# Question

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?

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?

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