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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 31 May 2010 14:37:01 +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/May/31/t1275316652xbns86twncmcg5g.htm/, Retrieved Mon, 29 Apr 2024 09:47:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=76740, Retrieved Mon, 29 Apr 2024 09:47:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact157
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [cijferreeks - Ins...] [2009-06-02 13:44:55] [74be16979710d4c4e7c6647856088456]
-  M    [Exponential Smoothing] [Inschrijvingen pe...] [2010-05-31 14:28:43] [74be16979710d4c4e7c6647856088456]
-    D      [Exponential Smoothing] [Champagne Exponen...] [2010-05-31 14:37:01] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
2851
2672
2755
2721
2946
3036
2282
2212
2922
4301
5764
7132
2541
2475
3031
3266
3776
3230
3028
1759
3595
4474
6838
8357
3113
3006
4047
3523
3937
3986
3260
1573
3528
5211
7614
9254
5375
3088
3718
4514
4520
4539
3663
1643
4739
5428
8314
10651
3633
4292
4154
4121
4647
4753
3965
1723
5048
6922
9858
11331
4016
3975
4510
4276
4968
4677
3523
1821
5222
6873
10803
13916
2639
2899
3370
3740
2927
3986
4217
1738
5221
6424
9842
13076
3934
3162
4286
4676
5010
4874
4633
1659
5951
6981
9851
12670




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76740&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76740&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76740&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.30842644344129
beta0
gamma0.632760470780569

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.30842644344129 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.632760470780569 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76740&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]0.30842644344129[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.632760470780569[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76740&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76740&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
alpha0.30842644344129
beta0
gamma0.632760470780569







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1325412393.50833868648147.491661313523
1424752389.7588888929285.2411111070837
1530312978.3564054691852.6435945308167
1632663224.5748616720941.425138327912
1737763723.4358524657452.5641475342582
1832303145.9564754495484.0435245504614
1930282495.85826039448532.141739605515
2017592615.11807012923-856.118070129231
2135953130.25669910364464.743300896364
2244744811.13642911062-337.136429110617
2368386258.72643224635579.273567753655
2483577934.66214742373422.337852576273
2531132940.7998191162172.200180883797
2630062897.56490597696108.435094023038
2740473580.3024470368466.697552963203
2835233995.14184564363-472.141845643626
2939374423.91370452947-486.913704529466
3039863610.94140603873375.05859396127
3132603148.77166912909111.228330870912
3215732417.20206583968-844.202065839685
3335283625.51605483856-97.5160548385575
3452114817.81581161119393.184188388806
3576147041.98015460674572.019845393255
3692548751.20258405828502.797415941719
3753753252.838656173982122.16134382602
3830883742.2695559007-654.269555900696
3937184483.8418231847-765.841823184696
4045144085.64765089121428.352349108791
4145204861.68281614564-341.682816145635
4245394410.85001290644128.149987093557
4336633653.356755915639.64324408436505
4416432264.44617605372-621.446176053724
4547394149.84148853392589.158511466083
4654286069.71709395816-641.717093958163
4783148362.0605378331-48.0605378330911
481065110014.2215488854636.778451114596
4936334500.74097486828-867.740974868284
5042923013.428062464471278.57193753553
5141544323.7759675356-169.775967535601
5241214656.04329075914-535.043290759142
5346474799.98302171796-152.983021717956
5447534607.07333369408145.926666305915
5539653775.00500753416189.994992465839
5617232059.76462237556-336.764622375558
5750484772.81180891231275.18819108769
5869226115.09205057554806.907949424456
5998589486.33781629371.662183710003
601133111851.8998112841-520.899811284056
6140164563.38971079182-547.389710791824
6239753997.45323471011-22.4532347101144
6345104273.31838761804236.681612381963
6442764569.22285121982-293.222851219819
6549684977.49285544872-9.49285544871782
6646774956.23587445028-279.23587445028
6735233982.17547180157-459.175471801574
6818211867.74768227565-46.7476822756498
6952225011.51465333456210.485346665436
7068736581.07120783537291.928792164632
71108039581.42652635451221.57347364551
721391611851.05862199172064.94137800828
7326394698.03096152302-2059.03096152302
7428993899.80834532273-1000.80834532273
7533703949.58307105529-579.583071055289
7637403765.04537858081-25.0453785808081
7729274299.35202261117-1372.35202261117
7839863774.43180886483211.56819113517
7942173056.309942512081160.69005748792
8017381733.494537051884.50546294811966
8152214831.36712436927389.632875630735
8264246427.2259168487-3.22591684869803
8398429545.7731737953296.226826204693
841307611678.25990474811397.7400952519
8539343307.99996998548626.00003001452
8631623789.18182936661-627.181829366613
8742864197.5076305948388.4923694051668
8846764504.02522974213171.974770257874
8950104413.97229349209596.027706507914
9048745413.85440538327-539.854405383268
9146334676.36618707742-43.3661870774158
9216592061.05277379123-402.052773791227
9359515569.97297961752381.02702038248
9469817130.64581122766-149.645811227659
95985110661.1481746792-810.148174679225
961267013072.6379617398-402.637961739832

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 2541 & 2393.50833868648 & 147.491661313523 \tabularnewline
14 & 2475 & 2389.75888889292 & 85.2411111070837 \tabularnewline
15 & 3031 & 2978.35640546918 & 52.6435945308167 \tabularnewline
16 & 3266 & 3224.57486167209 & 41.425138327912 \tabularnewline
17 & 3776 & 3723.43585246574 & 52.5641475342582 \tabularnewline
18 & 3230 & 3145.95647544954 & 84.0435245504614 \tabularnewline
19 & 3028 & 2495.85826039448 & 532.141739605515 \tabularnewline
20 & 1759 & 2615.11807012923 & -856.118070129231 \tabularnewline
21 & 3595 & 3130.25669910364 & 464.743300896364 \tabularnewline
22 & 4474 & 4811.13642911062 & -337.136429110617 \tabularnewline
23 & 6838 & 6258.72643224635 & 579.273567753655 \tabularnewline
24 & 8357 & 7934.66214742373 & 422.337852576273 \tabularnewline
25 & 3113 & 2940.7998191162 & 172.200180883797 \tabularnewline
26 & 3006 & 2897.56490597696 & 108.435094023038 \tabularnewline
27 & 4047 & 3580.3024470368 & 466.697552963203 \tabularnewline
28 & 3523 & 3995.14184564363 & -472.141845643626 \tabularnewline
29 & 3937 & 4423.91370452947 & -486.913704529466 \tabularnewline
30 & 3986 & 3610.94140603873 & 375.05859396127 \tabularnewline
31 & 3260 & 3148.77166912909 & 111.228330870912 \tabularnewline
32 & 1573 & 2417.20206583968 & -844.202065839685 \tabularnewline
33 & 3528 & 3625.51605483856 & -97.5160548385575 \tabularnewline
34 & 5211 & 4817.81581161119 & 393.184188388806 \tabularnewline
35 & 7614 & 7041.98015460674 & 572.019845393255 \tabularnewline
36 & 9254 & 8751.20258405828 & 502.797415941719 \tabularnewline
37 & 5375 & 3252.83865617398 & 2122.16134382602 \tabularnewline
38 & 3088 & 3742.2695559007 & -654.269555900696 \tabularnewline
39 & 3718 & 4483.8418231847 & -765.841823184696 \tabularnewline
40 & 4514 & 4085.64765089121 & 428.352349108791 \tabularnewline
41 & 4520 & 4861.68281614564 & -341.682816145635 \tabularnewline
42 & 4539 & 4410.85001290644 & 128.149987093557 \tabularnewline
43 & 3663 & 3653.35675591563 & 9.64324408436505 \tabularnewline
44 & 1643 & 2264.44617605372 & -621.446176053724 \tabularnewline
45 & 4739 & 4149.84148853392 & 589.158511466083 \tabularnewline
46 & 5428 & 6069.71709395816 & -641.717093958163 \tabularnewline
47 & 8314 & 8362.0605378331 & -48.0605378330911 \tabularnewline
48 & 10651 & 10014.2215488854 & 636.778451114596 \tabularnewline
49 & 3633 & 4500.74097486828 & -867.740974868284 \tabularnewline
50 & 4292 & 3013.42806246447 & 1278.57193753553 \tabularnewline
51 & 4154 & 4323.7759675356 & -169.775967535601 \tabularnewline
52 & 4121 & 4656.04329075914 & -535.043290759142 \tabularnewline
53 & 4647 & 4799.98302171796 & -152.983021717956 \tabularnewline
54 & 4753 & 4607.07333369408 & 145.926666305915 \tabularnewline
55 & 3965 & 3775.00500753416 & 189.994992465839 \tabularnewline
56 & 1723 & 2059.76462237556 & -336.764622375558 \tabularnewline
57 & 5048 & 4772.81180891231 & 275.18819108769 \tabularnewline
58 & 6922 & 6115.09205057554 & 806.907949424456 \tabularnewline
59 & 9858 & 9486.33781629 & 371.662183710003 \tabularnewline
60 & 11331 & 11851.8998112841 & -520.899811284056 \tabularnewline
61 & 4016 & 4563.38971079182 & -547.389710791824 \tabularnewline
62 & 3975 & 3997.45323471011 & -22.4532347101144 \tabularnewline
63 & 4510 & 4273.31838761804 & 236.681612381963 \tabularnewline
64 & 4276 & 4569.22285121982 & -293.222851219819 \tabularnewline
65 & 4968 & 4977.49285544872 & -9.49285544871782 \tabularnewline
66 & 4677 & 4956.23587445028 & -279.23587445028 \tabularnewline
67 & 3523 & 3982.17547180157 & -459.175471801574 \tabularnewline
68 & 1821 & 1867.74768227565 & -46.7476822756498 \tabularnewline
69 & 5222 & 5011.51465333456 & 210.485346665436 \tabularnewline
70 & 6873 & 6581.07120783537 & 291.928792164632 \tabularnewline
71 & 10803 & 9581.4265263545 & 1221.57347364551 \tabularnewline
72 & 13916 & 11851.0586219917 & 2064.94137800828 \tabularnewline
73 & 2639 & 4698.03096152302 & -2059.03096152302 \tabularnewline
74 & 2899 & 3899.80834532273 & -1000.80834532273 \tabularnewline
75 & 3370 & 3949.58307105529 & -579.583071055289 \tabularnewline
76 & 3740 & 3765.04537858081 & -25.0453785808081 \tabularnewline
77 & 2927 & 4299.35202261117 & -1372.35202261117 \tabularnewline
78 & 3986 & 3774.43180886483 & 211.56819113517 \tabularnewline
79 & 4217 & 3056.30994251208 & 1160.69005748792 \tabularnewline
80 & 1738 & 1733.49453705188 & 4.50546294811966 \tabularnewline
81 & 5221 & 4831.36712436927 & 389.632875630735 \tabularnewline
82 & 6424 & 6427.2259168487 & -3.22591684869803 \tabularnewline
83 & 9842 & 9545.7731737953 & 296.226826204693 \tabularnewline
84 & 13076 & 11678.2599047481 & 1397.7400952519 \tabularnewline
85 & 3934 & 3307.99996998548 & 626.00003001452 \tabularnewline
86 & 3162 & 3789.18182936661 & -627.181829366613 \tabularnewline
87 & 4286 & 4197.50763059483 & 88.4923694051668 \tabularnewline
88 & 4676 & 4504.02522974213 & 171.974770257874 \tabularnewline
89 & 5010 & 4413.97229349209 & 596.027706507914 \tabularnewline
90 & 4874 & 5413.85440538327 & -539.854405383268 \tabularnewline
91 & 4633 & 4676.36618707742 & -43.3661870774158 \tabularnewline
92 & 1659 & 2061.05277379123 & -402.052773791227 \tabularnewline
93 & 5951 & 5569.97297961752 & 381.02702038248 \tabularnewline
94 & 6981 & 7130.64581122766 & -149.645811227659 \tabularnewline
95 & 9851 & 10661.1481746792 & -810.148174679225 \tabularnewline
96 & 12670 & 13072.6379617398 & -402.637961739832 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76740&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]2541[/C][C]2393.50833868648[/C][C]147.491661313523[/C][/ROW]
[ROW][C]14[/C][C]2475[/C][C]2389.75888889292[/C][C]85.2411111070837[/C][/ROW]
[ROW][C]15[/C][C]3031[/C][C]2978.35640546918[/C][C]52.6435945308167[/C][/ROW]
[ROW][C]16[/C][C]3266[/C][C]3224.57486167209[/C][C]41.425138327912[/C][/ROW]
[ROW][C]17[/C][C]3776[/C][C]3723.43585246574[/C][C]52.5641475342582[/C][/ROW]
[ROW][C]18[/C][C]3230[/C][C]3145.95647544954[/C][C]84.0435245504614[/C][/ROW]
[ROW][C]19[/C][C]3028[/C][C]2495.85826039448[/C][C]532.141739605515[/C][/ROW]
[ROW][C]20[/C][C]1759[/C][C]2615.11807012923[/C][C]-856.118070129231[/C][/ROW]
[ROW][C]21[/C][C]3595[/C][C]3130.25669910364[/C][C]464.743300896364[/C][/ROW]
[ROW][C]22[/C][C]4474[/C][C]4811.13642911062[/C][C]-337.136429110617[/C][/ROW]
[ROW][C]23[/C][C]6838[/C][C]6258.72643224635[/C][C]579.273567753655[/C][/ROW]
[ROW][C]24[/C][C]8357[/C][C]7934.66214742373[/C][C]422.337852576273[/C][/ROW]
[ROW][C]25[/C][C]3113[/C][C]2940.7998191162[/C][C]172.200180883797[/C][/ROW]
[ROW][C]26[/C][C]3006[/C][C]2897.56490597696[/C][C]108.435094023038[/C][/ROW]
[ROW][C]27[/C][C]4047[/C][C]3580.3024470368[/C][C]466.697552963203[/C][/ROW]
[ROW][C]28[/C][C]3523[/C][C]3995.14184564363[/C][C]-472.141845643626[/C][/ROW]
[ROW][C]29[/C][C]3937[/C][C]4423.91370452947[/C][C]-486.913704529466[/C][/ROW]
[ROW][C]30[/C][C]3986[/C][C]3610.94140603873[/C][C]375.05859396127[/C][/ROW]
[ROW][C]31[/C][C]3260[/C][C]3148.77166912909[/C][C]111.228330870912[/C][/ROW]
[ROW][C]32[/C][C]1573[/C][C]2417.20206583968[/C][C]-844.202065839685[/C][/ROW]
[ROW][C]33[/C][C]3528[/C][C]3625.51605483856[/C][C]-97.5160548385575[/C][/ROW]
[ROW][C]34[/C][C]5211[/C][C]4817.81581161119[/C][C]393.184188388806[/C][/ROW]
[ROW][C]35[/C][C]7614[/C][C]7041.98015460674[/C][C]572.019845393255[/C][/ROW]
[ROW][C]36[/C][C]9254[/C][C]8751.20258405828[/C][C]502.797415941719[/C][/ROW]
[ROW][C]37[/C][C]5375[/C][C]3252.83865617398[/C][C]2122.16134382602[/C][/ROW]
[ROW][C]38[/C][C]3088[/C][C]3742.2695559007[/C][C]-654.269555900696[/C][/ROW]
[ROW][C]39[/C][C]3718[/C][C]4483.8418231847[/C][C]-765.841823184696[/C][/ROW]
[ROW][C]40[/C][C]4514[/C][C]4085.64765089121[/C][C]428.352349108791[/C][/ROW]
[ROW][C]41[/C][C]4520[/C][C]4861.68281614564[/C][C]-341.682816145635[/C][/ROW]
[ROW][C]42[/C][C]4539[/C][C]4410.85001290644[/C][C]128.149987093557[/C][/ROW]
[ROW][C]43[/C][C]3663[/C][C]3653.35675591563[/C][C]9.64324408436505[/C][/ROW]
[ROW][C]44[/C][C]1643[/C][C]2264.44617605372[/C][C]-621.446176053724[/C][/ROW]
[ROW][C]45[/C][C]4739[/C][C]4149.84148853392[/C][C]589.158511466083[/C][/ROW]
[ROW][C]46[/C][C]5428[/C][C]6069.71709395816[/C][C]-641.717093958163[/C][/ROW]
[ROW][C]47[/C][C]8314[/C][C]8362.0605378331[/C][C]-48.0605378330911[/C][/ROW]
[ROW][C]48[/C][C]10651[/C][C]10014.2215488854[/C][C]636.778451114596[/C][/ROW]
[ROW][C]49[/C][C]3633[/C][C]4500.74097486828[/C][C]-867.740974868284[/C][/ROW]
[ROW][C]50[/C][C]4292[/C][C]3013.42806246447[/C][C]1278.57193753553[/C][/ROW]
[ROW][C]51[/C][C]4154[/C][C]4323.7759675356[/C][C]-169.775967535601[/C][/ROW]
[ROW][C]52[/C][C]4121[/C][C]4656.04329075914[/C][C]-535.043290759142[/C][/ROW]
[ROW][C]53[/C][C]4647[/C][C]4799.98302171796[/C][C]-152.983021717956[/C][/ROW]
[ROW][C]54[/C][C]4753[/C][C]4607.07333369408[/C][C]145.926666305915[/C][/ROW]
[ROW][C]55[/C][C]3965[/C][C]3775.00500753416[/C][C]189.994992465839[/C][/ROW]
[ROW][C]56[/C][C]1723[/C][C]2059.76462237556[/C][C]-336.764622375558[/C][/ROW]
[ROW][C]57[/C][C]5048[/C][C]4772.81180891231[/C][C]275.18819108769[/C][/ROW]
[ROW][C]58[/C][C]6922[/C][C]6115.09205057554[/C][C]806.907949424456[/C][/ROW]
[ROW][C]59[/C][C]9858[/C][C]9486.33781629[/C][C]371.662183710003[/C][/ROW]
[ROW][C]60[/C][C]11331[/C][C]11851.8998112841[/C][C]-520.899811284056[/C][/ROW]
[ROW][C]61[/C][C]4016[/C][C]4563.38971079182[/C][C]-547.389710791824[/C][/ROW]
[ROW][C]62[/C][C]3975[/C][C]3997.45323471011[/C][C]-22.4532347101144[/C][/ROW]
[ROW][C]63[/C][C]4510[/C][C]4273.31838761804[/C][C]236.681612381963[/C][/ROW]
[ROW][C]64[/C][C]4276[/C][C]4569.22285121982[/C][C]-293.222851219819[/C][/ROW]
[ROW][C]65[/C][C]4968[/C][C]4977.49285544872[/C][C]-9.49285544871782[/C][/ROW]
[ROW][C]66[/C][C]4677[/C][C]4956.23587445028[/C][C]-279.23587445028[/C][/ROW]
[ROW][C]67[/C][C]3523[/C][C]3982.17547180157[/C][C]-459.175471801574[/C][/ROW]
[ROW][C]68[/C][C]1821[/C][C]1867.74768227565[/C][C]-46.7476822756498[/C][/ROW]
[ROW][C]69[/C][C]5222[/C][C]5011.51465333456[/C][C]210.485346665436[/C][/ROW]
[ROW][C]70[/C][C]6873[/C][C]6581.07120783537[/C][C]291.928792164632[/C][/ROW]
[ROW][C]71[/C][C]10803[/C][C]9581.4265263545[/C][C]1221.57347364551[/C][/ROW]
[ROW][C]72[/C][C]13916[/C][C]11851.0586219917[/C][C]2064.94137800828[/C][/ROW]
[ROW][C]73[/C][C]2639[/C][C]4698.03096152302[/C][C]-2059.03096152302[/C][/ROW]
[ROW][C]74[/C][C]2899[/C][C]3899.80834532273[/C][C]-1000.80834532273[/C][/ROW]
[ROW][C]75[/C][C]3370[/C][C]3949.58307105529[/C][C]-579.583071055289[/C][/ROW]
[ROW][C]76[/C][C]3740[/C][C]3765.04537858081[/C][C]-25.0453785808081[/C][/ROW]
[ROW][C]77[/C][C]2927[/C][C]4299.35202261117[/C][C]-1372.35202261117[/C][/ROW]
[ROW][C]78[/C][C]3986[/C][C]3774.43180886483[/C][C]211.56819113517[/C][/ROW]
[ROW][C]79[/C][C]4217[/C][C]3056.30994251208[/C][C]1160.69005748792[/C][/ROW]
[ROW][C]80[/C][C]1738[/C][C]1733.49453705188[/C][C]4.50546294811966[/C][/ROW]
[ROW][C]81[/C][C]5221[/C][C]4831.36712436927[/C][C]389.632875630735[/C][/ROW]
[ROW][C]82[/C][C]6424[/C][C]6427.2259168487[/C][C]-3.22591684869803[/C][/ROW]
[ROW][C]83[/C][C]9842[/C][C]9545.7731737953[/C][C]296.226826204693[/C][/ROW]
[ROW][C]84[/C][C]13076[/C][C]11678.2599047481[/C][C]1397.7400952519[/C][/ROW]
[ROW][C]85[/C][C]3934[/C][C]3307.99996998548[/C][C]626.00003001452[/C][/ROW]
[ROW][C]86[/C][C]3162[/C][C]3789.18182936661[/C][C]-627.181829366613[/C][/ROW]
[ROW][C]87[/C][C]4286[/C][C]4197.50763059483[/C][C]88.4923694051668[/C][/ROW]
[ROW][C]88[/C][C]4676[/C][C]4504.02522974213[/C][C]171.974770257874[/C][/ROW]
[ROW][C]89[/C][C]5010[/C][C]4413.97229349209[/C][C]596.027706507914[/C][/ROW]
[ROW][C]90[/C][C]4874[/C][C]5413.85440538327[/C][C]-539.854405383268[/C][/ROW]
[ROW][C]91[/C][C]4633[/C][C]4676.36618707742[/C][C]-43.3661870774158[/C][/ROW]
[ROW][C]92[/C][C]1659[/C][C]2061.05277379123[/C][C]-402.052773791227[/C][/ROW]
[ROW][C]93[/C][C]5951[/C][C]5569.97297961752[/C][C]381.02702038248[/C][/ROW]
[ROW][C]94[/C][C]6981[/C][C]7130.64581122766[/C][C]-149.645811227659[/C][/ROW]
[ROW][C]95[/C][C]9851[/C][C]10661.1481746792[/C][C]-810.148174679225[/C][/ROW]
[ROW][C]96[/C][C]12670[/C][C]13072.6379617398[/C][C]-402.637961739832[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76740&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76740&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
1325412393.50833868648147.491661313523
1424752389.7588888929285.2411111070837
1530312978.3564054691852.6435945308167
1632663224.5748616720941.425138327912
1737763723.4358524657452.5641475342582
1832303145.9564754495484.0435245504614
1930282495.85826039448532.141739605515
2017592615.11807012923-856.118070129231
2135953130.25669910364464.743300896364
2244744811.13642911062-337.136429110617
2368386258.72643224635579.273567753655
2483577934.66214742373422.337852576273
2531132940.7998191162172.200180883797
2630062897.56490597696108.435094023038
2740473580.3024470368466.697552963203
2835233995.14184564363-472.141845643626
2939374423.91370452947-486.913704529466
3039863610.94140603873375.05859396127
3132603148.77166912909111.228330870912
3215732417.20206583968-844.202065839685
3335283625.51605483856-97.5160548385575
3452114817.81581161119393.184188388806
3576147041.98015460674572.019845393255
3692548751.20258405828502.797415941719
3753753252.838656173982122.16134382602
3830883742.2695559007-654.269555900696
3937184483.8418231847-765.841823184696
4045144085.64765089121428.352349108791
4145204861.68281614564-341.682816145635
4245394410.85001290644128.149987093557
4336633653.356755915639.64324408436505
4416432264.44617605372-621.446176053724
4547394149.84148853392589.158511466083
4654286069.71709395816-641.717093958163
4783148362.0605378331-48.0605378330911
481065110014.2215488854636.778451114596
4936334500.74097486828-867.740974868284
5042923013.428062464471278.57193753553
5141544323.7759675356-169.775967535601
5241214656.04329075914-535.043290759142
5346474799.98302171796-152.983021717956
5447534607.07333369408145.926666305915
5539653775.00500753416189.994992465839
5617232059.76462237556-336.764622375558
5750484772.81180891231275.18819108769
5869226115.09205057554806.907949424456
5998589486.33781629371.662183710003
601133111851.8998112841-520.899811284056
6140164563.38971079182-547.389710791824
6239753997.45323471011-22.4532347101144
6345104273.31838761804236.681612381963
6442764569.22285121982-293.222851219819
6549684977.49285544872-9.49285544871782
6646774956.23587445028-279.23587445028
6735233982.17547180157-459.175471801574
6818211867.74768227565-46.7476822756498
6952225011.51465333456210.485346665436
7068736581.07120783537291.928792164632
71108039581.42652635451221.57347364551
721391611851.05862199172064.94137800828
7326394698.03096152302-2059.03096152302
7428993899.80834532273-1000.80834532273
7533703949.58307105529-579.583071055289
7637403765.04537858081-25.0453785808081
7729274299.35202261117-1372.35202261117
7839863774.43180886483211.56819113517
7942173056.309942512081160.69005748792
8017381733.494537051884.50546294811966
8152214831.36712436927389.632875630735
8264246427.2259168487-3.22591684869803
8398429545.7731737953296.226826204693
841307611678.25990474811397.7400952519
8539343307.99996998548626.00003001452
8631623789.18182936661-627.181829366613
8742864197.5076305948388.4923694051668
8846764504.02522974213171.974770257874
8950104413.97229349209596.027706507914
9048745413.85440538327-539.854405383268
9146334676.36618707742-43.3661870774158
9216592061.05277379123-402.052773791227
9359515569.97297961752381.02702038248
9469817130.64581122766-149.645811227659
95985110661.1481746792-810.148174679225
961267013072.6379617398-402.637961739832







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
973630.219953699592669.588570824244590.85133657494
983366.476796167632338.436582245134394.51701009014
994293.275676884283113.511733880065473.03961988851
1004610.166448813273330.655899314015889.67699831253
1014642.18423422723301.714573514025982.65389494038
1024941.062993047593499.413808012016382.71217808317
1034592.600294047163162.748543348576022.45204474576
1041853.22234945944790.7809150675652915.66378385131
1056031.354945016763856.097545145898206.61234488763
1067277.25030701814701.799161773529852.70145226268
10710674.81871724467013.0651144768214336.5723200123
10813682.57049693359149.6832868392618215.4577070277

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 3630.21995369959 & 2669.58857082424 & 4590.85133657494 \tabularnewline
98 & 3366.47679616763 & 2338.43658224513 & 4394.51701009014 \tabularnewline
99 & 4293.27567688428 & 3113.51173388006 & 5473.03961988851 \tabularnewline
100 & 4610.16644881327 & 3330.65589931401 & 5889.67699831253 \tabularnewline
101 & 4642.1842342272 & 3301.71457351402 & 5982.65389494038 \tabularnewline
102 & 4941.06299304759 & 3499.41380801201 & 6382.71217808317 \tabularnewline
103 & 4592.60029404716 & 3162.74854334857 & 6022.45204474576 \tabularnewline
104 & 1853.22234945944 & 790.780915067565 & 2915.66378385131 \tabularnewline
105 & 6031.35494501676 & 3856.09754514589 & 8206.61234488763 \tabularnewline
106 & 7277.2503070181 & 4701.79916177352 & 9852.70145226268 \tabularnewline
107 & 10674.8187172446 & 7013.06511447682 & 14336.5723200123 \tabularnewline
108 & 13682.5704969335 & 9149.68328683926 & 18215.4577070277 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76740&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]3630.21995369959[/C][C]2669.58857082424[/C][C]4590.85133657494[/C][/ROW]
[ROW][C]98[/C][C]3366.47679616763[/C][C]2338.43658224513[/C][C]4394.51701009014[/C][/ROW]
[ROW][C]99[/C][C]4293.27567688428[/C][C]3113.51173388006[/C][C]5473.03961988851[/C][/ROW]
[ROW][C]100[/C][C]4610.16644881327[/C][C]3330.65589931401[/C][C]5889.67699831253[/C][/ROW]
[ROW][C]101[/C][C]4642.1842342272[/C][C]3301.71457351402[/C][C]5982.65389494038[/C][/ROW]
[ROW][C]102[/C][C]4941.06299304759[/C][C]3499.41380801201[/C][C]6382.71217808317[/C][/ROW]
[ROW][C]103[/C][C]4592.60029404716[/C][C]3162.74854334857[/C][C]6022.45204474576[/C][/ROW]
[ROW][C]104[/C][C]1853.22234945944[/C][C]790.780915067565[/C][C]2915.66378385131[/C][/ROW]
[ROW][C]105[/C][C]6031.35494501676[/C][C]3856.09754514589[/C][C]8206.61234488763[/C][/ROW]
[ROW][C]106[/C][C]7277.2503070181[/C][C]4701.79916177352[/C][C]9852.70145226268[/C][/ROW]
[ROW][C]107[/C][C]10674.8187172446[/C][C]7013.06511447682[/C][C]14336.5723200123[/C][/ROW]
[ROW][C]108[/C][C]13682.5704969335[/C][C]9149.68328683926[/C][C]18215.4577070277[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76740&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76740&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
973630.219953699592669.588570824244590.85133657494
983366.476796167632338.436582245134394.51701009014
994293.275676884283113.511733880065473.03961988851
1004610.166448813273330.655899314015889.67699831253
1014642.18423422723301.714573514025982.65389494038
1024941.062993047593499.413808012016382.71217808317
1034592.600294047163162.748543348576022.45204474576
1041853.22234945944790.7809150675652915.66378385131
1056031.354945016763856.097545145898206.61234488763
1067277.25030701814701.799161773529852.70145226268
10710674.81871724467013.0651144768214336.5723200123
10813682.57049693359149.6832868392618215.4577070277



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')