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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 11 Dec 2012 06:13:51 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/11/t13552245003xaxunahfnyx3vu.htm/, Retrieved Thu, 28 Mar 2024 17:39:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=198417, Retrieved Thu, 28 Mar 2024 17:39:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact112
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [Monthly US soldie...] [2010-11-02 12:07:39] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [Soldiers] [2010-11-30 14:09:25] [b98453cac15ba1066b407e146608df68]
- R P       [Exponential Smoothing] [paper single expo...] [2012-12-11 11:13:51] [d0f95aac7f57db23d4da86d121b837fb] [Current]
-   P         [Exponential Smoothing] [paper double expo...] [2012-12-11 11:30:08] [1edfe4f7de973a74350ac08c1294a22c]
-   P         [Exponential Smoothing] [paper triple expo...] [2012-12-11 11:39:36] [1edfe4f7de973a74350ac08c1294a22c]
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Dataseries X:
37
30
47
35
30
43
82
40
47
19
52
136
80
42
54
66
81
63
137
72
107
58
36
52
79
77
54
84
48
96
83
66
61
53
30
74
69
59
42
65
70
100
63
105
82
81
75
102
121
98
76
77
63
37
35
23
40
29
37
51
20
28
13
22
25
13
16
13
16
17
9
17
25
14
8
7
10
7
10
3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=198417&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=198417&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=198417&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 time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.365156398722376
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.365156398722376 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=198417&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]0.365156398722376[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=198417&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=198417&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
alpha0.365156398722376
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
23037-7
34734.443905208943412.5560947910566
43539.0288435648624-4.02884356486239
53037.5576855577014-7.55768555770143
64334.79794831677518.20205168322494
78237.792979971556344.2070200284437
84053.9354562033907-13.9354562033907
94748.8468352016072-1.84683520160717
101948.1724515103546-29.1724515103546
115237.519944174930414.4800558250696
1213642.807429213311893.1925707866882
138076.83729274945893.1627072505411
144277.9921755392796-35.9921755392796
155464.8494023371727-10.8494023371727
166660.88767365144065.11232634855941
178162.754472329974118.2455276700259
186369.4169435067502-6.41694350675019
1913767.073755525020469.9262444749796
207292.6077711336843-20.6077711336843
2110785.082711640813221.9172883591868
225893.0859497278137-35.0859497278137
233680.2740906794509-44.2740906794509
245264.1071231702347-12.1071231702347
257959.686129674503619.3138703254964
267766.738713007952810.2612869920472
275470.4856876122255-16.4856876122255
288464.465833293283219.5341667067168
294871.5988592599504-23.5988592599504
309662.981584798630733.0184152013693
318375.03847038508297.96152961491713
326677.9456738675876-11.9456738675876
336173.5836346177873-12.5836346177873
345368.9886399179179-15.9886399179179
353063.1502857450222-33.1502857450222
367451.045246785752222.9547532142478
376959.42732180302789.57267819697222
385962.9228464995624-3.92284649956236
394261.4903939990415-19.4903939990415
406554.373351916671310.6266480833287
417058.253740461269611.7462595387304
4210062.542962292890837.4570377071092
436376.220639288827-13.220639288827
4410571.393038257311433.6069617426886
458283.6648353792722-1.66483537927222
468183.0569100877116-2.05691008771157
477582.3058162075871-7.30581620758709
4810279.63805067149722.361949328503
4912187.803659556705433.1963404432946
509899.9255156837408-1.92551568374081
517699.2224013109826-23.2224013109826
527790.7425928785784-13.7425928785784
536385.7243971539289-22.7243971539289
543777.4264381260632-40.4264381260632
553562.664465566777-27.664465566777
562352.5626089478336-29.5626089478336
574041.7676331276048-1.76763312760479
582941.1221705804663-12.1221705804663
593736.69568242660490.304317573395132
605136.806805935773814.1931940642262
612041.9895415666344-21.9895415666344
622833.9599197586062-5.9599197586062
631331.7836169228792-18.7836169228792
642224.92465901234-2.92465901233998
652523.8567010599031.14329894009703
661324.2741839835319-11.2741839835319
671620.1573435615719-4.15734356157191
681318.6392629583767-5.63926295837666
691616.5800500050473-0.580050005047347
701716.36824103412540.631758965874639
71916.5989318629647-7.59893186296472
721713.82413326974783.17586673025219
732514.983821327788910.0161786722111
741418.6412930606934-4.64129306069337
75816.9464952012354-8.94649520123543
76713.6796252323653-6.67962523236528
771011.2405173376997-1.24051733769967
78710.7875344941126-3.78753449411259
79109.404492038205660.59550796179434
8039.62194558094498-6.62194558094498

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 30 & 37 & -7 \tabularnewline
3 & 47 & 34.4439052089434 & 12.5560947910566 \tabularnewline
4 & 35 & 39.0288435648624 & -4.02884356486239 \tabularnewline
5 & 30 & 37.5576855577014 & -7.55768555770143 \tabularnewline
6 & 43 & 34.7979483167751 & 8.20205168322494 \tabularnewline
7 & 82 & 37.7929799715563 & 44.2070200284437 \tabularnewline
8 & 40 & 53.9354562033907 & -13.9354562033907 \tabularnewline
9 & 47 & 48.8468352016072 & -1.84683520160717 \tabularnewline
10 & 19 & 48.1724515103546 & -29.1724515103546 \tabularnewline
11 & 52 & 37.5199441749304 & 14.4800558250696 \tabularnewline
12 & 136 & 42.8074292133118 & 93.1925707866882 \tabularnewline
13 & 80 & 76.8372927494589 & 3.1627072505411 \tabularnewline
14 & 42 & 77.9921755392796 & -35.9921755392796 \tabularnewline
15 & 54 & 64.8494023371727 & -10.8494023371727 \tabularnewline
16 & 66 & 60.8876736514406 & 5.11232634855941 \tabularnewline
17 & 81 & 62.7544723299741 & 18.2455276700259 \tabularnewline
18 & 63 & 69.4169435067502 & -6.41694350675019 \tabularnewline
19 & 137 & 67.0737555250204 & 69.9262444749796 \tabularnewline
20 & 72 & 92.6077711336843 & -20.6077711336843 \tabularnewline
21 & 107 & 85.0827116408132 & 21.9172883591868 \tabularnewline
22 & 58 & 93.0859497278137 & -35.0859497278137 \tabularnewline
23 & 36 & 80.2740906794509 & -44.2740906794509 \tabularnewline
24 & 52 & 64.1071231702347 & -12.1071231702347 \tabularnewline
25 & 79 & 59.6861296745036 & 19.3138703254964 \tabularnewline
26 & 77 & 66.7387130079528 & 10.2612869920472 \tabularnewline
27 & 54 & 70.4856876122255 & -16.4856876122255 \tabularnewline
28 & 84 & 64.4658332932832 & 19.5341667067168 \tabularnewline
29 & 48 & 71.5988592599504 & -23.5988592599504 \tabularnewline
30 & 96 & 62.9815847986307 & 33.0184152013693 \tabularnewline
31 & 83 & 75.0384703850829 & 7.96152961491713 \tabularnewline
32 & 66 & 77.9456738675876 & -11.9456738675876 \tabularnewline
33 & 61 & 73.5836346177873 & -12.5836346177873 \tabularnewline
34 & 53 & 68.9886399179179 & -15.9886399179179 \tabularnewline
35 & 30 & 63.1502857450222 & -33.1502857450222 \tabularnewline
36 & 74 & 51.0452467857522 & 22.9547532142478 \tabularnewline
37 & 69 & 59.4273218030278 & 9.57267819697222 \tabularnewline
38 & 59 & 62.9228464995624 & -3.92284649956236 \tabularnewline
39 & 42 & 61.4903939990415 & -19.4903939990415 \tabularnewline
40 & 65 & 54.3733519166713 & 10.6266480833287 \tabularnewline
41 & 70 & 58.2537404612696 & 11.7462595387304 \tabularnewline
42 & 100 & 62.5429622928908 & 37.4570377071092 \tabularnewline
43 & 63 & 76.220639288827 & -13.220639288827 \tabularnewline
44 & 105 & 71.3930382573114 & 33.6069617426886 \tabularnewline
45 & 82 & 83.6648353792722 & -1.66483537927222 \tabularnewline
46 & 81 & 83.0569100877116 & -2.05691008771157 \tabularnewline
47 & 75 & 82.3058162075871 & -7.30581620758709 \tabularnewline
48 & 102 & 79.638050671497 & 22.361949328503 \tabularnewline
49 & 121 & 87.8036595567054 & 33.1963404432946 \tabularnewline
50 & 98 & 99.9255156837408 & -1.92551568374081 \tabularnewline
51 & 76 & 99.2224013109826 & -23.2224013109826 \tabularnewline
52 & 77 & 90.7425928785784 & -13.7425928785784 \tabularnewline
53 & 63 & 85.7243971539289 & -22.7243971539289 \tabularnewline
54 & 37 & 77.4264381260632 & -40.4264381260632 \tabularnewline
55 & 35 & 62.664465566777 & -27.664465566777 \tabularnewline
56 & 23 & 52.5626089478336 & -29.5626089478336 \tabularnewline
57 & 40 & 41.7676331276048 & -1.76763312760479 \tabularnewline
58 & 29 & 41.1221705804663 & -12.1221705804663 \tabularnewline
59 & 37 & 36.6956824266049 & 0.304317573395132 \tabularnewline
60 & 51 & 36.8068059357738 & 14.1931940642262 \tabularnewline
61 & 20 & 41.9895415666344 & -21.9895415666344 \tabularnewline
62 & 28 & 33.9599197586062 & -5.9599197586062 \tabularnewline
63 & 13 & 31.7836169228792 & -18.7836169228792 \tabularnewline
64 & 22 & 24.92465901234 & -2.92465901233998 \tabularnewline
65 & 25 & 23.856701059903 & 1.14329894009703 \tabularnewline
66 & 13 & 24.2741839835319 & -11.2741839835319 \tabularnewline
67 & 16 & 20.1573435615719 & -4.15734356157191 \tabularnewline
68 & 13 & 18.6392629583767 & -5.63926295837666 \tabularnewline
69 & 16 & 16.5800500050473 & -0.580050005047347 \tabularnewline
70 & 17 & 16.3682410341254 & 0.631758965874639 \tabularnewline
71 & 9 & 16.5989318629647 & -7.59893186296472 \tabularnewline
72 & 17 & 13.8241332697478 & 3.17586673025219 \tabularnewline
73 & 25 & 14.9838213277889 & 10.0161786722111 \tabularnewline
74 & 14 & 18.6412930606934 & -4.64129306069337 \tabularnewline
75 & 8 & 16.9464952012354 & -8.94649520123543 \tabularnewline
76 & 7 & 13.6796252323653 & -6.67962523236528 \tabularnewline
77 & 10 & 11.2405173376997 & -1.24051733769967 \tabularnewline
78 & 7 & 10.7875344941126 & -3.78753449411259 \tabularnewline
79 & 10 & 9.40449203820566 & 0.59550796179434 \tabularnewline
80 & 3 & 9.62194558094498 & -6.62194558094498 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=198417&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]2[/C][C]30[/C][C]37[/C][C]-7[/C][/ROW]
[ROW][C]3[/C][C]47[/C][C]34.4439052089434[/C][C]12.5560947910566[/C][/ROW]
[ROW][C]4[/C][C]35[/C][C]39.0288435648624[/C][C]-4.02884356486239[/C][/ROW]
[ROW][C]5[/C][C]30[/C][C]37.5576855577014[/C][C]-7.55768555770143[/C][/ROW]
[ROW][C]6[/C][C]43[/C][C]34.7979483167751[/C][C]8.20205168322494[/C][/ROW]
[ROW][C]7[/C][C]82[/C][C]37.7929799715563[/C][C]44.2070200284437[/C][/ROW]
[ROW][C]8[/C][C]40[/C][C]53.9354562033907[/C][C]-13.9354562033907[/C][/ROW]
[ROW][C]9[/C][C]47[/C][C]48.8468352016072[/C][C]-1.84683520160717[/C][/ROW]
[ROW][C]10[/C][C]19[/C][C]48.1724515103546[/C][C]-29.1724515103546[/C][/ROW]
[ROW][C]11[/C][C]52[/C][C]37.5199441749304[/C][C]14.4800558250696[/C][/ROW]
[ROW][C]12[/C][C]136[/C][C]42.8074292133118[/C][C]93.1925707866882[/C][/ROW]
[ROW][C]13[/C][C]80[/C][C]76.8372927494589[/C][C]3.1627072505411[/C][/ROW]
[ROW][C]14[/C][C]42[/C][C]77.9921755392796[/C][C]-35.9921755392796[/C][/ROW]
[ROW][C]15[/C][C]54[/C][C]64.8494023371727[/C][C]-10.8494023371727[/C][/ROW]
[ROW][C]16[/C][C]66[/C][C]60.8876736514406[/C][C]5.11232634855941[/C][/ROW]
[ROW][C]17[/C][C]81[/C][C]62.7544723299741[/C][C]18.2455276700259[/C][/ROW]
[ROW][C]18[/C][C]63[/C][C]69.4169435067502[/C][C]-6.41694350675019[/C][/ROW]
[ROW][C]19[/C][C]137[/C][C]67.0737555250204[/C][C]69.9262444749796[/C][/ROW]
[ROW][C]20[/C][C]72[/C][C]92.6077711336843[/C][C]-20.6077711336843[/C][/ROW]
[ROW][C]21[/C][C]107[/C][C]85.0827116408132[/C][C]21.9172883591868[/C][/ROW]
[ROW][C]22[/C][C]58[/C][C]93.0859497278137[/C][C]-35.0859497278137[/C][/ROW]
[ROW][C]23[/C][C]36[/C][C]80.2740906794509[/C][C]-44.2740906794509[/C][/ROW]
[ROW][C]24[/C][C]52[/C][C]64.1071231702347[/C][C]-12.1071231702347[/C][/ROW]
[ROW][C]25[/C][C]79[/C][C]59.6861296745036[/C][C]19.3138703254964[/C][/ROW]
[ROW][C]26[/C][C]77[/C][C]66.7387130079528[/C][C]10.2612869920472[/C][/ROW]
[ROW][C]27[/C][C]54[/C][C]70.4856876122255[/C][C]-16.4856876122255[/C][/ROW]
[ROW][C]28[/C][C]84[/C][C]64.4658332932832[/C][C]19.5341667067168[/C][/ROW]
[ROW][C]29[/C][C]48[/C][C]71.5988592599504[/C][C]-23.5988592599504[/C][/ROW]
[ROW][C]30[/C][C]96[/C][C]62.9815847986307[/C][C]33.0184152013693[/C][/ROW]
[ROW][C]31[/C][C]83[/C][C]75.0384703850829[/C][C]7.96152961491713[/C][/ROW]
[ROW][C]32[/C][C]66[/C][C]77.9456738675876[/C][C]-11.9456738675876[/C][/ROW]
[ROW][C]33[/C][C]61[/C][C]73.5836346177873[/C][C]-12.5836346177873[/C][/ROW]
[ROW][C]34[/C][C]53[/C][C]68.9886399179179[/C][C]-15.9886399179179[/C][/ROW]
[ROW][C]35[/C][C]30[/C][C]63.1502857450222[/C][C]-33.1502857450222[/C][/ROW]
[ROW][C]36[/C][C]74[/C][C]51.0452467857522[/C][C]22.9547532142478[/C][/ROW]
[ROW][C]37[/C][C]69[/C][C]59.4273218030278[/C][C]9.57267819697222[/C][/ROW]
[ROW][C]38[/C][C]59[/C][C]62.9228464995624[/C][C]-3.92284649956236[/C][/ROW]
[ROW][C]39[/C][C]42[/C][C]61.4903939990415[/C][C]-19.4903939990415[/C][/ROW]
[ROW][C]40[/C][C]65[/C][C]54.3733519166713[/C][C]10.6266480833287[/C][/ROW]
[ROW][C]41[/C][C]70[/C][C]58.2537404612696[/C][C]11.7462595387304[/C][/ROW]
[ROW][C]42[/C][C]100[/C][C]62.5429622928908[/C][C]37.4570377071092[/C][/ROW]
[ROW][C]43[/C][C]63[/C][C]76.220639288827[/C][C]-13.220639288827[/C][/ROW]
[ROW][C]44[/C][C]105[/C][C]71.3930382573114[/C][C]33.6069617426886[/C][/ROW]
[ROW][C]45[/C][C]82[/C][C]83.6648353792722[/C][C]-1.66483537927222[/C][/ROW]
[ROW][C]46[/C][C]81[/C][C]83.0569100877116[/C][C]-2.05691008771157[/C][/ROW]
[ROW][C]47[/C][C]75[/C][C]82.3058162075871[/C][C]-7.30581620758709[/C][/ROW]
[ROW][C]48[/C][C]102[/C][C]79.638050671497[/C][C]22.361949328503[/C][/ROW]
[ROW][C]49[/C][C]121[/C][C]87.8036595567054[/C][C]33.1963404432946[/C][/ROW]
[ROW][C]50[/C][C]98[/C][C]99.9255156837408[/C][C]-1.92551568374081[/C][/ROW]
[ROW][C]51[/C][C]76[/C][C]99.2224013109826[/C][C]-23.2224013109826[/C][/ROW]
[ROW][C]52[/C][C]77[/C][C]90.7425928785784[/C][C]-13.7425928785784[/C][/ROW]
[ROW][C]53[/C][C]63[/C][C]85.7243971539289[/C][C]-22.7243971539289[/C][/ROW]
[ROW][C]54[/C][C]37[/C][C]77.4264381260632[/C][C]-40.4264381260632[/C][/ROW]
[ROW][C]55[/C][C]35[/C][C]62.664465566777[/C][C]-27.664465566777[/C][/ROW]
[ROW][C]56[/C][C]23[/C][C]52.5626089478336[/C][C]-29.5626089478336[/C][/ROW]
[ROW][C]57[/C][C]40[/C][C]41.7676331276048[/C][C]-1.76763312760479[/C][/ROW]
[ROW][C]58[/C][C]29[/C][C]41.1221705804663[/C][C]-12.1221705804663[/C][/ROW]
[ROW][C]59[/C][C]37[/C][C]36.6956824266049[/C][C]0.304317573395132[/C][/ROW]
[ROW][C]60[/C][C]51[/C][C]36.8068059357738[/C][C]14.1931940642262[/C][/ROW]
[ROW][C]61[/C][C]20[/C][C]41.9895415666344[/C][C]-21.9895415666344[/C][/ROW]
[ROW][C]62[/C][C]28[/C][C]33.9599197586062[/C][C]-5.9599197586062[/C][/ROW]
[ROW][C]63[/C][C]13[/C][C]31.7836169228792[/C][C]-18.7836169228792[/C][/ROW]
[ROW][C]64[/C][C]22[/C][C]24.92465901234[/C][C]-2.92465901233998[/C][/ROW]
[ROW][C]65[/C][C]25[/C][C]23.856701059903[/C][C]1.14329894009703[/C][/ROW]
[ROW][C]66[/C][C]13[/C][C]24.2741839835319[/C][C]-11.2741839835319[/C][/ROW]
[ROW][C]67[/C][C]16[/C][C]20.1573435615719[/C][C]-4.15734356157191[/C][/ROW]
[ROW][C]68[/C][C]13[/C][C]18.6392629583767[/C][C]-5.63926295837666[/C][/ROW]
[ROW][C]69[/C][C]16[/C][C]16.5800500050473[/C][C]-0.580050005047347[/C][/ROW]
[ROW][C]70[/C][C]17[/C][C]16.3682410341254[/C][C]0.631758965874639[/C][/ROW]
[ROW][C]71[/C][C]9[/C][C]16.5989318629647[/C][C]-7.59893186296472[/C][/ROW]
[ROW][C]72[/C][C]17[/C][C]13.8241332697478[/C][C]3.17586673025219[/C][/ROW]
[ROW][C]73[/C][C]25[/C][C]14.9838213277889[/C][C]10.0161786722111[/C][/ROW]
[ROW][C]74[/C][C]14[/C][C]18.6412930606934[/C][C]-4.64129306069337[/C][/ROW]
[ROW][C]75[/C][C]8[/C][C]16.9464952012354[/C][C]-8.94649520123543[/C][/ROW]
[ROW][C]76[/C][C]7[/C][C]13.6796252323653[/C][C]-6.67962523236528[/C][/ROW]
[ROW][C]77[/C][C]10[/C][C]11.2405173376997[/C][C]-1.24051733769967[/C][/ROW]
[ROW][C]78[/C][C]7[/C][C]10.7875344941126[/C][C]-3.78753449411259[/C][/ROW]
[ROW][C]79[/C][C]10[/C][C]9.40449203820566[/C][C]0.59550796179434[/C][/ROW]
[ROW][C]80[/C][C]3[/C][C]9.62194558094498[/C][C]-6.62194558094498[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=198417&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=198417&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
23037-7
34734.443905208943412.5560947910566
43539.0288435648624-4.02884356486239
53037.5576855577014-7.55768555770143
64334.79794831677518.20205168322494
78237.792979971556344.2070200284437
84053.9354562033907-13.9354562033907
94748.8468352016072-1.84683520160717
101948.1724515103546-29.1724515103546
115237.519944174930414.4800558250696
1213642.807429213311893.1925707866882
138076.83729274945893.1627072505411
144277.9921755392796-35.9921755392796
155464.8494023371727-10.8494023371727
166660.88767365144065.11232634855941
178162.754472329974118.2455276700259
186369.4169435067502-6.41694350675019
1913767.073755525020469.9262444749796
207292.6077711336843-20.6077711336843
2110785.082711640813221.9172883591868
225893.0859497278137-35.0859497278137
233680.2740906794509-44.2740906794509
245264.1071231702347-12.1071231702347
257959.686129674503619.3138703254964
267766.738713007952810.2612869920472
275470.4856876122255-16.4856876122255
288464.465833293283219.5341667067168
294871.5988592599504-23.5988592599504
309662.981584798630733.0184152013693
318375.03847038508297.96152961491713
326677.9456738675876-11.9456738675876
336173.5836346177873-12.5836346177873
345368.9886399179179-15.9886399179179
353063.1502857450222-33.1502857450222
367451.045246785752222.9547532142478
376959.42732180302789.57267819697222
385962.9228464995624-3.92284649956236
394261.4903939990415-19.4903939990415
406554.373351916671310.6266480833287
417058.253740461269611.7462595387304
4210062.542962292890837.4570377071092
436376.220639288827-13.220639288827
4410571.393038257311433.6069617426886
458283.6648353792722-1.66483537927222
468183.0569100877116-2.05691008771157
477582.3058162075871-7.30581620758709
4810279.63805067149722.361949328503
4912187.803659556705433.1963404432946
509899.9255156837408-1.92551568374081
517699.2224013109826-23.2224013109826
527790.7425928785784-13.7425928785784
536385.7243971539289-22.7243971539289
543777.4264381260632-40.4264381260632
553562.664465566777-27.664465566777
562352.5626089478336-29.5626089478336
574041.7676331276048-1.76763312760479
582941.1221705804663-12.1221705804663
593736.69568242660490.304317573395132
605136.806805935773814.1931940642262
612041.9895415666344-21.9895415666344
622833.9599197586062-5.9599197586062
631331.7836169228792-18.7836169228792
642224.92465901234-2.92465901233998
652523.8567010599031.14329894009703
661324.2741839835319-11.2741839835319
671620.1573435615719-4.15734356157191
681318.6392629583767-5.63926295837666
691616.5800500050473-0.580050005047347
701716.36824103412540.631758965874639
71916.5989318629647-7.59893186296472
721713.82413326974783.17586673025219
732514.983821327788910.0161786722111
741418.6412930606934-4.64129306069337
75816.9464952012354-8.94649520123543
76713.6796252323653-6.67962523236528
771011.2405173376997-1.24051733769967
78710.7875344941126-3.78753449411259
79109.404492038205660.59550796179434
8039.62194558094498-6.62194558094498







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
817.20389978007156-36.933000232125451.3407997922685
827.20389978007156-39.783539906719254.1913394668624
837.20389978007156-42.470772176096756.8785717362399
847.20389978007156-45.019912600738659.4277121608818
857.20389978007156-47.4502869325661.8580864927031
867.20389978007156-49.777094163982564.1848937241256
877.20389978007156-52.012544021337666.4203435814808
887.20389978007156-54.166620521768768.5744200819118
897.20389978007156-56.247611689330970.6554112494741
907.20389978007156-58.262487422712572.6702869828556
917.20389978007156-60.217175552631274.6249751127743
927.20389978007156-62.116767734394276.5245672945373

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
81 & 7.20389978007156 & -36.9330002321254 & 51.3407997922685 \tabularnewline
82 & 7.20389978007156 & -39.7835399067192 & 54.1913394668624 \tabularnewline
83 & 7.20389978007156 & -42.4707721760967 & 56.8785717362399 \tabularnewline
84 & 7.20389978007156 & -45.0199126007386 & 59.4277121608818 \tabularnewline
85 & 7.20389978007156 & -47.45028693256 & 61.8580864927031 \tabularnewline
86 & 7.20389978007156 & -49.7770941639825 & 64.1848937241256 \tabularnewline
87 & 7.20389978007156 & -52.0125440213376 & 66.4203435814808 \tabularnewline
88 & 7.20389978007156 & -54.1666205217687 & 68.5744200819118 \tabularnewline
89 & 7.20389978007156 & -56.2476116893309 & 70.6554112494741 \tabularnewline
90 & 7.20389978007156 & -58.2624874227125 & 72.6702869828556 \tabularnewline
91 & 7.20389978007156 & -60.2171755526312 & 74.6249751127743 \tabularnewline
92 & 7.20389978007156 & -62.1167677343942 & 76.5245672945373 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=198417&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]81[/C][C]7.20389978007156[/C][C]-36.9330002321254[/C][C]51.3407997922685[/C][/ROW]
[ROW][C]82[/C][C]7.20389978007156[/C][C]-39.7835399067192[/C][C]54.1913394668624[/C][/ROW]
[ROW][C]83[/C][C]7.20389978007156[/C][C]-42.4707721760967[/C][C]56.8785717362399[/C][/ROW]
[ROW][C]84[/C][C]7.20389978007156[/C][C]-45.0199126007386[/C][C]59.4277121608818[/C][/ROW]
[ROW][C]85[/C][C]7.20389978007156[/C][C]-47.45028693256[/C][C]61.8580864927031[/C][/ROW]
[ROW][C]86[/C][C]7.20389978007156[/C][C]-49.7770941639825[/C][C]64.1848937241256[/C][/ROW]
[ROW][C]87[/C][C]7.20389978007156[/C][C]-52.0125440213376[/C][C]66.4203435814808[/C][/ROW]
[ROW][C]88[/C][C]7.20389978007156[/C][C]-54.1666205217687[/C][C]68.5744200819118[/C][/ROW]
[ROW][C]89[/C][C]7.20389978007156[/C][C]-56.2476116893309[/C][C]70.6554112494741[/C][/ROW]
[ROW][C]90[/C][C]7.20389978007156[/C][C]-58.2624874227125[/C][C]72.6702869828556[/C][/ROW]
[ROW][C]91[/C][C]7.20389978007156[/C][C]-60.2171755526312[/C][C]74.6249751127743[/C][/ROW]
[ROW][C]92[/C][C]7.20389978007156[/C][C]-62.1167677343942[/C][C]76.5245672945373[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=198417&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=198417&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
817.20389978007156-36.933000232125451.3407997922685
827.20389978007156-39.783539906719254.1913394668624
837.20389978007156-42.470772176096756.8785717362399
847.20389978007156-45.019912600738659.4277121608818
857.20389978007156-47.4502869325661.8580864927031
867.20389978007156-49.777094163982564.1848937241256
877.20389978007156-52.012544021337666.4203435814808
887.20389978007156-54.166620521768768.5744200819118
897.20389978007156-56.247611689330970.6554112494741
907.20389978007156-58.262487422712572.6702869828556
917.20389978007156-60.217175552631274.6249751127743
927.20389978007156-62.116767734394276.5245672945373



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