5 3 00 252y0043 Open this document in Page Layout view ECO252 QBA2 Name FINAL EXAM May 4 2000 key Note If this is the only thing you look at before taking the final you are badly cheating yourself People who used last year s final and did not read the problems carefully got very wrong answers to them If you can t be bothered to think there is not much point to taking this course or this exam Note If you still think that a large p value means that a coefficient is significant you need a conference with an audiologist Further note that a p value is a probability and can only be compared with another probability like the significance level Note Have you reread Things that You Should Never Do On a Statistics Exam I think I could have graded this exam by just looking for violations of these rules I 16 points Do all the following 1 2 task Hand in your fourth regression problem 2 points and answer the following questions a For the regression of revenue against gdp and gdpsq gdp squared what coefficients are significant at the 5 level Why What about the 10 level 2 b In the same regression which coefficients have signs that are are not reasonable Explain why 1 c Do an F test to show if addition of both yearsq and gdp improves the regression over your results with year alone 4 d Overall which of the regressions seems most successful in predicting rev Why 3 The following pages show the regression of the variable time the time in minutes it takes to do a on an automobile assembly line against months of experience exp The intent was to fit the model y 0 1 x 2 x 2 3 x 3 where x is months of experience Accordingly exp expsq and expcu represent respectively the months of experience of a given worker experience squared and experience to the third power a What is our equation that relates time against exp expsq and expcu What time does it predict for someone with experience of 12 months Show your work 2 b Look at these equations and do appropriate tests 05 to show whether we are justified in including experience squared or cubed in the equation 4 Solution 1 a The result from the computer output see document 252cp400s is copied below MTB regress rev on 2 gdp gdpsq resid pred Regression Analysis The regression equation is rev 65 7 26 5 gdp 2 88 gdpsq Predictor Constant gdp gdpsq s 1 085 Coef 65 67 26 54 2 877 Stdev 67 70 21 92 1 769 R sq 94 5 t ratio 0 97 1 21 1 63 p 0 360 0 261 0 143 R sq adj 93 1 Since all these p values are above both 5 and 10 none of them are significant at either level The rule on p value If the p value is less than the significance level reject the null hypothesis if the p value is greater or equal than the significance level do not reject the null hypothesis 5 3 00 252y0043 b We would expect sales to go up with gdp a negative coefficient doesn t look right There is nothing wrong with a negative regression coefficient unless you have a good reason to believe that it shouldn t be negative c The result from the computer output see document 252cp400s is copied below MTB regress rev on 3 year yearsq gdp resid pred Regression Analysis The regression equation is rev 16 7 0 870 year 0 0588 yearsq 1 77 gdp Predictor Constant year yearsq gdp Coef 16 705 0 8698 0 05882 1 773 s 0 3800 Stdev 7 684 0 2159 0 01301 1 382 R sq 99 4 t ratio 2 17 4 03 4 52 1 28 p 0 066 0 005 0 000 0 240 R sq adj 99 2 Analysis of Variance SOURCE Regression Error Total DF 3 7 10 SS 169 255 1 011 170 265 SOURCE year yearsq gdp DF 1 1 1 SEQ SS 166 173 2 844 0 238 MS 56 418 0 144 F 390 81 p 0 000 If we look at the sequential sums of squares at the end of the ANOVA we see that yearsq and gdp together account for 2 844 0 238 3 082 We can use this to itemize the ANOVA as follows SOURCE year yearsq gdp Error Total DF 1 2 7 10 SS 166 173 3 082 1 011 170 265 MS 166 173 1 541 0 144 F p 10 701 2 7 Since F 05 4 74 we can conclude that the addition of these two variables improves the regression though a look at the p values for the coefficients makes it look like this improvement is due to yearsq alone d If our criteria are a high R 2 and significant low p value coefficients we don t seem to be able to improve on rev 6 85 0 653 year 0 0576 yearsq Predictor Constant year yearsq s 0 3950 Coef 6 8545 0 6533 0 05758 Stdev 0 3009 0 1400 0 01348 R sq 99 3 t ratio 22 78 4 67 4 27 p 0 000 0 000 0 003 R sq adj 99 1 Any higher R 2 seems to be accompanied by insignificant coefficients and often unreasonable signs on these coefficients In particular the negative insignificant coefficient of gdp in the equation toward the top of this page disqualifies it This is what STEPWISE should have made you suspect 2 See below 2 5 3 00 252y0043 Worksheet size 100000 cells MTB RETR C MINITAB 2X0041 1 MTW Retrieving worksheet from file C MINITAB 2X0041 1 MTW Worksheet was saved on 5 1 2000 MTB regress time on 1 exp Regression Analysis The regression equation is time 19 7 0 441 exp Predictor Constant exp Coef 19 7488 0 44116 s 1 141 Stdev 0 5407 0 04098 R sq 89 9 t ratio 36 52 10 77 p 0 000 0 000 R sq adj 89 1 Analysis of Variance SOURCE Regression Error Total DF 1 13 14 SS 150 82 16 92 167 73 Unusual Observations Obs exp time 1 25 0 11 000 MS 150 82 1 30 Fit 8 720 F 115 90 Stdev Fit 0 642 p 0 000 Residual 2 280 St Resid 2 42R R denotes an obs with a large st resid MTB regress time on 2 exp expsq Regression Analysis The regression equation is time 20 8 0 636 exp 0 000331 expsq Predictor Constant exp expsq Coef 20 8233 0 63565 0 0003314 s 0 9982 Stdev 0 6752 0 09427 0 0001485 R sq 92 9 t ratio 30 84 6 74 2 23 p 0 000 0 000 0 046 R sq adj 91 7 Analysis of Variance SOURCE Regression Error Total DF 2 12 14 SS 155 776 11 957 167 733 SOURCE exp expsq DF 1 1 SEQ SS 150 817 4 959 Unusual Observations Obs …
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