Question

2 Using data from 50 workers, a researcher estimates Wage BoIEducation + 2Experience B3Age E, 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. 10 points Standard Coefficients t Stat P-Value 0.1310 0.0003 0.0022 Error 4.24 Intercept Education Experience Age 6.52 1.32 1.54 0.34 0.12 3.88 3.25 -0.20 0.39 0.01 0.05 0.8424 eBook a-1. Interpret the point estimate for B1. References As Education increases by 1 year, Wage is predicted to increase by 1.32/hour. As Education increases by 1 year, Wage is predicted to increase by 0.39/hour. As Education increases by 1 year, Wage is predicted to increase by 1.32/hour, holding Age and Experience constant As Education increases by 1 year, Wage is predicted to increase by 0.39/hour, holding Age and Experience constant a-2. Interpret the point estimate for B2 As Experience increases by 1 year, Wage is predicted to increase by 1.32/hour. As Experience increases by 1 year, Wage is predicted to increase by 0.39/hour. As Experience increases by 1 year, Wage is predicted to increase by 1.32/hour, holding Age and Education constant. As Experience increases by 1 year, Wage is predicted to increase by 0.39/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.) Age Education+ Experience+ + c. Predict the hourly wage rate for a 32-year-old worker with 5 years of higher education and 3 years of experience. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

Solution:

Given:

Intercept Education Experience Age Coefficients 6.52 1.32 0.39 -0.01 Standard ΕΡΓΟΙ 4.24 0.34 0.12 0.05 t Stat 1.54 3.88 3.25 -0.20 p-Value 0.1310 0.0003 0.0022 0.8424

Part a-1) Interpret the point estimate of $\beta_{1}$ :

$\beta_{1}$ is the population slope coefficient of Education variable.

Thus slope coefficient of Education is b₁ = 1.32.

Thus correct answer is:

As Education increases by 1 year , Wage is predicted to increase by 1.32 / hour , holding Age and Experience constant.

Part a-2) Interpret the point estimate of $\beta_{2}$ :

$\beta_{2}$ is the population slope coefficient of Experience variable.

Thus slope coefficient of Experience is b₂ = 0.39

Thus correct answer is:

As Experience increases by 1 year , Wage is predicted to increase by 0.39/hour, holding Age and Education constant.

Part b) Sample Regression Equation:

ý = bo + b1 x Education + b2 x Experience + b3 x Age

y = 6.52+ (1.32 x Education + 0.39 x Experience +/-0.01] x Age

Part c) Predict hourly wage rate for a 32 year old worker with 5 years of higher education and 3 years of experience.

Thus put Education = 5 , Experience = 3 , Age = 32 in above sample regression equation.

y = 6.52+ (1.32 x Education + 0.39 x Experience +/-0.01] x Age

y = 6.52+ 1.32 x 5 + 0.39 x 3+1 -0.01 x 32

y = 6.52+ 6.6 +1.17 – 0.32

y = 13.97