Econ 444 Elementary Econometrics (Fall 2007)
ANSWERS TO HOMEWORK EXERCISE: 1
(1.a)
False.
The stochastic error term
°
i
is for the population regression
and is not directly observable unless the population regression is, while the
residual is for the sample regression and can be computed from a sample.
(1.b)
False. The sample regression computed from the OLS is usually dif
ferent from the population regression just as the sample average is usually
di/erent from the population mean.
(1.c)
False. The individual residual term is usually di/erent from zero. (Note
that the sum of the residual is always zero when OLS is used as we will learn
in Chapter 2.
However, the individual residual term does not have to be
zero, and is usually not equal to zero as we have seen in examples in class.)
(2.a)
Let
X
1
= 9
; X
2
= 12
, and
X
3
= 16
.
When the price is $9, the
expected demand is
E
(
Y
1
j
X
1
) = (1
=
2)
°
21 + (1
=
2)
°
25 = 23
.
When the
price is $12,
E
(
Y
1
j
X
2
) = (1
=
2)
°
12 + (1
=
2)
°
16 = 14
. When the price is $16,
E
(
Y
3
j
X
3
) = (1
=
2)
°
0 + (1
=
2)
°
4 = 2
.
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 Fall '07
 OGAKI
 Econometrics, Linear Regression, Regression Analysis, Errors and residuals in statistics, Studentized residual, population regression

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