There has been a lot of discussion regarding the relationship between Scholastic Aptitude Test (SAT) scores and test-takers’ family income (New York Times, August 27,

2009). It is generally believed that the wealthier a student’s family, the higher the SAT score. Another commonly used predictor for SAT scores is the student’s grade point average (GPA). Consider the following data collected on 24 students. The entire data set, labeled SAT, can be found on the text website.

a. Estimate three models:

(i) SAT = β0 + β0Income +
,

(ii) SAT = β0 + β0GPA +
, and

(iii) SAT = β0 + β0Income + β2GPA +
.

b. Use goodness-of-it measures to select the best-fitting model.

c. Predict SAT given the mean value of the explanatory variable(s).

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SAT Income GPA 1651 47,000 2.79 1581 34,000 2.97 1940 113,000 3.96