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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Definitions:

Stretch Reflex

A muscle contraction in response to stretching within the muscle, a mechanism that helps maintain muscle tone and posture.

Golgi Tendon Reflex

A protective reflex mechanism that prevents muscle damage during excessive force by causing muscle relaxation.

Reciprocal Innervation

The coordination of muscle groups achieved through the activation of one muscle and the simultaneous inhibition of its antagonist.

Obturator Nerve

A nerve in the pelvic region that innervates the adductor muscles of the thigh.