In the article “Statistical Fallacies in Sports” (Chance, Vol. 19, No. 4, pp. 50–56), S. Berry discussed, among other things, the relation between scores for the first and second rounds of the 2006 Masters golf tournament. You will find those scores on the WeissStats CD. Take these scores to be a sample of those of all Masters golf tournaments.
• For the estimations and predictions, use a first-round score of 72.
• For the correlation test, decide whether first-round and second-round scores are positively linearly correlated.
a. determine the sample regression equation.
b. find and interpret the standard error of the estimate.
c. decide, at the 5% significance level, whether the data provide sufficient evidence to conclude that the predictor variable is useful for predicting the response variable.
d. determine and interpret a point estimate for the conditional mean of the response variable corresponding to the specified value of the predictor variable.
e. find and interpret a 95% confidence interval for the conditional mean of the response variable corresponding to the specified value of the predictor variable.
f. determine and interpret the predicted value of the response variable corresponding to the specified value of the predictor variable.
g. find and interpret a 95% prediction interval for the value of the response variable corresponding to the specified value of the predictor variable.
h. compare and discuss the differences between the confidence interval that you obtained in part (e) and the prediction interval that you obtained in part (g).
i. perform and interpret the required correlation t-test at the 5% significance level.
j. perform a residual analysis to decide whether making the preceding inferences is reasonable. Explain your answer.