- When we say that the OLS estimator is "BLU", we are referring to the fact that:
- Among all possible estimators of the linear regression coefficient vector that are unbiased, this estimator has the greatest "efficiency", provided that the model satisfies certain assumptions.
- Among all possible linear estimators of the regression coefficient vector that are also unbiased, this estimator has the greatest "efficiency", provided that the model satisfies certain assumptions.
- Among all possible linear estimators of the regression coefficient vector that are also unbiased, this estimator has the greatest "efficiency".
- Among all possible linear estimators of the regression coefficient vector that are also unbiased, this estimator has the greatest "efficiency", provided that the model's error term is normally distributed.

- When we say that the usual OLS estimator is a "linear estimator" we mean that:
- It is being applied to a regression model that is itself linear.
- It is linear in the parameters, but not necessarily linear in the regressors.
- It is a linear function of the random sample data - the data for the dependent variable, y, in this case.
- It is a linear function of the X matrix.

- The connection between the expected value of an estimator and the mean of that estimator's sampling distribution is that:
- The expected value of an estimator always exists, but the mean of its sampling distribution may not. When they both exist, they are the same.
- There is really no connection in general - they relate to quite different concepts.
- They will both be zero if the estimator is unbiased.
- They are exactly the same thing.

- The usual estimator that we use for the error variance in a linear regresion model (namely, the sum of squared OLS residuals, divided by the degrees of freedom) is:
- An unbiased estimator, whose sampling distribution is proportional to a Chi-Square distribution with (n-k) degrees of freedom.
- An unbiased estimator.
- An unbiased estimator, whose sampling distribution is a Chi-Square distribution, with (n-k) degrees of freedom.
- An unbiased estimator, whose sampling distribution is Student-t with (n-k) degrees of freedom.

- The OLS estimator of the regession coefficient vector in a linear regression model, and the usual estimator of the variance of the model's error term are:
- Positively correlated, because the estimator of the error variance must yield positive values.
- Both unbiased estimators.
- Statistically independent if all of the assumptions (including normality of the error term) about the model hold.
- Statistically independent, as long as the errors are homoskedastic and uncorrelated.

- One connection between the variance of an estimator and the mean squared error of that estimator is:
- The mean squared error cannot be smaller than the variance.
- They will be same if the estimator is linear and unbiased.
- They will be same if the estimator is unbiased.
- Both A and C.

- The diagonal elements of the covariance matrix of an estimator of a vector of parameters are:
- The standard deviations of the estimators of the individual elements of the parameter vector.
- The variances of the estimators of the individual elements of the parameter vector.
- Either positive or negative, depending on whether this matrix is positive definite or negative definite.
- Of the same sign as any bias in the estimator for the corresponding parameter element, and therefore zero if this estimator is unbiased.

- Suppose that we choose to use the arithmetic mean of the squared OLS residuals as an estimator of the variance of the model's error term. Then:
- This estimator is a downward-biased estimator of the error's variance.
- This estimator is an upward-biased estimator of the error's variance.
- This estimator is biased, and the direction of its bias depends on the degrees of freedom, (n-k).
- It is impossible to tell anything about the the bias of this estimator unlesss we know the value of the error's variance.

- A statistic that follows a Student-t distribution is one which is constructed in the following way:
- By taking the ratio of a the square of a standard normal statistic to a chi-square statistic (that has been already divided by its degrees of freedom), where these 2 statistics are independent of each other.
- By taking the ratio of a standard normal statistic to the square root of a chi-square statistic (that has been already divided by its degrees of freedom), where these 2 statistics are independent of each other.
- By taking the ratio of the square root of a chi-square statistic (that has been already divided by its degrees of freedom) to a standard normal statistic, where these 2 statistics are independent of each other.
- By taking the ratio of the square roots of two independent chi-square statistics.

- The correct interpretation of a 95% confidence interval is:
- If we were to take an infinite number of samples of the same size, and construct the estimator and the confidence interval in each case, then 95% of the time the true value of the parameter being estimated would lie in one of these intervals.
- If we were to take an infinite number of samples of the same size, and construct the estimator and the confidence interval in each case, then 95% of all of these intervals would cover the true value of the parameter being estimated.
- There is a 95% chance that the true value of the parameter I am estimating lies in the interval I have constructed from this sample of data.
- None of the above.

- If we have constructed a 95% (2-sided) confidence interval that covers the value 2.0 for some parameter of interest, then the following is true:
- We cannot reject the hypothesis that the parameter is 2.0, at the 5% significance level, against the alternative hypothesis that it is not equal to 2.0.
- This interval is consistent with coming to the conclusion that we cannot reject the hypothesis that the parameter is 2.0 (against a 2-sided alternative) if were to obtain a p-value of 0.06.
- Both A and B.
- This interval is consistent with coming to the conclusion that we cannot reject the hypothesis that the parameter is 2.0 (against a 2-sided alternative) if were to obtain a p-value of 0.04.

- I have estimated a regression model by OLS and I calculate a 95% confidence interval for one of the regression coefficients as (0.85, 0.95). Using exactly the same data, I am asked to now calculate a 99% confidence interval, because my supervisor is hoping that this interv al will cover the value 1.00.
- This is worth doing, becasuse the new interval must be wider than the original one, and it is possible that it will cover 1.00
- This is a waste of time as the new interval must be narrower than the one I have calculated already
- This is a waste of time as the new interval must be (0.89, 0.99) and so it won't cover 1.00
- This is a waste of time. Although the new interval must be wider than the one I have calculated already, its upper limit cannot be above 0.99

- Suppose I am conducting a test and I have in mind an implicit significance level of 5%. My class-mate always uses a significance level of 10% for such tests.The econometrics package I am using reports a p-value of 0.015 for my test.
- I would reject the null hypothesis, but my class-mate would not reject it.
- My class-mate would reject the null hypothesis, but I would not reject it.
- Neither of us would reject the null hypothesis.
- My class-mate and I would both reject the null hypothesis.

- If a statistical test is "Unbiased", then:
- It must also be a "Most Powerful" test.
- It will correctly reject false hypotheses, on average.
- Its power never falls below the assigned significance level.
- Its power improves, on average, as the sample size increases.

- When the null hypothesis is true, the Power of a test is:
- The probability of rejecting this null hypothesis.
- Equal to the significance level.
- The probability of a Type II error.
- Both A and B.

- Check the EViews regression output located here. The following is true with respect to the regressor called P_SA:
- We would reject the hypothesis that this coefficient is zero, against the alternative that it is positive, at the 5% significance level, but not at the 1% significance level.
- We would reject the hypothesis that this coefficient is zero, against the alternative that it is positive, at the 1% significance level, but not at the 5% significance level.
- We would reject the hypothesis that this coefficient is zero, against a 2-sided alternative hypothesis, at both the 5% and 1% significance levels.
- We cannot reject the hypothesis that this coefficient is zero, against the alternative that it is positive, at either the 5% significance level or the 1% significance level.

- Check the EViews regression output for a confidence ellipse located here. The following is true:
- There is a 95% chance that the true values of C(4) and C(5) lie in this ellipse.
- Of all of the ellipses of this sort that could be created by re-estimating the model again and again with different samples of the same size, 95% would cover the true values of both C(4) and C(5) at once.
- The OLS estimators of C(4) and C(5) are negatively correlated
- Both B and C.