Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 29 Nov 2014 15:51:25 +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/Nov/29/t1417276603u1jihfnfck0iicv.htm/, Retrieved Fri, 17 May 2024 04:11:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=261197, Retrieved Fri, 17 May 2024 04:11:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact115
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-11-29 15:51:25] [c53b0bb515ebe5f6f1384250cc1174dd] [Current]
Feedback Forum

Post a new message
Dataseries X:
246,78
247,91
247,99
248,6
248,68
248,75
248,75
249,03
249,05
249,57
249,35
249,46
249,46
250,82
254,19
255,18
256,68
256,73
256,73
257,39
257,78
258,67
258,71
258,91
258,91
261,38
262,42
262,77
263,24
262,83
262,83
263,09
263,6
265,68
266,08
266,28
266,28
269,14
270,96
272,97
273,13
274,73
274,73
274,59
275,15
275,16
275,38
275,4
275,4
275,71
275,21
279,04
279,1
279,11
279,11
279,02
279,3
279,34
279,36
279,39
279,39
280,21
283
284,33
285,15
284,21
284,21
284,17
286,28
286,95
287,12
287,34




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261197&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261197&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261197&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0550056609527954
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0550056609527954 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261197&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]0.0550056609527954[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261197&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261197&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
beta0.0550056609527954
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3247.99249.04-1.04999999999998
4248.6249.062244056-0.462244055999577
5248.68249.646818016178-0.966818016177797
6248.75249.673637552177-0.923637552176871
7248.75249.692832258139-0.942832258138566
8249.03249.640971146612-0.61097114661203
9249.05249.88736427487-0.837364274869543
10249.57249.861304499472-0.291304499472119
11249.35250.36528110294-1.01528110294009
12249.46250.08943489482-0.62943489481998
13249.46250.164812412404-0.704812412403669
14250.82250.1260437398120.693956260188315
15254.19251.5242152625762.66578473742433
16255.18255.0408485140160.139151485984456
17256.68256.0385026334750.6414973665253
18256.73257.57378862012-0.843788620119881
19256.73257.577375469366-0.847375469365772
20257.39257.530765021598-0.140765021598156
21257.78258.183022148546-0.403022148546086
22258.67258.5508536488870.119146351113386
23258.71259.44740737268-0.737407372679797
24258.91259.446845792754-0.536845792754036
25258.91259.617316235094-0.707316235093913
26261.38259.578409838081.80159016192005
27262.42262.1475074957020.272492504297645
28262.77263.202496126006-0.432496126006015
29263.24263.528706390735-0.288706390735456
30262.83263.982825904892-1.15282590489181
31262.83263.50941395403-0.679413954029712
32263.09263.472042340428-0.382042340427745
33263.6263.711027848981-0.111027848980541
34265.68264.2149206887631.46507931123676
35266.08266.375508344626-0.295508344626114
36266.28266.759253712813-0.479253712812863
37266.28266.932892045575-0.65289204557547
38269.14266.8969792870782.2430207129222
39270.96269.8803581239231.07964187607712
40272.97271.7597445389091.21025546109121
41273.13273.836315440468-0.706315440467904
42274.73273.9574640928240.772535907176234
43274.73275.599957941008-0.869957941007783
44274.59275.552105329462-0.962105329461565
45275.15275.359184089908-0.209184089908263
46275.16275.907677780782-0.747677780781999
47275.38275.87655127027-0.496551270270459
48275.4276.069238139452-0.669238139452261
49275.4276.052426253257-0.652426253256863
50275.71276.016539115974-0.306539115973521
51275.21276.309677729291-1.0996777292915
52279.04275.7491892289573.29081077104331
53279.1279.760202450489-0.660202450488555
54279.11279.783887578337-0.673887578336803
55279.11279.756819946683-0.646819946682513
56279.02279.721241187998-0.701241187997823
57279.3279.592668952965-0.292668952964618
58279.34279.856570503766-0.516570503766502
59279.36279.868156201778-0.508156201778036
60279.39279.860204734032-0.470204734031995
61279.39279.864340811853-0.474340811853438
62280.21279.8382493819810.371750618019462
63283280.6786977704342.32130222956573
64284.33283.5963825338430.733617466157227
65285.15284.9667356474550.183264352544711
66284.21285.796816224296-1.58681622429606
67284.21284.769532349068-0.559532349068036
68284.17284.738754902383-0.568754902383034
69286.28284.6674701630571.6125298369426
70286.95286.8661684325440.0838315674554906
71287.12287.540779643321-0.420779643321055
72287.34287.687634380925-0.347634380924774

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 247.99 & 249.04 & -1.04999999999998 \tabularnewline
4 & 248.6 & 249.062244056 & -0.462244055999577 \tabularnewline
5 & 248.68 & 249.646818016178 & -0.966818016177797 \tabularnewline
6 & 248.75 & 249.673637552177 & -0.923637552176871 \tabularnewline
7 & 248.75 & 249.692832258139 & -0.942832258138566 \tabularnewline
8 & 249.03 & 249.640971146612 & -0.61097114661203 \tabularnewline
9 & 249.05 & 249.88736427487 & -0.837364274869543 \tabularnewline
10 & 249.57 & 249.861304499472 & -0.291304499472119 \tabularnewline
11 & 249.35 & 250.36528110294 & -1.01528110294009 \tabularnewline
12 & 249.46 & 250.08943489482 & -0.62943489481998 \tabularnewline
13 & 249.46 & 250.164812412404 & -0.704812412403669 \tabularnewline
14 & 250.82 & 250.126043739812 & 0.693956260188315 \tabularnewline
15 & 254.19 & 251.524215262576 & 2.66578473742433 \tabularnewline
16 & 255.18 & 255.040848514016 & 0.139151485984456 \tabularnewline
17 & 256.68 & 256.038502633475 & 0.6414973665253 \tabularnewline
18 & 256.73 & 257.57378862012 & -0.843788620119881 \tabularnewline
19 & 256.73 & 257.577375469366 & -0.847375469365772 \tabularnewline
20 & 257.39 & 257.530765021598 & -0.140765021598156 \tabularnewline
21 & 257.78 & 258.183022148546 & -0.403022148546086 \tabularnewline
22 & 258.67 & 258.550853648887 & 0.119146351113386 \tabularnewline
23 & 258.71 & 259.44740737268 & -0.737407372679797 \tabularnewline
24 & 258.91 & 259.446845792754 & -0.536845792754036 \tabularnewline
25 & 258.91 & 259.617316235094 & -0.707316235093913 \tabularnewline
26 & 261.38 & 259.57840983808 & 1.80159016192005 \tabularnewline
27 & 262.42 & 262.147507495702 & 0.272492504297645 \tabularnewline
28 & 262.77 & 263.202496126006 & -0.432496126006015 \tabularnewline
29 & 263.24 & 263.528706390735 & -0.288706390735456 \tabularnewline
30 & 262.83 & 263.982825904892 & -1.15282590489181 \tabularnewline
31 & 262.83 & 263.50941395403 & -0.679413954029712 \tabularnewline
32 & 263.09 & 263.472042340428 & -0.382042340427745 \tabularnewline
33 & 263.6 & 263.711027848981 & -0.111027848980541 \tabularnewline
34 & 265.68 & 264.214920688763 & 1.46507931123676 \tabularnewline
35 & 266.08 & 266.375508344626 & -0.295508344626114 \tabularnewline
36 & 266.28 & 266.759253712813 & -0.479253712812863 \tabularnewline
37 & 266.28 & 266.932892045575 & -0.65289204557547 \tabularnewline
38 & 269.14 & 266.896979287078 & 2.2430207129222 \tabularnewline
39 & 270.96 & 269.880358123923 & 1.07964187607712 \tabularnewline
40 & 272.97 & 271.759744538909 & 1.21025546109121 \tabularnewline
41 & 273.13 & 273.836315440468 & -0.706315440467904 \tabularnewline
42 & 274.73 & 273.957464092824 & 0.772535907176234 \tabularnewline
43 & 274.73 & 275.599957941008 & -0.869957941007783 \tabularnewline
44 & 274.59 & 275.552105329462 & -0.962105329461565 \tabularnewline
45 & 275.15 & 275.359184089908 & -0.209184089908263 \tabularnewline
46 & 275.16 & 275.907677780782 & -0.747677780781999 \tabularnewline
47 & 275.38 & 275.87655127027 & -0.496551270270459 \tabularnewline
48 & 275.4 & 276.069238139452 & -0.669238139452261 \tabularnewline
49 & 275.4 & 276.052426253257 & -0.652426253256863 \tabularnewline
50 & 275.71 & 276.016539115974 & -0.306539115973521 \tabularnewline
51 & 275.21 & 276.309677729291 & -1.0996777292915 \tabularnewline
52 & 279.04 & 275.749189228957 & 3.29081077104331 \tabularnewline
53 & 279.1 & 279.760202450489 & -0.660202450488555 \tabularnewline
54 & 279.11 & 279.783887578337 & -0.673887578336803 \tabularnewline
55 & 279.11 & 279.756819946683 & -0.646819946682513 \tabularnewline
56 & 279.02 & 279.721241187998 & -0.701241187997823 \tabularnewline
57 & 279.3 & 279.592668952965 & -0.292668952964618 \tabularnewline
58 & 279.34 & 279.856570503766 & -0.516570503766502 \tabularnewline
59 & 279.36 & 279.868156201778 & -0.508156201778036 \tabularnewline
60 & 279.39 & 279.860204734032 & -0.470204734031995 \tabularnewline
61 & 279.39 & 279.864340811853 & -0.474340811853438 \tabularnewline
62 & 280.21 & 279.838249381981 & 0.371750618019462 \tabularnewline
63 & 283 & 280.678697770434 & 2.32130222956573 \tabularnewline
64 & 284.33 & 283.596382533843 & 0.733617466157227 \tabularnewline
65 & 285.15 & 284.966735647455 & 0.183264352544711 \tabularnewline
66 & 284.21 & 285.796816224296 & -1.58681622429606 \tabularnewline
67 & 284.21 & 284.769532349068 & -0.559532349068036 \tabularnewline
68 & 284.17 & 284.738754902383 & -0.568754902383034 \tabularnewline
69 & 286.28 & 284.667470163057 & 1.6125298369426 \tabularnewline
70 & 286.95 & 286.866168432544 & 0.0838315674554906 \tabularnewline
71 & 287.12 & 287.540779643321 & -0.420779643321055 \tabularnewline
72 & 287.34 & 287.687634380925 & -0.347634380924774 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261197&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]247.99[/C][C]249.04[/C][C]-1.04999999999998[/C][/ROW]
[ROW][C]4[/C][C]248.6[/C][C]249.062244056[/C][C]-0.462244055999577[/C][/ROW]
[ROW][C]5[/C][C]248.68[/C][C]249.646818016178[/C][C]-0.966818016177797[/C][/ROW]
[ROW][C]6[/C][C]248.75[/C][C]249.673637552177[/C][C]-0.923637552176871[/C][/ROW]
[ROW][C]7[/C][C]248.75[/C][C]249.692832258139[/C][C]-0.942832258138566[/C][/ROW]
[ROW][C]8[/C][C]249.03[/C][C]249.640971146612[/C][C]-0.61097114661203[/C][/ROW]
[ROW][C]9[/C][C]249.05[/C][C]249.88736427487[/C][C]-0.837364274869543[/C][/ROW]
[ROW][C]10[/C][C]249.57[/C][C]249.861304499472[/C][C]-0.291304499472119[/C][/ROW]
[ROW][C]11[/C][C]249.35[/C][C]250.36528110294[/C][C]-1.01528110294009[/C][/ROW]
[ROW][C]12[/C][C]249.46[/C][C]250.08943489482[/C][C]-0.62943489481998[/C][/ROW]
[ROW][C]13[/C][C]249.46[/C][C]250.164812412404[/C][C]-0.704812412403669[/C][/ROW]
[ROW][C]14[/C][C]250.82[/C][C]250.126043739812[/C][C]0.693956260188315[/C][/ROW]
[ROW][C]15[/C][C]254.19[/C][C]251.524215262576[/C][C]2.66578473742433[/C][/ROW]
[ROW][C]16[/C][C]255.18[/C][C]255.040848514016[/C][C]0.139151485984456[/C][/ROW]
[ROW][C]17[/C][C]256.68[/C][C]256.038502633475[/C][C]0.6414973665253[/C][/ROW]
[ROW][C]18[/C][C]256.73[/C][C]257.57378862012[/C][C]-0.843788620119881[/C][/ROW]
[ROW][C]19[/C][C]256.73[/C][C]257.577375469366[/C][C]-0.847375469365772[/C][/ROW]
[ROW][C]20[/C][C]257.39[/C][C]257.530765021598[/C][C]-0.140765021598156[/C][/ROW]
[ROW][C]21[/C][C]257.78[/C][C]258.183022148546[/C][C]-0.403022148546086[/C][/ROW]
[ROW][C]22[/C][C]258.67[/C][C]258.550853648887[/C][C]0.119146351113386[/C][/ROW]
[ROW][C]23[/C][C]258.71[/C][C]259.44740737268[/C][C]-0.737407372679797[/C][/ROW]
[ROW][C]24[/C][C]258.91[/C][C]259.446845792754[/C][C]-0.536845792754036[/C][/ROW]
[ROW][C]25[/C][C]258.91[/C][C]259.617316235094[/C][C]-0.707316235093913[/C][/ROW]
[ROW][C]26[/C][C]261.38[/C][C]259.57840983808[/C][C]1.80159016192005[/C][/ROW]
[ROW][C]27[/C][C]262.42[/C][C]262.147507495702[/C][C]0.272492504297645[/C][/ROW]
[ROW][C]28[/C][C]262.77[/C][C]263.202496126006[/C][C]-0.432496126006015[/C][/ROW]
[ROW][C]29[/C][C]263.24[/C][C]263.528706390735[/C][C]-0.288706390735456[/C][/ROW]
[ROW][C]30[/C][C]262.83[/C][C]263.982825904892[/C][C]-1.15282590489181[/C][/ROW]
[ROW][C]31[/C][C]262.83[/C][C]263.50941395403[/C][C]-0.679413954029712[/C][/ROW]
[ROW][C]32[/C][C]263.09[/C][C]263.472042340428[/C][C]-0.382042340427745[/C][/ROW]
[ROW][C]33[/C][C]263.6[/C][C]263.711027848981[/C][C]-0.111027848980541[/C][/ROW]
[ROW][C]34[/C][C]265.68[/C][C]264.214920688763[/C][C]1.46507931123676[/C][/ROW]
[ROW][C]35[/C][C]266.08[/C][C]266.375508344626[/C][C]-0.295508344626114[/C][/ROW]
[ROW][C]36[/C][C]266.28[/C][C]266.759253712813[/C][C]-0.479253712812863[/C][/ROW]
[ROW][C]37[/C][C]266.28[/C][C]266.932892045575[/C][C]-0.65289204557547[/C][/ROW]
[ROW][C]38[/C][C]269.14[/C][C]266.896979287078[/C][C]2.2430207129222[/C][/ROW]
[ROW][C]39[/C][C]270.96[/C][C]269.880358123923[/C][C]1.07964187607712[/C][/ROW]
[ROW][C]40[/C][C]272.97[/C][C]271.759744538909[/C][C]1.21025546109121[/C][/ROW]
[ROW][C]41[/C][C]273.13[/C][C]273.836315440468[/C][C]-0.706315440467904[/C][/ROW]
[ROW][C]42[/C][C]274.73[/C][C]273.957464092824[/C][C]0.772535907176234[/C][/ROW]
[ROW][C]43[/C][C]274.73[/C][C]275.599957941008[/C][C]-0.869957941007783[/C][/ROW]
[ROW][C]44[/C][C]274.59[/C][C]275.552105329462[/C][C]-0.962105329461565[/C][/ROW]
[ROW][C]45[/C][C]275.15[/C][C]275.359184089908[/C][C]-0.209184089908263[/C][/ROW]
[ROW][C]46[/C][C]275.16[/C][C]275.907677780782[/C][C]-0.747677780781999[/C][/ROW]
[ROW][C]47[/C][C]275.38[/C][C]275.87655127027[/C][C]-0.496551270270459[/C][/ROW]
[ROW][C]48[/C][C]275.4[/C][C]276.069238139452[/C][C]-0.669238139452261[/C][/ROW]
[ROW][C]49[/C][C]275.4[/C][C]276.052426253257[/C][C]-0.652426253256863[/C][/ROW]
[ROW][C]50[/C][C]275.71[/C][C]276.016539115974[/C][C]-0.306539115973521[/C][/ROW]
[ROW][C]51[/C][C]275.21[/C][C]276.309677729291[/C][C]-1.0996777292915[/C][/ROW]
[ROW][C]52[/C][C]279.04[/C][C]275.749189228957[/C][C]3.29081077104331[/C][/ROW]
[ROW][C]53[/C][C]279.1[/C][C]279.760202450489[/C][C]-0.660202450488555[/C][/ROW]
[ROW][C]54[/C][C]279.11[/C][C]279.783887578337[/C][C]-0.673887578336803[/C][/ROW]
[ROW][C]55[/C][C]279.11[/C][C]279.756819946683[/C][C]-0.646819946682513[/C][/ROW]
[ROW][C]56[/C][C]279.02[/C][C]279.721241187998[/C][C]-0.701241187997823[/C][/ROW]
[ROW][C]57[/C][C]279.3[/C][C]279.592668952965[/C][C]-0.292668952964618[/C][/ROW]
[ROW][C]58[/C][C]279.34[/C][C]279.856570503766[/C][C]-0.516570503766502[/C][/ROW]
[ROW][C]59[/C][C]279.36[/C][C]279.868156201778[/C][C]-0.508156201778036[/C][/ROW]
[ROW][C]60[/C][C]279.39[/C][C]279.860204734032[/C][C]-0.470204734031995[/C][/ROW]
[ROW][C]61[/C][C]279.39[/C][C]279.864340811853[/C][C]-0.474340811853438[/C][/ROW]
[ROW][C]62[/C][C]280.21[/C][C]279.838249381981[/C][C]0.371750618019462[/C][/ROW]
[ROW][C]63[/C][C]283[/C][C]280.678697770434[/C][C]2.32130222956573[/C][/ROW]
[ROW][C]64[/C][C]284.33[/C][C]283.596382533843[/C][C]0.733617466157227[/C][/ROW]
[ROW][C]65[/C][C]285.15[/C][C]284.966735647455[/C][C]0.183264352544711[/C][/ROW]
[ROW][C]66[/C][C]284.21[/C][C]285.796816224296[/C][C]-1.58681622429606[/C][/ROW]
[ROW][C]67[/C][C]284.21[/C][C]284.769532349068[/C][C]-0.559532349068036[/C][/ROW]
[ROW][C]68[/C][C]284.17[/C][C]284.738754902383[/C][C]-0.568754902383034[/C][/ROW]
[ROW][C]69[/C][C]286.28[/C][C]284.667470163057[/C][C]1.6125298369426[/C][/ROW]
[ROW][C]70[/C][C]286.95[/C][C]286.866168432544[/C][C]0.0838315674554906[/C][/ROW]
[ROW][C]71[/C][C]287.12[/C][C]287.540779643321[/C][C]-0.420779643321055[/C][/ROW]
[ROW][C]72[/C][C]287.34[/C][C]287.687634380925[/C][C]-0.347634380924774[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261197&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261197&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
3247.99249.04-1.04999999999998
4248.6249.062244056-0.462244055999577
5248.68249.646818016178-0.966818016177797
6248.75249.673637552177-0.923637552176871
7248.75249.692832258139-0.942832258138566
8249.03249.640971146612-0.61097114661203
9249.05249.88736427487-0.837364274869543
10249.57249.861304499472-0.291304499472119
11249.35250.36528110294-1.01528110294009
12249.46250.08943489482-0.62943489481998
13249.46250.164812412404-0.704812412403669
14250.82250.1260437398120.693956260188315
15254.19251.5242152625762.66578473742433
16255.18255.0408485140160.139151485984456
17256.68256.0385026334750.6414973665253
18256.73257.57378862012-0.843788620119881
19256.73257.577375469366-0.847375469365772
20257.39257.530765021598-0.140765021598156
21257.78258.183022148546-0.403022148546086
22258.67258.5508536488870.119146351113386
23258.71259.44740737268-0.737407372679797
24258.91259.446845792754-0.536845792754036
25258.91259.617316235094-0.707316235093913
26261.38259.578409838081.80159016192005
27262.42262.1475074957020.272492504297645
28262.77263.202496126006-0.432496126006015
29263.24263.528706390735-0.288706390735456
30262.83263.982825904892-1.15282590489181
31262.83263.50941395403-0.679413954029712
32263.09263.472042340428-0.382042340427745
33263.6263.711027848981-0.111027848980541
34265.68264.2149206887631.46507931123676
35266.08266.375508344626-0.295508344626114
36266.28266.759253712813-0.479253712812863
37266.28266.932892045575-0.65289204557547
38269.14266.8969792870782.2430207129222
39270.96269.8803581239231.07964187607712
40272.97271.7597445389091.21025546109121
41273.13273.836315440468-0.706315440467904
42274.73273.9574640928240.772535907176234
43274.73275.599957941008-0.869957941007783
44274.59275.552105329462-0.962105329461565
45275.15275.359184089908-0.209184089908263
46275.16275.907677780782-0.747677780781999
47275.38275.87655127027-0.496551270270459
48275.4276.069238139452-0.669238139452261
49275.4276.052426253257-0.652426253256863
50275.71276.016539115974-0.306539115973521
51275.21276.309677729291-1.0996777292915
52279.04275.7491892289573.29081077104331
53279.1279.760202450489-0.660202450488555
54279.11279.783887578337-0.673887578336803
55279.11279.756819946683-0.646819946682513
56279.02279.721241187998-0.701241187997823
57279.3279.592668952965-0.292668952964618
58279.34279.856570503766-0.516570503766502
59279.36279.868156201778-0.508156201778036
60279.39279.860204734032-0.470204734031995
61279.39279.864340811853-0.474340811853438
62280.21279.8382493819810.371750618019462
63283280.6786977704342.32130222956573
64284.33283.5963825338430.733617466157227
65285.15284.9667356474550.183264352544711
66284.21285.796816224296-1.58681622429606
67284.21284.769532349068-0.559532349068036
68284.17284.738754902383-0.568754902383034
69286.28284.6674701630571.6125298369426
70286.95286.8661684325440.0838315674554906
71287.12287.540779643321-0.420779643321055
72287.34287.687634380925-0.347634380924774







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73287.888512522032285.998002500232289.779022543832
74288.437025044064285.688925062923291.185125025205
75288.985537566096285.52783552383292.443239608362
76289.534050088128285.434464110939293.633636065318
77290.08256261016285.3786933367294.786431883621
78290.631075132192285.345559678897295.916590585487
79291.179587654224285.326460720556297.032714587893
80291.728100176256285.315980608807298.140219743706
81292.276612698288285.310491233259299.242734163318
82292.825125220321285.307450381776300.342800058865
83293.373637742353285.305015505162301.442259979544
84293.922150264385285.301815869919302.54248465885

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 287.888512522032 & 285.998002500232 & 289.779022543832 \tabularnewline
74 & 288.437025044064 & 285.688925062923 & 291.185125025205 \tabularnewline
75 & 288.985537566096 & 285.52783552383 & 292.443239608362 \tabularnewline
76 & 289.534050088128 & 285.434464110939 & 293.633636065318 \tabularnewline
77 & 290.08256261016 & 285.3786933367 & 294.786431883621 \tabularnewline
78 & 290.631075132192 & 285.345559678897 & 295.916590585487 \tabularnewline
79 & 291.179587654224 & 285.326460720556 & 297.032714587893 \tabularnewline
80 & 291.728100176256 & 285.315980608807 & 298.140219743706 \tabularnewline
81 & 292.276612698288 & 285.310491233259 & 299.242734163318 \tabularnewline
82 & 292.825125220321 & 285.307450381776 & 300.342800058865 \tabularnewline
83 & 293.373637742353 & 285.305015505162 & 301.442259979544 \tabularnewline
84 & 293.922150264385 & 285.301815869919 & 302.54248465885 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261197&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]287.888512522032[/C][C]285.998002500232[/C][C]289.779022543832[/C][/ROW]
[ROW][C]74[/C][C]288.437025044064[/C][C]285.688925062923[/C][C]291.185125025205[/C][/ROW]
[ROW][C]75[/C][C]288.985537566096[/C][C]285.52783552383[/C][C]292.443239608362[/C][/ROW]
[ROW][C]76[/C][C]289.534050088128[/C][C]285.434464110939[/C][C]293.633636065318[/C][/ROW]
[ROW][C]77[/C][C]290.08256261016[/C][C]285.3786933367[/C][C]294.786431883621[/C][/ROW]
[ROW][C]78[/C][C]290.631075132192[/C][C]285.345559678897[/C][C]295.916590585487[/C][/ROW]
[ROW][C]79[/C][C]291.179587654224[/C][C]285.326460720556[/C][C]297.032714587893[/C][/ROW]
[ROW][C]80[/C][C]291.728100176256[/C][C]285.315980608807[/C][C]298.140219743706[/C][/ROW]
[ROW][C]81[/C][C]292.276612698288[/C][C]285.310491233259[/C][C]299.242734163318[/C][/ROW]
[ROW][C]82[/C][C]292.825125220321[/C][C]285.307450381776[/C][C]300.342800058865[/C][/ROW]
[ROW][C]83[/C][C]293.373637742353[/C][C]285.305015505162[/C][C]301.442259979544[/C][/ROW]
[ROW][C]84[/C][C]293.922150264385[/C][C]285.301815869919[/C][C]302.54248465885[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261197&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261197&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
73287.888512522032285.998002500232289.779022543832
74288.437025044064285.688925062923291.185125025205
75288.985537566096285.52783552383292.443239608362
76289.534050088128285.434464110939293.633636065318
77290.08256261016285.3786933367294.786431883621
78290.631075132192285.345559678897295.916590585487
79291.179587654224285.326460720556297.032714587893
80291.728100176256285.315980608807298.140219743706
81292.276612698288285.310491233259299.242734163318
82292.825125220321285.307450381776300.342800058865
83293.373637742353285.305015505162301.442259979544
84293.922150264385285.301815869919302.54248465885



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')