1. Dummy Variables (20 points) To study the effects of computer ownership on col

Question

1. Dummy Variables (20 points) To study the effects of computer ownership on college gpa, the following regression equation is estimated as colGPA=1.26+.157PC+447hsGPA+.0067ACT (n=105, R2=.237) where the dummy variable PC equals one if a student owns a personal computer and zero otherwise. Let noPC be a dummy variable equal to one if the student does not own a PC and zero otherwise. a) If noPC is used in place of PC in the regression equation, what happens to the intercept term in the estimated equation? What will be the coefficient on noPC? b) What will happen to the R-squared if noPC is used in place of PC? c) Should PC and noPC both be included as independent variables in the model? Explain.

Explanation / Answer

Let’s assume that the given model be,

ColGPA = 1.26 + 0.157*PC + 0.447*hsGPA + 0.0087*ACT.

So, if PC=1, => noPC=0, => ColGPA = (1.26 + 0.157) + 0.447*hsGPA + 0.0087*ACT.

So, if PC=0, => noPC=1, => ColGPA = 1.26 + 0.447*hsGPA + 0.0087*ACT.

So, which implied if we use “noPC” instead of “PC” then the regression model will look like.

ColGPA = (1.26 + 0.157) - 0.157*noPC + 0.447*hsGPA + 0.0087*ACT.

ColGPA = 1.417 - 0.157*noPC + 0.447*hsGPA + 0.0087*ACT.

=> the intercept will be “1.417”, if we use “noPC” instead of “PC” in the model, and the coefficient of “noPC” will be “-0.157”.

b).

The R^2 will remain same because we are not removing the variable, rather we are using the “different quality as 1” of the same variable.

c).

No, we can’t include both as independent variable. Since both variables are same rather they are showing different quality of the same variable. So, as we know if a qualitative variable have “M” character then we can introduce “M-1” dummy variable, so here we can’t introduce both of them together.

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