LECTURE 6: MULTIPLE REGRESSION MODEL
•
Multiple variables affect the dependent variable
•
Example: (Trivariate) Linear Population Regression Function (with Fixed
Regressors):
E(Y
i
|X) =
β
0
+
β
1
X
i1
+
β
2
X
i2
Or
Y
i
=
β
0
+
β
1
X
i1
+
β
2
X
i2
+
ε
i
Where E(
ε
i
) = 0
•
Note: E(Y|X) still gives the average value of Y for the fixed values of the X
variables.
•
Note: Still linear regression model (remember
≡
linear in parameters)
What is different?
•
β
1
,
β
2
are
partial
regression coefficients
•
β
1
measures the change in the mean value of Y per unit change of X
1
,
holding X
2
constant.
•
β
2
measures the change in the mean value of Y per unit change of X
2
,
holding X
1
constant.
•
GOAL: To find out what part of the change in the average value of Y can be
directly attributed to X
1
and what part to X
2
Example: Returns to Education and Experience
E(Y
i
|X) = 7 + .12X
1i
+ 0.09X
2i
where
Y = log (hourly wage)
X
1
= education

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