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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 14 May 2012 06:23:22 -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/2012/May/14/t1336991041awkh9cguatt1bj5.htm/, Retrieved Sun, 05 May 2024 10:23:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=166443, Retrieved Sun, 05 May 2024 10:23:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact178
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2012-05-14 10:23:22] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
2,35
2,35
2,35
2,35
2,35
2,35
2,35
2,36
2,36
2,36
2,36
2,36
2,36
2,37
2,37
2,39
2,4
2,41
2,41
2,42
2,44
2,44
2,44
2,44
2,44
2,45
2,45
2,46
2,47
2,48
2,48
2,48
2,49
2,5
2,5
2,5
2,5
2,5
2,5
2,5
2,51
2,52
2,54
2,56
2,57
2,57
2,58
2,59
2,6
2,6
2,62
2,62
2,63
2,63
2,63
2,63
2,63
2,63
2,63
2,64




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=166443&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=166443&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166443&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
alpha0.999952120979739
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999952120979739 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166443&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]0.999952120979739[/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=166443&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166443&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
alpha0.999952120979739
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
22.352.350
32.352.350
42.352.350
52.352.350
62.352.350
72.352.350
82.362.350.00999999999999979
92.362.35999952120984.78790202596002e-07
102.362.359999999977082.29238850124602e-11
112.362.368.88178419700125e-16
122.362.360
132.362.360
142.372.360.0100000000000002
152.372.36999952120984.78790202596002e-07
162.392.369999999977080.0200000000229239
172.42.389999042419590.0100009575804063
182.412.399999521163950.010000478836051
192.412.409999521186874.78813128701461e-07
202.422.409999999977070.010000000022925
212.442.41999952120980.0200004787902039
222.442.439999042396679.57603329077017e-07
232.442.439999999954154.584910229255e-11
242.442.442.22044604925031e-15
252.442.440
262.452.440.0100000000000002
272.452.44999952120984.78790202596002e-07
282.462.449999999977080.0100000000229237
292.472.45999952120980.0100004787902042
302.482.469999521186870.0100004788131263
312.482.479999521186874.78813127813282e-07
322.482.479999999977072.29252172800898e-11
332.492.480.0100000000000011
342.52.48999952120980.0100004787902024
352.52.499999521186874.78813126481015e-07
362.52.499999999977072.29252172800898e-11
372.52.58.88178419700125e-16
382.52.50
392.52.50
402.52.50
412.512.50.00999999999999979
422.522.50999952120980.0100004787902028
432.542.519999521186870.0200004788131265
442.562.539999042396670.0200009576033304
452.572.559999042373750.0100009576262541
462.572.569999521163954.78836053030562e-07
472.582.569999999977070.0100000000229263
482.592.57999952120980.0100004787902037
492.62.589999521186870.0100004788131267
502.62.599999521186874.78813127813282e-07
512.622.599999999977070.0200000000229252
522.622.619999042419599.57580406524272e-07
532.632.619999999954150.010000000045848
542.632.62999952120984.78790204816448e-07
552.632.629999999977082.29238850124602e-11
562.632.638.88178419700125e-16
572.632.630
582.632.630
592.632.630
602.642.630.0100000000000002

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 2.35 & 2.35 & 0 \tabularnewline
3 & 2.35 & 2.35 & 0 \tabularnewline
4 & 2.35 & 2.35 & 0 \tabularnewline
5 & 2.35 & 2.35 & 0 \tabularnewline
6 & 2.35 & 2.35 & 0 \tabularnewline
7 & 2.35 & 2.35 & 0 \tabularnewline
8 & 2.36 & 2.35 & 0.00999999999999979 \tabularnewline
9 & 2.36 & 2.3599995212098 & 4.78790202596002e-07 \tabularnewline
10 & 2.36 & 2.35999999997708 & 2.29238850124602e-11 \tabularnewline
11 & 2.36 & 2.36 & 8.88178419700125e-16 \tabularnewline
12 & 2.36 & 2.36 & 0 \tabularnewline
13 & 2.36 & 2.36 & 0 \tabularnewline
14 & 2.37 & 2.36 & 0.0100000000000002 \tabularnewline
15 & 2.37 & 2.3699995212098 & 4.78790202596002e-07 \tabularnewline
16 & 2.39 & 2.36999999997708 & 0.0200000000229239 \tabularnewline
17 & 2.4 & 2.38999904241959 & 0.0100009575804063 \tabularnewline
18 & 2.41 & 2.39999952116395 & 0.010000478836051 \tabularnewline
19 & 2.41 & 2.40999952118687 & 4.78813128701461e-07 \tabularnewline
20 & 2.42 & 2.40999999997707 & 0.010000000022925 \tabularnewline
21 & 2.44 & 2.4199995212098 & 0.0200004787902039 \tabularnewline
22 & 2.44 & 2.43999904239667 & 9.57603329077017e-07 \tabularnewline
23 & 2.44 & 2.43999999995415 & 4.584910229255e-11 \tabularnewline
24 & 2.44 & 2.44 & 2.22044604925031e-15 \tabularnewline
25 & 2.44 & 2.44 & 0 \tabularnewline
26 & 2.45 & 2.44 & 0.0100000000000002 \tabularnewline
27 & 2.45 & 2.4499995212098 & 4.78790202596002e-07 \tabularnewline
28 & 2.46 & 2.44999999997708 & 0.0100000000229237 \tabularnewline
29 & 2.47 & 2.4599995212098 & 0.0100004787902042 \tabularnewline
30 & 2.48 & 2.46999952118687 & 0.0100004788131263 \tabularnewline
31 & 2.48 & 2.47999952118687 & 4.78813127813282e-07 \tabularnewline
32 & 2.48 & 2.47999999997707 & 2.29252172800898e-11 \tabularnewline
33 & 2.49 & 2.48 & 0.0100000000000011 \tabularnewline
34 & 2.5 & 2.4899995212098 & 0.0100004787902024 \tabularnewline
35 & 2.5 & 2.49999952118687 & 4.78813126481015e-07 \tabularnewline
36 & 2.5 & 2.49999999997707 & 2.29252172800898e-11 \tabularnewline
37 & 2.5 & 2.5 & 8.88178419700125e-16 \tabularnewline
38 & 2.5 & 2.5 & 0 \tabularnewline
39 & 2.5 & 2.5 & 0 \tabularnewline
40 & 2.5 & 2.5 & 0 \tabularnewline
41 & 2.51 & 2.5 & 0.00999999999999979 \tabularnewline
42 & 2.52 & 2.5099995212098 & 0.0100004787902028 \tabularnewline
43 & 2.54 & 2.51999952118687 & 0.0200004788131265 \tabularnewline
44 & 2.56 & 2.53999904239667 & 0.0200009576033304 \tabularnewline
45 & 2.57 & 2.55999904237375 & 0.0100009576262541 \tabularnewline
46 & 2.57 & 2.56999952116395 & 4.78836053030562e-07 \tabularnewline
47 & 2.58 & 2.56999999997707 & 0.0100000000229263 \tabularnewline
48 & 2.59 & 2.5799995212098 & 0.0100004787902037 \tabularnewline
49 & 2.6 & 2.58999952118687 & 0.0100004788131267 \tabularnewline
50 & 2.6 & 2.59999952118687 & 4.78813127813282e-07 \tabularnewline
51 & 2.62 & 2.59999999997707 & 0.0200000000229252 \tabularnewline
52 & 2.62 & 2.61999904241959 & 9.57580406524272e-07 \tabularnewline
53 & 2.63 & 2.61999999995415 & 0.010000000045848 \tabularnewline
54 & 2.63 & 2.6299995212098 & 4.78790204816448e-07 \tabularnewline
55 & 2.63 & 2.62999999997708 & 2.29238850124602e-11 \tabularnewline
56 & 2.63 & 2.63 & 8.88178419700125e-16 \tabularnewline
57 & 2.63 & 2.63 & 0 \tabularnewline
58 & 2.63 & 2.63 & 0 \tabularnewline
59 & 2.63 & 2.63 & 0 \tabularnewline
60 & 2.64 & 2.63 & 0.0100000000000002 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166443&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]2.35[/C][C]2.35[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]2.35[/C][C]2.35[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]2.35[/C][C]2.35[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]2.35[/C][C]2.35[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]2.35[/C][C]2.35[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]2.35[/C][C]2.35[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]2.36[/C][C]2.35[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]9[/C][C]2.36[/C][C]2.3599995212098[/C][C]4.78790202596002e-07[/C][/ROW]
[ROW][C]10[/C][C]2.36[/C][C]2.35999999997708[/C][C]2.29238850124602e-11[/C][/ROW]
[ROW][C]11[/C][C]2.36[/C][C]2.36[/C][C]8.88178419700125e-16[/C][/ROW]
[ROW][C]12[/C][C]2.36[/C][C]2.36[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]2.36[/C][C]2.36[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]2.37[/C][C]2.36[/C][C]0.0100000000000002[/C][/ROW]
[ROW][C]15[/C][C]2.37[/C][C]2.3699995212098[/C][C]4.78790202596002e-07[/C][/ROW]
[ROW][C]16[/C][C]2.39[/C][C]2.36999999997708[/C][C]0.0200000000229239[/C][/ROW]
[ROW][C]17[/C][C]2.4[/C][C]2.38999904241959[/C][C]0.0100009575804063[/C][/ROW]
[ROW][C]18[/C][C]2.41[/C][C]2.39999952116395[/C][C]0.010000478836051[/C][/ROW]
[ROW][C]19[/C][C]2.41[/C][C]2.40999952118687[/C][C]4.78813128701461e-07[/C][/ROW]
[ROW][C]20[/C][C]2.42[/C][C]2.40999999997707[/C][C]0.010000000022925[/C][/ROW]
[ROW][C]21[/C][C]2.44[/C][C]2.4199995212098[/C][C]0.0200004787902039[/C][/ROW]
[ROW][C]22[/C][C]2.44[/C][C]2.43999904239667[/C][C]9.57603329077017e-07[/C][/ROW]
[ROW][C]23[/C][C]2.44[/C][C]2.43999999995415[/C][C]4.584910229255e-11[/C][/ROW]
[ROW][C]24[/C][C]2.44[/C][C]2.44[/C][C]2.22044604925031e-15[/C][/ROW]
[ROW][C]25[/C][C]2.44[/C][C]2.44[/C][C]0[/C][/ROW]
[ROW][C]26[/C][C]2.45[/C][C]2.44[/C][C]0.0100000000000002[/C][/ROW]
[ROW][C]27[/C][C]2.45[/C][C]2.4499995212098[/C][C]4.78790202596002e-07[/C][/ROW]
[ROW][C]28[/C][C]2.46[/C][C]2.44999999997708[/C][C]0.0100000000229237[/C][/ROW]
[ROW][C]29[/C][C]2.47[/C][C]2.4599995212098[/C][C]0.0100004787902042[/C][/ROW]
[ROW][C]30[/C][C]2.48[/C][C]2.46999952118687[/C][C]0.0100004788131263[/C][/ROW]
[ROW][C]31[/C][C]2.48[/C][C]2.47999952118687[/C][C]4.78813127813282e-07[/C][/ROW]
[ROW][C]32[/C][C]2.48[/C][C]2.47999999997707[/C][C]2.29252172800898e-11[/C][/ROW]
[ROW][C]33[/C][C]2.49[/C][C]2.48[/C][C]0.0100000000000011[/C][/ROW]
[ROW][C]34[/C][C]2.5[/C][C]2.4899995212098[/C][C]0.0100004787902024[/C][/ROW]
[ROW][C]35[/C][C]2.5[/C][C]2.49999952118687[/C][C]4.78813126481015e-07[/C][/ROW]
[ROW][C]36[/C][C]2.5[/C][C]2.49999999997707[/C][C]2.29252172800898e-11[/C][/ROW]
[ROW][C]37[/C][C]2.5[/C][C]2.5[/C][C]8.88178419700125e-16[/C][/ROW]
[ROW][C]38[/C][C]2.5[/C][C]2.5[/C][C]0[/C][/ROW]
[ROW][C]39[/C][C]2.5[/C][C]2.5[/C][C]0[/C][/ROW]
[ROW][C]40[/C][C]2.5[/C][C]2.5[/C][C]0[/C][/ROW]
[ROW][C]41[/C][C]2.51[/C][C]2.5[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]42[/C][C]2.52[/C][C]2.5099995212098[/C][C]0.0100004787902028[/C][/ROW]
[ROW][C]43[/C][C]2.54[/C][C]2.51999952118687[/C][C]0.0200004788131265[/C][/ROW]
[ROW][C]44[/C][C]2.56[/C][C]2.53999904239667[/C][C]0.0200009576033304[/C][/ROW]
[ROW][C]45[/C][C]2.57[/C][C]2.55999904237375[/C][C]0.0100009576262541[/C][/ROW]
[ROW][C]46[/C][C]2.57[/C][C]2.56999952116395[/C][C]4.78836053030562e-07[/C][/ROW]
[ROW][C]47[/C][C]2.58[/C][C]2.56999999997707[/C][C]0.0100000000229263[/C][/ROW]
[ROW][C]48[/C][C]2.59[/C][C]2.5799995212098[/C][C]0.0100004787902037[/C][/ROW]
[ROW][C]49[/C][C]2.6[/C][C]2.58999952118687[/C][C]0.0100004788131267[/C][/ROW]
[ROW][C]50[/C][C]2.6[/C][C]2.59999952118687[/C][C]4.78813127813282e-07[/C][/ROW]
[ROW][C]51[/C][C]2.62[/C][C]2.59999999997707[/C][C]0.0200000000229252[/C][/ROW]
[ROW][C]52[/C][C]2.62[/C][C]2.61999904241959[/C][C]9.57580406524272e-07[/C][/ROW]
[ROW][C]53[/C][C]2.63[/C][C]2.61999999995415[/C][C]0.010000000045848[/C][/ROW]
[ROW][C]54[/C][C]2.63[/C][C]2.6299995212098[/C][C]4.78790204816448e-07[/C][/ROW]
[ROW][C]55[/C][C]2.63[/C][C]2.62999999997708[/C][C]2.29238850124602e-11[/C][/ROW]
[ROW][C]56[/C][C]2.63[/C][C]2.63[/C][C]8.88178419700125e-16[/C][/ROW]
[ROW][C]57[/C][C]2.63[/C][C]2.63[/C][C]0[/C][/ROW]
[ROW][C]58[/C][C]2.63[/C][C]2.63[/C][C]0[/C][/ROW]
[ROW][C]59[/C][C]2.63[/C][C]2.63[/C][C]0[/C][/ROW]
[ROW][C]60[/C][C]2.64[/C][C]2.63[/C][C]0.0100000000000002[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166443&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166443&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
22.352.350
32.352.350
42.352.350
52.352.350
62.352.350
72.352.350
82.362.350.00999999999999979
92.362.35999952120984.78790202596002e-07
102.362.359999999977082.29238850124602e-11
112.362.368.88178419700125e-16
122.362.360
132.362.360
142.372.360.0100000000000002
152.372.36999952120984.78790202596002e-07
162.392.369999999977080.0200000000229239
172.42.389999042419590.0100009575804063
182.412.399999521163950.010000478836051
192.412.409999521186874.78813128701461e-07
202.422.409999999977070.010000000022925
212.442.41999952120980.0200004787902039
222.442.439999042396679.57603329077017e-07
232.442.439999999954154.584910229255e-11
242.442.442.22044604925031e-15
252.442.440
262.452.440.0100000000000002
272.452.44999952120984.78790202596002e-07
282.462.449999999977080.0100000000229237
292.472.45999952120980.0100004787902042
302.482.469999521186870.0100004788131263
312.482.479999521186874.78813127813282e-07
322.482.479999999977072.29252172800898e-11
332.492.480.0100000000000011
342.52.48999952120980.0100004787902024
352.52.499999521186874.78813126481015e-07
362.52.499999999977072.29252172800898e-11
372.52.58.88178419700125e-16
382.52.50
392.52.50
402.52.50
412.512.50.00999999999999979
422.522.50999952120980.0100004787902028
432.542.519999521186870.0200004788131265
442.562.539999042396670.0200009576033304
452.572.559999042373750.0100009576262541
462.572.569999521163954.78836053030562e-07
472.582.569999999977070.0100000000229263
482.592.57999952120980.0100004787902037
492.62.589999521186870.0100004788131267
502.62.599999521186874.78813127813282e-07
512.622.599999999977070.0200000000229252
522.622.619999042419599.57580406524272e-07
532.632.619999999954150.010000000045848
542.632.62999952120984.78790204816448e-07
552.632.629999999977082.29238850124602e-11
562.632.638.88178419700125e-16
572.632.630
582.632.630
592.632.630
602.642.630.0100000000000002







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
612.63999952120982.62719719415212.6528018482675
622.63999952120982.621894730079882.65810431233972
632.63999952120982.617825948073662.66217309434594
642.63999952120982.61439578653322.66560325588639
652.63999952120982.611373744134672.66862529828493
662.63999952120982.608641603598442.67135743882116
672.63999952120982.606129137676592.673869904743
682.63999952120982.60379058910112.67620845331849
692.63999952120982.601594174600012.67840486781958
702.63999952120982.599516752875812.68048228954379
712.63999952120982.597540854064572.68245818835502
722.63999952120982.595652905786362.68434613663324

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 2.6399995212098 & 2.6271971941521 & 2.6528018482675 \tabularnewline
62 & 2.6399995212098 & 2.62189473007988 & 2.65810431233972 \tabularnewline
63 & 2.6399995212098 & 2.61782594807366 & 2.66217309434594 \tabularnewline
64 & 2.6399995212098 & 2.6143957865332 & 2.66560325588639 \tabularnewline
65 & 2.6399995212098 & 2.61137374413467 & 2.66862529828493 \tabularnewline
66 & 2.6399995212098 & 2.60864160359844 & 2.67135743882116 \tabularnewline
67 & 2.6399995212098 & 2.60612913767659 & 2.673869904743 \tabularnewline
68 & 2.6399995212098 & 2.6037905891011 & 2.67620845331849 \tabularnewline
69 & 2.6399995212098 & 2.60159417460001 & 2.67840486781958 \tabularnewline
70 & 2.6399995212098 & 2.59951675287581 & 2.68048228954379 \tabularnewline
71 & 2.6399995212098 & 2.59754085406457 & 2.68245818835502 \tabularnewline
72 & 2.6399995212098 & 2.59565290578636 & 2.68434613663324 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166443&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]61[/C][C]2.6399995212098[/C][C]2.6271971941521[/C][C]2.6528018482675[/C][/ROW]
[ROW][C]62[/C][C]2.6399995212098[/C][C]2.62189473007988[/C][C]2.65810431233972[/C][/ROW]
[ROW][C]63[/C][C]2.6399995212098[/C][C]2.61782594807366[/C][C]2.66217309434594[/C][/ROW]
[ROW][C]64[/C][C]2.6399995212098[/C][C]2.6143957865332[/C][C]2.66560325588639[/C][/ROW]
[ROW][C]65[/C][C]2.6399995212098[/C][C]2.61137374413467[/C][C]2.66862529828493[/C][/ROW]
[ROW][C]66[/C][C]2.6399995212098[/C][C]2.60864160359844[/C][C]2.67135743882116[/C][/ROW]
[ROW][C]67[/C][C]2.6399995212098[/C][C]2.60612913767659[/C][C]2.673869904743[/C][/ROW]
[ROW][C]68[/C][C]2.6399995212098[/C][C]2.6037905891011[/C][C]2.67620845331849[/C][/ROW]
[ROW][C]69[/C][C]2.6399995212098[/C][C]2.60159417460001[/C][C]2.67840486781958[/C][/ROW]
[ROW][C]70[/C][C]2.6399995212098[/C][C]2.59951675287581[/C][C]2.68048228954379[/C][/ROW]
[ROW][C]71[/C][C]2.6399995212098[/C][C]2.59754085406457[/C][C]2.68245818835502[/C][/ROW]
[ROW][C]72[/C][C]2.6399995212098[/C][C]2.59565290578636[/C][C]2.68434613663324[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166443&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166443&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
612.63999952120982.62719719415212.6528018482675
622.63999952120982.621894730079882.65810431233972
632.63999952120982.617825948073662.66217309434594
642.63999952120982.61439578653322.66560325588639
652.63999952120982.611373744134672.66862529828493
662.63999952120982.608641603598442.67135743882116
672.63999952120982.606129137676592.673869904743
682.63999952120982.60379058910112.67620845331849
692.63999952120982.601594174600012.67840486781958
702.63999952120982.599516752875812.68048228954379
712.63999952120982.597540854064572.68245818835502
722.63999952120982.595652905786362.68434613663324



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')