Câu hỏi: Which of the following is a correct interpretation of a “95% confidence interval” for a regression parameter?

A. We are 95% sure that the interval contains the true value of the parameter

B. We are 95% sure that our estimate of the coefficient is correct

C. We are 95% sure that the interval contains our estimate of the coefficient

D. In repeated samples, we would derive the same estimate for the coefficient 95% of the time

Câu 1: The type I error associated with testing a hypothesis is equal to:

A. One minus the type II error

B. The confidence level

C. The size of the test

D. The size of the sample

Câu 2: Consider a standard normally distributed variable, a t-distributed variable with d degrees of freedom, and an F-distributed variable with (1, d) degrees of freedom. Which of the following statements is FALSE?

A. The standard normal is a special case of the t-distribution, the square of which is a special case of the F-distribution

B. Since the three distributions are related, the 5% critical values from each will be the same

C. Asymptotically, a given test conducted using any of the three distributions will lead to the same conclusion

D. The normal and t- distributions are symmetric about zero while the F- takes only positive values

Câu 3: What result is proved by the Gauss-Markov theorem?

A. That OLS gives unbiased coefficient estimates

B. That OLS gives minimum variance coefficient estimates

C. That OLS gives minimum variance coefficient estimates only among the class of linear unbiased estimators

D. That OLS ensures that the errors are distributed normally

Câu 4: Two researchers have identical models, data, coefficients and standard error estimates. They test the same hypothesis using a two-sided alternative, but researcher 1 uses a 5% size of test while researcher 2 uses a 10% test. Which one of the following statements is correct?

A. Researcher 2 will use a larger critical value from the t-tables

B. Researcher 2 will have a higher probability of type I error

C. Researcher 1 will be more likely to reject the null hypothesis

D. Both researchers will always reach the same conclusion

Câu 5: What is the relationship, if any, between t-distributed and F-distributed random variables?

A. A t-variate with z degrees of freedom is also an F(1, z)

B. The square of a t-variate with z degrees of freedom is also an F(1, z)

C. A t-variate with z degrees of freedom is also an F(z, 1)

D. There is no relationship between the two distributions

Câu 6: Which of the following would you expect to be a problem associated with adding lagged values of the dependent variable into a regression equation?

A. The assumption that the regressors are non-stochastic is violated

B. A model with many lags may lead to residual non-normality

C. Adding lags may induce multicollinearity with current values of variables

D. The standard errors of the coefficients will fall as a result of adding more explanatory variables