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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 04 Jan 2015 20:11:07 +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/2015/Jan/04/t14204023987j3v606yuimkip0.htm/, Retrieved Tue, 14 May 2024 13:51:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=271934, Retrieved Tue, 14 May 2024 13:51:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact147
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [] [2014-12-16 21:00:28] [8ae5f3921d0f515f24933d117e773272]
- R  D    [Exponential Smoothing] [] [2015-01-04 20:11:07] [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 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=271934&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=271934&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271934&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
alpha0.973542292398817
beta0.0235630691081967
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.973542292398817 \tabularnewline
beta & 0.0235630691081967 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271934&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]0.973542292398817[/C][/ROW]
[ROW][C]beta[/C][C]0.0235630691081967[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271934&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271934&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
alpha0.973542292398817
beta0.0235630691081967
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
321.9621.963.5527136788005e-15
422.121.970.130000000000003
522.1322.10954265177290.0204573482271329
622.1822.14291018351530.0370898164846984
722.1822.1933209537313-0.0133209537313448
822.2722.19434912920910.0756508707908701
922.322.28373054275930.0162694572407247
1022.0422.3156748543982-0.275674854398247
1122.0522.0570751485248-0.00707514852477686
1222.0622.05980631465440.000193685345617922
1322.0622.0696184410462-0.00961844104617171
1422.0622.0696574038007-0.00965740380072333
1521.9722.0694368972577-0.0994368972576893
1622.0321.97953120978920.0504687902107754
1722.0822.03672278503890.0432772149610976
1822.1322.08790582155220.0420941784477762
1922.1322.1389027474677-0.00890274746772235
2022.422.14004778336180.259952216638187
2122.422.4088977087231-0.00889770872309015
2222.1222.4158067511636-0.295806751163568
2322.2222.13661200505880.0833879949412371
2422.1422.2284922722866-0.0884922722865511
2522.1422.1510098488884-0.011009848888353
2622.1922.14870727956840.0412927204316134
2722.2922.19827071380210.0917292861979462
2822.2422.2990405150913-0.0590405150912972
2922.2622.25167516999250.00832483000750983
3022.2922.27008380602880.0199161939712198
3122.2922.3002339955161-0.0102339955161455
3222.2922.3007969361967-0.0107969361966553
3322.2922.3005641524405-0.0105641524405264
3422.3522.30031565561650.0496843443835076
3522.3922.35986135969230.0301386403076762
3622.4322.40106986390440.0289301360955676
3722.4322.4417654851875-0.0117654851875422
3822.1122.4425723019907-0.332572301990702
3922.1222.1234310246293-0.00343102462926836
4022.0522.1246439944687-0.0746439944687296
4122.0522.0548158197188-0.004815819718754
4222.0822.05285785309750.0271421469025412
4322.0822.082634949757-0.00263494975696688
4422.0922.08336233866340.00663766133662236
4522.0922.0932692722205-0.0032692722205141
4622.2422.09345639102990.146543608970113
4722.2522.24285434389090.00714565610905638
4822.2422.2567064129775-0.0167064129774914
4922.2422.2469542448756-0.00695424487557261
5022.2522.24653669695950.00346330304047626
5122.2822.25634051946270.0236594805372548
5222.2322.2863489149721-0.0563489149720908
5322.2922.23717312963910.05282687036091
5422.3122.295496418250.0145035817499988
5522.3122.316843071621-0.00684307162103082
5622.3122.3172508775052-0.00725087750517517
5722.3922.31709533456310.0729046654369334
5822.4222.39664700973940.0233529902606406
5922.4222.4284937427626-0.00849374276260662
6022.4222.4291414908751-0.00914149087510552
6122.1522.4289489262561-0.278948926256081
6221.9522.1596884233395-0.209688423339497
6321.9621.95304577135650.00695422864347606
6421.9721.9574734309480.0125265690520173
6521.6621.9676133546333-0.307613354633347
6621.6621.65902698218370.000973017816320976
6721.6821.65088481485430.0291151851456846
6821.7521.67080812961130.0791918703887262
6921.5521.7412998486549-0.191299848654879
7021.5921.54406808898010.0459319110198848
7121.5421.5788451421505-0.0388451421504534
7221.5421.53019705489020.00980294510979007

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 21.96 & 21.96 & 3.5527136788005e-15 \tabularnewline
4 & 22.1 & 21.97 & 0.130000000000003 \tabularnewline
5 & 22.13 & 22.1095426517729 & 0.0204573482271329 \tabularnewline
6 & 22.18 & 22.1429101835153 & 0.0370898164846984 \tabularnewline
7 & 22.18 & 22.1933209537313 & -0.0133209537313448 \tabularnewline
8 & 22.27 & 22.1943491292091 & 0.0756508707908701 \tabularnewline
9 & 22.3 & 22.2837305427593 & 0.0162694572407247 \tabularnewline
10 & 22.04 & 22.3156748543982 & -0.275674854398247 \tabularnewline
11 & 22.05 & 22.0570751485248 & -0.00707514852477686 \tabularnewline
12 & 22.06 & 22.0598063146544 & 0.000193685345617922 \tabularnewline
13 & 22.06 & 22.0696184410462 & -0.00961844104617171 \tabularnewline
14 & 22.06 & 22.0696574038007 & -0.00965740380072333 \tabularnewline
15 & 21.97 & 22.0694368972577 & -0.0994368972576893 \tabularnewline
16 & 22.03 & 21.9795312097892 & 0.0504687902107754 \tabularnewline
17 & 22.08 & 22.0367227850389 & 0.0432772149610976 \tabularnewline
18 & 22.13 & 22.0879058215522 & 0.0420941784477762 \tabularnewline
19 & 22.13 & 22.1389027474677 & -0.00890274746772235 \tabularnewline
20 & 22.4 & 22.1400477833618 & 0.259952216638187 \tabularnewline
21 & 22.4 & 22.4088977087231 & -0.00889770872309015 \tabularnewline
22 & 22.12 & 22.4158067511636 & -0.295806751163568 \tabularnewline
23 & 22.22 & 22.1366120050588 & 0.0833879949412371 \tabularnewline
24 & 22.14 & 22.2284922722866 & -0.0884922722865511 \tabularnewline
25 & 22.14 & 22.1510098488884 & -0.011009848888353 \tabularnewline
26 & 22.19 & 22.1487072795684 & 0.0412927204316134 \tabularnewline
27 & 22.29 & 22.1982707138021 & 0.0917292861979462 \tabularnewline
28 & 22.24 & 22.2990405150913 & -0.0590405150912972 \tabularnewline
29 & 22.26 & 22.2516751699925 & 0.00832483000750983 \tabularnewline
30 & 22.29 & 22.2700838060288 & 0.0199161939712198 \tabularnewline
31 & 22.29 & 22.3002339955161 & -0.0102339955161455 \tabularnewline
32 & 22.29 & 22.3007969361967 & -0.0107969361966553 \tabularnewline
33 & 22.29 & 22.3005641524405 & -0.0105641524405264 \tabularnewline
34 & 22.35 & 22.3003156556165 & 0.0496843443835076 \tabularnewline
35 & 22.39 & 22.3598613596923 & 0.0301386403076762 \tabularnewline
36 & 22.43 & 22.4010698639044 & 0.0289301360955676 \tabularnewline
37 & 22.43 & 22.4417654851875 & -0.0117654851875422 \tabularnewline
38 & 22.11 & 22.4425723019907 & -0.332572301990702 \tabularnewline
39 & 22.12 & 22.1234310246293 & -0.00343102462926836 \tabularnewline
40 & 22.05 & 22.1246439944687 & -0.0746439944687296 \tabularnewline
41 & 22.05 & 22.0548158197188 & -0.004815819718754 \tabularnewline
42 & 22.08 & 22.0528578530975 & 0.0271421469025412 \tabularnewline
43 & 22.08 & 22.082634949757 & -0.00263494975696688 \tabularnewline
44 & 22.09 & 22.0833623386634 & 0.00663766133662236 \tabularnewline
45 & 22.09 & 22.0932692722205 & -0.0032692722205141 \tabularnewline
46 & 22.24 & 22.0934563910299 & 0.146543608970113 \tabularnewline
47 & 22.25 & 22.2428543438909 & 0.00714565610905638 \tabularnewline
48 & 22.24 & 22.2567064129775 & -0.0167064129774914 \tabularnewline
49 & 22.24 & 22.2469542448756 & -0.00695424487557261 \tabularnewline
50 & 22.25 & 22.2465366969595 & 0.00346330304047626 \tabularnewline
51 & 22.28 & 22.2563405194627 & 0.0236594805372548 \tabularnewline
52 & 22.23 & 22.2863489149721 & -0.0563489149720908 \tabularnewline
53 & 22.29 & 22.2371731296391 & 0.05282687036091 \tabularnewline
54 & 22.31 & 22.29549641825 & 0.0145035817499988 \tabularnewline
55 & 22.31 & 22.316843071621 & -0.00684307162103082 \tabularnewline
56 & 22.31 & 22.3172508775052 & -0.00725087750517517 \tabularnewline
57 & 22.39 & 22.3170953345631 & 0.0729046654369334 \tabularnewline
58 & 22.42 & 22.3966470097394 & 0.0233529902606406 \tabularnewline
59 & 22.42 & 22.4284937427626 & -0.00849374276260662 \tabularnewline
60 & 22.42 & 22.4291414908751 & -0.00914149087510552 \tabularnewline
61 & 22.15 & 22.4289489262561 & -0.278948926256081 \tabularnewline
62 & 21.95 & 22.1596884233395 & -0.209688423339497 \tabularnewline
63 & 21.96 & 21.9530457713565 & 0.00695422864347606 \tabularnewline
64 & 21.97 & 21.957473430948 & 0.0125265690520173 \tabularnewline
65 & 21.66 & 21.9676133546333 & -0.307613354633347 \tabularnewline
66 & 21.66 & 21.6590269821837 & 0.000973017816320976 \tabularnewline
67 & 21.68 & 21.6508848148543 & 0.0291151851456846 \tabularnewline
68 & 21.75 & 21.6708081296113 & 0.0791918703887262 \tabularnewline
69 & 21.55 & 21.7412998486549 & -0.191299848654879 \tabularnewline
70 & 21.59 & 21.5440680889801 & 0.0459319110198848 \tabularnewline
71 & 21.54 & 21.5788451421505 & -0.0388451421504534 \tabularnewline
72 & 21.54 & 21.5301970548902 & 0.00980294510979007 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271934&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]3[/C][C]21.96[/C][C]21.96[/C][C]3.5527136788005e-15[/C][/ROW]
[ROW][C]4[/C][C]22.1[/C][C]21.97[/C][C]0.130000000000003[/C][/ROW]
[ROW][C]5[/C][C]22.13[/C][C]22.1095426517729[/C][C]0.0204573482271329[/C][/ROW]
[ROW][C]6[/C][C]22.18[/C][C]22.1429101835153[/C][C]0.0370898164846984[/C][/ROW]
[ROW][C]7[/C][C]22.18[/C][C]22.1933209537313[/C][C]-0.0133209537313448[/C][/ROW]
[ROW][C]8[/C][C]22.27[/C][C]22.1943491292091[/C][C]0.0756508707908701[/C][/ROW]
[ROW][C]9[/C][C]22.3[/C][C]22.2837305427593[/C][C]0.0162694572407247[/C][/ROW]
[ROW][C]10[/C][C]22.04[/C][C]22.3156748543982[/C][C]-0.275674854398247[/C][/ROW]
[ROW][C]11[/C][C]22.05[/C][C]22.0570751485248[/C][C]-0.00707514852477686[/C][/ROW]
[ROW][C]12[/C][C]22.06[/C][C]22.0598063146544[/C][C]0.000193685345617922[/C][/ROW]
[ROW][C]13[/C][C]22.06[/C][C]22.0696184410462[/C][C]-0.00961844104617171[/C][/ROW]
[ROW][C]14[/C][C]22.06[/C][C]22.0696574038007[/C][C]-0.00965740380072333[/C][/ROW]
[ROW][C]15[/C][C]21.97[/C][C]22.0694368972577[/C][C]-0.0994368972576893[/C][/ROW]
[ROW][C]16[/C][C]22.03[/C][C]21.9795312097892[/C][C]0.0504687902107754[/C][/ROW]
[ROW][C]17[/C][C]22.08[/C][C]22.0367227850389[/C][C]0.0432772149610976[/C][/ROW]
[ROW][C]18[/C][C]22.13[/C][C]22.0879058215522[/C][C]0.0420941784477762[/C][/ROW]
[ROW][C]19[/C][C]22.13[/C][C]22.1389027474677[/C][C]-0.00890274746772235[/C][/ROW]
[ROW][C]20[/C][C]22.4[/C][C]22.1400477833618[/C][C]0.259952216638187[/C][/ROW]
[ROW][C]21[/C][C]22.4[/C][C]22.4088977087231[/C][C]-0.00889770872309015[/C][/ROW]
[ROW][C]22[/C][C]22.12[/C][C]22.4158067511636[/C][C]-0.295806751163568[/C][/ROW]
[ROW][C]23[/C][C]22.22[/C][C]22.1366120050588[/C][C]0.0833879949412371[/C][/ROW]
[ROW][C]24[/C][C]22.14[/C][C]22.2284922722866[/C][C]-0.0884922722865511[/C][/ROW]
[ROW][C]25[/C][C]22.14[/C][C]22.1510098488884[/C][C]-0.011009848888353[/C][/ROW]
[ROW][C]26[/C][C]22.19[/C][C]22.1487072795684[/C][C]0.0412927204316134[/C][/ROW]
[ROW][C]27[/C][C]22.29[/C][C]22.1982707138021[/C][C]0.0917292861979462[/C][/ROW]
[ROW][C]28[/C][C]22.24[/C][C]22.2990405150913[/C][C]-0.0590405150912972[/C][/ROW]
[ROW][C]29[/C][C]22.26[/C][C]22.2516751699925[/C][C]0.00832483000750983[/C][/ROW]
[ROW][C]30[/C][C]22.29[/C][C]22.2700838060288[/C][C]0.0199161939712198[/C][/ROW]
[ROW][C]31[/C][C]22.29[/C][C]22.3002339955161[/C][C]-0.0102339955161455[/C][/ROW]
[ROW][C]32[/C][C]22.29[/C][C]22.3007969361967[/C][C]-0.0107969361966553[/C][/ROW]
[ROW][C]33[/C][C]22.29[/C][C]22.3005641524405[/C][C]-0.0105641524405264[/C][/ROW]
[ROW][C]34[/C][C]22.35[/C][C]22.3003156556165[/C][C]0.0496843443835076[/C][/ROW]
[ROW][C]35[/C][C]22.39[/C][C]22.3598613596923[/C][C]0.0301386403076762[/C][/ROW]
[ROW][C]36[/C][C]22.43[/C][C]22.4010698639044[/C][C]0.0289301360955676[/C][/ROW]
[ROW][C]37[/C][C]22.43[/C][C]22.4417654851875[/C][C]-0.0117654851875422[/C][/ROW]
[ROW][C]38[/C][C]22.11[/C][C]22.4425723019907[/C][C]-0.332572301990702[/C][/ROW]
[ROW][C]39[/C][C]22.12[/C][C]22.1234310246293[/C][C]-0.00343102462926836[/C][/ROW]
[ROW][C]40[/C][C]22.05[/C][C]22.1246439944687[/C][C]-0.0746439944687296[/C][/ROW]
[ROW][C]41[/C][C]22.05[/C][C]22.0548158197188[/C][C]-0.004815819718754[/C][/ROW]
[ROW][C]42[/C][C]22.08[/C][C]22.0528578530975[/C][C]0.0271421469025412[/C][/ROW]
[ROW][C]43[/C][C]22.08[/C][C]22.082634949757[/C][C]-0.00263494975696688[/C][/ROW]
[ROW][C]44[/C][C]22.09[/C][C]22.0833623386634[/C][C]0.00663766133662236[/C][/ROW]
[ROW][C]45[/C][C]22.09[/C][C]22.0932692722205[/C][C]-0.0032692722205141[/C][/ROW]
[ROW][C]46[/C][C]22.24[/C][C]22.0934563910299[/C][C]0.146543608970113[/C][/ROW]
[ROW][C]47[/C][C]22.25[/C][C]22.2428543438909[/C][C]0.00714565610905638[/C][/ROW]
[ROW][C]48[/C][C]22.24[/C][C]22.2567064129775[/C][C]-0.0167064129774914[/C][/ROW]
[ROW][C]49[/C][C]22.24[/C][C]22.2469542448756[/C][C]-0.00695424487557261[/C][/ROW]
[ROW][C]50[/C][C]22.25[/C][C]22.2465366969595[/C][C]0.00346330304047626[/C][/ROW]
[ROW][C]51[/C][C]22.28[/C][C]22.2563405194627[/C][C]0.0236594805372548[/C][/ROW]
[ROW][C]52[/C][C]22.23[/C][C]22.2863489149721[/C][C]-0.0563489149720908[/C][/ROW]
[ROW][C]53[/C][C]22.29[/C][C]22.2371731296391[/C][C]0.05282687036091[/C][/ROW]
[ROW][C]54[/C][C]22.31[/C][C]22.29549641825[/C][C]0.0145035817499988[/C][/ROW]
[ROW][C]55[/C][C]22.31[/C][C]22.316843071621[/C][C]-0.00684307162103082[/C][/ROW]
[ROW][C]56[/C][C]22.31[/C][C]22.3172508775052[/C][C]-0.00725087750517517[/C][/ROW]
[ROW][C]57[/C][C]22.39[/C][C]22.3170953345631[/C][C]0.0729046654369334[/C][/ROW]
[ROW][C]58[/C][C]22.42[/C][C]22.3966470097394[/C][C]0.0233529902606406[/C][/ROW]
[ROW][C]59[/C][C]22.42[/C][C]22.4284937427626[/C][C]-0.00849374276260662[/C][/ROW]
[ROW][C]60[/C][C]22.42[/C][C]22.4291414908751[/C][C]-0.00914149087510552[/C][/ROW]
[ROW][C]61[/C][C]22.15[/C][C]22.4289489262561[/C][C]-0.278948926256081[/C][/ROW]
[ROW][C]62[/C][C]21.95[/C][C]22.1596884233395[/C][C]-0.209688423339497[/C][/ROW]
[ROW][C]63[/C][C]21.96[/C][C]21.9530457713565[/C][C]0.00695422864347606[/C][/ROW]
[ROW][C]64[/C][C]21.97[/C][C]21.957473430948[/C][C]0.0125265690520173[/C][/ROW]
[ROW][C]65[/C][C]21.66[/C][C]21.9676133546333[/C][C]-0.307613354633347[/C][/ROW]
[ROW][C]66[/C][C]21.66[/C][C]21.6590269821837[/C][C]0.000973017816320976[/C][/ROW]
[ROW][C]67[/C][C]21.68[/C][C]21.6508848148543[/C][C]0.0291151851456846[/C][/ROW]
[ROW][C]68[/C][C]21.75[/C][C]21.6708081296113[/C][C]0.0791918703887262[/C][/ROW]
[ROW][C]69[/C][C]21.55[/C][C]21.7412998486549[/C][C]-0.191299848654879[/C][/ROW]
[ROW][C]70[/C][C]21.59[/C][C]21.5440680889801[/C][C]0.0459319110198848[/C][/ROW]
[ROW][C]71[/C][C]21.54[/C][C]21.5788451421505[/C][C]-0.0388451421504534[/C][/ROW]
[ROW][C]72[/C][C]21.54[/C][C]21.5301970548902[/C][C]0.00980294510979007[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271934&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271934&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
321.9621.963.5527136788005e-15
422.121.970.130000000000003
522.1322.10954265177290.0204573482271329
622.1822.14291018351530.0370898164846984
722.1822.1933209537313-0.0133209537313448
822.2722.19434912920910.0756508707908701
922.322.28373054275930.0162694572407247
1022.0422.3156748543982-0.275674854398247
1122.0522.0570751485248-0.00707514852477686
1222.0622.05980631465440.000193685345617922
1322.0622.0696184410462-0.00961844104617171
1422.0622.0696574038007-0.00965740380072333
1521.9722.0694368972577-0.0994368972576893
1622.0321.97953120978920.0504687902107754
1722.0822.03672278503890.0432772149610976
1822.1322.08790582155220.0420941784477762
1922.1322.1389027474677-0.00890274746772235
2022.422.14004778336180.259952216638187
2122.422.4088977087231-0.00889770872309015
2222.1222.4158067511636-0.295806751163568
2322.2222.13661200505880.0833879949412371
2422.1422.2284922722866-0.0884922722865511
2522.1422.1510098488884-0.011009848888353
2622.1922.14870727956840.0412927204316134
2722.2922.19827071380210.0917292861979462
2822.2422.2990405150913-0.0590405150912972
2922.2622.25167516999250.00832483000750983
3022.2922.27008380602880.0199161939712198
3122.2922.3002339955161-0.0102339955161455
3222.2922.3007969361967-0.0107969361966553
3322.2922.3005641524405-0.0105641524405264
3422.3522.30031565561650.0496843443835076
3522.3922.35986135969230.0301386403076762
3622.4322.40106986390440.0289301360955676
3722.4322.4417654851875-0.0117654851875422
3822.1122.4425723019907-0.332572301990702
3922.1222.1234310246293-0.00343102462926836
4022.0522.1246439944687-0.0746439944687296
4122.0522.0548158197188-0.004815819718754
4222.0822.05285785309750.0271421469025412
4322.0822.082634949757-0.00263494975696688
4422.0922.08336233866340.00663766133662236
4522.0922.0932692722205-0.0032692722205141
4622.2422.09345639102990.146543608970113
4722.2522.24285434389090.00714565610905638
4822.2422.2567064129775-0.0167064129774914
4922.2422.2469542448756-0.00695424487557261
5022.2522.24653669695950.00346330304047626
5122.2822.25634051946270.0236594805372548
5222.2322.2863489149721-0.0563489149720908
5322.2922.23717312963910.05282687036091
5422.3122.295496418250.0145035817499988
5522.3122.316843071621-0.00684307162103082
5622.3122.3172508775052-0.00725087750517517
5722.3922.31709533456310.0729046654369334
5822.4222.39664700973940.0233529902606406
5922.4222.4284937427626-0.00849374276260662
6022.4222.4291414908751-0.00914149087510552
6122.1522.4289489262561-0.278948926256081
6221.9522.1596884233395-0.209688423339497
6321.9621.95304577135650.00695422864347606
6421.9721.9574734309480.0125265690520173
6521.6621.9676133546333-0.307613354633347
6621.6621.65902698218370.000973017816320976
6721.6821.65088481485430.0291151851456846
6821.7521.67080812961130.0791918703887262
6921.5521.7412998486549-0.191299848654879
7021.5921.54406808898010.0459319110198848
7121.5421.5788451421505-0.0388451421504534
7221.5421.53019705489020.00980294510979007







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7321.529134814096221.330274534808321.7279950933841
7421.518528991647721.237792345862921.7992656374325
7521.507923169199221.161643715285321.8542026231132
7621.497317346750821.093738087898521.900896605603
7721.486711524302321.030910078546921.9425129700577
7821.476105701853820.971539255008821.9806721486989
7921.465499879405320.914668814639622.0163309441711
8021.454894056956920.859680426746622.0501076871671
8121.444288234508420.806148649416822.0824278196
8221.433682412059920.753766920930722.1135979031892
8321.423076589611520.702306362433822.1438468167891
8421.41247076716320.651591219709222.1733503146168

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 21.5291348140962 & 21.3302745348083 & 21.7279950933841 \tabularnewline
74 & 21.5185289916477 & 21.2377923458629 & 21.7992656374325 \tabularnewline
75 & 21.5079231691992 & 21.1616437152853 & 21.8542026231132 \tabularnewline
76 & 21.4973173467508 & 21.0937380878985 & 21.900896605603 \tabularnewline
77 & 21.4867115243023 & 21.0309100785469 & 21.9425129700577 \tabularnewline
78 & 21.4761057018538 & 20.9715392550088 & 21.9806721486989 \tabularnewline
79 & 21.4654998794053 & 20.9146688146396 & 22.0163309441711 \tabularnewline
80 & 21.4548940569569 & 20.8596804267466 & 22.0501076871671 \tabularnewline
81 & 21.4442882345084 & 20.8061486494168 & 22.0824278196 \tabularnewline
82 & 21.4336824120599 & 20.7537669209307 & 22.1135979031892 \tabularnewline
83 & 21.4230765896115 & 20.7023063624338 & 22.1438468167891 \tabularnewline
84 & 21.412470767163 & 20.6515912197092 & 22.1733503146168 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271934&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]21.5291348140962[/C][C]21.3302745348083[/C][C]21.7279950933841[/C][/ROW]
[ROW][C]74[/C][C]21.5185289916477[/C][C]21.2377923458629[/C][C]21.7992656374325[/C][/ROW]
[ROW][C]75[/C][C]21.5079231691992[/C][C]21.1616437152853[/C][C]21.8542026231132[/C][/ROW]
[ROW][C]76[/C][C]21.4973173467508[/C][C]21.0937380878985[/C][C]21.900896605603[/C][/ROW]
[ROW][C]77[/C][C]21.4867115243023[/C][C]21.0309100785469[/C][C]21.9425129700577[/C][/ROW]
[ROW][C]78[/C][C]21.4761057018538[/C][C]20.9715392550088[/C][C]21.9806721486989[/C][/ROW]
[ROW][C]79[/C][C]21.4654998794053[/C][C]20.9146688146396[/C][C]22.0163309441711[/C][/ROW]
[ROW][C]80[/C][C]21.4548940569569[/C][C]20.8596804267466[/C][C]22.0501076871671[/C][/ROW]
[ROW][C]81[/C][C]21.4442882345084[/C][C]20.8061486494168[/C][C]22.0824278196[/C][/ROW]
[ROW][C]82[/C][C]21.4336824120599[/C][C]20.7537669209307[/C][C]22.1135979031892[/C][/ROW]
[ROW][C]83[/C][C]21.4230765896115[/C][C]20.7023063624338[/C][C]22.1438468167891[/C][/ROW]
[ROW][C]84[/C][C]21.412470767163[/C][C]20.6515912197092[/C][C]22.1733503146168[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271934&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271934&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
7321.529134814096221.330274534808321.7279950933841
7421.518528991647721.237792345862921.7992656374325
7521.507923169199221.161643715285321.8542026231132
7621.497317346750821.093738087898521.900896605603
7721.486711524302321.030910078546921.9425129700577
7821.476105701853820.971539255008821.9806721486989
7921.465499879405320.914668814639622.0163309441711
8021.454894056956920.859680426746622.0501076871671
8121.444288234508420.806148649416822.0824278196
8221.433682412059920.753766920930722.1135979031892
8321.423076589611520.702306362433822.1438468167891
8421.41247076716320.651591219709222.1733503146168



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')