The following is an analysis that contains school level pass rates (as a percent) on a 10th grade math test.
a. the variable expend is expenditures per student, in dollars, and math 10 is the pass rate on teh exam. The following simper regression relates math10 to lexpend= log(expend):
math10= -69.34+11.16 lexpend
(25.53) (3.17)
n=-408, R^2=0.0297
a. Interpret the coefficient on lexpend. In particular, if expend increases by 10%, what is the estimated percentage point change in math10? What do you make of the large negative intercept estimate? (The minimum value of lexpend is 8.11 and its average value is 8.37).
b. Does the small R-squared in part (a) imply that spending is correlated with other factors affecting math10? Explain. Would you espect the R-squared to be much higher if expenditures were randomly assigned to schools that is, independent of other school and student characteristics rather than having the school districts determines spending?
c. When log of enrollment and the percent of students eligible for the federal free lunch program are included, the estimated equation becomes
math10= -23.14+7.75 lexpend - 1.26 lenroll - .34 ln chprg
(24.99) (3.04) (0.58) (0.36)
n = 408, R^2= 0.1893
Comment on what happens to the coefficient on lexpend. Is the spending coefficient still statistically different from zero?