A Second Course in Statistics: Regression Analysis

Transcription

1 FIFTH E D I T I 0 N A Second Course in Statistics: Regression Analysis WILLIAM MENDENHALL University of Florida TERRY SINCICH University of South Florida PRENTICE HALL Upper Saddle River, New Jersey 07458

2 Contents Preface xii CHAPTER! A Review of Basic Concepts (Optional) Statistics and Data Populations, Samples, and Random Sampling Describing Data Sets Graphically Describing Data Sets Numerically The Normal Probability Distribution Sampling Distributions and the Central Limit Theorem Estimating a Population Mean Testing a Hypothesis About a Population Mean Inferences About the Difference Between Two Population Means Comparing Two Population Variances 72 CHAPTER L Introduction to Regression Analysis Modeling a Response Overview of Regression Analysis Regression Applications Collecting the Data for Regression 97 CHAPTER 30 Simple Linear Regression Introduction The Straight-Line Probabilistic Model Fitting the Model: The Method of Least Squares Model Assumptions An Estimator of cr Assessing the Utility of the Model: Making Inferences About the Slope ^ The Coefficient of Correlation The Coefficient of Determination Using the Model for Estimation and Prediction Simple Linear Regression: An Example Using the Computer Regression Through the Origin (Optional) A Summary of the Steps to Follow in a Simple Linear Regression Analysis 162

3 Vi CONTENTS CHAPTER 4 Multiple Regression The General Linear Model Model Assumptions Fitting the Model: The Method of Least Squares Estimation of a 2, the Variance of e Inferences About the /3 Parameters The Multiple Coefficient of Determination, R Testing the Utility of a Model: The Analysis of Variance F Test Using the Model for Estimation and Prediction Other Linear Models A Test for Comparing Nested Models Stepwise Regression Other Variable Selection Techniques (Optional) Multiple Regression: A Complete Example A Summary of the Steps to Follow in a Multiple Regression Analysis 262 H A P T E R 5 Model Building Introduction: Why Model Building Is Important The Two Types of Independent Variables: Quantitative and Qualitative Models with a Single Quantitative Independent Variable First-Order Models with Two or More Quantitative Independent Variables Second-Order Models with Two or More Quantitative Independent Variables Coding Quantitative Independent Variables (Optional) Models with One Qualitative Independent Variable Models with Two Qualitative Independent Variables Models with Three or More Qualitative Independent Variables Models with Both Quantitative and Qualitative Independent Variables Model Building: An Example 335 CHAPTER D Some Regression Pitfalls Introduction Observational Data Versus Designed Experiments Deviating from the Assumptions Parameter Estimability and Interpretation Multicollinearity Extrapolation: Predicting Outside the Experimental Region Data Transformations 363

4 CONTENTS CHAPTER / Residual Analysis Introduction Plotting Residuals and Detecting Lack of Fit Detecting Unequal Variances Checking the Normality Assumption Detecting Outliers and Identifying Influential Observations Detecting Residual Correlation: The Durbin Watson Test 430 CHAPTER 80 Special Topics in Regression (Optional) Introduction Piecewise Linear Regression Inverse Prediction Weighted Least Squares Modeling Qualitative Dependent Variables Logistic Regression Ridge Regression Robust Regression Model Validation 489 CHAPTER 9u Time Series Modeling and Forecasting What Is a Time Series? Time Series Components Forecasting Using Smoothing Techniques (Optional) Forecasting: The Regression Approach Autocorrelation and Autoregressive Error Models Other Models for Autocorrelated Errors (Optional) Constructing Time Series Models Fitting Time Series Models with Autoregressive Errors Forecasting with Time Series Autoregressive Models Seasonal Time Series Models: An Example Forecasting Using Lagged Values of the Dependent Variable (Optional) 551 CHAPTER IU Principles of Experimental Design Introduction Experimental Design Terminology Controlling the Information in an Experiment 562

5 Viii CONTENTS 10.4 Noise-Reducing Designs Volume-Increasing Designs Selecting the Sample Size The Importance of Randomization 578 CHAPTER 11 The Analysis of Variance for Designed Experiments 58i 11.1 Introduction The Logic Behind an Analysis of Variance Completely Randomized Designs Randomized Block Designs Two-Factor Factorial Experiments More Complex Factorial Designs (Optional) Follow-Up Analysis: Tukey's Multiple Comparisons of Means Other Multiple Comparisons Methods (Optional) Checking ANOVA Assumptions 673 CASE STUDY 1 c Modeling the Sale Prices of Residential Properties in Four Neighborhoods The Problem The Data The Models Model Comparisons Interpreting the Prediction Equation 704 i 12.6 Predicting the Sale Price of a Property Conclusions 711 CASE STUDY lo An Analysis of Rain Levels in California The Problem The Data A Model for Average Annual Precipitation A Residual Analysis of the Model Adjustments to the Model Conclusions 721 CASE STUDY 14 Reluctance to Transmit Bad News: The MUM Effect The Problem 723

6 CONTENTS ix 14.2 The Design Analysis of Variance Models and Results Follow-Up Analysis Conclusions 727 CASE STUDY lo An Investigation of Factors Affecting the Sale Price of Condominium Units Sold at Public Auction The Problem The Data The Models The Regression Analyses An Analysis of the Residuals from Model What the Model 3 Regression Analysis Tells Us Comparing the Mean Sale Price for Two Types of Units (Optional) Conclusions 750 CASE STUDY 1 0 Modeling Daily Peak Electricity Demands The Problem The Data The Models The Regression and Autoregression Analyses Forecasting Daily Peak Electricity Demand Conclusions 765 APPENDIX A The Mechanics of a Multiple Regression Analysis 767 A.1 Introduction 768 A.2 Matrices and Matrix Multiplication 769 A. 3 Identity Matrices and Matrix Inversion 774 A.4 Solving Systems of Simultaneous Linear Equations 779 A. 5 The Least Squares Equations and Their Solution 782 A.6 Calculating SSE and s A.7 Standard Errors of Estimators, Test Statistics, and Confidence Intervals for /3 0, p lt...,& 789 A.8 A Confidence Interval for a Linear Function of the /3 Parameters; A Confidence Interval for E(y) 793 A.9 A Prediction Interval for Some Value of y to Be Observed in the Future 799 APPENDIX b A Procedure for Inverting a Matrix 805

7 CONTENTS APPENDIX 0 Useful Statistical Tables en Table 1 Normal Curve Areas 812 Table 2 Critical Values for Student's t 813 Table 3 Critical Values for the F Statistic: F lo 814 Table 4 Critical Values for the F Statistic: F Table 5 Critical Values for the F Statistic: F Table 6 Critical Values for the F Statistic: F ol 820 Table 7 Random Numbers 822 Table 8 Critical Values for the Durbin-Watson d Statistic (a =.05) 825 Table 9 Critical Values for the Durbin-Watson d Statistic (a =.01) 826 Table 10 Critical Values for the x 2 Statistic 827 Table 11 Percentage Points of the Studentized Range, q(p, v), Upper 5% 829 Table 12 Percentage Points of the Studentized Range, q(p, v), Upper 1% 831 APPENDIX DU SAS Tutorial 833 D.1 Introduction 834 D.2 Creating a SAS Data Set 834 D.3 Accessing an External Data File 835 D.4 Relative Frequency Distributions, Descriptive Statistics, Correlations, and Plots 836 D.5 Simple Linear Regression 837 D.6 Multiple Regression 838 D.7 Stepwise Regression 839 D.8 Residual Analysis and Regression Diagnostics 840 D.9 Logistic Regression 841 D.10 Time Series Forecasting Models and Durbin-Watson Test 842 D.11 Analysis of Variance 842 APPENDIX t E SPSS Tutorial 844 E.1 Introduction 845 E.2 Creating an SPSS Data File 845 E.3 Accessing an External Data File 846 E.4 Relative Frequency Distributions, Descriptive Statistics, Correlations, and Plots 847 E.5 Simple Linear Regression 848 E.6 Multiple Regression 849 E.7 Stepwise Regression 850 E.8 Residual Analysis and Regression Diagnostics 850

8 CONTENTS E.9 Logistic Regression 851 E. 10 Analysis of Variance 852 APPENDIX FP MINITAB Tutorial 854 F.1 Introduction 855 F.2 Creating a MINITAB Data Worksheet 855 F.3 Accessing an External Data File 856 F.4 Relative Frequency Distributions, Descriptive Statistics, Correlations, and Plots 857 F.5 Simple Linear Regression 858 F.6 Multiple Regression 859 F.7 Stepwise Regression 859 F.8 Residual Analysis and Regression Diagnostics 860 F.9 Time Series Smoothing Methods and Durbin Watson Test 861 F.10 Analysis of Variance 862 APPENDIX GU ASP Tutorial 864 G.1 Introduction 865 G.2 Hardware Requirements 865 G.3 Getting Started 865 G.4 The Main Menu 866 G.5 Alternative Commands Menu 866 G.6 Creating a Data Matrix 868 G.7 Accessing an External Data File 869 i G.8 Analyzing a Data Matrix G.9 Available Documentation 869 APPENDIX H APPENDIX I Data Set Sealed Bid Data for Fixed and Competitive Highway Construction Contracts 870 Data Set Real Estate Appraisals and Sales Data for Seven Neighborhoods in Tampa, Florida 874 A P P E N D I X J Data Set Condominium Sales Data 880 Answers to Odd-Numbered Exercises 884 Index 895