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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 computationWed, 20 Jan 2010 07:55:27 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Jan/20/t1263999794yvtrpgxcg2iv9hq.htm/, Retrieved Mon, 06 May 2024 06:48:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72307, Retrieved Mon, 06 May 2024 06:48:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W61
Estimated Impact175
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2010-01-20 14:55:27] [6fe3b5976049c9b6736c06f51fce3033] [Current]
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Dataseries X:
23.98
24.24
24.92
25.46
25.84
26.08
26.18
26.34
26.42
26.38
26.04
25.58
25.65
25.56
25.62
25.62
25.69
25.68
25.68
25.83
25.93
26.11
24.72
24.62
24.65
25.24
25.56
25.9
25.87
25.78
25.78
25.74
25.78
25.73
24.67
24.31
24.56
25
25.38
25.99
26.22
26.19
26.22
26.22
26.61
26.72
25.46
25.48
25.59
25.88
26
26.97
27.2
27.19
27.19
27.19
27.26
26.9
26.11
25.87
26.02
26.31
26.37
26.52
26.86
26.92
26.98
26.98
27.03
26.75
26.39
26.3
26.3
26.52
26.53
26.98
27.22
27.34
27.41
27.47
27.46
27.53
27.21
26.91
26.95
26.91
27.39
27.62
27.79
27.88
27.9
28.09
28.46
28.73
27.93
27.61
27.65
28.19
28.98
28.99
29.02
29
29.04
29.19
29.23
29.26
29.02
28.47
28.53
28.48
28.68
28.89
29.2
29.21
29.15
29.22
29.34
29.13
28.84
28.76




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72307&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72307&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72307&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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.843623991338351
beta0.0118408398755793
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.843623991338351 \tabularnewline
beta & 0.0118408398755793 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72307&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]0.843623991338351[/C][/ROW]
[ROW][C]beta[/C][C]0.0118408398755793[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72307&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72307&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
alpha0.843623991338351
beta0.0118408398755793
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1325.6525.58193643162390.0680635683760684
1425.5625.5776136070211-0.0176136070211399
1525.6225.6504188489409-0.0304188489409185
1625.6225.6421174210916-0.0221174210915933
1725.6925.7451816745618-0.0551816745618048
1825.6825.7685509088495-0.0885509088494842
1925.6826.0858011689778-0.405801168977835
2025.8325.75885786263150.0711421373685077
2125.9325.79540269291320.134597307086846
2226.1125.81515768173080.294842318269218
2324.7225.7084611169199-0.988461116919861
2424.6224.41259836715560.207401632844416
2524.6524.6828927457645-0.0328927457645385
2625.2424.57068241828670.66931758171328
2725.5625.21853828376440.341461716235578
2825.925.52651858724170.373481412758295
2925.8725.9633569948208-0.093356994820791
3025.7825.9541290667629-0.17412906676293
3125.7826.1535449529318-0.373544952931844
3225.7425.9326902118613-0.192690211861329
3325.7825.75824108727470.0217589127253106
3425.7325.70839268602340.0216073139765776
3524.6725.1683125548834-0.49831255488343
3624.3124.4756532429014-0.165653242901371
3724.5624.39262488427150.167375115728522
382524.56014627859770.439853721402251
3925.3824.96183207141300.418167928586954
4025.9925.33897685992570.651023140074287
4126.2225.93917239649790.280827603502068
4226.1926.2389411656517-0.0489411656517156
4326.2226.5199916444388-0.299991644438823
4426.2226.3974112576997-0.177411257699710
4526.6126.27748082444090.332519175559057
4626.7226.50097208250940.219027917490610
4725.4626.0593083445771-0.599308344577054
4825.4825.34562825763350.134371742366490
4925.5925.58294459542880.00705540457121145
5025.8825.67138285897840.208617141021605
512625.88584822193710.114151778062944
5226.9726.05114121225800.918858787742032
5327.226.83028564637790.369714353622147
5427.1927.16524741541610.0247525845839505
5527.1927.4817195097738-0.291719509773802
5627.1927.3978790297665-0.207879029766502
5727.2627.3442744935536-0.0842744935536395
5826.927.2065262154050-0.306526215405043
5926.1126.196399282182-0.0863992821820183
6025.8726.0381501473715-0.168150147371531
6126.0226.00531918174610.0146808182538791
6226.3126.13676266038540.173237339614595
6326.3726.31130805447080.0586919455292438
6426.5226.5597960663654-0.0397960663653905
6526.8626.43889243692090.421107563079147
6626.9226.75834956932670.161650430673344
6726.9827.1372733937366-0.157273393736567
6826.9827.1777585994591-0.197758599459089
6927.0327.1499148573228-0.119914857322790
7026.7526.9448828289851-0.194882828985058
7126.3926.06201688913290.327983110867081
7226.326.24335954705830.0566404529417461
7326.326.4337959219185-0.13379592191853
7426.5226.4683303504030.0516696495970237
7526.5326.52474686114620.00525313885380996
7626.9826.71455832771120.265441672288802
7727.2226.92809080974370.291909190256341
7827.3427.10154559601600.238454403983958
7927.4127.4997236433436-0.0897236433436355
8027.4727.5958718764446-0.125871876444609
8127.4627.646571836462-0.186571836461987
8227.5327.37864278240940.151357217590608
8327.2126.87815520143260.331844798567420
8426.9127.0288810252406-0.118881025240622
8526.9527.0482671031612-0.098267103161163
8626.9127.1489352796717-0.238935279671708
8727.3926.95718757413480.432812425865190
8827.6227.55691204236430.0630879576357088
8927.7927.61037809077720.179621909222831
9027.8827.68612905473440.193870945265640
9127.928.0003143676811-0.100314367681083
9228.0928.08670761637570.00329238362428441
9328.4628.24300419845050.216995801549508
9428.7328.37853237809640.351467621903563
9527.9328.0872395042733-0.157239504273267
9627.6127.7621466436877-0.152146643687651
9727.6527.7636275457869-0.113627545786905
9828.1927.83612169273360.35387830726636
9928.9828.26223425621110.717765743788853
10028.9929.0600858832815-0.0700858832815179
10129.0229.0336458364341-0.0136458364340761
1022928.96086854514770.0391314548522708
10329.0429.1092515046038-0.0692515046038444
10429.1929.2491051518121-0.0591051518120835
10529.2329.3966098727707-0.166609872770746
10629.2629.23614545796840.0238545420315681
10729.0228.59224633118240.427753668817598
10828.4728.7706333619727-0.300633361972665
10928.5328.6605567175041-0.130556717504103
11028.4828.7993925477856-0.319392547785629
11128.6828.7152123212211-0.0352123212210564
11228.8928.74790222487790.142097775122053
11329.228.90468055064570.295319449354302
11429.2129.09928248882240.110717511177633
11529.1529.290299356577-0.140299356577003
11629.2229.3702829534414-0.150282953441426
11729.3429.4216269154447-0.0816269154447475
11829.1329.3610593215966-0.231059321596614
11928.8428.56114158160080.278858418399228
12028.7628.49440010792220.265599892077816

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 25.65 & 25.5819364316239 & 0.0680635683760684 \tabularnewline
14 & 25.56 & 25.5776136070211 & -0.0176136070211399 \tabularnewline
15 & 25.62 & 25.6504188489409 & -0.0304188489409185 \tabularnewline
16 & 25.62 & 25.6421174210916 & -0.0221174210915933 \tabularnewline
17 & 25.69 & 25.7451816745618 & -0.0551816745618048 \tabularnewline
18 & 25.68 & 25.7685509088495 & -0.0885509088494842 \tabularnewline
19 & 25.68 & 26.0858011689778 & -0.405801168977835 \tabularnewline
20 & 25.83 & 25.7588578626315 & 0.0711421373685077 \tabularnewline
21 & 25.93 & 25.7954026929132 & 0.134597307086846 \tabularnewline
22 & 26.11 & 25.8151576817308 & 0.294842318269218 \tabularnewline
23 & 24.72 & 25.7084611169199 & -0.988461116919861 \tabularnewline
24 & 24.62 & 24.4125983671556 & 0.207401632844416 \tabularnewline
25 & 24.65 & 24.6828927457645 & -0.0328927457645385 \tabularnewline
26 & 25.24 & 24.5706824182867 & 0.66931758171328 \tabularnewline
27 & 25.56 & 25.2185382837644 & 0.341461716235578 \tabularnewline
28 & 25.9 & 25.5265185872417 & 0.373481412758295 \tabularnewline
29 & 25.87 & 25.9633569948208 & -0.093356994820791 \tabularnewline
30 & 25.78 & 25.9541290667629 & -0.17412906676293 \tabularnewline
31 & 25.78 & 26.1535449529318 & -0.373544952931844 \tabularnewline
32 & 25.74 & 25.9326902118613 & -0.192690211861329 \tabularnewline
33 & 25.78 & 25.7582410872747 & 0.0217589127253106 \tabularnewline
34 & 25.73 & 25.7083926860234 & 0.0216073139765776 \tabularnewline
35 & 24.67 & 25.1683125548834 & -0.49831255488343 \tabularnewline
36 & 24.31 & 24.4756532429014 & -0.165653242901371 \tabularnewline
37 & 24.56 & 24.3926248842715 & 0.167375115728522 \tabularnewline
38 & 25 & 24.5601462785977 & 0.439853721402251 \tabularnewline
39 & 25.38 & 24.9618320714130 & 0.418167928586954 \tabularnewline
40 & 25.99 & 25.3389768599257 & 0.651023140074287 \tabularnewline
41 & 26.22 & 25.9391723964979 & 0.280827603502068 \tabularnewline
42 & 26.19 & 26.2389411656517 & -0.0489411656517156 \tabularnewline
43 & 26.22 & 26.5199916444388 & -0.299991644438823 \tabularnewline
44 & 26.22 & 26.3974112576997 & -0.177411257699710 \tabularnewline
45 & 26.61 & 26.2774808244409 & 0.332519175559057 \tabularnewline
46 & 26.72 & 26.5009720825094 & 0.219027917490610 \tabularnewline
47 & 25.46 & 26.0593083445771 & -0.599308344577054 \tabularnewline
48 & 25.48 & 25.3456282576335 & 0.134371742366490 \tabularnewline
49 & 25.59 & 25.5829445954288 & 0.00705540457121145 \tabularnewline
50 & 25.88 & 25.6713828589784 & 0.208617141021605 \tabularnewline
51 & 26 & 25.8858482219371 & 0.114151778062944 \tabularnewline
52 & 26.97 & 26.0511412122580 & 0.918858787742032 \tabularnewline
53 & 27.2 & 26.8302856463779 & 0.369714353622147 \tabularnewline
54 & 27.19 & 27.1652474154161 & 0.0247525845839505 \tabularnewline
55 & 27.19 & 27.4817195097738 & -0.291719509773802 \tabularnewline
56 & 27.19 & 27.3978790297665 & -0.207879029766502 \tabularnewline
57 & 27.26 & 27.3442744935536 & -0.0842744935536395 \tabularnewline
58 & 26.9 & 27.2065262154050 & -0.306526215405043 \tabularnewline
59 & 26.11 & 26.196399282182 & -0.0863992821820183 \tabularnewline
60 & 25.87 & 26.0381501473715 & -0.168150147371531 \tabularnewline
61 & 26.02 & 26.0053191817461 & 0.0146808182538791 \tabularnewline
62 & 26.31 & 26.1367626603854 & 0.173237339614595 \tabularnewline
63 & 26.37 & 26.3113080544708 & 0.0586919455292438 \tabularnewline
64 & 26.52 & 26.5597960663654 & -0.0397960663653905 \tabularnewline
65 & 26.86 & 26.4388924369209 & 0.421107563079147 \tabularnewline
66 & 26.92 & 26.7583495693267 & 0.161650430673344 \tabularnewline
67 & 26.98 & 27.1372733937366 & -0.157273393736567 \tabularnewline
68 & 26.98 & 27.1777585994591 & -0.197758599459089 \tabularnewline
69 & 27.03 & 27.1499148573228 & -0.119914857322790 \tabularnewline
70 & 26.75 & 26.9448828289851 & -0.194882828985058 \tabularnewline
71 & 26.39 & 26.0620168891329 & 0.327983110867081 \tabularnewline
72 & 26.3 & 26.2433595470583 & 0.0566404529417461 \tabularnewline
73 & 26.3 & 26.4337959219185 & -0.13379592191853 \tabularnewline
74 & 26.52 & 26.468330350403 & 0.0516696495970237 \tabularnewline
75 & 26.53 & 26.5247468611462 & 0.00525313885380996 \tabularnewline
76 & 26.98 & 26.7145583277112 & 0.265441672288802 \tabularnewline
77 & 27.22 & 26.9280908097437 & 0.291909190256341 \tabularnewline
78 & 27.34 & 27.1015455960160 & 0.238454403983958 \tabularnewline
79 & 27.41 & 27.4997236433436 & -0.0897236433436355 \tabularnewline
80 & 27.47 & 27.5958718764446 & -0.125871876444609 \tabularnewline
81 & 27.46 & 27.646571836462 & -0.186571836461987 \tabularnewline
82 & 27.53 & 27.3786427824094 & 0.151357217590608 \tabularnewline
83 & 27.21 & 26.8781552014326 & 0.331844798567420 \tabularnewline
84 & 26.91 & 27.0288810252406 & -0.118881025240622 \tabularnewline
85 & 26.95 & 27.0482671031612 & -0.098267103161163 \tabularnewline
86 & 26.91 & 27.1489352796717 & -0.238935279671708 \tabularnewline
87 & 27.39 & 26.9571875741348 & 0.432812425865190 \tabularnewline
88 & 27.62 & 27.5569120423643 & 0.0630879576357088 \tabularnewline
89 & 27.79 & 27.6103780907772 & 0.179621909222831 \tabularnewline
90 & 27.88 & 27.6861290547344 & 0.193870945265640 \tabularnewline
91 & 27.9 & 28.0003143676811 & -0.100314367681083 \tabularnewline
92 & 28.09 & 28.0867076163757 & 0.00329238362428441 \tabularnewline
93 & 28.46 & 28.2430041984505 & 0.216995801549508 \tabularnewline
94 & 28.73 & 28.3785323780964 & 0.351467621903563 \tabularnewline
95 & 27.93 & 28.0872395042733 & -0.157239504273267 \tabularnewline
96 & 27.61 & 27.7621466436877 & -0.152146643687651 \tabularnewline
97 & 27.65 & 27.7636275457869 & -0.113627545786905 \tabularnewline
98 & 28.19 & 27.8361216927336 & 0.35387830726636 \tabularnewline
99 & 28.98 & 28.2622342562111 & 0.717765743788853 \tabularnewline
100 & 28.99 & 29.0600858832815 & -0.0700858832815179 \tabularnewline
101 & 29.02 & 29.0336458364341 & -0.0136458364340761 \tabularnewline
102 & 29 & 28.9608685451477 & 0.0391314548522708 \tabularnewline
103 & 29.04 & 29.1092515046038 & -0.0692515046038444 \tabularnewline
104 & 29.19 & 29.2491051518121 & -0.0591051518120835 \tabularnewline
105 & 29.23 & 29.3966098727707 & -0.166609872770746 \tabularnewline
106 & 29.26 & 29.2361454579684 & 0.0238545420315681 \tabularnewline
107 & 29.02 & 28.5922463311824 & 0.427753668817598 \tabularnewline
108 & 28.47 & 28.7706333619727 & -0.300633361972665 \tabularnewline
109 & 28.53 & 28.6605567175041 & -0.130556717504103 \tabularnewline
110 & 28.48 & 28.7993925477856 & -0.319392547785629 \tabularnewline
111 & 28.68 & 28.7152123212211 & -0.0352123212210564 \tabularnewline
112 & 28.89 & 28.7479022248779 & 0.142097775122053 \tabularnewline
113 & 29.2 & 28.9046805506457 & 0.295319449354302 \tabularnewline
114 & 29.21 & 29.0992824888224 & 0.110717511177633 \tabularnewline
115 & 29.15 & 29.290299356577 & -0.140299356577003 \tabularnewline
116 & 29.22 & 29.3702829534414 & -0.150282953441426 \tabularnewline
117 & 29.34 & 29.4216269154447 & -0.0816269154447475 \tabularnewline
118 & 29.13 & 29.3610593215966 & -0.231059321596614 \tabularnewline
119 & 28.84 & 28.5611415816008 & 0.278858418399228 \tabularnewline
120 & 28.76 & 28.4944001079222 & 0.265599892077816 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72307&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]25.65[/C][C]25.5819364316239[/C][C]0.0680635683760684[/C][/ROW]
[ROW][C]14[/C][C]25.56[/C][C]25.5776136070211[/C][C]-0.0176136070211399[/C][/ROW]
[ROW][C]15[/C][C]25.62[/C][C]25.6504188489409[/C][C]-0.0304188489409185[/C][/ROW]
[ROW][C]16[/C][C]25.62[/C][C]25.6421174210916[/C][C]-0.0221174210915933[/C][/ROW]
[ROW][C]17[/C][C]25.69[/C][C]25.7451816745618[/C][C]-0.0551816745618048[/C][/ROW]
[ROW][C]18[/C][C]25.68[/C][C]25.7685509088495[/C][C]-0.0885509088494842[/C][/ROW]
[ROW][C]19[/C][C]25.68[/C][C]26.0858011689778[/C][C]-0.405801168977835[/C][/ROW]
[ROW][C]20[/C][C]25.83[/C][C]25.7588578626315[/C][C]0.0711421373685077[/C][/ROW]
[ROW][C]21[/C][C]25.93[/C][C]25.7954026929132[/C][C]0.134597307086846[/C][/ROW]
[ROW][C]22[/C][C]26.11[/C][C]25.8151576817308[/C][C]0.294842318269218[/C][/ROW]
[ROW][C]23[/C][C]24.72[/C][C]25.7084611169199[/C][C]-0.988461116919861[/C][/ROW]
[ROW][C]24[/C][C]24.62[/C][C]24.4125983671556[/C][C]0.207401632844416[/C][/ROW]
[ROW][C]25[/C][C]24.65[/C][C]24.6828927457645[/C][C]-0.0328927457645385[/C][/ROW]
[ROW][C]26[/C][C]25.24[/C][C]24.5706824182867[/C][C]0.66931758171328[/C][/ROW]
[ROW][C]27[/C][C]25.56[/C][C]25.2185382837644[/C][C]0.341461716235578[/C][/ROW]
[ROW][C]28[/C][C]25.9[/C][C]25.5265185872417[/C][C]0.373481412758295[/C][/ROW]
[ROW][C]29[/C][C]25.87[/C][C]25.9633569948208[/C][C]-0.093356994820791[/C][/ROW]
[ROW][C]30[/C][C]25.78[/C][C]25.9541290667629[/C][C]-0.17412906676293[/C][/ROW]
[ROW][C]31[/C][C]25.78[/C][C]26.1535449529318[/C][C]-0.373544952931844[/C][/ROW]
[ROW][C]32[/C][C]25.74[/C][C]25.9326902118613[/C][C]-0.192690211861329[/C][/ROW]
[ROW][C]33[/C][C]25.78[/C][C]25.7582410872747[/C][C]0.0217589127253106[/C][/ROW]
[ROW][C]34[/C][C]25.73[/C][C]25.7083926860234[/C][C]0.0216073139765776[/C][/ROW]
[ROW][C]35[/C][C]24.67[/C][C]25.1683125548834[/C][C]-0.49831255488343[/C][/ROW]
[ROW][C]36[/C][C]24.31[/C][C]24.4756532429014[/C][C]-0.165653242901371[/C][/ROW]
[ROW][C]37[/C][C]24.56[/C][C]24.3926248842715[/C][C]0.167375115728522[/C][/ROW]
[ROW][C]38[/C][C]25[/C][C]24.5601462785977[/C][C]0.439853721402251[/C][/ROW]
[ROW][C]39[/C][C]25.38[/C][C]24.9618320714130[/C][C]0.418167928586954[/C][/ROW]
[ROW][C]40[/C][C]25.99[/C][C]25.3389768599257[/C][C]0.651023140074287[/C][/ROW]
[ROW][C]41[/C][C]26.22[/C][C]25.9391723964979[/C][C]0.280827603502068[/C][/ROW]
[ROW][C]42[/C][C]26.19[/C][C]26.2389411656517[/C][C]-0.0489411656517156[/C][/ROW]
[ROW][C]43[/C][C]26.22[/C][C]26.5199916444388[/C][C]-0.299991644438823[/C][/ROW]
[ROW][C]44[/C][C]26.22[/C][C]26.3974112576997[/C][C]-0.177411257699710[/C][/ROW]
[ROW][C]45[/C][C]26.61[/C][C]26.2774808244409[/C][C]0.332519175559057[/C][/ROW]
[ROW][C]46[/C][C]26.72[/C][C]26.5009720825094[/C][C]0.219027917490610[/C][/ROW]
[ROW][C]47[/C][C]25.46[/C][C]26.0593083445771[/C][C]-0.599308344577054[/C][/ROW]
[ROW][C]48[/C][C]25.48[/C][C]25.3456282576335[/C][C]0.134371742366490[/C][/ROW]
[ROW][C]49[/C][C]25.59[/C][C]25.5829445954288[/C][C]0.00705540457121145[/C][/ROW]
[ROW][C]50[/C][C]25.88[/C][C]25.6713828589784[/C][C]0.208617141021605[/C][/ROW]
[ROW][C]51[/C][C]26[/C][C]25.8858482219371[/C][C]0.114151778062944[/C][/ROW]
[ROW][C]52[/C][C]26.97[/C][C]26.0511412122580[/C][C]0.918858787742032[/C][/ROW]
[ROW][C]53[/C][C]27.2[/C][C]26.8302856463779[/C][C]0.369714353622147[/C][/ROW]
[ROW][C]54[/C][C]27.19[/C][C]27.1652474154161[/C][C]0.0247525845839505[/C][/ROW]
[ROW][C]55[/C][C]27.19[/C][C]27.4817195097738[/C][C]-0.291719509773802[/C][/ROW]
[ROW][C]56[/C][C]27.19[/C][C]27.3978790297665[/C][C]-0.207879029766502[/C][/ROW]
[ROW][C]57[/C][C]27.26[/C][C]27.3442744935536[/C][C]-0.0842744935536395[/C][/ROW]
[ROW][C]58[/C][C]26.9[/C][C]27.2065262154050[/C][C]-0.306526215405043[/C][/ROW]
[ROW][C]59[/C][C]26.11[/C][C]26.196399282182[/C][C]-0.0863992821820183[/C][/ROW]
[ROW][C]60[/C][C]25.87[/C][C]26.0381501473715[/C][C]-0.168150147371531[/C][/ROW]
[ROW][C]61[/C][C]26.02[/C][C]26.0053191817461[/C][C]0.0146808182538791[/C][/ROW]
[ROW][C]62[/C][C]26.31[/C][C]26.1367626603854[/C][C]0.173237339614595[/C][/ROW]
[ROW][C]63[/C][C]26.37[/C][C]26.3113080544708[/C][C]0.0586919455292438[/C][/ROW]
[ROW][C]64[/C][C]26.52[/C][C]26.5597960663654[/C][C]-0.0397960663653905[/C][/ROW]
[ROW][C]65[/C][C]26.86[/C][C]26.4388924369209[/C][C]0.421107563079147[/C][/ROW]
[ROW][C]66[/C][C]26.92[/C][C]26.7583495693267[/C][C]0.161650430673344[/C][/ROW]
[ROW][C]67[/C][C]26.98[/C][C]27.1372733937366[/C][C]-0.157273393736567[/C][/ROW]
[ROW][C]68[/C][C]26.98[/C][C]27.1777585994591[/C][C]-0.197758599459089[/C][/ROW]
[ROW][C]69[/C][C]27.03[/C][C]27.1499148573228[/C][C]-0.119914857322790[/C][/ROW]
[ROW][C]70[/C][C]26.75[/C][C]26.9448828289851[/C][C]-0.194882828985058[/C][/ROW]
[ROW][C]71[/C][C]26.39[/C][C]26.0620168891329[/C][C]0.327983110867081[/C][/ROW]
[ROW][C]72[/C][C]26.3[/C][C]26.2433595470583[/C][C]0.0566404529417461[/C][/ROW]
[ROW][C]73[/C][C]26.3[/C][C]26.4337959219185[/C][C]-0.13379592191853[/C][/ROW]
[ROW][C]74[/C][C]26.52[/C][C]26.468330350403[/C][C]0.0516696495970237[/C][/ROW]
[ROW][C]75[/C][C]26.53[/C][C]26.5247468611462[/C][C]0.00525313885380996[/C][/ROW]
[ROW][C]76[/C][C]26.98[/C][C]26.7145583277112[/C][C]0.265441672288802[/C][/ROW]
[ROW][C]77[/C][C]27.22[/C][C]26.9280908097437[/C][C]0.291909190256341[/C][/ROW]
[ROW][C]78[/C][C]27.34[/C][C]27.1015455960160[/C][C]0.238454403983958[/C][/ROW]
[ROW][C]79[/C][C]27.41[/C][C]27.4997236433436[/C][C]-0.0897236433436355[/C][/ROW]
[ROW][C]80[/C][C]27.47[/C][C]27.5958718764446[/C][C]-0.125871876444609[/C][/ROW]
[ROW][C]81[/C][C]27.46[/C][C]27.646571836462[/C][C]-0.186571836461987[/C][/ROW]
[ROW][C]82[/C][C]27.53[/C][C]27.3786427824094[/C][C]0.151357217590608[/C][/ROW]
[ROW][C]83[/C][C]27.21[/C][C]26.8781552014326[/C][C]0.331844798567420[/C][/ROW]
[ROW][C]84[/C][C]26.91[/C][C]27.0288810252406[/C][C]-0.118881025240622[/C][/ROW]
[ROW][C]85[/C][C]26.95[/C][C]27.0482671031612[/C][C]-0.098267103161163[/C][/ROW]
[ROW][C]86[/C][C]26.91[/C][C]27.1489352796717[/C][C]-0.238935279671708[/C][/ROW]
[ROW][C]87[/C][C]27.39[/C][C]26.9571875741348[/C][C]0.432812425865190[/C][/ROW]
[ROW][C]88[/C][C]27.62[/C][C]27.5569120423643[/C][C]0.0630879576357088[/C][/ROW]
[ROW][C]89[/C][C]27.79[/C][C]27.6103780907772[/C][C]0.179621909222831[/C][/ROW]
[ROW][C]90[/C][C]27.88[/C][C]27.6861290547344[/C][C]0.193870945265640[/C][/ROW]
[ROW][C]91[/C][C]27.9[/C][C]28.0003143676811[/C][C]-0.100314367681083[/C][/ROW]
[ROW][C]92[/C][C]28.09[/C][C]28.0867076163757[/C][C]0.00329238362428441[/C][/ROW]
[ROW][C]93[/C][C]28.46[/C][C]28.2430041984505[/C][C]0.216995801549508[/C][/ROW]
[ROW][C]94[/C][C]28.73[/C][C]28.3785323780964[/C][C]0.351467621903563[/C][/ROW]
[ROW][C]95[/C][C]27.93[/C][C]28.0872395042733[/C][C]-0.157239504273267[/C][/ROW]
[ROW][C]96[/C][C]27.61[/C][C]27.7621466436877[/C][C]-0.152146643687651[/C][/ROW]
[ROW][C]97[/C][C]27.65[/C][C]27.7636275457869[/C][C]-0.113627545786905[/C][/ROW]
[ROW][C]98[/C][C]28.19[/C][C]27.8361216927336[/C][C]0.35387830726636[/C][/ROW]
[ROW][C]99[/C][C]28.98[/C][C]28.2622342562111[/C][C]0.717765743788853[/C][/ROW]
[ROW][C]100[/C][C]28.99[/C][C]29.0600858832815[/C][C]-0.0700858832815179[/C][/ROW]
[ROW][C]101[/C][C]29.02[/C][C]29.0336458364341[/C][C]-0.0136458364340761[/C][/ROW]
[ROW][C]102[/C][C]29[/C][C]28.9608685451477[/C][C]0.0391314548522708[/C][/ROW]
[ROW][C]103[/C][C]29.04[/C][C]29.1092515046038[/C][C]-0.0692515046038444[/C][/ROW]
[ROW][C]104[/C][C]29.19[/C][C]29.2491051518121[/C][C]-0.0591051518120835[/C][/ROW]
[ROW][C]105[/C][C]29.23[/C][C]29.3966098727707[/C][C]-0.166609872770746[/C][/ROW]
[ROW][C]106[/C][C]29.26[/C][C]29.2361454579684[/C][C]0.0238545420315681[/C][/ROW]
[ROW][C]107[/C][C]29.02[/C][C]28.5922463311824[/C][C]0.427753668817598[/C][/ROW]
[ROW][C]108[/C][C]28.47[/C][C]28.7706333619727[/C][C]-0.300633361972665[/C][/ROW]
[ROW][C]109[/C][C]28.53[/C][C]28.6605567175041[/C][C]-0.130556717504103[/C][/ROW]
[ROW][C]110[/C][C]28.48[/C][C]28.7993925477856[/C][C]-0.319392547785629[/C][/ROW]
[ROW][C]111[/C][C]28.68[/C][C]28.7152123212211[/C][C]-0.0352123212210564[/C][/ROW]
[ROW][C]112[/C][C]28.89[/C][C]28.7479022248779[/C][C]0.142097775122053[/C][/ROW]
[ROW][C]113[/C][C]29.2[/C][C]28.9046805506457[/C][C]0.295319449354302[/C][/ROW]
[ROW][C]114[/C][C]29.21[/C][C]29.0992824888224[/C][C]0.110717511177633[/C][/ROW]
[ROW][C]115[/C][C]29.15[/C][C]29.290299356577[/C][C]-0.140299356577003[/C][/ROW]
[ROW][C]116[/C][C]29.22[/C][C]29.3702829534414[/C][C]-0.150282953441426[/C][/ROW]
[ROW][C]117[/C][C]29.34[/C][C]29.4216269154447[/C][C]-0.0816269154447475[/C][/ROW]
[ROW][C]118[/C][C]29.13[/C][C]29.3610593215966[/C][C]-0.231059321596614[/C][/ROW]
[ROW][C]119[/C][C]28.84[/C][C]28.5611415816008[/C][C]0.278858418399228[/C][/ROW]
[ROW][C]120[/C][C]28.76[/C][C]28.4944001079222[/C][C]0.265599892077816[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72307&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72307&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
1325.6525.58193643162390.0680635683760684
1425.5625.5776136070211-0.0176136070211399
1525.6225.6504188489409-0.0304188489409185
1625.6225.6421174210916-0.0221174210915933
1725.6925.7451816745618-0.0551816745618048
1825.6825.7685509088495-0.0885509088494842
1925.6826.0858011689778-0.405801168977835
2025.8325.75885786263150.0711421373685077
2125.9325.79540269291320.134597307086846
2226.1125.81515768173080.294842318269218
2324.7225.7084611169199-0.988461116919861
2424.6224.41259836715560.207401632844416
2524.6524.6828927457645-0.0328927457645385
2625.2424.57068241828670.66931758171328
2725.5625.21853828376440.341461716235578
2825.925.52651858724170.373481412758295
2925.8725.9633569948208-0.093356994820791
3025.7825.9541290667629-0.17412906676293
3125.7826.1535449529318-0.373544952931844
3225.7425.9326902118613-0.192690211861329
3325.7825.75824108727470.0217589127253106
3425.7325.70839268602340.0216073139765776
3524.6725.1683125548834-0.49831255488343
3624.3124.4756532429014-0.165653242901371
3724.5624.39262488427150.167375115728522
382524.56014627859770.439853721402251
3925.3824.96183207141300.418167928586954
4025.9925.33897685992570.651023140074287
4126.2225.93917239649790.280827603502068
4226.1926.2389411656517-0.0489411656517156
4326.2226.5199916444388-0.299991644438823
4426.2226.3974112576997-0.177411257699710
4526.6126.27748082444090.332519175559057
4626.7226.50097208250940.219027917490610
4725.4626.0593083445771-0.599308344577054
4825.4825.34562825763350.134371742366490
4925.5925.58294459542880.00705540457121145
5025.8825.67138285897840.208617141021605
512625.88584822193710.114151778062944
5226.9726.05114121225800.918858787742032
5327.226.83028564637790.369714353622147
5427.1927.16524741541610.0247525845839505
5527.1927.4817195097738-0.291719509773802
5627.1927.3978790297665-0.207879029766502
5727.2627.3442744935536-0.0842744935536395
5826.927.2065262154050-0.306526215405043
5926.1126.196399282182-0.0863992821820183
6025.8726.0381501473715-0.168150147371531
6126.0226.00531918174610.0146808182538791
6226.3126.13676266038540.173237339614595
6326.3726.31130805447080.0586919455292438
6426.5226.5597960663654-0.0397960663653905
6526.8626.43889243692090.421107563079147
6626.9226.75834956932670.161650430673344
6726.9827.1372733937366-0.157273393736567
6826.9827.1777585994591-0.197758599459089
6927.0327.1499148573228-0.119914857322790
7026.7526.9448828289851-0.194882828985058
7126.3926.06201688913290.327983110867081
7226.326.24335954705830.0566404529417461
7326.326.4337959219185-0.13379592191853
7426.5226.4683303504030.0516696495970237
7526.5326.52474686114620.00525313885380996
7626.9826.71455832771120.265441672288802
7727.2226.92809080974370.291909190256341
7827.3427.10154559601600.238454403983958
7927.4127.4997236433436-0.0897236433436355
8027.4727.5958718764446-0.125871876444609
8127.4627.646571836462-0.186571836461987
8227.5327.37864278240940.151357217590608
8327.2126.87815520143260.331844798567420
8426.9127.0288810252406-0.118881025240622
8526.9527.0482671031612-0.098267103161163
8626.9127.1489352796717-0.238935279671708
8727.3926.95718757413480.432812425865190
8827.6227.55691204236430.0630879576357088
8927.7927.61037809077720.179621909222831
9027.8827.68612905473440.193870945265640
9127.928.0003143676811-0.100314367681083
9228.0928.08670761637570.00329238362428441
9328.4628.24300419845050.216995801549508
9428.7328.37853237809640.351467621903563
9527.9328.0872395042733-0.157239504273267
9627.6127.7621466436877-0.152146643687651
9727.6527.7636275457869-0.113627545786905
9828.1927.83612169273360.35387830726636
9928.9828.26223425621110.717765743788853
10028.9929.0600858832815-0.0700858832815179
10129.0229.0336458364341-0.0136458364340761
1022928.96086854514770.0391314548522708
10329.0429.1092515046038-0.0692515046038444
10429.1929.2491051518121-0.0591051518120835
10529.2329.3966098727707-0.166609872770746
10629.2629.23614545796840.0238545420315681
10729.0228.59224633118240.427753668817598
10828.4728.7706333619727-0.300633361972665
10928.5328.6605567175041-0.130556717504103
11028.4828.7993925477856-0.319392547785629
11128.6828.7152123212211-0.0352123212210564
11228.8928.74790222487790.142097775122053
11329.228.90468055064570.295319449354302
11429.2129.09928248882240.110717511177633
11529.1529.290299356577-0.140299356577003
11629.2229.3702829534414-0.150282953441426
11729.3429.4216269154447-0.0816269154447475
11829.1329.3610593215966-0.231059321596614
11928.8428.56114158160080.278858418399228
12028.7628.49440010792220.265599892077816







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12128.88864891232828.347254504180529.4300433204755
12229.109441871859228.397625466499329.821258277219
12329.343684055735728.492047306958230.1953208045131
12429.438694931934228.464541929998130.4128479338703
12529.503024882303728.417756321946830.5882934426606
12629.420139446621928.231928616068830.6083502771749
12729.477911881608228.192943416767330.7628803464491
12829.675508199090528.298641002627331.0523753955537
12929.866685844741228.401844066170331.3315276233122
13029.854743642243628.305164044575731.4043232399115
13129.334930702286527.703327732289730.9665336722833
13229.033517396082827.322198051819630.7448367403461

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 28.888648912328 & 28.3472545041805 & 29.4300433204755 \tabularnewline
122 & 29.1094418718592 & 28.3976254664993 & 29.821258277219 \tabularnewline
123 & 29.3436840557357 & 28.4920473069582 & 30.1953208045131 \tabularnewline
124 & 29.4386949319342 & 28.4645419299981 & 30.4128479338703 \tabularnewline
125 & 29.5030248823037 & 28.4177563219468 & 30.5882934426606 \tabularnewline
126 & 29.4201394466219 & 28.2319286160688 & 30.6083502771749 \tabularnewline
127 & 29.4779118816082 & 28.1929434167673 & 30.7628803464491 \tabularnewline
128 & 29.6755081990905 & 28.2986410026273 & 31.0523753955537 \tabularnewline
129 & 29.8666858447412 & 28.4018440661703 & 31.3315276233122 \tabularnewline
130 & 29.8547436422436 & 28.3051640445757 & 31.4043232399115 \tabularnewline
131 & 29.3349307022865 & 27.7033277322897 & 30.9665336722833 \tabularnewline
132 & 29.0335173960828 & 27.3221980518196 & 30.7448367403461 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72307&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]28.888648912328[/C][C]28.3472545041805[/C][C]29.4300433204755[/C][/ROW]
[ROW][C]122[/C][C]29.1094418718592[/C][C]28.3976254664993[/C][C]29.821258277219[/C][/ROW]
[ROW][C]123[/C][C]29.3436840557357[/C][C]28.4920473069582[/C][C]30.1953208045131[/C][/ROW]
[ROW][C]124[/C][C]29.4386949319342[/C][C]28.4645419299981[/C][C]30.4128479338703[/C][/ROW]
[ROW][C]125[/C][C]29.5030248823037[/C][C]28.4177563219468[/C][C]30.5882934426606[/C][/ROW]
[ROW][C]126[/C][C]29.4201394466219[/C][C]28.2319286160688[/C][C]30.6083502771749[/C][/ROW]
[ROW][C]127[/C][C]29.4779118816082[/C][C]28.1929434167673[/C][C]30.7628803464491[/C][/ROW]
[ROW][C]128[/C][C]29.6755081990905[/C][C]28.2986410026273[/C][C]31.0523753955537[/C][/ROW]
[ROW][C]129[/C][C]29.8666858447412[/C][C]28.4018440661703[/C][C]31.3315276233122[/C][/ROW]
[ROW][C]130[/C][C]29.8547436422436[/C][C]28.3051640445757[/C][C]31.4043232399115[/C][/ROW]
[ROW][C]131[/C][C]29.3349307022865[/C][C]27.7033277322897[/C][C]30.9665336722833[/C][/ROW]
[ROW][C]132[/C][C]29.0335173960828[/C][C]27.3221980518196[/C][C]30.7448367403461[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72307&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72307&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
12128.88864891232828.347254504180529.4300433204755
12229.109441871859228.397625466499329.821258277219
12329.343684055735728.492047306958230.1953208045131
12429.438694931934228.464541929998130.4128479338703
12529.503024882303728.417756321946830.5882934426606
12629.420139446621928.231928616068830.6083502771749
12729.477911881608228.192943416767330.7628803464491
12829.675508199090528.298641002627331.0523753955537
12929.866685844741228.401844066170331.3315276233122
13029.854743642243628.305164044575731.4043232399115
13129.334930702286527.703327732289730.9665336722833
13229.033517396082827.322198051819630.7448367403461



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; 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')