Econ 444 Elementary Econometrics (Fall 2007)
SUMMARY of CHAPTER 2
and
HOMEWORK EXERCISE: 2
Due at the beginning of class on Monday, October 8
1 KEY TERMS, CONCEPTS, and Formulas
The least squares principle, Ordinary Least Squares (OLS), Multiple Regre
sion
The Formulas for OLS estimates for K=1:
^
1
=
[(
P
N
i
=1
(
X
i
X
))
±
(
Y
i
Y
)]
P
N
i
=1
(
X
i
X
)
2
:
(1)
^
&
0
=
Y
^
1
X;
(2)
Two features of the OLS estimators.
(1) The estimated regression obtained by the OLS passes through the
sample mean values of
X
and
Y
:
Y
=
^
&
0
+
^
1
±
X:
(3)
(2) The sample mean value of the residuals is always equal to zero (except
for the rounding error):
e
=
1
N
N
X
i
=1
e
i
= 0
:
(4)
The
total sum of squares
, or TSS, is
TSS
=
N
X
i
=1
(
Y
i
Y
)
2
:
(5)
The
explained sum of squares
, or ESS, is
1
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=
N
X
i
=1
(
^
Y
i
Y
)
2
:
(6)
The residual sum of squares, or RSS, is
RSS
=
N
X
i
=1
e
2
i
:
(7)
TSS
=
ESS
+
RSS:
(8)
R
2
, the coe¢ cient of determination, by
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 Fall '07
 OGAKI
 Econometrics, Regression Analysis, OLS, Adjusted R2, ne R2

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