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 | 6.69 | 4.23 | 1.58 | 0.1206 |
Education | 1.13 | 0.34 | 3.32 | 0.0018 |
Experience | 0.37 | 0.10 | 3.70 | 0.0006 |
Age | −0.09 | 0.06 | −1.50 | 0.1404 |
a-1. Interpret the point estimate for β_{1}.
As Education increases by 1 year, Wage is predicted to increase by 1.13/hour.
As Education increases by 1 year, Wage is predicted to increase by 0.37/hour.
As Education increases by 1 year, Wage is predicted to increase by 1.13/hour, holding Age and Experience constant.
As Education increases by 1 year, Wage is predicted to increase by 0.37/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 1.13/hour.
As Experience increases by 1 year, Wage is predicted to increase by 0.37/hour.
As Experience increases by 1 year, Wage is predicted to increase by 1.13/hour, holding Age and Education constant.
As Experience increases by 1 year, Wage is predicted to increase by 0.37/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 36-year-old worker with 5 years of higher education and 4 years of experience. (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Ans.
a1. Option c
Increase in education by 1 units increases the predicted wage by 1.13 is what the coefficient of the education i.e. b1 means. Provided other things are constant.
a2. Option d
Increase in experience by 1 units increases the predicted wage by 0.37 is what the coefficient of the experience i.e. b2 means. Provided other things are constant.
b. Sample regression equation,
Predicted Wage = 6.69 + 1.13*Education + 0.37*Experience - 0.09*Age
c) At Education = 5 years, Experience = 4 years and Age = 36 years, using the regression equation, we get,
Predicted wage = 6.69 + 1.13*5 + 0.37*4 - 0.09*36 = $10.58 per hour
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