INTRODUCTORY REGRESSION ANALYSIS

Transcription

1 ;»»>? INTRODUCTORY REGRESSION ANALYSIS With Computer Application for Business and Economics Allen Webster Routledge Taylor & Francis Croup NEW YORK AND LONDON

2 TABLE OF CONTENT IN DETAIL INTRODUCTORY REGRESSION ANALYSIS Preface xvii Chapter 1:» 1 A Review of Basic Concepts 1 Introduction The Importance of Making Systematic Decisions The Process of Statistical Analysis 4 Data Collection. 4 Organizing the Data 4 Analyzing the Data 5 Interpreting the Results 5 Prediction and Forecasting Our "Arabic" Number System Some Basic Definitions 6 Populations and Samples 7 Sampling Error 8 Sources of Sampling Error: Sampling Bias and Plain Bad Luck, 8 A Sampling Distribution ' 9 Types of Variables Levels of Data Measurement 12 Nominal Data 12 Ordinal Data 12 Interval Data 13 Ratio Data Properties of Good Estimators 15 A Good Estimator Is Unbiased 15 A Good Estimator Is Efficient 16

3 XDDI TABLE OF CONTENTS IN DETAIL A Good Estimator Is Consistent 17 A Good Estimator Is Sufficient Other Considerations Probability Distributions The Development and Application of Models "In God We Trust Everybody Else Has to Bring Data" 22 Chapter Problems, 23 Appendix: Excel Commands and Common Probability Distributions 24 The Normal Distribution -" 25 Student's f-distribution 27 The F-Distribution 27 The Chi-Square Distribution 28 Chapter 2: An Introduction to Regression and Correlation Analysis 29 Introduction The Simple Regression Model Estimating the Model: Ordinary Least Squares 35 Multiple Regression: A Look Ahead 39 Calculating the Residuals ' Why the Process Is Called Ordinary Least Squares Properties and Assumptions of the OLS Model The Gauss-Markov Theorem Measures of Goodness of Fit 46 The Standard Error of the Estimate 46 The Coefficient of Determination 48 How r 2 Can Be Used as a Measure of Goodness of Fit Limitations of Regression and Correlation Regression Through the Origin Computer Applications 58 Using Excel 58 Using Minitab 60 Using SPSS Review Problems 62 Chapter Problems 63 Conceptual Problems 63 Computational Problems 64 Computer Problems 70

4 TABLE OF CONTENTS IN DETAIL B XI Chapter 3: Statistical Inferences in the Simple Regression Model 71 Introduction Confidence Interval Estimation 72 Conditional Mean Interval 73 The Predictive Interval 76 Factors that Affect the Width of the Interval 79 Confidence Interval for the Population Regression Coefficient,,8, 80 Confidence Interval for the Correlation Coefficient, p Hypothesis Testing: Checking for Statistical Significance 84 Hypothesis Test for the Population Regression Coefficient, j8, 85 The Meaning of the "Level of Significance" 88 The Hypothesis Test for the Population Correlation Coefficient, p Large Samples and the Standard Normal Distribution The p-value and Its Role in Inferential Analysis 94 How to Detect and Interpret an Extremely Small p-value Computer Applications 99 Using Excel 99 Using Minitab 100 Using SPSS ( Review Problem 104 Chapter Problems 109 Conceptual Problems 109 Computational Problems 110 Computer Problems 117 Chapter 4: Multiple Regression: Using Two or More Predictor Variables 119 Introduction 120 Additional Assumptions The Multiple Regression Model 122 The Adjusted Coefficient of Determination 123 Analyzing the Model 124 A Change in the Coefficient for GDP The Issue of Multicollinearity 129 The Problems of Multicollinearity ' 129 Detecting Multicollinearity 131 Treating the Problem of Multicollinearity Analysis of Variance: Using the F-Test for Significance Dummy Variables 142 Allowing for More Responses in a Qualitative Variable 147 Using Dummy Variables to Deseasonalize Time Series Data 148 Interpreting a Computer's Printout 150

5 XII DOB TABLE OF CONTENTS IN DETAIL 4.5 Interaction Between Independent Variables Incorporating Slope Dummies Control Variables A Partial F-Test Computer Applications 164 Excel 164 Minitab 166 SPSS Review Problem Chapter Problems 168 Conceptual Problems " 168 Computational Problems 169 Computer Problem 174 Chapter 5: Residual Analysis and Model Specification 175 Introduction Using Residuals to Evaluate the Model 176 A Test for Randomness 177 Testing the Assumption of a Constant Variance, 178 The Presence of Autocorrelation 181 Checking for Linearity 181 Test for Normality Standardized Regression Coefficients Proper Model Specification: Getting it Right 189 Consequences of an Omitted Variable 189 All Combinations 191 Backward Elimination, Forward Selection, and Stepwise Regression Reseating the Variables 193 Rescaling the Dependent Variable 195 Rescaling an Independent Variable The Lagrange Multiplier Test for Significant Variables 197 Chapter Problems 198 Conceptual Problems, 198 Computer Problems ' 199 Chapter 6: Using Qualitative and Limited Dependent Variables 200 Introduction Logit Analysis 201 An Example of a Logit Model 203 The Log-Likelihood Statistic 205 Classification Tables 207 Maximum Likelihood and the Use of Iterations 209

6 TABLE OF CONTENTS IN DETAIL IDD XI The Linear Probability Model and Weighted Least Squares 211 The Linear Probability Model 211 Weighted Least Squares Discriminant Analysis 215 Evaluation ' 218 Cross-Validation 219 The Eigenvalue and Wilks' Lambda 221 Chapter Problems 224 Conceptual Problems 224 Computational Problems -" 224 Computer Problem 228 Chapter 7: Heteroscedasticity 229 Introduction Consequences of Heteroscedasticity Detecting Heteroscedasticity 232 Using Plots of Residuals 232 The Park Test 233 The Glejser Test, 236 White's Test ' v 237 The Goldfeld-Quandt Test Remedial Measures > 244 If the Population Error Variances Are Known 244 Weighted Least Squares with of Unknown 245 Applying WLS to Our Income/Consumption Data 247 Heteroscedasticity, Elasticities, and the Use of Logs 251 Elasticity of Demand and Total Sales Revenue 252 How Elasticity Relates to Heteroscedasticity 254 How Logs Estimate Elasticities 255 Chapter Problems 259 Conceptual Problems 259 Computational Problems 260 Appendix: Logs and Elasticity 261 Chapter 8: Autocorrelation, 264 Introduction The Nature of Autocorrelation Causes of Autocorrelation 270 Model Misspecification 271 The Issue of Stickiness The Consequences of Autocorrelation 272

7 XBV DOB TABLE OF CONTENTS IN DETAIL 8.4 Detecting Autocorrelation 274 The Durbin-Watson Statistic 274 The Durbin-Watson ft-statistic 280 A Simple Hypothesis Test 280 A Nonparametric Runs Test 281 The Lagrangian Multiplier Test 284 The Breusch-Godfrey Test Correcting for Autocorrelation 285 Generalized Least Squares The Cochrane-Orcutt Method 286 Modification of the Cochrane-Orcutt Method 289 Incorporating a Lagged Value of the Dependent Variable 290 First-Differencing 290 Summary 291 Chapter Problems 293 Conceptual Problems 293 Computational Problems 293 Appendix: Transforming Data to Eliminate Autocorrelation 295 Chapter 9: Non-Linear Regression and the Selection of 1 the Proper Functional Form. 297 Introduction 298 _ 9.1 The Nature of Curvilinear Models Polynomials Quadratics and Cubics 303 The Average Cost Curve 303 The Revenue Function 305 Solving Quadratic Equations and the Vertex 306 Cubic Functions The Use of Logarithmic Transformations: The Double-Log Model 312 The Demand Curve as an Example 313 The Cobb-Douglas Production Function Other Logarithmic Transformations 319 The Log-Linear Model 319 The Linear-Log Model, 323 The Reciprocal Model 325 An Exponential Model 326 Continuous Growth Models 329 Mixed Models 330 Chapter Problems 331 Conceptual Problems 331 Computational Problems 331 Appendix: With Respect to Exponential Functions 335

8 TABLE OF CONTENTS IN DETAIL Q XV Chapter 10: Simultaneous Equations: Two-Stage Least Squares 337 Introduction The Two-Equation Model Simultaneity Bias The Reduced-Form Equations The Identification Problem 341 Finding the Proxy An Illustration of 2SLS Applying 2SLS to Our Market for Bread ' A Comparison of 2SLS and OLS The Durbin-Wu-Hausman Test for Simultaneity A Macroeconomic Model 354 Chapter Problems 355 Conceptual Problems 355 Computational Problems 356 Chapter 11: Forecasting with Time Series Data and Distributed Lag Models 357 Introduction ' A Simple Time Series Model Autoregressive Models Distributed Lag Models 367 The Koyck Transformation (Geometric Lag) 367 The Problem of Autocorrelation 369 Stationarity and the Dickey-Fuller Test 371 Cointegration \ 373 The Almon (Polynomial) Lag Granger Causality Methods of Forecasting: Moving Averages and Exponential Smoothing 379 Moving Average 380 First-Differencing 383 Single Exponential Smoothing 385 Double Exponential Smoothing Autoregressive Moving Averages 391 The ARMA Model 392 Integration-ARIMA 394 Box-Jenkins Methodology 396 Chapter Problems 396 Conceptual Problems 396 Computational Problems 397 Appendix: The Koyck Transformation 398

9 XVI D D I TABLE OF CONTENTS IN DETAIL APPENDICES 399 Appendix A: Answers to Selected Even Problems 400 Appendix B: Statistical Tables 433 B.1 Chi-Square Table " 433 B.2 Durbin-Watson Values 435 B.3 F-Distribution Table 437 B.4 f-values for a Two-Tailed Test Example: f O5>19 = ± B.5 The Normal Distribution Table 463 Notes Index '. 470