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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 13 Aug 2016 13:48:43 +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/Aug/13/t1471092566k26mzx0je2s665x.htm/, Retrieved Wed, 01 May 2024 17:01:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=296514, Retrieved Wed, 01 May 2024 17:01:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact171
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [] [2016-08-13 09:35:09] [74be16979710d4c4e7c6647856088456]
- RMP     [Exponential Smoothing] [] [2016-08-13 12:48:43] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
29312
29336
29357
29380
29402
29426
29448
29471
29495
29517
29540
29563
29586
29609
29631
29654
29677
29700
29723
29746
29769
29792
29815
29837
29861
29884
29905
29928
29951
29974
29996
30020
30043
30065
30089
30111
30134
30158
30179
30202
30224
30248
30270
30293
30317
30339
30362
30385
30408
30431
30452
30476
30498
30521
30544
30567
30590
30613
30636
30659
30682
30705
30727
30750
30773
30796
30818
30842
30865
30887
30911
30933
30956
30980
31001
31024
31046
31070
31092
31115
31139
31161
31184
31207
31230
31253
31274
31298
31320
31343
31366
31389
31412
31435
31458
31481
31504
31527
31548
31571
31594
31617
31640
31663
31686
31709
31732
31754




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=296514&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=296514&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296514&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
alpha0.628749767969885
beta0.218314234003923
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.628749767969885 \tabularnewline
beta & 0.218314234003923 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296514&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]0.628749767969885[/C][/ROW]
[ROW][C]beta[/C][C]0.218314234003923[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296514&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296514&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
alpha0.628749767969885
beta0.218314234003923
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
32935729360-3
42938029381.7019556242-1.70195562416484
52940229403.9864373689-1.98643736889426
62942629425.81938290960.180617090427404
72944829449.039655848-1.03965584797334
82947129471.3499740746-0.349974074593774
92949529494.04589035650.954109643535048
102951729517.6927148566-0.692714856617386
112954029540.209013313-0.209013313007745
122956329563.0007487853-0.000748785292671528
132958629585.9233277490.0766722509797546
142960929608.90510958970.0948904102915549
152963129631.9113712283-0.911371228281496
162965429654.1598467016-0.159846701586503
172967729676.85890168530.141098314652481
182970029699.76654364180.233456358215335
192972329722.76430108930.235698910710198
202974629745.79582175780.204178242212947
212976929768.83555034460.164449655410863
222979229791.87287277760.127127222447598
232981529814.90417886070.0958211393153761
242983729837.9289541423-0.928954142298608
252986129860.18188929080.818110709235043
262988429883.64558904540.354410954627383
272990529906.866385915-1.86638591504743
282992829928.4346677608-0.43466776083369
292995129950.84347738330.156522616733128
302997429973.64548289920.354517100837256
312999629996.6206401993-0.620640199340414
323002030018.89747538151.10252461854543
333004330042.40908811120.590911888812116
343006530065.6801359904-0.680135990394774
353008930088.05865392740.941346072555461
363011130111.5858922266-0.585892226561555
373013430134.0724572889-0.0724572889448609
383015830156.87189859771.12810140227884
393017930180.5810397711-1.58103977106657
403020230202.3697875982-0.369787598192488
413022430224.8693510444-0.869351044435462
423024830246.93548259781.064517402192
433027030270.363654495-0.363654495020455
443029330292.84394660030.156053399743541
453031730315.67242559741.32757440260684
463033930339.4197276855-0.419727685453836
473036230362.0108000603-0.0108000602667744
483038530384.8575031140.142496886001027
493040830407.82015142560.179848574392963
503043130430.83097152150.169028478503606
513045230453.8581901828-1.85819018276015
523047630475.35573106110.64426893885684
533049830498.5151281229-0.515128122933675
543052130520.8748454770.125154523004312
553054430543.65431973470.345680265269039
563056730566.61989931160.380100688355014
573059030589.65929525170.340704748316057
583061330612.7206878490.279312150985788
593063630635.78181965410.218180345880683
603065930658.83446338140.165536618642363
613068230681.87672976520.123270234766096
623070530704.90934186180.0906581382187142
633072730727.9338933017-0.933893301709759
643075030750.1860673751-0.186067375063431
653077330772.88289628360.117103716420388
663079630795.786418190.213581810039614
673081830818.7799179876-0.77991798759831
683084230841.04169955670.95830044327522
693086530864.52792669430.472073305736558
703088730887.7732377855-0.773237785520905
713091130910.12942131390.870578686066438
723093330933.6386540717-0.638654071659403
733095630956.1112922167-0.111292216690345
743098030978.90023247691.09976752312286
753100131002.6015858829-1.60158588289778
763102431024.3846222371-0.384622237063013
773104631046.8800290206-0.880029020583606
783107031068.94315169931.05684830069004
793109231092.3691538517-0.369153851701412
803111531114.84788556940.152114430649817
813113931137.67524458951.32475541045278
823116131161.4217439369-0.421743936884013
833118431184.0122415332-0.0122415332152741
843120731206.85853333650.141466663513711
853123031229.82088755770.179112442256155
863125331252.83149742730.168502572672878
873127431275.8585658536-1.85856585355214
883129831297.35599939070.644000609318027
893132031320.5153197698-0.515319769750931
903134331342.87498234890.125017651076632
913136631365.65441748370.345582516263676
923138931388.61996911870.380030881260609
933141231411.65934510330.340654896728665
943143531434.72072344920.27927655077292
953145831457.78184507680.218154923153634
963148131480.8344815360.165518463967601
973150431503.87674272960.123257270352042
983152731526.90935111980.0906488802465901
993154831549.9338999129-1.93389991286313
1003157131571.4200573042-0.420057304156217
1013159431593.80038370850.199616291505663
1023161731616.59773007740.402269922640698
1033164031639.57771246040.422287539644458
1043166331662.62824622470.371753775347315
1053168631685.69803568730.301964312744531
1063170931708.76539418010.234605819929129
1073173231731.82260420970.177395790342416
1083175431754.8681936838-0.868193683825666

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 29357 & 29360 & -3 \tabularnewline
4 & 29380 & 29381.7019556242 & -1.70195562416484 \tabularnewline
5 & 29402 & 29403.9864373689 & -1.98643736889426 \tabularnewline
6 & 29426 & 29425.8193829096 & 0.180617090427404 \tabularnewline
7 & 29448 & 29449.039655848 & -1.03965584797334 \tabularnewline
8 & 29471 & 29471.3499740746 & -0.349974074593774 \tabularnewline
9 & 29495 & 29494.0458903565 & 0.954109643535048 \tabularnewline
10 & 29517 & 29517.6927148566 & -0.692714856617386 \tabularnewline
11 & 29540 & 29540.209013313 & -0.209013313007745 \tabularnewline
12 & 29563 & 29563.0007487853 & -0.000748785292671528 \tabularnewline
13 & 29586 & 29585.923327749 & 0.0766722509797546 \tabularnewline
14 & 29609 & 29608.9051095897 & 0.0948904102915549 \tabularnewline
15 & 29631 & 29631.9113712283 & -0.911371228281496 \tabularnewline
16 & 29654 & 29654.1598467016 & -0.159846701586503 \tabularnewline
17 & 29677 & 29676.8589016853 & 0.141098314652481 \tabularnewline
18 & 29700 & 29699.7665436418 & 0.233456358215335 \tabularnewline
19 & 29723 & 29722.7643010893 & 0.235698910710198 \tabularnewline
20 & 29746 & 29745.7958217578 & 0.204178242212947 \tabularnewline
21 & 29769 & 29768.8355503446 & 0.164449655410863 \tabularnewline
22 & 29792 & 29791.8728727776 & 0.127127222447598 \tabularnewline
23 & 29815 & 29814.9041788607 & 0.0958211393153761 \tabularnewline
24 & 29837 & 29837.9289541423 & -0.928954142298608 \tabularnewline
25 & 29861 & 29860.1818892908 & 0.818110709235043 \tabularnewline
26 & 29884 & 29883.6455890454 & 0.354410954627383 \tabularnewline
27 & 29905 & 29906.866385915 & -1.86638591504743 \tabularnewline
28 & 29928 & 29928.4346677608 & -0.43466776083369 \tabularnewline
29 & 29951 & 29950.8434773833 & 0.156522616733128 \tabularnewline
30 & 29974 & 29973.6454828992 & 0.354517100837256 \tabularnewline
31 & 29996 & 29996.6206401993 & -0.620640199340414 \tabularnewline
32 & 30020 & 30018.8974753815 & 1.10252461854543 \tabularnewline
33 & 30043 & 30042.4090881112 & 0.590911888812116 \tabularnewline
34 & 30065 & 30065.6801359904 & -0.680135990394774 \tabularnewline
35 & 30089 & 30088.0586539274 & 0.941346072555461 \tabularnewline
36 & 30111 & 30111.5858922266 & -0.585892226561555 \tabularnewline
37 & 30134 & 30134.0724572889 & -0.0724572889448609 \tabularnewline
38 & 30158 & 30156.8718985977 & 1.12810140227884 \tabularnewline
39 & 30179 & 30180.5810397711 & -1.58103977106657 \tabularnewline
40 & 30202 & 30202.3697875982 & -0.369787598192488 \tabularnewline
41 & 30224 & 30224.8693510444 & -0.869351044435462 \tabularnewline
42 & 30248 & 30246.9354825978 & 1.064517402192 \tabularnewline
43 & 30270 & 30270.363654495 & -0.363654495020455 \tabularnewline
44 & 30293 & 30292.8439466003 & 0.156053399743541 \tabularnewline
45 & 30317 & 30315.6724255974 & 1.32757440260684 \tabularnewline
46 & 30339 & 30339.4197276855 & -0.419727685453836 \tabularnewline
47 & 30362 & 30362.0108000603 & -0.0108000602667744 \tabularnewline
48 & 30385 & 30384.857503114 & 0.142496886001027 \tabularnewline
49 & 30408 & 30407.8201514256 & 0.179848574392963 \tabularnewline
50 & 30431 & 30430.8309715215 & 0.169028478503606 \tabularnewline
51 & 30452 & 30453.8581901828 & -1.85819018276015 \tabularnewline
52 & 30476 & 30475.3557310611 & 0.64426893885684 \tabularnewline
53 & 30498 & 30498.5151281229 & -0.515128122933675 \tabularnewline
54 & 30521 & 30520.874845477 & 0.125154523004312 \tabularnewline
55 & 30544 & 30543.6543197347 & 0.345680265269039 \tabularnewline
56 & 30567 & 30566.6198993116 & 0.380100688355014 \tabularnewline
57 & 30590 & 30589.6592952517 & 0.340704748316057 \tabularnewline
58 & 30613 & 30612.720687849 & 0.279312150985788 \tabularnewline
59 & 30636 & 30635.7818196541 & 0.218180345880683 \tabularnewline
60 & 30659 & 30658.8344633814 & 0.165536618642363 \tabularnewline
61 & 30682 & 30681.8767297652 & 0.123270234766096 \tabularnewline
62 & 30705 & 30704.9093418618 & 0.0906581382187142 \tabularnewline
63 & 30727 & 30727.9338933017 & -0.933893301709759 \tabularnewline
64 & 30750 & 30750.1860673751 & -0.186067375063431 \tabularnewline
65 & 30773 & 30772.8828962836 & 0.117103716420388 \tabularnewline
66 & 30796 & 30795.78641819 & 0.213581810039614 \tabularnewline
67 & 30818 & 30818.7799179876 & -0.77991798759831 \tabularnewline
68 & 30842 & 30841.0416995567 & 0.95830044327522 \tabularnewline
69 & 30865 & 30864.5279266943 & 0.472073305736558 \tabularnewline
70 & 30887 & 30887.7732377855 & -0.773237785520905 \tabularnewline
71 & 30911 & 30910.1294213139 & 0.870578686066438 \tabularnewline
72 & 30933 & 30933.6386540717 & -0.638654071659403 \tabularnewline
73 & 30956 & 30956.1112922167 & -0.111292216690345 \tabularnewline
74 & 30980 & 30978.9002324769 & 1.09976752312286 \tabularnewline
75 & 31001 & 31002.6015858829 & -1.60158588289778 \tabularnewline
76 & 31024 & 31024.3846222371 & -0.384622237063013 \tabularnewline
77 & 31046 & 31046.8800290206 & -0.880029020583606 \tabularnewline
78 & 31070 & 31068.9431516993 & 1.05684830069004 \tabularnewline
79 & 31092 & 31092.3691538517 & -0.369153851701412 \tabularnewline
80 & 31115 & 31114.8478855694 & 0.152114430649817 \tabularnewline
81 & 31139 & 31137.6752445895 & 1.32475541045278 \tabularnewline
82 & 31161 & 31161.4217439369 & -0.421743936884013 \tabularnewline
83 & 31184 & 31184.0122415332 & -0.0122415332152741 \tabularnewline
84 & 31207 & 31206.8585333365 & 0.141466663513711 \tabularnewline
85 & 31230 & 31229.8208875577 & 0.179112442256155 \tabularnewline
86 & 31253 & 31252.8314974273 & 0.168502572672878 \tabularnewline
87 & 31274 & 31275.8585658536 & -1.85856585355214 \tabularnewline
88 & 31298 & 31297.3559993907 & 0.644000609318027 \tabularnewline
89 & 31320 & 31320.5153197698 & -0.515319769750931 \tabularnewline
90 & 31343 & 31342.8749823489 & 0.125017651076632 \tabularnewline
91 & 31366 & 31365.6544174837 & 0.345582516263676 \tabularnewline
92 & 31389 & 31388.6199691187 & 0.380030881260609 \tabularnewline
93 & 31412 & 31411.6593451033 & 0.340654896728665 \tabularnewline
94 & 31435 & 31434.7207234492 & 0.27927655077292 \tabularnewline
95 & 31458 & 31457.7818450768 & 0.218154923153634 \tabularnewline
96 & 31481 & 31480.834481536 & 0.165518463967601 \tabularnewline
97 & 31504 & 31503.8767427296 & 0.123257270352042 \tabularnewline
98 & 31527 & 31526.9093511198 & 0.0906488802465901 \tabularnewline
99 & 31548 & 31549.9338999129 & -1.93389991286313 \tabularnewline
100 & 31571 & 31571.4200573042 & -0.420057304156217 \tabularnewline
101 & 31594 & 31593.8003837085 & 0.199616291505663 \tabularnewline
102 & 31617 & 31616.5977300774 & 0.402269922640698 \tabularnewline
103 & 31640 & 31639.5777124604 & 0.422287539644458 \tabularnewline
104 & 31663 & 31662.6282462247 & 0.371753775347315 \tabularnewline
105 & 31686 & 31685.6980356873 & 0.301964312744531 \tabularnewline
106 & 31709 & 31708.7653941801 & 0.234605819929129 \tabularnewline
107 & 31732 & 31731.8226042097 & 0.177395790342416 \tabularnewline
108 & 31754 & 31754.8681936838 & -0.868193683825666 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296514&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]29357[/C][C]29360[/C][C]-3[/C][/ROW]
[ROW][C]4[/C][C]29380[/C][C]29381.7019556242[/C][C]-1.70195562416484[/C][/ROW]
[ROW][C]5[/C][C]29402[/C][C]29403.9864373689[/C][C]-1.98643736889426[/C][/ROW]
[ROW][C]6[/C][C]29426[/C][C]29425.8193829096[/C][C]0.180617090427404[/C][/ROW]
[ROW][C]7[/C][C]29448[/C][C]29449.039655848[/C][C]-1.03965584797334[/C][/ROW]
[ROW][C]8[/C][C]29471[/C][C]29471.3499740746[/C][C]-0.349974074593774[/C][/ROW]
[ROW][C]9[/C][C]29495[/C][C]29494.0458903565[/C][C]0.954109643535048[/C][/ROW]
[ROW][C]10[/C][C]29517[/C][C]29517.6927148566[/C][C]-0.692714856617386[/C][/ROW]
[ROW][C]11[/C][C]29540[/C][C]29540.209013313[/C][C]-0.209013313007745[/C][/ROW]
[ROW][C]12[/C][C]29563[/C][C]29563.0007487853[/C][C]-0.000748785292671528[/C][/ROW]
[ROW][C]13[/C][C]29586[/C][C]29585.923327749[/C][C]0.0766722509797546[/C][/ROW]
[ROW][C]14[/C][C]29609[/C][C]29608.9051095897[/C][C]0.0948904102915549[/C][/ROW]
[ROW][C]15[/C][C]29631[/C][C]29631.9113712283[/C][C]-0.911371228281496[/C][/ROW]
[ROW][C]16[/C][C]29654[/C][C]29654.1598467016[/C][C]-0.159846701586503[/C][/ROW]
[ROW][C]17[/C][C]29677[/C][C]29676.8589016853[/C][C]0.141098314652481[/C][/ROW]
[ROW][C]18[/C][C]29700[/C][C]29699.7665436418[/C][C]0.233456358215335[/C][/ROW]
[ROW][C]19[/C][C]29723[/C][C]29722.7643010893[/C][C]0.235698910710198[/C][/ROW]
[ROW][C]20[/C][C]29746[/C][C]29745.7958217578[/C][C]0.204178242212947[/C][/ROW]
[ROW][C]21[/C][C]29769[/C][C]29768.8355503446[/C][C]0.164449655410863[/C][/ROW]
[ROW][C]22[/C][C]29792[/C][C]29791.8728727776[/C][C]0.127127222447598[/C][/ROW]
[ROW][C]23[/C][C]29815[/C][C]29814.9041788607[/C][C]0.0958211393153761[/C][/ROW]
[ROW][C]24[/C][C]29837[/C][C]29837.9289541423[/C][C]-0.928954142298608[/C][/ROW]
[ROW][C]25[/C][C]29861[/C][C]29860.1818892908[/C][C]0.818110709235043[/C][/ROW]
[ROW][C]26[/C][C]29884[/C][C]29883.6455890454[/C][C]0.354410954627383[/C][/ROW]
[ROW][C]27[/C][C]29905[/C][C]29906.866385915[/C][C]-1.86638591504743[/C][/ROW]
[ROW][C]28[/C][C]29928[/C][C]29928.4346677608[/C][C]-0.43466776083369[/C][/ROW]
[ROW][C]29[/C][C]29951[/C][C]29950.8434773833[/C][C]0.156522616733128[/C][/ROW]
[ROW][C]30[/C][C]29974[/C][C]29973.6454828992[/C][C]0.354517100837256[/C][/ROW]
[ROW][C]31[/C][C]29996[/C][C]29996.6206401993[/C][C]-0.620640199340414[/C][/ROW]
[ROW][C]32[/C][C]30020[/C][C]30018.8974753815[/C][C]1.10252461854543[/C][/ROW]
[ROW][C]33[/C][C]30043[/C][C]30042.4090881112[/C][C]0.590911888812116[/C][/ROW]
[ROW][C]34[/C][C]30065[/C][C]30065.6801359904[/C][C]-0.680135990394774[/C][/ROW]
[ROW][C]35[/C][C]30089[/C][C]30088.0586539274[/C][C]0.941346072555461[/C][/ROW]
[ROW][C]36[/C][C]30111[/C][C]30111.5858922266[/C][C]-0.585892226561555[/C][/ROW]
[ROW][C]37[/C][C]30134[/C][C]30134.0724572889[/C][C]-0.0724572889448609[/C][/ROW]
[ROW][C]38[/C][C]30158[/C][C]30156.8718985977[/C][C]1.12810140227884[/C][/ROW]
[ROW][C]39[/C][C]30179[/C][C]30180.5810397711[/C][C]-1.58103977106657[/C][/ROW]
[ROW][C]40[/C][C]30202[/C][C]30202.3697875982[/C][C]-0.369787598192488[/C][/ROW]
[ROW][C]41[/C][C]30224[/C][C]30224.8693510444[/C][C]-0.869351044435462[/C][/ROW]
[ROW][C]42[/C][C]30248[/C][C]30246.9354825978[/C][C]1.064517402192[/C][/ROW]
[ROW][C]43[/C][C]30270[/C][C]30270.363654495[/C][C]-0.363654495020455[/C][/ROW]
[ROW][C]44[/C][C]30293[/C][C]30292.8439466003[/C][C]0.156053399743541[/C][/ROW]
[ROW][C]45[/C][C]30317[/C][C]30315.6724255974[/C][C]1.32757440260684[/C][/ROW]
[ROW][C]46[/C][C]30339[/C][C]30339.4197276855[/C][C]-0.419727685453836[/C][/ROW]
[ROW][C]47[/C][C]30362[/C][C]30362.0108000603[/C][C]-0.0108000602667744[/C][/ROW]
[ROW][C]48[/C][C]30385[/C][C]30384.857503114[/C][C]0.142496886001027[/C][/ROW]
[ROW][C]49[/C][C]30408[/C][C]30407.8201514256[/C][C]0.179848574392963[/C][/ROW]
[ROW][C]50[/C][C]30431[/C][C]30430.8309715215[/C][C]0.169028478503606[/C][/ROW]
[ROW][C]51[/C][C]30452[/C][C]30453.8581901828[/C][C]-1.85819018276015[/C][/ROW]
[ROW][C]52[/C][C]30476[/C][C]30475.3557310611[/C][C]0.64426893885684[/C][/ROW]
[ROW][C]53[/C][C]30498[/C][C]30498.5151281229[/C][C]-0.515128122933675[/C][/ROW]
[ROW][C]54[/C][C]30521[/C][C]30520.874845477[/C][C]0.125154523004312[/C][/ROW]
[ROW][C]55[/C][C]30544[/C][C]30543.6543197347[/C][C]0.345680265269039[/C][/ROW]
[ROW][C]56[/C][C]30567[/C][C]30566.6198993116[/C][C]0.380100688355014[/C][/ROW]
[ROW][C]57[/C][C]30590[/C][C]30589.6592952517[/C][C]0.340704748316057[/C][/ROW]
[ROW][C]58[/C][C]30613[/C][C]30612.720687849[/C][C]0.279312150985788[/C][/ROW]
[ROW][C]59[/C][C]30636[/C][C]30635.7818196541[/C][C]0.218180345880683[/C][/ROW]
[ROW][C]60[/C][C]30659[/C][C]30658.8344633814[/C][C]0.165536618642363[/C][/ROW]
[ROW][C]61[/C][C]30682[/C][C]30681.8767297652[/C][C]0.123270234766096[/C][/ROW]
[ROW][C]62[/C][C]30705[/C][C]30704.9093418618[/C][C]0.0906581382187142[/C][/ROW]
[ROW][C]63[/C][C]30727[/C][C]30727.9338933017[/C][C]-0.933893301709759[/C][/ROW]
[ROW][C]64[/C][C]30750[/C][C]30750.1860673751[/C][C]-0.186067375063431[/C][/ROW]
[ROW][C]65[/C][C]30773[/C][C]30772.8828962836[/C][C]0.117103716420388[/C][/ROW]
[ROW][C]66[/C][C]30796[/C][C]30795.78641819[/C][C]0.213581810039614[/C][/ROW]
[ROW][C]67[/C][C]30818[/C][C]30818.7799179876[/C][C]-0.77991798759831[/C][/ROW]
[ROW][C]68[/C][C]30842[/C][C]30841.0416995567[/C][C]0.95830044327522[/C][/ROW]
[ROW][C]69[/C][C]30865[/C][C]30864.5279266943[/C][C]0.472073305736558[/C][/ROW]
[ROW][C]70[/C][C]30887[/C][C]30887.7732377855[/C][C]-0.773237785520905[/C][/ROW]
[ROW][C]71[/C][C]30911[/C][C]30910.1294213139[/C][C]0.870578686066438[/C][/ROW]
[ROW][C]72[/C][C]30933[/C][C]30933.6386540717[/C][C]-0.638654071659403[/C][/ROW]
[ROW][C]73[/C][C]30956[/C][C]30956.1112922167[/C][C]-0.111292216690345[/C][/ROW]
[ROW][C]74[/C][C]30980[/C][C]30978.9002324769[/C][C]1.09976752312286[/C][/ROW]
[ROW][C]75[/C][C]31001[/C][C]31002.6015858829[/C][C]-1.60158588289778[/C][/ROW]
[ROW][C]76[/C][C]31024[/C][C]31024.3846222371[/C][C]-0.384622237063013[/C][/ROW]
[ROW][C]77[/C][C]31046[/C][C]31046.8800290206[/C][C]-0.880029020583606[/C][/ROW]
[ROW][C]78[/C][C]31070[/C][C]31068.9431516993[/C][C]1.05684830069004[/C][/ROW]
[ROW][C]79[/C][C]31092[/C][C]31092.3691538517[/C][C]-0.369153851701412[/C][/ROW]
[ROW][C]80[/C][C]31115[/C][C]31114.8478855694[/C][C]0.152114430649817[/C][/ROW]
[ROW][C]81[/C][C]31139[/C][C]31137.6752445895[/C][C]1.32475541045278[/C][/ROW]
[ROW][C]82[/C][C]31161[/C][C]31161.4217439369[/C][C]-0.421743936884013[/C][/ROW]
[ROW][C]83[/C][C]31184[/C][C]31184.0122415332[/C][C]-0.0122415332152741[/C][/ROW]
[ROW][C]84[/C][C]31207[/C][C]31206.8585333365[/C][C]0.141466663513711[/C][/ROW]
[ROW][C]85[/C][C]31230[/C][C]31229.8208875577[/C][C]0.179112442256155[/C][/ROW]
[ROW][C]86[/C][C]31253[/C][C]31252.8314974273[/C][C]0.168502572672878[/C][/ROW]
[ROW][C]87[/C][C]31274[/C][C]31275.8585658536[/C][C]-1.85856585355214[/C][/ROW]
[ROW][C]88[/C][C]31298[/C][C]31297.3559993907[/C][C]0.644000609318027[/C][/ROW]
[ROW][C]89[/C][C]31320[/C][C]31320.5153197698[/C][C]-0.515319769750931[/C][/ROW]
[ROW][C]90[/C][C]31343[/C][C]31342.8749823489[/C][C]0.125017651076632[/C][/ROW]
[ROW][C]91[/C][C]31366[/C][C]31365.6544174837[/C][C]0.345582516263676[/C][/ROW]
[ROW][C]92[/C][C]31389[/C][C]31388.6199691187[/C][C]0.380030881260609[/C][/ROW]
[ROW][C]93[/C][C]31412[/C][C]31411.6593451033[/C][C]0.340654896728665[/C][/ROW]
[ROW][C]94[/C][C]31435[/C][C]31434.7207234492[/C][C]0.27927655077292[/C][/ROW]
[ROW][C]95[/C][C]31458[/C][C]31457.7818450768[/C][C]0.218154923153634[/C][/ROW]
[ROW][C]96[/C][C]31481[/C][C]31480.834481536[/C][C]0.165518463967601[/C][/ROW]
[ROW][C]97[/C][C]31504[/C][C]31503.8767427296[/C][C]0.123257270352042[/C][/ROW]
[ROW][C]98[/C][C]31527[/C][C]31526.9093511198[/C][C]0.0906488802465901[/C][/ROW]
[ROW][C]99[/C][C]31548[/C][C]31549.9338999129[/C][C]-1.93389991286313[/C][/ROW]
[ROW][C]100[/C][C]31571[/C][C]31571.4200573042[/C][C]-0.420057304156217[/C][/ROW]
[ROW][C]101[/C][C]31594[/C][C]31593.8003837085[/C][C]0.199616291505663[/C][/ROW]
[ROW][C]102[/C][C]31617[/C][C]31616.5977300774[/C][C]0.402269922640698[/C][/ROW]
[ROW][C]103[/C][C]31640[/C][C]31639.5777124604[/C][C]0.422287539644458[/C][/ROW]
[ROW][C]104[/C][C]31663[/C][C]31662.6282462247[/C][C]0.371753775347315[/C][/ROW]
[ROW][C]105[/C][C]31686[/C][C]31685.6980356873[/C][C]0.301964312744531[/C][/ROW]
[ROW][C]106[/C][C]31709[/C][C]31708.7653941801[/C][C]0.234605819929129[/C][/ROW]
[ROW][C]107[/C][C]31732[/C][C]31731.8226042097[/C][C]0.177395790342416[/C][/ROW]
[ROW][C]108[/C][C]31754[/C][C]31754.8681936838[/C][C]-0.868193683825666[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296514&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296514&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
32935729360-3
42938029381.7019556242-1.70195562416484
52940229403.9864373689-1.98643736889426
62942629425.81938290960.180617090427404
72944829449.039655848-1.03965584797334
82947129471.3499740746-0.349974074593774
92949529494.04589035650.954109643535048
102951729517.6927148566-0.692714856617386
112954029540.209013313-0.209013313007745
122956329563.0007487853-0.000748785292671528
132958629585.9233277490.0766722509797546
142960929608.90510958970.0948904102915549
152963129631.9113712283-0.911371228281496
162965429654.1598467016-0.159846701586503
172967729676.85890168530.141098314652481
182970029699.76654364180.233456358215335
192972329722.76430108930.235698910710198
202974629745.79582175780.204178242212947
212976929768.83555034460.164449655410863
222979229791.87287277760.127127222447598
232981529814.90417886070.0958211393153761
242983729837.9289541423-0.928954142298608
252986129860.18188929080.818110709235043
262988429883.64558904540.354410954627383
272990529906.866385915-1.86638591504743
282992829928.4346677608-0.43466776083369
292995129950.84347738330.156522616733128
302997429973.64548289920.354517100837256
312999629996.6206401993-0.620640199340414
323002030018.89747538151.10252461854543
333004330042.40908811120.590911888812116
343006530065.6801359904-0.680135990394774
353008930088.05865392740.941346072555461
363011130111.5858922266-0.585892226561555
373013430134.0724572889-0.0724572889448609
383015830156.87189859771.12810140227884
393017930180.5810397711-1.58103977106657
403020230202.3697875982-0.369787598192488
413022430224.8693510444-0.869351044435462
423024830246.93548259781.064517402192
433027030270.363654495-0.363654495020455
443029330292.84394660030.156053399743541
453031730315.67242559741.32757440260684
463033930339.4197276855-0.419727685453836
473036230362.0108000603-0.0108000602667744
483038530384.8575031140.142496886001027
493040830407.82015142560.179848574392963
503043130430.83097152150.169028478503606
513045230453.8581901828-1.85819018276015
523047630475.35573106110.64426893885684
533049830498.5151281229-0.515128122933675
543052130520.8748454770.125154523004312
553054430543.65431973470.345680265269039
563056730566.61989931160.380100688355014
573059030589.65929525170.340704748316057
583061330612.7206878490.279312150985788
593063630635.78181965410.218180345880683
603065930658.83446338140.165536618642363
613068230681.87672976520.123270234766096
623070530704.90934186180.0906581382187142
633072730727.9338933017-0.933893301709759
643075030750.1860673751-0.186067375063431
653077330772.88289628360.117103716420388
663079630795.786418190.213581810039614
673081830818.7799179876-0.77991798759831
683084230841.04169955670.95830044327522
693086530864.52792669430.472073305736558
703088730887.7732377855-0.773237785520905
713091130910.12942131390.870578686066438
723093330933.6386540717-0.638654071659403
733095630956.1112922167-0.111292216690345
743098030978.90023247691.09976752312286
753100131002.6015858829-1.60158588289778
763102431024.3846222371-0.384622237063013
773104631046.8800290206-0.880029020583606
783107031068.94315169931.05684830069004
793109231092.3691538517-0.369153851701412
803111531114.84788556940.152114430649817
813113931137.67524458951.32475541045278
823116131161.4217439369-0.421743936884013
833118431184.0122415332-0.0122415332152741
843120731206.85853333650.141466663513711
853123031229.82088755770.179112442256155
863125331252.83149742730.168502572672878
873127431275.8585658536-1.85856585355214
883129831297.35599939070.644000609318027
893132031320.5153197698-0.515319769750931
903134331342.87498234890.125017651076632
913136631365.65441748370.345582516263676
923138931388.61996911870.380030881260609
933141231411.65934510330.340654896728665
943143531434.72072344920.27927655077292
953145831457.78184507680.218154923153634
963148131480.8344815360.165518463967601
973150431503.87674272960.123257270352042
983152731526.90935111980.0906488802465901
993154831549.9338999129-1.93389991286313
1003157131571.4200573042-0.420057304156217
1013159431593.80038370850.199616291505663
1023161731616.59773007740.402269922640698
1033164031639.57771246040.422287539644458
1043166331662.62824622470.371753775347315
1053168631685.69803568730.301964312744531
1063170931708.76539418010.234605819929129
1073173231731.82260420970.177395790342416
1083175431754.8681936838-0.868193683825666







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
10931777.137196391931775.615851382631778.6585414012
11031799.952075677231798.035676878631801.8684744759
11131822.766954962631820.408775441231825.1251344839
11231845.581834247931842.741590006531848.4220784893
11331868.396713533231865.038480030431871.754947036
11431891.211592818531887.302569514131895.120616123
11531914.026472103931909.536216212131918.5167279956
11631936.841351389231931.741277427931941.9414253505
11731959.656230674531953.91926716431965.3931941851
11831982.471109959931976.07145344431988.8707664757
11932005.285989245231998.198921316532012.3730571738
12032028.100868530532020.302615325532035.8991217356

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 31777.1371963919 & 31775.6158513826 & 31778.6585414012 \tabularnewline
110 & 31799.9520756772 & 31798.0356768786 & 31801.8684744759 \tabularnewline
111 & 31822.7669549626 & 31820.4087754412 & 31825.1251344839 \tabularnewline
112 & 31845.5818342479 & 31842.7415900065 & 31848.4220784893 \tabularnewline
113 & 31868.3967135332 & 31865.0384800304 & 31871.754947036 \tabularnewline
114 & 31891.2115928185 & 31887.3025695141 & 31895.120616123 \tabularnewline
115 & 31914.0264721039 & 31909.5362162121 & 31918.5167279956 \tabularnewline
116 & 31936.8413513892 & 31931.7412774279 & 31941.9414253505 \tabularnewline
117 & 31959.6562306745 & 31953.919267164 & 31965.3931941851 \tabularnewline
118 & 31982.4711099599 & 31976.071453444 & 31988.8707664757 \tabularnewline
119 & 32005.2859892452 & 31998.1989213165 & 32012.3730571738 \tabularnewline
120 & 32028.1008685305 & 32020.3026153255 & 32035.8991217356 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296514&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]109[/C][C]31777.1371963919[/C][C]31775.6158513826[/C][C]31778.6585414012[/C][/ROW]
[ROW][C]110[/C][C]31799.9520756772[/C][C]31798.0356768786[/C][C]31801.8684744759[/C][/ROW]
[ROW][C]111[/C][C]31822.7669549626[/C][C]31820.4087754412[/C][C]31825.1251344839[/C][/ROW]
[ROW][C]112[/C][C]31845.5818342479[/C][C]31842.7415900065[/C][C]31848.4220784893[/C][/ROW]
[ROW][C]113[/C][C]31868.3967135332[/C][C]31865.0384800304[/C][C]31871.754947036[/C][/ROW]
[ROW][C]114[/C][C]31891.2115928185[/C][C]31887.3025695141[/C][C]31895.120616123[/C][/ROW]
[ROW][C]115[/C][C]31914.0264721039[/C][C]31909.5362162121[/C][C]31918.5167279956[/C][/ROW]
[ROW][C]116[/C][C]31936.8413513892[/C][C]31931.7412774279[/C][C]31941.9414253505[/C][/ROW]
[ROW][C]117[/C][C]31959.6562306745[/C][C]31953.919267164[/C][C]31965.3931941851[/C][/ROW]
[ROW][C]118[/C][C]31982.4711099599[/C][C]31976.071453444[/C][C]31988.8707664757[/C][/ROW]
[ROW][C]119[/C][C]32005.2859892452[/C][C]31998.1989213165[/C][C]32012.3730571738[/C][/ROW]
[ROW][C]120[/C][C]32028.1008685305[/C][C]32020.3026153255[/C][C]32035.8991217356[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296514&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296514&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
10931777.137196391931775.615851382631778.6585414012
11031799.952075677231798.035676878631801.8684744759
11131822.766954962631820.408775441231825.1251344839
11231845.581834247931842.741590006531848.4220784893
11331868.396713533231865.038480030431871.754947036
11431891.211592818531887.302569514131895.120616123
11531914.026472103931909.536216212131918.5167279956
11631936.841351389231931.741277427931941.9414253505
11731959.656230674531953.91926716431965.3931941851
11831982.471109959931976.07145344431988.8707664757
11932005.285989245231998.198921316532012.3730571738
12032028.100868530532020.302615325532035.8991217356



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')