Dummy Variables

#1
I have a question regarding Dummy Variables.. Never been good at it..

Question is like this..

Create the dummy variable for Education Level.

D1 = 1 -> if the worker is in Education Level 1
0 -> if the worker is not in Education Level 1
Create similar dummy variables for D2 (Education Level 2), D3, etc.

Also create a dummy variable M for Males and a dummy variable F for Females;

M = 1 -> if the worker is Male
0 -> if the worker is not a Male

and given this equation:
Y = β0 + β1X1 + β2X2 + β3X3 + ε (2)

Y = β0 + β1X1 + β2X2 + β3X3 + αM + γ1D1 + γ2D2 + γ3D3 + γ4D4 + ε (3)

a. Estimae equation (3) (drop D5, i.e., using D5 as the base case). Write down the estimated equation with its standard errors.

b. Why might these Dummy Variables be appropriate?

c. Interpret the coefficient of D2 for this model.

d. Perform an abbreviated hypothesis test on the coefficient of the variable D2 setting out clearly what is being tested.

e. has the inclusion of the dummy variables in (3) improved the relationship estimated in (2)? test the hypothesis α = γ1 = γ2 = γ3 = γ4 = 0 (abbreviated)

f. is there evidence of wage difference between Males and females? test (abbreviated) whatever statistical hypothesis is needed to substantiate your conclusion.

g. Predict the wage of a male graduate with a Starting Wage of 30,000 who has worked for 18 years with 4 years of Previous Experience. Also determine the 90% confidence interval for this prediction.



any help to these questions would be appreciated so much.. :wave: and it's a good practice too..