The data in the file "sat.txt" (https://ideone.com/1BFk9c) data on SAT.

Key points of data is here:

• The column expend contains the mean expenses per pupil (in $ per pupil),
• the ratio is the pupil/teacher ratio,
• salary is the mean salary of teachers,
• takers is the percentage of pupils that take the SAT.
• Variables verbal and math are partial scores of the total SAT score in total and not used in the analysis.
• All data are per state.

I could like to figure out 3 things below. If you can do in R or Python, it would be great:

1) I can't fit a multiple linear regression model to these data taking the column total as the response variable and expend, ratio, salary, takers as explanatory variables. Use both the step-up and the step-down methods to find the best model. In case step-up and step-down yield two different models, choose the best one and motivate your choice.

2) Investigate whether the square of takers is useful as an additional explanatory variable.

Expand the data set in the following way: sat$takers2=(sat$takers)^2.

Find again the best model, using step-up and step-down, now using expend, ratio, salary, takers, and takers2 as possible explanatory variables.

3) which models (1) or (2) is better?