Chapter 13, Problem 78PS

An analyst has the objective of predicting the return on average tangible common (ROATCE) of banks. The analyst begins by using efficiency ratio, a measure of a bank’s ability to turn resources into revenue. A sample of 100 American banks is selected and stored in AmericanBanks.

a. Construct a scatter plot and, assuming a linear relationship, use the least-squares method to compute the regression coefficients $b_0$ and $b_1.$

b. Interpret the meaning of $Y$ Intercept, $b_0,$ and the slope, $b_1,$ in this problem.

c. Use the prediction line developed in (a) to predict the mean ROATCE for a bank with an efficiency ratio of $60\%.$

d. Determine the coefficient of determination, $r^2,$ 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 efficiency ratio and ROATCE?

g. Construct a $95\%$ confidence interval estimate of the mean ROATCE of banks with an efficiency ratio of $60\%$ and a $95\%$ prediction interval of the ROATCE for a particular bank with an efficiency ratio of $60\%.$

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

i. What conclusions can you reach concerning the relationship between efficiency ratio and ROATCE?