R studio
rich the tutorievans_2e_ple_case_solution_ch9.xlsx
Case Chapter 9
XLMiner may be used for forecasting these variables |
As there is a lot of data to forecast, instructors may wish to restrict the assignment to only a portion of the data, or assign different time series to different students or groups. |
Also, there is not a unique answer to many of these forecasts; students should provide logic and justification for their choices. |
First thing to do is to chart the data |
Mower Sales: |
An important focus on this case is for students to select the proper forecasting procedure. |
For NA and World Mower Sales, we see a seasonal pattern with no trend, so use Holt-Winter no trend option. |
For SA and Europe, we have a stable seasonal pattern with trend, so use Holt-Winters additive model. |
For Pacific, we might use a double exponential smoothing model or perhaps regression. |
Note that XLMiner does not optimize Holt-Winter models, so students need to experiment to find the best models, so it would be difficult to expect the "best" model. |
A sample result for NA mower sales is given in the worksheet Mower Fcst NA |
Because XLMiner does optimize double exponential smoothing, the result is given in the worksheet Mower Fcst Pacific |
There is not enough data for China to make an effective forecast. |
Tractor Sales: |
For NA and World tractor sales, we see seasonal data with increasing amplitude, suggesting that Holt-Winters multiplicative models are appropriate. |
SA: use double exponential smoothing or regression. |
The data for Europe and Pacific are somewhat irregular; students might experiment with different types of smoothing models. |
A smoothing model would also be appropriate for China. |
Industry Mower Sales: |
Similar logic can be applied. All except Pacific region would use Holt Winter no trend model, and Pacific would probably use double exponential smoothing. |
Industry Tractor Sales: |
NA: Holt Winter multiplicative |
World: Holt Winter multiplicative |
Europe: exponential smoothing or moving average |
SA, Pacific, and China: smoothing model |
Unit production costs follow a close linear trend except for an apparent anomoly in in 2011. |
It will be interesting to see how students handle it. They might question the integrity of the data. |
For example, we see that a linear trendline will underestimate the data for tractors. |
For mowers, there appears to be a decreasing return, so a polynomial trendline might be adequate as would a double exponential smoothing model. |
Mower Unit Sales
Mower Unit Sales | ||||||
Month | NA | SA | Europe | Pacific | China | World |
Jan-10 | 6000 | 200 | 720 | 100 | 0 | 7020 |
Feb-10 | 7950 | 220 | 990 | 120 | 0 | 9280 |
Mar-10 | 8100 | 250 | 1320 | 110 | 0 | 9780 |
Apr-10 | 9050 | 280 | 1650 | 120 | 0 | 11100 |
May-10 | 9900 | 310 | 1590 | 130 | 0 | 11930 |
Jun-10 | 10200 | 300 | 1620 | 120 | 0 | 12240 |
Jul-10 | 8730 | 280 | 1590 | 140 | 0 | 10740 |
Aug-10 | 8140 | 250 | 1560 | 130 | 0 | 10080 |
Sep-10 | 6480 | 230 | 1590 | 130 | 0 | 8430 |
Oct-10 | 5990 | 220 | 1320 | 120 | 0 | 7650 |
Nov-10 | 5320 | 210 | 990 | 130 | 0 | 6650 |
Dec-10 | 4640 | 180 | 660 | 140 | 0 | 5620 |
Jan-11 | 5980 | 210 | 690 | 140 | 0 | 7020 |
Feb-11 | 7620 | 240 | 1020 | 150 | 0 | 9030 |
Mar-11 | 8370 | 250 | 1290 | 140 | 0 | 10050 |
Apr-11 | 8830 | 290 | 1620 | 150 | 0 | 10890 |
May-11 | 9310 | 330 | 1650 | 130 | 0 | 11420 |
Jun-11 | 10230 | 310 | 1590 | 140 | 0 | 12270 |
Jul-11 | 8720 | 290 | 1560 | 150 | 0 | 10720 |
Aug-11 | 7710 | 270 | 1530 | 140 | 0 | 9650 |
Sep-11 | 6320 | 250 | 1590 | 150 | 0 | 8310 |
Oct-11 | 5840 | 250 | 1260 | 160 | 0 | 7510 |
Nov-11 | 4960 | 240 | 900 | 150 | 0 | 6250 |
Dec-11 | 4350 | 210 | 660 | 150 | 0 | 5370 |
Jan-12 | 6020 | 220 | 570 | 160 | 0 | 6970 |
Feb-12 | 7920 | 250 | 840 | 150 | 0 | 9160 |
Mar-12 | 8430 | 270 | 1110 | 160 | 0 | 9970 |
Apr-12 | 9040 | 310 | 1500 | 170 | 0 | 11020 |
May-12 | 9820 | 360 | 1440 | 160 | 0 | 11780 |
Jun-12 | 10370 | 330 | 1410 | 170 | 0 | 12280 |
Jul-12 | 9050 | 310 | 1440 | 160 | 0 | 10960 |
Aug-12 | 7620 | 300 | 1410 | 170 | 0 | 9500 |
Sep-12 | 6420 | 280 | 1350 | 180 | 0 | 8230 |
Oct-12 | 5890 | 270 | 1080 | 180 | 0 | 7420 |
Nov-12 | 5340 | 260 | 840 | 190 | 0 | 6630 |
Dec-12 | 4430 | 230 | 510 | 180 | 0 | 5350 |
Jan-13 | 6100 | 250 | 480 | 200 | 0 | 7030 |
Feb-13 | 8010 | 270 | 750 | 190 | 0 | 9220 |
Mar-13 | 8430 | 280 | 1140 | 200 | 0 | 10050 |
Apr-13 | 9110 | 320 | 1410 | 210 | 0 | 11050 |
May-13 | 9730 | 380 | 1340 | 190 | 0 | 11640 |
Jun-13 | 10120 | 360 | 1360 | 200 | 0 | 12040 |
Jul-13 | 9080 | 320 | 1410 | 200 | 0 | 11010 |
Aug-13 | 7820 | 310 | 1490 | 210 | 0 | 9830 |
Sep-13 | 6540 | 300 | 1310 | 220 | 0 | 8370 |
Oct-13 | 6010 | 290 | 980 | 210 | 0 | 7490 |
Nov-13 | 5270 | 270 | 770 | 220 | 0 | 6530 |
Dec-13 | 5380 | 260 | 430 | 230 | 0 | 6300 |
Jan-14 | 6210 | 270 | 400 | 200 | 0 | 7080 |
Feb-14 | 8030 | 280 | 750 | 190 | 0 | 9250 |
Mar-14 | 8540 | 300 | 970 | 210 | 0 | 10020 |
Apr-14 | 9120 | 340 | 1310 | 220 | 5 | 10995 |
May-14 | 9570 | 390 | 1260 | 200 | 16 | 11436 |
Jun-14 | 10230 | 380 | 1240 | 210 | 22 | 12082 |
Jul-14 | 9580 | 350 | 1300 | 230 | 26 | 11486 |
Aug-14 | 7680 | 340 | 1250 | 220 | 14 | 9504 |
Sep-14 | 6870 | 320 | 1210 | 220 | 15 | 8635 |
Oct-14 | 5930 | 310 | 970 | 230 | 11 | 7451 |
Nov-14 | 5260 | 300 | 650 | 240 | 3 | 6453 |
Dec-14 | 4830 | 290 | 300 | 230 | 1 | 5651 |
Tractor Unit Sales
Tractor Unit Sales | ||||||
Month | NA | SA | Eur | Pac | China | World |
Jan-10 | 570 | 250 | 560 | 212 | 0 | 1592 |
Feb-10 | 611 | 270 | 600 | 230 | 0 | 1711 |
Mar-10 | 630 | 260 | 680 | 240 | 0 | 1810 |
Apr-10 | 684 | 270 | 650 | 263 | 0 | 1867 |
May-10 | 650 | 280 | 580 | 269 | 0 | 1779 |
Jun-10 | 600 | 270 | 590 | 280 | 0 | 1740 |
Jul-10 | 512 | 264 | 760 | 290 | 0 | 1826 |
Aug-10 | 500 | 280 | 645 | 270 | 0 | 1695 |
Sep-10 | 478 | 290 | 650 | 263 | 0 | 1681 |
Oct-10 | 455 | 280 | 670 | 258 | 0 | 1663 |
Nov-10 | 407 | 290 | 888 | 240 | 0 | 1825 |
Dec-10 | 360 | 280 | 850 | 230 | 0 | 1720 |
Jan-11 | 571 | 320 | 620 | 250 | 0 | 1761 |
Feb-11 | 650 | 350 | 760 | 275 | 0 | 2035 |
Mar-11 | 740 | 390 | 742 | 270 | 0 | 2142 |
Apr-11 | 840 | 440 | 780 | 280 | 0 | 2340 |
May-11 | 830 | 470 | 690 | 290 | 0 | 2280 |
Jun-11 | 760 | 490 | 721 | 300 | 0 | 2271 |
Jul-11 | 681 | 481 | 680 | 312 | 0 | 2154 |
Aug-11 | 670 | 460 | 711 | 305 | 0 | 2146 |
Sep-11 | 640 | 460 | 695 | 290 | 0 | 2085 |
Oct-11 | 620 | 440 | 650 | 260 | 0 | 1970 |
Nov-11 | 570 | 436 | 680 | 250 | 0 | 1936 |
Dec-11 | 533 | 420 | 657 | 240 | 0 | 1850 |
Jan-12 | 620 | 510 | 610 | 250 | 10 | 2000 |
Feb-12 | 792 | 590 | 680 | 250 | 12 | 2324 |
Mar-12 | 890 | 610 | 730 | 260 | 20 | 2510 |
Apr-12 | 960 | 600 | 820 | 270 | 22 | 2672 |
May-12 | 1040 | 620 | 810 | 290 | 20 | 2780 |
Jun-12 | 1032 | 640 | 807 | 310 | 24 | 2813 |
Jul-12 | 1006 | 590 | 760 | 340 | 20 | 2716 |
Aug-12 | 910 | 600 | 720 | 320 | 31 | 2581 |
Sep-12 | 803 | 670 | 660 | 313 | 30 | 2476 |
Oct-12 | 730 | 630 | 630 | 290 | 37 | 2317 |
Nov-12 | 699 | 710 | 603 | 280 | 32 | 2324 |
Dec-12 | 647 | 570 | 570 | 260 | 33 | 2080 |
Jan-13 | 730 | 650 | 500 | 287 | 35 | 2202 |
Feb-13 | 930 | 680 | 590 | 290 | 50 | 2540 |
Mar-13 | 1160 | 724 | 620 | 300 | 63 | 2867 |
Apr-13 | 1510 | 730 | 730 | 310 | 68 | 3348 |
May-13 | 1650 | 760 | 740 | 330 | 70 | 3550 |
Jun-13 | 1490 | 800 | 720 | 340 | 82 | 3432 |
Jul-13 | 1460 | 840 | 670 | 350 | 80 | 3400 |
Aug-13 | 1390 | 830 | 610 | 341 | 90 | 3261 |
Sep-13 | 1360 | 820 | 599 | 330 | 100 | 3209 |
Oct-13 | 1340 | 810 | 560 | 320 | 102 | 3132 |
Nov-13 | 1240 | 827 | 550 | 300 | 110 | 3027 |
Dec-13 | 1103 | 750 | 520 | 290 | 114 | 2777 |
Jan-14 | 1250 | 780 | 480 | 200 | 111 | 2821 |
Feb-14 | 1550 | 805 | 523 | 210 | 121 | 3209 |
Mar-14 | 1820 | 830 | 560 | 220 | 123 | 3553 |
Apr-14 | 2010 | 890 | 570 | 230 | 120 | 3820 |
May-14 | 2230 | 930 | 590 | 253 | 130 | 4133 |
Jun-14 | 2490 | 980 | 600 | 270 | 136 | 4476 |
Jul-14 | 2440 | 1002 | 580 | 280 | 134 | 4436 |
Aug-14 | 2334 | 970 | 570 | 250 | 132 | 4256 |
Sep-14 | 2190 | 960 | 550 | 230 | 137 | 4067 |
Oct-14 | 2080 | 930 | 530 | 220 | 130 | 3890 |
Nov-14 | 2050 | 920 | 517 | 190 | 139 | 3816 |
Dec-14 | 2004 | 902 | 490 | 190 | 131 | 3717 |
Industry Mower Total Sales
Industry Mower Total Sales | |||||
Month | NA | SA | Eur | Pac | World |
Jan-10 | 60000 | 571 | 13091 | 1045 | 74662 |
Feb-10 | 77184 | 611 | 17679 | 1111 | 96585 |
Mar-10 | 77885 | 658 | 22759 | 1068 | 102369 |
Apr-10 | 86190 | 778 | 27966 | 1237 | 116171 |
May-10 | 96117 | 886 | 27895 | 1313 | 126210 |
Jun-10 | 97143 | 882 | 30566 | 1176 | 129768 |
Jul-10 | 84757 | 848 | 29444 | 1359 | 116409 |
Aug-10 | 79804 | 735 | 28364 | 1238 | 110141 |
Sep-10 | 64800 | 657 | 28393 | 1215 | 95065 |
Oct-10 | 59307 | 595 | 24444 | 1154 | 85500 |
Nov-10 | 52157 | 553 | 18000 | 1262 | 71972 |
Dec-10 | 45049 | 462 | 12453 | 1386 | 59349 |
Jan-11 | 58627 | 553 | 12778 | 1443 | 73401 |
Feb-11 | 76200 | 615 | 18214 | 1515 | 96545 |
Mar-11 | 82871 | 658 | 23889 | 1373 | 108791 |
Apr-11 | 84904 | 784 | 29455 | 1442 | 116584 |
May-11 | 93100 | 846 | 29464 | 1215 | 124625 |
Jun-11 | 93000 | 838 | 27414 | 1333 | 122585 |
Jul-11 | 83048 | 763 | 27368 | 1415 | 112594 |
Aug-11 | 74854 | 694 | 27321 | 1296 | 104164 |
Sep-11 | 60769 | 625 | 29444 | 1402 | 92241 |
Oct-11 | 55619 | 610 | 23774 | 1468 | 81470 |
Nov-11 | 48155 | 571 | 17308 | 1351 | 67386 |
Dec-11 | 42647 | 512 | 12941 | 1389 | 57489 |
Jan-12 | 57885 | 537 | 10962 | 1509 | 70892 |
Feb-12 | 77647 | 595 | 15273 | 1402 | 94917 |
Mar-12 | 81845 | 659 | 20556 | 1524 | 104583 |
Apr-12 | 86095 | 756 | 26786 | 1574 | 115211 |
May-12 | 91776 | 878 | 24828 | 1468 | 118949 |
Jun-12 | 100680 | 825 | 24737 | 1560 | 127801 |
Jul-12 | 86190 | 756 | 24828 | 1441 | 113216 |
Aug-12 | 71887 | 714 | 25179 | 1545 | 99325 |
Sep-12 | 60000 | 651 | 24545 | 1667 | 86863 |
Oct-12 | 55566 | 643 | 19286 | 1698 | 77193 |
Nov-12 | 50857 | 619 | 15273 | 1810 | 68558 |
Dec-12 | 42596 | 548 | 9107 | 1731 | 53982 |
Jan-13 | 58095 | 581 | 8571 | 1887 | 69135 |
Feb-13 | 75566 | 614 | 13158 | 1845 | 91182 |
Mar-13 | 80286 | 622 | 19655 | 1923 | 102486 |
Apr-13 | 85140 | 727 | 25179 | 1981 | 113027 |
May-13 | 90093 | 826 | 23103 | 1810 | 115832 |
Jun-13 | 95472 | 783 | 24286 | 1942 | 122482 |
Jul-13 | 87308 | 681 | 24737 | 1961 | 114686 |
Aug-13 | 74476 | 646 | 26607 | 2000 | 103729 |
Sep-13 | 61698 | 625 | 22982 | 2075 | 87381 |
Oct-13 | 57238 | 617 | 16897 | 2019 | 76771 |
Nov-13 | 50673 | 587 | 13750 | 2095 | 67105 |
Dec-13 | 51238 | 591 | 7818 | 2150 | 61797 |
Jan-14 | 59712 | 563 | 7547 | 1852 | 69673 |
Feb-14 | 77961 | 571 | 13889 | 1743 | 94165 |
Mar-14 | 83725 | 625 | 18302 | 1892 | 104544 |
Apr-14 | 90297 | 723 | 25192 | 2037 | 118250 |
May-14 | 91143 | 848 | 24706 | 1887 | 118583 |
Jun-14 | 99320 | 792 | 25306 | 1944 | 127363 |
Jul-14 | 93922 | 745 | 27083 | 2170 | 123919 |
Aug-14 | 73143 | 739 | 26042 | 2037 | 101961 |
Sep-14 | 66699 | 667 | 26304 | 2018 | 95688 |
Oct-14 | 56476 | 660 | 22558 | 2072 | 81766 |
Nov-14 | 51068 | 625 | 14773 | 2182 | 68648 |
Dec-14 | 46893 | 608 | 6977 | 2035 | 56510 |
Industry Tractor Total Sales
Industry Tractor Total Sales | ||||||
Month | NA | SA | Eur | Pac | China | World |
Jan-10 | 8143 | 984 | 5091 | 987 | 278 | 15483 |
Feb-10 | 8592 | 1051 | 5310 | 1090 | 283 | 16325 |
Mar-10 | 8630 | 1016 | 6071 | 1127 | 285 | 17129 |
Apr-10 | 8947 | 1027 | 5856 | 1209 | 288 | 17327 |
May-10 | 8442 | 1057 | 5273 | 1221 | 286 | 16278 |
Jun-10 | 7500 | 1019 | 5315 | 1327 | 287 | 15448 |
Jul-10 | 6145 | 977 | 7170 | 1324 | 289 | 15905 |
Aug-10 | 5882 | 1057 | 5926 | 1268 | 290 | 14422 |
Sep-10 | 5595 | 1086 | 6075 | 1209 | 293 | 14258 |
Oct-10 | 5233 | 1045 | 6321 | 1168 | 295 | 14061 |
Nov-10 | 4494 | 1078 | 8381 | 1127 | 298 | 15378 |
Dec-10 | 3913 | 1029 | 7944 | 1085 | 301 | 14272 |
Jan-11 | 5938 | 1172 | 5688 | 1185 | 306 | 14289 |
Feb-11 | 6633 | 1273 | 7037 | 1286 | 302 | 16530 |
Mar-11 | 7327 | 1423 | 6981 | 1286 | 303 | 17320 |
Apr-11 | 8077 | 1612 | 7500 | 1346 | 307 | 18842 |
May-11 | 7830 | 1728 | 6571 | 1388 | 309 | 17826 |
Jun-11 | 7103 | 1815 | 6990 | 1449 | 312 | 17669 |
Jul-11 | 6239 | 1776 | 6667 | 1490 | 315 | 16487 |
Aug-11 | 6036 | 1685 | 6762 | 1449 | 318 | 16250 |
Sep-11 | 5664 | 1679 | 6635 | 1394 | 321 | 15692 |
Oct-11 | 5345 | 1618 | 6311 | 1256 | 315 | 14844 |
Nov-11 | 4831 | 1564 | 6476 | 1214 | 318 | 14402 |
Dec-11 | 4454 | 1522 | 6250 | 1171 | 320 | 13716 |
Jan-12 | 5299 | 1835 | 5922 | 1208 | 333 | 14597 |
Feb-12 | 6529 | 2115 | 6667 | 1214 | 313 | 16836 |
Mar-12 | 7120 | 2202 | 7228 | 1256 | 606 | 18412 |
Apr-12 | 7619 | 2151 | 8200 | 1311 | 571 | 19852 |
May-12 | 8387 | 2214 | 7941 | 1415 | 556 | 20513 |
Jun-12 | 8110 | 2278 | 7921 | 1520 | 526 | 20355 |
Jul-12 | 7752 | 2100 | 7677 | 1675 | 513 | 19716 |
Aug-12 | 6894 | 2128 | 7200 | 1584 | 769 | 18575 |
Sep-12 | 6015 | 2367 | 6735 | 1527 | 750 | 17394 |
Oct-12 | 5368 | 2211 | 6495 | 1422 | 732 | 16226 |
Nov-12 | 4964 | 2483 | 6061 | 1366 | 714 | 15587 |
Dec-12 | 4444 | 1986 | 5816 | 1262 | 698 | 14207 |
Jan-13 | 5000 | 2257 | 5051 | 1373 | 714 | 14394 |
Feb-13 | 6284 | 2353 | 6082 | 1436 | 1063 | 17218 |
Mar-13 | 7785 | 2457 | 6327 | 1478 | 1264 | 19310 |
Apr-13 | 9934 | 2517 | 7604 | 1512 | 1333 | 22901 |
May-13 | 10645 | 2612 | 7789 | 1642 | 1556 | 24244 |
Jun-13 | 9491 | 2749 | 7347 | 1667 | 1739 | 22993 |
Jul-13 | 9182 | 2887 | 6979 | 1733 | 1702 | 22483 |
Aug-13 | 8528 | 2833 | 6489 | 1700 | 1915 | 21465 |
Sep-13 | 8293 | 2789 | 6316 | 1642 | 2083 | 21123 |
Oct-13 | 8221 | 2765 | 5833 | 1576 | 2128 | 20523 |
Nov-13 | 7470 | 2746 | 5789 | 1493 | 2292 | 19789 |
Dec-13 | 6509 | 2534 | 5591 | 1450 | 2245 | 18329 |
Jan-14 | 7267 | 2635 | 5106 | 1010 | 2292 | 18311 |
Feb-14 | 8807 | 2703 | 5474 | 1045 | 2449 | 20477 |
Mar-14 | 10168 | 2795 | 6022 | 1106 | 2400 | 22489 |
Apr-14 | 11044 | 2997 | 6064 | 1150 | 2353 | 23607 |
May-14 | 12120 | 3131 | 6344 | 1244 | 2600 | 25439 |
Jun-14 | 13459 | 3311 | 6593 | 1357 | 2653 | 27374 |
Jul-14 | 13048 | 3390 | 6304 | 1421 | 2600 | 26764 |
Aug-14 | 12275 | 3277 | 6064 | 1263 | 2549 | 25428 |
Sep-14 | 11347 | 3232 | 5789 | 1173 | 2453 | 23995 |
Oct-14 | 10667 | 3131 | 5699 | 1128 | 2517 | 23142 |
Nov-14 | 10459 | 3087 | 5604 | 974 | 2541 | 22666 |
Dec-14 | 10082 | 3030 | 5444 | 979 | 2453 | 21989 |
Unit Production Costs
Unit Production Costs | ||
Month | Tractor | Mower |
Jan-10 | $1,750 | $50 |
Feb-10 | $1,755 | $50 |
Mar-10 | $1,763 | $51 |
Apr-10 | $1,770 | $51 |
May-10 | $1,778 | $51 |
Jun-10 | $1,785 | $51 |
Jul-10 | $1,792 | $51 |
Aug-10 | $1,795 | $51 |
Sep-10 | $1,801 | $52 |
Oct-10 | $1,804 | $52 |
Nov-10 | $1,810 | $52 |
Dec-10 | $1,813 | $52 |
Jan-11 | $1,835 | $55 |
Feb-11 | $1,841 | $55 |
Mar-11 | $1,848 | $55 |
Apr-11 | $1,854 | $55 |
May-11 | $1,860 | $56 |
Jun-11 | $1,866 | $56 |
Jul-11 | $1,872 | $56 |
Aug-11 | $1,878 | $56 |
Sep-11 | $1,885 | $56 |
Oct-11 | $1,892 | $57 |
Nov-11 | $1,897 | $57 |
Dec-11 | $1,903 | $57 |
Jan-12 | $1,925 | $59 |
Feb-12 | $1,931 | $59 |
Mar-12 | $1,938 | $59 |
Apr-12 | $1,944 | $59 |
May-12 | $1,950 | $59 |
Jun-12 | $1,956 | $60 |
Jul-12 | $1,963 | $60 |
Aug-12 | $1,969 | $60 |
Sep-12 | $1,976 | $60 |
Oct-12 | $1,983 | $60 |
Nov-12 | $1,990 | $61 |
Dec-12 | $1,996 | $61 |
Jan-13 | $1,940 | $59 |
Feb-13 | $1,946 | $59 |
Mar-13 | $1,952 | $59 |
Apr-13 | $1,958 | $59 |
May-13 | $1,964 | $60 |
Jun-13 | $1,970 | $60 |
Jul-13 | $1,976 | $60 |
Aug-13 | $1,983 | $60 |
Sep-13 | $1,990 | $60 |
Oct-13 | $1,996 | $60 |
Nov-13 | $2,012 | $61 |
Dec-13 | $2,008 | $61 |
Jan-14 | $2,073 | $63 |
Feb-14 | $2,077 | $63 |
Mar-14 | $2,081 | $63 |
Apr-14 | $2,086 | $63 |
May-14 | $2,092 | $63 |
Jun-14 | $2,098 | $63 |
Jul-14 | $2,104 | $64 |
Aug-14 | $2,110 | $64 |
Sep-14 | $2,116 | $64 |
Oct-14 | $2,122 | $64 |
Nov-14 | $2,129 | $64 |
Dec-14 | $2,135 | $64 |
Mower Fcst NA
XLMiner : Time Series - Holt Winter(No Trend) Forecasting Method | Date: 08-Oct-2012 08:45:51 | (Ver: 4.0.0P) | |
Output Navigator | |||
Inputs | Fitted Model | Forecast | |
Elapsed Time | Error Measures(Training) | Error Measures(Validation) | |
Inputs | |||
Data | |||
# Records in input data | 60 | ||
Input data | Mower Unit Sales!$B$4:$B$63 | ||
Selected variable | NA | ||
Parameters/Options | |||
Alpha (Level) | 0.2 | ||
Beta (Trend) | N.A. | ||
Gamma (Seasonality) | 0.05 | ||
Season length | 12 | ||
Number of seasons | 5 | ||
Forecast | Yes | ||
#Forecasts | 12 | ||
Fitted Model | |||
Time | Actual | Forecast | Residuals |
1 | 6000 | 5985.7795995934 | 14.2204004066 |
2 | 7950 | 7810.303334132 | 139.696665868 |
3 | 8100 | 8302.2317348871 | -202.2317348871 |
4 | 9050 | 8908.9947519494 | 141.0052480506 |
5 | 9900 | 9566.6594261212 | 333.3405738788 |
6 | 10200 | 10195.4211404279 | 4.5788595721 |
7 | 8730 | 9002.2790803789 | -272.2790803789 |
8 | 8140 | 7721.361218111 | 418.638781889 |
9 | 6480 | 6535.2849175665 | -55.2849175666 |
10 | 5990 | 5930.3892284407 | 59.6107715593 |
11 | 5320 | 5239.0911213412 | 80.9088786588 |
12 | 4640 | 4748.8374209496 | -108.8374209497 |
13 | 5980 | 6063.9483146367 | -83.9483146367 |
14 | 7620 | 7891.5168752532 | -271.5168752532 |
15 | 8370 | 8287.1059814834 | 82.8940185166 |
16 | 8830 | 8968.6087118495 | -138.6087118495 |
17 | 9310 | 9577.8128860408 | -267.8128860408 |
18 | 10230 | 10066.2276354007 | 163.7723645993 |
19 | 8720 | 8905.3123733326 | -185.3123733326 |
20 | 7710 | 7678.4595372206 | 31.5404627794 |
21 | 6320 | 6418.5867074902 | -98.5867074902 |
22 | 5840 | 5820.7477387984 | 19.2522612016 |
23 | 4960 | 5136.4096751633 | -176.4096751633 |
24 | 4350 | 4602.4671886197 | -252.4671886197 |
25 | 6020 | 5841.469892645 | 178.530107355 |
26 | 7920 | 7663.3169567811 | 256.6830432189 |
27 | 8430 | 8172.0926731999 | 257.9073268001 |
28 | 9040 | 8873.1400497835 | 166.8599502165 |
29 | 9820 | 9536.1713229061 | 283.8286770938 |
30 | 10370 | 10156.8237515656 | 213.1762484344 |
31 | 9050 | 8980.5702496427 | 69.4297503573 |
32 | 7620 | 7795.5280183133 | -175.5280183133 |
33 | 6420 | 6476.7183766721 | -56.7183766721 |
34 | 5890 | 5885.6492486915 | 4.3507513085 |
35 | 5340 | 5183.1487523924 | 156.8512476076 |
36 | 4430 | 4700.8388803607 | -270.8388803607 |
37 | 6100 | 5983.5134624651 | 116.4865375349 |
38 | 8010 | 7833.2553050143 | 176.7446949857 |
39 | 8430 | 8334.5356806588 | 95.4643193411 |
40 | 9110 | 9008.8108731609 | 101.1891268391 |
41 | 9730 | 9671.5644179994 | 58.4355820006 |
42 | 10120 | 10248.8889327706 | -128.8889327706 |
43 | 9080 | 8996.6537031251 | 83.3462968749 |
44 | 7820 | 7802.4031108645 | 17.5968891355 |
45 | 6540 | 6518.3032673712 | 21.6967326288 |
46 | 6010 | 5940.0421048885 | 69.9578951115 |
47 | 5270 | 5248.7485218257 | 21.2514781743 |
48 | 5380 | 4718.8097247758 | 661.1902752242 |
49 | 6210 | 6266.1439263363 | -56.1439263363 |
50 | 8030 | 8157.7996043291 | -127.7996043292 |
51 | 8540 | 8609.9836160512 | -69.9836160512 |
52 | 9120 | 9270.0957516861 | -150.0957516861 |
53 | 9570 | 9895.5624263681 | -325.5624263681 |
54 | 10230 | 10396.9289635414 | -166.9289635414 |
55 | 9580 | 9128.2150185378 | 451.7849814622 |
56 | 7680 | 7977.8461406715 | -297.8461406715 |
57 | 6870 | 6612.4078853044 | 257.5921146956 |
58 | 5930 | 6070.7508489666 | -140.7508489666 |
59 | 5260 | 5325.1835532845 | -65.1835532845 |
60 | 4830 | 4797.1828946893 | 32.8171053107 |
Error Measures (Training) | |||
MAPE | 2.1426514221 | ||
MAD | 156.4699224035 | ||
MSE | 39436.1547549712 | ||
Forecast | |||
Time | Forecast | LCI | UCI |
61 | 6169.18233134 | 5779.9549786184 | 6558.4096840617 |
62 | 8043.8152425909 | 7654.5878898693 | 8433.0425953126 |
63 | 8518.9461683267 | 8129.718815605 | 8908.1735210483 |
64 | 9184.0348848411 | 8794.8075321195 | 9573.2622375628 |
65 | 9828.9023206981 | 9439.6749679765 | 10218.1296734198 |
66 | 10402.374679002 | 10013.1473262803 | 10791.6020317236 |
67 | 9186.2978205198 | 8797.0704677981 | 9575.5251732414 |
68 | 7922.4237475825 | 7533.1963948609 | 8311.6511003042 |
69 | 6636.0848714818 | 6246.8575187601 | 7025.3122242034 |
70 | 6030.4308474524 | 5641.2034947307 | 6419.658200174 |
71 | 5316.8039188336 | 4927.576566112 | 5706.0312715552 |
72 | 4805.0589999639 | 4415.8316472422 | 5194.2863526855 |
Elapsed Time | |||
Overall (secs) | 1.00 |
Time Plot of Actual Vs Forecast (Training Data)
Actual 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 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 6000 7950 8100 9050 9900 10200 8730 8140 6480 5990 5320 4640 5980 7620 8370 8830 9310 10230 8720 7710 6320 5840 4960 4350 6020 7920 8430 9040 9820 10370 9050 7620 6420 5890 5340 4430 6100 8010 8430 9110 9730 10120 9080 7820 6540 6010 5270 5380 6210 8030 8540 9120 9570 10230 9580 7680 6870 5930 5260 4830 Forecast 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 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 5985.7795995934048 7810.3033341320315 8302.2317348870874 8908.9947519494053 9566.6594261211903 10195.421140427874 9002.2790803788521 7721.3612181109647 6535.2849175665542 5930.3892284406738 5239.0911213411637 4748.8374209496515 6063.9483146367056 7891.5168752532163 8287.1059814834352 8968.6087118495343 9577.8128860408033 10066.227635400708 8905.3123733326065 7678.4595372205504 6418.5867074902217 5820.7477387984081 5136.4096751632969 4602.4671886196775 5841.4698926450428 7663.3169567810937 8172.0926731999471 8873.1400497834893 9536.1713229061534 10156.823751565593 8980.5702496427257 7795.5280183132782 6476.7183766720882 5885.6492486915231 5183.1487523923879 4700.8388803606949 5983.5134624651291 7833.2553050143224 8334.5356806588516 9008.8108731608718 9671.5644179993669 10248.888932770584 8996.6537031251228 7802.403110864494 6518.3032673711641 5940.0421048884991 5248.748521825737 4718.8097247758087 6266.1439263362618 8157.7996043291541 8609.9836160512259 9270.0957516860653 9895.5624263681038 10396.928963541375 9128.2150185377704 7977.8461406714814 6612.407885304392 6070.7508489666261 5325.1835532845416 4797.1828946892983Time
NA
Mower Fcst Pacific
XLMiner : Time Series - Double Exponential Smoothing | Date: 08-Oct-2012 09:01:31 | (Ver: 4.0.0P) | |
Output Navigator | |||
Inputs | Fitted Model | Forecast | |
Elapsed Time | Error Measures(Training) | Error Measures(Validation) | |
Inputs | |||
Data | |||
# Records in input data | 60 | ||
Input data | Mower Unit Sales!$A$4:$G$63 | ||
Selected variable | Pacific | ||
Parameters/Options | |||
Optimization Selected | Yes | ||
Alpha (Level) | 2.69555480756071E-16 | ||
Beta (Trend) | 0.4377648438 | ||
Gamma (Seasonality) | N.A. | ||
Season length | N.A. | ||
Number of seasons | N.A. | ||
Forecast | Yes | ||
#Forecasts | 12 | ||
Fitted Model | |||
Time | Actual | Forecast | Residuals |
1 | 100 | 111.5737704918 | -11.5737704918 |
2 | 120 | 113.6390664073 | 6.3609335927 |
3 | 110 | 115.7043623229 | -5.7043623229 |
4 | 120 | 117.7696582384 | 2.2303417616 |
5 | 130 | 119.8349541539 | 10.1650458461 |
6 | 120 | 121.9002500695 | -1.9002500695 |
7 | 140 | 123.965545985 | 16.034454015 |
8 | 130 | 126.0308419005 | 3.9691580995 |
9 | 130 | 128.0961378161 | 1.9038621839 |
10 | 120 | 130.1614337316 | -10.1614337316 |
11 | 130 | 132.2267296471 | -2.2267296471 |
12 | 140 | 134.2920255627 | 5.7079744373 |
13 | 140 | 136.3573214782 | 3.6426785218 |
14 | 150 | 138.4226173937 | 11.5773826063 |
15 | 140 | 140.4879133093 | -0.4879133093 |
16 | 150 | 142.5532092248 | 7.4467907752 |
17 | 130 | 144.6185051403 | -14.6185051403 |
18 | 140 | 146.6838010558 | -6.6838010558 |
19 | 150 | 148.7490969714 | 1.2509030286 |
20 | 140 | 150.8143928869 | -10.8143928869 |
21 | 150 | 152.8796888024 | -2.8796888024 |
22 | 160 | 154.944984718 | 5.055015282 |
23 | 150 | 157.0102806335 | -7.0102806335 |
24 | 150 | 159.075576549 | -9.075576549 |
25 | 160 | 161.1408724646 | -1.1408724646 |
26 | 150 | 163.2061683801 | -13.2061683801 |
27 | 160 | 165.2714642956 | -5.2714642956 |
28 | 170 | 167.3367602112 | 2.6632397888 |
29 | 160 | 169.4020561267 | -9.4020561267 |
30 | 170 | 171.4673520422 | -1.4673520422 |
31 | 160 | 173.5326479578 | -13.5326479578 |
32 | 170 | 175.5979438733 | -5.5979438733 |
33 | 180 | 177.6632397888 | 2.3367602112 |
34 | 180 | 179.7285357044 | 0.2714642956 |
35 | 190 | 181.7938316199 | 8.2061683801 |
36 | 180 | 183.8591275354 | -3.8591275354 |
37 | 200 | 185.924423451 | 14.075576549 |
38 | 190 | 187.9897193665 | 2.0102806335 |
39 | 200 | 190.055015282 | 9.944984718 |
40 | 210 | 192.1203111976 | 17.8796888024 |
41 | 190 | 194.1856071131 | -4.1856071131 |
42 | 200 | 196.2509030286 | 3.7490969714 |
43 | 200 | 198.3161989442 | 1.6838010558 |
44 | 210 | 200.3814948597 | 9.6185051403 |
45 | 220 | 202.4467907752 | 17.5532092248 |
46 | 210 | 204.5120866907 | 5.4879133093 |
47 | 220 | 206.5773826063 | 13.4226173937 |
48 | 230 | 208.6426785218 | 21.3573214782 |
49 | 200 | 210.7079744373 | -10.7079744373 |
50 | 190 | 212.7732703529 | -22.7732703529 |
51 | 210 | 214.8385662684 | -4.8385662684 |
52 | 220 | 216.9038621839 | 3.0961378161 |
53 | 200 | 218.9691580995 | -18.9691580995 |
54 | 210 | 221.034454015 | -11.034454015 |
55 | 230 | 223.0997499305 | 6.9002500695 |
56 | 220 | 225.1650458461 | -5.1650458461 |
57 | 220 | 227.2303417616 | -7.2303417616 |
58 | 230 | 229.2956376771 | 0.7043623229 |
59 | 240 | 231.3609335927 | 8.6390664073 |
60 | 230 | 233.4262295082 | -3.4262295082 |
Error Measures (Training) | |||
MAPE | 4.4537757707 | ||
MAD | 7.4981661573 | ||
MSE | 86.1379549875 | ||
Forecast | |||
Time | Forecast | LCI | UCI |
61 | 235.4915254237 | 217.3006604668 | 253.6823903806 |
62 | 237.5568213393 | 219.3659563824 | 255.7476862962 |
63 | 239.6221172548 | 221.4312522979 | 257.8129822117 |
64 | 241.6874131703 | 223.4965482134 | 259.8782781272 |
65 | 243.7527090859 | 225.561844129 | 261.9435740428 |
66 | 245.8180050014 | 227.6271400445 | 264.0088699583 |
67 | 247.8833009169 | 229.69243596 | 266.0741658738 |
68 | 249.9485968325 | 231.7577318756 | 268.1394617893 |
69 | 252.013892748 | 233.8230277911 | 270.2047577049 |
70 | 254.0791886635 | 235.8883237066 | 272.2700536204 |
71 | 256.1444845791 | 237.9536196222 | 274.3353495359 |
72 | 258.2097804946 | 240.0189155377 | 276.4006454515 |
Elapsed Time | |||
Overall (secs) | 1.00 |
Time Plot of Actual Vs Forecast (Training Data)
Actual 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 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 100 120 110 120 130 120 140 130 130 120 130 140 140 150 140 150 130 140 150 140 150 160 150 150 160 150 160 170 160 170 160 170 180 180 190 180 200 190 200 210 190 200 200 210 220 210 220 230 200 190 210 220 200 210 230 220 220 230 240 230 Forecast 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 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 111.57377049180326 113.63906640733535 115.70436232286744 117.76965823839953 119.83495415393162 121.90025006946371 123.9655459849958 126.03084190052789 128.09613781605998 130.16143373159207 132.22672964712416 134.29202556265625 136.35732147818834 138.42261739372043 140.48791330925252 142.55320922478461 144.6185051403167 146.68380105584879 148.74909697138088 150.81439288691297 152.87968880244506 154.94498471797715 157.01028063350924 159.07557654904133 161.14087246457342 163.20616838010551 165.2714642956376 167.33676021116969 169.40205612670178 171.46735204223387 173.53264795776596 175.59794387329805 177.66323978883014 179.72853570436223 181.79383161989432 183.85912753542641 185.9244234509585 187.98971936649059 190.05501528202268 192.12031119755477 194.18560711308686 196.25090302861895 198.31619894415104 200.38149485968313 202.44679077521522 204.51208669074731 206.5773826062794 208.64267852181149 210.70797443734358 212.77327035287567 214.83856626840776 216.90386218393985 218.96915809947194 221.03445401500403 223.09974993053612 225.16504584606821 227.2303417616003 229.29563767713239 231.36093359266448 233.42622950819657Time
Pacific