Use the following data to predict the wage you would have to pay to hire a parti
ID: 3262479 • Letter: U
Question
Use the following data to predict the wage you would have to pay to hire a particular individual. The data set is in the excel file New Wage.xlsx that was e-mailed to your msmc account, and is provided in text format at the back of this handout.
a. Specify a regression equation. Explain how it tests what you want to know.
b. Estimate a regression equation to explain wages. Attach your excel results.
c. Tell me about the t-stats, the f-stat and the R squared. What information do they give?
d. You have a nonwhite female with 20 years in the industry and an MBA. How much will you have to pay to hire her? What if she was a white male?
e. Does this industry discriminate against nonwhites or/and females? Explain.
Annual Income in $1000
Years of Experience
Education
Sex
M = Male
F = Female
Race
w = White
o = Other
77.80
12
Masters
m
w
77.10
13
Masters
m
w
76.19
15
Masters
m
w
77.52
24
Masters
f
w
66.13
2
Masters
f
w
76.62
22
Masters
m
o
72.56
9
Masters
f
o
78.43
7
Masters
m
w
57.98
12
BA
m
w
56.64
15
BA
m
w
61.63
27
BA
f
w
54.45
23
BA
f
w
65.19
24
BA
m
w
59.00
17
BA
m
w
58.88
1
BA
m
w
51.66
5
BA
f
w
56.23
15
BA
f
o
49.72
2
BA
f
o
55.25
1
BA
m
o
56.15
16
BA
m
o
52.44
18
BA
m
o
57.00
23
BA
m
o
55.73
22
BA
f
o
50.61
18
BA
f
w
51.73
15
BA
f
w
54.66
16
BA
f
w
54.41
18
BA
m
o
59.31
12
BA
m
o
56.65
11
BA
f
w
38.36
10
Some Col
f
w
42.94
12
Some Col
f
w
43.33
13
Some Col
f
o
41.35
15
Some Col
f
o
42.51
22
Some Col
f
o
47.39
19
Some Col
f
o
48.90
23
Some Col
f
w
48.02
12
Some Col
m
w
48.19
15
Some Col
m
o
53.74
16
Some Col
m
w
43.74
12
Some Col
m
o
51.61
12
Some Col
m
w
48.99
10
Some Col
m
w
38.70
7
HiSch
m
w
38.79
12
HiSch
m
o
40.34
13
HiSch
m
o
32.73
15
HiSch
m
o
30.97
6
HiSch
m
w
33.64
4
HiSch
m
w
38.05
8
HiSch
m
o
36.82
16
HiSch
m
o
33.60
13
HiSch
m
o
29.12
16
HiSch
f
o
30.50
2
HiSch
f
w
34.28
4
HiSch
f
w
30.52
6
HiSch
f
w
32.70
1
HiSch
f
w
34.26
2
HiSch
f
w
32.15
7
HiSch
m
w
38.41
5
HiSch
m
w
38.31
5
HiSch
m
w
30.29
3
HiSch
m
w
34.23
8
HiSch
m
w
37.95
9
HiSch
m
o
28.58
19
HiSch
f
o
35.44
34
HiSch
f
o
38.57
32
HiSch
f
w
34.06
12
HiSch
f
w
31.63
19
HiSch
f
w
32.84
23
HiSch
f
o
29.69
15
HiSch
f
o
26.32
2
HiSch
f
o
34.92
7
HiSch
m
w
32.28
4
HiSch
m
w
37.95
17
HiSch
m
w
38.40
18
HiSch
f
w
33.56
2
HiSch
f
w
Annual Income in $1000
Years of Experience
Education
Sex
M = Male
F = Female
Race
w = White
o = Other
77.80
12
Masters
m
w
77.10
13
Masters
m
w
76.19
15
Masters
m
w
77.52
24
Masters
f
w
66.13
2
Masters
f
w
76.62
22
Masters
m
o
72.56
9
Masters
f
o
78.43
7
Masters
m
w
57.98
12
BA
m
w
56.64
15
BA
m
w
61.63
27
BA
f
w
54.45
23
BA
f
w
65.19
24
BA
m
w
59.00
17
BA
m
w
58.88
1
BA
m
w
51.66
5
BA
f
w
56.23
15
BA
f
o
49.72
2
BA
f
o
55.25
1
BA
m
o
56.15
16
BA
m
o
52.44
18
BA
m
o
57.00
23
BA
m
o
55.73
22
BA
f
o
50.61
18
BA
f
w
51.73
15
BA
f
w
54.66
16
BA
f
w
54.41
18
BA
m
o
59.31
12
BA
m
o
56.65
11
BA
f
w
38.36
10
Some Col
f
w
42.94
12
Some Col
f
w
43.33
13
Some Col
f
o
41.35
15
Some Col
f
o
42.51
22
Some Col
f
o
47.39
19
Some Col
f
o
48.90
23
Some Col
f
w
48.02
12
Some Col
m
w
48.19
15
Some Col
m
o
53.74
16
Some Col
m
w
43.74
12
Some Col
m
o
51.61
12
Some Col
m
w
48.99
10
Some Col
m
w
38.70
7
HiSch
m
w
38.79
12
HiSch
m
o
40.34
13
HiSch
m
o
32.73
15
HiSch
m
o
30.97
6
HiSch
m
w
33.64
4
HiSch
m
w
38.05
8
HiSch
m
o
36.82
16
HiSch
m
o
33.60
13
HiSch
m
o
29.12
16
HiSch
f
o
30.50
2
HiSch
f
w
34.28
4
HiSch
f
w
30.52
6
HiSch
f
w
32.70
1
HiSch
f
w
34.26
2
HiSch
f
w
32.15
7
HiSch
m
w
38.41
5
HiSch
m
w
38.31
5
HiSch
m
w
30.29
3
HiSch
m
w
34.23
8
HiSch
m
w
37.95
9
HiSch
m
o
28.58
19
HiSch
f
o
35.44
34
HiSch
f
o
38.57
32
HiSch
f
w
34.06
12
HiSch
f
w
31.63
19
HiSch
f
w
32.84
23
HiSch
f
o
29.69
15
HiSch
f
o
26.32
2
HiSch
f
o
34.92
7
HiSch
m
w
32.28
4
HiSch
m
w
37.95
17
HiSch
m
w
38.40
18
HiSch
f
w
33.56
2
HiSch
f
w
Explanation / Answer
a. Specify a regression equation. Explain how it tests what you want to know.
Income^ = b0 + b1*male + b2 * white + b3*Masters + b4 *BA +b5*Some col + b5*year_experience
for n categories we need n-1 dummy variabe
For male , male = 1 , for female male = 0
similarly for white white= 1 , for other white =0
for Masters masters = 1 ,BA = Somecol =0
for BA masters = 0 , BA = 1 , Somecol =0
for Somecol , masters= 0 ,BA =0 ,Somecol = 1
for Hisch masters = 0 , BA = 0 , Somecol =0
b. Estimate a regression equation to explain wages. Attach your excel results.
Income^ = 28.14 + 4.319*male + 2.11 * white + 39.966*Masters + 21.0502 *BA +11.529*Some col +0.22344*year_experience
c. Tell me about the t-stats, the f-stat and the R squared. What information do they give?
if t-stat > t-critical ,the variable is significant
if f-stat > f-critical . the model is significant
R^2 gies % of variation explained by the model , 0.9612 (about 96 %)
d. You have a nonwhite female with 20 years in the industry and an MBA. How much will you have to pay to hire her? What if she was a white male?
white =0 , male = 0 , year_exper = 20 , MAster0 ,BA = 1 , Some col = 0
ncome^ = 28.14 + 4.319*male + 2.11 * white + 39.966*Masters + 21.0502 *BA +11.529*Some col +0.22344*year_experience
=28.14 +21.0502 +0.22344*20 = 53.659
hence 53659 dollars
e. Does this industry discriminate against nonwhites or/and females? Explain.
p-value for b1 is 1.69*10^(-8) <0.05 , hence Male is significant
p-value for b2 = 0.00365 < 0.05 , hence white is significant
hence this industry discriminates against nonwhites or/and females.
Please rate my solution
Annual Income in $1000 Years of Experience Education Sex Race M = Male w = White F = Female o = Other male White Masters BA Some col years of experience 77.8 12+A4:B4:B69 Masters m w 1 1 1 0 0 12 77.1 13 Masters m w 1 1 1 0 0 13 76.19 15 Masters m w 1 1 1 0 0 15 77.52 24 Masters f w 0 1 1 0 0 24 66.13 2 Masters f w 0 1 1 0 0 2 76.62 22 Masters m o 1 0 1 0 0 22 72.56 9 Masters f o 0 0 1 0 0 9 78.43 7 Masters m w 1 1 1 0 0 7 57.98 12 BA m w 1 1 0 1 0 12 56.64 15 BA m w 1 1 0 1 0 15 61.63 27 BA f w 0 1 0 1 0 27 54.45 23 BA f w 0 1 0 1 0 23 65.19 24 BA m w 1 1 0 1 0 24 59 17 BA m w 1 1 0 1 0 17 58.88 1 BA m w 1 1 0 1 0 1 51.66 5 BA f w 0 1 0 1 0 5 56.23 15 BA f o 0 0 0 1 0 15 49.72 2 BA f o 0 0 0 1 0 2 55.25 1 BA m o 1 0 0 1 0 1 56.15 16 BA m o 1 0 0 1 0 16 52.44 18 BA m o 1 0 0 1 0 18 57 23 BA m o 1 0 0 1 0 23 55.73 22 BA f o 0 0 0 1 0 22 50.61 18 BA f w 0 1 0 1 0 18 51.73 15 BA f w 0 1 0 1 0 15 54.66 16 BA f w 0 1 0 1 0 16 54.41 18 BA m o 1 0 0 1 0 18 59.31 12 BA m o 1 0 0 1 0 12 56.65 11 BA f w 0 1 0 1 0 11 38.36 10 Some Col f w 0 1 0 0 1 10 42.94 12 Some Col f w 0 1 0 0 1 12 43.33 13 Some Col f o 0 0 0 0 1 13 41.35 15 Some Col f o 0 0 0 0 1 15 42.51 22 Some Col f o 0 0 0 0 1 22 47.39 19 Some Col f o 0 0 0 0 1 19 48.9 23 Some Col f w 0 1 0 0 1 23 48.02 12 Some Col m w 1 1 0 0 1 12 48.19 15 Some Col m o 1 0 0 0 1 15 53.74 16 Some Col m w 1 1 0 0 1 16 43.74 12 Some Col m o 1 0 0 0 1 12 51.61 12 Some Col m w 1 1 0 0 1 12 48.99 10 Some Col m w 1 1 0 0 1 10 38.7 7 HiSch m w 1 1 0 0 0 7 38.79 12 HiSch m o 1 0 0 0 0 12 40.34 13 HiSch m o 1 0 0 0 0 13 32.73 15 HiSch m o 1 0 0 0 0 15 30.97 6 HiSch m w 1 1 0 0 0 6 33.64 4 HiSch m w 1 1 0 0 0 4 38.05 8 HiSch m o 1 0 0 0 0 8 36.82 16 HiSch m o 1 0 0 0 0 16 33.6 13 HiSch m o 1 0 0 0 0 13 29.12 16 HiSch f o 0 0 0 0 0 16 30.5 2 HiSch f w 0 1 0 0 0 2 34.28 4 HiSch f w 0 1 0 0 0 4 30.52 6 HiSch f w 0 1 0 0 0 6 32.7 1 HiSch f w 0 1 0 0 0 1 34.26 2 HiSch f w 0 1 0 0 0 2 32.15 7 HiSch m w 1 1 0 0 0 7 38.41 5 HiSch m w 1 1 0 0 0 5 38.31 5 HiSch m w 1 1 0 0 0 5 30.29 3 HiSch m w 1 1 0 0 0 3 34.23 8 HiSch m w 1 1 0 0 0 8 37.95 9 HiSch m o 1 0 0 0 0 9 28.58 19 HiSch f o 0 0 0 0 0 19 35.44 34 HiSch f o 0 0 0 0 0 34 38.57 32 HiSch f w 0 1 0 0 0 32 34.06 12 HiSch f w 0 1 0 0 0 12 31.63 19 HiSch f w 0 1 0 0 0 19 32.84 23 HiSch f o 0 0 0 0 0 23 29.69 15 HiSch f o 0 0 0 0 0 15 26.32 2 HiSch f o 0 0 0 0 0 2 34.92 7 HiSch m w 1 1 0 0 0 7 32.28 4 HiSch m w 1 1 0 0 0 4 37.95 17 HiSch m w 1 1 0 0 0 17 38.4 18 HiSch f w 0 1 0 0 0 18 33.56 2 HiSch f w 0 1 0 0 0 2Related Questions
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