We run a regression on data collected from employees of a firm: = 0 + 11 + 22 + 33 +

: salary in $1000;

1: years of education;

2: years of experience;

3: an indicator for being a union member, takes value 1 if is a union member, value 0 if not.

Regression Statistics

R Square .........................0.5113

Adjusted R Square

Standard Error ...............3.6614

Observations...................40

ANOVA

df SS MS F

Regression 490.9441

Residual

Total 960.1414

Coefficient s Standard Error....... t Stat P-value Lower 95% ......Upper 95%

Intercept 2.0575 3.2222 0.6385...... 0.5273 .......-4.4840 .........8.5989

1: education ...........0.4834 0.1464 3.3024 0.0022 0.1862 0.7805

2: experience 1.4825 0.6256

3: union member1.1500 1.3031 0.8825 0.3835 -1.4954 3.7955

1) (2') Use the information from the table to test for the overall significance of all independent

variables at the 95% level.

2) (1') Interpret the estimated coefficient in front of "education", 0.4834.

3) (2') Use the information from the table to test the following hypothesis at the 95% level

0: 2 < 1; : 2 1.

4) (1') According to the point estimates, what is the predicted salary level of a union member with

12 years of education and 2 years of experience?

5) (3') In the regression above, "education" is included as a numerical variable. How would you run

the regression if you want to learn the relationship between "education level" and salary? There

are three different levels of education among all employees: high school degree, college degree,

and graduate degree. Explain how you would define new variables and write down the new

regression model. Explain what each slope parameter related to education mean.