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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 07 Dec 2016 11:34:38 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/07/t1481106933pi8cpa0743mdpov.htm/, Retrieved Tue, 07 May 2024 06:08:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=297981, Retrieved Tue, 07 May 2024 06:08:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact90
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Additief exponent...] [2016-12-07 10:34:38] [6b2845a830bced35782aaf33b6e68e42] [Current]
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Dataseries X:
2620
2940
3080
3120
2420
2930
2780
2890
3000
3380
3460
2810
3530
3590
3840
3520
2820
3310
2870
3340
3660
3650
3670
3050
3770
3480
3780
2750
3600
3550
2750
3480
3870
3640
3340
3030
3850
3400
3450
3000
3190
4100
2960
3640
4210
4040
3470
3380
4490
3670
3650
3520
3470
3570
3440
3580
4120
4370
3250
3260
3610
3600
3620
3020
3240
3360
3450
3640
3690
3870
3810
3430
3910
3800
4140
3350
3360
3310
2850
3630
4340
4260
3690
2990
3620
3590
3940
2970
3470
4310
3060
3480
4190
3470
2650
2620
3620
3090
3620
2820
3060
3600
2940
3550
4590
3120
2800
3380
3490
2940
3500
2980
3040
4160
3110
3890




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297981&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=297981&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297981&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.172765202577926
beta0.0451012729291031
gamma0.48799554925451

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.172765202577926 \tabularnewline
beta & 0.0451012729291031 \tabularnewline
gamma & 0.48799554925451 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297981&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]0.172765202577926[/C][/ROW]
[ROW][C]beta[/C][C]0.0451012729291031[/C][/ROW]
[ROW][C]gamma[/C][C]0.48799554925451[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297981&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297981&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.172765202577926
beta0.0451012729291031
gamma0.48799554925451







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1335303296.25534188034233.744658119657
1435903411.00914103489178.990858965108
1538403683.94807332947156.051926670528
1635203391.63990211471128.360097885289
1728202734.2977194587685.7022805412425
1833103261.5035365661348.4964634338662
1928703185.15936421907-315.159364219074
2033403214.78241925944125.217580740564
2136603327.71297309968332.287026900317
2236503759.42374585773-109.423745857727
2336703828.96964525068-158.96964525068
2430503159.55039019543-109.550390195432
2537703975.09177665652-205.091776656516
2634803993.14916090484-513.149160904844
2737804133.07977108752-353.07977108752
2827503733.49494672498-983.49494672498
2936002850.04141899331749.958581006691
3035503465.3628673919884.6371326080211
3127503237.11581509467-487.115815094671
3234803402.1216732959777.8783267040303
3338703577.41250059275292.587499407252
3436403810.59001482815-170.590014828147
3533403835.72916819342-495.729168193423
3630303111.6171722836-81.6171722836029
3738503877.170974938-27.1709749379975
3834003786.74983300645-386.749833006453
3934503999.2623398488-549.262339848799
4030003295.89158127283-295.89158127283
4131903220.96016024734-30.9601602473399
4241003416.65529919119683.344700808806
4329603049.57082198847-89.5708219884709
4436403502.97291310917137.027086890832
4542103767.25230956895442.747690431053
4640403832.65806428563207.34193571437
4734703788.0455897081-318.045589708096
4833803259.39651767259120.603482327409
4944904081.03571540857408.964284591429
5036703923.37411745252-253.374117452522
5136504096.93221292507-446.932212925068
5235203517.927420713172.07257928683202
5334703608.14932352915-138.149323529146
5435704079.57235037685-509.572350376855
5534403190.97325038131249.026749618687
5635803793.58195960344-213.581959603438
5741204117.205927102712.79407289728988
5843704004.64691019846365.353089801542
5932503769.5465389644-519.546538964401
6032603375.89725237469-115.897252374692
6136104263.97728760316-653.977287603158
6236003637.90912753492-37.9091275349188
6336203754.8441862408-134.844186240797
6430203397.73544376775-377.735443767753
6532403349.49529986853-109.495299868529
6633603659.91471352756-299.914713527563
6734503099.39189254982350.608107450179
6836403519.210981496120.789018504001
6936903976.96591514383-286.965915143832
7038703947.46411759088-77.4641175908764
7138103261.94489055917548.055109440831
7234303207.31356195055222.686438049446
7339103930.93705063578-20.9370506357814
7438003662.13130082979137.868699170208
7541403770.86932687679369.130673123207
7633503407.27091034271-57.2709103427073
7733603529.67098172811-169.670981728113
7833103759.34548739577-449.345487395766
7928503440.97059337856-590.970593378555
8036303603.3628003963426.6371996036642
8143403877.53273518034462.467264819657
8242604065.20605918648194.79394081352
8336903684.484899230145.51510076985915
8429903405.79446318287-415.794463182875
8536203916.8080571899-296.808057189898
8635903658.344628378-68.3446283780036
8739403817.10222697917122.897773020828
8829703229.20060148505-259.200601485052
8934703260.13639144791209.863608552092
9043103434.2342195225875.765780477497
9130603289.69930325852-229.69930325852
9234803768.72085467694-288.720854676936
9341904166.7835927581223.2164072418809
9434704169.52764076024-699.527640760236
9526503549.93515348018-899.935153480177
9626202929.72777373428-309.727773734276
9736203492.91622283816127.083777161837
9830903389.0341502921-299.034150292103
9936203572.4610666595247.5389333404846
10028202804.0271447842215.9728552157803
10130603060.73773860549-0.737738605494997
10236003454.50530357619145.494696423806
10329402719.09130025381220.908699746194
10435503237.19523046171312.804769538286
10545903854.85191975921735.148080240788
10631203684.12427471974-564.124274719743
10728003003.37153461456-203.371534614562
10833802743.54131665027636.458683349727
10934903655.6818003949-165.681800394902
11029403336.06942873563-396.069428735628
11135003648.75057702184-148.750577021841
11229802838.24390962272141.756090377276
11330403115.50177967518-75.5017796751836
11441603560.36443994077599.635560059226
11531102942.37205587914167.62794412086
11638903496.47124086381393.528759136191

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 3530 & 3296.25534188034 & 233.744658119657 \tabularnewline
14 & 3590 & 3411.00914103489 & 178.990858965108 \tabularnewline
15 & 3840 & 3683.94807332947 & 156.051926670528 \tabularnewline
16 & 3520 & 3391.63990211471 & 128.360097885289 \tabularnewline
17 & 2820 & 2734.29771945876 & 85.7022805412425 \tabularnewline
18 & 3310 & 3261.50353656613 & 48.4964634338662 \tabularnewline
19 & 2870 & 3185.15936421907 & -315.159364219074 \tabularnewline
20 & 3340 & 3214.78241925944 & 125.217580740564 \tabularnewline
21 & 3660 & 3327.71297309968 & 332.287026900317 \tabularnewline
22 & 3650 & 3759.42374585773 & -109.423745857727 \tabularnewline
23 & 3670 & 3828.96964525068 & -158.96964525068 \tabularnewline
24 & 3050 & 3159.55039019543 & -109.550390195432 \tabularnewline
25 & 3770 & 3975.09177665652 & -205.091776656516 \tabularnewline
26 & 3480 & 3993.14916090484 & -513.149160904844 \tabularnewline
27 & 3780 & 4133.07977108752 & -353.07977108752 \tabularnewline
28 & 2750 & 3733.49494672498 & -983.49494672498 \tabularnewline
29 & 3600 & 2850.04141899331 & 749.958581006691 \tabularnewline
30 & 3550 & 3465.36286739198 & 84.6371326080211 \tabularnewline
31 & 2750 & 3237.11581509467 & -487.115815094671 \tabularnewline
32 & 3480 & 3402.12167329597 & 77.8783267040303 \tabularnewline
33 & 3870 & 3577.41250059275 & 292.587499407252 \tabularnewline
34 & 3640 & 3810.59001482815 & -170.590014828147 \tabularnewline
35 & 3340 & 3835.72916819342 & -495.729168193423 \tabularnewline
36 & 3030 & 3111.6171722836 & -81.6171722836029 \tabularnewline
37 & 3850 & 3877.170974938 & -27.1709749379975 \tabularnewline
38 & 3400 & 3786.74983300645 & -386.749833006453 \tabularnewline
39 & 3450 & 3999.2623398488 & -549.262339848799 \tabularnewline
40 & 3000 & 3295.89158127283 & -295.89158127283 \tabularnewline
41 & 3190 & 3220.96016024734 & -30.9601602473399 \tabularnewline
42 & 4100 & 3416.65529919119 & 683.344700808806 \tabularnewline
43 & 2960 & 3049.57082198847 & -89.5708219884709 \tabularnewline
44 & 3640 & 3502.97291310917 & 137.027086890832 \tabularnewline
45 & 4210 & 3767.25230956895 & 442.747690431053 \tabularnewline
46 & 4040 & 3832.65806428563 & 207.34193571437 \tabularnewline
47 & 3470 & 3788.0455897081 & -318.045589708096 \tabularnewline
48 & 3380 & 3259.39651767259 & 120.603482327409 \tabularnewline
49 & 4490 & 4081.03571540857 & 408.964284591429 \tabularnewline
50 & 3670 & 3923.37411745252 & -253.374117452522 \tabularnewline
51 & 3650 & 4096.93221292507 & -446.932212925068 \tabularnewline
52 & 3520 & 3517.92742071317 & 2.07257928683202 \tabularnewline
53 & 3470 & 3608.14932352915 & -138.149323529146 \tabularnewline
54 & 3570 & 4079.57235037685 & -509.572350376855 \tabularnewline
55 & 3440 & 3190.97325038131 & 249.026749618687 \tabularnewline
56 & 3580 & 3793.58195960344 & -213.581959603438 \tabularnewline
57 & 4120 & 4117.20592710271 & 2.79407289728988 \tabularnewline
58 & 4370 & 4004.64691019846 & 365.353089801542 \tabularnewline
59 & 3250 & 3769.5465389644 & -519.546538964401 \tabularnewline
60 & 3260 & 3375.89725237469 & -115.897252374692 \tabularnewline
61 & 3610 & 4263.97728760316 & -653.977287603158 \tabularnewline
62 & 3600 & 3637.90912753492 & -37.9091275349188 \tabularnewline
63 & 3620 & 3754.8441862408 & -134.844186240797 \tabularnewline
64 & 3020 & 3397.73544376775 & -377.735443767753 \tabularnewline
65 & 3240 & 3349.49529986853 & -109.495299868529 \tabularnewline
66 & 3360 & 3659.91471352756 & -299.914713527563 \tabularnewline
67 & 3450 & 3099.39189254982 & 350.608107450179 \tabularnewline
68 & 3640 & 3519.210981496 & 120.789018504001 \tabularnewline
69 & 3690 & 3976.96591514383 & -286.965915143832 \tabularnewline
70 & 3870 & 3947.46411759088 & -77.4641175908764 \tabularnewline
71 & 3810 & 3261.94489055917 & 548.055109440831 \tabularnewline
72 & 3430 & 3207.31356195055 & 222.686438049446 \tabularnewline
73 & 3910 & 3930.93705063578 & -20.9370506357814 \tabularnewline
74 & 3800 & 3662.13130082979 & 137.868699170208 \tabularnewline
75 & 4140 & 3770.86932687679 & 369.130673123207 \tabularnewline
76 & 3350 & 3407.27091034271 & -57.2709103427073 \tabularnewline
77 & 3360 & 3529.67098172811 & -169.670981728113 \tabularnewline
78 & 3310 & 3759.34548739577 & -449.345487395766 \tabularnewline
79 & 2850 & 3440.97059337856 & -590.970593378555 \tabularnewline
80 & 3630 & 3603.36280039634 & 26.6371996036642 \tabularnewline
81 & 4340 & 3877.53273518034 & 462.467264819657 \tabularnewline
82 & 4260 & 4065.20605918648 & 194.79394081352 \tabularnewline
83 & 3690 & 3684.48489923014 & 5.51510076985915 \tabularnewline
84 & 2990 & 3405.79446318287 & -415.794463182875 \tabularnewline
85 & 3620 & 3916.8080571899 & -296.808057189898 \tabularnewline
86 & 3590 & 3658.344628378 & -68.3446283780036 \tabularnewline
87 & 3940 & 3817.10222697917 & 122.897773020828 \tabularnewline
88 & 2970 & 3229.20060148505 & -259.200601485052 \tabularnewline
89 & 3470 & 3260.13639144791 & 209.863608552092 \tabularnewline
90 & 4310 & 3434.2342195225 & 875.765780477497 \tabularnewline
91 & 3060 & 3289.69930325852 & -229.69930325852 \tabularnewline
92 & 3480 & 3768.72085467694 & -288.720854676936 \tabularnewline
93 & 4190 & 4166.78359275812 & 23.2164072418809 \tabularnewline
94 & 3470 & 4169.52764076024 & -699.527640760236 \tabularnewline
95 & 2650 & 3549.93515348018 & -899.935153480177 \tabularnewline
96 & 2620 & 2929.72777373428 & -309.727773734276 \tabularnewline
97 & 3620 & 3492.91622283816 & 127.083777161837 \tabularnewline
98 & 3090 & 3389.0341502921 & -299.034150292103 \tabularnewline
99 & 3620 & 3572.46106665952 & 47.5389333404846 \tabularnewline
100 & 2820 & 2804.02714478422 & 15.9728552157803 \tabularnewline
101 & 3060 & 3060.73773860549 & -0.737738605494997 \tabularnewline
102 & 3600 & 3454.50530357619 & 145.494696423806 \tabularnewline
103 & 2940 & 2719.09130025381 & 220.908699746194 \tabularnewline
104 & 3550 & 3237.19523046171 & 312.804769538286 \tabularnewline
105 & 4590 & 3854.85191975921 & 735.148080240788 \tabularnewline
106 & 3120 & 3684.12427471974 & -564.124274719743 \tabularnewline
107 & 2800 & 3003.37153461456 & -203.371534614562 \tabularnewline
108 & 3380 & 2743.54131665027 & 636.458683349727 \tabularnewline
109 & 3490 & 3655.6818003949 & -165.681800394902 \tabularnewline
110 & 2940 & 3336.06942873563 & -396.069428735628 \tabularnewline
111 & 3500 & 3648.75057702184 & -148.750577021841 \tabularnewline
112 & 2980 & 2838.24390962272 & 141.756090377276 \tabularnewline
113 & 3040 & 3115.50177967518 & -75.5017796751836 \tabularnewline
114 & 4160 & 3560.36443994077 & 599.635560059226 \tabularnewline
115 & 3110 & 2942.37205587914 & 167.62794412086 \tabularnewline
116 & 3890 & 3496.47124086381 & 393.528759136191 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297981&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]3530[/C][C]3296.25534188034[/C][C]233.744658119657[/C][/ROW]
[ROW][C]14[/C][C]3590[/C][C]3411.00914103489[/C][C]178.990858965108[/C][/ROW]
[ROW][C]15[/C][C]3840[/C][C]3683.94807332947[/C][C]156.051926670528[/C][/ROW]
[ROW][C]16[/C][C]3520[/C][C]3391.63990211471[/C][C]128.360097885289[/C][/ROW]
[ROW][C]17[/C][C]2820[/C][C]2734.29771945876[/C][C]85.7022805412425[/C][/ROW]
[ROW][C]18[/C][C]3310[/C][C]3261.50353656613[/C][C]48.4964634338662[/C][/ROW]
[ROW][C]19[/C][C]2870[/C][C]3185.15936421907[/C][C]-315.159364219074[/C][/ROW]
[ROW][C]20[/C][C]3340[/C][C]3214.78241925944[/C][C]125.217580740564[/C][/ROW]
[ROW][C]21[/C][C]3660[/C][C]3327.71297309968[/C][C]332.287026900317[/C][/ROW]
[ROW][C]22[/C][C]3650[/C][C]3759.42374585773[/C][C]-109.423745857727[/C][/ROW]
[ROW][C]23[/C][C]3670[/C][C]3828.96964525068[/C][C]-158.96964525068[/C][/ROW]
[ROW][C]24[/C][C]3050[/C][C]3159.55039019543[/C][C]-109.550390195432[/C][/ROW]
[ROW][C]25[/C][C]3770[/C][C]3975.09177665652[/C][C]-205.091776656516[/C][/ROW]
[ROW][C]26[/C][C]3480[/C][C]3993.14916090484[/C][C]-513.149160904844[/C][/ROW]
[ROW][C]27[/C][C]3780[/C][C]4133.07977108752[/C][C]-353.07977108752[/C][/ROW]
[ROW][C]28[/C][C]2750[/C][C]3733.49494672498[/C][C]-983.49494672498[/C][/ROW]
[ROW][C]29[/C][C]3600[/C][C]2850.04141899331[/C][C]749.958581006691[/C][/ROW]
[ROW][C]30[/C][C]3550[/C][C]3465.36286739198[/C][C]84.6371326080211[/C][/ROW]
[ROW][C]31[/C][C]2750[/C][C]3237.11581509467[/C][C]-487.115815094671[/C][/ROW]
[ROW][C]32[/C][C]3480[/C][C]3402.12167329597[/C][C]77.8783267040303[/C][/ROW]
[ROW][C]33[/C][C]3870[/C][C]3577.41250059275[/C][C]292.587499407252[/C][/ROW]
[ROW][C]34[/C][C]3640[/C][C]3810.59001482815[/C][C]-170.590014828147[/C][/ROW]
[ROW][C]35[/C][C]3340[/C][C]3835.72916819342[/C][C]-495.729168193423[/C][/ROW]
[ROW][C]36[/C][C]3030[/C][C]3111.6171722836[/C][C]-81.6171722836029[/C][/ROW]
[ROW][C]37[/C][C]3850[/C][C]3877.170974938[/C][C]-27.1709749379975[/C][/ROW]
[ROW][C]38[/C][C]3400[/C][C]3786.74983300645[/C][C]-386.749833006453[/C][/ROW]
[ROW][C]39[/C][C]3450[/C][C]3999.2623398488[/C][C]-549.262339848799[/C][/ROW]
[ROW][C]40[/C][C]3000[/C][C]3295.89158127283[/C][C]-295.89158127283[/C][/ROW]
[ROW][C]41[/C][C]3190[/C][C]3220.96016024734[/C][C]-30.9601602473399[/C][/ROW]
[ROW][C]42[/C][C]4100[/C][C]3416.65529919119[/C][C]683.344700808806[/C][/ROW]
[ROW][C]43[/C][C]2960[/C][C]3049.57082198847[/C][C]-89.5708219884709[/C][/ROW]
[ROW][C]44[/C][C]3640[/C][C]3502.97291310917[/C][C]137.027086890832[/C][/ROW]
[ROW][C]45[/C][C]4210[/C][C]3767.25230956895[/C][C]442.747690431053[/C][/ROW]
[ROW][C]46[/C][C]4040[/C][C]3832.65806428563[/C][C]207.34193571437[/C][/ROW]
[ROW][C]47[/C][C]3470[/C][C]3788.0455897081[/C][C]-318.045589708096[/C][/ROW]
[ROW][C]48[/C][C]3380[/C][C]3259.39651767259[/C][C]120.603482327409[/C][/ROW]
[ROW][C]49[/C][C]4490[/C][C]4081.03571540857[/C][C]408.964284591429[/C][/ROW]
[ROW][C]50[/C][C]3670[/C][C]3923.37411745252[/C][C]-253.374117452522[/C][/ROW]
[ROW][C]51[/C][C]3650[/C][C]4096.93221292507[/C][C]-446.932212925068[/C][/ROW]
[ROW][C]52[/C][C]3520[/C][C]3517.92742071317[/C][C]2.07257928683202[/C][/ROW]
[ROW][C]53[/C][C]3470[/C][C]3608.14932352915[/C][C]-138.149323529146[/C][/ROW]
[ROW][C]54[/C][C]3570[/C][C]4079.57235037685[/C][C]-509.572350376855[/C][/ROW]
[ROW][C]55[/C][C]3440[/C][C]3190.97325038131[/C][C]249.026749618687[/C][/ROW]
[ROW][C]56[/C][C]3580[/C][C]3793.58195960344[/C][C]-213.581959603438[/C][/ROW]
[ROW][C]57[/C][C]4120[/C][C]4117.20592710271[/C][C]2.79407289728988[/C][/ROW]
[ROW][C]58[/C][C]4370[/C][C]4004.64691019846[/C][C]365.353089801542[/C][/ROW]
[ROW][C]59[/C][C]3250[/C][C]3769.5465389644[/C][C]-519.546538964401[/C][/ROW]
[ROW][C]60[/C][C]3260[/C][C]3375.89725237469[/C][C]-115.897252374692[/C][/ROW]
[ROW][C]61[/C][C]3610[/C][C]4263.97728760316[/C][C]-653.977287603158[/C][/ROW]
[ROW][C]62[/C][C]3600[/C][C]3637.90912753492[/C][C]-37.9091275349188[/C][/ROW]
[ROW][C]63[/C][C]3620[/C][C]3754.8441862408[/C][C]-134.844186240797[/C][/ROW]
[ROW][C]64[/C][C]3020[/C][C]3397.73544376775[/C][C]-377.735443767753[/C][/ROW]
[ROW][C]65[/C][C]3240[/C][C]3349.49529986853[/C][C]-109.495299868529[/C][/ROW]
[ROW][C]66[/C][C]3360[/C][C]3659.91471352756[/C][C]-299.914713527563[/C][/ROW]
[ROW][C]67[/C][C]3450[/C][C]3099.39189254982[/C][C]350.608107450179[/C][/ROW]
[ROW][C]68[/C][C]3640[/C][C]3519.210981496[/C][C]120.789018504001[/C][/ROW]
[ROW][C]69[/C][C]3690[/C][C]3976.96591514383[/C][C]-286.965915143832[/C][/ROW]
[ROW][C]70[/C][C]3870[/C][C]3947.46411759088[/C][C]-77.4641175908764[/C][/ROW]
[ROW][C]71[/C][C]3810[/C][C]3261.94489055917[/C][C]548.055109440831[/C][/ROW]
[ROW][C]72[/C][C]3430[/C][C]3207.31356195055[/C][C]222.686438049446[/C][/ROW]
[ROW][C]73[/C][C]3910[/C][C]3930.93705063578[/C][C]-20.9370506357814[/C][/ROW]
[ROW][C]74[/C][C]3800[/C][C]3662.13130082979[/C][C]137.868699170208[/C][/ROW]
[ROW][C]75[/C][C]4140[/C][C]3770.86932687679[/C][C]369.130673123207[/C][/ROW]
[ROW][C]76[/C][C]3350[/C][C]3407.27091034271[/C][C]-57.2709103427073[/C][/ROW]
[ROW][C]77[/C][C]3360[/C][C]3529.67098172811[/C][C]-169.670981728113[/C][/ROW]
[ROW][C]78[/C][C]3310[/C][C]3759.34548739577[/C][C]-449.345487395766[/C][/ROW]
[ROW][C]79[/C][C]2850[/C][C]3440.97059337856[/C][C]-590.970593378555[/C][/ROW]
[ROW][C]80[/C][C]3630[/C][C]3603.36280039634[/C][C]26.6371996036642[/C][/ROW]
[ROW][C]81[/C][C]4340[/C][C]3877.53273518034[/C][C]462.467264819657[/C][/ROW]
[ROW][C]82[/C][C]4260[/C][C]4065.20605918648[/C][C]194.79394081352[/C][/ROW]
[ROW][C]83[/C][C]3690[/C][C]3684.48489923014[/C][C]5.51510076985915[/C][/ROW]
[ROW][C]84[/C][C]2990[/C][C]3405.79446318287[/C][C]-415.794463182875[/C][/ROW]
[ROW][C]85[/C][C]3620[/C][C]3916.8080571899[/C][C]-296.808057189898[/C][/ROW]
[ROW][C]86[/C][C]3590[/C][C]3658.344628378[/C][C]-68.3446283780036[/C][/ROW]
[ROW][C]87[/C][C]3940[/C][C]3817.10222697917[/C][C]122.897773020828[/C][/ROW]
[ROW][C]88[/C][C]2970[/C][C]3229.20060148505[/C][C]-259.200601485052[/C][/ROW]
[ROW][C]89[/C][C]3470[/C][C]3260.13639144791[/C][C]209.863608552092[/C][/ROW]
[ROW][C]90[/C][C]4310[/C][C]3434.2342195225[/C][C]875.765780477497[/C][/ROW]
[ROW][C]91[/C][C]3060[/C][C]3289.69930325852[/C][C]-229.69930325852[/C][/ROW]
[ROW][C]92[/C][C]3480[/C][C]3768.72085467694[/C][C]-288.720854676936[/C][/ROW]
[ROW][C]93[/C][C]4190[/C][C]4166.78359275812[/C][C]23.2164072418809[/C][/ROW]
[ROW][C]94[/C][C]3470[/C][C]4169.52764076024[/C][C]-699.527640760236[/C][/ROW]
[ROW][C]95[/C][C]2650[/C][C]3549.93515348018[/C][C]-899.935153480177[/C][/ROW]
[ROW][C]96[/C][C]2620[/C][C]2929.72777373428[/C][C]-309.727773734276[/C][/ROW]
[ROW][C]97[/C][C]3620[/C][C]3492.91622283816[/C][C]127.083777161837[/C][/ROW]
[ROW][C]98[/C][C]3090[/C][C]3389.0341502921[/C][C]-299.034150292103[/C][/ROW]
[ROW][C]99[/C][C]3620[/C][C]3572.46106665952[/C][C]47.5389333404846[/C][/ROW]
[ROW][C]100[/C][C]2820[/C][C]2804.02714478422[/C][C]15.9728552157803[/C][/ROW]
[ROW][C]101[/C][C]3060[/C][C]3060.73773860549[/C][C]-0.737738605494997[/C][/ROW]
[ROW][C]102[/C][C]3600[/C][C]3454.50530357619[/C][C]145.494696423806[/C][/ROW]
[ROW][C]103[/C][C]2940[/C][C]2719.09130025381[/C][C]220.908699746194[/C][/ROW]
[ROW][C]104[/C][C]3550[/C][C]3237.19523046171[/C][C]312.804769538286[/C][/ROW]
[ROW][C]105[/C][C]4590[/C][C]3854.85191975921[/C][C]735.148080240788[/C][/ROW]
[ROW][C]106[/C][C]3120[/C][C]3684.12427471974[/C][C]-564.124274719743[/C][/ROW]
[ROW][C]107[/C][C]2800[/C][C]3003.37153461456[/C][C]-203.371534614562[/C][/ROW]
[ROW][C]108[/C][C]3380[/C][C]2743.54131665027[/C][C]636.458683349727[/C][/ROW]
[ROW][C]109[/C][C]3490[/C][C]3655.6818003949[/C][C]-165.681800394902[/C][/ROW]
[ROW][C]110[/C][C]2940[/C][C]3336.06942873563[/C][C]-396.069428735628[/C][/ROW]
[ROW][C]111[/C][C]3500[/C][C]3648.75057702184[/C][C]-148.750577021841[/C][/ROW]
[ROW][C]112[/C][C]2980[/C][C]2838.24390962272[/C][C]141.756090377276[/C][/ROW]
[ROW][C]113[/C][C]3040[/C][C]3115.50177967518[/C][C]-75.5017796751836[/C][/ROW]
[ROW][C]114[/C][C]4160[/C][C]3560.36443994077[/C][C]599.635560059226[/C][/ROW]
[ROW][C]115[/C][C]3110[/C][C]2942.37205587914[/C][C]167.62794412086[/C][/ROW]
[ROW][C]116[/C][C]3890[/C][C]3496.47124086381[/C][C]393.528759136191[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297981&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297981&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1335303296.25534188034233.744658119657
1435903411.00914103489178.990858965108
1538403683.94807332947156.051926670528
1635203391.63990211471128.360097885289
1728202734.2977194587685.7022805412425
1833103261.5035365661348.4964634338662
1928703185.15936421907-315.159364219074
2033403214.78241925944125.217580740564
2136603327.71297309968332.287026900317
2236503759.42374585773-109.423745857727
2336703828.96964525068-158.96964525068
2430503159.55039019543-109.550390195432
2537703975.09177665652-205.091776656516
2634803993.14916090484-513.149160904844
2737804133.07977108752-353.07977108752
2827503733.49494672498-983.49494672498
2936002850.04141899331749.958581006691
3035503465.3628673919884.6371326080211
3127503237.11581509467-487.115815094671
3234803402.1216732959777.8783267040303
3338703577.41250059275292.587499407252
3436403810.59001482815-170.590014828147
3533403835.72916819342-495.729168193423
3630303111.6171722836-81.6171722836029
3738503877.170974938-27.1709749379975
3834003786.74983300645-386.749833006453
3934503999.2623398488-549.262339848799
4030003295.89158127283-295.89158127283
4131903220.96016024734-30.9601602473399
4241003416.65529919119683.344700808806
4329603049.57082198847-89.5708219884709
4436403502.97291310917137.027086890832
4542103767.25230956895442.747690431053
4640403832.65806428563207.34193571437
4734703788.0455897081-318.045589708096
4833803259.39651767259120.603482327409
4944904081.03571540857408.964284591429
5036703923.37411745252-253.374117452522
5136504096.93221292507-446.932212925068
5235203517.927420713172.07257928683202
5334703608.14932352915-138.149323529146
5435704079.57235037685-509.572350376855
5534403190.97325038131249.026749618687
5635803793.58195960344-213.581959603438
5741204117.205927102712.79407289728988
5843704004.64691019846365.353089801542
5932503769.5465389644-519.546538964401
6032603375.89725237469-115.897252374692
6136104263.97728760316-653.977287603158
6236003637.90912753492-37.9091275349188
6336203754.8441862408-134.844186240797
6430203397.73544376775-377.735443767753
6532403349.49529986853-109.495299868529
6633603659.91471352756-299.914713527563
6734503099.39189254982350.608107450179
6836403519.210981496120.789018504001
6936903976.96591514383-286.965915143832
7038703947.46411759088-77.4641175908764
7138103261.94489055917548.055109440831
7234303207.31356195055222.686438049446
7339103930.93705063578-20.9370506357814
7438003662.13130082979137.868699170208
7541403770.86932687679369.130673123207
7633503407.27091034271-57.2709103427073
7733603529.67098172811-169.670981728113
7833103759.34548739577-449.345487395766
7928503440.97059337856-590.970593378555
8036303603.3628003963426.6371996036642
8143403877.53273518034462.467264819657
8242604065.20605918648194.79394081352
8336903684.484899230145.51510076985915
8429903405.79446318287-415.794463182875
8536203916.8080571899-296.808057189898
8635903658.344628378-68.3446283780036
8739403817.10222697917122.897773020828
8829703229.20060148505-259.200601485052
8934703260.13639144791209.863608552092
9043103434.2342195225875.765780477497
9130603289.69930325852-229.69930325852
9234803768.72085467694-288.720854676936
9341904166.7835927581223.2164072418809
9434704169.52764076024-699.527640760236
9526503549.93515348018-899.935153480177
9626202929.72777373428-309.727773734276
9736203492.91622283816127.083777161837
9830903389.0341502921-299.034150292103
9936203572.4610666595247.5389333404846
10028202804.0271447842215.9728552157803
10130603060.73773860549-0.737738605494997
10236003454.50530357619145.494696423806
10329402719.09130025381220.908699746194
10435503237.19523046171312.804769538286
10545903854.85191975921735.148080240788
10631203684.12427471974-564.124274719743
10728003003.37153461456-203.371534614562
10833802743.54131665027636.458683349727
10934903655.6818003949-165.681800394902
11029403336.06942873563-396.069428735628
11135003648.75057702184-148.750577021841
11229802838.24390962272141.756090377276
11330403115.50177967518-75.5017796751836
11441603560.36443994077599.635560059226
11531102942.37205587914167.62794412086
11638903496.47124086381393.528759136191







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1174307.300759689383617.617275304534996.98424407423
1183488.06972805622787.234262143134188.90519396927
1193057.808653576252345.036121802213770.58118535029
1203181.126539462762455.63080345853906.62227546702
1213663.520386095022924.516832635984402.52393955406
1223284.843458957552531.551345456484038.13557245863
1233774.193010253883005.837564713874542.5484557939
1243116.220063916112332.034334432033900.40579340019
1253289.739766460862488.966221576584090.51331134513
1264029.235418990123211.127305542834847.34353243741
1273137.623555018392301.446024437173973.80108559962
1283757.022012611292902.053029965974611.99099525661

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
117 & 4307.30075968938 & 3617.61727530453 & 4996.98424407423 \tabularnewline
118 & 3488.0697280562 & 2787.23426214313 & 4188.90519396927 \tabularnewline
119 & 3057.80865357625 & 2345.03612180221 & 3770.58118535029 \tabularnewline
120 & 3181.12653946276 & 2455.6308034585 & 3906.62227546702 \tabularnewline
121 & 3663.52038609502 & 2924.51683263598 & 4402.52393955406 \tabularnewline
122 & 3284.84345895755 & 2531.55134545648 & 4038.13557245863 \tabularnewline
123 & 3774.19301025388 & 3005.83756471387 & 4542.5484557939 \tabularnewline
124 & 3116.22006391611 & 2332.03433443203 & 3900.40579340019 \tabularnewline
125 & 3289.73976646086 & 2488.96622157658 & 4090.51331134513 \tabularnewline
126 & 4029.23541899012 & 3211.12730554283 & 4847.34353243741 \tabularnewline
127 & 3137.62355501839 & 2301.44602443717 & 3973.80108559962 \tabularnewline
128 & 3757.02201261129 & 2902.05302996597 & 4611.99099525661 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297981&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]117[/C][C]4307.30075968938[/C][C]3617.61727530453[/C][C]4996.98424407423[/C][/ROW]
[ROW][C]118[/C][C]3488.0697280562[/C][C]2787.23426214313[/C][C]4188.90519396927[/C][/ROW]
[ROW][C]119[/C][C]3057.80865357625[/C][C]2345.03612180221[/C][C]3770.58118535029[/C][/ROW]
[ROW][C]120[/C][C]3181.12653946276[/C][C]2455.6308034585[/C][C]3906.62227546702[/C][/ROW]
[ROW][C]121[/C][C]3663.52038609502[/C][C]2924.51683263598[/C][C]4402.52393955406[/C][/ROW]
[ROW][C]122[/C][C]3284.84345895755[/C][C]2531.55134545648[/C][C]4038.13557245863[/C][/ROW]
[ROW][C]123[/C][C]3774.19301025388[/C][C]3005.83756471387[/C][C]4542.5484557939[/C][/ROW]
[ROW][C]124[/C][C]3116.22006391611[/C][C]2332.03433443203[/C][C]3900.40579340019[/C][/ROW]
[ROW][C]125[/C][C]3289.73976646086[/C][C]2488.96622157658[/C][C]4090.51331134513[/C][/ROW]
[ROW][C]126[/C][C]4029.23541899012[/C][C]3211.12730554283[/C][C]4847.34353243741[/C][/ROW]
[ROW][C]127[/C][C]3137.62355501839[/C][C]2301.44602443717[/C][C]3973.80108559962[/C][/ROW]
[ROW][C]128[/C][C]3757.02201261129[/C][C]2902.05302996597[/C][C]4611.99099525661[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297981&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297981&T=3

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1174307.300759689383617.617275304534996.98424407423
1183488.06972805622787.234262143134188.90519396927
1193057.808653576252345.036121802213770.58118535029
1203181.126539462762455.63080345853906.62227546702
1213663.520386095022924.516832635984402.52393955406
1223284.843458957552531.551345456484038.13557245863
1233774.193010253883005.837564713874542.5484557939
1243116.220063916112332.034334432033900.40579340019
1253289.739766460862488.966221576584090.51331134513
1264029.235418990123211.127305542834847.34353243741
1273137.623555018392301.446024437173973.80108559962
1283757.022012611292902.053029965974611.99099525661



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')