Problem Set 4
Economics 103 – Spring 2008
Prof. Ackerberg
Due: Tuesday, May 27 at the beginning of class
True/False – You must explain your answer for full credit.
1) If your regression suffers from “Imperfect Multicollinearity”, your estimated
coefficients will be biased.
False, “Imperfect Multicollinearity” does not cause bias.
However, it can lead to
imprecise estimates, i.e. high standard errors and large confidence intervals.
2) When testing hypotheses in a multiple regression model, you always need to use an
F
STAT
.
False, if you are testing a hypothesis regarding a single coefficient, you can use a
t
STAT
.
3)
Just because a coefficient is statistically significant does not mean that it is
economically significant.
True, “statistical significance” means that we can reject the null hypothesis that the
coefficient equals zero.
“Economic significance” means that the coefficient is large
in an economic sense, i.e. that the effect is economically large.
The two do not
necessarily coincide – e.g. a coefficient can be statistically significant but not
economically significant.
We saw an example of this in class (Lecture note 11)
4) In a nonlinear regression model, the effect of a change in
X
i
on
Y
i
varies depending on
the level of
X
i
.
True, in a linear model, the effect of a unit change in
X
i
(on
Y
i
) is constant, i.e.
always the same.
In a nonlinear model this is not the case.
For example, if
Y
i
=
10
+ 2
X
i
+ 1
X
i
2
, the effect of increasing
X
i
from 1 to 2 is to increase
Y
i
by 4.
The effect
of increasing
X
i
from 2 to 3 is to increase
Y
i
by 6.
5) The adjustedR
2
always increases when you add an additional regressor variable to the
regression.
False, R
2
always increases when you add an additional regressor variable to the
regression.
AdjustedR
2
does not always increase.
If AdjustedR
2
does increase, it
tells us that the additional regressor has improved the fit of the model.
If it does not
increase, the additional regressor is not improving the fit of the model (and often we
choose not to include the variable)
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View Full Document6)
In the following polynomial regression model
Y
i
=
100 + 5.4
X
i
 0.1
X
i
2
the relationship between
X
i
and
Y
i
is concave (you can answer this either with or without
calculus).
True.
Using Calculus, the derivative of this function is 5.4 – 0.2
X
i
, and the second
derivative is 0.2.
Since the second derivative is negative, the function is concave.
One can also do this by plugging in various values of
X
i
.
When
X
i
= 1,
Y
i
= 105.3,
when
X
i
= 2,
Y
i
= 110.4, and when
X
i
= 3,
Y
i
= 115.3.
Since the effect of increasing
X
i
by one unit decreases as
X
i
increases, the function is concave (you could also plot
these points and see that the function looks concave (the function looks like a cave
when viewed from below).
Longer Answer:
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 Spring '07
 SandraBlack
 Economics, Econometrics, Linear Regression, Regression Analysis, per capita, robust standard errors, robust linear regression, Linear regression Number

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