ECON 1150
Fall 2010
Problem Set 3: Due 10/25/10
Please be sure that the pages are stapled together in the correct order.
Please write neatly.
Parts within each question receive equal weight. You do not need to attach Stata output
with your answers, but be sure to write out all equations in standard form; and include the
sample size and the
R
squared.
1.
Provide a short answer to each of the following questions.
(i) Suppose that the results of a multiple and simple regression, using the same set of
data, are
and
Are
x
1
and
x
2
positively or negatively correlated in the sample?
Justify your answer.
(Hint: use formula (3.23) on page 84)
Using equation connecting coefficients’ estimates of the simple and multiple regression,
one can obtain
, a slope coefficient form a simple regression of
x
2
on
x
1
:
The negative sign of the slope coefficient indicates negative correlation between
x
2
and
x
1.
(ii) Comment on the following statement:
“Multiple regression analysis is useless unless
all of the explanatory variables are uncorrelated.”
As long as there is no perfect collinearity between the independent variables, regression
makes sense, since inclusion of each independent variable allows a researcher to hold it
fixed in the analysis.
It is true that if the explanatory variables are highly correlated that
it may be difficult to estimate each partial effect, but that depends on other factors, such
as the sample size and how big the population effect is.
In any case, correlations among
the explanatory variables are certainly allowed, and fully expected, in multiple
regression.
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 Fall '08
 Staff
 Statistics, Econometrics, Regression Analysis, New Jersey

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