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Statistics - Regression

In the following regression, X = weekly pay, Y = income tax withheld, and n = 35 McDonald's employees. (a) Write the regression equation. (b) Is the regression model significant? . (c) What is your conclusion about the slope? (d) In your own words, describe the fit of this regression. How well does the independent variable explain the dependent variable? ...

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Week 5 E-text Assignments

Be sure to answer the question asked in each problem, and explain why, with reference to your output. You need to interpret the results of the first three questions. On the fourth problem, please follow the instructions in that problem.

12.48 In the following regression, X = weekly pay, Y = income tax withheld, and n = 35 McDonald's employees. (a) Write the regression equation. (b) Is the regression model significant? . (c) What is your conclusion about the slope? (d) In your own words, describe the fit of this regression. How well does the independent variable explain the dependent variable?

(a) y = 0.0343x + 30.7963
(b) Since the p- values are less than 0.05, both the variables (x = weekly pay) and (y = income tax withheld) have a significant influence in the regression.
(c) Dof = 35 - 1 = 34, critical value of t corresponding to 34 dof at  = 0.05 (two-tailed) is 2.032.
Since the t- value for the slope (2.889) is greater than the critical value (2.032), the null hypothesis is rejected. Therefore, the population 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.

12.50 In the following regression, X = total assets ($ billions), Y = total revenue ($ billions), and n = 64 large banks. a) Write the regression equation. (b) Is the regression model significant? . (c) What is your conclusion about the slope? (d) In your own words, describe ...

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