Suppose that you are interested in estimating the ceteris paribus relationship betweenyand. For this purpose, you can collect data on two control variables,and. (For concreteness, you might think ofyas final exam score,as class attendance,as GPA up through the previous semester, andas SAT or ACT score.) Letbe the simple regression estimate fromyonand letbe the multiple regression estimate fromyon,,.

Ifis highly correlated withandin the sample, andandhave large partial effects ony, would you expectandto be similar or very different? Explain.

Ifis almost uncorrelated withand, butandare highly correlated, willandtend to be similar or very different? Explain.

Ifis highly correlated withand, andandhave small partial effects ony, would you expectorto be smaller? Explain.

Ifis almost uncorrelated withand,andhave large partial effects ony, andandare highly correlated, would you expectorto be smaller? Explain.