5 01 03 252y0341 Introduction This is long but that s because I gave a relatively thorough explanation of everything that I did When I worked it out in the classroom it was much much shorter The easiest sections were probably 1a 2a 2b 2c 7b 7c and 7d in Part I There are some very easy sections in part I if you just follow suggestions and look at p values and R squared After doing the above I might have computed the spare parts in 3b in Part II Spare Parts Computation SSx x 2 nx 2 990401 11 260 636 2 x 2867 260 636 x n y 11 y n 13083 1189 36 11 243158 6 xy nx y 4369154 11 260 636 1189 36 Sxy 959263 6 y SSy 2 4462195 7 ny 2 20022545 11 1189 36 2 And not recomputed them every time I needed them in Problems 4 and 5 Only then would I have tried the multiple regression Many of you seem to have no idea what a statistical test is We have been doing them every day The most common examples of this were in part II 7 10 06087 and p 2 09709 Hey look They re different Whoopee Problem 1b p 3 115 103 And you think that you will get credit for this Whether these two proportions come from the same population or not chances are they will be somewhat different you need one of the three statistical tests shown in the solution to show that they are significantly different Problem 3c Many of you started with x 2 nx 2 990401 11 260 363 2 243158 6 s x2 24315 86 n 1 10 10 s 24315 86 155 90 This is fine and you got some credit for knowing how to compute a sample variance though you probably had already computed the numerator somewhere else in this exam But then you told me that this wasn t 200 Where was your test 5 01 03 252y0341 ECO252 QBA2 Name KEY FINAL EXAM Hour of Class Registered Circle May 6 2003 I 18 points Do all the following Note that answers without reasons receive no credit A researcher wishes to use demographic information to predict sales of a large chain of nationwide sports stores The researcher assembles the following data for a random sample of 38 stores Use 10 in this problem That s why p values above 10 mean that the null hypothesis of insignificance is not rejected Row 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 Sales Age 1695713 3403862 2710353 529215 663687 2546324 2787046 612696 891822 1124968 909501 2631167 882973 1078573 844320 1849119 3860007 826574 604683 1903612 2356808 2788572 634878 2371627 2627838 1868116 2236797 1318876 1868098 1695219 2700194 1156050 643858 2188687 830352 1226906 566904 826518 33 1574 32 6667 35 6553 33 0728 35 7585 33 8132 30 9797 30 7843 32 3164 32 5312 31 4400 33 1613 31 8736 33 4072 34 0470 28 8879 36 1056 32 8083 33 0538 33 4996 32 6809 28 5166 32 8945 30 5024 30 2922 31 2911 33 0498 32 9348 31 8381 31 0794 32 1807 31 6944 34 0263 34 7315 30 5613 33 5183 32 3952 29 9108 Growth Income 0 8299 0 6619 0 9688 0 0821 0 4646 2 1796 1 8048 0 0569 0 1577 0 3664 2 2256 1 5158 0 1413 1 0400 1 6836 2 3596 0 7840 0 1164 1 1498 0 0606 1 6338 1 1256 1 4884 4 7937 1 8922 1 8667 1 7896 0 2707 3 0129 23 4630 0 7041 0 1569 0 7084 0 1353 0 3848 0 7417 0 6693 0 1111 26748 5 53063 8 36090 1 32058 1 47843 4 50181 0 30710 1 29141 7 25980 2 18730 9 31109 2 35614 1 23038 4 34531 7 30350 4 38964 9 49392 8 25595 7 29622 6 31586 1 39674 6 28879 0 24287 1 46711 2 33449 8 31694 5 25459 2 47047 3 26433 2 33396 7 26179 4 33454 6 42271 5 46514 8 27030 8 42910 1 40561 4 22326 0 HS 73 5949 88 4557 73 5362 79 1780 84 1838 93 4996 78 0234 70 2949 70 6674 63 7395 76 9059 82 9452 65 2127 73 4944 80 2201 87 5973 85 3041 65 5884 80 6176 80 3790 79 8526 81 2371 70 2244 87 1046 80 2057 75 2914 77 6162 85 1753 74 1792 81 6991 73 4140 73 7161 78 6493 80 9503 66 8057 77 8905 79 3622 58 3610 College 17 8350 31 9439 18 6198 20 6284 35 2032 41 7057 28 0250 15 0882 10 9829 13 2458 19 5500 20 8135 16 9796 32 9920 22 3185 24 5670 30 8790 17 4545 18 6356 38 3249 23 7780 16 9300 19 1429 30 8843 26 5570 28 3600 19 2490 35 4994 18 6375 41 1130 17 8566 26 5426 29 8734 24 5374 14 1390 20 8340 19 0309 10 6729 In the data above Sales is the total sales in the last month Age is the median customer age Growth is the population growth rate in the last ten years Income is median family income HS is percent Don t forget that it is in per cent of potential customers with a high school diploma College is percent of potential customers with a college degree To start with the researcher runs sales against each independent variable individually with the following results Comments that answer the question on Page 3 appear in red MTB regress c1 1 c2 Regression Analysis Sales versus Age The regression equation is Sales 931626 21783 Age Predictor Constant Coef 931626 SE Coef 2851421 T 0 33 P 0 746 2 Age is insignificant 21783 87750 S 919493 R Sq 0 2 0 25 The p value above 10 shows us that the slope 0 805 5 01 03 252y0341 R Sq adj 0 0 Extremely low R sq Little explanation of Y Analysis of Variance Source DF SS MS Regression 1 52099324721 52099324721 Residual Error 36 3 04368E 13 8 45467E 11 Total 37 3 04889E 13 F 0 06 P 0 805 Same p value same conclusion Unusual Observations Obs Age Sales Fit SE Fit Residual St Resid 17 36 1 3860007 1718106 353724 2141901 2 52R 22 28 5 2788572 1552797 376045 1235775 1 47 X R denotes an observation with a large standardized residual X denotes an observation whose X value gives it large influence MTB regress c1 1 c3 Regression Analysis Sales versus Growth The regression equation is Sales 1595571 26834 Growth Predictor Constant Growth is insignificant S 914467 Coef 1595571 26834 SE Coef 161301 39601 T 9 89 0 68 P 0 000 0 502 The p value above 10 shows us that the slope R Sq adj 0 0 Extremely low R sq Little explanation …
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