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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 20 May 2014 08:41:31 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/May/20/t1400589847plqomo5tx5m2lto.htm/, Retrieved Wed, 15 May 2024 17:19:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234984, Retrieved Wed, 15 May 2024 17:19:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact143
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bootstrap Plot - Central Tendency] [bootstrap plot oe...] [2014-04-21 17:33:30] [74976ff3bfb104667fd389bfeeadbb92]
- RMPD    [Exponential Smoothing] [Exponential smoot...] [2014-05-20 12:41:31] [5251501093c7f29df32c3ec23cad27f5] [Current]
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Dataseries X:
0,45
0,44
0,42
0,43
0,43
0,47
0,47
0,47
0,47
0,48
0,48
0,48
0,49
0,49
0,47
0,5
0,51
0,5
0,49
0,5
0,51
0,51
0,5
0,53
0,5
0,49
0,46
0,46
0,47
0,49
0,5
0,5
0,51
0,5
0,52
0,5
0,48
0,47
0,43
0,42
0,45
0,5
0,52
0,52
0,51
0,52
0,52
0,51
0,51
0,51
0,48
0,49
0,47
0,51
0,5
0,51
0,51
0,52
0,51
0,52
0,48
0,49
0,47
0,44
0,44
0,47
0,51
0,51
0,52
0,52
0,52
0,52




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=234984&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=234984&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234984&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
alpha1
beta0.0535850126857
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0535850126857 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234984&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]0.0535850126857[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234984&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234984&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
beta0.0535850126857
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
30.420.43-0.01
40.430.4094641498731430.020535850126857
50.430.4205645636627020.00943543633729776
60.470.4210701616385310.0489298383614685
70.470.463692067647840.00630793235215998
80.470.4640300782829510.00596992171704896
90.470.4643499766138920.00565002338610826
100.480.4646527331887110.0153472668112892
110.480.4754751166754850.00452488332451539
120.480.475717582605830.0042824173941699
130.490.4759470559962220.0140529440037779
140.490.4867000831789360.00329991682106401
150.470.486876909263654-0.0168769092636545
160.50.4659725598666660.0340274401333339
170.510.4977959206778730.0122040793221273
180.50.508449876423166-0.00844987642316619
190.490.497997089687838-0.00799708968783824
200.50.4875685655354670.0124314344645333
210.510.498234704108950.0117652958910498
220.510.5088651476385230.00113485236147681
230.50.508925958716709-0.00892595871670931
240.530.4984476611056420.0315523388943577
250.50.53013839358556-0.03013839358556
260.490.498523427382951-0.0085234273829512
270.460.48806669941851-0.0280666994185101
280.460.4565627449741240.0034372550258765
290.470.4567469303282890.0132530696717109
300.490.4674570962347720.0225429037652278
310.50.4886650580190040.0113349419809956
320.50.4992724410288480.000727558971152231
330.510.4993114272855470.0106885727144535
340.50.509884174590043-0.00988417459004254
350.520.4993545309692470.0206454690307526
360.50.520460818689163-0.0204608186891626
370.480.499364425460144-0.019364425460144
380.470.478326782476211-0.00832678247621088
390.430.467880591731592-0.037880591731592
400.420.425850759743113-0.00585075974311289
410.450.4155372467080570.0344627532919429
420.50.447383933780390.0526160662196099
430.520.500203366356240.0197966336437605
440.520.521264169221175-0.00126416922117456
450.510.521196428697421-0.0111964286974211
460.520.5105964679236350.0094035320763648
470.520.521100356309238-0.00110035630923766
480.510.521041393702448-0.0110413937024483
490.510.510449740480835-0.000449740480834793
500.510.510425641131464-0.000425641131464038
510.480.510402833146035-0.030402833146035
520.490.4787736969462230.0112263030537765
530.470.489375258537774-0.0193752585377736
540.510.4683370350632380.0416629649367617
550.50.510569545567899-0.0105695455678986
560.510.5000031763345610.00999682366543941
570.510.51053885625749-0.000538856257489839
580.520.5105099816380960.00949001836190355
590.510.521018504392407-0.0110185043924066
600.520.5104280776947620.00957192230523796
610.480.520940989272915-0.0409409892729148
620.490.4787471658433610.0112528341566395
630.470.489350149104394-0.0193501491043941
640.440.468313271119165-0.028313271119165
650.440.4367961041270710.00320389587292913
660.470.4369677849280650.0330322150719345
670.510.4687378165917320.0412621834082682
680.510.510948851213104-0.000948851213103508
690.520.5108980070088130.00910199299118741
700.520.521385737418711-0.00138573741871051
710.520.52131148266155-0.00131148266154979
720.520.521241206846494-0.00124120684649365

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 0.42 & 0.43 & -0.01 \tabularnewline
4 & 0.43 & 0.409464149873143 & 0.020535850126857 \tabularnewline
5 & 0.43 & 0.420564563662702 & 0.00943543633729776 \tabularnewline
6 & 0.47 & 0.421070161638531 & 0.0489298383614685 \tabularnewline
7 & 0.47 & 0.46369206764784 & 0.00630793235215998 \tabularnewline
8 & 0.47 & 0.464030078282951 & 0.00596992171704896 \tabularnewline
9 & 0.47 & 0.464349976613892 & 0.00565002338610826 \tabularnewline
10 & 0.48 & 0.464652733188711 & 0.0153472668112892 \tabularnewline
11 & 0.48 & 0.475475116675485 & 0.00452488332451539 \tabularnewline
12 & 0.48 & 0.47571758260583 & 0.0042824173941699 \tabularnewline
13 & 0.49 & 0.475947055996222 & 0.0140529440037779 \tabularnewline
14 & 0.49 & 0.486700083178936 & 0.00329991682106401 \tabularnewline
15 & 0.47 & 0.486876909263654 & -0.0168769092636545 \tabularnewline
16 & 0.5 & 0.465972559866666 & 0.0340274401333339 \tabularnewline
17 & 0.51 & 0.497795920677873 & 0.0122040793221273 \tabularnewline
18 & 0.5 & 0.508449876423166 & -0.00844987642316619 \tabularnewline
19 & 0.49 & 0.497997089687838 & -0.00799708968783824 \tabularnewline
20 & 0.5 & 0.487568565535467 & 0.0124314344645333 \tabularnewline
21 & 0.51 & 0.49823470410895 & 0.0117652958910498 \tabularnewline
22 & 0.51 & 0.508865147638523 & 0.00113485236147681 \tabularnewline
23 & 0.5 & 0.508925958716709 & -0.00892595871670931 \tabularnewline
24 & 0.53 & 0.498447661105642 & 0.0315523388943577 \tabularnewline
25 & 0.5 & 0.53013839358556 & -0.03013839358556 \tabularnewline
26 & 0.49 & 0.498523427382951 & -0.0085234273829512 \tabularnewline
27 & 0.46 & 0.48806669941851 & -0.0280666994185101 \tabularnewline
28 & 0.46 & 0.456562744974124 & 0.0034372550258765 \tabularnewline
29 & 0.47 & 0.456746930328289 & 0.0132530696717109 \tabularnewline
30 & 0.49 & 0.467457096234772 & 0.0225429037652278 \tabularnewline
31 & 0.5 & 0.488665058019004 & 0.0113349419809956 \tabularnewline
32 & 0.5 & 0.499272441028848 & 0.000727558971152231 \tabularnewline
33 & 0.51 & 0.499311427285547 & 0.0106885727144535 \tabularnewline
34 & 0.5 & 0.509884174590043 & -0.00988417459004254 \tabularnewline
35 & 0.52 & 0.499354530969247 & 0.0206454690307526 \tabularnewline
36 & 0.5 & 0.520460818689163 & -0.0204608186891626 \tabularnewline
37 & 0.48 & 0.499364425460144 & -0.019364425460144 \tabularnewline
38 & 0.47 & 0.478326782476211 & -0.00832678247621088 \tabularnewline
39 & 0.43 & 0.467880591731592 & -0.037880591731592 \tabularnewline
40 & 0.42 & 0.425850759743113 & -0.00585075974311289 \tabularnewline
41 & 0.45 & 0.415537246708057 & 0.0344627532919429 \tabularnewline
42 & 0.5 & 0.44738393378039 & 0.0526160662196099 \tabularnewline
43 & 0.52 & 0.50020336635624 & 0.0197966336437605 \tabularnewline
44 & 0.52 & 0.521264169221175 & -0.00126416922117456 \tabularnewline
45 & 0.51 & 0.521196428697421 & -0.0111964286974211 \tabularnewline
46 & 0.52 & 0.510596467923635 & 0.0094035320763648 \tabularnewline
47 & 0.52 & 0.521100356309238 & -0.00110035630923766 \tabularnewline
48 & 0.51 & 0.521041393702448 & -0.0110413937024483 \tabularnewline
49 & 0.51 & 0.510449740480835 & -0.000449740480834793 \tabularnewline
50 & 0.51 & 0.510425641131464 & -0.000425641131464038 \tabularnewline
51 & 0.48 & 0.510402833146035 & -0.030402833146035 \tabularnewline
52 & 0.49 & 0.478773696946223 & 0.0112263030537765 \tabularnewline
53 & 0.47 & 0.489375258537774 & -0.0193752585377736 \tabularnewline
54 & 0.51 & 0.468337035063238 & 0.0416629649367617 \tabularnewline
55 & 0.5 & 0.510569545567899 & -0.0105695455678986 \tabularnewline
56 & 0.51 & 0.500003176334561 & 0.00999682366543941 \tabularnewline
57 & 0.51 & 0.51053885625749 & -0.000538856257489839 \tabularnewline
58 & 0.52 & 0.510509981638096 & 0.00949001836190355 \tabularnewline
59 & 0.51 & 0.521018504392407 & -0.0110185043924066 \tabularnewline
60 & 0.52 & 0.510428077694762 & 0.00957192230523796 \tabularnewline
61 & 0.48 & 0.520940989272915 & -0.0409409892729148 \tabularnewline
62 & 0.49 & 0.478747165843361 & 0.0112528341566395 \tabularnewline
63 & 0.47 & 0.489350149104394 & -0.0193501491043941 \tabularnewline
64 & 0.44 & 0.468313271119165 & -0.028313271119165 \tabularnewline
65 & 0.44 & 0.436796104127071 & 0.00320389587292913 \tabularnewline
66 & 0.47 & 0.436967784928065 & 0.0330322150719345 \tabularnewline
67 & 0.51 & 0.468737816591732 & 0.0412621834082682 \tabularnewline
68 & 0.51 & 0.510948851213104 & -0.000948851213103508 \tabularnewline
69 & 0.52 & 0.510898007008813 & 0.00910199299118741 \tabularnewline
70 & 0.52 & 0.521385737418711 & -0.00138573741871051 \tabularnewline
71 & 0.52 & 0.52131148266155 & -0.00131148266154979 \tabularnewline
72 & 0.52 & 0.521241206846494 & -0.00124120684649365 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234984&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]0.42[/C][C]0.43[/C][C]-0.01[/C][/ROW]
[ROW][C]4[/C][C]0.43[/C][C]0.409464149873143[/C][C]0.020535850126857[/C][/ROW]
[ROW][C]5[/C][C]0.43[/C][C]0.420564563662702[/C][C]0.00943543633729776[/C][/ROW]
[ROW][C]6[/C][C]0.47[/C][C]0.421070161638531[/C][C]0.0489298383614685[/C][/ROW]
[ROW][C]7[/C][C]0.47[/C][C]0.46369206764784[/C][C]0.00630793235215998[/C][/ROW]
[ROW][C]8[/C][C]0.47[/C][C]0.464030078282951[/C][C]0.00596992171704896[/C][/ROW]
[ROW][C]9[/C][C]0.47[/C][C]0.464349976613892[/C][C]0.00565002338610826[/C][/ROW]
[ROW][C]10[/C][C]0.48[/C][C]0.464652733188711[/C][C]0.0153472668112892[/C][/ROW]
[ROW][C]11[/C][C]0.48[/C][C]0.475475116675485[/C][C]0.00452488332451539[/C][/ROW]
[ROW][C]12[/C][C]0.48[/C][C]0.47571758260583[/C][C]0.0042824173941699[/C][/ROW]
[ROW][C]13[/C][C]0.49[/C][C]0.475947055996222[/C][C]0.0140529440037779[/C][/ROW]
[ROW][C]14[/C][C]0.49[/C][C]0.486700083178936[/C][C]0.00329991682106401[/C][/ROW]
[ROW][C]15[/C][C]0.47[/C][C]0.486876909263654[/C][C]-0.0168769092636545[/C][/ROW]
[ROW][C]16[/C][C]0.5[/C][C]0.465972559866666[/C][C]0.0340274401333339[/C][/ROW]
[ROW][C]17[/C][C]0.51[/C][C]0.497795920677873[/C][C]0.0122040793221273[/C][/ROW]
[ROW][C]18[/C][C]0.5[/C][C]0.508449876423166[/C][C]-0.00844987642316619[/C][/ROW]
[ROW][C]19[/C][C]0.49[/C][C]0.497997089687838[/C][C]-0.00799708968783824[/C][/ROW]
[ROW][C]20[/C][C]0.5[/C][C]0.487568565535467[/C][C]0.0124314344645333[/C][/ROW]
[ROW][C]21[/C][C]0.51[/C][C]0.49823470410895[/C][C]0.0117652958910498[/C][/ROW]
[ROW][C]22[/C][C]0.51[/C][C]0.508865147638523[/C][C]0.00113485236147681[/C][/ROW]
[ROW][C]23[/C][C]0.5[/C][C]0.508925958716709[/C][C]-0.00892595871670931[/C][/ROW]
[ROW][C]24[/C][C]0.53[/C][C]0.498447661105642[/C][C]0.0315523388943577[/C][/ROW]
[ROW][C]25[/C][C]0.5[/C][C]0.53013839358556[/C][C]-0.03013839358556[/C][/ROW]
[ROW][C]26[/C][C]0.49[/C][C]0.498523427382951[/C][C]-0.0085234273829512[/C][/ROW]
[ROW][C]27[/C][C]0.46[/C][C]0.48806669941851[/C][C]-0.0280666994185101[/C][/ROW]
[ROW][C]28[/C][C]0.46[/C][C]0.456562744974124[/C][C]0.0034372550258765[/C][/ROW]
[ROW][C]29[/C][C]0.47[/C][C]0.456746930328289[/C][C]0.0132530696717109[/C][/ROW]
[ROW][C]30[/C][C]0.49[/C][C]0.467457096234772[/C][C]0.0225429037652278[/C][/ROW]
[ROW][C]31[/C][C]0.5[/C][C]0.488665058019004[/C][C]0.0113349419809956[/C][/ROW]
[ROW][C]32[/C][C]0.5[/C][C]0.499272441028848[/C][C]0.000727558971152231[/C][/ROW]
[ROW][C]33[/C][C]0.51[/C][C]0.499311427285547[/C][C]0.0106885727144535[/C][/ROW]
[ROW][C]34[/C][C]0.5[/C][C]0.509884174590043[/C][C]-0.00988417459004254[/C][/ROW]
[ROW][C]35[/C][C]0.52[/C][C]0.499354530969247[/C][C]0.0206454690307526[/C][/ROW]
[ROW][C]36[/C][C]0.5[/C][C]0.520460818689163[/C][C]-0.0204608186891626[/C][/ROW]
[ROW][C]37[/C][C]0.48[/C][C]0.499364425460144[/C][C]-0.019364425460144[/C][/ROW]
[ROW][C]38[/C][C]0.47[/C][C]0.478326782476211[/C][C]-0.00832678247621088[/C][/ROW]
[ROW][C]39[/C][C]0.43[/C][C]0.467880591731592[/C][C]-0.037880591731592[/C][/ROW]
[ROW][C]40[/C][C]0.42[/C][C]0.425850759743113[/C][C]-0.00585075974311289[/C][/ROW]
[ROW][C]41[/C][C]0.45[/C][C]0.415537246708057[/C][C]0.0344627532919429[/C][/ROW]
[ROW][C]42[/C][C]0.5[/C][C]0.44738393378039[/C][C]0.0526160662196099[/C][/ROW]
[ROW][C]43[/C][C]0.52[/C][C]0.50020336635624[/C][C]0.0197966336437605[/C][/ROW]
[ROW][C]44[/C][C]0.52[/C][C]0.521264169221175[/C][C]-0.00126416922117456[/C][/ROW]
[ROW][C]45[/C][C]0.51[/C][C]0.521196428697421[/C][C]-0.0111964286974211[/C][/ROW]
[ROW][C]46[/C][C]0.52[/C][C]0.510596467923635[/C][C]0.0094035320763648[/C][/ROW]
[ROW][C]47[/C][C]0.52[/C][C]0.521100356309238[/C][C]-0.00110035630923766[/C][/ROW]
[ROW][C]48[/C][C]0.51[/C][C]0.521041393702448[/C][C]-0.0110413937024483[/C][/ROW]
[ROW][C]49[/C][C]0.51[/C][C]0.510449740480835[/C][C]-0.000449740480834793[/C][/ROW]
[ROW][C]50[/C][C]0.51[/C][C]0.510425641131464[/C][C]-0.000425641131464038[/C][/ROW]
[ROW][C]51[/C][C]0.48[/C][C]0.510402833146035[/C][C]-0.030402833146035[/C][/ROW]
[ROW][C]52[/C][C]0.49[/C][C]0.478773696946223[/C][C]0.0112263030537765[/C][/ROW]
[ROW][C]53[/C][C]0.47[/C][C]0.489375258537774[/C][C]-0.0193752585377736[/C][/ROW]
[ROW][C]54[/C][C]0.51[/C][C]0.468337035063238[/C][C]0.0416629649367617[/C][/ROW]
[ROW][C]55[/C][C]0.5[/C][C]0.510569545567899[/C][C]-0.0105695455678986[/C][/ROW]
[ROW][C]56[/C][C]0.51[/C][C]0.500003176334561[/C][C]0.00999682366543941[/C][/ROW]
[ROW][C]57[/C][C]0.51[/C][C]0.51053885625749[/C][C]-0.000538856257489839[/C][/ROW]
[ROW][C]58[/C][C]0.52[/C][C]0.510509981638096[/C][C]0.00949001836190355[/C][/ROW]
[ROW][C]59[/C][C]0.51[/C][C]0.521018504392407[/C][C]-0.0110185043924066[/C][/ROW]
[ROW][C]60[/C][C]0.52[/C][C]0.510428077694762[/C][C]0.00957192230523796[/C][/ROW]
[ROW][C]61[/C][C]0.48[/C][C]0.520940989272915[/C][C]-0.0409409892729148[/C][/ROW]
[ROW][C]62[/C][C]0.49[/C][C]0.478747165843361[/C][C]0.0112528341566395[/C][/ROW]
[ROW][C]63[/C][C]0.47[/C][C]0.489350149104394[/C][C]-0.0193501491043941[/C][/ROW]
[ROW][C]64[/C][C]0.44[/C][C]0.468313271119165[/C][C]-0.028313271119165[/C][/ROW]
[ROW][C]65[/C][C]0.44[/C][C]0.436796104127071[/C][C]0.00320389587292913[/C][/ROW]
[ROW][C]66[/C][C]0.47[/C][C]0.436967784928065[/C][C]0.0330322150719345[/C][/ROW]
[ROW][C]67[/C][C]0.51[/C][C]0.468737816591732[/C][C]0.0412621834082682[/C][/ROW]
[ROW][C]68[/C][C]0.51[/C][C]0.510948851213104[/C][C]-0.000948851213103508[/C][/ROW]
[ROW][C]69[/C][C]0.52[/C][C]0.510898007008813[/C][C]0.00910199299118741[/C][/ROW]
[ROW][C]70[/C][C]0.52[/C][C]0.521385737418711[/C][C]-0.00138573741871051[/C][/ROW]
[ROW][C]71[/C][C]0.52[/C][C]0.52131148266155[/C][C]-0.00131148266154979[/C][/ROW]
[ROW][C]72[/C][C]0.52[/C][C]0.521241206846494[/C][C]-0.00124120684649365[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234984&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234984&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
30.420.43-0.01
40.430.4094641498731430.020535850126857
50.430.4205645636627020.00943543633729776
60.470.4210701616385310.0489298383614685
70.470.463692067647840.00630793235215998
80.470.4640300782829510.00596992171704896
90.470.4643499766138920.00565002338610826
100.480.4646527331887110.0153472668112892
110.480.4754751166754850.00452488332451539
120.480.475717582605830.0042824173941699
130.490.4759470559962220.0140529440037779
140.490.4867000831789360.00329991682106401
150.470.486876909263654-0.0168769092636545
160.50.4659725598666660.0340274401333339
170.510.4977959206778730.0122040793221273
180.50.508449876423166-0.00844987642316619
190.490.497997089687838-0.00799708968783824
200.50.4875685655354670.0124314344645333
210.510.498234704108950.0117652958910498
220.510.5088651476385230.00113485236147681
230.50.508925958716709-0.00892595871670931
240.530.4984476611056420.0315523388943577
250.50.53013839358556-0.03013839358556
260.490.498523427382951-0.0085234273829512
270.460.48806669941851-0.0280666994185101
280.460.4565627449741240.0034372550258765
290.470.4567469303282890.0132530696717109
300.490.4674570962347720.0225429037652278
310.50.4886650580190040.0113349419809956
320.50.4992724410288480.000727558971152231
330.510.4993114272855470.0106885727144535
340.50.509884174590043-0.00988417459004254
350.520.4993545309692470.0206454690307526
360.50.520460818689163-0.0204608186891626
370.480.499364425460144-0.019364425460144
380.470.478326782476211-0.00832678247621088
390.430.467880591731592-0.037880591731592
400.420.425850759743113-0.00585075974311289
410.450.4155372467080570.0344627532919429
420.50.447383933780390.0526160662196099
430.520.500203366356240.0197966336437605
440.520.521264169221175-0.00126416922117456
450.510.521196428697421-0.0111964286974211
460.520.5105964679236350.0094035320763648
470.520.521100356309238-0.00110035630923766
480.510.521041393702448-0.0110413937024483
490.510.510449740480835-0.000449740480834793
500.510.510425641131464-0.000425641131464038
510.480.510402833146035-0.030402833146035
520.490.4787736969462230.0112263030537765
530.470.489375258537774-0.0193752585377736
540.510.4683370350632380.0416629649367617
550.50.510569545567899-0.0105695455678986
560.510.5000031763345610.00999682366543941
570.510.51053885625749-0.000538856257489839
580.520.5105099816380960.00949001836190355
590.510.521018504392407-0.0110185043924066
600.520.5104280776947620.00957192230523796
610.480.520940989272915-0.0409409892729148
620.490.4787471658433610.0112528341566395
630.470.489350149104394-0.0193501491043941
640.440.468313271119165-0.028313271119165
650.440.4367961041270710.00320389587292913
660.470.4369677849280650.0330322150719345
670.510.4687378165917320.0412621834082682
680.510.510948851213104-0.000948851213103508
690.520.5108980070088130.00910199299118741
700.520.521385737418711-0.00138573741871051
710.520.52131148266155-0.00131148266154979
720.520.521241206846494-0.00124120684649365







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
730.5211746967618790.4832244929375650.559124900586192
740.5223493935237570.4672229977403980.577475789307116
750.5235240902856360.454210488623820.592837691947452
760.5246987870475150.442571712886930.606825861208099
770.5258734838093930.4317000636386140.620046903980173
780.5270481805712720.4212938596437170.632802501498827
790.5282228773331510.41117947920750.645266275458802
800.529397574095030.4012474833163690.65754766487369
810.5305722708569080.3914244598419680.669720081871849
820.5317469676187870.3816588920568870.681835043180687
830.5329216643806660.3719133793034160.693929949457915
840.5340963611425440.3621600462662510.706032676018837

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 0.521174696761879 & 0.483224492937565 & 0.559124900586192 \tabularnewline
74 & 0.522349393523757 & 0.467222997740398 & 0.577475789307116 \tabularnewline
75 & 0.523524090285636 & 0.45421048862382 & 0.592837691947452 \tabularnewline
76 & 0.524698787047515 & 0.44257171288693 & 0.606825861208099 \tabularnewline
77 & 0.525873483809393 & 0.431700063638614 & 0.620046903980173 \tabularnewline
78 & 0.527048180571272 & 0.421293859643717 & 0.632802501498827 \tabularnewline
79 & 0.528222877333151 & 0.4111794792075 & 0.645266275458802 \tabularnewline
80 & 0.52939757409503 & 0.401247483316369 & 0.65754766487369 \tabularnewline
81 & 0.530572270856908 & 0.391424459841968 & 0.669720081871849 \tabularnewline
82 & 0.531746967618787 & 0.381658892056887 & 0.681835043180687 \tabularnewline
83 & 0.532921664380666 & 0.371913379303416 & 0.693929949457915 \tabularnewline
84 & 0.534096361142544 & 0.362160046266251 & 0.706032676018837 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234984&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]0.521174696761879[/C][C]0.483224492937565[/C][C]0.559124900586192[/C][/ROW]
[ROW][C]74[/C][C]0.522349393523757[/C][C]0.467222997740398[/C][C]0.577475789307116[/C][/ROW]
[ROW][C]75[/C][C]0.523524090285636[/C][C]0.45421048862382[/C][C]0.592837691947452[/C][/ROW]
[ROW][C]76[/C][C]0.524698787047515[/C][C]0.44257171288693[/C][C]0.606825861208099[/C][/ROW]
[ROW][C]77[/C][C]0.525873483809393[/C][C]0.431700063638614[/C][C]0.620046903980173[/C][/ROW]
[ROW][C]78[/C][C]0.527048180571272[/C][C]0.421293859643717[/C][C]0.632802501498827[/C][/ROW]
[ROW][C]79[/C][C]0.528222877333151[/C][C]0.4111794792075[/C][C]0.645266275458802[/C][/ROW]
[ROW][C]80[/C][C]0.52939757409503[/C][C]0.401247483316369[/C][C]0.65754766487369[/C][/ROW]
[ROW][C]81[/C][C]0.530572270856908[/C][C]0.391424459841968[/C][C]0.669720081871849[/C][/ROW]
[ROW][C]82[/C][C]0.531746967618787[/C][C]0.381658892056887[/C][C]0.681835043180687[/C][/ROW]
[ROW][C]83[/C][C]0.532921664380666[/C][C]0.371913379303416[/C][C]0.693929949457915[/C][/ROW]
[ROW][C]84[/C][C]0.534096361142544[/C][C]0.362160046266251[/C][C]0.706032676018837[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234984&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234984&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
730.5211746967618790.4832244929375650.559124900586192
740.5223493935237570.4672229977403980.577475789307116
750.5235240902856360.454210488623820.592837691947452
760.5246987870475150.442571712886930.606825861208099
770.5258734838093930.4317000636386140.620046903980173
780.5270481805712720.4212938596437170.632802501498827
790.5282228773331510.41117947920750.645266275458802
800.529397574095030.4012474833163690.65754766487369
810.5305722708569080.3914244598419680.669720081871849
820.5317469676187870.3816588920568870.681835043180687
830.5329216643806660.3719133793034160.693929949457915
840.5340963611425440.3621600462662510.706032676018837



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