Remainder of answer to ISolution Continues in 252z987112/14/98 252y9871 ECO252 QBA2 Name FINAL EXAM Hour of Class Registered (Circle) December 14, 1998 MWF 10 11 TR 12:30 2:00 I. (16 points) Do all the following.Hand in your fourth regression problem(2 points) and answer the following questions. If you did not do this problem you can have a copy of the problem output for a 2-point penalty.1. In the regression of ‘price’ against ‘oldpr’,’chassets’,’chincome’ and ‘chsales’, which coefficients are significant at the 5% level. Why? (3)2. Which coefficients are significant at the 1% level? Why?(1)3. Comparing the regressions that you did, noting t-tests, Rsq, Rsq(adj), which seems best? Why?(2)4. Compare the regression against ‘oldpr’ with the regression against ‘oldpr’, ‘chassets’ and ‘chincome’ using an F test. Do the added variables have additional explanatory power? (4)5. Using the regression against ‘oldpr’ and ‘chassets’ observation, give a confidence and prediction intervalfor price in the first observation. (3)6. In the regression against ‘oldpr’, ‘chassets’, ‘chincome’ and ‘eps’, are the signs of the coefficients as expected? Why?(2)7. If a company has an old price of 20, a 25% change in assets in 1992, and a 30% change in income in 1992, what price does the regression against ‘oldpr’, ‘chassets’ and ‘chincome’ predict? (2) Solution: 1),2) From the computer output: VariableCoefficient t pConstant -36.240 -4.14 .003 S5 S1Oldpr 2.4072 8.96 .000 S5 S1Chassets 0.1783 1.18 .273 Chincome 0.15782 2.63 .030 S5Chinsales 0.3217 1.02 .339The easiest way to do this problem is to compare the p-value to .05 and .01. Those significant at the 1% level are marked S1 and those significant at the 5% level are marked S5. You can also compare the t coefficient against 2t. In particular, 306.28025.t and 355.38005.t ; this yields the same results.3) The regression against Oldpr, Chassets and Chincome has significant coefficients and a relatively large2Radjusted (87.0) and is preferred. The addition of Chsales doesn’t raise 2Radjusted and creates two insignificant coefficients. No other regression has as high an 2Radjusted.4) The first two ANOVAs below come from the printout. The last one is figured out from the difference between the Regression sums of squares in the first two.Regression 1 Regression 2 DifferenceSource SS DF Source SS DF Source SS DF MSRegr. 3904.7 1 Regr. 4600.2 3 Regression 1 3904.7 1Error 1195.7 11 Error 500.1 9 Regression 2 695.5 2 342.75Total 5100.3 12 Total 5100.3 12 Error 500.1 9 55.57Total 5100.3 12If we take the ratio of the mean squares in the difference ANOVA we find that 258.657.5575.342F. Since 26.49,205.Fis less than the computed F, we conclude that the effect of the new variables is significant.5) Reading the standard deviation and the es from the printout, the confidence interval is 87.393.5112025.t, and the prediction interval is 2212025.182.987,393.51 t. Since no onegot this, I never finished getting the values.1See bottom of page 3 for rest of answer.212/14/98 252y9871II. Do at least 4 of the following 6 Problems (at least 15 each) (or do sections adding to at least 60 points - Anything extra you do helps, and grades wrap around) . Show your work! State H0 and H1where applicable. Use a significance level of 5% unless noted otherwise.1. The data below shows salary, months employed and gender for 9 employees. yis salary in thousands, y x1x2x1 is months employed andx2is a dummy variable with 1 for female.Salary Months Gender a) Compute the simple regression equation of salary against gender (6) 7.5 6 0 b) Compute R2. (4) 8.6 10 0 c) Compute se.(3) 9.1 12 0 d) Compute 1bs and do a significance test on 1b. (4)10.3 18 0 e) Do a prediction interval for salary for an employee with 17 years service.(4)13.0 30 0 6.2 5 1 8.7 13 1 9.4 15 1 9.8 21 1,64.786,6.822yy,0.2364,0.130211xx,0.4,0.4222xx9 and 0.54,1.34?,2121nxxyxyx. You do not need all of these.Solution: No! yxyx1 If you think this is true, you didn’t learn anything from me in ECO251. yx1 45.0 86.0 109.2 185.4 390.0 31.0 113.1 141.0 205.81306.5So 5.13061yxUsing capital letter instead of small ones17778.996.82 Y44444.1490.1301XOur spare parts are: 22222.48644444.1490.236422121XnX 38889.11317778.944444.1495.130611YXnYX 55556.2817778.9664.786222YnYa)233204.022222.48638889.1132121111XnXYXnYXb 80928.544444.14233204.017778.910 XbYb, so that our equation is1233204.08093.5ˆXY .b) 92601.55556.2822222.48238889.1132222222YnYXnXYXnXYR312/14/98 252y9871c) 54939.0301831.0738889.113233204.055556.2821222eesnYXnXYbYnYsd) 00062077.02222.4821301831.0122221XnXsseb. 0249152.01bs,so that 35991.90249151.233204.01101bsbt Since 365.27025.2025.ttn,0 is significant. (0H is 01. We reject it.)e) If 170X, 77375.917233204.080928.5ˆ0100 XbbY so that 12222.4864444.1417913018.0365.2774.911ˆ2222022025.00XnXXXnstYenY 378.1774.958263.0365.2774.9 Remainder of answer to I6) Logic says that all the independent variables should be related to higher prices, so that the coefficients should all be positive. However, the coefficient of Eps is negative.7) Using coefficients from the printout: Price .46.2430147.25282.02032.24.33 Solution Continues in
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