An analyst has the objective of predicting the return on equity (ROE) of banks. The analyst begins by using the leverage ratio, a financial measurement that looks at how much capital comes in the form of debt. A sample of 25 American banks is selected and stored in AmericanBanks . (Data extracted from K. Badenhausen, "Full List: America's Best and Worst Banks 2015," onforb.es/1Cvw05F.)

a. Construct a scatter plot and, assuming a linear relationship, use the least-squares method to compute the regression coefficients b0 and b1.

b. Interpret the meaning of the Y intercept, b0, and the slope, b1, in this problem.

c. Use the prediction line developed in (a) to predict the mean ROE for a bank with a leverage ratio of 9%.

d. Determine the coefficient of determination, r2, and interpret its meaning in this problem.

e. Perform a residual analysis on your results and evaluate the regression assumptions.

f. At the 0.05 level of significance, is there evidence of a linear relationship between leverage ratio and ROE?

g. Construct a 95% confidence interval estimate of the mean ROE of banks with a leverage ratio of 9% and a 95% prediction interval of the ROE for a particular bank with a leverage ratio of 9%.

h. Construct a 95% confidence interval estimate of the population slope.

i. What conclusions can you reach concerning the relationship between leverage ratio and ROE?