Figure 14.9 (page 329) plots the average SAT Mathematics score of each state’s high school seniors against the percentage of each state’s seniors who took the exam. In addition to two clusters, the plot shows an overall roughly straight-line pattern. The least-squares regression line for predicting average SAT Math score from percentage taking is average
Math SAT score = 588.4 − (1.228 × percentage taking)
(a) What does the slope b = −1.228 tell us about the relationship between these variables?
(b) In New York State, the percentage of high school seniors who took the SAT was 76%. Predict their average score. (The actual average score in New York was 502.)
(c) On page 345, we mention that using least-squares regression to do prediction outside the range of available data is risky. For what range of data is it reasonable to use the least-squares regression line for predicting average SAT Math score from percentage taking?
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The StatBoards video Computing a Correlation describes how to compute the correlation in thecontext of an example exploring the relationship between the cost of attending a baseball game andthe team’s performance.State average SAT Math score62560057555052550047545020406080100Percent of seniors taking the SATFigure 14.9 Scatterplot of average SAT Mathematics score for each state against the proportion ofthe state’s high school seniors who took the SAT.