The following two equations were estimated using the data in MEAPSINGLE. The key explanatory variable is lexppp, the log of expenditures per student at the school level.

math4 5 24.49 1 9 .01 lexppp 2 .422 free 2 .752 lmedinc 2 .274 pctsgle 159.242 14.042 1.0712 15.3582 1.1612 n 5 229, R2 5 .472, R2 5 .462.

math4 5 149.38 1 1 .93 lexppp 2 .060 free 2 10 .78 lmedinc 2 .397 pctsgle 1 .667 read4 141.702 12.822 1.0542 13.762 1.1112 1.0422 n 5 229, R2 5 .749, R2 5 .743.

(i) If you are a policy maker trying to estimate the causal effect of per-student spending on math test performance, explain why the first equation is more relevant than the second. What is the estimated effect of a 10% increase in expenditures per student?

(ii) Does adding read4 to the regression have strange effects on coefficients and statistical significance other than blexppp?

(iii) How would you explain to someone with only basic knowledge of regression why, in this case, you prefer the equation with the smaller adjusted R-squared?