1、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 mo
2、del 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 bProof?,Inference in the OLS Model,Properties of aProof?,Gauss-Markov Theorem,The OLS estimator is found to have minimum variance
3、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, aIf u is normal, then,Inference Procedure,Sampling distribut
4、ion 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 reg
5、ression 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,
