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1
Introduction to Business Statistics
L
e
c
t
u
r
e
2
6
Multiple Regression Analysis
Introduction:
Including more independent variables in a regression
sometimes can greatly increase its prediction and explanation power.
Example:
Dependent variable
Y
Independent variables
X
Market value of a flat
size, # of rooms, # of bath rooms, age,
location, view
Salary
experience, education, performance
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The Model:
}
part
random
part
systematic
2
2
1
1
0
ε
β
+
+
+
+
+
=
4
4
4
4
43
4
4
4
4
42
1
L
k
k
X
X
X
Y
Assumptions:
•
Random errors are normally distributed with mean zero and
variance
2
σ
.
•
Random errors for different values of
Y
are independent.
•
Regression parameters
k
,
,
,
1
0
L
are constants.
•
Independent variables
k
X
X
X
,
,
,
2
1
L
are constants measured without
error.
3
The population regression equation:
k
k
Y
X
X
X
β
μ
+
+
+
+
=
L
2
2
1
1
0
,
where
0
is the intercept and
k
,
,
1
L
are called
partial slopes
.
Interpretation of
i
(
k
i
,
,
1
L
=
): When we increase
X
i
by one unit
keeping all other
X’s
fixed, on the average
Y
will increase by
i
.
Method of least squares for fitting:
Find
k
b
b
b
,
,
,
1
0
L
such that
∑
+
+
−
=
=
n
i
ki
k
i
i
X
X
Y
L
1
2
1
1
0
)]
(
[
L
is minimized.
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This note was uploaded on 02/13/2012 for the course ISOM 111 taught by Professor Hu,inchi during the Fall '10 term at HKUST.
 Fall '10
 Hu,Inchi

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