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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, 04 Dec 2009 12:29:39 -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/04/t1259955026c64xu2glnn6agsz.htm/, Retrieved Sun, 28 Apr 2024 00:32:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=64070, Retrieved Sun, 28 Apr 2024 00:32:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact146
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]
-   PD    [Exponential Smoothing] [WS9] [2009-12-04 01:00:44] [37a8d600db9abe09a2528d150ccff095]
-   PD        [Exponential Smoothing] [Exponential smoot...] [2009-12-04 19:29:39] [d1081bd6cdf1fed9ed45c42dbd523bf1] [Current]
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Dataseries X:
7.3
7.6
7.5
7.6
7.9
7.9
8.1
8.2
8
7.5
6.8
6.5
6.6
7.6
8
8.1
7.7
7.5
7.6
7.8
7.8
7.8
7.5
7.5
7.1
7.5
7.5
7.6
7.7
7.7
7.9
8.1
8.2
8.2
8.2
7.9
7.3
6.9
6.6
6.7
6.9
7
7.1
7.2
7.1
6.9
7
6.8
6.4
6.7
6.6
6.4
6.3
6.2
6.5
6.8
6.8
6.4
6.1
5.8
6.1
7.2
7.3
6.9
6.1
5.8
6.2
7.1
7.7
7.9
7.7
7.4
7.5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64070&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]3 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=64070&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64070&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 time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64070&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[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64070&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64070&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
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
136.66.60287968271151-0.00287968271150874
147.67.63453373333942-0.0345337333394165
1588.02308015304527-0.0230801530452709
168.18.091732643438560.0082673565614435
177.77.653748556834430.0462514431655654
187.57.426524536876950.0734754631230476
197.68.13654148519345-0.536541485193451
207.87.719908321933410.0800916780665908
217.87.585052313022180.214947686977819
227.87.268876941790020.531123058209976
237.57.057257787661120.442742212338883
247.57.189833180492890.310166819507109
257.17.65028232418406-0.550282324184056
267.58.213173299187-0.713173299186991
277.57.91746455154151-0.417464551541512
287.67.585764991458640.0142350085413643
297.77.181076124742520.518923875257484
307.77.426524536876950.273475463123048
317.98.3536149252818-0.453614925281800
328.18.024790476815560.0752095231844354
338.27.876926276537930.323073723462064
348.27.641815369497550.558184630502446
358.27.419327308334370.78067269166563
367.97.861161568676360.0388384313236427
377.38.05845907272605-0.75845907272605
386.98.44462912552602-1.54462912552602
396.67.28377094251895-0.683770942518955
406.76.675023217894780.0249767821052238
416.96.330265746977060.569734253022936
4276.654582193506040.345417806493963
437.17.59385788497258-0.493857884972579
447.27.21177139712982-0.0117713971298175
457.17.001304385990670.098695614009328
466.96.616234693301840.283765306698156
4776.24260136614630.757398633853702
486.86.710312903218990.089687096781014
496.46.93597301423556-0.535973014235562
506.77.40307790700039-0.703077907000387
516.67.07253973951144-0.472539739511437
526.46.67502321789478-0.275023217894776
536.36.046662287721910.253337712278086
546.26.075625435977850.124374564022149
556.56.72556412461918-0.225564124619183
566.86.602007087365510.197992912634492
576.86.6121391013030.187860898697001
586.46.33653087252120.0634691274788057
596.15.790014465304730.309985534695268
605.85.84717640412596-0.0471764041259561
616.15.915531142880580.184468857119423
627.27.055894167491840.144105832508158
637.37.60061774703023-0.300617747030233
646.97.38337793066667-0.483377930666666
656.16.51933471981383-0.419334719813833
665.85.88263985013512-0.0826398501351218
676.26.29141724444248-0.0914172444424848
687.16.297124932483350.802875067516647
697.76.904013064818750.795986935181247
707.97.175642334863140.724357665136859
717.77.147775167829430.552224832170569
727.47.381641291402450.0183587085975470
737.57.54823813704856-0.0482381370485570

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 6.6 & 6.60287968271151 & -0.00287968271150874 \tabularnewline
14 & 7.6 & 7.63453373333942 & -0.0345337333394165 \tabularnewline
15 & 8 & 8.02308015304527 & -0.0230801530452709 \tabularnewline
16 & 8.1 & 8.09173264343856 & 0.0082673565614435 \tabularnewline
17 & 7.7 & 7.65374855683443 & 0.0462514431655654 \tabularnewline
18 & 7.5 & 7.42652453687695 & 0.0734754631230476 \tabularnewline
19 & 7.6 & 8.13654148519345 & -0.536541485193451 \tabularnewline
20 & 7.8 & 7.71990832193341 & 0.0800916780665908 \tabularnewline
21 & 7.8 & 7.58505231302218 & 0.214947686977819 \tabularnewline
22 & 7.8 & 7.26887694179002 & 0.531123058209976 \tabularnewline
23 & 7.5 & 7.05725778766112 & 0.442742212338883 \tabularnewline
24 & 7.5 & 7.18983318049289 & 0.310166819507109 \tabularnewline
25 & 7.1 & 7.65028232418406 & -0.550282324184056 \tabularnewline
26 & 7.5 & 8.213173299187 & -0.713173299186991 \tabularnewline
27 & 7.5 & 7.91746455154151 & -0.417464551541512 \tabularnewline
28 & 7.6 & 7.58576499145864 & 0.0142350085413643 \tabularnewline
29 & 7.7 & 7.18107612474252 & 0.518923875257484 \tabularnewline
30 & 7.7 & 7.42652453687695 & 0.273475463123048 \tabularnewline
31 & 7.9 & 8.3536149252818 & -0.453614925281800 \tabularnewline
32 & 8.1 & 8.02479047681556 & 0.0752095231844354 \tabularnewline
33 & 8.2 & 7.87692627653793 & 0.323073723462064 \tabularnewline
34 & 8.2 & 7.64181536949755 & 0.558184630502446 \tabularnewline
35 & 8.2 & 7.41932730833437 & 0.78067269166563 \tabularnewline
36 & 7.9 & 7.86116156867636 & 0.0388384313236427 \tabularnewline
37 & 7.3 & 8.05845907272605 & -0.75845907272605 \tabularnewline
38 & 6.9 & 8.44462912552602 & -1.54462912552602 \tabularnewline
39 & 6.6 & 7.28377094251895 & -0.683770942518955 \tabularnewline
40 & 6.7 & 6.67502321789478 & 0.0249767821052238 \tabularnewline
41 & 6.9 & 6.33026574697706 & 0.569734253022936 \tabularnewline
42 & 7 & 6.65458219350604 & 0.345417806493963 \tabularnewline
43 & 7.1 & 7.59385788497258 & -0.493857884972579 \tabularnewline
44 & 7.2 & 7.21177139712982 & -0.0117713971298175 \tabularnewline
45 & 7.1 & 7.00130438599067 & 0.098695614009328 \tabularnewline
46 & 6.9 & 6.61623469330184 & 0.283765306698156 \tabularnewline
47 & 7 & 6.2426013661463 & 0.757398633853702 \tabularnewline
48 & 6.8 & 6.71031290321899 & 0.089687096781014 \tabularnewline
49 & 6.4 & 6.93597301423556 & -0.535973014235562 \tabularnewline
50 & 6.7 & 7.40307790700039 & -0.703077907000387 \tabularnewline
51 & 6.6 & 7.07253973951144 & -0.472539739511437 \tabularnewline
52 & 6.4 & 6.67502321789478 & -0.275023217894776 \tabularnewline
53 & 6.3 & 6.04666228772191 & 0.253337712278086 \tabularnewline
54 & 6.2 & 6.07562543597785 & 0.124374564022149 \tabularnewline
55 & 6.5 & 6.72556412461918 & -0.225564124619183 \tabularnewline
56 & 6.8 & 6.60200708736551 & 0.197992912634492 \tabularnewline
57 & 6.8 & 6.612139101303 & 0.187860898697001 \tabularnewline
58 & 6.4 & 6.3365308725212 & 0.0634691274788057 \tabularnewline
59 & 6.1 & 5.79001446530473 & 0.309985534695268 \tabularnewline
60 & 5.8 & 5.84717640412596 & -0.0471764041259561 \tabularnewline
61 & 6.1 & 5.91553114288058 & 0.184468857119423 \tabularnewline
62 & 7.2 & 7.05589416749184 & 0.144105832508158 \tabularnewline
63 & 7.3 & 7.60061774703023 & -0.300617747030233 \tabularnewline
64 & 6.9 & 7.38337793066667 & -0.483377930666666 \tabularnewline
65 & 6.1 & 6.51933471981383 & -0.419334719813833 \tabularnewline
66 & 5.8 & 5.88263985013512 & -0.0826398501351218 \tabularnewline
67 & 6.2 & 6.29141724444248 & -0.0914172444424848 \tabularnewline
68 & 7.1 & 6.29712493248335 & 0.802875067516647 \tabularnewline
69 & 7.7 & 6.90401306481875 & 0.795986935181247 \tabularnewline
70 & 7.9 & 7.17564233486314 & 0.724357665136859 \tabularnewline
71 & 7.7 & 7.14777516782943 & 0.552224832170569 \tabularnewline
72 & 7.4 & 7.38164129140245 & 0.0183587085975470 \tabularnewline
73 & 7.5 & 7.54823813704856 & -0.0482381370485570 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64070&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]6.6[/C][C]6.60287968271151[/C][C]-0.00287968271150874[/C][/ROW]
[ROW][C]14[/C][C]7.6[/C][C]7.63453373333942[/C][C]-0.0345337333394165[/C][/ROW]
[ROW][C]15[/C][C]8[/C][C]8.02308015304527[/C][C]-0.0230801530452709[/C][/ROW]
[ROW][C]16[/C][C]8.1[/C][C]8.09173264343856[/C][C]0.0082673565614435[/C][/ROW]
[ROW][C]17[/C][C]7.7[/C][C]7.65374855683443[/C][C]0.0462514431655654[/C][/ROW]
[ROW][C]18[/C][C]7.5[/C][C]7.42652453687695[/C][C]0.0734754631230476[/C][/ROW]
[ROW][C]19[/C][C]7.6[/C][C]8.13654148519345[/C][C]-0.536541485193451[/C][/ROW]
[ROW][C]20[/C][C]7.8[/C][C]7.71990832193341[/C][C]0.0800916780665908[/C][/ROW]
[ROW][C]21[/C][C]7.8[/C][C]7.58505231302218[/C][C]0.214947686977819[/C][/ROW]
[ROW][C]22[/C][C]7.8[/C][C]7.26887694179002[/C][C]0.531123058209976[/C][/ROW]
[ROW][C]23[/C][C]7.5[/C][C]7.05725778766112[/C][C]0.442742212338883[/C][/ROW]
[ROW][C]24[/C][C]7.5[/C][C]7.18983318049289[/C][C]0.310166819507109[/C][/ROW]
[ROW][C]25[/C][C]7.1[/C][C]7.65028232418406[/C][C]-0.550282324184056[/C][/ROW]
[ROW][C]26[/C][C]7.5[/C][C]8.213173299187[/C][C]-0.713173299186991[/C][/ROW]
[ROW][C]27[/C][C]7.5[/C][C]7.91746455154151[/C][C]-0.417464551541512[/C][/ROW]
[ROW][C]28[/C][C]7.6[/C][C]7.58576499145864[/C][C]0.0142350085413643[/C][/ROW]
[ROW][C]29[/C][C]7.7[/C][C]7.18107612474252[/C][C]0.518923875257484[/C][/ROW]
[ROW][C]30[/C][C]7.7[/C][C]7.42652453687695[/C][C]0.273475463123048[/C][/ROW]
[ROW][C]31[/C][C]7.9[/C][C]8.3536149252818[/C][C]-0.453614925281800[/C][/ROW]
[ROW][C]32[/C][C]8.1[/C][C]8.02479047681556[/C][C]0.0752095231844354[/C][/ROW]
[ROW][C]33[/C][C]8.2[/C][C]7.87692627653793[/C][C]0.323073723462064[/C][/ROW]
[ROW][C]34[/C][C]8.2[/C][C]7.64181536949755[/C][C]0.558184630502446[/C][/ROW]
[ROW][C]35[/C][C]8.2[/C][C]7.41932730833437[/C][C]0.78067269166563[/C][/ROW]
[ROW][C]36[/C][C]7.9[/C][C]7.86116156867636[/C][C]0.0388384313236427[/C][/ROW]
[ROW][C]37[/C][C]7.3[/C][C]8.05845907272605[/C][C]-0.75845907272605[/C][/ROW]
[ROW][C]38[/C][C]6.9[/C][C]8.44462912552602[/C][C]-1.54462912552602[/C][/ROW]
[ROW][C]39[/C][C]6.6[/C][C]7.28377094251895[/C][C]-0.683770942518955[/C][/ROW]
[ROW][C]40[/C][C]6.7[/C][C]6.67502321789478[/C][C]0.0249767821052238[/C][/ROW]
[ROW][C]41[/C][C]6.9[/C][C]6.33026574697706[/C][C]0.569734253022936[/C][/ROW]
[ROW][C]42[/C][C]7[/C][C]6.65458219350604[/C][C]0.345417806493963[/C][/ROW]
[ROW][C]43[/C][C]7.1[/C][C]7.59385788497258[/C][C]-0.493857884972579[/C][/ROW]
[ROW][C]44[/C][C]7.2[/C][C]7.21177139712982[/C][C]-0.0117713971298175[/C][/ROW]
[ROW][C]45[/C][C]7.1[/C][C]7.00130438599067[/C][C]0.098695614009328[/C][/ROW]
[ROW][C]46[/C][C]6.9[/C][C]6.61623469330184[/C][C]0.283765306698156[/C][/ROW]
[ROW][C]47[/C][C]7[/C][C]6.2426013661463[/C][C]0.757398633853702[/C][/ROW]
[ROW][C]48[/C][C]6.8[/C][C]6.71031290321899[/C][C]0.089687096781014[/C][/ROW]
[ROW][C]49[/C][C]6.4[/C][C]6.93597301423556[/C][C]-0.535973014235562[/C][/ROW]
[ROW][C]50[/C][C]6.7[/C][C]7.40307790700039[/C][C]-0.703077907000387[/C][/ROW]
[ROW][C]51[/C][C]6.6[/C][C]7.07253973951144[/C][C]-0.472539739511437[/C][/ROW]
[ROW][C]52[/C][C]6.4[/C][C]6.67502321789478[/C][C]-0.275023217894776[/C][/ROW]
[ROW][C]53[/C][C]6.3[/C][C]6.04666228772191[/C][C]0.253337712278086[/C][/ROW]
[ROW][C]54[/C][C]6.2[/C][C]6.07562543597785[/C][C]0.124374564022149[/C][/ROW]
[ROW][C]55[/C][C]6.5[/C][C]6.72556412461918[/C][C]-0.225564124619183[/C][/ROW]
[ROW][C]56[/C][C]6.8[/C][C]6.60200708736551[/C][C]0.197992912634492[/C][/ROW]
[ROW][C]57[/C][C]6.8[/C][C]6.612139101303[/C][C]0.187860898697001[/C][/ROW]
[ROW][C]58[/C][C]6.4[/C][C]6.3365308725212[/C][C]0.0634691274788057[/C][/ROW]
[ROW][C]59[/C][C]6.1[/C][C]5.79001446530473[/C][C]0.309985534695268[/C][/ROW]
[ROW][C]60[/C][C]5.8[/C][C]5.84717640412596[/C][C]-0.0471764041259561[/C][/ROW]
[ROW][C]61[/C][C]6.1[/C][C]5.91553114288058[/C][C]0.184468857119423[/C][/ROW]
[ROW][C]62[/C][C]7.2[/C][C]7.05589416749184[/C][C]0.144105832508158[/C][/ROW]
[ROW][C]63[/C][C]7.3[/C][C]7.60061774703023[/C][C]-0.300617747030233[/C][/ROW]
[ROW][C]64[/C][C]6.9[/C][C]7.38337793066667[/C][C]-0.483377930666666[/C][/ROW]
[ROW][C]65[/C][C]6.1[/C][C]6.51933471981383[/C][C]-0.419334719813833[/C][/ROW]
[ROW][C]66[/C][C]5.8[/C][C]5.88263985013512[/C][C]-0.0826398501351218[/C][/ROW]
[ROW][C]67[/C][C]6.2[/C][C]6.29141724444248[/C][C]-0.0914172444424848[/C][/ROW]
[ROW][C]68[/C][C]7.1[/C][C]6.29712493248335[/C][C]0.802875067516647[/C][/ROW]
[ROW][C]69[/C][C]7.7[/C][C]6.90401306481875[/C][C]0.795986935181247[/C][/ROW]
[ROW][C]70[/C][C]7.9[/C][C]7.17564233486314[/C][C]0.724357665136859[/C][/ROW]
[ROW][C]71[/C][C]7.7[/C][C]7.14777516782943[/C][C]0.552224832170569[/C][/ROW]
[ROW][C]72[/C][C]7.4[/C][C]7.38164129140245[/C][C]0.0183587085975470[/C][/ROW]
[ROW][C]73[/C][C]7.5[/C][C]7.54823813704856[/C][C]-0.0482381370485570[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64070&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64070&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
136.66.60287968271151-0.00287968271150874
147.67.63453373333942-0.0345337333394165
1588.02308015304527-0.0230801530452709
168.18.091732643438560.0082673565614435
177.77.653748556834430.0462514431655654
187.57.426524536876950.0734754631230476
197.68.13654148519345-0.536541485193451
207.87.719908321933410.0800916780665908
217.87.585052313022180.214947686977819
227.87.268876941790020.531123058209976
237.57.057257787661120.442742212338883
247.57.189833180492890.310166819507109
257.17.65028232418406-0.550282324184056
267.58.213173299187-0.713173299186991
277.57.91746455154151-0.417464551541512
287.67.585764991458640.0142350085413643
297.77.181076124742520.518923875257484
307.77.426524536876950.273475463123048
317.98.3536149252818-0.453614925281800
328.18.024790476815560.0752095231844354
338.27.876926276537930.323073723462064
348.27.641815369497550.558184630502446
358.27.419327308334370.78067269166563
367.97.861161568676360.0388384313236427
377.38.05845907272605-0.75845907272605
386.98.44462912552602-1.54462912552602
396.67.28377094251895-0.683770942518955
406.76.675023217894780.0249767821052238
416.96.330265746977060.569734253022936
4276.654582193506040.345417806493963
437.17.59385788497258-0.493857884972579
447.27.21177139712982-0.0117713971298175
457.17.001304385990670.098695614009328
466.96.616234693301840.283765306698156
4776.24260136614630.757398633853702
486.86.710312903218990.089687096781014
496.46.93597301423556-0.535973014235562
506.77.40307790700039-0.703077907000387
516.67.07253973951144-0.472539739511437
526.46.67502321789478-0.275023217894776
536.36.046662287721910.253337712278086
546.26.075625435977850.124374564022149
556.56.72556412461918-0.225564124619183
566.86.602007087365510.197992912634492
576.86.6121391013030.187860898697001
586.46.33653087252120.0634691274788057
596.15.790014465304730.309985534695268
605.85.84717640412596-0.0471764041259561
616.15.915531142880580.184468857119423
627.27.055894167491840.144105832508158
637.37.60061774703023-0.300617747030233
646.97.38337793066667-0.483377930666666
656.16.51933471981383-0.419334719813833
665.85.88263985013512-0.0826398501351218
676.26.29141724444248-0.0914172444424848
687.16.297124932483350.802875067516647
697.76.904013064818750.795986935181247
707.97.175642334863140.724357665136859
717.77.147775167829430.552224832170569
727.47.381641291402450.0183587085975470
737.57.54823813704856-0.0482381370485570







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
748.676084951865057.787363428944819.5648064747853
759.159593747648997.8669802862906510.4522072090073
769.265166494935677.6837754251710310.8465575647003
778.755232718740957.0160573032490410.4944081342329
788.444748059010146.545771894384910.3437242236354
799.161940041124066.9174126358778411.4064674463703
809.307267140382166.8591994109801411.7553348697842
819.051492427490176.5093290899818611.5936557649985
828.43570098728025.9043850857461610.9670168888142
837.632677667051255.1750784679929810.0902768661095
847.317076443877834.798152194241819.83600069351385
857.46361946825984-216.657454182507231.584693119026

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
74 & 8.67608495186505 & 7.78736342894481 & 9.5648064747853 \tabularnewline
75 & 9.15959374764899 & 7.86698028629065 & 10.4522072090073 \tabularnewline
76 & 9.26516649493567 & 7.68377542517103 & 10.8465575647003 \tabularnewline
77 & 8.75523271874095 & 7.01605730324904 & 10.4944081342329 \tabularnewline
78 & 8.44474805901014 & 6.5457718943849 & 10.3437242236354 \tabularnewline
79 & 9.16194004112406 & 6.91741263587784 & 11.4064674463703 \tabularnewline
80 & 9.30726714038216 & 6.85919941098014 & 11.7553348697842 \tabularnewline
81 & 9.05149242749017 & 6.50932908998186 & 11.5936557649985 \tabularnewline
82 & 8.4357009872802 & 5.90438508574616 & 10.9670168888142 \tabularnewline
83 & 7.63267766705125 & 5.17507846799298 & 10.0902768661095 \tabularnewline
84 & 7.31707644387783 & 4.79815219424181 & 9.83600069351385 \tabularnewline
85 & 7.46361946825984 & -216.657454182507 & 231.584693119026 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64070&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]74[/C][C]8.67608495186505[/C][C]7.78736342894481[/C][C]9.5648064747853[/C][/ROW]
[ROW][C]75[/C][C]9.15959374764899[/C][C]7.86698028629065[/C][C]10.4522072090073[/C][/ROW]
[ROW][C]76[/C][C]9.26516649493567[/C][C]7.68377542517103[/C][C]10.8465575647003[/C][/ROW]
[ROW][C]77[/C][C]8.75523271874095[/C][C]7.01605730324904[/C][C]10.4944081342329[/C][/ROW]
[ROW][C]78[/C][C]8.44474805901014[/C][C]6.5457718943849[/C][C]10.3437242236354[/C][/ROW]
[ROW][C]79[/C][C]9.16194004112406[/C][C]6.91741263587784[/C][C]11.4064674463703[/C][/ROW]
[ROW][C]80[/C][C]9.30726714038216[/C][C]6.85919941098014[/C][C]11.7553348697842[/C][/ROW]
[ROW][C]81[/C][C]9.05149242749017[/C][C]6.50932908998186[/C][C]11.5936557649985[/C][/ROW]
[ROW][C]82[/C][C]8.4357009872802[/C][C]5.90438508574616[/C][C]10.9670168888142[/C][/ROW]
[ROW][C]83[/C][C]7.63267766705125[/C][C]5.17507846799298[/C][C]10.0902768661095[/C][/ROW]
[ROW][C]84[/C][C]7.31707644387783[/C][C]4.79815219424181[/C][C]9.83600069351385[/C][/ROW]
[ROW][C]85[/C][C]7.46361946825984[/C][C]-216.657454182507[/C][C]231.584693119026[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64070&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64070&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
748.676084951865057.787363428944819.5648064747853
759.159593747648997.8669802862906510.4522072090073
769.265166494935677.6837754251710310.8465575647003
778.755232718740957.0160573032490410.4944081342329
788.444748059010146.545771894384910.3437242236354
799.161940041124066.9174126358778411.4064674463703
809.307267140382166.8591994109801411.7553348697842
819.051492427490176.5093290899818611.5936557649985
828.43570098728025.9043850857461610.9670168888142
837.632677667051255.1750784679929810.0902768661095
847.317076443877834.798152194241819.83600069351385
857.46361946825984-216.657454182507231.584693119026



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')