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SUMMARY of CHAPTER 4
and
HOMEWORK EXERCISE: 3
Due at the beginning of class on Wednesday, October 17
1 KEY TERMS AND CONCEPTS
variance, correlation, sample variance, sample correlation coe¢ cient, Clas
sical Assumptions, perfect multicollinearity, normal distributions, sampling
distributions of OLS estimators, Linear unbiased estimators, Variances of
OLS estimators, GaussMarkov theorem, BLUE
2 FORMULAS AND RESULTS
The Classical Assumptions
I. The regression model is linear.
Y
i
=
&
0
+
1
X
1
i
+
:::
+
K
X
Ki
+
±
i
;
i
= 1
;
2
; ::::::; N
(1)
II. The error term has a zero population mean.
E
[
±
i
] = 0
;
i
= 1
;
2
; :::; N:
(2)
III. All explanatory variables are given and nonrandom.
IV. The error terms are uncorrelated with each other.
Cor
(
±
i
; ±
j
) = 0
;
fori
6
=
j:
(3)
V. The error term has a constant variance (no heteroskedasticity)
V ar
(
±
i
) =
²
2
;
i
= 1
;
2
; :::::; N
(4)
VI. There is no perfect linear relationship between the explanatory vari
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 Fall '07
 OGAKI
 Econometrics

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