SOLUTION: 12.50 In the following regression, X = total assets ($ billions), Y = total revenue ($ billions), and n = 64 large banks. (a) Write the fittedregression equation. (b) State the deg
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Question 178531This question is from textbook
: 12.50 In the following regression, X = total assets ($ billions), Y = total revenue ($ billions), and n = 64 large banks. (a) Write the fittedregression 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 α= .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 theslope. (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 3,260.0981 1 3,260.0981 66.97 1.90E-
Residual 3,018.3339 62 48.6828
Total 6,278.4320 63
Regression output confidence interval
variables coefficients std. error t (df =62) p-value 95% lower 95% upper
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
This question is from textbook
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
In the following regression, X = total assets ($ billions), Y = total revenue ($ billions), and n = 64 large banks.
(a) Write the fitted regression equation.
Y = 6.5763 + 0.0452X
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(b) State the degrees of freedom for a two- tailed test for zero slope, and use Appendix D to find the critical value at α= .05.
df = 62 ; crit. value = 1.96 (I do not have the same D-chart you may have)
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(c) What is your conclusion about the slope?
Since p-value = 1.9E-11, reject hypothesis that the slope is zero
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(d) Interpret the 95 percent confidence limits for the slope.
With 95% confidence we can say the slope is between 0.0342 and 0.0563
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(e) Verify that F = t2 for the slope.
66.97 = 8.8183^2
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(f) In your own words, describe the fit of this regression.
Since R^2 is 51.9% the fit is good.
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R2 0.519
Std. Error 6.977
n 64
-------------------------
ANOVA table
Source........ SS.... df MS......... F.. p-value
Regression 3,260.0981 1 3,260.0981 66.97 1.90E-
Residual.. 3,018.3339 62 48.6828
Total..... 6,278.4320 63
-----------------------------------
Regression output confidence interval
variables coefficients std. error t (df =62) 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.....1.90E-11.. 0.0342.... 0.0563
=========================================================================
Cheers,
Stan H.
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