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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 31 Jul 2015 16:32:12 +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/Jul/31/t1438356745hqcjm59ftmdt29u.htm/, Retrieved Fri, 17 May 2024 03:22:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279802, Retrieved Fri, 17 May 2024 03:22:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact157
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-07-31 15:32:12] [517bf63cbd197750110a40d4d2cd39d6] [Current]
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Dataseries X:
43200
41600
44000
35200
45600
44800
48000
49600
55200
48000
45600
56800
48000
36000
42400
32000
44800
36800
48800
44000
46400
52000
51200
60800
44000
36800
40800
29600
42400
32800
46400
44000
39200
56000
50400
57600
43200
40000
36000
29600
39200
35200
48000
46400
40000
53600
49600
64000
51200
31200
31200
31200
36800
36800
49600
45600
40800
51200
47200
68000
53600
31200
32800
27200
37600
43200
54400
53600
43200
50400
44800
64000
48800
39200
35200
26400
39200
47200
55200
52000
38400
55200
43200
66400
55200
40000
36800
24800
39200
37600
56800
56800
43200
56000
41600
64800
55200
40800
31200
21600
42400
40800
53600
61600
45600
51200
38400
66400




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279802&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 Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279802&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279802&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 Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.616435516556531
beta0.0182153483451634
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.616435516556531 \tabularnewline
beta & 0.0182153483451634 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279802&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]0.616435516556531[/C][/ROW]
[ROW][C]beta[/C][C]0.0182153483451634[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279802&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279802&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
alpha0.616435516556531
beta0.0182153483451634
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
344000400004000
43520040910.6564168918-5710.65641689176
54560035771.1967231249828.80327687595
64480040321.17547194374478.82452805629
74800041623.5281810246376.471818976
84960044167.25685094625432.74314905377
95520046190.2396834549009.76031654602
104800050519.3898249041-2519.38982490405
114560047713.2731539368-2113.27315393675
125680045133.772149947311666.2278500527
134800051179.440227394-3179.440227394
143600048038.0106115696-12038.0106115696
154240039300.67372754243099.3262724576
163200039929.3299816678-7929.32998166782
174480033670.49564402211129.504355978
183680039285.172311613-2485.17231161299
194880036479.373759700312320.6262402997
204400042938.73851801211061.2614819879
214640042469.3474130233930.65258697695
225200043812.88657319978187.1134268003
235120047872.18909072323327.81090927684
246080048973.411567284611826.5884327154
254400055446.3782416173-11446.3782416173
263680047444.5350207058-10644.5350207058
274080039817.4533452262982.54665477384
282960039368.7503796652-9768.75037966524
294240032182.876802997810217.1231970022
303280037431.729391913-4631.72939191295
314640033475.214085384212924.7859146158
324400040486.285452483513.71454752001
333920041735.4922318813-2535.49223188127
345600039227.283108661916772.7168913381
355040048809.6737721141590.32622788602
365760049050.95672184598549.04327815406
374320053677.8336929433-10477.8336929433
384000046458.2166557294-6458.21665572943
393600041643.9176713224-5643.9176713224
402960037268.2082776454-7668.20827764535
413920031558.55110950937641.44889049073
423520035372.1130448818-172.113044881793
434800034367.185306063513632.8146939365
444640042025.182583884374.81741611996
454000044025.3445483482-4025.3445483482
465360040802.149398942312797.8506010577
474960048093.07102900731506.9289709927
486400048440.788235701715559.2117642983
495120057625.5396182015-6425.53961820155
503120053185.9596909562-21985.9596909562
513120038907.5129025057-7707.51290250575
523120033344.2633514029-2144.26335140293
533680031186.3213620465613.67863795403
543680033873.68403303122926.31596696882
554960034937.319303127614662.6806968724
564560043400.30782362742199.69217637263
574080044205.3670140963-3405.36701409626
585120041517.03118510459682.96881489555
594720047005.5364779317194.46352206829
606800046647.173659931121352.8263400689
615360059571.3392376202-5971.33923762022
623120055584.8689868349-24384.8689868349
633280039973.8373743108-7173.83737431082
642720034891.7448624618-7691.7448624618
653760029404.02834913018195.97165086986
664320033802.0937577919397.906242209
675440039046.599551252515353.4004487475
685360048134.68049518725465.3195048128
694320051188.7649738794-7988.76497387945
705040045859.57138929834540.4286107017
714480048304.8003247635-3504.80032476354
726400045751.310447879818248.6895521202
734880056812.3513505933-8012.35135059327
743920051595.1865495762-12395.1865495762
753520043537.1060298785-8337.10602987849
762640037886.956545628-11486.956545628
773920030166.14503303289033.85496696718
784720035196.527997825712003.4720021743
795520042192.270411369213007.7295886308
805200049953.13130100272046.86869899731
813840050980.311690859-12580.311690859
825520042849.519448637112350.4805513629
834320050225.6314540061-7025.63145400611
846640045578.731927795120821.2680722049
855520058331.4437293963-3131.4437293963
864000056283.6915682098-16283.6915682098
873680045945.5838583184-9145.58385831839
882480039904.9672716964-15104.9672716964
893920030021.16764308199178.8323569181
903760035209.82990628262390.17009371743
915680036240.557874974220559.4421250258
925680048702.32393201498097.67606798511
934320053573.1402581006-10373.1402581006
945600046941.41366623089058.58633376919
954160052389.808624388-10789.808624388
966480045481.793671652819318.2063283472
975520057350.3446421143-2150.34464211432
984080055960.7729720522-15160.7729720522
993120046380.8771253959-15180.8771253959
1002160036618.1285549328-15018.1285549328
1014240026787.071610507515612.9283894925
1024080036013.39721144234786.60278855774
1035360038619.737987191214980.2620128088
1046160047678.019537719213921.9804622808
1054560056240.2629320959-10640.2629320959
1065120049541.99200674611658.00799325385
1073840050443.4291601204-12043.4291601204
1086640042763.583124158923636.4168758411

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 44000 & 40000 & 4000 \tabularnewline
4 & 35200 & 40910.6564168918 & -5710.65641689176 \tabularnewline
5 & 45600 & 35771.196723124 & 9828.80327687595 \tabularnewline
6 & 44800 & 40321.1754719437 & 4478.82452805629 \tabularnewline
7 & 48000 & 41623.528181024 & 6376.471818976 \tabularnewline
8 & 49600 & 44167.2568509462 & 5432.74314905377 \tabularnewline
9 & 55200 & 46190.239683454 & 9009.76031654602 \tabularnewline
10 & 48000 & 50519.3898249041 & -2519.38982490405 \tabularnewline
11 & 45600 & 47713.2731539368 & -2113.27315393675 \tabularnewline
12 & 56800 & 45133.7721499473 & 11666.2278500527 \tabularnewline
13 & 48000 & 51179.440227394 & -3179.440227394 \tabularnewline
14 & 36000 & 48038.0106115696 & -12038.0106115696 \tabularnewline
15 & 42400 & 39300.6737275424 & 3099.3262724576 \tabularnewline
16 & 32000 & 39929.3299816678 & -7929.32998166782 \tabularnewline
17 & 44800 & 33670.495644022 & 11129.504355978 \tabularnewline
18 & 36800 & 39285.172311613 & -2485.17231161299 \tabularnewline
19 & 48800 & 36479.3737597003 & 12320.6262402997 \tabularnewline
20 & 44000 & 42938.7385180121 & 1061.2614819879 \tabularnewline
21 & 46400 & 42469.347413023 & 3930.65258697695 \tabularnewline
22 & 52000 & 43812.8865731997 & 8187.1134268003 \tabularnewline
23 & 51200 & 47872.1890907232 & 3327.81090927684 \tabularnewline
24 & 60800 & 48973.4115672846 & 11826.5884327154 \tabularnewline
25 & 44000 & 55446.3782416173 & -11446.3782416173 \tabularnewline
26 & 36800 & 47444.5350207058 & -10644.5350207058 \tabularnewline
27 & 40800 & 39817.4533452262 & 982.54665477384 \tabularnewline
28 & 29600 & 39368.7503796652 & -9768.75037966524 \tabularnewline
29 & 42400 & 32182.8768029978 & 10217.1231970022 \tabularnewline
30 & 32800 & 37431.729391913 & -4631.72939191295 \tabularnewline
31 & 46400 & 33475.2140853842 & 12924.7859146158 \tabularnewline
32 & 44000 & 40486.28545248 & 3513.71454752001 \tabularnewline
33 & 39200 & 41735.4922318813 & -2535.49223188127 \tabularnewline
34 & 56000 & 39227.2831086619 & 16772.7168913381 \tabularnewline
35 & 50400 & 48809.673772114 & 1590.32622788602 \tabularnewline
36 & 57600 & 49050.9567218459 & 8549.04327815406 \tabularnewline
37 & 43200 & 53677.8336929433 & -10477.8336929433 \tabularnewline
38 & 40000 & 46458.2166557294 & -6458.21665572943 \tabularnewline
39 & 36000 & 41643.9176713224 & -5643.9176713224 \tabularnewline
40 & 29600 & 37268.2082776454 & -7668.20827764535 \tabularnewline
41 & 39200 & 31558.5511095093 & 7641.44889049073 \tabularnewline
42 & 35200 & 35372.1130448818 & -172.113044881793 \tabularnewline
43 & 48000 & 34367.1853060635 & 13632.8146939365 \tabularnewline
44 & 46400 & 42025.18258388 & 4374.81741611996 \tabularnewline
45 & 40000 & 44025.3445483482 & -4025.3445483482 \tabularnewline
46 & 53600 & 40802.1493989423 & 12797.8506010577 \tabularnewline
47 & 49600 & 48093.0710290073 & 1506.9289709927 \tabularnewline
48 & 64000 & 48440.7882357017 & 15559.2117642983 \tabularnewline
49 & 51200 & 57625.5396182015 & -6425.53961820155 \tabularnewline
50 & 31200 & 53185.9596909562 & -21985.9596909562 \tabularnewline
51 & 31200 & 38907.5129025057 & -7707.51290250575 \tabularnewline
52 & 31200 & 33344.2633514029 & -2144.26335140293 \tabularnewline
53 & 36800 & 31186.321362046 & 5613.67863795403 \tabularnewline
54 & 36800 & 33873.6840330312 & 2926.31596696882 \tabularnewline
55 & 49600 & 34937.3193031276 & 14662.6806968724 \tabularnewline
56 & 45600 & 43400.3078236274 & 2199.69217637263 \tabularnewline
57 & 40800 & 44205.3670140963 & -3405.36701409626 \tabularnewline
58 & 51200 & 41517.0311851045 & 9682.96881489555 \tabularnewline
59 & 47200 & 47005.5364779317 & 194.46352206829 \tabularnewline
60 & 68000 & 46647.1736599311 & 21352.8263400689 \tabularnewline
61 & 53600 & 59571.3392376202 & -5971.33923762022 \tabularnewline
62 & 31200 & 55584.8689868349 & -24384.8689868349 \tabularnewline
63 & 32800 & 39973.8373743108 & -7173.83737431082 \tabularnewline
64 & 27200 & 34891.7448624618 & -7691.7448624618 \tabularnewline
65 & 37600 & 29404.0283491301 & 8195.97165086986 \tabularnewline
66 & 43200 & 33802.093757791 & 9397.906242209 \tabularnewline
67 & 54400 & 39046.5995512525 & 15353.4004487475 \tabularnewline
68 & 53600 & 48134.6804951872 & 5465.3195048128 \tabularnewline
69 & 43200 & 51188.7649738794 & -7988.76497387945 \tabularnewline
70 & 50400 & 45859.5713892983 & 4540.4286107017 \tabularnewline
71 & 44800 & 48304.8003247635 & -3504.80032476354 \tabularnewline
72 & 64000 & 45751.3104478798 & 18248.6895521202 \tabularnewline
73 & 48800 & 56812.3513505933 & -8012.35135059327 \tabularnewline
74 & 39200 & 51595.1865495762 & -12395.1865495762 \tabularnewline
75 & 35200 & 43537.1060298785 & -8337.10602987849 \tabularnewline
76 & 26400 & 37886.956545628 & -11486.956545628 \tabularnewline
77 & 39200 & 30166.1450330328 & 9033.85496696718 \tabularnewline
78 & 47200 & 35196.5279978257 & 12003.4720021743 \tabularnewline
79 & 55200 & 42192.2704113692 & 13007.7295886308 \tabularnewline
80 & 52000 & 49953.1313010027 & 2046.86869899731 \tabularnewline
81 & 38400 & 50980.311690859 & -12580.311690859 \tabularnewline
82 & 55200 & 42849.5194486371 & 12350.4805513629 \tabularnewline
83 & 43200 & 50225.6314540061 & -7025.63145400611 \tabularnewline
84 & 66400 & 45578.7319277951 & 20821.2680722049 \tabularnewline
85 & 55200 & 58331.4437293963 & -3131.4437293963 \tabularnewline
86 & 40000 & 56283.6915682098 & -16283.6915682098 \tabularnewline
87 & 36800 & 45945.5838583184 & -9145.58385831839 \tabularnewline
88 & 24800 & 39904.9672716964 & -15104.9672716964 \tabularnewline
89 & 39200 & 30021.1676430819 & 9178.8323569181 \tabularnewline
90 & 37600 & 35209.8299062826 & 2390.17009371743 \tabularnewline
91 & 56800 & 36240.5578749742 & 20559.4421250258 \tabularnewline
92 & 56800 & 48702.3239320149 & 8097.67606798511 \tabularnewline
93 & 43200 & 53573.1402581006 & -10373.1402581006 \tabularnewline
94 & 56000 & 46941.4136662308 & 9058.58633376919 \tabularnewline
95 & 41600 & 52389.808624388 & -10789.808624388 \tabularnewline
96 & 64800 & 45481.7936716528 & 19318.2063283472 \tabularnewline
97 & 55200 & 57350.3446421143 & -2150.34464211432 \tabularnewline
98 & 40800 & 55960.7729720522 & -15160.7729720522 \tabularnewline
99 & 31200 & 46380.8771253959 & -15180.8771253959 \tabularnewline
100 & 21600 & 36618.1285549328 & -15018.1285549328 \tabularnewline
101 & 42400 & 26787.0716105075 & 15612.9283894925 \tabularnewline
102 & 40800 & 36013.3972114423 & 4786.60278855774 \tabularnewline
103 & 53600 & 38619.7379871912 & 14980.2620128088 \tabularnewline
104 & 61600 & 47678.0195377192 & 13921.9804622808 \tabularnewline
105 & 45600 & 56240.2629320959 & -10640.2629320959 \tabularnewline
106 & 51200 & 49541.9920067461 & 1658.00799325385 \tabularnewline
107 & 38400 & 50443.4291601204 & -12043.4291601204 \tabularnewline
108 & 66400 & 42763.5831241589 & 23636.4168758411 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279802&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]3[/C][C]44000[/C][C]40000[/C][C]4000[/C][/ROW]
[ROW][C]4[/C][C]35200[/C][C]40910.6564168918[/C][C]-5710.65641689176[/C][/ROW]
[ROW][C]5[/C][C]45600[/C][C]35771.196723124[/C][C]9828.80327687595[/C][/ROW]
[ROW][C]6[/C][C]44800[/C][C]40321.1754719437[/C][C]4478.82452805629[/C][/ROW]
[ROW][C]7[/C][C]48000[/C][C]41623.528181024[/C][C]6376.471818976[/C][/ROW]
[ROW][C]8[/C][C]49600[/C][C]44167.2568509462[/C][C]5432.74314905377[/C][/ROW]
[ROW][C]9[/C][C]55200[/C][C]46190.239683454[/C][C]9009.76031654602[/C][/ROW]
[ROW][C]10[/C][C]48000[/C][C]50519.3898249041[/C][C]-2519.38982490405[/C][/ROW]
[ROW][C]11[/C][C]45600[/C][C]47713.2731539368[/C][C]-2113.27315393675[/C][/ROW]
[ROW][C]12[/C][C]56800[/C][C]45133.7721499473[/C][C]11666.2278500527[/C][/ROW]
[ROW][C]13[/C][C]48000[/C][C]51179.440227394[/C][C]-3179.440227394[/C][/ROW]
[ROW][C]14[/C][C]36000[/C][C]48038.0106115696[/C][C]-12038.0106115696[/C][/ROW]
[ROW][C]15[/C][C]42400[/C][C]39300.6737275424[/C][C]3099.3262724576[/C][/ROW]
[ROW][C]16[/C][C]32000[/C][C]39929.3299816678[/C][C]-7929.32998166782[/C][/ROW]
[ROW][C]17[/C][C]44800[/C][C]33670.495644022[/C][C]11129.504355978[/C][/ROW]
[ROW][C]18[/C][C]36800[/C][C]39285.172311613[/C][C]-2485.17231161299[/C][/ROW]
[ROW][C]19[/C][C]48800[/C][C]36479.3737597003[/C][C]12320.6262402997[/C][/ROW]
[ROW][C]20[/C][C]44000[/C][C]42938.7385180121[/C][C]1061.2614819879[/C][/ROW]
[ROW][C]21[/C][C]46400[/C][C]42469.347413023[/C][C]3930.65258697695[/C][/ROW]
[ROW][C]22[/C][C]52000[/C][C]43812.8865731997[/C][C]8187.1134268003[/C][/ROW]
[ROW][C]23[/C][C]51200[/C][C]47872.1890907232[/C][C]3327.81090927684[/C][/ROW]
[ROW][C]24[/C][C]60800[/C][C]48973.4115672846[/C][C]11826.5884327154[/C][/ROW]
[ROW][C]25[/C][C]44000[/C][C]55446.3782416173[/C][C]-11446.3782416173[/C][/ROW]
[ROW][C]26[/C][C]36800[/C][C]47444.5350207058[/C][C]-10644.5350207058[/C][/ROW]
[ROW][C]27[/C][C]40800[/C][C]39817.4533452262[/C][C]982.54665477384[/C][/ROW]
[ROW][C]28[/C][C]29600[/C][C]39368.7503796652[/C][C]-9768.75037966524[/C][/ROW]
[ROW][C]29[/C][C]42400[/C][C]32182.8768029978[/C][C]10217.1231970022[/C][/ROW]
[ROW][C]30[/C][C]32800[/C][C]37431.729391913[/C][C]-4631.72939191295[/C][/ROW]
[ROW][C]31[/C][C]46400[/C][C]33475.2140853842[/C][C]12924.7859146158[/C][/ROW]
[ROW][C]32[/C][C]44000[/C][C]40486.28545248[/C][C]3513.71454752001[/C][/ROW]
[ROW][C]33[/C][C]39200[/C][C]41735.4922318813[/C][C]-2535.49223188127[/C][/ROW]
[ROW][C]34[/C][C]56000[/C][C]39227.2831086619[/C][C]16772.7168913381[/C][/ROW]
[ROW][C]35[/C][C]50400[/C][C]48809.673772114[/C][C]1590.32622788602[/C][/ROW]
[ROW][C]36[/C][C]57600[/C][C]49050.9567218459[/C][C]8549.04327815406[/C][/ROW]
[ROW][C]37[/C][C]43200[/C][C]53677.8336929433[/C][C]-10477.8336929433[/C][/ROW]
[ROW][C]38[/C][C]40000[/C][C]46458.2166557294[/C][C]-6458.21665572943[/C][/ROW]
[ROW][C]39[/C][C]36000[/C][C]41643.9176713224[/C][C]-5643.9176713224[/C][/ROW]
[ROW][C]40[/C][C]29600[/C][C]37268.2082776454[/C][C]-7668.20827764535[/C][/ROW]
[ROW][C]41[/C][C]39200[/C][C]31558.5511095093[/C][C]7641.44889049073[/C][/ROW]
[ROW][C]42[/C][C]35200[/C][C]35372.1130448818[/C][C]-172.113044881793[/C][/ROW]
[ROW][C]43[/C][C]48000[/C][C]34367.1853060635[/C][C]13632.8146939365[/C][/ROW]
[ROW][C]44[/C][C]46400[/C][C]42025.18258388[/C][C]4374.81741611996[/C][/ROW]
[ROW][C]45[/C][C]40000[/C][C]44025.3445483482[/C][C]-4025.3445483482[/C][/ROW]
[ROW][C]46[/C][C]53600[/C][C]40802.1493989423[/C][C]12797.8506010577[/C][/ROW]
[ROW][C]47[/C][C]49600[/C][C]48093.0710290073[/C][C]1506.9289709927[/C][/ROW]
[ROW][C]48[/C][C]64000[/C][C]48440.7882357017[/C][C]15559.2117642983[/C][/ROW]
[ROW][C]49[/C][C]51200[/C][C]57625.5396182015[/C][C]-6425.53961820155[/C][/ROW]
[ROW][C]50[/C][C]31200[/C][C]53185.9596909562[/C][C]-21985.9596909562[/C][/ROW]
[ROW][C]51[/C][C]31200[/C][C]38907.5129025057[/C][C]-7707.51290250575[/C][/ROW]
[ROW][C]52[/C][C]31200[/C][C]33344.2633514029[/C][C]-2144.26335140293[/C][/ROW]
[ROW][C]53[/C][C]36800[/C][C]31186.321362046[/C][C]5613.67863795403[/C][/ROW]
[ROW][C]54[/C][C]36800[/C][C]33873.6840330312[/C][C]2926.31596696882[/C][/ROW]
[ROW][C]55[/C][C]49600[/C][C]34937.3193031276[/C][C]14662.6806968724[/C][/ROW]
[ROW][C]56[/C][C]45600[/C][C]43400.3078236274[/C][C]2199.69217637263[/C][/ROW]
[ROW][C]57[/C][C]40800[/C][C]44205.3670140963[/C][C]-3405.36701409626[/C][/ROW]
[ROW][C]58[/C][C]51200[/C][C]41517.0311851045[/C][C]9682.96881489555[/C][/ROW]
[ROW][C]59[/C][C]47200[/C][C]47005.5364779317[/C][C]194.46352206829[/C][/ROW]
[ROW][C]60[/C][C]68000[/C][C]46647.1736599311[/C][C]21352.8263400689[/C][/ROW]
[ROW][C]61[/C][C]53600[/C][C]59571.3392376202[/C][C]-5971.33923762022[/C][/ROW]
[ROW][C]62[/C][C]31200[/C][C]55584.8689868349[/C][C]-24384.8689868349[/C][/ROW]
[ROW][C]63[/C][C]32800[/C][C]39973.8373743108[/C][C]-7173.83737431082[/C][/ROW]
[ROW][C]64[/C][C]27200[/C][C]34891.7448624618[/C][C]-7691.7448624618[/C][/ROW]
[ROW][C]65[/C][C]37600[/C][C]29404.0283491301[/C][C]8195.97165086986[/C][/ROW]
[ROW][C]66[/C][C]43200[/C][C]33802.093757791[/C][C]9397.906242209[/C][/ROW]
[ROW][C]67[/C][C]54400[/C][C]39046.5995512525[/C][C]15353.4004487475[/C][/ROW]
[ROW][C]68[/C][C]53600[/C][C]48134.6804951872[/C][C]5465.3195048128[/C][/ROW]
[ROW][C]69[/C][C]43200[/C][C]51188.7649738794[/C][C]-7988.76497387945[/C][/ROW]
[ROW][C]70[/C][C]50400[/C][C]45859.5713892983[/C][C]4540.4286107017[/C][/ROW]
[ROW][C]71[/C][C]44800[/C][C]48304.8003247635[/C][C]-3504.80032476354[/C][/ROW]
[ROW][C]72[/C][C]64000[/C][C]45751.3104478798[/C][C]18248.6895521202[/C][/ROW]
[ROW][C]73[/C][C]48800[/C][C]56812.3513505933[/C][C]-8012.35135059327[/C][/ROW]
[ROW][C]74[/C][C]39200[/C][C]51595.1865495762[/C][C]-12395.1865495762[/C][/ROW]
[ROW][C]75[/C][C]35200[/C][C]43537.1060298785[/C][C]-8337.10602987849[/C][/ROW]
[ROW][C]76[/C][C]26400[/C][C]37886.956545628[/C][C]-11486.956545628[/C][/ROW]
[ROW][C]77[/C][C]39200[/C][C]30166.1450330328[/C][C]9033.85496696718[/C][/ROW]
[ROW][C]78[/C][C]47200[/C][C]35196.5279978257[/C][C]12003.4720021743[/C][/ROW]
[ROW][C]79[/C][C]55200[/C][C]42192.2704113692[/C][C]13007.7295886308[/C][/ROW]
[ROW][C]80[/C][C]52000[/C][C]49953.1313010027[/C][C]2046.86869899731[/C][/ROW]
[ROW][C]81[/C][C]38400[/C][C]50980.311690859[/C][C]-12580.311690859[/C][/ROW]
[ROW][C]82[/C][C]55200[/C][C]42849.5194486371[/C][C]12350.4805513629[/C][/ROW]
[ROW][C]83[/C][C]43200[/C][C]50225.6314540061[/C][C]-7025.63145400611[/C][/ROW]
[ROW][C]84[/C][C]66400[/C][C]45578.7319277951[/C][C]20821.2680722049[/C][/ROW]
[ROW][C]85[/C][C]55200[/C][C]58331.4437293963[/C][C]-3131.4437293963[/C][/ROW]
[ROW][C]86[/C][C]40000[/C][C]56283.6915682098[/C][C]-16283.6915682098[/C][/ROW]
[ROW][C]87[/C][C]36800[/C][C]45945.5838583184[/C][C]-9145.58385831839[/C][/ROW]
[ROW][C]88[/C][C]24800[/C][C]39904.9672716964[/C][C]-15104.9672716964[/C][/ROW]
[ROW][C]89[/C][C]39200[/C][C]30021.1676430819[/C][C]9178.8323569181[/C][/ROW]
[ROW][C]90[/C][C]37600[/C][C]35209.8299062826[/C][C]2390.17009371743[/C][/ROW]
[ROW][C]91[/C][C]56800[/C][C]36240.5578749742[/C][C]20559.4421250258[/C][/ROW]
[ROW][C]92[/C][C]56800[/C][C]48702.3239320149[/C][C]8097.67606798511[/C][/ROW]
[ROW][C]93[/C][C]43200[/C][C]53573.1402581006[/C][C]-10373.1402581006[/C][/ROW]
[ROW][C]94[/C][C]56000[/C][C]46941.4136662308[/C][C]9058.58633376919[/C][/ROW]
[ROW][C]95[/C][C]41600[/C][C]52389.808624388[/C][C]-10789.808624388[/C][/ROW]
[ROW][C]96[/C][C]64800[/C][C]45481.7936716528[/C][C]19318.2063283472[/C][/ROW]
[ROW][C]97[/C][C]55200[/C][C]57350.3446421143[/C][C]-2150.34464211432[/C][/ROW]
[ROW][C]98[/C][C]40800[/C][C]55960.7729720522[/C][C]-15160.7729720522[/C][/ROW]
[ROW][C]99[/C][C]31200[/C][C]46380.8771253959[/C][C]-15180.8771253959[/C][/ROW]
[ROW][C]100[/C][C]21600[/C][C]36618.1285549328[/C][C]-15018.1285549328[/C][/ROW]
[ROW][C]101[/C][C]42400[/C][C]26787.0716105075[/C][C]15612.9283894925[/C][/ROW]
[ROW][C]102[/C][C]40800[/C][C]36013.3972114423[/C][C]4786.60278855774[/C][/ROW]
[ROW][C]103[/C][C]53600[/C][C]38619.7379871912[/C][C]14980.2620128088[/C][/ROW]
[ROW][C]104[/C][C]61600[/C][C]47678.0195377192[/C][C]13921.9804622808[/C][/ROW]
[ROW][C]105[/C][C]45600[/C][C]56240.2629320959[/C][C]-10640.2629320959[/C][/ROW]
[ROW][C]106[/C][C]51200[/C][C]49541.9920067461[/C][C]1658.00799325385[/C][/ROW]
[ROW][C]107[/C][C]38400[/C][C]50443.4291601204[/C][C]-12043.4291601204[/C][/ROW]
[ROW][C]108[/C][C]66400[/C][C]42763.5831241589[/C][C]23636.4168758411[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279802&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279802&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
344000400004000
43520040910.6564168918-5710.65641689176
54560035771.1967231249828.80327687595
64480040321.17547194374478.82452805629
74800041623.5281810246376.471818976
84960044167.25685094625432.74314905377
95520046190.2396834549009.76031654602
104800050519.3898249041-2519.38982490405
114560047713.2731539368-2113.27315393675
125680045133.772149947311666.2278500527
134800051179.440227394-3179.440227394
143600048038.0106115696-12038.0106115696
154240039300.67372754243099.3262724576
163200039929.3299816678-7929.32998166782
174480033670.49564402211129.504355978
183680039285.172311613-2485.17231161299
194880036479.373759700312320.6262402997
204400042938.73851801211061.2614819879
214640042469.3474130233930.65258697695
225200043812.88657319978187.1134268003
235120047872.18909072323327.81090927684
246080048973.411567284611826.5884327154
254400055446.3782416173-11446.3782416173
263680047444.5350207058-10644.5350207058
274080039817.4533452262982.54665477384
282960039368.7503796652-9768.75037966524
294240032182.876802997810217.1231970022
303280037431.729391913-4631.72939191295
314640033475.214085384212924.7859146158
324400040486.285452483513.71454752001
333920041735.4922318813-2535.49223188127
345600039227.283108661916772.7168913381
355040048809.6737721141590.32622788602
365760049050.95672184598549.04327815406
374320053677.8336929433-10477.8336929433
384000046458.2166557294-6458.21665572943
393600041643.9176713224-5643.9176713224
402960037268.2082776454-7668.20827764535
413920031558.55110950937641.44889049073
423520035372.1130448818-172.113044881793
434800034367.185306063513632.8146939365
444640042025.182583884374.81741611996
454000044025.3445483482-4025.3445483482
465360040802.149398942312797.8506010577
474960048093.07102900731506.9289709927
486400048440.788235701715559.2117642983
495120057625.5396182015-6425.53961820155
503120053185.9596909562-21985.9596909562
513120038907.5129025057-7707.51290250575
523120033344.2633514029-2144.26335140293
533680031186.3213620465613.67863795403
543680033873.68403303122926.31596696882
554960034937.319303127614662.6806968724
564560043400.30782362742199.69217637263
574080044205.3670140963-3405.36701409626
585120041517.03118510459682.96881489555
594720047005.5364779317194.46352206829
606800046647.173659931121352.8263400689
615360059571.3392376202-5971.33923762022
623120055584.8689868349-24384.8689868349
633280039973.8373743108-7173.83737431082
642720034891.7448624618-7691.7448624618
653760029404.02834913018195.97165086986
664320033802.0937577919397.906242209
675440039046.599551252515353.4004487475
685360048134.68049518725465.3195048128
694320051188.7649738794-7988.76497387945
705040045859.57138929834540.4286107017
714480048304.8003247635-3504.80032476354
726400045751.310447879818248.6895521202
734880056812.3513505933-8012.35135059327
743920051595.1865495762-12395.1865495762
753520043537.1060298785-8337.10602987849
762640037886.956545628-11486.956545628
773920030166.14503303289033.85496696718
784720035196.527997825712003.4720021743
795520042192.270411369213007.7295886308
805200049953.13130100272046.86869899731
813840050980.311690859-12580.311690859
825520042849.519448637112350.4805513629
834320050225.6314540061-7025.63145400611
846640045578.731927795120821.2680722049
855520058331.4437293963-3131.4437293963
864000056283.6915682098-16283.6915682098
873680045945.5838583184-9145.58385831839
882480039904.9672716964-15104.9672716964
893920030021.16764308199178.8323569181
903760035209.82990628262390.17009371743
915680036240.557874974220559.4421250258
925680048702.32393201498097.67606798511
934320053573.1402581006-10373.1402581006
945600046941.41366623089058.58633376919
954160052389.808624388-10789.808624388
966480045481.793671652819318.2063283472
975520057350.3446421143-2150.34464211432
984080055960.7729720522-15160.7729720522
993120046380.8771253959-15180.8771253959
1002160036618.1285549328-15018.1285549328
1014240026787.071610507515612.9283894925
1024080036013.39721144234786.60278855774
1035360038619.737987191214980.2620128088
1046160047678.019537719213921.9804622808
1054560056240.2629320959-10640.2629320959
1065120049541.99200674611658.00799325385
1073840050443.4291601204-12043.4291601204
1086640042763.583124158923636.4168758411







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
10957343.46498904336737.527687882177949.402290204
11057353.020007522533024.377491155181681.66252389
11157362.57502600229700.333295988685024.8167560155
11257372.130044481526636.775257317988107.4848316452
11357381.68506296123760.602910678291002.7672152438
11457391.240081440521025.705843169993756.7743197111
11557400.7950999218400.873955927496400.7162439126
11657410.350118399515863.875649307198956.8245874919
11757419.90513687913398.2488247104101441.561449048
11857429.460155358510991.4265027923103867.493807925
11957439.0151738388633.57648844733106244.453859229
12057448.57019231756316.84891238862108580.291472246

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 57343.464989043 & 36737.5276878821 & 77949.402290204 \tabularnewline
110 & 57353.0200075225 & 33024.3774911551 & 81681.66252389 \tabularnewline
111 & 57362.575026002 & 29700.3332959886 & 85024.8167560155 \tabularnewline
112 & 57372.1300444815 & 26636.7752573179 & 88107.4848316452 \tabularnewline
113 & 57381.685062961 & 23760.6029106782 & 91002.7672152438 \tabularnewline
114 & 57391.2400814405 & 21025.7058431699 & 93756.7743197111 \tabularnewline
115 & 57400.79509992 & 18400.8739559274 & 96400.7162439126 \tabularnewline
116 & 57410.3501183995 & 15863.8756493071 & 98956.8245874919 \tabularnewline
117 & 57419.905136879 & 13398.2488247104 & 101441.561449048 \tabularnewline
118 & 57429.4601553585 & 10991.4265027923 & 103867.493807925 \tabularnewline
119 & 57439.015173838 & 8633.57648844733 & 106244.453859229 \tabularnewline
120 & 57448.5701923175 & 6316.84891238862 & 108580.291472246 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279802&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]109[/C][C]57343.464989043[/C][C]36737.5276878821[/C][C]77949.402290204[/C][/ROW]
[ROW][C]110[/C][C]57353.0200075225[/C][C]33024.3774911551[/C][C]81681.66252389[/C][/ROW]
[ROW][C]111[/C][C]57362.575026002[/C][C]29700.3332959886[/C][C]85024.8167560155[/C][/ROW]
[ROW][C]112[/C][C]57372.1300444815[/C][C]26636.7752573179[/C][C]88107.4848316452[/C][/ROW]
[ROW][C]113[/C][C]57381.685062961[/C][C]23760.6029106782[/C][C]91002.7672152438[/C][/ROW]
[ROW][C]114[/C][C]57391.2400814405[/C][C]21025.7058431699[/C][C]93756.7743197111[/C][/ROW]
[ROW][C]115[/C][C]57400.79509992[/C][C]18400.8739559274[/C][C]96400.7162439126[/C][/ROW]
[ROW][C]116[/C][C]57410.3501183995[/C][C]15863.8756493071[/C][C]98956.8245874919[/C][/ROW]
[ROW][C]117[/C][C]57419.905136879[/C][C]13398.2488247104[/C][C]101441.561449048[/C][/ROW]
[ROW][C]118[/C][C]57429.4601553585[/C][C]10991.4265027923[/C][C]103867.493807925[/C][/ROW]
[ROW][C]119[/C][C]57439.015173838[/C][C]8633.57648844733[/C][C]106244.453859229[/C][/ROW]
[ROW][C]120[/C][C]57448.5701923175[/C][C]6316.84891238862[/C][C]108580.291472246[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279802&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279802&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
10957343.46498904336737.527687882177949.402290204
11057353.020007522533024.377491155181681.66252389
11157362.57502600229700.333295988685024.8167560155
11257372.130044481526636.775257317988107.4848316452
11357381.68506296123760.602910678291002.7672152438
11457391.240081440521025.705843169993756.7743197111
11557400.7950999218400.873955927496400.7162439126
11657410.350118399515863.875649307198956.8245874919
11757419.90513687913398.2488247104101441.561449048
11857429.460155358510991.4265027923103867.493807925
11957439.0151738388633.57648844733106244.453859229
12057448.57019231756316.84891238862108580.291472246



Parameters (Session):
par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = additive ;
R code (references can be found in the software module):
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')