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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 26 Apr 2016 19:46:06 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Apr/26/t1461696398fyoz6v988gcdeuq.htm/, Retrieved Fri, 03 May 2024 21:47:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294963, Retrieved Fri, 03 May 2024 21:47:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact69
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-04-26 18:46:06] [be6cd4bb5de010eb7c002bb036e110fa] [Current]
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Dataseries X:
81432
81935
82229
82963
82975
82892
82692
82648
83479
84176
84589
84857
84586
84635
84927
85563
86962
87780
88515
88800
89218
89626
89939
90663
91302
91560
92290
93281
94535
94855
95536
96008
96627
96738
96212
94198
93123
93022
93993
94876
95251
96216
96632
97023
97799
98001
98069
98172
98448
98157
98009
98020
97802
98006
98262
98629
99043
99289
99682
99979




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294963&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294963&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294963&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999929814973248
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999929814973248 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294963&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]0.999929814973248[/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=294963&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294963&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
alpha0.999929814973248
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
28193581432503
38222981934.9646969316294.035303068449
48296382228.9793631244734.020636875604
58297582962.94848274212.0515172580344
68289282974.9991541639-82.999154163932
78269282892.0058252978-200.005825297849
88264882692.0140374142-44.0140374142065
98347982648.0030891264830.996910873611
108417683478.9416764596697.058323540419
118458984175.9510769429413.048923057082
128485784588.9710101503268.028989849714
138458684856.9811883782-270.98118837818
148463584586.01901882248.9809811780433
158492784634.9965622685292.003437731473
168556384926.9795057309636.020494269091
178696285562.95536088461399.0446391154
188778086961.9018080146818.098191985424
198851587779.9425817565735.057418243479
208880088514.9484099754285.051590024566
218921888799.9799936465418.020006353472
228962689217.9706612547408.029338745328
238993989625.9713624499313.028637550058
249066389938.9780300767724.021969923313
259130290662.9491844987639.050815501323
269156091301.9551482014258.044851798579
279229091559.9818891152730.018110884819
289328192289.9487636594991.051236340645
299453593280.93044304251254.06955695753
309485594534.9119830946320.088016905414
319553694854.977534614681.022465386035
329600895535.95220242472.047797579959
339662796007.9668693127619.033130687298
349673896626.9565531432111.043446856842
359621296737.9922064127-525.992206412717
369419896212.0369167771-2014.03691677707
379312394198.1413552349-1075.14135523488
389302293123.0754588248-101.07545882478
399399393022.0070939838970.992906016225
409487693992.9318508369883.068149163082
419525194875.9380218383375.06197816167
429621695250.973676265965.026323734972
439663296215.9322696016416.067730398354
449702396631.9707982752391.029201724785
459779997022.972555605776.027444394989
469800197798.945534493202.054465506953
479806998000.985818801968.014181198072
489817298068.9952264229103.004773577122
499844898171.9927706072276.007229392781
509815798447.9806284252-290.980628425212
519800998157.0204224832-148.020422483183
529802098009.010388817310.989611182682
539780298019.9992286938-217.999228693836
549800697802.0153002817203.984699718305
559826298005.9856833284256.014316671601
569862998261.9820316283367.017968371671
579904398628.9742408341414.025759165932
589928999042.970941591246.029058408982
599968299288.982732444393.017267556046
609997999681.9724160726297.02758392744

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 81935 & 81432 & 503 \tabularnewline
3 & 82229 & 81934.9646969316 & 294.035303068449 \tabularnewline
4 & 82963 & 82228.9793631244 & 734.020636875604 \tabularnewline
5 & 82975 & 82962.948482742 & 12.0515172580344 \tabularnewline
6 & 82892 & 82974.9991541639 & -82.999154163932 \tabularnewline
7 & 82692 & 82892.0058252978 & -200.005825297849 \tabularnewline
8 & 82648 & 82692.0140374142 & -44.0140374142065 \tabularnewline
9 & 83479 & 82648.0030891264 & 830.996910873611 \tabularnewline
10 & 84176 & 83478.9416764596 & 697.058323540419 \tabularnewline
11 & 84589 & 84175.9510769429 & 413.048923057082 \tabularnewline
12 & 84857 & 84588.9710101503 & 268.028989849714 \tabularnewline
13 & 84586 & 84856.9811883782 & -270.98118837818 \tabularnewline
14 & 84635 & 84586.019018822 & 48.9809811780433 \tabularnewline
15 & 84927 & 84634.9965622685 & 292.003437731473 \tabularnewline
16 & 85563 & 84926.9795057309 & 636.020494269091 \tabularnewline
17 & 86962 & 85562.9553608846 & 1399.0446391154 \tabularnewline
18 & 87780 & 86961.9018080146 & 818.098191985424 \tabularnewline
19 & 88515 & 87779.9425817565 & 735.057418243479 \tabularnewline
20 & 88800 & 88514.9484099754 & 285.051590024566 \tabularnewline
21 & 89218 & 88799.9799936465 & 418.020006353472 \tabularnewline
22 & 89626 & 89217.9706612547 & 408.029338745328 \tabularnewline
23 & 89939 & 89625.9713624499 & 313.028637550058 \tabularnewline
24 & 90663 & 89938.9780300767 & 724.021969923313 \tabularnewline
25 & 91302 & 90662.9491844987 & 639.050815501323 \tabularnewline
26 & 91560 & 91301.9551482014 & 258.044851798579 \tabularnewline
27 & 92290 & 91559.9818891152 & 730.018110884819 \tabularnewline
28 & 93281 & 92289.9487636594 & 991.051236340645 \tabularnewline
29 & 94535 & 93280.9304430425 & 1254.06955695753 \tabularnewline
30 & 94855 & 94534.9119830946 & 320.088016905414 \tabularnewline
31 & 95536 & 94854.977534614 & 681.022465386035 \tabularnewline
32 & 96008 & 95535.95220242 & 472.047797579959 \tabularnewline
33 & 96627 & 96007.9668693127 & 619.033130687298 \tabularnewline
34 & 96738 & 96626.9565531432 & 111.043446856842 \tabularnewline
35 & 96212 & 96737.9922064127 & -525.992206412717 \tabularnewline
36 & 94198 & 96212.0369167771 & -2014.03691677707 \tabularnewline
37 & 93123 & 94198.1413552349 & -1075.14135523488 \tabularnewline
38 & 93022 & 93123.0754588248 & -101.07545882478 \tabularnewline
39 & 93993 & 93022.0070939838 & 970.992906016225 \tabularnewline
40 & 94876 & 93992.9318508369 & 883.068149163082 \tabularnewline
41 & 95251 & 94875.9380218383 & 375.06197816167 \tabularnewline
42 & 96216 & 95250.973676265 & 965.026323734972 \tabularnewline
43 & 96632 & 96215.9322696016 & 416.067730398354 \tabularnewline
44 & 97023 & 96631.9707982752 & 391.029201724785 \tabularnewline
45 & 97799 & 97022.972555605 & 776.027444394989 \tabularnewline
46 & 98001 & 97798.945534493 & 202.054465506953 \tabularnewline
47 & 98069 & 98000.9858188019 & 68.014181198072 \tabularnewline
48 & 98172 & 98068.9952264229 & 103.004773577122 \tabularnewline
49 & 98448 & 98171.9927706072 & 276.007229392781 \tabularnewline
50 & 98157 & 98447.9806284252 & -290.980628425212 \tabularnewline
51 & 98009 & 98157.0204224832 & -148.020422483183 \tabularnewline
52 & 98020 & 98009.0103888173 & 10.989611182682 \tabularnewline
53 & 97802 & 98019.9992286938 & -217.999228693836 \tabularnewline
54 & 98006 & 97802.0153002817 & 203.984699718305 \tabularnewline
55 & 98262 & 98005.9856833284 & 256.014316671601 \tabularnewline
56 & 98629 & 98261.9820316283 & 367.017968371671 \tabularnewline
57 & 99043 & 98628.9742408341 & 414.025759165932 \tabularnewline
58 & 99289 & 99042.970941591 & 246.029058408982 \tabularnewline
59 & 99682 & 99288.982732444 & 393.017267556046 \tabularnewline
60 & 99979 & 99681.9724160726 & 297.02758392744 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294963&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]81935[/C][C]81432[/C][C]503[/C][/ROW]
[ROW][C]3[/C][C]82229[/C][C]81934.9646969316[/C][C]294.035303068449[/C][/ROW]
[ROW][C]4[/C][C]82963[/C][C]82228.9793631244[/C][C]734.020636875604[/C][/ROW]
[ROW][C]5[/C][C]82975[/C][C]82962.948482742[/C][C]12.0515172580344[/C][/ROW]
[ROW][C]6[/C][C]82892[/C][C]82974.9991541639[/C][C]-82.999154163932[/C][/ROW]
[ROW][C]7[/C][C]82692[/C][C]82892.0058252978[/C][C]-200.005825297849[/C][/ROW]
[ROW][C]8[/C][C]82648[/C][C]82692.0140374142[/C][C]-44.0140374142065[/C][/ROW]
[ROW][C]9[/C][C]83479[/C][C]82648.0030891264[/C][C]830.996910873611[/C][/ROW]
[ROW][C]10[/C][C]84176[/C][C]83478.9416764596[/C][C]697.058323540419[/C][/ROW]
[ROW][C]11[/C][C]84589[/C][C]84175.9510769429[/C][C]413.048923057082[/C][/ROW]
[ROW][C]12[/C][C]84857[/C][C]84588.9710101503[/C][C]268.028989849714[/C][/ROW]
[ROW][C]13[/C][C]84586[/C][C]84856.9811883782[/C][C]-270.98118837818[/C][/ROW]
[ROW][C]14[/C][C]84635[/C][C]84586.019018822[/C][C]48.9809811780433[/C][/ROW]
[ROW][C]15[/C][C]84927[/C][C]84634.9965622685[/C][C]292.003437731473[/C][/ROW]
[ROW][C]16[/C][C]85563[/C][C]84926.9795057309[/C][C]636.020494269091[/C][/ROW]
[ROW][C]17[/C][C]86962[/C][C]85562.9553608846[/C][C]1399.0446391154[/C][/ROW]
[ROW][C]18[/C][C]87780[/C][C]86961.9018080146[/C][C]818.098191985424[/C][/ROW]
[ROW][C]19[/C][C]88515[/C][C]87779.9425817565[/C][C]735.057418243479[/C][/ROW]
[ROW][C]20[/C][C]88800[/C][C]88514.9484099754[/C][C]285.051590024566[/C][/ROW]
[ROW][C]21[/C][C]89218[/C][C]88799.9799936465[/C][C]418.020006353472[/C][/ROW]
[ROW][C]22[/C][C]89626[/C][C]89217.9706612547[/C][C]408.029338745328[/C][/ROW]
[ROW][C]23[/C][C]89939[/C][C]89625.9713624499[/C][C]313.028637550058[/C][/ROW]
[ROW][C]24[/C][C]90663[/C][C]89938.9780300767[/C][C]724.021969923313[/C][/ROW]
[ROW][C]25[/C][C]91302[/C][C]90662.9491844987[/C][C]639.050815501323[/C][/ROW]
[ROW][C]26[/C][C]91560[/C][C]91301.9551482014[/C][C]258.044851798579[/C][/ROW]
[ROW][C]27[/C][C]92290[/C][C]91559.9818891152[/C][C]730.018110884819[/C][/ROW]
[ROW][C]28[/C][C]93281[/C][C]92289.9487636594[/C][C]991.051236340645[/C][/ROW]
[ROW][C]29[/C][C]94535[/C][C]93280.9304430425[/C][C]1254.06955695753[/C][/ROW]
[ROW][C]30[/C][C]94855[/C][C]94534.9119830946[/C][C]320.088016905414[/C][/ROW]
[ROW][C]31[/C][C]95536[/C][C]94854.977534614[/C][C]681.022465386035[/C][/ROW]
[ROW][C]32[/C][C]96008[/C][C]95535.95220242[/C][C]472.047797579959[/C][/ROW]
[ROW][C]33[/C][C]96627[/C][C]96007.9668693127[/C][C]619.033130687298[/C][/ROW]
[ROW][C]34[/C][C]96738[/C][C]96626.9565531432[/C][C]111.043446856842[/C][/ROW]
[ROW][C]35[/C][C]96212[/C][C]96737.9922064127[/C][C]-525.992206412717[/C][/ROW]
[ROW][C]36[/C][C]94198[/C][C]96212.0369167771[/C][C]-2014.03691677707[/C][/ROW]
[ROW][C]37[/C][C]93123[/C][C]94198.1413552349[/C][C]-1075.14135523488[/C][/ROW]
[ROW][C]38[/C][C]93022[/C][C]93123.0754588248[/C][C]-101.07545882478[/C][/ROW]
[ROW][C]39[/C][C]93993[/C][C]93022.0070939838[/C][C]970.992906016225[/C][/ROW]
[ROW][C]40[/C][C]94876[/C][C]93992.9318508369[/C][C]883.068149163082[/C][/ROW]
[ROW][C]41[/C][C]95251[/C][C]94875.9380218383[/C][C]375.06197816167[/C][/ROW]
[ROW][C]42[/C][C]96216[/C][C]95250.973676265[/C][C]965.026323734972[/C][/ROW]
[ROW][C]43[/C][C]96632[/C][C]96215.9322696016[/C][C]416.067730398354[/C][/ROW]
[ROW][C]44[/C][C]97023[/C][C]96631.9707982752[/C][C]391.029201724785[/C][/ROW]
[ROW][C]45[/C][C]97799[/C][C]97022.972555605[/C][C]776.027444394989[/C][/ROW]
[ROW][C]46[/C][C]98001[/C][C]97798.945534493[/C][C]202.054465506953[/C][/ROW]
[ROW][C]47[/C][C]98069[/C][C]98000.9858188019[/C][C]68.014181198072[/C][/ROW]
[ROW][C]48[/C][C]98172[/C][C]98068.9952264229[/C][C]103.004773577122[/C][/ROW]
[ROW][C]49[/C][C]98448[/C][C]98171.9927706072[/C][C]276.007229392781[/C][/ROW]
[ROW][C]50[/C][C]98157[/C][C]98447.9806284252[/C][C]-290.980628425212[/C][/ROW]
[ROW][C]51[/C][C]98009[/C][C]98157.0204224832[/C][C]-148.020422483183[/C][/ROW]
[ROW][C]52[/C][C]98020[/C][C]98009.0103888173[/C][C]10.989611182682[/C][/ROW]
[ROW][C]53[/C][C]97802[/C][C]98019.9992286938[/C][C]-217.999228693836[/C][/ROW]
[ROW][C]54[/C][C]98006[/C][C]97802.0153002817[/C][C]203.984699718305[/C][/ROW]
[ROW][C]55[/C][C]98262[/C][C]98005.9856833284[/C][C]256.014316671601[/C][/ROW]
[ROW][C]56[/C][C]98629[/C][C]98261.9820316283[/C][C]367.017968371671[/C][/ROW]
[ROW][C]57[/C][C]99043[/C][C]98628.9742408341[/C][C]414.025759165932[/C][/ROW]
[ROW][C]58[/C][C]99289[/C][C]99042.970941591[/C][C]246.029058408982[/C][/ROW]
[ROW][C]59[/C][C]99682[/C][C]99288.982732444[/C][C]393.017267556046[/C][/ROW]
[ROW][C]60[/C][C]99979[/C][C]99681.9724160726[/C][C]297.02758392744[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294963&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294963&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
28193581432503
38222981934.9646969316294.035303068449
48296382228.9793631244734.020636875604
58297582962.94848274212.0515172580344
68289282974.9991541639-82.999154163932
78269282892.0058252978-200.005825297849
88264882692.0140374142-44.0140374142065
98347982648.0030891264830.996910873611
108417683478.9416764596697.058323540419
118458984175.9510769429413.048923057082
128485784588.9710101503268.028989849714
138458684856.9811883782-270.98118837818
148463584586.01901882248.9809811780433
158492784634.9965622685292.003437731473
168556384926.9795057309636.020494269091
178696285562.95536088461399.0446391154
188778086961.9018080146818.098191985424
198851587779.9425817565735.057418243479
208880088514.9484099754285.051590024566
218921888799.9799936465418.020006353472
228962689217.9706612547408.029338745328
238993989625.9713624499313.028637550058
249066389938.9780300767724.021969923313
259130290662.9491844987639.050815501323
269156091301.9551482014258.044851798579
279229091559.9818891152730.018110884819
289328192289.9487636594991.051236340645
299453593280.93044304251254.06955695753
309485594534.9119830946320.088016905414
319553694854.977534614681.022465386035
329600895535.95220242472.047797579959
339662796007.9668693127619.033130687298
349673896626.9565531432111.043446856842
359621296737.9922064127-525.992206412717
369419896212.0369167771-2014.03691677707
379312394198.1413552349-1075.14135523488
389302293123.0754588248-101.07545882478
399399393022.0070939838970.992906016225
409487693992.9318508369883.068149163082
419525194875.9380218383375.06197816167
429621695250.973676265965.026323734972
439663296215.9322696016416.067730398354
449702396631.9707982752391.029201724785
459779997022.972555605776.027444394989
469800197798.945534493202.054465506953
479806998000.985818801968.014181198072
489817298068.9952264229103.004773577122
499844898171.9927706072276.007229392781
509815798447.9806284252-290.980628425212
519800998157.0204224832-148.020422483183
529802098009.010388817310.989611182682
539780298019.9992286938-217.999228693836
549800697802.0153002817203.984699718305
559826298005.9856833284256.014316671601
569862998261.9820316283367.017968371671
579904398628.9742408341414.025759165932
589928999042.970941591246.029058408982
599968299288.982732444393.017267556046
609997999681.9724160726297.02758392744







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6199978.979153111198941.0820877234101016.876218499
6299978.979153111198511.2225550644101446.735751158
6399978.979153111198181.3728158173101776.585490405
6499978.979153111197903.2942886271102054.664017595
6599978.979153111197658.3010691414102299.657237081
6699978.979153111197436.8096304029102521.148675819
6799978.979153111197233.1268273376102724.831478885
6899978.979153111197043.5432216479102914.415084574
6999978.979153111196865.4822090795103092.476097143
7099978.979153111196697.0677689839103260.890537238
7199978.979153111196536.8836509449103421.074655277
7299978.979153111196383.8295652911103574.128740931

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 99978.9791531111 & 98941.0820877234 & 101016.876218499 \tabularnewline
62 & 99978.9791531111 & 98511.2225550644 & 101446.735751158 \tabularnewline
63 & 99978.9791531111 & 98181.3728158173 & 101776.585490405 \tabularnewline
64 & 99978.9791531111 & 97903.2942886271 & 102054.664017595 \tabularnewline
65 & 99978.9791531111 & 97658.3010691414 & 102299.657237081 \tabularnewline
66 & 99978.9791531111 & 97436.8096304029 & 102521.148675819 \tabularnewline
67 & 99978.9791531111 & 97233.1268273376 & 102724.831478885 \tabularnewline
68 & 99978.9791531111 & 97043.5432216479 & 102914.415084574 \tabularnewline
69 & 99978.9791531111 & 96865.4822090795 & 103092.476097143 \tabularnewline
70 & 99978.9791531111 & 96697.0677689839 & 103260.890537238 \tabularnewline
71 & 99978.9791531111 & 96536.8836509449 & 103421.074655277 \tabularnewline
72 & 99978.9791531111 & 96383.8295652911 & 103574.128740931 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294963&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]99978.9791531111[/C][C]98941.0820877234[/C][C]101016.876218499[/C][/ROW]
[ROW][C]62[/C][C]99978.9791531111[/C][C]98511.2225550644[/C][C]101446.735751158[/C][/ROW]
[ROW][C]63[/C][C]99978.9791531111[/C][C]98181.3728158173[/C][C]101776.585490405[/C][/ROW]
[ROW][C]64[/C][C]99978.9791531111[/C][C]97903.2942886271[/C][C]102054.664017595[/C][/ROW]
[ROW][C]65[/C][C]99978.9791531111[/C][C]97658.3010691414[/C][C]102299.657237081[/C][/ROW]
[ROW][C]66[/C][C]99978.9791531111[/C][C]97436.8096304029[/C][C]102521.148675819[/C][/ROW]
[ROW][C]67[/C][C]99978.9791531111[/C][C]97233.1268273376[/C][C]102724.831478885[/C][/ROW]
[ROW][C]68[/C][C]99978.9791531111[/C][C]97043.5432216479[/C][C]102914.415084574[/C][/ROW]
[ROW][C]69[/C][C]99978.9791531111[/C][C]96865.4822090795[/C][C]103092.476097143[/C][/ROW]
[ROW][C]70[/C][C]99978.9791531111[/C][C]96697.0677689839[/C][C]103260.890537238[/C][/ROW]
[ROW][C]71[/C][C]99978.9791531111[/C][C]96536.8836509449[/C][C]103421.074655277[/C][/ROW]
[ROW][C]72[/C][C]99978.9791531111[/C][C]96383.8295652911[/C][C]103574.128740931[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294963&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294963&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
6199978.979153111198941.0820877234101016.876218499
6299978.979153111198511.2225550644101446.735751158
6399978.979153111198181.3728158173101776.585490405
6499978.979153111197903.2942886271102054.664017595
6599978.979153111197658.3010691414102299.657237081
6699978.979153111197436.8096304029102521.148675819
6799978.979153111197233.1268273376102724.831478885
6899978.979153111197043.5432216479102914.415084574
6999978.979153111196865.4822090795103092.476097143
7099978.979153111196697.0677689839103260.890537238
7199978.979153111196536.8836509449103421.074655277
7299978.979153111196383.8295652911103574.128740931



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')