1
ECO 6416
Bivariate Regression
Statistical model to study relationship between
dependent variable and one or more
independent variables.
Flexible modeling approach
Widely used statistical method in business &
economics
Can do anything that analysis of variance can
do, plus more
Illustrative example
Framework and regression model
Estimation
Inference
Simple regression
Examples
Transition to multiple regression
To study the influence of advertising on profits,
the
Boston Celtics
compiled annual data on Ad
expenditures in $100,000s
and profits in
millions of dollars
. The sample (for each of the
Slide #4
last five years) is:
Year
1
2
3
4
5
Ad Expenditures (x)
2
3
4.5
5.5
7
Profit (y)
3
6
8
10
11
Ad Expenditures (x)
2
3
4.5
5.5
7
Profit (y)
3
6
8
10
11
The
Celtics
need answers to these questions
Slide #5
need answers to these questions
1. Does advertising increase profit?
2. How much does another $100,000 spent on
advertising increase profit?
3. What will our profit be if we spend $800,000
on advertising?
4. How much will we need to spend on ads to
generate $12,000,000 in profit?
Slide #6

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Surprisingly, one statistical decision-making
tool can provide answers to
all
of these
questions -- and more.
The tool is called
regression analysis
.
Slide #7
Note: You would never really use a regression with
only five observations!
Regression analysis is a statistical technique
A
ttempts to "explain" movements in one
variable, the
dependent variable
. . .
Slide #8
as function of movements in a set of other
variables, the
independent variables
. . .
through the quantification of one or more
equations
Slide #9
equations.
Northwestern Memorial Hospital, which has the
largest birthing facility in the Midwest, uses a
simple regression model
to forecast delivery
volume based on previous delivery volumes.
Slide #10
(Source: Jerry Lassa, Northwestern Memorial
Hospital, Chicago, IL.)
IRI, the largest market research firm in the United
States uses
simple regression
on adjusted weekly
sales data to determine baseline sales when
there is no special promotion. (Source: Doug
Slide #11
Honnold, IRI, Inc., Chicago, IL.)
0
1
value of dependent variable for population element i.
X
value of independent variable for population
i
i
i
i
i
Y
X
u
Y
β
β
=
+
+
=
=
0
1
value of independent variable for population
element i.
,
population parameters governing
X, Y relationship.
a random
i
u
β
β
=
=
"error" for population element i.