Statistical Analysis of Factors Affecting Wheat Production a Case Study at Walmara Woreda

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Volume-6, Issue-5, September-October 2016 International Journal of Engineering and Management Research Page Number: 43-53

Statistical Analysis of Factors Affecting Wheat Production A Case Study at Walmara Woreda

Agatamudi Lakshmana Rao1, Hirko Ketema2 1,2Department of Statistics, College of Natural Sciences, Jimma Uniiversity, Jimma, ETHIOPIA

ABSTRACT and decline in productivity of crops and livestock This research is done based on the major factors enterprise. (Food agricultural organization .FAO 2006). that affect the production of wheat crop in the case of In our country, although there is favorable Walmara woreda. The aim of this study is to identify the climatic condition and rich in natural resources, food main factors that affect wheat production and to see the problem was not eliminating. The above situations are linear relationship between production of wheat which is true in the case of Oromia Special Zone Surrounding dependent variable and land size, pesticide, fertilizer, temperature and rainfall which are independent variables. Finfinne in Walmara Woreda. Walmara Woreda is one The data collection was done through secondary sources of 12 Woreda in Oromia Special Zone Surrounding that obtained from Oromia special zone Surrounding Finfinne. Administratively this Woreda is structured into Finfinne in Walmara woreda agriculture and rural 34 rural Kebeles and has total area of 83598.6 hectare. development office,Walmara woreda agricultural research Agriculture is the main economic source of the center and Walmara woreda cooperative association. In Woreda and approximately 96% of population directly this research we analysis both descriptive and inferential or indirectly depends on the livelihood on the sector. The statistics. major crops grown in Walmara Woreda are wheat, teff, From multiple linear regression model analysis maize, beans, barely and etc. Wheat production was the result finding indicate that some variables like land size and rainfall has negative effect on production. But other highest portion of all other crops. By considering these variables like pesticide, fertilizer and temperature has and other related concepts the study tries to asses with positive relationship with production. And some the identification of overall factor of wheat crop independent variables like land size, fertilizer, temperature production in this Woreda. and rainfall in the multiple linear regression analysis in the Wheat is the second cultivated species in the model is significant. That means at least one of the world next to maize 27 millions of production (Penal at parameters or coefficients of explanatory variables are as 2000).It is more adapted to drought and productive in different from zero. marginal area than maize. Wheat is the staple food for poor people living in marginal environments of the Keywords--- Wheat production, data collection, multiple Andean Zone North African, East Asia and Ethiopia linear regression and secondary sources (Efermetal 2000).It is traditional growth as rain fed crop often in place when the rainfalls limited, wheat is an indigenous, metalloid species and one of the I. INTRODUCTION predominant crop species growth in Ethiopia, but currently the size of land under cultivation is shirked. It 1.1 Back ground of the study is possesses immense diversity and Ethiopia has been Ethiopia is one of among the nation in recognized as secondary center of diversity for wheat developing country in the world and characterize by the (Hallan 1971).In Ethiopia wheat is mainly growth in low income and lower technology. The country was heavy black clay loom soil (vet soil) of low lands with mainly depending on agricultural activities and endow altitude ranges of 1800-2800m inclusively under rainfall with good climatic conditions and fertile soil for crop conditions (Tesfaye and Getachew 1991) thought the production. Various studies indicate that farmers in degree of production of varies. Wheat grown is all developing countries are depending on a farm income administrative region of Ethiopia, but 64% of the area and they are characterizing by the low income and and 69% of the production is contracted in the central deficiency in supply of food. This because, of and northern region. Wheat grain is widely used in bread technological backwardness, rapid population growth and to produce superior past products, also, popularly

43 Copyright © 2016. Vandana Publications. All Rights Reserved. www.ijemr.net ISSN (ONLINE): 2250-0758, ISSN (PRINT): 2394-6962 eaten in many areas as bulgur and cracks drum product of shortage of food as well as they are not competent on similarly to couscous (Di Solemn et al, 1975). the market without that the life of hand to mouth. So that In Ethiopia wheat is traditionally consumed in the aim of this study is to solve the above problem by different forms (Tesfaye and Getachew 1991) listed the underling the constraints and different strategies to adapt most common recipes in Ethiopia dabo (Ethiopia bread), by society to cope with the constraints and annual Ambush (bread from North Ethiopia), Kitta(unleavened production to identify weather the problem is really the bread), Injera (thin bread), Nitro(boiled problem of production. Therefore, the study attempts to grain),Dabokolo(ground and seasoned dough shaped and answer the following basic questions: deep fried), and Kinches(crushed kernels cooked with 1. What are the major challenges of wheat production in milk or water and mixed with spiced better).Wheat are the study area? traditional used inflate bread and specially bred 2. What are those factor affect wheat production in the particularly in Mediterranean countries and Ethiopia study area? (Quail, 1988), wheat has yellowish color a characteristics test and smell fine and uniform crumb II. METHODOLOGY structure and more prolonged shelf all which appeal to some consumer (Liuetal 1996) in Italy in the 10 last 2.1. Descriptions of the Study Area years the share of wheat used for bread making has This study was conducted in Oromia Special increased from 4%-10% . It has been reported that Zone Surrounding Finfinne in Walmara woreda. wheat used for baking performance improves as Gluten Walmara is one of the Woredas in the Oromia Region of becomes stronger, but loaf volumes achieved for best Ethiopia. It is one of 11 Woreda in Oromia Special Zone performing wheat verities are substantially lower than Surrounding Finfinne and the total population live in the that for (Palumboetal 2000). Woreda is estimated about 83,823 from whom 42,115 Agriculture or farming is the rearing of animals men and 41,708 women. It is bordered on the south by and production of cereal crops plants through cultivating the Sebeta Hawas, on the west by West Shewa Zone, on the soil (Mann ion, 1995 a.p.2). It is a manifestation of the North by Mulo, on the Northeast by the Sululta, and the interaction between people and the environment on the East by the city of Addis Ababa. The target through the nature of this interaction has evolved over a population of those farmers lives in the Woreda. The period of at least 10,000years. Near East around 10,000 district has 23 peasant associations and one town. Its years BP (Macneish, 1992).The domestication of plants total land area is about 83598.6 hectare. (Source: and animals spread from the near east into south Eastern Walmara Woreda Agricultural and rural development Europe where the combination of improved cultivation office). methods and an extensive trading network supported 2.2. Method of Data Collection first the Greek and then the Roman empires. It was this In our study, the data collection will be done by that gave rise to the term agriculture, which is derived using secondary source of data. The data was collect data from the Latin word ,”Agra “and the Greek word , “agro from Walmara Woreda agricultural and rural “,both meaning field and symbolizing the integral link development office, Walmara woreda research center between land based production and accompanying of and Walmara woreda cooperative association of the year the natural environment (Mannion,1995). 2000-2007 E.C. Thus, this study was based on secondary Agricultural geography includes work that source of data. spans a wide range of issues pertaining to the nature of 2.3. Method of Data Analysis/Statistical Analysis this hierarchy including the spatial distribution of cereal 2.3.1 Variable Identification /Variable Considered In crops and livestock. The system of management the Study employed the nature of linkages to the boarder The study variables to this research are: economic, social cultural, political and ecological Dependent (response) variable: systems, and the broad spectrum of food production, Yield of wheat crop(Y) (quintal) processing, marketing and consumption. The principal Independent (factor or explanatory) variables are: focus for research by agricultural geographers on the last • Land size(X1)(hectare) four decades has been the economic, social, and political • Pesticides(X2)(Lt) characteristics of agriculture and its linkages to both the • fertilizer uses(X3)(quintal) suppliers of inputs to the- agro-ecosystem and to the • rain fall(X )(mm) processing, sale and consumption of food products. 4 • Temperature(X )( P) However it should not be for gotten that at the heart of 5 2.4. Methods of statistical analysis farming activity, underlying the chain of food supply To accomplish the℃ data, the two broad areas of from farmers to consumers is a set of activities directly statistics which are descriptive and inferential statistics dependent up on the physical condition with in which will used. farming takes place. (Munton, 1992) 2.4.1 Descriptive statistics 1.2. Statement of Problem Descriptive statistics are utilized numerical and Even if the majority of the people in the Oromia graphical to present that information in a convenient Special Zone Surrounding Finfinne depends on form. It describes the data collected through charts, agriculture, most private land holds are face to problem frequency distribution, statistical graphs and so on. 44 Copyright © 2016. Vandana Publications. All Rights Reserved. www.ijemr.net ISSN (ONLINE): 2250-0758, ISSN (PRINT): 2394-6962

Descriptive statistics describe patterns and general trends β1 is the change in total production of wheat when the in data set in most cases, descriptive statistics are used to temperature(X1) increases by one, keeping rainfall(X2), examine or explore one variable at a time. Always pesticides(X3), fertilizer(X4) and land size (X5) constant. analyses of statistical data begin by describing the raw β2 is the change in total production when X2 increase by data. In general descriptive statistics is very important in one unit that is the production increase by β2 unit drawing conclusion or making decision clearly. keeping X1, X3, X4 and X5 constant. 2.4.2. Inferential statistics β3 is the change in total production when X3 increase by It is used for conclusion and prediction of one unit ,the production increase by β3 units keeping analysis, such as ANOVA, Multiple Regression, X1,X2,X4 and X5 constant correlations and so on. β4 is the change in total production when X4 increase by 2.4.2.1 Multiple linear regression models one unit ,the production increase by β4 units keeping The primary objective of regression is to X1,X2,X3 and X5 constant develop a regression model, to explain the relation β5 is the change in total production when X5 increase by between one or more variables in a given population. A one unit ,the production increase by β5 units keeping particular form of regression model depends up on the X1,X2,X3 and X4 constant. nature of the problem under study and the type of data 2.4.2.2 Assumptions of the Multiple Linear Regression variables. Multiple linear regressions contain two or model more independent variables and one dependent variable. The model based on several simplifying The general form of a multiple linear regression model is assumptions, which are as follows: given by  The regression model is linear in the parameter. Yi = β0 + β1X1i + β2X2i + - - - + βkXki +εi,i=1, 2, . . ., n  For given Xi’s, the mean value of the Where β0 is the intercept and β1, β2 . . . βk is coefficient disturbance εi is zero.E (ε) =0 and Var 2 of the variable X1, X2,…..,Xk (ε) =δ . Constant (βo) is the value of dependent variable (Yi)  For given Xi’s, the variance of εi when the all independent variables (Xi) are zero. constant or Homoscedasticity.ε~ N (0, 2 β1 is the change in dependent variable (Yi) when the δ2), δ is constant. independent variable (X1) increases by one, keeping  For given Xi’s, there is no other independent variables are constant. autocorrelation in the disturbances. β2 is the change in dependent variable (Yi) when the Ε(εi εj)=0 independent variable (X2) increases by one, keeping  The number∀ of observations must be 𝒊𝒊≠𝒋𝒋 other independent variables are constant. greater than the𝒊𝒊𝒊𝒊 number of regress. β3 is the change in dependent variable (Yi) when the n observation (n>k). independent variable (X3) increases by one, keeping  There must be sufficient variability in the other independent variables are constant…etc. values taken by the regress. The regression model is correctly specified. Y=β 0 +β 1 X 1 +β 2 X 2 +β3X3+β4X4+β5X5+εi,Where  There is no exact linear relationship between Y=yield of wheat crop, X1=temperature in 0 the regress. =1(cixi) 0 (C ),X2=rainfall in (mm),X3=pesticides in  The stochastic𝑘𝑘 (disturbance) term εi is normally (Lt),X =fertilizer in (quintal),X =land in (hectare), ε 𝑖𝑖 𝑖𝑖 4 5 i distributed. ∑ ≠ ∀𝑐𝑐 ≠ 𝟎𝟎 =the random error term. 2.4.2.3 Hypothesis testing for significance of regression The above model shows that: Constant (βo) is the value of wheat production when the all independent variables(X1, X2, X3, X4 and X5) are zero.

model Sum of squares Degree of freedom Mean sum of square F tab

Regression SSR k-1 MSR=SSR/k-1 Fcal=MSR/MSE

Error SSE n-k MSE=SSE/n-k

Total SST n-1

Hypothesis: Ho: β1=β2=---= β5= 0 versus H1:βi≠0, for To test Ho: β1=β2---=β5, first we compute F calculated at least one i and F tabulation as follow.

The total sum squares is given by: SST=SSR+SSE MSR= , MSE= , F = , Where MSR is 1 cal Where SSR=sum square of regression, SSE=sum 𝑆𝑆𝑆𝑆𝑆𝑆 𝑆𝑆𝑆𝑆𝑆𝑆 𝑀𝑀𝑀𝑀𝑀𝑀 mean square regression and MSE is mean square square of residual (errors) 𝐾𝐾 𝑛𝑛−𝑘𝑘− 𝑀𝑀𝑀𝑀𝑀𝑀 45 Copyright © 2016. Vandana Publications. All Rights Reserved. www.ijemr.net ISSN (ONLINE): 2250-0758, ISSN (PRINT): 2394-6962 residual. We compare Fcal with Fα (k, n-k-1) and we There is linear relationship between dependent reject Ho and independent variable is called linearity assumption. If Fcal>Fα (k, n-k-1). Multiple regression models the linear (straight-line) Where ‘k’ represents number of independent variables relationship between Y and the X’s. Any curvilinear and ‘n’ is number of observation relationship is ignored. This is most easily evaluated by If Ho is rejected it means that the contribution of Xi in scatter plots early on in your analysis. estimating Y is significant. ii. Homoscedasticity: If Ho is accepted it means that the contribution of Xiin Error terms have constant variance and points in estimating Y is not significant. the graph are dispersed at random fashion have no any Test of individual regression coefficients trend; this indicates that the assumptions of Null hypothesis: Ho: βi=0 (individual factors have no homoscedasticity hold. effect) iii. Normality of Error Term Alternative hypothesis: H1: ≠0, βi where i=1, The error terms are normally distributed with 2…5(individual factor has effect on the response mean zero and variance σ2can be tested by plotting variable). residual against the cumulative probability. Test statistic (t ) = iv. Autocorrelation test ( ) 𝜷𝜷𝜷𝜷 A test that the residuals from a linear regression Decision rule: reject Ho if t > ( ) 𝒔𝒔𝒔𝒔 𝜷𝜷𝜷𝜷 cal or multiple regressions are independent. If Ho is rejected, it means that the contribution of Xiin The error terms should be independent. There is no 𝒕𝒕 𝜶𝜶⁄𝟐𝟐 𝒏𝒏 − 𝟏𝟏 estimating Y is significant. relation between successive error terms. If Ho is accepted, it means that the contribution of Xi in v. Multicollinearity estimating Y is not significant. Collinearity, or multicollinearity, is the t- Distribution used to test the significance of one existence of near-linear relationships among the set of parameter. When the numbers of observation are less independent variables. The presence of multicollinearity than 30 and the distribution of the population is normally causes all kinds of problems with regression analysis, so distributed. you could say that we assume the data do not exhibit it. Use of F-test: To test for the significance of the overall We can test the presence of multicollinearity by variance model, before considering the significance of individual variables. inflation factor, given by; VIF= 2 𝟏𝟏 Where R i is coefficient of determination𝟐𝟐 obtained from Use of t-test: It is used to determine if the individual 𝟏𝟏−𝑹𝑹 𝒊𝒊 coefficient for each independent variable represents a Xi on the other explanatory variables. If value of VIF significant contribution to the overall model. less than 10,(tolerance greater than 0.1), then there is no The coefficient of multiple determinations (R2) multicollinarity in the data. It is the amount of variation explained by the regression model. 1-R2 is the amount of unexplained variation, III. RESULT AND DISCUSSION called the error or residual variation. R2 is depend on the number of data pairs (n) and the 3.1 Descriptive Analysis number of variables(k),adjusted R2 is depend on the The main objective of this study was to identify number of degrees of freedom. Adjusted R2 is less than impacts that affect the yield of wheat crop in Walmara R2 and take account the fact when n and k are Woreda. The secondary data were used that collected on approximately equal. the yield of wheat crop issues during the period of 1998 2.4.2.4 Model Diagnosis up to 2007 E.C. i. Linearity

Table 3.1: Descriptive Statistics

Descriptive Statistics

N Mi ni m u m Maximum Me an Std. Deviati on yield (quintal) 10 405365 548269 471925.20 47321.495 land s ize (hectare) 10 14120 15265 14766.80 342.549

pesticide (lts) 10 1120 2504 1755.00 586.168 fertilizer (quintal) 10 2263 7865 4054.70 1842.963 temprature (c) 10 17 24 20.50 2.593

rainfall (mm) 10 800 1150 933.90 129.135 Valid N (listwise) 10

The descriptive statistics of SPSS output with The mean values of cultivated land size, 10 years of wheat crop production are given in the above pesticide, fertilizer, temperature and rainfall are 14766.8, table. 1755.00, 4054.70, 20.50 and 933.90 respectively which The maximum yield of wheat crop is 548269qu shows that land size is the most used up factor. which is recorded in 2005; at the year of maximum crop From the output the standard deviation of production of yield recorded the amount of cultivated land size, wheat in quintal, cultivated land size in hectare, pesticide pesticide, fertilizer, temperature and rainfall was 15203 in liter, fertilizer in quintal, temperature in Celsius and hectare, 1120Lt, 7865qu, 22 and 1150mm rainfall millimeter are respectively. 47321.495,342.549,586.168,1842.963,2.593 and 129.135 The minimum yield of℃ wheat crop respectively. was405365qu which was recorded in 1999, at the year 3.1.1 Testing the Assumptions of Multiple Linear when the minimum wheat crop production recorded the Regression amount of cultivated land size, pesticide, fertilizer , Normality assumption temperature and rainfall was14939hectare,2406Lt, The error terms are normally distributed with 3201qu ,24 and 956mm respectively. mean zero and variance σ2can be tested by plotting residual against the cumulative probability. ℃

Figure 3.1: Histogram residual

The above Figure shows that the error terms are Homoscadeasticity: This plot should always be normally distributed approximately with mean zero and examined. The preferred pattern to look for is a point constant variance. This implies that independent variable cloud or a horizontal band. A wedge or bowtie pattern is X and error terms are independent. This means the an indicator of non-constant variance, a violation of a models are well defined. critical regression assumption. The sloping or curved The shape of the histogram should band signifies inadequate specification of the model. approximately follow the shape of the normal curve. The sloping band with increasing or decreasing This histogram is acceptably close to normal curve. variability suggests non-constant variance and Therefore, the assumption of normality holds. inadequate specification of the model.

Figure 3.2 scatter plot of residual versus predicted value

As it is seen from the graph of the residuals hetroscedasticity in the data. That means the error term versus the fitted value (the production of wheat) above, εi’s are independently and identically distributed random there is no systematic relationship between the residuals variables having normal distribution with mean zero and and fitted value the fitted value means that the constant variance δ2ε. production of wheat. This indicates that there is no Linearity assumption:

Fig.3.3 Scatter plot matrix of dependent variable (yield) and independent variables.

A matrix scatter plot is one plot made up of wheat crop and independent variables like land size, individual scatter plots, and is used when you would like pesticide, fertilizer, temperature and rainfall to examine the correlation among several continuous, 3.2 Inferential statistics preferably normally distributed, variables. The scatter 3.2.1 Multiple linear regression analysis plot matrix generates all pair wise scatter plots on a The statistical model that was used in the study single page. is multiple linear regression models. The general model The conditioning plot, also called a co-pilot or for multiple linear regression analysis is used to check subset plot, generates scatter plots of Y versus X the effects of many quantitative independent variables on dependent on the value of a third variable. From the fig single response. 4.4 above scatter plot matrix of dependent variable Mathematically, the model is given as: (yield) and independent variables the position of all point Y = β + β X + β X + ...... + β X + ε in plot are closed to the fitted line. Therefore we can say o 1 1 2 2 k k ij there is linear relationship between average yield of

Before we use the results and interpret, we have to check The model summary table reports the strength of the model adequacy and whether assumptions are satisfied relationship between the model and the dependent or not. variable. Table 3.2 Model Summary

Model Summaryb

Adjusted St d. Error of Durbin- Model R R Square R Square the Estimate W atson 1 .990a .981 .957 9863.850 2.257 a. Predic tors: (Constant), rainfall (mm), temprature (c), pestic ide (lts), land size (hec tare), fertiliz er (quintal) b. Dependent Variable: y ield (quintal)

According to the given fitted model, the value of R = fertilizer, temperature and rainfall are jointly and 99% this indicates that there is strong relationship linearly. Hence the model is adequate. between variables and also the value of R2 = 98.1% of 3.2.1.1 Hypothesis testing for the model the variation in the production of wheat crop is explained Overall Hypothesis Testing: by the five explanatory variables; land, pesticides, This method is used to test the effect of the independent variables on the dependent variable.

Tab1e 3.3.ANOVA analysis

ANOVA table is a useful test of model’s ability Step 2; α=0.05 to explain any variation in the dependent variable; it Step 3; Test statistics, Fcal=40.628 does not directly address the strength of that relationship Step4; P-value =0.002 Test for significance of regression Step5; Decision; since p-value=0.002 is < α-value= 0.05 The objectives are to determine if we reject Ho. there is a linear relationship between the response Therefore, we can conclude that the overall variable and any one of the regress or independent regression model is statistically significant, that means at variables. least one of the parameters or coefficients of explanatory The hypotheses are as follow. variables are different from zero. Step 1; Ho: β1=β2=β3= β4= β5=0VS H1: βi≠0, for at 3.2.1.2 Interpretation of the model coefficient least one i is defer

The regression coefficients are the least squares Decision rule Reject Ho, since p-value is less estimates of the parameters. than α value i.e.0.017<0.05 The value indicates how much change in Y We conclude that area of the land has significant effect occurs for a one-unit change in x when the remaining X’s on yield of wheat crop production. are held constant. These coefficients are often called Test for pesticide partial-regression coefficients since the effect of the Null hypothesis: Pesticide has no significant effect on other X’s is removed. These coefficients are the values of yield of wheat production. βo, β1, β2, β3, β4 and β5 Alternative hypothesis: Pesticide has significant effect The fitted model for Production on yield of wheat production. Average yield of wheat in quintal(Y) = 1443148- Level of significance: α=0.05 6l.024*land size +3.832*pesticide + 40.118*fertilizer + Test statistics t 4856.986*temperature -149.822*rainfall. Decision rule: we fail to Reject Ho since p-value is Or Y =1443148- greater than α value i.e.0.685 >0.05 6l.024X1+3.832X2+40.118X3+4856.986X4-149.822X5. We counclude that the pesticide has no  Firstly, the slope of land size β1=-61.024 is significant effect on the yield of wheat crops i.e.when negative indicating that there is inverse the pesticide is in interval of (1120-2504) the change in relationship between land size and the yield of wheat crop production is due to other factors, production of wheat crop. β1=-61.024 is the not pesticide. change in yield of wheat crop(Yi) when the Test for fertilizer land size (X1) increases by one, keeping other Null hypothesis: fertilizer has no significant effect on independent variables are constant. production.  Secondly, the slope of fertilizer β3= 40.118 is Alternative hypothesis: fertilizer has significant effect on positive indicating that there is direct production. relationship between fertilizer and the Level of significance: α=0.05 production of wheat crop. If the effects of Test statistics t (p value=.001) remaining independent variable are fixed, then Decision rule: Reject Ho, since p-value is less than α for each change of one unit in fertilizer, yield of value i.e.0.001<0.05. wheat (y) changed by 40.118units(quintals). We conclude that effect the fertilizer is statistically  Thirdly, the slope of temperature β4= 4856.986 siginificant on yield of wheat crop. i.e.the parametre is implies change in yield of wheat(Y) occurs for differ from zero. a one-unit change in temperature(X4) when the Test for temperature remaining independent variables are held Null hypothesis: Temperature has no significant effect constant is 4856.986quintal. on production  Fourthly, the slope of rainfall β5 =-149.822 Alternative hypothesis: temperature has significant negative indicating that there is inverse effect on production (negative) relationship between rainfall and the Level of significance: α=0.05 production of wheat crop. If the effects of Test statistics t remaining independent variable are fixed, then Decision rule: Reject Ho since p-value is less than α for each change of one unit in rainfall, yield of value i.e.0.036 <0.05 wheat (y) changes by -149.822 units. The We counclude that the temperature has significant effect amount of change in the production of wheat on the yield of wheat crops. crop when land size, fertilizer, temperature and Test for rainfall rainfall changed by one unit is, -61.024 quintal, Null hypothesis: Rainfall has no significant effect on 40.118 quintal, 4856.986 quintal and -149.822 production quintal respectively; assuming that the effect of Alternative hypothesis: Rainfall has significant effect on other independent variables on production of production wheat crop remains constant. Level of significance: α=0.05 3.2.1.3 Test of individual parameters Test statistics t Since we have rejected the null hypothesis on Decision rule: fail to Reject Ho since p-value is greater overall test of significance we have to identify which than α value i.e.0.035>0.05 variable is responsible for the rejection. We counclue that the rainfall is statistically siginificant Test for area of land size i.e. the parametre is differ from zero. Null hypothesis: area of land has no significant effect on From table of multiple regressions for the production. model, land size, fertilizer, temperature and rainfall has a Alternative hypothesis: area of land has significant effect significance effect both individually and in group on the on production. production. Because their p - values are less than the Level of significance: α=0.05 significance level value, 0.0 Test statistics t (p-value= 0.017) 3.3 Test of model diagnosis

50 Copyright © 2016. Vandana Publications. All Rights Reserved. www.ijemr.net ISSN (ONLINE): 2250-0758, ISSN (PRINT): 2394-6962 i. linearity: Variables with a high VIF are candidates for exclusion The below Figure 1.2 is approximately normal from the model. We can test the presence of it show that there is approximately a linear relationship multicollinearity by variance inflation factor, given by; between response variables and explanatory variables. VIF= ii. Homoscedasticity 𝟏𝟏 The above𝟐𝟐 table 4.4 or collinearity statistics tells as Since the points, in the Figure 1.3 indicating a 𝟏𝟏−𝑹𝑹 𝒙𝒙 whether multicollinearity exists in the model or not. sharp downward and upward curve at both extremis From the above result, we see that the variance inflation indicating the tail of distribution is to be considered factor (VIF) is less than 10(tolerance level is greater than normal. Points in the plot are not dispersed at random 0.1); hence, we can conclude that there is no problem of fashion; this indicates that the assumption of multicollinearity presents in the data. homoscedasticity is hold. This means the models are 3.4 Correlation coefficient well defined. In statistical terms, correlation is a method of iii. Normality of Error Term assessing a possible two-way linear association between The above Figure 4.1 shows that the error terms two continuous variables. Correlation is measured by a are approximately normally distributed with mean zero statistic called the correlation coefficient, which and constant variance. This implies that independent represents the strength of the putative linear association variable X and error terms are independent. This means between the variables in question. It is a dimensionless the models are well defined. quantity that takes a value in the range−1 to +1. A iv. Autocorrelation correlation coefficient of zero indicates that no linear The above table 4.2 shows that the value of relationship exists between two continuous variables, Durbin –Watson test 2.257 is positive this indicates that and a correlation coefficient −1of or +1 indicates a there is a positive autocorrelation .This implies that our perfect linear relationship. The strength of relationship model is well defined. can be anywhere between−1 and +1. The stronger the v. Multicolinearity correlation, the closer the correlation coefficient comes The variance inflation factor (VIF) is a measure to ±1. If the coefficient is a positive number, the of multicollinearity. It is the reciprocal of 1-Rx2 where variables are directly related (i.e., as the value of one Rx2, is the R2 (coefficient of determination) obtained variable goes up, the value of the other also tends to do when X variable is regressed on the remaining so).If, on the other hand, the coefficient is a negative independent variables. Collinearity or multicollinearity, number, the variables are inversely related (i.e., as the is the existence of near-linear relationships among the set value of one variable goes up, the value of the other of independent variables. tends to go down). Any other form of relationship The presence of multicollinearity causes all between two continuous variables that is not linear is not kinds of problems with regression analysis, so you could correlation in statistical terms. To emphasize this point, a say that we assume the data do not exhibit it. A VIF of mathematical relationship does not necessarily mean that 10 or more for large data sets indicates a collinearity there is correlation problem since the correlation of independent variable X Pearson Correlation Coefficient with the remaining independent variables is 90 percent. yield (quintal) Pearson 1 .280 -.686 .859 -.212 .642 Correlation Sig. (2-tailed) .434 .028 .001 .557 .046 land size (hectare) Pearson .280 1 -.004 .666 .390 .524 Correlation Sig. (2-tailed) .434 .991 .036 .266 .120 pesticide (Lt) Pearson -.686 -.004 1 -.528 .387 -.471 Correlation Sig. (2-tailed) .028 .991 .117 .270 .170 fertilizer (quintal) Pearson .859 .666 -.528 1 .147 .844 Correlation Sig. (2-tailed) .001 .036 .117 .686 .002 Temperature in celsius Pearson -.212 .390 .387 .147 1 .051 Correlation Sig. (2-tailed) .557 .266 .270 .686 .889 rainfall (mm) Pearson .642 .524 -.471 .844 .051 1 Correlation Sig. (2-tailed) .046 .120 .170 .002 .889

51 Copyright © 2016. Vandana Publications. All Rights Reserved. www.ijemr.net ISSN (ONLINE): 2250-0758, ISSN (PRINT): 2394-6962 yield (quintal) Pearson 1 .280 -.686 .859 -.212 .642 Correlation Sig. (2-tailed) .434 .028 .001 .557 .046 land size (hectare) Pearson .280 1 -.004 .666 .390 .524 Correlation Sig. (2-tailed) .434 .991 .036 .266 .120 pesticide (Lt) Pearson -.686 -.004 1 -.528 .387 -.471 Correlation Sig. (2-tailed) .028 .991 .117 .270 .170 fertilizer (quintal) Pearson .859 .666 -.528 1 .147 .844 Correlation Sig. (2-tailed) .001 .036 .117 .686 .002 Temperature in celsius Pearson -.212 .390 .387 .147 1 .051 Correlation Sig. (2-tailed) .557 .266 .270 .686 .889 rainfall (mm) Pearson .642 .524 -.471 .844 .051 1 Correlation Sig. (2-tailed) .046 .120 .170 .002 .889 N 10 10 10 10 10 10

Interpretation is weak positive relationship between the two From the above Pearson Correlation Coefficient variables. we understand the following: • The Pearson correlation between fertilizer in • The Pearson correlation between yield of quintal and temperature in centigrade is.319 production and land size is 0.280 there is weak there is weak positive relationship between the positive linear relationship between yield wheat two variables production and area of land, the other • The Pearson correlation between fertilizer in independent variables remain constant. quintal and rainfall in millimetre is 0.844there • The Pearson correlation between yield of is weak positive linear relationship between the production and fertilizer is 0.859 there is strong two variables. positive linear relationship between the yield of • The Pearson correlation between rainfall in production and fertilizer the other independent millimetre and temperature in centigrade variables remain constant. is0.051there is weak positive linear relationship • The Pearson correlation between yield of wheat between the two variables production and temperature is -0.212 there is weak negative linear relationship between the IV. CONCLUSIONS two variables yield of wheat production and temperature. Depending up on the analysis of data result and • The Pearson correlation between production discussion, we conclude the following main points. The and rainfall is 0.642 there is a moderate positive multiple linear regression analysis indicates that the linear relationship between the two variables relationships between the amount of wheat production yield of wheat production and rainfall. and land size and rainfall are negative but pesticide, • The Pearson correlation between land size in fertilizer and temperature are positive. The average hectare and fertilizer in quintal is 0.666 there is production of wheat in the Walmara woreda for the past strong positive linear relationship between the 10 years is 471925.20 quintal per hectare. The average two variables land size in hectare and fertilizer land size, pesticide, fertilizer, temperature and rainfall in in quintal. the past 10 years 14766.80hectare, 1755.00Lt, • The Pearson correlation between land size in 4054.70quintal, 20.50 and 933.90mm respectively. hectare and temperature in Celsius is 0.390 From multiple linear regression model analysis result there is weak positive relationship between the finding indicate that some℃ variable like land size and two variables land size in hectare and rainfall are negatively affect the production , but there is temperature in Celsius. a positive relationship between production and other • The Pearson correlation between land size in variables like pesticide, fertilizer and temperature. And hectare and rainfall in millimetre is 0.524 there some independent variables like land size, fertilizer, temperature and rainfall in the multiple linear regression

52 Copyright © 2016. Vandana Publications. All Rights Reserved. www.ijemr.net ISSN (ONLINE): 2250-0758, ISSN (PRINT): 2394-6962 analysis in the model is significant. We conclude that the [4] Eferm etal. (2000)Wheat is the staple food for poor overall regression model is statistically significant.That people living in marginal Environments of the Andean means at least one of the parameters or coefficients of Zone North African, EastAsia and Ethiopia explanatory variables are different from zero. [5] Ellis 1995, peasant economics, from household and agrarian development; camp ridge REFERENCE University press. [6] FAO/food agricultural organization (2006). [1] Bluman.Allan G Elementary statistics; a step by step [7] Hallan (1971).Ethiopia has been recognized as approach. secondary center of diversity for wheat. [2] Cochran W.G (1997): sampling techniquies”3rd [8] Mannion (1995 a.p.2).Agriculture or farming is the edition, johnsWiley and sons,inc…New York” rearing of animals and production of cereal crops plants [3] CSA / central statistical agency (1997). through cultivating the soil. [9] NSAP, (2007). Agriculture in Ethiopia contributes 46.3to GDP.