simple2 - Simple Linear Regression Model The equation that...

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 .

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
  