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.
. 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.
Annual Salary(in $1000.00) |
Education(in years) |
Experience(in years) |
Gender |
130 |
20 |
18 |
0 |
80 |
19 |
16 |
1 |
62 |
18 |
8 |
1 |
176 |
18 |
30 |
0 |
44 |
14 |
9 |
1 |
139 |
16 |
22 |
0 |
165 |
18 |
27 |
0 |
112 |
19 |
20 |
1 |
92 |
16 |
17 |
1 |
84 |
18 |
13 |
1 |
106 |
14 |
17 |
0 |
103 |
22 |
24 |
1 |
98 |
16 |
18 |
0 |
93 |
17 |
14 |
1 |
79 |
16 |
14 |
1 |
92 |
16 |
14 |
0 |
79 |
14 |
16 |
0 |
98 |
20 |
18 |
1 |
111 |
19 |
25 |
1 |
45 |
15 |
10 |
0 |
82 |
16 |
13 |
0 |
100 |
19 |
21 |
1 |
88 |
15 |
15 |
0 |
76 |
18 |
13 |
1 |
123 |
16 |
21 |
0 |
120 |
17 |
22 |
0 |
50 |
18 |
7 |
1 |
30 |
17 |
4 |
1 |
135 |
16 |
19 |
0 |
84 |
14 |
17 |
0 |
50 |
16 |
6 |
1 |
65 |
15 |
9 |
0 |
83 |
17 |
12 |
1 |
105 |
21 |
21 |
1 |
70 |
17 |
10 |
1 |
99 |
15 |
12 |
0 |
89 |
18 |
8 |
0 |
93 |
15 |
14 |
0 |
68 |
17 |
11 |
1 |
57 |
15 |
10 |
0 |
Show all of your work in each question. In parts (d), (e), and (g) make sure...
a Using the Excel’s Regression Tool, develop the estimated regression equation to show how income (y annual income in $1000s) is related to the independent variables education (level of education attained in number of years), age (Develop the dummy variable for the gender variable first. b. Use the t test to test whether each of the coefficients obtained in part (a) are significant at .05 level of significance. What are your conclusions? c. Use the F test to test...
a. Using the Excel’s Regression Tool, develop the estimated regression equation to show how income (y annual income in $1000s) is related to the independent variables education(level of education attained in number of years), age ( Develop the dummy variable for the gender variable first. [ 6 points] Use the t test to test whether each of the coefficients obtained in part (a) are significant at .05 level of significance. What are your conclusions? [3 points] Use the F test...
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