7. (15 pts) A researcher estimates the following two models by Least Squares: (A): Y = X,B,+X,*:ß, +ɛ, . = = (B): Y = X,
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7. (15 pts) A researcher estimates the following two models by Least Squares: (A): Y = X,B,+X,*:ß, +ɛ, . = = (B): Y = X,*:B,+X, B. +v; where X,* = residuals from the regression of X, on X,, X,* = residuals from the regression of X, on X, , X, and X, are defined as matrices of explanatory variables. Show how the estimates of ß, and ß, from (A) compare with those from (B).