Let D1 and D2 be defined as in the previous exercise. (a) In the OLS regression Y D1b1 D2b2 bu, show that b1 is

Let D1 and D2 be defined as in the previous exercise.

(a) In the OLS regression Y ÆD1b°1 ÅD2b°2 Å bu, show that b°1 is the sample mean of the dependent variable among the men of the sample (Y 1), and that b°2 is the sample mean among the women (Y 2).

(b) Let X (n £k) be an additionalmatrix of regressors. Describe in words the transformations Y ¤

Æ Y ¡D1Y 1 ¡D2Y 2 X ¤

Æ X ¡D1X 0

1 ¡D2X 0

2 where X1 and X2 are the k £1 means of the regressors for men and women, respectively.

(c) Compare e¯ from the OLS regression Y ¤
Æ X ¤e¯
Åee with b¯ from the OLS regression Y ÆD1b®
1 ÅD2b®
2 ÅXb¯
Åbe.