Answer Happy

Question 3 Consider the linear function y; = Bo + Bixi + u₁. Suppose that the following results were obtained from a sample with 12 observations: . Sample average of y = 10 . Sample average of x = 10 • Sample variance of y = 25 . Sample variance of x = 40 . Sample covariance of y and x = 20. Suppose that the CLM Assumptions hold here and answer the following questions. (14 points) (i) Calculate the OLS estimates of Bo and B₁, and the R². [Hint: R² is equaled to the square of "coefficient of correlation", r. See eq. (C.15) in Appendix C.] (3 points) Estimate the variance of error term, o, and Var (B₁). [Hint: See eq. (2.61).] (2 points) (iii) Test the null hypothesis that x has no effect on y against the alternative that x has effect on y. What is the t-statistic? Is x statistically significant? (2 points) (iv) Suppose that we add the term ß₂z to the original model and that x and z are negatively correlated. What is the likely bias in estimates of ₁ obtained from the simple regression of y on x? (2 points) Based on question (iv), when <0 and R² = 0.7 from regressing y on x and z, what is the t-statistic for the coefficient on z? Can we say that "z is statistically significant?" (5 points) (v)