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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 18 May 2013 11:16:35 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/May/18/t1368890294msohdoh1zw0itku.htm/, Retrieved Mon, 29 Apr 2024 00:46:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=209065, Retrieved Mon, 29 Apr 2024 00:46:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact103
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Inschrijving nieu...] [2013-05-18 15:16:35] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
99,23
101,14
100,8
98,93
100,97
101,69
102,14
102,52
103,4
105,83
104,35
106,61
105,63
106,73
106,19
107,26
106,27
107,45
107,63
107,45
107,74
108,15
108,99
108,83
110,78
110,66
108,51
108,29
109,33
107,06
108,02
109,43
109,85
110,5
109,9
110,92
108,36
109,01
108,03
106,28
106,6
108,06
107,42
107,58
107,59
109,66
107,85
110,74
108,8
109,18
108,38
108,59
109,52
108,71
109,78
109,77
109,34
111,86
110,74
110,67
111,36
112,21
110,2
110,99
110,43
110,72
111,19
111,52
111,99
111,65
114,45
115,58




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=209065&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=209065&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=209065&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.69078213740303
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.69078213740303 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=209065&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]0.69078213740303[/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=209065&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=209065&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
alpha0.69078213740303
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2101.1499.231.91
3100.8100.549393882440.25060611756021
498.93100.722508111974-1.7925081119743
5100.9799.48427552707241.48572447292757
6101.69100.5105874540731.17941254592667
7102.14101.3253045734280.814695426571504
8102.52101.8880816215280.631918378471966
9103.4102.3245995496731.07540045032685
10105.83103.0674669713142.76253302868588
11104.35104.975775441516-0.625775441516225
12106.61104.5435009444912.06649905550869
13105.63105.971001578997-0.341001578996952
14106.73105.73544377940.994556220600373
15106.19106.422465451233-0.232465451233438
16107.26106.2618824699580.998117530041966
17106.27106.95136423074-0.68136423073986
18107.45106.4806899910790.969310008920601
19107.63107.1502720308480.479727969152265
20107.45107.481659542751-0.0316595427507451
21107.74107.459789696140.280210303859803
22108.15107.6533539687630.496646031237191
23108.99107.9964281757540.993571824246416
24108.83108.682769844170.147230155830059
25110.78108.7844738059041.99552619409559
26110.66110.1629476555050.497052344494506
27108.51110.506302536437-1.99630253643659
28108.29109.127292403414-0.837292403413826
29109.33108.5489057673520.781094232647689
30107.06109.088471710894-2.02847171089385
31108.02107.6872396867810.332760313218984
32109.43107.9171045671891.51289543281068
33109.85108.9621857079340.887814292066423
34110.5109.5754719622240.924528037775829
35109.9110.214119416248-0.314119416247976
36110.92109.9971313344920.922868665507593
37108.36110.634632523794-2.27463252379403
38109.01109.063357007201-0.0533570072011287
39108.03109.026498939721-0.996498939721306
40106.28108.338135272221-2.05813527222077
41106.6106.916412189812-0.316412189811544
42108.06106.6978403010331.36215969896685
43107.42107.63879588937-0.218795889369744
44107.58107.4876555972560.0923444027440752
45107.59107.5514454611610.0385545388393211
46109.66107.5780782479072.08192175209329
47107.85109.016232605724-1.16623260572358
48110.74108.2106199536332.52938004636727
49108.8109.957870508367-1.15787050836688
50109.18109.1580342437610.0219657562387283
51108.38109.173207795806-0.793207795805543
52108.59108.625274019214-0.035274019214242
53109.52108.6009073568270.919092643173357
54108.71109.235800137349-0.525800137349336
55109.78108.8725867946240.907413205375647
56109.77109.4994116281410.270588371858523
57109.34109.68632924201-0.346329242010313
58111.86109.4470911879692.41290881203074
59110.74111.113885494502-0.37388549450246
60110.67110.855612073466-0.185612073466061
61111.36110.7273945686290.632605431370635
62112.21111.1643871006441.04561289935566
63110.2111.886677814157-1.68667781415741
64110.99110.7215509085830.268449091416514
65110.43110.906990745736-0.476990745736074
66110.72110.5774940588750.142505941124952
67111.19110.6759346174780.51406538252202
68111.52111.0310418011810.488958198818551
69111.99111.3688053908620.62119460913793
70111.65111.797915530706-0.147915530705603
71114.45111.695738124252.75426187575032
72115.58113.5983330297481.98166697025184

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 101.14 & 99.23 & 1.91 \tabularnewline
3 & 100.8 & 100.54939388244 & 0.25060611756021 \tabularnewline
4 & 98.93 & 100.722508111974 & -1.7925081119743 \tabularnewline
5 & 100.97 & 99.4842755270724 & 1.48572447292757 \tabularnewline
6 & 101.69 & 100.510587454073 & 1.17941254592667 \tabularnewline
7 & 102.14 & 101.325304573428 & 0.814695426571504 \tabularnewline
8 & 102.52 & 101.888081621528 & 0.631918378471966 \tabularnewline
9 & 103.4 & 102.324599549673 & 1.07540045032685 \tabularnewline
10 & 105.83 & 103.067466971314 & 2.76253302868588 \tabularnewline
11 & 104.35 & 104.975775441516 & -0.625775441516225 \tabularnewline
12 & 106.61 & 104.543500944491 & 2.06649905550869 \tabularnewline
13 & 105.63 & 105.971001578997 & -0.341001578996952 \tabularnewline
14 & 106.73 & 105.7354437794 & 0.994556220600373 \tabularnewline
15 & 106.19 & 106.422465451233 & -0.232465451233438 \tabularnewline
16 & 107.26 & 106.261882469958 & 0.998117530041966 \tabularnewline
17 & 106.27 & 106.95136423074 & -0.68136423073986 \tabularnewline
18 & 107.45 & 106.480689991079 & 0.969310008920601 \tabularnewline
19 & 107.63 & 107.150272030848 & 0.479727969152265 \tabularnewline
20 & 107.45 & 107.481659542751 & -0.0316595427507451 \tabularnewline
21 & 107.74 & 107.45978969614 & 0.280210303859803 \tabularnewline
22 & 108.15 & 107.653353968763 & 0.496646031237191 \tabularnewline
23 & 108.99 & 107.996428175754 & 0.993571824246416 \tabularnewline
24 & 108.83 & 108.68276984417 & 0.147230155830059 \tabularnewline
25 & 110.78 & 108.784473805904 & 1.99552619409559 \tabularnewline
26 & 110.66 & 110.162947655505 & 0.497052344494506 \tabularnewline
27 & 108.51 & 110.506302536437 & -1.99630253643659 \tabularnewline
28 & 108.29 & 109.127292403414 & -0.837292403413826 \tabularnewline
29 & 109.33 & 108.548905767352 & 0.781094232647689 \tabularnewline
30 & 107.06 & 109.088471710894 & -2.02847171089385 \tabularnewline
31 & 108.02 & 107.687239686781 & 0.332760313218984 \tabularnewline
32 & 109.43 & 107.917104567189 & 1.51289543281068 \tabularnewline
33 & 109.85 & 108.962185707934 & 0.887814292066423 \tabularnewline
34 & 110.5 & 109.575471962224 & 0.924528037775829 \tabularnewline
35 & 109.9 & 110.214119416248 & -0.314119416247976 \tabularnewline
36 & 110.92 & 109.997131334492 & 0.922868665507593 \tabularnewline
37 & 108.36 & 110.634632523794 & -2.27463252379403 \tabularnewline
38 & 109.01 & 109.063357007201 & -0.0533570072011287 \tabularnewline
39 & 108.03 & 109.026498939721 & -0.996498939721306 \tabularnewline
40 & 106.28 & 108.338135272221 & -2.05813527222077 \tabularnewline
41 & 106.6 & 106.916412189812 & -0.316412189811544 \tabularnewline
42 & 108.06 & 106.697840301033 & 1.36215969896685 \tabularnewline
43 & 107.42 & 107.63879588937 & -0.218795889369744 \tabularnewline
44 & 107.58 & 107.487655597256 & 0.0923444027440752 \tabularnewline
45 & 107.59 & 107.551445461161 & 0.0385545388393211 \tabularnewline
46 & 109.66 & 107.578078247907 & 2.08192175209329 \tabularnewline
47 & 107.85 & 109.016232605724 & -1.16623260572358 \tabularnewline
48 & 110.74 & 108.210619953633 & 2.52938004636727 \tabularnewline
49 & 108.8 & 109.957870508367 & -1.15787050836688 \tabularnewline
50 & 109.18 & 109.158034243761 & 0.0219657562387283 \tabularnewline
51 & 108.38 & 109.173207795806 & -0.793207795805543 \tabularnewline
52 & 108.59 & 108.625274019214 & -0.035274019214242 \tabularnewline
53 & 109.52 & 108.600907356827 & 0.919092643173357 \tabularnewline
54 & 108.71 & 109.235800137349 & -0.525800137349336 \tabularnewline
55 & 109.78 & 108.872586794624 & 0.907413205375647 \tabularnewline
56 & 109.77 & 109.499411628141 & 0.270588371858523 \tabularnewline
57 & 109.34 & 109.68632924201 & -0.346329242010313 \tabularnewline
58 & 111.86 & 109.447091187969 & 2.41290881203074 \tabularnewline
59 & 110.74 & 111.113885494502 & -0.37388549450246 \tabularnewline
60 & 110.67 & 110.855612073466 & -0.185612073466061 \tabularnewline
61 & 111.36 & 110.727394568629 & 0.632605431370635 \tabularnewline
62 & 112.21 & 111.164387100644 & 1.04561289935566 \tabularnewline
63 & 110.2 & 111.886677814157 & -1.68667781415741 \tabularnewline
64 & 110.99 & 110.721550908583 & 0.268449091416514 \tabularnewline
65 & 110.43 & 110.906990745736 & -0.476990745736074 \tabularnewline
66 & 110.72 & 110.577494058875 & 0.142505941124952 \tabularnewline
67 & 111.19 & 110.675934617478 & 0.51406538252202 \tabularnewline
68 & 111.52 & 111.031041801181 & 0.488958198818551 \tabularnewline
69 & 111.99 & 111.368805390862 & 0.62119460913793 \tabularnewline
70 & 111.65 & 111.797915530706 & -0.147915530705603 \tabularnewline
71 & 114.45 & 111.69573812425 & 2.75426187575032 \tabularnewline
72 & 115.58 & 113.598333029748 & 1.98166697025184 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=209065&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]101.14[/C][C]99.23[/C][C]1.91[/C][/ROW]
[ROW][C]3[/C][C]100.8[/C][C]100.54939388244[/C][C]0.25060611756021[/C][/ROW]
[ROW][C]4[/C][C]98.93[/C][C]100.722508111974[/C][C]-1.7925081119743[/C][/ROW]
[ROW][C]5[/C][C]100.97[/C][C]99.4842755270724[/C][C]1.48572447292757[/C][/ROW]
[ROW][C]6[/C][C]101.69[/C][C]100.510587454073[/C][C]1.17941254592667[/C][/ROW]
[ROW][C]7[/C][C]102.14[/C][C]101.325304573428[/C][C]0.814695426571504[/C][/ROW]
[ROW][C]8[/C][C]102.52[/C][C]101.888081621528[/C][C]0.631918378471966[/C][/ROW]
[ROW][C]9[/C][C]103.4[/C][C]102.324599549673[/C][C]1.07540045032685[/C][/ROW]
[ROW][C]10[/C][C]105.83[/C][C]103.067466971314[/C][C]2.76253302868588[/C][/ROW]
[ROW][C]11[/C][C]104.35[/C][C]104.975775441516[/C][C]-0.625775441516225[/C][/ROW]
[ROW][C]12[/C][C]106.61[/C][C]104.543500944491[/C][C]2.06649905550869[/C][/ROW]
[ROW][C]13[/C][C]105.63[/C][C]105.971001578997[/C][C]-0.341001578996952[/C][/ROW]
[ROW][C]14[/C][C]106.73[/C][C]105.7354437794[/C][C]0.994556220600373[/C][/ROW]
[ROW][C]15[/C][C]106.19[/C][C]106.422465451233[/C][C]-0.232465451233438[/C][/ROW]
[ROW][C]16[/C][C]107.26[/C][C]106.261882469958[/C][C]0.998117530041966[/C][/ROW]
[ROW][C]17[/C][C]106.27[/C][C]106.95136423074[/C][C]-0.68136423073986[/C][/ROW]
[ROW][C]18[/C][C]107.45[/C][C]106.480689991079[/C][C]0.969310008920601[/C][/ROW]
[ROW][C]19[/C][C]107.63[/C][C]107.150272030848[/C][C]0.479727969152265[/C][/ROW]
[ROW][C]20[/C][C]107.45[/C][C]107.481659542751[/C][C]-0.0316595427507451[/C][/ROW]
[ROW][C]21[/C][C]107.74[/C][C]107.45978969614[/C][C]0.280210303859803[/C][/ROW]
[ROW][C]22[/C][C]108.15[/C][C]107.653353968763[/C][C]0.496646031237191[/C][/ROW]
[ROW][C]23[/C][C]108.99[/C][C]107.996428175754[/C][C]0.993571824246416[/C][/ROW]
[ROW][C]24[/C][C]108.83[/C][C]108.68276984417[/C][C]0.147230155830059[/C][/ROW]
[ROW][C]25[/C][C]110.78[/C][C]108.784473805904[/C][C]1.99552619409559[/C][/ROW]
[ROW][C]26[/C][C]110.66[/C][C]110.162947655505[/C][C]0.497052344494506[/C][/ROW]
[ROW][C]27[/C][C]108.51[/C][C]110.506302536437[/C][C]-1.99630253643659[/C][/ROW]
[ROW][C]28[/C][C]108.29[/C][C]109.127292403414[/C][C]-0.837292403413826[/C][/ROW]
[ROW][C]29[/C][C]109.33[/C][C]108.548905767352[/C][C]0.781094232647689[/C][/ROW]
[ROW][C]30[/C][C]107.06[/C][C]109.088471710894[/C][C]-2.02847171089385[/C][/ROW]
[ROW][C]31[/C][C]108.02[/C][C]107.687239686781[/C][C]0.332760313218984[/C][/ROW]
[ROW][C]32[/C][C]109.43[/C][C]107.917104567189[/C][C]1.51289543281068[/C][/ROW]
[ROW][C]33[/C][C]109.85[/C][C]108.962185707934[/C][C]0.887814292066423[/C][/ROW]
[ROW][C]34[/C][C]110.5[/C][C]109.575471962224[/C][C]0.924528037775829[/C][/ROW]
[ROW][C]35[/C][C]109.9[/C][C]110.214119416248[/C][C]-0.314119416247976[/C][/ROW]
[ROW][C]36[/C][C]110.92[/C][C]109.997131334492[/C][C]0.922868665507593[/C][/ROW]
[ROW][C]37[/C][C]108.36[/C][C]110.634632523794[/C][C]-2.27463252379403[/C][/ROW]
[ROW][C]38[/C][C]109.01[/C][C]109.063357007201[/C][C]-0.0533570072011287[/C][/ROW]
[ROW][C]39[/C][C]108.03[/C][C]109.026498939721[/C][C]-0.996498939721306[/C][/ROW]
[ROW][C]40[/C][C]106.28[/C][C]108.338135272221[/C][C]-2.05813527222077[/C][/ROW]
[ROW][C]41[/C][C]106.6[/C][C]106.916412189812[/C][C]-0.316412189811544[/C][/ROW]
[ROW][C]42[/C][C]108.06[/C][C]106.697840301033[/C][C]1.36215969896685[/C][/ROW]
[ROW][C]43[/C][C]107.42[/C][C]107.63879588937[/C][C]-0.218795889369744[/C][/ROW]
[ROW][C]44[/C][C]107.58[/C][C]107.487655597256[/C][C]0.0923444027440752[/C][/ROW]
[ROW][C]45[/C][C]107.59[/C][C]107.551445461161[/C][C]0.0385545388393211[/C][/ROW]
[ROW][C]46[/C][C]109.66[/C][C]107.578078247907[/C][C]2.08192175209329[/C][/ROW]
[ROW][C]47[/C][C]107.85[/C][C]109.016232605724[/C][C]-1.16623260572358[/C][/ROW]
[ROW][C]48[/C][C]110.74[/C][C]108.210619953633[/C][C]2.52938004636727[/C][/ROW]
[ROW][C]49[/C][C]108.8[/C][C]109.957870508367[/C][C]-1.15787050836688[/C][/ROW]
[ROW][C]50[/C][C]109.18[/C][C]109.158034243761[/C][C]0.0219657562387283[/C][/ROW]
[ROW][C]51[/C][C]108.38[/C][C]109.173207795806[/C][C]-0.793207795805543[/C][/ROW]
[ROW][C]52[/C][C]108.59[/C][C]108.625274019214[/C][C]-0.035274019214242[/C][/ROW]
[ROW][C]53[/C][C]109.52[/C][C]108.600907356827[/C][C]0.919092643173357[/C][/ROW]
[ROW][C]54[/C][C]108.71[/C][C]109.235800137349[/C][C]-0.525800137349336[/C][/ROW]
[ROW][C]55[/C][C]109.78[/C][C]108.872586794624[/C][C]0.907413205375647[/C][/ROW]
[ROW][C]56[/C][C]109.77[/C][C]109.499411628141[/C][C]0.270588371858523[/C][/ROW]
[ROW][C]57[/C][C]109.34[/C][C]109.68632924201[/C][C]-0.346329242010313[/C][/ROW]
[ROW][C]58[/C][C]111.86[/C][C]109.447091187969[/C][C]2.41290881203074[/C][/ROW]
[ROW][C]59[/C][C]110.74[/C][C]111.113885494502[/C][C]-0.37388549450246[/C][/ROW]
[ROW][C]60[/C][C]110.67[/C][C]110.855612073466[/C][C]-0.185612073466061[/C][/ROW]
[ROW][C]61[/C][C]111.36[/C][C]110.727394568629[/C][C]0.632605431370635[/C][/ROW]
[ROW][C]62[/C][C]112.21[/C][C]111.164387100644[/C][C]1.04561289935566[/C][/ROW]
[ROW][C]63[/C][C]110.2[/C][C]111.886677814157[/C][C]-1.68667781415741[/C][/ROW]
[ROW][C]64[/C][C]110.99[/C][C]110.721550908583[/C][C]0.268449091416514[/C][/ROW]
[ROW][C]65[/C][C]110.43[/C][C]110.906990745736[/C][C]-0.476990745736074[/C][/ROW]
[ROW][C]66[/C][C]110.72[/C][C]110.577494058875[/C][C]0.142505941124952[/C][/ROW]
[ROW][C]67[/C][C]111.19[/C][C]110.675934617478[/C][C]0.51406538252202[/C][/ROW]
[ROW][C]68[/C][C]111.52[/C][C]111.031041801181[/C][C]0.488958198818551[/C][/ROW]
[ROW][C]69[/C][C]111.99[/C][C]111.368805390862[/C][C]0.62119460913793[/C][/ROW]
[ROW][C]70[/C][C]111.65[/C][C]111.797915530706[/C][C]-0.147915530705603[/C][/ROW]
[ROW][C]71[/C][C]114.45[/C][C]111.69573812425[/C][C]2.75426187575032[/C][/ROW]
[ROW][C]72[/C][C]115.58[/C][C]113.598333029748[/C][C]1.98166697025184[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=209065&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=209065&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
2101.1499.231.91
3100.8100.549393882440.25060611756021
498.93100.722508111974-1.7925081119743
5100.9799.48427552707241.48572447292757
6101.69100.5105874540731.17941254592667
7102.14101.3253045734280.814695426571504
8102.52101.8880816215280.631918378471966
9103.4102.3245995496731.07540045032685
10105.83103.0674669713142.76253302868588
11104.35104.975775441516-0.625775441516225
12106.61104.5435009444912.06649905550869
13105.63105.971001578997-0.341001578996952
14106.73105.73544377940.994556220600373
15106.19106.422465451233-0.232465451233438
16107.26106.2618824699580.998117530041966
17106.27106.95136423074-0.68136423073986
18107.45106.4806899910790.969310008920601
19107.63107.1502720308480.479727969152265
20107.45107.481659542751-0.0316595427507451
21107.74107.459789696140.280210303859803
22108.15107.6533539687630.496646031237191
23108.99107.9964281757540.993571824246416
24108.83108.682769844170.147230155830059
25110.78108.7844738059041.99552619409559
26110.66110.1629476555050.497052344494506
27108.51110.506302536437-1.99630253643659
28108.29109.127292403414-0.837292403413826
29109.33108.5489057673520.781094232647689
30107.06109.088471710894-2.02847171089385
31108.02107.6872396867810.332760313218984
32109.43107.9171045671891.51289543281068
33109.85108.9621857079340.887814292066423
34110.5109.5754719622240.924528037775829
35109.9110.214119416248-0.314119416247976
36110.92109.9971313344920.922868665507593
37108.36110.634632523794-2.27463252379403
38109.01109.063357007201-0.0533570072011287
39108.03109.026498939721-0.996498939721306
40106.28108.338135272221-2.05813527222077
41106.6106.916412189812-0.316412189811544
42108.06106.6978403010331.36215969896685
43107.42107.63879588937-0.218795889369744
44107.58107.4876555972560.0923444027440752
45107.59107.5514454611610.0385545388393211
46109.66107.5780782479072.08192175209329
47107.85109.016232605724-1.16623260572358
48110.74108.2106199536332.52938004636727
49108.8109.957870508367-1.15787050836688
50109.18109.1580342437610.0219657562387283
51108.38109.173207795806-0.793207795805543
52108.59108.625274019214-0.035274019214242
53109.52108.6009073568270.919092643173357
54108.71109.235800137349-0.525800137349336
55109.78108.8725867946240.907413205375647
56109.77109.4994116281410.270588371858523
57109.34109.68632924201-0.346329242010313
58111.86109.4470911879692.41290881203074
59110.74111.113885494502-0.37388549450246
60110.67110.855612073466-0.185612073466061
61111.36110.7273945686290.632605431370635
62112.21111.1643871006441.04561289935566
63110.2111.886677814157-1.68667781415741
64110.99110.7215509085830.268449091416514
65110.43110.906990745736-0.476990745736074
66110.72110.5774940588750.142505941124952
67111.19110.6759346174780.51406538252202
68111.52111.0310418011810.488958198818551
69111.99111.3688053908620.62119460913793
70111.65111.797915530706-0.147915530705603
71114.45111.695738124252.75426187575032
72115.58113.5983330297481.98166697025184







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73114.96723317508112.70588599567117.228580354489
74114.96723317508112.218807812987117.715658537173
75114.96723317508111.80590546727118.12856088289
76114.96723317508111.441025044334118.493441305826
77114.96723317508111.110512458394118.823953891765
78114.96723317508110.806170138825119.128296211334
79114.96723317508110.522618850208119.411847499952
80114.96723317508110.256103013215119.678363336944
81114.96723317508110.003877625938119.930588724222
82114.96723317508109.763864149883120.170602200276
83114.96723317508109.534443825441120.400022524718
84114.96723317508109.314326752476120.620139597684

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 114.96723317508 & 112.70588599567 & 117.228580354489 \tabularnewline
74 & 114.96723317508 & 112.218807812987 & 117.715658537173 \tabularnewline
75 & 114.96723317508 & 111.80590546727 & 118.12856088289 \tabularnewline
76 & 114.96723317508 & 111.441025044334 & 118.493441305826 \tabularnewline
77 & 114.96723317508 & 111.110512458394 & 118.823953891765 \tabularnewline
78 & 114.96723317508 & 110.806170138825 & 119.128296211334 \tabularnewline
79 & 114.96723317508 & 110.522618850208 & 119.411847499952 \tabularnewline
80 & 114.96723317508 & 110.256103013215 & 119.678363336944 \tabularnewline
81 & 114.96723317508 & 110.003877625938 & 119.930588724222 \tabularnewline
82 & 114.96723317508 & 109.763864149883 & 120.170602200276 \tabularnewline
83 & 114.96723317508 & 109.534443825441 & 120.400022524718 \tabularnewline
84 & 114.96723317508 & 109.314326752476 & 120.620139597684 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=209065&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]73[/C][C]114.96723317508[/C][C]112.70588599567[/C][C]117.228580354489[/C][/ROW]
[ROW][C]74[/C][C]114.96723317508[/C][C]112.218807812987[/C][C]117.715658537173[/C][/ROW]
[ROW][C]75[/C][C]114.96723317508[/C][C]111.80590546727[/C][C]118.12856088289[/C][/ROW]
[ROW][C]76[/C][C]114.96723317508[/C][C]111.441025044334[/C][C]118.493441305826[/C][/ROW]
[ROW][C]77[/C][C]114.96723317508[/C][C]111.110512458394[/C][C]118.823953891765[/C][/ROW]
[ROW][C]78[/C][C]114.96723317508[/C][C]110.806170138825[/C][C]119.128296211334[/C][/ROW]
[ROW][C]79[/C][C]114.96723317508[/C][C]110.522618850208[/C][C]119.411847499952[/C][/ROW]
[ROW][C]80[/C][C]114.96723317508[/C][C]110.256103013215[/C][C]119.678363336944[/C][/ROW]
[ROW][C]81[/C][C]114.96723317508[/C][C]110.003877625938[/C][C]119.930588724222[/C][/ROW]
[ROW][C]82[/C][C]114.96723317508[/C][C]109.763864149883[/C][C]120.170602200276[/C][/ROW]
[ROW][C]83[/C][C]114.96723317508[/C][C]109.534443825441[/C][C]120.400022524718[/C][/ROW]
[ROW][C]84[/C][C]114.96723317508[/C][C]109.314326752476[/C][C]120.620139597684[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=209065&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=209065&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
73114.96723317508112.70588599567117.228580354489
74114.96723317508112.218807812987117.715658537173
75114.96723317508111.80590546727118.12856088289
76114.96723317508111.441025044334118.493441305826
77114.96723317508111.110512458394118.823953891765
78114.96723317508110.806170138825119.128296211334
79114.96723317508110.522618850208119.411847499952
80114.96723317508110.256103013215119.678363336944
81114.96723317508110.003877625938119.930588724222
82114.96723317508109.763864149883120.170602200276
83114.96723317508109.534443825441120.400022524718
84114.96723317508109.314326752476120.620139597684



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')