The following two equations were estimated using the data in MEAPSINGLE. The key

Question

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 = 24.49 + 9.01 lexppp - .422 free - .752 lmedinc - .274 pctsgle (59.24) (4.04) (.071) (5.358) (.161) n = 229, R^2 = .472, R^2 = .462. math 4 = 149.38 + 1.93 lexppp - .060 free - 10.78 Imedinc - .397 pctsgle + .667 read4 (41.70) (2.82) (.054) (3.76) (.111) (.042) n = 229, R^2 = .749, R^2 = .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 beta_lexppp? 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?

Explanation / Answer

Part-i

In first regression model test statistic for lexppp = 9.01/4.04=2.23

In second regression model test statistic for lexppp = 1.93/2.82 =0.68

As lexppp is the key explanatory variable and is significant in first model and non-signifcant in second model so we would keep using first model.

For 1% increase in lexppp there is on an average an increase of 0.0901 in the math test performance, holding other predictors fixed.

So, For 10% increase in lexppp there is on an average an increase of 0.901 in the math test performance, holding other predictors fixed.

Part-ii

We observe that adding read4 in the first regression model will make the standard error of free , lmedinc and pctshle to decrease and high inflation of coefficient of lmedinc.

Part-iii

We prefer the equation with smaller adjusted R-square when in that regression model the key explanatory variable is significant.

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