Using data from 50 workers, a researcher estimates Wage = β_{0} + β_{1}Education + β_{2}Experience + β_{3}Age + ε, where Wage is the hourly wage rate and Education, Experience, and Age are the years of higher education, the years of experience, and the age of the worker, respectively. The regression results are shown in the following table.
Coefficients | Standard Error |
t Stat | p-Value | |
Intercept | 7.56 | 4.35 | 1.74 | 0.0889 |
Education | 1.53 | 0.38 | 4.03 | 0.0002 |
Experience | 0.42 | 0.12 | 3.50 | 0.0010 |
Age | −0.04 | 0.07 | −0.57 | 0.5705 |
a-1. Interpret the point estimate for β_{1}.
As Education increases by 1 year, Wage is predicted to increase by 1.53/hour.
As Education increases by 1 year, Wage is predicted to increase by 0.42/hour.
As Education increases by 1 year, Wage is predicted to increase by 1.53/hour, holding Age and Experience constant.
As Education increases by 1 year, Wage is predicted to increase by 0.42/hour, holding Age and Experience constant.
a-2. Interpret the point estimate for β_{2}.
As Experience increases by 1 year, Wage is predicted to increase by 1.53/hour.
As Experience increases by 1 year, Wage is predicted to increase by 0.42/hour.
As Experience increases by 1 year, Wage is predicted to increase by 1.53/hour, holding Age and Education constant.
As Experience increases by 1 year, Wage is predicted to increase by 0.42/hour, holding Age and Education constant.
b. What is the sample regression equation? (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)
c. Predict the hourly wage rate for a 24-year-old worker with 4 years of higher education and 4 years of experience. (Do not round intermediate calculations. Round your answer to 2 decimal places.)
We know that the regression coefficients explains the marginal effect of that particular variable holding other variables constant so,
Answer a-1: As Education increases by 1 year, Wage is predicted to increase by 1.53/hour, holding Age and Experience constant.
Answer a-2: As Experience increases by 1 year, Wage is predicted to increase by 0.42/hour, holding Age and Education constant.
Answer b:
The sample regression equation is given as:
Answer c.
Here, Education = 4, Experience = 4 and Age = 24, so the predicted hourly wage is given using the above sample regression equation as:
The hourly wage rate for a 24-year-old worker with 4 years of higher education and 4 years of experience is 14.40
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