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.

(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?

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math4 = 24.49 + 9.01 lexppp – .422 free – .752 Imedinc (.071) .274 pctsgle (.161) (59.24) (4.04) n = 229, R2 = 472, R = .462. (5.358) math4 = 149.38 + 1.93 lexppp - .060 free (41.70) (2.82) n = 229, R? = .749, R2 = .743. 10.78 Imedinc - .397 pctsgle + .667 read4 (.054) (3.76) (.111) (.042)