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. A portion of the regression results is shown in the following table.
Coefficients | Standard Error | t Stat | p-value | |
Intercept | 7.58 | 4.42 | 1.71 | 0.0931 |
Education | 1.68 | 0.37 | 4.54 | 0.0000 |
Experience | 0.35 | 0.18 | 1.94 | 0.0580 |
Age | −0.06 | 0.05 | −1.20 | 0.2363 |
a-1. Interpret the point estimate for β_{1}.
As Education increases by 1 year, Wage is predicted to increase by 1.68/hour.
As Education increases by 1 year, Wage is predicted to increase by 0.35/hour.
As Education increases by 1 year, Wage is predicted to increase by 1.68/hour, holding Age and Experience constant.
As Education increases by 1 year, Wage is predicted to increase by 0.35/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 1.68/hour.
As Experience increases by 1 year, Wage is predicted to increase by 0.35/hour.
As Experience increases by 1 year, Wage is predicted to increase by 1.68/hour, holding Age and Education constant.
As Experience increases by 1 year, Wage is predicted to increase by 0.35/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.)
y-hat = + Education + Experience + Age
c. Predict the hourly wage rate for a 29-year-old worker with 3 years of higher education and 2 years of experience. (Do not round intermediate calculations. Round your answer to 2 decimal places.)
y-hat =
a-1
As Education increases by 1 year, Wage is predicted to increase by 1.68/hour, holding Age and Experience constant. Option C is correct here.
a-2
As Experience increases by 1 year, Wage is predicted to increase by 0.35/hour, holding Age and Education constant. Option D is correct here.
b.
y-hat = 7.58 + 1.68 * Education + 0.35 * Experience -0.06 * Age
c.
Age = 29; Education = 3; Experience = 2
y^ = 7.58 + 1.68 * 3 + 0.35 * 2 - .06 * 29 = 11.58
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