计量经济学Test bank questions Chapter 3

Multiple Choice Test Bank Questions No Feedback – Chapter 3 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?

(a)The standard normal is a special case of the t-distribution, the square of which is a

special case of the F-distribution.

(b)* Since the three distributions are related, the 5% critical values from each will be the

same.

(c)Asymptotically, a given test conducted using any of the three distributions will lead to

the same conclusion.

(d)The normal and t- distributions are symmetric about zero while the F- takes only

positive values.

2. If our regression equation is y = Xβ+ u, where we have T observations and k regressors, what will be the dimension of β? using the standard matrix notation

(a) T?k

(b) T? 1

(c) * k? 1

(d) k?k

Question 3 refers to the following regression estimated on 64 observations: y t = β1 + β2X2t + β3X3t + β4X4t + u t

3. Which of the following null hypotheses could we test using an F-test?

(i) β2 = 0

(ii) β2 = 1 and β3 + β4 = 1

(iii) β3β4 = 1

(iv) β2 -β3 -β4 = 1

(a) (i) and (ii) only

(b) (ii) and (iv) only

(c) (i), (ii), (iii) and (iv)

(d)* (i), (ii), and (iv) only

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The regression equation is

y t = β1+ β2X2t + β3X3t + u t

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4. Which of the following is the correct value for

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(a) * 2.89

(b) 1.30

(c) 0.84

?β from the information given in the question (d) We cannot determine the value of

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5. Consider the following regression estimated using 84 observations:

y t = β1 + β2X2t + β3X3t + β4X4t + u t

Suppose that a researcher wishes to test the null hypothesis: β2 = 1 and β3 + β4 = 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

(a) 19.48

(b) 2.76

(c) * 2.37

(d) 3.11

6.What is the relationship, if any, between t-distributed and F-distributed random

variables?

(a)A t-variate with z degrees of freedom is also an F(1, z)

(b)* The square of a t-variate with z degrees of freedom is also an F(1, z)

(c)A t-variate with z degrees of freedom is also an F(z, 1)

(d)There is no relationship between the two distributions.

7. Which one of the following statements must hold for EVERY CASE concerning the residual sums of squares for the restricted and unrestricted regressions?

(a)URSS > RRSS

(b)URSS ≥ RRSS

(c)RRSS > URSS

(d)* RRSS ≥ URSS

8. Which one of the following is the most appropriate as a definition of R2 in the context that the term is usually used?

(a)It is the proportion of the total variability of y that is explained by the model

(b)* It is the proportion of the total variability of y about its mean value that is explained

by the model

(c)It is the correlation between the fitted values and the residuals

(d)It is the correlation between the fitted values and the mean.

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

(a) (ii) and (iv) only

(b) (i) and (iii) only

(c) * (i), (ii), and (iii) only

(i), (ii), (iii), and (iv)

10. Consider the following two regressions

t t t t u y x y +++=-13221βββ

t t t t u y x y +++=?-13221γγγ

Which of the following statements are true?

(i) The RSS will be the same for the two models

(ii) The R 2 will be the same for the two models

(iii) The adjusted R 2 will be different for the two models

(iv) The regression F -test will be the same for the two models

(a) (ii) and (iv) only

(b) * (i) and (iii) only

(c) (i), (ii), and (iii) only

(d) (i), (ii), (iii), and (iv).

11. Which of the following are often considered disadvantages of the use of adjusted R 2 as a variable addition / variable deletion rule?

(i) Adjusted R 2 always rises as more variables are added

(ii) Adjusted R 2 often leads to large models with many marginally significant or

marginally insignificant variables

(iii) Adjusted R 2 cannot be compared for models with different explanatory variables (iv) Adjusted R 2 cannot be compared for models with different explained variables.

(a) * (ii) and (iv) only

(b) (i) and (iii) only

(c) (i), (ii), and (iii) only

(d) (i), (ii), (iii), and (iv).