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Regression Analysis CALIFORNIA STATE UNIVERSITY, SACRAMENTO College of Business Administration NOTES FOR DATA ANALYSIS [Eleventh Edition] Manfred W. Hopfe, Ph.D. Stanley A. Taylor, Ph.D. Last Revised July 2008 by Min Li, Ph.D. 1 NOTES FOR DATA ANALYSIS [Tenth Edition] As stated in previous editions, the topics presented in this publication, which we have produced to assist our students, have been heavily influenced by the Making Statistics More Effective in Schools of Business Conferences held throughout the United States. The first conference was held at the University of Chicago in 1986. The School of Business Administration at California State University, Sacramento, hosted the tenth annual conference June 15-17, 1995. Most recent conferences were held at Babson College, (June 1999) and Syracuse University (June 2000). As with any publication in its developmental stages, there will be errors. If you find any errors, we ask for your feedback since this is a dynamic publication we continually revise. Throughout the semester you will be provided additional handouts to supplement the material in this book. Manfred W. Hopfe, Ph.D. Stanley A. Taylor, Ph.D. Carmichael, California August 2000 2 TABLE OF CONTENTS REVIEW................................................................................................................................................................ 5 Statistics vs. Parameters.................................................................................................................................... 5 Mean and Variance ........................................................................................................................................... 6 Sampling Distributions ..................................................................................................................................... 7 Normal Distribution .......................................................................................................................................... 7 Chi-Square ()χ 2 Distribution and the F Distribution ................................................................................... 10 Student’s t Distribution ................................................................................................................................... 11 Confidence Intervals ....................................................................................................................................... 12 Hypothesis Testing .......................................................................................................................................... 15 P-Values ......................................................................................................................................................... 16 VARIATION ........................................................................................................................................................ 21 QUALITY -- COMMON VS. SPECIFIC VARIATION ..................................................................................... 22 Common Causes and Specific Causes ............................................................................................................. 22 Stable and Unstable Processes ......................................................................................................................... 23 Quality ............................................................................................................................................................. 24 CONTROL CHARTS ........................................................................................................................................... 43 Types of Control Charts................................................................................................................................... 47 Continuous Data .............................................................................................................................................. 48 X-Bar and R Charts .................................................................................................................................... 48 P Charts ...................................................................................................................................................... 52 C Charts ...................................................................................................................................................... 54 Conclusion ....................................................................................................................................................... 55 .................................................................................................................................................................................. TRANSFORMATIONS & RANDOM WALK .................................................................................................... 57 Random Walk .................................................................................................................................................. 57 MODEL BUILDING ............................................................................................................................................ 61 Specification .................................................................................................................................................... 61 Estimation ........................................................................................................................................................ 62 Diagnostic Checking ........................................................................................................................................ 62 REGRESSION ANALYSIS ................................................................................................................................. 64 Simple Linear Regression ................................................................................................................................ 64 Estimation ................................................................................................................................................. 74 Diagnostic Checking ................................................................................................................................... 75 Estimation ................................................................................................................................................. 77 Diagnostic Checking ................................................................................................................................... 77 Update ......................................................................................................................................................... 78 Using Model ............................................................................................................................................... 78 Explanation ................................................................................................................................................. 78 Forecasting.................................................................................................................................................. 79 The Concept of Stock Beta .............................................................................................................................. 81 Summary ..................................................................................................................................................... 86 Multiple Linear Regression ............................................................................................................................. 87 Specification ............................................................................................................................................... 87 Estimation ................................................................................................................................................... 87 Diagnostic Checking ................................................................................................................................... 88 Specification ............................................................................................................................................... 92 Estimation ................................................................................................................................................... 93 3 Diagnostic Checking ................................................................................................................................... 95 Dummy Variables ................................................................................................................................................ 96 Outliers ............................................................................................................................................................ 99 Multicollinearity ............................................................................................................................................ 104 Predicting Values ........................................................................................................................................... 106 Cross-Sectional Data ...............................................................................................................................
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