Question

1) Which of the following does not generally decrease the variance of the OLS estimator of slope βˆ1?

a) Increasing the variance of the error term, b) Increasing the sample size, c) None of the above, d) Increasing the variance of the independent variable

2) If the independent variable is a binary variable then which of the following is true?

a)β0 is a population mean for the group with a value of 1 for the independent variable,

b) β1 is the difference between two population means

c) β0 is the difference between two population means

d) β1 is a population mean for the group with a value of 0 for the independent variable

3) Which of the following is *not* a consequence of the 3
least squares assumptions

a) The OLS estimators are consistent.

b) The OLS estimators are unbiased.

c) The OLS estimators are approximately normally distributed in large samples.

d) The OLS estimators are efficient.

Answer #1

Q.1) Option a) is correct.

If increasing the variance of the error term then generally does not decrease the variance of the OLS estimator of slope βˆ1 it will increase.

Q.2) Option c) is correct.

If the independent variable is a binary variable then is the difference between two population mean.

Q.3) Option c) is correct.

The least square estimates are linear, consistent as well as efficient but it is not necessory they are normally distribted in large samples .

1. The Central Limit Theorem
A. States that the OLS estimator is BLUE
B. states that the mean of the sampling distribution of the
mean is equal to the population mean
C. none of these
D. states that the mean of the sampling distribution of the
mean is equal to the population standard deviation divided by the
square root of the sample size
2. Consider the regression equation Ci= β0+β1 Yi+ ui where C is
consumption and Y is disposable...

1. Consider the bivariate model: Yi = β0+β1Xi+ui . Explain what
it means for the OLS estimator, βˆ 1, to be consistent. (You may
want to draw a picture.)
2. (Circle all that applies) Which of the following regression
functions is/are linear in the parameters a) Yi = β1 + β2 1 Xi b)
Yi = β1 + β 3 2Xi c) Yi = β1 + β2Xi

Answer the following questions in technical or non-technical
language.
(a) What is the Central Limit Theorem?
(b) What does it mean for an estimator to be unbiased or
consistent?
(c) What is the difference between point estimators and interval
estimators of parameters?
(d) Under what conditions should we use t-tests rather than
z-tests for population means?
(e) Why are conjugate families of distributions convenient for
Bayesian analysis?

Which of the following statements is correct regarding the
implication of the existence of heteroscedasticity?
A) The OLS estimator is biased.
B) The OLS estimator is unbiased and still best. There is no
other estimator with smaller variance.
C) The OLS estimator is biased but the standard errors usually
computed for the OLS estimator are correct.
D) The standard errors usually computed for the OLS estimator
are incorrect.

a. If ? ̅1 is the mean of a random sample of size n from a
normal population with mean ? and variance ?1 2 and ? ̅2 is the
mean of a random sample of size n from a normal population with
mean ? and variance ?2 2, and the two samples are independent, show
that ?? ̅1 + (1 − ?)? ̅2 where 0 ≤ ? ≤ 1 is an unbiased estimator
of ?.
b. Find the value...

Consider the following statements concerning confidence interval
estimates:
A. The use of the pooled variance estimator when constructing a
confidence interval for the difference between means requires the
assumption that the population variances are equal.
B. The width of a confidence interval estimate for the proportion,
or for mean when the population standard deviation is known, is
inversely proportional to the square root of the sample size.
C. To determine the sample size required to achieve a desired
precision in...

Discuss whether each of the following statements is correct or
not.
(a) A large t-value implies a low p-value.
(b) The law of iterated expectations implies that if the
conditional mean of Y given X is zero, then the mean of Y is
zero.
(c) A sample correlation of 0.97 between the regressors causes
OLS estimators to be biased.
(d) Measurement error in the independent variable causes OLS
estimators to be biased.

which of the following is an unbiased point estimator for the
expected value of any sampled random variables?
a) the sample varlance
b) the p-value
c) the sample mean
d) the margin of error

1) Which is NOT a fundamental assumption of OLS (Ordinary Least
Squares)?
a) The regression model is nonlinear
in the coefficients and error term.
b) Observations of the
error term are uncorrelated with each other.
c) No independent variable is a
perfect linear function of any other explanatory variables.
d) The error term has
homoscedasticity.
e) All independent variables will be uncorrelated
with the error term.
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2) You test a model that...

1. When the error-terms are heteroskedastic, then:
a) WLS is more efficient than OLS in large samples, if the
functional form of the heteroskedasticity is known.
b) OLS coefficients are biased.
c) OLS is still BLUE but t and F distributions are invalid.
d) there are only two solutions: either use WLS if the
functional form of the heteroskedasticity is known or use GLS if
the functional form of the heteroskedasticity is known.
e) None of the above
2. Which...

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