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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 30 Nov 2014 20:11:25 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Nov/30/t1417378386ea9t4o9kj0jx1zw.htm/, Retrieved Fri, 17 May 2024 02:09:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=261607, Retrieved Fri, 17 May 2024 02:09:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact65
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-11-30 20:11:25] [77e76d07a5b02a0482982fb19d5d5436] [Current]
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Dataseries X:
21,94
21,95
21,96
22,1
22,13
22,18
22,18
22,27
22,3
22,04
22,05
22,06
22,06
22,06
21,97
22,03
22,08
22,13
22,13
22,4
22,4
22,12
22,22
22,14
22,14
22,19
22,29
22,24
22,26
22,29
22,29
22,29
22,29
22,35
22,39
22,43
22,43
22,11
22,12
22,05
22,05
22,08
22,08
22,09
22,09
22,24
22,25
22,24
22,24
22,25
22,28
22,23
22,29
22,31
22,31
22,31
22,39
22,42
22,42
22,42
22,15
21,95
21,96
21,97
21,66
21,66
21,68
21,75
21,55
21,59
21,54
21,54




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261607&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]1 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=261607&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261607&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 time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.984497672555413
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.984497672555413 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261607&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]0.984497672555413[/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=261607&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261607&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
alpha0.984497672555413
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
221.9521.940.00999999999999801
321.9621.94984497672560.0101550232744501
422.121.9598425735040.140157426496007
522.1322.09782723368070.0321727663193307
622.1822.12950124724170.0504987527582799
722.1822.17921715179920.000782848200802988
822.2722.17998786403080.0900121359691504
922.322.26860460239420.031395397605781
1022.0422.2995132982661-0.259513298266064
1122.0522.04402306012590.00597693987405634
1222.0622.0499073435210.010092656479042
1322.0622.05984354033450.000156459665525688
1422.0622.0599975745112.42548896878247e-06
1521.9722.0599999623993-0.0899999623992755
1622.0321.97139520888710.058604791112888
1722.0822.02909148933830.0509085106616496
1822.1322.0792107995980.0507892004019936
1922.1322.12921264918470.000787350815279808
2022.422.12998779422980.270012205770151
2122.422.39581418237210.00418581762788151
2222.1222.3999351100845-0.279935110084509
2322.2222.12433964573980.0956603542602323
2422.1422.2185170418648-0.0785170418647887
2522.1422.141217196893-0.0012171968929664
2622.1922.14001886938480.0499811306152012
2722.2922.18922517614720.100774823852845
2822.2422.2884377556825-0.0484377556824604
2922.2622.24075089794930.0192491020507326
3022.2922.2597015941170.030298405883002
3122.2922.2895303041910.000469695809048432
3222.2922.28999271862187.2813782310277e-06
3322.2922.28999988712171.12878311142595e-07
3422.3522.28999999825010.0600000017498807
3522.3922.34906986032620.0409301396738009
3622.4322.38936548757240.0406345124275731
3722.4322.42937007048280.000629929517202754
3822.1122.4299902346264-0.31999023462636
3922.1222.11496059339620.00503940660375335
4022.0522.1199218774687-0.0699218774687047
4122.0522.0510839518401-0.00108395184006227
4222.0822.05001680377640.0299831962236361
4322.0822.07953519067430.000464809325691817
4422.0922.07999279437360.0100072056263656
4522.0922.08984486502160.000155134978424343
4622.2422.08999759504680.150002404953231
4722.2522.23767461360090.0123253863990627
4822.2422.2498089278242-0.00980892782416021
4922.2422.240152061211-0.000152061211011301
5022.2522.24000235730270.00999764269731429
5122.2822.24984501326920.0301549867307713
5222.2322.2795325275216-0.0495325275216132
5322.2922.23076786946080.0592321305392005
5422.3122.28908176411710.0209182358828599
5522.3122.30967571865780.000324281342219734
5622.3122.30999497288445.02711555228075e-06
5722.3922.3099999220680.0800000779319916
5822.4222.38875981259630.0312401874036929
5922.4222.41951570438540.000484295614562313
6022.4222.41999249229087.50770919566435e-06
6122.1522.419999883613-0.269999883613036
6221.9522.1541856266058-0.204185626605767
6321.9621.95316535244310.00683464755688235
6421.9721.95989404705560.010105952944393
6521.6621.9698433342083-0.309843334208317
6621.6621.6648032928234-0.0048032928234214
6721.6821.66007446221820.0199255377818375
6821.7521.67969110778880.0703088922112052
6921.5521.7489100485307-0.198910048530674
7021.5921.55308356870430.0369164312956585
7121.5421.589427709394-0.0494277093939708
7221.5421.5407662445359-0.000766244535860494

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 21.95 & 21.94 & 0.00999999999999801 \tabularnewline
3 & 21.96 & 21.9498449767256 & 0.0101550232744501 \tabularnewline
4 & 22.1 & 21.959842573504 & 0.140157426496007 \tabularnewline
5 & 22.13 & 22.0978272336807 & 0.0321727663193307 \tabularnewline
6 & 22.18 & 22.1295012472417 & 0.0504987527582799 \tabularnewline
7 & 22.18 & 22.1792171517992 & 0.000782848200802988 \tabularnewline
8 & 22.27 & 22.1799878640308 & 0.0900121359691504 \tabularnewline
9 & 22.3 & 22.2686046023942 & 0.031395397605781 \tabularnewline
10 & 22.04 & 22.2995132982661 & -0.259513298266064 \tabularnewline
11 & 22.05 & 22.0440230601259 & 0.00597693987405634 \tabularnewline
12 & 22.06 & 22.049907343521 & 0.010092656479042 \tabularnewline
13 & 22.06 & 22.0598435403345 & 0.000156459665525688 \tabularnewline
14 & 22.06 & 22.059997574511 & 2.42548896878247e-06 \tabularnewline
15 & 21.97 & 22.0599999623993 & -0.0899999623992755 \tabularnewline
16 & 22.03 & 21.9713952088871 & 0.058604791112888 \tabularnewline
17 & 22.08 & 22.0290914893383 & 0.0509085106616496 \tabularnewline
18 & 22.13 & 22.079210799598 & 0.0507892004019936 \tabularnewline
19 & 22.13 & 22.1292126491847 & 0.000787350815279808 \tabularnewline
20 & 22.4 & 22.1299877942298 & 0.270012205770151 \tabularnewline
21 & 22.4 & 22.3958141823721 & 0.00418581762788151 \tabularnewline
22 & 22.12 & 22.3999351100845 & -0.279935110084509 \tabularnewline
23 & 22.22 & 22.1243396457398 & 0.0956603542602323 \tabularnewline
24 & 22.14 & 22.2185170418648 & -0.0785170418647887 \tabularnewline
25 & 22.14 & 22.141217196893 & -0.0012171968929664 \tabularnewline
26 & 22.19 & 22.1400188693848 & 0.0499811306152012 \tabularnewline
27 & 22.29 & 22.1892251761472 & 0.100774823852845 \tabularnewline
28 & 22.24 & 22.2884377556825 & -0.0484377556824604 \tabularnewline
29 & 22.26 & 22.2407508979493 & 0.0192491020507326 \tabularnewline
30 & 22.29 & 22.259701594117 & 0.030298405883002 \tabularnewline
31 & 22.29 & 22.289530304191 & 0.000469695809048432 \tabularnewline
32 & 22.29 & 22.2899927186218 & 7.2813782310277e-06 \tabularnewline
33 & 22.29 & 22.2899998871217 & 1.12878311142595e-07 \tabularnewline
34 & 22.35 & 22.2899999982501 & 0.0600000017498807 \tabularnewline
35 & 22.39 & 22.3490698603262 & 0.0409301396738009 \tabularnewline
36 & 22.43 & 22.3893654875724 & 0.0406345124275731 \tabularnewline
37 & 22.43 & 22.4293700704828 & 0.000629929517202754 \tabularnewline
38 & 22.11 & 22.4299902346264 & -0.31999023462636 \tabularnewline
39 & 22.12 & 22.1149605933962 & 0.00503940660375335 \tabularnewline
40 & 22.05 & 22.1199218774687 & -0.0699218774687047 \tabularnewline
41 & 22.05 & 22.0510839518401 & -0.00108395184006227 \tabularnewline
42 & 22.08 & 22.0500168037764 & 0.0299831962236361 \tabularnewline
43 & 22.08 & 22.0795351906743 & 0.000464809325691817 \tabularnewline
44 & 22.09 & 22.0799927943736 & 0.0100072056263656 \tabularnewline
45 & 22.09 & 22.0898448650216 & 0.000155134978424343 \tabularnewline
46 & 22.24 & 22.0899975950468 & 0.150002404953231 \tabularnewline
47 & 22.25 & 22.2376746136009 & 0.0123253863990627 \tabularnewline
48 & 22.24 & 22.2498089278242 & -0.00980892782416021 \tabularnewline
49 & 22.24 & 22.240152061211 & -0.000152061211011301 \tabularnewline
50 & 22.25 & 22.2400023573027 & 0.00999764269731429 \tabularnewline
51 & 22.28 & 22.2498450132692 & 0.0301549867307713 \tabularnewline
52 & 22.23 & 22.2795325275216 & -0.0495325275216132 \tabularnewline
53 & 22.29 & 22.2307678694608 & 0.0592321305392005 \tabularnewline
54 & 22.31 & 22.2890817641171 & 0.0209182358828599 \tabularnewline
55 & 22.31 & 22.3096757186578 & 0.000324281342219734 \tabularnewline
56 & 22.31 & 22.3099949728844 & 5.02711555228075e-06 \tabularnewline
57 & 22.39 & 22.309999922068 & 0.0800000779319916 \tabularnewline
58 & 22.42 & 22.3887598125963 & 0.0312401874036929 \tabularnewline
59 & 22.42 & 22.4195157043854 & 0.000484295614562313 \tabularnewline
60 & 22.42 & 22.4199924922908 & 7.50770919566435e-06 \tabularnewline
61 & 22.15 & 22.419999883613 & -0.269999883613036 \tabularnewline
62 & 21.95 & 22.1541856266058 & -0.204185626605767 \tabularnewline
63 & 21.96 & 21.9531653524431 & 0.00683464755688235 \tabularnewline
64 & 21.97 & 21.9598940470556 & 0.010105952944393 \tabularnewline
65 & 21.66 & 21.9698433342083 & -0.309843334208317 \tabularnewline
66 & 21.66 & 21.6648032928234 & -0.0048032928234214 \tabularnewline
67 & 21.68 & 21.6600744622182 & 0.0199255377818375 \tabularnewline
68 & 21.75 & 21.6796911077888 & 0.0703088922112052 \tabularnewline
69 & 21.55 & 21.7489100485307 & -0.198910048530674 \tabularnewline
70 & 21.59 & 21.5530835687043 & 0.0369164312956585 \tabularnewline
71 & 21.54 & 21.589427709394 & -0.0494277093939708 \tabularnewline
72 & 21.54 & 21.5407662445359 & -0.000766244535860494 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261607&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]21.95[/C][C]21.94[/C][C]0.00999999999999801[/C][/ROW]
[ROW][C]3[/C][C]21.96[/C][C]21.9498449767256[/C][C]0.0101550232744501[/C][/ROW]
[ROW][C]4[/C][C]22.1[/C][C]21.959842573504[/C][C]0.140157426496007[/C][/ROW]
[ROW][C]5[/C][C]22.13[/C][C]22.0978272336807[/C][C]0.0321727663193307[/C][/ROW]
[ROW][C]6[/C][C]22.18[/C][C]22.1295012472417[/C][C]0.0504987527582799[/C][/ROW]
[ROW][C]7[/C][C]22.18[/C][C]22.1792171517992[/C][C]0.000782848200802988[/C][/ROW]
[ROW][C]8[/C][C]22.27[/C][C]22.1799878640308[/C][C]0.0900121359691504[/C][/ROW]
[ROW][C]9[/C][C]22.3[/C][C]22.2686046023942[/C][C]0.031395397605781[/C][/ROW]
[ROW][C]10[/C][C]22.04[/C][C]22.2995132982661[/C][C]-0.259513298266064[/C][/ROW]
[ROW][C]11[/C][C]22.05[/C][C]22.0440230601259[/C][C]0.00597693987405634[/C][/ROW]
[ROW][C]12[/C][C]22.06[/C][C]22.049907343521[/C][C]0.010092656479042[/C][/ROW]
[ROW][C]13[/C][C]22.06[/C][C]22.0598435403345[/C][C]0.000156459665525688[/C][/ROW]
[ROW][C]14[/C][C]22.06[/C][C]22.059997574511[/C][C]2.42548896878247e-06[/C][/ROW]
[ROW][C]15[/C][C]21.97[/C][C]22.0599999623993[/C][C]-0.0899999623992755[/C][/ROW]
[ROW][C]16[/C][C]22.03[/C][C]21.9713952088871[/C][C]0.058604791112888[/C][/ROW]
[ROW][C]17[/C][C]22.08[/C][C]22.0290914893383[/C][C]0.0509085106616496[/C][/ROW]
[ROW][C]18[/C][C]22.13[/C][C]22.079210799598[/C][C]0.0507892004019936[/C][/ROW]
[ROW][C]19[/C][C]22.13[/C][C]22.1292126491847[/C][C]0.000787350815279808[/C][/ROW]
[ROW][C]20[/C][C]22.4[/C][C]22.1299877942298[/C][C]0.270012205770151[/C][/ROW]
[ROW][C]21[/C][C]22.4[/C][C]22.3958141823721[/C][C]0.00418581762788151[/C][/ROW]
[ROW][C]22[/C][C]22.12[/C][C]22.3999351100845[/C][C]-0.279935110084509[/C][/ROW]
[ROW][C]23[/C][C]22.22[/C][C]22.1243396457398[/C][C]0.0956603542602323[/C][/ROW]
[ROW][C]24[/C][C]22.14[/C][C]22.2185170418648[/C][C]-0.0785170418647887[/C][/ROW]
[ROW][C]25[/C][C]22.14[/C][C]22.141217196893[/C][C]-0.0012171968929664[/C][/ROW]
[ROW][C]26[/C][C]22.19[/C][C]22.1400188693848[/C][C]0.0499811306152012[/C][/ROW]
[ROW][C]27[/C][C]22.29[/C][C]22.1892251761472[/C][C]0.100774823852845[/C][/ROW]
[ROW][C]28[/C][C]22.24[/C][C]22.2884377556825[/C][C]-0.0484377556824604[/C][/ROW]
[ROW][C]29[/C][C]22.26[/C][C]22.2407508979493[/C][C]0.0192491020507326[/C][/ROW]
[ROW][C]30[/C][C]22.29[/C][C]22.259701594117[/C][C]0.030298405883002[/C][/ROW]
[ROW][C]31[/C][C]22.29[/C][C]22.289530304191[/C][C]0.000469695809048432[/C][/ROW]
[ROW][C]32[/C][C]22.29[/C][C]22.2899927186218[/C][C]7.2813782310277e-06[/C][/ROW]
[ROW][C]33[/C][C]22.29[/C][C]22.2899998871217[/C][C]1.12878311142595e-07[/C][/ROW]
[ROW][C]34[/C][C]22.35[/C][C]22.2899999982501[/C][C]0.0600000017498807[/C][/ROW]
[ROW][C]35[/C][C]22.39[/C][C]22.3490698603262[/C][C]0.0409301396738009[/C][/ROW]
[ROW][C]36[/C][C]22.43[/C][C]22.3893654875724[/C][C]0.0406345124275731[/C][/ROW]
[ROW][C]37[/C][C]22.43[/C][C]22.4293700704828[/C][C]0.000629929517202754[/C][/ROW]
[ROW][C]38[/C][C]22.11[/C][C]22.4299902346264[/C][C]-0.31999023462636[/C][/ROW]
[ROW][C]39[/C][C]22.12[/C][C]22.1149605933962[/C][C]0.00503940660375335[/C][/ROW]
[ROW][C]40[/C][C]22.05[/C][C]22.1199218774687[/C][C]-0.0699218774687047[/C][/ROW]
[ROW][C]41[/C][C]22.05[/C][C]22.0510839518401[/C][C]-0.00108395184006227[/C][/ROW]
[ROW][C]42[/C][C]22.08[/C][C]22.0500168037764[/C][C]0.0299831962236361[/C][/ROW]
[ROW][C]43[/C][C]22.08[/C][C]22.0795351906743[/C][C]0.000464809325691817[/C][/ROW]
[ROW][C]44[/C][C]22.09[/C][C]22.0799927943736[/C][C]0.0100072056263656[/C][/ROW]
[ROW][C]45[/C][C]22.09[/C][C]22.0898448650216[/C][C]0.000155134978424343[/C][/ROW]
[ROW][C]46[/C][C]22.24[/C][C]22.0899975950468[/C][C]0.150002404953231[/C][/ROW]
[ROW][C]47[/C][C]22.25[/C][C]22.2376746136009[/C][C]0.0123253863990627[/C][/ROW]
[ROW][C]48[/C][C]22.24[/C][C]22.2498089278242[/C][C]-0.00980892782416021[/C][/ROW]
[ROW][C]49[/C][C]22.24[/C][C]22.240152061211[/C][C]-0.000152061211011301[/C][/ROW]
[ROW][C]50[/C][C]22.25[/C][C]22.2400023573027[/C][C]0.00999764269731429[/C][/ROW]
[ROW][C]51[/C][C]22.28[/C][C]22.2498450132692[/C][C]0.0301549867307713[/C][/ROW]
[ROW][C]52[/C][C]22.23[/C][C]22.2795325275216[/C][C]-0.0495325275216132[/C][/ROW]
[ROW][C]53[/C][C]22.29[/C][C]22.2307678694608[/C][C]0.0592321305392005[/C][/ROW]
[ROW][C]54[/C][C]22.31[/C][C]22.2890817641171[/C][C]0.0209182358828599[/C][/ROW]
[ROW][C]55[/C][C]22.31[/C][C]22.3096757186578[/C][C]0.000324281342219734[/C][/ROW]
[ROW][C]56[/C][C]22.31[/C][C]22.3099949728844[/C][C]5.02711555228075e-06[/C][/ROW]
[ROW][C]57[/C][C]22.39[/C][C]22.309999922068[/C][C]0.0800000779319916[/C][/ROW]
[ROW][C]58[/C][C]22.42[/C][C]22.3887598125963[/C][C]0.0312401874036929[/C][/ROW]
[ROW][C]59[/C][C]22.42[/C][C]22.4195157043854[/C][C]0.000484295614562313[/C][/ROW]
[ROW][C]60[/C][C]22.42[/C][C]22.4199924922908[/C][C]7.50770919566435e-06[/C][/ROW]
[ROW][C]61[/C][C]22.15[/C][C]22.419999883613[/C][C]-0.269999883613036[/C][/ROW]
[ROW][C]62[/C][C]21.95[/C][C]22.1541856266058[/C][C]-0.204185626605767[/C][/ROW]
[ROW][C]63[/C][C]21.96[/C][C]21.9531653524431[/C][C]0.00683464755688235[/C][/ROW]
[ROW][C]64[/C][C]21.97[/C][C]21.9598940470556[/C][C]0.010105952944393[/C][/ROW]
[ROW][C]65[/C][C]21.66[/C][C]21.9698433342083[/C][C]-0.309843334208317[/C][/ROW]
[ROW][C]66[/C][C]21.66[/C][C]21.6648032928234[/C][C]-0.0048032928234214[/C][/ROW]
[ROW][C]67[/C][C]21.68[/C][C]21.6600744622182[/C][C]0.0199255377818375[/C][/ROW]
[ROW][C]68[/C][C]21.75[/C][C]21.6796911077888[/C][C]0.0703088922112052[/C][/ROW]
[ROW][C]69[/C][C]21.55[/C][C]21.7489100485307[/C][C]-0.198910048530674[/C][/ROW]
[ROW][C]70[/C][C]21.59[/C][C]21.5530835687043[/C][C]0.0369164312956585[/C][/ROW]
[ROW][C]71[/C][C]21.54[/C][C]21.589427709394[/C][C]-0.0494277093939708[/C][/ROW]
[ROW][C]72[/C][C]21.54[/C][C]21.5407662445359[/C][C]-0.000766244535860494[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261607&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261607&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
221.9521.940.00999999999999801
321.9621.94984497672560.0101550232744501
422.121.9598425735040.140157426496007
522.1322.09782723368070.0321727663193307
622.1822.12950124724170.0504987527582799
722.1822.17921715179920.000782848200802988
822.2722.17998786403080.0900121359691504
922.322.26860460239420.031395397605781
1022.0422.2995132982661-0.259513298266064
1122.0522.04402306012590.00597693987405634
1222.0622.0499073435210.010092656479042
1322.0622.05984354033450.000156459665525688
1422.0622.0599975745112.42548896878247e-06
1521.9722.0599999623993-0.0899999623992755
1622.0321.97139520888710.058604791112888
1722.0822.02909148933830.0509085106616496
1822.1322.0792107995980.0507892004019936
1922.1322.12921264918470.000787350815279808
2022.422.12998779422980.270012205770151
2122.422.39581418237210.00418581762788151
2222.1222.3999351100845-0.279935110084509
2322.2222.12433964573980.0956603542602323
2422.1422.2185170418648-0.0785170418647887
2522.1422.141217196893-0.0012171968929664
2622.1922.14001886938480.0499811306152012
2722.2922.18922517614720.100774823852845
2822.2422.2884377556825-0.0484377556824604
2922.2622.24075089794930.0192491020507326
3022.2922.2597015941170.030298405883002
3122.2922.2895303041910.000469695809048432
3222.2922.28999271862187.2813782310277e-06
3322.2922.28999988712171.12878311142595e-07
3422.3522.28999999825010.0600000017498807
3522.3922.34906986032620.0409301396738009
3622.4322.38936548757240.0406345124275731
3722.4322.42937007048280.000629929517202754
3822.1122.4299902346264-0.31999023462636
3922.1222.11496059339620.00503940660375335
4022.0522.1199218774687-0.0699218774687047
4122.0522.0510839518401-0.00108395184006227
4222.0822.05001680377640.0299831962236361
4322.0822.07953519067430.000464809325691817
4422.0922.07999279437360.0100072056263656
4522.0922.08984486502160.000155134978424343
4622.2422.08999759504680.150002404953231
4722.2522.23767461360090.0123253863990627
4822.2422.2498089278242-0.00980892782416021
4922.2422.240152061211-0.000152061211011301
5022.2522.24000235730270.00999764269731429
5122.2822.24984501326920.0301549867307713
5222.2322.2795325275216-0.0495325275216132
5322.2922.23076786946080.0592321305392005
5422.3122.28908176411710.0209182358828599
5522.3122.30967571865780.000324281342219734
5622.3122.30999497288445.02711555228075e-06
5722.3922.3099999220680.0800000779319916
5822.4222.38875981259630.0312401874036929
5922.4222.41951570438540.000484295614562313
6022.4222.41999249229087.50770919566435e-06
6122.1522.419999883613-0.269999883613036
6221.9522.1541856266058-0.204185626605767
6321.9621.95316535244310.00683464755688235
6421.9721.95989404705560.010105952944393
6521.6621.9698433342083-0.309843334208317
6621.6621.6648032928234-0.0048032928234214
6721.6821.66007446221820.0199255377818375
6821.7521.67969110778880.0703088922112052
6921.5521.7489100485307-0.198910048530674
7021.5921.55308356870430.0369164312956585
7121.5421.589427709394-0.0494277093939708
7221.5421.5407662445359-0.000766244535860494







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7321.540011878573721.342685956854421.737337800293
7421.540011878573721.263105482904221.8169182742432
7521.540011878573721.201756376707221.8782673804402
7621.540011878573721.149939555634421.930084201513
7721.540011878573721.104241239700921.9757825174465
7821.540011878573721.062900065385322.0171236917621
7921.540011878573721.024865962483722.0551577946637
8021.540011878573720.989453119271422.090570637876
8121.540011878573720.956184352651222.1238394044962
8221.540011878573720.924711778943422.155311978204
8321.540011878573720.894772508118522.1852512490289
8421.540011878573720.866162134368322.2138616227791

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 21.5400118785737 & 21.3426859568544 & 21.737337800293 \tabularnewline
74 & 21.5400118785737 & 21.2631054829042 & 21.8169182742432 \tabularnewline
75 & 21.5400118785737 & 21.2017563767072 & 21.8782673804402 \tabularnewline
76 & 21.5400118785737 & 21.1499395556344 & 21.930084201513 \tabularnewline
77 & 21.5400118785737 & 21.1042412397009 & 21.9757825174465 \tabularnewline
78 & 21.5400118785737 & 21.0629000653853 & 22.0171236917621 \tabularnewline
79 & 21.5400118785737 & 21.0248659624837 & 22.0551577946637 \tabularnewline
80 & 21.5400118785737 & 20.9894531192714 & 22.090570637876 \tabularnewline
81 & 21.5400118785737 & 20.9561843526512 & 22.1238394044962 \tabularnewline
82 & 21.5400118785737 & 20.9247117789434 & 22.155311978204 \tabularnewline
83 & 21.5400118785737 & 20.8947725081185 & 22.1852512490289 \tabularnewline
84 & 21.5400118785737 & 20.8661621343683 & 22.2138616227791 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261607&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]21.5400118785737[/C][C]21.3426859568544[/C][C]21.737337800293[/C][/ROW]
[ROW][C]74[/C][C]21.5400118785737[/C][C]21.2631054829042[/C][C]21.8169182742432[/C][/ROW]
[ROW][C]75[/C][C]21.5400118785737[/C][C]21.2017563767072[/C][C]21.8782673804402[/C][/ROW]
[ROW][C]76[/C][C]21.5400118785737[/C][C]21.1499395556344[/C][C]21.930084201513[/C][/ROW]
[ROW][C]77[/C][C]21.5400118785737[/C][C]21.1042412397009[/C][C]21.9757825174465[/C][/ROW]
[ROW][C]78[/C][C]21.5400118785737[/C][C]21.0629000653853[/C][C]22.0171236917621[/C][/ROW]
[ROW][C]79[/C][C]21.5400118785737[/C][C]21.0248659624837[/C][C]22.0551577946637[/C][/ROW]
[ROW][C]80[/C][C]21.5400118785737[/C][C]20.9894531192714[/C][C]22.090570637876[/C][/ROW]
[ROW][C]81[/C][C]21.5400118785737[/C][C]20.9561843526512[/C][C]22.1238394044962[/C][/ROW]
[ROW][C]82[/C][C]21.5400118785737[/C][C]20.9247117789434[/C][C]22.155311978204[/C][/ROW]
[ROW][C]83[/C][C]21.5400118785737[/C][C]20.8947725081185[/C][C]22.1852512490289[/C][/ROW]
[ROW][C]84[/C][C]21.5400118785737[/C][C]20.8661621343683[/C][C]22.2138616227791[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261607&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261607&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
7321.540011878573721.342685956854421.737337800293
7421.540011878573721.263105482904221.8169182742432
7521.540011878573721.201756376707221.8782673804402
7621.540011878573721.149939555634421.930084201513
7721.540011878573721.104241239700921.9757825174465
7821.540011878573721.062900065385322.0171236917621
7921.540011878573721.024865962483722.0551577946637
8021.540011878573720.989453119271422.090570637876
8121.540011878573720.956184352651222.1238394044962
8221.540011878573720.924711778943422.155311978204
8321.540011878573720.894772508118522.1852512490289
8421.540011878573720.866162134368322.2138616227791



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')