SECTION A – Answer ALL questions. Each question has only ONE correct answer. Each
question carries equal weight.
1. What is the value of b1 in the following sample regression function
= 1 + 2 +
= 8.6747 = 12 2 = 0.7241
where b1 and b2 are OLS estimates and ui is a residual.
a. 5.7187
b. 17.364
c. 0.0145
d. 8.6892
2. In the two-variable Ordinary Least Squares (OLS) regression model of the form Y = a + bX,
an unbiased estimator of the slope coefficient (b) is given by the expression:
a.
cov(X,Y)
Var(X)
b. cov(X,Y)
Var(Y)
c.
Var(X)
Var(Y)
d. Var(X)
cov(X,Y)
3. Which of the following assumptions are required to show consistency, unbiasedness and
efficiency of the OLS estimators
I. (
) = 0
II. (
) =
2
III. (
, ) = 0; ≠
IV. ~ (0,
2
)
a. II and IV only
b. I and III only
c. I, II, and III only
d. I, II, III, and IV
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continued
Continued
4. Which one of the following is NOT the BLUE property of the OLS estimators in the simple
regression models
a. b1 and b2 have the lowest variances.
b. b1 and b2 are linear functions of X.
c. E(b1) = β1 and E(b2) = β2.
d. None of the above.
5. What is the value of the coefficient of determination (R2
) in the following estimation results
where se are standard errors
Y i = 0.000518 + 0.707Xi
se = (0.000315) (0.035)
RSS = 0.157 and TSS = 0.208
a. 0.198
b. 0.245
c. 0.755
d. 0.548
6. If the estimates of the coefficients of interest change substantially across specifications,
then:
a. this can be expected from sample variation.
b. you should change the scale of variables to make the changes appear to be smaller.
c. this often provides evidence that the original specification had omitted variable bias.
d. you should choose the specification that your coefficient of interest is most significant.
7. Which of the following is a test of the significance of a sub-group of coefficients
a. Adjusted R2
.
b. t- test.
c. Chow test.
d. Wald test.
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8. Imagine you regressed earnings of individuals on a constant, a binary variable (“Male”)
which takes on the value 1 for males and is 0 otherwise, and another binary variable
(“Female”) which takes on the value 1 for females and is 0 otherwise. Because females
typically earn less than males, you would expect
a. the coefficient for Male to have a positive sign, and for Female a negative sign.
b. both coefficients to be the same distance from the constant, one above and the other
below.
c. none of the OLS estimators to exist because there is perfect multicollinearity.
d. this to yield a difference in means statistic.
9. When you have an omitted variable problem, the assumption that E(ui Xi) = 0 is violated.
This implies that
a) the sum of the residuals is no longer zero.
b) there is another estimator called weighted least squares, which is BLUE.
c) the sum of the residuals times any of the explanatory variables is no longer zero.
d) the OLS estimator is no longer consistent.
10.If you had a two regressor regression model, then omitting one variable which is relevant
a) will have no effect on the coefficient of the included variable if the correlation
between the excluded and the included variable is negative.
b) will always bias the coefficient of the included variable upwards.
c) can result in a negative value for the coefficient of the included variable, even
though the coefficient will have a significant positive effect on Y if the omitted
variable were included.
d) makes the sum of the product between the included variable and the residuals
different from 0.
11. The Augmented Dickey Fuller (ADF) t-statistic
a) has a normal distribution in large samples.
b) has the identical distribution whether or not a trend is included or not.
c) is a two-sided test.
d) is an extension of the Dickey-Fuller test when the underlying model is AR(p) rather
than AR(1).
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12.What would be then consequences for the OLS estimator if heteroscedasticity is present
in a regression model but ignored
a) It will be biased.
b) It will be inconsistent.
c) It will be inefficient.
d) All of a, c, and b will be true.
13.The regression coefficient estimated in the presence of autocorrelation in the sample data
are NOT
a) Unbiased estimator.
b) Consistent estimator.
c) Efficient estimator.
d) Linear estimator.
14.With heteroskedastic errors, the weighted least squares estimator is BLUE. You should
use OLS with heteroskedasticity-robust standard errors because
a) the exact form of the conditional variance is rarely known.
b) the Gauss-Markov theorem holds.
c) this method is simpler.
d) our spreadsheet program does not have a command for weighted least squares.
15.The AR(p) model
a) is defined as Yt = β0 + βpYt-p + ut.
b) represents Yt as a linear function of p of its lagged values.
c) can be represented as follows: Yt = β0 + β1Xt + βpYt-p + ut.
d) can be written as Yt = β0 + β1Yt-1 + ut-p.
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SECTION B – Answer TWO questions
16.Consider the following multiple regression model that relates the logarithm of demand for
pizza ( ) to logarithm of total expenditure ( ), the number of children in the
household ( ), and logarithm of pizza price ( ):
