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Introduction to Regression Analysis
We wish to study the
relationship between 2 or more variables
We define:
y
=
the
dependent
variable
x
=
independent (predictor)
variable
We wish to
predict
y
on the basis of
x
.
Example:
y
=
sales of a product
x
=
price of the product
Assuming a
linear (straight line) relationship
between y and x, we wish to find a
prediction
equation
Predicted value of y
intercept
y
ˆ
= b
0
+ b
1
x
slope
Simple Linear Regression
One
Straight Line
Predictor
Relationship
Variable
We use data concerning both
x
and
y
to find numerical values for b
0
and b
1
.

Multiple Regression
We predict
y
by using
more than one
independent (predictor) variable.
Example:
y
=
sales
x
1
=
price
x
2
=
advertising budget
x
3
=
type of advertising ( TV, radio, print, etc.)
The
prediction equation
might have the following form:
y
ˆ
=
b
0
+ b
1
x
1
+ b
2
x
2
+ b
3
x
3
We find
numerical values
of
b
0
, b
1
, b
2
,
and
b
3
by using data concerning
y
,
x
1
,
x
2
,
and
x
3
.
Alternatively, ( as one possible example) the prediction equation could have the form:

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