An analyst has the objective of predicting the return on average tangible common equity (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 .

Source: Data extracted from K. Badenhausen, “America’s Best Banks 2017,” available at bit.ly/2tpw1Er.

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 ROATCE for a bank with an efficiency ratio of 60%.

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 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?