Chapter 14, Problem 4PS

Profitability remains a challenge for banks and thrifts with less than $\text{\$2}$ billion of assets. The business problem facing a bank analyst relates to the factors that affect return on average assets (ROAA), an indicator of how profitable a company is relative to its total assets. Data collected on a sample of 199 community banks and stored in CommunityBanks include the ROAA $\left(\%\right)$ , the efficiency ratio capital $\left(\%\right)$ as a measure of capital adequacy.

a. State the multiple regression equation.

b. Interpret the meaning of the slopes, $b_1$ and $b_2,$ in this problem.

c. Predict the mean ROAA when the efficiency ratio is $60\%$ and the risk-based capital is $15\%$ .

d. construct a $95\%$ confidence interval estimate for the mean ROAA when the efficiency ratio is $60\%$ and the total risk-based capital is $15\%.$

e. Construct a $95\%$ prediction interval for ROAA for a particular community bank when the efficacy ratio is $60\%$ and the total risk-based capital is $15\%.$

f. Explain why the interval in (d) is narrower than the interval in (e).

g. What conclusions can you reach concerning ROAA?