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Contents 13
Chapter 6 Linear Regression with Multiple Regressors 228
6.1 Omitted Variable Bias 228
Definition of Omitted Variable Bias 229
A Formula for Omitted Variable Bias 231
Addressing Omitted Variable Bias by Dividing the Data into
Groups 233
6.2 The Multiple Regression Model 235
The Population Regression Line 235
The Population Multiple Regression Model 236
6.3 The OLS Estimator in Multiple Regression 238
The OLS Estimator 239
Application to Test Scores and the Student–Teacher Ratio 240
6.4 Measures of Fit in Multiple Regression 242
The Standard Error of the Regression (SER) 242
The R2 242
The “Adjusted R2” 243
Application to Test Scores 244
6.5 The Least Squares Assumptions in Multiple
Regression 245
Assumption #1: The Conditional Distribution of ui Given X1i, X2i, c, Xki Has a
Mean of Zero 245
Assumption #2: (X1i, X2i, c, Xki, Yi), i = 1, c, n, Are i.i.d. 245
Assumption #3: Large Outliers Are Unlikely 245
Assumption #4: No Perfect Multicollinearity 246
6.6 The Distribution of the OLS Estimators in Multiple
Regression 247
6.7 Multicollinearity 248
Examples of Perfect Multicollinearity 249
Imperfect Multicollinearity 251
6.8 Conclusion 252
Appendix 6.1 Derivation of Equation (6.1) 260
Appendix 6.2 Distribution of the OLS Estimators When There Are Two
Regressors and Homoskedastic Errors 260
Appendix 6.3 The Frisch–Waugh Theorem 261
