5 3 99 252x9943 ECO252 QBA2 Name FINAL EXAM Hour of Class Registered Circle May 5 1999 MWF 10 11 TR 12 30 2 00 I 16 points Do all the following 1 Hand in your fourth regression problem 2 points and answer the following questions a For the regression of the number of hours of work against the number of machines what coefficients are significant at the 1 level Why What about the 5 level 2 b Would you say that the regression of number of hours of work against the number of machines and months of experience is more successful than the regression against machines alone Why 3 c What was the surprise that occurred when you did the stepwise regression 2 2 The following pages show the regression of the variable mins the winning time in minutes in a triathlon against some of the following independent variables female A dummy variable that is 1 if the contestant is female swim Number of miles of swimming bike Number of miles of biking run Number of miles of running c6 swim multiplied by female c7 bike multiplied by female c8 run multiplied by female c9 swim squared c10 bike squared c11 run squared a In the regression of mins against female swim bike and run which coefficients have signs that look wrong Why Which coefficients are not significant at the 99 confidence level 3 b Look at the regression of mins against run c8 and c11 and the regression of mins against run and c8 Use 10 Does either seem to be an improvement over the regression of mins against run alone Why 2 c Explain the meaning of the F test in the regression of mins against female swim bike and run What is being tested and what are the conclusions 2 d The printout concludes with a printout of the data and of a correlation matrix What does this suggest about the problems that are occurring with these regressions 2 5 3 99 252x9943 Worksheet size 100000 cells MTB RETR C MINITAB LR13 49 MTW Retrieving worksheet from file C MINITAB LR13 49 MTW Worksheet was saved on 5 3 1999 MTB regress c1 on 4 c2 c3 c4 c5 Regression Analysis The regression equation is mins 24 6 35 5 female 25 0 swim 7 13 bike 6 37 run Predictor Constant female swim bike run Coef 24 57 35 47 25 01 7 130 6 372 s 33 02 Stdev 20 13 14 77 45 75 1 331 5 384 R sq 98 0 t ratio 1 22 2 40 0 55 5 36 1 18 p 0 241 0 030 0 593 0 000 0 255 R sq adj 97 4 Analysis of Variance SOURCE Regression Error Total DF 4 15 19 SS 786104 16351 802455 SOURCE female swim bike run DF 1 1 1 1 SEQ SS 6291 726098 52189 1526 MS 196526 1090 Unusual Observations Obs female mins 1 0 00 489 25 18 1 00 660 48 Fit 547 00 582 47 F 180 29 Stdev Fit 17 48 17 48 p 0 000 Residual 57 75 78 01 St Resid 2 06R 2 79R R denotes an obs with a large st resid MTB regress c1 on 1 c5 Regression Analysis The regression equation is mins 19 2 23 6 run Predictor Constant run s 57 74 Coef 19 25 23 615 Stdev 23 19 1 582 R sq 92 5 t ratio 0 83 14 92 p 0 417 0 000 R sq adj 92 1 2 5 3 99 252x9943 Analysis of Variance SOURCE Regression Error Total DF 1 18 19 SS 742445 60011 802455 MS 742445 3334 Unusual Observations Obs run mins 1 26 2 489 2 12 18 6 589 1 Fit 599 5 420 0 F 222 69 Stdev Fit 25 7 16 4 p 0 000 Residual 110 2 169 1 St Resid 2 13R 3 05R R denotes an obs with a large st resid MTB regress c1 on 2 c5 c8 Regression Analysis The regression equation is mins 19 2 22 1 run 3 02 C8 Predictor Constant run C8 Coef 19 25 22 106 3 017 s 54 36 Stdev 21 83 1 705 1 659 R sq 93 7 t ratio 0 88 12 96 1 82 p 0 390 0 000 0 087 R sq adj 93 0 Analysis of Variance SOURCE Regression Error Total DF 2 17 19 SS 752216 50240 802455 SOURCE run C8 DF 1 1 SEQ SS 742445 9771 Unusual Observations Obs run mins 2 18 6 505 1 11 26 2 540 9 12 18 6 589 1 MS 376108 2955 Fit 391 9 639 0 448 0 F 127 27 Stdev Fit 21 9 32 5 21 9 p 0 000 Residual 113 2 98 1 141 0 St Resid 2 27R 2 25R 2 83R R denotes an obs with a large st resid 3 5 3 99 252x9943 MTB regress c1 on 2 c5 c11 Regression Analysis The regression equation is mins 102 39 6 run 0 519 C11 Predictor Constant run C11 Coef 101 71 39 550 0 5192 s 54 11 Stdev 49 18 8 654 0 2778 R sq 93 8 t ratio 2 07 4 57 1 87 p 0 054 0 000 0 079 R sq adj 93 1 Analysis of Variance SOURCE Regression Error Total DF 2 17 19 SS 752675 49780 802455 SOURCE run C11 DF 1 1 SEQ SS 742445 10230 Unusual Observations Obs run mins 12 18 6 589 1 MS 376337 2928 Fit 454 3 F 128 52 Stdev Fit 24 0 p 0 000 Residual 134 8 St Resid 2 78R R denotes an obs with a large st resid MTB regress c1 on 3 c5 c8 c11 Regression Analysis The regression equation is mins 102 38 0 run 3 02 C8 0 519 C11 Predictor Constant run C8 C11 s 50 01 Coef 101 71 38 042 3 017 0 5192 Stdev 45 45 8 033 1 526 0 2567 R sq 95 0 t ratio 2 24 4 74 1 98 2 02 p 0 040 0 000 0 066 0 060 R sq adj 94 1 4 5 3 99 252x9943 Analysis of Variance SOURCE Regression Error Total DF 3 16 19 SS 762446 40009 802455 SOURCE run C8 C11 DF 1 1 1 SEQ SS 742445 9771 10230 Unusual Observations Obs run mins 12 18 6 589 1 MS 254149 2501 Fit 482 3 F 101 64 Stdev Fit 26 3 p 0 000 Residual 106 7 St Resid 2 51R R denotes an obs with a large st resid 5 5 3 99 252x9943 MTB print c1 c11 Data Display Row mins female swim bike run C6 C7 C8 C9 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 489 250 505 150 245 500 204 400 114 533 108 267 79 417 566 500 74 983 116 117 540 933 589 067 280 100 235 033 127 167 120 750 90 317 660 …
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