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 20 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. Complete parts (a) through (g) below. Efficiency Total Risk-Based RDA (%) Ratio (%) Capital (%) 1.22 46.88 12.90 0.78 69.82 11.35 0.94 63.74 18.40 1.62 28.26 20.28 1.06 57.09 14.62 1.01 59.70 18.69 0.73 61.73 12.50 0.60 63.31 13.94 1.11 69.82 17.50 0.79 65.87 12.80 0.96 49.12 12.91 0.94 62.48 15.58 1.27 46.87 26.72 1.07 54.72 16.02 0.92 61.80 17.72 0.96 51.04 17.44 1.74 72.02 22.27 1.17 57.04 14.81 0.96 73.28 14.90 1.55 71.04 14.30 a. State the multiple regression equation. Let X₁ represent the efficiency ratio (%) and let X2; represent the total risk-based capital (%). 1i (Round the constant to two decimal places as needed. Round the coefficients to four decimal places as needed.) b. Interpret the meaning of the slopes, b₁ and b₂, in this problem. Choose the correct answer below. A. For each increase of 1% in the RDA, the Efficiency Ratio is estimated to increase by b₁% and the Risk-Based Capital is estimated to increase by b₂%. OB. For a given Risk-Based Capital, for each increase of 1% in the Efficiency Ratio, the RDA is estimated to increase by b₁ %. For a given Efficiency Ratio, for each increase of 1% in Risk-Based Capital, the RDA is estimated to increase by b₂%. OC. For each increase of 1% in both the Efficiency Ratio and the Risk-Based Capital, the RDA is estimated to increase by (b₁ +b2) %. OD. The slopes, b₁ and b₂, cannot be interpreted individually. c. Predict the mean ROA when the efficiency ratio is 60% and the total risk-based capital is 10%. %☐ (Round to two decimal places as needed.) d. Construct a 95% confidence interval estimate for the mean ROA when the efficiency ratio is 60% and the total risk-based capital is 10%. ☐ % ≤ Hy 1x 50% (Round to one decimal place as needed.) e. Construct a 95% prediction interval for the ROA of a particular community bank when the efficiency ratio is 60% and the total risk-based capital is 10%. ☐ % ≤Y x ≤ % (Round to one decimal place as needed.) f. Explain why the interval in (d) is narrower than the interval in (e). Choose the correct answer below. A. The interval in (e) is narrower because it is estimating the mean value, whereas the prediction interval is estimating an individual value. O B. The interval in (e) is narrower because it is estimating an individual value, whereas the prediction interval is estimating a mean value. O C. The interval in part (e) is narrower because it uses multiplied variables, whereas the prediction interval in part (f) is only measuring a single variable. OD. The interval in part (e) is not narrower than the interval in (f). g. What conclusions can you reach concerning ROA? OA. The model uses both the efficiency ratio and the total risk-based capital to predict ROA. OB. The model uses the efficiency ratio or the total risk-based capital to predict ROA, but not both. OC. The model uses the efficiency ratio to predict ROA. The total risk-based capital only affects the efficiency ratio directly. OD. The model uses the total risk-based capital to predict ROA. The efficiency ratio only affects the total risk-based capital directly.