计量经济学章节义2.pptVIP

Econometric Theory Lecturer: Dr.Jingtao Yi Room 715 Business School, RUC Lecture 2: Two-Variable Linear Regression II 1. The two-variable linear regression model; 2. Inference in the model; 3. Analysis of variance in the model. Two-variable Linear Regression Model The two-variable linear regression model is specified as: Inference in the OLS Model Properties of a and b Sampling distribution of a and b X is non-stochastic, then Inference in the OLS Model Properties of b Proof? Inference in the OLS Model Properties of a Proof? Gauss-Markov Theorem The OLS estimator is found to have minimum variance in the class of linear unbiased estimators. “Linear”, “Unbiased”, and Efficient Therefore, the OLS estimator is said to be a best linear unbiased estimator (BLUE). Gauss-Markov Theorem Proof? Inference Procedure Sampling distribution of b, a If u is normal, then Inference Procedure Sampling distribution of b Inference Procedure Note: is distributed independently of Sampling distribution of a Similarly, tests on the intercept a are based on the t distribution. Analysis of Variance in the OLS Model Derive the F-test F-statistic To test the null hypothesis F-statistic In the two-variable linear regression model, note that Prediction in the OLS Model Predictions: a point prediction and an interval prediction Prediction in the OLS Model Properties of the OLS predictor Prediction in the OLS Model The prediction error variance is a minimum in the class of linear unbiased predictors. Note that is unknown. So derive a 95 percent confidence interval for as Prediction in the OLS Model Due to the random drawing , predict the mean of