Simple Linear Regression Model
y
=
b
0
+
b
1
x
+
e
where:
b
0
and
b
1
are called parameters of the model
,
e
is a random variable called the error term
.
The simple linear regression model
is:
The equation that describes how
y
is related to
x
and
an error term is called the regression model
.
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Estimation Process
Regression Model
y
=
b
0
+
b
1
x
+
e
Regression Equation
E
(
y
) =
b
0
+
b
1
x
Unknown Parameters
b
0
,
b
1
Sample Data:
x
y
x
1
y
1
.
.
.
.
x
n
y
n
b
0
and
b
1
provide estimates of
b
0
and
b
1
Estimated
Regression Equation
Sample Statistics
b
0
,
b
1
0
1
ˆ
y
b
b x
Estimation Process
Unknown
Relationship
Population
Random Sample
Y
X
i
i
i
b
b
e
0
1
i
i
i
X
Y
e
b
b
ˆ
ˆ
ˆ
1
0
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