1. (22 points, 2 points each) Multiple Choice Questions: choose the one alternative that best completes the statement or answers the question. Please write your answer in the following box.
1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11)
1) Daily stock prices for 200 stocks from 1 March 1990 to 1 March 2020 is an example of using
A) time series data.
B) panel data.
C) cross-sectional data.
D) experimental data.
2) In a linear regression model Yi = β0 + β1X1i + β2X2i + β3X3i + ui, which one of the following statements is NOT true?
3) In a linear regression model Yi = β1X1i + β2X2i + β3X3i + β4X4i + ui, which one of the following statements is true?
4) In a linear regression model Yi = β0 +β1X1i +β2X2i +β3X3i +ui, which of the following statements about the assumption that E (ui|X1i, X2i, X3i) = 0 is not correct?
A) It says that the conditional distribution of the error given the explanatory variables has a zero mean.
B) It implies that ui and X2 are uncorrelated.
C) It implies that u2 and X2i are uncorrelated.
D) It cannot hold if ui and X1i are correlated.
5) An example of a randomized controlled experiment is when
A) random variables are controlled for by holding other factors constant.
B) one U.S. state increases the cigarette tax and an adjacent state does not, and cigarette consumption differences are observed.
C) households receive government bonus in 2017 but not in 2016.
D) some 2nd graders in a specific elementary school are randomly assigned to attend piano lessons at school while others are not, and their end-of-year performance is compared.
6) In a linear regression model Yi = β0 + β1Xi + ui, which of the following factors makes V ar(β1) smaller?
A) a smaller value of sample size
B) a larger variation in Yi
C) a larger value of the error variance
D) a larger variation in Xi
7) Which of the following statement is true?
A) As you add irrelevant independent variables to a linear regression model, T SS will decrease. 2
B) As you remove independent variables from a linear regression model, R will decrease. 2
C) As n increases, the difference between R and R increases. 2
D) R is usually preferred to R because it takes into account the degrees of freedom in the regression.
8) Consider the following multiple regression models A) to D) below. M ale is a binary variable which takes on the value one if the individual is male, and is zero otherwise; F emale = 1 if the individual is a female, and is zero otherwise; M arried is a binary variable which is unity for married individuals and is zero otherwise, and Single = 1 — M arried. Regressing weekly earnings (Earn) on a set of explanatory variables, you will experience perfect multicollinearity in the following cases unless:
A) Earn = β0 + β1M arried + β2Single + β3Schooling + u.
B) Earn = β0 + β1M ale + β2F emale + β3Schooling + u.
C) Earn = β1M ale + β2F emale + β3M arried + β4Schooling + u.
D) Earn = β1M ale + β2F emale + β3M arried + β4Single + β5Schooling + u.
9) Which of the following statements is true when two or more regressors in a multiple regression model are highly correlated?
A) The OLS estimators of some slope coefficients are inconsistent.
B) R2 is close to zero.
C) The sign of a slope coefficient estimate might be wrong.
D) The OLS assumptions are violated.
10) You have collected data for the 50 U.S. states and estimated the following relationship between the change in the unemployment rate from the previous year (Aur ) and the growth rate of the respective state real GDP (gCDP ). The results are as follows
Aˆur = 2.81 — 0.23 gCDP , n = 50, R2 = 0.36, SER = 0.78.
Assuming that the estimator has a normal distribution, the 95% confidence interval for the slope is ap- proximately the interval
A) [2.57, 3.05]
B) [-0.31,-0.15]
C) [-0.31, 0.15]
D) [-0.33, -0.13]
11) Given the information in the above question, we can also calculate the explained sum of squares (ESS) which is approximately given by
A) 16.4268 B) 29.2032 C) 45.6300 D) 17.1113
2. (8 points, 2 points each) Please first state whether you agree or disagree with each of the following claims. Then explain briefly why you agree or disagree with them.
(a) 0 ≤ R2 ≤ 1, when there is an intercept term in the linear regression model Yi = β0 + β1X1i +
β2X2i + ui.
b) The OLS estimation is commonly used by applied researchers as the OLS estimators are always unbiased and consistent.
c) In the case of omitted relevant independent variables that may be correlated with other regressors, the confidence interval of a slope coefficient is generally valid.
d) For the simple linear regression (SLR) model: Yi = β0 +β1Xi +ui, i = 1, ..., n, the OLS etstimator is consistent if (i) Cov(Xi, ui) = 0 for i = 1, 2, ..., n, (ii) (Yi, Xi), i = 1, 2, • • • , n, are IID, (iii) Large outliers are unlikely.
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