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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.

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#### Solution Summary

The solution provides step by step method for the calculation of regression analysis. The solution also provides conclusion about the slope and interpretation of the 95 percent confidence limits for the slope. Formula for the calculation and Interpretations of the results are also included.

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