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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 11 Dec 2014 18:49:21 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Dec/11/t1418323826s2wvecxfuvxjryy.htm/, Retrieved Thu, 16 May 2024 13:00:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=266274, Retrieved Thu, 16 May 2024 13:00:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact51
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-12-11 18:49:21] [bdd4dd5e616b71837cf1c04213e8fe07] [Current]
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Dataseries X:
204,12
203,27
203,73
203,7
203,44
203,34
203,34
203,05
202,71
202,51
203,45
203,04
203,04
202,87
202,92
202,87
203,17
203,88
203,88
203,45
203,22
202,11
202,5
202,86
202,86
203,8
203,78
204,53
204,44
204,14
204,14
204,04
204,68
205,01
204,93
204,34
204,34
203,87
202,47
201,95
201,86
200,33
200,33
200,33
200,75
201,86
202,77
202,85
202,85
202,84
202,94
203,05
203,45
204,19
204,18
204,47
204,78
206,05
206,32
206,36
205,21
205,35
205,94
204,57
204,27
204,86
204,66
204,79
205,58
205,63
205,12
204,96




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266274&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266274&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266274&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'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.22411210008796
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.22411210008796 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266274&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]0.22411210008796[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266274&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266274&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
beta0.22411210008796
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3203.73202.421.30999999999997
4203.7203.1735868511150.526413148884785
5203.44203.2615624074260.178437592574312
6203.34203.0415524310320.298447568967845
7203.34203.008438142480.331561857520285
8203.05203.082745166678-0.0327451666776426
9202.71202.785406578606-0.0754065786057936
10202.51202.4285070519140.0814929480859803
11203.45202.2467706076521.20322939234811
12203.04203.456428873659-0.416428873658589
13203.04202.9531021242460.0868978757542891
14202.87202.972576989674-0.102576989674162
15202.92202.7795882450980.140411754902374
16202.87202.8610562183660.00894378163420129
17203.17202.8130606280510.356939371949409
18203.88203.1930550603020.686944939697781
19203.88204.057007733383-0.177007733382709
20203.45204.017338158522-0.567338158522489
21203.22203.460190812356-0.240190812355962
22202.11203.176361144977-1.06636114497704
23202.5201.8273767093240.672623290675944
24202.86202.3681197275650.491880272434514
25202.86202.8383560484130.0216439515873503
26203.8202.8432067198570.956793280142904
27203.78203.99763567122-0.217635671219966
28204.53203.9288608838890.601139116111199
29204.44204.813583433646-0.373583433645507
30204.14204.639858865773-0.499858865773149
31204.14204.227834445617-0.0878344456171192
32204.04204.20814968355-0.168149683549814
33204.68204.070465304840.609534695159681
34205.01204.8470694054490.162930594550943
35204.93205.213584123162-0.283584123162427
36204.34205.070029489769-0.730029489768896
37204.34204.3164210476910.0235789523093501
38203.87204.321705376211-0.451705376210583
39202.47203.750472735727-1.28047273572702
40201.95202.063503301818-0.113503301817843
41201.86201.5180658384810.341934161519504
42200.33201.50469742151-1.17469742151047
43200.33199.7114335154080.618566484592151
44200.33199.8500617493140.47993825068616
45200.75199.9576217185880.79237828141234
46201.86200.5552032792991.30479672070095
47202.77201.9576240125630.812375987436781
48202.85203.049687301169-0.199687301168723
49202.85203.084934960743-0.234934960742891
50202.84203.032283193307-0.192283193306707
51202.94202.979190203043-0.0391902030431481
52203.05203.070407204336-0.0204072043362373
53203.45203.1758337029160.274166297084435
54204.19203.6372776875280.552722312471531
55204.18204.501149445742-0.321149445741924
56204.47204.4191759690150.0508240309853534
57204.78204.7205662493340.059433750666301
58206.05205.0438860720121.00611392798839
59206.32206.539368377341-0.219368377340857
60206.36206.760205269602-0.400205269602083
61205.21206.710514426165-1.50051442616532
62205.35205.2242309869050.125769013094867
63205.94205.3924173445560.547582655444188
64204.57206.105137243439-1.53513724343915
65204.27204.391094411889-0.121094411888748
66204.86204.0639556889310.796044311068556
67204.66204.832358851248-0.172358851248106
68204.79204.5937311471260.196268852873857
69205.58204.7677173719260.812282628074456
70205.63205.739759737568-0.109759737568311
71205.12205.765161252277-0.64516125227675
72204.96205.110572809134-0.150572809133621

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 203.73 & 202.42 & 1.30999999999997 \tabularnewline
4 & 203.7 & 203.173586851115 & 0.526413148884785 \tabularnewline
5 & 203.44 & 203.261562407426 & 0.178437592574312 \tabularnewline
6 & 203.34 & 203.041552431032 & 0.298447568967845 \tabularnewline
7 & 203.34 & 203.00843814248 & 0.331561857520285 \tabularnewline
8 & 203.05 & 203.082745166678 & -0.0327451666776426 \tabularnewline
9 & 202.71 & 202.785406578606 & -0.0754065786057936 \tabularnewline
10 & 202.51 & 202.428507051914 & 0.0814929480859803 \tabularnewline
11 & 203.45 & 202.246770607652 & 1.20322939234811 \tabularnewline
12 & 203.04 & 203.456428873659 & -0.416428873658589 \tabularnewline
13 & 203.04 & 202.953102124246 & 0.0868978757542891 \tabularnewline
14 & 202.87 & 202.972576989674 & -0.102576989674162 \tabularnewline
15 & 202.92 & 202.779588245098 & 0.140411754902374 \tabularnewline
16 & 202.87 & 202.861056218366 & 0.00894378163420129 \tabularnewline
17 & 203.17 & 202.813060628051 & 0.356939371949409 \tabularnewline
18 & 203.88 & 203.193055060302 & 0.686944939697781 \tabularnewline
19 & 203.88 & 204.057007733383 & -0.177007733382709 \tabularnewline
20 & 203.45 & 204.017338158522 & -0.567338158522489 \tabularnewline
21 & 203.22 & 203.460190812356 & -0.240190812355962 \tabularnewline
22 & 202.11 & 203.176361144977 & -1.06636114497704 \tabularnewline
23 & 202.5 & 201.827376709324 & 0.672623290675944 \tabularnewline
24 & 202.86 & 202.368119727565 & 0.491880272434514 \tabularnewline
25 & 202.86 & 202.838356048413 & 0.0216439515873503 \tabularnewline
26 & 203.8 & 202.843206719857 & 0.956793280142904 \tabularnewline
27 & 203.78 & 203.99763567122 & -0.217635671219966 \tabularnewline
28 & 204.53 & 203.928860883889 & 0.601139116111199 \tabularnewline
29 & 204.44 & 204.813583433646 & -0.373583433645507 \tabularnewline
30 & 204.14 & 204.639858865773 & -0.499858865773149 \tabularnewline
31 & 204.14 & 204.227834445617 & -0.0878344456171192 \tabularnewline
32 & 204.04 & 204.20814968355 & -0.168149683549814 \tabularnewline
33 & 204.68 & 204.07046530484 & 0.609534695159681 \tabularnewline
34 & 205.01 & 204.847069405449 & 0.162930594550943 \tabularnewline
35 & 204.93 & 205.213584123162 & -0.283584123162427 \tabularnewline
36 & 204.34 & 205.070029489769 & -0.730029489768896 \tabularnewline
37 & 204.34 & 204.316421047691 & 0.0235789523093501 \tabularnewline
38 & 203.87 & 204.321705376211 & -0.451705376210583 \tabularnewline
39 & 202.47 & 203.750472735727 & -1.28047273572702 \tabularnewline
40 & 201.95 & 202.063503301818 & -0.113503301817843 \tabularnewline
41 & 201.86 & 201.518065838481 & 0.341934161519504 \tabularnewline
42 & 200.33 & 201.50469742151 & -1.17469742151047 \tabularnewline
43 & 200.33 & 199.711433515408 & 0.618566484592151 \tabularnewline
44 & 200.33 & 199.850061749314 & 0.47993825068616 \tabularnewline
45 & 200.75 & 199.957621718588 & 0.79237828141234 \tabularnewline
46 & 201.86 & 200.555203279299 & 1.30479672070095 \tabularnewline
47 & 202.77 & 201.957624012563 & 0.812375987436781 \tabularnewline
48 & 202.85 & 203.049687301169 & -0.199687301168723 \tabularnewline
49 & 202.85 & 203.084934960743 & -0.234934960742891 \tabularnewline
50 & 202.84 & 203.032283193307 & -0.192283193306707 \tabularnewline
51 & 202.94 & 202.979190203043 & -0.0391902030431481 \tabularnewline
52 & 203.05 & 203.070407204336 & -0.0204072043362373 \tabularnewline
53 & 203.45 & 203.175833702916 & 0.274166297084435 \tabularnewline
54 & 204.19 & 203.637277687528 & 0.552722312471531 \tabularnewline
55 & 204.18 & 204.501149445742 & -0.321149445741924 \tabularnewline
56 & 204.47 & 204.419175969015 & 0.0508240309853534 \tabularnewline
57 & 204.78 & 204.720566249334 & 0.059433750666301 \tabularnewline
58 & 206.05 & 205.043886072012 & 1.00611392798839 \tabularnewline
59 & 206.32 & 206.539368377341 & -0.219368377340857 \tabularnewline
60 & 206.36 & 206.760205269602 & -0.400205269602083 \tabularnewline
61 & 205.21 & 206.710514426165 & -1.50051442616532 \tabularnewline
62 & 205.35 & 205.224230986905 & 0.125769013094867 \tabularnewline
63 & 205.94 & 205.392417344556 & 0.547582655444188 \tabularnewline
64 & 204.57 & 206.105137243439 & -1.53513724343915 \tabularnewline
65 & 204.27 & 204.391094411889 & -0.121094411888748 \tabularnewline
66 & 204.86 & 204.063955688931 & 0.796044311068556 \tabularnewline
67 & 204.66 & 204.832358851248 & -0.172358851248106 \tabularnewline
68 & 204.79 & 204.593731147126 & 0.196268852873857 \tabularnewline
69 & 205.58 & 204.767717371926 & 0.812282628074456 \tabularnewline
70 & 205.63 & 205.739759737568 & -0.109759737568311 \tabularnewline
71 & 205.12 & 205.765161252277 & -0.64516125227675 \tabularnewline
72 & 204.96 & 205.110572809134 & -0.150572809133621 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266274&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]203.73[/C][C]202.42[/C][C]1.30999999999997[/C][/ROW]
[ROW][C]4[/C][C]203.7[/C][C]203.173586851115[/C][C]0.526413148884785[/C][/ROW]
[ROW][C]5[/C][C]203.44[/C][C]203.261562407426[/C][C]0.178437592574312[/C][/ROW]
[ROW][C]6[/C][C]203.34[/C][C]203.041552431032[/C][C]0.298447568967845[/C][/ROW]
[ROW][C]7[/C][C]203.34[/C][C]203.00843814248[/C][C]0.331561857520285[/C][/ROW]
[ROW][C]8[/C][C]203.05[/C][C]203.082745166678[/C][C]-0.0327451666776426[/C][/ROW]
[ROW][C]9[/C][C]202.71[/C][C]202.785406578606[/C][C]-0.0754065786057936[/C][/ROW]
[ROW][C]10[/C][C]202.51[/C][C]202.428507051914[/C][C]0.0814929480859803[/C][/ROW]
[ROW][C]11[/C][C]203.45[/C][C]202.246770607652[/C][C]1.20322939234811[/C][/ROW]
[ROW][C]12[/C][C]203.04[/C][C]203.456428873659[/C][C]-0.416428873658589[/C][/ROW]
[ROW][C]13[/C][C]203.04[/C][C]202.953102124246[/C][C]0.0868978757542891[/C][/ROW]
[ROW][C]14[/C][C]202.87[/C][C]202.972576989674[/C][C]-0.102576989674162[/C][/ROW]
[ROW][C]15[/C][C]202.92[/C][C]202.779588245098[/C][C]0.140411754902374[/C][/ROW]
[ROW][C]16[/C][C]202.87[/C][C]202.861056218366[/C][C]0.00894378163420129[/C][/ROW]
[ROW][C]17[/C][C]203.17[/C][C]202.813060628051[/C][C]0.356939371949409[/C][/ROW]
[ROW][C]18[/C][C]203.88[/C][C]203.193055060302[/C][C]0.686944939697781[/C][/ROW]
[ROW][C]19[/C][C]203.88[/C][C]204.057007733383[/C][C]-0.177007733382709[/C][/ROW]
[ROW][C]20[/C][C]203.45[/C][C]204.017338158522[/C][C]-0.567338158522489[/C][/ROW]
[ROW][C]21[/C][C]203.22[/C][C]203.460190812356[/C][C]-0.240190812355962[/C][/ROW]
[ROW][C]22[/C][C]202.11[/C][C]203.176361144977[/C][C]-1.06636114497704[/C][/ROW]
[ROW][C]23[/C][C]202.5[/C][C]201.827376709324[/C][C]0.672623290675944[/C][/ROW]
[ROW][C]24[/C][C]202.86[/C][C]202.368119727565[/C][C]0.491880272434514[/C][/ROW]
[ROW][C]25[/C][C]202.86[/C][C]202.838356048413[/C][C]0.0216439515873503[/C][/ROW]
[ROW][C]26[/C][C]203.8[/C][C]202.843206719857[/C][C]0.956793280142904[/C][/ROW]
[ROW][C]27[/C][C]203.78[/C][C]203.99763567122[/C][C]-0.217635671219966[/C][/ROW]
[ROW][C]28[/C][C]204.53[/C][C]203.928860883889[/C][C]0.601139116111199[/C][/ROW]
[ROW][C]29[/C][C]204.44[/C][C]204.813583433646[/C][C]-0.373583433645507[/C][/ROW]
[ROW][C]30[/C][C]204.14[/C][C]204.639858865773[/C][C]-0.499858865773149[/C][/ROW]
[ROW][C]31[/C][C]204.14[/C][C]204.227834445617[/C][C]-0.0878344456171192[/C][/ROW]
[ROW][C]32[/C][C]204.04[/C][C]204.20814968355[/C][C]-0.168149683549814[/C][/ROW]
[ROW][C]33[/C][C]204.68[/C][C]204.07046530484[/C][C]0.609534695159681[/C][/ROW]
[ROW][C]34[/C][C]205.01[/C][C]204.847069405449[/C][C]0.162930594550943[/C][/ROW]
[ROW][C]35[/C][C]204.93[/C][C]205.213584123162[/C][C]-0.283584123162427[/C][/ROW]
[ROW][C]36[/C][C]204.34[/C][C]205.070029489769[/C][C]-0.730029489768896[/C][/ROW]
[ROW][C]37[/C][C]204.34[/C][C]204.316421047691[/C][C]0.0235789523093501[/C][/ROW]
[ROW][C]38[/C][C]203.87[/C][C]204.321705376211[/C][C]-0.451705376210583[/C][/ROW]
[ROW][C]39[/C][C]202.47[/C][C]203.750472735727[/C][C]-1.28047273572702[/C][/ROW]
[ROW][C]40[/C][C]201.95[/C][C]202.063503301818[/C][C]-0.113503301817843[/C][/ROW]
[ROW][C]41[/C][C]201.86[/C][C]201.518065838481[/C][C]0.341934161519504[/C][/ROW]
[ROW][C]42[/C][C]200.33[/C][C]201.50469742151[/C][C]-1.17469742151047[/C][/ROW]
[ROW][C]43[/C][C]200.33[/C][C]199.711433515408[/C][C]0.618566484592151[/C][/ROW]
[ROW][C]44[/C][C]200.33[/C][C]199.850061749314[/C][C]0.47993825068616[/C][/ROW]
[ROW][C]45[/C][C]200.75[/C][C]199.957621718588[/C][C]0.79237828141234[/C][/ROW]
[ROW][C]46[/C][C]201.86[/C][C]200.555203279299[/C][C]1.30479672070095[/C][/ROW]
[ROW][C]47[/C][C]202.77[/C][C]201.957624012563[/C][C]0.812375987436781[/C][/ROW]
[ROW][C]48[/C][C]202.85[/C][C]203.049687301169[/C][C]-0.199687301168723[/C][/ROW]
[ROW][C]49[/C][C]202.85[/C][C]203.084934960743[/C][C]-0.234934960742891[/C][/ROW]
[ROW][C]50[/C][C]202.84[/C][C]203.032283193307[/C][C]-0.192283193306707[/C][/ROW]
[ROW][C]51[/C][C]202.94[/C][C]202.979190203043[/C][C]-0.0391902030431481[/C][/ROW]
[ROW][C]52[/C][C]203.05[/C][C]203.070407204336[/C][C]-0.0204072043362373[/C][/ROW]
[ROW][C]53[/C][C]203.45[/C][C]203.175833702916[/C][C]0.274166297084435[/C][/ROW]
[ROW][C]54[/C][C]204.19[/C][C]203.637277687528[/C][C]0.552722312471531[/C][/ROW]
[ROW][C]55[/C][C]204.18[/C][C]204.501149445742[/C][C]-0.321149445741924[/C][/ROW]
[ROW][C]56[/C][C]204.47[/C][C]204.419175969015[/C][C]0.0508240309853534[/C][/ROW]
[ROW][C]57[/C][C]204.78[/C][C]204.720566249334[/C][C]0.059433750666301[/C][/ROW]
[ROW][C]58[/C][C]206.05[/C][C]205.043886072012[/C][C]1.00611392798839[/C][/ROW]
[ROW][C]59[/C][C]206.32[/C][C]206.539368377341[/C][C]-0.219368377340857[/C][/ROW]
[ROW][C]60[/C][C]206.36[/C][C]206.760205269602[/C][C]-0.400205269602083[/C][/ROW]
[ROW][C]61[/C][C]205.21[/C][C]206.710514426165[/C][C]-1.50051442616532[/C][/ROW]
[ROW][C]62[/C][C]205.35[/C][C]205.224230986905[/C][C]0.125769013094867[/C][/ROW]
[ROW][C]63[/C][C]205.94[/C][C]205.392417344556[/C][C]0.547582655444188[/C][/ROW]
[ROW][C]64[/C][C]204.57[/C][C]206.105137243439[/C][C]-1.53513724343915[/C][/ROW]
[ROW][C]65[/C][C]204.27[/C][C]204.391094411889[/C][C]-0.121094411888748[/C][/ROW]
[ROW][C]66[/C][C]204.86[/C][C]204.063955688931[/C][C]0.796044311068556[/C][/ROW]
[ROW][C]67[/C][C]204.66[/C][C]204.832358851248[/C][C]-0.172358851248106[/C][/ROW]
[ROW][C]68[/C][C]204.79[/C][C]204.593731147126[/C][C]0.196268852873857[/C][/ROW]
[ROW][C]69[/C][C]205.58[/C][C]204.767717371926[/C][C]0.812282628074456[/C][/ROW]
[ROW][C]70[/C][C]205.63[/C][C]205.739759737568[/C][C]-0.109759737568311[/C][/ROW]
[ROW][C]71[/C][C]205.12[/C][C]205.765161252277[/C][C]-0.64516125227675[/C][/ROW]
[ROW][C]72[/C][C]204.96[/C][C]205.110572809134[/C][C]-0.150572809133621[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266274&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266274&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
3203.73202.421.30999999999997
4203.7203.1735868511150.526413148884785
5203.44203.2615624074260.178437592574312
6203.34203.0415524310320.298447568967845
7203.34203.008438142480.331561857520285
8203.05203.082745166678-0.0327451666776426
9202.71202.785406578606-0.0754065786057936
10202.51202.4285070519140.0814929480859803
11203.45202.2467706076521.20322939234811
12203.04203.456428873659-0.416428873658589
13203.04202.9531021242460.0868978757542891
14202.87202.972576989674-0.102576989674162
15202.92202.7795882450980.140411754902374
16202.87202.8610562183660.00894378163420129
17203.17202.8130606280510.356939371949409
18203.88203.1930550603020.686944939697781
19203.88204.057007733383-0.177007733382709
20203.45204.017338158522-0.567338158522489
21203.22203.460190812356-0.240190812355962
22202.11203.176361144977-1.06636114497704
23202.5201.8273767093240.672623290675944
24202.86202.3681197275650.491880272434514
25202.86202.8383560484130.0216439515873503
26203.8202.8432067198570.956793280142904
27203.78203.99763567122-0.217635671219966
28204.53203.9288608838890.601139116111199
29204.44204.813583433646-0.373583433645507
30204.14204.639858865773-0.499858865773149
31204.14204.227834445617-0.0878344456171192
32204.04204.20814968355-0.168149683549814
33204.68204.070465304840.609534695159681
34205.01204.8470694054490.162930594550943
35204.93205.213584123162-0.283584123162427
36204.34205.070029489769-0.730029489768896
37204.34204.3164210476910.0235789523093501
38203.87204.321705376211-0.451705376210583
39202.47203.750472735727-1.28047273572702
40201.95202.063503301818-0.113503301817843
41201.86201.5180658384810.341934161519504
42200.33201.50469742151-1.17469742151047
43200.33199.7114335154080.618566484592151
44200.33199.8500617493140.47993825068616
45200.75199.9576217185880.79237828141234
46201.86200.5552032792991.30479672070095
47202.77201.9576240125630.812375987436781
48202.85203.049687301169-0.199687301168723
49202.85203.084934960743-0.234934960742891
50202.84203.032283193307-0.192283193306707
51202.94202.979190203043-0.0391902030431481
52203.05203.070407204336-0.0204072043362373
53203.45203.1758337029160.274166297084435
54204.19203.6372776875280.552722312471531
55204.18204.501149445742-0.321149445741924
56204.47204.4191759690150.0508240309853534
57204.78204.7205662493340.059433750666301
58206.05205.0438860720121.00611392798839
59206.32206.539368377341-0.219368377340857
60206.36206.760205269602-0.400205269602083
61205.21206.710514426165-1.50051442616532
62205.35205.2242309869050.125769013094867
63205.94205.3924173445560.547582655444188
64204.57206.105137243439-1.53513724343915
65204.27204.391094411889-0.121094411888748
66204.86204.0639556889310.796044311068556
67204.66204.832358851248-0.172358851248106
68204.79204.5937311471260.196268852873857
69205.58204.7677173719260.812282628074456
70205.63205.739759737568-0.109759737568311
71205.12205.765161252277-0.64516125227675
72204.96205.110572809134-0.150572809133621







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73204.916827620663203.740200865329206.093454375996
74204.873655241325203.013821645171206.733488837479
75204.830482861988202.308050916009207.352914807966
76204.78731048265201.588159385632207.986461579669
77204.744138103313200.843655192978208.644621013648
78204.700965723975200.070703099791209.33122834816
79204.657793344638199.26795713962210.047629549656
80204.6146209653198.435151291625210.794090638976
81204.571448585963197.572524609249211.570372562677
82204.528276206626196.680558070834212.375994342417
83204.485103827288195.759844734349213.210362920227
84204.441931447951194.811022498004214.072840397897

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 204.916827620663 & 203.740200865329 & 206.093454375996 \tabularnewline
74 & 204.873655241325 & 203.013821645171 & 206.733488837479 \tabularnewline
75 & 204.830482861988 & 202.308050916009 & 207.352914807966 \tabularnewline
76 & 204.78731048265 & 201.588159385632 & 207.986461579669 \tabularnewline
77 & 204.744138103313 & 200.843655192978 & 208.644621013648 \tabularnewline
78 & 204.700965723975 & 200.070703099791 & 209.33122834816 \tabularnewline
79 & 204.657793344638 & 199.26795713962 & 210.047629549656 \tabularnewline
80 & 204.6146209653 & 198.435151291625 & 210.794090638976 \tabularnewline
81 & 204.571448585963 & 197.572524609249 & 211.570372562677 \tabularnewline
82 & 204.528276206626 & 196.680558070834 & 212.375994342417 \tabularnewline
83 & 204.485103827288 & 195.759844734349 & 213.210362920227 \tabularnewline
84 & 204.441931447951 & 194.811022498004 & 214.072840397897 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266274&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]204.916827620663[/C][C]203.740200865329[/C][C]206.093454375996[/C][/ROW]
[ROW][C]74[/C][C]204.873655241325[/C][C]203.013821645171[/C][C]206.733488837479[/C][/ROW]
[ROW][C]75[/C][C]204.830482861988[/C][C]202.308050916009[/C][C]207.352914807966[/C][/ROW]
[ROW][C]76[/C][C]204.78731048265[/C][C]201.588159385632[/C][C]207.986461579669[/C][/ROW]
[ROW][C]77[/C][C]204.744138103313[/C][C]200.843655192978[/C][C]208.644621013648[/C][/ROW]
[ROW][C]78[/C][C]204.700965723975[/C][C]200.070703099791[/C][C]209.33122834816[/C][/ROW]
[ROW][C]79[/C][C]204.657793344638[/C][C]199.26795713962[/C][C]210.047629549656[/C][/ROW]
[ROW][C]80[/C][C]204.6146209653[/C][C]198.435151291625[/C][C]210.794090638976[/C][/ROW]
[ROW][C]81[/C][C]204.571448585963[/C][C]197.572524609249[/C][C]211.570372562677[/C][/ROW]
[ROW][C]82[/C][C]204.528276206626[/C][C]196.680558070834[/C][C]212.375994342417[/C][/ROW]
[ROW][C]83[/C][C]204.485103827288[/C][C]195.759844734349[/C][C]213.210362920227[/C][/ROW]
[ROW][C]84[/C][C]204.441931447951[/C][C]194.811022498004[/C][C]214.072840397897[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266274&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266274&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
73204.916827620663203.740200865329206.093454375996
74204.873655241325203.013821645171206.733488837479
75204.830482861988202.308050916009207.352914807966
76204.78731048265201.588159385632207.986461579669
77204.744138103313200.843655192978208.644621013648
78204.700965723975200.070703099791209.33122834816
79204.657793344638199.26795713962210.047629549656
80204.6146209653198.435151291625210.794090638976
81204.571448585963197.572524609249211.570372562677
82204.528276206626196.680558070834212.375994342417
83204.485103827288195.759844734349213.210362920227
84204.441931447951194.811022498004214.072840397897



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')