Profitability remains a challenge for banks and thrifts with less than $ 2 billion of assets. The business problem facing a bank analyst relates to the factors that affect ­return on assets (ROA), an indicator of how profitable a company is relative to its total assets. Data collected from a sample of 200 community banks and stored in Community Banks include the ROA (%), the efficiency ratio (%), as a measure of bank productivity (the lower the efficiency ratio, the better), and total risk based capital (%), as a measure of capital adequacy. (Data extracted from “ Rising Tide: The Top 200 Community Banks,” bit. ly/ 1ldN8gC.)
a. State the multiple regression equation.
b. Interpret the meaning of the slopes, b1 and b2, in this problem.
c. Predict the mean ROA when the efficiency ratio is 60% and the total risk based capital is 15%.
d. Construct a 95% confidence interval estimate for the mean ROA when the efficiency ratio is 60% and the total risk based capital is 15%.
e. Construct a 95% prediction interval for the ROA for a particular community bank when the efficiency ratio is 60% and the total risk based capital is 15%.
f. E xplain why the interval in (d) is narrower than the interval in (e).
g. What conclusions can you reach concerning ROA?