# Solution

Ignoring the fact that rep78 is a categorical variable gives:

reg price weight foreign rep78

The coefficient on rep78 is about 150, though with a 95% confidence interval of -492 to 792 it's statistically indistuinguishable from zero.

That suggests that the contribution of rep78 to a car's price is 150 times its value of rep78, i.e. for cars with a rep78 of one it contrubutes 150, for cars with a rep78 of two it contributes 300, etc.

Now run the regression with i.rep78:

reg price weight foreign i.rep78

The coefficient on each value of i.rep78 represents its change from the base level of one. If the first model is right, we'd thus expect the coefficient on 2.rep78 to be 150 (a rep78 of two contributes 300, but we have to subtract the 150 contributed by a rep78 of one), 3.rep78 to be 300, etc. We can test the hypothesis that all those values are correct with:

test (2.rep78=150) (3.rep78=300) (4.rep78=450) (5.rep78==600)

The result does not reject this hypothesis, however that probably has more to do with the fact that we can't say much of anything about the effect of rep78 than it actually being linear.

Last Revised: 1/18/2011