You Have Read the Analysis in Chapter 9 and Want $\widehat {\text { TestScr }}$

question 18

Essay

You have read the analysis in chapter 9 and want to explore the relationship between poverty and test scores. You decide to start your analysis by running a regression of test scores on the percent of students who are eligible to receive a free/reduced price lunch both in California and in Massachusetts. The results are as follows: $\widehat {\text { TestScr }}$ _CA = 681.44 - 0.610×PctLch_{CA
(0.99)(0.018)
n = 420, R}^{2 = 0.75, SER = 9.45} $\widehat {\text { TestScr }}$ _MA = 731.89 - 0.788×PctLch_{MA
(0.95)(0.045)
n = 220, R}^{2 = 0.61, SER = 9.41}
Numbers in parenthesis are heteroskedasticity-robust standard errors.
a. Calculate a t-statistic to test whether or not the two slope coefficients are the same.
b. Your textbook compares the slope coefficients for the student-teacher ratio instead of the percent eligible for a free lunch. The authors remark: "Because the two standardized tests are different, the coefficients themselves cannot be compared directly: One point on the Massachusetts test is not the same as one point on the California test." What solution do they suggest?

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Definitions:

Cross-Sequential Design

is a research method that combines both longitudinal and cross-sectional designs to study changes over time in different cohorts.

Cognitive Development

The development of thinking, problem solving, and memory.

Longitudinal Design

A research strategy that involves following the same group of individuals over an extended period to observe changes or developments.

Cross-Sectional Design

A research method used to examine a population at a single point in time, allowing for the comparison of different population groups at the same time.