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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 21 Dec 2012 04:10:29 -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/21/t1356081095el394irp98yzthd.htm/, Retrieved Sat, 27 Apr 2024 01:18:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=203332, Retrieved Sat, 27 Apr 2024 01:18:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact49
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [oefening 10: siga...] [2012-12-21 09:10:29] [4ab20b1300d6ce8ed8a6f2d2c22a072d] [Current]
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Dataseries X:
104,4
104,4
104,4
104,4
104,4
104,41
104,42
104,68
106,02
106,35
106,38
106,47
106,5
106,56
113,07
116,26
118
118,02
118,04
118,12
118,12
118,17
118,22
118,22
118,23
118,23
118,23
119,94
120,88
121,14
121,16
121,2
121,2
121,2
121,2
121,2
121,22
121,22
121,95
123,05
123,44
123,65
123,79
123,87
123,91
123,94
124,28
126,28
126,68
126,69
126,69
126,99
128,79
128,84
128,95
128,97
128,97
128,97
128,97
128,97
128,97
128,98
128,99
129,07
129,76
130,47
130,76
130,88
131,04
131,06
131,13
131,15




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203332&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203332&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203332&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0943573923710635
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0943573923710635 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203332&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0943573923710635[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203332&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203332&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
alpha1
beta0.0943573923710635
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3104.4104.40
4104.4104.40
5104.4104.40
6104.41104.40.00999999999999091
7104.42104.4109435739240.00905642607629886
8104.68104.4217981146720.258201885327537
9106.02104.7061613712771.31383862872272
10106.35106.170131758280.179868241720087
11106.38106.517103656539-0.137103656538997
12106.47106.534166913023-0.0641669130234277
13106.5106.618112290434-0.118112290434041
14106.56106.636967522702-0.0769675227017075
15113.07106.6897050679626.38029493203767
16116.26113.8017330603082.45826693969231
17118117.2236887184890.776311281510928
18118.02119.036939426681-1.01693942668068
19118.04118.96098367418-0.920983674179752
20118.12118.894082056268-0.774082056267844
21118.12118.901041691957-0.781041691957171
22118.17118.827344634571-0.657344634571018
23118.22118.815319308964-0.595319308963781
24118.22118.809146531342-0.589146531341811
25118.23118.75355620092-0.523556200919941
26118.23118.714154803041-0.484154803041434
27118.23118.668471218323-0.438471218322519
28119.94118.6270982175321.31290178246815
29120.88120.4609802061650.419019793835133
30121.14121.440517821263-0.300517821263
31121.16121.672161743288-0.512161743287606
32121.2121.643835496719-0.443835496718748
33121.2121.641956336607-0.441956336606665
34121.2121.600254489143-0.400254489142597
35121.2121.562487519262-0.362487519262288
36121.2121.528284142178-0.328284142177637
37121.22121.497308106565-0.277308106564988
38121.22121.491142036746-0.271142036746156
39121.95121.4655577811970.484442218803395
40123.05122.2412684857170.808731514282641
41123.44123.4175782825330.0224217174666421
42123.65123.809693937326-0.159693937325983
43123.79124.004625633822-0.21462563382245
44123.87124.124374118679-0.254374118678982
45123.91124.180372040154-0.270372040153745
46123.94124.194860439475-0.254860439474783
47124.28124.2008124729870.079187527012607
48126.28124.5482844015451.73171559845538
49126.68126.711684569743-0.0316845697431631
50126.69127.108694896364-0.418694896363817
51126.69127.079187937744-0.389187937743841
52126.99127.042465178796-0.0524651787960693
53128.79127.3375147013351.45248529866541
54128.84129.274567426574-0.434567426573949
55128.95129.283562777393-0.333562777393041
56128.97129.362088663526-0.392088663526181
57128.97129.345092199658-0.375092199657587
58128.97129.309699477799-0.339699477799172
59128.97129.277646320884-0.307646320884231
60128.97129.248617616273-0.278617616273038
61128.97129.222327984533-0.252327984532883
62128.98129.19851897389-0.218518973890127
63128.99129.18790009333-0.197900093330219
64129.07129.179226756574-0.109226756573634
65129.76129.2489204046460.511079595353834
66130.47129.9871445425580.482855457442184
67130.76130.7427055244140.0172944755857998
68130.88131.034337386033-0.154337386032893
69131.04131.139774512741-0.099774512741476
70131.06131.290360049894-0.230360049894074
71131.13131.28862387628-0.15862387627962
72131.15131.343656540946-0.19365654094608

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 104.4 & 104.4 & 0 \tabularnewline
4 & 104.4 & 104.4 & 0 \tabularnewline
5 & 104.4 & 104.4 & 0 \tabularnewline
6 & 104.41 & 104.4 & 0.00999999999999091 \tabularnewline
7 & 104.42 & 104.410943573924 & 0.00905642607629886 \tabularnewline
8 & 104.68 & 104.421798114672 & 0.258201885327537 \tabularnewline
9 & 106.02 & 104.706161371277 & 1.31383862872272 \tabularnewline
10 & 106.35 & 106.17013175828 & 0.179868241720087 \tabularnewline
11 & 106.38 & 106.517103656539 & -0.137103656538997 \tabularnewline
12 & 106.47 & 106.534166913023 & -0.0641669130234277 \tabularnewline
13 & 106.5 & 106.618112290434 & -0.118112290434041 \tabularnewline
14 & 106.56 & 106.636967522702 & -0.0769675227017075 \tabularnewline
15 & 113.07 & 106.689705067962 & 6.38029493203767 \tabularnewline
16 & 116.26 & 113.801733060308 & 2.45826693969231 \tabularnewline
17 & 118 & 117.223688718489 & 0.776311281510928 \tabularnewline
18 & 118.02 & 119.036939426681 & -1.01693942668068 \tabularnewline
19 & 118.04 & 118.96098367418 & -0.920983674179752 \tabularnewline
20 & 118.12 & 118.894082056268 & -0.774082056267844 \tabularnewline
21 & 118.12 & 118.901041691957 & -0.781041691957171 \tabularnewline
22 & 118.17 & 118.827344634571 & -0.657344634571018 \tabularnewline
23 & 118.22 & 118.815319308964 & -0.595319308963781 \tabularnewline
24 & 118.22 & 118.809146531342 & -0.589146531341811 \tabularnewline
25 & 118.23 & 118.75355620092 & -0.523556200919941 \tabularnewline
26 & 118.23 & 118.714154803041 & -0.484154803041434 \tabularnewline
27 & 118.23 & 118.668471218323 & -0.438471218322519 \tabularnewline
28 & 119.94 & 118.627098217532 & 1.31290178246815 \tabularnewline
29 & 120.88 & 120.460980206165 & 0.419019793835133 \tabularnewline
30 & 121.14 & 121.440517821263 & -0.300517821263 \tabularnewline
31 & 121.16 & 121.672161743288 & -0.512161743287606 \tabularnewline
32 & 121.2 & 121.643835496719 & -0.443835496718748 \tabularnewline
33 & 121.2 & 121.641956336607 & -0.441956336606665 \tabularnewline
34 & 121.2 & 121.600254489143 & -0.400254489142597 \tabularnewline
35 & 121.2 & 121.562487519262 & -0.362487519262288 \tabularnewline
36 & 121.2 & 121.528284142178 & -0.328284142177637 \tabularnewline
37 & 121.22 & 121.497308106565 & -0.277308106564988 \tabularnewline
38 & 121.22 & 121.491142036746 & -0.271142036746156 \tabularnewline
39 & 121.95 & 121.465557781197 & 0.484442218803395 \tabularnewline
40 & 123.05 & 122.241268485717 & 0.808731514282641 \tabularnewline
41 & 123.44 & 123.417578282533 & 0.0224217174666421 \tabularnewline
42 & 123.65 & 123.809693937326 & -0.159693937325983 \tabularnewline
43 & 123.79 & 124.004625633822 & -0.21462563382245 \tabularnewline
44 & 123.87 & 124.124374118679 & -0.254374118678982 \tabularnewline
45 & 123.91 & 124.180372040154 & -0.270372040153745 \tabularnewline
46 & 123.94 & 124.194860439475 & -0.254860439474783 \tabularnewline
47 & 124.28 & 124.200812472987 & 0.079187527012607 \tabularnewline
48 & 126.28 & 124.548284401545 & 1.73171559845538 \tabularnewline
49 & 126.68 & 126.711684569743 & -0.0316845697431631 \tabularnewline
50 & 126.69 & 127.108694896364 & -0.418694896363817 \tabularnewline
51 & 126.69 & 127.079187937744 & -0.389187937743841 \tabularnewline
52 & 126.99 & 127.042465178796 & -0.0524651787960693 \tabularnewline
53 & 128.79 & 127.337514701335 & 1.45248529866541 \tabularnewline
54 & 128.84 & 129.274567426574 & -0.434567426573949 \tabularnewline
55 & 128.95 & 129.283562777393 & -0.333562777393041 \tabularnewline
56 & 128.97 & 129.362088663526 & -0.392088663526181 \tabularnewline
57 & 128.97 & 129.345092199658 & -0.375092199657587 \tabularnewline
58 & 128.97 & 129.309699477799 & -0.339699477799172 \tabularnewline
59 & 128.97 & 129.277646320884 & -0.307646320884231 \tabularnewline
60 & 128.97 & 129.248617616273 & -0.278617616273038 \tabularnewline
61 & 128.97 & 129.222327984533 & -0.252327984532883 \tabularnewline
62 & 128.98 & 129.19851897389 & -0.218518973890127 \tabularnewline
63 & 128.99 & 129.18790009333 & -0.197900093330219 \tabularnewline
64 & 129.07 & 129.179226756574 & -0.109226756573634 \tabularnewline
65 & 129.76 & 129.248920404646 & 0.511079595353834 \tabularnewline
66 & 130.47 & 129.987144542558 & 0.482855457442184 \tabularnewline
67 & 130.76 & 130.742705524414 & 0.0172944755857998 \tabularnewline
68 & 130.88 & 131.034337386033 & -0.154337386032893 \tabularnewline
69 & 131.04 & 131.139774512741 & -0.099774512741476 \tabularnewline
70 & 131.06 & 131.290360049894 & -0.230360049894074 \tabularnewline
71 & 131.13 & 131.28862387628 & -0.15862387627962 \tabularnewline
72 & 131.15 & 131.343656540946 & -0.19365654094608 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203332&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]104.4[/C][C]104.4[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]104.4[/C][C]104.4[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]104.4[/C][C]104.4[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]104.41[/C][C]104.4[/C][C]0.00999999999999091[/C][/ROW]
[ROW][C]7[/C][C]104.42[/C][C]104.410943573924[/C][C]0.00905642607629886[/C][/ROW]
[ROW][C]8[/C][C]104.68[/C][C]104.421798114672[/C][C]0.258201885327537[/C][/ROW]
[ROW][C]9[/C][C]106.02[/C][C]104.706161371277[/C][C]1.31383862872272[/C][/ROW]
[ROW][C]10[/C][C]106.35[/C][C]106.17013175828[/C][C]0.179868241720087[/C][/ROW]
[ROW][C]11[/C][C]106.38[/C][C]106.517103656539[/C][C]-0.137103656538997[/C][/ROW]
[ROW][C]12[/C][C]106.47[/C][C]106.534166913023[/C][C]-0.0641669130234277[/C][/ROW]
[ROW][C]13[/C][C]106.5[/C][C]106.618112290434[/C][C]-0.118112290434041[/C][/ROW]
[ROW][C]14[/C][C]106.56[/C][C]106.636967522702[/C][C]-0.0769675227017075[/C][/ROW]
[ROW][C]15[/C][C]113.07[/C][C]106.689705067962[/C][C]6.38029493203767[/C][/ROW]
[ROW][C]16[/C][C]116.26[/C][C]113.801733060308[/C][C]2.45826693969231[/C][/ROW]
[ROW][C]17[/C][C]118[/C][C]117.223688718489[/C][C]0.776311281510928[/C][/ROW]
[ROW][C]18[/C][C]118.02[/C][C]119.036939426681[/C][C]-1.01693942668068[/C][/ROW]
[ROW][C]19[/C][C]118.04[/C][C]118.96098367418[/C][C]-0.920983674179752[/C][/ROW]
[ROW][C]20[/C][C]118.12[/C][C]118.894082056268[/C][C]-0.774082056267844[/C][/ROW]
[ROW][C]21[/C][C]118.12[/C][C]118.901041691957[/C][C]-0.781041691957171[/C][/ROW]
[ROW][C]22[/C][C]118.17[/C][C]118.827344634571[/C][C]-0.657344634571018[/C][/ROW]
[ROW][C]23[/C][C]118.22[/C][C]118.815319308964[/C][C]-0.595319308963781[/C][/ROW]
[ROW][C]24[/C][C]118.22[/C][C]118.809146531342[/C][C]-0.589146531341811[/C][/ROW]
[ROW][C]25[/C][C]118.23[/C][C]118.75355620092[/C][C]-0.523556200919941[/C][/ROW]
[ROW][C]26[/C][C]118.23[/C][C]118.714154803041[/C][C]-0.484154803041434[/C][/ROW]
[ROW][C]27[/C][C]118.23[/C][C]118.668471218323[/C][C]-0.438471218322519[/C][/ROW]
[ROW][C]28[/C][C]119.94[/C][C]118.627098217532[/C][C]1.31290178246815[/C][/ROW]
[ROW][C]29[/C][C]120.88[/C][C]120.460980206165[/C][C]0.419019793835133[/C][/ROW]
[ROW][C]30[/C][C]121.14[/C][C]121.440517821263[/C][C]-0.300517821263[/C][/ROW]
[ROW][C]31[/C][C]121.16[/C][C]121.672161743288[/C][C]-0.512161743287606[/C][/ROW]
[ROW][C]32[/C][C]121.2[/C][C]121.643835496719[/C][C]-0.443835496718748[/C][/ROW]
[ROW][C]33[/C][C]121.2[/C][C]121.641956336607[/C][C]-0.441956336606665[/C][/ROW]
[ROW][C]34[/C][C]121.2[/C][C]121.600254489143[/C][C]-0.400254489142597[/C][/ROW]
[ROW][C]35[/C][C]121.2[/C][C]121.562487519262[/C][C]-0.362487519262288[/C][/ROW]
[ROW][C]36[/C][C]121.2[/C][C]121.528284142178[/C][C]-0.328284142177637[/C][/ROW]
[ROW][C]37[/C][C]121.22[/C][C]121.497308106565[/C][C]-0.277308106564988[/C][/ROW]
[ROW][C]38[/C][C]121.22[/C][C]121.491142036746[/C][C]-0.271142036746156[/C][/ROW]
[ROW][C]39[/C][C]121.95[/C][C]121.465557781197[/C][C]0.484442218803395[/C][/ROW]
[ROW][C]40[/C][C]123.05[/C][C]122.241268485717[/C][C]0.808731514282641[/C][/ROW]
[ROW][C]41[/C][C]123.44[/C][C]123.417578282533[/C][C]0.0224217174666421[/C][/ROW]
[ROW][C]42[/C][C]123.65[/C][C]123.809693937326[/C][C]-0.159693937325983[/C][/ROW]
[ROW][C]43[/C][C]123.79[/C][C]124.004625633822[/C][C]-0.21462563382245[/C][/ROW]
[ROW][C]44[/C][C]123.87[/C][C]124.124374118679[/C][C]-0.254374118678982[/C][/ROW]
[ROW][C]45[/C][C]123.91[/C][C]124.180372040154[/C][C]-0.270372040153745[/C][/ROW]
[ROW][C]46[/C][C]123.94[/C][C]124.194860439475[/C][C]-0.254860439474783[/C][/ROW]
[ROW][C]47[/C][C]124.28[/C][C]124.200812472987[/C][C]0.079187527012607[/C][/ROW]
[ROW][C]48[/C][C]126.28[/C][C]124.548284401545[/C][C]1.73171559845538[/C][/ROW]
[ROW][C]49[/C][C]126.68[/C][C]126.711684569743[/C][C]-0.0316845697431631[/C][/ROW]
[ROW][C]50[/C][C]126.69[/C][C]127.108694896364[/C][C]-0.418694896363817[/C][/ROW]
[ROW][C]51[/C][C]126.69[/C][C]127.079187937744[/C][C]-0.389187937743841[/C][/ROW]
[ROW][C]52[/C][C]126.99[/C][C]127.042465178796[/C][C]-0.0524651787960693[/C][/ROW]
[ROW][C]53[/C][C]128.79[/C][C]127.337514701335[/C][C]1.45248529866541[/C][/ROW]
[ROW][C]54[/C][C]128.84[/C][C]129.274567426574[/C][C]-0.434567426573949[/C][/ROW]
[ROW][C]55[/C][C]128.95[/C][C]129.283562777393[/C][C]-0.333562777393041[/C][/ROW]
[ROW][C]56[/C][C]128.97[/C][C]129.362088663526[/C][C]-0.392088663526181[/C][/ROW]
[ROW][C]57[/C][C]128.97[/C][C]129.345092199658[/C][C]-0.375092199657587[/C][/ROW]
[ROW][C]58[/C][C]128.97[/C][C]129.309699477799[/C][C]-0.339699477799172[/C][/ROW]
[ROW][C]59[/C][C]128.97[/C][C]129.277646320884[/C][C]-0.307646320884231[/C][/ROW]
[ROW][C]60[/C][C]128.97[/C][C]129.248617616273[/C][C]-0.278617616273038[/C][/ROW]
[ROW][C]61[/C][C]128.97[/C][C]129.222327984533[/C][C]-0.252327984532883[/C][/ROW]
[ROW][C]62[/C][C]128.98[/C][C]129.19851897389[/C][C]-0.218518973890127[/C][/ROW]
[ROW][C]63[/C][C]128.99[/C][C]129.18790009333[/C][C]-0.197900093330219[/C][/ROW]
[ROW][C]64[/C][C]129.07[/C][C]129.179226756574[/C][C]-0.109226756573634[/C][/ROW]
[ROW][C]65[/C][C]129.76[/C][C]129.248920404646[/C][C]0.511079595353834[/C][/ROW]
[ROW][C]66[/C][C]130.47[/C][C]129.987144542558[/C][C]0.482855457442184[/C][/ROW]
[ROW][C]67[/C][C]130.76[/C][C]130.742705524414[/C][C]0.0172944755857998[/C][/ROW]
[ROW][C]68[/C][C]130.88[/C][C]131.034337386033[/C][C]-0.154337386032893[/C][/ROW]
[ROW][C]69[/C][C]131.04[/C][C]131.139774512741[/C][C]-0.099774512741476[/C][/ROW]
[ROW][C]70[/C][C]131.06[/C][C]131.290360049894[/C][C]-0.230360049894074[/C][/ROW]
[ROW][C]71[/C][C]131.13[/C][C]131.28862387628[/C][C]-0.15862387627962[/C][/ROW]
[ROW][C]72[/C][C]131.15[/C][C]131.343656540946[/C][C]-0.19365654094608[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203332&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203332&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
3104.4104.40
4104.4104.40
5104.4104.40
6104.41104.40.00999999999999091
7104.42104.4109435739240.00905642607629886
8104.68104.4217981146720.258201885327537
9106.02104.7061613712771.31383862872272
10106.35106.170131758280.179868241720087
11106.38106.517103656539-0.137103656538997
12106.47106.534166913023-0.0641669130234277
13106.5106.618112290434-0.118112290434041
14106.56106.636967522702-0.0769675227017075
15113.07106.6897050679626.38029493203767
16116.26113.8017330603082.45826693969231
17118117.2236887184890.776311281510928
18118.02119.036939426681-1.01693942668068
19118.04118.96098367418-0.920983674179752
20118.12118.894082056268-0.774082056267844
21118.12118.901041691957-0.781041691957171
22118.17118.827344634571-0.657344634571018
23118.22118.815319308964-0.595319308963781
24118.22118.809146531342-0.589146531341811
25118.23118.75355620092-0.523556200919941
26118.23118.714154803041-0.484154803041434
27118.23118.668471218323-0.438471218322519
28119.94118.6270982175321.31290178246815
29120.88120.4609802061650.419019793835133
30121.14121.440517821263-0.300517821263
31121.16121.672161743288-0.512161743287606
32121.2121.643835496719-0.443835496718748
33121.2121.641956336607-0.441956336606665
34121.2121.600254489143-0.400254489142597
35121.2121.562487519262-0.362487519262288
36121.2121.528284142178-0.328284142177637
37121.22121.497308106565-0.277308106564988
38121.22121.491142036746-0.271142036746156
39121.95121.4655577811970.484442218803395
40123.05122.2412684857170.808731514282641
41123.44123.4175782825330.0224217174666421
42123.65123.809693937326-0.159693937325983
43123.79124.004625633822-0.21462563382245
44123.87124.124374118679-0.254374118678982
45123.91124.180372040154-0.270372040153745
46123.94124.194860439475-0.254860439474783
47124.28124.2008124729870.079187527012607
48126.28124.5482844015451.73171559845538
49126.68126.711684569743-0.0316845697431631
50126.69127.108694896364-0.418694896363817
51126.69127.079187937744-0.389187937743841
52126.99127.042465178796-0.0524651787960693
53128.79127.3375147013351.45248529866541
54128.84129.274567426574-0.434567426573949
55128.95129.283562777393-0.333562777393041
56128.97129.362088663526-0.392088663526181
57128.97129.345092199658-0.375092199657587
58128.97129.309699477799-0.339699477799172
59128.97129.277646320884-0.307646320884231
60128.97129.248617616273-0.278617616273038
61128.97129.222327984533-0.252327984532883
62128.98129.19851897389-0.218518973890127
63128.99129.18790009333-0.197900093330219
64129.07129.179226756574-0.109226756573634
65129.76129.2489204046460.511079595353834
66130.47129.9871445425580.482855457442184
67130.76130.7427055244140.0172944755857998
68130.88131.034337386033-0.154337386032893
69131.04131.139774512741-0.099774512741476
70131.06131.290360049894-0.230360049894074
71131.13131.28862387628-0.15862387627962
72131.15131.343656540946-0.19365654094608







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73131.345383614727129.434630337194133.256136892259
74131.540767229454128.708196747333134.373337711575
75131.73615084418128.105387290889135.366914397472
76131.931534458907127.550557963542136.312510954273
77132.126918073634127.016145099861137.237691047407
78132.322301688361126.488898597233138.155704779489
79132.517685303088125.961486679684139.073883926491
80132.713068917814125.429494361225139.996643474404
81132.908452532541124.890113736169140.926791328914
82133.103836147268124.341493525588141.866178768948
83133.299219761995123.782385022731142.816054501259
84133.494603376722123.211935707687143.777271045756

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 131.345383614727 & 129.434630337194 & 133.256136892259 \tabularnewline
74 & 131.540767229454 & 128.708196747333 & 134.373337711575 \tabularnewline
75 & 131.73615084418 & 128.105387290889 & 135.366914397472 \tabularnewline
76 & 131.931534458907 & 127.550557963542 & 136.312510954273 \tabularnewline
77 & 132.126918073634 & 127.016145099861 & 137.237691047407 \tabularnewline
78 & 132.322301688361 & 126.488898597233 & 138.155704779489 \tabularnewline
79 & 132.517685303088 & 125.961486679684 & 139.073883926491 \tabularnewline
80 & 132.713068917814 & 125.429494361225 & 139.996643474404 \tabularnewline
81 & 132.908452532541 & 124.890113736169 & 140.926791328914 \tabularnewline
82 & 133.103836147268 & 124.341493525588 & 141.866178768948 \tabularnewline
83 & 133.299219761995 & 123.782385022731 & 142.816054501259 \tabularnewline
84 & 133.494603376722 & 123.211935707687 & 143.777271045756 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203332&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]131.345383614727[/C][C]129.434630337194[/C][C]133.256136892259[/C][/ROW]
[ROW][C]74[/C][C]131.540767229454[/C][C]128.708196747333[/C][C]134.373337711575[/C][/ROW]
[ROW][C]75[/C][C]131.73615084418[/C][C]128.105387290889[/C][C]135.366914397472[/C][/ROW]
[ROW][C]76[/C][C]131.931534458907[/C][C]127.550557963542[/C][C]136.312510954273[/C][/ROW]
[ROW][C]77[/C][C]132.126918073634[/C][C]127.016145099861[/C][C]137.237691047407[/C][/ROW]
[ROW][C]78[/C][C]132.322301688361[/C][C]126.488898597233[/C][C]138.155704779489[/C][/ROW]
[ROW][C]79[/C][C]132.517685303088[/C][C]125.961486679684[/C][C]139.073883926491[/C][/ROW]
[ROW][C]80[/C][C]132.713068917814[/C][C]125.429494361225[/C][C]139.996643474404[/C][/ROW]
[ROW][C]81[/C][C]132.908452532541[/C][C]124.890113736169[/C][C]140.926791328914[/C][/ROW]
[ROW][C]82[/C][C]133.103836147268[/C][C]124.341493525588[/C][C]141.866178768948[/C][/ROW]
[ROW][C]83[/C][C]133.299219761995[/C][C]123.782385022731[/C][C]142.816054501259[/C][/ROW]
[ROW][C]84[/C][C]133.494603376722[/C][C]123.211935707687[/C][C]143.777271045756[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203332&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203332&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
73131.345383614727129.434630337194133.256136892259
74131.540767229454128.708196747333134.373337711575
75131.73615084418128.105387290889135.366914397472
76131.931534458907127.550557963542136.312510954273
77132.126918073634127.016145099861137.237691047407
78132.322301688361126.488898597233138.155704779489
79132.517685303088125.961486679684139.073883926491
80132.713068917814125.429494361225139.996643474404
81132.908452532541124.890113736169140.926791328914
82133.103836147268124.341493525588141.866178768948
83133.299219761995123.782385022731142.816054501259
84133.494603376722123.211935707687143.777271045756



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')