Polynomials, Dummy Variables, and Joint F tests

I need some help following the instructions and creating a log file using Stata.

Please download the do-file for this assignment

Please submit:
a) A printed Stata smcl (log) file documenting that you've completed each of the operations directed below and showing results. (NB: Be sure to run only your corrected Do file so your printed log file does not contain errors.)
b) A printed write-up, which includes typed answers to the questions below.

Estimate the following four OLS regressions with total expenditures per pupil as the dependent variable.

1. Independent variables:
- percent of the school's students who are black;
- percent of the school's students who are eligible for free lunches;
- total enrollment in the school.

a. Interpret the results on the coefficient for the percent of a school's students who are black.

2. Independent variables:
- percent of the school's students who are black;
- percent of the school's students who are eligible for free lunches;
- total enrollment in the school;
- year dummies (See the Exercise 5 do-file for models of how to do this.) Browse your data to make sure the dummy was properly created (see cribsheet for how to browse).

a. Interpret the result on the coefficient for the percent of a school's students who are black. Does it substantively differ from the previous result? If so, why?

b. If you include all four year dummies in the model, one of them will be dropped by Stata. Why?

3. Independent variables:
- percent of the school's students who are black;
- percent of the school's students who are eligible for free lunches;
- a polynomial in total enrollment in the school (See the Exercise 5 do-file for how to create a polynomial, and be -re to use both totreg and totregsq)
- year dummies
- a dummy variable if a school is a middle school

a. Interpret the results on the coefficient for the percent of a school's students who are black.

4. Independent variables:
- percent of the school's students who are black
- percent of the school's student who are eligible for free lunches
- a polynomial in total enrollment in the school
- year dummies
- a dummy variable if the school is a middle school
- dummy variables for the boroughs of New York City

a. If you include five borough dummies in the model, one of them will be dropped by Stata. Why?
b. Interpret the results on the coefficient for the percent of a school's students who are black.
c. Use test to see if the polynomial is statistically significant. Is it?
d. Test to see if the borough dummies are statistically significant. Are they?
e. Finally, at what enrollment is total expenditures per pupil minimized? Show your work. Note: This is not a Stata exercise.