PEARSON CO Mathematics with Applications In the Management, Natural, and Social Sciences 13th edition
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IQ and grades Exercise 3 included the plot shown below of school grade point average (GPA) against IQ test score for 78 seventh-grade students. (GPA was recorded on a 12-point scale with A+=12, A=11, A-=10, B+=9, ..., D-=1 and F=0. Calculation shows that the mean and standard deviation of the IQ scores are $overline{x}=108.9$ and $s_{x}=13.17$. For the GPAs, these values are $overline{y}=7.447$ and $s_{y}=2.10$. The correlation between IQ and GPA is $r=0.6337$. (a) Find the equation of the least-squares line for predicting GPA from IQ. Show your work. (b) What percent of the observed variation in these students' GPAs can be explained by the linear relationship between GPA and IQ? (c) One student has an IQ of 103 but a very low GPA of 0.53. Find and interpret the residual for this student.
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