Question

Using data from 50 workers, a researcher estimates Wage = β0 + β1 Education + β2 Experience +β3 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 7.42 4.14 1.40 0.0524 Education 1.53 0.39 3.65 0.0002 Experience 0.47 0.20 3.53 0.0026 Age −0.07 0.08 −0.19 0.8130 a-1. What is the point estimate for β1? 1.53 0.47 a-2. Interpret this value. As Education increases by 1 unit, Wage is predicted to increase by 1.53 units, holding Age and Experience constant. Same interpretation by using 0.47 or -0.07 a-3. What is the point estimate for β2? 0.47 1.53 a-4. Interpret this value. Same interpretation by using 1.53 or -0.07 As Experience increases by 1 unit, Wage is predicted to increase by 0.47 units, holding Age and Education constant. b. What is the sample regression equation? (Negative value should be indicated by a minus sign. Round your answers to 2 decimal places.) y-hat = + Education + Experience + Age c. What is the predicted value for Age = 40, Education = 4 and Experience = 3. (Do not round intermediate calculations. Round your answer to 2 decimal places.) y-hat

Answer 1

Using data from 50 workers, a researcher estimates Wage = β0 + β1 Education + β2 Experience +β3 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   7.42 4.14 1.40 0.0524

Education 1.53 0.39 3.65 0.0002

Experience 0.47 0.20 3.53 0.0026

Age −0.07 0.08 −0.19 0.8130

a-1. What is the point estimate for β1? 1.53

a-2. Interpret this value. As Education increases by 1 unit, Wage is predicted to increase by 1.53 units, holding Age and Experience constant.

What is the point estimate for β2? 0.47

a-4. Interpret this value. As Experience increases by 1 unit, Wage is predicted to increase by 0.47 units, holding Age and Education constant.

b. What is the sample regression equation? (Negative value should be indicated by a minus sign. Round your answers to 2 decimal places.)

y-hat =7.42 + 1.53*Education + 0.47*Experience + (-0.07)*Age

c. What is the predicted value for Age = 40, Education = 4 and Experience = 3. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

y-hat =7.42 + 1.53*4 + 0.47*3 + (-0.07)*40

=12.15