A researcher interviews 50 employees of a large manufacturer and collects data on each worker’s hourly wage (Wage), years of higher education (EDUC), experience (EXPER), and age (AGE).
Data:
Wage EDUC EXPER AGE Gender
37.85 11 2 40 1
21.72 4 1 39 0
14.34 4 2 38 0
21.26 5 9 53 1
24.65 6 15 59 1
25.65 6 12 36 1
15.45 9 5 45 0
20.39 4 12 37 0
29.13 5 14 37 1
27.33 11 3 43 1
18.02 8 5 32 0
20.39 9 18 40 1
24.18 7 1 49 1
17.29 4 10 43 0
15.61 1 9 31 0
35.07 9 22 45 0
40.33 11 3 31 1
20.39 4 14 55 0
16.61 6 5 30 1
16.33 9 3 28 0
23.15 6 15 60 1
20.39 4 13 32 0
14.88 4 9 58 1
13.88 5 4 28 0
17.65 6 5 40 1
15.45 6 2 37 0
26.35 4 18 52 1
19.15 6 4 44 0
16.61 6 4 57 0
18.39 9 3 30 1
15.45 5 8 43 0
18.02 7 6 31 1
13.44 4 3 33 0
17.66 6 23 51 1
16.96 4 15 37 0
14.34 4 9 45 0
15.45 6 3 55 0
17.43 5 14 57 0
35.89 9 16 36 1
20.39 4 20 60 1
11.81 4 5 35 0
15.45 9 10 34 0
17.66 5 4 28 1
13.87 6 1 25 0
16.35 7 10 43 1
15.45 9 2 42 1
23.67 4 17 47 0
16.02 11 2 46 1
23.15 4 15 52 0
24.18 8 11 64 0
a. Estimate: Wage = β0 + β1EDUC + β2EXPER + β3AGE + ε. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.) Show the regression equation.
b. Are the signs as expected?
Coefficients Is the sign expected?
EDUC
EXPER
AGE
c. Interpret the coefficient of EDUC.
For a 1 year increase in higher education, wage is predicted to increase by $1.44/hour holding higher education, experience and age constant.
For a 1 year increase in higher education, wage is predicted to increase by $1.44/hour holding experience and age constant.
For a 1 year increase in higher education, wage is predicted to increase by $1.44/hour.
d. Interpret the coefficient of determination.
25.24% of the sample variation in Age is explained by the estimated regression model.
25.24% of the sample variation in wage is explained by the estimated regression model.
34.24% of the sample variation in Experience is explained by the estimated regression model.
34.24% of the sample variation in wage is explained by the estimated regression model.
e. Predict the hourly wage of a 40-year-old employee who has 5 years of higher education and 8 years of experience. (Round intermediate coefficient values and final answer to 2 decimal places.)