93 câu trắc nghiệm Kinh tế lượng – Phần 1

KTL_002_C3_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?
○ The standard normal is a special case of the t-distribution, the square of which is a special case of the F-distribution.
● Since the three distributions are related, the 5% critical values from each will be the same.
○ Asymptotically, a given test conducted using any of the three distributions will lead to the same conclusion.
○ The normal and t- distributions are symmetric about zero while the F- takes only positive values.

KTL_002_C3_2: If our regression equation is \(Y = X\beta + U\), where we have T observations and k regressors, what will be the dimension of \(\hat \beta \) using the standard matrix notation
○ T x k
○ T x 1
● k x 1
○ k x k

Question 3 refers to the following regression estimated on 64 observations:
\({Y_t} = {\beta _1} + {\beta _2}{X_{2t}} + {\beta _3}{X_{3t}} + {\beta _4}{X_{4t}} + {U_t}\)

KTL_002_C3_3: Which of the following null hypotheses could we test using an F-test?
(i) \({\beta _2}\) = 0
(ii) \({\beta _2}\) = 1 and \({\beta _3}\) + \({\beta _4}\) = 1
(iii) \({\beta _3}\)\({\beta _4}\) = 1
(iv) \({\beta _2}\) – \({\beta _3}\) – \({\beta _4}\) = 1

○ (i) and (ii) only
○ (ii) and (iv) only
○ (i), (ii), (iii) and (iv)
● (i), (ii), and (iv) only

For question 4, you are given the following data

\(\begin{array}{l}{(X’X)^{ – 1}} = \left[ {\begin{array}{ccccccccccccccc}{1.3}&{2.1}&{ – 1.4}\\{2.1}&{0.8}&{1.9}\\{ – 1.4}&{1.9}&{3.4}\end{array}} \right]\quad ,\quad (X’y) = \left[ {\begin{array}{ccccccccccccccc}{ – 1.6}\\{2.9}\\{0.8}\end{array}} \right]\quad ,\quad \\{s^2} = 0.86\quad ,\quad \quad T = 103\end{array}\)

The regression equation is
\({Y_t} = {\beta _1} + {\beta _2}{X_{2t}} + {\beta _3}{X_{3t}} + {U_t}\)

KTL_002_C3_4: Which of the following is the correct value for?
● 2.89
○ 1.30
○ 0.84
○ We cannot determine the value of from the information given in the question

KTL_002_C3_5: Consider the following regression estimated using 84 observations:
\({Y_t} = {\beta _1} + {\beta _2}{X_{2t}} + {\beta _3}{X_{3t}} + {\beta _4}{X_{4t}} + {U_t}\)

Suppose that a researcher wishes to test the null hypothesis: \({\beta _2}\) = 1 and \({\beta _3}\) + \({\beta _4}\) = 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
○ 19.48
○ 2.76
● 2.37
○ 3.11

KTL_002_C3_6: What is the relationship, if any, between t-distributed and F-distributed random variables?
○ A t-variate with z degrees of freedom is also an F(1, z)
● The square of a t-variate with z degrees of freedom is also an F(1, z)
○ A t-variate with z degrees of freedom is also an F(z, 1)
○ There is no relationship between the two distributions.

KTL_002_C3_7: Which one of the following statements must hold for EVERY CASE concerning the residual sums of squares for the restricted and unrestricted regressions?
○ URSS > RRSS
○ URSS \( \ge \) RRSS
○ RRSS > URSS
● RRSS \( \ge \) URSS

KTL_002_C3_8: Which one of the following is the most appropriate as a definition of \({R^2}\) in the context that the term is usually used?
○ It is the proportion of the total variability of y that is explained by the model
● It is the proportion of the total variability of y about its mean value that is explained by the model
○ It is the correlation between the fitted values and the residuals
○ It is the correlation between the fitted values and the mean.

KTL_002_C3_9: Suppose that the value of \({R^2}\) 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
(iv) The fitted line will be horizontal with respect to all of the explanatory variables

○ (ii) and (iv) only
○ (i) and (iii) only
● (i), (ii), and (iii) only
○ (i), (ii), (iii), and (iv)

KTL_002_C3_10: Consider the following two regressions

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

○ (ii) and (iv) only
● (i) and (iii) only
○ (i), (ii), and (iii) only
○ (i), (ii), (iii), and (iv).

KTL_002_C3_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.

● (ii) and (iv) only
○ (i) and (iii) only
○ (i), (ii), and (iii) only
○ (i), (ii), (iii), and (iv).