1
III.
Simple Regression.
A.
Introduction
B.
Population Regression Equation
C.
Sample Regression Equation
D.
Ordinary Least Squares
E.
Classical Regression Model.
F.
Properties of OLS Estimators (
BLUE
)
G.
Estimator for
σ
2
H.
Inference (we’ve done this before!)
F. Properties of OLS Estimators
•
What properties do we want for our estimators?
•
What are we trying to describe?
U
d
l
d
i
Unbiased and Min. Variance
Sampling Distribution
•
Use expected values to determine
Center:
Variance:
1
1
ˆ
[
]
E
β
β
=
2
1
1
1
ˆ
ˆ
(
)
[ (
) ]
Var
E
β
β
β
=
−
CRMA # 6
: We assume that the disturbances
are normally distributed.
•
Linear combinations of normally distributed
variables are also normally distributed.
•
Y is a linear combination of u.
•
OLS estimators
‐
linear combinations of Y.
•
OLS estimators are normally distributed.

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