In the following regression, X = weekly pay, Y = income tax withheld…2. In the following regression, X = total assets

  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 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 0.370 Std. Error 286.793 n 15 ANOVA table Source SS df MS F p-value Regression 628,298.2 1 628,298.2 7.64 .0161 Residual 1,069,251.8 13 82,250.1 Total 1,697,550.0 14 Regression output confidence interval variables coefficients std. error t (df = 13) p-value 95% lower 95% upper Intercept 1,743.57 288.82 6.037 .0000 1,119.61 2,367.53 Slope -1.2163 0.4401 -2.764 .0161 -2.1671 -0.2656
  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 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 0.519 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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