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Author's title

Single Exponential Smoothing model_Gem consumptieprijs roze zalm_Dominique ...

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 16 Jul 2008 05:00:01 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Jul/16/t12162061010y14sqahgv4lf86.htm/, Retrieved Tue, 28 May 2024 20:09:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13853, Retrieved Tue, 28 May 2024 20:09:54 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact323
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [Nietje van Santfo...] [2008-05-24 10:16:40] [f48bfde976615948c8f49c9cb95da62c]
-   PD    [Exponential Smoothing] [Single Exponentia...] [2008-07-16 11:00:01] [d41d8cd98f00b204e9800998ecf8427e] [Current]
-   PD      [Exponential Smoothing] [Double Ex Sm_Gem ...] [2008-08-01 12:08:39] [74be16979710d4c4e7c6647856088456]
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Dataseries X:
11.73
11.74
11.65
11.38
11.53
11.75
11.82
11.83
11.63
11.55
11.4
11.4
11.63
11.46
11.35
11.7
11.52
11.64
11.9
11.73
11.7
11.54
11.97
11.64
11.98
11.79
11.66
11.96
11.83
12.36
12.53
12.55
12.53
12.24
12.34
12.05
12.22
12.23
11.92
12.13
12.1
12.15
12.23
12.08
12.02
11.93
12.16
11.87
11.93
11.79
11.43
11.63
11.93
11.89
11.83
11.59
12.04
11.81
11.9
11.72
11.91
11.94
11.91
11.84
12.01
11.89
11.8
11.7
11.5
11.76
11.61
11.27
11.64
11.39
11.54
11.62
11.59
11.44
11.31
11.56
11.4
11.51
11.5
11.24
11.8
11.87
11.86
12.11
11.92
12.61
13.34
13.31
13.47
13.3
13.18
13.24




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13853&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13853&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13853&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.779534626319323
beta0
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.779534626319323 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13853&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]0.779534626319323[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13853&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13853&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
alpha0.779534626319323
beta0
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
211.7411.730.00999999999999979
311.6511.7377953462632-0.087795346263194
411.3811.6693558338213-0.289355833821338
511.5311.44379294203010.0862070579698919
611.7511.51099432875080.239005671249243
711.8211.69730752537620.122692474623765
811.8311.79295055773430.0370494422657348
911.6311.8218318808662-0.191831880866223
1011.5511.6722922872990-0.122292287299038
1111.411.5769612148176-0.176961214817647
1211.411.4390138203518-0.0390138203517605
1311.6311.40860119648260.221398803517438
1411.4611.5811892300501-0.121189230050073
1511.3511.4867180288891-0.136718028889065
1611.711.38014159132790.319858408672086
1711.5211.6294822964072-0.109482296407201
1811.6411.54413705538880.0958629446111683
1911.911.61886554009420.281134459905831
2011.7311.8380195862423-0.108019586242346
2111.711.7538145784458-0.0538145784457527
2211.5411.7118642511465-0.171864251146511
2311.9711.57789011635140.392109883648637
2411.6411.8835533479775-0.243553347977517
2511.9811.69369507987300.286304920126955
2611.7911.9168796787976-0.126879678797595
2711.6611.8179725757986-0.157972575798595
2811.9611.69482748295470.265172517045265
2911.8311.9015386419398-0.071538641939771
3012.3611.84577179342790.514228206572138
3112.5312.24663048628090.283369513719069
3212.5512.46752683426820.0824731657317876
3312.5312.5318175226983-0.00181752269831392
3412.2412.5304007008209-0.290400700820856
3512.3412.30402329902360.0359767009764003
3612.0512.3320683831754-0.282068383175440
3712.2212.11218631150030.107813688499721
3812.2312.19623081487700.0337691851229831
3911.9212.2225550639830-0.30255506398297
4012.1311.9867029152400.143297084760015
4112.112.09840795466100.00159204533896684
4212.1512.09964900912940.050350990870573
4312.2312.13889934998250.0911006500174736
4412.0812.2099154611513-0.129915461151345
4512.0212.1086418606896-0.0886418606896289
4611.9312.0395424609407-0.109542460940689
4712.1611.95415031958520.205849680414810
4811.8712.1146172732853-0.244617273285302
4911.9311.92392963856360.00607036143640727
5011.7911.9286616954975-0.138661695497547
5111.4311.8205701025131-0.390570102513063
5211.6311.51610718359900.113892816400959
5311.9311.60489057767260.325109422327381
5411.8911.85832462971950.0316753702805155
5511.8311.8830166776546-0.0530166776546341
5611.5911.8416883416504-0.251688341650437
5712.0411.64548856429300.394511435706967
5811.8111.9530238889056-0.143023888905562
5911.911.84153181511280.05846818488717
6011.7211.8871097897704-0.167109789770420
6111.9111.75684192224740.153158077752565
6211.9411.87623394715610.063766052843933
6311.9111.9259417933316-0.0159417933316188
6411.8411.913514613424-0.0735146134239955
6512.0111.85620742671950.153792573280489
6611.8911.9760940628624-0.0860940628624043
6711.811.9089807597406-0.108980759740648
6811.711.8240264839202-0.124026483920227
6911.511.7273435451238-0.227343545123773
7011.7611.55012137962960.209878620370397
7111.6111.7137290315325-0.103729031532456
7211.2711.6328686596983-0.362868659698339
7311.6411.34999997465740.2900000253426
7411.3911.5760650360454-0.186065036045438
7511.5411.43102089770070.108979102299333
7611.6211.51597388148820.104026118511808
7711.5911.5970658429097-0.00706584290974277
7811.4411.5915577736975-0.151557773697464
7911.3111.4734132412124-0.163413241212423
8011.5611.34602696128830.213973038711734
8111.411.5128263540628-0.112826354062827
8211.5111.42487430430950.0851256956905093
8311.511.49123273168980.00876726831023689
8411.2411.4980671209158-0.258067120915825
8511.811.29689486424740.503105135752596
8611.8711.68908273824560.180917261754363
8711.8611.83011400828200.0298859917179612
8812.1111.85341117366810.256588826331917
8911.9212.0534310485204-0.133431048520448
9012.6111.94941692597270.660583074027334
9113.3412.46436430573740.875635694262566
9213.3113.14695264945630.163047350543737
9313.4713.27405370493470.195946295065269
9413.313.4268006268371-0.126800626837092
9513.1813.3279551475786-0.147955147578585
9613.2413.21261898689890.0273810131011079

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 11.74 & 11.73 & 0.00999999999999979 \tabularnewline
3 & 11.65 & 11.7377953462632 & -0.087795346263194 \tabularnewline
4 & 11.38 & 11.6693558338213 & -0.289355833821338 \tabularnewline
5 & 11.53 & 11.4437929420301 & 0.0862070579698919 \tabularnewline
6 & 11.75 & 11.5109943287508 & 0.239005671249243 \tabularnewline
7 & 11.82 & 11.6973075253762 & 0.122692474623765 \tabularnewline
8 & 11.83 & 11.7929505577343 & 0.0370494422657348 \tabularnewline
9 & 11.63 & 11.8218318808662 & -0.191831880866223 \tabularnewline
10 & 11.55 & 11.6722922872990 & -0.122292287299038 \tabularnewline
11 & 11.4 & 11.5769612148176 & -0.176961214817647 \tabularnewline
12 & 11.4 & 11.4390138203518 & -0.0390138203517605 \tabularnewline
13 & 11.63 & 11.4086011964826 & 0.221398803517438 \tabularnewline
14 & 11.46 & 11.5811892300501 & -0.121189230050073 \tabularnewline
15 & 11.35 & 11.4867180288891 & -0.136718028889065 \tabularnewline
16 & 11.7 & 11.3801415913279 & 0.319858408672086 \tabularnewline
17 & 11.52 & 11.6294822964072 & -0.109482296407201 \tabularnewline
18 & 11.64 & 11.5441370553888 & 0.0958629446111683 \tabularnewline
19 & 11.9 & 11.6188655400942 & 0.281134459905831 \tabularnewline
20 & 11.73 & 11.8380195862423 & -0.108019586242346 \tabularnewline
21 & 11.7 & 11.7538145784458 & -0.0538145784457527 \tabularnewline
22 & 11.54 & 11.7118642511465 & -0.171864251146511 \tabularnewline
23 & 11.97 & 11.5778901163514 & 0.392109883648637 \tabularnewline
24 & 11.64 & 11.8835533479775 & -0.243553347977517 \tabularnewline
25 & 11.98 & 11.6936950798730 & 0.286304920126955 \tabularnewline
26 & 11.79 & 11.9168796787976 & -0.126879678797595 \tabularnewline
27 & 11.66 & 11.8179725757986 & -0.157972575798595 \tabularnewline
28 & 11.96 & 11.6948274829547 & 0.265172517045265 \tabularnewline
29 & 11.83 & 11.9015386419398 & -0.071538641939771 \tabularnewline
30 & 12.36 & 11.8457717934279 & 0.514228206572138 \tabularnewline
31 & 12.53 & 12.2466304862809 & 0.283369513719069 \tabularnewline
32 & 12.55 & 12.4675268342682 & 0.0824731657317876 \tabularnewline
33 & 12.53 & 12.5318175226983 & -0.00181752269831392 \tabularnewline
34 & 12.24 & 12.5304007008209 & -0.290400700820856 \tabularnewline
35 & 12.34 & 12.3040232990236 & 0.0359767009764003 \tabularnewline
36 & 12.05 & 12.3320683831754 & -0.282068383175440 \tabularnewline
37 & 12.22 & 12.1121863115003 & 0.107813688499721 \tabularnewline
38 & 12.23 & 12.1962308148770 & 0.0337691851229831 \tabularnewline
39 & 11.92 & 12.2225550639830 & -0.30255506398297 \tabularnewline
40 & 12.13 & 11.986702915240 & 0.143297084760015 \tabularnewline
41 & 12.1 & 12.0984079546610 & 0.00159204533896684 \tabularnewline
42 & 12.15 & 12.0996490091294 & 0.050350990870573 \tabularnewline
43 & 12.23 & 12.1388993499825 & 0.0911006500174736 \tabularnewline
44 & 12.08 & 12.2099154611513 & -0.129915461151345 \tabularnewline
45 & 12.02 & 12.1086418606896 & -0.0886418606896289 \tabularnewline
46 & 11.93 & 12.0395424609407 & -0.109542460940689 \tabularnewline
47 & 12.16 & 11.9541503195852 & 0.205849680414810 \tabularnewline
48 & 11.87 & 12.1146172732853 & -0.244617273285302 \tabularnewline
49 & 11.93 & 11.9239296385636 & 0.00607036143640727 \tabularnewline
50 & 11.79 & 11.9286616954975 & -0.138661695497547 \tabularnewline
51 & 11.43 & 11.8205701025131 & -0.390570102513063 \tabularnewline
52 & 11.63 & 11.5161071835990 & 0.113892816400959 \tabularnewline
53 & 11.93 & 11.6048905776726 & 0.325109422327381 \tabularnewline
54 & 11.89 & 11.8583246297195 & 0.0316753702805155 \tabularnewline
55 & 11.83 & 11.8830166776546 & -0.0530166776546341 \tabularnewline
56 & 11.59 & 11.8416883416504 & -0.251688341650437 \tabularnewline
57 & 12.04 & 11.6454885642930 & 0.394511435706967 \tabularnewline
58 & 11.81 & 11.9530238889056 & -0.143023888905562 \tabularnewline
59 & 11.9 & 11.8415318151128 & 0.05846818488717 \tabularnewline
60 & 11.72 & 11.8871097897704 & -0.167109789770420 \tabularnewline
61 & 11.91 & 11.7568419222474 & 0.153158077752565 \tabularnewline
62 & 11.94 & 11.8762339471561 & 0.063766052843933 \tabularnewline
63 & 11.91 & 11.9259417933316 & -0.0159417933316188 \tabularnewline
64 & 11.84 & 11.913514613424 & -0.0735146134239955 \tabularnewline
65 & 12.01 & 11.8562074267195 & 0.153792573280489 \tabularnewline
66 & 11.89 & 11.9760940628624 & -0.0860940628624043 \tabularnewline
67 & 11.8 & 11.9089807597406 & -0.108980759740648 \tabularnewline
68 & 11.7 & 11.8240264839202 & -0.124026483920227 \tabularnewline
69 & 11.5 & 11.7273435451238 & -0.227343545123773 \tabularnewline
70 & 11.76 & 11.5501213796296 & 0.209878620370397 \tabularnewline
71 & 11.61 & 11.7137290315325 & -0.103729031532456 \tabularnewline
72 & 11.27 & 11.6328686596983 & -0.362868659698339 \tabularnewline
73 & 11.64 & 11.3499999746574 & 0.2900000253426 \tabularnewline
74 & 11.39 & 11.5760650360454 & -0.186065036045438 \tabularnewline
75 & 11.54 & 11.4310208977007 & 0.108979102299333 \tabularnewline
76 & 11.62 & 11.5159738814882 & 0.104026118511808 \tabularnewline
77 & 11.59 & 11.5970658429097 & -0.00706584290974277 \tabularnewline
78 & 11.44 & 11.5915577736975 & -0.151557773697464 \tabularnewline
79 & 11.31 & 11.4734132412124 & -0.163413241212423 \tabularnewline
80 & 11.56 & 11.3460269612883 & 0.213973038711734 \tabularnewline
81 & 11.4 & 11.5128263540628 & -0.112826354062827 \tabularnewline
82 & 11.51 & 11.4248743043095 & 0.0851256956905093 \tabularnewline
83 & 11.5 & 11.4912327316898 & 0.00876726831023689 \tabularnewline
84 & 11.24 & 11.4980671209158 & -0.258067120915825 \tabularnewline
85 & 11.8 & 11.2968948642474 & 0.503105135752596 \tabularnewline
86 & 11.87 & 11.6890827382456 & 0.180917261754363 \tabularnewline
87 & 11.86 & 11.8301140082820 & 0.0298859917179612 \tabularnewline
88 & 12.11 & 11.8534111736681 & 0.256588826331917 \tabularnewline
89 & 11.92 & 12.0534310485204 & -0.133431048520448 \tabularnewline
90 & 12.61 & 11.9494169259727 & 0.660583074027334 \tabularnewline
91 & 13.34 & 12.4643643057374 & 0.875635694262566 \tabularnewline
92 & 13.31 & 13.1469526494563 & 0.163047350543737 \tabularnewline
93 & 13.47 & 13.2740537049347 & 0.195946295065269 \tabularnewline
94 & 13.3 & 13.4268006268371 & -0.126800626837092 \tabularnewline
95 & 13.18 & 13.3279551475786 & -0.147955147578585 \tabularnewline
96 & 13.24 & 13.2126189868989 & 0.0273810131011079 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13853&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]2[/C][C]11.74[/C][C]11.73[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]3[/C][C]11.65[/C][C]11.7377953462632[/C][C]-0.087795346263194[/C][/ROW]
[ROW][C]4[/C][C]11.38[/C][C]11.6693558338213[/C][C]-0.289355833821338[/C][/ROW]
[ROW][C]5[/C][C]11.53[/C][C]11.4437929420301[/C][C]0.0862070579698919[/C][/ROW]
[ROW][C]6[/C][C]11.75[/C][C]11.5109943287508[/C][C]0.239005671249243[/C][/ROW]
[ROW][C]7[/C][C]11.82[/C][C]11.6973075253762[/C][C]0.122692474623765[/C][/ROW]
[ROW][C]8[/C][C]11.83[/C][C]11.7929505577343[/C][C]0.0370494422657348[/C][/ROW]
[ROW][C]9[/C][C]11.63[/C][C]11.8218318808662[/C][C]-0.191831880866223[/C][/ROW]
[ROW][C]10[/C][C]11.55[/C][C]11.6722922872990[/C][C]-0.122292287299038[/C][/ROW]
[ROW][C]11[/C][C]11.4[/C][C]11.5769612148176[/C][C]-0.176961214817647[/C][/ROW]
[ROW][C]12[/C][C]11.4[/C][C]11.4390138203518[/C][C]-0.0390138203517605[/C][/ROW]
[ROW][C]13[/C][C]11.63[/C][C]11.4086011964826[/C][C]0.221398803517438[/C][/ROW]
[ROW][C]14[/C][C]11.46[/C][C]11.5811892300501[/C][C]-0.121189230050073[/C][/ROW]
[ROW][C]15[/C][C]11.35[/C][C]11.4867180288891[/C][C]-0.136718028889065[/C][/ROW]
[ROW][C]16[/C][C]11.7[/C][C]11.3801415913279[/C][C]0.319858408672086[/C][/ROW]
[ROW][C]17[/C][C]11.52[/C][C]11.6294822964072[/C][C]-0.109482296407201[/C][/ROW]
[ROW][C]18[/C][C]11.64[/C][C]11.5441370553888[/C][C]0.0958629446111683[/C][/ROW]
[ROW][C]19[/C][C]11.9[/C][C]11.6188655400942[/C][C]0.281134459905831[/C][/ROW]
[ROW][C]20[/C][C]11.73[/C][C]11.8380195862423[/C][C]-0.108019586242346[/C][/ROW]
[ROW][C]21[/C][C]11.7[/C][C]11.7538145784458[/C][C]-0.0538145784457527[/C][/ROW]
[ROW][C]22[/C][C]11.54[/C][C]11.7118642511465[/C][C]-0.171864251146511[/C][/ROW]
[ROW][C]23[/C][C]11.97[/C][C]11.5778901163514[/C][C]0.392109883648637[/C][/ROW]
[ROW][C]24[/C][C]11.64[/C][C]11.8835533479775[/C][C]-0.243553347977517[/C][/ROW]
[ROW][C]25[/C][C]11.98[/C][C]11.6936950798730[/C][C]0.286304920126955[/C][/ROW]
[ROW][C]26[/C][C]11.79[/C][C]11.9168796787976[/C][C]-0.126879678797595[/C][/ROW]
[ROW][C]27[/C][C]11.66[/C][C]11.8179725757986[/C][C]-0.157972575798595[/C][/ROW]
[ROW][C]28[/C][C]11.96[/C][C]11.6948274829547[/C][C]0.265172517045265[/C][/ROW]
[ROW][C]29[/C][C]11.83[/C][C]11.9015386419398[/C][C]-0.071538641939771[/C][/ROW]
[ROW][C]30[/C][C]12.36[/C][C]11.8457717934279[/C][C]0.514228206572138[/C][/ROW]
[ROW][C]31[/C][C]12.53[/C][C]12.2466304862809[/C][C]0.283369513719069[/C][/ROW]
[ROW][C]32[/C][C]12.55[/C][C]12.4675268342682[/C][C]0.0824731657317876[/C][/ROW]
[ROW][C]33[/C][C]12.53[/C][C]12.5318175226983[/C][C]-0.00181752269831392[/C][/ROW]
[ROW][C]34[/C][C]12.24[/C][C]12.5304007008209[/C][C]-0.290400700820856[/C][/ROW]
[ROW][C]35[/C][C]12.34[/C][C]12.3040232990236[/C][C]0.0359767009764003[/C][/ROW]
[ROW][C]36[/C][C]12.05[/C][C]12.3320683831754[/C][C]-0.282068383175440[/C][/ROW]
[ROW][C]37[/C][C]12.22[/C][C]12.1121863115003[/C][C]0.107813688499721[/C][/ROW]
[ROW][C]38[/C][C]12.23[/C][C]12.1962308148770[/C][C]0.0337691851229831[/C][/ROW]
[ROW][C]39[/C][C]11.92[/C][C]12.2225550639830[/C][C]-0.30255506398297[/C][/ROW]
[ROW][C]40[/C][C]12.13[/C][C]11.986702915240[/C][C]0.143297084760015[/C][/ROW]
[ROW][C]41[/C][C]12.1[/C][C]12.0984079546610[/C][C]0.00159204533896684[/C][/ROW]
[ROW][C]42[/C][C]12.15[/C][C]12.0996490091294[/C][C]0.050350990870573[/C][/ROW]
[ROW][C]43[/C][C]12.23[/C][C]12.1388993499825[/C][C]0.0911006500174736[/C][/ROW]
[ROW][C]44[/C][C]12.08[/C][C]12.2099154611513[/C][C]-0.129915461151345[/C][/ROW]
[ROW][C]45[/C][C]12.02[/C][C]12.1086418606896[/C][C]-0.0886418606896289[/C][/ROW]
[ROW][C]46[/C][C]11.93[/C][C]12.0395424609407[/C][C]-0.109542460940689[/C][/ROW]
[ROW][C]47[/C][C]12.16[/C][C]11.9541503195852[/C][C]0.205849680414810[/C][/ROW]
[ROW][C]48[/C][C]11.87[/C][C]12.1146172732853[/C][C]-0.244617273285302[/C][/ROW]
[ROW][C]49[/C][C]11.93[/C][C]11.9239296385636[/C][C]0.00607036143640727[/C][/ROW]
[ROW][C]50[/C][C]11.79[/C][C]11.9286616954975[/C][C]-0.138661695497547[/C][/ROW]
[ROW][C]51[/C][C]11.43[/C][C]11.8205701025131[/C][C]-0.390570102513063[/C][/ROW]
[ROW][C]52[/C][C]11.63[/C][C]11.5161071835990[/C][C]0.113892816400959[/C][/ROW]
[ROW][C]53[/C][C]11.93[/C][C]11.6048905776726[/C][C]0.325109422327381[/C][/ROW]
[ROW][C]54[/C][C]11.89[/C][C]11.8583246297195[/C][C]0.0316753702805155[/C][/ROW]
[ROW][C]55[/C][C]11.83[/C][C]11.8830166776546[/C][C]-0.0530166776546341[/C][/ROW]
[ROW][C]56[/C][C]11.59[/C][C]11.8416883416504[/C][C]-0.251688341650437[/C][/ROW]
[ROW][C]57[/C][C]12.04[/C][C]11.6454885642930[/C][C]0.394511435706967[/C][/ROW]
[ROW][C]58[/C][C]11.81[/C][C]11.9530238889056[/C][C]-0.143023888905562[/C][/ROW]
[ROW][C]59[/C][C]11.9[/C][C]11.8415318151128[/C][C]0.05846818488717[/C][/ROW]
[ROW][C]60[/C][C]11.72[/C][C]11.8871097897704[/C][C]-0.167109789770420[/C][/ROW]
[ROW][C]61[/C][C]11.91[/C][C]11.7568419222474[/C][C]0.153158077752565[/C][/ROW]
[ROW][C]62[/C][C]11.94[/C][C]11.8762339471561[/C][C]0.063766052843933[/C][/ROW]
[ROW][C]63[/C][C]11.91[/C][C]11.9259417933316[/C][C]-0.0159417933316188[/C][/ROW]
[ROW][C]64[/C][C]11.84[/C][C]11.913514613424[/C][C]-0.0735146134239955[/C][/ROW]
[ROW][C]65[/C][C]12.01[/C][C]11.8562074267195[/C][C]0.153792573280489[/C][/ROW]
[ROW][C]66[/C][C]11.89[/C][C]11.9760940628624[/C][C]-0.0860940628624043[/C][/ROW]
[ROW][C]67[/C][C]11.8[/C][C]11.9089807597406[/C][C]-0.108980759740648[/C][/ROW]
[ROW][C]68[/C][C]11.7[/C][C]11.8240264839202[/C][C]-0.124026483920227[/C][/ROW]
[ROW][C]69[/C][C]11.5[/C][C]11.7273435451238[/C][C]-0.227343545123773[/C][/ROW]
[ROW][C]70[/C][C]11.76[/C][C]11.5501213796296[/C][C]0.209878620370397[/C][/ROW]
[ROW][C]71[/C][C]11.61[/C][C]11.7137290315325[/C][C]-0.103729031532456[/C][/ROW]
[ROW][C]72[/C][C]11.27[/C][C]11.6328686596983[/C][C]-0.362868659698339[/C][/ROW]
[ROW][C]73[/C][C]11.64[/C][C]11.3499999746574[/C][C]0.2900000253426[/C][/ROW]
[ROW][C]74[/C][C]11.39[/C][C]11.5760650360454[/C][C]-0.186065036045438[/C][/ROW]
[ROW][C]75[/C][C]11.54[/C][C]11.4310208977007[/C][C]0.108979102299333[/C][/ROW]
[ROW][C]76[/C][C]11.62[/C][C]11.5159738814882[/C][C]0.104026118511808[/C][/ROW]
[ROW][C]77[/C][C]11.59[/C][C]11.5970658429097[/C][C]-0.00706584290974277[/C][/ROW]
[ROW][C]78[/C][C]11.44[/C][C]11.5915577736975[/C][C]-0.151557773697464[/C][/ROW]
[ROW][C]79[/C][C]11.31[/C][C]11.4734132412124[/C][C]-0.163413241212423[/C][/ROW]
[ROW][C]80[/C][C]11.56[/C][C]11.3460269612883[/C][C]0.213973038711734[/C][/ROW]
[ROW][C]81[/C][C]11.4[/C][C]11.5128263540628[/C][C]-0.112826354062827[/C][/ROW]
[ROW][C]82[/C][C]11.51[/C][C]11.4248743043095[/C][C]0.0851256956905093[/C][/ROW]
[ROW][C]83[/C][C]11.5[/C][C]11.4912327316898[/C][C]0.00876726831023689[/C][/ROW]
[ROW][C]84[/C][C]11.24[/C][C]11.4980671209158[/C][C]-0.258067120915825[/C][/ROW]
[ROW][C]85[/C][C]11.8[/C][C]11.2968948642474[/C][C]0.503105135752596[/C][/ROW]
[ROW][C]86[/C][C]11.87[/C][C]11.6890827382456[/C][C]0.180917261754363[/C][/ROW]
[ROW][C]87[/C][C]11.86[/C][C]11.8301140082820[/C][C]0.0298859917179612[/C][/ROW]
[ROW][C]88[/C][C]12.11[/C][C]11.8534111736681[/C][C]0.256588826331917[/C][/ROW]
[ROW][C]89[/C][C]11.92[/C][C]12.0534310485204[/C][C]-0.133431048520448[/C][/ROW]
[ROW][C]90[/C][C]12.61[/C][C]11.9494169259727[/C][C]0.660583074027334[/C][/ROW]
[ROW][C]91[/C][C]13.34[/C][C]12.4643643057374[/C][C]0.875635694262566[/C][/ROW]
[ROW][C]92[/C][C]13.31[/C][C]13.1469526494563[/C][C]0.163047350543737[/C][/ROW]
[ROW][C]93[/C][C]13.47[/C][C]13.2740537049347[/C][C]0.195946295065269[/C][/ROW]
[ROW][C]94[/C][C]13.3[/C][C]13.4268006268371[/C][C]-0.126800626837092[/C][/ROW]
[ROW][C]95[/C][C]13.18[/C][C]13.3279551475786[/C][C]-0.147955147578585[/C][/ROW]
[ROW][C]96[/C][C]13.24[/C][C]13.2126189868989[/C][C]0.0273810131011079[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13853&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13853&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
211.7411.730.00999999999999979
311.6511.7377953462632-0.087795346263194
411.3811.6693558338213-0.289355833821338
511.5311.44379294203010.0862070579698919
611.7511.51099432875080.239005671249243
711.8211.69730752537620.122692474623765
811.8311.79295055773430.0370494422657348
911.6311.8218318808662-0.191831880866223
1011.5511.6722922872990-0.122292287299038
1111.411.5769612148176-0.176961214817647
1211.411.4390138203518-0.0390138203517605
1311.6311.40860119648260.221398803517438
1411.4611.5811892300501-0.121189230050073
1511.3511.4867180288891-0.136718028889065
1611.711.38014159132790.319858408672086
1711.5211.6294822964072-0.109482296407201
1811.6411.54413705538880.0958629446111683
1911.911.61886554009420.281134459905831
2011.7311.8380195862423-0.108019586242346
2111.711.7538145784458-0.0538145784457527
2211.5411.7118642511465-0.171864251146511
2311.9711.57789011635140.392109883648637
2411.6411.8835533479775-0.243553347977517
2511.9811.69369507987300.286304920126955
2611.7911.9168796787976-0.126879678797595
2711.6611.8179725757986-0.157972575798595
2811.9611.69482748295470.265172517045265
2911.8311.9015386419398-0.071538641939771
3012.3611.84577179342790.514228206572138
3112.5312.24663048628090.283369513719069
3212.5512.46752683426820.0824731657317876
3312.5312.5318175226983-0.00181752269831392
3412.2412.5304007008209-0.290400700820856
3512.3412.30402329902360.0359767009764003
3612.0512.3320683831754-0.282068383175440
3712.2212.11218631150030.107813688499721
3812.2312.19623081487700.0337691851229831
3911.9212.2225550639830-0.30255506398297
4012.1311.9867029152400.143297084760015
4112.112.09840795466100.00159204533896684
4212.1512.09964900912940.050350990870573
4312.2312.13889934998250.0911006500174736
4412.0812.2099154611513-0.129915461151345
4512.0212.1086418606896-0.0886418606896289
4611.9312.0395424609407-0.109542460940689
4712.1611.95415031958520.205849680414810
4811.8712.1146172732853-0.244617273285302
4911.9311.92392963856360.00607036143640727
5011.7911.9286616954975-0.138661695497547
5111.4311.8205701025131-0.390570102513063
5211.6311.51610718359900.113892816400959
5311.9311.60489057767260.325109422327381
5411.8911.85832462971950.0316753702805155
5511.8311.8830166776546-0.0530166776546341
5611.5911.8416883416504-0.251688341650437
5712.0411.64548856429300.394511435706967
5811.8111.9530238889056-0.143023888905562
5911.911.84153181511280.05846818488717
6011.7211.8871097897704-0.167109789770420
6111.9111.75684192224740.153158077752565
6211.9411.87623394715610.063766052843933
6311.9111.9259417933316-0.0159417933316188
6411.8411.913514613424-0.0735146134239955
6512.0111.85620742671950.153792573280489
6611.8911.9760940628624-0.0860940628624043
6711.811.9089807597406-0.108980759740648
6811.711.8240264839202-0.124026483920227
6911.511.7273435451238-0.227343545123773
7011.7611.55012137962960.209878620370397
7111.6111.7137290315325-0.103729031532456
7211.2711.6328686596983-0.362868659698339
7311.6411.34999997465740.2900000253426
7411.3911.5760650360454-0.186065036045438
7511.5411.43102089770070.108979102299333
7611.6211.51597388148820.104026118511808
7711.5911.5970658429097-0.00706584290974277
7811.4411.5915577736975-0.151557773697464
7911.3111.4734132412124-0.163413241212423
8011.5611.34602696128830.213973038711734
8111.411.5128263540628-0.112826354062827
8211.5111.42487430430950.0851256956905093
8311.511.49123273168980.00876726831023689
8411.2411.4980671209158-0.258067120915825
8511.811.29689486424740.503105135752596
8611.8711.68908273824560.180917261754363
8711.8611.83011400828200.0298859917179612
8812.1111.85341117366810.256588826331917
8911.9212.0534310485204-0.133431048520448
9012.6111.94941692597270.660583074027334
9113.3412.46436430573740.875635694262566
9213.3113.14695264945630.163047350543737
9313.4713.27405370493470.195946295065269
9413.313.4268006268371-0.126800626837092
9513.1813.3279551475786-0.147955147578585
9613.2413.21261898689890.0273810131011079







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
9713.233963434714912.798258356799213.6696685126306
9813.233963434714912.681515127576813.786411741853
9913.233963434714912.585457961185213.8824689082446
10013.233963434714912.501898160073213.9660287093566
10113.233963434714912.426944362155714.0409825072742
10213.233963434714912.358383626466314.1095432429635
10313.233963434714912.294814768235114.1731121011947
10413.233963434714912.235284089334714.2326427800951
10513.233963434714912.17910768532214.2888191841078
10613.233963434714912.125775332827214.3421515366026
10713.233963434714912.074894374518914.3930324949110
10813.233963434714912.026154963374414.4417719060555

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 13.2339634347149 & 12.7982583567992 & 13.6696685126306 \tabularnewline
98 & 13.2339634347149 & 12.6815151275768 & 13.786411741853 \tabularnewline
99 & 13.2339634347149 & 12.5854579611852 & 13.8824689082446 \tabularnewline
100 & 13.2339634347149 & 12.5018981600732 & 13.9660287093566 \tabularnewline
101 & 13.2339634347149 & 12.4269443621557 & 14.0409825072742 \tabularnewline
102 & 13.2339634347149 & 12.3583836264663 & 14.1095432429635 \tabularnewline
103 & 13.2339634347149 & 12.2948147682351 & 14.1731121011947 \tabularnewline
104 & 13.2339634347149 & 12.2352840893347 & 14.2326427800951 \tabularnewline
105 & 13.2339634347149 & 12.179107685322 & 14.2888191841078 \tabularnewline
106 & 13.2339634347149 & 12.1257753328272 & 14.3421515366026 \tabularnewline
107 & 13.2339634347149 & 12.0748943745189 & 14.3930324949110 \tabularnewline
108 & 13.2339634347149 & 12.0261549633744 & 14.4417719060555 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13853&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]97[/C][C]13.2339634347149[/C][C]12.7982583567992[/C][C]13.6696685126306[/C][/ROW]
[ROW][C]98[/C][C]13.2339634347149[/C][C]12.6815151275768[/C][C]13.786411741853[/C][/ROW]
[ROW][C]99[/C][C]13.2339634347149[/C][C]12.5854579611852[/C][C]13.8824689082446[/C][/ROW]
[ROW][C]100[/C][C]13.2339634347149[/C][C]12.5018981600732[/C][C]13.9660287093566[/C][/ROW]
[ROW][C]101[/C][C]13.2339634347149[/C][C]12.4269443621557[/C][C]14.0409825072742[/C][/ROW]
[ROW][C]102[/C][C]13.2339634347149[/C][C]12.3583836264663[/C][C]14.1095432429635[/C][/ROW]
[ROW][C]103[/C][C]13.2339634347149[/C][C]12.2948147682351[/C][C]14.1731121011947[/C][/ROW]
[ROW][C]104[/C][C]13.2339634347149[/C][C]12.2352840893347[/C][C]14.2326427800951[/C][/ROW]
[ROW][C]105[/C][C]13.2339634347149[/C][C]12.179107685322[/C][C]14.2888191841078[/C][/ROW]
[ROW][C]106[/C][C]13.2339634347149[/C][C]12.1257753328272[/C][C]14.3421515366026[/C][/ROW]
[ROW][C]107[/C][C]13.2339634347149[/C][C]12.0748943745189[/C][C]14.3930324949110[/C][/ROW]
[ROW][C]108[/C][C]13.2339634347149[/C][C]12.0261549633744[/C][C]14.4417719060555[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13853&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13853&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
9713.233963434714912.798258356799213.6696685126306
9813.233963434714912.681515127576813.786411741853
9913.233963434714912.585457961185213.8824689082446
10013.233963434714912.501898160073213.9660287093566
10113.233963434714912.426944362155714.0409825072742
10213.233963434714912.358383626466314.1095432429635
10313.233963434714912.294814768235114.1731121011947
10413.233963434714912.235284089334714.2326427800951
10513.233963434714912.17910768532214.2888191841078
10613.233963434714912.125775332827214.3421515366026
10713.233963434714912.074894374518914.3930324949110
10813.233963434714912.026154963374414.4417719060555



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')