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In the following regression, X = total assets ($ billions), Y = total revenue ($

ID: 2959039 • Letter: I

Question

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 two-tailed test for zero slope, and use Appendix D to find the critical value at a = .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
Source          SS              df    MS             F          p-value
Regression   3260.0981    1    3260.0981  66.97   1.90E-11
Residual       3018.3339   62   48.6828
TOTAL         6278.4320   63

REGRESSION OUTPUT                                              Confidence Interval
Variables   Coefficients  Std. Error  t(df=33)  p-value  95%lower 95%upper
Intercept   6.5763          1.9254      3.416      0.0011   2.7275   10.4252
X1             0.0452          0.0055      8.183     190E-11  0.0342    0.0563

Explanation / Answer

(a) Write the fitted regression equation. Y = 6.5763 + 0.0452 X ------------------------------------------------------------------------------------------------------------- (b) State the degrees of freedom for a two-tailed test for zero slope, and use Appendix D to find the critical value at a = .05. Degrees of freedom = n-2 = 64-2 = 62 Critical value = t(0.05/2 , 62) = 1.9989 (check student t table) --------------------------------------------------------------------------------------------------------------- (c) What is your conclusion about the slope? The t value is 8.183. |t| = 8.183 > 1.9989(critical value). The null hypothesis is rejected. The slope is significantly different from 0. --------------------------------------------------------------------------------------------------------------- (d) Interpret the 95 percent confidence limits for the slope. The 95% confidence interval for the slope is (0.0342, 0.0563). --------------------------------------------------------------------------------------------------------------- (e) Verify that F = t2 for the slope. F = 66.97 t = 8.183 t^2=8.183^2= 66.96149?66.97 So F=t^2 -------------------------------------------------------------------------------------------------------------- (f) In your own words, describe the fit of this regression. The p-value is 1.90E-11 < 0.01. So the F is significant. So regression model is good fit to the data.
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