Question

Use the following data to predict the wage you would have to pay to hire a particular individual.

a. Specify a regression equation

b. Estimate a regression equation to explain wages

c. Explain the t-stats, f-stats, 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 nonwhite or females ?

Annual Income in $1000	Years of Experience	Education	Sex	Race
77.8	12	Masters	m	w
77.1	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	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	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 Coll.	f	w
42.94	12	Some Coll.	f	w
43.33	13	Some Coll.	f	o
41.35	15	Some Coll.	f	o
42.51	22	Some Coll.	f	o
47.39	19	Some Coll.	f	o
48.9	23	Some Coll.	f	w
48.02	12	SOme Coll.	m	w
48.19	15	Some Coll.	m	o
53.74	16	Some Coll.	m	w
43.74	12	Some Coll	m	o
51.61	12	Some Coll	m	w
48.99	10	SOme Coll.	m	w
38.7	7	High School	m	o
38.79	12	High School	m	o
40.34	13	High School	m	o
32.73	15	High School	m	o
30.97	6	High School	m	w
33.64	4	High School	m	w
38.05	8	High School	m	o
36.82	16	High School	m	o
33.6	13	High School	m	o
29.12	16	High School	m	o
30.5	2	High School	m	w
34.28	2	High School	f	w
30.52	4	High School	m	w
32.7	6	High School	m	w
34.26	1	High School	m	w
32.15	2	High School	m	w
38.41	7	High School	m	w
38.31	5	High School	m	w
30.29	5	High School	f	w
34.23	3	High School	m	w
37.95	8	High School	m	o
28.58	9	High School	m	o
35.44	34	High School	m	o
38.57	32	High School	m	w
34.06	12	High School	m	w
31.63	19	High School	f	w
32.84	23	High School	f	o
29.69	15	High School	f	o
26.32	2	High School	f	o
34.92	7	High School	m	w
32.28	4	High School	m	w
37.95	17	High School	m	w
38.4	18	High School	f	w
33.56	2	High School	f	w

Answer 1

a. Specify a regression equation

Let

Y=Annual Income in $1000  

Years of Experience

if the education=Masters, else 0

if education =BA, else 0

if education is Some college, else 0

if sex=m(ale), else 0

if race=w(hite), else 0

The regression equation that we wan to estimate is

where is the intercept, are the slope coefficients of respectively and is a random disturbance

b. Estimate a regression equation to explain wages

Prepare the following sheet

get this

set up the regression using data-->data analysis-->regression

get this

the estimated regression equation to explain the wages is

c. Explain the t-stats, f-stats, and the R Squared. What information do they give ?

Suppose we want to test the overall validity of the model. The hypotheses are

The f-stat and the corresponding significance F helps to test the above hypotheses.

The test statistics to test the above hypotheses is F=167.1897 and the p-value=4.4878E-39.

We will reject the null hypothesis if the p-value is less than the significance level. HEre, the p-value of 4.4878E-39 is less than 0.05 and hence we reject the null hypothesis.

We can say that the regression model to estimate the wages is significant.

We use the t-stats to test if the individual predictor variables can significantly explain the wages
The hypotheses are

The t-stat values are the test statistics to test the above hypotheses and the p-values are used to test if we can reject the null hypothesis.

If the p-value is less than the significance level we reject the null hypothesis.

Here,

only the p-value for the variable Race is not significant at 0.05.

So Race cannot explain variation in wages at 5% level of significance.

Finally the value of R-square from the output is

This indicates that 93.56% of the variations in wages is explained by the model (or the predictors)

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?

The values of variables are

Using the estimated equation we get

ans: You will have to pay $72,856 to hire a nonwhite female with 20 years in the industry and an MBA

if she was a white male (with 20 years in the industry and an MBA), then the variables are

Using the estimated equation we get

ans: You will have to pay $78,722 to hire a white male with 20 years in the industry and an MBA

e. Does this industry discriminate against nonwhite or females ?

Yes it does.

We can see the slope for white is positive 1.61. This means that a white candidate will be paid on an average $1,607 more than a non white candidate, while keeping other variables the same.

We can see the slope for male is positive 4.26. This means that a male candidate will be paid on an average $4,258 more than a female candidate, while keeping other variables the same.