We used the data in MEAP93 for Example 2.12. Now we want to explore the relationship between the math pass rate (math10) and spending per student (expend).

(i) Do you think each additional dollar spent has the same effect on the pass rate, or does a diminishing effect seem more appropriate? Explain.

(ii) In the population model math105 b01 b1 log1expend2 1 u, argue that b1/10 is the percentage point change in math10 given a 10% increase in expend.

(iii) Use the data in MEAP93 to estimate the model from part (ii). Report the estimated equation in the usual way, including the sample size and R-squared.

(iv) How big is the estimated spending effect? Namely, if spending increases by 10%, what is the estimated percentage point increase in math10?

(v) One might worry that regression analysis can produce fitted values for math10 that are greater than 100. Why is this not much of a worry in this data set?