2. In practicer 2 is unknown, so we use its estimator 2 then b,. b, b t(n-k) 2∑c(729) 3 (7.30) 7.3.3 Properties of oLS Estimators of Multiple regression BLUE 7.4 An Illustrative Example
2. In practice, is unknown, so we use its estimator, , then b1 , b2 , b3～t（n-k） (7.29) (7.30) 7.3.3 Properties of OLS Estimators of Multiple Regression －－BLUE 7.4 An IllustrativeExample 2 σ 2 σ ˆ n 3 e σ 2 2 t − ˆ = 2 σ ˆ = σ ˆ
7.5 Goodness of fit of Estimated Multiple regression: Multiple Coefficient of Determination, R2 Multiple coefficient of determination. R2 TSS=ESS+RSS (733 R (7.34) TSS R2=b 2y,xa+b, 2y x(7.36) ∑ R2 also lies between0 and 1(just as r2) R: coefficient of multiple correlation the degree of linear association between Y and all the X variables jointly R is always taken to be positive. (rcan be positive or negative 7.6 Hypothesis Testing: General Comments:
7.5 Goodness of Fit of Estimated Multiple Regression: Multiple Coefficient of Determination, R2 • Multiple coefficient of determination, R2 TSS=ESS+RSS (7.33) R2= (7.34) R2= (7.36) R2 also lies between 0 and 1（just as r 2） R: coefficient of multiple correlation, the degree of linear association between Y and all the X variables jointly. R is always taken to be positive.（r can be positive or negative） 7.6 Hypothesis Testing: General Comments: TSS ESS + 2 t 2 t 2t 3 t 3t y b y x b y x