计量经济学讲义(厦门大学黄长全)chap4.pptVIP

Chapter 3 多元线性回归模型(Multiple linear regression model) You are required to get familiar with matrix algebra for mastering this chapter! Classical Multiple linear regression model (CMLRM): 1. model 2. random sample Matrix form: 3. Model assumption: 1. 2. 3. is non-random. 4. 5. Normality assumption assumptions 1 and 5 imply that the errors are Independent. As in the case of the univariate linear regression models, we can estimate the regression coefficients of the multiple linear regression models by using the ordinary least squares procedure. In matrix form, the OLSE is 4. OLSE for the CMLRM 5. Properties of the OLSE for the CMLRM 1. 2. 3. The Gauss-Markov theorem is still true: The OLSE for the CMLRM is the BLUE. 6. Residual and Estimation of the population variance 1. Residual 1) P is idempotent (幂等的) 2) 3) 4) 2. Estimator for 7. Goodness-of-fit testing 1. 1) Total sum of squares: 2) Explained sum of squares: 2. Coefficient of determination: 3. Adjusted R-squared: 8. Hypothesis testing 1. Significance test for the population regression equation 1) Hypothesis: 2) F-statistic: 3) Testing Given a significance level , pick up the critical value . if , reject . otherwise, accept it. 2. Significance test for a single parameter 1) Hypothesis: 2) t-statistic: 9. Forecasting 1. Point forecast: Given , then a predictor 2. Interval forecast: Let then Let Then Homework: * * *