ECG 561, Intermediate Econometrics, Spring 2008
Study Questions for Midterm II
1.
Consider the following multiple regression:
y
i
= +
1
x
1i
+
2
x
2i
+ u
i
,
where the basic assumption about the error term hold.
Describe in detail how you could test the following hypotheses using the Fstatistic that compares a
restricted with an unrestricted regression model.
(a)
2
= 2
(b)
1
=
2
(c)
1
= 2
2
(d)
1
+
2
= 1
(e)
+
1
+
2
= 0
(f)
1
=
2
= 5
2.
A researcher estimates a multiple regression, in which y is the dependent variable and x
1
and x
2
are the
independent variables.
The researcher suspects that a basic assumption concerning the disturbance terms is
violated for the data he is examining.
Namely, he suspects that:
Cov(x
1
,u) 0.
He proposes to test the hypothesis by calculating the sample covariance between x
1
and
.
If the sample
covariance is far enough from zero then he proposes to reject the null hypothesis of uncorrelated x
1
and u.
What is wrong with his test procedure?
3.
True, False, or Uncertain (and explain):
In a simple linear regression, if the tstatistic for the slope
coefficient equals zero, then the R
2
for the regression equals zero, and the Fstatistic for the regression equals zero.
4.
True, False, or Uncertain (and explain): In a simple linear regression, the tstatistic for the slope equals
the overall Fstatistic for the regression.
5.
True, False, or Uncertain (and explain): If the Rsquared for a simple linear regression is zero, then the F
statistic testing H
o
:
o
=
1
= 0 will also be zero.
6.
You run a linear regression of corn yield (y) on fertilizer level (x), assuming the standard linear regression
model discussed in class.
When you present your research results to your thesis committee, you are asked to
perform two calculations:
(i)
Estimate the expected corn yield that would result from an application rate of 400 pounds per
acre and construct a 90% confidence interval around your estimate–an interval that in repeated
sampling would contain the true conditional expectation 90% of the time.
(ii)
Predict the corn yield that would result from an application rate of 400 pounds per acre and
construct a 90% confidence interval for the realized corn yield–an interval that in repeated
sampling would contain the realized corn yield 90% of the time.
Explain why the confidence interval that you would construct in (ii) would be larger, perhaps much larger,
than the confidence interval you would construct in (i).
Your answer should be primarily in words, but you may
use relevant formulas as well.
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7.
Consider the regression of
prate
on
rate
in Problem Set #3.
The variable
prate
is a percentage with values
in the range 3 to 100.
The variable
rate
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 Fall '08
 ERYURUK
 Linear Regression, Regression Analysis

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