Problem: You are worried about multicollinearity in your regression model. In particular, you are worried that X2 and X3 are collinear. You compute the correlation coefficient: r(X2,X3) = - 0.82. Which of the following statements do you think are true? (Circle more than one answer if you think more than one statement is true. Choose no answers if you think no answer is true.)
1. OLS is no longer the minimum-variance estimator.
2. If you have a small number of observations (50), it is still possible that you will obtain statistically significant estimates of β2 and β3.
3. The more observations you have, the greater your chance of obtaining statistically significant estimates of β2 and β3.
4. Your estimates of β2 and β3 are less likely to be biased than if the correlation coefficient were closer to 1.0.
5. Your adjusted R2 is likely to be lower than if the correlation coefficient were closer to 0.
6. Your t-statistics are likely to be larger than they would be if the correlation coefficient were closer to 1.0.
7. You expect the α1 in the following equation to be positive: X2= α0 + α1X3 + ε
8. If the t-statistic for X3 is low, it is unlikely that dropping X3 from your model will cause omitted variable bias.
9. Your t-statistic for β2 will probably rise if you drop X3 from your model.
10. You have a higher probability of obtaining an estimate of β2 that is dramatically different from the true value of β2.