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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 30 Nov 2015 10:34:32 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Nov/30/t1448879721p9aa2kpsbtsdaq1.htm/, Retrieved Tue, 14 May 2024 20:24:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284568, Retrieved Tue, 14 May 2024 20:24:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact135

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [] [2015-11-30 10:16:36] [ae29a80d97dbf7fdde7336bcf9526e8b]
- R PD    [Exponential Smoothing] [] [2015-11-30 10:34:32] [935c69a10ec4a64678755fcf1ddf3064] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
0,62
0,7
1,65
1,79
2,28
2,46
2,57
2,32
2,91
3,01
2,87
3,11
3,22
3,38
3,52
3,41
3,35
3,68
3,75
3,6
3,56
3,57
3,85
3,48
3,65
3,66
3,36
3,19
2,81
2,25
2,32
2,85
2,75
2,78
2,26
2,23
1,46
1,19
1,11
1
1,18
1,59
1,51
1,01
0,9
0,63
0,81
0,97
1,14
0,97
0,89
0,62
0,36
0,27
0,34
0,02
-0,12
0,09
-0,11
-0,38

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284568&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284568&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284568&T=0

As an alternative you can also use a QR Code:  
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'Gertrude Mary Cox' @ cox.wessa.net






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0981818103106977
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0981818103106977 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284568&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0981818103106977[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284568&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284568&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0981818103106977
gammaFALSE






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
31.650.780.87
41.791.81541817497031-0.0254181749703069
52.281.952922572536930.327077427463072
62.462.47503562647702-0.0150356264770184
72.572.65355940145035-0.0835594014503496
82.322.75535538814748-0.435355388147476
92.912.462611408010640.44738859198936
103.013.09653682988451-0.0865368298845097
112.873.1880404872679-0.318040487267899
123.113.016814696475840.0931853035241592
133.223.26596379827019-0.0459637982701944
143.383.371450989347270.00854901065272839
153.523.53229034668952-0.0122903466895212
163.413.6710836582022-0.261083658202198
173.353.53544999199737-0.185449991997367
183.683.457242176060960.222757823939039
193.753.80911294247617-0.0591129424761676
203.63.87330912677107-0.273309126771065
213.563.69647514193025-0.136475141930246
223.573.64307576543313-0.0730757654331256
233.853.645901054493060.204098945506939
243.483.94593985844544-0.465939858445437
253.653.530193039647350.119806960352646
263.663.7119559039026-0.0519559039025981
273.363.71685477920111-0.356854779201113
283.193.38181813096112-0.191818130961123
292.813.19298507961295-0.382985079612945
302.252.77538291117456-0.52538291117456
312.322.163799865849140.156200134150863
322.852.249135877790840.600864122209158
332.752.83812980506009-0.0881298050600861
342.782.729477061256960.0505229387430419
352.262.76443749484497-0.504437494844966
362.232.194910908412490.0350890915875062
371.462.16835601894671-0.708356018946713
381.191.32880834266205-0.138808342662046
391.111.045179888293260.0648201117067413
4010.9715440442051680.0284559557948316
411.180.8643379014592260.315662098540774
421.591.075330177740430.514669822259567
431.511.53586139260216-0.0258613926021625
441.011.45332227425933-0.443322274259326
450.90.90979609082149-0.00979609082149013
460.630.798834292890668-0.168834292890668
470.810.5122578363721360.297742163627864
480.970.7214907010029440.248509298997056
491.140.9058897938575170.234110206142483
500.971.0988751577088-0.128875157708797
510.890.91622196142087-0.0262219614208702
520.620.833647441778672-0.213647441778672
530.360.542671149176593-0.182671149176593
540.270.2647361650588990.00526383494110083
550.340.1752529779025930.164747022097407
560.020.261428138775413-0.241428138775413
57-0.12-0.0822757129494993-0.0377242870505007
580.09-0.2259795517447980.315979551744798
59-0.110.0150438926666692-0.125043892666669
60-0.38-0.197233143083641-0.182766856916359

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1.65 & 0.78 & 0.87 \tabularnewline
4 & 1.79 & 1.81541817497031 & -0.0254181749703069 \tabularnewline
5 & 2.28 & 1.95292257253693 & 0.327077427463072 \tabularnewline
6 & 2.46 & 2.47503562647702 & -0.0150356264770184 \tabularnewline
7 & 2.57 & 2.65355940145035 & -0.0835594014503496 \tabularnewline
8 & 2.32 & 2.75535538814748 & -0.435355388147476 \tabularnewline
9 & 2.91 & 2.46261140801064 & 0.44738859198936 \tabularnewline
10 & 3.01 & 3.09653682988451 & -0.0865368298845097 \tabularnewline
11 & 2.87 & 3.1880404872679 & -0.318040487267899 \tabularnewline
12 & 3.11 & 3.01681469647584 & 0.0931853035241592 \tabularnewline
13 & 3.22 & 3.26596379827019 & -0.0459637982701944 \tabularnewline
14 & 3.38 & 3.37145098934727 & 0.00854901065272839 \tabularnewline
15 & 3.52 & 3.53229034668952 & -0.0122903466895212 \tabularnewline
16 & 3.41 & 3.6710836582022 & -0.261083658202198 \tabularnewline
17 & 3.35 & 3.53544999199737 & -0.185449991997367 \tabularnewline
18 & 3.68 & 3.45724217606096 & 0.222757823939039 \tabularnewline
19 & 3.75 & 3.80911294247617 & -0.0591129424761676 \tabularnewline
20 & 3.6 & 3.87330912677107 & -0.273309126771065 \tabularnewline
21 & 3.56 & 3.69647514193025 & -0.136475141930246 \tabularnewline
22 & 3.57 & 3.64307576543313 & -0.0730757654331256 \tabularnewline
23 & 3.85 & 3.64590105449306 & 0.204098945506939 \tabularnewline
24 & 3.48 & 3.94593985844544 & -0.465939858445437 \tabularnewline
25 & 3.65 & 3.53019303964735 & 0.119806960352646 \tabularnewline
26 & 3.66 & 3.7119559039026 & -0.0519559039025981 \tabularnewline
27 & 3.36 & 3.71685477920111 & -0.356854779201113 \tabularnewline
28 & 3.19 & 3.38181813096112 & -0.191818130961123 \tabularnewline
29 & 2.81 & 3.19298507961295 & -0.382985079612945 \tabularnewline
30 & 2.25 & 2.77538291117456 & -0.52538291117456 \tabularnewline
31 & 2.32 & 2.16379986584914 & 0.156200134150863 \tabularnewline
32 & 2.85 & 2.24913587779084 & 0.600864122209158 \tabularnewline
33 & 2.75 & 2.83812980506009 & -0.0881298050600861 \tabularnewline
34 & 2.78 & 2.72947706125696 & 0.0505229387430419 \tabularnewline
35 & 2.26 & 2.76443749484497 & -0.504437494844966 \tabularnewline
36 & 2.23 & 2.19491090841249 & 0.0350890915875062 \tabularnewline
37 & 1.46 & 2.16835601894671 & -0.708356018946713 \tabularnewline
38 & 1.19 & 1.32880834266205 & -0.138808342662046 \tabularnewline
39 & 1.11 & 1.04517988829326 & 0.0648201117067413 \tabularnewline
40 & 1 & 0.971544044205168 & 0.0284559557948316 \tabularnewline
41 & 1.18 & 0.864337901459226 & 0.315662098540774 \tabularnewline
42 & 1.59 & 1.07533017774043 & 0.514669822259567 \tabularnewline
43 & 1.51 & 1.53586139260216 & -0.0258613926021625 \tabularnewline
44 & 1.01 & 1.45332227425933 & -0.443322274259326 \tabularnewline
45 & 0.9 & 0.90979609082149 & -0.00979609082149013 \tabularnewline
46 & 0.63 & 0.798834292890668 & -0.168834292890668 \tabularnewline
47 & 0.81 & 0.512257836372136 & 0.297742163627864 \tabularnewline
48 & 0.97 & 0.721490701002944 & 0.248509298997056 \tabularnewline
49 & 1.14 & 0.905889793857517 & 0.234110206142483 \tabularnewline
50 & 0.97 & 1.0988751577088 & -0.128875157708797 \tabularnewline
51 & 0.89 & 0.91622196142087 & -0.0262219614208702 \tabularnewline
52 & 0.62 & 0.833647441778672 & -0.213647441778672 \tabularnewline
53 & 0.36 & 0.542671149176593 & -0.182671149176593 \tabularnewline
54 & 0.27 & 0.264736165058899 & 0.00526383494110083 \tabularnewline
55 & 0.34 & 0.175252977902593 & 0.164747022097407 \tabularnewline
56 & 0.02 & 0.261428138775413 & -0.241428138775413 \tabularnewline
57 & -0.12 & -0.0822757129494993 & -0.0377242870505007 \tabularnewline
58 & 0.09 & -0.225979551744798 & 0.315979551744798 \tabularnewline
59 & -0.11 & 0.0150438926666692 & -0.125043892666669 \tabularnewline
60 & -0.38 & -0.197233143083641 & -0.182766856916359 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284568&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]1.65[/C][C]0.78[/C][C]0.87[/C][/ROW]
[ROW][C]4[/C][C]1.79[/C][C]1.81541817497031[/C][C]-0.0254181749703069[/C][/ROW]
[ROW][C]5[/C][C]2.28[/C][C]1.95292257253693[/C][C]0.327077427463072[/C][/ROW]
[ROW][C]6[/C][C]2.46[/C][C]2.47503562647702[/C][C]-0.0150356264770184[/C][/ROW]
[ROW][C]7[/C][C]2.57[/C][C]2.65355940145035[/C][C]-0.0835594014503496[/C][/ROW]
[ROW][C]8[/C][C]2.32[/C][C]2.75535538814748[/C][C]-0.435355388147476[/C][/ROW]
[ROW][C]9[/C][C]2.91[/C][C]2.46261140801064[/C][C]0.44738859198936[/C][/ROW]
[ROW][C]10[/C][C]3.01[/C][C]3.09653682988451[/C][C]-0.0865368298845097[/C][/ROW]
[ROW][C]11[/C][C]2.87[/C][C]3.1880404872679[/C][C]-0.318040487267899[/C][/ROW]
[ROW][C]12[/C][C]3.11[/C][C]3.01681469647584[/C][C]0.0931853035241592[/C][/ROW]
[ROW][C]13[/C][C]3.22[/C][C]3.26596379827019[/C][C]-0.0459637982701944[/C][/ROW]
[ROW][C]14[/C][C]3.38[/C][C]3.37145098934727[/C][C]0.00854901065272839[/C][/ROW]
[ROW][C]15[/C][C]3.52[/C][C]3.53229034668952[/C][C]-0.0122903466895212[/C][/ROW]
[ROW][C]16[/C][C]3.41[/C][C]3.6710836582022[/C][C]-0.261083658202198[/C][/ROW]
[ROW][C]17[/C][C]3.35[/C][C]3.53544999199737[/C][C]-0.185449991997367[/C][/ROW]
[ROW][C]18[/C][C]3.68[/C][C]3.45724217606096[/C][C]0.222757823939039[/C][/ROW]
[ROW][C]19[/C][C]3.75[/C][C]3.80911294247617[/C][C]-0.0591129424761676[/C][/ROW]
[ROW][C]20[/C][C]3.6[/C][C]3.87330912677107[/C][C]-0.273309126771065[/C][/ROW]
[ROW][C]21[/C][C]3.56[/C][C]3.69647514193025[/C][C]-0.136475141930246[/C][/ROW]
[ROW][C]22[/C][C]3.57[/C][C]3.64307576543313[/C][C]-0.0730757654331256[/C][/ROW]
[ROW][C]23[/C][C]3.85[/C][C]3.64590105449306[/C][C]0.204098945506939[/C][/ROW]
[ROW][C]24[/C][C]3.48[/C][C]3.94593985844544[/C][C]-0.465939858445437[/C][/ROW]
[ROW][C]25[/C][C]3.65[/C][C]3.53019303964735[/C][C]0.119806960352646[/C][/ROW]
[ROW][C]26[/C][C]3.66[/C][C]3.7119559039026[/C][C]-0.0519559039025981[/C][/ROW]
[ROW][C]27[/C][C]3.36[/C][C]3.71685477920111[/C][C]-0.356854779201113[/C][/ROW]
[ROW][C]28[/C][C]3.19[/C][C]3.38181813096112[/C][C]-0.191818130961123[/C][/ROW]
[ROW][C]29[/C][C]2.81[/C][C]3.19298507961295[/C][C]-0.382985079612945[/C][/ROW]
[ROW][C]30[/C][C]2.25[/C][C]2.77538291117456[/C][C]-0.52538291117456[/C][/ROW]
[ROW][C]31[/C][C]2.32[/C][C]2.16379986584914[/C][C]0.156200134150863[/C][/ROW]
[ROW][C]32[/C][C]2.85[/C][C]2.24913587779084[/C][C]0.600864122209158[/C][/ROW]
[ROW][C]33[/C][C]2.75[/C][C]2.83812980506009[/C][C]-0.0881298050600861[/C][/ROW]
[ROW][C]34[/C][C]2.78[/C][C]2.72947706125696[/C][C]0.0505229387430419[/C][/ROW]
[ROW][C]35[/C][C]2.26[/C][C]2.76443749484497[/C][C]-0.504437494844966[/C][/ROW]
[ROW][C]36[/C][C]2.23[/C][C]2.19491090841249[/C][C]0.0350890915875062[/C][/ROW]
[ROW][C]37[/C][C]1.46[/C][C]2.16835601894671[/C][C]-0.708356018946713[/C][/ROW]
[ROW][C]38[/C][C]1.19[/C][C]1.32880834266205[/C][C]-0.138808342662046[/C][/ROW]
[ROW][C]39[/C][C]1.11[/C][C]1.04517988829326[/C][C]0.0648201117067413[/C][/ROW]
[ROW][C]40[/C][C]1[/C][C]0.971544044205168[/C][C]0.0284559557948316[/C][/ROW]
[ROW][C]41[/C][C]1.18[/C][C]0.864337901459226[/C][C]0.315662098540774[/C][/ROW]
[ROW][C]42[/C][C]1.59[/C][C]1.07533017774043[/C][C]0.514669822259567[/C][/ROW]
[ROW][C]43[/C][C]1.51[/C][C]1.53586139260216[/C][C]-0.0258613926021625[/C][/ROW]
[ROW][C]44[/C][C]1.01[/C][C]1.45332227425933[/C][C]-0.443322274259326[/C][/ROW]
[ROW][C]45[/C][C]0.9[/C][C]0.90979609082149[/C][C]-0.00979609082149013[/C][/ROW]
[ROW][C]46[/C][C]0.63[/C][C]0.798834292890668[/C][C]-0.168834292890668[/C][/ROW]
[ROW][C]47[/C][C]0.81[/C][C]0.512257836372136[/C][C]0.297742163627864[/C][/ROW]
[ROW][C]48[/C][C]0.97[/C][C]0.721490701002944[/C][C]0.248509298997056[/C][/ROW]
[ROW][C]49[/C][C]1.14[/C][C]0.905889793857517[/C][C]0.234110206142483[/C][/ROW]
[ROW][C]50[/C][C]0.97[/C][C]1.0988751577088[/C][C]-0.128875157708797[/C][/ROW]
[ROW][C]51[/C][C]0.89[/C][C]0.91622196142087[/C][C]-0.0262219614208702[/C][/ROW]
[ROW][C]52[/C][C]0.62[/C][C]0.833647441778672[/C][C]-0.213647441778672[/C][/ROW]
[ROW][C]53[/C][C]0.36[/C][C]0.542671149176593[/C][C]-0.182671149176593[/C][/ROW]
[ROW][C]54[/C][C]0.27[/C][C]0.264736165058899[/C][C]0.00526383494110083[/C][/ROW]
[ROW][C]55[/C][C]0.34[/C][C]0.175252977902593[/C][C]0.164747022097407[/C][/ROW]
[ROW][C]56[/C][C]0.02[/C][C]0.261428138775413[/C][C]-0.241428138775413[/C][/ROW]
[ROW][C]57[/C][C]-0.12[/C][C]-0.0822757129494993[/C][C]-0.0377242870505007[/C][/ROW]
[ROW][C]58[/C][C]0.09[/C][C]-0.225979551744798[/C][C]0.315979551744798[/C][/ROW]
[ROW][C]59[/C][C]-0.11[/C][C]0.0150438926666692[/C][C]-0.125043892666669[/C][/ROW]
[ROW][C]60[/C][C]-0.38[/C][C]-0.197233143083641[/C][C]-0.182766856916359[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284568&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284568&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
31.650.780.87
41.791.81541817497031-0.0254181749703069
52.281.952922572536930.327077427463072
62.462.47503562647702-0.0150356264770184
72.572.65355940145035-0.0835594014503496
82.322.75535538814748-0.435355388147476
92.912.462611408010640.44738859198936
103.013.09653682988451-0.0865368298845097
112.873.1880404872679-0.318040487267899
123.113.016814696475840.0931853035241592
133.223.26596379827019-0.0459637982701944
143.383.371450989347270.00854901065272839
153.523.53229034668952-0.0122903466895212
163.413.6710836582022-0.261083658202198
173.353.53544999199737-0.185449991997367
183.683.457242176060960.222757823939039
193.753.80911294247617-0.0591129424761676
203.63.87330912677107-0.273309126771065
213.563.69647514193025-0.136475141930246
223.573.64307576543313-0.0730757654331256
233.853.645901054493060.204098945506939
243.483.94593985844544-0.465939858445437
253.653.530193039647350.119806960352646
263.663.7119559039026-0.0519559039025981
273.363.71685477920111-0.356854779201113
283.193.38181813096112-0.191818130961123
292.813.19298507961295-0.382985079612945
302.252.77538291117456-0.52538291117456
312.322.163799865849140.156200134150863
322.852.249135877790840.600864122209158
332.752.83812980506009-0.0881298050600861
342.782.729477061256960.0505229387430419
352.262.76443749484497-0.504437494844966
362.232.194910908412490.0350890915875062
371.462.16835601894671-0.708356018946713
381.191.32880834266205-0.138808342662046
391.111.045179888293260.0648201117067413
4010.9715440442051680.0284559557948316
411.180.8643379014592260.315662098540774
421.591.075330177740430.514669822259567
431.511.53586139260216-0.0258613926021625
441.011.45332227425933-0.443322274259326
450.90.90979609082149-0.00979609082149013
460.630.798834292890668-0.168834292890668
470.810.5122578363721360.297742163627864
480.970.7214907010029440.248509298997056
491.140.9058897938575170.234110206142483
500.971.0988751577088-0.128875157708797
510.890.91622196142087-0.0262219614208702
520.620.833647441778672-0.213647441778672
530.360.542671149176593-0.182671149176593
540.270.2647361650588990.00526383494110083
550.340.1752529779025930.164747022097407
560.020.261428138775413-0.241428138775413
57-0.12-0.0822757129494993-0.0377242870505007
580.09-0.2259795517447980.315979551744798
59-0.110.0150438926666692-0.125043892666669
60-0.38-0.197233143083641-0.182766856916359






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61-0.485177523960485-1.050484908685710.0801298607647436
62-0.590355047920971-1.429984639969260.24927454412732
63-0.695532571881456-1.773668640384750.382603496621834
64-0.800710095841942-2.103757360783380.502337169099497
65-0.905887619802427-2.428320992264720.616545752659864
66-1.01106514376291-2.751223792653060.729093505127236
67-1.1162426677234-3.074593904908660.842108569461862
68-1.22142019168388-3.399705492688620.95686510932085
69-1.32659771564437-3.727363243725931.0741678124372
70-1.43177523960485-4.058093102562851.19454262335315
71-1.53695276356534-4.392245951020651.31834042388997
72-1.64213028752582-4.730057953823531.44579737877188

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & -0.485177523960485 & -1.05048490868571 & 0.0801298607647436 \tabularnewline
62 & -0.590355047920971 & -1.42998463996926 & 0.24927454412732 \tabularnewline
63 & -0.695532571881456 & -1.77366864038475 & 0.382603496621834 \tabularnewline
64 & -0.800710095841942 & -2.10375736078338 & 0.502337169099497 \tabularnewline
65 & -0.905887619802427 & -2.42832099226472 & 0.616545752659864 \tabularnewline
66 & -1.01106514376291 & -2.75122379265306 & 0.729093505127236 \tabularnewline
67 & -1.1162426677234 & -3.07459390490866 & 0.842108569461862 \tabularnewline
68 & -1.22142019168388 & -3.39970549268862 & 0.95686510932085 \tabularnewline
69 & -1.32659771564437 & -3.72736324372593 & 1.0741678124372 \tabularnewline
70 & -1.43177523960485 & -4.05809310256285 & 1.19454262335315 \tabularnewline
71 & -1.53695276356534 & -4.39224595102065 & 1.31834042388997 \tabularnewline
72 & -1.64213028752582 & -4.73005795382353 & 1.44579737877188 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284568&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]-0.485177523960485[/C][C]-1.05048490868571[/C][C]0.0801298607647436[/C][/ROW]
[ROW][C]62[/C][C]-0.590355047920971[/C][C]-1.42998463996926[/C][C]0.24927454412732[/C][/ROW]
[ROW][C]63[/C][C]-0.695532571881456[/C][C]-1.77366864038475[/C][C]0.382603496621834[/C][/ROW]
[ROW][C]64[/C][C]-0.800710095841942[/C][C]-2.10375736078338[/C][C]0.502337169099497[/C][/ROW]
[ROW][C]65[/C][C]-0.905887619802427[/C][C]-2.42832099226472[/C][C]0.616545752659864[/C][/ROW]
[ROW][C]66[/C][C]-1.01106514376291[/C][C]-2.75122379265306[/C][C]0.729093505127236[/C][/ROW]
[ROW][C]67[/C][C]-1.1162426677234[/C][C]-3.07459390490866[/C][C]0.842108569461862[/C][/ROW]
[ROW][C]68[/C][C]-1.22142019168388[/C][C]-3.39970549268862[/C][C]0.95686510932085[/C][/ROW]
[ROW][C]69[/C][C]-1.32659771564437[/C][C]-3.72736324372593[/C][C]1.0741678124372[/C][/ROW]
[ROW][C]70[/C][C]-1.43177523960485[/C][C]-4.05809310256285[/C][C]1.19454262335315[/C][/ROW]
[ROW][C]71[/C][C]-1.53695276356534[/C][C]-4.39224595102065[/C][C]1.31834042388997[/C][/ROW]
[ROW][C]72[/C][C]-1.64213028752582[/C][C]-4.73005795382353[/C][C]1.44579737877188[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284568&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284568&T=3

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61-0.485177523960485-1.050484908685710.0801298607647436
62-0.590355047920971-1.429984639969260.24927454412732
63-0.695532571881456-1.773668640384750.382603496621834
64-0.800710095841942-2.103757360783380.502337169099497
65-0.905887619802427-2.428320992264720.616545752659864
66-1.01106514376291-2.751223792653060.729093505127236
67-1.1162426677234-3.074593904908660.842108569461862
68-1.22142019168388-3.399705492688620.95686510932085
69-1.32659771564437-3.727363243725931.0741678124372
70-1.43177523960485-4.058093102562851.19454262335315
71-1.53695276356534-4.392245951020651.31834042388997
72-1.64213028752582-4.730057953823531.44579737877188


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
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')