```Question 140333
In the following regression, X = weekly pay, Y = income tax withheld, and n = 35 McDonald’s employees.
(a) Write the fitted regression equation.
y = 30.7963 + 0.0343X
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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 &#945; = .05.
df= 33 ; critical value = 1.692
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Since 2.889 is greater than 1.692, Reject Ho.  The slope is not 0.
There is a linear relation between X and Y.
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(d) Interpret the 95 percent confidence limits for the slope.
We can be 95% confidence 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
(f) In your own words, describe the fit of this regression.
Based on p-values both the intercept and the slope are good.
Income tax withheld increases by 0.0343 for every increase of one
dollar of weekly pay.
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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
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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

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Cheers,
Stan H.

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