Static Method Sales JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC Total Year 1 2000 3000 3000 3000 4000 6000 7000 6000 10000 12000 14000 8000 78000 Year 2 3000 4000 3000 5000 5000 8000 3000 8000 12000 12000 16000 10000 89000 Year 3 2000 5000 5000 3000 4000 6000 7000 10000 15000 15000 18000 8000 98000 Year 4 5000 4000 4000 2000 5000 7000 10000 14000 16000 16000 20000 12000 115000 Year 5 5000 2000 3000 2000 7000 6000 8000 10000 20000 20000 22000 8000 113000 Color coding Given Data Forecast Red 1. Start by reformatting data Year Month Period 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Demand Dt 2000 3000 3000 3000 4000 6000 7000 6000 10000 12000 14000 8000 3000 4000 3000 5000 5000 8000 3000 8000 12000 12000 16000 p = 12 (even) Dt Deseaso (based on nalized Demand regressio Seasonal n) Dt Factor St Forecast 6068 0.33 2588 6138 0.49 2913 6208 0.48 2872 6278 0.48 2500 6348 0.63 3944 6419 0.93 5356 6542 6489 1.08 5534 6625 6559 0.91 7551 6667 6629 1.51 11489 6750 6700 1.79 11913 6875 6770 2.07 14377 7000 6840 1.17 7488 6917 6910 0.43 2948 6833 6981 0.57 3313 7000 7051 0.43 3262 7083 7121 0.70 2836 7167 7191 0.70 4468 7333 7262 1.10 6059 7375 7332 0.41 6253 7375 7402 1.08 8521 7500 7472 1.61 12950 7500 7543 1.59 13411 7375 7613 2.10 16167 Calculate Errors Et 588 -87 -128 -500 -56 -644 -1466 1551 1489 -87 377 -512 -52 -687 262 -2164 -532 -1941 3253 521 950 1411 167 2 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 DEC JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC 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 61 62 63 64 65 66 67 68 69 70 71 72 10000 2000 5000 5000 3000 4000 6000 7000 10000 15000 15000 18000 8000 5000 4000 4000 2000 5000 7000 10000 14000 16000 16000 20000 12000 5000 2000 3000 2000 7000 6000 8000 10000 20000 20000 22000 8000 7250 7333 7583 7792 8042 8250 8250 8292 8375 8292 8208 8208 8292 8458 8750 8958 9042 9167 9417 9583 9500 9375 9333 9417 9458 9333 9083 9083 9417 9667 9583 7683 7753 7824 7894 7964 8034 8105 8175 8245 8315 8386 8456 8526 8596 8667 8737 8807 8877 8948 9018 9088 9158 9229 9299 9369 9439 9510 9580 9650 9720 9791 9861 9931 10001 10072 10142 10212 Forecasts 1.30 0.26 0.64 0.63 0.38 0.50 0.74 0.86 1.21 1.80 1.79 2.13 0.94 0.58 0.46 0.46 0.23 0.56 0.78 1.11 1.54 1.75 1.73 2.15 1.28 0.53 0.21 0.31 0.21 0.72 0.61 0.81 1.01 2.00 1.99 2.17 0.78 8411 3308 3713 3652 3171 4992 6762 6972 9491 14411 14910 17958 9334 3667 4113 4042 3507 5516 7466 7691 10462 15871 16409 19748 10256 4027 4513 4432 3843 6039 8169 8410 11432 17332 17908 21538 11179 4386 4913 4822 4178 6563 8872 9129 12403 18793 19407 23328 12102 -1589 1308 -1287 -1348 171 992 762 -28 -509 -589 -90 -42 1334 -1333 113 42 1507 516 466 -2309 -3538 -129 409 -252 -1744 -973 2513 1432 1843 -961 2169 410 1432 -2668 -2092 -462 3179 Estimate of standard lor coding Given Data Forecast At 588 87 128 500 56 644 1466 1551 1489 87 377 512 52 687 262 2164 532 1941 3253 521 950 1411 167 bias MSE MAD Percent Error MAPE TS 588 501 373 -127 -183 -827 -2292 -742 747 660 1037 525 473 -214 48 -2117 -2648 -4589 -1336 -815 135 1546 1713 346273 176952 123433 155075 124678 173086 455240 698911 867560 781567 723454 685002 632517 621082 584250 840507 807704 972128 1478005 1417679 1393120 1420351 1359815 588 338 268 326 272 334 496 628 723 660 634 624 580 587 566 666 658 729 862 845 850 875 845 29 3 4 17 1 11 21 26 15 1 3 6 2 17 9 43 11 24 108 7 8 12 1 29 16 12 13 11 11 12 14 14 13 12 11 11 11 11 13 13 13 18 18 17 17 16 1.00 1.48 1.39 -0.39 -0.67 -2.48 -4.63 -1.18 1.03 1.00 1.64 0.84 0.82 -0.36 0.08 -3.18 -4.03 -6.29 -1.55 -0.96 0.16 1.77 2.03 Regression S 1589 1308 1287 1348 171 992 762 28 509 589 90 42 1334 1333 113 42 1507 516 466 2309 3538 129 409 252 1744 973 2513 1432 1843 961 2169 410 1432 2668 2092 462 3179 124 1432 145 -1203 -1032 -40 722 694 186 -404 -493 -536 798 -535 -422 -380 1127 1642 2108 -201 -3739 -3868 -3459 -3711 -5454 -6427 -3915 -2483 -640 -1601 568 978 2410 -257 -2349 -2812 368 1408374 1420438 1429544 1443909 1393389 1379266 1352665 1309056 1276231 1248087 1211615 1177049 1193763 1209503 1178008 1147848 1175927 1153731 1131425 1229085 1485675 1453028 1425079 1396112 1430356 1420490 1518356 1528783 1564679 1552568 1610944 1584712 1593039 1689953 1736276 1710467 1850424 Estimate of standard deviation of forecast error: 876 893 908 924 898 901 896 868 857 849 826 804 819 833 814 794 812 805 796 832 893 876 866 853 872 874 906 917 934 935 958 948 957 987 1006 996 1033 1291 16 65 26 27 6 25 13 0 5 4 1 0 17 27 3 1 75 10 7 23 25 1 3 1 15 19 126 48 92 14 36 5 14 13 10 2 40 16 18 19 19 19 19 19 18 18 17 17 16 16 16 16 16 17 17 17 17 17 17 16 16 16 16 18 19 20 20 21 20 20 20 20 20 20 0.14 1.60 0.16 -1.30 -1.15 -0.04 0.81 0.80 0.22 -0.48 -0.60 -0.67 0.97 -0.64 -0.52 -0.48 1.39 2.04 2.65 -0.24 -4.19 -4.41 -3.99 -4.35 -6.26 -7.36 -4.32 -2.71 -0.69 -1.71 0.59 1.03 2.52 -0.26 -2.34 -2.82 0.36 Graph Using Winter's Deseasonalized Demand Regression SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.974925619 0.950479963 0.949403441 226.9014716 48 ANOVA df 1 46 47 SS 45456339.83 2368276.778 47824616.61 MS 45456339.83 51484.27779 Coefficients 5997.260518 70.24578448 Standard Error 79.19340748 2.364070087 t Stat 75.72928996 29.7139179 Regression Residual Total Intercept X Variable 1 Average of Seasonal Factor St Month JAN Avg. Seasonal Factors Total 0.427 JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC 0.475 0.463 0.398 0.621 0.834 0.853 1.151 1.733 1.778 2.124 1.095 FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC Comparison between Demand and Forecast 25000 20000 15000 10000 5000 0 1 4 7 10 13 16 19 22 25 28 31 34 37 F 882.9169172 Significance F 1.14478E-31 P-value 6.1285E-50 1.14478E-31 Lower 95% 5837.852609 65.48716276 0.427 0.427 Upper 95% 6156.668427 75.00440621 Lower 95.0% 5837.852609 65.48716276 Upper 95.0% 6156.668427 75.00440621 0.475 0.463 0.398 0.621 0.834 0.853 1.151 1.733 1.778 2.124 1.095 0.475 0.463 0.398 0.621 0.834 0.853 1.151 1.733 1.778 2.124 1.095 Demand and Forecast demand forecast 37 40 43 46 49 52 55 58 61 64 67 70 Moving Average Sales JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC Total Year 1 2000 3000 3000 3000 4000 6000 7000 6000 10000 12000 14000 8000 78000 Year 2 3000 4000 3000 5000 5000 8000 3000 8000 12000 12000 16000 10000 89000 Year 3 2000 5000 5000 3000 4000 6000 7000 10000 15000 15000 18000 8000 98000 Year 4 5000 4000 4000 2000 5000 7000 10000 14000 16000 16000 20000 12000 115000 Year 5 5000 2000 3000 2000 7000 6000 8000 10000 20000 20000 22000 8000 113000 Color coding Given Data Forecast Red 1. Start by reformatting data p = 12 (even) Using a 12 period moving Average Year Month Period 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 3 3 JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC JAN FEB 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 Demand Dt 2000 3000 3000 3000 4000 6000 7000 6000 10000 12000 14000 8000 3000 4000 3000 5000 5000 8000 3000 8000 12000 12000 16000 10000 2000 5000 Level Forecast Calculate Errors 6500 6583 6667 6667 6833 6917 7083 6750 6917 7083 7083 7250 7417 7333 7417 6500 6583 6667 6667 6833 6917 7083 6750 6917 7083 7083 7250 7417 7333 Et At 3500 2583 3667 1667 1833 -1083 4083 -1250 -5083 -4917 -8917 -2750 5417 2333 3500 2583 3667 1667 1833 1083 4083 1250 5083 4917 8917 2750 5417 2333 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 MAR APR MAY JUN JUL AUG SEP OCT NOV DEC JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC 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 61 62 63 64 65 66 67 68 69 70 71 72 5000 3000 4000 6000 7000 10000 15000 15000 18000 8000 5000 4000 4000 2000 5000 7000 10000 14000 16000 16000 20000 12000 5000 2000 3000 2000 7000 6000 8000 10000 20000 20000 22000 8000 Forecasts 7583 7417 7333 7167 7500 7667 7917 8167 8333 8167 8417 8333 8250 8167 8250 8333 8583 8917 9000 9083 9250 9583 9583 9417 9333 9333 9500 9417 9250 8917 9250 9583 9750 9417 7417 7583 7417 7333 7167 7500 7667 7917 8167 8333 8167 8417 8333 8250 8167 8250 8333 8583 8917 9000 9083 9250 9583 9583 9417 9333 9333 9500 9417 9250 8917 9250 9583 9750 9417 9417 9417 9417 9417 9417 9417 9417 9417 9417 9417 9417 2417 4583 3417 1333 167 -2500 -7333 -7083 -9833 333 3167 4417 4333 6250 3167 1250 -1667 -5417 -7083 -7000 -10917 -2750 4583 7583 6417 7333 2333 3500 1417 -750 -11083 -10750 -12417 1750 2417 4583 3417 1333 167 2500 7333 7083 9833 333 3167 4417 4333 6250 3167 1250 1667 5417 7083 7000 10917 2750 4583 7583 6417 7333 2333 3500 1417 750 11083 10750 12417 1750 Estimate of standard deviation of forecas Color coding Red Given Data Forecast bias MSE MAD Percent Error MAPE TS 3500 6083 9750 11417 13250 12167 16250 15000 9917 5000 -3917 -6667 -1250 1083 942308 1351687 2157870 2196615 2265114 2204475 2966009 2895833 3988426 4905934 8149457 8125000 8973611 8837874 269 435 650 714 779 796 969 983 1179 1348 1678 1722 1870 1888 117 65 122 33 37 14 136 16 42 41 56 28 271 47 117 91 101 84 75 65 75 67 65 62 62 59 75 73 13.00 14.00 15.00 16.00 17.00 15.28 16.76 15.25 8.41 3.71 -2.33 -3.87 -0.67 0.57 Graph Using Winter's Model 3500 8083 11500 12833 13000 10500 3167 -3917 -13750 -13417 -10250 -5833 -1500 4750 7917 9167 7500 2083 -5000 -12000 -22917 -25667 -21083 -13500 -7083 250 2583 6083 7500 6750 -4333 -15083 -27500 -25750 8726852 9165427 9251916 9002778 8713262 8636285 10004209 11185662 13628770 13253279 13166104 13332968 13472578 14112326 14012703 13716270 13461886 13822759 14630556 15377717 17586141 17377315 17451389 18252500 18701934 19376469 19113601 18986497 18677778 18354291 20187378 21831777 24074859 23724653 Estimate of standard deviation of forecast error: 1907 2003 2052 2028 1968 1984 2146 2292 2507 2447 2466 2518 2564 2656 2669 2635 2612 2676 2774 2866 3037 3031 3063 3153 3217 3296 3278 3282 3248 3204 3342 3470 3621 3590 4488 48 153 85 22 2 25 49 47 55 4 63 110 108 313 63 18 17 39 44 44 55 23 92 379 214 367 33 58 18 8 55 54 56 22 71 76 77 74 70 68 67 66 66 63 63 65 67 75 75 73 71 70 69 69 68 67 68 76 79 87 85 85 83 81 81 80 80 78 1.83 4.04 5.61 6.33 6.61 5.29 1.48 -1.71 -5.48 -5.48 -4.16 -2.32 -0.58 1.79 2.97 3.48 2.87 0.78 -1.80 -4.19 -7.55 -8.47 -6.88 -4.28 -2.20 0.08 0.79 1.85 2.31 2.11 -1.30 -4.35 -7.59 -7.17 25000 20000 15000 10000 5000 Comparison between Demand & Forecast 0 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 47 49 51 53 55 57 59 61 63 65 67 69 71 Simple Exponential Smoothing Sales JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC Total Year 1 2000 3000 3000 3000 4000 6000 7000 6000 10000 12000 14000 8000 78000 Year 2 3000 4000 3000 5000 5000 8000 3000 8000 12000 12000 16000 10000 89000 Year 3 2000 5000 5000 3000 4000 6000 7000 10000 15000 15000 18000 8000 98000 1. Start by reformatting data Year 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 Month Period JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC JAN FEB MAR 0 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 Year 4 5000 4000 4000 2000 5000 7000 10000 14000 16000 16000 20000 12000 115000 Year 5 5000 2000 3000 2000 7000 6000 8000 10000 20000 20000 22000 8000 113000 Color coding Given Data Forecast Red p = 12 (even) Exponential Smoothing Alpha = 0.6 Demand Dt Level Forecast 2000 3000 3000 3000 4000 6000 7000 6000 10000 12000 14000 8000 3000 4000 3000 5000 5000 8000 3000 8000 12000 12000 16000 10000 2000 5000 5000 8217 4487 3595 3238 3095 3638 5055 6222 6089 8436 10574 12630 9852 5741 4696 3679 4471 4789 6715 4486 6594 9838 11135 14054 11622 5849 5339 5136 8217 4487 3595 3238 3095 3638 5055 6222 6089 8436 10574 12630 9852 5741 4696 3679 4471 4789 6715 4486 6594 9838 11135 14054 11622 5849 5339 Calculate Errors Et At bias 6217 1487 595 238 -905 -2362 -1945 222 -3911 -3564 -3426 4630 6852 1741 1696 -1321 -529 -3211 3715 -3514 -5406 -2162 -4865 4054 9622 849 339 6217 1487 595 238 905 2362 1945 222 3911 3564 3426 4630 6852 1741 1696 1321 529 3211 3715 3514 5406 2162 4865 4054 9622 849 339 6217 7703 8298 8536 7631 5269 3324 3546 -365 -3929 -7355 -2725 4127 5867 7564 6242 5714 2502 6217 2704 -2702 -4864 -9729 -5675 3947 4795 5135 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 APR MAY JUN JUL AUG SEP OCT NOV DEC JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC 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 61 62 63 64 65 66 67 68 69 70 71 72 3000 4000 6000 7000 10000 15000 15000 18000 8000 5000 4000 4000 2000 5000 7000 10000 14000 16000 16000 20000 12000 5000 2000 3000 2000 7000 6000 8000 10000 20000 20000 22000 8000 3854 3942 5177 6271 8508 12403 13961 16385 11354 7542 5417 4567 3027 4211 5884 8354 11741 14297 15319 18127 14451 8780 4712 3685 2674 5270 5708 7083 8833 15533 18213 20485 12994 Forecasts 5136 3854 3942 5177 6271 8508 12403 13961 16385 11354 7542 5417 4567 3027 4211 5884 8354 11741 14297 15319 18127 14451 8780 4712 3685 2674 5270 5708 7083 8833 15533 18213 20485 8780 4712 3685 2674 5270 5708 7083 8833 15533 18213 20485 12994 2136 -146 -2058 -1823 -3729 -6492 -2597 -4039 8385 6354 3542 1417 2567 -1973 -2789 -4116 -5646 -4259 -1703 -4681 6127 9451 6780 1712 1685 -4326 -730 -2292 -2917 -11167 -4467 -3787 12485 2136 146 2058 1823 3729 6492 2597 4039 8385 6354 3542 1417 2567 1973 2789 4116 5646 4259 1703 4681 6127 9451 6780 1712 1685 4326 730 2292 2917 11167 4467 3787 12485 7271 7125 5067 3243 -486 -6978 -9574 -13613 -5229 1125 4667 6083 8650 6677 3887 -228 -5875 -10133 -11837 -16518 -10391 -940 5841 7553 9238 4912 4181 1889 -1028 -12194 -16661 -20448 -7962 Estimate of standard deviation of forecast error or coding Given Data Forecast MSE MAD Percent Error MAPE TS 38646944 20428561 13736917 10316833 8417218 7944143 7349573 6437042 7421505 7949896 8294088 9389080 12278241 11617668 11034985 10454443 9855912 9881324 10087801 10200761 11106428 10814098 11372924 11583856 14823523 14281088 13756427 6217 3852 2766 2134 1888 1967 1964 1746 1987 2145 2261 2458 2796 2721 2653 2569 2449 2492 2556 2604 2737 2711 2805 2857 3128 3040 2940 311 50 20 8 23 39 28 4 39 30 24 58 228 44 57 26 11 40 124 44 45 18 30 41 481 17 7 311 180 127 97 82 75 68 60 58 55 52 53 66 65 64 62 59 58 61 60 60 58 57 56 73 71 68 1.00 2.00 3.00 4.00 4.04 2.68 1.69 2.03 -0.18 -1.83 -3.25 -1.11 1.48 2.16 2.85 2.43 2.33 1.00 2.43 1.04 -0.99 -1.79 -3.47 -1.99 1.26 1.58 1.75 Graph Using Winter's Model 25000 20000 15000 10000 5000 13428039 12965735 12674760 12373138 12421098 13321748 13128250 13219183 14804770 15495747 15418028 15074150 14861987 14594477 14432238 14490541 14885770 14957975 14695879 14849481 15322319 16832497 17415322 17131325 16856468 16891530 16588604 16382521 16241907 18144614 18175766 18110735 20406946 tandard deviation of forecast error: 2911 2816 2791 2759 2790 2902 2893 2926 3077 3166 3176 3131 3116 3089 3081 3106 3163 3188 3155 3188 3249 3376 3444 3410 3377 3395 3345 3326 3319 3456 3474 3479 3629 4537 71 4 34 26 37 43 17 22 105 127 89 35 128 39 40 41 40 27 11 23 51 189 339 57 84 62 12 29 29 56 22 17 156 68 66 65 64 63 62 61 60 61 63 64 63 65 64 63 63 62 62 60 60 60 62 68 67 68 68 67 66 65 65 64 64 65 2.50 2.53 1.82 1.18 -0.17 -2.40 -3.31 -4.65 -1.70 0.36 1.47 1.94 2.78 2.16 1.26 -0.07 -1.86 -3.18 -3.75 -5.18 -3.20 -0.28 1.70 2.22 2.74 1.45 1.25 0.57 -0.31 -3.53 -4.80 -5.88 -2.19 0 1 3 5 7 9 11 13 Comparison Between Demand and Forecast 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 65 67 69 71 73 75 Holts Model Sales JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC Total Year 1 2000 3000 3000 3000 4000 6000 7000 6000 10000 12000 14000 8000 78000 Year 2 3000 4000 3000 5000 5000 8000 3000 8000 12000 12000 16000 10000 89000 Year 3 2000 5000 5000 3000 4000 6000 7000 10000 15000 15000 18000 8000 98000 Year 4 5000 4000 4000 2000 5000 7000 10000 14000 16000 16000 20000 12000 115000 1. Start by reformatting data Year Month 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC JAN FEB MAR Period 0 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 Year 5 5000 2000 3000 2000 7000 6000 8000 10000 20000 20000 22000 8000 113000 Color coding Given Data Forecast Red p = 12 (even) Smoothing Constants Alpha = 0.5 Beta = 0.5 Demand Dt 2000 3000 3000 3000 4000 6000 7000 6000 10000 12000 14000 8000 3000 4000 3000 5000 5000 8000 3000 8000 12000 12000 16000 10000 2000 5000 5000 Level 5997 4034 3044 2538 2400 2981 4527 6168 6696 8786 11135 13525 11839 7536 4751 2670 2713 3305 5526 4754 6430 9660 11860 14995 13814 8270 5430 3903 Trend 70 -947 -968 -737 -437 72 809 1225 877 1483 1916 2153 234 -2035 -2410 -2245 -1102 -254 983 106 891 2061 2130 2633 726 -2409 -2624 -2076 Forecast 6068 3087 2075 1800 1963 3053 5335 7392 7573 10270 13051 15679 12073 5502 2341 425 1611 3051 6508 4860 7321 11721 13991 17628 14540 5861 2806 Calculate Errors Et 4068 87 -925 -1200 -2037 -2947 -1665 1392 -2427 -1730 -949 7679 9073 1502 -659 -4575 -3389 -4949 3508 -3140 -4679 -279 -2009 7628 12540 861 -2194 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 APR MAY JUN JUL AUG SEP OCT NOV DEC JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC 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 61 62 63 64 65 66 67 68 69 70 71 72 3000 4000 6000 7000 10000 15000 15000 18000 8000 5000 4000 4000 2000 5000 7000 10000 14000 16000 16000 20000 12000 5000 2000 3000 2000 7000 6000 8000 10000 20000 20000 22000 8000 2414 2315 3688 5452 8221 12550 15327 18134 14504 9563 5452 3033 1066 1815 3986 7325 11664 15417 17439 20091 17394 11197 5049 1713 -133 1977 3788 6246 8914 15519 19942 23168 17489 -1783 -940 216 990 1880 3104 2941 2874 -378 -2660 -3385 -2902 -2435 -842 664 2002 3170 3462 2742 2697 0 -3098 -4623 -3980 -2913 -401 705 1582 2125 4365 4394 3810 -935 Forecasts 1827 631 1375 3903 6442 10100 15655 18268 21008 14126 6903 2066 131 -1369 973 4651 9327 14833 18878 20181 22787 17394 8098 426 -2267 -3046 1576 4492 7828 11039 19884 24336 26978 16554 15620 14685 13751 12816 11882 10947 10012 9078 8143 7209 6274 -1173 -3369 -4625 -3097 -3558 -4900 655 268 13008 9126 2903 -1934 -1869 -6369 -6027 -5349 -4673 -1167 2878 181 10787 12394 6098 -2574 -4267 -10046 -4424 -3508 -2172 -8961 -116 2336 18978 Estimate of standard olor coding Given Data Forecast At bias MSE MAD Percent Error MAPE TS 4068 87 925 1200 2037 2947 1665 1392 2427 1730 949 7679 9073 1502 659 4575 3389 4949 3508 3140 4679 279 2009 7628 12540 861 2194 4068 4155 3230 2030 -7 -2954 -4618 -3226 -5653 -7383 -8332 -653 8420 9921 9262 4687 1298 -3651 -142 -3282 -7961 -8240 -10250 -2622 9918 10779 8585 16544608 8276099 5802515 4711661 4599288 5279785 4921400 4548593 4697726 4527277 4197593 8761335 14419528 13550661 12676255 13192105 13091721 13725015 13650507 13460959 13862588 13236009 12836044 14725667 20426345 19669198 19119017 4068 2077 1693 1570 1663 1877 1847 1790 1861 1848 1766 2259 2783 2691 2556 2682 2724 2847 2882 2895 2980 2857 2820 3021 3401 3304 3263 203 3 31 40 51 49 24 23 24 14 7 96 302 38 22 91 68 62 117 39 39 2 13 76 627 17 44 203 103 79 69 66 63 57 53 50 46 43 47 67 65 62 64 64 64 67 65 64 61 59 60 82 80 79 1.00 2.00 1.91 1.29 0.00 -1.57 -2.50 -1.80 -3.04 -4.00 -4.72 -0.29 3.03 3.69 3.62 1.75 0.48 -1.28 -0.05 -1.13 -2.67 -2.88 -3.63 -0.87 2.92 3.26 2.63 Regression Statis 1173 3369 4625 3097 3558 4900 655 268 13008 9126 2903 1934 1869 6369 6027 5349 4673 1167 2878 181 10787 12394 6098 2574 4267 10046 4424 3508 2172 8961 116 2336 18978 7412 4042 -582 -3679 -7237 -12137 -11482 -11214 1794 10919 13823 11889 10020 3651 -2376 -7725 -12398 -13565 -10687 -10506 281 12675 18773 16199 11933 1887 -2538 -6045 -8218 -17179 -17295 -14959 4019 18485332 18239320 18344340 18061906 17893139 18078365 17559256 17059617 21285846 22961331 22578895 22095838 21630761 22092614 22431491 22575274 22558494 22087439 21787365 21324502 23304503 25963577 26188084 25804495 25658318 27078468 26939536 26673410 26281353 27229174 26759936 26398874 31961602 Estimate of standard deviation of forecast error: 3188 3194 3242 3237 3247 3297 3220 3135 3409 3564 3547 3505 3464 3535 3595 3635 3659 3604 3588 3515 3667 3845 3890 3864 3872 3988 3996 3988 3955 4043 3975 3947 4198 5247 39 84 77 44 36 33 4 1 163 183 73 48 93 127 86 53 33 7 18 1 90 248 305 86 213 144 74 44 22 45 1 11 237 77 77 77 76 75 74 72 70 72 75 75 75 75 76 77 76 75 74 72 71 71 75 79 80 82 83 83 82 81 81 79 78 81 2.32 1.27 -0.18 -1.14 -2.23 -3.68 -3.57 -3.58 0.53 3.06 3.90 3.39 2.89 1.03 -0.66 -2.13 -3.39 -3.76 -2.98 -2.99 0.08 3.30 4.83 4.19 3.08 0.47 -0.64 -1.52 -2.08 -4.25 -4.35 -3.79 0.96 Graph Using Winter's Model Deseasonalized Demand Regression SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.974925619 0.950479963 0.949403441 226.9014716 48 ANOVA df Regression Residual Total Intercept X Variable 1 1 46 47 SS 45456339.83 2368276.778 47824616.61 MS 45456339.83 51484.27779 F 882.9169172 Coefficients 5997.260518 70.24578448 Standard Error 79.19340748 2.364070087 t Stat 75.72928996 29.7139179 P-value 6.1285E-50 1.14478E-31 Avg. Seasonal Factors JAN FEB MAR APR MAY JUN 0.427 0.475 0.463 0.398 0.621 0.834 JUL AUG SEP OCT NOV DEC 0.853 1.151 1.733 1.778 2.124 1.095 Comparison Between Demand & Forecast 30000 25000 20000 15000 10000 5000 0 1 -5000 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 Significance F 1.14478E-31 Lower 95% 5837.852609 65.48716276 Upper 95% 6156.668427 75.00440621 Lower 95.0% 5837.852609 65.48716276 Upper 95.0% 6156.668427 75.00440621 Between Demand & Forecast 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 75 Winter's Model Sales JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC Total Year 1 2000 3000 3000 3000 4000 6000 7000 6000 10000 12000 14000 8000 78000 Year 2 3000 4000 3000 5000 5000 8000 3000 8000 12000 12000 16000 10000 89000 Year 3 2000 5000 5000 3000 4000 6000 7000 10000 15000 15000 18000 8000 98000 Year 4 5000 4000 4000 2000 5000 7000 10000 14000 16000 16000 20000 12000 115000 Year 5 5000 2000 3000 2000 7000 6000 8000 10000 20000 20000 22000 8000 113000 Color coding Red 1. Start by reformatting data p = 12 (even) Smoothing Constants Alpha = 0.0004 Year Month Period Demand Dt Level Trend 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC JAN FEB MAR APR MAY JUN JUL 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 2000 3000 3000 3000 4000 6000 7000 6000 10000 12000 14000 8000 3000 4000 3000 5000 5000 8000 3000 5997 6067 6137 6207 6277 6347 6418 6490 6560 6631 6701 6772 6842 6913 6984 7055 7129 7202 7276 7349 70 70 70 70 70 70 71 71 71 71 71 70 71 71 71 71 73 73 74 73 Beta = 0.93202 Gamma = 0 Seasonal Factor St Forecast 0.43 0.47 0.46 0.40 0.62 0.83 0.85 1.15 1.73 1.78 2.12 1.09 0.43 0.47 0.46 0.40 0.62 0.83 0.85 2588 2912 2871 2499 3944 5355 5534 7553 11492 11916 14381 7490 2949 3314 3264 2838 4474 6070 6269 Calculate Errors Given Forec 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 AUG SEP OCT NOV DEC JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV 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 61 62 63 64 65 66 67 68 69 70 71 8000 12000 12000 16000 10000 2000 5000 5000 3000 4000 6000 7000 10000 15000 15000 18000 8000 5000 4000 4000 2000 5000 7000 10000 14000 16000 16000 20000 12000 5000 2000 3000 2000 7000 6000 8000 10000 20000 20000 22000 8000 7421 7494 7566 7638 7710 7782 7854 7928 8001 8074 8146 8218 8291 8363 8436 8508 8581 8654 8727 8800 8872 8943 9014 9086 9159 9233 9306 9379 9452 9527 9599 9670 9740 9810 9879 9948 10016 10085 10154 10224 10292 73 72 72 72 73 71 72 73 73 73 72 72 72 73 73 73 72 73 73 73 72 71 71 72 73 73 73 73 74 74 72 71 70 70 69 69 68 69 69 69 68 Forecasts 1.15 1.73 1.78 2.12 1.09 0.43 0.47 0.46 0.40 0.62 0.83 0.85 1.15 1.73 1.78 2.12 1.09 0.43 0.47 0.46 0.40 0.62 0.83 0.85 1.15 1.73 1.78 2.12 1.09 0.43 0.47 0.46 0.40 0.62 0.83 0.85 1.15 1.73 1.78 2.12 1.09 0.43 0.47 0.46 0.40 0.62 0.83 0.85 1.15 1.73 1.78 2.12 8543 12987 13453 16220 8440 3320 3727 3667 3186 5017 6797 7009 9544 14493 15000 18069 9394 3691 4141 4071 3533 5557 7521 7748 10542 16000 16546 19917 10347 4064 4556 4474 3879 6095 8244 8484 11531 17476 18055 21712 11268 4420 4949 4856 4207 6607 8929 9185 12476 18901 19514 23452 6 DEC 72 1.09 12164 Color coding Given Data Forecast Red Et At bias 588 -88 -129 -501 -56 -645 -1466 1553 1492 -84 381 -510 -51 -686 264 -2162 -526 -1930 3269 588 88 129 501 56 645 1466 1553 1492 84 381 510 51 686 264 2162 526 1930 3269 588 501 372 -129 -185 -830 -2296 -743 749 664 1046 536 485 -201 64 -2099 -2624 -4554 -1285 MSE MAD Percent Error MAPE TS 346284 176999 123522 155306 124877 173408 455551 699922 869449 783217 725237 686442 633837 622159 585331 840961 807739 969745 1481111 588 338 268 326 272 334 496 628 724 660 635 624 580 588 566 666 658 728 862 29 3 4 17 1 11 21 26 15 1 3 6 2 17 9 43 11 24 109 29 16 12 13 11 11 12 14 14 13 12 11 11 11 11 13 13 13 18 1.00 1.48 1.39 -0.39 -0.68 -2.48 -4.63 -1.18 1.03 1.01 1.65 0.86 0.84 -0.34 0.11 -3.15 -3.99 -6.25 -1.49 Regr 543 987 1453 220 -1560 1320 -1273 -1333 186 1017 797 9 -456 -507 0 69 1394 -1309 141 71 1533 557 521 -2252 -3458 0 546 -83 -1653 -936 2556 1474 1879 -905 2244 484 1531 -2524 -1945 -288 3268 543 987 1453 220 1560 1320 1273 1333 186 1017 797 9 456 507 0 69 1394 1309 141 71 1533 557 521 2252 3458 0 546 83 1653 936 2556 1474 1879 905 2244 484 1531 2524 1945 288 3268 -742 245 1698 1918 358 1679 405 -928 -742 275 1072 1081 625 118 118 188 1581 273 414 485 2019 2575 3097 845 -2613 -2613 -2066 -2149 -3802 -4738 -2182 -708 1172 266 2510 2994 4525 2001 56 -232 3036 1421813 1400489 1432798 1372611 1416813 1429864 1437229 1449811 1399269 1386662 1361619 1317699 1283027 1251922 1215101 1180521 1201698 1215508 1184047 1153817 1183745 1162431 1141224 1232575 1476260 1443454 1418563 1388526 1416523 1405499 1508081 1521128 1559780 1545814 1610406 1585392 1598915 1682599 1718846 1691121 1840941 Estimate of standard deviation of forecast error: 846 853 880 851 881 899 913 929 902 906 902 874 860 850 825 803 820 833 815 796 814 808 801 835 894 874 867 851 867 869 902 914 932 932 956 947 958 985 1002 990 1028 1285 7 8 12 1 16 66 25 27 6 25 13 0 5 3 0 0 17 26 4 2 77 11 7 23 25 0 3 0 14 19 128 49 94 13 37 6 15 13 10 1 41 Winter's model seems to result in lowest forecast error 18 17 17 17 16 18 19 19 19 19 19 18 18 17 17 16 16 17 16 16 17 17 17 17 17 17 17 16 16 16 18 19 20 20 21 20 20 20 20 20 20 -0.88 0.29 1.93 2.25 0.41 1.87 0.44 -1.00 -0.82 0.30 1.19 1.24 0.73 0.14 0.14 0.23 1.93 0.33 0.51 0.61 2.48 3.19 3.87 1.01 -2.92 -2.99 -2.38 -2.53 -4.38 -5.45 -2.42 Graph -0.77 Using 1.26 Winter's 0.29 Model 2.63 3.16 4.72 2.03 0.06 -0.23 2.95 Graph Using Winter's Model Deseasonalized Demand Regression SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.974925619 0.950479963 0.949403441 226.9014716 48 ANOVA df Regression Residual Total Intercept X Variable 1 1 46 47 SS 45456339.83 2368276.778 47824616.61 MS 45456339.83 51484.27779 F 882.9169172 Coefficients 5997.260518 70.24578448 Standard Error 79.19340748 2.364070087 t Stat 75.72928996 29.7139179 P-value 6.1285E-50 1.14478E-31 Avg. Seasonal Factors JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC 0.427 0.475 0.463 0.398 0.621 0.834 0.853 1.151 1.733 1.778 2.124 1.095 Comparison Between Demand and Foreca 25000 20000 15000 10000 5000 0 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 Significance F 1.14478E-31 Lower 95% 5837.852609 65.48716276 Upper 95% 6156.668427 75.00440621 Lower 95.0% 5837.852609 65.48716276 Upper 95.0% 6156.668427 75.00440621 etween Demand and Forecast 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 73 75
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