PAM 305  Introduction to Multivariate Analysis
Fall 2006
Suggested Solutions Homework 3
Due date: September 29th
Question 1
For the computer exercises in STATA we will use the same data set WAGE1.dta.
Suppose that the true model is
log(
wage
) =
β
o
+
β
1
educ
+
β
2
exper
+
β
3
tenure
+
u
(1)
Obtain the sample regression function
d
log(
wage
) =
ˆ
β
o
+
ˆ
β
1
educ
+
ˆ
β
2
exper
+
ˆ
β
3
tenure
(2)
a. As in the simple linear regression model, the coefficients have a percent
age interpretation. The only difference is that now they have a
ceteris
paribus
interpretation. Interpret
ˆ
β
1
.
ˆ
β
1
=0.092 is the ceteris paribus effect of education on wages, that is the
effect of education on wage, holding fixed tenure and experience. An extra
year of education will, on average, increase wages by
ˆ
β
1
×
100
percent,
i.e. 9.2%
b. If we take two people with the same levels of experience and job tenure,
what is the percentage difference in predicted wages if their education
differs by 1 year?
The percentage difference in predicted wages will be 9.2%.
Remember
that the beauty of multiple regression analysis is to allow us to explicitly
1
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control for many factors that simultaneously affect the dependent vari
able. We can study the effect of one explanatory variable on the explained
variable holding the others fixed, even though those other factors were not
being held fixed during the sampling process.
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 Fall '06
 LUCARELLI
 Linear Regression, Regression Analysis, exper

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