(#2) (Data exercise). This problem also uses the data set rental.dta. In question #1, you estimated the
following model for rental rates in college towns, using all 64 observations:
log(rent) = XXXXXXXXXXlog(pop XXXXXXXXXXlog(avginc XXXXXXXXXXpcstu
XXXXXXXXXX XXXXXXXXXX)
n=64, R?=.458
Now suppose that you accidently deleted a few observations from the data for year 1990 before running
the regression. Let’s assume that the observations were deleted at random, so the sample you have left
is still a random sample.
a) Do you think your estimates for 3; would change? Why or why not? If so, can you predict whethe
B11 will get bigger or smaller?
) Explain why you might expect the t-stat for 81 to get smaller.
¢) Is it possible that the t-stat will actually get bigger? Explain.
Now, try estimating the regression after dropping 4 observations. Do this as follows.
First, “keep” only the observations co
esponding to year 1990 by typing:
keep if year==90
(type describe to verify that you now have a data set with only 64 observations, and tab year to
verify that year is equal to 90 for all of them.)
First, re-estimate the regression using all 64 observations (in #1, you did this by adding “if year==90" to
the end of the command. Now, you no longer need this “if” condition).
Now, to estimate the regression using only the first 60 observations (i.e, ignoring the last 4), type
egress y x .. in 1\60
Try it again using only the last 60 observations:
egress y x .. in 5\64
d) What happened to £1 and to the t-statistic in each case?
(#3) (Data exercise). Use the data on housing prices (houseprices.dta) to estimate a simple linea
egression of price on number of bedrooms (bdrms).
a) Is the coefficient on bdrms statistically significant at a:
. 10% significance level? YES/ NO
. 5% level? YES / NO
. 1% level? YES/ NO
) Now control for both the size of the house and the size of the lot in your regression. Conditional on the
size of the house and the size of the lot, is the predicted effect of an additional bedroom on the sale price
of a house significant at the:
. 10% significance level? YES/ NO
5% level? YES / NO
1% level? YES/ NO
¢) A realtor tells you that you should expect to pay an extra $150 on average (8.15K) for each additional
square foot in this housing market, holding constant the size of the lot and the number of bedrooms.
Suppose that you decide you will trust this realtor’s advice unless you are 95% confident that the
statement is wrong based on your own regression analysis. Do you trust the realtor? [Hint: test the null
hypothesis that the statement is true.]
d) The p-value of .128 on bdrms in your estimated multiple regression model implies that...
e ..anadditional bedroom does not have a statistically significant effect on the home price (using
conventional thresholds for significance) once we control for the size of the house and the lot.
TRUE/ FALSE ?
e ..an additional bedroom does not have an economically meaningful effect on the home price (once we
control for the size of the house and the lot).
TRUE/ FALSE ?
e ..the true coefficient on bdrms in the price regression is zero (once we control for the size of the house
and the lot).
TRUE/ FALSE ?
e) Suppose you were able to collect additional data on housing prices and quadruple the size of you
andom sample (i.e., you now have 88 x 4 = 352 observations). If you re-estimate the multiple
egression model using the new sample, would you expect the new coefficient on bdrms to be
statistically significant at the 5% level? Explain.