SOLUTION: 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 fo

Question 137309: 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---coeffic.--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=33; 1.645
----------------------------
(c) What is your conclusion about the slope?
0.0343 is in the 95% confidence interval
---------------
(d) Interpret the 95 percent confidence limits for the slope.
With 95% condifidence we can say the slope is between the lower and the upper limit.
----------------
(e) Verify that F = t2 for the slope.
8.35 = 2.889^2
----------------------
(f) In your own words, describe the fit of this regression.
Since R^2 = 0.202 only 20% of the variation between X and y is explained
by the regression equation. R = sqrt(R^2) = 0.449 shows the Regression
equation weak as a linear predictor.
------------------------
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---coeffic.--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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