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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 14 Jan 2013 16:56:28 -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/2013/Jan/14/t13582006784kd7k8nvf31qrbb.htm/, Retrieved Sun, 28 Apr 2024 17:30:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=205378, Retrieved Sun, 28 Apr 2024 17:30:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact57
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Opg10PrijzenBlaze...] [2013-01-14 21:56:28] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
163,93
164,28
164,58
165,97
166,3
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
173,2
173,38
172,89
172,98
172,98
172,69
172,77
172,65
172,3
172,17
172,17
173,07
173,27
173,05
173,41
173,37
173,37
173,08
173,97
175,23
174,9
174,83




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=205378&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=205378&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205378&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
alpha0.830113043957641
beta0.00137966518934271
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.830113043957641 \tabularnewline
beta & 0.00137966518934271 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205378&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]0.830113043957641[/C][/ROW]
[ROW][C]beta[/C][C]0.00137966518934271[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205378&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205378&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
alpha0.830113043957641
beta0.00137966518934271
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13166.19165.6349679487180.555032051282041
14166.19166.1294927272380.0605072727619813
15166.35166.363575334201-0.0135753342007945
16166.52166.5003121219280.0196878780724319
17167.17167.0884336841410.081566315858737
18167.16167.0442647608140.115735239186137
19167.16167.63109245547-0.471092455469886
20167.16167.336913961045-0.176913961044846
21167.39166.9571509230810.432849076919297
22168.46167.7007225358760.759277464124125
23168.55167.8036361946370.746363805363501
24168.58168.5725181842470.00748181575343665
25168.58168.70151253746-0.121512537460376
26169.21168.5520651481550.657934851845027
27169.29169.2718283628660.018171637134401
28169.24169.442939920719-0.202939920718791
29169.53169.858882821146-0.328882821146379
30169.57169.4814447297880.0885552702122823
31169.57169.947629638378-0.377629638377755
32169.67169.782734008892-0.112734008891749
33170.04169.5616329490840.478367050916091
34170.39170.40029225792-0.0102922579203835
35170.57169.8631475256970.706852474303219
36170.48170.4746243161570.00537568384277165
37170.48170.580873555916-0.100873555915854
38170.48170.581918108272-0.101918108272116
39170.49170.562301110736-0.0723011107362197
40170.72170.6207135410670.0992864589325393
41171.11171.266456028845-0.156456028845241
42171.07171.103580013567-0.0335800135668762
43171.07171.389551276015-0.319551276015318
44171.07171.318307261859-0.24830726185931
45171.05171.085367864041-0.0353678640409214
46172.28171.4142463349090.86575366509129
47172.74171.726849660861.01315033914022
48172.86172.4744647185970.385535281402923
49172.86172.879722598607-0.0197225986067906
50173.24172.9495306632020.290469336798395
51173.2173.262697036265-0.0626970362651491
52173.38173.3602693159340.0197306840657916
53172.89173.898469982948-1.00846998294796
54172.98173.050171088499-0.0701710884985118
55172.98173.258112913662-0.278112913662426
56172.69173.234346390366-0.544346390366286
57172.77172.792473166497-0.022473166496809
58172.65173.285795745544-0.635795745544186
59172.3172.375915658196-0.0759156581956688
60172.17172.1105434970160.0594565029842045
61172.17172.173581934109-0.00358193410875174
62173.07172.3068154561390.763184543861115
63173.27172.9502612365280.31973876347152
64173.05173.377610559833-0.32761055983292
65173.41173.45071174905-0.0407117490498194
66173.37173.564185584263-0.194185584262499
67173.37173.63273197733-0.262731977329537
68173.08173.575398612595-0.495398612594499
69173.97173.2617679274220.708232072577516
70175.23174.2572507078260.972749292173717
71174.9174.7793911503640.120608849635602
72174.83174.7020095746930.12799042530736

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 166.19 & 165.634967948718 & 0.555032051282041 \tabularnewline
14 & 166.19 & 166.129492727238 & 0.0605072727619813 \tabularnewline
15 & 166.35 & 166.363575334201 & -0.0135753342007945 \tabularnewline
16 & 166.52 & 166.500312121928 & 0.0196878780724319 \tabularnewline
17 & 167.17 & 167.088433684141 & 0.081566315858737 \tabularnewline
18 & 167.16 & 167.044264760814 & 0.115735239186137 \tabularnewline
19 & 167.16 & 167.63109245547 & -0.471092455469886 \tabularnewline
20 & 167.16 & 167.336913961045 & -0.176913961044846 \tabularnewline
21 & 167.39 & 166.957150923081 & 0.432849076919297 \tabularnewline
22 & 168.46 & 167.700722535876 & 0.759277464124125 \tabularnewline
23 & 168.55 & 167.803636194637 & 0.746363805363501 \tabularnewline
24 & 168.58 & 168.572518184247 & 0.00748181575343665 \tabularnewline
25 & 168.58 & 168.70151253746 & -0.121512537460376 \tabularnewline
26 & 169.21 & 168.552065148155 & 0.657934851845027 \tabularnewline
27 & 169.29 & 169.271828362866 & 0.018171637134401 \tabularnewline
28 & 169.24 & 169.442939920719 & -0.202939920718791 \tabularnewline
29 & 169.53 & 169.858882821146 & -0.328882821146379 \tabularnewline
30 & 169.57 & 169.481444729788 & 0.0885552702122823 \tabularnewline
31 & 169.57 & 169.947629638378 & -0.377629638377755 \tabularnewline
32 & 169.67 & 169.782734008892 & -0.112734008891749 \tabularnewline
33 & 170.04 & 169.561632949084 & 0.478367050916091 \tabularnewline
34 & 170.39 & 170.40029225792 & -0.0102922579203835 \tabularnewline
35 & 170.57 & 169.863147525697 & 0.706852474303219 \tabularnewline
36 & 170.48 & 170.474624316157 & 0.00537568384277165 \tabularnewline
37 & 170.48 & 170.580873555916 & -0.100873555915854 \tabularnewline
38 & 170.48 & 170.581918108272 & -0.101918108272116 \tabularnewline
39 & 170.49 & 170.562301110736 & -0.0723011107362197 \tabularnewline
40 & 170.72 & 170.620713541067 & 0.0992864589325393 \tabularnewline
41 & 171.11 & 171.266456028845 & -0.156456028845241 \tabularnewline
42 & 171.07 & 171.103580013567 & -0.0335800135668762 \tabularnewline
43 & 171.07 & 171.389551276015 & -0.319551276015318 \tabularnewline
44 & 171.07 & 171.318307261859 & -0.24830726185931 \tabularnewline
45 & 171.05 & 171.085367864041 & -0.0353678640409214 \tabularnewline
46 & 172.28 & 171.414246334909 & 0.86575366509129 \tabularnewline
47 & 172.74 & 171.72684966086 & 1.01315033914022 \tabularnewline
48 & 172.86 & 172.474464718597 & 0.385535281402923 \tabularnewline
49 & 172.86 & 172.879722598607 & -0.0197225986067906 \tabularnewline
50 & 173.24 & 172.949530663202 & 0.290469336798395 \tabularnewline
51 & 173.2 & 173.262697036265 & -0.0626970362651491 \tabularnewline
52 & 173.38 & 173.360269315934 & 0.0197306840657916 \tabularnewline
53 & 172.89 & 173.898469982948 & -1.00846998294796 \tabularnewline
54 & 172.98 & 173.050171088499 & -0.0701710884985118 \tabularnewline
55 & 172.98 & 173.258112913662 & -0.278112913662426 \tabularnewline
56 & 172.69 & 173.234346390366 & -0.544346390366286 \tabularnewline
57 & 172.77 & 172.792473166497 & -0.022473166496809 \tabularnewline
58 & 172.65 & 173.285795745544 & -0.635795745544186 \tabularnewline
59 & 172.3 & 172.375915658196 & -0.0759156581956688 \tabularnewline
60 & 172.17 & 172.110543497016 & 0.0594565029842045 \tabularnewline
61 & 172.17 & 172.173581934109 & -0.00358193410875174 \tabularnewline
62 & 173.07 & 172.306815456139 & 0.763184543861115 \tabularnewline
63 & 173.27 & 172.950261236528 & 0.31973876347152 \tabularnewline
64 & 173.05 & 173.377610559833 & -0.32761055983292 \tabularnewline
65 & 173.41 & 173.45071174905 & -0.0407117490498194 \tabularnewline
66 & 173.37 & 173.564185584263 & -0.194185584262499 \tabularnewline
67 & 173.37 & 173.63273197733 & -0.262731977329537 \tabularnewline
68 & 173.08 & 173.575398612595 & -0.495398612594499 \tabularnewline
69 & 173.97 & 173.261767927422 & 0.708232072577516 \tabularnewline
70 & 175.23 & 174.257250707826 & 0.972749292173717 \tabularnewline
71 & 174.9 & 174.779391150364 & 0.120608849635602 \tabularnewline
72 & 174.83 & 174.702009574693 & 0.12799042530736 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205378&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]13[/C][C]166.19[/C][C]165.634967948718[/C][C]0.555032051282041[/C][/ROW]
[ROW][C]14[/C][C]166.19[/C][C]166.129492727238[/C][C]0.0605072727619813[/C][/ROW]
[ROW][C]15[/C][C]166.35[/C][C]166.363575334201[/C][C]-0.0135753342007945[/C][/ROW]
[ROW][C]16[/C][C]166.52[/C][C]166.500312121928[/C][C]0.0196878780724319[/C][/ROW]
[ROW][C]17[/C][C]167.17[/C][C]167.088433684141[/C][C]0.081566315858737[/C][/ROW]
[ROW][C]18[/C][C]167.16[/C][C]167.044264760814[/C][C]0.115735239186137[/C][/ROW]
[ROW][C]19[/C][C]167.16[/C][C]167.63109245547[/C][C]-0.471092455469886[/C][/ROW]
[ROW][C]20[/C][C]167.16[/C][C]167.336913961045[/C][C]-0.176913961044846[/C][/ROW]
[ROW][C]21[/C][C]167.39[/C][C]166.957150923081[/C][C]0.432849076919297[/C][/ROW]
[ROW][C]22[/C][C]168.46[/C][C]167.700722535876[/C][C]0.759277464124125[/C][/ROW]
[ROW][C]23[/C][C]168.55[/C][C]167.803636194637[/C][C]0.746363805363501[/C][/ROW]
[ROW][C]24[/C][C]168.58[/C][C]168.572518184247[/C][C]0.00748181575343665[/C][/ROW]
[ROW][C]25[/C][C]168.58[/C][C]168.70151253746[/C][C]-0.121512537460376[/C][/ROW]
[ROW][C]26[/C][C]169.21[/C][C]168.552065148155[/C][C]0.657934851845027[/C][/ROW]
[ROW][C]27[/C][C]169.29[/C][C]169.271828362866[/C][C]0.018171637134401[/C][/ROW]
[ROW][C]28[/C][C]169.24[/C][C]169.442939920719[/C][C]-0.202939920718791[/C][/ROW]
[ROW][C]29[/C][C]169.53[/C][C]169.858882821146[/C][C]-0.328882821146379[/C][/ROW]
[ROW][C]30[/C][C]169.57[/C][C]169.481444729788[/C][C]0.0885552702122823[/C][/ROW]
[ROW][C]31[/C][C]169.57[/C][C]169.947629638378[/C][C]-0.377629638377755[/C][/ROW]
[ROW][C]32[/C][C]169.67[/C][C]169.782734008892[/C][C]-0.112734008891749[/C][/ROW]
[ROW][C]33[/C][C]170.04[/C][C]169.561632949084[/C][C]0.478367050916091[/C][/ROW]
[ROW][C]34[/C][C]170.39[/C][C]170.40029225792[/C][C]-0.0102922579203835[/C][/ROW]
[ROW][C]35[/C][C]170.57[/C][C]169.863147525697[/C][C]0.706852474303219[/C][/ROW]
[ROW][C]36[/C][C]170.48[/C][C]170.474624316157[/C][C]0.00537568384277165[/C][/ROW]
[ROW][C]37[/C][C]170.48[/C][C]170.580873555916[/C][C]-0.100873555915854[/C][/ROW]
[ROW][C]38[/C][C]170.48[/C][C]170.581918108272[/C][C]-0.101918108272116[/C][/ROW]
[ROW][C]39[/C][C]170.49[/C][C]170.562301110736[/C][C]-0.0723011107362197[/C][/ROW]
[ROW][C]40[/C][C]170.72[/C][C]170.620713541067[/C][C]0.0992864589325393[/C][/ROW]
[ROW][C]41[/C][C]171.11[/C][C]171.266456028845[/C][C]-0.156456028845241[/C][/ROW]
[ROW][C]42[/C][C]171.07[/C][C]171.103580013567[/C][C]-0.0335800135668762[/C][/ROW]
[ROW][C]43[/C][C]171.07[/C][C]171.389551276015[/C][C]-0.319551276015318[/C][/ROW]
[ROW][C]44[/C][C]171.07[/C][C]171.318307261859[/C][C]-0.24830726185931[/C][/ROW]
[ROW][C]45[/C][C]171.05[/C][C]171.085367864041[/C][C]-0.0353678640409214[/C][/ROW]
[ROW][C]46[/C][C]172.28[/C][C]171.414246334909[/C][C]0.86575366509129[/C][/ROW]
[ROW][C]47[/C][C]172.74[/C][C]171.72684966086[/C][C]1.01315033914022[/C][/ROW]
[ROW][C]48[/C][C]172.86[/C][C]172.474464718597[/C][C]0.385535281402923[/C][/ROW]
[ROW][C]49[/C][C]172.86[/C][C]172.879722598607[/C][C]-0.0197225986067906[/C][/ROW]
[ROW][C]50[/C][C]173.24[/C][C]172.949530663202[/C][C]0.290469336798395[/C][/ROW]
[ROW][C]51[/C][C]173.2[/C][C]173.262697036265[/C][C]-0.0626970362651491[/C][/ROW]
[ROW][C]52[/C][C]173.38[/C][C]173.360269315934[/C][C]0.0197306840657916[/C][/ROW]
[ROW][C]53[/C][C]172.89[/C][C]173.898469982948[/C][C]-1.00846998294796[/C][/ROW]
[ROW][C]54[/C][C]172.98[/C][C]173.050171088499[/C][C]-0.0701710884985118[/C][/ROW]
[ROW][C]55[/C][C]172.98[/C][C]173.258112913662[/C][C]-0.278112913662426[/C][/ROW]
[ROW][C]56[/C][C]172.69[/C][C]173.234346390366[/C][C]-0.544346390366286[/C][/ROW]
[ROW][C]57[/C][C]172.77[/C][C]172.792473166497[/C][C]-0.022473166496809[/C][/ROW]
[ROW][C]58[/C][C]172.65[/C][C]173.285795745544[/C][C]-0.635795745544186[/C][/ROW]
[ROW][C]59[/C][C]172.3[/C][C]172.375915658196[/C][C]-0.0759156581956688[/C][/ROW]
[ROW][C]60[/C][C]172.17[/C][C]172.110543497016[/C][C]0.0594565029842045[/C][/ROW]
[ROW][C]61[/C][C]172.17[/C][C]172.173581934109[/C][C]-0.00358193410875174[/C][/ROW]
[ROW][C]62[/C][C]173.07[/C][C]172.306815456139[/C][C]0.763184543861115[/C][/ROW]
[ROW][C]63[/C][C]173.27[/C][C]172.950261236528[/C][C]0.31973876347152[/C][/ROW]
[ROW][C]64[/C][C]173.05[/C][C]173.377610559833[/C][C]-0.32761055983292[/C][/ROW]
[ROW][C]65[/C][C]173.41[/C][C]173.45071174905[/C][C]-0.0407117490498194[/C][/ROW]
[ROW][C]66[/C][C]173.37[/C][C]173.564185584263[/C][C]-0.194185584262499[/C][/ROW]
[ROW][C]67[/C][C]173.37[/C][C]173.63273197733[/C][C]-0.262731977329537[/C][/ROW]
[ROW][C]68[/C][C]173.08[/C][C]173.575398612595[/C][C]-0.495398612594499[/C][/ROW]
[ROW][C]69[/C][C]173.97[/C][C]173.261767927422[/C][C]0.708232072577516[/C][/ROW]
[ROW][C]70[/C][C]175.23[/C][C]174.257250707826[/C][C]0.972749292173717[/C][/ROW]
[ROW][C]71[/C][C]174.9[/C][C]174.779391150364[/C][C]0.120608849635602[/C][/ROW]
[ROW][C]72[/C][C]174.83[/C][C]174.702009574693[/C][C]0.12799042530736[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205378&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205378&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
13166.19165.6349679487180.555032051282041
14166.19166.1294927272380.0605072727619813
15166.35166.363575334201-0.0135753342007945
16166.52166.5003121219280.0196878780724319
17167.17167.0884336841410.081566315858737
18167.16167.0442647608140.115735239186137
19167.16167.63109245547-0.471092455469886
20167.16167.336913961045-0.176913961044846
21167.39166.9571509230810.432849076919297
22168.46167.7007225358760.759277464124125
23168.55167.8036361946370.746363805363501
24168.58168.5725181842470.00748181575343665
25168.58168.70151253746-0.121512537460376
26169.21168.5520651481550.657934851845027
27169.29169.2718283628660.018171637134401
28169.24169.442939920719-0.202939920718791
29169.53169.858882821146-0.328882821146379
30169.57169.4814447297880.0885552702122823
31169.57169.947629638378-0.377629638377755
32169.67169.782734008892-0.112734008891749
33170.04169.5616329490840.478367050916091
34170.39170.40029225792-0.0102922579203835
35170.57169.8631475256970.706852474303219
36170.48170.4746243161570.00537568384277165
37170.48170.580873555916-0.100873555915854
38170.48170.581918108272-0.101918108272116
39170.49170.562301110736-0.0723011107362197
40170.72170.6207135410670.0992864589325393
41171.11171.266456028845-0.156456028845241
42171.07171.103580013567-0.0335800135668762
43171.07171.389551276015-0.319551276015318
44171.07171.318307261859-0.24830726185931
45171.05171.085367864041-0.0353678640409214
46172.28171.4142463349090.86575366509129
47172.74171.726849660861.01315033914022
48172.86172.4744647185970.385535281402923
49172.86172.879722598607-0.0197225986067906
50173.24172.9495306632020.290469336798395
51173.2173.262697036265-0.0626970362651491
52173.38173.3602693159340.0197306840657916
53172.89173.898469982948-1.00846998294796
54172.98173.050171088499-0.0701710884985118
55172.98173.258112913662-0.278112913662426
56172.69173.234346390366-0.544346390366286
57172.77172.792473166497-0.022473166496809
58172.65173.285795745544-0.635795745544186
59172.3172.375915658196-0.0759156581956688
60172.17172.1105434970160.0594565029842045
61172.17172.173581934109-0.00358193410875174
62173.07172.3068154561390.763184543861115
63173.27172.9502612365280.31973876347152
64173.05173.377610559833-0.32761055983292
65173.41173.45071174905-0.0407117490498194
66173.37173.564185584263-0.194185584262499
67173.37173.63273197733-0.262731977329537
68173.08173.575398612595-0.495398612594499
69173.97173.2617679274220.708232072577516
70175.23174.2572507078260.972749292173717
71174.9174.7793911503640.120608849635602
72174.83174.7020095746930.12799042530736







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73174.813163060571174.011952388146175.614373732996
74175.081571272178174.039692243727176.123450300629
75175.017215551853173.780159207387176.25427189632
76175.069866759007173.664046822458176.475686695555
77175.464734726223173.907950387345177.021519065101
78175.587049952229173.892336573886177.281763330571
79175.806488829727173.983919421205177.629058238249
80175.929368217224173.98702514654177.871711287907
81176.233665442019174.178217270743178.289113613295
82176.687572349815174.524640849606178.850503850024
83176.257738085813173.992144398138178.523331773489
84176.081638148891173.717574884525178.445701413258

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 174.813163060571 & 174.011952388146 & 175.614373732996 \tabularnewline
74 & 175.081571272178 & 174.039692243727 & 176.123450300629 \tabularnewline
75 & 175.017215551853 & 173.780159207387 & 176.25427189632 \tabularnewline
76 & 175.069866759007 & 173.664046822458 & 176.475686695555 \tabularnewline
77 & 175.464734726223 & 173.907950387345 & 177.021519065101 \tabularnewline
78 & 175.587049952229 & 173.892336573886 & 177.281763330571 \tabularnewline
79 & 175.806488829727 & 173.983919421205 & 177.629058238249 \tabularnewline
80 & 175.929368217224 & 173.98702514654 & 177.871711287907 \tabularnewline
81 & 176.233665442019 & 174.178217270743 & 178.289113613295 \tabularnewline
82 & 176.687572349815 & 174.524640849606 & 178.850503850024 \tabularnewline
83 & 176.257738085813 & 173.992144398138 & 178.523331773489 \tabularnewline
84 & 176.081638148891 & 173.717574884525 & 178.445701413258 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205378&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]174.813163060571[/C][C]174.011952388146[/C][C]175.614373732996[/C][/ROW]
[ROW][C]74[/C][C]175.081571272178[/C][C]174.039692243727[/C][C]176.123450300629[/C][/ROW]
[ROW][C]75[/C][C]175.017215551853[/C][C]173.780159207387[/C][C]176.25427189632[/C][/ROW]
[ROW][C]76[/C][C]175.069866759007[/C][C]173.664046822458[/C][C]176.475686695555[/C][/ROW]
[ROW][C]77[/C][C]175.464734726223[/C][C]173.907950387345[/C][C]177.021519065101[/C][/ROW]
[ROW][C]78[/C][C]175.587049952229[/C][C]173.892336573886[/C][C]177.281763330571[/C][/ROW]
[ROW][C]79[/C][C]175.806488829727[/C][C]173.983919421205[/C][C]177.629058238249[/C][/ROW]
[ROW][C]80[/C][C]175.929368217224[/C][C]173.98702514654[/C][C]177.871711287907[/C][/ROW]
[ROW][C]81[/C][C]176.233665442019[/C][C]174.178217270743[/C][C]178.289113613295[/C][/ROW]
[ROW][C]82[/C][C]176.687572349815[/C][C]174.524640849606[/C][C]178.850503850024[/C][/ROW]
[ROW][C]83[/C][C]176.257738085813[/C][C]173.992144398138[/C][C]178.523331773489[/C][/ROW]
[ROW][C]84[/C][C]176.081638148891[/C][C]173.717574884525[/C][C]178.445701413258[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205378&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205378&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
73174.813163060571174.011952388146175.614373732996
74175.081571272178174.039692243727176.123450300629
75175.017215551853173.780159207387176.25427189632
76175.069866759007173.664046822458176.475686695555
77175.464734726223173.907950387345177.021519065101
78175.587049952229173.892336573886177.281763330571
79175.806488829727173.983919421205177.629058238249
80175.929368217224173.98702514654177.871711287907
81176.233665442019174.178217270743178.289113613295
82176.687572349815174.524640849606178.850503850024
83176.257738085813173.992144398138178.523331773489
84176.081638148891173.717574884525178.445701413258



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