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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 16 Jan 2009 01:57:26 -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/2009/Jan/16/t12320963212k15uungv0f4v50.htm/, Retrieved Sun, 05 May 2024 02:33:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36909, Retrieved Sun, 05 May 2024 02:33:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact220
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Gemiddelde prijs ...] [2008-09-23 09:31:20] [74be16979710d4c4e7c6647856088456]
- RMPD    [Exponential Smoothing] [Exponential Smoot...] [2009-01-16 08:57:26] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
5.44
	5.44
	5.44
	5.44
	5.49
	5.49
	5.49
	5.49
	5.49
	5.49
	5.6
	5.6
	5.6
	5.6
	5.6
	5.6
	5.6
	5.67
	5.67
	5.67
	5.67
	5.67
	5.67
	5.67
	5.67
	5.67
	5.82
	5.82
	5.95
	5.95
	5.95
	5.95
	5.95
	5.95
	6.02
	6.02
	6.05
	6.05
	6.05
	6.12
	6.12
	6.12
	6.12
	6.12
	6.12
	6.12
	6.12
	6.17
	6.17
	6.17
	6.17
	6.17
	6.28
	6.27
	6.28
	6.28
	6.27
	6.27
	6.28
	6.59
	6.59
	6.59
	6.59
	6.59
	6.63
	6.63
	6.63
	6.63
	6.63
	6.63
	6.63
	6.63
	6.63




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=36909&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=36909&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36909&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
alpha0.913036634752078
beta0.0354041768981070
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.913036634752078 \tabularnewline
beta & 0.0354041768981070 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36909&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]0.913036634752078[/C][/ROW]
[ROW][C]beta[/C][C]0.0354041768981070[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36909&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36909&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
alpha0.913036634752078
beta0.0354041768981070
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
35.445.440
45.445.440
55.495.440.0499999999999998
65.495.487268097264160.00273190273583523
75.495.4914669996754-0.00146699967539909
85.495.49178472913937-0.00178472913937089
95.495.49175466803915-0.00175466803915292
105.495.49169533363547-0.00169533363546925
115.65.491635371529830.10836462847017
125.65.595567107111960.00443289288803772
135.65.6047486552334-0.00474865523339929
145.65.6053936118012-0.00539361180119968
155.65.60527534921842-0.0052753492184161
165.65.60509453740459-0.0050945374045881
175.65.60491413089717-0.00491413089716541
185.675.604739591332920.0652604086670756
195.675.67074654019325-0.000746540193252265
205.675.67646259445232-0.00646259445232289
215.675.67675077639412-0.00675077639412258
225.675.67655761672232-0.00655761672231936
235.675.67632884191033-0.00632884191033423
245.675.67610436510275-0.00610436510274592
255.675.6758875183466-0.00588751834659629
265.675.67567834476413-0.00567834476412621
275.825.675476600067670.144523399932330
285.825.81708631466460.00291368533540304
295.955.8294953577810.120504642218999
305.955.95316460242786-0.00316460242786043
315.955.96381699936383-0.0138169993638328
325.955.9642967288543-0.0142967288542959
335.955.9638763015454-0.0138763015453991
345.955.9633911840153-0.0133911840152958
356.025.962916122380660.0570838776193376
366.026.02863262792523-0.00863262792523045
376.056.034068504021340.0159314959786645
386.056.06244731569702-0.0124473156970248
396.056.06451286931689-0.014512869316893
406.126.064223363803410.0557766361965903
416.126.12991374894779-0.00991374894778563
426.126.13530594089111-0.0153059408911078
436.126.13528009475628-0.0152800947562843
446.126.13478391328148-0.0147839132814775
456.126.13426286908296-0.0142628690829643
466.126.13375650565385-0.0137565056538458
476.126.13326778726893-0.0132677872689264
486.176.132796401329990.0372035986700148
496.176.1796098576399-0.0096098576398953
506.176.18337027170712-0.0133702717071200
516.176.18326509178431-0.0132650917843131
526.176.18282714677312-0.0128271467731160
536.286.182374420098480.0976255799015213
546.276.28592485647215-0.0159248564721501
556.286.28528480861395-0.00528480861394609
566.286.29418868116626-0.0141886811662548
576.276.29450433836242-0.0245043383624157
586.276.28460931228001-0.0146093122800091
596.286.28327655695657-0.00327655695656759
606.596.292185106695020.297814893304983
616.596.58562813983980.00437186016020075
626.596.6112882552479-0.0212882552479048
636.596.61283159577489-0.0228315957748872
646.596.61222777143749-0.0222277714374908
656.636.611456741226960.0185432587730414
666.636.64851057183333-0.0185105718333256
676.636.65113453765556-0.0211345376555592
686.636.6506795460611-0.020679546061106
696.636.64997150571282-0.0199715057128227
706.636.64926434701746-0.0192643470174625
716.636.64858012411803-0.0185801241180288
726.636.64792001351029-0.0179200135102908
736.636.64728333806896-0.0172833380689621

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 5.44 & 5.44 & 0 \tabularnewline
4 & 5.44 & 5.44 & 0 \tabularnewline
5 & 5.49 & 5.44 & 0.0499999999999998 \tabularnewline
6 & 5.49 & 5.48726809726416 & 0.00273190273583523 \tabularnewline
7 & 5.49 & 5.4914669996754 & -0.00146699967539909 \tabularnewline
8 & 5.49 & 5.49178472913937 & -0.00178472913937089 \tabularnewline
9 & 5.49 & 5.49175466803915 & -0.00175466803915292 \tabularnewline
10 & 5.49 & 5.49169533363547 & -0.00169533363546925 \tabularnewline
11 & 5.6 & 5.49163537152983 & 0.10836462847017 \tabularnewline
12 & 5.6 & 5.59556710711196 & 0.00443289288803772 \tabularnewline
13 & 5.6 & 5.6047486552334 & -0.00474865523339929 \tabularnewline
14 & 5.6 & 5.6053936118012 & -0.00539361180119968 \tabularnewline
15 & 5.6 & 5.60527534921842 & -0.0052753492184161 \tabularnewline
16 & 5.6 & 5.60509453740459 & -0.0050945374045881 \tabularnewline
17 & 5.6 & 5.60491413089717 & -0.00491413089716541 \tabularnewline
18 & 5.67 & 5.60473959133292 & 0.0652604086670756 \tabularnewline
19 & 5.67 & 5.67074654019325 & -0.000746540193252265 \tabularnewline
20 & 5.67 & 5.67646259445232 & -0.00646259445232289 \tabularnewline
21 & 5.67 & 5.67675077639412 & -0.00675077639412258 \tabularnewline
22 & 5.67 & 5.67655761672232 & -0.00655761672231936 \tabularnewline
23 & 5.67 & 5.67632884191033 & -0.00632884191033423 \tabularnewline
24 & 5.67 & 5.67610436510275 & -0.00610436510274592 \tabularnewline
25 & 5.67 & 5.6758875183466 & -0.00588751834659629 \tabularnewline
26 & 5.67 & 5.67567834476413 & -0.00567834476412621 \tabularnewline
27 & 5.82 & 5.67547660006767 & 0.144523399932330 \tabularnewline
28 & 5.82 & 5.8170863146646 & 0.00291368533540304 \tabularnewline
29 & 5.95 & 5.829495357781 & 0.120504642218999 \tabularnewline
30 & 5.95 & 5.95316460242786 & -0.00316460242786043 \tabularnewline
31 & 5.95 & 5.96381699936383 & -0.0138169993638328 \tabularnewline
32 & 5.95 & 5.9642967288543 & -0.0142967288542959 \tabularnewline
33 & 5.95 & 5.9638763015454 & -0.0138763015453991 \tabularnewline
34 & 5.95 & 5.9633911840153 & -0.0133911840152958 \tabularnewline
35 & 6.02 & 5.96291612238066 & 0.0570838776193376 \tabularnewline
36 & 6.02 & 6.02863262792523 & -0.00863262792523045 \tabularnewline
37 & 6.05 & 6.03406850402134 & 0.0159314959786645 \tabularnewline
38 & 6.05 & 6.06244731569702 & -0.0124473156970248 \tabularnewline
39 & 6.05 & 6.06451286931689 & -0.014512869316893 \tabularnewline
40 & 6.12 & 6.06422336380341 & 0.0557766361965903 \tabularnewline
41 & 6.12 & 6.12991374894779 & -0.00991374894778563 \tabularnewline
42 & 6.12 & 6.13530594089111 & -0.0153059408911078 \tabularnewline
43 & 6.12 & 6.13528009475628 & -0.0152800947562843 \tabularnewline
44 & 6.12 & 6.13478391328148 & -0.0147839132814775 \tabularnewline
45 & 6.12 & 6.13426286908296 & -0.0142628690829643 \tabularnewline
46 & 6.12 & 6.13375650565385 & -0.0137565056538458 \tabularnewline
47 & 6.12 & 6.13326778726893 & -0.0132677872689264 \tabularnewline
48 & 6.17 & 6.13279640132999 & 0.0372035986700148 \tabularnewline
49 & 6.17 & 6.1796098576399 & -0.0096098576398953 \tabularnewline
50 & 6.17 & 6.18337027170712 & -0.0133702717071200 \tabularnewline
51 & 6.17 & 6.18326509178431 & -0.0132650917843131 \tabularnewline
52 & 6.17 & 6.18282714677312 & -0.0128271467731160 \tabularnewline
53 & 6.28 & 6.18237442009848 & 0.0976255799015213 \tabularnewline
54 & 6.27 & 6.28592485647215 & -0.0159248564721501 \tabularnewline
55 & 6.28 & 6.28528480861395 & -0.00528480861394609 \tabularnewline
56 & 6.28 & 6.29418868116626 & -0.0141886811662548 \tabularnewline
57 & 6.27 & 6.29450433836242 & -0.0245043383624157 \tabularnewline
58 & 6.27 & 6.28460931228001 & -0.0146093122800091 \tabularnewline
59 & 6.28 & 6.28327655695657 & -0.00327655695656759 \tabularnewline
60 & 6.59 & 6.29218510669502 & 0.297814893304983 \tabularnewline
61 & 6.59 & 6.5856281398398 & 0.00437186016020075 \tabularnewline
62 & 6.59 & 6.6112882552479 & -0.0212882552479048 \tabularnewline
63 & 6.59 & 6.61283159577489 & -0.0228315957748872 \tabularnewline
64 & 6.59 & 6.61222777143749 & -0.0222277714374908 \tabularnewline
65 & 6.63 & 6.61145674122696 & 0.0185432587730414 \tabularnewline
66 & 6.63 & 6.64851057183333 & -0.0185105718333256 \tabularnewline
67 & 6.63 & 6.65113453765556 & -0.0211345376555592 \tabularnewline
68 & 6.63 & 6.6506795460611 & -0.020679546061106 \tabularnewline
69 & 6.63 & 6.64997150571282 & -0.0199715057128227 \tabularnewline
70 & 6.63 & 6.64926434701746 & -0.0192643470174625 \tabularnewline
71 & 6.63 & 6.64858012411803 & -0.0185801241180288 \tabularnewline
72 & 6.63 & 6.64792001351029 & -0.0179200135102908 \tabularnewline
73 & 6.63 & 6.64728333806896 & -0.0172833380689621 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36909&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]5.44[/C][C]5.44[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]5.44[/C][C]5.44[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]5.49[/C][C]5.44[/C][C]0.0499999999999998[/C][/ROW]
[ROW][C]6[/C][C]5.49[/C][C]5.48726809726416[/C][C]0.00273190273583523[/C][/ROW]
[ROW][C]7[/C][C]5.49[/C][C]5.4914669996754[/C][C]-0.00146699967539909[/C][/ROW]
[ROW][C]8[/C][C]5.49[/C][C]5.49178472913937[/C][C]-0.00178472913937089[/C][/ROW]
[ROW][C]9[/C][C]5.49[/C][C]5.49175466803915[/C][C]-0.00175466803915292[/C][/ROW]
[ROW][C]10[/C][C]5.49[/C][C]5.49169533363547[/C][C]-0.00169533363546925[/C][/ROW]
[ROW][C]11[/C][C]5.6[/C][C]5.49163537152983[/C][C]0.10836462847017[/C][/ROW]
[ROW][C]12[/C][C]5.6[/C][C]5.59556710711196[/C][C]0.00443289288803772[/C][/ROW]
[ROW][C]13[/C][C]5.6[/C][C]5.6047486552334[/C][C]-0.00474865523339929[/C][/ROW]
[ROW][C]14[/C][C]5.6[/C][C]5.6053936118012[/C][C]-0.00539361180119968[/C][/ROW]
[ROW][C]15[/C][C]5.6[/C][C]5.60527534921842[/C][C]-0.0052753492184161[/C][/ROW]
[ROW][C]16[/C][C]5.6[/C][C]5.60509453740459[/C][C]-0.0050945374045881[/C][/ROW]
[ROW][C]17[/C][C]5.6[/C][C]5.60491413089717[/C][C]-0.00491413089716541[/C][/ROW]
[ROW][C]18[/C][C]5.67[/C][C]5.60473959133292[/C][C]0.0652604086670756[/C][/ROW]
[ROW][C]19[/C][C]5.67[/C][C]5.67074654019325[/C][C]-0.000746540193252265[/C][/ROW]
[ROW][C]20[/C][C]5.67[/C][C]5.67646259445232[/C][C]-0.00646259445232289[/C][/ROW]
[ROW][C]21[/C][C]5.67[/C][C]5.67675077639412[/C][C]-0.00675077639412258[/C][/ROW]
[ROW][C]22[/C][C]5.67[/C][C]5.67655761672232[/C][C]-0.00655761672231936[/C][/ROW]
[ROW][C]23[/C][C]5.67[/C][C]5.67632884191033[/C][C]-0.00632884191033423[/C][/ROW]
[ROW][C]24[/C][C]5.67[/C][C]5.67610436510275[/C][C]-0.00610436510274592[/C][/ROW]
[ROW][C]25[/C][C]5.67[/C][C]5.6758875183466[/C][C]-0.00588751834659629[/C][/ROW]
[ROW][C]26[/C][C]5.67[/C][C]5.67567834476413[/C][C]-0.00567834476412621[/C][/ROW]
[ROW][C]27[/C][C]5.82[/C][C]5.67547660006767[/C][C]0.144523399932330[/C][/ROW]
[ROW][C]28[/C][C]5.82[/C][C]5.8170863146646[/C][C]0.00291368533540304[/C][/ROW]
[ROW][C]29[/C][C]5.95[/C][C]5.829495357781[/C][C]0.120504642218999[/C][/ROW]
[ROW][C]30[/C][C]5.95[/C][C]5.95316460242786[/C][C]-0.00316460242786043[/C][/ROW]
[ROW][C]31[/C][C]5.95[/C][C]5.96381699936383[/C][C]-0.0138169993638328[/C][/ROW]
[ROW][C]32[/C][C]5.95[/C][C]5.9642967288543[/C][C]-0.0142967288542959[/C][/ROW]
[ROW][C]33[/C][C]5.95[/C][C]5.9638763015454[/C][C]-0.0138763015453991[/C][/ROW]
[ROW][C]34[/C][C]5.95[/C][C]5.9633911840153[/C][C]-0.0133911840152958[/C][/ROW]
[ROW][C]35[/C][C]6.02[/C][C]5.96291612238066[/C][C]0.0570838776193376[/C][/ROW]
[ROW][C]36[/C][C]6.02[/C][C]6.02863262792523[/C][C]-0.00863262792523045[/C][/ROW]
[ROW][C]37[/C][C]6.05[/C][C]6.03406850402134[/C][C]0.0159314959786645[/C][/ROW]
[ROW][C]38[/C][C]6.05[/C][C]6.06244731569702[/C][C]-0.0124473156970248[/C][/ROW]
[ROW][C]39[/C][C]6.05[/C][C]6.06451286931689[/C][C]-0.014512869316893[/C][/ROW]
[ROW][C]40[/C][C]6.12[/C][C]6.06422336380341[/C][C]0.0557766361965903[/C][/ROW]
[ROW][C]41[/C][C]6.12[/C][C]6.12991374894779[/C][C]-0.00991374894778563[/C][/ROW]
[ROW][C]42[/C][C]6.12[/C][C]6.13530594089111[/C][C]-0.0153059408911078[/C][/ROW]
[ROW][C]43[/C][C]6.12[/C][C]6.13528009475628[/C][C]-0.0152800947562843[/C][/ROW]
[ROW][C]44[/C][C]6.12[/C][C]6.13478391328148[/C][C]-0.0147839132814775[/C][/ROW]
[ROW][C]45[/C][C]6.12[/C][C]6.13426286908296[/C][C]-0.0142628690829643[/C][/ROW]
[ROW][C]46[/C][C]6.12[/C][C]6.13375650565385[/C][C]-0.0137565056538458[/C][/ROW]
[ROW][C]47[/C][C]6.12[/C][C]6.13326778726893[/C][C]-0.0132677872689264[/C][/ROW]
[ROW][C]48[/C][C]6.17[/C][C]6.13279640132999[/C][C]0.0372035986700148[/C][/ROW]
[ROW][C]49[/C][C]6.17[/C][C]6.1796098576399[/C][C]-0.0096098576398953[/C][/ROW]
[ROW][C]50[/C][C]6.17[/C][C]6.18337027170712[/C][C]-0.0133702717071200[/C][/ROW]
[ROW][C]51[/C][C]6.17[/C][C]6.18326509178431[/C][C]-0.0132650917843131[/C][/ROW]
[ROW][C]52[/C][C]6.17[/C][C]6.18282714677312[/C][C]-0.0128271467731160[/C][/ROW]
[ROW][C]53[/C][C]6.28[/C][C]6.18237442009848[/C][C]0.0976255799015213[/C][/ROW]
[ROW][C]54[/C][C]6.27[/C][C]6.28592485647215[/C][C]-0.0159248564721501[/C][/ROW]
[ROW][C]55[/C][C]6.28[/C][C]6.28528480861395[/C][C]-0.00528480861394609[/C][/ROW]
[ROW][C]56[/C][C]6.28[/C][C]6.29418868116626[/C][C]-0.0141886811662548[/C][/ROW]
[ROW][C]57[/C][C]6.27[/C][C]6.29450433836242[/C][C]-0.0245043383624157[/C][/ROW]
[ROW][C]58[/C][C]6.27[/C][C]6.28460931228001[/C][C]-0.0146093122800091[/C][/ROW]
[ROW][C]59[/C][C]6.28[/C][C]6.28327655695657[/C][C]-0.00327655695656759[/C][/ROW]
[ROW][C]60[/C][C]6.59[/C][C]6.29218510669502[/C][C]0.297814893304983[/C][/ROW]
[ROW][C]61[/C][C]6.59[/C][C]6.5856281398398[/C][C]0.00437186016020075[/C][/ROW]
[ROW][C]62[/C][C]6.59[/C][C]6.6112882552479[/C][C]-0.0212882552479048[/C][/ROW]
[ROW][C]63[/C][C]6.59[/C][C]6.61283159577489[/C][C]-0.0228315957748872[/C][/ROW]
[ROW][C]64[/C][C]6.59[/C][C]6.61222777143749[/C][C]-0.0222277714374908[/C][/ROW]
[ROW][C]65[/C][C]6.63[/C][C]6.61145674122696[/C][C]0.0185432587730414[/C][/ROW]
[ROW][C]66[/C][C]6.63[/C][C]6.64851057183333[/C][C]-0.0185105718333256[/C][/ROW]
[ROW][C]67[/C][C]6.63[/C][C]6.65113453765556[/C][C]-0.0211345376555592[/C][/ROW]
[ROW][C]68[/C][C]6.63[/C][C]6.6506795460611[/C][C]-0.020679546061106[/C][/ROW]
[ROW][C]69[/C][C]6.63[/C][C]6.64997150571282[/C][C]-0.0199715057128227[/C][/ROW]
[ROW][C]70[/C][C]6.63[/C][C]6.64926434701746[/C][C]-0.0192643470174625[/C][/ROW]
[ROW][C]71[/C][C]6.63[/C][C]6.64858012411803[/C][C]-0.0185801241180288[/C][/ROW]
[ROW][C]72[/C][C]6.63[/C][C]6.64792001351029[/C][C]-0.0179200135102908[/C][/ROW]
[ROW][C]73[/C][C]6.63[/C][C]6.64728333806896[/C][C]-0.0172833380689621[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36909&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36909&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
35.445.440
45.445.440
55.495.440.0499999999999998
65.495.487268097264160.00273190273583523
75.495.4914669996754-0.00146699967539909
85.495.49178472913937-0.00178472913937089
95.495.49175466803915-0.00175466803915292
105.495.49169533363547-0.00169533363546925
115.65.491635371529830.10836462847017
125.65.595567107111960.00443289288803772
135.65.6047486552334-0.00474865523339929
145.65.6053936118012-0.00539361180119968
155.65.60527534921842-0.0052753492184161
165.65.60509453740459-0.0050945374045881
175.65.60491413089717-0.00491413089716541
185.675.604739591332920.0652604086670756
195.675.67074654019325-0.000746540193252265
205.675.67646259445232-0.00646259445232289
215.675.67675077639412-0.00675077639412258
225.675.67655761672232-0.00655761672231936
235.675.67632884191033-0.00632884191033423
245.675.67610436510275-0.00610436510274592
255.675.6758875183466-0.00588751834659629
265.675.67567834476413-0.00567834476412621
275.825.675476600067670.144523399932330
285.825.81708631466460.00291368533540304
295.955.8294953577810.120504642218999
305.955.95316460242786-0.00316460242786043
315.955.96381699936383-0.0138169993638328
325.955.9642967288543-0.0142967288542959
335.955.9638763015454-0.0138763015453991
345.955.9633911840153-0.0133911840152958
356.025.962916122380660.0570838776193376
366.026.02863262792523-0.00863262792523045
376.056.034068504021340.0159314959786645
386.056.06244731569702-0.0124473156970248
396.056.06451286931689-0.014512869316893
406.126.064223363803410.0557766361965903
416.126.12991374894779-0.00991374894778563
426.126.13530594089111-0.0153059408911078
436.126.13528009475628-0.0152800947562843
446.126.13478391328148-0.0147839132814775
456.126.13426286908296-0.0142628690829643
466.126.13375650565385-0.0137565056538458
476.126.13326778726893-0.0132677872689264
486.176.132796401329990.0372035986700148
496.176.1796098576399-0.0096098576398953
506.176.18337027170712-0.0133702717071200
516.176.18326509178431-0.0132650917843131
526.176.18282714677312-0.0128271467731160
536.286.182374420098480.0976255799015213
546.276.28592485647215-0.0159248564721501
556.286.28528480861395-0.00528480861394609
566.286.29418868116626-0.0141886811662548
576.276.29450433836242-0.0245043383624157
586.276.28460931228001-0.0146093122800091
596.286.28327655695657-0.00327655695656759
606.596.292185106695020.297814893304983
616.596.58562813983980.00437186016020075
626.596.6112882552479-0.0212882552479048
636.596.61283159577489-0.0228315957748872
646.596.61222777143749-0.0222277714374908
656.636.611456741226960.0185432587730414
666.636.64851057183333-0.0185105718333256
676.636.65113453765556-0.0211345376555592
686.636.6506795460611-0.020679546061106
696.636.64997150571282-0.0199715057128227
706.636.64926434701746-0.0192643470174625
716.636.64858012411803-0.0185801241180288
726.636.64792001351029-0.0179200135102908
736.636.64728333806896-0.0172833380689621







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
746.646669281359926.551004170549866.74233439216997
756.661835545478646.530188770540826.79348232041646
766.677001809597366.51551237049136.83849124870343
776.692168073716096.503979774052686.8803563733795
786.707334337834816.494360182492226.9203084931774
796.722500601953546.486010794532666.95899040937441
806.737666866072266.478548598536866.99678513360766
816.752833130190986.471725215959187.03394104442279
826.767999394309716.46536974678047.07062904183901
836.783165658428436.459359335357797.10697198149907
846.798331922547156.453602638522247.14306120657207
856.813498186665886.448029908007897.17896646532387

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
74 & 6.64666928135992 & 6.55100417054986 & 6.74233439216997 \tabularnewline
75 & 6.66183554547864 & 6.53018877054082 & 6.79348232041646 \tabularnewline
76 & 6.67700180959736 & 6.5155123704913 & 6.83849124870343 \tabularnewline
77 & 6.69216807371609 & 6.50397977405268 & 6.8803563733795 \tabularnewline
78 & 6.70733433783481 & 6.49436018249222 & 6.9203084931774 \tabularnewline
79 & 6.72250060195354 & 6.48601079453266 & 6.95899040937441 \tabularnewline
80 & 6.73766686607226 & 6.47854859853686 & 6.99678513360766 \tabularnewline
81 & 6.75283313019098 & 6.47172521595918 & 7.03394104442279 \tabularnewline
82 & 6.76799939430971 & 6.4653697467804 & 7.07062904183901 \tabularnewline
83 & 6.78316565842843 & 6.45935933535779 & 7.10697198149907 \tabularnewline
84 & 6.79833192254715 & 6.45360263852224 & 7.14306120657207 \tabularnewline
85 & 6.81349818666588 & 6.44802990800789 & 7.17896646532387 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36909&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]74[/C][C]6.64666928135992[/C][C]6.55100417054986[/C][C]6.74233439216997[/C][/ROW]
[ROW][C]75[/C][C]6.66183554547864[/C][C]6.53018877054082[/C][C]6.79348232041646[/C][/ROW]
[ROW][C]76[/C][C]6.67700180959736[/C][C]6.5155123704913[/C][C]6.83849124870343[/C][/ROW]
[ROW][C]77[/C][C]6.69216807371609[/C][C]6.50397977405268[/C][C]6.8803563733795[/C][/ROW]
[ROW][C]78[/C][C]6.70733433783481[/C][C]6.49436018249222[/C][C]6.9203084931774[/C][/ROW]
[ROW][C]79[/C][C]6.72250060195354[/C][C]6.48601079453266[/C][C]6.95899040937441[/C][/ROW]
[ROW][C]80[/C][C]6.73766686607226[/C][C]6.47854859853686[/C][C]6.99678513360766[/C][/ROW]
[ROW][C]81[/C][C]6.75283313019098[/C][C]6.47172521595918[/C][C]7.03394104442279[/C][/ROW]
[ROW][C]82[/C][C]6.76799939430971[/C][C]6.4653697467804[/C][C]7.07062904183901[/C][/ROW]
[ROW][C]83[/C][C]6.78316565842843[/C][C]6.45935933535779[/C][C]7.10697198149907[/C][/ROW]
[ROW][C]84[/C][C]6.79833192254715[/C][C]6.45360263852224[/C][C]7.14306120657207[/C][/ROW]
[ROW][C]85[/C][C]6.81349818666588[/C][C]6.44802990800789[/C][C]7.17896646532387[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36909&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36909&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
746.646669281359926.551004170549866.74233439216997
756.661835545478646.530188770540826.79348232041646
766.677001809597366.51551237049136.83849124870343
776.692168073716096.503979774052686.8803563733795
786.707334337834816.494360182492226.9203084931774
796.722500601953546.486010794532666.95899040937441
806.737666866072266.478548598536866.99678513360766
816.752833130190986.471725215959187.03394104442279
826.767999394309716.46536974678047.07062904183901
836.783165658428436.459359335357797.10697198149907
846.798331922547156.453602638522247.14306120657207
856.813498186665886.448029908007897.17896646532387



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')