Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 16 Aug 2015 12:47:39 +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/2015/Aug/16/t1439725674bxhmmc6yb7odhgu.htm/, Retrieved Wed, 23 Sep 2026 07:39:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=280116, Retrieved Wed, 23 Sep 2026 07:39:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact410
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-08-16 11:47:39] [f898ec974b62c60a8bec4044c4c271e3] [Current]
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Dataseries X:
5452304
5431998
5411406
5368792
5790356
5768048
5452304
5242380
5262686
5262686
5285280
5325892
5389098
5389098
5348486
5242380
5790356
5873868
5747742
5452304
5578716
5389098
5474612
5515510
5558124
5452304
5474612
5325892
5790356
5937074
5810948
5578716
5831254
5558124
5810948
5790356
5853562
5621330
5873868
5853562
6232512
6146998
5810948
5641636
5873868
5558124
5790356
5831254
5916768
5727436
5831254
5894460
6126692
5937074
5684536
5411406
5664230
4969250
5305586
5494918
5684536
5411406
5411406
5411406
5558124
5348486
5073354
4843124
5010148
4358068
4757610
4989842
5032456
4800224
4820530
4757610
4969250
4820530
4527380
4315454
4673812
3895606
4400968
4631198
4631198
4358068
4105530
4085224
4315454
4105530
3706274
3431142
3726580
3031886
3663374
3999424
4105530
3873298
3579862
3789786
3873298
3810092
3178318
2885168
3094806
2463318
3115398
3347630
3536962
3221218
2925780
3094806
3178318
3011294
2379806
2104674
2357212
1662518
2420418
2885168




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280116&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280116&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280116&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.405343002238637
beta0.0645195510983771
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.405343002238637 \tabularnewline
beta & 0.0645195510983771 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280116&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]0.405343002238637[/C][/ROW]
[ROW][C]beta[/C][C]0.0645195510983771[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280116&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280116&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
alpha0.405343002238637
beta0.0645195510983771
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1353890985388863.63888889234.361111107282
1453890985377036.1813322812061.8186677219
1553484865328848.3482287619637.6517712353
1652423805222230.5673678220149.4326321818
1757903565775708.2756459414647.7243540576
1858738685860241.3969620813626.6030379152
1957477425544924.73429575202817.26570425
2054523045438166.2878839314137.7121160738
2155787165485515.7252953993200.2747046063
2253890985550523.71056649-161425.710566491
2354746125528071.47412112-53459.4741211161
2455155105556326.16127142-40816.1612714222
2555581245599061.72797944-40937.7279794384
2654523045580027.64181511-127723.641815115
2754746125478476.93580877-3864.93580877222
2853258925360815.39019514-34923.3901951415
2957903565885436.30171403-95080.3017140264
3059370745918753.2669638518320.7330361493
3158109485711834.2003582599113.7996417526
3255787165442119.86471259136596.135287413
3358312545580603.87490091250650.125099092
3455581245556617.447910441506.55208955798
3558109485667272.15253536143675.847464637
3657903565790968.8988528-612.898852798156
3758535625858995.90553516-5433.90553515777
3856213305812741.32920127-191411.329201272
3958738685767359.25052785106508.749472152
4058535625687184.87127938166377.128720623
4162325126274110.42532825-41598.425328251
4261469986414420.91539258-267422.91539258
4358109486150129.1998602-339181.199860198
4456416365723989.03215305-82353.0321530495
4558738685834765.2996257639102.7003742382
4655581245564560.89793757-6436.89793757256
4757903565744016.26827346339.7317270031
4858312545727389.12225421103864.877745786
4959167685822563.9130737494204.0869262591
5057274365696375.2046307131060.7953692861
5158312545914420.19873791-83166.1987379072
5258944605784092.36824237110367.631757634
5361266926214304.76601672-87612.7660167245
5459370746190136.17947587-253062.179475873
5556845365877830.11926968-193294.119269676
5654114065656200.44242485-244794.442424851
5756642305761759.98184644-97529.9818464415
5849692505393922.00448774-424672.004487738
5953055865409124.74606951-103538.746069511
6054949185335925.48717927158992.512820734
6156845365419115.09905635265420.900943646
6254114065300671.1607099110734.839290104
6354114065461061.10175787-49655.1017578663
6454114065438254.91927534-26848.9192753443
6555581245670380.46957604-112256.469576038
6653484865512455.93334048-163969.933340482
6750733545248753.1307766-175399.130776595
6848431244981168.87817004-138044.878170039
6950101485197779.06504886-187631.065048861
7043580684576734.19473206-218666.194732063
7147576104849643.90962894-92033.9096289407
7249898424920764.8072833169077.192716687
7350324565011985.4457172920470.5542827081
7448002244677050.56020259123173.439797408
7548205304722213.8119778698316.1880221441
7647576104751926.850553355683.14944665134
7749692504926279.8845254342970.1154745733
7848205304784412.1907111336117.8092888705
7945273804584138.51213963-56758.5121396268
8043154544379081.53624384-63627.5362438438
8146738124590539.8665015783272.1334984275
8238956064062103.63161224-166497.631612238
8344009684434081.80052-33113.8005199991
8446311984629051.825067792146.17493220791
8546311984666648.17798401-35450.1779840058
8643580684371066.74671754-12998.7467175443
8741055304343638.30934882-238108.30934882
8840852244170487.08199386-85263.0819938602
8943154544316358.11148592-904.111485918052
9041055304137693.57086053-32163.5708605256
9137062743837789.26197948-131515.261979483
9234311423579666.67166637-148524.671666373
9337265803823168.40654778-96588.4065477815
9430318863047696.75801088-15810.7580108754
9536633743538410.40727768124963.592722324
9639994243800895.69690089198528.303099107
9741055303883345.23879165222184.761208352
9838732983699891.04013483173406.95986517
9935798623613378.67127908-33516.6712790807
10037897863618619.10595388171166.894046123
10138732983929874.57053191-56576.5705319066
10238100923719876.6418610790215.3581389277
10331783183423519.8278993-245201.827899298
10428851683119249.45650098-234081.456500978
10530948063366767.12023426-271961.120234263
10624633182571469.42936617-108151.429366174
10731153983109276.008535626121.99146437692
10833476303365037.56787157-17407.5678715659
10935369623366081.33188436170880.668115642
11032212183123538.4224122997679.5775877126
11129257802872014.5449793953765.4550206056
11230948063025365.9844318469440.0155681618
11331783183148312.7998599330005.2001400702
11430112943051320.24169847-40026.2416984737
11523798062489925.78807989-110119.788079886
11621046742237768.58080888-133094.580808876
11723572122497082.0228677-139870.022867702
11816625181849578.49384494-187060.493844938
11924204182418131.033024232286.96697577462
12028851682653023.48699732232144.513002685

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 5389098 & 5388863.63888889 & 234.361111107282 \tabularnewline
14 & 5389098 & 5377036.18133228 & 12061.8186677219 \tabularnewline
15 & 5348486 & 5328848.34822876 & 19637.6517712353 \tabularnewline
16 & 5242380 & 5222230.56736782 & 20149.4326321818 \tabularnewline
17 & 5790356 & 5775708.27564594 & 14647.7243540576 \tabularnewline
18 & 5873868 & 5860241.39696208 & 13626.6030379152 \tabularnewline
19 & 5747742 & 5544924.73429575 & 202817.26570425 \tabularnewline
20 & 5452304 & 5438166.28788393 & 14137.7121160738 \tabularnewline
21 & 5578716 & 5485515.72529539 & 93200.2747046063 \tabularnewline
22 & 5389098 & 5550523.71056649 & -161425.710566491 \tabularnewline
23 & 5474612 & 5528071.47412112 & -53459.4741211161 \tabularnewline
24 & 5515510 & 5556326.16127142 & -40816.1612714222 \tabularnewline
25 & 5558124 & 5599061.72797944 & -40937.7279794384 \tabularnewline
26 & 5452304 & 5580027.64181511 & -127723.641815115 \tabularnewline
27 & 5474612 & 5478476.93580877 & -3864.93580877222 \tabularnewline
28 & 5325892 & 5360815.39019514 & -34923.3901951415 \tabularnewline
29 & 5790356 & 5885436.30171403 & -95080.3017140264 \tabularnewline
30 & 5937074 & 5918753.26696385 & 18320.7330361493 \tabularnewline
31 & 5810948 & 5711834.20035825 & 99113.7996417526 \tabularnewline
32 & 5578716 & 5442119.86471259 & 136596.135287413 \tabularnewline
33 & 5831254 & 5580603.87490091 & 250650.125099092 \tabularnewline
34 & 5558124 & 5556617.44791044 & 1506.55208955798 \tabularnewline
35 & 5810948 & 5667272.15253536 & 143675.847464637 \tabularnewline
36 & 5790356 & 5790968.8988528 & -612.898852798156 \tabularnewline
37 & 5853562 & 5858995.90553516 & -5433.90553515777 \tabularnewline
38 & 5621330 & 5812741.32920127 & -191411.329201272 \tabularnewline
39 & 5873868 & 5767359.25052785 & 106508.749472152 \tabularnewline
40 & 5853562 & 5687184.87127938 & 166377.128720623 \tabularnewline
41 & 6232512 & 6274110.42532825 & -41598.425328251 \tabularnewline
42 & 6146998 & 6414420.91539258 & -267422.91539258 \tabularnewline
43 & 5810948 & 6150129.1998602 & -339181.199860198 \tabularnewline
44 & 5641636 & 5723989.03215305 & -82353.0321530495 \tabularnewline
45 & 5873868 & 5834765.29962576 & 39102.7003742382 \tabularnewline
46 & 5558124 & 5564560.89793757 & -6436.89793757256 \tabularnewline
47 & 5790356 & 5744016.268273 & 46339.7317270031 \tabularnewline
48 & 5831254 & 5727389.12225421 & 103864.877745786 \tabularnewline
49 & 5916768 & 5822563.91307374 & 94204.0869262591 \tabularnewline
50 & 5727436 & 5696375.20463071 & 31060.7953692861 \tabularnewline
51 & 5831254 & 5914420.19873791 & -83166.1987379072 \tabularnewline
52 & 5894460 & 5784092.36824237 & 110367.631757634 \tabularnewline
53 & 6126692 & 6214304.76601672 & -87612.7660167245 \tabularnewline
54 & 5937074 & 6190136.17947587 & -253062.179475873 \tabularnewline
55 & 5684536 & 5877830.11926968 & -193294.119269676 \tabularnewline
56 & 5411406 & 5656200.44242485 & -244794.442424851 \tabularnewline
57 & 5664230 & 5761759.98184644 & -97529.9818464415 \tabularnewline
58 & 4969250 & 5393922.00448774 & -424672.004487738 \tabularnewline
59 & 5305586 & 5409124.74606951 & -103538.746069511 \tabularnewline
60 & 5494918 & 5335925.48717927 & 158992.512820734 \tabularnewline
61 & 5684536 & 5419115.09905635 & 265420.900943646 \tabularnewline
62 & 5411406 & 5300671.1607099 & 110734.839290104 \tabularnewline
63 & 5411406 & 5461061.10175787 & -49655.1017578663 \tabularnewline
64 & 5411406 & 5438254.91927534 & -26848.9192753443 \tabularnewline
65 & 5558124 & 5670380.46957604 & -112256.469576038 \tabularnewline
66 & 5348486 & 5512455.93334048 & -163969.933340482 \tabularnewline
67 & 5073354 & 5248753.1307766 & -175399.130776595 \tabularnewline
68 & 4843124 & 4981168.87817004 & -138044.878170039 \tabularnewline
69 & 5010148 & 5197779.06504886 & -187631.065048861 \tabularnewline
70 & 4358068 & 4576734.19473206 & -218666.194732063 \tabularnewline
71 & 4757610 & 4849643.90962894 & -92033.9096289407 \tabularnewline
72 & 4989842 & 4920764.80728331 & 69077.192716687 \tabularnewline
73 & 5032456 & 5011985.44571729 & 20470.5542827081 \tabularnewline
74 & 4800224 & 4677050.56020259 & 123173.439797408 \tabularnewline
75 & 4820530 & 4722213.81197786 & 98316.1880221441 \tabularnewline
76 & 4757610 & 4751926.85055335 & 5683.14944665134 \tabularnewline
77 & 4969250 & 4926279.88452543 & 42970.1154745733 \tabularnewline
78 & 4820530 & 4784412.19071113 & 36117.8092888705 \tabularnewline
79 & 4527380 & 4584138.51213963 & -56758.5121396268 \tabularnewline
80 & 4315454 & 4379081.53624384 & -63627.5362438438 \tabularnewline
81 & 4673812 & 4590539.86650157 & 83272.1334984275 \tabularnewline
82 & 3895606 & 4062103.63161224 & -166497.631612238 \tabularnewline
83 & 4400968 & 4434081.80052 & -33113.8005199991 \tabularnewline
84 & 4631198 & 4629051.82506779 & 2146.17493220791 \tabularnewline
85 & 4631198 & 4666648.17798401 & -35450.1779840058 \tabularnewline
86 & 4358068 & 4371066.74671754 & -12998.7467175443 \tabularnewline
87 & 4105530 & 4343638.30934882 & -238108.30934882 \tabularnewline
88 & 4085224 & 4170487.08199386 & -85263.0819938602 \tabularnewline
89 & 4315454 & 4316358.11148592 & -904.111485918052 \tabularnewline
90 & 4105530 & 4137693.57086053 & -32163.5708605256 \tabularnewline
91 & 3706274 & 3837789.26197948 & -131515.261979483 \tabularnewline
92 & 3431142 & 3579666.67166637 & -148524.671666373 \tabularnewline
93 & 3726580 & 3823168.40654778 & -96588.4065477815 \tabularnewline
94 & 3031886 & 3047696.75801088 & -15810.7580108754 \tabularnewline
95 & 3663374 & 3538410.40727768 & 124963.592722324 \tabularnewline
96 & 3999424 & 3800895.69690089 & 198528.303099107 \tabularnewline
97 & 4105530 & 3883345.23879165 & 222184.761208352 \tabularnewline
98 & 3873298 & 3699891.04013483 & 173406.95986517 \tabularnewline
99 & 3579862 & 3613378.67127908 & -33516.6712790807 \tabularnewline
100 & 3789786 & 3618619.10595388 & 171166.894046123 \tabularnewline
101 & 3873298 & 3929874.57053191 & -56576.5705319066 \tabularnewline
102 & 3810092 & 3719876.64186107 & 90215.3581389277 \tabularnewline
103 & 3178318 & 3423519.8278993 & -245201.827899298 \tabularnewline
104 & 2885168 & 3119249.45650098 & -234081.456500978 \tabularnewline
105 & 3094806 & 3366767.12023426 & -271961.120234263 \tabularnewline
106 & 2463318 & 2571469.42936617 & -108151.429366174 \tabularnewline
107 & 3115398 & 3109276.00853562 & 6121.99146437692 \tabularnewline
108 & 3347630 & 3365037.56787157 & -17407.5678715659 \tabularnewline
109 & 3536962 & 3366081.33188436 & 170880.668115642 \tabularnewline
110 & 3221218 & 3123538.42241229 & 97679.5775877126 \tabularnewline
111 & 2925780 & 2872014.54497939 & 53765.4550206056 \tabularnewline
112 & 3094806 & 3025365.98443184 & 69440.0155681618 \tabularnewline
113 & 3178318 & 3148312.79985993 & 30005.2001400702 \tabularnewline
114 & 3011294 & 3051320.24169847 & -40026.2416984737 \tabularnewline
115 & 2379806 & 2489925.78807989 & -110119.788079886 \tabularnewline
116 & 2104674 & 2237768.58080888 & -133094.580808876 \tabularnewline
117 & 2357212 & 2497082.0228677 & -139870.022867702 \tabularnewline
118 & 1662518 & 1849578.49384494 & -187060.493844938 \tabularnewline
119 & 2420418 & 2418131.03302423 & 2286.96697577462 \tabularnewline
120 & 2885168 & 2653023.48699732 & 232144.513002685 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280116&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]5389098[/C][C]5388863.63888889[/C][C]234.361111107282[/C][/ROW]
[ROW][C]14[/C][C]5389098[/C][C]5377036.18133228[/C][C]12061.8186677219[/C][/ROW]
[ROW][C]15[/C][C]5348486[/C][C]5328848.34822876[/C][C]19637.6517712353[/C][/ROW]
[ROW][C]16[/C][C]5242380[/C][C]5222230.56736782[/C][C]20149.4326321818[/C][/ROW]
[ROW][C]17[/C][C]5790356[/C][C]5775708.27564594[/C][C]14647.7243540576[/C][/ROW]
[ROW][C]18[/C][C]5873868[/C][C]5860241.39696208[/C][C]13626.6030379152[/C][/ROW]
[ROW][C]19[/C][C]5747742[/C][C]5544924.73429575[/C][C]202817.26570425[/C][/ROW]
[ROW][C]20[/C][C]5452304[/C][C]5438166.28788393[/C][C]14137.7121160738[/C][/ROW]
[ROW][C]21[/C][C]5578716[/C][C]5485515.72529539[/C][C]93200.2747046063[/C][/ROW]
[ROW][C]22[/C][C]5389098[/C][C]5550523.71056649[/C][C]-161425.710566491[/C][/ROW]
[ROW][C]23[/C][C]5474612[/C][C]5528071.47412112[/C][C]-53459.4741211161[/C][/ROW]
[ROW][C]24[/C][C]5515510[/C][C]5556326.16127142[/C][C]-40816.1612714222[/C][/ROW]
[ROW][C]25[/C][C]5558124[/C][C]5599061.72797944[/C][C]-40937.7279794384[/C][/ROW]
[ROW][C]26[/C][C]5452304[/C][C]5580027.64181511[/C][C]-127723.641815115[/C][/ROW]
[ROW][C]27[/C][C]5474612[/C][C]5478476.93580877[/C][C]-3864.93580877222[/C][/ROW]
[ROW][C]28[/C][C]5325892[/C][C]5360815.39019514[/C][C]-34923.3901951415[/C][/ROW]
[ROW][C]29[/C][C]5790356[/C][C]5885436.30171403[/C][C]-95080.3017140264[/C][/ROW]
[ROW][C]30[/C][C]5937074[/C][C]5918753.26696385[/C][C]18320.7330361493[/C][/ROW]
[ROW][C]31[/C][C]5810948[/C][C]5711834.20035825[/C][C]99113.7996417526[/C][/ROW]
[ROW][C]32[/C][C]5578716[/C][C]5442119.86471259[/C][C]136596.135287413[/C][/ROW]
[ROW][C]33[/C][C]5831254[/C][C]5580603.87490091[/C][C]250650.125099092[/C][/ROW]
[ROW][C]34[/C][C]5558124[/C][C]5556617.44791044[/C][C]1506.55208955798[/C][/ROW]
[ROW][C]35[/C][C]5810948[/C][C]5667272.15253536[/C][C]143675.847464637[/C][/ROW]
[ROW][C]36[/C][C]5790356[/C][C]5790968.8988528[/C][C]-612.898852798156[/C][/ROW]
[ROW][C]37[/C][C]5853562[/C][C]5858995.90553516[/C][C]-5433.90553515777[/C][/ROW]
[ROW][C]38[/C][C]5621330[/C][C]5812741.32920127[/C][C]-191411.329201272[/C][/ROW]
[ROW][C]39[/C][C]5873868[/C][C]5767359.25052785[/C][C]106508.749472152[/C][/ROW]
[ROW][C]40[/C][C]5853562[/C][C]5687184.87127938[/C][C]166377.128720623[/C][/ROW]
[ROW][C]41[/C][C]6232512[/C][C]6274110.42532825[/C][C]-41598.425328251[/C][/ROW]
[ROW][C]42[/C][C]6146998[/C][C]6414420.91539258[/C][C]-267422.91539258[/C][/ROW]
[ROW][C]43[/C][C]5810948[/C][C]6150129.1998602[/C][C]-339181.199860198[/C][/ROW]
[ROW][C]44[/C][C]5641636[/C][C]5723989.03215305[/C][C]-82353.0321530495[/C][/ROW]
[ROW][C]45[/C][C]5873868[/C][C]5834765.29962576[/C][C]39102.7003742382[/C][/ROW]
[ROW][C]46[/C][C]5558124[/C][C]5564560.89793757[/C][C]-6436.89793757256[/C][/ROW]
[ROW][C]47[/C][C]5790356[/C][C]5744016.268273[/C][C]46339.7317270031[/C][/ROW]
[ROW][C]48[/C][C]5831254[/C][C]5727389.12225421[/C][C]103864.877745786[/C][/ROW]
[ROW][C]49[/C][C]5916768[/C][C]5822563.91307374[/C][C]94204.0869262591[/C][/ROW]
[ROW][C]50[/C][C]5727436[/C][C]5696375.20463071[/C][C]31060.7953692861[/C][/ROW]
[ROW][C]51[/C][C]5831254[/C][C]5914420.19873791[/C][C]-83166.1987379072[/C][/ROW]
[ROW][C]52[/C][C]5894460[/C][C]5784092.36824237[/C][C]110367.631757634[/C][/ROW]
[ROW][C]53[/C][C]6126692[/C][C]6214304.76601672[/C][C]-87612.7660167245[/C][/ROW]
[ROW][C]54[/C][C]5937074[/C][C]6190136.17947587[/C][C]-253062.179475873[/C][/ROW]
[ROW][C]55[/C][C]5684536[/C][C]5877830.11926968[/C][C]-193294.119269676[/C][/ROW]
[ROW][C]56[/C][C]5411406[/C][C]5656200.44242485[/C][C]-244794.442424851[/C][/ROW]
[ROW][C]57[/C][C]5664230[/C][C]5761759.98184644[/C][C]-97529.9818464415[/C][/ROW]
[ROW][C]58[/C][C]4969250[/C][C]5393922.00448774[/C][C]-424672.004487738[/C][/ROW]
[ROW][C]59[/C][C]5305586[/C][C]5409124.74606951[/C][C]-103538.746069511[/C][/ROW]
[ROW][C]60[/C][C]5494918[/C][C]5335925.48717927[/C][C]158992.512820734[/C][/ROW]
[ROW][C]61[/C][C]5684536[/C][C]5419115.09905635[/C][C]265420.900943646[/C][/ROW]
[ROW][C]62[/C][C]5411406[/C][C]5300671.1607099[/C][C]110734.839290104[/C][/ROW]
[ROW][C]63[/C][C]5411406[/C][C]5461061.10175787[/C][C]-49655.1017578663[/C][/ROW]
[ROW][C]64[/C][C]5411406[/C][C]5438254.91927534[/C][C]-26848.9192753443[/C][/ROW]
[ROW][C]65[/C][C]5558124[/C][C]5670380.46957604[/C][C]-112256.469576038[/C][/ROW]
[ROW][C]66[/C][C]5348486[/C][C]5512455.93334048[/C][C]-163969.933340482[/C][/ROW]
[ROW][C]67[/C][C]5073354[/C][C]5248753.1307766[/C][C]-175399.130776595[/C][/ROW]
[ROW][C]68[/C][C]4843124[/C][C]4981168.87817004[/C][C]-138044.878170039[/C][/ROW]
[ROW][C]69[/C][C]5010148[/C][C]5197779.06504886[/C][C]-187631.065048861[/C][/ROW]
[ROW][C]70[/C][C]4358068[/C][C]4576734.19473206[/C][C]-218666.194732063[/C][/ROW]
[ROW][C]71[/C][C]4757610[/C][C]4849643.90962894[/C][C]-92033.9096289407[/C][/ROW]
[ROW][C]72[/C][C]4989842[/C][C]4920764.80728331[/C][C]69077.192716687[/C][/ROW]
[ROW][C]73[/C][C]5032456[/C][C]5011985.44571729[/C][C]20470.5542827081[/C][/ROW]
[ROW][C]74[/C][C]4800224[/C][C]4677050.56020259[/C][C]123173.439797408[/C][/ROW]
[ROW][C]75[/C][C]4820530[/C][C]4722213.81197786[/C][C]98316.1880221441[/C][/ROW]
[ROW][C]76[/C][C]4757610[/C][C]4751926.85055335[/C][C]5683.14944665134[/C][/ROW]
[ROW][C]77[/C][C]4969250[/C][C]4926279.88452543[/C][C]42970.1154745733[/C][/ROW]
[ROW][C]78[/C][C]4820530[/C][C]4784412.19071113[/C][C]36117.8092888705[/C][/ROW]
[ROW][C]79[/C][C]4527380[/C][C]4584138.51213963[/C][C]-56758.5121396268[/C][/ROW]
[ROW][C]80[/C][C]4315454[/C][C]4379081.53624384[/C][C]-63627.5362438438[/C][/ROW]
[ROW][C]81[/C][C]4673812[/C][C]4590539.86650157[/C][C]83272.1334984275[/C][/ROW]
[ROW][C]82[/C][C]3895606[/C][C]4062103.63161224[/C][C]-166497.631612238[/C][/ROW]
[ROW][C]83[/C][C]4400968[/C][C]4434081.80052[/C][C]-33113.8005199991[/C][/ROW]
[ROW][C]84[/C][C]4631198[/C][C]4629051.82506779[/C][C]2146.17493220791[/C][/ROW]
[ROW][C]85[/C][C]4631198[/C][C]4666648.17798401[/C][C]-35450.1779840058[/C][/ROW]
[ROW][C]86[/C][C]4358068[/C][C]4371066.74671754[/C][C]-12998.7467175443[/C][/ROW]
[ROW][C]87[/C][C]4105530[/C][C]4343638.30934882[/C][C]-238108.30934882[/C][/ROW]
[ROW][C]88[/C][C]4085224[/C][C]4170487.08199386[/C][C]-85263.0819938602[/C][/ROW]
[ROW][C]89[/C][C]4315454[/C][C]4316358.11148592[/C][C]-904.111485918052[/C][/ROW]
[ROW][C]90[/C][C]4105530[/C][C]4137693.57086053[/C][C]-32163.5708605256[/C][/ROW]
[ROW][C]91[/C][C]3706274[/C][C]3837789.26197948[/C][C]-131515.261979483[/C][/ROW]
[ROW][C]92[/C][C]3431142[/C][C]3579666.67166637[/C][C]-148524.671666373[/C][/ROW]
[ROW][C]93[/C][C]3726580[/C][C]3823168.40654778[/C][C]-96588.4065477815[/C][/ROW]
[ROW][C]94[/C][C]3031886[/C][C]3047696.75801088[/C][C]-15810.7580108754[/C][/ROW]
[ROW][C]95[/C][C]3663374[/C][C]3538410.40727768[/C][C]124963.592722324[/C][/ROW]
[ROW][C]96[/C][C]3999424[/C][C]3800895.69690089[/C][C]198528.303099107[/C][/ROW]
[ROW][C]97[/C][C]4105530[/C][C]3883345.23879165[/C][C]222184.761208352[/C][/ROW]
[ROW][C]98[/C][C]3873298[/C][C]3699891.04013483[/C][C]173406.95986517[/C][/ROW]
[ROW][C]99[/C][C]3579862[/C][C]3613378.67127908[/C][C]-33516.6712790807[/C][/ROW]
[ROW][C]100[/C][C]3789786[/C][C]3618619.10595388[/C][C]171166.894046123[/C][/ROW]
[ROW][C]101[/C][C]3873298[/C][C]3929874.57053191[/C][C]-56576.5705319066[/C][/ROW]
[ROW][C]102[/C][C]3810092[/C][C]3719876.64186107[/C][C]90215.3581389277[/C][/ROW]
[ROW][C]103[/C][C]3178318[/C][C]3423519.8278993[/C][C]-245201.827899298[/C][/ROW]
[ROW][C]104[/C][C]2885168[/C][C]3119249.45650098[/C][C]-234081.456500978[/C][/ROW]
[ROW][C]105[/C][C]3094806[/C][C]3366767.12023426[/C][C]-271961.120234263[/C][/ROW]
[ROW][C]106[/C][C]2463318[/C][C]2571469.42936617[/C][C]-108151.429366174[/C][/ROW]
[ROW][C]107[/C][C]3115398[/C][C]3109276.00853562[/C][C]6121.99146437692[/C][/ROW]
[ROW][C]108[/C][C]3347630[/C][C]3365037.56787157[/C][C]-17407.5678715659[/C][/ROW]
[ROW][C]109[/C][C]3536962[/C][C]3366081.33188436[/C][C]170880.668115642[/C][/ROW]
[ROW][C]110[/C][C]3221218[/C][C]3123538.42241229[/C][C]97679.5775877126[/C][/ROW]
[ROW][C]111[/C][C]2925780[/C][C]2872014.54497939[/C][C]53765.4550206056[/C][/ROW]
[ROW][C]112[/C][C]3094806[/C][C]3025365.98443184[/C][C]69440.0155681618[/C][/ROW]
[ROW][C]113[/C][C]3178318[/C][C]3148312.79985993[/C][C]30005.2001400702[/C][/ROW]
[ROW][C]114[/C][C]3011294[/C][C]3051320.24169847[/C][C]-40026.2416984737[/C][/ROW]
[ROW][C]115[/C][C]2379806[/C][C]2489925.78807989[/C][C]-110119.788079886[/C][/ROW]
[ROW][C]116[/C][C]2104674[/C][C]2237768.58080888[/C][C]-133094.580808876[/C][/ROW]
[ROW][C]117[/C][C]2357212[/C][C]2497082.0228677[/C][C]-139870.022867702[/C][/ROW]
[ROW][C]118[/C][C]1662518[/C][C]1849578.49384494[/C][C]-187060.493844938[/C][/ROW]
[ROW][C]119[/C][C]2420418[/C][C]2418131.03302423[/C][C]2286.96697577462[/C][/ROW]
[ROW][C]120[/C][C]2885168[/C][C]2653023.48699732[/C][C]232144.513002685[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280116&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280116&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
1353890985388863.63888889234.361111107282
1453890985377036.1813322812061.8186677219
1553484865328848.3482287619637.6517712353
1652423805222230.5673678220149.4326321818
1757903565775708.2756459414647.7243540576
1858738685860241.3969620813626.6030379152
1957477425544924.73429575202817.26570425
2054523045438166.2878839314137.7121160738
2155787165485515.7252953993200.2747046063
2253890985550523.71056649-161425.710566491
2354746125528071.47412112-53459.4741211161
2455155105556326.16127142-40816.1612714222
2555581245599061.72797944-40937.7279794384
2654523045580027.64181511-127723.641815115
2754746125478476.93580877-3864.93580877222
2853258925360815.39019514-34923.3901951415
2957903565885436.30171403-95080.3017140264
3059370745918753.2669638518320.7330361493
3158109485711834.2003582599113.7996417526
3255787165442119.86471259136596.135287413
3358312545580603.87490091250650.125099092
3455581245556617.447910441506.55208955798
3558109485667272.15253536143675.847464637
3657903565790968.8988528-612.898852798156
3758535625858995.90553516-5433.90553515777
3856213305812741.32920127-191411.329201272
3958738685767359.25052785106508.749472152
4058535625687184.87127938166377.128720623
4162325126274110.42532825-41598.425328251
4261469986414420.91539258-267422.91539258
4358109486150129.1998602-339181.199860198
4456416365723989.03215305-82353.0321530495
4558738685834765.2996257639102.7003742382
4655581245564560.89793757-6436.89793757256
4757903565744016.26827346339.7317270031
4858312545727389.12225421103864.877745786
4959167685822563.9130737494204.0869262591
5057274365696375.2046307131060.7953692861
5158312545914420.19873791-83166.1987379072
5258944605784092.36824237110367.631757634
5361266926214304.76601672-87612.7660167245
5459370746190136.17947587-253062.179475873
5556845365877830.11926968-193294.119269676
5654114065656200.44242485-244794.442424851
5756642305761759.98184644-97529.9818464415
5849692505393922.00448774-424672.004487738
5953055865409124.74606951-103538.746069511
6054949185335925.48717927158992.512820734
6156845365419115.09905635265420.900943646
6254114065300671.1607099110734.839290104
6354114065461061.10175787-49655.1017578663
6454114065438254.91927534-26848.9192753443
6555581245670380.46957604-112256.469576038
6653484865512455.93334048-163969.933340482
6750733545248753.1307766-175399.130776595
6848431244981168.87817004-138044.878170039
6950101485197779.06504886-187631.065048861
7043580684576734.19473206-218666.194732063
7147576104849643.90962894-92033.9096289407
7249898424920764.8072833169077.192716687
7350324565011985.4457172920470.5542827081
7448002244677050.56020259123173.439797408
7548205304722213.8119778698316.1880221441
7647576104751926.850553355683.14944665134
7749692504926279.8845254342970.1154745733
7848205304784412.1907111336117.8092888705
7945273804584138.51213963-56758.5121396268
8043154544379081.53624384-63627.5362438438
8146738124590539.8665015783272.1334984275
8238956064062103.63161224-166497.631612238
8344009684434081.80052-33113.8005199991
8446311984629051.825067792146.17493220791
8546311984666648.17798401-35450.1779840058
8643580684371066.74671754-12998.7467175443
8741055304343638.30934882-238108.30934882
8840852244170487.08199386-85263.0819938602
8943154544316358.11148592-904.111485918052
9041055304137693.57086053-32163.5708605256
9137062743837789.26197948-131515.261979483
9234311423579666.67166637-148524.671666373
9337265803823168.40654778-96588.4065477815
9430318863047696.75801088-15810.7580108754
9536633743538410.40727768124963.592722324
9639994243800895.69690089198528.303099107
9741055303883345.23879165222184.761208352
9838732983699891.04013483173406.95986517
9935798623613378.67127908-33516.6712790807
10037897863618619.10595388171166.894046123
10138732983929874.57053191-56576.5705319066
10238100923719876.6418610790215.3581389277
10331783183423519.8278993-245201.827899298
10428851683119249.45650098-234081.456500978
10530948063366767.12023426-271961.120234263
10624633182571469.42936617-108151.429366174
10731153983109276.008535626121.99146437692
10833476303365037.56787157-17407.5678715659
10935369623366081.33188436170880.668115642
11032212183123538.4224122997679.5775877126
11129257802872014.5449793953765.4550206056
11230948063025365.9844318469440.0155681618
11331783183148312.7998599330005.2001400702
11430112943051320.24169847-40026.2416984737
11523798062489925.78807989-110119.788079886
11621046742237768.58080888-133094.580808876
11723572122497082.0228677-139870.022867702
11816625181849578.49384494-187060.493844938
11924204182418131.033024232286.96697577462
12028851682653023.48699732232144.513002685







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1212868392.192812532607282.347745023129502.03788004
1222509789.32960742225408.651607822794170.00760698
1232186738.178789551878271.380831182495204.97674791
1242320391.350868091987059.985080872653722.71665531
1252382699.116046852023756.594323652741641.63777005
1262222072.923658271836800.512434962607345.33488158
1271626441.448026591214145.010713752038737.88533942
1281399358.55695904959365.8752347411839351.23868335
1291706172.806402841237831.353980652174514.25882503
1301088541.34059269591216.4141757181585866.26700965
1311851645.315193391324718.450188452378572.18019832
1322228368.331985481671235.947449612785500.71652135

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 2868392.19281253 & 2607282.34774502 & 3129502.03788004 \tabularnewline
122 & 2509789.3296074 & 2225408.65160782 & 2794170.00760698 \tabularnewline
123 & 2186738.17878955 & 1878271.38083118 & 2495204.97674791 \tabularnewline
124 & 2320391.35086809 & 1987059.98508087 & 2653722.71665531 \tabularnewline
125 & 2382699.11604685 & 2023756.59432365 & 2741641.63777005 \tabularnewline
126 & 2222072.92365827 & 1836800.51243496 & 2607345.33488158 \tabularnewline
127 & 1626441.44802659 & 1214145.01071375 & 2038737.88533942 \tabularnewline
128 & 1399358.55695904 & 959365.875234741 & 1839351.23868335 \tabularnewline
129 & 1706172.80640284 & 1237831.35398065 & 2174514.25882503 \tabularnewline
130 & 1088541.34059269 & 591216.414175718 & 1585866.26700965 \tabularnewline
131 & 1851645.31519339 & 1324718.45018845 & 2378572.18019832 \tabularnewline
132 & 2228368.33198548 & 1671235.94744961 & 2785500.71652135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280116&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]121[/C][C]2868392.19281253[/C][C]2607282.34774502[/C][C]3129502.03788004[/C][/ROW]
[ROW][C]122[/C][C]2509789.3296074[/C][C]2225408.65160782[/C][C]2794170.00760698[/C][/ROW]
[ROW][C]123[/C][C]2186738.17878955[/C][C]1878271.38083118[/C][C]2495204.97674791[/C][/ROW]
[ROW][C]124[/C][C]2320391.35086809[/C][C]1987059.98508087[/C][C]2653722.71665531[/C][/ROW]
[ROW][C]125[/C][C]2382699.11604685[/C][C]2023756.59432365[/C][C]2741641.63777005[/C][/ROW]
[ROW][C]126[/C][C]2222072.92365827[/C][C]1836800.51243496[/C][C]2607345.33488158[/C][/ROW]
[ROW][C]127[/C][C]1626441.44802659[/C][C]1214145.01071375[/C][C]2038737.88533942[/C][/ROW]
[ROW][C]128[/C][C]1399358.55695904[/C][C]959365.875234741[/C][C]1839351.23868335[/C][/ROW]
[ROW][C]129[/C][C]1706172.80640284[/C][C]1237831.35398065[/C][C]2174514.25882503[/C][/ROW]
[ROW][C]130[/C][C]1088541.34059269[/C][C]591216.414175718[/C][C]1585866.26700965[/C][/ROW]
[ROW][C]131[/C][C]1851645.31519339[/C][C]1324718.45018845[/C][C]2378572.18019832[/C][/ROW]
[ROW][C]132[/C][C]2228368.33198548[/C][C]1671235.94744961[/C][C]2785500.71652135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280116&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280116&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
1212868392.192812532607282.347745023129502.03788004
1222509789.32960742225408.651607822794170.00760698
1232186738.178789551878271.380831182495204.97674791
1242320391.350868091987059.985080872653722.71665531
1252382699.116046852023756.594323652741641.63777005
1262222072.923658271836800.512434962607345.33488158
1271626441.448026591214145.010713752038737.88533942
1281399358.55695904959365.8752347411839351.23868335
1291706172.806402841237831.353980652174514.25882503
1301088541.34059269591216.4141757181585866.26700965
1311851645.315193391324718.450188452378572.18019832
1322228368.331985481671235.947449612785500.71652135



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par3 <- 'additive'
par2 <- 'Double'
par1 <- '12'
par1 <- as.numeric(par1)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')