\f3. (20 points) Use the data in GPA2 to estimate the following equation: sat = Bo + Bjhsize + Byhsize? + Byfemale + Bablack + Bs female x black + u. and answer the following questions. Here the variable sat is the combined SAT score,| lusize is the size of the student's high school graduating class in hundreds, female and black are gender and race dummies respectively (i) (9 points) In the estimation, Bo = B1 B2 = B3 = B4 (ii) (3 points) Is there strong evidence that hsize should be included in the model? From this equation, what is the optimal high school size? (iii) (4 points) Holding hsize fixed, what is the estimated difference in SAT score between nonblack females and nonblack males? (iv) (4 points) Holding hsize fixed. what is the estimated difference in SAT score between nonblack males and black males? (gift)