问题如下:
c. Using the results from part a and part b, and the correlation between the two explanatory variables, estimate the parameters for the full model:
Y=α+β1X1+β2X2
选项:
解释:
The key statement from the chapter is “the estimator β1 converges to β1+β2δ”
So, part a gives that:
β1+β2δ1=0
And part b gives that:
β2+β1δ2=−1.479
δ1=V[X1]Cov[X1,X2]=0.467/0.933=0.501
and
δ2=0.467/0.934=0.5
Note: In this case these quantities are essentially equal, but that will not usually be the case.
Plugging back in the 2 * 2 system of equations:
β1+0.501β2=0
β2+0.5β1=−1.479
Solving yields that
β1=0.989,β2=−1.9733
And plugging these back into the equation to find alpha:
Y=α+β1X1+β2X2=−2
Y=−2+0.989X1−1.9733X2