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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 28 Dec 2012 12:42:21 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/28/t13567165582z3gy38laqf2a83.htm/, Retrieved Mon, 29 Apr 2024 08:59:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=204849, Retrieved Mon, 29 Apr 2024 08:59:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact127
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-12-28 17:42:21] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
49,98
50,12
50,37
50,39
50,34
50,32
50,32
50,32
50,67
50,86
50,95
51,02
51,02
51,06
50,9
51,23
51,29
51,3
51,3
51,3
51,46
51,47
51,77
51,82
51,82
51,84
51,9
51,94
52,22
52,27
52,27
52,28
52,53
52,73
52,72
52,67
52,67
52,65
52,69
52,73
52,84
52,83
52,83
52,84
52,82
53,09
53,4
53,43
53,43
53,42
53,6
53,69
54,05
54,04
54,04
54,08
54,05
54,39
54,38
54,46
54,46
54,69
54,91
55,52
56,01
56,07
56,07
56,09
56,29
56,45
56,87
56,87




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204849&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204849&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204849&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999956670705821
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999956670705821 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204849&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]0.999956670705821[/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=204849&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204849&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
alpha0.999956670705821
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
250.1249.980.140000000000001
350.3750.11999393389880.250006066101186
450.3950.36998916741360.0200108325863866
550.3450.3899991329448-0.0499991329447482
650.3250.3400021664271-0.0200021664271404
750.3250.3200008666798-8.66679755517907e-07
850.3250.3200000000376-3.75521835849213e-11
950.6750.320.350000000000001
1050.8650.6699848347470.190015165252959
1150.9550.8599917667770.0900082332229957
1251.0250.94999610000680.0700038999932175
1351.0251.01999696678043.03321957773051e-06
1451.0651.01999999986860.0400000001314282
1550.951.0599982668282-0.159998266828232
1651.2350.9000069326120.329993067388024
1751.2951.22998570163330.0600142983666956
1851.351.28999739962280.0100026003771845
1951.351.29999956659444.33405617172866e-07
2051.351.29999999998121.87796445061394e-11
2151.4651.30.160000000000004
2251.4751.45999306731290.0100069326870695
2351.7751.46999956640670.300000433593333
2451.8251.7699870011930.0500129988070412
2551.8251.81999783297212.16702793665036e-06
2651.8451.81999999990610.0200000000939013
2751.951.83999913341410.0600008665858809
2851.9451.89999740020480.0400025997952014
2952.2251.93999826671560.280001733284415
3052.2752.21998786772250.0500121322774731
3152.2752.26999783300962.1669903915722e-06
3252.2852.26999999990610.0100000000938891
3352.5352.27999956670710.250000433292946
3452.7352.52998916765770.200010832342315
3552.7252.7299913336718-0.00999133367180605
3652.6752.7200004329174-0.0500004329174359
3752.6752.6700021664835-2.16648346906823e-06
3852.6552.6700000000939-0.0200000000938729
3952.6952.65000086658590.0399991334141134
4052.7352.68999826686580.0400017331342184
4152.8452.72999826675310.110001733246868
4252.8352.8399952337025-0.00999523370254707
4352.8352.8300004330864-4.33086420059681e-07
4452.8452.83000000001880.00999999998123968
4552.8252.8399995667071-0.0199995667070638
4653.0952.82000086656710.269999133432897
4753.453.08998830112810.310011698871875
4853.4353.39998656741190.030013432588099
4953.4353.42999869953911.30046085189406e-06
5053.4253.4299999999437-0.00999999994365197
5153.653.42000043329290.17999956670706
5253.6953.59999220074580.0900077992541739
5354.0553.68999610002560.360003899974409
5454.0454.0499844012851-0.00998440128510936
5554.0454.0400004326171-4.32617063950147e-07
5654.0854.04000000001870.039999999981255
5754.0554.0799982668282-0.0299982668282368
5854.3954.05000129980370.339998700196276
5954.3854.3899852680963-0.00998526809629396
6054.4654.38000043265460.0799995673453822
6154.4654.45999653367523.46632478454012e-06
6254.6954.45999999984980.230000000150191
6354.9154.68999003426230.220009965737667
6455.5254.90999046712350.610009532876532
6556.0155.51997356871750.490026431282494
6656.0756.00997876750060.0600212324994018
6756.0756.06999739932242.60067763946381e-06
6856.0956.06999999988730.0200000001126881
6956.2956.08999913341410.200000866585881
7056.4556.28999133410360.160008665896385
7156.8756.44999306693740.420006933062552
7256.8756.8699818013961.81986039606841e-05

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 50.12 & 49.98 & 0.140000000000001 \tabularnewline
3 & 50.37 & 50.1199939338988 & 0.250006066101186 \tabularnewline
4 & 50.39 & 50.3699891674136 & 0.0200108325863866 \tabularnewline
5 & 50.34 & 50.3899991329448 & -0.0499991329447482 \tabularnewline
6 & 50.32 & 50.3400021664271 & -0.0200021664271404 \tabularnewline
7 & 50.32 & 50.3200008666798 & -8.66679755517907e-07 \tabularnewline
8 & 50.32 & 50.3200000000376 & -3.75521835849213e-11 \tabularnewline
9 & 50.67 & 50.32 & 0.350000000000001 \tabularnewline
10 & 50.86 & 50.669984834747 & 0.190015165252959 \tabularnewline
11 & 50.95 & 50.859991766777 & 0.0900082332229957 \tabularnewline
12 & 51.02 & 50.9499961000068 & 0.0700038999932175 \tabularnewline
13 & 51.02 & 51.0199969667804 & 3.03321957773051e-06 \tabularnewline
14 & 51.06 & 51.0199999998686 & 0.0400000001314282 \tabularnewline
15 & 50.9 & 51.0599982668282 & -0.159998266828232 \tabularnewline
16 & 51.23 & 50.900006932612 & 0.329993067388024 \tabularnewline
17 & 51.29 & 51.2299857016333 & 0.0600142983666956 \tabularnewline
18 & 51.3 & 51.2899973996228 & 0.0100026003771845 \tabularnewline
19 & 51.3 & 51.2999995665944 & 4.33405617172866e-07 \tabularnewline
20 & 51.3 & 51.2999999999812 & 1.87796445061394e-11 \tabularnewline
21 & 51.46 & 51.3 & 0.160000000000004 \tabularnewline
22 & 51.47 & 51.4599930673129 & 0.0100069326870695 \tabularnewline
23 & 51.77 & 51.4699995664067 & 0.300000433593333 \tabularnewline
24 & 51.82 & 51.769987001193 & 0.0500129988070412 \tabularnewline
25 & 51.82 & 51.8199978329721 & 2.16702793665036e-06 \tabularnewline
26 & 51.84 & 51.8199999999061 & 0.0200000000939013 \tabularnewline
27 & 51.9 & 51.8399991334141 & 0.0600008665858809 \tabularnewline
28 & 51.94 & 51.8999974002048 & 0.0400025997952014 \tabularnewline
29 & 52.22 & 51.9399982667156 & 0.280001733284415 \tabularnewline
30 & 52.27 & 52.2199878677225 & 0.0500121322774731 \tabularnewline
31 & 52.27 & 52.2699978330096 & 2.1669903915722e-06 \tabularnewline
32 & 52.28 & 52.2699999999061 & 0.0100000000938891 \tabularnewline
33 & 52.53 & 52.2799995667071 & 0.250000433292946 \tabularnewline
34 & 52.73 & 52.5299891676577 & 0.200010832342315 \tabularnewline
35 & 52.72 & 52.7299913336718 & -0.00999133367180605 \tabularnewline
36 & 52.67 & 52.7200004329174 & -0.0500004329174359 \tabularnewline
37 & 52.67 & 52.6700021664835 & -2.16648346906823e-06 \tabularnewline
38 & 52.65 & 52.6700000000939 & -0.0200000000938729 \tabularnewline
39 & 52.69 & 52.6500008665859 & 0.0399991334141134 \tabularnewline
40 & 52.73 & 52.6899982668658 & 0.0400017331342184 \tabularnewline
41 & 52.84 & 52.7299982667531 & 0.110001733246868 \tabularnewline
42 & 52.83 & 52.8399952337025 & -0.00999523370254707 \tabularnewline
43 & 52.83 & 52.8300004330864 & -4.33086420059681e-07 \tabularnewline
44 & 52.84 & 52.8300000000188 & 0.00999999998123968 \tabularnewline
45 & 52.82 & 52.8399995667071 & -0.0199995667070638 \tabularnewline
46 & 53.09 & 52.8200008665671 & 0.269999133432897 \tabularnewline
47 & 53.4 & 53.0899883011281 & 0.310011698871875 \tabularnewline
48 & 53.43 & 53.3999865674119 & 0.030013432588099 \tabularnewline
49 & 53.43 & 53.4299986995391 & 1.30046085189406e-06 \tabularnewline
50 & 53.42 & 53.4299999999437 & -0.00999999994365197 \tabularnewline
51 & 53.6 & 53.4200004332929 & 0.17999956670706 \tabularnewline
52 & 53.69 & 53.5999922007458 & 0.0900077992541739 \tabularnewline
53 & 54.05 & 53.6899961000256 & 0.360003899974409 \tabularnewline
54 & 54.04 & 54.0499844012851 & -0.00998440128510936 \tabularnewline
55 & 54.04 & 54.0400004326171 & -4.32617063950147e-07 \tabularnewline
56 & 54.08 & 54.0400000000187 & 0.039999999981255 \tabularnewline
57 & 54.05 & 54.0799982668282 & -0.0299982668282368 \tabularnewline
58 & 54.39 & 54.0500012998037 & 0.339998700196276 \tabularnewline
59 & 54.38 & 54.3899852680963 & -0.00998526809629396 \tabularnewline
60 & 54.46 & 54.3800004326546 & 0.0799995673453822 \tabularnewline
61 & 54.46 & 54.4599965336752 & 3.46632478454012e-06 \tabularnewline
62 & 54.69 & 54.4599999998498 & 0.230000000150191 \tabularnewline
63 & 54.91 & 54.6899900342623 & 0.220009965737667 \tabularnewline
64 & 55.52 & 54.9099904671235 & 0.610009532876532 \tabularnewline
65 & 56.01 & 55.5199735687175 & 0.490026431282494 \tabularnewline
66 & 56.07 & 56.0099787675006 & 0.0600212324994018 \tabularnewline
67 & 56.07 & 56.0699973993224 & 2.60067763946381e-06 \tabularnewline
68 & 56.09 & 56.0699999998873 & 0.0200000001126881 \tabularnewline
69 & 56.29 & 56.0899991334141 & 0.200000866585881 \tabularnewline
70 & 56.45 & 56.2899913341036 & 0.160008665896385 \tabularnewline
71 & 56.87 & 56.4499930669374 & 0.420006933062552 \tabularnewline
72 & 56.87 & 56.869981801396 & 1.81986039606841e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204849&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]50.12[/C][C]49.98[/C][C]0.140000000000001[/C][/ROW]
[ROW][C]3[/C][C]50.37[/C][C]50.1199939338988[/C][C]0.250006066101186[/C][/ROW]
[ROW][C]4[/C][C]50.39[/C][C]50.3699891674136[/C][C]0.0200108325863866[/C][/ROW]
[ROW][C]5[/C][C]50.34[/C][C]50.3899991329448[/C][C]-0.0499991329447482[/C][/ROW]
[ROW][C]6[/C][C]50.32[/C][C]50.3400021664271[/C][C]-0.0200021664271404[/C][/ROW]
[ROW][C]7[/C][C]50.32[/C][C]50.3200008666798[/C][C]-8.66679755517907e-07[/C][/ROW]
[ROW][C]8[/C][C]50.32[/C][C]50.3200000000376[/C][C]-3.75521835849213e-11[/C][/ROW]
[ROW][C]9[/C][C]50.67[/C][C]50.32[/C][C]0.350000000000001[/C][/ROW]
[ROW][C]10[/C][C]50.86[/C][C]50.669984834747[/C][C]0.190015165252959[/C][/ROW]
[ROW][C]11[/C][C]50.95[/C][C]50.859991766777[/C][C]0.0900082332229957[/C][/ROW]
[ROW][C]12[/C][C]51.02[/C][C]50.9499961000068[/C][C]0.0700038999932175[/C][/ROW]
[ROW][C]13[/C][C]51.02[/C][C]51.0199969667804[/C][C]3.03321957773051e-06[/C][/ROW]
[ROW][C]14[/C][C]51.06[/C][C]51.0199999998686[/C][C]0.0400000001314282[/C][/ROW]
[ROW][C]15[/C][C]50.9[/C][C]51.0599982668282[/C][C]-0.159998266828232[/C][/ROW]
[ROW][C]16[/C][C]51.23[/C][C]50.900006932612[/C][C]0.329993067388024[/C][/ROW]
[ROW][C]17[/C][C]51.29[/C][C]51.2299857016333[/C][C]0.0600142983666956[/C][/ROW]
[ROW][C]18[/C][C]51.3[/C][C]51.2899973996228[/C][C]0.0100026003771845[/C][/ROW]
[ROW][C]19[/C][C]51.3[/C][C]51.2999995665944[/C][C]4.33405617172866e-07[/C][/ROW]
[ROW][C]20[/C][C]51.3[/C][C]51.2999999999812[/C][C]1.87796445061394e-11[/C][/ROW]
[ROW][C]21[/C][C]51.46[/C][C]51.3[/C][C]0.160000000000004[/C][/ROW]
[ROW][C]22[/C][C]51.47[/C][C]51.4599930673129[/C][C]0.0100069326870695[/C][/ROW]
[ROW][C]23[/C][C]51.77[/C][C]51.4699995664067[/C][C]0.300000433593333[/C][/ROW]
[ROW][C]24[/C][C]51.82[/C][C]51.769987001193[/C][C]0.0500129988070412[/C][/ROW]
[ROW][C]25[/C][C]51.82[/C][C]51.8199978329721[/C][C]2.16702793665036e-06[/C][/ROW]
[ROW][C]26[/C][C]51.84[/C][C]51.8199999999061[/C][C]0.0200000000939013[/C][/ROW]
[ROW][C]27[/C][C]51.9[/C][C]51.8399991334141[/C][C]0.0600008665858809[/C][/ROW]
[ROW][C]28[/C][C]51.94[/C][C]51.8999974002048[/C][C]0.0400025997952014[/C][/ROW]
[ROW][C]29[/C][C]52.22[/C][C]51.9399982667156[/C][C]0.280001733284415[/C][/ROW]
[ROW][C]30[/C][C]52.27[/C][C]52.2199878677225[/C][C]0.0500121322774731[/C][/ROW]
[ROW][C]31[/C][C]52.27[/C][C]52.2699978330096[/C][C]2.1669903915722e-06[/C][/ROW]
[ROW][C]32[/C][C]52.28[/C][C]52.2699999999061[/C][C]0.0100000000938891[/C][/ROW]
[ROW][C]33[/C][C]52.53[/C][C]52.2799995667071[/C][C]0.250000433292946[/C][/ROW]
[ROW][C]34[/C][C]52.73[/C][C]52.5299891676577[/C][C]0.200010832342315[/C][/ROW]
[ROW][C]35[/C][C]52.72[/C][C]52.7299913336718[/C][C]-0.00999133367180605[/C][/ROW]
[ROW][C]36[/C][C]52.67[/C][C]52.7200004329174[/C][C]-0.0500004329174359[/C][/ROW]
[ROW][C]37[/C][C]52.67[/C][C]52.6700021664835[/C][C]-2.16648346906823e-06[/C][/ROW]
[ROW][C]38[/C][C]52.65[/C][C]52.6700000000939[/C][C]-0.0200000000938729[/C][/ROW]
[ROW][C]39[/C][C]52.69[/C][C]52.6500008665859[/C][C]0.0399991334141134[/C][/ROW]
[ROW][C]40[/C][C]52.73[/C][C]52.6899982668658[/C][C]0.0400017331342184[/C][/ROW]
[ROW][C]41[/C][C]52.84[/C][C]52.7299982667531[/C][C]0.110001733246868[/C][/ROW]
[ROW][C]42[/C][C]52.83[/C][C]52.8399952337025[/C][C]-0.00999523370254707[/C][/ROW]
[ROW][C]43[/C][C]52.83[/C][C]52.8300004330864[/C][C]-4.33086420059681e-07[/C][/ROW]
[ROW][C]44[/C][C]52.84[/C][C]52.8300000000188[/C][C]0.00999999998123968[/C][/ROW]
[ROW][C]45[/C][C]52.82[/C][C]52.8399995667071[/C][C]-0.0199995667070638[/C][/ROW]
[ROW][C]46[/C][C]53.09[/C][C]52.8200008665671[/C][C]0.269999133432897[/C][/ROW]
[ROW][C]47[/C][C]53.4[/C][C]53.0899883011281[/C][C]0.310011698871875[/C][/ROW]
[ROW][C]48[/C][C]53.43[/C][C]53.3999865674119[/C][C]0.030013432588099[/C][/ROW]
[ROW][C]49[/C][C]53.43[/C][C]53.4299986995391[/C][C]1.30046085189406e-06[/C][/ROW]
[ROW][C]50[/C][C]53.42[/C][C]53.4299999999437[/C][C]-0.00999999994365197[/C][/ROW]
[ROW][C]51[/C][C]53.6[/C][C]53.4200004332929[/C][C]0.17999956670706[/C][/ROW]
[ROW][C]52[/C][C]53.69[/C][C]53.5999922007458[/C][C]0.0900077992541739[/C][/ROW]
[ROW][C]53[/C][C]54.05[/C][C]53.6899961000256[/C][C]0.360003899974409[/C][/ROW]
[ROW][C]54[/C][C]54.04[/C][C]54.0499844012851[/C][C]-0.00998440128510936[/C][/ROW]
[ROW][C]55[/C][C]54.04[/C][C]54.0400004326171[/C][C]-4.32617063950147e-07[/C][/ROW]
[ROW][C]56[/C][C]54.08[/C][C]54.0400000000187[/C][C]0.039999999981255[/C][/ROW]
[ROW][C]57[/C][C]54.05[/C][C]54.0799982668282[/C][C]-0.0299982668282368[/C][/ROW]
[ROW][C]58[/C][C]54.39[/C][C]54.0500012998037[/C][C]0.339998700196276[/C][/ROW]
[ROW][C]59[/C][C]54.38[/C][C]54.3899852680963[/C][C]-0.00998526809629396[/C][/ROW]
[ROW][C]60[/C][C]54.46[/C][C]54.3800004326546[/C][C]0.0799995673453822[/C][/ROW]
[ROW][C]61[/C][C]54.46[/C][C]54.4599965336752[/C][C]3.46632478454012e-06[/C][/ROW]
[ROW][C]62[/C][C]54.69[/C][C]54.4599999998498[/C][C]0.230000000150191[/C][/ROW]
[ROW][C]63[/C][C]54.91[/C][C]54.6899900342623[/C][C]0.220009965737667[/C][/ROW]
[ROW][C]64[/C][C]55.52[/C][C]54.9099904671235[/C][C]0.610009532876532[/C][/ROW]
[ROW][C]65[/C][C]56.01[/C][C]55.5199735687175[/C][C]0.490026431282494[/C][/ROW]
[ROW][C]66[/C][C]56.07[/C][C]56.0099787675006[/C][C]0.0600212324994018[/C][/ROW]
[ROW][C]67[/C][C]56.07[/C][C]56.0699973993224[/C][C]2.60067763946381e-06[/C][/ROW]
[ROW][C]68[/C][C]56.09[/C][C]56.0699999998873[/C][C]0.0200000001126881[/C][/ROW]
[ROW][C]69[/C][C]56.29[/C][C]56.0899991334141[/C][C]0.200000866585881[/C][/ROW]
[ROW][C]70[/C][C]56.45[/C][C]56.2899913341036[/C][C]0.160008665896385[/C][/ROW]
[ROW][C]71[/C][C]56.87[/C][C]56.4499930669374[/C][C]0.420006933062552[/C][/ROW]
[ROW][C]72[/C][C]56.87[/C][C]56.869981801396[/C][C]1.81986039606841e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204849&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204849&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
250.1249.980.140000000000001
350.3750.11999393389880.250006066101186
450.3950.36998916741360.0200108325863866
550.3450.3899991329448-0.0499991329447482
650.3250.3400021664271-0.0200021664271404
750.3250.3200008666798-8.66679755517907e-07
850.3250.3200000000376-3.75521835849213e-11
950.6750.320.350000000000001
1050.8650.6699848347470.190015165252959
1150.9550.8599917667770.0900082332229957
1251.0250.94999610000680.0700038999932175
1351.0251.01999696678043.03321957773051e-06
1451.0651.01999999986860.0400000001314282
1550.951.0599982668282-0.159998266828232
1651.2350.9000069326120.329993067388024
1751.2951.22998570163330.0600142983666956
1851.351.28999739962280.0100026003771845
1951.351.29999956659444.33405617172866e-07
2051.351.29999999998121.87796445061394e-11
2151.4651.30.160000000000004
2251.4751.45999306731290.0100069326870695
2351.7751.46999956640670.300000433593333
2451.8251.7699870011930.0500129988070412
2551.8251.81999783297212.16702793665036e-06
2651.8451.81999999990610.0200000000939013
2751.951.83999913341410.0600008665858809
2851.9451.89999740020480.0400025997952014
2952.2251.93999826671560.280001733284415
3052.2752.21998786772250.0500121322774731
3152.2752.26999783300962.1669903915722e-06
3252.2852.26999999990610.0100000000938891
3352.5352.27999956670710.250000433292946
3452.7352.52998916765770.200010832342315
3552.7252.7299913336718-0.00999133367180605
3652.6752.7200004329174-0.0500004329174359
3752.6752.6700021664835-2.16648346906823e-06
3852.6552.6700000000939-0.0200000000938729
3952.6952.65000086658590.0399991334141134
4052.7352.68999826686580.0400017331342184
4152.8452.72999826675310.110001733246868
4252.8352.8399952337025-0.00999523370254707
4352.8352.8300004330864-4.33086420059681e-07
4452.8452.83000000001880.00999999998123968
4552.8252.8399995667071-0.0199995667070638
4653.0952.82000086656710.269999133432897
4753.453.08998830112810.310011698871875
4853.4353.39998656741190.030013432588099
4953.4353.42999869953911.30046085189406e-06
5053.4253.4299999999437-0.00999999994365197
5153.653.42000043329290.17999956670706
5253.6953.59999220074580.0900077992541739
5354.0553.68999610002560.360003899974409
5454.0454.0499844012851-0.00998440128510936
5554.0454.0400004326171-4.32617063950147e-07
5654.0854.04000000001870.039999999981255
5754.0554.0799982668282-0.0299982668282368
5854.3954.05000129980370.339998700196276
5954.3854.3899852680963-0.00998526809629396
6054.4654.38000043265460.0799995673453822
6154.4654.45999653367523.46632478454012e-06
6254.6954.45999999984980.230000000150191
6354.9154.68999003426230.220009965737667
6455.5254.90999046712350.610009532876532
6556.0155.51997356871750.490026431282494
6656.0756.00997876750060.0600212324994018
6756.0756.06999739932242.60067763946381e-06
6856.0956.06999999988730.0200000001126881
6956.2956.08999913341410.200000866585881
7056.4556.28999133410360.160008665896385
7156.8756.44999306693740.420006933062552
7256.8756.8699818013961.81986039606841e-05







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7356.869999999211556.585134876793957.154865121629
7456.869999999211556.467148607369357.2728513910537
7556.869999999211556.376613386251257.3633866121718
7656.869999999211556.300288268783157.4397117296398
7756.869999999211556.233044300809457.5069556976135
7856.869999999211556.172250998734957.5677489996881
7956.869999999211556.116345719315657.6236542791073
8056.869999999211556.064310307366957.675689691056
8156.869999999211556.015437546558857.7245624518642
8256.869999999211555.969212515160457.7707874832625
8356.869999999211555.925246487779957.814753510643
8456.869999999211555.883237462781657.8567625356413

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 56.8699999992115 & 56.5851348767939 & 57.154865121629 \tabularnewline
74 & 56.8699999992115 & 56.4671486073693 & 57.2728513910537 \tabularnewline
75 & 56.8699999992115 & 56.3766133862512 & 57.3633866121718 \tabularnewline
76 & 56.8699999992115 & 56.3002882687831 & 57.4397117296398 \tabularnewline
77 & 56.8699999992115 & 56.2330443008094 & 57.5069556976135 \tabularnewline
78 & 56.8699999992115 & 56.1722509987349 & 57.5677489996881 \tabularnewline
79 & 56.8699999992115 & 56.1163457193156 & 57.6236542791073 \tabularnewline
80 & 56.8699999992115 & 56.0643103073669 & 57.675689691056 \tabularnewline
81 & 56.8699999992115 & 56.0154375465588 & 57.7245624518642 \tabularnewline
82 & 56.8699999992115 & 55.9692125151604 & 57.7707874832625 \tabularnewline
83 & 56.8699999992115 & 55.9252464877799 & 57.814753510643 \tabularnewline
84 & 56.8699999992115 & 55.8832374627816 & 57.8567625356413 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204849&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]73[/C][C]56.8699999992115[/C][C]56.5851348767939[/C][C]57.154865121629[/C][/ROW]
[ROW][C]74[/C][C]56.8699999992115[/C][C]56.4671486073693[/C][C]57.2728513910537[/C][/ROW]
[ROW][C]75[/C][C]56.8699999992115[/C][C]56.3766133862512[/C][C]57.3633866121718[/C][/ROW]
[ROW][C]76[/C][C]56.8699999992115[/C][C]56.3002882687831[/C][C]57.4397117296398[/C][/ROW]
[ROW][C]77[/C][C]56.8699999992115[/C][C]56.2330443008094[/C][C]57.5069556976135[/C][/ROW]
[ROW][C]78[/C][C]56.8699999992115[/C][C]56.1722509987349[/C][C]57.5677489996881[/C][/ROW]
[ROW][C]79[/C][C]56.8699999992115[/C][C]56.1163457193156[/C][C]57.6236542791073[/C][/ROW]
[ROW][C]80[/C][C]56.8699999992115[/C][C]56.0643103073669[/C][C]57.675689691056[/C][/ROW]
[ROW][C]81[/C][C]56.8699999992115[/C][C]56.0154375465588[/C][C]57.7245624518642[/C][/ROW]
[ROW][C]82[/C][C]56.8699999992115[/C][C]55.9692125151604[/C][C]57.7707874832625[/C][/ROW]
[ROW][C]83[/C][C]56.8699999992115[/C][C]55.9252464877799[/C][C]57.814753510643[/C][/ROW]
[ROW][C]84[/C][C]56.8699999992115[/C][C]55.8832374627816[/C][C]57.8567625356413[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204849&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204849&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
7356.869999999211556.585134876793957.154865121629
7456.869999999211556.467148607369357.2728513910537
7556.869999999211556.376613386251257.3633866121718
7656.869999999211556.300288268783157.4397117296398
7756.869999999211556.233044300809457.5069556976135
7856.869999999211556.172250998734957.5677489996881
7956.869999999211556.116345719315657.6236542791073
8056.869999999211556.064310307366957.675689691056
8156.869999999211556.015437546558857.7245624518642
8256.869999999211555.969212515160457.7707874832625
8356.869999999211555.925246487779957.814753510643
8456.869999999211555.883237462781657.8567625356413



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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=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')