Question

ROA   Efficiency Ratio   Total RiskBased Capital
1.02   66.32   13.15
0.73   61.73   12.50
0.97   55.14   15.44
1.40   67.44   18.00
3.75   76.32   17.57
0.63   80.33   15.69
1.35   58.07   14.80
1.32   57.05   13.16
0.87   58.22   14.35
1.17   52.55   13.94
4.41   86.31   10.96
1.75   55.68   17.42
1.12   62.30   17.88
1.34   54.66   14.76
1.55   64.99   13.30
1.07   68.31   18.28
1.14   71.41   15.29
1.14   74.06   14.70
1.74   72.02   22.27
0.96   59.25   13.21

PLEASE USE THE NUMBERS FROM PART A. Please show ALL excel formulas in a step by step process.

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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 (9 ), 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. Click the icon to view the data table. a. State the multiple regression equation Let X1i represent the efficiency ratio (%) and let X2i represent the total risk-based capital (%). (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. Regression coefficients in a multiple regression are called net regression coefficients; they estimate the mean change in Y per unit change in a particular x, holding constant the effect of the other X-variables. Use this information to interpret the meaning of the slopes b0.0032 and b20.0151 in this problem. C. Predict the mean ROA when the efficiency ratio is 55% and the total risk-based capital is 30%. You can use the multiple regression equation to predict values of the dependent variable. Substitute the given values of the X-variables into the multiple regression equation and simplify to find the prediction for Y. First, determine the values of X1i and X2i d. Construct a 95% confidence interval estimate for the mean ROA when the efficiency ratio is 55% and the total risk-based capital is 30%. set the values of the new observations to 55% for efficiency ratio and 30% for total risk-based capital. Use technology to determine the 95% confidence interval based on these new observations, rounding to one decimal place. Y 1 X s 3.2% -0.7% e. Construct a 95% prediction interval for the ROA of a particular community bank when the efficiency ratio is 55% and the total risk-based capital is 30%. f. Explain why the interval in (d) is narrower than the interval in (e). A confidence interval estimates a mean value and a prediction interval predicts an individual value. Use this information to determine why the interval in part (e) is narrower than the interval in part (f). g. What conclusions can you reach concerning ROA? Use the interpretation of each variable in the model to determine how the regression model predicts the ROA and what effect (if any) each variable has on the model

Answer 1

a) the equation $\hat{y} =$

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