# Statistics: Understanding Regression Analyses

Question 1: 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 £ = .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

Question 2: In the following regression, X = total assets ($ billions), Y = total revenue ($ billions), and n = 64 large banks.

(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 £ = .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 0.519

Std. Error 6.977

n 64

ANOVA table

Source SS df MS F p-value

Regression 3,260.0981 1 3,260.0981 66.97 1.90E-11

Residual 3,018.3339 62 48.6828

Total 6,278.4320 63

Regression output confidence interval

variables coefficients std. error t (df =62) p-value 95% lower 95% upper

Intercept 6.5763 1.9254 3.416 .0011 2.7275 10.4252

X1 0.0452 0.0055 8.183 1.90E-11 0.0342 0.0563

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#### Solution Preview

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Question 1:

(a) y = 0.0343x + 30.7963

(b) Degrees of freedom (Dof) = 35 - 1 = 34, critical value of t corresponding to 34 dof at alpha = 0.05 (two-tailed) is 2.032.

(c) Since the t- value for the slope (2.889) is greater than the critical value (2.032), the ...

#### Solution Summary

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