Posted: February 6th, 2017
Business Econ Homework Help, LynetteAnn Show all of your work in each question. In parts (d), (e), and (g) make sure to set up your null and alternative hypotheses and write your conclusions. Also, please round your numbers to 2 decimal points. Write legibly and neatly. You can use p-value approach or critical-value approach in writing the conclusions of your hypotheses. A large firm employing tens of thousands of workers has been accused of discriminating against its female managers. The accusation is based on a random sample of 40 managers. The mean annual salary of the 20 female managers is $79,500 while the mean annual salary of the 20 male managers is $103,250. The president of the firm points out that the company has a strict policy of equal pay for equal work and that the difference may be due to other variables. Accordingly, he found and recorded the number of years of education and the number of years of experience for each of the 40 managers in the sample. Also recorded are the salary and gender (1 = female and 0 = male). The data are in attached Excel document. The president wanted to know whether a regression analysis would shed some light on the issue. Use Microsoft Excel to run a regression of annual salary on years of education, years of experience, and gender and round up numbers in your regression results to 2 decimal points. Please use the level of significance of 10 percent (i.e. α = 0.10). On the basis of your Excel results answer following questions. (1 pts.) a. Write down the estimated regression equation.
(4.5 pts.) b. Clearly interpret the numerical values of estimated coefficients of our explanatory variables which are years of education, years of experience and gender.
( 1 pts.) c. Interpret the numerical value of adjusted R-square.
(4.5 pts.) d. At 10 percent level of significance, determine whether each explanatory variable makes a contribution to the regression model. Show your work.
(2 pts.) e. At 10 percent level of significance, determine whether there is a significant relationship between annual salary on the one hand and the three explanatory variables on the other hand. Show your work.
(1 pt.) f. Predict the annual salary of a female manager with 15 years of experience and 20 years of education. Show your work.
(6 pts.) g. Now, drop the education and gender variables from the full model and run a regression of annual salary on the years of experience. Using the hypothesis testing procedure reviewed in chapter 16(section 16.2), test the null hypothesis that managers years of education and gender add no explanatory power to the model. Here you compare SSE of your full model (model with all independent variables) with the SSE of reduced model(model with years of experience as the only Independent variable) and conduct a hypothesis test to decide which model has statistically lower SSE and thus would be preferred model. Please make sure to specify your null and alternative hypothesis in this part and conduct your test at 10% level of significance. Write down the conclusion of your hypothesis test.
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