Question 138776This question is from textbook APPLIED STATISTICS IN BUSINESS AND ECONOMICS
: 12.48 In the following regression, X = weekly pay, Y = income tax withheld, and n = 35 McDonald’s
employees. (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 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 0.202
Std. Error 6.816
n 35
ANOVA table
Source SS df MS F p-value
Regression 387.6959 1 387.6959 8.35 .0068
Residual 1,533.0614 33 46.4564
Total 1,920.7573 34
Regression output confidence interval
variables coefficients std. error t (df = 33) p-value 95% lower 95% upper
Intercept 30.7963 6.4078 4.806 .0000 17.7595 43.8331
Slope 0.0343 0.0119 2.889 .0068 0.0101 0.0584
This question is from textbook APPLIED STATISTICS IN BUSINESS AND ECONOMICS
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! In the following regression,
X = weekly pay, Y = income tax withheld, and n = 35 McDonald’s employees.
(a) Write the fitted regression equation.
Income Tax = 0.0343 (weekly pay) +30.7963
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(b) State the degrees of freedom for a two tailed for zero slope, and use Appendix D to find the critical value at α = .05.
df=33 ; t = 1.96
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(c) What is your conclusion about the slope?
Since p-value is less than 5% Reject Ho that the correlation is zero.
Accept the slope value of 0.0343
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(d) Interpret the 95 percent confidence limits for the slope.
With 95% confidence we can state that the slope is between 0.0101 and 0.0584
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(e) Verify that F = t2 for the slope.
8.35 = 2.889^2
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(f) In your own words, describe the fit of this regression.
Since R^2 is only 0.202 only 20.2% of the correlation between
the variables is explained by the regression equation.
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Cheers,
Stan H.
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R2 0.202 Std. Error 6.816 n 35
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ANOVA table
Source....... SS... df MS F p-value
Regression 387.6959 1 387.6959 8.35 .0068
Residual 1,533.0614 33 46.4564
Total 1, 920.7573 34
Regression output confidence interval
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variables coefficients std. error t (df = 33) p-value 95% lower 95% upper
Intercept 30.7963 ........6.4078... 4.806 .0000 17.7595 43.8331
Slope 0.0343 ........0.0119... 2.889....... .0068..... 0.0101 0.0584
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