Week 5 - 12.50 In the following regression, X = total...

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week 5 E-Text . 12.48 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 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 (a) y = 0.0343x + 30.7963 (b.) Degrees of freedom = 35 – 1 = 34, critical value of t corresponding to 34 degrees of freedom at α = 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 null hypothesis is rejected. Therefore, the slope is different from zero. (d) R^2 = 0.202 is very low. Only 20.2% of the variation in the dependent variable is explained by the variation in the independent variables. (e) t^2 = 2.889^2 = 8.346. Thus, F = t^2.
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Unformatted text preview: 12.50 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. (a) y = 0.0452x + 6.5763 (b) Degrees of freedom = 64 1 = 63, critical value of t corresponding to 63 degrees of freedom at = 0.05 (two-tailed) is 1.9983. (c) Since the t- value for the slope (8.183) is greater than the critical value (1.9983), the null hypothesis is rejected. Therefore, the slope is different from zero. (d) We are 95% confident that the true population slope lies between 0.0342 and 0.0563. (e) t^2 = 8.183^2 = 66.97 = F=t^2...
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