Monthly shampoo sales over three years | Holt's Linear Exponential Smoothing | |||||||||
AlphaLES | 0.157181 | Note: Ft is the forecast obtain at the period t-1 | ||||||||
BetaLES | 0.400793 | MSE(LES) | 5664.99 | |||||||
t | Yt | Lt | bt | Ft | Et | Et*Et | ||||
1 | 266 | 266 | 0 | |||||||
2 | 145.9 | 247.1226 | -7.56592 | 266 | -120.1 | 14424.01 | Note: | |||
3 | 183.1 | 230.6828 | -11.1225 | 239.5567 | -56.4567 | 3187.358 | Use Solver to minimize the MSE | |||
4 | 119.3 | 203.8013 | -17.4386 | 219.5603 | -100.26 | 10052.12 | by varying Alpha & Beta. | |||
5 | 180.3 | 185.4098 | -17.8205 | 186.3627 | -6.06271 | 36.75646 | ||||
6 | 168.5 | 167.7324 | -17.7632 | 167.5892 | 0.910762 | 0.829487 | ||||
7 | 231.8 | 162.8314 | -12.6081 | 149.9692 | 81.83076 | 6696.274 | ||||
8 | 224.5 | 161.8982 | -7.92888 | 150.2234 | 74.27663 | 5517.018 | ||||
9 | 192.8 | 160.0728 | -5.48267 | 153.9693 | 38.83067 | 1507.821 | ||||
10 | 122.9 | 149.609 | -7.47905 | 154.5901 | -31.6901 | 1004.262 | ||||
11 | 336.5 | 172.6812 | 4.765655 | 142.13 | 194.37 | 37779.71 | ||||
12 | 185.9 | 178.7755 | 5.298179 | 177.4468 | 8.453179 | 71.45624 | ||||
13 | 194.3 | 185.6811 | 5.942406 | 184.0737 | 10.22632 | 104.5777 | ||||
14 | 149.5 | 185.0025 | 3.28876 | 191.6235 | -42.1235 | 1774.386 | ||||
15 | 210.1 | 191.7191 | 4.662644 | 188.2912 | 21.80877 | 475.6224 | ||||
16 | 273.3 | 208.4718 | 9.50825 | 196.3818 | 76.91821 | 5916.411 | ||||
17 | 191.4 | 213.8022 | 7.833788 | 217.9801 | -26.5801 | 706.501 | ||||
18 | 287 | 231.91 | 11.95151 | 221.636 | 65.364 | 4272.452 | ||||
19 | 226 | 241.054 | 10.8263 | 243.8615 | -17.8615 | 319.032 | ||||
20 | 303.6 | 260.0096 | 14.08448 | 251.8803 | 51.71971 | 2674.929 | ||||
21 | 289.9 | 276.5785 | 15.0802 | 274.0941 | 15.8059 | 249.8265 | ||||
22 | 421.6 | 312.0829 | 23.26609 | 291.6587 | 129.9413 | 16884.75 | ||||
23 | 264.5 | 324.2129 | 18.80283 | 335.349 | -70.849 | 5019.584 | ||||
24 | 342.3 | 342.9033 | 18.75774 | 343.0158 | -0.71576 | 0.512318 | ||||
25 | 339.7 | 358.2092 | 17.37426 | 361.661 | -21.961 | 482.2854 | ||||
26 | 440.4 | 385.7713 | 21.45751 | 375.5834 | 64.81658 | 4201.189 | ||||
27 | 315.9 | 392.8737 | 15.70408 | 407.2288 | -91.3288 | 8340.955 | ||||
28 | 439.3 | 413.4067 | 17.63948 | 408.5778 | 30.72221 | 943.8542 | ||||
29 | 401.3 | 426.3707 | 15.76556 | 431.0462 | -29.7462 | 884.8365 | ||||
30 | 437.4 | 441.3918 | 15.46719 | 442.1362 | -4.73624 | 22.43195 | ||||
31 | 575.5 | 475.507 | 22.9412 | 456.859 | 118.641 | 14075.69 | ||||
32 | 407.6 | 484.1687 | 17.21805 | 498.4483 | -90.8483 | 8253.405 | ||||
33 | 682 | 529.7756 | 28.59612 | 501.3867 | 180.6133 | 32621.16 | ||||
34 | 475.3 | 545.3145 | 23.36286 | 558.3717 | -83.0717 | 6900.914 | ||||
35 | 581.3 | 570.6614 | 24.15805 | 568.6773 | 12.62266 | 159.3317 | ||||
36 | 646.9 | 603.0055 | 27.43896 | 594.8194 | 52.08058 | 2712.387 |