Economics 103
Winter 2009
Problem Set 2
Due Tuesday, February 3
Question 1:
True/False/Explain
1.
When the estimated slope coefficient in the simple regression model,
1
ö
β
, is zero,
then
R
2
=0.
2.
The variance of
Y
i
is equal to the variance of the error term in the regression.
3.
To obtain the slope estimator using the least squares principle, you divide the
sample covariance of
X
and
Y
by the sample variance of Y
4.
The population regression line and the sample regression line are the same on
average.
5.
We do not need any assumptions in order for OLS estimators to be BLUE (Best
linear unbiased estimator)
6.
The model y=
α
+
β
log(x) is linear in the variables but not linear in the parameters.
It therefore satisfies our linearity assumption.
7.
If the pvalue for a twosided test is .03, you fail to reject the null hypothesis at
the 5% confidence level.
8.
The assumptions made by the classical linear regression model (CLRM) are not
necessary to compute OLS estimators.
Question 2
Show that OLS estimators are unbiased.
(Use a simple bivariate regression function.)
What assumptions do you need?
Question 3
Sir Francis Galton, a cousin of James Darwin, examined the relationship between the
height of children and their parents towards the end of the 19
th
century. It is from
this study that the name “regression” originated. You decide to update his
findings by collecting data from 110 college students, and estimate the following
relationship (Standard errors in parenthesis):
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Studenth
= 19.6 + 0.73×
Midparh
,
R
2
=
0.45
(7.2)
(0.10)
where
Studenth
is the height of students in inches, and
Midparh
is the average of
the parental heights. (Following Galton’s methodology, both variables were
adjusted so that the average female height was equal to the average male height.)
1.
Interpret the estimated coefficients.
2.
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 Winter '07
 SandraBlack
 Economics, Regression Analysis, Errors and residuals in statistics, OLS, predicted value, College GPA

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