Write down your answers on blank papers. You can use formulae, graphs or examples to illustrate if needed. (Total 20 points, 5 points each) a. (5 points) Given the motivations for using the adjusted R instead of the R when comparing the goodness of fit of various multiple regression models? b. (5 points) Given the following sample regression model estimated using the ordinary least squares (OLS) estimation method: 3 = B1 + xe tt 2 Xt is it true that cov (B1, B) < 0? If it is true, explain why. If not, give an example when this does not hold. c. (5 points) If the magnitude of the covariance coefficient between two random variables is large, does it indicate a strong linear relationship between the two random variables? [Hint: Use an example to justify your answer.] d. (5 points) Is the following statement true? Explain. "When conducting hypothesis testing, we reject the null hypothesis at a 5% significance level if the p-value of the test statistic is larger than 0.05."