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