Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 06 Jun 2010 16:07:22 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Jun/06/t1275840530xtfndnnelchek0j.htm/, Retrieved Sat, 27 Apr 2024 18:12:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=77736, Retrieved Sat, 27 Apr 2024 18:12:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W61
Estimated Impact123
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Inschrijvingen ni...] [2010-06-06 16:07:22] [dd2ef098fd65ce7e9f689caa343b799f] [Current]
Feedback Forum

Post a new message
Dataseries X:
5.074
4.643
5.451
5.397
5.635
5.708
5.578
5.574
5.352
5.302
4.923
4.982
5.101
4.763
5.505
5.385
5.794
5.695
5.798
5.705
5.422
5.311
4.968
5.053
5.236
4.782
5.531
5.566
5.961
5.868
5.872
5.908
5.594
5.526
5.111
5.177
5.835
5.348
6.038
6.039
6.408
6.214
6.138
6.529
6.058
6.026
5.678
5.733
6.488
5.936
6.84
6.694
7.193
6.991
7.209
7.104
6.83
6.848
6.396
6.414
7.151
6.882
7.698
7.626
7.936
8.054
8.128
8.062
7.708
7.574
7.039
7.146
7.07
6.607
7.699
7.663
7.988
7.723
8.087
8.028
7.362




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77736&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77736&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77736&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.559630632692926
beta0.0234545572772744
gamma0.256002529557058

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.559630632692926 \tabularnewline
beta & 0.0234545572772744 \tabularnewline
gamma & 0.256002529557058 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77736&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]0.559630632692926[/C][/ROW]
[ROW][C]beta[/C][C]0.0234545572772744[/C][/ROW]
[ROW][C]gamma[/C][C]0.256002529557058[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77736&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77736&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
alpha0.559630632692926
beta0.0234545572772744
gamma0.256002529557058







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
135.1015.073015563475940.0279844365240587
144.7634.74491793654520.0180820634547976
155.5055.494878224314580.0101217756854188
165.3855.384962728943873.72710561293843e-05
175.7945.79975376250684-0.00575376250684023
185.6955.70034313780302-0.00534313780302309
195.7985.661115008425490.136884991574514
205.7055.73661660126565-0.0316166012656511
215.4225.49249451976837-0.0704945197683662
225.3115.40815241789843-0.09715241789843
234.9684.97144204584224-0.00344204584224439
245.0535.02943328355950.023566716440504
255.2365.164480193325480.0715198066745204
264.7824.85242116638604-0.0704211663860352
275.5315.55986841956288-0.0288684195628779
285.5665.424877313953090.141122686046906
295.9615.927665539863060.0333344601369365
305.8685.84869856677570.0193014332242951
315.8725.839823620812960.0321763791870442
325.9085.837339940395590.0706600596044149
335.5945.64068079502438-0.0466807950243826
345.5265.56654521918851-0.0405452191885098
355.1115.1601603579849-0.0491603579848992
365.1775.19919322455277-0.0221932245527690
375.8355.318502873740550.516497126259449
385.3485.21745634802680.130543651973195
396.0386.12779419212348-0.0897941921234828
406.0395.976874363853320.0621256361466758
416.4086.4682974133028-0.0602974133028047
426.2146.3342657063743-0.120265706374304
436.1386.2527012340951-0.114701234095095
446.5296.174796856065070.35420314393493
456.0586.10934525352416-0.0513452535241612
466.0266.03568235453588-0.00968235453587596
475.6785.61778374912620.0602162508737987
485.7335.73597020508194-0.00297020508193935
496.4885.952194689453570.535805310546427
505.9365.780556118668450.155443881331553
516.846.774415996784650.0655840032153456
526.6946.72742122244282-0.033421222442823
537.1937.21184406668911-0.0188440666891099
546.9917.09108209706072-0.100082097060715
557.2097.029794827945050.179205172054952
567.1047.18774743122067-0.083747431220667
576.836.80407769835850.0259223016415033
586.8486.782025836945720.0659741630542792
596.3966.3701083882310.0258916117689951
606.4146.48027661401617-0.0662766140161706
617.1516.760997354218470.390002645781527
626.8826.41534405158420.466655948415798
637.6987.70325146888048-0.00525146888047789
647.6267.601586114198850.0244138858011462
657.9368.1982358398763-0.262235839876304
668.0547.924767833493040.129232166506958
678.1288.036107151617350.0918928483826491
688.0628.12739902701665-0.0653990270166513
697.7087.73081600475976-0.0228160047597576
707.5747.6891884823673-0.115188482367305
717.0397.12332248022609-0.0843224802260876
727.1467.17434038702171-0.0283403870217143
737.077.57214065910529-0.50214065910529
746.6076.70755739519404-0.100557395194036
757.6997.601136601422250.097863398577747
767.6637.54993388216220.113066117837794
777.9888.1521536287938-0.164153628793799
787.7237.96754458481684-0.244544584816841
798.0877.851222216265150.235777783734851
808.0287.993122411740130.0348775882598753
817.3627.65033431707146-0.288334317071460

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 5.101 & 5.07301556347594 & 0.0279844365240587 \tabularnewline
14 & 4.763 & 4.7449179365452 & 0.0180820634547976 \tabularnewline
15 & 5.505 & 5.49487822431458 & 0.0101217756854188 \tabularnewline
16 & 5.385 & 5.38496272894387 & 3.72710561293843e-05 \tabularnewline
17 & 5.794 & 5.79975376250684 & -0.00575376250684023 \tabularnewline
18 & 5.695 & 5.70034313780302 & -0.00534313780302309 \tabularnewline
19 & 5.798 & 5.66111500842549 & 0.136884991574514 \tabularnewline
20 & 5.705 & 5.73661660126565 & -0.0316166012656511 \tabularnewline
21 & 5.422 & 5.49249451976837 & -0.0704945197683662 \tabularnewline
22 & 5.311 & 5.40815241789843 & -0.09715241789843 \tabularnewline
23 & 4.968 & 4.97144204584224 & -0.00344204584224439 \tabularnewline
24 & 5.053 & 5.0294332835595 & 0.023566716440504 \tabularnewline
25 & 5.236 & 5.16448019332548 & 0.0715198066745204 \tabularnewline
26 & 4.782 & 4.85242116638604 & -0.0704211663860352 \tabularnewline
27 & 5.531 & 5.55986841956288 & -0.0288684195628779 \tabularnewline
28 & 5.566 & 5.42487731395309 & 0.141122686046906 \tabularnewline
29 & 5.961 & 5.92766553986306 & 0.0333344601369365 \tabularnewline
30 & 5.868 & 5.8486985667757 & 0.0193014332242951 \tabularnewline
31 & 5.872 & 5.83982362081296 & 0.0321763791870442 \tabularnewline
32 & 5.908 & 5.83733994039559 & 0.0706600596044149 \tabularnewline
33 & 5.594 & 5.64068079502438 & -0.0466807950243826 \tabularnewline
34 & 5.526 & 5.56654521918851 & -0.0405452191885098 \tabularnewline
35 & 5.111 & 5.1601603579849 & -0.0491603579848992 \tabularnewline
36 & 5.177 & 5.19919322455277 & -0.0221932245527690 \tabularnewline
37 & 5.835 & 5.31850287374055 & 0.516497126259449 \tabularnewline
38 & 5.348 & 5.2174563480268 & 0.130543651973195 \tabularnewline
39 & 6.038 & 6.12779419212348 & -0.0897941921234828 \tabularnewline
40 & 6.039 & 5.97687436385332 & 0.0621256361466758 \tabularnewline
41 & 6.408 & 6.4682974133028 & -0.0602974133028047 \tabularnewline
42 & 6.214 & 6.3342657063743 & -0.120265706374304 \tabularnewline
43 & 6.138 & 6.2527012340951 & -0.114701234095095 \tabularnewline
44 & 6.529 & 6.17479685606507 & 0.35420314393493 \tabularnewline
45 & 6.058 & 6.10934525352416 & -0.0513452535241612 \tabularnewline
46 & 6.026 & 6.03568235453588 & -0.00968235453587596 \tabularnewline
47 & 5.678 & 5.6177837491262 & 0.0602162508737987 \tabularnewline
48 & 5.733 & 5.73597020508194 & -0.00297020508193935 \tabularnewline
49 & 6.488 & 5.95219468945357 & 0.535805310546427 \tabularnewline
50 & 5.936 & 5.78055611866845 & 0.155443881331553 \tabularnewline
51 & 6.84 & 6.77441599678465 & 0.0655840032153456 \tabularnewline
52 & 6.694 & 6.72742122244282 & -0.033421222442823 \tabularnewline
53 & 7.193 & 7.21184406668911 & -0.0188440666891099 \tabularnewline
54 & 6.991 & 7.09108209706072 & -0.100082097060715 \tabularnewline
55 & 7.209 & 7.02979482794505 & 0.179205172054952 \tabularnewline
56 & 7.104 & 7.18774743122067 & -0.083747431220667 \tabularnewline
57 & 6.83 & 6.8040776983585 & 0.0259223016415033 \tabularnewline
58 & 6.848 & 6.78202583694572 & 0.0659741630542792 \tabularnewline
59 & 6.396 & 6.370108388231 & 0.0258916117689951 \tabularnewline
60 & 6.414 & 6.48027661401617 & -0.0662766140161706 \tabularnewline
61 & 7.151 & 6.76099735421847 & 0.390002645781527 \tabularnewline
62 & 6.882 & 6.4153440515842 & 0.466655948415798 \tabularnewline
63 & 7.698 & 7.70325146888048 & -0.00525146888047789 \tabularnewline
64 & 7.626 & 7.60158611419885 & 0.0244138858011462 \tabularnewline
65 & 7.936 & 8.1982358398763 & -0.262235839876304 \tabularnewline
66 & 8.054 & 7.92476783349304 & 0.129232166506958 \tabularnewline
67 & 8.128 & 8.03610715161735 & 0.0918928483826491 \tabularnewline
68 & 8.062 & 8.12739902701665 & -0.0653990270166513 \tabularnewline
69 & 7.708 & 7.73081600475976 & -0.0228160047597576 \tabularnewline
70 & 7.574 & 7.6891884823673 & -0.115188482367305 \tabularnewline
71 & 7.039 & 7.12332248022609 & -0.0843224802260876 \tabularnewline
72 & 7.146 & 7.17434038702171 & -0.0283403870217143 \tabularnewline
73 & 7.07 & 7.57214065910529 & -0.50214065910529 \tabularnewline
74 & 6.607 & 6.70755739519404 & -0.100557395194036 \tabularnewline
75 & 7.699 & 7.60113660142225 & 0.097863398577747 \tabularnewline
76 & 7.663 & 7.5499338821622 & 0.113066117837794 \tabularnewline
77 & 7.988 & 8.1521536287938 & -0.164153628793799 \tabularnewline
78 & 7.723 & 7.96754458481684 & -0.244544584816841 \tabularnewline
79 & 8.087 & 7.85122221626515 & 0.235777783734851 \tabularnewline
80 & 8.028 & 7.99312241174013 & 0.0348775882598753 \tabularnewline
81 & 7.362 & 7.65033431707146 & -0.288334317071460 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77736&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]5.101[/C][C]5.07301556347594[/C][C]0.0279844365240587[/C][/ROW]
[ROW][C]14[/C][C]4.763[/C][C]4.7449179365452[/C][C]0.0180820634547976[/C][/ROW]
[ROW][C]15[/C][C]5.505[/C][C]5.49487822431458[/C][C]0.0101217756854188[/C][/ROW]
[ROW][C]16[/C][C]5.385[/C][C]5.38496272894387[/C][C]3.72710561293843e-05[/C][/ROW]
[ROW][C]17[/C][C]5.794[/C][C]5.79975376250684[/C][C]-0.00575376250684023[/C][/ROW]
[ROW][C]18[/C][C]5.695[/C][C]5.70034313780302[/C][C]-0.00534313780302309[/C][/ROW]
[ROW][C]19[/C][C]5.798[/C][C]5.66111500842549[/C][C]0.136884991574514[/C][/ROW]
[ROW][C]20[/C][C]5.705[/C][C]5.73661660126565[/C][C]-0.0316166012656511[/C][/ROW]
[ROW][C]21[/C][C]5.422[/C][C]5.49249451976837[/C][C]-0.0704945197683662[/C][/ROW]
[ROW][C]22[/C][C]5.311[/C][C]5.40815241789843[/C][C]-0.09715241789843[/C][/ROW]
[ROW][C]23[/C][C]4.968[/C][C]4.97144204584224[/C][C]-0.00344204584224439[/C][/ROW]
[ROW][C]24[/C][C]5.053[/C][C]5.0294332835595[/C][C]0.023566716440504[/C][/ROW]
[ROW][C]25[/C][C]5.236[/C][C]5.16448019332548[/C][C]0.0715198066745204[/C][/ROW]
[ROW][C]26[/C][C]4.782[/C][C]4.85242116638604[/C][C]-0.0704211663860352[/C][/ROW]
[ROW][C]27[/C][C]5.531[/C][C]5.55986841956288[/C][C]-0.0288684195628779[/C][/ROW]
[ROW][C]28[/C][C]5.566[/C][C]5.42487731395309[/C][C]0.141122686046906[/C][/ROW]
[ROW][C]29[/C][C]5.961[/C][C]5.92766553986306[/C][C]0.0333344601369365[/C][/ROW]
[ROW][C]30[/C][C]5.868[/C][C]5.8486985667757[/C][C]0.0193014332242951[/C][/ROW]
[ROW][C]31[/C][C]5.872[/C][C]5.83982362081296[/C][C]0.0321763791870442[/C][/ROW]
[ROW][C]32[/C][C]5.908[/C][C]5.83733994039559[/C][C]0.0706600596044149[/C][/ROW]
[ROW][C]33[/C][C]5.594[/C][C]5.64068079502438[/C][C]-0.0466807950243826[/C][/ROW]
[ROW][C]34[/C][C]5.526[/C][C]5.56654521918851[/C][C]-0.0405452191885098[/C][/ROW]
[ROW][C]35[/C][C]5.111[/C][C]5.1601603579849[/C][C]-0.0491603579848992[/C][/ROW]
[ROW][C]36[/C][C]5.177[/C][C]5.19919322455277[/C][C]-0.0221932245527690[/C][/ROW]
[ROW][C]37[/C][C]5.835[/C][C]5.31850287374055[/C][C]0.516497126259449[/C][/ROW]
[ROW][C]38[/C][C]5.348[/C][C]5.2174563480268[/C][C]0.130543651973195[/C][/ROW]
[ROW][C]39[/C][C]6.038[/C][C]6.12779419212348[/C][C]-0.0897941921234828[/C][/ROW]
[ROW][C]40[/C][C]6.039[/C][C]5.97687436385332[/C][C]0.0621256361466758[/C][/ROW]
[ROW][C]41[/C][C]6.408[/C][C]6.4682974133028[/C][C]-0.0602974133028047[/C][/ROW]
[ROW][C]42[/C][C]6.214[/C][C]6.3342657063743[/C][C]-0.120265706374304[/C][/ROW]
[ROW][C]43[/C][C]6.138[/C][C]6.2527012340951[/C][C]-0.114701234095095[/C][/ROW]
[ROW][C]44[/C][C]6.529[/C][C]6.17479685606507[/C][C]0.35420314393493[/C][/ROW]
[ROW][C]45[/C][C]6.058[/C][C]6.10934525352416[/C][C]-0.0513452535241612[/C][/ROW]
[ROW][C]46[/C][C]6.026[/C][C]6.03568235453588[/C][C]-0.00968235453587596[/C][/ROW]
[ROW][C]47[/C][C]5.678[/C][C]5.6177837491262[/C][C]0.0602162508737987[/C][/ROW]
[ROW][C]48[/C][C]5.733[/C][C]5.73597020508194[/C][C]-0.00297020508193935[/C][/ROW]
[ROW][C]49[/C][C]6.488[/C][C]5.95219468945357[/C][C]0.535805310546427[/C][/ROW]
[ROW][C]50[/C][C]5.936[/C][C]5.78055611866845[/C][C]0.155443881331553[/C][/ROW]
[ROW][C]51[/C][C]6.84[/C][C]6.77441599678465[/C][C]0.0655840032153456[/C][/ROW]
[ROW][C]52[/C][C]6.694[/C][C]6.72742122244282[/C][C]-0.033421222442823[/C][/ROW]
[ROW][C]53[/C][C]7.193[/C][C]7.21184406668911[/C][C]-0.0188440666891099[/C][/ROW]
[ROW][C]54[/C][C]6.991[/C][C]7.09108209706072[/C][C]-0.100082097060715[/C][/ROW]
[ROW][C]55[/C][C]7.209[/C][C]7.02979482794505[/C][C]0.179205172054952[/C][/ROW]
[ROW][C]56[/C][C]7.104[/C][C]7.18774743122067[/C][C]-0.083747431220667[/C][/ROW]
[ROW][C]57[/C][C]6.83[/C][C]6.8040776983585[/C][C]0.0259223016415033[/C][/ROW]
[ROW][C]58[/C][C]6.848[/C][C]6.78202583694572[/C][C]0.0659741630542792[/C][/ROW]
[ROW][C]59[/C][C]6.396[/C][C]6.370108388231[/C][C]0.0258916117689951[/C][/ROW]
[ROW][C]60[/C][C]6.414[/C][C]6.48027661401617[/C][C]-0.0662766140161706[/C][/ROW]
[ROW][C]61[/C][C]7.151[/C][C]6.76099735421847[/C][C]0.390002645781527[/C][/ROW]
[ROW][C]62[/C][C]6.882[/C][C]6.4153440515842[/C][C]0.466655948415798[/C][/ROW]
[ROW][C]63[/C][C]7.698[/C][C]7.70325146888048[/C][C]-0.00525146888047789[/C][/ROW]
[ROW][C]64[/C][C]7.626[/C][C]7.60158611419885[/C][C]0.0244138858011462[/C][/ROW]
[ROW][C]65[/C][C]7.936[/C][C]8.1982358398763[/C][C]-0.262235839876304[/C][/ROW]
[ROW][C]66[/C][C]8.054[/C][C]7.92476783349304[/C][C]0.129232166506958[/C][/ROW]
[ROW][C]67[/C][C]8.128[/C][C]8.03610715161735[/C][C]0.0918928483826491[/C][/ROW]
[ROW][C]68[/C][C]8.062[/C][C]8.12739902701665[/C][C]-0.0653990270166513[/C][/ROW]
[ROW][C]69[/C][C]7.708[/C][C]7.73081600475976[/C][C]-0.0228160047597576[/C][/ROW]
[ROW][C]70[/C][C]7.574[/C][C]7.6891884823673[/C][C]-0.115188482367305[/C][/ROW]
[ROW][C]71[/C][C]7.039[/C][C]7.12332248022609[/C][C]-0.0843224802260876[/C][/ROW]
[ROW][C]72[/C][C]7.146[/C][C]7.17434038702171[/C][C]-0.0283403870217143[/C][/ROW]
[ROW][C]73[/C][C]7.07[/C][C]7.57214065910529[/C][C]-0.50214065910529[/C][/ROW]
[ROW][C]74[/C][C]6.607[/C][C]6.70755739519404[/C][C]-0.100557395194036[/C][/ROW]
[ROW][C]75[/C][C]7.699[/C][C]7.60113660142225[/C][C]0.097863398577747[/C][/ROW]
[ROW][C]76[/C][C]7.663[/C][C]7.5499338821622[/C][C]0.113066117837794[/C][/ROW]
[ROW][C]77[/C][C]7.988[/C][C]8.1521536287938[/C][C]-0.164153628793799[/C][/ROW]
[ROW][C]78[/C][C]7.723[/C][C]7.96754458481684[/C][C]-0.244544584816841[/C][/ROW]
[ROW][C]79[/C][C]8.087[/C][C]7.85122221626515[/C][C]0.235777783734851[/C][/ROW]
[ROW][C]80[/C][C]8.028[/C][C]7.99312241174013[/C][C]0.0348775882598753[/C][/ROW]
[ROW][C]81[/C][C]7.362[/C][C]7.65033431707146[/C][C]-0.288334317071460[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77736&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77736&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
135.1015.073015563475940.0279844365240587
144.7634.74491793654520.0180820634547976
155.5055.494878224314580.0101217756854188
165.3855.384962728943873.72710561293843e-05
175.7945.79975376250684-0.00575376250684023
185.6955.70034313780302-0.00534313780302309
195.7985.661115008425490.136884991574514
205.7055.73661660126565-0.0316166012656511
215.4225.49249451976837-0.0704945197683662
225.3115.40815241789843-0.09715241789843
234.9684.97144204584224-0.00344204584224439
245.0535.02943328355950.023566716440504
255.2365.164480193325480.0715198066745204
264.7824.85242116638604-0.0704211663860352
275.5315.55986841956288-0.0288684195628779
285.5665.424877313953090.141122686046906
295.9615.927665539863060.0333344601369365
305.8685.84869856677570.0193014332242951
315.8725.839823620812960.0321763791870442
325.9085.837339940395590.0706600596044149
335.5945.64068079502438-0.0466807950243826
345.5265.56654521918851-0.0405452191885098
355.1115.1601603579849-0.0491603579848992
365.1775.19919322455277-0.0221932245527690
375.8355.318502873740550.516497126259449
385.3485.21745634802680.130543651973195
396.0386.12779419212348-0.0897941921234828
406.0395.976874363853320.0621256361466758
416.4086.4682974133028-0.0602974133028047
426.2146.3342657063743-0.120265706374304
436.1386.2527012340951-0.114701234095095
446.5296.174796856065070.35420314393493
456.0586.10934525352416-0.0513452535241612
466.0266.03568235453588-0.00968235453587596
475.6785.61778374912620.0602162508737987
485.7335.73597020508194-0.00297020508193935
496.4885.952194689453570.535805310546427
505.9365.780556118668450.155443881331553
516.846.774415996784650.0655840032153456
526.6946.72742122244282-0.033421222442823
537.1937.21184406668911-0.0188440666891099
546.9917.09108209706072-0.100082097060715
557.2097.029794827945050.179205172054952
567.1047.18774743122067-0.083747431220667
576.836.80407769835850.0259223016415033
586.8486.782025836945720.0659741630542792
596.3966.3701083882310.0258916117689951
606.4146.48027661401617-0.0662766140161706
617.1516.760997354218470.390002645781527
626.8826.41534405158420.466655948415798
637.6987.70325146888048-0.00525146888047789
647.6267.601586114198850.0244138858011462
657.9368.1982358398763-0.262235839876304
668.0547.924767833493040.129232166506958
678.1288.036107151617350.0918928483826491
688.0628.12739902701665-0.0653990270166513
697.7087.73081600475976-0.0228160047597576
707.5747.6891884823673-0.115188482367305
717.0397.12332248022609-0.0843224802260876
727.1467.17434038702171-0.0283403870217143
737.077.57214065910529-0.50214065910529
746.6076.70755739519404-0.100557395194036
757.6997.601136601422250.097863398577747
767.6637.54993388216220.113066117837794
777.9888.1521536287938-0.164153628793799
787.7237.96754458481684-0.244544584816841
798.0877.851222216265150.235777783734851
808.0287.993122411740130.0348775882598753
817.3627.65033431707146-0.288334317071460







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
827.437958660591257.21793606113727.6579812600453
836.940585797837556.659876952900967.22129464277413
847.033293104799886.691699281769057.37488692783072
857.375217872936696.969268688726217.78116705714716
866.822082783081866.395827065793297.24833850037044
877.817325201197037.292060276576018.34259012581805
887.706336586144937.148018637706828.26465453458304
898.212984346901987.581952049618068.8440166441859
908.104255932073397.444383432416728.76412843173005
918.179901931736537.478156802195028.88164706127805
928.162775867678287.427215101635028.89833663372153
937.75176068555115-1.2305905892820616.7341119603844

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
82 & 7.43795866059125 & 7.2179360611372 & 7.6579812600453 \tabularnewline
83 & 6.94058579783755 & 6.65987695290096 & 7.22129464277413 \tabularnewline
84 & 7.03329310479988 & 6.69169928176905 & 7.37488692783072 \tabularnewline
85 & 7.37521787293669 & 6.96926868872621 & 7.78116705714716 \tabularnewline
86 & 6.82208278308186 & 6.39582706579329 & 7.24833850037044 \tabularnewline
87 & 7.81732520119703 & 7.29206027657601 & 8.34259012581805 \tabularnewline
88 & 7.70633658614493 & 7.14801863770682 & 8.26465453458304 \tabularnewline
89 & 8.21298434690198 & 7.58195204961806 & 8.8440166441859 \tabularnewline
90 & 8.10425593207339 & 7.44438343241672 & 8.76412843173005 \tabularnewline
91 & 8.17990193173653 & 7.47815680219502 & 8.88164706127805 \tabularnewline
92 & 8.16277586767828 & 7.42721510163502 & 8.89833663372153 \tabularnewline
93 & 7.75176068555115 & -1.23059058928206 & 16.7341119603844 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77736&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]82[/C][C]7.43795866059125[/C][C]7.2179360611372[/C][C]7.6579812600453[/C][/ROW]
[ROW][C]83[/C][C]6.94058579783755[/C][C]6.65987695290096[/C][C]7.22129464277413[/C][/ROW]
[ROW][C]84[/C][C]7.03329310479988[/C][C]6.69169928176905[/C][C]7.37488692783072[/C][/ROW]
[ROW][C]85[/C][C]7.37521787293669[/C][C]6.96926868872621[/C][C]7.78116705714716[/C][/ROW]
[ROW][C]86[/C][C]6.82208278308186[/C][C]6.39582706579329[/C][C]7.24833850037044[/C][/ROW]
[ROW][C]87[/C][C]7.81732520119703[/C][C]7.29206027657601[/C][C]8.34259012581805[/C][/ROW]
[ROW][C]88[/C][C]7.70633658614493[/C][C]7.14801863770682[/C][C]8.26465453458304[/C][/ROW]
[ROW][C]89[/C][C]8.21298434690198[/C][C]7.58195204961806[/C][C]8.8440166441859[/C][/ROW]
[ROW][C]90[/C][C]8.10425593207339[/C][C]7.44438343241672[/C][C]8.76412843173005[/C][/ROW]
[ROW][C]91[/C][C]8.17990193173653[/C][C]7.47815680219502[/C][C]8.88164706127805[/C][/ROW]
[ROW][C]92[/C][C]8.16277586767828[/C][C]7.42721510163502[/C][C]8.89833663372153[/C][/ROW]
[ROW][C]93[/C][C]7.75176068555115[/C][C]-1.23059058928206[/C][C]16.7341119603844[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77736&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77736&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
827.437958660591257.21793606113727.6579812600453
836.940585797837556.659876952900967.22129464277413
847.033293104799886.691699281769057.37488692783072
857.375217872936696.969268688726217.78116705714716
866.822082783081866.395827065793297.24833850037044
877.817325201197037.292060276576018.34259012581805
887.706336586144937.148018637706828.26465453458304
898.212984346901987.581952049618068.8440166441859
908.104255932073397.444383432416728.76412843173005
918.179901931736537.478156802195028.88164706127805
928.162775867678287.427215101635028.89833663372153
937.75176068555115-1.2305905892820616.7341119603844



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=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')