 ECON | 3790 | Business and Economics | l...
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
Showing 1-6 out of 25
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
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
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?

Browse thousands of Study Materials & Solutions from your Favorite Schools Youngstown State Universi...
Youngstown_State_University
School:
Course:
Great resource for chem class. Had all the past labs and assignments  Leland P.
Santa Clara University
Introducing Study Plan
Using AI Tools to Help you understand and remember your course concepts better and faster than any other resource. Find the best videos to learn every concept in that course from Youtube and Tiktok without searching. Save All Relavent Videos & Materials and access anytime and anywhere Prepare Smart and Guarantee better grades