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Multiple Choice Test Bank Questions No Feedback – Chapter 4
Correct answers denoted by an asterisk.
1. Consider a standard normally distributed variable, a t-distributed variable with d
degrees of freedom, and an F-distributed variable with (1, d) degrees of freedom.
Which of the following statements is FALSE?
2. If our regression equation is y = X
+ u, where we have T observations and k
regressors, what will be the dimension of
ˆ
using the standard matrix notation
Question 3 refers to the following regression estimated on 64 observations:
yt =
1 +
2X2t +
3X3t +
4X4t + ut
3. Which of the following null hypotheses could we test using an F-test?
(i)
2 = 0
(ii)
2 = 1 and
3 +
4 = 1
(iii)
3
4 = 1
(iv)
2 -
3 -
4 = 1
For question 4, you are given the following data
103,86.0
,
8.0
9.2
6.1
)'(,
4.39.14.1
9.18.01.2
4.11.23.1
)'(
2
1
==
−
=
−
−
=
−
Ts
yXXX
The regression equation is
yt =
1 +
2X2t +
3X3t + ut
4. Which of the following is the correct value for
1
ˆ
?
5. Consider the following regression estimated using 84 observations:
yt =
1 +
2X2t +
3X3t +
4X4t + ut
Suppose that a researcher wishes to test the null hypothesis:
2 = 1 and
3 +
4 = 1. The
TABULATED value of the F-distribution that we would compare the result of testing
this hypothesis with at the 10% level would be approximately
6. What is the relationship, if any, between t-distributed and F-distributed random
variables?
7. Which one of the following statements must hold for EVERY CASE concerning the
residual sums of squares for the restricted and unrestricted regressions?
8. Which one of the following is the most appropriate as a definition of R2 in the context
that the term is usually used?
9. Suppose that the value of R2 for an estimated regression model is exactly one. Which
of the following are true?
(i) All of the data points must lie exactly on the line
(ii) All of the residuals must be zero
(iii) All of the variability of y about is mean have has been explained by the model
(i) The fitted line will be horizontal with respect to all of the explanatory variables
10. Consider the following two regressions
tttt uyxy +++= −13221
tttt uyxy +++= −13221
Which of the following statements are true?
(i) The RSS will be the same for the two models
(ii) The R2 will be the same for the two models
(iii) The adjusted R2 will be different for the two models
(iv) The regression F-test will be the same for the two models
11. Which of the following are often considered disadvantages of the use of adjusted R2
as a variable addition / variable deletion rule?
(i) Adjusted R2 always rises as more variables are added
(ii) Adjusted R2 often leads to large models with many marginally significant or
marginally insignificant variables
(iii) Adjusted R2 cannot be compared for models with different explanatory variables
(iv) Adjusted R2 cannot be compared for models with different explained variables.
12. Which of these is a mathematical expression of the residual sum of squares?
(I)
ˆˆ
'uu
(II)
12
ˆ ˆ ˆ
... T
u u u
(III)
12
ˆ ˆ ˆ
... T
u u u+ + +
13. If you are interested in conducting a multiple hypotheses test to determine whether
2
and
3
are both unity for a regression
1 2 2 3 3 4 4
y x x x u
= + + + +
, what would
the restricted regression be?
14. What would the restricted regression be if you are interested in testing the null
hypothesis
02
:0H
=
and
30
=
against the alternative hypothesis
12
:0H
or
30
for a regression
1 2 2 3 3 4 4
y x x x u
= + + + +
,?
15. Assuming that the restricted sum of squares of the restricted regression in question 3
is 436.1 and the unrestricted sum of squares is 397.2, what would the conclusion of the
hypothesis test be? (The significance level is 5%)
16. Which of these statements is a characteristic of the stepwise regression procedure?
(I) It chooses the jointly most ‘important’ explanatory variable from a set of candidate
variables
(II) It can start with no variables in the regression and then it selects first the variable
with the lowest p-value
(III) It can start with no variables in the regression and then it selects first the variable
with the highest p-value
17. Trying many variables in a regression without basing the selection of candidate
variables on a financial or economic theory is popularly referred to as
18. Why is R2 a commonly used and perhaps better measure of how well a regression
Use the following to answer questions 19 and 20.
Assuming you have two regression models
1 2 2 3 3t t t t
y x x u
= + + +
and
1 2 4 3 5t t t t
y x x v
= + + +
.
19. How can the two models be validly compared to determine the model that better
represents the data yt?
20. What is the relevant encompassing model required to compare the two regression
models?
21. Which of these statements is not true about quantile regressions?
