Consider the following model of student GPA, which is measured on as scale of 0
ID: 3171671 • Letter: C
Question
Consider the following model of student GPA, which is measured on as scale of 0 to 4.0.
GP A = 0 + 1(size of high school class) + 2(size of high school class)2 + 3(academic percentile in high school) + 4(combined SAT) + 5(female) + 6(athlete) + .
The last two variables are dummies, the first taking on a value of 1 if the student is female (and 0 otherwise) and the second taking on a value of 1 if the student is an athlete (and 0 otherwise).
This model was estimated on a sample of 4,137 college students, and produced the following coefficient estimates (estimated standard errors in parentheses):
ˆ0 = 1.241(0.079)
ˆ1 = 0.569(0.0164) ˆ2 = 0.00468(0.00225) ˆ3 = 0.0132(0.0006) ˆ4 = 0.0165(0.00007) ˆ5 = 0.155(0.018)
ˆ6 = 0.169(0.042)
a) The researcher ran the regression again, but this time she left out combined SAT. The estimated coefficient on “athlete” changed to 0.0054, with an estimated standard error of approximately 0.0448.
What does this new result tell you about the SATs of student athletes compared to non- athletes? Think about the new and the old results, and explain your answer carefully.
b) Refer to the example above. Suppose that, starting from the original regression, the researcher decides to include an additional variable, something totally irrelevant, such as the students shoe size.
Yes or no? Would this decision cause the estimators to become biased? Why or why not?
c) Why is it impossible to use the estimates on the previous page to compare the impact of sports participation on the predicted GPA of female students with the impact of sports participation on the predicted GPA of male students? What variable would you need to add to the regression to be able to do this?
Explanation / Answer
In the above regression question, we have six independent variable and name is mention in the question, the size of the sample is 4,137 college students. on the basis of the sample, we estimate the coefficient of the multiple regression coefficients.
a.
GP A directly affects the change the value of combined SAT and it is also highly correlated with athlete variable. after the delete combined SAT variable, it becomes insignificant its means the value of athlete changes they didn't affect significantly the dependent variable.
b.
Yes, because size of shoes not related to the GP A dependent variable. in the stepwise variable selection method, there is highly chance to eliminate from the main model on the basis of low correlation with the GP A dependent variable.
c.
In place of Female varible we add details of all male participation.