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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 22 May 2012 06:36:53 -0400
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/May/22/t1337683031a9irpcl2z8emd5m.htm/, Retrieved Fri, 03 May 2024 17:36:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167039, Retrieved Fri, 03 May 2024 17:36:05 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact117
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-05-22 10:36:53] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
163.93
164.28
164.58
165.97
166.30
166.27
166.27
166.44
166.26
166.64
166.07
166.19
166.19
166.19
166.35
166.52
167.17
167.16
167.16
167.16
167.39
168.46
168.55
168.58
168.58
169.21
169.29
169.24
169.53
169.57
169.57
169.67
170.04
170.39
170.57
170.48
170.48
170.48
170.49
170.72
171.11
171.07
171.07
171.07
171.05
172.28
172.74
172.86
172.86
173.24
173.20
173.38
172.89
172.98
172.98
172.69
172.77
172.65
172.30
172.17




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167039&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167039&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167039&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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999958201984458
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999958201984458 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167039&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]0.999958201984458[/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=167039&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167039&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
alpha0.999958201984458
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2164.28163.930.349999999999994
3164.58164.2799853706950.300014629305451
4165.97164.5799874599841.39001254001613
5166.3165.9699419002340.330058099765751
6166.27166.299986204226-0.0299862042264181
7166.27166.270001253364-1.25336381984198e-06
8166.44166.2700000000520.169999999947606
9166.26166.439992894337-0.179992894337374
10166.64166.2600075233460.379992476654195
11166.07166.639984117069-0.569984117068543
12166.19166.0700238242050.119976175795017
13166.19166.1899949852345.01476606018514e-06
14166.19166.189999999792.0961010704923e-10
15166.35166.190.159999999999997
16166.52166.3499933123180.170006687682502
17167.17166.5199928940580.650007105942137
18167.16167.169972830993-0.00997283099286506
19167.16167.160000416845-4.16844557094009e-07
20167.16167.160000000017-1.74225078808377e-11
21167.39167.160.22999999999999
22168.46167.3899903864561.07000961354359
23168.55168.4599552757220.0900447242784708
24168.58168.5499962363090.0300037636907859
25168.58168.5799987459021.25409778206631e-06
26169.21168.5799999999480.630000000052405
27169.29169.209973667250.0800263327497817
28169.24169.289996655058-0.049996655058095
29169.53169.2400020897610.289997910239038
30169.57169.5299878786630.0400121213371563
31169.57169.5699983275731.67242725979122e-06
32169.67169.569999999930.100000000069912
33170.04169.6699958201980.370004179801555
34170.39170.039984534560.350015465440464
35170.57170.3899853700480.18001462995187
36170.48170.569992475746-0.0899924757457029
37170.48170.480003761507-3.76150688907728e-06
38170.48170.480000000157-1.57228896568995e-10
39170.49170.480.0100000000000193
40170.72170.489999582020.230000417980136
41171.11170.7199903864390.390009613561062
42171.07171.109983698372-0.03998369837214
43171.07171.070001671239-1.67123923233703e-06
44171.07171.07000000007-6.98605617799331e-11
45171.05171.07-0.0199999999999818
46172.28171.050000835961.22999916403967
47172.74172.2799485884760.460051411524177
48172.86172.7399807707640.12001922923605
49172.86172.8599949834345.01656560913943e-06
50173.24172.859999999790.380000000209691
51173.2173.239984116754-0.0399841167541126
52173.38173.2000016712570.179998328743267
53172.89173.379992476427-0.489992476427062
54172.98172.8900204807130.0899795192868567
55172.98172.9799962390353.76096534182579e-06
56172.69172.979999999843-0.289999999842792
57172.77172.6900121214250.0799878785755084
58172.65172.769996656665-0.119996656665421
59172.3172.650005015622-0.350005015622116
60172.17172.300014629515-0.130014629515102

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 164.28 & 163.93 & 0.349999999999994 \tabularnewline
3 & 164.58 & 164.279985370695 & 0.300014629305451 \tabularnewline
4 & 165.97 & 164.579987459984 & 1.39001254001613 \tabularnewline
5 & 166.3 & 165.969941900234 & 0.330058099765751 \tabularnewline
6 & 166.27 & 166.299986204226 & -0.0299862042264181 \tabularnewline
7 & 166.27 & 166.270001253364 & -1.25336381984198e-06 \tabularnewline
8 & 166.44 & 166.270000000052 & 0.169999999947606 \tabularnewline
9 & 166.26 & 166.439992894337 & -0.179992894337374 \tabularnewline
10 & 166.64 & 166.260007523346 & 0.379992476654195 \tabularnewline
11 & 166.07 & 166.639984117069 & -0.569984117068543 \tabularnewline
12 & 166.19 & 166.070023824205 & 0.119976175795017 \tabularnewline
13 & 166.19 & 166.189994985234 & 5.01476606018514e-06 \tabularnewline
14 & 166.19 & 166.18999999979 & 2.0961010704923e-10 \tabularnewline
15 & 166.35 & 166.19 & 0.159999999999997 \tabularnewline
16 & 166.52 & 166.349993312318 & 0.170006687682502 \tabularnewline
17 & 167.17 & 166.519992894058 & 0.650007105942137 \tabularnewline
18 & 167.16 & 167.169972830993 & -0.00997283099286506 \tabularnewline
19 & 167.16 & 167.160000416845 & -4.16844557094009e-07 \tabularnewline
20 & 167.16 & 167.160000000017 & -1.74225078808377e-11 \tabularnewline
21 & 167.39 & 167.16 & 0.22999999999999 \tabularnewline
22 & 168.46 & 167.389990386456 & 1.07000961354359 \tabularnewline
23 & 168.55 & 168.459955275722 & 0.0900447242784708 \tabularnewline
24 & 168.58 & 168.549996236309 & 0.0300037636907859 \tabularnewline
25 & 168.58 & 168.579998745902 & 1.25409778206631e-06 \tabularnewline
26 & 169.21 & 168.579999999948 & 0.630000000052405 \tabularnewline
27 & 169.29 & 169.20997366725 & 0.0800263327497817 \tabularnewline
28 & 169.24 & 169.289996655058 & -0.049996655058095 \tabularnewline
29 & 169.53 & 169.240002089761 & 0.289997910239038 \tabularnewline
30 & 169.57 & 169.529987878663 & 0.0400121213371563 \tabularnewline
31 & 169.57 & 169.569998327573 & 1.67242725979122e-06 \tabularnewline
32 & 169.67 & 169.56999999993 & 0.100000000069912 \tabularnewline
33 & 170.04 & 169.669995820198 & 0.370004179801555 \tabularnewline
34 & 170.39 & 170.03998453456 & 0.350015465440464 \tabularnewline
35 & 170.57 & 170.389985370048 & 0.18001462995187 \tabularnewline
36 & 170.48 & 170.569992475746 & -0.0899924757457029 \tabularnewline
37 & 170.48 & 170.480003761507 & -3.76150688907728e-06 \tabularnewline
38 & 170.48 & 170.480000000157 & -1.57228896568995e-10 \tabularnewline
39 & 170.49 & 170.48 & 0.0100000000000193 \tabularnewline
40 & 170.72 & 170.48999958202 & 0.230000417980136 \tabularnewline
41 & 171.11 & 170.719990386439 & 0.390009613561062 \tabularnewline
42 & 171.07 & 171.109983698372 & -0.03998369837214 \tabularnewline
43 & 171.07 & 171.070001671239 & -1.67123923233703e-06 \tabularnewline
44 & 171.07 & 171.07000000007 & -6.98605617799331e-11 \tabularnewline
45 & 171.05 & 171.07 & -0.0199999999999818 \tabularnewline
46 & 172.28 & 171.05000083596 & 1.22999916403967 \tabularnewline
47 & 172.74 & 172.279948588476 & 0.460051411524177 \tabularnewline
48 & 172.86 & 172.739980770764 & 0.12001922923605 \tabularnewline
49 & 172.86 & 172.859994983434 & 5.01656560913943e-06 \tabularnewline
50 & 173.24 & 172.85999999979 & 0.380000000209691 \tabularnewline
51 & 173.2 & 173.239984116754 & -0.0399841167541126 \tabularnewline
52 & 173.38 & 173.200001671257 & 0.179998328743267 \tabularnewline
53 & 172.89 & 173.379992476427 & -0.489992476427062 \tabularnewline
54 & 172.98 & 172.890020480713 & 0.0899795192868567 \tabularnewline
55 & 172.98 & 172.979996239035 & 3.76096534182579e-06 \tabularnewline
56 & 172.69 & 172.979999999843 & -0.289999999842792 \tabularnewline
57 & 172.77 & 172.690012121425 & 0.0799878785755084 \tabularnewline
58 & 172.65 & 172.769996656665 & -0.119996656665421 \tabularnewline
59 & 172.3 & 172.650005015622 & -0.350005015622116 \tabularnewline
60 & 172.17 & 172.300014629515 & -0.130014629515102 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167039&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]164.28[/C][C]163.93[/C][C]0.349999999999994[/C][/ROW]
[ROW][C]3[/C][C]164.58[/C][C]164.279985370695[/C][C]0.300014629305451[/C][/ROW]
[ROW][C]4[/C][C]165.97[/C][C]164.579987459984[/C][C]1.39001254001613[/C][/ROW]
[ROW][C]5[/C][C]166.3[/C][C]165.969941900234[/C][C]0.330058099765751[/C][/ROW]
[ROW][C]6[/C][C]166.27[/C][C]166.299986204226[/C][C]-0.0299862042264181[/C][/ROW]
[ROW][C]7[/C][C]166.27[/C][C]166.270001253364[/C][C]-1.25336381984198e-06[/C][/ROW]
[ROW][C]8[/C][C]166.44[/C][C]166.270000000052[/C][C]0.169999999947606[/C][/ROW]
[ROW][C]9[/C][C]166.26[/C][C]166.439992894337[/C][C]-0.179992894337374[/C][/ROW]
[ROW][C]10[/C][C]166.64[/C][C]166.260007523346[/C][C]0.379992476654195[/C][/ROW]
[ROW][C]11[/C][C]166.07[/C][C]166.639984117069[/C][C]-0.569984117068543[/C][/ROW]
[ROW][C]12[/C][C]166.19[/C][C]166.070023824205[/C][C]0.119976175795017[/C][/ROW]
[ROW][C]13[/C][C]166.19[/C][C]166.189994985234[/C][C]5.01476606018514e-06[/C][/ROW]
[ROW][C]14[/C][C]166.19[/C][C]166.18999999979[/C][C]2.0961010704923e-10[/C][/ROW]
[ROW][C]15[/C][C]166.35[/C][C]166.19[/C][C]0.159999999999997[/C][/ROW]
[ROW][C]16[/C][C]166.52[/C][C]166.349993312318[/C][C]0.170006687682502[/C][/ROW]
[ROW][C]17[/C][C]167.17[/C][C]166.519992894058[/C][C]0.650007105942137[/C][/ROW]
[ROW][C]18[/C][C]167.16[/C][C]167.169972830993[/C][C]-0.00997283099286506[/C][/ROW]
[ROW][C]19[/C][C]167.16[/C][C]167.160000416845[/C][C]-4.16844557094009e-07[/C][/ROW]
[ROW][C]20[/C][C]167.16[/C][C]167.160000000017[/C][C]-1.74225078808377e-11[/C][/ROW]
[ROW][C]21[/C][C]167.39[/C][C]167.16[/C][C]0.22999999999999[/C][/ROW]
[ROW][C]22[/C][C]168.46[/C][C]167.389990386456[/C][C]1.07000961354359[/C][/ROW]
[ROW][C]23[/C][C]168.55[/C][C]168.459955275722[/C][C]0.0900447242784708[/C][/ROW]
[ROW][C]24[/C][C]168.58[/C][C]168.549996236309[/C][C]0.0300037636907859[/C][/ROW]
[ROW][C]25[/C][C]168.58[/C][C]168.579998745902[/C][C]1.25409778206631e-06[/C][/ROW]
[ROW][C]26[/C][C]169.21[/C][C]168.579999999948[/C][C]0.630000000052405[/C][/ROW]
[ROW][C]27[/C][C]169.29[/C][C]169.20997366725[/C][C]0.0800263327497817[/C][/ROW]
[ROW][C]28[/C][C]169.24[/C][C]169.289996655058[/C][C]-0.049996655058095[/C][/ROW]
[ROW][C]29[/C][C]169.53[/C][C]169.240002089761[/C][C]0.289997910239038[/C][/ROW]
[ROW][C]30[/C][C]169.57[/C][C]169.529987878663[/C][C]0.0400121213371563[/C][/ROW]
[ROW][C]31[/C][C]169.57[/C][C]169.569998327573[/C][C]1.67242725979122e-06[/C][/ROW]
[ROW][C]32[/C][C]169.67[/C][C]169.56999999993[/C][C]0.100000000069912[/C][/ROW]
[ROW][C]33[/C][C]170.04[/C][C]169.669995820198[/C][C]0.370004179801555[/C][/ROW]
[ROW][C]34[/C][C]170.39[/C][C]170.03998453456[/C][C]0.350015465440464[/C][/ROW]
[ROW][C]35[/C][C]170.57[/C][C]170.389985370048[/C][C]0.18001462995187[/C][/ROW]
[ROW][C]36[/C][C]170.48[/C][C]170.569992475746[/C][C]-0.0899924757457029[/C][/ROW]
[ROW][C]37[/C][C]170.48[/C][C]170.480003761507[/C][C]-3.76150688907728e-06[/C][/ROW]
[ROW][C]38[/C][C]170.48[/C][C]170.480000000157[/C][C]-1.57228896568995e-10[/C][/ROW]
[ROW][C]39[/C][C]170.49[/C][C]170.48[/C][C]0.0100000000000193[/C][/ROW]
[ROW][C]40[/C][C]170.72[/C][C]170.48999958202[/C][C]0.230000417980136[/C][/ROW]
[ROW][C]41[/C][C]171.11[/C][C]170.719990386439[/C][C]0.390009613561062[/C][/ROW]
[ROW][C]42[/C][C]171.07[/C][C]171.109983698372[/C][C]-0.03998369837214[/C][/ROW]
[ROW][C]43[/C][C]171.07[/C][C]171.070001671239[/C][C]-1.67123923233703e-06[/C][/ROW]
[ROW][C]44[/C][C]171.07[/C][C]171.07000000007[/C][C]-6.98605617799331e-11[/C][/ROW]
[ROW][C]45[/C][C]171.05[/C][C]171.07[/C][C]-0.0199999999999818[/C][/ROW]
[ROW][C]46[/C][C]172.28[/C][C]171.05000083596[/C][C]1.22999916403967[/C][/ROW]
[ROW][C]47[/C][C]172.74[/C][C]172.279948588476[/C][C]0.460051411524177[/C][/ROW]
[ROW][C]48[/C][C]172.86[/C][C]172.739980770764[/C][C]0.12001922923605[/C][/ROW]
[ROW][C]49[/C][C]172.86[/C][C]172.859994983434[/C][C]5.01656560913943e-06[/C][/ROW]
[ROW][C]50[/C][C]173.24[/C][C]172.85999999979[/C][C]0.380000000209691[/C][/ROW]
[ROW][C]51[/C][C]173.2[/C][C]173.239984116754[/C][C]-0.0399841167541126[/C][/ROW]
[ROW][C]52[/C][C]173.38[/C][C]173.200001671257[/C][C]0.179998328743267[/C][/ROW]
[ROW][C]53[/C][C]172.89[/C][C]173.379992476427[/C][C]-0.489992476427062[/C][/ROW]
[ROW][C]54[/C][C]172.98[/C][C]172.890020480713[/C][C]0.0899795192868567[/C][/ROW]
[ROW][C]55[/C][C]172.98[/C][C]172.979996239035[/C][C]3.76096534182579e-06[/C][/ROW]
[ROW][C]56[/C][C]172.69[/C][C]172.979999999843[/C][C]-0.289999999842792[/C][/ROW]
[ROW][C]57[/C][C]172.77[/C][C]172.690012121425[/C][C]0.0799878785755084[/C][/ROW]
[ROW][C]58[/C][C]172.65[/C][C]172.769996656665[/C][C]-0.119996656665421[/C][/ROW]
[ROW][C]59[/C][C]172.3[/C][C]172.650005015622[/C][C]-0.350005015622116[/C][/ROW]
[ROW][C]60[/C][C]172.17[/C][C]172.300014629515[/C][C]-0.130014629515102[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167039&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167039&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
2164.28163.930.349999999999994
3164.58164.2799853706950.300014629305451
4165.97164.5799874599841.39001254001613
5166.3165.9699419002340.330058099765751
6166.27166.299986204226-0.0299862042264181
7166.27166.270001253364-1.25336381984198e-06
8166.44166.2700000000520.169999999947606
9166.26166.439992894337-0.179992894337374
10166.64166.2600075233460.379992476654195
11166.07166.639984117069-0.569984117068543
12166.19166.0700238242050.119976175795017
13166.19166.1899949852345.01476606018514e-06
14166.19166.189999999792.0961010704923e-10
15166.35166.190.159999999999997
16166.52166.3499933123180.170006687682502
17167.17166.5199928940580.650007105942137
18167.16167.169972830993-0.00997283099286506
19167.16167.160000416845-4.16844557094009e-07
20167.16167.160000000017-1.74225078808377e-11
21167.39167.160.22999999999999
22168.46167.3899903864561.07000961354359
23168.55168.4599552757220.0900447242784708
24168.58168.5499962363090.0300037636907859
25168.58168.5799987459021.25409778206631e-06
26169.21168.5799999999480.630000000052405
27169.29169.209973667250.0800263327497817
28169.24169.289996655058-0.049996655058095
29169.53169.2400020897610.289997910239038
30169.57169.5299878786630.0400121213371563
31169.57169.5699983275731.67242725979122e-06
32169.67169.569999999930.100000000069912
33170.04169.6699958201980.370004179801555
34170.39170.039984534560.350015465440464
35170.57170.3899853700480.18001462995187
36170.48170.569992475746-0.0899924757457029
37170.48170.480003761507-3.76150688907728e-06
38170.48170.480000000157-1.57228896568995e-10
39170.49170.480.0100000000000193
40170.72170.489999582020.230000417980136
41171.11170.7199903864390.390009613561062
42171.07171.109983698372-0.03998369837214
43171.07171.070001671239-1.67123923233703e-06
44171.07171.07000000007-6.98605617799331e-11
45171.05171.07-0.0199999999999818
46172.28171.050000835961.22999916403967
47172.74172.2799485884760.460051411524177
48172.86172.7399807707640.12001922923605
49172.86172.8599949834345.01656560913943e-06
50173.24172.859999999790.380000000209691
51173.2173.239984116754-0.0399841167541126
52173.38173.2000016712570.179998328743267
53172.89173.379992476427-0.489992476427062
54172.98172.8900204807130.0899795192868567
55172.98172.9799962390353.76096534182579e-06
56172.69172.979999999843-0.289999999842792
57172.77172.6900121214250.0799878785755084
58172.65172.769996656665-0.119996656665421
59172.3172.650005015622-0.350005015622116
60172.17172.300014629515-0.130014629515102







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61172.170005434353171.501332963851172.838677904856
62172.170005434353171.224379520633173.115631348074
63172.170005434353171.011863014532173.328147854175
64172.170005434353170.832702416903173.507308451804
65172.170005434353170.674858332436173.665152536271
66172.170005434353170.532156127407173.8078547413
67172.170005434353170.400927751448173.939083117259
68172.170005434353170.27878325173174.061227616977
69172.170005434353170.164062553826174.175948314881
70172.170005434353170.055556963515174.284453905192
71172.170005434353169.952354011852174.387656856855
72172.170005434353169.853744799707174.486266069

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 172.170005434353 & 171.501332963851 & 172.838677904856 \tabularnewline
62 & 172.170005434353 & 171.224379520633 & 173.115631348074 \tabularnewline
63 & 172.170005434353 & 171.011863014532 & 173.328147854175 \tabularnewline
64 & 172.170005434353 & 170.832702416903 & 173.507308451804 \tabularnewline
65 & 172.170005434353 & 170.674858332436 & 173.665152536271 \tabularnewline
66 & 172.170005434353 & 170.532156127407 & 173.8078547413 \tabularnewline
67 & 172.170005434353 & 170.400927751448 & 173.939083117259 \tabularnewline
68 & 172.170005434353 & 170.27878325173 & 174.061227616977 \tabularnewline
69 & 172.170005434353 & 170.164062553826 & 174.175948314881 \tabularnewline
70 & 172.170005434353 & 170.055556963515 & 174.284453905192 \tabularnewline
71 & 172.170005434353 & 169.952354011852 & 174.387656856855 \tabularnewline
72 & 172.170005434353 & 169.853744799707 & 174.486266069 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167039&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]61[/C][C]172.170005434353[/C][C]171.501332963851[/C][C]172.838677904856[/C][/ROW]
[ROW][C]62[/C][C]172.170005434353[/C][C]171.224379520633[/C][C]173.115631348074[/C][/ROW]
[ROW][C]63[/C][C]172.170005434353[/C][C]171.011863014532[/C][C]173.328147854175[/C][/ROW]
[ROW][C]64[/C][C]172.170005434353[/C][C]170.832702416903[/C][C]173.507308451804[/C][/ROW]
[ROW][C]65[/C][C]172.170005434353[/C][C]170.674858332436[/C][C]173.665152536271[/C][/ROW]
[ROW][C]66[/C][C]172.170005434353[/C][C]170.532156127407[/C][C]173.8078547413[/C][/ROW]
[ROW][C]67[/C][C]172.170005434353[/C][C]170.400927751448[/C][C]173.939083117259[/C][/ROW]
[ROW][C]68[/C][C]172.170005434353[/C][C]170.27878325173[/C][C]174.061227616977[/C][/ROW]
[ROW][C]69[/C][C]172.170005434353[/C][C]170.164062553826[/C][C]174.175948314881[/C][/ROW]
[ROW][C]70[/C][C]172.170005434353[/C][C]170.055556963515[/C][C]174.284453905192[/C][/ROW]
[ROW][C]71[/C][C]172.170005434353[/C][C]169.952354011852[/C][C]174.387656856855[/C][/ROW]
[ROW][C]72[/C][C]172.170005434353[/C][C]169.853744799707[/C][C]174.486266069[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167039&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167039&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
61172.170005434353171.501332963851172.838677904856
62172.170005434353171.224379520633173.115631348074
63172.170005434353171.011863014532173.328147854175
64172.170005434353170.832702416903173.507308451804
65172.170005434353170.674858332436173.665152536271
66172.170005434353170.532156127407173.8078547413
67172.170005434353170.400927751448173.939083117259
68172.170005434353170.27878325173174.061227616977
69172.170005434353170.164062553826174.175948314881
70172.170005434353170.055556963515174.284453905192
71172.170005434353169.952354011852174.387656856855
72172.170005434353169.853744799707174.486266069



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')