In the following regression, X = weekly pay, Y = income tax withheld, and n = 35
ID: 2959003 • Letter: I
Question
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 two- tailed test for zero slope, and use Appendix D to find the critical value at a = .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 0.0068
Residual 1533.0614 33 46.4564
TOTAL 1920.7573 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 0.0000 17.7595 43.8331
Slope 0.0343 0.0119 2.889 0.0068 0.0101 0.0584
Explanation / Answer
(a) Write the fitted regression equation. y=30.7963+0.0343x ------------------------------------------------------------------------- (b) (b) State the degrees of freedom for a two- tailed test for zero slope, and use Appendix D to find the critical value at a = .05. df=35-2=33 critical value = |t(0.025, df=33)|=2.03 (check student t table) --------------------------------------------------------------------------------- (c) What is your conclusion about the slope? The p-value is 0.0068< 0.025, we reject Ho. -------------------------------------------------------------------------------------- (d) Interpret the 95 percent confidence limits for the slope. We have 95% confidence that the slope of the regression line is between 0.0101 and 0.0584. ------------------------------------------------------------------------------------------------ (e) Verify that F = t2 for the slope. F=8.35 t^2 =2.889^2=8.346 So F=t^2 -------------------------------------------------------------------------------------------------------- (f) In your own words, describe the fit of this regression. Good of fittness.Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.