Question

In: Statistics and Probability

Using data from 50 workers, a researcher estimates Wage = β0 + β1Education + β2Experience +...

Using data from 50 workers, a researcher estimates Wage = β0 + β1Education + β2Experience + β3Age + 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 β1.

  • 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 β2.

  • 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.)

Solutions

Expert Solution

1)  Interpret the point estimate for β1.

B1 = 1.13 for eduaction.

Answer:- As Education increases by 1 year, Wage is predicted to increase by 1.13/hour, holding Age and Experience constant.

2) Interpret the point estimate for β2.

B2 = 0.37 for experience

Answer:- As Experience increases by 1 year, Wage is predicted to increase by 0.37/hour, holding Age and Education constant.

3) What is the sample regression equation?

The regression equation for

Wage = β0 + β1Education + β2Experience + β3Age

is

Wage = 6.69 + 1.13*Education + 0.37*Experience + -0.09*Age

Answer:-

Wage = 6.69 + 1.13*Education + 0.37*Experience + -0.09*Age

4) Predict the hourly wage rate for a 36-year-old worker with 5 years of higher education and 4 years of experience.

Age = 36 , Education = 5, Expericence = 4

Wage = 6.69 + 1.13*Education + 0.37*Experience + -0.09*Age

Wage = 6.69 + (1.13*5) + (0.37*4) + (-0.09*36)

= 6.69 + 5.65 +1.48 - 3.24

= 10.58

Answer:-  Hourly wage rate for a 36-year-old worker with 5 years of higher education and 4 years of experience is 10.58

orchestra answered 2 years ago
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