University of California, Santa Barbara
Olivier Deschenes
Department of Economics
Winter 2011
Economics 140B
Individual Assignment 1: Answer Key
Due in class 01/20/11
Some of these exercises are from Stock and Watson.
Question 1:
Females are shorter and weigh less than males on average. One of your friends, a pre-med
student, tells you that in addition, females will weigh less for a given height. To test this
hypothesis, you collect the height and weight of 29 female and 81 male students at your
university. A regression of the weight on a constant, height, and a binary variable, which takes a
value of one for female and is zero otherwise, yields the follow result:
99
.
20
,
50
.
0
,
58
.
5
36
.
6
21
.
229
ˆ
2
SER
R
Height
Female
tudentw
S
(43.39)
(5.74)
(0.62)
Where
Studentw
is weight measured in pounds and
Height
is measured in inches
(heteroskedasticity-robust standard errors are in parentheses).
(a) Interpret the results. Does it make sense to have a negative intercept?
ANSWER:
For every additional inch in height, weight increases by roughly 5.6 pounds.
Female students weigh approximately 6.4 pounds less than male students, controlling
for height. The regression explains 50 percent of the weight variation among students. It
does not make sense to interpret the intercept, since there are no observations close to
the origin, or, put differently, there are no individuals who are zero inches tall.
(b) You decide that in order to give an interpretation to the intercept you should rescale the
height variable. One possibility is to subtract 5 ft. or 60 inches from your
Height
, because the
minimum height in your data set is 62 inches. The resulting new intercept is now 105.58. Can
you interpret this number now? What effect do you think the rescaling had on the two slope
coefficients and their t-statistics? Do you think that the R
2
has changed? What about the
standard error of the regression?
ANSWER:
There are now observations close to the origin and you can therefore
interpret the intercept. A student who is 5ft. tall will weight roughly 105.5 pounds, on
average. The two slopes will be unaffected, as will be the regression
R
2
. Since the
explanatory power of the regression is unaffected by rescaling, and the dependent
variable and the total sums of squares have remained unchanged, the sums of squared
residuals, and hence the
SER
, must remain the same.
(c) Use the information contained above to test the null hypothesis that males and females
weigh the same (conditional on height).