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英文版答案：
3.15 (i) The degrees of freedom of the first regression is n – k – 1 = 353 – 1 – 1 = 351.The degrees of freedom of the second regression is n – k – 1 = 353 – 2 – 1 = 350. The standard error is smaller than the simple regression equation because one more explanatory variable is included in the second regression. The SSR falls from 326.196 to 198.475 when another explanatory variable is added, and the degrees of freedom also falls by one, which affects the standard error.
(ii) Yes, there is a positive moderate correlation between years and rbisyr.
VIFyears = 1/(1-R_years^2 ) = 1/(1-0.597) = 2.48139; from this value, we can say that there is little collinearity between years and rbisyr.
(iii) The standard error for the coefficient on years in the multiple regression is:
se(β ̂_years )=σ ̂⁄〖[SST(1-R_years^2]〗^(1/2)
The standard error is smaller than the simple regression equation because one more explanatory variable is included in the second regression. The SSR falls from 326.196 to 198.475 when another explanatory variable is added. The degrees of freedom also falls by one, which affects the standard error. Therefore, the standard error for the coefficient of years in the multiple regression is smaller than its simple regression.
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