Question 193344: 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
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. Y 0.0343X + 30.7963
---------------------------
(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 = 34 ; I don't have your D-chart.
(c) What is your conclusion about the slope?
Since the p-value is greater than 5% the slope fail to reject Ho: rho = 0
(d) Interpret the 95 percent confidence limits for the slope.
We are 95% confident the slope is between 17.7595 and 43.8331
(e) Verify that F = t2 for the slope. 8.35 = 2.89^2
(f) In your own words, describe the fit of this regression.
It is not very good as seen in R^2 = 0.202. Only 20% of the
variation in Y is explained by the regression equation.
Cheers,
Stan H.
===============================================================
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
|
|
|
