11.70 Several states now require all high school seniors to pass an achievement test before they can graduate. On the test, the seniors must demonstrate their familiarity with basic verbal and mathematical skills. Suppose the educational testing company that creates and administers these exams wants to model the score Y on one of their exams as a function of the student’s IQ and socioeconomic status (SES). The SES is a categorical (or qualitative) variable with three levels: low, medium, and high.

1 if SES is medium X2 X3 10 if SES is low or high 1 if SES is high = 10 if SES is low or medium Data were collected for a random sample of 60 seniors who had taken the test, and the model was fit to these data, with the results shown in the SAS printout in Figure 11.63.
a Identify the least-squares equation.
b Interpret the value of and test to determine whether the data provide sufficient evidence to indicate that this model is useful for predicting achievement test scores.
c Sketch the relationship between predicted achievement test score and IQ for the three levels of SES. [Note: Three graphs of yN versus x1 R2 E(Y) = b0 + b1x1 + b2x2 + b3x3 must be drawn: the first for the low-SES model , the second for the medium-SES model , and the third for the high-SES model . Note that increase in predicted achievement test score per unit increase in IQ is the same for all three levels of SES; that is, all three lines are parallel.]