Recall from Chapter 1 (refer to page 30) that the Focus database and Focus sample contain information on the undergraduate students at the University of Wisconsin - Eau Claire (UWEC). Now would be a good time for you to review the discussion about these data sets. Open the Focus sample worksheet (FocusSample) in the technology of your choice and do the following.
a. Perform a residual analysis to decide whether considering the assumptions for regression inferences met by the variables high school percentile and cumulative GPA appears reasonable.
b. With high school percentile as the predictor variable and cumulative GPA as the response variable, determine and interpret the standard error of the estimate.
c. At the 5% significance level, do the data provide sufficient evidence to conclude that high school percentile is useful for predicting cumulative GPA of UWEC undergraduates?
d. Determine a point estimate for the mean cumulative GPA of all UWEC undergraduates who had high school percentiles of 74.
e. Find a 95% confidence interval for the mean cumulative GPA of all UWEC undergraduates who had high school percentiles of 74.
f. Determine the predicted cumulative GPA of a UWEC undergraduate who had a high school percentile of 74.
g. Find a 95% prediction interval for the cumulative GPA of a UWEC undergraduate who had a high school percentile of 74.
h. At the 5% significance level, do the data provide sufficient evidence to conclude that high school percentile and cumulative GPA are positively linearly correlated?