The following analysis was obtained using data in "meap93", which contains school-level pass rat

1. Interpret the coefficient on lexpend: The coefficient on lexpend is 11.16. This means that fo

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The following analysis was obtained using data in "meap93", which 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 math10 is the pass rate (in percentage) on the exam. The following simple regression relates math10 to lexpend = log(expend): widehat{math10} = -69.34 + 11.16 lexpend (25.53) (3.17) n = 408 R^2 = .0297 The figures in the brackets denote the corresponding standard errors. 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^2 in part (a) imply that spending is correlated with other factors affecting math10? Explain. Would you expect the R^2 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 determine spending? (c) When log of enrollment (lenroll) and the percent of students eligible for the federal free lunch program (lnchprg) are included, the estimated equation becomes widehat{math10} = -23.14 + 7.75 lexpend - 1.26 lenroll - .324 lnchprg (24.99) (3.04) (0.58) (0.36) n = 408 R^2 = .1893 The figures in the brackets denote the corresponding standard errors. Comment on what happens to the coefficient on lexpend. Is the spending coefficient statistically different from zero at 5% level of significance?

          The following analysis was obtained using data in "meap93", which 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 math10 is the pass rate (in percentage) on the exam. The following simple regression relates math10 to lexpend = log(expend):

widehat{math10} = -69.34 + 11.16 lexpend
(25.53) (3.17)
n = 408
R^2 = .0297

The figures in the brackets denote the corresponding standard errors. 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^2 in part (a) imply that spending is correlated with other factors affecting math10? Explain. Would you expect the R^2 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 determine spending?
(c) When log of enrollment (lenroll) and the percent of students eligible for the federal free lunch program (lnchprg) are included, the estimated equation becomes

widehat{math10} = -23.14 + 7.75 lexpend - 1.26 lenroll - .324 lnchprg
(24.99) (3.04) (0.58) (0.36)
n = 408
R^2 = .1893

The figures in the brackets denote the corresponding standard errors. Comment on what happens to the coefficient on lexpend. Is the spending coefficient statistically different from zero at 5% level of significance?

The following analysis was obtained using data in "meap93", which 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 math10 is the pass rate (in percentage) on the exam. The following simple regression relates math10 to lexpend = log(expend):

widehatmath10 = -69.34 + 11.16 lexpend
(25.53) (3.17)
n = 408
R^2 = .0297

The figures in the brackets denote the corresponding standard errors. 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^2 in part (a) imply that spending is correlated with other factors affecting math10? Explain. Would you expect the R^2 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 determine spending?
(c) When log of enrollment (lenroll) and the percent of students eligible for the federal free lunch program (lnchprg) are included, the estimated equation becomes

widehatmath10 = -23.14 + 7.75 lexpend - 1.26 lenroll - .324 lnchprg
(24.99) (3.04) (0.58) (0.36)
n = 408
R^2 = .1893

The figures in the brackets denote the corresponding standard errors. Comment on what happens to the coefficient on lexpend. Is the spending coefficient statistically different from zero at 5% level of significance?

Added by Jamie W.

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