Consider the Following Regression Using the California School Data Set $\widehat{\text { TestScore }}$

question 39

Essay

Consider the following regression using the California School data set from your textbook. $\widehat{\text { TestScore }}$ = 681.44 - 0.61LchPct
n=420, R²=0.75, SER=9.45
where TestScore is the test score and LchPct is the percent of students eligible for subsidized lunch (average = 44.7, max = 100, min = 0).
a. What is the effect of a 20 percentage point increase in the student eligible for subsidized lunch?
b. Your textbook started with the following regression in Chapter 4: $\widehat{\text { TestScore} }$ = 698.9 - 2.28STR
n=420, R²=0.051, SER=18.58
where STR is the student teacher ratio.
Your textbook tells you that in the multiple regression framework considered, the percentage of students eligible for subsidized lunch is a control variable, while the student teacher ratio is the variable of interest. Given that the regression R² is so much higher for the first equation than for the second equation, shouldn't the role of the two variables be reversed? That is, shouldn't the student teacher ratio be the control variable while the percent of students eligible for subsidized lunch be the variable of interest?

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