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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 11 Dec 2009 09:09:28 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/11/t1260547842x4g7q2wengswca0.htm/, Retrieved Sun, 28 Apr 2024 23:39:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=66452, Retrieved Sun, 28 Apr 2024 23:39:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact128
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [] [2009-11-27 15:04:36] [b98453cac15ba1066b407e146608df68]
-    D    [Exponential Smoothing] [Exponential smoot...] [2009-12-03 16:44:51] [d46757a0a8c9b00540ab7e7e0c34bfc4]
-    D      [Exponential Smoothing] [Exponential Smoot...] [2009-12-04 19:32:46] [4f1a20f787b3465111b61213cdeef1a9]
-    D          [Exponential Smoothing] [Experimental smoo...] [2009-12-11 16:09:28] [d1818fb1d9a1b0f34f8553ada228d3d5] [Current]
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Dataseries X:
8.3
8.2
8
7.9
7.6
7.6
8.3
8.4
8.4
8.4
8.4
8.6
8.9
8.8
8.3
7.5
7.2
7.4
8.8
9.3
9.3
8.7
8.2
8.3
8.5
8.6
8.5
8.2
8.1
7.9
8.6
8.7
8.7
8.5
8.4
8.5
8.7
8.7
8.6
8.5
8.3
8
8.2
8.1
8.1
8
7.9
7.9
8
8
7.9
8
7.7
7.2
7.5
7.3
7
7
7
7.2
7.3
7.1
6.8
6.4
6.1
6.5
7.7
7.9
7.5
6.9
6.6
6.9




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=66452&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=66452&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66452&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' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.00352340646797870
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.00352340646797870 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=66452&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]0.00352340646797870[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=66452&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66452&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
beta0.00352340646797870
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
138.98.9503140766282-0.0503140766281973
148.88.757959327267920.0420406727320852
158.38.244316094831130.0556839051688698
167.57.472424420550620.0275755794493833
177.27.21280290290433-0.0128029029043333
187.47.43515757080091-0.0351575708009104
198.88.525842027480930.274157972519067
209.38.872318873525670.427681126474331
219.39.279597586173770.0204024138262309
228.79.32643992965158-0.626439929651577
238.28.75478518261489-0.554785182614888
248.38.43891041178834-0.138910411788343
258.58.59475462049406-0.094754620494058
268.68.362991115487830.237008884512170
278.58.055914760946220.444085239053775
288.27.651996457042960.548003542957042
298.17.886155383552020.213844616447984
307.98.36500928681314-0.465009286813141
318.69.1018164327324-0.501816432732401
328.78.669593132450350.0304068675496527
338.78.679383246873880.0206167531261219
348.58.72320812946758-0.223208129467581
358.48.55246176408234-0.152461764082336
368.58.64419427175929-0.144194271759291
378.78.80129428351827-0.101294283518273
388.78.559210007762760.140789992237234
398.68.148936960138460.451063039861536
408.57.741438411716860.758561588283137
418.38.174357348412970.125642651587032
4288.57110904648884-0.571109046488839
438.29.21638133958279-1.01638133958279
448.18.26501134402285-0.165011344022849
458.18.079206822257260.0207931777427444
4688.12001412938259-0.120014129382588
477.98.047902750705-0.147902750704992
487.98.12814290430106-0.228142904301055
4988.17832367553149-0.178323675531486
5087.86874719452720.131252805472799
517.97.491607399373990.40839260062601
5287.109818330124760.890181669875243
537.77.692309190794510.00769080920548859
547.27.95013065469094-0.750130654690939
557.58.29281845025857-0.792818450258565
567.37.55771594955604-0.257715949556043
5777.27936065334012-0.279360653340116
5877.01493489161981-0.0149348916198146
5977.0396898750571-0.0396898750571033
607.27.20002038019794-2.03801979425933e-05
617.37.45181192963172-0.151811929631722
627.17.17843657501434-0.0784365750143401
636.86.646814668082130.153185331917874
646.46.117761617845420.282238382154585
656.16.15119200601735-0.0511920060173523
666.56.295340942525540.204659057474462
677.77.484795640886050.215204359113954
687.97.759112708465980.140887291534019
697.57.87825668532496-0.378256685324959
706.97.51644954893393-0.616449548933926
716.66.93842614275394-0.338426142753939
726.96.787288075495040.112711924504959

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 8.9 & 8.9503140766282 & -0.0503140766281973 \tabularnewline
14 & 8.8 & 8.75795932726792 & 0.0420406727320852 \tabularnewline
15 & 8.3 & 8.24431609483113 & 0.0556839051688698 \tabularnewline
16 & 7.5 & 7.47242442055062 & 0.0275755794493833 \tabularnewline
17 & 7.2 & 7.21280290290433 & -0.0128029029043333 \tabularnewline
18 & 7.4 & 7.43515757080091 & -0.0351575708009104 \tabularnewline
19 & 8.8 & 8.52584202748093 & 0.274157972519067 \tabularnewline
20 & 9.3 & 8.87231887352567 & 0.427681126474331 \tabularnewline
21 & 9.3 & 9.27959758617377 & 0.0204024138262309 \tabularnewline
22 & 8.7 & 9.32643992965158 & -0.626439929651577 \tabularnewline
23 & 8.2 & 8.75478518261489 & -0.554785182614888 \tabularnewline
24 & 8.3 & 8.43891041178834 & -0.138910411788343 \tabularnewline
25 & 8.5 & 8.59475462049406 & -0.094754620494058 \tabularnewline
26 & 8.6 & 8.36299111548783 & 0.237008884512170 \tabularnewline
27 & 8.5 & 8.05591476094622 & 0.444085239053775 \tabularnewline
28 & 8.2 & 7.65199645704296 & 0.548003542957042 \tabularnewline
29 & 8.1 & 7.88615538355202 & 0.213844616447984 \tabularnewline
30 & 7.9 & 8.36500928681314 & -0.465009286813141 \tabularnewline
31 & 8.6 & 9.1018164327324 & -0.501816432732401 \tabularnewline
32 & 8.7 & 8.66959313245035 & 0.0304068675496527 \tabularnewline
33 & 8.7 & 8.67938324687388 & 0.0206167531261219 \tabularnewline
34 & 8.5 & 8.72320812946758 & -0.223208129467581 \tabularnewline
35 & 8.4 & 8.55246176408234 & -0.152461764082336 \tabularnewline
36 & 8.5 & 8.64419427175929 & -0.144194271759291 \tabularnewline
37 & 8.7 & 8.80129428351827 & -0.101294283518273 \tabularnewline
38 & 8.7 & 8.55921000776276 & 0.140789992237234 \tabularnewline
39 & 8.6 & 8.14893696013846 & 0.451063039861536 \tabularnewline
40 & 8.5 & 7.74143841171686 & 0.758561588283137 \tabularnewline
41 & 8.3 & 8.17435734841297 & 0.125642651587032 \tabularnewline
42 & 8 & 8.57110904648884 & -0.571109046488839 \tabularnewline
43 & 8.2 & 9.21638133958279 & -1.01638133958279 \tabularnewline
44 & 8.1 & 8.26501134402285 & -0.165011344022849 \tabularnewline
45 & 8.1 & 8.07920682225726 & 0.0207931777427444 \tabularnewline
46 & 8 & 8.12001412938259 & -0.120014129382588 \tabularnewline
47 & 7.9 & 8.047902750705 & -0.147902750704992 \tabularnewline
48 & 7.9 & 8.12814290430106 & -0.228142904301055 \tabularnewline
49 & 8 & 8.17832367553149 & -0.178323675531486 \tabularnewline
50 & 8 & 7.8687471945272 & 0.131252805472799 \tabularnewline
51 & 7.9 & 7.49160739937399 & 0.40839260062601 \tabularnewline
52 & 8 & 7.10981833012476 & 0.890181669875243 \tabularnewline
53 & 7.7 & 7.69230919079451 & 0.00769080920548859 \tabularnewline
54 & 7.2 & 7.95013065469094 & -0.750130654690939 \tabularnewline
55 & 7.5 & 8.29281845025857 & -0.792818450258565 \tabularnewline
56 & 7.3 & 7.55771594955604 & -0.257715949556043 \tabularnewline
57 & 7 & 7.27936065334012 & -0.279360653340116 \tabularnewline
58 & 7 & 7.01493489161981 & -0.0149348916198146 \tabularnewline
59 & 7 & 7.0396898750571 & -0.0396898750571033 \tabularnewline
60 & 7.2 & 7.20002038019794 & -2.03801979425933e-05 \tabularnewline
61 & 7.3 & 7.45181192963172 & -0.151811929631722 \tabularnewline
62 & 7.1 & 7.17843657501434 & -0.0784365750143401 \tabularnewline
63 & 6.8 & 6.64681466808213 & 0.153185331917874 \tabularnewline
64 & 6.4 & 6.11776161784542 & 0.282238382154585 \tabularnewline
65 & 6.1 & 6.15119200601735 & -0.0511920060173523 \tabularnewline
66 & 6.5 & 6.29534094252554 & 0.204659057474462 \tabularnewline
67 & 7.7 & 7.48479564088605 & 0.215204359113954 \tabularnewline
68 & 7.9 & 7.75911270846598 & 0.140887291534019 \tabularnewline
69 & 7.5 & 7.87825668532496 & -0.378256685324959 \tabularnewline
70 & 6.9 & 7.51644954893393 & -0.616449548933926 \tabularnewline
71 & 6.6 & 6.93842614275394 & -0.338426142753939 \tabularnewline
72 & 6.9 & 6.78728807549504 & 0.112711924504959 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=66452&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]13[/C][C]8.9[/C][C]8.9503140766282[/C][C]-0.0503140766281973[/C][/ROW]
[ROW][C]14[/C][C]8.8[/C][C]8.75795932726792[/C][C]0.0420406727320852[/C][/ROW]
[ROW][C]15[/C][C]8.3[/C][C]8.24431609483113[/C][C]0.0556839051688698[/C][/ROW]
[ROW][C]16[/C][C]7.5[/C][C]7.47242442055062[/C][C]0.0275755794493833[/C][/ROW]
[ROW][C]17[/C][C]7.2[/C][C]7.21280290290433[/C][C]-0.0128029029043333[/C][/ROW]
[ROW][C]18[/C][C]7.4[/C][C]7.43515757080091[/C][C]-0.0351575708009104[/C][/ROW]
[ROW][C]19[/C][C]8.8[/C][C]8.52584202748093[/C][C]0.274157972519067[/C][/ROW]
[ROW][C]20[/C][C]9.3[/C][C]8.87231887352567[/C][C]0.427681126474331[/C][/ROW]
[ROW][C]21[/C][C]9.3[/C][C]9.27959758617377[/C][C]0.0204024138262309[/C][/ROW]
[ROW][C]22[/C][C]8.7[/C][C]9.32643992965158[/C][C]-0.626439929651577[/C][/ROW]
[ROW][C]23[/C][C]8.2[/C][C]8.75478518261489[/C][C]-0.554785182614888[/C][/ROW]
[ROW][C]24[/C][C]8.3[/C][C]8.43891041178834[/C][C]-0.138910411788343[/C][/ROW]
[ROW][C]25[/C][C]8.5[/C][C]8.59475462049406[/C][C]-0.094754620494058[/C][/ROW]
[ROW][C]26[/C][C]8.6[/C][C]8.36299111548783[/C][C]0.237008884512170[/C][/ROW]
[ROW][C]27[/C][C]8.5[/C][C]8.05591476094622[/C][C]0.444085239053775[/C][/ROW]
[ROW][C]28[/C][C]8.2[/C][C]7.65199645704296[/C][C]0.548003542957042[/C][/ROW]
[ROW][C]29[/C][C]8.1[/C][C]7.88615538355202[/C][C]0.213844616447984[/C][/ROW]
[ROW][C]30[/C][C]7.9[/C][C]8.36500928681314[/C][C]-0.465009286813141[/C][/ROW]
[ROW][C]31[/C][C]8.6[/C][C]9.1018164327324[/C][C]-0.501816432732401[/C][/ROW]
[ROW][C]32[/C][C]8.7[/C][C]8.66959313245035[/C][C]0.0304068675496527[/C][/ROW]
[ROW][C]33[/C][C]8.7[/C][C]8.67938324687388[/C][C]0.0206167531261219[/C][/ROW]
[ROW][C]34[/C][C]8.5[/C][C]8.72320812946758[/C][C]-0.223208129467581[/C][/ROW]
[ROW][C]35[/C][C]8.4[/C][C]8.55246176408234[/C][C]-0.152461764082336[/C][/ROW]
[ROW][C]36[/C][C]8.5[/C][C]8.64419427175929[/C][C]-0.144194271759291[/C][/ROW]
[ROW][C]37[/C][C]8.7[/C][C]8.80129428351827[/C][C]-0.101294283518273[/C][/ROW]
[ROW][C]38[/C][C]8.7[/C][C]8.55921000776276[/C][C]0.140789992237234[/C][/ROW]
[ROW][C]39[/C][C]8.6[/C][C]8.14893696013846[/C][C]0.451063039861536[/C][/ROW]
[ROW][C]40[/C][C]8.5[/C][C]7.74143841171686[/C][C]0.758561588283137[/C][/ROW]
[ROW][C]41[/C][C]8.3[/C][C]8.17435734841297[/C][C]0.125642651587032[/C][/ROW]
[ROW][C]42[/C][C]8[/C][C]8.57110904648884[/C][C]-0.571109046488839[/C][/ROW]
[ROW][C]43[/C][C]8.2[/C][C]9.21638133958279[/C][C]-1.01638133958279[/C][/ROW]
[ROW][C]44[/C][C]8.1[/C][C]8.26501134402285[/C][C]-0.165011344022849[/C][/ROW]
[ROW][C]45[/C][C]8.1[/C][C]8.07920682225726[/C][C]0.0207931777427444[/C][/ROW]
[ROW][C]46[/C][C]8[/C][C]8.12001412938259[/C][C]-0.120014129382588[/C][/ROW]
[ROW][C]47[/C][C]7.9[/C][C]8.047902750705[/C][C]-0.147902750704992[/C][/ROW]
[ROW][C]48[/C][C]7.9[/C][C]8.12814290430106[/C][C]-0.228142904301055[/C][/ROW]
[ROW][C]49[/C][C]8[/C][C]8.17832367553149[/C][C]-0.178323675531486[/C][/ROW]
[ROW][C]50[/C][C]8[/C][C]7.8687471945272[/C][C]0.131252805472799[/C][/ROW]
[ROW][C]51[/C][C]7.9[/C][C]7.49160739937399[/C][C]0.40839260062601[/C][/ROW]
[ROW][C]52[/C][C]8[/C][C]7.10981833012476[/C][C]0.890181669875243[/C][/ROW]
[ROW][C]53[/C][C]7.7[/C][C]7.69230919079451[/C][C]0.00769080920548859[/C][/ROW]
[ROW][C]54[/C][C]7.2[/C][C]7.95013065469094[/C][C]-0.750130654690939[/C][/ROW]
[ROW][C]55[/C][C]7.5[/C][C]8.29281845025857[/C][C]-0.792818450258565[/C][/ROW]
[ROW][C]56[/C][C]7.3[/C][C]7.55771594955604[/C][C]-0.257715949556043[/C][/ROW]
[ROW][C]57[/C][C]7[/C][C]7.27936065334012[/C][C]-0.279360653340116[/C][/ROW]
[ROW][C]58[/C][C]7[/C][C]7.01493489161981[/C][C]-0.0149348916198146[/C][/ROW]
[ROW][C]59[/C][C]7[/C][C]7.0396898750571[/C][C]-0.0396898750571033[/C][/ROW]
[ROW][C]60[/C][C]7.2[/C][C]7.20002038019794[/C][C]-2.03801979425933e-05[/C][/ROW]
[ROW][C]61[/C][C]7.3[/C][C]7.45181192963172[/C][C]-0.151811929631722[/C][/ROW]
[ROW][C]62[/C][C]7.1[/C][C]7.17843657501434[/C][C]-0.0784365750143401[/C][/ROW]
[ROW][C]63[/C][C]6.8[/C][C]6.64681466808213[/C][C]0.153185331917874[/C][/ROW]
[ROW][C]64[/C][C]6.4[/C][C]6.11776161784542[/C][C]0.282238382154585[/C][/ROW]
[ROW][C]65[/C][C]6.1[/C][C]6.15119200601735[/C][C]-0.0511920060173523[/C][/ROW]
[ROW][C]66[/C][C]6.5[/C][C]6.29534094252554[/C][C]0.204659057474462[/C][/ROW]
[ROW][C]67[/C][C]7.7[/C][C]7.48479564088605[/C][C]0.215204359113954[/C][/ROW]
[ROW][C]68[/C][C]7.9[/C][C]7.75911270846598[/C][C]0.140887291534019[/C][/ROW]
[ROW][C]69[/C][C]7.5[/C][C]7.87825668532496[/C][C]-0.378256685324959[/C][/ROW]
[ROW][C]70[/C][C]6.9[/C][C]7.51644954893393[/C][C]-0.616449548933926[/C][/ROW]
[ROW][C]71[/C][C]6.6[/C][C]6.93842614275394[/C][C]-0.338426142753939[/C][/ROW]
[ROW][C]72[/C][C]6.9[/C][C]6.78728807549504[/C][C]0.112711924504959[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=66452&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66452&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
138.98.9503140766282-0.0503140766281973
148.88.757959327267920.0420406727320852
158.38.244316094831130.0556839051688698
167.57.472424420550620.0275755794493833
177.27.21280290290433-0.0128029029043333
187.47.43515757080091-0.0351575708009104
198.88.525842027480930.274157972519067
209.38.872318873525670.427681126474331
219.39.279597586173770.0204024138262309
228.79.32643992965158-0.626439929651577
238.28.75478518261489-0.554785182614888
248.38.43891041178834-0.138910411788343
258.58.59475462049406-0.094754620494058
268.68.362991115487830.237008884512170
278.58.055914760946220.444085239053775
288.27.651996457042960.548003542957042
298.17.886155383552020.213844616447984
307.98.36500928681314-0.465009286813141
318.69.1018164327324-0.501816432732401
328.78.669593132450350.0304068675496527
338.78.679383246873880.0206167531261219
348.58.72320812946758-0.223208129467581
358.48.55246176408234-0.152461764082336
368.58.64419427175929-0.144194271759291
378.78.80129428351827-0.101294283518273
388.78.559210007762760.140789992237234
398.68.148936960138460.451063039861536
408.57.741438411716860.758561588283137
418.38.174357348412970.125642651587032
4288.57110904648884-0.571109046488839
438.29.21638133958279-1.01638133958279
448.18.26501134402285-0.165011344022849
458.18.079206822257260.0207931777427444
4688.12001412938259-0.120014129382588
477.98.047902750705-0.147902750704992
487.98.12814290430106-0.228142904301055
4988.17832367553149-0.178323675531486
5087.86874719452720.131252805472799
517.97.491607399373990.40839260062601
5287.109818330124760.890181669875243
537.77.692309190794510.00769080920548859
547.27.95013065469094-0.750130654690939
557.58.29281845025857-0.792818450258565
567.37.55771594955604-0.257715949556043
5777.27936065334012-0.279360653340116
5877.01493489161981-0.0149348916198146
5977.0396898750571-0.0396898750571033
607.27.20002038019794-2.03801979425933e-05
617.37.45181192963172-0.151811929631722
627.17.17843657501434-0.0784365750143401
636.86.646814668082130.153185331917874
646.46.117761617845420.282238382154585
656.16.15119200601735-0.0511920060173523
666.56.295340942525540.204659057474462
677.77.484795640886050.215204359113954
687.97.759112708465980.140887291534019
697.57.87825668532496-0.378256685324959
706.97.51644954893393-0.616449548933926
716.66.93842614275394-0.338426142753939
726.96.787288075495040.112711924504959







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
737.140199201947426.43866414456977.84173425932513
747.020478209794666.035637317038558.00531910255077
756.571746830253055.411765447468767.73172821303735
765.911587180570254.652438895329767.17073546581075
775.680493558113274.279737580391457.08124953583509
785.861182252188764.25193040145197.47043410292563
796.747395750517954.762881256877018.73191024415889
806.797045338112964.674540198952988.91955047727293
816.775987057862484.542683640071119.00929047565385
826.789097961123384.439720617376829.13847530486994
836.826270320877834.35744818949799.29509245225776
847.02004704166552-71.240119692433985.2802137757649

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 7.14019920194742 & 6.4386641445697 & 7.84173425932513 \tabularnewline
74 & 7.02047820979466 & 6.03563731703855 & 8.00531910255077 \tabularnewline
75 & 6.57174683025305 & 5.41176544746876 & 7.73172821303735 \tabularnewline
76 & 5.91158718057025 & 4.65243889532976 & 7.17073546581075 \tabularnewline
77 & 5.68049355811327 & 4.27973758039145 & 7.08124953583509 \tabularnewline
78 & 5.86118225218876 & 4.2519304014519 & 7.47043410292563 \tabularnewline
79 & 6.74739575051795 & 4.76288125687701 & 8.73191024415889 \tabularnewline
80 & 6.79704533811296 & 4.67454019895298 & 8.91955047727293 \tabularnewline
81 & 6.77598705786248 & 4.54268364007111 & 9.00929047565385 \tabularnewline
82 & 6.78909796112338 & 4.43972061737682 & 9.13847530486994 \tabularnewline
83 & 6.82627032087783 & 4.3574481894979 & 9.29509245225776 \tabularnewline
84 & 7.02004704166552 & -71.2401196924339 & 85.2802137757649 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=66452&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]7.14019920194742[/C][C]6.4386641445697[/C][C]7.84173425932513[/C][/ROW]
[ROW][C]74[/C][C]7.02047820979466[/C][C]6.03563731703855[/C][C]8.00531910255077[/C][/ROW]
[ROW][C]75[/C][C]6.57174683025305[/C][C]5.41176544746876[/C][C]7.73172821303735[/C][/ROW]
[ROW][C]76[/C][C]5.91158718057025[/C][C]4.65243889532976[/C][C]7.17073546581075[/C][/ROW]
[ROW][C]77[/C][C]5.68049355811327[/C][C]4.27973758039145[/C][C]7.08124953583509[/C][/ROW]
[ROW][C]78[/C][C]5.86118225218876[/C][C]4.2519304014519[/C][C]7.47043410292563[/C][/ROW]
[ROW][C]79[/C][C]6.74739575051795[/C][C]4.76288125687701[/C][C]8.73191024415889[/C][/ROW]
[ROW][C]80[/C][C]6.79704533811296[/C][C]4.67454019895298[/C][C]8.91955047727293[/C][/ROW]
[ROW][C]81[/C][C]6.77598705786248[/C][C]4.54268364007111[/C][C]9.00929047565385[/C][/ROW]
[ROW][C]82[/C][C]6.78909796112338[/C][C]4.43972061737682[/C][C]9.13847530486994[/C][/ROW]
[ROW][C]83[/C][C]6.82627032087783[/C][C]4.3574481894979[/C][C]9.29509245225776[/C][/ROW]
[ROW][C]84[/C][C]7.02004704166552[/C][C]-71.2401196924339[/C][C]85.2802137757649[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=66452&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66452&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
737.140199201947426.43866414456977.84173425932513
747.020478209794666.035637317038558.00531910255077
756.571746830253055.411765447468767.73172821303735
765.911587180570254.652438895329767.17073546581075
775.680493558113274.279737580391457.08124953583509
785.861182252188764.25193040145197.47043410292563
796.747395750517954.762881256877018.73191024415889
806.797045338112964.674540198952988.91955047727293
816.775987057862484.542683640071119.00929047565385
826.789097961123384.439720617376829.13847530486994
836.826270320877834.35744818949799.29509245225776
847.02004704166552-71.240119692433985.2802137757649



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; 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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')