Answer keys for HW3
(i) The approximate difference is just the coefficient on
times 100, or –28.3%.
2.86, which is very statistically significant.
.283) – 1)
24.7%, and so the estimate is somewhat smaller in magnitude.
(iii) The proportionate difference is .181
.158 = .023, or about 2.3%.
One equation that can
be estimated to obtain the standard error of this difference is
is a dummy variable for the transportation industry.
Now, the base group is
and so the coefficient
directly measures the difference between the consumer products and
finance industries, and we can use the
(i) If the appropriate factors have been controlled for,
> 0 signals discrimination against
a white person has a greater chance of having a loan approved, other relevant factors
(ii) The simple regression results are
.708 + .201
The coefficient on
means that, in the sample of 1,989 loan applications, an application
submitted by a white application was 20.1% more likely to be approved than that of a nonwhite
This is a practically large difference and the
statistic is about 10.
(We have a large
sample size, so standard errors are pretty small.)
(iii) When we add the other explanatory variables as controls, we obtain
The coefficient has fallen by some margin because we are now controlling for factors that
should affect loan approval rates, and some of these clearly differ by race.
(On average, white
people have financial characteristics – such as higher incomes and stronger credit histories – that
make them better loan risks.)
But the race effect is still strong and very significant (
(iv) When we add the interaction
to the regression, its coefficient and
are about .0081 and 3.53, respectively.
Therefore, there is an interactive effect: