Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 04 Aug 2011 04:10:28 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Aug/04/t1312445707pwws3mwz9nyn7wt.htm/, Retrieved Wed, 15 May 2024 22:36:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=123373, Retrieved Wed, 15 May 2024 22:36:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsMarin Peeters
Estimated Impact227
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks 1 - Sta...] [2011-08-04 08:10:28] [3f8170910ab21fde7eba151af40022ac] [Current]
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Dataseries X:
5740
5639
5538
5336
7380
7279
5740
4718
4819
4819
4920
5133
4516
3898
3392
3392
5336
5538
3999
2258
3179
3179
3898
4313
4212
3179
3696
3493
5234
4819
3179
1954
3078
3392
3696
4100
3280
2572
2876
2977
5639
5639
4100
3898
4516
4212
5032
6054
6257
4819
4414
3999
6773
6976
6459
6976
6874
6054
6976
7998
8413
7178
6358
6976
9638
10458
10256
10660
10559
9537
11278
11693
12300
10458
9739
10559
12513
14254
13839
13839
14042
13333
15176
15176
14862
13120
13434
13637
14973
16714
15479
16097
15580
15277
17636
17119
16400
15378
16400
16917
17534
18354
17534
18040
17423
17322
19883
20096
19276
17838
19063
19579
20197
21118
20197
20916
20602
19478
21837
21837




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ yule.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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123373&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123373&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123373&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'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999952904241852
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999952904241852 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123373&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]0.999952904241852[/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=123373&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123373&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
alpha0.999952904241852
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
256395740-101
355385639.00475667157-101.004756671573
453365538.00475689559-202.004756895592
573805336.009513567182043.99048643282
672797379.9037367184-100.903736718395
757407279.00475213798-1539.00475213798
847185740.0724805956-1022.0724805956
948194718.04813527836100.951864721645
1048194818.99524559540.00475440460559184
1149204818.99999977609101.000000223912
1251334919.99524332842213.004756671584
1345165132.9899683795-616.989968379496
1438984516.02905761033-618.029057610331
1533923898.02910654703-506.029106547026
1633923392.02383182442-0.0238318244178117
1753363392.000001122381943.99999887762
1855385335.90844584621202.091554153787
1939995537.99048234504-1538.99048234504
2022583999.07247992355-1741.07247992355
2131792258.08199712843920.918002871567
2231793178.956628668460.0433713315374007
2338983178.99999795739719.000002042606
2443133897.9661381498415.033861850205
2542124312.98045366562-100.980453665619
2631794212.00475575102-1033.00475575102
2736963179.04865014214516.951349857858
2834933695.97565378425-202.975653784253
2952343493.00955929231740.9904407077
3048195233.91800673527-414.918006735266
3131794819.0195408781-1640.0195408781
3219543179.07723796366-1225.07723796366
3330781954.057695941311123.94230405869
3433923077.94706708508314.052932914924
3536963391.98520943903304.014790560974
3641003695.98568219295404.01431780705
3732804099.9809726394-819.9809726394
3825723280.03861762557-708.038617625573
3928762572.03334561549303.966654384505
4029772875.98568445996101.01431554004
4156392976.995242654232662.00475734577
4256395638.874630867760.125369132240849
4341005638.99999409565-1538.99999409565
4438984100.07248037151-202.072480371512
4545163898.00951675666617.990483243336
4642124515.97089526966-303.970895269664
4750324212.01431573977819.985684260232
4860545031.961382152531022.03861784747
4962576053.95186631644203.048133683564
5048196256.9904372942-1437.9904372942
5144144819.06772324985-405.067723249854
5239994414.01907697153-415.019076971527
5367733999.019545638082773.98045436192
5469766772.86935728741203.130642712586
5564596975.99043340838-516.990433408379
5669766459.02434805642516.975651943583
5768746975.97565263973-101.975652639728
5860546874.00480262067-820.004802620674
5969766054.03861874786921.961381252136
6079986975.956579529771022.04342047023
6184137997.95186609025415.048133909747
6271788412.98045299347-1234.98045299347
6363587178.05816234073-820.058162340732
6469766358.03862126088617.961378739119
6596386975.970896640362662.02910335964
66104589637.87462972117820.125370278834
671025610457.9613755739-201.96137557391
681066010256.0095115241403.9904884759
691055910659.9809737617-100.980973761662
70953710559.0047557755-1022.00475577552
71112789537.04813208881740.9518679112
721169311277.9180085519415.081991448118
731230011692.9804513989607.019548601082
741045812299.9714119541-1841.97141195415
75973910458.0867490401-719.086749040132
76105599739.03386593562819.96613406438
771251310558.96138307331954.03861692674
781425412512.90797306991741.09202693012
791383914253.918001951-414.918001950986
801383913839.0195408779-0.0195408778708952
811404213839.0000009203202.999999079708
821333314041.9904395611-708.990439561139
831517613333.03339044231842.96660955773
841517615175.91320409030.0867959097176936
851486215175.9999959123-313.999995912282
861312014862.0147880679-1742.01478806787
871343413120.0820415071313.917958492852
881363713433.9852157957203.014784204252
891497313636.99043886481336.00956113518
901671414972.93707961681741.06292038317
911547916713.9180033218-1234.91800332178
921609715479.0581593996617.941840600382
931558016096.9708975605-516.970897560526
941527715580.0243471364-303.024347136361
951763615277.01427116142358.98572883863
961711917635.8889017786-516.888901778639
971640017119.0243432747-719.024343274708
981537816400.0338629966-1022.03386299657
991640015378.04813345961021.95186654037
1001691716399.9518704021517.048129597944
1011753416916.9756492263617.024350773663
1021835417533.9709407704820.029059229597
1031753418353.9613801098-819.961380109751
1041804017534.0386167028505.961383297152
1051742318039.9761713651-616.976171365059
1061732217423.0290569605-101.029056960549
1071988317322.004758042560.99524195997
1082009619882.8793879875213.120612012535
1091927620095.9899629232-819.989962923199
1101783819276.038618049-1438.03861804898
1111906317838.0677255191224.93227448104
1121957919062.9423108859516.057689114146
1132019719578.9756958719618.024304128117
1142111820196.9708936768921.029106323156
1152019721117.956623436-920.956623435963
1162091620197.0433731504718.956626849598
1172060220915.9661401926-313.966140192584
1181947820602.0147864734-1124.01478647341
1192183719478.05293632852358.94706367146
1202183721836.88890359960.111096400392853

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 5639 & 5740 & -101 \tabularnewline
3 & 5538 & 5639.00475667157 & -101.004756671573 \tabularnewline
4 & 5336 & 5538.00475689559 & -202.004756895592 \tabularnewline
5 & 7380 & 5336.00951356718 & 2043.99048643282 \tabularnewline
6 & 7279 & 7379.9037367184 & -100.903736718395 \tabularnewline
7 & 5740 & 7279.00475213798 & -1539.00475213798 \tabularnewline
8 & 4718 & 5740.0724805956 & -1022.0724805956 \tabularnewline
9 & 4819 & 4718.04813527836 & 100.951864721645 \tabularnewline
10 & 4819 & 4818.9952455954 & 0.00475440460559184 \tabularnewline
11 & 4920 & 4818.99999977609 & 101.000000223912 \tabularnewline
12 & 5133 & 4919.99524332842 & 213.004756671584 \tabularnewline
13 & 4516 & 5132.9899683795 & -616.989968379496 \tabularnewline
14 & 3898 & 4516.02905761033 & -618.029057610331 \tabularnewline
15 & 3392 & 3898.02910654703 & -506.029106547026 \tabularnewline
16 & 3392 & 3392.02383182442 & -0.0238318244178117 \tabularnewline
17 & 5336 & 3392.00000112238 & 1943.99999887762 \tabularnewline
18 & 5538 & 5335.90844584621 & 202.091554153787 \tabularnewline
19 & 3999 & 5537.99048234504 & -1538.99048234504 \tabularnewline
20 & 2258 & 3999.07247992355 & -1741.07247992355 \tabularnewline
21 & 3179 & 2258.08199712843 & 920.918002871567 \tabularnewline
22 & 3179 & 3178.95662866846 & 0.0433713315374007 \tabularnewline
23 & 3898 & 3178.99999795739 & 719.000002042606 \tabularnewline
24 & 4313 & 3897.9661381498 & 415.033861850205 \tabularnewline
25 & 4212 & 4312.98045366562 & -100.980453665619 \tabularnewline
26 & 3179 & 4212.00475575102 & -1033.00475575102 \tabularnewline
27 & 3696 & 3179.04865014214 & 516.951349857858 \tabularnewline
28 & 3493 & 3695.97565378425 & -202.975653784253 \tabularnewline
29 & 5234 & 3493.0095592923 & 1740.9904407077 \tabularnewline
30 & 4819 & 5233.91800673527 & -414.918006735266 \tabularnewline
31 & 3179 & 4819.0195408781 & -1640.0195408781 \tabularnewline
32 & 1954 & 3179.07723796366 & -1225.07723796366 \tabularnewline
33 & 3078 & 1954.05769594131 & 1123.94230405869 \tabularnewline
34 & 3392 & 3077.94706708508 & 314.052932914924 \tabularnewline
35 & 3696 & 3391.98520943903 & 304.014790560974 \tabularnewline
36 & 4100 & 3695.98568219295 & 404.01431780705 \tabularnewline
37 & 3280 & 4099.9809726394 & -819.9809726394 \tabularnewline
38 & 2572 & 3280.03861762557 & -708.038617625573 \tabularnewline
39 & 2876 & 2572.03334561549 & 303.966654384505 \tabularnewline
40 & 2977 & 2875.98568445996 & 101.01431554004 \tabularnewline
41 & 5639 & 2976.99524265423 & 2662.00475734577 \tabularnewline
42 & 5639 & 5638.87463086776 & 0.125369132240849 \tabularnewline
43 & 4100 & 5638.99999409565 & -1538.99999409565 \tabularnewline
44 & 3898 & 4100.07248037151 & -202.072480371512 \tabularnewline
45 & 4516 & 3898.00951675666 & 617.990483243336 \tabularnewline
46 & 4212 & 4515.97089526966 & -303.970895269664 \tabularnewline
47 & 5032 & 4212.01431573977 & 819.985684260232 \tabularnewline
48 & 6054 & 5031.96138215253 & 1022.03861784747 \tabularnewline
49 & 6257 & 6053.95186631644 & 203.048133683564 \tabularnewline
50 & 4819 & 6256.9904372942 & -1437.9904372942 \tabularnewline
51 & 4414 & 4819.06772324985 & -405.067723249854 \tabularnewline
52 & 3999 & 4414.01907697153 & -415.019076971527 \tabularnewline
53 & 6773 & 3999.01954563808 & 2773.98045436192 \tabularnewline
54 & 6976 & 6772.86935728741 & 203.130642712586 \tabularnewline
55 & 6459 & 6975.99043340838 & -516.990433408379 \tabularnewline
56 & 6976 & 6459.02434805642 & 516.975651943583 \tabularnewline
57 & 6874 & 6975.97565263973 & -101.975652639728 \tabularnewline
58 & 6054 & 6874.00480262067 & -820.004802620674 \tabularnewline
59 & 6976 & 6054.03861874786 & 921.961381252136 \tabularnewline
60 & 7998 & 6975.95657952977 & 1022.04342047023 \tabularnewline
61 & 8413 & 7997.95186609025 & 415.048133909747 \tabularnewline
62 & 7178 & 8412.98045299347 & -1234.98045299347 \tabularnewline
63 & 6358 & 7178.05816234073 & -820.058162340732 \tabularnewline
64 & 6976 & 6358.03862126088 & 617.961378739119 \tabularnewline
65 & 9638 & 6975.97089664036 & 2662.02910335964 \tabularnewline
66 & 10458 & 9637.87462972117 & 820.125370278834 \tabularnewline
67 & 10256 & 10457.9613755739 & -201.96137557391 \tabularnewline
68 & 10660 & 10256.0095115241 & 403.9904884759 \tabularnewline
69 & 10559 & 10659.9809737617 & -100.980973761662 \tabularnewline
70 & 9537 & 10559.0047557755 & -1022.00475577552 \tabularnewline
71 & 11278 & 9537.0481320888 & 1740.9518679112 \tabularnewline
72 & 11693 & 11277.9180085519 & 415.081991448118 \tabularnewline
73 & 12300 & 11692.9804513989 & 607.019548601082 \tabularnewline
74 & 10458 & 12299.9714119541 & -1841.97141195415 \tabularnewline
75 & 9739 & 10458.0867490401 & -719.086749040132 \tabularnewline
76 & 10559 & 9739.03386593562 & 819.96613406438 \tabularnewline
77 & 12513 & 10558.9613830733 & 1954.03861692674 \tabularnewline
78 & 14254 & 12512.9079730699 & 1741.09202693012 \tabularnewline
79 & 13839 & 14253.918001951 & -414.918001950986 \tabularnewline
80 & 13839 & 13839.0195408779 & -0.0195408778708952 \tabularnewline
81 & 14042 & 13839.0000009203 & 202.999999079708 \tabularnewline
82 & 13333 & 14041.9904395611 & -708.990439561139 \tabularnewline
83 & 15176 & 13333.0333904423 & 1842.96660955773 \tabularnewline
84 & 15176 & 15175.9132040903 & 0.0867959097176936 \tabularnewline
85 & 14862 & 15175.9999959123 & -313.999995912282 \tabularnewline
86 & 13120 & 14862.0147880679 & -1742.01478806787 \tabularnewline
87 & 13434 & 13120.0820415071 & 313.917958492852 \tabularnewline
88 & 13637 & 13433.9852157957 & 203.014784204252 \tabularnewline
89 & 14973 & 13636.9904388648 & 1336.00956113518 \tabularnewline
90 & 16714 & 14972.9370796168 & 1741.06292038317 \tabularnewline
91 & 15479 & 16713.9180033218 & -1234.91800332178 \tabularnewline
92 & 16097 & 15479.0581593996 & 617.941840600382 \tabularnewline
93 & 15580 & 16096.9708975605 & -516.970897560526 \tabularnewline
94 & 15277 & 15580.0243471364 & -303.024347136361 \tabularnewline
95 & 17636 & 15277.0142711614 & 2358.98572883863 \tabularnewline
96 & 17119 & 17635.8889017786 & -516.888901778639 \tabularnewline
97 & 16400 & 17119.0243432747 & -719.024343274708 \tabularnewline
98 & 15378 & 16400.0338629966 & -1022.03386299657 \tabularnewline
99 & 16400 & 15378.0481334596 & 1021.95186654037 \tabularnewline
100 & 16917 & 16399.9518704021 & 517.048129597944 \tabularnewline
101 & 17534 & 16916.9756492263 & 617.024350773663 \tabularnewline
102 & 18354 & 17533.9709407704 & 820.029059229597 \tabularnewline
103 & 17534 & 18353.9613801098 & -819.961380109751 \tabularnewline
104 & 18040 & 17534.0386167028 & 505.961383297152 \tabularnewline
105 & 17423 & 18039.9761713651 & -616.976171365059 \tabularnewline
106 & 17322 & 17423.0290569605 & -101.029056960549 \tabularnewline
107 & 19883 & 17322.00475804 & 2560.99524195997 \tabularnewline
108 & 20096 & 19882.8793879875 & 213.120612012535 \tabularnewline
109 & 19276 & 20095.9899629232 & -819.989962923199 \tabularnewline
110 & 17838 & 19276.038618049 & -1438.03861804898 \tabularnewline
111 & 19063 & 17838.067725519 & 1224.93227448104 \tabularnewline
112 & 19579 & 19062.9423108859 & 516.057689114146 \tabularnewline
113 & 20197 & 19578.9756958719 & 618.024304128117 \tabularnewline
114 & 21118 & 20196.9708936768 & 921.029106323156 \tabularnewline
115 & 20197 & 21117.956623436 & -920.956623435963 \tabularnewline
116 & 20916 & 20197.0433731504 & 718.956626849598 \tabularnewline
117 & 20602 & 20915.9661401926 & -313.966140192584 \tabularnewline
118 & 19478 & 20602.0147864734 & -1124.01478647341 \tabularnewline
119 & 21837 & 19478.0529363285 & 2358.94706367146 \tabularnewline
120 & 21837 & 21836.8889035996 & 0.111096400392853 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123373&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]5639[/C][C]5740[/C][C]-101[/C][/ROW]
[ROW][C]3[/C][C]5538[/C][C]5639.00475667157[/C][C]-101.004756671573[/C][/ROW]
[ROW][C]4[/C][C]5336[/C][C]5538.00475689559[/C][C]-202.004756895592[/C][/ROW]
[ROW][C]5[/C][C]7380[/C][C]5336.00951356718[/C][C]2043.99048643282[/C][/ROW]
[ROW][C]6[/C][C]7279[/C][C]7379.9037367184[/C][C]-100.903736718395[/C][/ROW]
[ROW][C]7[/C][C]5740[/C][C]7279.00475213798[/C][C]-1539.00475213798[/C][/ROW]
[ROW][C]8[/C][C]4718[/C][C]5740.0724805956[/C][C]-1022.0724805956[/C][/ROW]
[ROW][C]9[/C][C]4819[/C][C]4718.04813527836[/C][C]100.951864721645[/C][/ROW]
[ROW][C]10[/C][C]4819[/C][C]4818.9952455954[/C][C]0.00475440460559184[/C][/ROW]
[ROW][C]11[/C][C]4920[/C][C]4818.99999977609[/C][C]101.000000223912[/C][/ROW]
[ROW][C]12[/C][C]5133[/C][C]4919.99524332842[/C][C]213.004756671584[/C][/ROW]
[ROW][C]13[/C][C]4516[/C][C]5132.9899683795[/C][C]-616.989968379496[/C][/ROW]
[ROW][C]14[/C][C]3898[/C][C]4516.02905761033[/C][C]-618.029057610331[/C][/ROW]
[ROW][C]15[/C][C]3392[/C][C]3898.02910654703[/C][C]-506.029106547026[/C][/ROW]
[ROW][C]16[/C][C]3392[/C][C]3392.02383182442[/C][C]-0.0238318244178117[/C][/ROW]
[ROW][C]17[/C][C]5336[/C][C]3392.00000112238[/C][C]1943.99999887762[/C][/ROW]
[ROW][C]18[/C][C]5538[/C][C]5335.90844584621[/C][C]202.091554153787[/C][/ROW]
[ROW][C]19[/C][C]3999[/C][C]5537.99048234504[/C][C]-1538.99048234504[/C][/ROW]
[ROW][C]20[/C][C]2258[/C][C]3999.07247992355[/C][C]-1741.07247992355[/C][/ROW]
[ROW][C]21[/C][C]3179[/C][C]2258.08199712843[/C][C]920.918002871567[/C][/ROW]
[ROW][C]22[/C][C]3179[/C][C]3178.95662866846[/C][C]0.0433713315374007[/C][/ROW]
[ROW][C]23[/C][C]3898[/C][C]3178.99999795739[/C][C]719.000002042606[/C][/ROW]
[ROW][C]24[/C][C]4313[/C][C]3897.9661381498[/C][C]415.033861850205[/C][/ROW]
[ROW][C]25[/C][C]4212[/C][C]4312.98045366562[/C][C]-100.980453665619[/C][/ROW]
[ROW][C]26[/C][C]3179[/C][C]4212.00475575102[/C][C]-1033.00475575102[/C][/ROW]
[ROW][C]27[/C][C]3696[/C][C]3179.04865014214[/C][C]516.951349857858[/C][/ROW]
[ROW][C]28[/C][C]3493[/C][C]3695.97565378425[/C][C]-202.975653784253[/C][/ROW]
[ROW][C]29[/C][C]5234[/C][C]3493.0095592923[/C][C]1740.9904407077[/C][/ROW]
[ROW][C]30[/C][C]4819[/C][C]5233.91800673527[/C][C]-414.918006735266[/C][/ROW]
[ROW][C]31[/C][C]3179[/C][C]4819.0195408781[/C][C]-1640.0195408781[/C][/ROW]
[ROW][C]32[/C][C]1954[/C][C]3179.07723796366[/C][C]-1225.07723796366[/C][/ROW]
[ROW][C]33[/C][C]3078[/C][C]1954.05769594131[/C][C]1123.94230405869[/C][/ROW]
[ROW][C]34[/C][C]3392[/C][C]3077.94706708508[/C][C]314.052932914924[/C][/ROW]
[ROW][C]35[/C][C]3696[/C][C]3391.98520943903[/C][C]304.014790560974[/C][/ROW]
[ROW][C]36[/C][C]4100[/C][C]3695.98568219295[/C][C]404.01431780705[/C][/ROW]
[ROW][C]37[/C][C]3280[/C][C]4099.9809726394[/C][C]-819.9809726394[/C][/ROW]
[ROW][C]38[/C][C]2572[/C][C]3280.03861762557[/C][C]-708.038617625573[/C][/ROW]
[ROW][C]39[/C][C]2876[/C][C]2572.03334561549[/C][C]303.966654384505[/C][/ROW]
[ROW][C]40[/C][C]2977[/C][C]2875.98568445996[/C][C]101.01431554004[/C][/ROW]
[ROW][C]41[/C][C]5639[/C][C]2976.99524265423[/C][C]2662.00475734577[/C][/ROW]
[ROW][C]42[/C][C]5639[/C][C]5638.87463086776[/C][C]0.125369132240849[/C][/ROW]
[ROW][C]43[/C][C]4100[/C][C]5638.99999409565[/C][C]-1538.99999409565[/C][/ROW]
[ROW][C]44[/C][C]3898[/C][C]4100.07248037151[/C][C]-202.072480371512[/C][/ROW]
[ROW][C]45[/C][C]4516[/C][C]3898.00951675666[/C][C]617.990483243336[/C][/ROW]
[ROW][C]46[/C][C]4212[/C][C]4515.97089526966[/C][C]-303.970895269664[/C][/ROW]
[ROW][C]47[/C][C]5032[/C][C]4212.01431573977[/C][C]819.985684260232[/C][/ROW]
[ROW][C]48[/C][C]6054[/C][C]5031.96138215253[/C][C]1022.03861784747[/C][/ROW]
[ROW][C]49[/C][C]6257[/C][C]6053.95186631644[/C][C]203.048133683564[/C][/ROW]
[ROW][C]50[/C][C]4819[/C][C]6256.9904372942[/C][C]-1437.9904372942[/C][/ROW]
[ROW][C]51[/C][C]4414[/C][C]4819.06772324985[/C][C]-405.067723249854[/C][/ROW]
[ROW][C]52[/C][C]3999[/C][C]4414.01907697153[/C][C]-415.019076971527[/C][/ROW]
[ROW][C]53[/C][C]6773[/C][C]3999.01954563808[/C][C]2773.98045436192[/C][/ROW]
[ROW][C]54[/C][C]6976[/C][C]6772.86935728741[/C][C]203.130642712586[/C][/ROW]
[ROW][C]55[/C][C]6459[/C][C]6975.99043340838[/C][C]-516.990433408379[/C][/ROW]
[ROW][C]56[/C][C]6976[/C][C]6459.02434805642[/C][C]516.975651943583[/C][/ROW]
[ROW][C]57[/C][C]6874[/C][C]6975.97565263973[/C][C]-101.975652639728[/C][/ROW]
[ROW][C]58[/C][C]6054[/C][C]6874.00480262067[/C][C]-820.004802620674[/C][/ROW]
[ROW][C]59[/C][C]6976[/C][C]6054.03861874786[/C][C]921.961381252136[/C][/ROW]
[ROW][C]60[/C][C]7998[/C][C]6975.95657952977[/C][C]1022.04342047023[/C][/ROW]
[ROW][C]61[/C][C]8413[/C][C]7997.95186609025[/C][C]415.048133909747[/C][/ROW]
[ROW][C]62[/C][C]7178[/C][C]8412.98045299347[/C][C]-1234.98045299347[/C][/ROW]
[ROW][C]63[/C][C]6358[/C][C]7178.05816234073[/C][C]-820.058162340732[/C][/ROW]
[ROW][C]64[/C][C]6976[/C][C]6358.03862126088[/C][C]617.961378739119[/C][/ROW]
[ROW][C]65[/C][C]9638[/C][C]6975.97089664036[/C][C]2662.02910335964[/C][/ROW]
[ROW][C]66[/C][C]10458[/C][C]9637.87462972117[/C][C]820.125370278834[/C][/ROW]
[ROW][C]67[/C][C]10256[/C][C]10457.9613755739[/C][C]-201.96137557391[/C][/ROW]
[ROW][C]68[/C][C]10660[/C][C]10256.0095115241[/C][C]403.9904884759[/C][/ROW]
[ROW][C]69[/C][C]10559[/C][C]10659.9809737617[/C][C]-100.980973761662[/C][/ROW]
[ROW][C]70[/C][C]9537[/C][C]10559.0047557755[/C][C]-1022.00475577552[/C][/ROW]
[ROW][C]71[/C][C]11278[/C][C]9537.0481320888[/C][C]1740.9518679112[/C][/ROW]
[ROW][C]72[/C][C]11693[/C][C]11277.9180085519[/C][C]415.081991448118[/C][/ROW]
[ROW][C]73[/C][C]12300[/C][C]11692.9804513989[/C][C]607.019548601082[/C][/ROW]
[ROW][C]74[/C][C]10458[/C][C]12299.9714119541[/C][C]-1841.97141195415[/C][/ROW]
[ROW][C]75[/C][C]9739[/C][C]10458.0867490401[/C][C]-719.086749040132[/C][/ROW]
[ROW][C]76[/C][C]10559[/C][C]9739.03386593562[/C][C]819.96613406438[/C][/ROW]
[ROW][C]77[/C][C]12513[/C][C]10558.9613830733[/C][C]1954.03861692674[/C][/ROW]
[ROW][C]78[/C][C]14254[/C][C]12512.9079730699[/C][C]1741.09202693012[/C][/ROW]
[ROW][C]79[/C][C]13839[/C][C]14253.918001951[/C][C]-414.918001950986[/C][/ROW]
[ROW][C]80[/C][C]13839[/C][C]13839.0195408779[/C][C]-0.0195408778708952[/C][/ROW]
[ROW][C]81[/C][C]14042[/C][C]13839.0000009203[/C][C]202.999999079708[/C][/ROW]
[ROW][C]82[/C][C]13333[/C][C]14041.9904395611[/C][C]-708.990439561139[/C][/ROW]
[ROW][C]83[/C][C]15176[/C][C]13333.0333904423[/C][C]1842.96660955773[/C][/ROW]
[ROW][C]84[/C][C]15176[/C][C]15175.9132040903[/C][C]0.0867959097176936[/C][/ROW]
[ROW][C]85[/C][C]14862[/C][C]15175.9999959123[/C][C]-313.999995912282[/C][/ROW]
[ROW][C]86[/C][C]13120[/C][C]14862.0147880679[/C][C]-1742.01478806787[/C][/ROW]
[ROW][C]87[/C][C]13434[/C][C]13120.0820415071[/C][C]313.917958492852[/C][/ROW]
[ROW][C]88[/C][C]13637[/C][C]13433.9852157957[/C][C]203.014784204252[/C][/ROW]
[ROW][C]89[/C][C]14973[/C][C]13636.9904388648[/C][C]1336.00956113518[/C][/ROW]
[ROW][C]90[/C][C]16714[/C][C]14972.9370796168[/C][C]1741.06292038317[/C][/ROW]
[ROW][C]91[/C][C]15479[/C][C]16713.9180033218[/C][C]-1234.91800332178[/C][/ROW]
[ROW][C]92[/C][C]16097[/C][C]15479.0581593996[/C][C]617.941840600382[/C][/ROW]
[ROW][C]93[/C][C]15580[/C][C]16096.9708975605[/C][C]-516.970897560526[/C][/ROW]
[ROW][C]94[/C][C]15277[/C][C]15580.0243471364[/C][C]-303.024347136361[/C][/ROW]
[ROW][C]95[/C][C]17636[/C][C]15277.0142711614[/C][C]2358.98572883863[/C][/ROW]
[ROW][C]96[/C][C]17119[/C][C]17635.8889017786[/C][C]-516.888901778639[/C][/ROW]
[ROW][C]97[/C][C]16400[/C][C]17119.0243432747[/C][C]-719.024343274708[/C][/ROW]
[ROW][C]98[/C][C]15378[/C][C]16400.0338629966[/C][C]-1022.03386299657[/C][/ROW]
[ROW][C]99[/C][C]16400[/C][C]15378.0481334596[/C][C]1021.95186654037[/C][/ROW]
[ROW][C]100[/C][C]16917[/C][C]16399.9518704021[/C][C]517.048129597944[/C][/ROW]
[ROW][C]101[/C][C]17534[/C][C]16916.9756492263[/C][C]617.024350773663[/C][/ROW]
[ROW][C]102[/C][C]18354[/C][C]17533.9709407704[/C][C]820.029059229597[/C][/ROW]
[ROW][C]103[/C][C]17534[/C][C]18353.9613801098[/C][C]-819.961380109751[/C][/ROW]
[ROW][C]104[/C][C]18040[/C][C]17534.0386167028[/C][C]505.961383297152[/C][/ROW]
[ROW][C]105[/C][C]17423[/C][C]18039.9761713651[/C][C]-616.976171365059[/C][/ROW]
[ROW][C]106[/C][C]17322[/C][C]17423.0290569605[/C][C]-101.029056960549[/C][/ROW]
[ROW][C]107[/C][C]19883[/C][C]17322.00475804[/C][C]2560.99524195997[/C][/ROW]
[ROW][C]108[/C][C]20096[/C][C]19882.8793879875[/C][C]213.120612012535[/C][/ROW]
[ROW][C]109[/C][C]19276[/C][C]20095.9899629232[/C][C]-819.989962923199[/C][/ROW]
[ROW][C]110[/C][C]17838[/C][C]19276.038618049[/C][C]-1438.03861804898[/C][/ROW]
[ROW][C]111[/C][C]19063[/C][C]17838.067725519[/C][C]1224.93227448104[/C][/ROW]
[ROW][C]112[/C][C]19579[/C][C]19062.9423108859[/C][C]516.057689114146[/C][/ROW]
[ROW][C]113[/C][C]20197[/C][C]19578.9756958719[/C][C]618.024304128117[/C][/ROW]
[ROW][C]114[/C][C]21118[/C][C]20196.9708936768[/C][C]921.029106323156[/C][/ROW]
[ROW][C]115[/C][C]20197[/C][C]21117.956623436[/C][C]-920.956623435963[/C][/ROW]
[ROW][C]116[/C][C]20916[/C][C]20197.0433731504[/C][C]718.956626849598[/C][/ROW]
[ROW][C]117[/C][C]20602[/C][C]20915.9661401926[/C][C]-313.966140192584[/C][/ROW]
[ROW][C]118[/C][C]19478[/C][C]20602.0147864734[/C][C]-1124.01478647341[/C][/ROW]
[ROW][C]119[/C][C]21837[/C][C]19478.0529363285[/C][C]2358.94706367146[/C][/ROW]
[ROW][C]120[/C][C]21837[/C][C]21836.8889035996[/C][C]0.111096400392853[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123373&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123373&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
256395740-101
355385639.00475667157-101.004756671573
453365538.00475689559-202.004756895592
573805336.009513567182043.99048643282
672797379.9037367184-100.903736718395
757407279.00475213798-1539.00475213798
847185740.0724805956-1022.0724805956
948194718.04813527836100.951864721645
1048194818.99524559540.00475440460559184
1149204818.99999977609101.000000223912
1251334919.99524332842213.004756671584
1345165132.9899683795-616.989968379496
1438984516.02905761033-618.029057610331
1533923898.02910654703-506.029106547026
1633923392.02383182442-0.0238318244178117
1753363392.000001122381943.99999887762
1855385335.90844584621202.091554153787
1939995537.99048234504-1538.99048234504
2022583999.07247992355-1741.07247992355
2131792258.08199712843920.918002871567
2231793178.956628668460.0433713315374007
2338983178.99999795739719.000002042606
2443133897.9661381498415.033861850205
2542124312.98045366562-100.980453665619
2631794212.00475575102-1033.00475575102
2736963179.04865014214516.951349857858
2834933695.97565378425-202.975653784253
2952343493.00955929231740.9904407077
3048195233.91800673527-414.918006735266
3131794819.0195408781-1640.0195408781
3219543179.07723796366-1225.07723796366
3330781954.057695941311123.94230405869
3433923077.94706708508314.052932914924
3536963391.98520943903304.014790560974
3641003695.98568219295404.01431780705
3732804099.9809726394-819.9809726394
3825723280.03861762557-708.038617625573
3928762572.03334561549303.966654384505
4029772875.98568445996101.01431554004
4156392976.995242654232662.00475734577
4256395638.874630867760.125369132240849
4341005638.99999409565-1538.99999409565
4438984100.07248037151-202.072480371512
4545163898.00951675666617.990483243336
4642124515.97089526966-303.970895269664
4750324212.01431573977819.985684260232
4860545031.961382152531022.03861784747
4962576053.95186631644203.048133683564
5048196256.9904372942-1437.9904372942
5144144819.06772324985-405.067723249854
5239994414.01907697153-415.019076971527
5367733999.019545638082773.98045436192
5469766772.86935728741203.130642712586
5564596975.99043340838-516.990433408379
5669766459.02434805642516.975651943583
5768746975.97565263973-101.975652639728
5860546874.00480262067-820.004802620674
5969766054.03861874786921.961381252136
6079986975.956579529771022.04342047023
6184137997.95186609025415.048133909747
6271788412.98045299347-1234.98045299347
6363587178.05816234073-820.058162340732
6469766358.03862126088617.961378739119
6596386975.970896640362662.02910335964
66104589637.87462972117820.125370278834
671025610457.9613755739-201.96137557391
681066010256.0095115241403.9904884759
691055910659.9809737617-100.980973761662
70953710559.0047557755-1022.00475577552
71112789537.04813208881740.9518679112
721169311277.9180085519415.081991448118
731230011692.9804513989607.019548601082
741045812299.9714119541-1841.97141195415
75973910458.0867490401-719.086749040132
76105599739.03386593562819.96613406438
771251310558.96138307331954.03861692674
781425412512.90797306991741.09202693012
791383914253.918001951-414.918001950986
801383913839.0195408779-0.0195408778708952
811404213839.0000009203202.999999079708
821333314041.9904395611-708.990439561139
831517613333.03339044231842.96660955773
841517615175.91320409030.0867959097176936
851486215175.9999959123-313.999995912282
861312014862.0147880679-1742.01478806787
871343413120.0820415071313.917958492852
881363713433.9852157957203.014784204252
891497313636.99043886481336.00956113518
901671414972.93707961681741.06292038317
911547916713.9180033218-1234.91800332178
921609715479.0581593996617.941840600382
931558016096.9708975605-516.970897560526
941527715580.0243471364-303.024347136361
951763615277.01427116142358.98572883863
961711917635.8889017786-516.888901778639
971640017119.0243432747-719.024343274708
981537816400.0338629966-1022.03386299657
991640015378.04813345961021.95186654037
1001691716399.9518704021517.048129597944
1011753416916.9756492263617.024350773663
1021835417533.9709407704820.029059229597
1031753418353.9613801098-819.961380109751
1041804017534.0386167028505.961383297152
1051742318039.9761713651-616.976171365059
1061732217423.0290569605-101.029056960549
1071988317322.004758042560.99524195997
1082009619882.8793879875213.120612012535
1091927620095.9899629232-819.989962923199
1101783819276.038618049-1438.03861804898
1111906317838.0677255191224.93227448104
1121957919062.9423108859516.057689114146
1132019719578.9756958719618.024304128117
1142111820196.9708936768921.029106323156
1152019721117.956623436-920.956623435963
1162091620197.0433731504718.956626849598
1172060220915.9661401926-313.966140192584
1181947820602.0147864734-1124.01478647341
1192183719478.05293632852358.94706367146
1202183721836.88890359960.111096400392853







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12121836.999994767819804.212032876923869.7879566588
12221836.999994767818962.271384191624711.7286053441
12321836.999994767818316.218508943625357.7814805921
12421836.999994767817771.567673675825902.4323158598
12521836.999994767817291.719184538826382.2808049969
12621836.999994767816857.902151755226816.0978377805
12721836.999994767816458.965686886327215.0343026493
12821836.999994767816087.644317545627586.35567199
12921836.999994767815738.891403600927935.1085859348
13021836.999994767815409.032502930228264.9674866054
13121836.999994767815095.293700173128578.7062893625
13221836.999994767814795.519933798128878.4800557376

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 21836.9999947678 & 19804.2120328769 & 23869.7879566588 \tabularnewline
122 & 21836.9999947678 & 18962.2713841916 & 24711.7286053441 \tabularnewline
123 & 21836.9999947678 & 18316.2185089436 & 25357.7814805921 \tabularnewline
124 & 21836.9999947678 & 17771.5676736758 & 25902.4323158598 \tabularnewline
125 & 21836.9999947678 & 17291.7191845388 & 26382.2808049969 \tabularnewline
126 & 21836.9999947678 & 16857.9021517552 & 26816.0978377805 \tabularnewline
127 & 21836.9999947678 & 16458.9656868863 & 27215.0343026493 \tabularnewline
128 & 21836.9999947678 & 16087.6443175456 & 27586.35567199 \tabularnewline
129 & 21836.9999947678 & 15738.8914036009 & 27935.1085859348 \tabularnewline
130 & 21836.9999947678 & 15409.0325029302 & 28264.9674866054 \tabularnewline
131 & 21836.9999947678 & 15095.2937001731 & 28578.7062893625 \tabularnewline
132 & 21836.9999947678 & 14795.5199337981 & 28878.4800557376 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123373&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]121[/C][C]21836.9999947678[/C][C]19804.2120328769[/C][C]23869.7879566588[/C][/ROW]
[ROW][C]122[/C][C]21836.9999947678[/C][C]18962.2713841916[/C][C]24711.7286053441[/C][/ROW]
[ROW][C]123[/C][C]21836.9999947678[/C][C]18316.2185089436[/C][C]25357.7814805921[/C][/ROW]
[ROW][C]124[/C][C]21836.9999947678[/C][C]17771.5676736758[/C][C]25902.4323158598[/C][/ROW]
[ROW][C]125[/C][C]21836.9999947678[/C][C]17291.7191845388[/C][C]26382.2808049969[/C][/ROW]
[ROW][C]126[/C][C]21836.9999947678[/C][C]16857.9021517552[/C][C]26816.0978377805[/C][/ROW]
[ROW][C]127[/C][C]21836.9999947678[/C][C]16458.9656868863[/C][C]27215.0343026493[/C][/ROW]
[ROW][C]128[/C][C]21836.9999947678[/C][C]16087.6443175456[/C][C]27586.35567199[/C][/ROW]
[ROW][C]129[/C][C]21836.9999947678[/C][C]15738.8914036009[/C][C]27935.1085859348[/C][/ROW]
[ROW][C]130[/C][C]21836.9999947678[/C][C]15409.0325029302[/C][C]28264.9674866054[/C][/ROW]
[ROW][C]131[/C][C]21836.9999947678[/C][C]15095.2937001731[/C][C]28578.7062893625[/C][/ROW]
[ROW][C]132[/C][C]21836.9999947678[/C][C]14795.5199337981[/C][C]28878.4800557376[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123373&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123373&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
12121836.999994767819804.212032876923869.7879566588
12221836.999994767818962.271384191624711.7286053441
12321836.999994767818316.218508943625357.7814805921
12421836.999994767817771.567673675825902.4323158598
12521836.999994767817291.719184538826382.2808049969
12621836.999994767816857.902151755226816.0978377805
12721836.999994767816458.965686886327215.0343026493
12821836.999994767816087.644317545627586.35567199
12921836.999994767815738.891403600927935.1085859348
13021836.999994767815409.032502930228264.9674866054
13121836.999994767815095.293700173128578.7062893625
13221836.999994767814795.519933798128878.4800557376



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=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')