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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 01 Jun 2008 12:30:05 -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/Jun/01/t1212345064kh4srvidozqj9uz.htm/, Retrieved Sat, 18 May 2024 17:22:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13730, Retrieved Sat, 18 May 2024 17:22:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact213
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Glenn Van Passen ...] [2008-06-01 18:30:05] [7568f24034461b5d7b2d183bbb217711] [Current]
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Dataseries X:
11835.70
11542.20
13093.70
11180.20
12035.70
12112.00
10875.20
9897.30
11672.10
12385.70
11405.60
9830.90
11025.10
10853.80
12252.60
11839.40
11669.10
11601.40
11178.40
9516.40
12102.80
12989.00
11610.20
10205.50
11356.20
11307.10
12648.60
11947.20
11714.10
12192.50
11268.80
9097.40
12639.80
13040.10
11687.30
11191.70
11391.90
11793.10
13933.20
12778.10
11810.30
13698.40
11956.60
10723.80
13938.90
13979.80
13807.40
12973.90
12509.80
12934.10
14908.30
13772.10
13012.60
14049.90
11816.50
11593.20
14466.20
13615.90
14733.90
13880.70
13527.50
13584.00
16170.20
13260.60
14741.90
15486.50
13154.50
12621.20
15031.60
15452.40
15428.00
13105.90
14716.80
14180.00
16202.20
14392.40
15140.60
15960.10
14729.90
13705.20
15728.50
17315.60
16152.80




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13730&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13730&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13730&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.17805872722291
beta0.0478690546647562
gamma0.58355895556279

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.17805872722291 \tabularnewline
beta & 0.0478690546647562 \tabularnewline
gamma & 0.58355895556279 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13730&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]0.17805872722291[/C][/ROW]
[ROW][C]beta[/C][C]0.0478690546647562[/C][/ROW]
[ROW][C]gamma[/C][C]0.58355895556279[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13730&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13730&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
alpha0.17805872722291
beta0.0478690546647562
gamma0.58355895556279







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1311025.111016.38706208368.7129379164071
1410853.810863.0373765497-9.23737654965407
1512252.612273.6993659766-21.0993659766045
1611839.411825.130842669214.2691573308184
1711669.111636.94065256632.1593474339898
1811601.411564.684899835436.7151001646198
1911178.411134.455308659043.9446913409683
209516.49470.6463891949445.7536108050554
2112102.812033.630344951569.1696550485485
221298912921.956371728567.0436282714709
2311610.211570.746097402839.4539025971972
2410205.510168.118155725237.3818442748252
2511356.211256.999949136099.200050863983
2611307.111110.8717665178196.228233482154
2712648.612595.683215864552.916784135472
2811947.212171.4217199111-224.221719911111
2911714.111948.9203377463-234.820337746269
3012192.511831.5898388765360.910161123458
3111268.811455.4714702502-186.671470250218
329097.49714.8118448612-617.41184486121
3312639.812194.7233343156445.076665684384
3413040.113161.7591863968-121.659186396799
3511687.311742.6771031474-55.3771031473989
3611191.710302.6732522839889.02674771613
3711391.911606.5901758006-214.690175800575
3811793.111450.1689564520342.93104354804
3913933.212929.11315193861004.08684806136
4012778.112530.2145032048247.885496795167
4111810.312392.0803782404-581.780378240381
4213698.412518.30330634711180.09669365291
4311956.612003.9300753699-47.3300753699023
4410723.89981.22134570794742.578654292056
4513938.913514.9818584203423.918141579677
4613979.814297.4127364848-317.612736484789
4713807.412785.61108965441021.78891034562
4812973.911914.89533147881059.00466852118
4912509.812827.3061342329-317.506134232914
5012934.112974.9410424626-40.8410424626109
5114908.314927.8086018990-19.5086018990442
5213772.113919.7558657906-147.655865790593
5313012.613279.7565899022-267.156589902186
5414049.914435.3190521728-385.419052172778
5511816.512961.0793369486-1144.57933694863
5611593.211013.8774169365579.32258306352
5714466.214568.3003079413-102.100307941249
5813615.914918.4772920713-1302.57729207126
5914733.913823.4566599641910.443340035932
6013880.712892.6787134222988.021286577774
6113527.513123.3740067632404.125993236834
621358413542.703934732441.296065267572
6316170.215607.1920689984563.007931001555
6413260.614584.3120785899-1323.71207858991
6514741.913642.74579529371099.15420470629
6615486.515050.1933174055436.306682594521
6713154.513238.1520312516-83.652031251555
6812621.212242.4751487302378.724851269786
6915031.615701.1610463770-669.561046376955
7015452.415359.751994964692.6480050353839
711542815610.6308813893-182.630881389294
7213105.914443.2602639418-1337.36026394177
7314716.813961.0841708753755.715829124656
741418014274.0196794399-94.0196794398598
7516202.216673.7299494038-471.529949403815
7614392.414460.7603890167-68.3603890166632
7715140.614918.8105645343221.789435465673
7815960.115877.070252962983.0297470370679
7914729.913663.63451169661066.26548830342
8013705.213052.2723736871652.927626312925
8115728.516210.1127280847-481.612728084703
8217315.616276.65313456111038.94686543892
8316152.816578.8065691304-426.006569130441

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 11025.1 & 11016.3870620836 & 8.7129379164071 \tabularnewline
14 & 10853.8 & 10863.0373765497 & -9.23737654965407 \tabularnewline
15 & 12252.6 & 12273.6993659766 & -21.0993659766045 \tabularnewline
16 & 11839.4 & 11825.1308426692 & 14.2691573308184 \tabularnewline
17 & 11669.1 & 11636.940652566 & 32.1593474339898 \tabularnewline
18 & 11601.4 & 11564.6848998354 & 36.7151001646198 \tabularnewline
19 & 11178.4 & 11134.4553086590 & 43.9446913409683 \tabularnewline
20 & 9516.4 & 9470.64638919494 & 45.7536108050554 \tabularnewline
21 & 12102.8 & 12033.6303449515 & 69.1696550485485 \tabularnewline
22 & 12989 & 12921.9563717285 & 67.0436282714709 \tabularnewline
23 & 11610.2 & 11570.7460974028 & 39.4539025971972 \tabularnewline
24 & 10205.5 & 10168.1181557252 & 37.3818442748252 \tabularnewline
25 & 11356.2 & 11256.9999491360 & 99.200050863983 \tabularnewline
26 & 11307.1 & 11110.8717665178 & 196.228233482154 \tabularnewline
27 & 12648.6 & 12595.6832158645 & 52.916784135472 \tabularnewline
28 & 11947.2 & 12171.4217199111 & -224.221719911111 \tabularnewline
29 & 11714.1 & 11948.9203377463 & -234.820337746269 \tabularnewline
30 & 12192.5 & 11831.5898388765 & 360.910161123458 \tabularnewline
31 & 11268.8 & 11455.4714702502 & -186.671470250218 \tabularnewline
32 & 9097.4 & 9714.8118448612 & -617.41184486121 \tabularnewline
33 & 12639.8 & 12194.7233343156 & 445.076665684384 \tabularnewline
34 & 13040.1 & 13161.7591863968 & -121.659186396799 \tabularnewline
35 & 11687.3 & 11742.6771031474 & -55.3771031473989 \tabularnewline
36 & 11191.7 & 10302.6732522839 & 889.02674771613 \tabularnewline
37 & 11391.9 & 11606.5901758006 & -214.690175800575 \tabularnewline
38 & 11793.1 & 11450.1689564520 & 342.93104354804 \tabularnewline
39 & 13933.2 & 12929.1131519386 & 1004.08684806136 \tabularnewline
40 & 12778.1 & 12530.2145032048 & 247.885496795167 \tabularnewline
41 & 11810.3 & 12392.0803782404 & -581.780378240381 \tabularnewline
42 & 13698.4 & 12518.3033063471 & 1180.09669365291 \tabularnewline
43 & 11956.6 & 12003.9300753699 & -47.3300753699023 \tabularnewline
44 & 10723.8 & 9981.22134570794 & 742.578654292056 \tabularnewline
45 & 13938.9 & 13514.9818584203 & 423.918141579677 \tabularnewline
46 & 13979.8 & 14297.4127364848 & -317.612736484789 \tabularnewline
47 & 13807.4 & 12785.6110896544 & 1021.78891034562 \tabularnewline
48 & 12973.9 & 11914.8953314788 & 1059.00466852118 \tabularnewline
49 & 12509.8 & 12827.3061342329 & -317.506134232914 \tabularnewline
50 & 12934.1 & 12974.9410424626 & -40.8410424626109 \tabularnewline
51 & 14908.3 & 14927.8086018990 & -19.5086018990442 \tabularnewline
52 & 13772.1 & 13919.7558657906 & -147.655865790593 \tabularnewline
53 & 13012.6 & 13279.7565899022 & -267.156589902186 \tabularnewline
54 & 14049.9 & 14435.3190521728 & -385.419052172778 \tabularnewline
55 & 11816.5 & 12961.0793369486 & -1144.57933694863 \tabularnewline
56 & 11593.2 & 11013.8774169365 & 579.32258306352 \tabularnewline
57 & 14466.2 & 14568.3003079413 & -102.100307941249 \tabularnewline
58 & 13615.9 & 14918.4772920713 & -1302.57729207126 \tabularnewline
59 & 14733.9 & 13823.4566599641 & 910.443340035932 \tabularnewline
60 & 13880.7 & 12892.6787134222 & 988.021286577774 \tabularnewline
61 & 13527.5 & 13123.3740067632 & 404.125993236834 \tabularnewline
62 & 13584 & 13542.7039347324 & 41.296065267572 \tabularnewline
63 & 16170.2 & 15607.1920689984 & 563.007931001555 \tabularnewline
64 & 13260.6 & 14584.3120785899 & -1323.71207858991 \tabularnewline
65 & 14741.9 & 13642.7457952937 & 1099.15420470629 \tabularnewline
66 & 15486.5 & 15050.1933174055 & 436.306682594521 \tabularnewline
67 & 13154.5 & 13238.1520312516 & -83.652031251555 \tabularnewline
68 & 12621.2 & 12242.4751487302 & 378.724851269786 \tabularnewline
69 & 15031.6 & 15701.1610463770 & -669.561046376955 \tabularnewline
70 & 15452.4 & 15359.7519949646 & 92.6480050353839 \tabularnewline
71 & 15428 & 15610.6308813893 & -182.630881389294 \tabularnewline
72 & 13105.9 & 14443.2602639418 & -1337.36026394177 \tabularnewline
73 & 14716.8 & 13961.0841708753 & 755.715829124656 \tabularnewline
74 & 14180 & 14274.0196794399 & -94.0196794398598 \tabularnewline
75 & 16202.2 & 16673.7299494038 & -471.529949403815 \tabularnewline
76 & 14392.4 & 14460.7603890167 & -68.3603890166632 \tabularnewline
77 & 15140.6 & 14918.8105645343 & 221.789435465673 \tabularnewline
78 & 15960.1 & 15877.0702529629 & 83.0297470370679 \tabularnewline
79 & 14729.9 & 13663.6345116966 & 1066.26548830342 \tabularnewline
80 & 13705.2 & 13052.2723736871 & 652.927626312925 \tabularnewline
81 & 15728.5 & 16210.1127280847 & -481.612728084703 \tabularnewline
82 & 17315.6 & 16276.6531345611 & 1038.94686543892 \tabularnewline
83 & 16152.8 & 16578.8065691304 & -426.006569130441 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13730&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]11025.1[/C][C]11016.3870620836[/C][C]8.7129379164071[/C][/ROW]
[ROW][C]14[/C][C]10853.8[/C][C]10863.0373765497[/C][C]-9.23737654965407[/C][/ROW]
[ROW][C]15[/C][C]12252.6[/C][C]12273.6993659766[/C][C]-21.0993659766045[/C][/ROW]
[ROW][C]16[/C][C]11839.4[/C][C]11825.1308426692[/C][C]14.2691573308184[/C][/ROW]
[ROW][C]17[/C][C]11669.1[/C][C]11636.940652566[/C][C]32.1593474339898[/C][/ROW]
[ROW][C]18[/C][C]11601.4[/C][C]11564.6848998354[/C][C]36.7151001646198[/C][/ROW]
[ROW][C]19[/C][C]11178.4[/C][C]11134.4553086590[/C][C]43.9446913409683[/C][/ROW]
[ROW][C]20[/C][C]9516.4[/C][C]9470.64638919494[/C][C]45.7536108050554[/C][/ROW]
[ROW][C]21[/C][C]12102.8[/C][C]12033.6303449515[/C][C]69.1696550485485[/C][/ROW]
[ROW][C]22[/C][C]12989[/C][C]12921.9563717285[/C][C]67.0436282714709[/C][/ROW]
[ROW][C]23[/C][C]11610.2[/C][C]11570.7460974028[/C][C]39.4539025971972[/C][/ROW]
[ROW][C]24[/C][C]10205.5[/C][C]10168.1181557252[/C][C]37.3818442748252[/C][/ROW]
[ROW][C]25[/C][C]11356.2[/C][C]11256.9999491360[/C][C]99.200050863983[/C][/ROW]
[ROW][C]26[/C][C]11307.1[/C][C]11110.8717665178[/C][C]196.228233482154[/C][/ROW]
[ROW][C]27[/C][C]12648.6[/C][C]12595.6832158645[/C][C]52.916784135472[/C][/ROW]
[ROW][C]28[/C][C]11947.2[/C][C]12171.4217199111[/C][C]-224.221719911111[/C][/ROW]
[ROW][C]29[/C][C]11714.1[/C][C]11948.9203377463[/C][C]-234.820337746269[/C][/ROW]
[ROW][C]30[/C][C]12192.5[/C][C]11831.5898388765[/C][C]360.910161123458[/C][/ROW]
[ROW][C]31[/C][C]11268.8[/C][C]11455.4714702502[/C][C]-186.671470250218[/C][/ROW]
[ROW][C]32[/C][C]9097.4[/C][C]9714.8118448612[/C][C]-617.41184486121[/C][/ROW]
[ROW][C]33[/C][C]12639.8[/C][C]12194.7233343156[/C][C]445.076665684384[/C][/ROW]
[ROW][C]34[/C][C]13040.1[/C][C]13161.7591863968[/C][C]-121.659186396799[/C][/ROW]
[ROW][C]35[/C][C]11687.3[/C][C]11742.6771031474[/C][C]-55.3771031473989[/C][/ROW]
[ROW][C]36[/C][C]11191.7[/C][C]10302.6732522839[/C][C]889.02674771613[/C][/ROW]
[ROW][C]37[/C][C]11391.9[/C][C]11606.5901758006[/C][C]-214.690175800575[/C][/ROW]
[ROW][C]38[/C][C]11793.1[/C][C]11450.1689564520[/C][C]342.93104354804[/C][/ROW]
[ROW][C]39[/C][C]13933.2[/C][C]12929.1131519386[/C][C]1004.08684806136[/C][/ROW]
[ROW][C]40[/C][C]12778.1[/C][C]12530.2145032048[/C][C]247.885496795167[/C][/ROW]
[ROW][C]41[/C][C]11810.3[/C][C]12392.0803782404[/C][C]-581.780378240381[/C][/ROW]
[ROW][C]42[/C][C]13698.4[/C][C]12518.3033063471[/C][C]1180.09669365291[/C][/ROW]
[ROW][C]43[/C][C]11956.6[/C][C]12003.9300753699[/C][C]-47.3300753699023[/C][/ROW]
[ROW][C]44[/C][C]10723.8[/C][C]9981.22134570794[/C][C]742.578654292056[/C][/ROW]
[ROW][C]45[/C][C]13938.9[/C][C]13514.9818584203[/C][C]423.918141579677[/C][/ROW]
[ROW][C]46[/C][C]13979.8[/C][C]14297.4127364848[/C][C]-317.612736484789[/C][/ROW]
[ROW][C]47[/C][C]13807.4[/C][C]12785.6110896544[/C][C]1021.78891034562[/C][/ROW]
[ROW][C]48[/C][C]12973.9[/C][C]11914.8953314788[/C][C]1059.00466852118[/C][/ROW]
[ROW][C]49[/C][C]12509.8[/C][C]12827.3061342329[/C][C]-317.506134232914[/C][/ROW]
[ROW][C]50[/C][C]12934.1[/C][C]12974.9410424626[/C][C]-40.8410424626109[/C][/ROW]
[ROW][C]51[/C][C]14908.3[/C][C]14927.8086018990[/C][C]-19.5086018990442[/C][/ROW]
[ROW][C]52[/C][C]13772.1[/C][C]13919.7558657906[/C][C]-147.655865790593[/C][/ROW]
[ROW][C]53[/C][C]13012.6[/C][C]13279.7565899022[/C][C]-267.156589902186[/C][/ROW]
[ROW][C]54[/C][C]14049.9[/C][C]14435.3190521728[/C][C]-385.419052172778[/C][/ROW]
[ROW][C]55[/C][C]11816.5[/C][C]12961.0793369486[/C][C]-1144.57933694863[/C][/ROW]
[ROW][C]56[/C][C]11593.2[/C][C]11013.8774169365[/C][C]579.32258306352[/C][/ROW]
[ROW][C]57[/C][C]14466.2[/C][C]14568.3003079413[/C][C]-102.100307941249[/C][/ROW]
[ROW][C]58[/C][C]13615.9[/C][C]14918.4772920713[/C][C]-1302.57729207126[/C][/ROW]
[ROW][C]59[/C][C]14733.9[/C][C]13823.4566599641[/C][C]910.443340035932[/C][/ROW]
[ROW][C]60[/C][C]13880.7[/C][C]12892.6787134222[/C][C]988.021286577774[/C][/ROW]
[ROW][C]61[/C][C]13527.5[/C][C]13123.3740067632[/C][C]404.125993236834[/C][/ROW]
[ROW][C]62[/C][C]13584[/C][C]13542.7039347324[/C][C]41.296065267572[/C][/ROW]
[ROW][C]63[/C][C]16170.2[/C][C]15607.1920689984[/C][C]563.007931001555[/C][/ROW]
[ROW][C]64[/C][C]13260.6[/C][C]14584.3120785899[/C][C]-1323.71207858991[/C][/ROW]
[ROW][C]65[/C][C]14741.9[/C][C]13642.7457952937[/C][C]1099.15420470629[/C][/ROW]
[ROW][C]66[/C][C]15486.5[/C][C]15050.1933174055[/C][C]436.306682594521[/C][/ROW]
[ROW][C]67[/C][C]13154.5[/C][C]13238.1520312516[/C][C]-83.652031251555[/C][/ROW]
[ROW][C]68[/C][C]12621.2[/C][C]12242.4751487302[/C][C]378.724851269786[/C][/ROW]
[ROW][C]69[/C][C]15031.6[/C][C]15701.1610463770[/C][C]-669.561046376955[/C][/ROW]
[ROW][C]70[/C][C]15452.4[/C][C]15359.7519949646[/C][C]92.6480050353839[/C][/ROW]
[ROW][C]71[/C][C]15428[/C][C]15610.6308813893[/C][C]-182.630881389294[/C][/ROW]
[ROW][C]72[/C][C]13105.9[/C][C]14443.2602639418[/C][C]-1337.36026394177[/C][/ROW]
[ROW][C]73[/C][C]14716.8[/C][C]13961.0841708753[/C][C]755.715829124656[/C][/ROW]
[ROW][C]74[/C][C]14180[/C][C]14274.0196794399[/C][C]-94.0196794398598[/C][/ROW]
[ROW][C]75[/C][C]16202.2[/C][C]16673.7299494038[/C][C]-471.529949403815[/C][/ROW]
[ROW][C]76[/C][C]14392.4[/C][C]14460.7603890167[/C][C]-68.3603890166632[/C][/ROW]
[ROW][C]77[/C][C]15140.6[/C][C]14918.8105645343[/C][C]221.789435465673[/C][/ROW]
[ROW][C]78[/C][C]15960.1[/C][C]15877.0702529629[/C][C]83.0297470370679[/C][/ROW]
[ROW][C]79[/C][C]14729.9[/C][C]13663.6345116966[/C][C]1066.26548830342[/C][/ROW]
[ROW][C]80[/C][C]13705.2[/C][C]13052.2723736871[/C][C]652.927626312925[/C][/ROW]
[ROW][C]81[/C][C]15728.5[/C][C]16210.1127280847[/C][C]-481.612728084703[/C][/ROW]
[ROW][C]82[/C][C]17315.6[/C][C]16276.6531345611[/C][C]1038.94686543892[/C][/ROW]
[ROW][C]83[/C][C]16152.8[/C][C]16578.8065691304[/C][C]-426.006569130441[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13730&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13730&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
1311025.111016.38706208368.7129379164071
1410853.810863.0373765497-9.23737654965407
1512252.612273.6993659766-21.0993659766045
1611839.411825.130842669214.2691573308184
1711669.111636.94065256632.1593474339898
1811601.411564.684899835436.7151001646198
1911178.411134.455308659043.9446913409683
209516.49470.6463891949445.7536108050554
2112102.812033.630344951569.1696550485485
221298912921.956371728567.0436282714709
2311610.211570.746097402839.4539025971972
2410205.510168.118155725237.3818442748252
2511356.211256.999949136099.200050863983
2611307.111110.8717665178196.228233482154
2712648.612595.683215864552.916784135472
2811947.212171.4217199111-224.221719911111
2911714.111948.9203377463-234.820337746269
3012192.511831.5898388765360.910161123458
3111268.811455.4714702502-186.671470250218
329097.49714.8118448612-617.41184486121
3312639.812194.7233343156445.076665684384
3413040.113161.7591863968-121.659186396799
3511687.311742.6771031474-55.3771031473989
3611191.710302.6732522839889.02674771613
3711391.911606.5901758006-214.690175800575
3811793.111450.1689564520342.93104354804
3913933.212929.11315193861004.08684806136
4012778.112530.2145032048247.885496795167
4111810.312392.0803782404-581.780378240381
4213698.412518.30330634711180.09669365291
4311956.612003.9300753699-47.3300753699023
4410723.89981.22134570794742.578654292056
4513938.913514.9818584203423.918141579677
4613979.814297.4127364848-317.612736484789
4713807.412785.61108965441021.78891034562
4812973.911914.89533147881059.00466852118
4912509.812827.3061342329-317.506134232914
5012934.112974.9410424626-40.8410424626109
5114908.314927.8086018990-19.5086018990442
5213772.113919.7558657906-147.655865790593
5313012.613279.7565899022-267.156589902186
5414049.914435.3190521728-385.419052172778
5511816.512961.0793369486-1144.57933694863
5611593.211013.8774169365579.32258306352
5714466.214568.3003079413-102.100307941249
5813615.914918.4772920713-1302.57729207126
5914733.913823.4566599641910.443340035932
6013880.712892.6787134222988.021286577774
6113527.513123.3740067632404.125993236834
621358413542.703934732441.296065267572
6316170.215607.1920689984563.007931001555
6413260.614584.3120785899-1323.71207858991
6514741.913642.74579529371099.15420470629
6615486.515050.1933174055436.306682594521
6713154.513238.1520312516-83.652031251555
6812621.212242.4751487302378.724851269786
6915031.615701.1610463770-669.561046376955
7015452.415359.751994964692.6480050353839
711542815610.6308813893-182.630881389294
7213105.914443.2602639418-1337.36026394177
7314716.813961.0841708753755.715829124656
741418014274.0196794399-94.0196794398598
7516202.216673.7299494038-471.529949403815
7614392.414460.7603890167-68.3603890166632
7715140.614918.8105645343221.789435465673
7815960.115877.070252962983.0297470370679
7914729.913663.63451169661066.26548830342
8013705.213052.2723736871652.927626312925
8115728.516210.1127280847-481.612728084703
8217315.616276.65313456111038.94686543892
8316152.816578.8065691304-426.006569130441







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8414697.962153364613965.140352594215430.783954135
8515534.753823062514769.997684884016299.5099612411
8615298.689950428414505.727613185516091.6522876714
8717716.418176616116863.502869693018569.3334835393
8815635.296646448614780.656057761216489.9372351359
8916311.603196394615411.472759471217211.7336333181
9017248.740208433316293.081012702618204.3994041639
9115351.430112298514407.636842846816295.2233817502
9214282.943158594713333.171054662115232.7152625274
9316924.030963325715853.814338829617994.2475878217
9417857.364452885416713.559218404719001.169687366
9517231.997029543316334.198432972918129.7956261136

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
84 & 14697.9621533646 & 13965.1403525942 & 15430.783954135 \tabularnewline
85 & 15534.7538230625 & 14769.9976848840 & 16299.5099612411 \tabularnewline
86 & 15298.6899504284 & 14505.7276131855 & 16091.6522876714 \tabularnewline
87 & 17716.4181766161 & 16863.5028696930 & 18569.3334835393 \tabularnewline
88 & 15635.2966464486 & 14780.6560577612 & 16489.9372351359 \tabularnewline
89 & 16311.6031963946 & 15411.4727594712 & 17211.7336333181 \tabularnewline
90 & 17248.7402084333 & 16293.0810127026 & 18204.3994041639 \tabularnewline
91 & 15351.4301122985 & 14407.6368428468 & 16295.2233817502 \tabularnewline
92 & 14282.9431585947 & 13333.1710546621 & 15232.7152625274 \tabularnewline
93 & 16924.0309633257 & 15853.8143388296 & 17994.2475878217 \tabularnewline
94 & 17857.3644528854 & 16713.5592184047 & 19001.169687366 \tabularnewline
95 & 17231.9970295433 & 16334.1984329729 & 18129.7956261136 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13730&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]84[/C][C]14697.9621533646[/C][C]13965.1403525942[/C][C]15430.783954135[/C][/ROW]
[ROW][C]85[/C][C]15534.7538230625[/C][C]14769.9976848840[/C][C]16299.5099612411[/C][/ROW]
[ROW][C]86[/C][C]15298.6899504284[/C][C]14505.7276131855[/C][C]16091.6522876714[/C][/ROW]
[ROW][C]87[/C][C]17716.4181766161[/C][C]16863.5028696930[/C][C]18569.3334835393[/C][/ROW]
[ROW][C]88[/C][C]15635.2966464486[/C][C]14780.6560577612[/C][C]16489.9372351359[/C][/ROW]
[ROW][C]89[/C][C]16311.6031963946[/C][C]15411.4727594712[/C][C]17211.7336333181[/C][/ROW]
[ROW][C]90[/C][C]17248.7402084333[/C][C]16293.0810127026[/C][C]18204.3994041639[/C][/ROW]
[ROW][C]91[/C][C]15351.4301122985[/C][C]14407.6368428468[/C][C]16295.2233817502[/C][/ROW]
[ROW][C]92[/C][C]14282.9431585947[/C][C]13333.1710546621[/C][C]15232.7152625274[/C][/ROW]
[ROW][C]93[/C][C]16924.0309633257[/C][C]15853.8143388296[/C][C]17994.2475878217[/C][/ROW]
[ROW][C]94[/C][C]17857.3644528854[/C][C]16713.5592184047[/C][C]19001.169687366[/C][/ROW]
[ROW][C]95[/C][C]17231.9970295433[/C][C]16334.1984329729[/C][C]18129.7956261136[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13730&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13730&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
8414697.962153364613965.140352594215430.783954135
8515534.753823062514769.997684884016299.5099612411
8615298.689950428414505.727613185516091.6522876714
8717716.418176616116863.502869693018569.3334835393
8815635.296646448614780.656057761216489.9372351359
8916311.603196394615411.472759471217211.7336333181
9017248.740208433316293.081012702618204.3994041639
9115351.430112298514407.636842846816295.2233817502
9214282.943158594713333.171054662115232.7152625274
9316924.030963325715853.814338829617994.2475878217
9417857.364452885416713.559218404719001.169687366
9517231.997029543316334.198432972918129.7956261136



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