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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 15 Jan 2012 07:54:33 -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/Jan/15/t1326632132fkxt6t1ggeve1my.htm/, Retrieved Fri, 03 May 2024 13:40:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=161073, Retrieved Fri, 03 May 2024 13:40:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact120
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [double] [2012-01-15 12:54:33] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
123,46
123,24
123,86
124,28
124,78
125,19
125,46
127,60
127,80
126,63
127,06
126,77
127,05
128,23
128,60
128,97
129,34
129,71
130,08
130,45
128,82
132,19
131,56
131,93
132,30
130,67
133,05
132,42
133,79
134,16
134,53
136,90
135,27
136,64
136,01
136,38
136,75
138,12
137,50
137,87
138,24
138,61
138,98
140,35
139,72
143,09
140,46
141,83
143,20
140,57
141,95
141,32
142,69
143,06
144,43
143,80
144,17
144,54
146,91
145,28
144,65
145,02
144,40
146,77
146,14
147,51
148,88
148,25
147,62
150,99
148,36
149,73
150,10




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=161073&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=161073&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161073&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
alpha0.394923819862098
beta0.142120499984187
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.394923819862098 \tabularnewline
beta & 0.142120499984187 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161073&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]0.394923819862098[/C][/ROW]
[ROW][C]beta[/C][C]0.142120499984187[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161073&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161073&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
alpha0.394923819862098
beta0.142120499984187
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3123.86123.020.840000000000003
4124.28123.1788824961011.10111750389889
5124.78123.5026886839681.27731131603213
6125.19123.967769364551.22223063545016
7125.46124.4796972310160.980302768983677
8127.6124.9511032490922.64889675090812
9127.8126.2301507969451.56984920305457
10126.63127.171167331695-0.541167331695362
11127.06127.248119177995-0.18811917799475
12126.77127.453939627775-0.683939627774791
13127.05127.425561448878-0.375561448877605
14128.23127.4978901070150.732109892985221
15128.6128.0487555267480.551244473251813
16128.97128.5591324562080.410867543791625
17129.34129.0371318608980.302868139101747
18129.71129.4894787387510.220521261248706
19130.08129.9216820193210.158317980678902
20130.45130.3382056197250.111794380274944
21128.82130.742630599695-1.92263059969483
22132.19130.2357016484761.9542983515241
23131.56131.3695527435290.190447256470975
24131.93131.8175062159570.112493784043181
25132.3132.2409879181080.0590120818920639
26130.67132.646660579744-1.97666057974376
27133.05132.1374540426780.91254595732164
28132.42132.820482245333-0.400482245332654
29133.79132.9624865594410.827513440558988
30134.16133.6359012777540.52409872224618
31134.53134.2189062653340.311093734666116
32136.9134.7352511962922.16474880370828
33135.27136.105149027626-0.835149027625846
34136.64136.2434415302110.39655846978917
35136.01136.890422208944-0.880422208944367
36136.38136.983677544671-0.603677544671399
37136.75137.152343469192-0.40234346919226
38138.12137.3779387762180.742061223782088
39137.5138.097136256239-0.597136256239253
40137.87138.25393742215-0.383937422149671
41138.24138.47338671834-0.233386718339517
42138.61138.739192830728-0.1291928307283
43138.98139.038896414828-0.0588964148279842
44140.35139.3630560624450.986943937554514
45139.72140.155636953103-0.435636953102687
46143.09140.3619558689682.72804413103154
47140.46141.970804110902-1.51080411090192
48141.83141.8208336573580.00916634264203253
49143.2142.2716502186170.928349781382906
50140.57143.137579489999-2.56757948999882
51141.95142.478773074181-0.528773074181061
52141.32142.595461550952-1.27546155095226
53142.69142.3456774241790.344322575820939
54143.06142.7549103463750.30508965362506
55144.43143.1657729501151.26422704988468
56143.8144.026378739944-0.226378739944323
57144.17144.28560288971-0.115602889709521
58144.54144.582086644511-0.0420866445109311
59146.91144.9052415282412.00475847175937
60145.28146.149264923076-0.869264923076287
61144.65146.209478987405-1.55947898740541
62145.02145.909582557336-0.889582557335785
63144.4145.824314788096-1.4243147880963
64146.77145.4479263341161.32207366588369
65146.14146.230355824746-0.090355824746382
66147.51146.4499118849911.06008811500914
67148.88147.183304983051.69669501694975
68148.25148.263339322797-0.0133393227972647
69147.62148.667291675884-1.04729167588363
70150.99148.6041305163492.38586948365071
71148.36150.030717625652-1.67071762565166
72149.73149.761489873008-0.0314898730080415
73150.1150.13786478118-0.0378647811795929

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 123.86 & 123.02 & 0.840000000000003 \tabularnewline
4 & 124.28 & 123.178882496101 & 1.10111750389889 \tabularnewline
5 & 124.78 & 123.502688683968 & 1.27731131603213 \tabularnewline
6 & 125.19 & 123.96776936455 & 1.22223063545016 \tabularnewline
7 & 125.46 & 124.479697231016 & 0.980302768983677 \tabularnewline
8 & 127.6 & 124.951103249092 & 2.64889675090812 \tabularnewline
9 & 127.8 & 126.230150796945 & 1.56984920305457 \tabularnewline
10 & 126.63 & 127.171167331695 & -0.541167331695362 \tabularnewline
11 & 127.06 & 127.248119177995 & -0.18811917799475 \tabularnewline
12 & 126.77 & 127.453939627775 & -0.683939627774791 \tabularnewline
13 & 127.05 & 127.425561448878 & -0.375561448877605 \tabularnewline
14 & 128.23 & 127.497890107015 & 0.732109892985221 \tabularnewline
15 & 128.6 & 128.048755526748 & 0.551244473251813 \tabularnewline
16 & 128.97 & 128.559132456208 & 0.410867543791625 \tabularnewline
17 & 129.34 & 129.037131860898 & 0.302868139101747 \tabularnewline
18 & 129.71 & 129.489478738751 & 0.220521261248706 \tabularnewline
19 & 130.08 & 129.921682019321 & 0.158317980678902 \tabularnewline
20 & 130.45 & 130.338205619725 & 0.111794380274944 \tabularnewline
21 & 128.82 & 130.742630599695 & -1.92263059969483 \tabularnewline
22 & 132.19 & 130.235701648476 & 1.9542983515241 \tabularnewline
23 & 131.56 & 131.369552743529 & 0.190447256470975 \tabularnewline
24 & 131.93 & 131.817506215957 & 0.112493784043181 \tabularnewline
25 & 132.3 & 132.240987918108 & 0.0590120818920639 \tabularnewline
26 & 130.67 & 132.646660579744 & -1.97666057974376 \tabularnewline
27 & 133.05 & 132.137454042678 & 0.91254595732164 \tabularnewline
28 & 132.42 & 132.820482245333 & -0.400482245332654 \tabularnewline
29 & 133.79 & 132.962486559441 & 0.827513440558988 \tabularnewline
30 & 134.16 & 133.635901277754 & 0.52409872224618 \tabularnewline
31 & 134.53 & 134.218906265334 & 0.311093734666116 \tabularnewline
32 & 136.9 & 134.735251196292 & 2.16474880370828 \tabularnewline
33 & 135.27 & 136.105149027626 & -0.835149027625846 \tabularnewline
34 & 136.64 & 136.243441530211 & 0.39655846978917 \tabularnewline
35 & 136.01 & 136.890422208944 & -0.880422208944367 \tabularnewline
36 & 136.38 & 136.983677544671 & -0.603677544671399 \tabularnewline
37 & 136.75 & 137.152343469192 & -0.40234346919226 \tabularnewline
38 & 138.12 & 137.377938776218 & 0.742061223782088 \tabularnewline
39 & 137.5 & 138.097136256239 & -0.597136256239253 \tabularnewline
40 & 137.87 & 138.25393742215 & -0.383937422149671 \tabularnewline
41 & 138.24 & 138.47338671834 & -0.233386718339517 \tabularnewline
42 & 138.61 & 138.739192830728 & -0.1291928307283 \tabularnewline
43 & 138.98 & 139.038896414828 & -0.0588964148279842 \tabularnewline
44 & 140.35 & 139.363056062445 & 0.986943937554514 \tabularnewline
45 & 139.72 & 140.155636953103 & -0.435636953102687 \tabularnewline
46 & 143.09 & 140.361955868968 & 2.72804413103154 \tabularnewline
47 & 140.46 & 141.970804110902 & -1.51080411090192 \tabularnewline
48 & 141.83 & 141.820833657358 & 0.00916634264203253 \tabularnewline
49 & 143.2 & 142.271650218617 & 0.928349781382906 \tabularnewline
50 & 140.57 & 143.137579489999 & -2.56757948999882 \tabularnewline
51 & 141.95 & 142.478773074181 & -0.528773074181061 \tabularnewline
52 & 141.32 & 142.595461550952 & -1.27546155095226 \tabularnewline
53 & 142.69 & 142.345677424179 & 0.344322575820939 \tabularnewline
54 & 143.06 & 142.754910346375 & 0.30508965362506 \tabularnewline
55 & 144.43 & 143.165772950115 & 1.26422704988468 \tabularnewline
56 & 143.8 & 144.026378739944 & -0.226378739944323 \tabularnewline
57 & 144.17 & 144.28560288971 & -0.115602889709521 \tabularnewline
58 & 144.54 & 144.582086644511 & -0.0420866445109311 \tabularnewline
59 & 146.91 & 144.905241528241 & 2.00475847175937 \tabularnewline
60 & 145.28 & 146.149264923076 & -0.869264923076287 \tabularnewline
61 & 144.65 & 146.209478987405 & -1.55947898740541 \tabularnewline
62 & 145.02 & 145.909582557336 & -0.889582557335785 \tabularnewline
63 & 144.4 & 145.824314788096 & -1.4243147880963 \tabularnewline
64 & 146.77 & 145.447926334116 & 1.32207366588369 \tabularnewline
65 & 146.14 & 146.230355824746 & -0.090355824746382 \tabularnewline
66 & 147.51 & 146.449911884991 & 1.06008811500914 \tabularnewline
67 & 148.88 & 147.18330498305 & 1.69669501694975 \tabularnewline
68 & 148.25 & 148.263339322797 & -0.0133393227972647 \tabularnewline
69 & 147.62 & 148.667291675884 & -1.04729167588363 \tabularnewline
70 & 150.99 & 148.604130516349 & 2.38586948365071 \tabularnewline
71 & 148.36 & 150.030717625652 & -1.67071762565166 \tabularnewline
72 & 149.73 & 149.761489873008 & -0.0314898730080415 \tabularnewline
73 & 150.1 & 150.13786478118 & -0.0378647811795929 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161073&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]123.86[/C][C]123.02[/C][C]0.840000000000003[/C][/ROW]
[ROW][C]4[/C][C]124.28[/C][C]123.178882496101[/C][C]1.10111750389889[/C][/ROW]
[ROW][C]5[/C][C]124.78[/C][C]123.502688683968[/C][C]1.27731131603213[/C][/ROW]
[ROW][C]6[/C][C]125.19[/C][C]123.96776936455[/C][C]1.22223063545016[/C][/ROW]
[ROW][C]7[/C][C]125.46[/C][C]124.479697231016[/C][C]0.980302768983677[/C][/ROW]
[ROW][C]8[/C][C]127.6[/C][C]124.951103249092[/C][C]2.64889675090812[/C][/ROW]
[ROW][C]9[/C][C]127.8[/C][C]126.230150796945[/C][C]1.56984920305457[/C][/ROW]
[ROW][C]10[/C][C]126.63[/C][C]127.171167331695[/C][C]-0.541167331695362[/C][/ROW]
[ROW][C]11[/C][C]127.06[/C][C]127.248119177995[/C][C]-0.18811917799475[/C][/ROW]
[ROW][C]12[/C][C]126.77[/C][C]127.453939627775[/C][C]-0.683939627774791[/C][/ROW]
[ROW][C]13[/C][C]127.05[/C][C]127.425561448878[/C][C]-0.375561448877605[/C][/ROW]
[ROW][C]14[/C][C]128.23[/C][C]127.497890107015[/C][C]0.732109892985221[/C][/ROW]
[ROW][C]15[/C][C]128.6[/C][C]128.048755526748[/C][C]0.551244473251813[/C][/ROW]
[ROW][C]16[/C][C]128.97[/C][C]128.559132456208[/C][C]0.410867543791625[/C][/ROW]
[ROW][C]17[/C][C]129.34[/C][C]129.037131860898[/C][C]0.302868139101747[/C][/ROW]
[ROW][C]18[/C][C]129.71[/C][C]129.489478738751[/C][C]0.220521261248706[/C][/ROW]
[ROW][C]19[/C][C]130.08[/C][C]129.921682019321[/C][C]0.158317980678902[/C][/ROW]
[ROW][C]20[/C][C]130.45[/C][C]130.338205619725[/C][C]0.111794380274944[/C][/ROW]
[ROW][C]21[/C][C]128.82[/C][C]130.742630599695[/C][C]-1.92263059969483[/C][/ROW]
[ROW][C]22[/C][C]132.19[/C][C]130.235701648476[/C][C]1.9542983515241[/C][/ROW]
[ROW][C]23[/C][C]131.56[/C][C]131.369552743529[/C][C]0.190447256470975[/C][/ROW]
[ROW][C]24[/C][C]131.93[/C][C]131.817506215957[/C][C]0.112493784043181[/C][/ROW]
[ROW][C]25[/C][C]132.3[/C][C]132.240987918108[/C][C]0.0590120818920639[/C][/ROW]
[ROW][C]26[/C][C]130.67[/C][C]132.646660579744[/C][C]-1.97666057974376[/C][/ROW]
[ROW][C]27[/C][C]133.05[/C][C]132.137454042678[/C][C]0.91254595732164[/C][/ROW]
[ROW][C]28[/C][C]132.42[/C][C]132.820482245333[/C][C]-0.400482245332654[/C][/ROW]
[ROW][C]29[/C][C]133.79[/C][C]132.962486559441[/C][C]0.827513440558988[/C][/ROW]
[ROW][C]30[/C][C]134.16[/C][C]133.635901277754[/C][C]0.52409872224618[/C][/ROW]
[ROW][C]31[/C][C]134.53[/C][C]134.218906265334[/C][C]0.311093734666116[/C][/ROW]
[ROW][C]32[/C][C]136.9[/C][C]134.735251196292[/C][C]2.16474880370828[/C][/ROW]
[ROW][C]33[/C][C]135.27[/C][C]136.105149027626[/C][C]-0.835149027625846[/C][/ROW]
[ROW][C]34[/C][C]136.64[/C][C]136.243441530211[/C][C]0.39655846978917[/C][/ROW]
[ROW][C]35[/C][C]136.01[/C][C]136.890422208944[/C][C]-0.880422208944367[/C][/ROW]
[ROW][C]36[/C][C]136.38[/C][C]136.983677544671[/C][C]-0.603677544671399[/C][/ROW]
[ROW][C]37[/C][C]136.75[/C][C]137.152343469192[/C][C]-0.40234346919226[/C][/ROW]
[ROW][C]38[/C][C]138.12[/C][C]137.377938776218[/C][C]0.742061223782088[/C][/ROW]
[ROW][C]39[/C][C]137.5[/C][C]138.097136256239[/C][C]-0.597136256239253[/C][/ROW]
[ROW][C]40[/C][C]137.87[/C][C]138.25393742215[/C][C]-0.383937422149671[/C][/ROW]
[ROW][C]41[/C][C]138.24[/C][C]138.47338671834[/C][C]-0.233386718339517[/C][/ROW]
[ROW][C]42[/C][C]138.61[/C][C]138.739192830728[/C][C]-0.1291928307283[/C][/ROW]
[ROW][C]43[/C][C]138.98[/C][C]139.038896414828[/C][C]-0.0588964148279842[/C][/ROW]
[ROW][C]44[/C][C]140.35[/C][C]139.363056062445[/C][C]0.986943937554514[/C][/ROW]
[ROW][C]45[/C][C]139.72[/C][C]140.155636953103[/C][C]-0.435636953102687[/C][/ROW]
[ROW][C]46[/C][C]143.09[/C][C]140.361955868968[/C][C]2.72804413103154[/C][/ROW]
[ROW][C]47[/C][C]140.46[/C][C]141.970804110902[/C][C]-1.51080411090192[/C][/ROW]
[ROW][C]48[/C][C]141.83[/C][C]141.820833657358[/C][C]0.00916634264203253[/C][/ROW]
[ROW][C]49[/C][C]143.2[/C][C]142.271650218617[/C][C]0.928349781382906[/C][/ROW]
[ROW][C]50[/C][C]140.57[/C][C]143.137579489999[/C][C]-2.56757948999882[/C][/ROW]
[ROW][C]51[/C][C]141.95[/C][C]142.478773074181[/C][C]-0.528773074181061[/C][/ROW]
[ROW][C]52[/C][C]141.32[/C][C]142.595461550952[/C][C]-1.27546155095226[/C][/ROW]
[ROW][C]53[/C][C]142.69[/C][C]142.345677424179[/C][C]0.344322575820939[/C][/ROW]
[ROW][C]54[/C][C]143.06[/C][C]142.754910346375[/C][C]0.30508965362506[/C][/ROW]
[ROW][C]55[/C][C]144.43[/C][C]143.165772950115[/C][C]1.26422704988468[/C][/ROW]
[ROW][C]56[/C][C]143.8[/C][C]144.026378739944[/C][C]-0.226378739944323[/C][/ROW]
[ROW][C]57[/C][C]144.17[/C][C]144.28560288971[/C][C]-0.115602889709521[/C][/ROW]
[ROW][C]58[/C][C]144.54[/C][C]144.582086644511[/C][C]-0.0420866445109311[/C][/ROW]
[ROW][C]59[/C][C]146.91[/C][C]144.905241528241[/C][C]2.00475847175937[/C][/ROW]
[ROW][C]60[/C][C]145.28[/C][C]146.149264923076[/C][C]-0.869264923076287[/C][/ROW]
[ROW][C]61[/C][C]144.65[/C][C]146.209478987405[/C][C]-1.55947898740541[/C][/ROW]
[ROW][C]62[/C][C]145.02[/C][C]145.909582557336[/C][C]-0.889582557335785[/C][/ROW]
[ROW][C]63[/C][C]144.4[/C][C]145.824314788096[/C][C]-1.4243147880963[/C][/ROW]
[ROW][C]64[/C][C]146.77[/C][C]145.447926334116[/C][C]1.32207366588369[/C][/ROW]
[ROW][C]65[/C][C]146.14[/C][C]146.230355824746[/C][C]-0.090355824746382[/C][/ROW]
[ROW][C]66[/C][C]147.51[/C][C]146.449911884991[/C][C]1.06008811500914[/C][/ROW]
[ROW][C]67[/C][C]148.88[/C][C]147.18330498305[/C][C]1.69669501694975[/C][/ROW]
[ROW][C]68[/C][C]148.25[/C][C]148.263339322797[/C][C]-0.0133393227972647[/C][/ROW]
[ROW][C]69[/C][C]147.62[/C][C]148.667291675884[/C][C]-1.04729167588363[/C][/ROW]
[ROW][C]70[/C][C]150.99[/C][C]148.604130516349[/C][C]2.38586948365071[/C][/ROW]
[ROW][C]71[/C][C]148.36[/C][C]150.030717625652[/C][C]-1.67071762565166[/C][/ROW]
[ROW][C]72[/C][C]149.73[/C][C]149.761489873008[/C][C]-0.0314898730080415[/C][/ROW]
[ROW][C]73[/C][C]150.1[/C][C]150.13786478118[/C][C]-0.0378647811795929[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161073&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161073&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
3123.86123.020.840000000000003
4124.28123.1788824961011.10111750389889
5124.78123.5026886839681.27731131603213
6125.19123.967769364551.22223063545016
7125.46124.4796972310160.980302768983677
8127.6124.9511032490922.64889675090812
9127.8126.2301507969451.56984920305457
10126.63127.171167331695-0.541167331695362
11127.06127.248119177995-0.18811917799475
12126.77127.453939627775-0.683939627774791
13127.05127.425561448878-0.375561448877605
14128.23127.4978901070150.732109892985221
15128.6128.0487555267480.551244473251813
16128.97128.5591324562080.410867543791625
17129.34129.0371318608980.302868139101747
18129.71129.4894787387510.220521261248706
19130.08129.9216820193210.158317980678902
20130.45130.3382056197250.111794380274944
21128.82130.742630599695-1.92263059969483
22132.19130.2357016484761.9542983515241
23131.56131.3695527435290.190447256470975
24131.93131.8175062159570.112493784043181
25132.3132.2409879181080.0590120818920639
26130.67132.646660579744-1.97666057974376
27133.05132.1374540426780.91254595732164
28132.42132.820482245333-0.400482245332654
29133.79132.9624865594410.827513440558988
30134.16133.6359012777540.52409872224618
31134.53134.2189062653340.311093734666116
32136.9134.7352511962922.16474880370828
33135.27136.105149027626-0.835149027625846
34136.64136.2434415302110.39655846978917
35136.01136.890422208944-0.880422208944367
36136.38136.983677544671-0.603677544671399
37136.75137.152343469192-0.40234346919226
38138.12137.3779387762180.742061223782088
39137.5138.097136256239-0.597136256239253
40137.87138.25393742215-0.383937422149671
41138.24138.47338671834-0.233386718339517
42138.61138.739192830728-0.1291928307283
43138.98139.038896414828-0.0588964148279842
44140.35139.3630560624450.986943937554514
45139.72140.155636953103-0.435636953102687
46143.09140.3619558689682.72804413103154
47140.46141.970804110902-1.51080411090192
48141.83141.8208336573580.00916634264203253
49143.2142.2716502186170.928349781382906
50140.57143.137579489999-2.56757948999882
51141.95142.478773074181-0.528773074181061
52141.32142.595461550952-1.27546155095226
53142.69142.3456774241790.344322575820939
54143.06142.7549103463750.30508965362506
55144.43143.1657729501151.26422704988468
56143.8144.026378739944-0.226378739944323
57144.17144.28560288971-0.115602889709521
58144.54144.582086644511-0.0420866445109311
59146.91144.9052415282412.00475847175937
60145.28146.149264923076-0.869264923076287
61144.65146.209478987405-1.55947898740541
62145.02145.909582557336-0.889582557335785
63144.4145.824314788096-1.4243147880963
64146.77145.4479263341161.32207366588369
65146.14146.230355824746-0.090355824746382
66147.51146.4499118849911.06008811500914
67148.88147.183304983051.69669501694975
68148.25148.263339322797-0.0133393227972647
69147.62148.667291675884-1.04729167588363
70150.99148.6041305163492.38586948365071
71148.36150.030717625652-1.67071762565166
72149.73149.761489873008-0.0314898730080415
73150.1150.13786478118-0.0378647811795929







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
74150.509596858373148.350407173441152.668786543304
75150.896282639587148.527614517356153.264950761818
76151.282968420802148.673406112688153.892530728915
77151.669654202017148.790565175064154.54874322897
78152.056339983231148.881757103781155.230922862682
79152.443025764446148.9493661975155.936685331392
80152.829711545661148.995449036598156.663974054723
81153.216397326875149.021747741485157.411046912266
82153.60308310809149.029727789858158.176438426322
83153.989768889305149.020621740568158.958916038041
84154.376454670519148.995470380368159.75743896067
85154.763140451734148.955158209026160.571122694442

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
74 & 150.509596858373 & 148.350407173441 & 152.668786543304 \tabularnewline
75 & 150.896282639587 & 148.527614517356 & 153.264950761818 \tabularnewline
76 & 151.282968420802 & 148.673406112688 & 153.892530728915 \tabularnewline
77 & 151.669654202017 & 148.790565175064 & 154.54874322897 \tabularnewline
78 & 152.056339983231 & 148.881757103781 & 155.230922862682 \tabularnewline
79 & 152.443025764446 & 148.9493661975 & 155.936685331392 \tabularnewline
80 & 152.829711545661 & 148.995449036598 & 156.663974054723 \tabularnewline
81 & 153.216397326875 & 149.021747741485 & 157.411046912266 \tabularnewline
82 & 153.60308310809 & 149.029727789858 & 158.176438426322 \tabularnewline
83 & 153.989768889305 & 149.020621740568 & 158.958916038041 \tabularnewline
84 & 154.376454670519 & 148.995470380368 & 159.75743896067 \tabularnewline
85 & 154.763140451734 & 148.955158209026 & 160.571122694442 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161073&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]74[/C][C]150.509596858373[/C][C]148.350407173441[/C][C]152.668786543304[/C][/ROW]
[ROW][C]75[/C][C]150.896282639587[/C][C]148.527614517356[/C][C]153.264950761818[/C][/ROW]
[ROW][C]76[/C][C]151.282968420802[/C][C]148.673406112688[/C][C]153.892530728915[/C][/ROW]
[ROW][C]77[/C][C]151.669654202017[/C][C]148.790565175064[/C][C]154.54874322897[/C][/ROW]
[ROW][C]78[/C][C]152.056339983231[/C][C]148.881757103781[/C][C]155.230922862682[/C][/ROW]
[ROW][C]79[/C][C]152.443025764446[/C][C]148.9493661975[/C][C]155.936685331392[/C][/ROW]
[ROW][C]80[/C][C]152.829711545661[/C][C]148.995449036598[/C][C]156.663974054723[/C][/ROW]
[ROW][C]81[/C][C]153.216397326875[/C][C]149.021747741485[/C][C]157.411046912266[/C][/ROW]
[ROW][C]82[/C][C]153.60308310809[/C][C]149.029727789858[/C][C]158.176438426322[/C][/ROW]
[ROW][C]83[/C][C]153.989768889305[/C][C]149.020621740568[/C][C]158.958916038041[/C][/ROW]
[ROW][C]84[/C][C]154.376454670519[/C][C]148.995470380368[/C][C]159.75743896067[/C][/ROW]
[ROW][C]85[/C][C]154.763140451734[/C][C]148.955158209026[/C][C]160.571122694442[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161073&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161073&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
74150.509596858373148.350407173441152.668786543304
75150.896282639587148.527614517356153.264950761818
76151.282968420802148.673406112688153.892530728915
77151.669654202017148.790565175064154.54874322897
78152.056339983231148.881757103781155.230922862682
79152.443025764446148.9493661975155.936685331392
80152.829711545661148.995449036598156.663974054723
81153.216397326875149.021747741485157.411046912266
82153.60308310809149.029727789858158.176438426322
83153.989768889305149.020621740568158.958916038041
84154.376454670519148.995470380368159.75743896067
85154.763140451734148.955158209026160.571122694442



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