Question 183491: 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 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 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 3,260.0981 1 3,260.0981 66.97 1.90E-11
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
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.
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(a) Write the fitted regression equation.
Y = 0.0452X + 6.5763
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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: t = 2.00
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(c) What is your conclusion about the slope?
The p-value is less than 5% so reject Ho 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 = 8.183^2
(f) In your own words, describe the fit of this regression.
The p-value for the Regression of 1.90E-11 is strong evidence that
X and Y are strongly related.
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Cheers,
Stan H.
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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-11
Residual...3,018.3339.. 62.... 48.6828
Total..... 6,278.4320.. 63
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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
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