A finance executive would like to determine if a relationship exists between the current earnings per share (EPS) of a bank and the following independent variables:
• Total assets ($ billions)
• Previous period’s EPS
• Previous period’s return on average assets (ROAA)
• Previous period’s return on average equity (ROAE)
ROAA measures how effectively assets are utilized, and ROAE measures a firm’s profitability. The Excel file Bank EPS.xlsx contains these data for several banks.
a. Construct a regression model using all four independent variables.
b. Interpret the meaning of the regression coefficients.
c. Predict the average EPS for a bank that has $ 2.6 billion in total assets and the following results from the previous period: ROAA = 1.5%, EPS = $ 1.80, ROAE = 8%.
d. Construct a 95% confidence interval for the average EPS for a bank described in part c. Interpret the meaning of the interval.
e. Construct a 95% prediction interval for the EPS for a bank described in part c. Interpret the meaning of the interval.