Contrary to their name, dummy variables are not easy to understand without a lit

Question

Contrary to their name, dummy variables are not easy to understand without a little practice.

1.) Specify a dummy variable that would allow you to distinguish between undergrad students and grad students in your econometrics class.

2.) Specify a regresion equation to explain the grade (measured on a scale of 4.0) each student in your class received on his or her first econometrics test (Y) as a functions of the student's grade in a previous course in statistics (G), the number of hours the student studied for the test (H), and the dummy variable you created above (D). Are there other variables you would want to add? Explain.

3.) What is the hypothesized coefficent of D? Does the sign depend on the exact way in which you defined D?

4.) Suppose that you collected the data and ran the regression and found an estimated coefficient for D that had the expected sign and an absolute value of 0.5. What would this mean in real world terms? What would have happened if you only have undergrad or only grad students in your class?

Explanation / Answer

1) We can specify dummy variable

Undergrad stuent=0

Grad student=1

2) Y=G+H+D

Here we assume that more number of hours(H) a student studied higher is th score(Y)

Second more the previous score of Statistics(G) better the understanding and better the score (Y)

Third we assume that Grad students (D) will understand the subject better than undergrad student hence higher (Y)

score

3)The hypothesized coefficent (D) is 1

Yes the sign depends on the exact way you define D

For example here we gave values 0 and 1

but if you define D as -1 for undergrad and +1 for grad

or lets say you defined -1 for grad and +1 for under grad the equation will have opposite signs

4)

When we get +0.5 as the coefficint of D in our regression model

we conclude that the score (Y) is dependent on D

and 1 unit change in D will cause 0.5 units increase in Y keeping all other factors constant

Also we infer that being a grad or undergrad effects only 0.5 times on the score keeping every other variable constant

If we had onlty undergrad or only grad the dummy variable D will not have any significance as it would have become a constant for the entire dataset

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