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University of California, Santa Barbara
Olivier Deschenes
Department of Economics
Winter 2011
Economics 140B
Individual Assignment 1
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 premed
student, tells you that in addition, females will weigh less for a given height. To test this
hypothesis, you collect 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 females and is zero otherwise, yields the following result:
tudentw
S
ˆ
=
–229.21 – 6.36
Female
+ 5.58
Height
,
R
2
=0.50,
SER
= 20.99
(43.39)
(5.74)
(0.62)
where
Studentw
is weight measured in pounds and
Height
is measured in inches
(heteroskedasticityrobust standard errors in parentheses).
(a) Interpret the results. Does it make sense to have a negative intercept?
(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
statistic? Do you think that the regression
R
2
has changed? What about
the standard error of the regression?
(c) Use the information contained above to test the null hypothesis that males and females
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