Question: Let us consider a multiple linear regression equation of the type: Y = ???? +????X +???? X +.......+???? X +???? Let j ???? be the

Let us consider a multiple linear regression equation of the type:

Y = ???? +????X +???? X +.......+???? X +????
Let j ˆ????
be the OLS estimate of ????j when the jth explanatory variable linearly depends on the remaining (k-1)
explanatory variables, j0 ˆ????
be the OLS estimate of ????j in case of orthogonality and let 2j R be the coefficient of multiple determination which is obtained from a regression equation of the jth explanatory variable on the remaining (k-1)
explanatory variables. Then show that j 2j j0 var(????ˆ ) 1 ˆ =var(???? ) 1???? R . Also, shows that the magnitude of j var(????ˆ ) relative to j0 var(????ˆ ) will rise sharply if the degree of relationship of j X with the remaining (k-1) explanatory variables is very high.

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