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# Regression Analysis

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Instructions: Choose one or more of the data sets A-I below, or as assigned by your instructor. Choose the dependent variable (the response variable to be "explained") and the independent variable (the predictor or explanatory variable) as you judge appropriate. Use a spreadsheet or a statistical package (e.g., MegaStat or MINITAB) to obtain the bivariate regression and required graphs. Write your answers to exercises 12.28 through 12.43 (or those assigned by your instructor) in a concise report, labeling your answers to each question. Insert tables and graphs in your report as appropriate. You may work with a partner if your instructor allows it.

12.50 In the following regression, X = total assets (\$ billions), Y = total revenue (\$ billions), and n = 64 large banks. (a) Write the fitted regression equation. (b) State the degrees of freedom for a twotailed test for zero slope, and use Appendix D to find the critical value at &#945; = .05. (c) What is your conclusion about the slope? (d) Interpret the 95 percent confidence limits for the slope. (e) Verify that F = t2 for the slope. (f) In your own words, describe the fit of this regression.

R² 0.519
Std. Error 6.977
n 64

ANOVA table
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Source SS df MS F p-value
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Regression 3,260.0981 1 3,260.0981 66.97 1.90E-11
Residual 3,018.3339 62 48.6828
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Total 6,278.4320 63
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Regression output confidence interval
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Variables coefficients std. error t (df = 62) p-value 95% lower 95% upper
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Intercept 6.5763 1.9254 3.416 . 0011 2.7275 10.4252
X1 0.0452 0.0055 8.183 1.90E-11 0.0342 0.0563

(a) Write the fitted regression equation.
(b) State the degrees of freedom for a twotailed test for zero slope, and use Appendix D to find the critical value at &#945; = .05. (c) What is your conclusion about the slope?
(d) Interpret the 95 percent confidence limits for the slope.
(e) Verify that F = t2 for the slope.
(f) In your own words, describe the fit of this regression.