could you please show the reason why you choose this option thanks Consider the

Question

could you please show the reason why you choose this option

thanks

Consider the following multiple regression model uY=0+1X1+2X2+u Which of the following explains why two perfectly collinear regressors cannot be included in a linear multiple regressions? (Check all that apply)

A. For the case of two regressors and homoskedasticity, it can be shown mathematically that the variance of the estimated coefficient ModifyingAbove beta 1 with caret1 goes to infinity as the correlation between Upper X 1X1 and Upper X 2X2 goes to one.

B. Intuitively, if one regressor is a linear function of another, OLS cannot identify the partial effect of one while holding the other constant.

C. Perfectly collinear regressors cannot be included in a linear multiple regression because it shrinks the estimated coefficients ModifyingAbove beta 1 with caret1 and ModifyingAbove beta 2 with caret2 towards zero.

D. None of the above are correct.

Suppose you are interested in estimating the effect of the studentdash–teacher ratio (STR) on test performance using the model TestScore=0+1STR+u Which of the following regressors, if added to the model, would be perfectly collinear with STR? (Check all that apply)

A. An indicator variable that equals one if a student is a native English speaker.

B. The teacherdash–security officer ratio if the studentdash–security officer ratio is 1:10.

C. The studentdash–faculty parking ratio, if every teacher has a parking spot.

D. The number of teachers expressed as a percentage of the number of students.

Explanation / Answer

2)

D. The number of teachers expressed as a percentage of the number of students.   is correct

as ratio can be expressed as percentage also hence ir would be perfectly collinear with STR

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