12.48 In the following regression, x=wkly pay, y=income taxwithheld, and n=35 Mc

Question

12.48 In the following regression, x=wkly pay, y=income taxwithheld, and n=35 McDonalds employees. a) Write the fitted regresion equation b)State the degrees of freedom for a two tailed test for 0slope and use appendix D to find the critical value at aa=.05 c)What is your conclusion about the slope d)Interpret 95% confidence linits for the lope e)Verify that f=t^2 for the slope f) Describe the fit of this regression R2                  0.202 stdError          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               1920.7573   34          RegressionOutput                                                                                               Confidence Interval Variables            Coeffecients            stderror         t(df=33)            p-value   95%lower    95% upper intercept              30.7963                  6.4078            4.806               .0000        17.7595      43.8331 slope                    .0343                     0.0119            2.889               .0068         0.0101         0.0584 12.48 In the following regression, x=wkly pay, y=income taxwithheld, and n=35 McDonalds employees. a) Write the fitted regresion equation b)State the degrees of freedom for a two tailed test for 0slope and use appendix D to find the critical value at aa=.05 c)What is your conclusion about the slope d)Interpret 95% confidence linits for the lope e)Verify that f=t^2 for the slope f) Describe the fit of this regression R2                  0.202 stdError          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               1920.7573   34          RegressionOutput                                                                                               Confidence Interval Variables            Coeffecients            stderror         t(df=33)            p-value   95%lower    95% upper intercept              30.7963                  6.4078            4.806               .0000        17.7595      43.8331 slope                    .0343                     0.0119            2.889               .0068         0.0101         0.0584

Explanation / Answer

b.     DF = 33, t.025 =2.035

c.     t = 2.889 so we will reject thenull hypothesis that the slope is zero.

d.     We are 95% confident that the slopeis contained in the interval .0101 to .0584. This CI does notcontain zero, hence, there is a relationship between the weekly payand the income tax withheld.

e.     (2.889)2 =8.3463

f.     The value of R-squared assigns only20% of the variation in income withholding to the weekly pay. Whilethe F statistic is significant, the fit is only a modestfit.

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