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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 computationTue, 05 Jul 2016 17:31:41 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Jul/05/t1467736340f9cwqppahh4plyq.htm/, Retrieved Fri, 03 May 2024 10:02:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=295813, Retrieved Fri, 03 May 2024 10:02:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact129
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2016-07-05 16:31:41] [fcb50c3fd850be3d4e9c7b78a2663ee0] [Current]
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Dataseries X:
1020
970
1030
970
1070
1650
1010
980
1050
1010
1040
1120
1090
1060
990
950
1540
870
1070
1050
1020
960
1100
1190
1040
1090
1050
850
1100
850
1040
990
1040
1100
1030
1290
1040
1170
1040
860
1090
870
1080
1000
980
1080
1040
1280
1140
1220
1080
790
1020
830
1150
1030
900
1140
1010
1270
1090
1090
980
850
1010
810
1070
1040
880
1110
1010
1230
490
1040
1010
860
1010
800
1130
1040
940
1070
1030
1320
1040
1070
1070
770
1010
810
1150
1030
890
1010
1120
1250
990
1020
1110
830
1030
870
1260
980
940
970
1100
1320




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295813&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295813&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295813&T=0

As an alternative you can also use a QR Code:  

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

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







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.00161353096763133
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.00161353096763133 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295813&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]0.00161353096763133[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295813&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295813&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
alpha0.00161353096763133
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
29701020-50
310301019.9193234516210.0806765483815
49701019.9355889354-49.935588935404
510701019.8550163162750.1449836837301
616501019.93592680031630.064073199685
710101020.95255469401-10.9525546940146
89801020.93488240784-40.9348824078411
910501020.8688327074229.1311672925802
1010101020.91583674797-10.9158367479696
1110401020.8982237073419.1017762926608
1211201020.9290450149299.0709549850758
1310901021.0888990687968.9111009312145
1410601021.2000892641538.7999107358484
159901021.26269412167-31.2626941216653
169501021.21225079657-71.2122507965684
1715401021.09734762463518.902652375367
188701021.93461312343-151.934613123427
1910701021.689461920148.3105380799025
2010501021.7674124693528.2325875306476
2110201021.81296662363-1.81296662362945
229601021.81004134584-61.810041345839
2311001021.7103089300278.2896910699831
2411901021.836631771168.163368228995
2510401022.1079685732617.8920314267366
2610901022.1368379200467.8631620799557
2710501022.2463372336227.7536627663783
288501022.29111862796-172.29111862796
2911001022.0131215726177.9868784273934
308501022.13895581602-172.138955816018
3110401021.8612042800718.1387957199266
329901021.89047178868-31.890471788683
3310401021.8390155248818.1609844751204
3411001021.8683188357378.1316811642671
3510301021.994386722848.00561327715548
3612901022.00730402778267.992695972218
3710401022.4397185418317.5602814581677
3811701022.46805259977147.531947400235
3910401022.7060999656117.2939000343894
408601022.73400420887-162.734004208867
4110901022.4714278535967.5285721464104
428701022.58038729595-152.580387295948
4310801022.3341941159957.6658058840073
4410001022.42723967956-22.4272396795599
459801022.39105263382-42.3910526338184
4610801022.3226533576457.6773466423566
4710401022.4157175425817.5842824574183
4812801022.44409032687257.55590967313
4911401022.85966476302117.140335236976
5012201023.04867432149196.951325678512
5110801023.3664613845956.6335386154137
527901023.45784135295-233.457841352949
5310201023.08114989629-3.0811498962895
548301023.07617836552-193.076178365516
5511501022.76464397261127.235356027389
5610301022.969942159747.03005784026084
579001022.98128537577-122.981285375769
5811401022.78285126338117.217148736624
5910101022.9719847628-12.9719847627998
6012701022.95105406367247.048945936327
6110901023.3496751884666.6503248115376
6210901023.4572175515566.5427824484515
639801023.5645863917-43.5645863917015
648501023.49429358247-173.494293582467
6510101023.21435516706-13.214355167064
668101023.19303339578-213.193033395785
6710701022.8490398343247.1509601656826
6810401022.925119368717.0748806313017
698801022.95267021737-142.952670217366
7011101022.7220116570687.2779883429356
7110101022.86283739405-12.8628373940483
7212301022.84208280758207.157917192419
734901023.17633852216-533.176338522161
7410401022.3160419887517.6839580112525
7510101022.34457560263-12.344575602629
768601022.32465724761-162.324657247612
7710101022.06274138633-12.0627413863328
788001022.04327777955-222.043277779551
7911301021.6850040747108.3149959253
8010401021.8597736748818.1402263251158
819401021.88904349182-81.8890434918196
8210701021.7569129842448.243087015764
8310301021.834754699118.16524530088986
8413201021.84792957526298.152070424739
8510401022.3290071739617.6709928260448
8610701022.3575198681147.6424801318911
8710701022.4343924851847.5656075148236
887701022.5111410659-252.511141065896
8910101022.10370652011-12.1037065201141
908101022.08417681482-212.084176814821
9111501021.74197242779128.258027572214
9210301021.948920727128.05107927287941
938901021.96191139285-131.96191139285
9410101021.74898676227-11.7489867622701
9511201021.7300294082998.2699705917091
9612501021.88859104903228.111408950971
979901022.25665587144-32.2566558714412
9810201022.20460875828-2.20460875828041
9911101022.2010515537887.7989484462225
1008301022.34271787602-192.342717876021
10110301022.032366944337.96763305567026
1028701022.045222967-152.045222967004
10312601021.79989329127238.200106708734
1049801022.18423653993-42.1842365399339
1059401022.11617096793-82.1161709679309
1069701021.98367398313-51.9836739831309
10711001021.8997967153578.100203284652
10813201022.02581381193297.974186188074

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 970 & 1020 & -50 \tabularnewline
3 & 1030 & 1019.91932345162 & 10.0806765483815 \tabularnewline
4 & 970 & 1019.9355889354 & -49.935588935404 \tabularnewline
5 & 1070 & 1019.85501631627 & 50.1449836837301 \tabularnewline
6 & 1650 & 1019.93592680031 & 630.064073199685 \tabularnewline
7 & 1010 & 1020.95255469401 & -10.9525546940146 \tabularnewline
8 & 980 & 1020.93488240784 & -40.9348824078411 \tabularnewline
9 & 1050 & 1020.86883270742 & 29.1311672925802 \tabularnewline
10 & 1010 & 1020.91583674797 & -10.9158367479696 \tabularnewline
11 & 1040 & 1020.89822370734 & 19.1017762926608 \tabularnewline
12 & 1120 & 1020.92904501492 & 99.0709549850758 \tabularnewline
13 & 1090 & 1021.08889906879 & 68.9111009312145 \tabularnewline
14 & 1060 & 1021.20008926415 & 38.7999107358484 \tabularnewline
15 & 990 & 1021.26269412167 & -31.2626941216653 \tabularnewline
16 & 950 & 1021.21225079657 & -71.2122507965684 \tabularnewline
17 & 1540 & 1021.09734762463 & 518.902652375367 \tabularnewline
18 & 870 & 1021.93461312343 & -151.934613123427 \tabularnewline
19 & 1070 & 1021.6894619201 & 48.3105380799025 \tabularnewline
20 & 1050 & 1021.76741246935 & 28.2325875306476 \tabularnewline
21 & 1020 & 1021.81296662363 & -1.81296662362945 \tabularnewline
22 & 960 & 1021.81004134584 & -61.810041345839 \tabularnewline
23 & 1100 & 1021.71030893002 & 78.2896910699831 \tabularnewline
24 & 1190 & 1021.836631771 & 168.163368228995 \tabularnewline
25 & 1040 & 1022.10796857326 & 17.8920314267366 \tabularnewline
26 & 1090 & 1022.13683792004 & 67.8631620799557 \tabularnewline
27 & 1050 & 1022.24633723362 & 27.7536627663783 \tabularnewline
28 & 850 & 1022.29111862796 & -172.29111862796 \tabularnewline
29 & 1100 & 1022.01312157261 & 77.9868784273934 \tabularnewline
30 & 850 & 1022.13895581602 & -172.138955816018 \tabularnewline
31 & 1040 & 1021.86120428007 & 18.1387957199266 \tabularnewline
32 & 990 & 1021.89047178868 & -31.890471788683 \tabularnewline
33 & 1040 & 1021.83901552488 & 18.1609844751204 \tabularnewline
34 & 1100 & 1021.86831883573 & 78.1316811642671 \tabularnewline
35 & 1030 & 1021.99438672284 & 8.00561327715548 \tabularnewline
36 & 1290 & 1022.00730402778 & 267.992695972218 \tabularnewline
37 & 1040 & 1022.43971854183 & 17.5602814581677 \tabularnewline
38 & 1170 & 1022.46805259977 & 147.531947400235 \tabularnewline
39 & 1040 & 1022.70609996561 & 17.2939000343894 \tabularnewline
40 & 860 & 1022.73400420887 & -162.734004208867 \tabularnewline
41 & 1090 & 1022.47142785359 & 67.5285721464104 \tabularnewline
42 & 870 & 1022.58038729595 & -152.580387295948 \tabularnewline
43 & 1080 & 1022.33419411599 & 57.6658058840073 \tabularnewline
44 & 1000 & 1022.42723967956 & -22.4272396795599 \tabularnewline
45 & 980 & 1022.39105263382 & -42.3910526338184 \tabularnewline
46 & 1080 & 1022.32265335764 & 57.6773466423566 \tabularnewline
47 & 1040 & 1022.41571754258 & 17.5842824574183 \tabularnewline
48 & 1280 & 1022.44409032687 & 257.55590967313 \tabularnewline
49 & 1140 & 1022.85966476302 & 117.140335236976 \tabularnewline
50 & 1220 & 1023.04867432149 & 196.951325678512 \tabularnewline
51 & 1080 & 1023.36646138459 & 56.6335386154137 \tabularnewline
52 & 790 & 1023.45784135295 & -233.457841352949 \tabularnewline
53 & 1020 & 1023.08114989629 & -3.0811498962895 \tabularnewline
54 & 830 & 1023.07617836552 & -193.076178365516 \tabularnewline
55 & 1150 & 1022.76464397261 & 127.235356027389 \tabularnewline
56 & 1030 & 1022.96994215974 & 7.03005784026084 \tabularnewline
57 & 900 & 1022.98128537577 & -122.981285375769 \tabularnewline
58 & 1140 & 1022.78285126338 & 117.217148736624 \tabularnewline
59 & 1010 & 1022.9719847628 & -12.9719847627998 \tabularnewline
60 & 1270 & 1022.95105406367 & 247.048945936327 \tabularnewline
61 & 1090 & 1023.34967518846 & 66.6503248115376 \tabularnewline
62 & 1090 & 1023.45721755155 & 66.5427824484515 \tabularnewline
63 & 980 & 1023.5645863917 & -43.5645863917015 \tabularnewline
64 & 850 & 1023.49429358247 & -173.494293582467 \tabularnewline
65 & 1010 & 1023.21435516706 & -13.214355167064 \tabularnewline
66 & 810 & 1023.19303339578 & -213.193033395785 \tabularnewline
67 & 1070 & 1022.84903983432 & 47.1509601656826 \tabularnewline
68 & 1040 & 1022.9251193687 & 17.0748806313017 \tabularnewline
69 & 880 & 1022.95267021737 & -142.952670217366 \tabularnewline
70 & 1110 & 1022.72201165706 & 87.2779883429356 \tabularnewline
71 & 1010 & 1022.86283739405 & -12.8628373940483 \tabularnewline
72 & 1230 & 1022.84208280758 & 207.157917192419 \tabularnewline
73 & 490 & 1023.17633852216 & -533.176338522161 \tabularnewline
74 & 1040 & 1022.31604198875 & 17.6839580112525 \tabularnewline
75 & 1010 & 1022.34457560263 & -12.344575602629 \tabularnewline
76 & 860 & 1022.32465724761 & -162.324657247612 \tabularnewline
77 & 1010 & 1022.06274138633 & -12.0627413863328 \tabularnewline
78 & 800 & 1022.04327777955 & -222.043277779551 \tabularnewline
79 & 1130 & 1021.6850040747 & 108.3149959253 \tabularnewline
80 & 1040 & 1021.85977367488 & 18.1402263251158 \tabularnewline
81 & 940 & 1021.88904349182 & -81.8890434918196 \tabularnewline
82 & 1070 & 1021.75691298424 & 48.243087015764 \tabularnewline
83 & 1030 & 1021.83475469911 & 8.16524530088986 \tabularnewline
84 & 1320 & 1021.84792957526 & 298.152070424739 \tabularnewline
85 & 1040 & 1022.32900717396 & 17.6709928260448 \tabularnewline
86 & 1070 & 1022.35751986811 & 47.6424801318911 \tabularnewline
87 & 1070 & 1022.43439248518 & 47.5656075148236 \tabularnewline
88 & 770 & 1022.5111410659 & -252.511141065896 \tabularnewline
89 & 1010 & 1022.10370652011 & -12.1037065201141 \tabularnewline
90 & 810 & 1022.08417681482 & -212.084176814821 \tabularnewline
91 & 1150 & 1021.74197242779 & 128.258027572214 \tabularnewline
92 & 1030 & 1021.94892072712 & 8.05107927287941 \tabularnewline
93 & 890 & 1021.96191139285 & -131.96191139285 \tabularnewline
94 & 1010 & 1021.74898676227 & -11.7489867622701 \tabularnewline
95 & 1120 & 1021.73002940829 & 98.2699705917091 \tabularnewline
96 & 1250 & 1021.88859104903 & 228.111408950971 \tabularnewline
97 & 990 & 1022.25665587144 & -32.2566558714412 \tabularnewline
98 & 1020 & 1022.20460875828 & -2.20460875828041 \tabularnewline
99 & 1110 & 1022.20105155378 & 87.7989484462225 \tabularnewline
100 & 830 & 1022.34271787602 & -192.342717876021 \tabularnewline
101 & 1030 & 1022.03236694433 & 7.96763305567026 \tabularnewline
102 & 870 & 1022.045222967 & -152.045222967004 \tabularnewline
103 & 1260 & 1021.79989329127 & 238.200106708734 \tabularnewline
104 & 980 & 1022.18423653993 & -42.1842365399339 \tabularnewline
105 & 940 & 1022.11617096793 & -82.1161709679309 \tabularnewline
106 & 970 & 1021.98367398313 & -51.9836739831309 \tabularnewline
107 & 1100 & 1021.89979671535 & 78.100203284652 \tabularnewline
108 & 1320 & 1022.02581381193 & 297.974186188074 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295813&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]970[/C][C]1020[/C][C]-50[/C][/ROW]
[ROW][C]3[/C][C]1030[/C][C]1019.91932345162[/C][C]10.0806765483815[/C][/ROW]
[ROW][C]4[/C][C]970[/C][C]1019.9355889354[/C][C]-49.935588935404[/C][/ROW]
[ROW][C]5[/C][C]1070[/C][C]1019.85501631627[/C][C]50.1449836837301[/C][/ROW]
[ROW][C]6[/C][C]1650[/C][C]1019.93592680031[/C][C]630.064073199685[/C][/ROW]
[ROW][C]7[/C][C]1010[/C][C]1020.95255469401[/C][C]-10.9525546940146[/C][/ROW]
[ROW][C]8[/C][C]980[/C][C]1020.93488240784[/C][C]-40.9348824078411[/C][/ROW]
[ROW][C]9[/C][C]1050[/C][C]1020.86883270742[/C][C]29.1311672925802[/C][/ROW]
[ROW][C]10[/C][C]1010[/C][C]1020.91583674797[/C][C]-10.9158367479696[/C][/ROW]
[ROW][C]11[/C][C]1040[/C][C]1020.89822370734[/C][C]19.1017762926608[/C][/ROW]
[ROW][C]12[/C][C]1120[/C][C]1020.92904501492[/C][C]99.0709549850758[/C][/ROW]
[ROW][C]13[/C][C]1090[/C][C]1021.08889906879[/C][C]68.9111009312145[/C][/ROW]
[ROW][C]14[/C][C]1060[/C][C]1021.20008926415[/C][C]38.7999107358484[/C][/ROW]
[ROW][C]15[/C][C]990[/C][C]1021.26269412167[/C][C]-31.2626941216653[/C][/ROW]
[ROW][C]16[/C][C]950[/C][C]1021.21225079657[/C][C]-71.2122507965684[/C][/ROW]
[ROW][C]17[/C][C]1540[/C][C]1021.09734762463[/C][C]518.902652375367[/C][/ROW]
[ROW][C]18[/C][C]870[/C][C]1021.93461312343[/C][C]-151.934613123427[/C][/ROW]
[ROW][C]19[/C][C]1070[/C][C]1021.6894619201[/C][C]48.3105380799025[/C][/ROW]
[ROW][C]20[/C][C]1050[/C][C]1021.76741246935[/C][C]28.2325875306476[/C][/ROW]
[ROW][C]21[/C][C]1020[/C][C]1021.81296662363[/C][C]-1.81296662362945[/C][/ROW]
[ROW][C]22[/C][C]960[/C][C]1021.81004134584[/C][C]-61.810041345839[/C][/ROW]
[ROW][C]23[/C][C]1100[/C][C]1021.71030893002[/C][C]78.2896910699831[/C][/ROW]
[ROW][C]24[/C][C]1190[/C][C]1021.836631771[/C][C]168.163368228995[/C][/ROW]
[ROW][C]25[/C][C]1040[/C][C]1022.10796857326[/C][C]17.8920314267366[/C][/ROW]
[ROW][C]26[/C][C]1090[/C][C]1022.13683792004[/C][C]67.8631620799557[/C][/ROW]
[ROW][C]27[/C][C]1050[/C][C]1022.24633723362[/C][C]27.7536627663783[/C][/ROW]
[ROW][C]28[/C][C]850[/C][C]1022.29111862796[/C][C]-172.29111862796[/C][/ROW]
[ROW][C]29[/C][C]1100[/C][C]1022.01312157261[/C][C]77.9868784273934[/C][/ROW]
[ROW][C]30[/C][C]850[/C][C]1022.13895581602[/C][C]-172.138955816018[/C][/ROW]
[ROW][C]31[/C][C]1040[/C][C]1021.86120428007[/C][C]18.1387957199266[/C][/ROW]
[ROW][C]32[/C][C]990[/C][C]1021.89047178868[/C][C]-31.890471788683[/C][/ROW]
[ROW][C]33[/C][C]1040[/C][C]1021.83901552488[/C][C]18.1609844751204[/C][/ROW]
[ROW][C]34[/C][C]1100[/C][C]1021.86831883573[/C][C]78.1316811642671[/C][/ROW]
[ROW][C]35[/C][C]1030[/C][C]1021.99438672284[/C][C]8.00561327715548[/C][/ROW]
[ROW][C]36[/C][C]1290[/C][C]1022.00730402778[/C][C]267.992695972218[/C][/ROW]
[ROW][C]37[/C][C]1040[/C][C]1022.43971854183[/C][C]17.5602814581677[/C][/ROW]
[ROW][C]38[/C][C]1170[/C][C]1022.46805259977[/C][C]147.531947400235[/C][/ROW]
[ROW][C]39[/C][C]1040[/C][C]1022.70609996561[/C][C]17.2939000343894[/C][/ROW]
[ROW][C]40[/C][C]860[/C][C]1022.73400420887[/C][C]-162.734004208867[/C][/ROW]
[ROW][C]41[/C][C]1090[/C][C]1022.47142785359[/C][C]67.5285721464104[/C][/ROW]
[ROW][C]42[/C][C]870[/C][C]1022.58038729595[/C][C]-152.580387295948[/C][/ROW]
[ROW][C]43[/C][C]1080[/C][C]1022.33419411599[/C][C]57.6658058840073[/C][/ROW]
[ROW][C]44[/C][C]1000[/C][C]1022.42723967956[/C][C]-22.4272396795599[/C][/ROW]
[ROW][C]45[/C][C]980[/C][C]1022.39105263382[/C][C]-42.3910526338184[/C][/ROW]
[ROW][C]46[/C][C]1080[/C][C]1022.32265335764[/C][C]57.6773466423566[/C][/ROW]
[ROW][C]47[/C][C]1040[/C][C]1022.41571754258[/C][C]17.5842824574183[/C][/ROW]
[ROW][C]48[/C][C]1280[/C][C]1022.44409032687[/C][C]257.55590967313[/C][/ROW]
[ROW][C]49[/C][C]1140[/C][C]1022.85966476302[/C][C]117.140335236976[/C][/ROW]
[ROW][C]50[/C][C]1220[/C][C]1023.04867432149[/C][C]196.951325678512[/C][/ROW]
[ROW][C]51[/C][C]1080[/C][C]1023.36646138459[/C][C]56.6335386154137[/C][/ROW]
[ROW][C]52[/C][C]790[/C][C]1023.45784135295[/C][C]-233.457841352949[/C][/ROW]
[ROW][C]53[/C][C]1020[/C][C]1023.08114989629[/C][C]-3.0811498962895[/C][/ROW]
[ROW][C]54[/C][C]830[/C][C]1023.07617836552[/C][C]-193.076178365516[/C][/ROW]
[ROW][C]55[/C][C]1150[/C][C]1022.76464397261[/C][C]127.235356027389[/C][/ROW]
[ROW][C]56[/C][C]1030[/C][C]1022.96994215974[/C][C]7.03005784026084[/C][/ROW]
[ROW][C]57[/C][C]900[/C][C]1022.98128537577[/C][C]-122.981285375769[/C][/ROW]
[ROW][C]58[/C][C]1140[/C][C]1022.78285126338[/C][C]117.217148736624[/C][/ROW]
[ROW][C]59[/C][C]1010[/C][C]1022.9719847628[/C][C]-12.9719847627998[/C][/ROW]
[ROW][C]60[/C][C]1270[/C][C]1022.95105406367[/C][C]247.048945936327[/C][/ROW]
[ROW][C]61[/C][C]1090[/C][C]1023.34967518846[/C][C]66.6503248115376[/C][/ROW]
[ROW][C]62[/C][C]1090[/C][C]1023.45721755155[/C][C]66.5427824484515[/C][/ROW]
[ROW][C]63[/C][C]980[/C][C]1023.5645863917[/C][C]-43.5645863917015[/C][/ROW]
[ROW][C]64[/C][C]850[/C][C]1023.49429358247[/C][C]-173.494293582467[/C][/ROW]
[ROW][C]65[/C][C]1010[/C][C]1023.21435516706[/C][C]-13.214355167064[/C][/ROW]
[ROW][C]66[/C][C]810[/C][C]1023.19303339578[/C][C]-213.193033395785[/C][/ROW]
[ROW][C]67[/C][C]1070[/C][C]1022.84903983432[/C][C]47.1509601656826[/C][/ROW]
[ROW][C]68[/C][C]1040[/C][C]1022.9251193687[/C][C]17.0748806313017[/C][/ROW]
[ROW][C]69[/C][C]880[/C][C]1022.95267021737[/C][C]-142.952670217366[/C][/ROW]
[ROW][C]70[/C][C]1110[/C][C]1022.72201165706[/C][C]87.2779883429356[/C][/ROW]
[ROW][C]71[/C][C]1010[/C][C]1022.86283739405[/C][C]-12.8628373940483[/C][/ROW]
[ROW][C]72[/C][C]1230[/C][C]1022.84208280758[/C][C]207.157917192419[/C][/ROW]
[ROW][C]73[/C][C]490[/C][C]1023.17633852216[/C][C]-533.176338522161[/C][/ROW]
[ROW][C]74[/C][C]1040[/C][C]1022.31604198875[/C][C]17.6839580112525[/C][/ROW]
[ROW][C]75[/C][C]1010[/C][C]1022.34457560263[/C][C]-12.344575602629[/C][/ROW]
[ROW][C]76[/C][C]860[/C][C]1022.32465724761[/C][C]-162.324657247612[/C][/ROW]
[ROW][C]77[/C][C]1010[/C][C]1022.06274138633[/C][C]-12.0627413863328[/C][/ROW]
[ROW][C]78[/C][C]800[/C][C]1022.04327777955[/C][C]-222.043277779551[/C][/ROW]
[ROW][C]79[/C][C]1130[/C][C]1021.6850040747[/C][C]108.3149959253[/C][/ROW]
[ROW][C]80[/C][C]1040[/C][C]1021.85977367488[/C][C]18.1402263251158[/C][/ROW]
[ROW][C]81[/C][C]940[/C][C]1021.88904349182[/C][C]-81.8890434918196[/C][/ROW]
[ROW][C]82[/C][C]1070[/C][C]1021.75691298424[/C][C]48.243087015764[/C][/ROW]
[ROW][C]83[/C][C]1030[/C][C]1021.83475469911[/C][C]8.16524530088986[/C][/ROW]
[ROW][C]84[/C][C]1320[/C][C]1021.84792957526[/C][C]298.152070424739[/C][/ROW]
[ROW][C]85[/C][C]1040[/C][C]1022.32900717396[/C][C]17.6709928260448[/C][/ROW]
[ROW][C]86[/C][C]1070[/C][C]1022.35751986811[/C][C]47.6424801318911[/C][/ROW]
[ROW][C]87[/C][C]1070[/C][C]1022.43439248518[/C][C]47.5656075148236[/C][/ROW]
[ROW][C]88[/C][C]770[/C][C]1022.5111410659[/C][C]-252.511141065896[/C][/ROW]
[ROW][C]89[/C][C]1010[/C][C]1022.10370652011[/C][C]-12.1037065201141[/C][/ROW]
[ROW][C]90[/C][C]810[/C][C]1022.08417681482[/C][C]-212.084176814821[/C][/ROW]
[ROW][C]91[/C][C]1150[/C][C]1021.74197242779[/C][C]128.258027572214[/C][/ROW]
[ROW][C]92[/C][C]1030[/C][C]1021.94892072712[/C][C]8.05107927287941[/C][/ROW]
[ROW][C]93[/C][C]890[/C][C]1021.96191139285[/C][C]-131.96191139285[/C][/ROW]
[ROW][C]94[/C][C]1010[/C][C]1021.74898676227[/C][C]-11.7489867622701[/C][/ROW]
[ROW][C]95[/C][C]1120[/C][C]1021.73002940829[/C][C]98.2699705917091[/C][/ROW]
[ROW][C]96[/C][C]1250[/C][C]1021.88859104903[/C][C]228.111408950971[/C][/ROW]
[ROW][C]97[/C][C]990[/C][C]1022.25665587144[/C][C]-32.2566558714412[/C][/ROW]
[ROW][C]98[/C][C]1020[/C][C]1022.20460875828[/C][C]-2.20460875828041[/C][/ROW]
[ROW][C]99[/C][C]1110[/C][C]1022.20105155378[/C][C]87.7989484462225[/C][/ROW]
[ROW][C]100[/C][C]830[/C][C]1022.34271787602[/C][C]-192.342717876021[/C][/ROW]
[ROW][C]101[/C][C]1030[/C][C]1022.03236694433[/C][C]7.96763305567026[/C][/ROW]
[ROW][C]102[/C][C]870[/C][C]1022.045222967[/C][C]-152.045222967004[/C][/ROW]
[ROW][C]103[/C][C]1260[/C][C]1021.79989329127[/C][C]238.200106708734[/C][/ROW]
[ROW][C]104[/C][C]980[/C][C]1022.18423653993[/C][C]-42.1842365399339[/C][/ROW]
[ROW][C]105[/C][C]940[/C][C]1022.11617096793[/C][C]-82.1161709679309[/C][/ROW]
[ROW][C]106[/C][C]970[/C][C]1021.98367398313[/C][C]-51.9836739831309[/C][/ROW]
[ROW][C]107[/C][C]1100[/C][C]1021.89979671535[/C][C]78.100203284652[/C][/ROW]
[ROW][C]108[/C][C]1320[/C][C]1022.02581381193[/C][C]297.974186188074[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295813&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295813&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
29701020-50
310301019.9193234516210.0806765483815
49701019.9355889354-49.935588935404
510701019.8550163162750.1449836837301
616501019.93592680031630.064073199685
710101020.95255469401-10.9525546940146
89801020.93488240784-40.9348824078411
910501020.8688327074229.1311672925802
1010101020.91583674797-10.9158367479696
1110401020.8982237073419.1017762926608
1211201020.9290450149299.0709549850758
1310901021.0888990687968.9111009312145
1410601021.2000892641538.7999107358484
159901021.26269412167-31.2626941216653
169501021.21225079657-71.2122507965684
1715401021.09734762463518.902652375367
188701021.93461312343-151.934613123427
1910701021.689461920148.3105380799025
2010501021.7674124693528.2325875306476
2110201021.81296662363-1.81296662362945
229601021.81004134584-61.810041345839
2311001021.7103089300278.2896910699831
2411901021.836631771168.163368228995
2510401022.1079685732617.8920314267366
2610901022.1368379200467.8631620799557
2710501022.2463372336227.7536627663783
288501022.29111862796-172.29111862796
2911001022.0131215726177.9868784273934
308501022.13895581602-172.138955816018
3110401021.8612042800718.1387957199266
329901021.89047178868-31.890471788683
3310401021.8390155248818.1609844751204
3411001021.8683188357378.1316811642671
3510301021.994386722848.00561327715548
3612901022.00730402778267.992695972218
3710401022.4397185418317.5602814581677
3811701022.46805259977147.531947400235
3910401022.7060999656117.2939000343894
408601022.73400420887-162.734004208867
4110901022.4714278535967.5285721464104
428701022.58038729595-152.580387295948
4310801022.3341941159957.6658058840073
4410001022.42723967956-22.4272396795599
459801022.39105263382-42.3910526338184
4610801022.3226533576457.6773466423566
4710401022.4157175425817.5842824574183
4812801022.44409032687257.55590967313
4911401022.85966476302117.140335236976
5012201023.04867432149196.951325678512
5110801023.3664613845956.6335386154137
527901023.45784135295-233.457841352949
5310201023.08114989629-3.0811498962895
548301023.07617836552-193.076178365516
5511501022.76464397261127.235356027389
5610301022.969942159747.03005784026084
579001022.98128537577-122.981285375769
5811401022.78285126338117.217148736624
5910101022.9719847628-12.9719847627998
6012701022.95105406367247.048945936327
6110901023.3496751884666.6503248115376
6210901023.4572175515566.5427824484515
639801023.5645863917-43.5645863917015
648501023.49429358247-173.494293582467
6510101023.21435516706-13.214355167064
668101023.19303339578-213.193033395785
6710701022.8490398343247.1509601656826
6810401022.925119368717.0748806313017
698801022.95267021737-142.952670217366
7011101022.7220116570687.2779883429356
7110101022.86283739405-12.8628373940483
7212301022.84208280758207.157917192419
734901023.17633852216-533.176338522161
7410401022.3160419887517.6839580112525
7510101022.34457560263-12.344575602629
768601022.32465724761-162.324657247612
7710101022.06274138633-12.0627413863328
788001022.04327777955-222.043277779551
7911301021.6850040747108.3149959253
8010401021.8597736748818.1402263251158
819401021.88904349182-81.8890434918196
8210701021.7569129842448.243087015764
8310301021.834754699118.16524530088986
8413201021.84792957526298.152070424739
8510401022.3290071739617.6709928260448
8610701022.3575198681147.6424801318911
8710701022.4343924851847.5656075148236
887701022.5111410659-252.511141065896
8910101022.10370652011-12.1037065201141
908101022.08417681482-212.084176814821
9111501021.74197242779128.258027572214
9210301021.948920727128.05107927287941
938901021.96191139285-131.96191139285
9410101021.74898676227-11.7489867622701
9511201021.7300294082998.2699705917091
9612501021.88859104903228.111408950971
979901022.25665587144-32.2566558714412
9810201022.20460875828-2.20460875828041
9911101022.2010515537887.7989484462225
1008301022.34271787602-192.342717876021
10110301022.032366944337.96763305567026
1028701022.045222967-152.045222967004
10312601021.79989329127238.200106708734
1049801022.18423653993-42.1842365399339
1059401022.11617096793-82.1161709679309
1069701021.98367398313-51.9836739831309
10711001021.8997967153578.100203284652
10813201022.02581381193297.974186188074







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1091022.5066043889729.4462677147521315.56694106304
1101022.5066043889729.4458862263171315.56732255147
1111022.5066043889729.445504738381315.56770403941
1121022.5066043889729.4451232509391315.56808552685
1131022.5066043889729.4447417639941315.5684670138
1141022.5066043889729.4443602775461315.56884850024
1151022.5066043889729.4439787915951315.5692299862
1161022.5066043889729.443597306141315.56961147165
1171022.5066043889729.4432158211821315.56999295661
1181022.5066043889729.442834336721315.57037444107
1191022.5066043889729.4424528527551315.57075592504
1201022.5066043889729.4420713692871315.5711374085

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 1022.5066043889 & 729.446267714752 & 1315.56694106304 \tabularnewline
110 & 1022.5066043889 & 729.445886226317 & 1315.56732255147 \tabularnewline
111 & 1022.5066043889 & 729.44550473838 & 1315.56770403941 \tabularnewline
112 & 1022.5066043889 & 729.445123250939 & 1315.56808552685 \tabularnewline
113 & 1022.5066043889 & 729.444741763994 & 1315.5684670138 \tabularnewline
114 & 1022.5066043889 & 729.444360277546 & 1315.56884850024 \tabularnewline
115 & 1022.5066043889 & 729.443978791595 & 1315.5692299862 \tabularnewline
116 & 1022.5066043889 & 729.44359730614 & 1315.56961147165 \tabularnewline
117 & 1022.5066043889 & 729.443215821182 & 1315.56999295661 \tabularnewline
118 & 1022.5066043889 & 729.44283433672 & 1315.57037444107 \tabularnewline
119 & 1022.5066043889 & 729.442452852755 & 1315.57075592504 \tabularnewline
120 & 1022.5066043889 & 729.442071369287 & 1315.5711374085 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295813&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]109[/C][C]1022.5066043889[/C][C]729.446267714752[/C][C]1315.56694106304[/C][/ROW]
[ROW][C]110[/C][C]1022.5066043889[/C][C]729.445886226317[/C][C]1315.56732255147[/C][/ROW]
[ROW][C]111[/C][C]1022.5066043889[/C][C]729.44550473838[/C][C]1315.56770403941[/C][/ROW]
[ROW][C]112[/C][C]1022.5066043889[/C][C]729.445123250939[/C][C]1315.56808552685[/C][/ROW]
[ROW][C]113[/C][C]1022.5066043889[/C][C]729.444741763994[/C][C]1315.5684670138[/C][/ROW]
[ROW][C]114[/C][C]1022.5066043889[/C][C]729.444360277546[/C][C]1315.56884850024[/C][/ROW]
[ROW][C]115[/C][C]1022.5066043889[/C][C]729.443978791595[/C][C]1315.5692299862[/C][/ROW]
[ROW][C]116[/C][C]1022.5066043889[/C][C]729.44359730614[/C][C]1315.56961147165[/C][/ROW]
[ROW][C]117[/C][C]1022.5066043889[/C][C]729.443215821182[/C][C]1315.56999295661[/C][/ROW]
[ROW][C]118[/C][C]1022.5066043889[/C][C]729.44283433672[/C][C]1315.57037444107[/C][/ROW]
[ROW][C]119[/C][C]1022.5066043889[/C][C]729.442452852755[/C][C]1315.57075592504[/C][/ROW]
[ROW][C]120[/C][C]1022.5066043889[/C][C]729.442071369287[/C][C]1315.5711374085[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295813&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295813&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
1091022.5066043889729.4462677147521315.56694106304
1101022.5066043889729.4458862263171315.56732255147
1111022.5066043889729.445504738381315.56770403941
1121022.5066043889729.4451232509391315.56808552685
1131022.5066043889729.4447417639941315.5684670138
1141022.5066043889729.4443602775461315.56884850024
1151022.5066043889729.4439787915951315.5692299862
1161022.5066043889729.443597306141315.56961147165
1171022.5066043889729.4432158211821315.56999295661
1181022.5066043889729.442834336721315.57037444107
1191022.5066043889729.4424528527551315.57075592504
1201022.5066043889729.4420713692871315.5711374085



Parameters (Session):
par1 = 0 ; par2 = no ; par3 = 512 ;
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=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')