Finite sample properties of OLS estimators

QUESTION 1
Which of the following statements is correct?
Finite sample properties of OLS estimators hold for
any sample size n with the additional restriction that n
must be at least as large as the numbers of
parameters in the regression model.
Asymptotic properties of OLS estimators are defined as the
sample size grows without bound.
Asymptotic properties are also called large sample
properties.
All of the above.
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a.
b.
QUESTION 2
Let be the OLS estimator of βj for some independent
variable j. Which of the following statements is correct?
being unbiased means that for each sample size n,
has a probability distribution with mean value βj
.
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c.
d.
being consistent means that the probability distribution
of becomes more and more tightly distributed around its
mean value βj as the sample size n grows.
Under Assumptions MLR.1 through MLR.4, is both
unbiased and consistent.
All of the above.
a.
b.
c.
d.
QUESTION 3
Consider the following population model, y = β0 + β1x1 + …+ βkxk

• u. Which of the following statements is correct?
  Assumption MLR.4 requires that any function of the
  explanatory variables in uncorrelated with u, while
  Assumption MLR.4’ requires that each xj
  is uncorrelated
  with u (and that u has a zero mean in the population).
  Assumption MLR.4’ is weaker than Assumption MLR.4.
  Under Assumption MLR.4’, OLS is consistent, but biased.
  Correlation between u and any of x1
  , x2
  , …, xk generally
  causes all of the OLS estimators to be inconsistent.
  The problem of inconsistency in OLS estimators does
  not go away by adding more observations to the
  sample. The direction of the inconsistency or
  asymptotic bias is obtained similarly to the way the
  direction of the omitted variable bias is obtained.
  All of the above.
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  a.
  b.
  QUESTION 4
  Consider the following population model, y = β0 + β1x1 + …+
  βkxk + u. Which of the following statements is correct?
  Under the classical linear model (CLM) assumptions
  MLR.1 through MLR.6,
  and , where n is the sample
  size.
  Under the Gauss-Markov Assumptions MLR.1 through
  MLR.5, both and follow
  an asymptotic standard normal distribution.
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  Question Completion Status:
  d.All of the above.
  a.
  b.
  c.
  d.
  QUESTION 5
  Which of the following statements is incorrect?
  To test multiple exclusion restrictions, an alternative to the
  F statistic is the Lagrange multiplier (LM) statistic.
  The LM statistic is also called score statistic or n-R-squared statistic.
  The LM statistic requires estimation of the unrestricted model only.
  Asymptotically, the F and LM statistics have the same probability of
  Type I error. That is, they reject the null hypothesis with the same
  frequency when the null is true.
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  a.
  b.
  c.
  d.
  QUESTION 6
  If = Cov(x1
  ,x2
  ) / Var(x1
  ) where x1
  and x2
  are two independent variables
  in a regression equation, which of the following statements is true?
  δ1
  If x2
  has a positive partial effect on the dependent variable, and >
  0, then the inconsistency in the simple regression slope estimator
  associated with x1
  is negative.
  δ1
  If x2 has a positive partial effect on the dependent variable, and

0, then the inconsistency in the simple regression slope estimator
associated with x1
is positive.
δ1
If x1 has a positive partial effect on the dependent variable, and
0, then the inconsistency in the simple regression slope estimator
associated with x1
is negative.
δ1
If x1
has a positive partial effect on the dependent variable, and >
0, then the inconsistency in the simple regression slope estimator
associated with x1
is positive.
δ1
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QUESTION 7
This question is about how to use Excel to plot histogram for
residuals.
Use wagedata.xlsx to estimate the equation:
wage = β0 + β1‍educ + β2exper + β3tenure + u (1)
The estimated equation should be:
= -2.7683 + 0.5933educ + 0.0202exper + 0.1810tenure.
Note: below is how you run regression using Data Analysis in
Excel. The same as what you have learned in the past. But,
remember to select “Residuals”.
7-1.jpg
Then, use your output to plot a histogram for residuals in
Excel. Note: to create a histogram in Excel, two types of data
are required—the data you want to analyze (residuals) and the
bin numbers that represent the intervals by which you want to
measure the frequency (you can use 25 bin numbers here: -9,
-8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,
12, 13, 14, and 15 since the residuals range from -8.0018 to
14.5411). Below shows how you do this.
Choose “Histogram” under Data Analysis. Click on “Ok”.
7-2.jpg
In your output sheet, create a “Bins” column (from -9 to 15)
next to your “Residuals” column. Then select your Input Range
(all Residuals from C26 to C525) and Bin Range (all Bins from
D26 to D51). Output Range: you can select any cell of the
sheet. Select “Labels”. Select “Chart Output”. Then, click on
“Ok.
7-3.jpg
Your histogram of th

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