Success in college. Colleges use SAT scores in the

Chapter 8, Problem 38

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Success in college. Colleges use SAT scores in the ad-missions process because they believe these scores pro-vide some insight into how a high school student willperform at the college level. Suppose the entering fresh-men at a certain college have mean combined SAT Scoresof 1833, with a standard deviation of 123. In the first se-mester these students attained a mean GPA of 2.66, with astandard deviation of 0.56. A scatterplot showed the asso-ciation to be reasonably linear, and the correlation be-tween SAT score and GPA was 0.47.a) Write the equation of the regression line.b) Explain what the y-intercept of the regression lineindicates.c) Interpret the slope of the regression line.d) Predict the GPA of a freshman who scored a combined2100.TBOCK_C08_0321570448 pp3.qxd 11/21/08 5:01 PM Page 196e) Based upon these statistics, how effective do you thinkSAT scores would be in predicting academic successduring the first semester of the freshman year at thiscollege? Explain.f) As a student, would you rather have a positive or anegative residual in this context? Explain.