Question

1. Using a dataset, the following equation was estimated:

   sat_hat = 1,028.10 + 21.30hsize - 5.19hsize^2 - 40.09female - 150.81black + 50.31 female x black

                         (6.29)    (3.83)    (.53)    (4.29)   (12.71)          (18.15)

   The variable sat is the combined SAT score; hsize is size of the student’s high school graduating class, in hundreds; female is a gender dummy variable; and black is a race dummy variable equal to one for blacks, and zero otherwise. What is the estimated difference in SAT score between black females and nonblack females?

   		100.5
   		120.2
   		140.6
   		160.3

Answer 1

The correct answer is (a) 100.5.

It is given that we have the following regression equation :

sat_hat = 1,028.10 + 21.30hsize - 5.19hsize^2 - 40.09female - 150.81black + 50.31*female*black

For black females :

we have, Black = 1 and female = 1

Hence, we have sat_hat = 1,028.10 + 21.30hsize - 5.19hsize^2 - 40.09*1 - 150.81*1 + 50.31*1*1

=> sat_hat = 887.51 + 21.30hsize - 5.19hsize^2

Hence SAT score for Black female = 887.51 + 21.30hsize - 5.19hsize^2

For non black females :

we have, Black = 0 and female = 1

Hence, we have sat_hat = 1,028.10 + 21.30hsize - 5.19hsize^2 - 40.09*1 - 150.81*0 + 50.31*1*0

=> sat_hat = 988.01 + 21.30hsize - 5.19hsize^2

Hence SAT score for Non Black female = 988.01 + 21.30hsize - 5.19hsize^2

Thus, difference in score between non black females and black females = 988.01 + 21.30hsize - 5.19hsize^2 - (887.51 + 21.30hsize - 5.19hsize^2) = 100.5

=> difference in score between non black females and black females = 100.5

Hence, the correct answer is (a) 100.5.