Econ 120B Ramu RamanathanEcon 120B Ramu RamanathanSpring 2003 First Midterm AnswersI. Carefully explain whether the following statements are correct or not.I.1 (5 points) A high p-value means that the corresponding regression coefficient is significantly different from zero.False: A high p-value means that the probability of making a Type I error(rejecting a true hypothesis) is high. Thus we should not reject that = 0 but conclude that it is not significantly different from zero.I.2 (5 points) If the errors are serially correlated or heteroscedastic, thencoefficients cannot be unbiased or consistent.False: For unbiasedness and consistency proofs, we do not use Assumptions3.5 and 3.6 and hence coefficients can still be unbiased and consistent.I.3 (5 points) The p-value is the probability that the null hypothesis is true. Complete nonsense: The null hypothesis (say,0) is true or not and is not arandom event. So it is meaningless to talk about the probability of the nullhypothesis being true.II.An investigator gathered the following data on the salaries and employment characteristics of 49 employees in a certain company. WAGE = Wage rate per month (actual dollars) – dependent variable EDUC = Years of education beyond 8th grade when hired EXPER = Number of years at the company AGE = Age of employee in yearsThree models were estimated (the values in parentheses are standard errors).(A) WAGE = 1120.25 + 112.452 EDUC R2 = 0.1696 (241.489) (36.297) (B) WAGE = 1580.29 + 27.15 EXPER R2 = 0.0687 (157.393) (14.59) 1(C) WAGE = 1645.77 + 4.117 AGE R2 = 0.0043 (397.387) (9.117)II.1 (5 points) What do the low values for R2 indicate? Which is the “best” model and why?R2 measures the fraction of the variance of Y that is explained by the model. Lowvalues indicate that a lot of the variation is unexplained. Because Model A hasthe highest R2, it has the best goodness of fit.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:Fc = 221 RR(n-2) = 8304.01696.0 47 = 9.6(3 points) State its distribution and degrees of freedom under the null. F(1,47) or F-distribution with 1 d.f. for numerator and 47 d.f. for the denominator.(3 points) The critical value lies in the range F* is in the range (7.08, 7.31).(4 points) Do you reject the null hypothesis or not? What do you conclude in terms of the goodness of fit?Since Fc > F*, the null hypothesis is rejected and we conclude that thecorrelation between WAGE and EDUC is not zero.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: H0: = 0 H1: ≠ 0.(3 points) Compute the test statistic: tc = 297.36452.112 = 3.098.(2 points) State its distribution and degrees of freedom under the null. Under the null, tc has the t-distribution with 47 degrees of freedom.2(3 points) The critical value lies in the range )005.0(*47t is in (2.66-2.704).(3 points) Do you reject the null hypothesis or not? What do you conclude in terms of the significance of the coefficient?Since | tc| > t*, we reject the null hypothesis and conclude that is significantlydifferent from zero.(3 points) Explain why the two-variable model is inadequate.The best model explains only17% of the variation in WAGE whichmeans that more variables should be added. A possible multiple regressionmodel isWAGE = 1 + 2EDUC + 3EXPER + 4AGE +