Answer Happy

8. [18 marks] Suppose we are interested in determining if there is a linear relationship between Y, a student's CMAV (cumulative major average) after three terms and X, a student's high school Calculus grade (which has been rescaled on a 1 to 10 scale). A random sample of 20 students yielded the following summary statistics: x = 7.85, y = 80.35 Sxy = 188.05, Sxx = 260.55, Syy = 348.06, a. [3] Using the summary information given, determine the equation for the least squares line of best fit. = b. [2] Interpret the estimated slope coefficient and intercept terms, found in part a., in the context of the question. c. [2] What is the residual sample variance, S?? d. [5] Test Ho: B1 = 0 by calculating a p-value. Be sure to show all steps clearly and show all relevant work in your solution (as noted in question 1). e. [3] Construct a 90% confidence interval for the mean CMAV when x = 8. f. [3] Construct a 95% prediction interval for Y when x = 7.5.