Econ 120B Ramu RamanathanEcon 120B Ramu RamanathanSpring 2003 Makeup exam 1 (20%)I. Carefully explain whether the following statements are correct or not.I.1 (5 points) If the variance of ut is large then regression coefficients will be less precisely estimated.I.2 (5 points) Estimators can be BLUE even if the errors are not normally distributed.I.3 (5 points) If you choose a higher level of significance, a regression coefficient is less likely to be sigificant.II.The Registrar's Office at UCSD supplied me with the data for 427 first year undergraduate students on the GPA in college (COLGPA, the dependent variable), GPA in high school (HSGPA), Verbal SAT scores (VSAT), and math SAT scores (MSAT). Three alternative models were estimated and the results are given below. Values in parentheses are standard errors. (A) COLGPA = 0.92058 + 0.52417 HSGPA R2 = 0.165 (0.20463) (0.05712)(B) COLGPA = 1.99740 + 0.00157 VSAT R2 = 0.070 (0.14128) (0.00028)(C) COLGPA = 1.62845 + 0.00205 MSAT R2 = 0.124 (0.15135) (0.00026) II.1 (5 points) What do the low values for R2 indicate? Which is the “best” model and why?II.2 Test your best model for overall goodness of fit (that is, that the correlation between WAGE and your independent variable is zero) at the 1% level. (4 points) Compute the test statistic:(3 points) State its distribution and degrees of freedom under the null. 1(3 points) The critical value lies in the range (4 points) Do you reject the null hypothesis or not? What do you conclude in terms of the goodness of fit?I.3 In your best model, test (at the 1 percent level) the null hypothesis that the regression coefficient for the slope term is significantly different from zero by carrying out the following steps (choose the level 10%).(2 points) State the null hypothesis and the alternative: (3 points) Compute the test statistic:(2 points) State its distribution and degrees of freedom under the null. (3 points) State the range for the critical value.(3 points) Do you reject the null hypothesis or not? What do you conclude in terms of the significance of the coefficient?(3 points) Explain why the two-variable model is
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