Introduction to Econometrics (Econ 107)
Drake University, Fall 1995
William M. Boal
Name: _________________________________
QUIZ 3 -- November 3, 1995
INSTRUCTIONS: Closed-book, closed-notes, calculators permitted. Please write your answers on this
sheet.
(1) [Classical assumptions for least squares: 24 pts] Which of the following are classical assumptions?
Write "YES" for classical assumptions and "NO" otherwise.
a. The mean of the error term is zero: E(εi) = 0.
b. The mean of the regressor is zero: E(xi) = 0.
c. The variance of the error term is zero: Var(εi) = 0.
d. The covariance between the error term and the regressor is zero:
Cov(xi,εi) = 0.
e. The covariance between the regressor and dependent variables is
zero: Cov(xi,yi) = 0.
f. The covariance between the error term and the dependent variable is
zero: Cov(εi,yi) = 0.
g. The covariance between the error terms for different observations is
zero: Cov(εj,εi) = 0, for i≠j.
h. The true intercept is zero.
(2) [Properties of least squares: 21 pts] Under the classical assumptions, which of the following properties
hold? Write "TRUE" or "FALSE."
a. The least squares estimators are unbiased.
b. The reverse least squares estimators are unbiased.
c. Greater variance in the error term increases the variance of the least-
squares estimators.
d. Greater variation in the regressor increases the variance of the least-
squares estimators.
e. The least squares estimators for the intercept and slope are
uncorrelated with each other.
f. The covariance of the least squares estimators for the intercept and
slope is negative if the sample mean of the regressors is positive.
g. The least squares estimators have the smallest variance among all
linear estimators with zero bias.
(3) [Properties of least squares: 15 pts] Suppose the true slope is positive, but in our data the error term is
negatively correlated with the regressor. The the least squares estimator of the slope will be (check only
one box): biased upward (estimated slope too steep).
biased downward (estimated slope too flat or perhaps even negative).
unbiased.
