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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 20 Dec 2010 19:50:00 +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/2010/Dec/20/t1292874550jj984ixm1hfq209.htm/, Retrieved Fri, 03 May 2024 17:27:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=113098, Retrieved Fri, 03 May 2024 17:27:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102 - Sofie Baert
Estimated Impact88
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2010-12-20 19:50:00] [1ce81d942cb901782da36327f25f651a] [Current]
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Dataseries X:
6,59
6,59
6,59
6,59
6,63
6,63
6,63
6,63
6,63
6,63
6,63
6,63
6,63
6,63
6,63
6,63
6,63
6,63
6,63
6,63
6,63
6,79
6,79
6,79
6,81
6,80
6,80
6,85
6,85
6,85
6,85
6,85
6,85
6,86
6,86
6,88
6,88
6,88
6,91
6,91
6,91
6,91
6,99
6,99
6,99
7,02
7,02
7,05
7,05
7,05
7,05
7,10
7,10
7,10
7,10
7,12
7,13
7,18
7,24
7,24
7,24
7,27
7,27
7,27
7,27
7,30
7,30
7,57
7,76
7,94
7,94
7,96




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113098&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113098&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113098&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.153603670908544
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.153603670908544 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113098&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]0.153603670908544[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113098&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113098&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
alpha1
beta0.153603670908544
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
36.596.590
46.596.590
56.636.590.04
66.636.63614414683634-0.00614414683634212
76.636.63520038332768-0.00520038332767836
86.636.63440158535842-0.00440158535841562
96.636.63372548568955-0.00372548568954567
106.636.63315323741171-0.00315323741171447
116.636.63266888857003-0.002668888570029
126.636.63225893748843-0.00225893748842676
136.636.63191195639785-0.00191195639785136
146.636.63161827287652-0.00161827287652461
156.636.63136970022216-0.00136970022215799
166.636.63115930923999-0.00115930923999041
176.636.63098123508501-0.00098123508500958
186.636.63083051377393-0.000830513773927954
196.636.63070294380951-0.000702943809512746
206.636.63059496905993-0.000594969059928729
216.636.63050357962825-0.000503579628246875
226.796.630426227948750.159573772051247
236.796.81493734511655-0.0249373451165482
246.796.81110687736393-0.0211068773639331
256.816.807864783519420.00213521648058279
266.86.82819276060902-0.0281927606090182
276.86.81386224908643-0.0138622490864275
286.856.81173295673970.0382670432602961
296.856.8676109150593-0.0176109150593016
306.856.86490581385813-0.0149058138581344
316.856.86261622613165-0.0126162261316454
326.856.86067832748481-0.0106783274848121
336.856.85903809718398-0.00903809718398119
346.866.85764981227850.00235018772150664
356.866.86801080973984-0.00801080973984103
366.886.866780319956850.0132196800431474
376.886.88881091133972-0.00881091133971612
386.886.88745752301389-0.00745752301388602
396.916.886312020103070.0236879798969323
406.916.91995058077165-0.0099505807716449
416.916.91842213503745-0.00842213503744826
426.916.91712846417881-0.00712846417880808
436.996.9160335059130.0739664940869966
446.997.007395030929-0.0173950309290012
456.997.00472309032274-0.0147230903227387
467.027.002461569602050.0175384303979511
477.027.03515553689315-0.0151555368931477
487.057.032827590791770.0171724092082304
497.057.0654653358845-0.0154653358844978
507.057.0630898035208-0.0130898035208054
517.057.06107916164854-0.0110791616485377
527.17.059377361748730.040622638251266
537.17.11561714810612-0.0156171481061183
547.17.1132182968279-0.0132182968278958
557.17.11118791791197-0.0111879179119718
567.127.109469412650870.0105305873491304
577.137.13108694952452-0.00108694952451938
587.187.140919990087460.0390800099125386
597.247.196922823069170.0430771769308311
607.247.26353963557812-0.0235396355781221
617.247.25992386114147-0.0199238611414732
627.277.256863482931470.0131365170685287
637.277.28888130017615-0.0188813001761492
647.277.28598106315757-0.0159810631575663
657.277.28352631319154-0.0135263131915435
667.37.281448621831460.0185513781685369
677.37.31429818161856-0.014298181618563
687.577.312101928434640.257898071565365
697.767.621716018947310.13828398105269
707.947.832956946064850.107043053935151
717.948.02939915209455-0.0893991520945514
727.968.01566711415672-0.0556671141567167

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 6.59 & 6.59 & 0 \tabularnewline
4 & 6.59 & 6.59 & 0 \tabularnewline
5 & 6.63 & 6.59 & 0.04 \tabularnewline
6 & 6.63 & 6.63614414683634 & -0.00614414683634212 \tabularnewline
7 & 6.63 & 6.63520038332768 & -0.00520038332767836 \tabularnewline
8 & 6.63 & 6.63440158535842 & -0.00440158535841562 \tabularnewline
9 & 6.63 & 6.63372548568955 & -0.00372548568954567 \tabularnewline
10 & 6.63 & 6.63315323741171 & -0.00315323741171447 \tabularnewline
11 & 6.63 & 6.63266888857003 & -0.002668888570029 \tabularnewline
12 & 6.63 & 6.63225893748843 & -0.00225893748842676 \tabularnewline
13 & 6.63 & 6.63191195639785 & -0.00191195639785136 \tabularnewline
14 & 6.63 & 6.63161827287652 & -0.00161827287652461 \tabularnewline
15 & 6.63 & 6.63136970022216 & -0.00136970022215799 \tabularnewline
16 & 6.63 & 6.63115930923999 & -0.00115930923999041 \tabularnewline
17 & 6.63 & 6.63098123508501 & -0.00098123508500958 \tabularnewline
18 & 6.63 & 6.63083051377393 & -0.000830513773927954 \tabularnewline
19 & 6.63 & 6.63070294380951 & -0.000702943809512746 \tabularnewline
20 & 6.63 & 6.63059496905993 & -0.000594969059928729 \tabularnewline
21 & 6.63 & 6.63050357962825 & -0.000503579628246875 \tabularnewline
22 & 6.79 & 6.63042622794875 & 0.159573772051247 \tabularnewline
23 & 6.79 & 6.81493734511655 & -0.0249373451165482 \tabularnewline
24 & 6.79 & 6.81110687736393 & -0.0211068773639331 \tabularnewline
25 & 6.81 & 6.80786478351942 & 0.00213521648058279 \tabularnewline
26 & 6.8 & 6.82819276060902 & -0.0281927606090182 \tabularnewline
27 & 6.8 & 6.81386224908643 & -0.0138622490864275 \tabularnewline
28 & 6.85 & 6.8117329567397 & 0.0382670432602961 \tabularnewline
29 & 6.85 & 6.8676109150593 & -0.0176109150593016 \tabularnewline
30 & 6.85 & 6.86490581385813 & -0.0149058138581344 \tabularnewline
31 & 6.85 & 6.86261622613165 & -0.0126162261316454 \tabularnewline
32 & 6.85 & 6.86067832748481 & -0.0106783274848121 \tabularnewline
33 & 6.85 & 6.85903809718398 & -0.00903809718398119 \tabularnewline
34 & 6.86 & 6.8576498122785 & 0.00235018772150664 \tabularnewline
35 & 6.86 & 6.86801080973984 & -0.00801080973984103 \tabularnewline
36 & 6.88 & 6.86678031995685 & 0.0132196800431474 \tabularnewline
37 & 6.88 & 6.88881091133972 & -0.00881091133971612 \tabularnewline
38 & 6.88 & 6.88745752301389 & -0.00745752301388602 \tabularnewline
39 & 6.91 & 6.88631202010307 & 0.0236879798969323 \tabularnewline
40 & 6.91 & 6.91995058077165 & -0.0099505807716449 \tabularnewline
41 & 6.91 & 6.91842213503745 & -0.00842213503744826 \tabularnewline
42 & 6.91 & 6.91712846417881 & -0.00712846417880808 \tabularnewline
43 & 6.99 & 6.916033505913 & 0.0739664940869966 \tabularnewline
44 & 6.99 & 7.007395030929 & -0.0173950309290012 \tabularnewline
45 & 6.99 & 7.00472309032274 & -0.0147230903227387 \tabularnewline
46 & 7.02 & 7.00246156960205 & 0.0175384303979511 \tabularnewline
47 & 7.02 & 7.03515553689315 & -0.0151555368931477 \tabularnewline
48 & 7.05 & 7.03282759079177 & 0.0171724092082304 \tabularnewline
49 & 7.05 & 7.0654653358845 & -0.0154653358844978 \tabularnewline
50 & 7.05 & 7.0630898035208 & -0.0130898035208054 \tabularnewline
51 & 7.05 & 7.06107916164854 & -0.0110791616485377 \tabularnewline
52 & 7.1 & 7.05937736174873 & 0.040622638251266 \tabularnewline
53 & 7.1 & 7.11561714810612 & -0.0156171481061183 \tabularnewline
54 & 7.1 & 7.1132182968279 & -0.0132182968278958 \tabularnewline
55 & 7.1 & 7.11118791791197 & -0.0111879179119718 \tabularnewline
56 & 7.12 & 7.10946941265087 & 0.0105305873491304 \tabularnewline
57 & 7.13 & 7.13108694952452 & -0.00108694952451938 \tabularnewline
58 & 7.18 & 7.14091999008746 & 0.0390800099125386 \tabularnewline
59 & 7.24 & 7.19692282306917 & 0.0430771769308311 \tabularnewline
60 & 7.24 & 7.26353963557812 & -0.0235396355781221 \tabularnewline
61 & 7.24 & 7.25992386114147 & -0.0199238611414732 \tabularnewline
62 & 7.27 & 7.25686348293147 & 0.0131365170685287 \tabularnewline
63 & 7.27 & 7.28888130017615 & -0.0188813001761492 \tabularnewline
64 & 7.27 & 7.28598106315757 & -0.0159810631575663 \tabularnewline
65 & 7.27 & 7.28352631319154 & -0.0135263131915435 \tabularnewline
66 & 7.3 & 7.28144862183146 & 0.0185513781685369 \tabularnewline
67 & 7.3 & 7.31429818161856 & -0.014298181618563 \tabularnewline
68 & 7.57 & 7.31210192843464 & 0.257898071565365 \tabularnewline
69 & 7.76 & 7.62171601894731 & 0.13828398105269 \tabularnewline
70 & 7.94 & 7.83295694606485 & 0.107043053935151 \tabularnewline
71 & 7.94 & 8.02939915209455 & -0.0893991520945514 \tabularnewline
72 & 7.96 & 8.01566711415672 & -0.0556671141567167 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113098&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]6.59[/C][C]6.59[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]6.59[/C][C]6.59[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]6.63[/C][C]6.59[/C][C]0.04[/C][/ROW]
[ROW][C]6[/C][C]6.63[/C][C]6.63614414683634[/C][C]-0.00614414683634212[/C][/ROW]
[ROW][C]7[/C][C]6.63[/C][C]6.63520038332768[/C][C]-0.00520038332767836[/C][/ROW]
[ROW][C]8[/C][C]6.63[/C][C]6.63440158535842[/C][C]-0.00440158535841562[/C][/ROW]
[ROW][C]9[/C][C]6.63[/C][C]6.63372548568955[/C][C]-0.00372548568954567[/C][/ROW]
[ROW][C]10[/C][C]6.63[/C][C]6.63315323741171[/C][C]-0.00315323741171447[/C][/ROW]
[ROW][C]11[/C][C]6.63[/C][C]6.63266888857003[/C][C]-0.002668888570029[/C][/ROW]
[ROW][C]12[/C][C]6.63[/C][C]6.63225893748843[/C][C]-0.00225893748842676[/C][/ROW]
[ROW][C]13[/C][C]6.63[/C][C]6.63191195639785[/C][C]-0.00191195639785136[/C][/ROW]
[ROW][C]14[/C][C]6.63[/C][C]6.63161827287652[/C][C]-0.00161827287652461[/C][/ROW]
[ROW][C]15[/C][C]6.63[/C][C]6.63136970022216[/C][C]-0.00136970022215799[/C][/ROW]
[ROW][C]16[/C][C]6.63[/C][C]6.63115930923999[/C][C]-0.00115930923999041[/C][/ROW]
[ROW][C]17[/C][C]6.63[/C][C]6.63098123508501[/C][C]-0.00098123508500958[/C][/ROW]
[ROW][C]18[/C][C]6.63[/C][C]6.63083051377393[/C][C]-0.000830513773927954[/C][/ROW]
[ROW][C]19[/C][C]6.63[/C][C]6.63070294380951[/C][C]-0.000702943809512746[/C][/ROW]
[ROW][C]20[/C][C]6.63[/C][C]6.63059496905993[/C][C]-0.000594969059928729[/C][/ROW]
[ROW][C]21[/C][C]6.63[/C][C]6.63050357962825[/C][C]-0.000503579628246875[/C][/ROW]
[ROW][C]22[/C][C]6.79[/C][C]6.63042622794875[/C][C]0.159573772051247[/C][/ROW]
[ROW][C]23[/C][C]6.79[/C][C]6.81493734511655[/C][C]-0.0249373451165482[/C][/ROW]
[ROW][C]24[/C][C]6.79[/C][C]6.81110687736393[/C][C]-0.0211068773639331[/C][/ROW]
[ROW][C]25[/C][C]6.81[/C][C]6.80786478351942[/C][C]0.00213521648058279[/C][/ROW]
[ROW][C]26[/C][C]6.8[/C][C]6.82819276060902[/C][C]-0.0281927606090182[/C][/ROW]
[ROW][C]27[/C][C]6.8[/C][C]6.81386224908643[/C][C]-0.0138622490864275[/C][/ROW]
[ROW][C]28[/C][C]6.85[/C][C]6.8117329567397[/C][C]0.0382670432602961[/C][/ROW]
[ROW][C]29[/C][C]6.85[/C][C]6.8676109150593[/C][C]-0.0176109150593016[/C][/ROW]
[ROW][C]30[/C][C]6.85[/C][C]6.86490581385813[/C][C]-0.0149058138581344[/C][/ROW]
[ROW][C]31[/C][C]6.85[/C][C]6.86261622613165[/C][C]-0.0126162261316454[/C][/ROW]
[ROW][C]32[/C][C]6.85[/C][C]6.86067832748481[/C][C]-0.0106783274848121[/C][/ROW]
[ROW][C]33[/C][C]6.85[/C][C]6.85903809718398[/C][C]-0.00903809718398119[/C][/ROW]
[ROW][C]34[/C][C]6.86[/C][C]6.8576498122785[/C][C]0.00235018772150664[/C][/ROW]
[ROW][C]35[/C][C]6.86[/C][C]6.86801080973984[/C][C]-0.00801080973984103[/C][/ROW]
[ROW][C]36[/C][C]6.88[/C][C]6.86678031995685[/C][C]0.0132196800431474[/C][/ROW]
[ROW][C]37[/C][C]6.88[/C][C]6.88881091133972[/C][C]-0.00881091133971612[/C][/ROW]
[ROW][C]38[/C][C]6.88[/C][C]6.88745752301389[/C][C]-0.00745752301388602[/C][/ROW]
[ROW][C]39[/C][C]6.91[/C][C]6.88631202010307[/C][C]0.0236879798969323[/C][/ROW]
[ROW][C]40[/C][C]6.91[/C][C]6.91995058077165[/C][C]-0.0099505807716449[/C][/ROW]
[ROW][C]41[/C][C]6.91[/C][C]6.91842213503745[/C][C]-0.00842213503744826[/C][/ROW]
[ROW][C]42[/C][C]6.91[/C][C]6.91712846417881[/C][C]-0.00712846417880808[/C][/ROW]
[ROW][C]43[/C][C]6.99[/C][C]6.916033505913[/C][C]0.0739664940869966[/C][/ROW]
[ROW][C]44[/C][C]6.99[/C][C]7.007395030929[/C][C]-0.0173950309290012[/C][/ROW]
[ROW][C]45[/C][C]6.99[/C][C]7.00472309032274[/C][C]-0.0147230903227387[/C][/ROW]
[ROW][C]46[/C][C]7.02[/C][C]7.00246156960205[/C][C]0.0175384303979511[/C][/ROW]
[ROW][C]47[/C][C]7.02[/C][C]7.03515553689315[/C][C]-0.0151555368931477[/C][/ROW]
[ROW][C]48[/C][C]7.05[/C][C]7.03282759079177[/C][C]0.0171724092082304[/C][/ROW]
[ROW][C]49[/C][C]7.05[/C][C]7.0654653358845[/C][C]-0.0154653358844978[/C][/ROW]
[ROW][C]50[/C][C]7.05[/C][C]7.0630898035208[/C][C]-0.0130898035208054[/C][/ROW]
[ROW][C]51[/C][C]7.05[/C][C]7.06107916164854[/C][C]-0.0110791616485377[/C][/ROW]
[ROW][C]52[/C][C]7.1[/C][C]7.05937736174873[/C][C]0.040622638251266[/C][/ROW]
[ROW][C]53[/C][C]7.1[/C][C]7.11561714810612[/C][C]-0.0156171481061183[/C][/ROW]
[ROW][C]54[/C][C]7.1[/C][C]7.1132182968279[/C][C]-0.0132182968278958[/C][/ROW]
[ROW][C]55[/C][C]7.1[/C][C]7.11118791791197[/C][C]-0.0111879179119718[/C][/ROW]
[ROW][C]56[/C][C]7.12[/C][C]7.10946941265087[/C][C]0.0105305873491304[/C][/ROW]
[ROW][C]57[/C][C]7.13[/C][C]7.13108694952452[/C][C]-0.00108694952451938[/C][/ROW]
[ROW][C]58[/C][C]7.18[/C][C]7.14091999008746[/C][C]0.0390800099125386[/C][/ROW]
[ROW][C]59[/C][C]7.24[/C][C]7.19692282306917[/C][C]0.0430771769308311[/C][/ROW]
[ROW][C]60[/C][C]7.24[/C][C]7.26353963557812[/C][C]-0.0235396355781221[/C][/ROW]
[ROW][C]61[/C][C]7.24[/C][C]7.25992386114147[/C][C]-0.0199238611414732[/C][/ROW]
[ROW][C]62[/C][C]7.27[/C][C]7.25686348293147[/C][C]0.0131365170685287[/C][/ROW]
[ROW][C]63[/C][C]7.27[/C][C]7.28888130017615[/C][C]-0.0188813001761492[/C][/ROW]
[ROW][C]64[/C][C]7.27[/C][C]7.28598106315757[/C][C]-0.0159810631575663[/C][/ROW]
[ROW][C]65[/C][C]7.27[/C][C]7.28352631319154[/C][C]-0.0135263131915435[/C][/ROW]
[ROW][C]66[/C][C]7.3[/C][C]7.28144862183146[/C][C]0.0185513781685369[/C][/ROW]
[ROW][C]67[/C][C]7.3[/C][C]7.31429818161856[/C][C]-0.014298181618563[/C][/ROW]
[ROW][C]68[/C][C]7.57[/C][C]7.31210192843464[/C][C]0.257898071565365[/C][/ROW]
[ROW][C]69[/C][C]7.76[/C][C]7.62171601894731[/C][C]0.13828398105269[/C][/ROW]
[ROW][C]70[/C][C]7.94[/C][C]7.83295694606485[/C][C]0.107043053935151[/C][/ROW]
[ROW][C]71[/C][C]7.94[/C][C]8.02939915209455[/C][C]-0.0893991520945514[/C][/ROW]
[ROW][C]72[/C][C]7.96[/C][C]8.01566711415672[/C][C]-0.0556671141567167[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113098&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113098&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
36.596.590
46.596.590
56.636.590.04
66.636.63614414683634-0.00614414683634212
76.636.63520038332768-0.00520038332767836
86.636.63440158535842-0.00440158535841562
96.636.63372548568955-0.00372548568954567
106.636.63315323741171-0.00315323741171447
116.636.63266888857003-0.002668888570029
126.636.63225893748843-0.00225893748842676
136.636.63191195639785-0.00191195639785136
146.636.63161827287652-0.00161827287652461
156.636.63136970022216-0.00136970022215799
166.636.63115930923999-0.00115930923999041
176.636.63098123508501-0.00098123508500958
186.636.63083051377393-0.000830513773927954
196.636.63070294380951-0.000702943809512746
206.636.63059496905993-0.000594969059928729
216.636.63050357962825-0.000503579628246875
226.796.630426227948750.159573772051247
236.796.81493734511655-0.0249373451165482
246.796.81110687736393-0.0211068773639331
256.816.807864783519420.00213521648058279
266.86.82819276060902-0.0281927606090182
276.86.81386224908643-0.0138622490864275
286.856.81173295673970.0382670432602961
296.856.8676109150593-0.0176109150593016
306.856.86490581385813-0.0149058138581344
316.856.86261622613165-0.0126162261316454
326.856.86067832748481-0.0106783274848121
336.856.85903809718398-0.00903809718398119
346.866.85764981227850.00235018772150664
356.866.86801080973984-0.00801080973984103
366.886.866780319956850.0132196800431474
376.886.88881091133972-0.00881091133971612
386.886.88745752301389-0.00745752301388602
396.916.886312020103070.0236879798969323
406.916.91995058077165-0.0099505807716449
416.916.91842213503745-0.00842213503744826
426.916.91712846417881-0.00712846417880808
436.996.9160335059130.0739664940869966
446.997.007395030929-0.0173950309290012
456.997.00472309032274-0.0147230903227387
467.027.002461569602050.0175384303979511
477.027.03515553689315-0.0151555368931477
487.057.032827590791770.0171724092082304
497.057.0654653358845-0.0154653358844978
507.057.0630898035208-0.0130898035208054
517.057.06107916164854-0.0110791616485377
527.17.059377361748730.040622638251266
537.17.11561714810612-0.0156171481061183
547.17.1132182968279-0.0132182968278958
557.17.11118791791197-0.0111879179119718
567.127.109469412650870.0105305873491304
577.137.13108694952452-0.00108694952451938
587.187.140919990087460.0390800099125386
597.247.196922823069170.0430771769308311
607.247.26353963557812-0.0235396355781221
617.247.25992386114147-0.0199238611414732
627.277.256863482931470.0131365170685287
637.277.28888130017615-0.0188813001761492
647.277.28598106315757-0.0159810631575663
657.277.28352631319154-0.0135263131915435
667.37.281448621831460.0185513781685369
677.37.31429818161856-0.014298181618563
687.577.312101928434640.257898071565365
697.767.621716018947310.13828398105269
707.947.832956946064850.107043053935151
717.948.02939915209455-0.0893991520945514
727.968.01566711415672-0.0556671141567167







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
738.027116441073367.93460224505358.11963063709323
748.094232882146727.95299180632148.23547395797205
758.161349323220087.975407469756618.34729117668355
768.228465764293447.998598958649928.45833256993696
778.29558220536688.021454414607778.56970999612583
788.362698646440168.043480629056138.68191666382419
798.429815087513528.064431840813028.79519833421402
808.496931528586888.084179488651278.90968356852248
818.564047969660248.10265658602649.02543935329408
828.63116441073368.119830779925699.1424980415415
838.698280851806968.13569010930759.26087159430641
848.765397292880328.150234979902369.38055960585827

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 8.02711644107336 & 7.9346022450535 & 8.11963063709323 \tabularnewline
74 & 8.09423288214672 & 7.9529918063214 & 8.23547395797205 \tabularnewline
75 & 8.16134932322008 & 7.97540746975661 & 8.34729117668355 \tabularnewline
76 & 8.22846576429344 & 7.99859895864992 & 8.45833256993696 \tabularnewline
77 & 8.2955822053668 & 8.02145441460777 & 8.56970999612583 \tabularnewline
78 & 8.36269864644016 & 8.04348062905613 & 8.68191666382419 \tabularnewline
79 & 8.42981508751352 & 8.06443184081302 & 8.79519833421402 \tabularnewline
80 & 8.49693152858688 & 8.08417948865127 & 8.90968356852248 \tabularnewline
81 & 8.56404796966024 & 8.1026565860264 & 9.02543935329408 \tabularnewline
82 & 8.6311644107336 & 8.11983077992569 & 9.1424980415415 \tabularnewline
83 & 8.69828085180696 & 8.1356901093075 & 9.26087159430641 \tabularnewline
84 & 8.76539729288032 & 8.15023497990236 & 9.38055960585827 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113098&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]8.02711644107336[/C][C]7.9346022450535[/C][C]8.11963063709323[/C][/ROW]
[ROW][C]74[/C][C]8.09423288214672[/C][C]7.9529918063214[/C][C]8.23547395797205[/C][/ROW]
[ROW][C]75[/C][C]8.16134932322008[/C][C]7.97540746975661[/C][C]8.34729117668355[/C][/ROW]
[ROW][C]76[/C][C]8.22846576429344[/C][C]7.99859895864992[/C][C]8.45833256993696[/C][/ROW]
[ROW][C]77[/C][C]8.2955822053668[/C][C]8.02145441460777[/C][C]8.56970999612583[/C][/ROW]
[ROW][C]78[/C][C]8.36269864644016[/C][C]8.04348062905613[/C][C]8.68191666382419[/C][/ROW]
[ROW][C]79[/C][C]8.42981508751352[/C][C]8.06443184081302[/C][C]8.79519833421402[/C][/ROW]
[ROW][C]80[/C][C]8.49693152858688[/C][C]8.08417948865127[/C][C]8.90968356852248[/C][/ROW]
[ROW][C]81[/C][C]8.56404796966024[/C][C]8.1026565860264[/C][C]9.02543935329408[/C][/ROW]
[ROW][C]82[/C][C]8.6311644107336[/C][C]8.11983077992569[/C][C]9.1424980415415[/C][/ROW]
[ROW][C]83[/C][C]8.69828085180696[/C][C]8.1356901093075[/C][C]9.26087159430641[/C][/ROW]
[ROW][C]84[/C][C]8.76539729288032[/C][C]8.15023497990236[/C][C]9.38055960585827[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113098&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113098&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
738.027116441073367.93460224505358.11963063709323
748.094232882146727.95299180632148.23547395797205
758.161349323220087.975407469756618.34729117668355
768.228465764293447.998598958649928.45833256993696
778.29558220536688.021454414607778.56970999612583
788.362698646440168.043480629056138.68191666382419
798.429815087513528.064431840813028.79519833421402
808.496931528586888.084179488651278.90968356852248
818.564047969660248.10265658602649.02543935329408
828.63116441073368.119830779925699.1424980415415
838.698280851806968.13569010930759.26087159430641
848.765397292880328.150234979902369.38055960585827



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')