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ECON  3790  Business and Economics  lecture not...
ECON  3790  Business and Economics  lecture_notes Econ 3790: Business and Economics Statistics Instructor: Yogesh Uppal yuppal@ysu.edu The equation that describes how the dependent variable y is related to the independent variables x , x , . . . x and an error term is called the multiple regression model . Chapter 15: Multiple Regression Model y y = = 0 0 + + 1 1 x x 1 1 + + 2 2 x x 2 2 + + . . . + . . . + p p x x p p + + whe
ECON  3790  Business and Economic...
ECON  3790  Business and Economics  lecture_notes Econ 3790: Business and Economics Statistics Instructor: Yogesh Uppal yuppal@ysu.edu The equation that describes how the dependent variable y is related to the independent variables x , x , . . . x and an error term is called the multiple regression model . Chapter 15: Multiple Regression Model y y = = 0 0 + + 1 1 x x 1 1 + + 2 2 x x 2 2 + + . . . + . . . + p p x x p p + + whe
Page 1
Econ 3790: Business and
Economics Statistics
Instructor: Yogesh Uppal
yuppal@ysu.edu
Page 2
The equation that describes how the
dependent variable
y
is related to the
independent variables
x
,
x
, . . .
x
and an
error term is called the multiple
regression
model
.
Chapter 15:
Multiple Regression Model
y
y
=
=
0
0
+
+
1
1
x
x
1
1
+
+
2
2
x
x
2
2
+
+
. . . +
. . . +
p
p
x
x
p
p
+
+
where:
where:
0
0
,
,
1
1
,
,
2
2
, . . . ,
, . . . ,
p
p
are the
are the
parameters
parameters
, and
, and
is a random variable called the
is a random variable called the
error term
error term
Page 3
A simple random sample is used to compute
A simple random sample is used to compute
sample statistics
sample statistics
b
b
0
0
,
,
b
b
1
1
,
,
b
b
2
2
,
,
. . . ,
. . . ,
b
b
p
p
that are used as the
that are used as the
point estimators of the parameters
point estimators of the parameters
0
0
,
,
1
1
,
,
2
2
, . . . ,
, . . . ,
p
p
.
.
Estimated Multiple Regression Equation
Estimated Multiple Regression Equation
^
^
y
y
=
=
b
b
0
0
+
+
b
b
1
1
x
x
1
1
+
+
b
b
2
2
x
x
2
2
+ . . . +
+ . . . +
b
b
p
p
x
x
p
p
The
The
estimated multiple regression equation
estimated multiple regression equation
is:
is:
Page 4
Interpreting the Coefficients
Interpreting the Coefficients
In multiple regression analysis, we interpret each
In multiple regression analysis, we interpret each
regression coefficient as follows:
regression coefficient as follows:
b
b
i
i
represents an estimate of the change in
represents an estimate of the change in
y
y
corresponding to a 1
corresponding to a 1


unit increase in
unit increase in
x
x
i
i
when all
when all
other independent variables are held constant.
other independent variables are held constant.
Page 5
Example: Car Sales
Example: Car Sales
Suppose we believe that number of cars sold (
Suppose we believe that number of cars sold (
y
y
) is
) is
not only related to the number of ads (
not only related to the number of ads (
x
x
1
1
), but also to the
), but also to the
minimum down payment required at the
(
minimum down payment required at the
(
x
x
2
2
). The
). The
regression model can be given by:
regression model can be given by:
Multiple Regression Model
Multiple Regression Model
where
where
y
y
= number of cars sold
= number of cars sold
x
x
1
1
= number of ads
= number of ads
x
x
2
2
= minimum down payment required (
= minimum down payment required (
‘
‘
000)
000)
y
y
=
=
0
0
+
+
1
1
x
x
1
1
+
+
2
2
x
x
2
2
+
+
Page 6
Estimated Regression Equation
Estimated Regression Equation
y = 14.4 + 3.7 *
y = 14.4 + 3.7 *
x
x
1
1
–
–
25*
25*
x
x
2
2
Interpretation?
Interpretation?
Estimated values of y?
Estimated values of y?
Error?
Error?
Prediction?
Prediction?
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