Is there evidence that hsize2 should be included in the model? Explain.

Assignment 5

Instructions

You must use STATA and must turn in a copy of your Do-file. The Do-file must perform every task below neatly and correctly.

The work you hand in must be your own. You must NOT copy any answers from anyone or anywhere else. Please review FIU’s policy on academic misconduct for more information.

Questions

1. The data for this question can be downloaded here. Consider the following regression equation:

sat^=1,028.1+19.3hsize−2.18hsize2−45.09female−169.81black+62.31female⋅black+e (6.29)(3.83)(0.53)(4.29)(12.71)(18.15)

The standard error for each parameter estimates is in parenthesis. n=4,137 and R2=0858.

sat is the combined SAT score

hsize is the size of the student’s high-school graduating class, in hundreds

female is a dummy variable for gender

black is a race binary variable (=1 for blacks, =0 otherwise)

1. a) Is there evidence that hsize2 should be included in the model? Explain.
2. b) What is the optimal high-school graduating class size?
3. c) Holding hszie fixed, what is the estimated difference in SAT scores between non-black females and non-black males? Is the difference statistically significant?
4. d) Is there a difference in SAT score between black and non-black males? If so, what is it?
5. e) Is there a difference in SAT score between black and non-black females? If so, what is it?

2. The data for this question can be downloaded here. Consider the following regression equation:

log(salary )=β0+β1 years +β2 gamesyr +β3 bavg +β4 hrunsyr +β5 rbisyr +β6 runsyr +β7 fldperc +β8 allstar +β9 frstbase +β10 scndbase +β11 thrdbase +β12 shrtstop +β13 catcher +e,

The model above explains MLB player salary by position. Outfield is the base group.

1. a) State the null hypothesis that catchers and outfielders earn -on average- the same amount, while controlling for other factors.
2. b) Test the hypothesis from (2.a) using the supplied dataset, and comment on the difference in salary.
3. c) State and test the null hypothesis that there is no average salary across positions (when all other factors are controlled for)
4. d) Are the results from (2.a), (2.b), and (2.c) consistent? Explain why or why not.