SAT Scores and Exam Completion Times DS 12.12.1 gives the

Chapter 12, Problem 12.12.1

(choose chapter or problem)

SAT Scores and Exam Completion Times DS 12.12.1 gives the times taken by a class of n =14 students to nish a math test together with the math SAT scores of the students. Perform the following linear regression analysis with time as the dependent variable and SAT as the explanatory variable. (a) Calculate the point estimates 0, 1, and 2. (b) Calculate the sample correlation coefcient r. (c) Calculate a two-sided 95% condence interval for the slope parameter 1. (d) Is there any evidence that the time taken to nish the test depends upon the SAT score? (e) How does the predicted time taken to nish the test change as the SAT score increases by 10 points? (f) What is the predicted time for a student with an SAT score of 550? Construct a two-sided 95% condence interval for the expected time for a student with an SAT score of 550. Construct a two-sided 95% prediction interval for the time taken by a student with an SAT score of 550. (g) Plot the residuals against the SAT scores. Do there appear to be any problems with the regression analysis? Are there any points that are obvious outliers? Obtain a normal scores plot of the residuals.