计量经济学PPT-7.1

1、 Multiple Regression Analysis: Inference Standard Errors for Predictions in the Multiple Regression Model Var(u0 = 2 + Var( . Hence an estimator for Var(u0 is given by se2 = 2 + se( 2 , 0 where se( is the standard error of the intercept in the regression of y on (xj cj , j = 1, ., 4, and 2 = n 1 u2

2、/(n k 1. i= i It can be shown that if u N (0, 2 , t(n k 1 y0 se0 Hence the (1 % prediction interval for y0 is given by ( t/2 se0 , + t/2 se0 , where t/2 is the the constant that satises P(t > t/2 = /2 where t had the t(n k 1 distribution. 36 / 38 Multiple Regression Analysis: Inference Standard E

3、rrors for Predictions in the Multiple Regression Model Example: Suppose we have the following model y = 0 + 1 x1 + 2 x2 + 3 x3 + 4 x4 + u. We have a sample of 4137 observations. The estimated model is y = (0.075 1.493 + 0.00149 x1 (0.00007 (0.00227 0.01386 x2 (0.00056 0.06088 x3 (0.01650 +0.00546 x4

4、 , = 0.56 37 / 38 Multiple Regression Analysis: Inference Standard Errors for Predictions in the Multiple Regression Model Objectives: Construct a 95% condence interval for E(yjx1 = 1200 , x2 = 30, x3 = 5, x4 = 25. Construct a 95% condence interval for y when x1 = 1200 , x2 = 30, x3 = 5, x4 = 25. Dene a new set of regressors: x1 x2 x3 x4 = x1 = x2 = x3 = x4 1200. 30. 5. 25. Running the regression of y on these new regressors we obtain y = (0.020 2.700 + 0.00149 x1 (0.00007 (0.00