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.

$4=24\mathrm{.}49+9\mathrm{.}010\mathrm{.}4220\mathrm{.}7520\mathrm{.}274$

$(59\mathrm{.}24)(4\mathrm{.}04)(0\mathrm{.}071)(5\mathrm{.}358)(0\mathrm{.}161)$

N $=229,$ R$2=0\mathrm{.}472,2=0\mathrm{.}462.$

$4=149\mathrm{.}38+1\mathrm{.}930\mathrm{.}06010\mathrm{.}780\mathrm{.}397+0\mathrm{.}6674$

$(41\mathrm{.}70)(2\mathrm{.}82)(0\mathrm{.}054)(3\mathrm{.}76)(0\mathrm{.}111)(0\mathrm{.}042)$

N $=229,$ R$2=0\mathrm{.}749,2=0\mathrm{.}743.$

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?