Knitted Fabrics Presented to the University of Manitoba in Partial

Ttre Physícal Properties That Influence The Drape Of Knitted Fabrics

Marian Louise Gaucher

A Thesis presented to the University of Manitoba in partial fulfil-lment of the requiremenÈs for the degree of Master of Science t-n The FaculÊy of Graduate Studies

Winnipeg, Manitoba, 1979 THE PHYSICAL PROPERTIES THAT TNFLUENCE THE DRAPE OF

KNITTED FABRICS

MARIAN LOUIST GAUCHER

A dissertation submitted to the Faculty of Graduate Studies of the university of Manitoba in partial fulfillment of the requirements of the degree of

MASTER OF SCIENCE

6 ßtg

Fer¡nission has been granted to the LIBRAR.Y OF THE UNIVER- slrY oF MANITOEA to lend or sell copies of this dissertation, to the NATIONAL LIBRAR,Y OF CANADA ro microfilrn rhis dissertation and to lend or sell copies of the film, and UNIVERSITY MICROFILMS to pubListr an abstract of this dissertation.

The author reserves other publication rights, and neither the dissertatioll nor extensive extracts from it may be printed or other- wise reproduced without the author's written pennission.

ffiultluðed Fa@q/-,r 0F M,Af.tålEgôi "- . ASSTRACT

The drape of a fabric is defined as a description of Èhe deformaÈion

of a fabric produced by gravity r*'hen only part of it is directly sup-

ported (Cusick, 1965). Several physical properties have been suggested

as contributors to the drape of rvoven fabrics, but the literature lacks

infomation concerning Èhe physical properties Èhat influence Èhe drape

of knitted fabrícs. The present research investigated certain deformation properties and certain sËructural characteristics in order to determine the best predictors of the drape coeffícient of twenty knitted

fabrics. The deformation properties included stiffness, shear, and extensibility, útrile the structural characÈeristics included weight, thickness; and density. The measurements obtained were bending length, secondary shear modulus, extension at a 100 grarn load, fabric weight,

fabric thickness¡ and fabric density. The study also investigated the reliability of the properties as predictors for the two main types of knitted constructions- warp knits and r¿eft knits.

Regression anal-ysis Iras performed and several predictor equations were developed. The variables that predicted Èhe drape coefficient varied according to the knit structure. For the Ëwenty fabrics, the best

..predictor variables nere bending length, thickness, secondary shear nodulus, and transformaÈions of these variables. Bending length, thick-

nessr and extension were the best predictor variables for Èhe warp knit subgroup, drile bending length and secondary shear modulus were the best predictor variabl-es for the ¡reft knit subgroup.

-1- ACKNOIITLEDGEMENTS

The auÈhor trishes to express her appreciation to many Persons who con- tributed guidance, encouragement, and inspiration t,o¡¡ards this research. The guidance and encouragement of Professor Martin King, as thesis advi- sor is gratefully acknowledged. The inspiration and advise of Dr. Mar- garet Morton and Mrs. June Jackson as co"*iËtee members is gratefully acknowl-edged. Appreciation is also extended to Professor Bruce John- ston, DepartmenÈ of SËatisÈics for his guidance and enÈhusíasm. The author is also gratefuL to the members of the DeparÈment of Clothing and Textiles, University of Manitoba, for their encouragemenÈ and interest extended throughout this research projecÈ. The author also expresses appreciation to her fanily and friends for Ëheir support and encouragement. A spe'ciaL thank you is extended to her fíancíe, Miles, for his encouregement, enthusiasm, and assisËance ryith the conPuter work.

-11 - TA3I,E OF CONTENTS

LIST OF TABLES

LIST OF FIGI]RES

LIST OF PIATES v].L

Chapter Page

1. INTRODUCTION

Focussed Statement of the Problem 2 JusÈification for the Research Project 3 Thesis Format 3

2. REVIEI.I OF LITERATIIRE

The Knit Structure . . 6 I{eft Knits 6 l{arp Knits 9 Drape 11 The Measurement of Drape tt Résearch ReLated to Drape . . T2 The Defomation Properties . 15 Sti ffnes s 15 Shear . . t9 Extension . . 29 The Structural Characteristics . . 32 The Measurenent of the Structural Characteristics 32 The Structural Characteristics and the Knit Structure . . 33 Research Related Ëo the Structural Characteristics and Drape . . 33

3. EXPERII.MNTAI METIIOD 35

Pretes t 36 Fabric Selection and Preparation . 36 Selection of Fabri cs for Screening 36 Fabric Screening 37 Fabric Preparation 39 Physical Analysis of Fabrics 4T Drape.... .ara 4L The Deformation Properties 42

- 11¡- - The Structural Characteristics 51 Statistical Analysis 51

4. RESULTS AI{D DISCUSSION 54 Description of the Data 54 The Mean Data for Each Fabric 56 The Univariate SÊa tis tícs 60 Sinple Linear Correlation 67 The Drape Coeffici enË and the Defonnation Properties . 67 The Drape Coefficient and the Structural Characteristics 69 Regression Analysis 70 All Knit Group 75 I{arp Knit Subgroup 80 Weft KniÈ Subgroup 82 Directional and Face and Back ComponenËs . 85 Study of Residuals 88 Transf oraaÈi on Variabl es .89 The PredicÈor Equations .96 The Fabric propérties as PredicÈors of the Drape Coefficient 101 The Deformation Properties 103 The Structural Characteristics 106

5. SIMMARY AI{D RECOMMENDATIONS 108

Surmary 108 Inplications of Èhe Research Proj ect TL2 Recornmendati ons for Further Study 712

RE'ERENCES CITED 116

APPENDICES A. Statistics Tables T2T 81. Computer Printout - Multiple Linear Regressíon . 131 82. Cmputer Printout Stepwise Regression 150 83. Computer Printout All Possible Subsets Regres sion 159

-1V- LIST OF TABLES

Tabl-e page l. Description of Fabric Gharacteristics 40

2. Varíable Abbreviations . 55

3. Mean Drape coefficients and secondary shear ModuLus values . 57

4. Mean Bending Length Values . . 5g

5. Mean Extensíon values and structural, characteristics 59

6. Univariate StaËistics . 64 7. Correlation Matrix - All Knit Group . . 7I

8. Correlation Matrix - I'Iarp Knit Subgroup 72

9. Correlation Matrix - Í{eft Knit Subgroup 73

10. Variable Combinations Including Bending Length . . 76 11. Transformation VariabLe Abbreviations . g9

12. univariate statistics - Transformation variabLes . . 91

13. Multiple Regression Constants to predict the Mean Drape coefficient with rr¡o and Three rndependent variables 9g

L4. Multiple Regression Constants to predict the Mean Drape coefficient with More Than Three rndependent variables 100

15. Multiple Regression Constants to predict The Mean Drape Coefficient With One Independent Variable . . . LOz 16. R2 Values, F-Ratios, t-statistics, and Standard Error of the Estimate Values For the Variable Conbinations I{trich Include Bending Length . . . L2I ; :.. -.':: -.'.. -'-".. :':'-; ;; ::l. :

LIST OF FIGURES

Figure Page

1. Plain Weft Knit Structure 7

2. Warp Knit Structure . . 10

3. Forms of Shear Strain . . 20 4. Sinple Shear Test 2L

5. Spivakrs Shearing Apparatus . . 25

6. Hysteresis Curve 28

-vl - LIST OF PLATES

PIATE Page

I. The Tnstron tensile Ëest.er and four components of theshearíngapparaÈus ...... 46 :_..:.... II. The mount,ing frame of the shearing apparatus . . . . . 47 : '

III. The enËire shearing apparatus assembled on Èhe "' Inst,rontensiLet,ester . . . 48

-v11 - Chapter 1

INTRODUCTION

Fabric drape is one of the visual components in the aesthetic assess- menÈ of fabrics. Cusick (1965) defines the drape of a fabric as "a defomation of the fabric produced by gravity when only part of it is directly supported.rr since the particular type and style of a garment determines the amount of drape required, some prediction of how a fabric wiLl- drape is necessary.

Several physical properties have been suggesÈed as contributors to

Ëhe drape of woven fabrics (chu et al, 1963; cusick, L965; sudnik, 1972, L978; Kin and vaughn, 1974; Morooka and Niwa , 1976), but the literature lacks infomation concerning the physical properties that influence the drape of knitted fabrics. The drape of woven fabrics is influenced by a conbínation of certain deformation properties and structural character- istícs. stiffness, shear, and extension are the relevant measures of deformation, while fabríc weight and thickness are the appropriate structural characteristícs.

The type of basic woven construction is a factor in the drape of rùoven fabrics, for example, twiLl, satin, and plain rúeaves (cooper,

1960; chu et al, 1963; Howorth, L964). Researchers found than when yarns are woven inËo fabrics a wide range of stiffness is possible depending on the fibre movement permitted. -1- FOCUSSED STATEI'IENT OF TITE PROBLH'{

The major Purpose of this research project is to determine if certain deformation ProPerÈies and structural characterisÈics predict the drape coefficient of knitted fabrics. The deformation properties include stiffness, shear, and extension, while the structural characteristics incl-ude fabric weight, fabric thickness, and fabric density. Since density is calcul-ated fron weight and thickness, it is proposed that it could influence the drape coefficient.

In addition to studying knitted fabrics in general, the research project will also investigate Èhe reLiability of the properties and characteristics as predicËors of the drape coefficient for the tryo main types of knitted constructions-- warp knits and weft knits.

All of the directional and face and back components of the deformation properties will be measured in order to determine ¡shich ones are the most reLíable predictors of the drape coefficient.

Once Èhe properties Èhat influence the drape coefficient in knitted fabrics are detemined, equations r¡il1 be developed so predict,ions concerning the drape of a knitted fabric cen be made if one or more of the fabric properties are known.

The objectives of this study are:

1. To determine r¡hether the fabric properties of stiffness, shear, extension, weight, thickness, and density are reliable predictors of the drape coefficient ín knitted fabrics. 3

2. To determine which directional and/or face and back components

of these propertíes are the most reliabLe predictors of the drape coefficient in knirted fabrics. This would be limited to the pro-

perties found to be the most reliable in objective /É1. 3. 1o deternine whether the reLationships existing in objectives

/É1 and lf2 are consisËant for Èhe warp knit and wefÈ knit subgroups. 4. To develop predictor equations in order to make predictions

concerning the drape coefficient of a knitted fabric if measure-

ments of one or more of the fabric properties are known.

JUSTIFICATION FOR THE RESEARCH PROJECT

The major justification for Èhe research project was to establish a better understanding of the physical properÈies that contribute to the drape of knítted fabrics. The findings would fill- a void in the current literature concerning the drape of knitted fabrics and its relation to various physical properties. In addition, both knitted fabric and garment manufacturers could utilize the predictor equations Ëo allor¿ knitted fabrics to be designed or nodified to give the drape desired. Ulti- mately, this would ensure consuruer satisfaction in this area of aesËhetic assessnent.

THESIS FORMAT

The renainder of the thesís is presented in four chapters. Chapter is a revie¡¡ of the current literature. Chapter 3 outlines the experi- 4

Bental meÈhods end materials. Chapter 4 includes a presenÈation of the results of the study and a discussion of these results. Chapter 5 includes a surnnary of the research project, inplications of the research findings, and several recon'mendations for future study. ChapÈer 2

REVIEI{ OF LITERATURE

The reviel¡ of Litereture deals with two main topic areas-- a basic review of the knit structure and a discussion on fabric drape and its related defomation properties and structural characteristics. The basic types of knits are reviewed, including their structurel arrangements, properties, and end uses. The literature on fabric drape and its related physical properties is linited to woven fabrics. This area of discussion, therefore, focusses on the properËies thet infl-uence drape in woven fabrics. These properties include three deformation properties-- stiffness, shear, and extension, and two structural characteristics-- weight and thickness. Since fabric density is also included in the research, it is discussed as rsell. Drape is defined, the method of measurement is discussed, and the properÈíes Èhat influence drape in rroven fabrics are briefly mentioned. The deformation properties and structural characteristics are defined and discussed in terms of their measuremenÈs and their relationships with drape. In addition, the relationships of the knit structure rsith each deformation property and strucÈural characteristic are discussed.

-5- '..;'.1: :)aa - a

THE KNIT STRUCIT]RE

A knitted fabric is composed of a series of interconnected loops.

The properties of the fabric depend on the method of production and the geometric relationships of these loops (Thomas , L}TI). The two basic types of knitted fabrics are named after the general- direction of loop fo¡:matíon in the fabric. In ¡yeft knitting Èhe yarn is introduced in a weftwise direction, at right angles to the direction of fabric growth.

In warp knitting the yarn follows a warpwise progression (Thomas, 1971). The vertical or lengthwise coh¡mns of interconnected loops, corresponding to Ëhe warp direction in a rsoven fabric, are caLled wales. The horizontal or crosswise rows of inÈerconnected loops, corresponding to the rreft dircÈion in a noven fabric, are called courses (tyte, Lg76). weft Knits The basic t)pes of weft knits are pl-ain or singl-e jersey¡ purl, rib, interlock, and double knits. The basic repeat unit of each of these structures is a loop of yarn inÈerconnected by a previously formed loop in Ëhe såme course (smirfitt, L975).

The plain or single jersey is Èhe sinplest in construction (see Fig- ure l). All loops are interconnected in the same direction, are side by side in the same plane, and are drawn to one side of the fabric. The wales ere on the face side while the courses are on the reverse side. The different loop structure of the face and back tends to cause curling of the fabric edges. The loops are easily distorted, primarily along 7 the courses, making the ¡¡eft direction very extensible. For this reason plain knits are used widely in sweaters, sportswear, underwear, and hosiery (Laberth, L964; Wignall, 7964; Snirfirt , I975).

(a) ¡'ace

(b) Back

Figure l: Plain Weft Knit Structure (Stout, 1967) In the purl kniÈ the courses are interconnected on opposite sides, resulting in sirnilar appeerances of both sides of the fabric. The simpl-est fom is a l/L purl where alternate courses are knitted on opposite sides. Extensibility is particularly high in Èhe walewise direction (I,Iignall, L964; Smirfitt, L975). For this reason, purl knits are used primarily in infant and childrenrs wear and in non-fitted end uses such as scarves.

In Èhe rib knít the wales are interconnected on opposite sides. The wales lie in different planes producing a thick fabric with high laÈeral extension and negligible longitudinal extension. Both sides of fabric have similar appearances. The simplest form is a L/L rib where alternate wal-es are knitted to the front and the back (i,Iignall, 1964; Srnirfitt, 1975). Rib knits are utilized where a close fit is importanr, such as lrristbands, waistbands, underwear, sweeÈers, and socks (Corbman,

197 5)

The ínÈerLock knit is fo¡med by interlocking two, l X l rib structures. The l-ateral extensibility is not as high es that in rib knits due Èo one set of ribs being between the other, interferring with the nobility of the l-oops (Snirfitt, L975). The excellent longitudinal extensibility of the interlock knit contribuÈes to its success in end uses such as shirts, dresses, suits, coats, and sportswear (Labarthe,

L964; Corbman, f975). 9

A double knit is a t)pe of jersey construction composed of trso sides of fabric interlocked. one side of the fabric has a fine ribbed appearancer while the other side can assume various patt.erns, such as honeycomb or diamond. A double knit fabric is thicker, heavier, and more stable that a single knit and due to balanced yarn tension across the fabric, it has no eurling tendancy (Stoutr 196T). Double knits have been used in sportsrrear, suiÈs, dresses, æd slacks (corbuan, rg7Ð.

I{arp Knits

rn warp knitting many yarns from a nerp beam are fed into the knitting needles simultaneously, forning adjacent warpwise 1oops. The fabric is forued by interconnecting individual warp yarns into these warpwise 1-oops (see Figure 2). The yarns folLow a zigzag progression

¡shich helps to close the structure, rnaking ít more conpact and dimen- sionally stable than a weft knit (Thonas, r97r; Darlington, L97L;

Joseph, L972). The ¡vales are on the face of the fabric, while the courses are on the back. The two basic classifications of warp knits are tricot and raschel (l,yle, 1976). The basic differences between the tricot and raschel structures are the type of needle used and the number of sets of yarns used.

A tricot knit is classified according to the number of sets of yarns used in íts structure. It has vertical waLes on the face and horizonÈal ribs on the back (lyle, L976). The difference in the loop geometry on the face and back tends to cause curling of the fabric. Tricot knits do 10 not extend as easily as ¡¡eft knits. End uses ínclude lingerie and outerwear items (Labarthe , L964).

Figure 2: I{arp Knit Structure (Co¡¡an and Jungennan, f 969)

The raschel knit machine is very versatile, allowing e great number of yarn sets to be used. This leads to many different possibíliÈies of structural design, from an open-work crochet to solid structures with three-dimensíonal effects (Lyle, I976). This versatility extends Ëhe properties and end uses of the fabric. End uses incl-ude dresses, suits, drapesr æd lingerie. 1l

DRAPE

Cusick (1965) defines Èhe drape of a fabric asrra description of the defomation of a fabric produced by gravity when only part of it is directly supported't. The major mode of deformation in drape is bending, but the occurence of multi-directional curveture irnplies thaÈ shearing is also taking pl-ace. There are also tensile and compressive deforma- tions occurring in draping but these are usualLy snall due to yarn stiffness (Hearl-e, Grosberg, and Backer, L969; Morooka and Niwa, 1976; Sudnik, 1978). Fabric weight and thickness are Ëhe structural characteristics that influence drape (Chu et al, 1963; Kim and Vaughn, L974;

Morooka and Niwa, I976; Sudnik, 1978), however, no relationships between drape and fabric density have been reported in the literature.

The Measurement of Drape

The drapemeLer is the instrument that is generally adopted to Eeasure drape (Chu ét al-, 1950, L963; Cusick, 7965, 1968; Kin and Vaughn, L974;

Sudnik, 1972, 1978). The drapemeter aLlows measurement of drape when the fabric is distorted inÈo multi-directional curvature. A circular specimen is supported by a smaller horizonÈal disc a1-lowing an annular ring of fabric to drape under its own weight. Three different specimen sizes may be used, allowing different ratios of the supported and unsup- ported areas, and thus, enabling more accurate measurenent of three ranges of drape. The specimen size used depends on the drapeability of the fabrics, however, the results using different specimen sizes are not directly comparable (Cusick, L968; Sudnik, L972). I2 Drape is quantitatively expressed by the drape coefficient. It is

calculated as the ratio of the area of the shadow projected ¡shen Ëhe fabric is alLowed to drape, to Èhe area of the annular ring of fabric ¡ñich is allowed to drape. The drape coefficient is expressed as a percentage with a theoretical maximrm of one-hundred and a minimum of. zero. A high drape coefficient corresponds to low drapeability or e stiff fabric (Cusick, f968).

very drapeable fabrics tend to form pLeats under the projection of the disc. These pleats are referred to as re-entrant folds. The extent of this folding cennot be measured and therefore, Èhe drapemeter is linited in this respecr (Chu er al, 1963).

Research Related to Drape

The major research in the area of drape has been accomplished by Chu

er al (1950, 1963), Cusick (tg6s, tg68), sudnik (tglz, tgTg), Kim and

Vaughn Q974)¡ and Morooka and Ni¡ra Q976). Al-1 have done research on Iroven fabrics and there has been general egreement on the deformation

properties and structural characÈeristics vtrich relate to drape. The defornation properties are stiffness, shear, and extension. The struc-

tural characterisÈics are weight and thickness. Studíes have also shown that the type of woven construction influences drape. Researchers found that rstren yarns are woven into fabrics a wide range of stiffnesses is possible depending on the fibre movement permitted (Cooper, 1960; Chu et a1, 1963). 13

Predictor equations have been established for rroven and nonwoven

fabrics by Cusick (1965) and for woven fabrics by Morooka and Niwa

(1976). In Cusickrs equations the dependent variable ¡yas the drape coefficient (OC), whiLe the índependent variables included bending length (c), bending length squared (ê), the shear angle at a specified

load (A)r and the shear angle at a specified load squared (A2). One set of equations ¡ras derived for the entire group of fabrics only. The significance of the sinple regression of DC on c wes Èested, followed by

testing the significance of the difference made by incLuding additional variables. The regression of DC on c was significant at a level higher

than 0.001. The difference made by the addition of &ø and Èo c " A and J were highly significant at a level higher than 0.001. However, the difference made by the further addition of A2 r¡as of lesser significance than the 0.05 leveL.

Morooka and Niwa Q976) measured sixteen properties including ten- siLe, bending, shearing, compressional, and surface properties, weight, and thickness. Bending, weight, and shear were the most accurate predictors of the drape coefficient. I{hen these three variables were incLuded in the regression equation, the correlation coefficienÈ was 0.78. High correlation resulted when the ratio of bending rigidity to weight was related to the drape coefficient. Shear did not have to be included for high correlaÈion, but weight lras necessary. Correlation improved when warp and weft directions rùere considered separately. T4

Past research has not established predictor equations concerning the drape of knitted fabrics. 15

THE DEFORMATION PROPERTIES

St i ffnes s

Stiffness is defined as the resistance offered by a fabric to bending. Bending is considered to be the major mode of fabric defomaËion in draping (Hearle, Grosberg and Backer, L969).

The Measurement Of Stiffness

Stiffness is measured most often by the cantilever method or one of

the hanging loop uethods. In the cantilever method a fabric strip of a specified size is extended over a horizontal edge unÈil the tip of the strip subtends a specified angle (¿bbott, 1951; Kaswel1, 1953). In

Peircers Heart Loop test a specimen of known dimensions is fomed into a

heart-shaped loop and suspended from a horizontal bar (Abbott, 1951;

Brown, 1978; Peirce, 1930). Brown (1978) conducÈed a study to determine whether Peircets Heart Loop Test could be used to measure the stiffness

of singLe jersey fabrics with and without a tendancy Èo curl. An increase in strip width did decrease the curling edge effect and the variability. Evenso, meaningful results were obtained for the various strip widths tested.

One measure of stiffness is the bending lengÈh, c, which is calculated through the use of the following equations: lof(e), " = t(e) = (cos o/ran e)1/3 l6 A = 32.85 d/lo

d=1-1o and 1o = 0.1337L where 1 is the loop length and L is the strip lengÈh (Peirce, 1932; ASTI{, 1978). The bending length is expressed in centimeters. Fabrics with a bending length of less than 2 cm are too flexibLe to be tesÈed by the cantilever method and a heart Loop nethod is advised (Kaswel1,

1963).

AnoÈher measure of the stiffness is the flexural rigidity which measures Èhe actual forces produced in bending and is Èherefore dependent on fabric weight. L7 Stiffness and the KniÈ Structure

Researchers state thet the bending characteristics of warp- and rveft-knitted fabrics are determined by fabric thickness, fabric veight, run-in-ratio, fabric tightness (yarn linear density in tex/loop length), stitch type, fabric directions, fabric face and back, and overall con-

struction (Knapton, L973; Hanilton and postLe, L974; Knapton and Lo, 1975; Gibson and Postle, f97S).

Knapton and Lo OglS) stated that structurally unbal-anced knitted fabrícs resulting froro different warp and weft counts, the differenÈ number of loops on the face and back, and/or different stitch errange- ments on each side, have differenÈ directional and/or face and back bending characÈeristics.

Gibson and Postle (f978) found that overall fabric construction also det,ermines bending characteristics. They measured Ëhe frictional bending moment (one-half Èhe hysteresis at zero defornation) and the flexi- bíLity (the slope in the linear region of the hysteresis curve) of several types of knitted fabrics. plain knits had very low frictional bending monents and very high flexibiliÈies. Polyester double knits and warp knits had l-ow frictional bending moments and high flexibilities.

I{oo1- doubl-e knits had medirn to high frictional bending mornents and 1ow flexibilities. However, generally plain knits were similar to double knits. 18

Research Related to Stiffness and Drape F.L. Peírce discovered that stiffness !Ías an importanÈ factor contrí- buting Eo drape as early as 1930. He found that stiffness and drape lùere negatively related¡ and more recently, other researchers have found sinílar trends. Cusick (1965) tested woven and nonwoven fabrics and reported that when drape coefficient values were plotted against bending length values the gradient increased as bending lengËh increased. Also, the coefficients of detemination were high for the nultiple regression equations developed. Sudnikrs ¡¡ork Q972) on rroven, nonwoven, and knitted fabrics and Kimrs and Vaughn's work (1974) on noven fabrics also resulted in hígh correlation between bendíng length and drape coefficient values. Morooka and Niwa (1976) found bending properties were Ëhe most closely related to the drape coefficient but weight was also included in ther predictor equation.

Despite the fact that bending Length is very highly correlared with drape, it cannot be equated with ít (chu et al, 1963). The strip test exhibits monopLanar defomation only, whil-e the drape test exhibits nul- tiplanar defo¡mation. 19

Shear

The American Society for Testing and Materials defines a shearing force as ttthe force that causes adjacent layers of an object Èo slide relative to each other in a direction parallel to their plane of con- tact, to obÈain a separatíon in the object and a change in positiont'

(ASTU, L972).

Shear strain cen occur in various forms. Pure shear strain is defined as the deformatíon by extension in one direction and the con- traction in the perpendicular direction, so that the area remains constant (Hearle, Grosberg, and Backer, L969; HamilËon, lg7Ð, (see Figure 3a). Sinpl-e shear strain also maintains constant area, but the sides rshich are initiall-y perpendicul-ar to the dírection of shear move through a defor^nation angle (Hearle, Grosberg, and Backer, 1969; Hamilton, 1975), (see Figure 3b). Sinple shear straín et constant lengËh of sides is the Ëne. of shear deformation encountered most often in l-aboretory situations. ltris results in a decrease in area (Hearle, Grosberg, and Backer; L969; Hamilton, 1975), (see Figure 3c). 20

a. Pure Shear Strain (Hearl-e, Grosberg, and Backer, 1969)

b. Sinpl-e Shear Strain (Ilearle, Grosberg, and Backer, 1969)

c. Sinple Shear Strain at Constant Length of Sides (Hanilton, 1975)

Figure Forms of Shear Strain ::ì:a:::,::t.:::.i:::t:;:.:t;:-::,::ì-,';.;:t::i;:::-:-ì:::.ì.:t-i:.1ì:,:tt:,,;::,::l::,,:,,i:11::;:::::t:1,::i:::.,.:.:.

2T Hearle et el (f969) define a shear stress as rrthe force ecting tangentially on a plane in the material which must be balanced by an equal force in the opposite direction on e parall-el plane, and then by second couple Èo prevent rotation.rf

A sirnple shear test is illustrated in Figure 4. The shearing force, S, is calculaÈed as follows: S=F-I{(tan9) ¡shere F is the shear stress per unit width of the specimen, expressed in E/cm, I{ is the tensiLe load applied to the fabric in grams, and tanQ is the shear strain (g is the angle of inclination in the deformed state) (cusick, 1961; spivak and Treloar, 1968). The value I{(Èano) is usually negligible compared r,rith F, so iÈ is sometímes ignored (Spivak, f966).

Figure 4: Sinple Shear Test (Spivak and lreLoar, f968) 22

shear has been reported es an important aspect of drape of woven,

knitted, and nonwoven fabrics by many researchers (Morner and Eeg-

Olofsson, L957; Cusick, 1965; Treloar, L965; Carnaby and postLe, L974:' Hanilton and Postle, 1976; Goswami, L977, and Gibson and postl-e, l97B).

Shear is especially inportant when fabrics are required to drape around the chest or in the sl-eeves of e garment where the fabric deforns with nultidirectional curvature (Sudnik, 1972).

rn most !ùoven fabrics shearing can be expLained by a change in angle between intersecting yarns. Bending and twisÈing of the yarns between intersections also contributes to the shear deformation (Cusick, 1966). The resistance Èo shear defornaÈion is provided nainly by the frictional conÈact of yarns at the intersections (Skelton , 1976).

very Little research on Èhe shearing of knitted fabrics has been reported in Èhe l-iterature but the najor causes of defomation are thought to be interfibre and interyarn sl-ippage, twisting and bending of the yarns, and j¡rming (Carnaby and postle, Lg7Ð.

The MeasuremenÈ of Shear Several researchers have developed equip,rnent to measure the shearing properties of textí1e materiaLs (Dreby, I94I; Morner and Eeg-Olofsson,

L957; Behre, 196l; Treloar, L965; Spivak, L966; Carnaby and posrle, L974; Hamilton and PostLe, L976). Many have adapted vertical strain geuge testing instruments, while others have designed equip,Bent that can operate independently. rn all of the tests the fabric specimen is 23 mounted under tension along two paraL1el edges. A shearing force is applied through an angle untíl a conpressive stress develops which leads to buckling of the fabric (Hearle, Grosberg, and Backer, 1969).

Dreby (f941) ¡¡as one of the first to develop an instrument to study the shear of textíle fabrics. Drebyrs Planoflex was sinple in design and measured the shear angle required to produce buckLing.

Later, Morner and Eeg-OLofsson (f957) devel-oped an apparatus which is mounted on an Instron tensile tester. It was the first to yield a fabric hysteresis curve. The specimen is held between two clamps. The top clamp rests on two knife edges, one of r*rich is rigidly mounted, while Èhe other is connected to the sÈrain geuge of the Instron by a rigid rod. The botÈom clarnp is moved through a connection to Ëhe rnstron crosshead. HorizonËal movement of the botton clamp shears the specimen.

The appareËus measures Rcos9 ¡vhere R is the resisÈance offered Èo shearing and 0 ié the shear angl-e. Dawes and Orsen (f971) were successful- in utilizing this neËhod to measure the shearing behavior of the warp-knitted components of fabric laminates. Ttris method was also used by Cusick

(f96f) to study wovens.

Behre (1961) developed an instrument sinilar to Ëhat of Morner and Eeg-Olofsson, however, R could be measured directly. Behre tested various novens and noffùovens (Behre, 1961; Lindberg, Behre, and Dalberg, r961). 24

Treloar (1965) deveLoped an apperetus that is manually operated. The

specimen is mounted between Èwo clamps. A verÈical load is suspended fron Èhe center of the bottorn clamp from where a horizontal load is applied. Measurements of the dispLacements are nade with a Ëravelling venier microscope.

Spivakrs apparatus (1966) utilizes the Instron tensil-e tesÈer to' aPPly and measure the load and the resulting shear deformation. This aPParaËus is illustrated in Fígure 5. The specimen is mounted between Èwo vertical clamps, F1 and F2. cLarnp F2 is attached to Èhe cross-head of an rnstron tensile tester and clamp F, is suspended from the load cell. A normal load I{ is applied perpendicul-ar to cl-amp F, to prevenÈ premature buckling of the specimen. Vertical movement of clanp F, shears Èhe speci-men.

The apparatus has several advantages. It. can be adapted to different specimen dimensions. However, Treloar (1965) found that the maximum shear straín which can be applied without the onset of buckling increases as the ratio of width to length of the specimen decreases. The shearing characteristics are much less sensítive to the magnitude of the normal load with a specimen ratio of width to length of one to ten.

A second advantage of this apparatus is that the specimen is mounted verticaLly. Ttris eLininates the clamp weight so that low normal loads may be used. The application of as 1o¡ a normal load as possible is important in drape since the forces causing defornation during drape are small (Spivak, 1966). Spivakrs r¡ork on wovens included experimentation 25 with normal- Loads frorn 0 to 120 g/cm of. the specimen rsidth. IIe found that a combination of a low normal load and a long, nerrow specimen resulted in the shearing stress being less sensitive to the normal load.

Goswami (1977) and Spivak and Treloar (1965) who used the same apperatus for woven fabrics, used nomal- loads of.2.5 g/cm and 10 E/cm, respectively. A further advantage of the apparatus is Èhe absence of possibl-e frictional coupl-es. Kín and Vaughn (1974) also utilized Spivakrs apparatus.

specimen

cross-head

Figure 5: Spivakrs Shearing Apparatus (Spivak, L966) 26

Carnaby and Postle (1974) Ìrere among the first to study the shearing properties of knits. Their instrument wtrich is similar in design to those previously mentioned, consists of a top clamp ¡¡hich is rotated through an angle while a fixed bottom clanp provides the tensile and shearing stress. A square specimen is used. The shearing force obtained ís equival-ent to that defined by Morner and Eeg-Olofsson (1957) and TreLoar (1965) for shearing at constant length of sides. However, Carnaby and Postle found that in order Èo ensure shear at constant length of sides in knitted fabrics, some constraint had to be included. l{ithout this constraint they found deformation occurred thaÈ could not be classified as shear (Carnaby and Postle, L974).

More recently, Hamilton and Postle (I976) have devised a shearing ePPeratus to accoÍrnodaÈe this constraint required rshen shearing knitted fabrics. The apparatus operat,es independently of an Instron tensile tester. Thç specimen is mounÈed beÈ¡¡een two clamps. A stepper-motor is attached to a strain gauge which moves the botÈo'n clamp. The shear strain is measured by a potentiometer.

Various meesures of shear can be obtained from the hysteresís curves yielded by the various instrrments. A typical hysÈeresis curve is ilLustrated in Fígure 6. Spivak and Treloar used the resistance to shearing at a specified angle, the hysteresis at zero strain ()fY), and the relative energy loss of the hysteresis ((ABc+DEF)-(BCD+EFA)/(ABC+DEF)) to measure shear. Goswami measured the latÈer two in addition to the shear stress and strain aË the buckling point B. 27

Carnaby and Postle used the secondary shear modulus G, ie. the slope of the curve in the linear region, and the coercive force (xO), ie. haLf the r¡idth of the hysteresis loop at zero strain, and the shear strain. Some measurements are more reliable than others. For instance, the mean shearing modulus at zero strain (Cusick, 1961) and the esÈimaËe of the buckling point (Treloar, L965; Spivak, 1966) are subject Èo high experimental error. The first invoLves the small forces in Èhe initial stages of shear and a rapidly changing slope. The later involves error because definition of the poinË aÈ which buckLing occurs is highly subjective. The other Eeasures of shear are reliable, their usege depending on Èhe type of shear characteristic which is meaningful to the researcher. 28

SHEAR SIRAIN,

SHEAR STRESS, F, (g/c*)

Figure 6: Hysteresis Curve (Spivak, 1966 Carnaby and Postl-e, I974)

Shear and the KniÈ Structure

Shear in knitted fabrics is not dependent on structural- characteris- tics such as fabric thickness, weighÈ, and tightness, but is more a function of fabric type (Gibson and postle, l97B). Gibson and postle Q978) measured the frictional shear stress (one-half the hysÈeresis at zero deformation) and the shearability (the slope in the linear region of the hysteresis curve) of several knitted fabrics. They found that weft-knitted fabrics had medír¡m frictional shear stress and reasonable shearability, whíle narp knits had high frictíonal stress and low shearability. _:-_:: :: 1 - - -: " :1

29 The shearing behavior of a knitted fabric tends to be independent of the direction of the applied strain for warp knits and double knits (Gibson and Postle, 1978) but for the plain-kniËted structure the application of the tension nodifies the Loop shape and therefore values of the shear Eeasurements vary according to direction (Hanilton and postle,

L977 ) .

Research Related to Shear and Drape Ïn generalr the research índicates moderate to high correl-ation between the drape coefficient and shear Eeasurements. cusick (1965) reported t.hat woven and nonwoven fabrics with a high shear angle at a specified load have higher than average drape coefficients and those with a low shear angl-e at a specified load have lower than average drape coefficients. Research by Kim and vaughn (L97Ð indicated a high positive correl-ation between the shear stiffness and the drape coefficient for r¡oven fábrics. Morooka and Niwa (1976) found that shear rras related closeLy to the drape coefficient but lras noÈ necessary for high corre1a- tion if bending and weíght measurenenÈs were included. Sudnikts shear

Beasurements (1978) on woven, knitted, and nonwoven fabrics showed on1_y moderate agreement with drape and shear meesurements.

Extension

The extensibility of a fabric under a tensile stress is a third com-

Ponent of the drape of ¡soven fabrics. Extensibility is defined as the ease of sÈretching (Kaswell, 1963). The number of studies relating 30

extension to drape has been linited, although this factor was incLuded

in reseerch by Chu et al (t963) and Kin and Vaughn (L97Ð.

The Measurement of Extension

One method of measuring extensibiLity is with a vertical strain gauge testing machine such as the Instron tensile tester. Other instruments are available, but the rnstron tensiLe tester is one of the most pre-

c ise.

Extensibility can be expressed in several nays. The ratio of tensile stress to strain or Youngrs modulus is one measurement of extensíbil-ity.

Low modulus materials have high extensibility. peirce (1930) advised that to reLate extension to handle and stiffness, the measure of extensibility should be taken fron the initial slope, because the tensile deformaÈion experienced in bending is smaL1. Two other methods of des- cribing exÈensibility are the load at a specified extension or the extension et a specified load. Doyle (f953) advised that the l-aÈter is a more appropriate meesure when a wide r¿mge of extensibilities has to be consídered. Kin and Vaughn Q974) measured the percent extension of woven fabrícs at a load of 1000 grems. 31 Extension and the Knit Structure

Knits have a low resistance to extension due to their low bending and Èortional restraints (Hearle, Grosberg, and Backer, Lg6g). I{hen a plain knit undergoes extension the loop strucÈure changes shape (Doyle, 1953). Ttris initiar load is taken up by bending and Èwisting coupl-es in the yarn and frictional constraints a loop intersections. As adjacent loops compress and bend into high curvature the load rises. slippage of the loops over each other also occurs (Hearle, Grosberg, and Backer , 1969). l{hen a warp knit undergoes extension the loop structure changes shape and sinilar couples and constraints occur (Hearle, Grosberg, and Backer, 1969). Howeverr es the loop exËends, yarns move from the crosslink into the loop.

Extension in plain knits varies according to fabric tightness, fabric direction and yarn structure (Doyle, f953). In double knits exÈension depends on fabric tightness, fabric direction, stitch type, and stitch arrangements (Knapton and Lo, 1975). In warp knits extension depends on fabric tightness, fabric direction, and yarn stiffness (Cook and Gros- berg, 196f ).

Research Related to Extension and Drape

Research by Peirce in 1930 indicated that the drape of woven fabrics increased es extensibility increased. Other researchers found sinilar results in testing various noven constructions (Chu et al, 1963; Kin and Vaughn, 1974). Kin and Vaughn (1974) found very high correlaÈion ber- 32 ween the percent extension at a specified load and the drape coeffi- cíent. Morooka and Niwa (1976) found that extension was a poor predictor of the drape coefficient. The literature did not report reLaËion- ships between drape and exÈension for knitted fabrics.

TTTE STRUCIT'RAL CHARACTERISTICS

The structural characteristics that are discussed are fabric weight,

fabric thickness, and fabric density. Fabric density is defined as

fabric weight divided by fabric thickness. Density is a measure of the degree of compactness of the structure.

The Measurement of the Structural Characteristics

To measure fabric weight, specimens of knov¡n dimensions are taken

from fabric in moisture equilibrium ¡¡ith the standard atmosphere and weighed. Fabric weight is usuaLly expressed in g/*2.

To measure fabric thickness Èhe specimen is subjected to a low speci-

,., fied compression between two parallel planes. their perpendicular sepa- i, Éation is taken as the thickness of the specimen at the pressure t applied. Thickness is usuall-y expressed in centimeters.

Fabric density is calculated as fabric weight divided by fabric thickness. 33 The SÈructural Characteristics and the Knit Structure

The weight of the neft knit structure is related to Ëhe Loop length

and Èhe linear density of the yarn (Hearle, Grosberg, and Backer, 1969;

Knapton, 1973). Tfhen these ere held constant the weight depends on the knit structure.

Postle (1971) and Knapton and Lo Q975) have found that the thickness of weft knits is Largely dependent on the yarn diameter but is nargi- na1Ly affected by the loop length and tightness of the strucËure.

The density of weft knits is markedly dependent on tightness and increases linearly r.rith an increase in tightness (Postle, I}TI; Knapton, L973; Knapton and Lo, L975). Fibre specific gravity is also influential but the type of knitted structure and yarn do not contribuÈe.

Infomation regarding Ëhe structural characterisÈics of warp knits was not found in the literature.

Research Related to the Structural Characteristics and Drape

Chu et al (t963) and Morooka and Niwa (L976) stated that for wovens, fabric weight and the drape coefficient are negatively rel-ated. Ho¡r ever, Kin and Vaughn (L974) found that weight and the drape coefficient were positively related, but the correlation nas poor. sudnik (197S) stated that the drape of woven fabrics is weight dependent, but did not explain the relationships involved. The weight of knitted fabrics as related to drape has not been discussed in the literaËure. The appar- 34 ently confLicting results and the lack of research indicate further investigation into the relationship bet¡¡een weight and the drape coeffi- cienË is necessarv.

Thickness has not been related to drape very often in previous research. Kin and vaughn Q974) and Morooka and Niwa found that for woven fabrics, thickness tends to decrease as the drape coefficient decreases but the correlation is l-or¿. Fabric thickness has been found to influence the bending characteristics of knitted fabrics (Knapton, 1973, Harnilüon and Postle, L974; Knapton and Lo, 1975; Gíbson and postle, 1978), therefore it ís possibly a good predicror of drape in knitted fabrics.

No relationships between density and drape have been reported in Èhe Literature. However, since weight and thickness have been found to influence drape (Chu et al, L963; Kim and Vaughn, L974; Morooka and Niwa, 1976;'Sudnik, 1973) it is proposed Ëhat density may influence drape as well. Chapter 3

EXPERII.{ENTAL METHOD

In addition to measuring Èhe drape of several knitted fabrics, the

PresenÈ research project investigated three deforrnation properties and Ëhree structural characteristics in order to determine the accuracy of these properÈies and characterisÈics as predictors of the drape of knitted fabrics. The deformation properties included stiffness, shear, and extensibility, while the structural characteristics included weight, thickness, and density.

This chapter is presented in four sections. They are: (i) pretest, (ii) raUric Selection and Preparation, (iii) physicaL Analysis of Fabricsr to1 (iv) Statistical Analysis. The 'Pretestr section outlines the justifícations and overall result.s of the pretest only, as the specific influences of the pretest are mentioned in tPhysical Analysis of Fabrics.r fFabric Selection and Preparationr includes the selecÈion of fabrics for screening, the fabric screening procedure, and fabric preparation. 'Physical Analysis of Fabrics' discusses each of the properties tested in rel-ation to its nethod, equipment, measurement, specímen size, and sarnple size. fstatisticaL Analysis' includes an outline of the statistical modeL and a description of the methods of analysis.

-35- 36

All testing I€s done according to standard test methods except for shear where no standard method exists for textiles. All fabric cutting and testing lras conducted in Èhe standard atmosphere of 21 + I C and 65

+ 2 7. rel-ative hunidity. .- 3

PRETEST

In order to determine the feasibility of the study in terms of time, equipment; and t.est meËhodsi a pretest ¡sas conducted. The pretesÈ fabrics incLuded one rùarp knit and tt¡o ¡¡eft knits. The knits exhibited differenÈ degrees of drape. Ttre seven physical properties-- drape, stiffness, shear, extensibility, weight, thickness, and density-- were measured.

The pretest indicated the most appropríate method of testing and specimen sizes, the most reliable measurement,s, and the variabil-ity and limitations of the equipment and the ËesÈ methods.

FABRIC SELECTION AND PREPARATION

Selection of Fabrics for Screening Forty-two warp- and weft-knitted fabrics were sel-ected from the l{in- nipeg market for screening purposes. Because of the exploratory nature of the study and the need for a wide range of drape coefficient values, a variety of different knít constructions was chosen. Fabrics whose end use is apparel were chosen because this end use encompasses all types of knitted constructions. Fibre content was not a controlled variable in 37 fabric selection because fabric construction is Èhe predominant variable in drape.

The fabric consËructions selected were of two main types-- warp knits and rseft knits. The warp kniÈs included tricot and raschel, the two most prevalenË warp knits. The weft knits included pLaín or single jer- seyr rib, interlock, and double knits. I'Iarp- and r+eft-knitted pile fabrics were also selected for screening. PurL knits were not selecÈed because of their linited application in apparel and their linited avail- abi lity.

Fabric Screening

Prior to the screening procedure the fabrics \ùere laundered according to the Canadian National Standard CAI{2-4.2-l'477 Method 58-L977 (CCSI, 1977) in order to remove any water-soluble finishes and soíl and to relax the fabrics.

The purpose of screening the fabrics was to Linit the number of fabrics to be tested, wtrile maintaining a wide range of drape coefficients for the entire group of fabrics chosen, as well as for the warp- and l¡eft-knitted subgroups.

The drape coefficients of the forty-two fabrics Ìrere detennined according to the Brirish srandard Merhod BS:5058-1973 (Bsr, L974), except that the face and back were each tested once on one drape specimen. Ttre drape coefficíenÈs ranged fron 15 to 70"1 fot the forty-two 38 fabrics. From these, twenty fabrics were chosen for the research project, including ten narp knits and ten weft kniÈs. The range of drape

coefficients for each of these subgroups was also 15 to 707..

Fabrics were excluded fron the group of forty-t¡so for several rea- sons. Rib knits were excl.uded because of Èheir directional drape characteristics. They also had poor draping properties, and thus, did not provide a good range of drape. Pile knits were excluded because of the difference in Èhe drape coefficients between the face and the back. Other types of fabrics with very different face and back drape coefficients were also excluded. Fabrics with a tendancy to curl were excluded. Iùhen two or more fabrics had the same drape coefficient, only one was used in the sÈudy. This selection was made randomly.

In order to ensure that the drape properties of the twenty fabrics were due to construction rather than finishes, the presence of finishes was determined on all fabrics using the A¡nerican Association of TexÈile Chemists and Colorists tesË method 94-L977 (¿¡tcc, Lg77), tdentificarion of Finishes in Textiles. Finish deÈection included exÈractions with trichloroethyl-ene, ethanol, and 0.lN hydrochloric acid. The acetone extractíon specified in the test method ¡¡as omiÈted because it was unlikely that the fabrics contained alkyd resins, cellulose acetaÈe, chlorinated rubber, or polyvinyl chloride. I{ater extraction was omitted because the fabrics had previously been l_aundered. 39 Fabric yíelding less than lZ residue nere retained for the study. Fabrics yielding greater than r"Á residue with minimal loss of dye or

brightenerr and fabrics yiel-ding greater than 2"Å resídue, rüere tested further for bending length and shrinkage (fabric count) before and after extraction. If the bending lengths and/or fabric counts were signifi- canÈly different before and after extraction, the fabric was either

repLaced by one with a sinilar drape coefficient or drycleaned to remove

the finísh, so as to ensure that the finish did not influence the drape of any of the twenÈy fabric samples.

The final twenÈy fabrics chosen for Ëhe study included ten warp knits and Èen weft knits. The warp knits included eight tricot and tr¡o ras-

chel knits. The weft knits included five single, three double, and two interlock knits. A descripÈion of the fabric characteristics ís

included in Table 1. Fabríc count was determined according to the Cana- dian Natíonal Standard CÆ{2-4.2-ltt77 Method 7-L977 (ccSn, Lg77). Fabric

weight was determined according to the canadian National standard cAu2-4.2-Ì'177 Merhod 5.A-L977 (CCSB, Ig77 ).

Fabric Preparation

Ttre fabric preparation for all tests was done in a standard atmo-

sphere of 2l + I C and 65 + 2% reLative humidity. I{alewise specimens were cut from the lengthwise dirction parallel to the fabric wales. Coursewise specimens were cut from the widthwise direction parallel to the fabric courses. Specirnens Ìrere cut for each test so that they did not contain the same waLes or courses. Table I Description of Fabric Characteristics*

Fabric*nk Fabric Count Type of Knit Fibre Content I,Ieieht (wales/cn) (courses/c¡n) Gl^2)

A r5.6 L7 .4 tricot 85115 nylon/spandex 200.22 B 22.0 25.6 tricot l00Z nylon 7 4.95 c 16.0 15.4 tricoÈ 100% nylon 24.46 D 11. I 14.4 tricot 1002 triacetate 165.92 E 5.0 16.0 rasche 1 50 / 50 polyester/acetate 207.28 F L2.0 14.0 tricoÈ 1002 polyester r94.42 G 18.8 19.6 tricot 100% nylon 88.86 H 19.0 16.2 tricot 1002 nylon 167 .L6 I 8.0 7.4 rasche 1 1002 rayon 177 .75 J 8.0 6.0 tricot 1002 polyester I 33. 85

K 9.0 8.0 singl-e 90/10 cotton/flax L92.27 L 13.8 18.4 single 50 | 50 polyester/cotton r59.76 I'I 8.6 L2.0 single 50 / S0 polyester/cotton 227 .OL N 15 .0 17 .0 interlock 1002 polyester r37.02 o 5.0 7.0 single 1002 polyester 138.77 P 13.8 2r.0 single 100% nylon I52.12 a L2.4 9.0 double 1002 polyester 252.47 R 13.6 11.0 double 1002 nylon 237 .27 S 12.0 13.6 interlock l00Z polyester r53. l I T IL.4 r3.0 double 1002 polyester 215.11

+r Values are mean determinations according to standard test methods Fabrics A-J are warp knits, fabrics K-T are weft knits 4T

PHYSICAL ANAIYSIS OF FABRICS

Drape

To assess drape, the British standard Method BS:5058-1973 (nst,

1974), Assessment of Drape of Fabrics, was utilized. Two, 30-cn-dianeter fabric circles !¡ere Èested using a Rotrakote model tester with an l8-c¡n-diarneter disc. Each specimen was Èested three Èimes on each side yielding six face and síx back drape coefficients which ¡¡ere averaged to yield Èhree mean values. They were: (i) drape coefficient face, (ii) drape coefficíent back, and (iii) drape coefficient overall.

The test method suggests a specimen diameÈer of 24 cm if the drape coefficient of a 3O-cn-diameter specimen is Less than 357. and a specimen diameter of 36 cn if the drape coefficient of a 3O-cn-diameter specimen is greater than 852. The 36-cm-diameter specimen size was not selected because screeníng indicated Èhat none of the fabrics had drape coefficients greater than 85%. The 24-cm-diameter specimen size was not selected because initial trials indicated it was noÈ as capable of dis- crinínaÈing among the fabrics as the 30-cn size. The 3O-cro-diameter specimen was utilized throughout this study because it was proposed that for most fabrics this size would be the most accurate and most discrirni- natory.

Drape was quentitatively expressed by the drape coefficient which was calculated as the mass of the shaded area of the paper ring divided by the Èot.al mass of the paper ríng and expressed as a percentage. Drape coefficient results obtained during screening were not used in the test- iog. 42 Ttre pretest and the screening trials confirmed the línitation of the drape tester mentioned by Chu et al (1963). Very drapeable fabrics forned re-entrant folds under the projection of the disc. Since t,he specinen and the disc are both opaque, the size of these folds could not be measured. The occurance of re-entrent folds was noted and Èhe fabrics were included in the project. There rsere three fabrics rrhose face and back exhibited re-entrant foldíng and three fabrics whose face or back exhibited re-entranË folding.

The Deformatíon Properties

All of the defo¡:mation properÈies have face and back and/or directional componenËs. All such components were tesÈed because past research indicated that these properties can vary due Ëo the dífferent structural arrangements of the face and back or warp and l¡eft directions

(Doyle, 1953; Cook and Grosberg, L96L; Knapton and Lo, Lg75; Hamil-Èon and Postle L977, 1978).

Stiffness To obtain a measure of fabric stiffness, the American Society for Testing and Materials 1975 Designation: Dl388-64, Stiffness of Fabrics, rvas used (lStt'1, 1978). The pretesÈ included meesurements by both Èhe cantilever and heart loop methods.

The heart loop method r¡ad used for Èhe research project because the Pretest fabrics ¡¿ere too línp to be assessed by the cantilever method.

@uxtvr,tç

c3ü: ÂÁ,åi.lryffdÂ

@ {¡en¿nrF-9 43

In addition, the heart loop method eli¡ninated fabric curl and reduced variabíl-ity. The bending length was calculated accordíng to the formula outlined in the Review of Literature, page 15, and rras exPressed in centimeters.

The 15 cm strip lengÈh used was deÈermined by a bending length triaL for each fabric, as sPecified in the test method. The appropriaËe specimen width was determined in the pretest. Widths of 2.5r 3.5 and 5.5 c¡¡ were tested for ease of handl-ing, tendancy to curl, and variability.

A width of 3.5 cm rùas chosen because it ¡ras sufficient to elirninaÈe curl and it rsas the easiest to handle. The variabil-ity of the results was similar for all three widths.

Four walewise and four coursewise specimens rdere tested on the face and back. The nine mean values of bending length obtained were: (i) bending length wale¡yise, (ii) bending length coursewise, (iii) bending length waleçige face-in, (iv) bending Length coursewise face-in, (v) bending length walewise face-out, (vi) bending length coursewise face-out, (vii) bending length face-in (víii) bending length face-out¡ and (ix) bending length overall.

Shear

Since no sÈandard method for measuring the shearing properties of textile fabrics exists, a method reporÈed in the literaÈure was followed. The appartus developed by Spivak (1966) was adopted because it is simpLe in design, relatively inexpensive¡ and has several operational 44 advantages (See Chapter 2, page 24). I,lhile there nas no evidence in the literature thaÈ Spivakr s epparatus had been used to test knitted fabrics, the pretest results indicated that the apparetus was accuraÈe for knitted fabrics. The specimens did shear et constant length of sides and thus the shearing problem encountered by Carnaby and PostLe

Q974) did not occur. It was thought that this problem was avoided by using long, narrot¡ specimens and extra screws to prevent fabric slippage. In addition to the shearing apparaËus, the Instron tensile tester (ltodel TM) was used to apply and record the shearing force. The apparatus is pictured in Plates I through III.

Four components of the apparatus ¡¡ere atÈached to the Instron throughouË the testing (see PLATE I). These included the base (A), which was aÈtached to the cross-head, the uprights (B), extending fron the base, the puLley (C), and the thin rod (D), which connected the apparatus to the load cell. The mounting frame consisted of two plaËes

(E1 and E2) and two clamps (f1 and F2) (see PLATE II). The plates rrere screwed together as one and the fabric specimen was sandr¡iched between the plates and clamps ¡sith its shorter dinension perpendicular to the clamps. The entire frame was fixed to the uprights and the rod to the load cell and the normaL load (lÍ) were ettached (see PLATE III). A normal load of 5g/cn wìs utilized ín the present research. Ihis load was high enough to delay fabric buckling, but low enough so as not to dis- tort the knit structure. The load was sirnilar to that used by other researchers (Spivat and Treloar, L965; Goswami, 1977). ,.:...: :-:.r :: t.t-.:..

To test Èhe fabricrs shear properties, Èhe screws that held the plaÈes togeÈher nere removed, leaving one clamp (F1 ) and plate (Q ) suspended fron the load cell. This clamp and pLate unit remained sËation- ary. The other clamp (F, ) and plate (9 ) unit was rigidly fixed ro rhe Instron cross-head. As the cross-head moved vertically downwards, the fabric r¡as sheared through an angle, referred to as 0. The cross-head speed was adjusted each time to allor¡ the fabric specimen to buckle in about one minute. 46

PI,ATE I: The lnstron tensile tester and four components of the shearins ânnâïarus: A-base, B*uprights, C-pulley, D-connecting rod, PIATE 1I; The mounting framei El and Er-plates, F, and Fr-clamps, W

PI*ATE IIll The entire shearing apparatus assembled on the fnstron tensíle tester; S-fabric specimen, 1'J*no rma I load, 49

The specimen size for the shear test nas 5.5 by 20 cm, but Èhe actual dimensions sheared vere 2 by 20 cn. The larger síze allowed the edges of the specimen to be held securely between the plates and clamps. rn addition, three holes rtere punched in each specimen to ¿ssemmed¿Èe the clamping screrùs which also prevented specimen slippage. I,fider specimens could have been used but long, narrord specimens were known to delay the oriset of buckling (Treloar, 1965).

The Instron tensile tester recorded curves of shear stress versus shear strain which is equal to the tengent of the shear angle, e. The shearing force, s, was calculated according to the following for-mula: S=F-I{(tanO)

¡vhere ÏI is the normal load, 0 is Èhe shear angle, and F is the shear stress per uniË fabric width. since l{(tan0) was small, it was eliminated, and the above equation was approximated as S = F.

The measúrement used to express the shear characteristics of the fabrics was the secondary shear moduLus. this modulus is equal to the slope in the Linear portion of the shear sÈress-strain curve (see Figure

6r page 28). Seven walewise and seven courser¿ise specimens rùere tested to yiel-d three mean values: (i) secondary shear modulus walewise, (ii) secondary shear moduLus coursewise, and (iii) secondary shear modulus overall. The slope was not measured at the beginning of the curve because this measurement is subject to experimental error (cusick,

1961). consequently, iÈ was measured at one-half the buckling point as a point of reference for all samples. Shear stress at a specific strain 50

or sheer stiain at a specific stress nere not Eeesured because of the wide range of shear behaviors exhibited by the different fabrics.

Extension

Extensibility was determined with reference to the ASTM 1975 Designa- tion D1682-64 (AsrM, 1978), Breaking Load and Elongarion of TexÈiLe Fabrics. The Grab Method r¡as performed using the Instron Èensile tester

(Uoaet fU). Pneumatic rubber forced jaws, measuring 25.4 m wide by 38.1 m long, clamped gauge the specimen. The lengÈh was 75.0 "rm and the air pressure was 380 kN/r2. The cross-head speed was adjusted to ensure extension of the specimen to a specified load within 20 + 3 sec- onds. A low load of 100 g was chosen to símulate the extension occurring in drape. The pretest indicated that at this 1oad, the extension was at least 12. A lower percenÈage extension would have lacked accuracy. The reason for measuring percent extension at a specified load rather than-the mean load at e specified extension ¡¡as due to the wide range of exËensibiLities within the fabrics selected.

Specimens rùere extended ¡¡ith and without pretensioníng during the

Pretest. Pretensioning wes not found to improve Ëhe reproduceability, and merely gave consistently lower exËension values. Therefore, it ¡¡as decided Èo test the specimens wiÈhout pretensioning. Each specimen was centrally mounted in the top jarl and allo¡¡ed to hang freely before being fixed in Èhe bottom cl-arnp. 51

Five r¡aler¡íse and five coursewise specimens rdere tested. They measured 150 rm by 100 rm, and yielded Èhree mean values: (i) extension valewise, (ii) extension coursewise, and (iii) extension overal1.

The Structural GharacÈeristics Fabric weight sas deÈermined according t.o the Canadian National Stan- dard CAÌ,I2-4.2-þ177 Method 5^-L977 (CcSn, 1977). Five die cuÈ specimens of 6.129 cm diameter ¡¡ere taken from the fabric in moisture equil-ibrir¡m r¡ith the conditioned atmosphere and weighed on a Sartorius Autornatic Preweighing Balance.

Fabric thickness at a given pressure was determined according to the standard CGSB 4-GP-2 Method 37-L977 (CCSB, L97I). A Frazier Compressom- eter with a 25.4 rnm diameter pressure foot, \üas used. The pressure applied was 0.69 KN/n2. Five thickness measurements vrere taken from each fabric and the mean value was expressed in centimeters.

Fabric density was calculated from the mean values of fabric weight and fabric thickness. IË was determined following the relationship: fabric density, mg/cm3 = fabric weight/fabric thickness.

STATISTICAI ANAIYSIS The results of the research project nere analyzed in terms of their descriptive statistics, simpl-e linear correl-ation, and nuLtiple linear regression. The descriptive statistics included the mean data for each ,r":, :-t". :..:.. .. t-":_...... -,.--.

52 fabric and the univariate statistics for the three knit groups. The dispersions of the data were studied with reference to the hístograms. However, these histograms are not incl-uded in the thesis. Sinple linear correlation analysis between the drape coefficients and each of the independent variables ¡sas also performed but emphasis ¡sas placed on multiple linear regression analysis.

The mosË reliabl-e predictors of the drape coefficient in knitted fabrics were established using regression analysis. The Biomedical Com- puter Program (SlDp) developed by the Health Sciences Cornputing Faculty, Uníversity of California, was used (Dixon, 1973). Multiple linear regression (plR), stepwise regression (pzn), and all possible subsets regression (pgn), rrere the analyses used. The PlR analysis estimated nultiple Linear regression equations using various combinations of índe- pendent variables that were specified by Èhe researcher. rn Èhe p2R analysis, independenÈ variables were entered into and removed from a multiple linear regression eguation in a stepwise manner. The p9R analysis developed regression equations using the best subsets of predictor variables. In the P2R and P9R anal-yses the variabLes were selected for entry into the equations by the computer. In thís study, P2R and P9R were used to confirm the analysis using PlR. All three methods of analysis were used to develop predictor equations for the warp and weft knit subgroups as well as for the entire group of knitted fabrics.

Predictor equations were developed where higþ correlations were identified, according to the follolring model3

y = a * b1*1 * bz*Z + ... + bnxn + e 53 r¡here:

y is the dependenÈ or predicted variable, ie. drape coefficient, )q x_ are the independenÈ predictor variables, ie. bending L'r... p or length, shear, extension, weight, thickness, and density, br b^ are the regression coefficients, LÞ' ,... a is the intercept,

p is the number of independent variabLese and

e is the error which is assumed to be normallv distributed ¡sith Eean zero and a constant variance. Several transformation variables were also included in the regression analvsis. ChapËer 4

RESULTS AND DISCI'SSION

The results of this research project, ettained by the preceding rneth-

ods are reported and discussed in terms of: (i) description of the data, (ii) simple Linear regression, and (iii) regression analysis.

Each section includes discussions of the all knit group and Èhe warp and weft knit subgroups. Comparisons were made wíth the research findings mentioned in the rRevier¡ of LiteraÈurer. The tables presented in this chapËer include: variabl.e abbreviations, meen resulËs, univariate statistics, correlation mat.rices, and predictor equaËion constants.

Throughout this chapter several abbreviaËions were used for the variables. These are listed and defined in Table 2.

DESCRIPTION OF TTIE DATA

The mean results of each independent variable and the dependent variable (drape coefficient), for each of the twenÈy fabrics are presdnted and briefly discussed. Tables 3, 4, and 5 contain Èh.ese results. In addition, the univariate sÈatistics of each variable for the three knit groups are recorded and discussed. These univariaÈe statistics include the means, standard deviations, and the ranges of the data. They are presented in Tables 6a (a11 knit group), 6b (warp knit subgroup), and 6c

-54- 55

(¡¡eft knit subgroup). The dispersions of the data are mentioned ¡sith reference to the histograms.

Table 2 Variable Abbreviations

AbbreviaÈion Variable

DC face drape coefficient face DCback drape coefficient back DCmean drape coefficient mean blwalein bending length ¡rale¡¡ise face-in blwaleout bending length wale¡rise face-out blcoursein bending length coursewise face-in blcourseout bendíng length courser¡ise face-out blmeanin bending length mean face in bl-meanout bending length mean face out blmean bending length overall mean blwalemean bending length walewise mean blcoursemean bending lengÊh courser¡ise tnean shearwale secondary shear modulus walewise shearcourse secondary shear modulus coursewise shearmean secondary shear modulus mean extwale extension waler¿ise (100 g l-oad) extcourse extension coursewise (100 g load) exÈmean extension mean ( 100 g load) weight fabric weight thickness fabric thickness density fabric density 56

The Mean DaÈa for Each Fabric

The mean data (see Tables 3, 4, and 5) illustrate that the face and back components of the drape coefficient and the bending length values for each fabric are similar. In addition, Èhe directional components of the bending length, secondary shear modulus, and extension values for each fabric are generally sinilar.

Most of the mean values for the seven properËies are similar for the warp and weft knit subgroups, with one exception. Generally, the extension of the fabrics rùas slightly greater in the coursewise direction, but for Èhe warp knits Èhe coursewise extension was often more Lhan twice the walewise extension. Ttris suggests that extension for Èhe warp knit subgroup is more directionally dependent than extension for Èhe rseft knit subgroup.

An additional observation related to the mean data was the occurrance of re-enËrant folding in drape. The fabrics with drape coefficients of less than 25"/. fomed re-enÈranÈ folds under the projection of the drapemeter disc. Ttre face and back of fabrics H, L, and N and Èhe face or back of fabrics A, D, and G formed re-entranË folds. Three of Lhese fabrics were narp knits while three were weft knits. The re-entrant folding rùas not associated with fabric edge curling. Because the folding under the disc could noÈ be measured, there is error involved in the drape coefficients of the fabrics which exhibited re-entrant folding.

The amount of error involved is ninimal, but could noÈ accurately be estimated. Table 3 Mean Drape Coefficients and Secondary Shear Modulus Values

Mean Drape Coefficients(Z) Mean Secondary Shear Modulus Values (g/crn)

Fabric* Face*k Back# Overall W¿lsr^7isg*** Ç9u¡g grÂ7lgg**rìk Mean Mean Direction Direction

A 23.70 28.85 26.28 1226 914 1070 B 30.10 29 .02 29.56 320 330 325 C 37.09 35.35 36.22 320 330 325 D 27.12 25.94 26.53 434 518 476 E s7 .66 59. 11 58 .39 266 269 268 F 66.56 65.87 66.22 L289 I327 1308 G 26.72 24.33 25.53 480 504 492 H 77 .52 L7 .86 L7 .70 164 169 767 I 45.34 39.43 42.39 288 258 273 J 48.63 49.30 48.97 543 580 562

K 34.99 32.65 33.82 347 4r4 382 L 2r.38 18. t2 19.75 203 189 196 M 54.52 50.33 52.42 59r 655 623 N 18.99 18.60 18 .80 230 244 237 o 39 .48 35.88 37.68 r54 246 200 P 29.39 29.6r 29.50 381 560 47r q 49.46 46.37 47.89 447 347 397 R 67.IL 64.22 65.67 669 73r 700 S 29.08 29.O4 29.06 386 420 403 T 59 .85 63 .33 6r.59 4TT 364 388

Fabrics A-J are warp knits, fabrics K-T are weft kni ts ** Mean of 6 observaËions, mean standard deviation equal to 15.827. *ir* Mean of 7 observations, mean standard deviation equal to 295.90 g/"rn (Jl *J Tabl-e 4 Mean Bending Length Values (cn)

Walewise Direction Coursewise Direction

Face- Face- Face- Face- Face-in Face-out OveraLl Fabric* in** OuË*nk Mean in** out** Mean Mean Mean Mean

A t.L2 .92 L.02 .92 .97 .95 1.02 .95 .99 B .93 1.31 L.T2 1.11 .99 t .05 1.02 1.15 1.09 c 1. 15 1.57 I .36 .88 1.18 1 .03 r.02 1.38 1. 20 D .78 r.23 1 .01 I .38 1 .01 I.20 I .08 7.r2 1.10 E L.45 r.20 I .33 I .59 1.66 I .63 I.52 r.43 r.48 F 1.57 1.98 1.78 2.t4 1 .87 2.01 1 .86 1.93 1.90 G .87 I.37 T.T2 1.01 .86 .94 .94 T.I2 I .03 H 1.04 I .01 I .03 .83 .82 .83 .94 .92 .93 I 1.32 1.43 I .38 r.24 L.2T 1.23 r.28 t.32 1.30 J r.49 1.10 I .30 1.72 r.94 1.83 1.61 r.52 r.57

K 1.01 7.25 1. 13 1.16 I .06 1.11 r .09 1. 16 1. 13 L .78 1.05 .92 .90 .82 .86 .84 .94 .89 M .98 1 .39 1.19 r.26 I .00 1. 13 t.t2 1.20 1. 16 N 1.04 I .14 1.09 .86 .88 .87 .95 t .01 .98 o .98 r.25 T.T2 1 .43 L.42 1.43 r.2l t.34 1.28 P .95 1.10 I .03 I .04 .89 .97 I .00 I .00 1 .00 a 1 .61 1.87 r.74 r.64 r.74 1.69 1.63 I .81 r.72 R I .59 I.7 T 1 .65 r.44 1.41 t.43 7.52 1.56 1.54 s r.46 t.52 r.49 -87 .87 .87 T.I7 I.20 1. 19 T 2.00 1.78 t .89 1.80 I .69 r.75 1.90 r.74 1.82

* Fabrics A-J are warp knits, fabrics K-T are weft knits Mean of 4 observations, mean standard deviation equal to 0.30 cm Ltl æ Table 5 Mean Extension Values and Structural Characteristics

Mean ExÈension Values Fabric Geometric Characteristics

Fabric* I.Ialewise# Coursewise# Mean I.ieight MeAn*ick Density Direction Direction Thickness (%) (7") (i() (el^2) (cm) (togl"oP )

A 13. 93 11.37 12.65 200.22 .070 287 .68 B 10. 10 18. 51 14. 31 74.95 .049 r54.53 c 8.87 46.42 27 .65 24.46 .02L 1r8.75 D 5.55 7 .07 6.3r 165.92 .050 335.19 E 7.25 16.05 11 .65 207 .28 . r40 r47.85 F 1.48 2.69 2.09 194.42 .070 278.13 G 4.02 13.46 8.74 88 .86 .031 286.64 H 7 .95 12.59 10.27 167 .16 .051 325.85 I 4.43 11.4r 7.92 177 .75 . r09 163.52 J 3.07 r.72 2.40 I 33. 85 .045 297.44

K 11.94 12.47 T2.2L r92.27 .095 202.60 L t2.L3 L8.67 l5 .40 159.76 .056 287.33 M 4.32 7 .37 5.85 227 .0I .096 236.47 N 6.52 12.63 9 .58 I37 .02 .063 2t7.84 o 10.90 5. 88 8.39 138.77 .0 73 r91. 14 P 26.67 28.03 27 .35 r52.12 .083 183.71 a 3.94 5.03 4.49 252.47 .113 224.42 R 7. 10 I .14 7 .62 237.27 . I04 227.93 S 2.23 T4.27 8.22 153. I 1 .061 252.24 T 5.25 5.20 5.23 215. l1 .109 I98.26 * Fabrics A-J are warp knits, fabrics K-T are ¡¿eft knits Mean of 5 observations, mean standard deviation is equal to I.867" Mean of 5 observations, mean standard deviation is equal to .03 cm (¡ \o 60 The Unívariate Statistícs The Drape Coefficient

The overall mean drape coefficients of the twenty selected fabrics

(a11 knit group) ranged fron 17.69 to 66.22% ¡sith a mean of 38.707" and a standard deviation of 15.82% (see Table 6a). The r-tesr indicared thar the face and back drape coefficient values were not significantly different at the 0.10 level. The data nere nonnally distributed between the minimum and maximum vaLues on the histogran. The warp knit subgroup and wefÈ knit subgroup drape coefficient values vrere noÈ significantly different (see Tables 6b and 6c) and there \ùere no significant differences between DCface and DCback. The ranges and standard deviations were similar for the two groups. The drape coefficienË range in this research was larger Èhan Sudnik's (1972) range for knitted fabrics. His drape coefficient values using a 3O-cm-specimen size ranged from 20.8 to 40.57., however, he tested tricot knits only. No measures of variability were given.

The Bending LengËh

The overall mean bending Lengths (calculated from blwalemean and blcoursemean) for the tr¡enty fabrics ranged from 0.89 to 1.90 cn, with a mean of L.26 cm and a standard deviation of 0.30 cm (see Tabl-e 6a). The other bending length mean values did not vary significantly (0.10 level) from Èhe overall mean and no significanÈ differences \Íere identified between the face (bLneanin) and back (blneanouË) and directional conponents (bh¡alenean and blcoursemean). Most of the data for each bending 61

length variable were close to the minimum bending length value on the

h istogram.

The warp knit subgroup and weft knit subgroup bending length values nere not significantly different (see Tables 6b and 6c). As for the all knit group, there rrere no significant differences identified between the overall mean and the other bending length values or between the face and back and directional components. The ranges and sËandard deviations l¡ere similar for the two groups. The range of bending length values could not be compared to the range found by Brown (1978), who also used the heart loop method for knitted fabrics, because different strip widths were used.

The Secondary Shear Modulus

The overall mean secondary shear modulus values for the twenty fabrics ranged from 152.14 to l30B.86 g/cm, wirh a mean of 454.3L g/cn and a standard deviation of 295.90 g/"r (see Table 6a). There nas no significanÈ difference (0.10 level) between the directional components.

This is in agreement with Gibson and Postle (1978) who stated rhat the shearing behavior of a knitted fabric tends to be independent of the direction of the applied strain. Most of the data r^¡ere in Èhe lower region on the histogran. The meen, standard deviation, and range for the warp knit subgroup were larger than those for the weft knit sub- grouP, howeverr the means were not signifícanÈly different (0.10 level)

(see Tables 6b and 6c). This does not concur with statenents bv Gibson 62 and Postle ¡rho reporÈed that shear in knitted fabrics is a function of fabric Èype. As for the all knit group, there nere no significant differences between the directional componenÈs for the subgroups. Measures of the ranges and variabl-ities of the secondary shear modulus values for knitted fabrics were not available in the literature.

The ExÈension

The overall mean exÈensions at a 100 g load for the t¡senty fabrics ranged from 2.09 to 27.65i¿, with a rnean of 10.427" and a standard deviation of 6.867" (see Table 6a). There nas a significant difference between the directional components for Èhe all knit group at the 0.05 level. Most of the data were close to the minimr:m value on the histogran. There were no significant differences between the warp and weft knit subgroupsf extension values. However, as for the all knit group, there was a significant difference between the directional components for the warp kniÈ group (see Table 6b). There rùes no significant difference between the directional components for the weft knit subgroup

(see Table 6c). The ranges for the warp and r¡eft knit subgroups were similar with one exception. The maximum percent extension in the coursewise direction for the warp knit group !¡as 46.4271. I.Iith the exception of this fabric the maxiuun percent exEension in coursewise direction for the warp knit subgroup was 18.5I"Á. Ranges and variabili- ties of the percent extension at a 100 g load ¡rere not found in the literature. 63

Fabric T{eight

The weights for the twenty selected fabrics ranged fron 24.46 to

252.47 g/^2, rvith a mean of L64.99 glnL and a standard deviation of

56.4L g/r2 (se" Table 6a). The mean weight val-ues for the warp and weft knit subgroups were significanÈly different at the 0.05 level (see Tables 6b and 6c). Most of the data were in the upper region on the histogram. Standard deviations were sirnilar for the two subgroups, but the range for the weft knit subgroup was narro\{er.

Fabric Thickness

The thíckness values for the twenty selected fabrics ranged froro 0.02 to 0.14 crn ¡¡ith a mean of 0.07 cn and a standard deviation of 0.03 cn

(see Table 6a). The distribution of the daËa rras nornal on the histogram. The mean thickness values for the warp and weft knit subgroups were significantly different at the 0.05 level (see Tables 6b and 6c). The standard deviatíons were similar, but the range was greaLer for the warp knit subgroup.

Fabric Density

The range of densities for the ¡¡eft knit subgroup !úas narrower than that for the warp knit subgroup (see Tables 6a, 6b, and 6c). The warp knits had a density range of 118.75 to 335.19 ng/cn3 to 183.71 "orp"r"d to 287.33 ng/cn3 for the weft knits. The rneans, however, rùere not significantly different. The data appeared normally distributed on the histogram. 64

Table 6a Univariate Statistics - All Knit Group

Varí ab 1e Mean Standard Minimum Maximr¡m Deviation

DCface (%) 39.23 r5.90 17.52 67 .IT DCback (%) 38 .16 15.84 L7 .86 65.87 DCroean ( %) 38. 70 15.82 L7.69 66.22 extwale (Z) 7.88 5. 65 1.48 26.67 extcourse (%) L2.95 10. 06 r.72 46.42 extnean (Z) L0.42 6. 86 2.09 27 .65 shearwale (e/cn) 448.52 3I2.4I 14t.43 1288.57 shearcourse (g/cr) 460.11 286.45 162.86 1327 .14 shearmean (g/cn) 454.3r 295.90 152.14 1307.86 blwalein (cn) L.2I .33 .78 2.00 blwaleout (cm) I .36 .30 ot r.99 blcoursein (cm) r.26 .37 .83 2.14 blcourseout (cm) T.2I .38 .82 7.94 bhoeanin (cn) I.23 .32 .84 on blneanout (cm) 1 .30 .30 o, .93 blmean (cm) r.26 .30 .89 .90 blwalemean (cn) L.28 .29 .92 1.89 blcoursemean (cn) r.24 .37 .83 2.01 weight (e/#) 764.99 56.4r 24.46 252.47 thickness (cn) .07 .03 .02 .14 density (ng/cn3) 230. 88 61.68 118 . 75 335.19 65

Table 6b Univariate Statistics - I,Iarp Knit Subgroup

Variable Mean Standard Minimum Maximu DeviaÈion

DCf ace ("Á) 38.04 15. 99 17 .52 66.56 DCback (Z) 37 .5r r5.84 17 .86 65.87 DCmean (%) 37.78 15.85 17.69 66.22 extwale (Z) 6.67 3.72 r .48 13. 93 extcourse (Á) 14.13 12.55 I.72 46.42 extmean (% ) 10.40 7 .29 2.09 27 .65 shearrsale (g/cn) 515.04 41 1.85 r4r.43 7288.57 shearcourse (g/cn) 503. 14 369.24 162.86 1327 .r4 shear-mean (g/cm) 509 .09 387.29 r52.14 1307. 86 blwalein (cm) 1.17 ,Q .78 L .57 blwaleout (cn) I .31 .31 .92 1. 98 blcoursein (cn) I.28 .43 .83 2.t5 blcourseout (crn) t.25 .42 .82 r.94 blmeanin (cm) 7.23 .32 .93 1.86 blmeanout (cm) L.32 .31 ot 1.93 bl-mean (cm) r.25 .31 .92 1 .89 blwalemean (cn) r.24 .24 I .00 1. 78 blcoursemean (cn) 7.27 .4r .83 2.OL weight (e/.2) r43.49 61.52 24.46 207 .28 thickness (cro) .06 .04 .02 .14 densiry (*e/"# ) 239.56 82.99 118. 75 335.19 66

Table 6c Univariate Statistics - I.IefÈ Knit Subgroup

Variable Mean Standard Miniuum Maximum Deviation

DCface (%) 40.42 16.58 18. 99 67 .II DCback (%) 38 .81 16.66 18.12 64.22 DCmean (%) 39 .62 16.58 18.80 65 .67 extwale (Z) 9.10 7.08 2.23 26.67 extcourse (Z) LI.7 6 7 .26 5.03 28.03 exÈmean (Z ) 10.43 6.79 4.49 27 .35 shearwale (g/cn) 382.00 I 63. 09 r54.29 668.57 shearcourse (g/cn) 4r7 .07 181.04 188 .5 7 73r.43 shearmean (g/crn) 399.54 167.87 r95.7r 700.00 blwalein (cn) r.24 .39 .78 2.00 blwaleout (cn) r .41 .30 .05 1. 87 blcoursein (cn) r.24 .33 .86 1. 80 blcourseout (cn) 1.18 .36 .82 r.74 blneanin (crn) 1.24 .33 .84 1. 90 blmeanout (cm) L.29 .31 .93 1.81 blmean (cm) L.27 .32 .89 L.82 blwalemean (cn) L.32 .34 .92 1. 89 blcoursemean (cm) I.2T .34 .86 r.75 weight (e/n¿) 186.49 43.67 r37.02 252.47 thickness (cm)^ .09 .02 .06 .ti density (rg/cn') 222.L9 31 .28 I 83. 71 287.33 67

SIMPLE LINEAR CORRELATION

The sinple linear correlation beÈween the drape coefficients and each of the independenË variables are briefly discussed. The correlation matrices are presented in Table 7 (a11 knit group), Table I (warp knit subgroup), and Table 9 (weft knit subgroup).

The Drape Coefficient and the Defomation Properties The Drape Coefficient and the Bending Length

Generally, the highest correlation rùas found between the nine bending length variables and the drape coeffícients. The high, positive corre- laÈion concurs with the findings of Peirce (1930), Kim and Vaughn (1974)

and Morooka and ttiwa (1976) for \roven fabrics; Cusick (f965) for rùoven

and nonr¡oven fabrics; and Sudnik (1972) for lroven, nonwoven, and knitted fabrics. The correLation coefficient,s (r) in the present research ranged fron 0.67 to 0.90 for the al-l knit group, from 0.53 to 0.96 for the warp knit subgroup, and from 0.67 to 0.85 for the weft knit sub- grouP.

The correlations did not vary with the components of Èhe drape coefficient variable, however, they did vary with the bending l-ength variables. For instance, in the warp knit subgroup, correlation of blwaleout with DCnean resulted in an r value of 0.58, whereas, correlation of blmean with DCnean resulted in an r value of 0.96. 68

Ttre Drape Coefficient and the Secondary Shear Modulus The secondary shear modulus values were found Èo be positively correlated with the drape coefficient in this research. This is in agreenenË with the results reported by Cusick (1965) for woven and nonwoven fabrics, Sudnik (1972) for woven, nonwoven, and knitted fabrics, and Kirn and VaughrL (1974) and Morooka and Niwa 0976) for woven fabrics. In the present research the correlaÈion coefficients ranged from 0.35 to 0.46 for the all knit group and from 0.27 to 0.45 for the warp knit subgroup.

These values were lower than the Spearman rank coefficient,s reported by

Kim and Vaughn Q974) for rüoven fabrics and by Sudnik (1972) for woven, nonwoven and knitted fabrics. Kim and Vaughn reported a coefficient, of 0.89 between the drape coefficient and the initial shear modulus, while

Sudnik reported a coefficient of 0.59 between the drape coefficient and the shear angle. In Èhe present research, correlations between the drape coefficient values and the secondary shear modul-us values were higher for the r¿eft knit subgroup. The r values ranged from 0.60 to

0.77. The correlations did not vary with the face and back components of the drape coefficient or Èhe directional conponents of the shear modulus values for any of the three knit groups.

The Drape Coefficient and ExÈension

The values for percent extension at a 100 g load nere negatively related to Èhe drape coefficient values in this research. This concurs yvith the findings of Peirce (1930), Chu et al (1963), and Kim and Vaughn 0974) for woven fabrics. These researchers, however, found that exten- 69 sion and the drape coefficient were highly correlated. For instance,

Kim and Vaughn reported a Spearman rank coefficient of O. g8 between the percent exËension at a 1000 g l-oad for woven fabrics. However, the r values in this research ranged from -0.36 to -0.42 for the all knit group, from -0.19 to -0.58 for the warp knit subgroup, and from -0.35 to -0.65 for the weft knit subgroup. These low correlations, however, con-

cur ¡sith the findings of Morooka and Niwa Q976) for wovens. The degree

of correlation did not vary with the drape coefficient face and back

comPonents for any group, but varied with the directional components of the extension for Èhe warp and weft knit subgroups.

Tt¡e Drape Coefficíent and the Structural Characteristics

The Drape Coefficient and Fabric lfeight Fabric weight was found Èo be positively related to the drape coeffi-

cient valuesr concurring with research by Kin and Vaughn (1974) but not ¡yith Chu et al (f963) and Morooka and Niwa (1976). All researchers tested lùoven fabrics. In the present research the r value was 0.82 for the weft knit subgroup, 0.32 for the warp knit subgroup, and 0.51 for the all knit group. The degree of correLation did not vary with the face and back conponents of the drape coeffícienË.

The Drape CoefficienÈ and Fabric Thickness Correlation rùas positive between fabric thickness and the drape coefficient valuesr supporting previous findings for woven fabrics (Kin and Vaughn, 1974; Morooka and Niwa, L976). The r values were approximately 70

0.60 for the aLl knit group, 0.52 for the warp knit subgroup, and 0.85 for Èhe ¡¡eft knit subgroup. The Spearman rank coefficient reported by

Kin and Vaughn was 0.55. Again, the degree of correlaÈion did not vary with the face and back components of the drape coefficient.

The Drape Coefficient and Fabric Density Fabric density was negaÈively related to the drape coefficient values in this research but the correlation rüas poor for all three knit groups. The r value ranged from -0.22 to -0.33. In most cases, the correlations were higher beËween weight and the drape coefficient and thickness and Èhe drape coefficient then between density and the drape coefficient.

Past research was not available in the literature for comparison. The degree of correlation did not vary with the face and back components of Èhe drape coefficient.

REGRESSION ANALYSIS In order to develop the best predictor equations, three differenÈ strategies of estinating regression equations were performed using the

BMDP computer program. They were: nultiple linear regression analysis (PfR), stepwise regression analysis (pZn), æd all possible subsets regression analysis (pgn). Multiple f-inear regression !üas the original analysis used and the other tno were used subsequently to confim the findings. Approxinately 150 program executions r¡ere completed for each of the all knit group and the warp and weft knít subgroups. Sanple program executions are included in Appendix B. Table 7 Correlation Matrix - AlL Knit Group

DCF DCB DCM Ef{ EC mt SüT SC SM BI,{I B}TO BCI BCO B['{I BI'IO B['f BT{I,T BCM WT TII DEN DCF 1.0 DCB .99 1.0 DCM 1.0 1.0 1.0 EI{ -.39 -.36 - .37 1.0 EC -.36 -.36 -.36 .49 1.0 EM -.42 -.4I -.42 .76 .93 1 .0 SI,J .35 .47 .38 -.14 -.40 -.35 1.0 sc .42 .46 .44 -.LL -.39 -.33 .95 I .0 sM .39 .44 .41 -. r3 -.40 -.35 .99 .99 1.0 BWr .74 .79 .77 -.44 -.34 -.43 .28 .23 .26 t .0 BWO .70 .67 .69 -.5r -.17 -.33 .26 .30 .28 .67 1.0 BCr .84 .85 .84 -.40 -.59 -.59 .41 .47 .45 .65 .59 r.0 BCO .81 .83 .82 -.40 -.43 -.48 .29 .30 .30 .76 .54 .9r 1.0 BMr .87 .90 .89 -.46 - .52 -.57 .38 .39 .39 .90 .69 .92 .92 1.0 BMO .83 .82 .83 -.48 -.32 -.43 .29 .31 .30 .76 .83 .85 .87 .89 1.0 BM .88 .90 .89 -.49 -.44 -.53 .35 .37 .37 .87 .7 I .91 .93 .98 .94 1.0 BI,üM .79 .80 .80 -.52 -.28 -.42 .29 .29 .29 .92 .90 .68 .72 .88 .87 .91 I .0 BCM .84 .86 .85 -.41 -.52 -.55 .36 .39 .38 .72 .58 .98 .98 .94 .88 .94 .72 1.0 r{T .50 . 51 .51 -.14 -.65 -.53 .38 .34 .37 .46 .25 .46 .34 .51 .24 .43 .40 .47 I.0 lH .60 .59 .60 .001 -.36 -.26 .06 .04 .05 .51 .26 .45 .40 .52 .33 .47 .43 .44 .80 1.0 DBI -.27 -.25 -.26 -.24 -.51 -.48 .38 .37 .38 -.18 -.23 .002 - .14 -.09 - .28 -.L5 -.22 -.07 .22 -.35 1.0

K.r

DCF - drape coefficient face SM - secondary shear moduLus BMI bending Length mean face in DCB - drape coefficient back mean BMO bending length mean face out DCM - drape coefficient mean BI,II - bending length wal-ewise BM bending length overall mean EI.f - extension wal"ewise face ín BI,tM bending length waLewise mean EC - extension coursewise BI,IO - bending length walewise BCM bending length coursewise mean EM - extension mean face out I{T weight Sll - secondary shear modulus BCI - bending 1-ength coursewise TTI th ickness walewise face in DEN dens ity SC - secondary shear modulus BCO - bending length courser¿ise coursewise face out Table I Correlation MaÈrix - Ilarp Knit Subgroup

DCF DCB DCM EW EC EX'f SI^I sc SM Èt{I BI,IO BCI BCO Bil'f I Iß{O ûil't BI,üM BCM WT 1]T DEN DCF 1.0 DCB .98 1.0 DCr{ 1.0 1.0 1.0 Et{ -.58 -.48 -.53 1.0 EC -.L9 -.22 -.2L .44 1.0 Elf -.31 -.31 -.31 .63 .97 1.0 sr{ .27 .36 .32 -.03 -.49 -.42 1.0 sc .38 .45 .42 -.24 -.54 -.53 .97 1.0 sM .33 .4L .37 -.t3 -.52 -.48 .99 .99 1.0 BI'f I .87 .89 .88 -.39 -.22 -.29 .31 .35 .33 1.0 BWO .62 .53 .58 -.57 .74 -.02 .22 .38 .30 .34 1.0 BCr .87 .87 .87 -.69 -.56 -.66 .44 .60 .52 .70 .51 1.0 BCO .91 .93 .92 -.55 -.31 -.41 .30 .4r .36 .89 .38 .88 I .0 BMr .94 .95 .95 -.62 -.46 -.55 .42 .54 .48 .88 .48 .95 .96 1.0 BMO .87 .83 .85 -.54 -.I0 -.22 .26 .41 .33 .67 .76 .81 .79 .81 I .0 BM .96 .96 .96 -.66 -.32 -.44 .38 .52 .45 .86 .63 .95 .94 .98 .89 1.0 B!'lltl .90 .86 .88 -.59 -.04 -.18 .32 .44 .38 .80 .84 .73 .76 .82 .87 .90 1.0 BClf .91 .93 .93 -.64 -.45 -.55 .38 .52 .45 .82 .46 .97 .97 .98 .83 .97 .77 1.0 r{T .29 .36 .32 -.10 -.70 -.63 .46 .42 .45 .40 -.19 .44 .28 .45 .04 .29 .11 .37 1.0 Trr .51 .52 .52 -.03 -.28 -.25 .04 -.01 .01 .51 -.06 .36 .34 .45 . 15 .34 .26 .36 .73 1.0 DEN -.33 -.27 -.30 -.22 -.68 -.64 .42 .45 .44 -.22 -.29 .11 -.10 -.02 -.34 -.I2 -.32 .01 .38 -.31 1.0

4eI.

DCF - drape coefficient face SM secondary shear modulus BMI bending length mean face in DCB - drape coefficient back mean BMO bending length mean face out DCM - drape coefficient mean BWI - bending length walewise BM bending length overall mean E'tI - extension walewise face in BI,II'í bending length walewise mean EC - extension coursewise BIIO - bending length r¿alewise BCM bending length coursewise mean B{ - extension mean face out WT weight SI,f - secondary shear moduLus BCI - bending length coursewise rïI th ickness { lualewise face in DEN density l\) SC - secondary shear modulus BCO - bending length coursewise coursewise face out Table 9 Correlation Matrix - l{eft Knit Subgroup

DCF DCB DCM Et^I EC H'l sw sc SM BÌ^TO B!üI BCI BCO BMI BMO BM BWM BCM T.TT TTI DEN DCF 1.0 DCB .99 1.0 DC'I'Í 1.0 1.0 1.0 Er{ -.36 -.35 -.35 1.0 EC -.65 -.62 -.64 .79 1.0 EM -.53 -.51 -.52 .95 .95 1.0 sw .77 .76 .77 -.26 -.25 -.27 1.0 sc .62 .60 .61 .06 .02 .04 .90 1.0 slt .7L .69 .70 -.09 -.tl -.11 .97 .98 1.0 BI{T .67 .74 .70 -.s1 -.s4 -.55 .47 .20 .34 1.0 Blro .78 .81 .80 -.61 -.68 -.68 .62 .31 .47 .92 1.0 BCr .84 .85 .84 -.27 -.70 -.51 .37 .17 .27 .69 .76 1.0 BCO .73 .74 .74 -.34 -.73 -.57 .26 .02 .74 .74 .80 .96 1.0 BMI .81 .85 .83 -.44 -.66 -.s8 .46 .20 .33 .93 .92 .91 .91 1.0 BMO .80 .81 .81 -.49 -.74 -.65 .45 .16 .31 .86 .94 .91 .96 .96 1.0 BM .81 .84 .83 -.47 -.71 -.62 .46 .18 .32 .91 .94 .92 .94 .99 .99 1.0 BI{l,l .73 .78 .76 -.57 -.6L -.62 .55 .25 .40 .98 .97 .74 .78 .95 .92 .94 1.0 .79 BCM .80 .80 -.31 -.72 -.55 .32 .09 .20 .72 .79 .99 .99 .92 .95 .94 .77 t .0 r{T .83 .80 .82 - .41 -.55 -.51 .80 .52 .67 .58 .78 .70 .64 .69 .74 .72 .68 .67 1.0 .84 Tn .85 .85 -.16 -.50 -.36 .69 .52 .61 .61 .7 4 .84 .76 .78 .79 .79 .81 DEN .68 .88 1.0 -.22 -.27 -.24 -.39 -.06 -.17 .02 -.15 -.07 -. 16 -.07 -.42 - .38 - .30 -.25 -.28 -.12 -.40 .04 -.42 1.0

T9T

DCF drape - coefficient face SM secondary shear modulus BMI bending length mean face in DCB drape coefficient back - mean BMO bending length mean face out DCM drape coefficient meen - BhII bending length walewise BM bending length overaLl mean ET{ extension walewise - face in BWM bending length walewíse mean EC extension coursewise - BI^TO bending 1-ength walewise BgM bendíng length coursewise mean m{ extension mean - face out I,TT weight SIII - secondary shear rnodulus BCI bending length coursewise ÏTI th ickness walewise face in DEN density SC - secondary shear moduLus BCO - bending length courser¡ise { coursewise face out 74

The estination of multipl-e regression equations utilizíng PIR

included all the independenË variables specified by the researcher. The

possibLe conbinations of variables which included bending lengÈh were

selected for the analysis. One of the bending length variables was always included because the literature indicated that it night be a good predictor of the drape coefficient and because the r value was high in simple linear correlation in the present research. The criteria uti- 2 lized, to choose the best predictor equation included the R value (coefficient of mulÈiple determination), the probability level of the F-ratio (indicates ntrether alL the regression coefficients are significantly different from zero), Ëhe standard error of the esÈimate (a measure of the variation of the Y value about the regression l-ine), and the probability level of the t-statistic (indicates whether the individual regression coefficient for each variable is significanily different from zero in the presence of the other variables). Appendix A, Table 16 contains the R2 and standard error of the estimaÈe values as well as the

F-ratios and the t-stetisËics for all of the conbinations thaÈ were attempted.

The stepwise method of analysis entered variables into a uulÈiple linear regression equation in a stepwise manner. Forward stepping (beginning with no predictors) was performed. The F-to-enter and F-to-

remove values were 3.9 and 4.0, respectively. AË each step, the variable that had the highest partial correlation with Èhe drepe coefficienË nes added. The criteria utilized to choose the best predictor equation were sinilar to those for muLtíple linear regression analysis (PfR). 75 The all possible subsets method identified the best subseËs of pred-

ictor variables. In the analysis the best subset nas Èhe subset that maximized R2. Stepwíse and all possibl-e subsets regression analyses

índicated the best regression equations and thereby combinations which did not include bending lengÈh were analyzed.

By using these Èhree Èypes of regression analysis and studying transfomation variables as ¡¿ell as the original independent variables, one best predictor equation was idenÈified for each of the all knit group

and the warp and weft knit subgroups. In addition, several other good predictor equations were developed. The number of variables introduced into the regression equation was linited for each anal-ysis in order to ensure thaÈ an adequate number of degrees of freedom remained for error.

Also, because the independent variables of the same measurement rúere linearly correlated with each other (see Tables 7, 8, and 9), only one was introduced at a Èime into the equation.

All Knit Group Multiple Linear Regression Analysis Since the literature indicated that bending Length was the physical- property nost highly correlated with the drape coefficient, bending length lres grouped with the secondary shear modulus (shear)¡ extension, weight, thickness, and density in two, three, four, five, and six varía- ble combínations. This was done in order to examine the relationships between the drape coefficient and all Èhe possible combinations of vari- 76

ables r¡hich included bending lengÈh. A listing of these combinations is presenÈed in Table 10. Only the overall tnean measurements were utilized

in this analysis. The BMDP-PIR comPuter program was utilized.

Table 10

VariabLe Combinations Including Bending Length

g 2 variable combinations bl - bending l-ength b1-sh sh - shear b1-rh ext - percent extension b1-ext rút - weight b1-den th - thickness b1-wË den - density

¿ variable combinations 4 variabl-e combinations b1-sh-ext b1-sh-exÈ-wt b1- sh- th b1-sh-ext-th b1-sh-den b1-sh-ext-den bL-sh-wt b1-sh-den-wË b1-ext-th b1-sh-den-Èh b1-ext-¡sÈ b1-ext-¡¡t-den bl-ext-den b1-ext-th-¡rt b1-den-¡¡t b1-ext-den-th b1-den-th b1-wt-th-den b1-¡¡t-Ëh b1-sh-rvt-th

I variable combinations 6 variable combinations b1- sh-vrt-th-den b1-sh-ext-wt-th-den b1-sh-rst-th-ext b1-sh-wt-den-ext b1-sh-den-ext-th b1-den-th-ext-rüt 77

For the al-l knit group the F-ratios ínvariably had probabílity levels of 0.01 or lèss (see Appendix A, Table 16a).

Analysis of the two-variable cornbinations indicated that the blmean- thickness conbination had the highest R2 value (0.84) and the lowesr standard error of the estimate (6.71). It was the only combination where boÈh variables had probability levels of 0.10 or less in the t-test. Therefore, the addition of thickness as a variable added new information. The R2 values for Ëhe other two-variabLe conbinations ranged from 0.80 to 0.81 and Ëhe standard errors of the esÈimate ranged fron 7.2L to 7.46.

Analysis of the three-variable combinations indicated that Ëhe addition of a third variable did not increase the R 2 value or decrease the standard error of the estimate enough to justify using a third variable in the equation. The blmean-shearmean-thíckness combination had an R2 value of 0.85 and a standard error of the estimate equal to 6.58¡ but shearmean did not contribute additional information. ThaÈ is, the probability leveI of the t-statistic for shearmean was greaÈer than 0.10.

In the blmean-shearmean-density and blmean-weight-density combinations all three variables had probability levels equal to 0. l0 or less in the t-test. Í{hen shearmean and density were both included with blmean, they added new infomation. The same was true for weight and density. The R2 value ¡¡as 0.84 and the standard error of the esËimete was 6.8 for both of these three-variable combinations. Generally, for the other three variable combinations, the probabiliy levels of the t-statistics r¡ere 78 greater than 0.10 for all of the the variables except blmean and thickness. For these combinations the R2 values ranged fron 0.81 to 0.84 and the standard errors of the estirnates ranged fron 6.58 to 7.47.

In all of the four-variable combinations the R2 val-ues ranged from 0.83 to 0.87 and the sÈandard errors of the estimates ranged fron 6.33 to 7.2L. However, these changes lrere not appreciable and therefore there was no justificaÈíon to include a fourth variable in the equation.

As in the three-variable combinations, in most cases only blnean and thickness had t-test probabiLity levels of 0.10 or less. None of the four-variable combinations resulted in t-test probability levels of 0.10 or less for all of the variables.

The ranges of the R2 values and the standard errors of Èhe estimates for Ëhe five-variable conbinations were similar to those for the four- variable combinations. In addition, only one or two variables had t-test probability levels of 0.10 or less. None of the five-variable combinations rrere considered useful.

The six-variable combination had an R2 value of 0.87 and a standard error of the estimate equal to 7.03, but only blmean had a t-test probability of 0.10 or less.

The nultíple linear regression analysis yielded four useful variable combinations for the prediction of the drape coefficient. They were:

(i) blnean-thickness, (ii) blnean-shearmean-density, (iii) blmean- weight-density, md (iv) blmean-shearmean-thickness, the best being blmean-thickness. 79 SÈepwise Regression Analysis

Stepwise regression analysis Ìres used to confirm the conclusions

arrived at by rnultiple linear regression analysis. The BMDP-P2R program was used.

In order to deÈermine which independenÈ variables were the best pred-

ictors, each of the eighteen independent variables had an equal chance of being entered into the equation. That is, in addiËion to the overall ueansr æY of the directional and face and back means could be entered

int.o the equaËion. The analysis entered blmean and thickness into the equation. Shearcourse ldes the next variable for enËry into the equation buÈ the F-l-evel was insufficient for further stepping. stepwise regres-

sion analysis confirmed the besË tr¡o- and three-variable conbinations as indicated in the nultiple linear regression anaLysis.

A1l- Possible Subsets Analysis

The all possíble subsets analysis also allowed entry of any of the eighteen independenÈ variables inÈo the equation. The esÈination of the

best subseÈs of predictor variables carried out via BMDP-P9R indicated that the blmean-thickness conbination was the best trvo-variable subset.

This is consistent r¡ith the muLtiple linear and stepwise regression ana-

lyses conclusions. The best three-variable subset was blmean-shearc-

ourse-Èhickness with an R2 val-ue of 0.86. In addition, the blmean- shearmean-thickness combination had an R2 value of 0.85. These results are in agreement with stepr¡ise and nultiple l-inear regression analyses, respectiveLy. Either three-variable conbination is useful. 80

I{arp Knit Subgroup Multiple Linear Regression Analysis

The procedure followed and criÈeria used for selecting the predictor variables for the warp kniÈ subgroup were identical to thaË for the all knit group. Like the all knit group, the F-ratios for the warp knit

subgroup invariably had a probability level of 0.01 or less (see Appen-

dix A, Table 16b ).

The two-variable combination analysis indicated that bl-mean-thickness

and blmean-density were good predictor combinations. The former had an

R2 value of 0.97 and a standerd error of the estimate equal to 3.15, while the latter had an R2 value of 0.96 and a standard error of the estimate equal to 3.41. These were the only combinations where both variables had t-test probaLil-ity l-evels of 0.10 or less. In the other t¡¿o-variable combinaÈions the R2 values ranged from 0.93 to 0.94 and the standard error of the estimate ranged fron 4.28 to 4.73.

Analysis of the three-variable cornbinations indicated that in four of the cmbinations the addition of the third variable appreciably affected the R2 and standard error of the estimate values. In addition, the Ëhírd variable added new infomaÈion, as the t-test probability 1evels were 0.10 or less for all the variables. The four combinations rúere: blmean-extnean-thickness (n2=0.99, standard error of the estimate=1.87)t blmean-weight-density (R2=0.98, standard error of the estimaÈe=2.40), blmean-¡veight-thickness (n2=0.99, standard error of the estimate=2.26), and blmean-thickness-density (n2=0.99, sÈandard error of the esti- 81

rnate=2.17). In the other three-variable combinations the R2 values

ranged from 0.94 to 0.97 and the standard error of the estimate ranged from 3.30 to 4.7I.

In the four-variable combinations the R2 and standard error of the estimaÈe values did not change enough to justify including a fourth var-

iable in the equation. In all of Èhe four variable groups the R2 values

ranged from 0.97 to 0.99 and the standard errors of the estimaÈes ranged

from 1.88 to 3.86. In addition, there was always one variable and some- times two or three variables that had probability levels greater than 0.10 in the È-test.

In the five-variable combinations the R2 val,res were 0.99 and Ëhe

standard errors of the estimates ranged from 1.76 to 2.80, but only one or trùo variables had t-test probability levels equal to 0.10 or less.

In the six-variable combination all six variables had t-test probability levels of 0.05 or less. The R2 value was 0.99 and the standard error of the estimaÈe was 0.73.

The multiple linear regression analysis yielded seven acceptable variable conbinations for prediction of the drape coefficient. They were: blmean- thicknes s, blmean-dens i ty, blnean-thicknes s-dens i t y, blmean- exhean-thicknes s, blmean-wei ght-density, bhnean-wei ght-thicknes s, and blmean-shearmeen-exËmean-weight-thickness-dens i ty, the bes È being blmean-extnean-thicknes s . 82

Stepwise Regression Analysis

Stepwise regression analysis confirmed the conclusions arrived at by nuLtiple linear regression analysis. The stepwise analysis entered blmean, thickness, and extmean into the equation. This three-variable conbination was superior to blmean-thickness as Èhe standard error of the estimate decreased from 3.15 to 1.87.

All Possible Subsets Regression Analysis All possible subsets regression analysis confirmed bhnean-thickness as the best two-variable combination for prediction, and bluean-extmean- thickness as the best three-variable combination.

VJeft Knit Subgroup

Multiple Linear Regression Analysis The procedure and criËeria used for variable selection for the weft

knit subgroup were the same as those used for the all knit group and the

warp knit subgroup. The probability levels of the F-ratios varied and will be quoËed where applicabl-e (see Appendix A, Table 16c).

Of the two-variabl-e cornbinaÈions, Èhe blmean-sheer:rnean combinaÈion had the highest R2 and F values and the lo¡rest standard error of the estimate. The R2 value was 0.90, the F-ratio had a probabiliÈy level of less than 0.01, and the standard error of the estimate was 6.01. This was the only combination where both variables had t-test probability

levels of 0.10 or less. The other two-variable conbinations had R2 83 velues renging from 0.69 to 0.79, standard errors of the estimates ranging fron 8.62 to 10.52, and F-ratio probability levels bet¡¡een 0.10 and

0.01 .

The ranges of the regression coefficienÈs, the sÈandard errors of the estimates, and the probability levels for the F-raÈios for the three- variabLe combinations were sinilar to those for the tr¡o-variable combinations. In addition, blmean and shearmean nere the only variables with t-test probability levels of 0.10 or less. The blmean-shearmean-thickness combination had the highest R2 value and lowest standard error of the estinate value.

The four-variable combinations had regression coefficients ranging frorn 0.80 to 0.91, but Èhe standard errors of the esÈimaËes did not decrease and the F-ratios had probability l-evels of 0.05 or 0.r0. rn addition, the probability levels of the Ë-tesËs !üere usual-1y greater than 0. I0 for all of the variables. Sinilar results were observed for the five- and six-variable combinations.

MuLtiple linear regression analysis of the weft-knit group yielded one good variable combination: blmean-sheannean.

Stepwise Regression Analysis Stepwise regression analysis lras able to confirm the conclusions arrived at by nultiple l-inear regression anaLysís. I,Ihen al-l eighteen independent variables had an equal chance of being entered into the 84 equation, the analysis entered thickness, only. The R2 value was 0.72 and Èhe standard error of the estimate vas 9.27. Thickness was the variable most highly correlated with the drape coefficienË in sirnple linear

correlation (see Table 6c). I{hen the Ëolerance levels were lowered, Ëhe stepwise analysis entered thickness, blmean, and shearcourse into the equation. The R2 value was 0.91 and Èhe standard error of the estimate vas 6.26. Ho¡sever, multiple linear regression analysis indicated that the blmean-shearmean combination had an R2 value of 0.90 and a standard error of the estimate equal to 6.01. The inclusion of thickness as a third variabl-e did not improve prediction. In addition, Èhe Ëhickness- bLuean conbination had an R2 value of 0.79 and a standard error of the estimate equal to 8.46 and therefore, the blmean-sheercourse combination rres a better two-variable predicËor combination.

By arranging for bending Length to be entered into the equation before any other variables, the analysis entered blcoursein, sheatmean, and thickness into the equation. The blcoursein-shearnean combination had an R2 value of 0.95 and a standard error of the estimate equal to

4.07, while the blcoursein-shearmean-thickness combination had an R 2 value of 0.97 and a standard error of the estimate equal to 3.25. The addition of thickness, therefore, did noÈ improve prediction appreciably. 85 All Possible Subsets Regression Analysis 4L1 possible subset regression analysis confi::med blcoursein-shearmeen as the best two-variable cornbination for prediction and bl-coursein-

shearmean-thickness as Èhe best three-variabl-e combination.

Directional and Face and Back ComponenÈs Extensive analysis was not done on the face and back and directional

components of the variables because the correlation matrices (Tables 7r8, and 9) indicated thet the components rsithin each variable were linearly related and that the correlations between the drape coeffi-

cients and the corûponents of each variable were similar. Howeverr ana- l-ysis of the directional and face and back components of the independent

variables of the best two- and three-variable predictor equations was carried out using nu1-tiple linear regression analysis. Stepwise and all possible subsets regression analyses indicaÈed the best. regression equa-

tions and thereby included analysis of all the directional and face and

back components.

All Knit Group Multiple linear regression analysis of the direcÈiona1 components of the bending length in the bending length-thickness combination indicated

that the meen conponent was the best predictor. In addition, the coursewise direction Ì{es found to be superior to Èhe ¡¡alewise direction. In the bending l-ength-shear-thickness combination the same trends were present for bending length and the direction of shear was found to have very little influence (for an exarnple, see page 79). 86

SÈepwise regression analysis confimed these findings by entering blmean,and thickness into the equation. Shearcourse Ìres next in line for entry.

All possible subsets regression analysis indicated blmean-shearcourse-thickness was the best three-variabLe combination. In addition, blmean-shearmean-thickness and blmean-shearrvale-thickness had R2 values essentiaLly as high, so lrere acceptable. Ttris roethod of analysis indicated ËhaË blmean lres a better predictor than bl coursemean r¡hích Iras e better predictor than bl¡salemean.

The face-in varíables (blwalein, blcoursein and bhneanin) and the face-out variables (blwaleout, b1-courseout and blmeanout) were equally good predictors. The mean variables r+ere betÈer for prediction than the coursewise variables which were better than Èhe walewise variables.

l,Iarp Knit Subgroup Multiple linear regression analysís of the directional components of bending length in the bending length-thickness conbination indicated the same trends as for Èhe all knit group. Analysis of Èhe bending length- extension-thickness combination indicated the same trends for bending length and showed that the mean, waLewise, and coursewise conponents of extension rvere all equally good predictors.

Stepwise regression analysis entered blmean and extmean into the eguaÈion. 87

The all possible subsets analysís confimed these results. It indicated thaÈ exËmean, exÈwale, and exÈcourse rrere equally good predic-

tors and Èhat the bending length conponents fo1lo¡yed the tendancies rnen- tioned for the al-l knit group.

Weft Knit Subgroup Multiple linear regression analysis of the directions of the bending lengÈh-shear combínation indicated that the coursersise component of bending length was e better predictor Ëhan the mean, but they were both satisfactory. Ho¡¡ever, the walewise component nas a poor predicÈor. The mean, walewise, and coursewise conponents of shear were equally good.

Stepwise regression analysis entered blcoursein and shearmean into the equation and all possibLe subsets analysis confimed these as the best subset. The coursewise variables were better for prediction than the the mean variabl-es which were better than the wale¡¡ise variables.

Analysis of the directional and face and back components indicated that the walewise direction of bending length was a poor predicËor for the all knit group and the warp and weft knit subgroups. However, blmean was the best predictor for the all knit group and warp knit subgroup, whereas blcoursein lras Ëhe best predictor for the ¡¡eft knit grouP. 88

Study of Residuals

The computer plots and listings of Èhe residuals were sÈudied. (en example is presented in Appendix 81.) The residuals are the differences between the fitted or calculated value, Y, and the observed value, y. IÈ ryas proposed that the observations which were not close to the line were either inaccuraÈe values, were contributing to a nonlinear curve, or were influenced by a variable not accounÈed for in this research project.

hrhile some fabrics gave high residuals depending on the predictor equation, fabrícs M and Q invariably had residuals larger than one standard error. The equations predicted Ëhe drape coefficient of fabric M too high and the drape coefficient of fabric Q too low. Both fabrics were weft knits (M was a single knit and Q was a double knit), but they did noË appear to have features Èhat would distinguísh them frm the other fabrícs.

Fabrics M and Q were partially retested in order to determine the accurecy of their measurements and to observe any peculiarities. The retested results were not appreciably different from the original results. Fabric M was also drycleaned to remove the finish, but the DC results did not change. It was thought that fabric Mrs tendancy t.o curl was influencing its draping and bending properties. The behavior ofQ couLd not be accounted for. 89

In order to determine whether nonlinear curves would lead to smaller residuals, transformations of the variables were performed. This is discussed in the foll-owíng section.

Trans formation Variables

Some of the independent variables were transformed into ner¡ variables because it was proposed Èhat improved equations would result in that the

R2 values would increase and the sÈandard errors of the estimates and

the size of the residuals would decrease. The variables that were transformed were linited to those included in the best two- and three-

variable predíctor equations for each knit group. The variables ¡sere rnultiplied in pairs and squared in order to obtain transformation varia- b1es. These partícu1ar transformation variables were analyzed because of the exploraËory nature of this parË of the analysis. The transformation variables developed for the all knit group and warp and ¡¡eft knit subgroups are presented in Table 11. lable 12 contains the univariate statisÈics. Table 1l Transformation Variable Abbreviations Abbreviation Defínit ion thick2 thickness blmeanthick blmean x thickness shearcourse2 shearcourse extmean2 extmean blmean2 blmean blmeansheercourse blmean x shearcourse blmeanextmean blmean x extmean Ëhickextmean thickness x extmean thickshearcourse thickness x shearcourse blcoursein2 blcoursein shearmean2 shearmean blcourseinshearmean bLcoursein x shear.mean thickblcoursein thickness x blcoursein thicksheantreen thickness x shearmean Table 12 Univariate Statistics - Transformation Variables

Variable Standard Minimum Maximum Deviation

All Knit Group blmean r.68 0.84 0.79 3.59 thick2 0.01 0.01 0.00 0.02 shearcourse2 289651 .38 401676.56 26522.40 1761308.00 bl thick 0. 10 0.06 0.03 o.2I extnean2 153.17 215.87 4.37 764.52 blshearcourse 6 10. 93 518.82 r55.93 2513.61 blexûnean 12.08 7 .12 3.73 33.07 thextmean 0.72 0.50 0. ll 2.26 blcourse in2 I.72 1.04 0.69 4.60 shearcoursethi ck 34.50 23.88 3 .35 92.77 sheamean2 289578.88 418835 .63 23147.49 17 10489 .00 blcourseshearmean 619.69 584.00 r34.19 2805 .35 th ickblcourse in 0.10 0.06 0.02 0.22 thicksheannean 34.20 24.27 3. 13 91.42 Vlarp Knit Subgroup bLmean 1.66 0. 85 0. 86 3.59 thick2 0.01 0.01 0.00 0.02 shearcourse2 37 5856 .38 5437 55 .00 26522.40 1761308.00 blrhick 0.08 0 .06 0.02 0.2L extrnean2 155.95 223.55 4.37 764.52 blshearcourse 684.20 692.07 155.93 2513.61 blexûnean T2.T6 8.56 3.73 33 .07 thextmean 0.60 0..46 0. 11 1.63 blcourse in2 1.81 I.24 0.69 4.60 shearcoursethick 3I.75 27.30 3.35 92.77 shearmean2 394167 .88 569147.00 23147 .49 17 10489 .00 blcourseshear:u¡ean 730.35 786 .89 r34.r9 2805 .35 \o th ickblcourse in 0.09 0.06 0.02 0.22 thickshearmean 32.45 28.70 3. 13 91.42 Table 12 (continued)

VariabLe Mean Standard Minimum Maximum Deviation fleft Knit Subgroup blmean r.70 0.87 0.79 3.31 thick2 0.01 0.00 0.00 0.01 shearcourse2 203446.69 168619.06 35559.02 534988.310 blrhick 0. 11 0.05 0.05 0.20 extmean2 150. 38 279.98 20.t6 748.02 blshearcourse 537 .67 278.16 167.64 LT24.2T blextmean 12.00 5.79 6.78 27 .19 Èhextmean 0. 84 0.54 0.50 2.26 blcourse in2 r.64 0. 86 0.74 3.24 shearcoursethick 37.25 21.02 10 .48 76.r4 shearmean2 184990.25 148666.69 38303.96 4900000.00 blcourseshearmean 509.04 27I.33 176.93 1005 .20 th ickbLcourse in 0.11 0.05 0.05 0.20 thicksheannean 35.94 20.32 10. 88 72.87

\o 92 Stepwise and multiple Linear regression analyses were performed in order to determine which of the transformation variables were the best predictors of the drape coefficient.

All Knit Group Stepwise regression analysis rras performed on the best two-variable combination (blmean-thickness) and the related transformation variables

(blmean2, thick2, and blmeanthick). The transformation variables were forced into the regression but were not allowed entry into the equation until aft.er Èhe original two variables were enÈered. The remainder of

the variables ¡sere excluded fron the analysis. The stepwise anal-ysis entered blmean and thickness into the equation but no transformation variables.

The analysis was repeated on the best three-variable combination (blmean-shearcourse-thickness) and the related transformaÈion variables

(b1mean2, shearcourse2, thick2, blmeanshearcourse, blmeanthick, and thickshearcourse). The best equation included blmean, shearcourse,

thickness, thickshearcourse, and thick2. The R2 value was 0.93, the sÈandard error of the estímate was 4.89, and the F-ratio was highly sig: nificant. I{ithout the transformation variables the R2 val.re was 0.84 and the standard error of the estimaÈe was 6.71. The other transformation variables Èhat were entered into the equation did noË increase R2 or decrease the standard error of the estimate enough to warrant using them in the equation. 93

I{hen all Èhe independent variables, including the transformation variables had an equal chance of being entered into the equation, the anaLysis entered blmean, shearwal-e, and thickshearcourse. The R2 value was 0.91 and the standard error of the estimaÈe was 5.29.

MuLtiple linear regression analysis indicated that several variable

combinations could predict the drape coefficient equally as well as blmean-thickness. They Ìrere: bhnean2-thick2, blmean2-thick, and bl-nean-thick2. On the other hand, blmean2-blmeanthick-thick2, blmean- blneanthick-thick, bLmean2-blmeanthick-thick, bhnean-blmeanthick-Èhick2 were not good predicËor combinations.

ltarp Knit Subgroup

The same stepwise procedure was performed on the blmean-thickness combination for the warp kniÈ subgroup as for the all knit group. The analysis enÈered blmean, thickness, and thick2 into the equation. The R2 value was 0.99 and the standard error of Èhe estimate was 2.10. With blmean and thickness, only, the R2 value was 0.97 and the standard error of the estimate was 3.15. The transfomation variable did not improve predic tion.

I{hen the analysis nas repeated on the best Ëhree-variable combinat.ion (blmean-extmean-thickness) and the related transformation variables (blnean2, extmean2, thick2, blmeanextmean, blneanthick, and thickextmean) some transformation variabl-es were entered in addition to the original three variables. Ilowever, the transformation variables did not 94

increase the R2.rr1.r" and decrease Èhe standard error of the estimate enough to warrent using then in the equation.

T{hen all the independenÈ variables, including the transformation variables had an equal chance for entry inÈo the equatíon, the analysis

entered bLmean and thickextmean. The R2 val,re was 0.99 and the standard

error of the estimate ¡yas 1.49.

Multiple linear regression analysis indicaÈed that the following variable combinations could predict the drape coefficient equally as well as blmean-thickness: blmean2-thick2, blmean2-thick, blmean-thíek2, blmean2-blmeanthick-thick2, and bLmean-blneanthick-thick2. On the oÈher hand, blmean2-blueanthick, and blmean-blmeanthick-thick were poor pred-

íctor combinations.

l{eft KniË Subgroup

The same stepwise procedure was performed for the best two-variable combination (blcoursein-sheamean) and the rel-ated transformation variables (blcoursein2, shearmean2, and blcourseinsheannean) for Èhe wefÈ knit subgroup es for the aLl knit group. The analysis entered some of

Èhe transfomation variables into Èhe equaÈion but the variables did not increase the R2value or decrease the standard error of the estimate enough to rùarrant using them in the equation.

The analysis was repeated, but in addition, thickness and the related thickness transformation varíables were allowed entry into the equaÈion 95

after the analysis entered the originaL t¡so varíables. The analysis

enÈered blcoursein, shearmean, and thickness into the equaÈion.

Ìfhen Èhe nine bending length variables were allo¡ved entry into the ,1.',,",-',-' equation before the other independent variables, including Èhe transformation variables, the analysis entered blcoursein and shearmean2 into theequation.TheR2va1uewas0.97andËhestandarderroroftheesti. mate wes 3.3I. ...' Multiple linear regression analysis indicated that several variable

combinations could predict the drape coefficient equally as well as blcoursein-shearmean. They were: blcoursein2-shearmean2, blcoursein- shearmean2, and bl-coursein2-sheannean. However, Èhe addition of blcourseinshearmean into these conbinations decreased the R2 values appreciab3.y.

For Ëhe all knít group and the warp and weft knit subgroups, transformation of the variables permitted developmenÈ of variable combina- ,:,,,:,,'.,,::, tions that predicted the drape coefficient es welL as or better than :.: , those previousl-y developed. The most useful- of these nere: ' ' ' l. blmean-shearcourse-thickness-thickshearcourse-thick2 (a11 knit group)

2. blmean-shearwale-thickshearcourse (a11 knit group) ',,,:",,:',' ,:.,,' 3. blmean-thickness-thick2 (warp knit subgroup)

4. blmean-thickextmean (warp knit subgroup) 5. blcoursein-shearmean2 (weft knit subgroup) 96

TIIE PREDICTOR EQUATIONS The regression equations selected to describe the relationships between the mean drape coefficient and the relevant predicËor variables include one best equation and several other good equations for each knit

group. The R2 val-ues, standard errors of the estimates, and nultiple regression line constants are recorded in Table 13. The rnultiple regression line consËants include the intercept, ar and the partial regression coefficients, þ . The best sinple equaËions are indicated with asterisks. An example of the equaÈion format is: J = - 2I.435 + 40.701X1 + 119.005X2, where Y is the mean drape coefficient, X1 is the mean bending lengtht

and X2is the thickness for the all knit group.

The predictor equations have been kept as símp1e as possible in order

to allos a reasoneble number of degrees of freedom remaining for error

and so that a minimrm amount of testing and calculation have to be done to predict the drape coefficient. However, there were trfo insÈances

¡chere the R 2 val-ue nas extremely high when five or six independenÈ vari-

ables were included in the regression equation. The R2 values, sÈandard errors of the estimates, and multiple regression constants for these equations are presented in Table 14. The blmean-shearcourse-thickness-

Èhickshearcourse-thick2 combination is actually the best predictor equa-

tion for the all knit group. Ilowever, because several property measurements and calculations are required, a simpler conbination such as

bknean-thickness may be more useful. The warp knit conbination in Table 97

14 involves six independent variables¡ but is not as useful because the warp knit sample size was ten and therefore only three degrees of freedom remain for error. In addition Ëo Èhese predíctor equations, four equaÈions have been developed in order that Èhe drape coefficient may be predicted r¡ith one independent variable. The R2 values, standard errors of the estimaÈes, and rnultiple regression consÈanÈs for Êhese equations are presented in Table 15. These equations are not as good for prediction, buË measurenents of only one ProPerËy are required. Table 13 Mul-tiple Regression Constants to Predict the Mean Drape Coefficient I'Iith Tlrto and Three Independent Variabl-es

Coe ffic ient Standard Independent Variables Y intercept Regression Coefficients of Multiple Error of Knit Deternilation the EsÈ. Group Xl x'z x3 a b1 b2 b3

ALL KNIT * blmean th ick -21.453 40.701 119.005 .839 6.708

blmean shear density - 4.052 40.482 0.011 -0.058 .844 6.797 mean

blmean shear thick -2T.6TT 37 .643 0.007 129.4I4 .854 6.584 mean

blmean weight density -10.184 40.052 0.060 -0.049 .847 6.748

blmean shear thick -27.789 36 .858 0.009 133.351 . 861 6.422 course

bLmean thick shear -13.113 36.686 0.420 -0.0 20 .906 5.287 shear wale course

T{ARP KNIT blmean th ick 25.968 46.070 93.993 .969 3.147

blmean dens ity 14.677 48.725 -0.036 .964 3.4r4

dens 2.169 blmean th ick ity -18.149 45.985 74.8r2 -0.027 .988 \o @ * blmean extmean thick -34.459 49.477 0. 357 t02.047 .99r 1.869 Table 13 (continued)

Coe fficient Standard Independent Variables Y intercept Regression Coefficients of Multíple Error of Knit Determination the Est. Group X1 X2 X3 a b1 b2 b3 R2 lfARP blmean weight density -13.960 45.787 0.043 -0.050 .984 2.402 KNIT blmean weight th ick -23.253 46.525 - 0.049 r53.467 .986 2.263

blmean thick 32.II5 5r.465 8.901 .993 r .489 extmean

blmean th ick th ick2 -17 .7Ll 46.446 -r83. 150 L700.602 .988 2. 105

Ï.TEF'T KNIT blmean shear 23.692 34.862 0.048 .898 6.010 meen

blcourse shear 24.349 35 .307 0.051 .953 4.065 in mean

blcourse shear th ick -22.197 49 .566 0.067 -308.724 .97 4 3.248 in mean

blcourse shear -15 .5 31 35.747 0.001 .969 3.314 in mean2

* Best simple predictor equations iç.:k Sheamean2 = shearmean/1000

\o \o 100

Table 14 Mul-tiple Regression Constants to PredicÈ the Mean Drape Coefficient With More Than Three Independent Variables

ALL KNIT GROUP

X1- blmean bl= 34.123 a = 11'411 X2- shearcourse b2= -0.035 R2 = 0.930 X3- thickness b3= -584.668 * S = 0.964 X4- thickshearcourse b4= 0.693 X5- thick2 b5= 3092.255

WARP KNIT GROUP

X 1- blmean b1= 48.963 a = -49.149 2 X. Z- shearmean b 2= 0'006 ¡ = 0.999 X extmean b3= 0.517 * S = 0.733 3 - X 4- weight b 4= -o'145 X 5- thickness b 5= 339 '760 X b6 0.069 6 - density =

* Standard error of the estimate Table 15

Multiple Regression Constants to Predict the Mean Drape Goefficient With One Independent Variable

Independent Y Intercept Regression Coe ffic ient Standard Error Variable Coe ffic ient of Multiple of the Determination Est imate

Knit Group X b ¡2

All- Knit blmean -19.686 46.325 0.797 7 .327

T,Iarp Knit blmean -24.776 49.873 0.929 4.493 t{eft Knit blcourse in -12.777 42.246 0.71I 9.4s4

I{efr Knir thickness -17 .279 668.732 0.722 9 .275

H ts L02

The predictors of the drape coefficient have been influenced by the knit strucÈure. The best simpl-e equation for the all knit group includes blmean and thickness. Blmean, extmean, and thickness are the best predictor variables for the warp knit subgroup, while blcoursein and shearmeen ere the besË predictor variables for the weft kniÈ subgroup. For Ëhe conditions of Èest used, the regression equaÈions describe Èhese rel-ationships quantitatively.

Needless to say, not all of the possible corobinations of variables and their relaËed transfomations have been analyzed because of the num- erous possibiliÈies. However, the variables wtrich are the most reliable predictors of the drape coefficienË have been determined and transformations of these to the second porder and multiplication of these variables in pairs have been performed.

The eguaËions developed could not be compared direcÈly to those by other researchers (Cusick, 1965; Morooka and Niwa, L976) because of the different measurements involved. However, the variables in Cusickrs equations were bending and shear measurements; the same as Èhe best predictor variabLes found for the ¡veft knit subgroup in the presenr research.

TITE FABRIC PROPERTIES AS PREDICTORS OF TITE DRAPE COEFFICIENT

The bending length, secondary shear modulus, extension, and thickness variables were included in at leasË one of the besÈ predictor equations. lleíghÈ and density were included in sme of the additional good predic- Ëor equations. 103

The results of this research project ere compared to the findings of previous researchers rshere possible. However, this is linited on Èwo eccounts. The past research deaLt prínarily with rroven fabrics and sim- p1-e linear correlaÈion statistical analysis rather than multiple linear regression analysis was utilized.

The Deformation Properties

Bending Length

Bending lengËh lras expected to be an accurate predictor of the drape coefficient because past research indicaËed that for wovens, nonwoven, and knits, stiffness Eeesurements were highly correlated with Èhe drape coefficient both in sinpl-e and multiple linear correlations (Peirce,

1930; Cusick, 1965; Sudnik, 1972, 1978; Kin and Vaughn, 1974; Morooka and Niwa, L976). Hearle, Grosberg, and Backer (1969) staÈed that bending is the major mode of fabric deformation in draping. All- of the best and good predicÈor equations developed in the present research included a bending length variable. Ho¡vever, one or two additional- independent variables rrere necessary for high correl-ation (n2 irr"r"r"ed from approxinately 0.70 to 0.90).

There lrere no significant differences between the face and back and betr¿een the directional components of the bending length data. These findings do not agree with the findings of Knapton and Lo (1975) ¡rho stated that structurally unbalanced knitted fabrics have different direcËional and/or face and back bending characteristics. The sinilari- 704 ties in the face and back cmponents of bending length in the present

research may be due to the fact that the fabrics rilere screened in order to obtain sinilar face and back drape coefficients. rn the present research there were dissinilarities in the sinple linear correlation coefficients bet¡seen the drape coefficient and the bending length varia-

bles. In addition, the best bending length predictor variable ¡sas dif-

ferenË for the various knit groups. For the all knit group and the warp knit subgroup Èhe blmean variable was Èhe best, while for the weft knit subgroup, blcoursein was the best.

Secondary Shear Modulus

The secondary shear modulus was expected to be an accuraEe predictor

of the drape coefficient for al-L three knit groups because past research

indicated that for Itrovens r noilùovens, and knits, shear measurenenÈs were

moderately to highly correlated with the drape coefficient in sinple and nultiple linear correlations (cusick, Lg6s; Kin and vaughn, L974;

Morooka and Niwa, 1976; sudnik, 1978). rn this research, the secondary shear modulus was included in the best predictor equation for the weft knit group (blcoursein-sheamean) and the best three-variable equation for the all knit group (blmean-shearcourse-thickness). rt was also included in some of the good predíctor equations.

The ¡valewise and coursewise directions of the secondary shear modulus univariate statistics were not significantly different. In addition, there was little difference bet¡seen the correlations of the drape coef- 105

ficient with sheansal-e and the drape coefficient with shearcourse. The fabric direction was not irnportant in the predictor equations. This is

in agreenent with Gibson and Postle (1978) ¡sho found that bending lengÈh was dependent on fabric direction, but shear nas not.

Extension

Since controversy existed in the literature concerning the degree of association between the drape coefficient and extension for wovens

(Peirce, 1930; Chu et al, 1963; Kin and Vaughn, Ig74i Morooka and Niwa, L976), it was uncertain whether exÈension would be a good predictor of the drape coefficient for knitted fabrics. The present research indicated that the simple linear correlation between the drape coefficient and extension was poor for all three knit groups. However, extension was included in the best predictor equation for the warp knit subgroup (blnean-extension-thickness). This rnay be related Èo the findings of cook and Grosberg (1961) who reported that for warp knits, yarn stiffness influenced extensibilitv.

The literature stated that fabric direction ¡sas an important factor

ín the extension of knitted fabrics (Doyle, L953; cook and Grosberg, t96r; Knapton and to, 1975). rn this research projecÈ there were differences in the data depending on the fabric direction, especially for the warp knit subgroup. rn addítion, the sinple linear correlations were dependent on fabric direcÈion for both kniÈ groups. However, the direction of extension was not an irnportant factor with respect to the predictor equations. 106 The Structural Characteristics

Fabric Weight

Fabric weight was expecÈed to be an accurete predictor of the drape coefficient because it was an importanÈ variabLe in the equations developed by Morooka and Niwa 0976) for lroven fabrics and because past research indicated that the stiffness of knitted fabrics was infl-uenced by fabríc weight (Knapton, L973, 1974; Knapton and Lo, 1975). On the other hand, some question existed, sínce Kím and Vaughn Q974) indicated that weight and Ëhe drape coefficient were not highl-y related. In addition, Morooka and Niwa Q976) found weight and the drape coefficient were negetively related, while Kim and Vaughn 0974) found a positive relationship. In the present research the sirople linear correlation between weight and the drape coefficient was l-or+. Weight rües not included in any of the best predicËor equations, but rres an important variable in three of Èhe good predictor equations for the warp knit group. They were: bl-mean-weight-density, blmean-weight-thickness, and b lmean- sheermeen-ext ens i on- th i cknes s-we i gh t-dens i t y .

Fabric thiekness Since past research indicated that fabric thickness has an influence on knitted fabric stiffness (KnapÈon, L973, 1974; Knapton and Lo, 1975) it was expected that thickness would be a good predictor of the drape coefficient. On the other hand, Kim and Vaughn (1974) and Morooka and

Niwa (1976)found correlation lres poor between Èhickness and the drape coefficient. In the presenË research projecË the sirnple linear correla- 107 tion was generally higher than that reported in the literature, especially for the rùeft knit subgroup. Blmean and thickness formulated the best predictor equation for the al-l knit group and blmean, thick- nessr and extension formulated the best predictor equation for Èhe warp knit subrgroup. Thickness, therefore, was an important variable with respecÈ to all three knit groups.

Fabric Density

Since past results were not available for comparison, it ¡ras uncer- Ëain whether a rel-ationship between density and the drape coefficient existed. Hor¿ever, since weight and thickness influenced the drape of wovens (Chu et al, L963; Kim and Vaughn, 7974; Morooka and Niwa, Lg76) iË was felt density would influence drape as well. Fabric density was found to be poorly correlated with the drape coefficient in sinple linear correlation and was not íncluded in any of the besÈ equations.

However, it was an important predictor variable in two of the good equations. They lf,ere3 the blmean-shearmean-density corubination for the al-1 knit group and the blnean-density combination for the warp knit subgroup. Chapter 5

SI]MMARY AI{D RECOMMENDATIONS

SI]MMARY

The present research project investigated certain deformaËion proper-

ties and structural characteristics to deÈermine their reLiabiliÈy as predictors of Èhe drape coefficient in knitted fabrics. The deformation properties incLuded stiffness, shear, and extension, while the structural charateristics included weight, thickness, and densiÈy. The study also investigated the reliabiliÈy of these predictors for the two main tyPes of knitted construcÈions-- rrarp knits and weft knits. Predictor equaÈíons were developed in order to enable prediction of the drape of a knítted fabric if one or more of the property meesurements are known.

Twenty fabrics were selected for the sÈudy, including Ëen warp knits and ten weft knits. The warp knits included tricot and raschel knits, strile the weft knits included single jersey, rib, interlock, and double knits. The fabrics selected had sinilar face and back draping properties. The measurements of the fabric properties rrere made according Èo standard test methods, except for shear, where no standard tesÈ method for texËil-es exists. All of the directional and face and back components of the deformaÈion properties were measured. To assess drape, the British Standard Method BS:5058-1973 was used. Ttre Cusick Drape Tester

-108- 109

enabled calculaÈion of the drape coefficienÈ. Stiffness was quantita-

tively expressed by Ëhe bending lengÈh. The HearÈ Loop MeÈhod specified

in the Anerican Society for Testing and Materials 1975 Designation

D1388-64 was followed. The apparatus used to measure shear was based on

the one developed by S.M. Spivak for woven fabrics. Tfris appears to be the first tine this apparatus has been used successfully Èo measure the shearing properties of knitted fabrics. The secondary shear modulus was the measurement taken from the stress-strain curve. Extensibility was measured wiÈh reference to ASTM 1975 Designation DI682-64. The Instron tensile tester was employed to measure the percent extension at a load of 100 grems. To measure fabric weight, the Canadian National Standard CAII2-4.2-y177 Method 5.A-I977 rsas followed. The assessment of fabric thickness ¡sas made according to the standard CGSB 4-GP-2-I957 using a

Etazíer Compressometer. Fabric density was calculated from the Eeasure- ments of weight and thickness.

The most reliable predictors of the drape coefficient in knitted fabrics were established using regression analysis. Multiple linear, sËepwise, and all possible subsets analyses were perforrned. In addition, some of the independent variables were multiplied in pairs and squared in order to obtain transformation variables. IË was proposed that inproved equations rsould result. PredicËor equations were developed for the entire group of knitted fabrics (a11 knit group) as well as for the warp and weft knit subgroups. 110

The regression analyses resulted in one best predictor equation as well as several other good predictor equatíons for the all knit group

and for the warp and weft. knit subgroups. Some of the transformation variables were included in some of Èhe good predictor equations.

In meeting the objecrives of the present research several concl-usions have been dra¡rn. For the twenty fabrics the mosÈ reliable predictor variables were bending length, thickness, secondary shear modulus, and

transformaÈions of rhese three variables. I{eight and density were included in some of the good predictor equations, but extension was noÈ.

The mean bending lengÈh componenÈ lras a better predictor than the coursewise, which rdes a betÈer predictor than the walewise. The face-in and face-out components rùere equally good predictors and followed the tendancies mentioned for the mean, waler¡ise, and courservise components.

The walewise, coursewise, and mean secondary shear modulus componenËs were equally good for prediction.

The equations for the varp and weft knit subgroups differed from those for the all knit group. Ttre best equation for the warp knit subgroup included bendíng length, thickness, and extension. I.feight and density were included in some of the good equations but the secondary modulus shear rùas noÈ. The mean component of bending lengËh was the besË variable component for prediction. This was followed by the courser¡ise component. The mean, walewise, and coursewise components of extension rsere equally good. For the weft knit subgroup the bending 111 length and secondary shear modulus variables were the best for prediction. Thickness was the only other variable that was included in a good predictor equation. The coursewise direction was the best component of bending length, followed by the mean, while all the secondary shear modulus components rùere equally good predicËors. For both the warp and weft knit subgroups the bending length face-in and face-out variables nere equally good predictors and followed the the trends mentioned for the mean, ¡valewise, and coursewise conponents.

The best predíetor equation for the all knit group was: + Y = 11.411 34.123 Xt - 0.035 xZ -584.668 x3 + 0.693 LX¡ * 30s2.225 ç r+here Y is the mean drape coefficient, X1 is the mean bending length, X, is the coursewise secondary shear modulus, and \ is the fabric thickness.

The besÈ simple predictor equation for this knit group rùas: I = - 2I.t+85 + 40.70I L + 119.005 x2 where Y is the mean drape coefficient, X, is the mean bending length¡ and þis the fabric thickness. The best predictor equation for the warp knit subgroup was:

J = - 34.459 + 49.477 Xt + 0.357 X2+ 102.047 x,3

¡rhere Y is the mean drape coefficient, X, is the mean bending lengËh, þ is the mean extension, and \ is the fabric thickness.

The best predictor equation for the weft knit subgroup was:

J = - 24.349 + 35.307 X1 + 0.051 X2 rt2

where Y is the mean drape coefficient, x, is Èhe coursewise face-in

bending length, and X, is the mean secondary shear modulus.

IMPLICATIONS OF TTTE RESEARCIT PROJECT

The present reseerch project has provided a better understanding of

the physical properties thaË infl-uence the drepe of knitted fabrics, and Èherefore has fi1led a void in the current literature. Additional

insighÈ into the shearing properËies of knitted fabrics has also been accomplished.

Several predictor equations have been developed. The equations would be of particular interest to knitted fabric and garment manufacturers,

as knitted fabrics ¡.'ith sinilar face and back draping properÈies can be

designed, nodified, or selected to give the drape desired. The drape

coefficient cen. be predicted with one variable or several different. combinations of variables, allowing flexibility in the types of physical

ProPerties measured. In addition to predicting the drape coefficient, a defornation Property or structural characteristic mighË be predicted if measurements of the drape coefficient and other relevent independent variabLes are knorm.

RECOMMENDATIONS FOR FURTTIER S]]I'DY The research project led to several reco'r"nendations for further study and analysis. This research project nas Lirnited to a sample size of twenty fabrics for the aLl knit group and sanple sizes of ten for the 113 warP and lüeft knit subgroups. A recornmendation for further study is to incorporate a larger sanple size in order to obt,ain a rnore precise estimate of the variability. A different group of fabrics could be sÈudied to check the validity of the resuLts of the present research. In addition, the study of a different group of fabrics may extend the present research results to a wider range of fabrics. The fabrics chosen for

study could include both warp and rseft knits or the fabric sample could be linited to one basic type of knitted fabric, ie. either warp kniÈs or rseft knits. In addiÈion, since past research indicates that single and doubl-e knits vary in several properties (Doyl-e, 1953; Knapton and Lo,

1975; Harnilton and Postle, 1977; Gibson and postLe, 1978), it may be worth studyíng different stitch structures, for example, tricot, ras- che1, milanese, double, or single. Rib knits and/or pile knits could be studied as they were eliminated from this research project due to their directional and face and back draping properties, respectively.

The fabrics incorporated in this research were limited to those sui- table for apparel. Exanination of knitted fabrics ¡vith other end uses is recottrmended.

The physical properties measured in this research project were limited to those which influence the drape of woven fabrics as suggested by the literature. In addition, the high residuals in Èhis research indicate that wíth some fabrics, other factors may be influencing drape.

Consideratíon of other properties would be useful, for example, compressive and surface properties. 714

The measurements Èaken in this research were limited to one type for each physical property. Additional study could be conducted, altering

the testing methods and/or equipment used and/or the types of measure- ¡nents taken to determine if better correlation could be obtained. For example, flexural rigidity rather than bending length could be calculated as a measure of sËiffness.

Re-entrant fol-ding in the draping of very limp fabrics was encoun-

Ëered in this study. In extreme cases the results from the Cusick drape tester may be liraited. The extent of this linitation and alternative meÈhods of measuring the draping properties of very linp fabrics could be derived.

Further regression analysis could be conducted to include the devel-

opment c,f additional linear regression equations and quadratic equations. More extensive analysis night be worthwhile utilizing the trans-

formation variables fomulated in this research project es well as developing additional transfomation variables. Further statistical

analysis of the various face and back components of the measurements

¡¡ould also be useful .

Further understanding of the relationships between drape and oÈher properties of knitted fabrics could be achieved through an alternative theoretical approach. A theoretical model based on the elemenËs of the knit sÈructure could be deveLoped using the variables identified as reliable predictors of the drape coefficienË in the present research. 115 The present research has resulted in additional knor¡ledge concerning

the shearing properties of knitted fabrics. A shearing apparatus based

on the one developed by S.M. Spivak has been used Ëo measure the shearing properties of knitted fabrics successfully. A suggestion for further study is additional research on the shearing properÈies of knitted fabrics utilizing Spivakr s shearing apparatus and/or other appara- tuses.

Throughout the present study several equations have been developed in order that the drape coefficients of knitted fabrics could be predicted if measurements of one or tuore physical properties ere known. The tr¡o basic types of knitted fabrics- rtrarp knits and weft knits, have been studied separatelyr as well as the entire group of knitted fabrics. The reconrmendations for further study are expected to provide additional informaÈion into the drape of knitted fabrics and their relaÈed physical properties. REFERE.¡CES CITED

- 116 - l17

Abbott, N.J., "The Measurement of Stiffness in Textile Fabrics, Part I: A Comparison of Five Methods of LaboraÈory Evaluationrrl Textile Research Journal, 2L, 435-44I, 1951. Abbott, N.J., ttThe Measurement of Stiffness in Textile Fabrics Part II: A Study of Èhe Peirce CanÈilever Test For Stiffness of Textile Fabricsr" IglLþ Research Journal, 2L, 44L-444, 1951. Anonymous, 'rDrapetester Developed at Manchester Universityr" Textile Month, 77, Aug. f968.

AATCC, Technical Manual, N.C. Research Triangle Park, Vol 53, 1977.

ASTM, Glossary of Te¡ms Relating to Rubber and Rubber Technology, Special Technical Publication, Philidelphia A¡nerican Society of Testing and Materials, No. 1844, L972. ASIM Standards, Part 32, Textiles - Yarns, Fabrics, and General Test Methods, Philidelphia, American Society For Testing and MaÈeríals, L978. Behre, 8., rrMechanical Properties of Textiles Fabrics, Part I: Shearingr" TextiLe Research Journal, 31, 87-93, 1961. Brand, R.H. r ttMeasurement of Fabric Aesthetics, Analysis of Aesthetic Components rrr Textile Research Journal, 34, 79r-804, 1964.

Brown, Peterr ttleasuremenÈ of Single Jersy Fabric Stiffness: A Sinple Methodrrr Textile Research Journal, 48, 295-299, f978.

BSI, Methods of Test For Textiles, B.S. Handbook No. 11, London, British Standards Institution, 1974.

Carnaby, S.A. and R. PosÈle, ttThe Shear Properties of I,Ioo1 l{eft- .Knitted Structure"r" 4g! of the Textile Institute, 65, T87-T101,1974.

CGSB, Canadian Standard Textile Test Methods, Ottawa, Canadian c o vffiããts p eõTñã tññ;Tõ eã; 197ï .

CGSB, National Standard of Canada CAN2-4.2-y177 Textile Test Methods, OÈtawa, Canadial Government Specifications Board, 1977. chu, c.c., c. L. cunrmings and N. A. Teixerra, rrMechanics of Elastic Perfomance of lextile Material Part V: A Studv of the Factors Affecting the Drape of Fabrics - The Developmenf of a Drape Meterrrr Textile Research Journal, 2O, 539-548, 1950. Chu, C.C., W. J. Eanburger and M. M. Platt, Determination of Factors l{trich Influence the Draglng Properties of Cotton rãEffi ,-wFo@offieñ-IiEïTí;ãEn Rõeãcr' ana DevelopmenÈ Division, 1963. 118 Cook, D.L. and P. Grosberg, ttThe Load-ExÈension Properties of hlarp- Knitted Fabricsrr' Textile Research Journal, 31, 636-643, 196f. Cooper, D.N.E., ItThe Stiffness of Woven Textiles rtt Journal of the Textile Institute, 51, T317-T335, 1960. corbnnan, Bernard P., Textiles: Fibre to Fabric, Fifth Edition, New York, McGra¡y-Hil1 BooETõ:, TW co¡sanr Mary L. and Martha E. Jungeman, rntroduction To Textiles, New York, Appl et on-Cent ur¡rC ro f t s - t'teredffi-TõÇT .1OOO .-

Cusick, G.E., ttThe Dependence tt of Fabric Drape on Bending and Shear Stiffness, Journal of the Textile Institute, 56, T596-T606, r 965. ttThe Cusick, G.8., Measurement of Fabric Drapertl Journal of the Textile Institute, 59, 253-260, 1968. ttThe cusick, G.E., Resistance of Fabric Èo shearing Forces, A study of the Experimental Method Due to Morner and Eeg-Olofssonrrl Journal of the Textile Institute, 52, T395-T406, 1961. Daniel, cuÈhberÈ and Fred s. I{ood, Fitting Equations to Data: $ggp"t"r Anelysis g! 4ulrífaçror para for s"tAti* ang Engineers, New York, Interscience, I97L. Darlington, K.D., ttltarp Knitting for Outerweerr" Textile Institute and Industry, 9, 158-159, 1971.

Dawes, V.II. and J.D. Owen, rrThe Assessment of Fabric Handle, Part I: Stiffness and Liveliness rrf Journal of the Textile Institute, 62, 233-244, Ig7L.

Díxon, W.J., ed., Biomedical Computer program, California, universiry or c@7-

Doyle, P.J., "Fundamental Aspects of the Design of Knitted Fabricsr, Journal of the Textíle rnstitute, 44, p56l-p575, 1953.

Drebyf E.c., 'rThe Planoflex, A simple Device for Evaluating the PLiability of Fabricsrtr American Dyestuff Reporter, 30, 65r-654, 1941. Dunn, 01ive Jean and Virginia A. Clark, Applied Statistics: Ênalysi:_of Variance and Regression, NeÌr york, John Wiley and Sons, L974.

Gibson, viki L. and Ronald Rostle, "An Analysis of the Bending and Shear Properties of f{oven, Double-Knitted and t{arp-Knitted Outerwear Fabricsrrt Textile Research Journal, 48, 14-27, Lg7g. 119

Goswami, 8.C., Shear Behaviour of Fabrics, Textile Research InstiÈute Notes on Research, No. 281, Kno:nrille University of Tennessee, May 1977.

Harnilton, R.J., Bending and Shear Properties of Knitted StrucÈures, Ph.D. Thesis, University of New SouÈh T{ales, 1975. Hanilton, R.J. and R. Postle, rrBending and Recovery Properties of I{oo1 Plain Knitted Fabricsrrr .Textile Research Journal , 44, 336-343, I974.

Hamilton, R.J. and R. Postle, ttThe Bending and Shear Properties of l{oo1 Punto-Di-Rona Doubl-e-Knitted Fabricsr" Journal of the Textile Institute, 68, 5-11, L977. Hamilton, R.J. and R. Postle, ttshear Properties of I'Iool Plain- Knitted Fabricsrl Textile Research Journal, 46, 265-272, 1976. Hearle, J.i{.S., P. Grosberg, and S. Backer, Structural Mechanics of Fibres, Yarns, and Fabrics, Vol. À, New York, tfiley- Interscience, L969.

Howorth, W.S., ttThe Handle of Suiting, Lingerie and Dress Fabricsr'l Journal of the Textile Institute, 55, T25I-T260, 1964.

Joseph, Marjory, Introductory Textile Science, 2nd Edition, New York, Holt, RineharÈ and l{inston Inc., 1972.

Kaswell, 8.R., Textile Fibres, Yarns, and Fabrics¡ New York, Reinhold Publishing Corporation, 1953. Kaswell, E.R., Iùell-ington Sears llandbook of Industrial Textiles, New York, t{ellington Sears Co. Inc., 1963. Kim, C.J. and E.A. Vaughn, "Physical Properties Associated I{ith Fabric Handr" AATCC Book of Papers National Technical Conference 78-95, L974.

KnapËon, J.J.F., rrFurther Consíderations of the Geonetry of Relaxed Wool Double-Jersey Structure"r" &g! of the Textile Instítute, 64, 223-229, 1973. Knapton, J.J.F. and I.I{.K. Lo, "KniÈting High-Quality Double Jersey Cloth VII: The InfLuence of Structure on Sme Mechanical Propertiesr" Þ!!E Institute and Industrv, I3, 355-359, 1975. Labarthe, Ju1es, Elements of Textiles, New York, MacMillan Publ ishing con!ãiffiã .7 tEA .

Lindberg, J., Bengt Behre and B. Dahlberg, rrPart III: Shearing and Buckling of Various Corrmercial- Fabrics rrr Textile Research Journal, 31, 99-122, f961. r20

Lyle, Dorothy Siegert, Modern Textiles, New York, John I{iley and Sons, L976.

Morner, B. and I. Eeg-Olofsson, t'MeesurmenÈ of the Shearing Properties of Fabricsrtt Textile Research Journal, 27, 611-615, L957.

Morooka, Harr¡mi and Masako Niwa, "Re1ation Between Drape Goefficients and Mechanical Properties of Fabricsrtt Journal of the TexÈile Machinery Society of Japan, 22, 67-73, 1976. ttThe Peirce, I.T., Handle of Cloth as a Measurable QuanÈityrrl Journal of the Textile Institute, 2I, T377-T416, 1.930.

Postle, R., "The Thickness and Bulk Density of Plain-KnitËed Fabricsrt' Journal of the Textile InsÈitute, 62, T2I9-T23I, 197L. Skeleton, John, ItFundmenÈals of Fabric Shearr" Textile Research Journal, 46, 862-869, L976. Snirfitt, J.4., An Introduction to I,Ieft Knitting, England, Merrow Publishing Co. Ltd-@ Spivak, S.M., "The Behaviour of Fabrics in Shear, ParË I: Instrumental Method and the Effect of TesÈ Conditionsrfr TexÈile Research Journal, 36, 1056-1063, 1966.

Spivak, S.M. and L.R.G. Treloar, "The Behavior of Fabrics in Shear, Part III: The ReLation Between Bias Extension and Simple Shearrrl Textile Research Journal, 38, 963-97L, 1968

Stout, Evelyn E., Introduction to Textiles, New York, John l,liley and Sons Inc., L967 . Sudnik, 2.M., ttobjective Measurement of Fabric Drape, Practical Experience in the Laborat.oryrtt Textile Institute and Industry, 10, t4-18, I972.

Sudnik, M.P., "Rapid Assessments of Fabric Stiffness and Associated Fabric Aesthetic"r" Þt:iþ Institute and Industry, 16, 155-159, t 978.

Thomas, D.G.B., An Introduction to l{arp Knitting, England, Merrow Publishing Collta., TfZT. Treloar, L.R.G, rrThe Effect of Test Piece Dimensions on the Behaviour of Fabrics in Shearr" IgIgiþ InsÈiÈute and Indust,ry, 56, T533-T550, r965. Wignall, Earry, Knitting, London, Sir. Isaac Pitman and Sons Ltd., L964. APPENDIX A

Statistics Tables

-L2L- Table l6a

R2 Values, F-Ratios, t-sÈatistics, and Standard Error of the Estinate values For the varíable combinations hrhich Include Bending Length - All Knit Group Variable Combinations ¡ 2 F-Ratio Standard t-statistics Error of Est imate b lmean-sheannean .81 35.14 7 .38 7.43, 0. 86 bLrnean-dens ity .81 37 .14 7.22 7 .32, -1.25 b lmean-exËmean .80 34.19 7 .46 7.14, 0. 60 blmean-weight .81 37 .18 7.2I 7 .r4, I.26 b lmean-thickness .84 44.30 6.7r 7.L3, 2.r2 blrnean-shearmean- .81 23.08 7 .47 6.gg, ex trnean 0.99, 0. 78 blmean-shearmean- .85 31.26 6. s8 6.19, thickness I.29, 2.32 blmean-sheatrnean- .84 28.96 6. 80 6.93, 1.79, dens ity -2.01 blmean-shearmean- .82 23.93 7.36 weight 6,63, 0.59, 1.05 blmean-exüneen- .84 28 .80 6.8r thickness 6.51, 0. 70. 2.10 blmean-exûnean- .83 26.04 7. 11 7 .I5, t.23 , H weight l\) I .66 l\) blmean-extmean- .81 23.43 7 .42 5.63 dens ity , -0.27 , -1.09 Table 16a (continued)

Variable Combinations R2 F-Ratio S tandard t- s tat is tic s Error of Estimate

b lmean-dens ity- .85 29.46 6.75 6.83, -1.95, weighÈ -1.09 b lmean-dens ity- .84 28.75 6.82 7 .03, -0. 68 , th icknes s I.75 blmean-weight- .84 28.06 6.89 6 .94, th ickness -0.36, 1.63

b lnean-shearmean- .84 r9 .08 7 .21. 6.77 extmean-weight , 0.72, 1.28 , 1.46 b lmean-shearmean- .86 23.66 6. 58 6.09, r.46, exûnean-th icknes s 0.99, 2.36 b lmean-sheannean- .85 20. 98 6.93 4.52, 1.83, extnean-dens it y -0.62, -l .89 b lmean-shearmean- .87 25.28 6.40 6 .04, I.67, we igh t-dens it y r.75 , -2.48 b lmean-shearmean- .87 25.89 6 .33 6.07 g6, th ickness-density , l. l. g5, -1.51 blmean-exËmean- .85 20.78 6.96 s .46, 0.19, we igh t-dens it y T.79 , -1 .80 blmean-extmean- .84 20.25 7 .04 6.I7 weight-thickness , 0. 59, 0.05, 1. 1s (,t\) Table 16a (continued)

Variable Cornbinations F-Ratio Standard t-statistics Error of Es t ima te

blmean-extmean- .84 20.35 7 .02 5.66, 0.30, th ickness-dens itv I.70, -0.26 b lmean-weight- .85 20.72 6.97 6.59, 0.56 , th icknes s-density -0.02, -0.79 b lmean-shearmean- .87 24.94 6.44 6.12, 1.82, we ight-th ickness -1 .31 , 2.43

b lmean-shearmean- .87 19 .33 6.55 5 .23, r.69 , we ight-th ickness- -0. 3l , -0. 87 dens ity 1.93

bl-mean-sheal:ttrean- .87 r8 .77 6.64 5.86 t.7I, extmean-weight- , -0.03. 0. 55 th ickness -0.68

b lmean-shearrnean- .87 r8 .92 6.62 4.50, 1.61, extmean-\,re ight- -0. 17 , t.57, dens ity -1.96

blmean-shearmean- .87 19 .34 6.55 4.61, 1.79 , extmean- thi ckness -0.05, 0.04, dens ity -0. 55

blmean-extmean- .85 15.51 7 .20 5.14, 0.19 weight-thickness- , 0.50 , o. 04, dens ity -0. 55 blmean-shearmean- .87 14.96 7 .03 4.41 , 1.65, N) extmean-weight- F, -0.05 , -0.03, th ickness-dens itv 0. 50, -0.59 Table 16b

R2 VaLues, F Ratiosr t-statistics and Standard Error of the Estimate values For the variable cornbinations l{hich Include Bglgl¡rg Lengrh - Warp Knir Subgroup 2 Variable Cornbinations R F-ratio Standard Error of t- s taË istic s Estimate

b luean-shearrnean .93 49.87 4.60 9.24, -0.79 b lnean-dens it y .96 93.50 3.41 13.02, -2.62, bLmean-exËmean .94 58 .31 4.28 70.22, 1 .35, blmean-weight .93 47.r4 4.73 9 .r4, 0.48 bl-mean-thickness .97 1 10. 70 3. 15 12.64, 3.05 blmean-shearmean- .94 34.14 4.57 9.22, extmean -0.37 1.05 blmean-sheal:tnean- .97 67 ,37 3.30 10.90, -0.62, thickness 2.77 blmean-shearmeen- .97 55.17 3.63 9.88, 0.43, dens ity -2.30 blrnean-shearrnean- .94 3r.94 4.7 r 8.gg, -1.20 , weight 0.82 blmean-exhnean- .99 213.77 1.87 21 .05 , 3.72, thickness s.54 blmean-extnean- .96 P 55.02 3.64 1l.gg, 2.47, l\) weight (.¡l 1.92 bLmean-exùnean- .97 55.93 3. 6l 8.72, -0.52, dens ity r.96 Table 16b (continued)

Variable Combinations R2 F-ratio Standard Error of t-statis t ic s EsÈírnate b Lmean-dens ity- .98 t28.69 2.40 16 .20. -4.59 , weight 2.85 b Lmean-dens ity- .99 r58.25 2.r7 l8 .31, -2.96, th icknes s 3.37 b lmean-weight- .99 145 .30 2.26 17.72, -2.75, thickness 4.95 b lmean-sheannean- .97 40 .03 3. 70 tL.47 , -0. 89 extmean-weight 2.78 , 2.03 b lmean-shearmean- .99 I 36 .39 2.O3 18 .03, o.32, extmean-th icknes s 3.30, 5.05 b lmean-sheannean- .97 36. 68 3.86 6 .70, o.49 , extmean-dens iÈy -0. 55 , -1.84 b lmean-sheannean- .98 80. 83 2.62 12.74, 0.16, we ight-density 2.55, -3.79 b lmean-shear:mean- .99 109.57 2,26 14.36, 0.73, th ickness-density 3.24, -2.79 blmean-extmean- .99 84.24 2.57 12.25, 0 .48, we ight-dens ity 2.6I, -2.65 blmean-extmean- .99 158.63 1.88 19 .70, r.92, we ight-th icknes s -0.96 , 4.18 F l\) Table f6b (continued)

Variable Courbinations R2 F-ratio Standard Error of t-statistics Es t ima te

blmean-exÈmean- .99 138.88 2.OI 16.07 1.41, th ickness-densiÈy , 3.79 , -0.44 blmean-¡veight- .99 100.17 2.36 16. 50, -0.25, th ickness-dens itv 1.10, -0. 7I

b lmean-shearmean- .99 134. 51 2.04 15 .31, t.54, we ight-th icknes s -3.26 , 5.20 b lmean-shearmean- .99 86.43 2.28 13.66, 7.17 , we ight-Èh icknes s - -0.96 , 1.63, dens ity -0. 13 blmean-shealrneen- .99 151.06 1.73 16.52, 1. 39 extmean-weight- r.73, - 1. 70, th icknes s 4.36 b l-mean-shearmean- .99 53.93 2. 88 9.22, 0.03, extnean-weight- 0.41, 2.24, dens ity -2.07 blmean-shearmean- .99 95.26 2.17 12.35 0.53, extmean-thickness , 1 .19, 3.44, density -0. 60 blmean-extmean- .99 123.12 1.91 15 . 30, 1.91, we ight-th icknes s- -1.24, 2.25, dens ity 0.92 F {N) blmean-sheermeån- .99 70I.48 0.73 36.99 4.92, ex tmean-hrei , ght- 6 .00, -5.66 th icknes , s-density 7 .65, 4.38 Table 16c

R2 Values, F Ratios, t-statistics, and Standard Error of the Estimate Values For the Variable Combinations I,ltrich Include Bending Length - I^Ieft Knit Subgroup

Variable Combinations R2 F-ratio Standard t-sÈa t is t ic s Error of Es t imate b lmean-shear:rnean .90 30.74 6 .01 5 .26, 3.81 blmean-dens ity .69 7 .67 I0.52 3.74 , -0.07 blmean-exÈmean .69 7.69 10. 52 3.04, -0.06 blmean-weight .79 13. 15 8.62 1.99 , 1.86 b lmean-thickness .79 12.95 8.67 r.47 , I .82 bLmean-shearmean- .90 18,55 6.33 3.57, 3.65, exÈmean -0. 55 blmean-shearmean- .90 17 .93 6.43 2.73, 2.59 , thickness 0.34 blmean-shearmean- .90 17 .66 6.48 4.66, 3.53, dens ity -0.17 blmean-shearmean- .90 77 .65 6.48 3. 30, 2.53, weight 0. 16 blmean-extnean- .80 7 .92 9,r2 0.78, -0.59 , l\) th i cknes s I .83 æ blmean-exEneen- .80 7 .54 9.29 r.73 , o.14 , weight r.73 bLmean-exùnean- .69 4.39 11 .36 2.39, -0.09, dens ity -0. 10 Table 16c (continued)

Variable Conbinatíons F-ratio Standard L- stat í st ic s Error of Es t imate

b lmean-dens ity- .81 8.47 8.88 1 .39, -0. 78 , we ight r.96

b lmean-dens ity- .80 7 .90 9.13 1 .33, 0.56, th ickness r.82 blmean-¡,rcight- .80 8.19 8. 99 1 .36, 0 .71, th ickness 0.65 blmean-sheel:ttrean- .90 11.59 6.94 2.71, 2.40, extrnean-weight -0.48. 0.02 b lmean-shealrnean- .91 12.16 6.79 I.74, 2.4r, extmean-th icknes s -0.62, 0.47 b lmean-shearmean- .91 12.12 6.80 2.66, 3.43, extmean-density -0.66 , -0.45 b lmean-sheannean- .90 11.19 7 .05 2.47, 2.t2, we igh t-dens i t y 0.25 , -0.25 b lmean-sheannean- .90 7 .04 7.04 2.44, 2.25, th ickness-density 0.26 , -0.0 2 b lmean-ex tmean- .81 5 .35 9.68 0.93, -0 .21, we ight-dens ity 1.81, -0.73 blmean-extmean- .81 5.19 9.80 0 .82, -o .24, weight-th ickness 0.44, 0.63

l\) \o Table 16c (continued)

Variable Combinations F-ratio Standard t-s tat is t ic s Error of Estimate blmean-extmean- .80 5 .09 9.88 0.77 , -0.36, th ickness-density r.7I , 0. 33 b lmean-weight- .80 8.19 8.99 1.36, 0.71, th ickness-densitv 0.65 , redundant b lmean-shearmean- .90 11.21 7 .04 2.44, 2.r9 , we ight-th icknes s -0.03 , 0.27 b lmean-shearmean- .90 TT.2T 7.04 2.44, 2.t9, we ight-th icknes s- -0.03, 0.27, dens ity redundant bl-mean-shearmeen- .91 8.09 7 .46 1.51, 2.15, exÈmean-weight- -0.68, -0.39, th ickness 0.57 b lmean-sheannean- .91 7.83 7.57 I .7I, 2.04 , extmean-\{e igh t- -0.58, 0. 1g , dens ity -0.45 blmean-shearmean- .91 7 .93 7 .53 1.55, 2.I5 , extmean-thickness -0.62, 0 .29 , density -0.26 blmean-extmean- .81 5.19 9. B0 0.82, -0 .24, we ight-th icknes s- 0.44, 0.63, dens ity redundant (,ts blmean-shearmean- .91 8.09 7 .46 1.51, 2.15 , extmean-\deight- -0.68, -0.38, th ickness-density 0.57, redundant APPENDIX 81

Cornputer Printout

Multiple Linear Regression

-131- BIIDPIR . IIULÎIPLE LINTAB REGRESSICI'| PROcRÀn REVISED tOttEËBEn, 1979 HEÀLTH SCIENCES COIIPUT¡NG fACTI,ITI IIÀNUÀL DÀTE -- 197'' UNIYERSITÍ OF CÀLIFOnNIÀ, LOs ÀN(;tLES coPTRIGHT lcl 1977, RECENIS Op UNMIttSITy Ct¡ CALIFURNTÀ

TII THfS YERSION OF B'IDPIR

¡lE¡ oPTro!¡ - To PaINT THË CORIIELAÎICN Of THE REGRESSTON COEFFTCIEÙTS, SPECIFt 88Ec Ir TflE pnIttl ptntc8Àpt. IP LESS ÎHIII TIO VÀRIÀBLES EI{TEREU îHE EQUÀTIOil,ÎHE CORRELÀÎIOTI OP Tï8 NEGRESSIOü COETIICIEìÎs IS IOl P8ITÎID. IET OPÎIOTI - SPECIFY NOI{I' Iil THE PLCÎ PARAGHÀPH 1O PBINl THE TTORIIÀL PEOBâAILIÎT PLOT OF B8sI¡'UTLS. uEr oPlIOtl - sPlc¡rI D[oRll It{ 1!E P¡.oT PAIiÀGRAPH TO PRINT TltD DETREÈDED iloBüAr pEOBtBILItr pLOr OF ¡ESID0t¿S.

PROGRÀi COìlnOL IilPOnËÀlr(rtl

,/PEOBLEII TITLE IS INEGRISSICII 1O PREDICT DRÀPE COBFFICIEIIlI. /I¡TPUT VARIÂBLES ÀRE 2q. FORúÀT IS . (J(1X,F6..11 ,F-r.0,_l (1XrF5.2l , 3 ( lx,88. 3l .2t. À l//9 ( 1¡, F5. 31,/ 1r.,88..t.1x. P5.¿tr1rrF8. t¡,2r,lll .. ,/Vf RIÀ8LE l{ÀltEs ¡ R E DcFÀc E, Dc8Àct(, DcttE¡N, IDENl, ExT l{ÀLE, ExTcouBs. EItËEÀil,SH!ARtÀL,SHEÀnC00,SHEÀRüEÀ, FÀ8R IC1, BtíALE IN,ðLrÀ LEOU, BLCOU Fril. ELCOUHOU, BL[EÀNI N. BLúEAì¡OU, BLI|EÀÈ, Bf ÀIIÍE. ELCOURñ E, BEIGHT,THTCK NES,DENSITT, FA8RIC2, ÈLilpÀN2,lHICKz,SHEARCO2, ELlHICK, !XTMEÀN2, BLSBElCO.BLErT!|EÀ, 1HEX1ItBA, BLCOU It{2, s 8 t a coT H ,s ft! ÀR ü E2 , ELcoIs lih, 1H B Lco u I, 1HSnEAHn. BLÀIIKS ÀRE I'I5S¡NG. LÀBEL5 ARE FABEICI,F¡BRIC2. ÀDD IS 1q. ,/TRlt{SFORll BLñEAN2=BLl'tEAt¡*BLttEAN. lHICK2 :1 HICK N ES*THICK NES. S HEÀ RC O 2 =SH EÀ RCOU +5H E A RCO U. E LT H ICK= ELtl El ll f TH ICK N Es . Et(1lt EAN 2=E XTIIEA tlt E IlltEâN. ELS H IACO= BLIEÀ II*S H E À FCOU. 1¡I E XTt' E À=TH¡C K NE S IE X lII E AII. 8L EXTI'EA= ßT,ñEAN I ETlI,IE ÀN . . sHEÀCO1il=SHEÀHCOUTIHtCKIES. BLCOUI N2= BLCOU RINt ELCOUR I II. S H E ÀIì II E ¿ -SI'I¡1P flEÀ r Sh EA R It E A. BLCOIS Hlt= ELcoU RIN*SHt ÀRttE¡. IHBLCO U I=BLcoUH I ttrllt ICK NES. T IIS H TA F i= 5 II E À R TI EAIT TI ICK N ES .

(,H l\) ,/REGR ESS DEPEflDtsÙ1 IS DCttt À1{. INDEPTNDENT AFE ELüEÀI{,lHICKNES. ,/PR Il¡1 DÂ1À. COIiRELÀTIOI¡. covÀRIÂilc8. Itr gu. /PLOT RESIDUALS. v ÀRIÀULES AltE ELr'tEÀN, TItICKNES. PiI;IP ÀRE BLIIDÀIi,IHICKNES. NO P I.IA L. /ÊÃD

PBOBL EIt Îf TL E . . . . .RE(;RDSSICN 1C PFEDICl DRÀFE CO!:FFlCIEIIl TUIBEN OP YÀRIAELES SEA! IN. ztl

TUI'BE8 OF YÀRIÀBLÊS ÀDDED BY.THÀN:;¡ORIIAT¡CNS. . ltI ÎOTAL NUNBER OF VÀRIÀBLES !I' ltoirBE8 oF cAsEs To REIID lr,t. . . 1000000 CTSE LÀBELING VÀRIÀBLES. . . . F¡IBRIC1 FÀIìRIC2 LIIIIlS AND IIISSING VÀI.I'E CfIECKÈD IJIFO6E TRANSFOR¡IÀTI()N5 BLAIIKS À88.. . I1ISSING rilPUl UNIÎ ¡IUIIB ER 5 NEIIND IIIPUÎ UNIl PHIOR TO READING. . DAlA. . . NO

I NPUT FORII IT (3(1X.F6.31,FJ.0,J(1X,F5.21,3llX,pB.3).ZX.^1/9(lX,p5.3l,/1X.FS.q11I, F5.rtrlI,pg. tlr2xrÀ11

ITt COITROL LÀI'GUAGE 1BÀNSIOBIIÀTICTS ÀRE t¡ERfORIIED *fr

YÀRII8LE5 TO BE USBD 1 DCFÀCE 2 DCIJÀCK 3 DCMEÀI{ ¡¡ IDENT 5 E IT I{I LE 6 EXTCOURS 7 ETTüNAN I SH EÀRl,lÀL 9 s I EA RCOU t0 S H EÀRIt EI 1¿ BLIIALEIN 1J tsI.9ALECU lq tsLC0uhItl 15 B LCO U ROU 16 BLI' E AI¡T N 17 BLIIEÀNOU 18 IiLIIEAN 19 Bl¡ ÀLEüD 20 BLCOU RIIE 21 ¡ EI GTIT 2¿ THICKNES 23 OT.NSITY ¿5 BLIIEAN2 ¿6 îltIcK2 27 SH E À BCO2 28 BLTHICK 29 EXlIIEAN2 3O BLSHEACO 31 BLEITIIEÀ 32 lHE TTI' EÀ 3J BLCOUIN2 34 S I,EACOTh 35 SHEÀRIIE¿ 36 BLCOI SHII 3'l lUB LCOÛ T 38 lHSHEARII REGRESSIOH ITITERCEPl. .NoN-ZERO GROU P IIIG Y IR I IBL I IEIGHI VÀRIABLE PRINl COVARIÀIICE ñÀlRIX tEs PRIIII COANELÀlION NÀlRIX YES PRIIIl COPRELÀTIOII OF REGRESSION COEFFICIENlS. TE5 PRI IIT BESI DUÀLS . . YES PRIIIl NONilâ[ PNOBÀBILIlT PLOT. tEs PRIIIl DETREIIDED NORI'À¡. PNOEASILIlT PLOT. . . NO

?0 F TTB IIN LE llE À tl SlINDAND DEVIÀlION COEIFICIENT flINI¡IUII üÀ xI üu rl OF VARIÀTION 1 DCFTCE 19.23392 15.89880 0.q0523 t?.52399 67.10799 2 DCBÀCK J8.157Jb 15.83948 0.q 15l1 1?.8ó099 65.86899 3 DCi EAtl 38.69566 t 5.8 I 52 0 0.4 087 1 1 t.69199 66.21599 { IDE¡IT 0.00000 1.02598 rt+r+*+t**r* - 1.00000 1. 00000 5 EXlrÀLE 7.88250 5.6q50¡¡ 0.71615 1.48000 26.67000 6 ÉTTCOURS 12.9rt598 10.0552? 0.77671 1.72000 46.42000 7 EIlIIEÀII r0.q1599 6.U5?qr¡ 0.b58J6 2.09000 27.611999 SH EART ÀL 'tl2.4121 8 4¡¡8.52002 1 C.69b54 14 1.42899 1 2d8. 57080 9 5HEÀRCOU r¡60.10596 286.r¡5J11 0.02258 .t62.85699 132't.14282 1O SHEÀRIIEÀ ¡154.3132J 295.89ó7J 0.651J1 152.1tr299 I 307.85693 I2 ELÍÀLEIH 1.2050e 0. llj26 0.2765q 0.7?600 1. 99800 1 3 BLI ÀL EOU l. -ì5994 0.29921 C.22001 0.91800 1.98400 lrf BLcouRlll 1.26145 Q..l72tt7 0.29527 C.83000 2. 1¡¡500 I5 BLCOUROU I.i1385 u,11925 0.J1244 0.82200 1.93800 I6 BLITEANII{ 1.2.t355 0. J¿089 0. 260 t3 0.8r¡400 't. 90000 I7 BLII EANOU r.30465 0.10045 0.2JU¿g 0.(i1700 r.92800 18 BLIIEÀN 1.26025 0. to4-t2 0.24179 0.88900 1.891t00 BIALEñE I9 1. 282'ì 5 u.¿8e01 0.¿¿511 0.91500 1 .89000 20 BLCCURËE | .2 J79t) 0.36715 0.29ô?5 0.82600 2.00900 2l lErcnl 164.9eÉ59 56.41J21 0..t¿t1e2 24.46259 252.469f9 22 lHICtillES 0 . o'l tt25 0.01091 0.r¡1621 C.02060 0.14020 23 DEIISIlT 2J0.e752.t 61.6u¿¡6C 0. ¿bl1r| 1l f,.75240 JJ5. 1u7¡r¡ 25 BLnEÀt{2 1.67É43 0.rJq15C 0.501,rb 0,'t9oJ2 J.587Zt 26 THICK2 0.00óit2 0.0049? \).-t t.t41 0.00042 0.0tr66 27 SHEARCO2 2U9651. J 7500 f¡016 /f,.5b25C 1. ltJr,'t6 Zb,))-¿. lglt\q

2ö B LlHIC T 0.09775 0.056 3tl 0. 5 7ó rJJ 0.02464 0.20ó65 29 EX T ItEÀ II2 15.1. 16629 215.8l4Ir7 l.¡r0941 4.368r0 ?6tt.5219'l 30 BLSHEÀCO 610.9Jr¡TJ 51 8.82080 0.It492J 155.92816 2511.60718 3t BLEXÎII EÀ l¿.078¿19 7.11b81 0.5iJ9¿2 J.7 307 9 31.06917 32 TH E TTII EÀ 0.72 109 0. 5018 r¡ 0.69595 0.10?55 2.26458 33 BLCOÚ IN 2 1.72JQ4 1.044C8 0. f, 05 95 0.68890 4. 601 02 3tl SH E ÀCO TH 34.499r¡t' 2 J.8't66 0 0.69¿09 J. l5¡r85 92.7 67 ztl 35 SHEIRñE¿ 289578.87500 q198J5.62500 1. ¡l i¡ó 16 231q?.48828 t+*rt+rtt*rr 36 ÐLCOISÚi 619.ó91t2 58r¡.00.t8u 0.9r¡241 134.1901 I 2805.352?9 3? TH B LCOUI 0. c9855 0.05815 0.59208 0.01rJ17 0.22t34 38 THS 8EÀNi 34.1956e 2 q. ¿b ge6 0. r0971 3. 1J414 91.41916

(, ñ COYÀRI ÀIICE ItÀTRI X

DCFACE TCBÀCK DC¡lE¡ll I DËNT E XT IIÀL E ETT CO U RS EIl II EÀII S UEÀBT IL SHEIRCOU sHEtnñEt I 2 3 ¡l 5 6 7 I 9 10

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L, BLI'ÀLEIN RLTIALEOII I}LCOURIN E LCO U ROt¡ TJLII EÀN IN BLIIEÀNOU BL¡tEII BII T LEIIE BLCO UR It E IEIGHT '12 1J tll 15 16 17 t8 19 20 21 BLIÀLEIII 12 0.11tr ELIÀLEOO 'tl 0.c668 0.0ú95 BLCOU B I II lrr 0.c810 0. 0662 0.1J87 BLCOURO U 15 0.0e62 ù.06t8 0. 1 266 0. 14 J8 ELttEA r¡ r rl t6 0.0960 0. 0665 0.1c99 0. 1 124 0.1010 BLIIEÀNOU t7 0.0 t6rl 0.0747 cì. cì946 0.09r,7 0 .08 55 0.0903 ELIt EÀ N 18 0.0888 fJ.07rI 0.1037 0.1077 0.096¿ 0.0862 o. 0929 B IALEII B 19 0.0889 0.0 ,81 0.0716 0. 07 90 0.08 l3 0.0756 0. 0799 0.0835 BLCOU Bü E 20 0.0886 0.t¡640 0.lJlT 0. 1.162 0.11rl 0.096? 0.1 057 0.0763 0. l3rt9 TElGHT 21 6.6872 4.2 t q5 9.7 Ë75 1 . ¿82J 9.1916 4.0895 7.47tt? 6.rt532 8. 496 5 3 182 . {rt97 InICKt ES 22 0.0052 0.002q 0.00s1 0. 00 47 0 .00 52 0. 001 1 0.0041¡ 0.0038 0.0009 I .3 982 I¡E}IS ITI 2J - J. ó852 - r¡.20 c8 0. 0¡ld8 -3. ¿r,14 - 1 .8190 -5.ltt38 -2.7786 -3.9.r13 - 1.6r92 ?50.8lrt2 BLíEtX2 25 0.2qtt2 0. 196 5 0. 2 865 0.293( 0.2ó 5J o .235? 0.2552 o.2203 0.28 99 21.109? I 8rCK2 26 0.0009 0.0004 0.0008 0. 00 08 0.0008 0. 000s 0.0007 0.0006 0.0008 0.1999 SH E ÀRCO 2 27 32250.q57C q27q4.5586 73856.1250 51231.0547 5J09 1.52J4 { 3 6r¡2. 082 0 50029.0 39 1 37q 90 . 83 20 ó2570.89{5 aaaa*aattt DI.lHTC K 2A 0.01r¡0 0.0090 0.0145 0.0lql 0.01r¡3 0.0108 0.0r30 0.01 t5 .0.01tttl 2 0 ()071 .q21 EXTITEAN 2 29 -22.2655 -l¿.¿824 -J5.1268 -25. -28.78 q5 -18.1420 - 23.9r¡ | 0 -17.2521 -30.6t95 -6.r13.523q '131 BLSH EI CO 30 7.r.0126 I 1. 660t| . É 268 10¡r.8468 l0 3. 3678 88.5817 98.322tr 78.2220 | | 8.378? 1 0399.0508 ELEXlttEt 31 -0.5q12 -0. J168 -1.158q -0. 7564 -0.8.r95 -o . q'rz9 -0.6933 -0.rr28{ -0.9575 -19tt.5937 1HEXlftEt 32 - 0.02:3 -0.0510 -0. 0q26 -0.0q21 -0.0339 -0. 0 tt7 0 -0. 0402 -0.0381 - 0. 0rl2 3 3.9 t2¡. DLCOoI t{ 2 33 0.2320 0.1v15 0.3851 0.1575 0.3086 0.2ó55 o .2917 0.2 | t6 0.37 lrf 25.533 1 SHEACOIt 3q J.3798 3.0210 q.9381 3.571J 4.1620 2.9552 t.7286 3.2012 lf. 257 | 898.q807 SHEÀRüE 2 J5 3333r1.3320 36J6ó.39tr5 ó?563.1¿50 fr8 7 03. 51 95 50488.2969 391ztt.1797 rtó09 t.5391 3485t.2656 58153.5781 +taaata+'lr BLCOTS H tl 3ó 7 9.5992 a7.5U t7 1 53.3576 121.6ð62 1 t 6.52 6rt 99.8376 I 10.5851 I ¡.5509 137.5609 1 l6?8.9023 T HELCO U I l7 0.013.1 0.0c87 0. c 1óq 0.0156 0.0149 0.01r3 0.0r35 0.0r l0 0.01ó0 2.tt623 lHSH EI R It 38 3.7020 3.0289 .¡.9067 J. 7¡¡ 09 tl .30?1 3.0r¡(t5 3.8rr53 3.3 662 tt.3257 939.1 377

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(, @ BL TALEI¡I BLIIÀLEOU BLCOUFII{ B LCO U ROU B LII EÀ!¡ T I{ BL! E âIIOU BLUETII B f TLBTIE 8LCO0 B n E f EIGEl 12 1.1 14 t5 16 l7 l8 t9 20 2l öLfTLEI X 12 t .0000 DLl ÀLEOU l3 0.66 I ? 1.0000 B LCOUn [ [ 14 0.65 26 0. 59q r 1.0c00 8¡.COU nOU t5 0. ?6 t0 0.5t¡4u 0.9 r03 1. 0000 BLITEA TI II 16 0.d981 0.6927 0.9193 0.92J5 1.0000 BLI EÀ IIOU 17 0.7 6 15 0.irtl.l 0. 8457 0.86 58 0. d873 t.0000 BLöEÀ È l8 0.87q3 0.7d00 u.9 lJ5 0.9J 16 0.98q3 0.9¿tl0 | B¡ALEIIE t9 .0000 o.9232 0.9c37 0.ó834 0.720r¡ 0.8761 0.8702 0. 9076 1.0000 BLCOURIE 20 o.7 2 36 0.5827 0.97 t0 0. e7't7 0.9¡t28 0.8758 0. 9rt rt 1 0.7185 t.0000 TEIGHT 27 0. 46 21 o. 2q97 0. 4620 0.3¿t0¡l .t 0.5082 0.241 3 0. 3tt8 0. J958 0. cr 00 t .0000 1 HICK N ES 22 0.5090 0.2ó32 0.4r¡68 0. r¡03, 0.52J6 0.334? 0. tt660 o.tr297 rt350 DEN SIl T 2l 0. 0. 80 20 -0.1793 -0.22't 6 0. 002 t -c. 1q0r¡ -0.0919 -o .277 5 -0 . l rt?8 -0.22r1 -0.0715 BLT EÀT 2 25 0.87C6 0. ?ú01 0.9 rq0 0.21 s I c.9193 0.9826 0.9323 0.995t1 0.9057 0. 93 ¡l4q lnICr2 26 o.5227 ¡t q4¿J r1394 79 0. ? 0. 2?5 0. 0. 0.5281 0.36.t0 0. 482q o. ¡r¡ 39 SltEâBco 2 2'l 0.2q09 0.3557 ¡¡93? 0.(t5tt 0.7r35 0. 0.3J63 0.rt119 0.3ó1 6 0 ..r 087 0.3230 0..t21t0 o.2781 BLl HICK 2A 0.7q72 0.:363 0. 6 886 0.66e2 0.7877 0. ó.t02 0. 7 5tt8 0. 7 081 0.69.t6 EIlIIEA T 2 29 -0.3095 ¡¡ 0.76r t -0.1902 -0. J9q -0. 3 I 6rr -0.¿t155 -0.2797 -0.36.t0 -o .2 765 B¡.5 flEtCO JO o. ta 32? 0. -0.386 1 -o.5266 526 0 o .6922 0. 53 ¿9 0.6209 0. 5ó8 3 0.ó2t9 0.521? 0.62 | BLEIIIt E T 3t I 0.3553 - 0.2282 -0.1488 -0.¡t370 -0.2a02 -0.3720 1 IHEIITtBI -0.221 -0.3r97 -0.2083 -0.3663 -0.l¡8.t? J2 -0. t512 -0.3t96 -0 .22t7 -0.2212 -0.2106 -0.3120 -0 .2632 -0.2627 ELCOL I lt 2 33 0.6667 0.6130 0.9904 -0.2296 0. t J82 0.9029 0.9211 0.8r¡6q 0.9 tó8 0.70t3 0.9682 0. {335 sHEtcolñ Jll 0.q248 0.t1229 0. 555J c.l9t¡4 0.54 32 0.¡¡119 SIIEÀRIIB2 0.5125 0.4639 0. {85t1 0.6670 35 0.2J88 0 . ¿902 0. ¡tJ3t 0. J0 66 0 .37 57 0.3r09 0.3 6f3 o.2879 BLCOIS HI t6 0. ¡¡0 90 0.5010 0.3780 0.2920 0.7 c50 0.5¡¡ 94 0.62 18 0.5ó90 0. 62 trl 0..r950 0.órt12 0.3505 16BLco rf I J? 0.6893 0. q982 o .7 537 0.7031 0.?954 0.6q4 I 0.7ó0t 0. 655 | 0.7rl5l 0. ?rt8 0 lts HEt B rl 38 0.1¡577 0.4 t7 I o.5tt28 0.l¡06t| 0.55J 1 0. ¿||75 0.s2 00 0.0 799 0. 48 52 0.6860

IfiICKrES DE I{S IT T BLttEtt¡2 T fIICK 2 S HEÀRC02 BLlHICK E XlüE ¡ t2 BLSIIEÀCO BLBIII E¡ T H PIlI I¡ 22 2J 25 26 21 26 29 30 31 32 lHICf,t¡ES 22 1.0000 DETSITI 23 -0.35q9 1.0000 8LõEAT2 25 0.4qó2 - 0. l0r¡0 I .0000 1íIC(2 26 o.97? 1 -0.q27 ta 0. tt560 1.0000 SHEARCO2 27 -0.0000 0.3¿90 0.¡.r65 -0. 06 76 1.0000 BLTHICK 2g 0.9227 -0.J21l 0.7411 0.9241 0.1226 r.0000 ETTIIEÀII2 29 -0.2812 -0.q680 -0.36J7 -0.2202 -0.1895 -0. 3 58 rl | .0000 BLSHEÀCO 1 JO 0. 08? 0 .2780 0.6511 0. 04 94 0.95',r8 0.2937 -0.2677 BTEXTIIEÀ J1 - 0.1262 - 1.0000 0.6q00 -0.314¡¡ -0.0155 -0.3101 -0.2119 0.9rr69 -0.3 915 t THETTIIE¡ 32 0.4649 - c.48 00 .0000 -o.2717 0.46Þl¡ -0 .21 21 0.2188 0.5675 -0.27 17 0.ó24t 1.0000 BLCOUI il¿ 33 0.3894 0.0q05 0.9 267 0. l8 2q 0 .56 37 0. 648 1 -0.q228 0.7385 -0.438rr -0.2631 SHEACOTH 3q 0.r¡878 0.1c7J 0 .5 ¿62 0.4055 0 sHErRnB2 .8 168 0.5251 -o.2t7t 0.8389 -0.268ó 0.0908 15 0.0005 0. Jqlr¡ 0.4c-ìl -0.0661 0.9828 0. t099 t4 BLCO IS filt 36 0.1039 -0.20 0.9128 -0.3062 -0.2 t35 o.29 ltr 0. 6542 0. 0480 0.9587 0. 291 9 q9 lll BLCOU I :!7 -0.r071 0 .99 36 -0. ft -0.2919 o.9r 00 -0.29I5 o.7q77' c.9118 0.17s5 0.9862 -0.3631 0.3rtl3 0.2288 THSHEA R II J8 0. ¿t 696 0.1284 t¡ - 0-22ttl 0.5J66 0. I 14 0.81 58 0.5369 -0.2?3q o.8257 -0.29q0 0.0490

F \o BLCOI'Iil2 SHEÀCOlH SHEÀRItE2 BLCOIS IIII THBLCOf'I lHSHEÀRII 13 l¡¡ 35 36 3't 38

B LCOUI II2 t3 r .0000 S H EÀCOÎ H 3rf 0.56e5 1.0000 SHEABö82 l5 0.50 ll 0.B0lrr 1 .0000 BLCOTS HÉ 3ó 0.7627 0.8155 e.9195 1 .0000 lnB LCO0 I t7 0.7 12 0 0.548q 0. t531 0.lr¡93 1.0000 lltsHEtarl 3E 0.5593 c.988J 0.8256 0.80e7 0.551t r.0000

EEGRESSIOII lITLE. . .REGRESSION TO PRËDICÎ DNÀPE COEIIICTEIT DEPEI¡DEIIT YåRIÀBLE. 3 DCTl EA r¡ TOLERÀNCE 0.0t00 ¡LL DTTA COIISIDERED ÀS A SIlIGLE GROII P

üULTIPLE R C.9160 SÎD. ERROR OF EST. 6.708I¡ TULTIPLE 8.5QUÀ88 C.8390 ÀTALTSIS OT YTRIII{CE SUII OP SQUÀREs DI NETN SQUÀNE 8 RÀTIO P (rrr Ll REGRESSTOil J98?.250 2 1993.625 ¡r4.300 0.0000 0 RESIDUÀL 7b5.043 l7 45.003

S,T D. R EG VTII IBLE COEFFICIEIIl sTD. ERROR coEFF T P(2 ÎÀrll TOLERTIICE rltlERcEPl -¡1.41451 ELüEAll l8 q0.70119 5.706 0.?8rr 7.130 0.000 0.7a2873 lnrcKDES 22 1 19.00529 56.280 0.233 2.115 0.050 0.782673

CORNELÀlIOII I'ATRIX OF IìEGIr!,SSICII CODFFICIENlS

BLIIEA!{ TIIICKNES 18 ¿2 BLÌ|EAil l8 1.0000 TH¡CKNES 22 -0.rt660 1.0000

+. LTST OF PREDTClED VåLUES, RESIIIU]I[5, AND V¡IiIÀELIS NoTÈ - llDGÀlIvE cÀsü NUI'tllgR DENclEs À cAsit l¡IT[ ¡tIssINc vÀLUEs. THE NI'IftJER CP STANDÀBD DEVIÀlIONS FNOÉ TIIIi ¡IEÀN IS DENOlED BÏ UP 1O 3 ÀSTERISKS 10 lHE R CF EACH REsIDI'ÀT ON IÀRIABtE. IGIIl ItIS.SING VALUES ANE DENOTTI Br ilOhE TIIÀN THREE ASTERISKS.

CISB RESIDUÀL PREDICTED V¡RIABLES LÀBEL l¡O. tt.lLUE l DCI¡ÀCE 2 DCBÀCfi ] DCIIEÀN q rD8ù1 7 EXTIIEÀII 5 EXlrtlE 6 I IICOUn S 8 SHÐÀÂIÂL 9 5HEÀRCOU 10 SHETRTET 12 BI,T ÀLEI¡ l3 BLIILEOU I4 BLCOURIN 15 tsLCOUROU l6 BLüEÀiltll 17 DL IIETUO U 18 BLIIEÀTI l9 Bf Àt EüE 2O BLCOI'RITE 21 IJEIGHl 22 THTCKIES 2t DE IIS ITT 25 BLËEÀn2 26 ÎH ICK 2 27 SHEÀRCOI 28 tsLTHICK 2 9 E:(TN EAil 2 30 BLSUEACO 3J BLCOUTN2 J 1 BLEtlt'E¡ 32 lHEIlII EI 34 SHEACOTH 35 SHEÀEñE2 36 ELCOISRü 37 lHBLCOOI 38 Tnsfl Etat

-0. rf t 87 26. 6947 2 J .6980 28.8540 26.2760 t .0000 1 t¿.f,500 3.9300r | 1.3700 1225.71 )9r] 9lrt.2859r t070.0000.. r. t1l0 0.91 80. 0.9180 0.9680 1.0160 0. 9{3 0t 0.9790 tt5 l.0t 60 0.9q30 200.22 0.0ó96 287 . 67 9q 0.958tr 0.00 ¡t8 *rf+¡|*++f,** 0.0681 '160.0225 .| 895.0857 2. 3 8rt3 0. 88 0¿l 0.8tt27 63.6341* +taJlfa,t¡tta+|l 982.259A 0.0639 7 tt.l7 20. 1.Cl8J ¿8.538t 30.0970 29.0170 29.55?0 1.0000 1 0. 1000 18. 51 00 l¡¡.J100 J2 0.00 00 3 30. 0 000 32 5.00 00 0. 933 0 t . J090 l. 1130 0 .99 00 1.0230 1.5000 1.0520 1. 0 860 t. t2 t0 ta+rrttrr+ 7 4.94 56r 0.0485 15t.5278r t. 1?9 q 0.002q 0.0527 20tt .7761 35 0. 3796 t5.5q07 1.2J88 0.69r0 16.0050 tttt'|+*t¡t¡¡ t61.72q9 0.0srt 0 1 5.7625 6.52511 29.6956 37.09c0 .r5.3520 36.221 0 1.0000 8.8?00 rt6.4200t*. 27.6500+* 141.¡¡290 162.8570* 15 2. 1rt30r 1. 1rt?0 l.57rt0 0.8820t 1.1u00 1.0 t50 t. 3770 t.1960 1.36t0 l.0Jl0 24. 4626++ 0. 02 06r I | 8.752¡rr t. .f 30 tf ¿6522.7984 0.0001rt 0.02ttó* 76q.5220s; 190.77ó8 3 3. 069rf .t 0.5ó 96 o.7719 3. 35 rt 9* 231rt7.¡t881 ttr¡.1901 0.0 182t 3. t3t1. -2.6965 29.2275 27.1230 25.9390 2ó.s3t0 | .0000 5.5500 7. 0? 6.3100 q76. 00 43q.2859 517.8569 07 1 I 0.7?60t 1.2320 r. 1790 t.0l t0 t.0780 1.1220 r.1000 r. 00 q0 1.1950 165.9t84 0.0¿t95 :ll+ù*ù+t*r 3¡5.1877. t.2t00 0.0025 0.054r¡ 39.816 I 569.6021 ó.9q10 t.(r016 lttt*t+ttr 0.3t 23 25.613e 656.5027 0.0683 2 ¡.56 5ó

N .t. t4l4 55.243ó 57.6580* 59.1 1 20. 58.3850+ 1.0000 ?.2500 t6.0500 11.ó500 265.71 39 2ó8. 5 708 267 .1C28 r. q{90 t.1990 1.59J0 1.65 50r r. 521 0 1.,t270 l.lt7tt0 t .32 rlo l. ó240r 20'l .27 69 0.lt¡02r* I 07. 8rr 5 2r 2.1727 0. 0 I 9?.. 72130.2500 0.20 67 * 135.7 225 395.8?33 17.172r t.6333r 2.5376 3?. ó5J6 7t3ó5.2s00 s2 5. 55 8l 0.2233r. 3 7. ¡t53rl 2.2qq0 6J.9720 66.5610* 65.86 90* 66.2160t 1.0000 1..t800r 2.6900r 2.0900* 1 28 8.57 08++ 1327.1428r++ 1307.85ó9rr 1. 574 0r l. 98 ttor r 2. I 450*r 1.8720+ 1.8ó00+ 1.9280+. 1.89¡¡0r. 1. ?790r 2.0090r* 19 {.4 t 50 0.0699 27 8.1326 3.587 2r' 0.00q9 * | *** t* tt i*+t 0.1324 ¡r.f68 I 251 3. 60?2.tr 3.9585+ 0.llr6l. r¡.6010** 92.767 2r* +r**+++ *a taa* 2805.3523rr* 0. 1rr99 91.t192.r

t.q295 24.0955. ¿6.7 200 24.3¿90 25.5250 r .0000 .r.0200 I 3. q600 8.7400 480.0000 50rr.2859 q9 2.1428 0.86?0* t. 37 30 l. 011 0 0.8600 0.9390 1. I r70 1.0280 1.1200 0.9J6C 88.8751* 0.0310i 286 .63lr I 1.0568 0.0010. +++++trr+t 0.01 1 9t 76.3876 5t8.q058 8. 9 8tt7 0.27 09 1.0221 15.6329 a+*tarr**l q97.5562 0.031 3. t 5. 25 6rl -tr.62't1 22. -t190 17.524)+ 17.8610r 'l'l .6920+ 1.0000 7.9500 12.5900

H +- N) 10.¿l:)O 16r¡.0000 168.57t0r 166.2U60 1.0380 1.0t10r c.8 J0'J* 0.8220i 0. 93r10 0.9r?0r 0.9250* 1.02 50 0.8¿60* 167.1613 0.051J 125.C536r 0.8556 0. 00 26 ¿u416.1797 O. U¡¡75 105.4729 t55.9282 9. rr99 ? 0.5269 0.6dt 9 8.647?r 27651.0113 138.017¿l 0. 0 026 8. 53 05.

- 1.987¿ tlq. J72¿ r¡5. J 42 i) 39.4290 4¿.3850 1.0000 .t. f¡ 30 0 tt.rt100 7.9200 287.8569 257 . A569 27 2.8569 1. t220 l.¡¡300 1. 2JiJ0 1.2060 r.2u00 1.ft80 1.2990 r. 17 ó0 1 .2 ¿2t) 177.148J 0.1087. 163.521ór 1.687¡l 0.01 t8r 66490.1875 0.r412 62.726q 33 rt. 95 61 r0.288r 0. 86 09 1.5J26 28. O290 7r¡ 450.8 ?50 33't.7966 0. 1 J{6 29.6595

10 1. 5077 47. ¡¡553 {8.6290 49.¿980 r¡8.9ó3 0 1.0000 3. 070 0 1.72001 2.3'r00r 542.8569 580.0000 56 t. q290 1. r¡8ó0 1.1000 1.71n0. ¡.9J80r 1.6020r l.5r 90 1.5610 1.2930 1.8280* 1J3.$501 0.0450 297.tr$tt3. 2. tt367 0.00 20 tt+t*t*r** 0.0702 5.7 121 905.3799 3. ?308* 0. | 0?5. 2.9515] 26.1000 f,t**+aattt 96{.530.r 0.0?73 25.26tt3 rr56J 1l -l.6J3l 15. J4.99J0 12.65J0 13.823 0 - t.0000 1 1.9¡t00 1 2. q?00 1¿.2100 347.1428 41U.2859 380.71¡t8 l.0rt0 t.2510 1.1600 1.0590 1.0860 1. r5s0 1.1200 r. t3 10 1.1100 19 2.2653 0. 0 950 202.597tt l. 2 590 0.0090 rtttttr*** 0.106fi 149.081¡l {6rt.0000 1 t.6752 1. r599 1.345ó 39.t57r +ll+¡l*tt+* q41.6292 0.1102 36.16?9

12 -1.6t85 21. J655 21 .377 0] 18.1170r l9 . 7tt7 0. - r.0000 t2.1300 1 0.6700 q000 15. 202,8570 1 88.571 0 195.?t40 0.78t¡0r l. 00 50t 0.9040 0.82 20* 0.8r¡f¡0t 0.9ltt0r 0.8890r 0.91 50t 0.8630ù 15e.7551 0. 0556 287.i2A9 0.790.t. 0.0031 J5559.0195 0.0494 237. I 600 167. ó39ó 1 3.690ó 0.8562 0.8172 'I 0.t¡8q5* 38303.9órt8 176.925tt 0.050 3 t0.88t7 tl 15.2603 r+ J7.162b 54.5200 50. J260 52.Ít230 - 1 .0000 4.3200 7. 37 00 5.8500 59 1. r¡290 655.0000 ó23.2t{8 0.9830 1. 39 20 1.26ft0 0.99?0 1.1240 1. t950 1.1590 1. t8 80 l.1Jl0 227.006Aj 0.09ó0 236. t¡656 l.3rt33 0.0092 *a'¡t*t+tl* 0.1111 14.2225 759.1.t1t5 6.780 t 0.56 16 1.5977 62.8800r +*trù++t+a ?87. ?rt30 0.1213 59.8286r

14 -7.1520 + 25.9500 lB.99l0* t8.6030+ 18.7980r - 1.0000 6. 520 0 | 2.63 00 9.5600 230.0000 2qq.2860 237 .1r30 t.0380 1.1000 0.86J0+ 0. 88 20 0.9490 l.0tt0 0.9800 1.0890 0.8710 1J?.0204 0.06J0 21't .83't I 0. 9ó0 ¡¡ 0.0040 59675.64r¡5 0.06 1 7 91. ?764 239..t003 9. 3 88t¡ 0.6035 0.7396 15.J900 562 16. 7 96 9 20 3.91t29 0.05q2 1q.9{00 -1.2197 J8.rJ957 39.4760 15.6750 37.6760 - I .0000 t0.9000 5.8800 8.1900 l5¡¡.2860 245. 7 1 40 2 0 0.0000 0.9830 1.25r0 1.4280 1.4170 t.2060 l.3lrr0 1.2700 t. t1?0 l. l¡210 1J8.7687 0.07¿6 191.1t¡19 1.61:9 0.00f,3 +r 60J75. J6tl 0.0922 70. tl¡;,"t l1 2.0566 10..)551 0. ó0 91 g) ¿.0J9¿ 1¡.8388 40000.0000 285.5999 0. 1 ',:, 7 1x, \) ¡tO 16 0.6229 2d.87b1 29.J9ù0 29 .607 0 29.¡¡990 - t.0000 2ó. 6 70 0r f. 28. 03 00* '¿7. Jr)"tJ++ 381.4290 56 0. 000 0 0?0.?t4E 0.91r?0 1. t000 1 .0.ÌrJ0 0.88 90 0.9930 0.9950. 0. 99rt 0 1.î2.f0 0.9blr0 152.r156 0.0828 t I l. 71rt9 0.9880 0. 0069 j. 0.c82J 7 tt8.O220t' 55ó. bl99 27 .1959+. 2.26tt6t 1.077r¡ r¡6. J68C t**++t+**+ q88.6016 0. 0859 3A. 97 52

17 -1l.fr71l rt t, 1.75b1 {¡', . r¡ 5tt') Itlr. Jl 10 47. 885 0 -1.0000 3.9400 5.0300 ¿t.rtrcI r¡47.1rt2rJ 347 . 1tt ¿Íl 397 .1tr28 1.6050+ 1 .87 20r 1.t,ll')r 1.7q40* 1.b2l0r 1.8080. 1.7 t50* l. 7t 90* 1.brlj)* 2'r.1. l¡tr 94r 0.11-¿5r ¿¿t!.4169 2,9q12r 0.0127t

t**r***ttr Q.19?9* 20. 160 I 595.3rr96 7. ?003 0.5051 2.t' 198 39.0535 ***tf****l 650. 1223 0. 18.t2t q tr. 6? 85

l6 12. 155J | 5.r.511ô 67.1 080r 6q.2¿50* 65. ó 67 0* - t.0000 ?.1000 8.1{00 7.6 ¿J0 668.57C8 731.4290 700.0000 1.5930. t. ?1 20r 1.'t160 t.r¡050 1.5150 1. 5590 t.5370 1.6530t l.l¡2'10 237.27 211 0.10q1 227 .9269 2. l62tl 0.0r08 t I ++*+*r** 0. ló00+ 58.06¡¡ ll I 12q.2061 1 1. 7119 0.79t2 2.06¿1 76.1f¡ l7* *tr*tt+a*t 1005. t997 0.1095 ?2.8700. t9 -rt.?6c5 JJ.8165 29 .0't50 29.0380 29.0560 - r .0000 2.2300+ 1tt.2100 8.2200 385.7139 420.0000 402.8569 1. q550 I .52 00 0. t r40t 0.8670 1.1650 t. 1960 1.1800 1. tt900 0.rt710 153. 10 88 0.060? 252.2389 t.392q 0. 00 37 ttt+*t*tti 0.07 16 67.568q rt95. 59 96 9.6996 0. rt9 90 0.76J9 25.49r¡0 ùt ftr**tfl J52 . 096 9 0.0531 2 f . o53tl

20 -3.9230 65.513U 59.8460* 6t.33t¡0* 61.5900r - 1 .0000 5.2500 5.2000 5.2J00 ¡t 1 l. q290 364.2ö59 307.8579 1.9980+. t. ?8 20. 1 . rJ010* 1.ó910* 1.9000*t 1.?380+ t. I l90r 1.0900.* 1.7¿r70* 215.1088 0. | 085r t98.257r 3.3088. 0.0118. I fttt tt tt I 0. l9?r¡* 27 .3529 662.6357 9.513.1 0.5675 3.24J6* 39.5250 I t*t*';f **t 698.5317 0. t95lrr rt2.0826

SEEIIL CORRELÀlIOi OF RESIDUÀf,S =.0.q650

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25. -12 + +

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P PO t¿ +

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2.0 + +

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F \or APPENDIX 82

Computer Printout

Stepwise Regression

- 150 - EÚDP2R . SIEPSISE REGRESSfC'{ PROGIIÀ¡I REVISED NOVEIIBES, 19?8 HEA¡.18 SCIENCES CO¡IPI¡TING FACILITI IIÀIIUAL DåTE 1977 ulrIvEusIlt oF cÀLIPonNIÀ, Lcs Â¡rGELls 90024 coPtRIGHT (Cl 1977, REGEI{'IS OF ('XTVERSTTY CF CALIPORNTA

III lHIS YERSION OP BItDP2R .- IIET OPTIOII . TO PRINT THE CORRELÀTIOI OT THE REGRESSION COEPPIC¡EIITs, SPECIPI RREG I¡ ÎflE PNIilI PTBIGIIPH. IF LESS ÎHÀ[ ltao VÀRIA8LÈ5 ENTERED lHE EQUllror, lll¡j COnRELÀTÍOI Cr IHE REGRESSIOI COEppICIEltlS IS IOl pBfITED. .. lHE II{lLEV OPTICI¡ IS IIOl AVÀILÀÈLE.

-- llEt oPlIoN - SPECIPY llORltAL IN THE ELCÎ PÀRÀGRÀPH TO PFfùÎ THE llORtÀL PROBTBIL¡ÎI PLOÎ OF BESIDUILS. .- IIE| OPTIOII. SPEC¡PY DNORITÀ[ III THE ELOÎ PÀRÀGRAPH 10 PNINT lHE [ElNEilDED NONü¡L PSOBTEILIÎT PLOÎ OI AESII'U¡LS. -- llEl OPTIOÈ - 10 SPECIFI IIIDEPEI{DEllT VÀRIÀALES IN THE REGRESSIoN PIRÀcRÀPtl, 511¡E IIDEP¡ftRIÀBLE LI51. lHE LEYBLS OPTIOT sTILL ËÀr BE USED TO spEclFT THE INDEPENDEì|Î VÀRIABLES IF ¡N ITDEP= STttEËBtll IS toT sPECfttPD.

PAOGRII CONTEOL INFCNIÀTIOT¡

./PROELEII TITLE IS IR¡IGSESSICN TO PREDICÎ DRÀPE COEPFICIENT" /IilPUT VÀRÌABLES ÂRE 2¿r. PORËåT IS . (3(1X,t6.3¡,FJ.0,J(lX,F5.21 , 3 ( ¡X,FB. 3l .¿t.^1/9 | 1 I,85.3),/ 1.Í. F8. 0,1X, t 5. { , 1 x , F I . 4 , 2 X , A 1 I | . /YÀ8I rBLE llÀíES ÀR E DCP tCE, DCE tCK, DCltt À¡t, I DEN 1, EXl¡tÀLE, Ef,lCOURS, EITIEÀH ,SH EÀti gA L, SH t,A RCC t¡, SHEÀRttEÀ, ¡¿ÀB R lC 1 , BLfl ÀLEIn, BtH ÀLIOU, BLCOU fi 1N, BLCOUBOU. BLü EÂilIN. BLttEÀt¡ou, BLItEAN,BTA t Eü8, ELC0U RË8, taEIcHl,THlCK t{tS. I ENS]1T. FABR IC2, BLtt EAN 2 , TH IC K2 , SHEÀ RCO2 , E LI fll C K , EX I nE AN 2 , BLSH EÀCO, BLEXl ItEA, TB EXtüEA, BLCOU IN 2, sHËACOTH TSHEtRnE2, BLCOISHñ, TÌ¡ BLCOUI. lUSBE À8It. BLAIIKS ÀRE IIISSTIG. I,ABELS A8E PAEFICl,F¡BRIC2. ÀDD 1S 1q. /18 A tSFO Ri E L dEâI¡2=BLI,IEÀI¡I ELII EAN. 1H TC K2 =THIC K IIE S I1H I CK NËS . SBEIRC02=StlEÂHccU *S HÊlncOU. BLlUICK=BLüEÀ II*TH ICKNES. EXTü EANZ= EXT l,lEANrrtTü E ÀN. BI.SHEÀCO=BL I.tSÀ NI SHE A RCO U. 1¡l E Xî llEÀ=T HICK NESTEXTIt EÂN. ts BL BIl¡'EÀ =B LiEÀ N. E Tl fT E À II . \JI SHEÀCOTfl=5H EÀRCOUtT H ICK tl 85. BLCoUf N 2=BLC OU RI tl + ELCc URI N. SH EÀRú É2=S HEÀRlttÀrs tl I ÀRll EÀ. DLCOI SHü-BLCOUN IN*SHEI R IIEÀ. 1H BLCOU I = B LCoU R Il{ rT H¡cfi lt I S. lHS H E¡ R ã =SII EAR T'DI I1H ICK ¡¡E S. /BEc RE 55 DEPENDENT IS DCI'EÀII. lITLE IS 'SPECIFTING CRDER OF ENTRf OF VÀRIIEL,Es INTO EQUATION' üEÎHOD tS F. LEVELS ÀnE 4r0,6+1,0,12r1,1 l*û. /?rD

PROBLEII TTTLE. . . .REcRES:;lCN 1C PFEDICT DÂÀtii COeFFICIENT

rU!IBE8 OF YARIÄ8LES 1O R¡ÀT IN. . . 24 NUüBEN 08 VÀRIAELÈS ADDEI BY 1RÀNSFORI'ÀlIOIIS. . I¡¡ TOTÀL IIUIIBER OF VÀR IÀBLÈS ]8 NUãBER OF CASES TO REÀD It¡. . . 1o000oo CÀSE LÀBELIIIG VARIå8LES. . . . FÀBRIC1 FÀBRIC2 I,IIIITS ÀTID IIISSING VÀLUE CfiECI(ED BE¡OFE 1RÀIISFORüÀlIONS BLÀ¡|KS¡I8E.. . ¡rISSIt¡c ITIPUÎ UilTT NUIIßER 5 RETIND IIIPUT UII IT PRICR TO RljÀDII{G. . DÀ1¡. . . NO IIPUÎ FORÚA1 (l(1r,F6.Jl,FJ.0,J(1x,F5.21, Jl1r,F8.3l,2t..È1/g11t,F5.3i tt.2Í.^11 /1x.F8.4,1X. F5.¡rrl rrFg. it+ COIITBOL LÀ¡GUÀGE TRÀNSFORI'ATICNS ÀItE PERFOAí!D +'r

VÀRIÀBLES TO EE USEC 1 DCPÀCT 2 DCtsÀCK 3 DCttEÀt'f rl IDENl 5 EITTILE ó EXTCOT¡RS 7 EXlI'EAN I SHEARIÀL 9 S H EÀ ¡ICOU l0 S HETRNE¡ I2 BI.I' A L EI I¡ 1l 8LIÀLEOU ltl BLCOURIN t5 B LCOTROU l6 8Ll| EtX I tl 17 BLËEÀilOu ld B L I.'EÀ N l9 BIALEIIE 20 BLCOUNËE 21 UEIGHT 22 THICKTES 23 DENSITY 25 BLIIEAN 2 26 1ilrcx2 27 sflEtRco2 28 BLTHICK 29 EXlI'EÀN2 t0 BLSIIEÀCO JI BIEfTIIEA t2 THEIÎIIET J3 BLCOUIT{2 lt¡ S HEACOl H 35 SHEARIIE2 l6 BLCOISHIT 37 lIIBLCOUI 38 TSSHEtSü

.IIIÎBRCEP REGR ESSIOI¡ 1 . NON Z ERO ¡EIGHT UÀRIAELE PRT[T COVARIÀNCE T'TlNII NO PRTNl CORRELAIION íÂTBII l¡o PRINÎ INOVÀ tÎ EÀC8 SÎEP. . YES PRI ìI1 STEP OUÎPUT YES PRINT AEGRESSION COEPFICIENT SUIIIANY TAtsLE. TES PRTTIl PARTIÀL CORRELÀTICN SUüT'ÀRT TÀBLE . . NO PRINT F-RÀTIO SIIIII'ÀRT 1ÀBLE. ilo P&tNT SUIIIIÀBf TAELE YES PRINT RESI[UÀLS ÀIID DÀTÀ. . NO PRIIIT CORRELÀlIOI{ OP REGRESSICII CO¡;FPICITNTS NÙ PRINT TORTIAL PROBÀBILTTT PLOT . NO PRII¡T DETREIIDED NOR!TL FIOEÀtsILITY FLCl. . t¡o F lJt UUIIBEB OF CASES 8EÀD. . l\) YTRITELE STÀNDARD CCEFFICIENT S¡IILLEST LÂRGEST S IIILLESÎ LIRG ESl ilo. NÀttE üEÀll DI;VIÀIION OF VÀNIÀTTON SKÈI'NDSS I(URTOSIS YALUE YÀLUE SlD SCCEE stD scoSE 1 DC!^CE 19.23)9 15.8yfrn 0.4052 0..1511 -t.Jl3rt 1?.52rt0 67.1080 -1.3655 r.7512 2 DCEÀCK 38. 15?t¡ 1s.8395 0.4151 0.45'16 -',t.2115 17.8ót0 65.8690 -1.28tC t.7rl95 3 DCiEÀl¡ 18.695t 15.8152 0.4087 0.405r¡ -1.2727 17.6920 6ó.2t60 -t.3281 t. ?rf 0î .r rD ENl 0. 0000 1.0260 26r¡8160.0000 -0.0000 -2.0975 -t.0000 1.0000 -0.97¡t? o.97tt1 5 ErrftLE I.8825 5.6450 0.7161 t. t Jfrs 3.tr362 1.4800 26.6700 -t.13rt2 t. 328 t 6 ETTCOURS 12.9t¡ó0 10.0553 a.77b7 1.8211 3.598q 1.'1200 rt6..t200 -1.tt6t¡ 3.3290 7 ËrÎËEÀN 10. q 160 6.t5rq 0.6584 1..'119J 1.1r¡01 2.0900 27.6500 -1.21tt2 2.5132 I sH EAntÀL qq8.5200 J'l¿.tt1¿1 0.6965 1.57¡¡1 1.70ó8 141.¿1290 1288.5?08 -0.9830 2.6889 9 SflEtRCOU 460.1060 ¿86.45J1 0.6226 1.41rt¿t 1.7'162 162.8570 132?.1028 -1.0377 3.0268 10 sHEÀRilEt 051r.3132 295.8967 0.ó5lJ t.tt76tl l.ó166 t52.1.130 130?.8569 -1.0212 2.8846 12 BLIÀLEIN l. 2051 0.Jll3 0.2765 0.6156 -0.ó808 0.7760 1.9980 -1.2816 2. 379 3 lJ BLTILEO0 r.3599 0.¿992 A.2200 0.5523 -0.8rr23 0.9180 1.9800 -1. rr??l 2.085? lq BLCOUSrlt 1.2614 0.3725 tJ.2953 0.64ó2 -0.6290 0.8300 2.1¡t50 -1.1583 2.3722 15 BLCOUFOo 1.2138 0.J793 0.3124 0.6412 -1.1959 0.8220 t.9380 -1.0¡32 l. 9o9t¡ tó BtËEÀilrì 1.2JJ5 0.3209 0.¿60t 0.7702 -0.8212 0.8r¡rr0 1.9000 -1.21tt0 2.0769 17 BLiEÀiOU 1.30r¡ó 0.3004 0.2103 0.¡¡738 -0.9315 0.91?0 1.9280 -1.2902 2. O7tr1 18 BLúEAil 1.2602 0.J0r¡, 0.2q1n 0.7117 -0.8r¡37 0.8890 t.89r¡0 -t.2181 2.0798 t 9 Br tLEilE 1. 282'' o.2a90 0.225J 0.7303 -0.6273 0.9150 1.8900 -1.2'r2q 2. t0t2 20 BLCOUEüE 7.23'19 0.J673 0.2968 0.6508 -1.0276 0.82ó0 2.0090 -t. t21l 2. 099 1 27 ¡ ElcHl 164.9886 56.rt1J2 C.3419 -0.6799 -0.0163 ztt.tt626 252.9690 -2.tt910 t. 5507 22 THTCKIIES 0.07rll 0.0f09 0.qr62 0.2622 -0.8?21 0.0206 0.1q02 -1.?36t 2. r3t8 2l DE[Srlt 230.8752 61.6U46 0.2672 -0.0045 -1.1896 11B.752rr 335.18?? -1.81?7 t. 691 t 25 BLnEÀil2 1.676q 0.urt15 0.5020 0.9489 -0.r¡33.t 0.7903 1.5872 -t.0530 2.2707 26 THTCKz 0.0064 0.0050 0.7734 0.9256 0.1122 0.000rr 0.0197 -1.2075 2.6650 27 SHEARCO2 289651.3?50 r¡01ó?6.5625 r.3868 2.5090 6.2t93 26322.J9A4 1?ó130S.0000 -0.6551 3.6638 28 BLrHrCf, 0.0977 0.05ó4 0.5?68 0.6432 -0.9631 0.0206 0.2067 -1.2967 1 .931s 29 ErIilEAil2 153.1663 215.87qtt 1.q094 2.0981 3.1508 0.3681 76tt.5220 -0.689¡ 2.8120 t0 BLsflEtco 610.93¡¡J 518.S2C8 0.8492 2.J955 6.2062 155.9282 2513.6072 -0.8?70 3. 66? 3 3l BLEXlilEA 12.0785 7.11ó8 0.5892 1.5658 2.03ó3 3.7308 33.069r¡ -1.1?30 2.9495 32 îHËrliEr 0.7211 0.501c 0.óe59 1.srt5? 2.3090 0.t075 2.2646 -1.2226 3.0?56 33 BLCOUTI2 1.?230 1.0.tr¡l 0.6060 1.0851 0.(93t 0.6889 l¡.ó010 -C.9905 2.7565 3rt sHBÀcoÎ¡t ll¡.0995 ¿J.A766 0.6921 0.8500 -0.2126 3.1549 92.1672 -1.30rrq 2.1¡¡r00 J5 SHËÀRilE¿ 289578.e?50 4188J5.6250 1.4qó4 2.3038 4.5rr02 231q7.4883 r?t0rr89.0000 -0.616t 3. i925 36 BLCOISHil ó19.6911 584.00¿¡9 0.9rf2¡¡ 2.5140 6.9223 13q. l90l 2805.3521 -0.8313 t.7tt25 37 tñBLCOUT 0. C986 0.058r¡ 0.5921 0.5901 -0.878? 0.0182 0.221t -1.3?76 2.1385 38 lHSHEÀRË 34.1957 24.¿6A9 C.7097 0.8357 -0.3682 3. 13t¡1 91.tr192 -1.2799 2.t579 IIOlE. KURTOSIS VÀLUES GREÀ1ER THÀN ZERO INDICATE À DISTRIBUTIOùI TIl¡I HEIVIEN lTILS THTT NORÜTL DISlSTBUTIOII

H l¡ L' RE6NESSION ÎITLE. .SPECIFYING ORDER OF ElIÎRf OF VAEITBLES INÎO EQUTTION STEPPING ÀLGORIlHI'. E tAxIüutt !lultBER oF SlEPS . 76 DEPEIIDENT VARIABLE. . I DCI' BÀN tIIIIItIUtt ÀCCEPTABLE F 1O EI{1ER . r¡ . 000, l¡ .00 0 rÀIIItUd TCCEPTABLE I TO FEI'IOVE. . J.900, 3.900 IIIIIIITUII IC(EPTABLE TOLERÀ¡¡CE. . 0.01000 SUBSCRIPIS OF lHE I¡IDEPENDII{T VÀRIÀBLES .l2tt 56 7 A 9 10 l2 t3 ltl 15 16 l7 18 19 20 21 22 ':3 25 26 27 28 29 30 ¡l 32 33 3rt 35 J6 ll 38

slEP ïO. 0 sÎD. EIROR Of ESÎ. 15.8152 TTILfSIS OF YÀBIAIICE SUII OP SQUÀREs DT üE¡N SQUÀRE RESTD0IL tt752.2891 19 250.1205 YIRIÀBLEs III EQU¡lION TtBIIBLES ¡rO1 I¡ Eou¡lrOl SÎD. EIiBOR STD REG T TO P¡BIIII I TO r¡8I¡BLE COEPFICIETÎ O8 COEFF COEFF ÎOLERÀIICE BEITOVE LEY EL. TTBIIBLß CO8I. ÎOLBBIICB 8IÎEA LIYEL (r-IiTBACEPI 38.696 ) DCPICE t 0.9966 I 1.00000 26rt2.80 0 DCBTCK 2 0.99ó59 1.00000 2622.26 0 I DE IIT tt -0.05973 1.00000 0.06 0 ETTITLE 5 -O.37217 1 .00000 2.90 | E rlCOU BS 6 -0.35869 t.00000 2.66 t EXlíEtll ? -0.tf1623 r.00000 3.77 | SHEAB TTL I 0.38312 t.00000 3.10 t 5 íE ARCOU 9 0. {392q t.00000 rt.30 t SHB TA Ë EÀ t0 0.rr1{86 1.00000 3.7q I BLT TL EIII 12 0.76802 t.00000 25.89 t B LT ÀLEOU | 3 0.687?3 1.00 000 t6. I 5 1 DLCOO R III 1 | 0.84308 t.00000 ql¡.21r 1 B LCO 0 800 r5 0.82198 1.00000 3?.rt9 1 BLT BT ü IN I 6 0.8883 t 1.00000 67.35 1 BLIIEÀTOU t? 0.825ó3 1. 00000 38.50 | B.LII EÀII I 0 0.8925? r.00000 70.53 t B¡A LEIIE t 9 0.79866 r.00000 31.?0 1 BLCOU RT E 20 0.85185 t . 00 000 rr?.6 | I ¡IEI GHl 2 I 0.50ó33 1.00000 6.21 I lUICKTES 22 0.5979? 1.00000 10.02 I DËN SITI 23 -0.26117 t.00000 1.12 I BLII EÀN 2 25 0.8?20t r.00000 57 .12 0 THICK2 26 0.6r95ó r.00000 11.2 1 0 5 HEÀRCO 2 27 0.03 | 32 1.00000 4.11 0 BLTHI CK 2A 0. ?9068 r.00000 30.02 0 EITITEÀI¡2 29 -0.28020 1.00000 1.53 0 BLSHEÀCO 30 0.61939 1.00000 71.20 0 BL EXTII EÀ 3 I -0. r9939 r.00000 0.75 0 P ÎH E XÎã Et 32 -0.06676 1.00000 0.08 0 (¡l BLCOU II{ 2 3l 0.82264 r. c0000 37.68 0 r SH E ÂCOlH 34 0.67111 1.00000 1rr.75 0 SHEÀRNE2 J5 0.37?15 1.00000 2.98 0 BLCOtSHn 36 0.60179 1.00000 10.22 0 l IIBLCOU I 37 0.81 t?5 1 .00 000 34.78 2 THSHEÀRII 3I 0. 651r¡ { 1.00000 13.27 2 VTRIIBLI EIITERED I8 BLIlCAN

IULTIPLE R O. d926 T0LlIPLE R-SQIJÀRE 0.7967 / TDJUSTED R-sQUåRE 0. 1854 51D. EB80R Ot EsT. 7.J267 t¡¡LtsIs oF VIRIANcE SUII OF SÙUAR5S DF I.IEåN SQUARE F 841 IO REGnESSTOìI 3786.0J42 1 378ó.014 70.53 RESTDUÀL 966.25586 1t 53.680t8 VTRIA!LES IN EOUIlIO¡¡ vtRIIBLES üOt Iì EQUÀTIOI S1D. ER¡iOR STD FEG FTO PIRÎTIL F TO YÀRITBLE COEPTICIEI{T OF COEFF COETS TOLDRÀNCE R EIIOY E LEV EL. YInIIBLE CO8R. ÎOLEBAIICE ETTER IBYBL (r-rÈ1ÊRcEPl -19.686 I BL¡Etil 18 rt6..J25 5.516 0.tt9J 1 .00000 70.53 DCFTCE 1 0.98521 0.22156 561.90 0 DCB TCK 2 0.983t 1 0.19575 tt90.52 0 I DE IIl 0 -0.0921¡l 0.99958 0. 15 0 ETl IÀL B 5 0.169?9 0.?5?95 0.50 1 E IlCOURS 6 0.093¡t3 0. 80273 0.15 1 ETl IIEAII ? 0. t439 t 0.72115 0.3 6 I SH E ÀN ¡TL I 0. t5830 0.87q36 0. tl ¡¡ I S H E ÀRCOU 9 0.2503 3 0. 859rt? 1.1t| 1 SHE À4il EI t0 0.20rr90 0.8ó¿r15 0.711 1 DI,I TL E T¡ r2 -0.056118 0.23559 0.05 I ts LI' I LEOO 13 -0.03007 0.39t58 0.02 t BI.COUN IN trt 0. t5093 0.165115 0.lt 0 I BLCOUROU 1 5 -0.0s?95 0. 13220 0.06 I DLII DÀII III l6 0.12261 0.03t1ó 0.26 t B Ltt El t¡ot t7 -0.09369 0. tl4r¡8 0. r5 1 BIIÀL EIt E I 9 - 0. 060rt 9 0. t7 623 0.06 1 B LCOUSttE 20 0.06179 0.10870 0. 0? 1 r EI GHl 21 0.29tr3 0.81092 1 .57 t THI CT IIES 22 0.115633 0.78287 ft.4? 1 D Elt s llr 23 -O.28977 0.97815 1.56 1 BTi ET N2 2 5 -0.37916 0.00923 2.85 0 lHICK2 26 0.078rr0 0.76126 5.05 0 SHE ÀRCOz 27 0.1615? 0.83293 0. q6 0 BLT HICK 28 0. 39543 0. r1302{ 3.t5 0 ErlÉEt!¡2 29 0.10633 0.8675r1 0.19 0 BLS H EÀCO 30 0.18203 0.6tJ21 0.5I 0 B LE XTITEA 3r 0.20116 0.89?80 o.'t2 0 THEXTIIET t2 0.3865t 0.930?{ 2.99 0 BLCOUI N2 33 0.02rr25 0. 15955 0.0 | 0 5 I E ÀCOTH 34 0.5s188 0.?3736 7.tt5 0 SHE¡RI'82 35 0.t238rt 0.86730 0.26 0 BLCO lS l{tl 3ó 0.133q2 0.6tJ84 0.ll 0 1H B LCOUT t7 0.r15502 0.1t2229 tt.4ll 2 lIISHBÀRI! 0. q8635 0.72963 5.27 2 38 ts vl L¡ slEP [O. 2 YÀBIÀBLE E[lEAED 22 THtCt(N ES

TULlIPLE R 0.9160 ñULlIPLE n-SQUARE 0.rr19c ÀDJUSTTD R -S0UARE c.B2r)l sTD. ERROR OT EST. 6. /orJ4

ÀNÀLTSIS OF VARIÀ¡¡CE ifr:,t cP 5):,ÀtDi; î¡ :TtÀì,¡:;0u,thi F RÀT IO . REGRESSION l')tl'1.¿q'|1 2 l9¡¡3.ô2r¡ 44. t0 NES1DIJÀL /D5. C1;19 , 1i (5.00,1'r2

v ÀR t,ilrLEs It{ E0UATIoN vÂRrÀBLES ì0T Iil EQUAIIOn 5TD. DNNOR SlD REG FTO PARTIIL T TO VAHIÀB¡.8 COETTICIENl CT CO[,fF COErF TOLERÀNCII R E¡IOVE LEVEL. VÀRIABI.E CORR. TOLERAIICE ENlER. LEVEL , (!-IUTERCEPÎ -i 1.¡¡J4 t BLËEIN 18 40.7fjl 5.'/08 0.7811 0.78¿8't 50.811 . oar^a¿ t 0.9814ó 0. t7705 ql9.q2 THICKNES 22 119.005 5ô.280 0.2J.| 0 0.78 ¿A-t 4.4 7 . DCB¡C|( ? 0.97877 0. t5610 f 64.9.1 0 . IDDNT rt 0.10809 0. s4123 0.1 9 0 . ExTrrLs 5 0.0392{ 0.69016 0. 02 1 . EXTcoUnS 6 0. 20tt59 0. ??061 0.7 0 t . EXlúErt{ 7 0.17127 0.72090 0.q8 1 . sHEÀRfAL ð 0.24243 0.86129 r .00 I . sHE[&COU 9 0.3707] 0.8362t 2.55 1 . sHEÃRËEr 10 0.J0752 0.8¡¡ót5 1.6? 1 . BT||LEIN 12 -0.19017 o.222ql 0.6 0 1 . BLLÀLEOU t3 0.06002 0.37875 0.06 1 . ELCOURIN tq 0. tt982 0.16488 0.32 1 . ELCOUROU t5 -0.0t686 0. t3t03 0. 00 I . BLItBAìrr l6 -0.08306 0.025?ó 0.11 1 . BLt'tEANor¡ rt 0.0?738 0. 10071 0.10 t . BrÀLEtrE t9 -0.07732 0.176r7 0.10 I . BLcoûRttE 20 0.07813 0.10867 0.r0 t . rErGHl 2t -0.08891 0.35208 0.r3 1 . DEff sIlt 2t -o.16721 0.873611 0.1¡6 1 . BLnEÀt2 25 -0.J2ó9rr 0.0088r¡ 1.91 0 . THrcxz 26 0. 16588 0.0r¡196 0.05 0 . SHEAECO2 27 0.3tt3ó 0.?865? 1.72 0 . BLTHICK 28 -0.33ó55 0.0t3?6 2.0.r 0 . ErTnEA12 29 0. 19070 0.85 tó3 0.60 0 . BLSHBACO 30 0.3508rt 0.57 130 2.25 0 . 8LErlilEt J I 0.21221 0. 897trr 0.7 5 0 . lREXlüEt 32 0. t12t6 0.fi89?3 0.2 0 0 . BLCOUTN2 13 0.08250 0. 15772 0. r1 0 . srEtcoTH 3{ 0.r¡7859 0.65818 ft .75 0 . sHEÀ8trE2 35 0.2q982 0.83072 | .0? 0 . ELCOrSHi 36 0.29815 0.56983 1.56 0 . IHBLCOUI 37 0.06098 0.02?66 0.06 2 . THSHEARi 30 0. rr0005 0.ó5153 3.06 2 I I I + F * F.IEVELS( ¡I.OOO, J.9OOI OK TCLEFANCE lNSUFFICIENT FOR FURTHER SlEPPING \¡ STEPfISE REGRESSICN C0¿FFICIEN'tS

YÀRIÀBLES O T.II{ÎCPÎ l DCt'ÀCE 2 DCBÀCK 4 IDhNT 5 DXTIIALE ó EXTCOURS 7 EXTII EÀl{ SH ET RTÀ L SH EABCOU 10 sREtntEt SlE P o 38.6957r 0.991¡1 0."951 -0.92c¡ -1.04J5 -0.5642 -0.9599 0.01911 0.02r¡3 0.0222 1 -19.bÙ58+ 0.9J88 1.000t1 -0.rr4C6 0.¿46r¡ 0.0/40 0.1762 0.0039 0.0067 0.0053 2 -21.{3q5r 0.9J,J9 0.99¿q 0. tzðo 0.05J1 0.1¿t67 0.1867 0.0053 0.0090 0 .007 2

ÌtotE - 1l RËGRESSION COEPTICTE¡¡1S FOR VARrÀBIES I¡I lHE EQUA'TION ÀBE INDICATED BY AN ASTBSISK 2l lHE REtfArllIllc coEPPTCTENTS ÀRt THCSE ÍIHICH fOULU BE ()81ÀII¡ED IF TIIÀ1 VÀRITBLE fERE 1() BÜÎER Iil lNE TBIî S18P

stdPflIs¡: RLGEESSTCI{ COEPFICIENTs VÀRIÀDLES I2 BLII¡LEIII 1J BLrÀtEOU lrl ELC0uRlN 15 BLCOUBOU Ió BLIIEÀIIIN I? BLIIEÀNOU 18 BLI'E¡T I9 BT¡fEIE 20 BLCO0S|IE 2l TEIGHÎ S1-.: 0 36.4q7q J6. J51J 35.7978 34.21 14 ¡r3.781r¡ q3.4600 q6.3255 { 3. 70r¡ 2 36.6?t9 0.1019 ?.10q7 15..t199 -6.5723 rtó.3255t -3.5557 3.638r¡ 0.01109 I -2.4900 -1.1455 -2.9970 q. 2 '1 .6'la2 ¿.0662 5.8662 -0.7791 -10.2J21 s. 1501 00. ?012r - 0l¡lt ó rl. o9rt3 -0.0169

E 01E. 1I REGNESSION COEFFICIENTS PO8 YÀRIABL¡5 IN TIIE EQUATIOII ARE INDICATED BI ÀII ISlERISÍ 2l THE REüÀrt¡lNG CoEFFTCTENIS AItE THOSE ¡IIIICH f¡OUTD BE OtsTÀT¡IED IF TB¡1 VÀRIÀBLE ¡ERE 1O EüÎEB II IHE XEIl 51BP

STEPIISE EEGFESSICN COETFICIEI¡TS

YÀRIÀELE5 22 THICKTES 2J DENSIÎY 25 BI.üEAN2 26 THICKz 27 SHEARCO2 28 BLTHICK 29 Erlä8rr2 30 BLSRBICO 31 8L8r1t8¡ 32 lnlrlllEr SlEP 0205 0.0 t89 -2.10110 0 305. 996 3 -0.06?0 1ó.3886 1973.0191 0.0000 221.7801 -0. -0.rt¡t3t -0.03J9 -J3.q181 78tt.¿725 0.0000 76.2q73 0.0038 0. 003 2 0.2127 5.6931 1 119.00s1 2.0266 2 | 19 .005 3* -0.0184 -26.22qA 1010.9082 0.0000 -322.91s5 0-006 I 0.0057 0.1998

UOTE - 1l nEGRESSIOII COEFFTCTENIi FOti VARrÀBLES IN lHE EOUÀlIOII ÀAE INDICATED BY AI{ ASTERISK 2I THE REüÀINING COEPTIClENTS ÀRE lHOSI IHICH I{OULD BE OETAINED IP ÎHÀT YÀRIABLE IERE 1O ETÎER IÈ lHE ÜBI1 51EP

\¡L'I STEPI'ISE RI;GRlSSICN COETFICIENTS

YTRITELES J3 BLCOT'II¡2 t4 slrEÀcollt 35 sHEARtrt2 36 BLCOISHI,! 37 THBLCOUI 38 lHSIIEÀR¡I SlE P 0 12. rt609 0.4r¡45 0.0000 0.016J 220.0095 0.42.15 1 0.¿t146 0. t 920 c.0000 0.0021 85.5741 0.1ó73 2 1.2626 c.1568 0.('000 0.004J J9.8',rt¿t 0. 1298

üo1E- t) REGRESSIoN cOEFFICIENTS FOti VAtìIÀbl.!s lli lllf'j E:JUÀlIoN AFI IND¡CATED tsY Al¡ ASTERISK 2l 1íE RErtÀINtNG CoE.FFIcl¿N15 ÀRI TITOSE rHICH r(.,rtLD BE O¡JTÀINtD rP tHÀT VARIABLE IfERE 1O ElllER IÙ Îfl8 tlEIT SlEP

SUIIIIIRT lABLE SÎEP VÀR IÀBL E ¡'ULTIPLD I NCIìEA5E F-TO. r.TO- IIUII I¡O. ENTBRED RTIIOVID BER OF ITDEPEIIDBñT F FSç IN RSQ ENlER RE!OVE VARTTBLESINCLI'DED I 18 BLttEÀt¡ 0.8926 0.7967 0.796't 70.5285 2 22 ÎHICKilES 0.9160 I 0.8J90 0.0¡¡2J 4.¿t711 2

H L,r @ A,?PENDIX 83

Computer Printout All Possible Subsets Regression

-t59- BIlDPgR - ÀLL POSSTBLE SUBSEl'S RUGRESSTON FFOGFÀlf BEVrSËD NOVEIBER,.1977 197u IIEALTÍI SCIEIICES COúPUTING TÀCILITY IIÀI.IU ÁL DAÎE uïIvERSrlY OF CALIFORNIA, LoS ÀNGELES, CÀ 90024 coptRIGHT (Cl 19?7,1978, nEGElllS CF llNrVERSrtY 0F CALIfORNTÀ .. IF lHENT ÀRE TEÏER lIIAN THRIE INDEPENDENl VÂRIÀI]L85, TIIEN tlEIH0D=RoilE. L ILL BE 0SED. -- rF sÎÀîrslrcs. rs stÀTED rN THE EICT PÀFÀG8åPH, ltlEN SlAlISTICS À5 II¡ BItDP6D I¡ ILL ÂCCCT'IEÀNY EÀCII PI.OT. -.10 LIflIT lHE NItttBER CP VÀIIIABLIS IN THE FEPOIì1TD 5U85ETS, III THE PRII{1 PÀRÀGRÀPII STIITE hÀTVAR=1HT IÂXII'I¡II NUI'BER OF Y[8IÀBLES THÀÎ TOU DESIRE. A SUBSET IIllH G8EÀTER TtìÀÌI üTIVIR VARIÀBLES TILL IICT BE REPORTED OIiLESS I1 IS ONE OP lHE BEST SUBSEÎS 8I lIIE CP OR ADJUSÎED F-SQUÀRED

CRIl ER I¡. , .- 10 OBTÀIII THE COVÀFIÀNCE IIATRIX OF THE &EGRESSIO¡¡ COEFEICIEIITS, II¡CIt¡DE CRÊG III THE üÀTNII S1ÀTTüÞNT OF TTIE PRIIIT PARAGRIPlI , E. G.. ItÀTRIx=coRR, RESI [, cREG. .. IP 8ESIDUÂTS IRE CCËPUÎED OR IT TOU STÀTE HISÎOGEÀII. fN lHE PLOT PÀNAGNAPN, À HISlOGRAI' OT THE STÀNDÀI{DIZED (sluDEHlIZEDl RESTDUÀLS tfrLL BE lttDE.

PBOGATi CONTAOL INFCEIIÀTICII /PROELEII TIÎLE IS IREGBESSICII TO PREDICT DRÀPE COEFFICIENÎI. /rNPOl VARrÀBLES tHE 2q. roBüÀT IS | (3(1I,tó.31,FJ.0,3flX,F5.2' , 3 (lr,F8. Jl .2X.^1,t9(1X.F5. Jl /1X.F8. ¡¡,1N, F 5. 4 , 1 X , F I . 4 , 2 r , À | I . . /vaBrÀBlE llÀtEs ÀFE DCràcE,DcBtcK, ccüt¡[,TDENT,Err!ÀLE.ETTCOURS, EXTIE ÀN ,SHEÂR tà L,SHEA ACOU, SIIEARItEÀ, FÀBn ICI , 8 L ¡I À L E I I{, BLI À L EOU, B LCOU 6 I N, gLCO U RO U, BLII E AN I I{, BLüEÀNOU, ELttEÀ t¡, B¡tA I EltE, BLCOU RflE. r E I G HT ,1 HICK N ¡ S, D I,IIS I TY , PA BR ICz, BLtt EAN 2, THrCK2, SHEA 8CO2, ELl ltrCK, tXT tiEAN 2, ELS[[ACO, BT EXT ilEA,Tt EXTtTEA, BLCOU IN 2, sH EÀCOTH,SHEAniE2, BLCOISH11, THBLCOUI, lHStìEåRH. BLÀNKS ÀNE üISS1NG. LÀBTLS ARE FåETICI, F¡ERIC2. ADD IS 1I¡. ,/TRÀl¡sFoRü BLütÀN2=BLltEÀNi ELlt¡AN. I Hlc K2 =Ttt Ic K NE s *ltllCK N¿s. SH EA FC02=S llEÀRcoU +s bE¡RcOU. BLTUICK=BLItEA NITH ICI( NES. ETlN I AN2= EXT I'EÀN I T XTTI I ÀN. 8I,SHTÀ CO=BLüEA N+SII EÀ 8COU. I ll E X ¡ ü EÀ=T H lC K N !.S * EXTII E Àl{ . F BL E X 1 I.|E À =U LIIEÀ N * E XT II ! A Ii . c¡, SHEÀCCt ll= S ll !. å ICCU tT l' ICX N f S. BLCO U I il2=B¡.C CURI !¡ TBLCCURT N. SH¡ A Rll t2=S fl ! À R It E A rS t t À Br'! t Â. BLCO I SHIt:ß L(:OORIì.¡ISHEARIIEA. THBLC0t I=BLCoU R tN*THtCK N tS. I l'l5HEÀ R il=SHLÀ R tf EA*TH tcK NLS. ,/REc SESS DUPENDENl 1S DCItTAN. üìlttioD=Rs0. frlt{ûfR=5. INDbPINITENT AiìlÌ f',7,9,10,17,1q.20 To 23 '¿5 TO 28. J0 . ttl . /EtlD

PROBLET TIlLE. .:llii;1ä.jiilCN'f(ì t¡.t.DIC1 l)ì[t.L L(r,:i'trlCIt.N.

IIUIIBER OF VARIÀELES 10 REAT IN. . . 2q NUIIBÉ8 OF IÀNIABLTS ÀDDEI EI lRAIISFCRNÀ1IONS. . 14 101ÀL rUñEtR O8 VÀnIÀBLES ld lluðBE8 0F cÀsEs 1() REÀD ¡Ì. . . 1000000 CTSELABELIIIGVÀRIIBLES... . 8ÀBRICI FÀBRIC2 LIIIIlS ÀIID ITISSIIIG YTLUE CIIECI(ED BEFOFE TRINsFORI'ATIONS BLtllKstRE.. . ütssING ItPUl U!¡IT ilott8ER 5 EEfIIID ITPUÎ UIIIT PRIOR TO REÀDIIIG. . DTTI. . . NO IùPUÎ ronËÀ1 (l(1I,f6.J1,F3.0,J(11,P5.21, 31lI,F8.J¡ (¡X,F5.31 F5.¡t,1r,P8. llr2lrll¡ .2X,.A1/9 /7t.tB.q.1t. frf coilnol LtilcuÀcE 1RÀisFoR[ÀTIcts ånt ptRFoSüED +*+

VÀ8IÀBLES TO BE USED 1 DCFÀC! 2 DC BÀCK 3 DCtt EÀt¡ ¿t fDEXI 5 EIIfTLE 6 EXTCOURS 7 u xl ttEÀ ì¡ I SHEANIAL 9 S H EA RCOU t0 sllE tRrE I 12 BLTILEIN 13 I LH ÀLËO U l¿l BLCOURIII t5 BLCOU ROU t6 Ef,II EÀII III 17 BLðEÀNOU t8 BLIIEÀN l9 BfALEIIE 20 BLCOURIIE 21 TBIGHT 22 îHICKIE5 2J DDilSIlr 25 BLIIEÂN2 26 T HICK2 27 sflEAnco 2 26 ELTHICK 29 EXTlttÀil2 JO BL SII EÀCO 31 B L Efl!EA 12 ÎH E ITIIE A 33 BLCOUTN2 34 5H EÀCO 1 H 35 SH EÀR IIE2 36 BLCOIS HII 37 TgBLCOUI 38 lHSHEÀRII

ITDEPITDEIIl YTBIABLES ÀRE 6 ETTCOURS 7 EXTTIEÀ I¡ 9 SHEÀRCOU 10 sHEIRIIEA l7 BLII E¡IIOU 18 BLII EÀ N 20 BLCOUR I.|E 2l TEIGHT 2Z lIIICKNES 2f DBNS ¡17 25 BLËEAÌ¡2 26 lHICK2 27 SHEÀRCO2 28 B LTH ICK l0 8LS HETCO . 3.t sHEÀcoTh

DEPEI¡DENl VÀNITBLE. . ] DCI'EAN NUIIBEB OF '8EST' REGRESSIOIS. . q SELECIIOi CEIÎERION . nJl| F TEIGHT VÀRITELE c¡, PBECIS[OII . DOUELN lOLER¡NCE FOR IIAlRII ItIVERSION. 0.0001000 PRI.IICORRELÀÎIOnnÀlRII ....lBs PRIIIÎ COYASITìICE iTIRIT NO PRITTBESIDUÀ¡,S.. NO PRINT COVÀRl¡NCE !tÂT81I tOR REGRESSIOn COE8S. . llo PBIT'T COREELTlION ItÀlRIX FOR REGRESSION COEFS . NO tA¡l . to. oF vÀRs. Il¡ Àt¡Y REPCñTED SUBsEl 16

DÀÎt TPTEB lttlrSrORflÂr ICNS lOn FIRST 5 CÀSES c¡sEs t¡1H zEBo lEIGSlS ÀllD drSSrr{G DAlÀ l¡C1 INCLUDED. cà58 CâSE CÀSl LTBEL NUIIBEB I¡EIGIIÎ 6 EXTCOUSS 7 Ð(TðEÀN 9 SHEtRCOU 1O SHEARãET 17 Bt ttEtt|ou 18 Bf,ñET II 20 BLCOUEäE 21 ¡Erc[1 22 lHICKNES 2J DËNSIlY 25 BLIIEÀT2 26 THICT(2 27 sflErnco2 28 BLTH ICK 30 BLSüttco 3¡t SltEÀccltl 3 DCI'EÀN r a 1 1.00c00 11.370C0 1¿.65000 9 t.t. 285I 9 1 070.00000 0.91r300 0.9 790 0 0.9rr3 00 200.22 Utr9 0.06960 2Al.679q4 0.95844 0.00ttElr 83 59 | 8. 62500 0.0ó8t4 895.085ó9 63.6Jq28 26.2'' 599 B B 2 1.00000 I 8.50999 14. J 1 00 0 330.00000 3 25.00 000 t.50000 t.08600 1.0s200 7t¡.9.t559 0.otf 850 15t1.52779 1.17939 0.00235 108900.00000 0.05267 358.37960 1ó.00r¡99 29.55699 c c J 1.00000 ¿r6.q2000 27.6tt9,r9 1ó2. t5ó99 152.1r¡299 1 .37700 1.19600 1.01t00 '¿tt . q6259 0.0206c 118.75240 t. 430tt 1 0.00002 26522.3984t1 0.0 2tt6ll t 9¡.776 82 J.15485 J6 . 2209 9 D D r¡ 1.00000 '¡.0?000 6.11000 517.85ó93 rt?6.0? 178 1. t2200 1.t0000 t.t9500 . 165.9t840 0.0495C 335.1877tl 1.21000 0.00245 26 8t ?5. 7500 0 0.05 {q5 569.6rt2 09 25.61:91 26.53C99 I E 5 1.00000 ló.0r¡999 11.65000 2ó8.57080 267.1tr282 1.q2700 t.lt?1r00 1.62r100 207.2 1888 0.14020 trt7.8r¡520 2.17268 0.01966 72130.25000 0. 20 6ó5 J 95.87329 37.6536t 58.38¡t99 iuiBES ()F c¡sls REÀ!. . . . 20

H o, N) t'IIIYÀRIÂTE SUNüARY STÀTISTICS S IIT LLEST LÀRGESl STÀND ¡ I{ U COEFTJICIENT SIIÀLLEST LARGESl STÀIIDÀRD SlTIIDARD VÀRTABLE ¡1EAN DEVIAT ¡OII OF VÀRIATION VÀLU E YÀLUE sCO8E scoaE s (E f !rEss f,¡IBTOSIS

6 EXTCOURS 12.94600 10.0552e 0.7767'10 1.72000 rt6. rt2000 -1.12 l. 33 1.82 3.60 7 EXlfrEÀN l0.rr160C 6.857¡¡5 0.658_t58 2.09000 27.64999 -1.21 2.31 r .32 l.lll 9 sHEÀ8COU 460. l0?C9 286.45r¡16 0.622581 1 ó2.85699 1327.14282 1 q5q.t1r¡r¡2 - .0¿l 1.0¡ l.lal t.?8 10 SHEÀRt'tEÀ 295.A9762 0.651J06 152.1tt299 t 307.85ó93 -t.02 2.88 t.{8 1-62 17 B¿üEÀI¡OU 1.10465 0. 100.r5 o.2r02.t1 0.91700 1.92800 - 1.29 2.07 0. q? -0.91 18 BtiEÀil 1.260¿5 0.J0r¡?2 0.24 1790 0.88900 1.89rt00 - 1.22 2. 08 0.71 - 0.811 20 BLCOURüE 1.2r 190 0.3é735 o . 296'1 5J c.82600 2. 00900 -t.12 2. r0 0.65 - 1.03 21 tEIcHl 16q.98864 56. ¡¡ 1121 0.341922 2tt.46259 252.1t69!9 -2. ttg t. 55 -0.68 -0.02 22 TifrcKilEs c.c7425 0.03c91 0.41621t 0.02060 0. lr¡020 - 1.7q 2.13 o.26 -0.87 2J DEISITI 2J0.8'530 61.ó8r¡69 0.267178 1 1 €.75240 33 5. | 8?7r¡ -1.82 1.69 -0. 00 -t.19 25 DLíEtr¡z 1.6?óq4 0.84 1 50 0.50 1955 0.790J2 3.58721 - 1.05 2.27 0.95 -0.¡3 26 ÎHICK2 0.006r¡2 0.0049? 0.7r1401 0.000¡12 0.01966 -1.21 2.66 0.93 . 0.lr 27 SHETflCOz 289ó5t.?0¿15 401ô77. J6ö16 l. J86?6C 26 52 2 .39 €q ¡t't 76 1 3 08 . 00000 -0. ó6 l. 66 2.5r 6.24 2E BLTHICK O.C9'I?5 0.05ó38 0.576825 0.02¡t64 0.20665 - 1.30 1. 93 0. 6q -0.96 30 BLSHEÀCO 6IO.9J5JJ 51U.82118 0.84922t1 1s5.92816 2513.60716 -0.88 1.67 2. tt0 6.21 30 sHEtcotlt J4.49956 2J.8?661 0.ö92085 3.35485 92.?6't2'r - t.30 2. 0rl 0.85 -0.2t J DCðErr¡ 38.ó9574 15.61511 0.40rJ707 l?.69199 óó.21599 - 1.33 l. ?lr 0. {1 - 1.27 TILUES FOR KORTOSIS GRTITEF ÎHÀN ZERC INDICATE DISTRIBOlIONS SITII HET9 IE8 TAILS THÀN lHE I¡ORIIÀ[ DISTRIBUlICII.

F o. L¡) co R REL tlIOrlS

gEIGHI SHEIRCO2 EXTCOURS EXTIIEÀN SHDARCOU SHEIAIIEA IJLIIDÀNOT' BLilNÀN BLCOUEIIE ÎHICKI¡ES DEÈSTlT BLiETII2 lHICX2 6 7 9 l0 lt 18 20 21 22 21 25 26 27

E IlCOU R S 6 t.000 EXÎI'EÀN 7 0.91.1 1.000 SHEÀ RCO O 9 -0. l9 1 -0. JJo 1.000 SHEÀRItEI 10 -0.40 c -0.145 0.987 1 .000 BLTET NOU 17 -0.J1? -0.4J0 0.312 0. J02 1.000 8Ln ÊA rl 18 -0.4r¡lr -0.528 0.J75 0.3r9 0.9q1 1.000 20 -0.516 -0.5rr 0. 394 0.380 0.87tt 0.9t¡4 1.000 BLCOUßIIE 0.410 1.000 T EICHT 2l -0.611? -0.5J1' 0.J41 0.367 0.2t¡1 0.t¡35 0.435 0.802 1.000 THICKIIE S 22 -0 .355 -0.260 0. 0r¡0 0.053 0. 3J5 0.466 355 | .000 DEilS rll 23 -0.51.1 _0.477 C.370 c.JSl -0.278 -0.1q8 -0.071 0.216 -0. 0. l¡ q5 0.r¡4ó t.000 X 2 25 -0.r¡53 -0.529 0.q02 0.398 0.9J2 0.995 0.938 -0.10q BL;E¡ 0. q 56 1.000 26 -0.250 -0.201 -0.038 -0.02 1 0.364 0.r¡82 0.r¡51 0. 713 o .97'l -0.427 lHI CK2 -0.000 0.329 0.rr rr? -0.0ó8 | .000 s hEtRco 2 27 -0.310 -0.J03 c.960 0.951 0.)6¿ 0.409 0.42q 0.2?8 ?ó1 0. 923 0.7tlt 0.924 0.123 BLlHICK 2A -0..t26 -0.402 0.1JJ o. 1rt8 0.640 0.755 0.695 0. -0.322 0.621 0.J55 0.109 0.278 0.651 0.01¡9 0.958 ELS H EICO 30 -0..136 -0.r¡15 0.931 c.9c6 0.568 0.622 q 0. 088 0.107 0.526 0. rr05 0.8r 7 sH EtcolH 3q -0. 18 -0.32q 0.867 0.85? 0.012 0.512 0.t¡85 0.667 0.506 0.598 0.872 0. ó20 0.03r DCË EtI 3 -0.359 -0.r¡16 0.ltl9 0.415 0.826 0.891 0.852 -0.261

ELlR ICX ELSHEÀCO SHEÀCOTH DCI'EAN 28 J0 3tt 3 BLTHTCÍ 2ð 1.000 DLSHEÀCo 30 0.294 1.000 SHEACOTn .3q 0.525 0.8J9 I . 000 DCü Et lr 3 0 .791 0.619 0.6?1 1.000

o, N FOn EACH SItBSEI SELDCTED BY ÌOUR CRITrRICN, rfiE R-SQUATìnD, tDJ0STED R-S0UÀRED, !lÂlLol¡S' CD, Àt¡D lHF VIRIÀÉLE NÀ¡1ES ÀRE PNI[îÈD. lHE REGRESSICN COEfFICIENTS AND 1-SIAlISTICS ÀNE P&IIIÎED 10 THE RIGIIl OF TIIE V¡RIÀDLE IiÀÌtT,S.

üTIT OTHER SI¡8SBT5 IIAY ALSO BE TIEP('NlLD IhAT ATIE NOT ICCOIIPÀIIIED BY REGRESSICN COEFPICIENTS ÀND T.S1ÀTISTICS. scüE oP THEs8 SUBSETS f1Àl BE 00118 GCCD ÀLIHOUGH THEY ARE IIOT IIECESSÀRILT BETTER 1HÀN ANY SUi]5ET lIiÀ1 HA5 !¡OT BEEN PE II{18 D.

rrr* suBsEls rITH 1 vÀR IÀBLES .r*f ÀDJUSTED B.SQU IRED R-SQUtnED CP

0. ?96ó75 0.78s3?e 51.77 VÀRIABLE CO EFFIC IENl 1- STÀ TI S1 IC 18 BLITEAN ¡t6. J2 55 8. q0 I IIT ERC BPl -19.6859

0. ?6019¡l 0.7rr70d3 61. 86 VAH I ÀII LE COEFFICIEI{T T-STATISTIC 25 BLñEÀt{2 16.3$86 7 .56 I NlENCEPl 11.2272

0.7256.t2 0.710rt00 75.qq VÀN I ÀB LE COEFFICIENl 1- STA TIST IC 2O BLCOUR¡IE 36.6738 6.90 I ilTEACEPl -6.70276

0.681óó0 0.66 3974 90. 10 VARIÀBLE COEFTICIEIIT T. STATIST IC 17 BLIIEÀNOO 43.r¡599 6.21 INTERCEPT -18.00q2

0. 625 t79 0. 60 43 56 1c8.93 VAR¡.ÀBLE COEFFICIENT T- STTlIsT IC 28 BLlIIICK 221 .7A0 5. q8 IIITERCEFl 17.0171

0. ¡t 50 391 0. ¡¡19857 1ó7.19 SHE ACOlH

0. J838rt8 0.J49618 1 89.37 rHIC K 2

0.38J639 0.3.t9397 189 . 44 ELsIIEÀCO

0.357566 0 . t2187 7 198.1¿ THICKNES

0. 256 368 0.21 5055 2J1 .86 rE IGHl

o. L¡ {r+*t ST BSETS tIlH 2 V^RIÀBLEs t+tt T DJ U STED N.SQUTNED 8-SQUARED CP ì 0.858602 0.8r¡1967 3J. t3 VÀRlÀBLE CO EI¡F I C lEN 1 T. STA 1IS1 IC 18 BLI,tEAN 3 8.617 ? 7 .01 Jlt 5HEÀCOlh 0.191957 2 .71 INlERCEPl -16.5940 0.803208 0.s2tt'162 JA.26 VÀiìIÀBLE CCEFFICIIINT 1. STATISlIC 1d BLIIEÀN rtO.1592 7 .06 ?b rtlrcK2 7t4.27Q 2 .25 INTERCEPT -16.9508 0.83e015 0.8200?f, 19.66 VåRlABLE COESFICIIINT 1-STATISTIC 18 0I.1,!tÀN 40.70 l2 7.11 22 Tll tcKNFS 119.0{Jb 2.11 .,,T, -(..f i -,1 lr,r/

0.828qó7 c. ö0d287 4J.17 VAIIIÀBLE COEFFICIENT 1- STA 1 IST IC 18 BLúEAN ]5. ó?60 't6.247q 4.49 28 trLltflc¡( 1 .78 MIERCEIT -1J.7160 0.825905 c. 80 54 2q t¡4.01 VARITBLE CO! FICIENl T-STÀlISTIC 18 BL¡IEÀN 1JÙ.2J9 2.51 25 BLIrEÀ¡r2 -J3. ¡tJ7d -1.69 INlERCEPl -79.t1617

o.622 t21 0 .80 I 8ó5 Ir5.09 DLI'EAI{2 SHEÀCOTH

0.822586 0.80 17 I { r.5. 1 J BLIIEAN2 THICK2

0.81.t875 0.79 r095 tt1 .7 0 lHICKIIES BLIIEÀI¡2 0.81 t908 0.7920t5 48.02 BLIIEÀN IEIGHl

0.8lJ?rt7 0.?9 r835 .t8.08 ELIIEAII DENSITT

II+I SOBSElS IITH ] VARIÂBLES ***t ÀDJUSTED 8-SQUtBED R-SQUTBED 0.908ó11 0.u9147ó 18. 46 YÀRIÀBLE COEPTICIEIIl 1- STÂ TI S1 IC I{' BLIIEAN 159.805 1.88 25 BLIIEÀN2 -44.5873 -2.96 l4 sHEÀCOlfr 0 . 2261 51 J. 8l IIITERCEPT -95. ?512 0.90339rf 0.865281 20.20 VIRIABLE COEFFICIENT T-STÀ1IS1IC I O SHEARIIEÀ -0.0222¿t2 -2.72 18 BLüEttl 16.55 lf' 7 .6tl o\ J4 SHEÀCOlH 0.rt4t5l4 tt.0l o, INTERCEPl -l¿.5018 0.89rr650 0.87 4897 21. 11 ITNIÀBL8 c0ETFIcIENT T-SltlrslIC 18 BLñEÀN - J8.3ft9t 7.83 27 SüEARCO2 -0.00 00 1 29600 -2.14 34 SHEÀCOlH 0.371512 3.?s INlDRCEI'T - 18.?479

0.89q229 0.87rt397 23.25 VÀ RI A BLE COEFFICIENT T.STAlI5lIC 18 BLttEÀN 3 5.8269 7.08 2J DENSIlÍ -0.0501094 -2.J2 ]O SHEACOlH 0.224102 3.49 INlERCEPT - 2.617 qtt

0.89285.r O.A7276q 2t.71 VA R I AtsLE COEFFICIENT T-STÀTISTIC 9 SHEASCOU -0.02 07879 -2.26 I8 BLIIEÀN 36.7755 7.)4 l4 sHEACOttl 0. tt2025q l. 53 I NTljI(CEPT - 12 .5tt q4

0.88898r1 0.86816rJ 25.00 tsLI.IRAN BLSEÌ.ACO SHjrÀCOTH

0.8865¿6 0.865250 25.e2 D LllDÀ il ÎilICK2 SBEÀCOTH

0.876082 0.852848 ¿9 ..lo E ¡.CCU Rt.I E DENSTTI SHEACOTIT

0.87 5 889 0.85261rì '29. ) l fiI1'|nÂN lHICKN F5 SilEACOrrl

0.tTrr9r3 0.85 1 5J 1 2t).t,-l SIIETIRCOU tsLCCIllilE SIrtÀCOTrl

S1¡TISTICS FOR SOBSET ¡tlllots. Cp 'B!ST' 17.00 SQUTRED nULIIPLE CORRELÀ1I0¡l 0.991C0 ttULlIPLE CORIIELÀÎICN 0.9''549 tDJUSÎED SQUÀRED llULT. COR8. c.9q299 nESfDUAL nEÀr¡ SQUÀRE 1q.¿581't7 sTttDÀ8D ERROn OF EST. 1.776000 r-sTÀTrSlrC 20.tq TIIttERIlOR DEGREES CF IREEDCII 16 D!IIOIIIIITlOR DEGREES Of FREEDCII ] sIGfIrICÀrCE 0.0 1 46

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PNOBLEII TUIIBEB I COIIPI,ETED.

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