d. The 95% confidence interval estimate for the mean ROA when the efficiency ratio is 50% and the total risk-based capital is 20% is (0.945, 1.035).
e. The 95% prediction interval for the ROA of a particular community bank when the efficiency ratio is 50 and the total risk-based capital is 20% is (0.845, 1.135).
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.
RDA Efficiency Ratio Total RiskBased Capital
0.82 50.93 13.39
0.81 69.59 13.27
2.68 79.68 12.58
1.38 62.70 17.39
1.07 73.36 23.15
0.91 65.00 14.70
0.68 72.80 14.14
0.97 63.30 24.93
0.88 62.28 20.57
0.92 65.20 18.80
1.06 57.09 14.62
1.50 54.70 26.60
0.54 74.69 15.33
1.07 65.84 14.47
0.96 62.11 13.89
0.71 68.34 11.10
0.90 69.94 13.09
1.07 70.15 16.61
1.22 46.88 12.90
0.60 72.79 13.88
a. State the multiple regression equation. Let Upper X Subscript 1 I represent the efficiency ratio(%) and let Upper X Subscript 2 i
represent the total risk-based capital(%).
Answer: Y=.54+.0050X1i+.0102X2i
b. Interpret the meaning of the slopes, b 1 and b 2,in this problem. Choose the correct answer below.
Answer:
For a given Risk-Based Capital, for each increase of 1% in the Efficiency Ratio, the RDA is estimated to increase by b 1. For a given Efficiency Ratio, for each increase Risk-Based Capital, the RDA is estimated to increase by b 2
c. Predict the mean ROA when the efficiency ratio is 50% and the total risk-based capital is 20%
Answer: .99%
(This is where I am stuck)
d. Construct a 95% confidence interval estimate for the mean ROA when the efficiency ratio is 50% and the total risk-based capital is 20%.
e. Construct a 95% prediction interval for the ROA of a particular community bank when the efficiency ratio is 50 and the total risk-based capital is 20%.
I can't seem to answer d and e.
1 answer