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Multiple Choice Test Bank Questions No Feedback – Chapter 3
Correct answers denoted by an asterisk.
1. Regression is concerned with describing and evaluating the relationship between
2. What does a positive linear relationship between x and y in a simple regression
imply?
3. Which of these is not a reason for adding a disturbance term to a regression model
t t t
y x u
= + +
?
4. Which of these is not a standard method for estimating econometric models?
5. The method of estimating econometric models which involves fitting a line to the
data by minimising the sum of squared residuals is the
6. Suppose you have 5-year annual data on the excess returns on a fund manager’s
portfolio (“fund ABC”) and the excess returns on a market index (where
ABC
r
is the
return on fund ABC,
f
r
is the risk-free rate and
M
r
is the return on the market index):
Year t
Excess return on fund ABC
,,ABC t f t
rr−
Excess return on market index
,,M t f t
rr−
1
14.0
16.0
2
32.0
21.7
3
11.6
6.0
4
21.2
16.2
5
17.4
11.0
What is the estimated alpha (
ˆ
) for Fund ABC?
7. Given the data in question 6, what is the estimated beta (
ˆ
) of Fund ABC?
8. Suppose that the unbiased estimator of the standard deviation of the disturbance (s)
is 5.1. What is the nearest value to the standard errors of the estimated CAPM alpha
(
ˆ
) of Fund ABC from question 6?
9. The estimated alpha (
ˆ
) and beta (
ˆ
) of a rival fund, Fund DEF, are 2.3 and 3.1,
respectively. If the expected market risk premium is 12%, what would we expect the
excess return of Fund DEF to be?
10. What is the most appropriate interpretation of the assumption
( )
cov , 0
ij
uu =
concerning the regression disturbance terms?
11. The estimators
ˆ
and
ˆ
determined by OLS will be the Best Linear Unbiased
Estimators (BLUE) if which of the following assumptions hold?
(I) The errors have zero mean
(II) The variance of the errors is constant and finite over all values of the independent
variable(s)
(III) The errors are linearly independent of one another
(IV)There is no relationship between the error and corresponding independent
variables
Suppose you have calculated the following regression results:
ˆ1.25 0.64
tt
yx=+
. The standard errors of
ˆ
and
ˆ
are 1.22 and 0.58, respectively.
13. Using the test of significance approach, what is the test statistic value of a
hypothesis to test whether the true value of
statistically different from zero?
14. Assuming there are 1000 observations in your sample, what are the test statistic
and critical value of a two-sided hypothesis test of whether the true value
of
statistically different from zero be given a 5% significance level?
15. Consider a bivariate regression model with coefficient standard errors calculated
using the usual formulae. Which of the following statements is/are correct regarding
the standard error estimator for the slope coefficient?
(i) It varies positively with the square root of the residual variance (s)
(ii) It varies positively with the spread of X about its mean value
(iii) It varies positively with the spread of X about zero
(iv) It varies positively with the sample size T
16. In a time series regression of the excess return of a mutual fund on a constant and
the excess return on a market index, which of the following statements should be true
for the fund manager to be considered to have “beaten the market” in a statistical
sense?
17. What result is proved by the Gauss-Markov theorem?
18. The type I error associated with testing a hypothesis is equal to
19. Which of the following is a correct interpretation of a “95% confidence interval”
for a regression parameter?
20. Which of the following statements is correct concerning the conditions required
for OLS to be a usable estimation technique?
21. Which of the following is NOT a good reason for including a disturbance term in
a regression equation?
22. Which of the following is NOT correct with regard to the p-value attached to a
test statistic?
23. Which one of the following is NOT an assumption of the classical linear
regression model?
24. Which of the following is the most accurate definition of the term “the OLS
estimator”?
25. Two researchers have identical models, data, coefficients and standard error
estimates. They test the same hypothesis using a two-sided alternative, but researcher
1 uses a 5% size of test while researcher 2 uses a 10% test. Which one of the
following statements is correct?
26. Consider an increase in the size of the test used to examine a hypothesis from 5%
to 10%. Which one of the following would be an implication?
27. What is the relationship, if any, between the normal and t-distributions?
