The following table gives the variables to work with from the STAR data set. Choose the x1,
x2, and y corresponding to the ﬁfth, sixth, and seventh digits of your student number. As well,
pick any other x you want from either of the ﬁrst two columns of the table to use as your x3.
x1 x2 y
1 freem frac s ed frac lt hs z math score
2 frpm frac s hs frac own z math score
3 enrollment s ed frac grd z math score
4 edi s med income z math score
5 re asian frac s ms frac now married z elarts score
6 charter s sex frac female z elarts score
7 re hl frac s age frac 75 older z elarts score
8 ed frac lt hs z rev total d :5 math score + :5 elarts score
9 yrcal s te days d :5 math score + :5 elarts score
0 te avgyr s te salary avg d :5 math score + :5 elarts score
1. (25 points). Conduct a heteroskedasticity – robust F test of the joint hypothesis that both of your
coefﬁcients from the regression of y on x1 and x2 equal zero. Take a screenshot that shows the
relevant commands and results written to the R console. Interpret the result of your F-test.
2. (25 points) Consider the following (generic) population regression model:
Yi = 0 + 1X1;i + 2X2;i + 3X3;i + ui; i = 1; :::; n (?)
Transform the regression to allow you to easily test the null hypothesis that 1 + 3 = 1. State
the new null hypothesis associated to this transformed regression. Without actually running it in
R, consider what would happen if you ran this regression and conducted this hypothesis test using your variables y, x1, x2, and x3 from the STAR data set. Would you expect to reject or accept the null hypothesis? Why?
3. (25 points). Continuing with the previous question, add two additional regressors to your un-
transformed model (your version of ? with Y = y, X1 = x1, X=x2, X3 = x3): the square of
x3 and the cube of x3. Show the results run in R. Assuming homoskedasticity of your errors (just this once!), construct the homoskedasticity-only F test of the joint hypothesis that the coefﬁcients on the square of x3 the cube of x3 are both equal to zero. Can you reject this hypothesis? What does rejecting/failing to reject this null hypothesis tell you about the relationship between x3 and y in this speciﬁc multiple regression framework?
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