Using a dataset on SAT scores, class size and demographic characteristics of a sample of students, the following model is estimated:
sat = β0 + β1 ⋅ hsize + β2 ⋅ hsize^2 + β3 ⋅ female + β4 ⋅ black + β5 ⋅ (female ⋅ black)
sat = 1028.09 + 19.29 ⋅ hsize − 2.19 ⋅ hsize^2 − 45.09 ⋅ female + 169.81 ⋅ black + 62.30 ⋅ (female ⋅ black)
(Standard errors in parentheses: (12.713) (6.29) (3.832) (0.527) (18.154) (4.291))
Where:
sat: combined SAT score
hsize: size of student’s high school graduating class (in hundreds)
female: dummy variable for gender (1 = female)
black: dummy variable for race (1 = Black)
(a) Is there strong evidence that hsize should be included in the model?
(b) Holding hsize fixed, what is the estimated difference in SAT score between nonblack females and nonblack males? How statistically significant is this estimated difference?
(c) What is the estimated difference in SAT score between black males and nonblack males? How statistically significant is this estimated difference?
(d) What is the estimated difference in SAT score between black females and nonblack females? (Hint: plug in values for black and female to get the required group)
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