Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 05 May 2013 09:31:29 -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/2013/May/05/t1367760882uf91gquund4fkea.htm/, Retrieved Mon, 29 Apr 2024 07:18:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=208723, Retrieved Mon, 29 Apr 2024 07:18:58 +0000
QR Codes:

Original text written by user:Gem farma consumptieprijzen additief, double exponential smoothing
IsPrivate?No (this computation is public)
User-defined keywordsGem farma consumptieprijzen additief, double exponential smoothing
Estimated Impact151
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-05-05 13:31:29] [0941a6a4eb2aa1312aa94e558e86fae5] [Current]
Feedback Forum

Post a new message
Dataseries X:
 105,71 
 105,82 
 105,82 
 105,72 
 105,76 
 105,80 
 105,09 
 105,06 
 105,16 
 105,20 
 105,21 
 105,23 
 105,19 
 105,16 
 104,88 
 104,52 
 104,09 
 104,35 
 104,48 
 104,47 
 104,55 
 104,59 
 104,59 
 104,72 
 104,65 
 104,72 
 104,92 
 105,05 
 103,74 
 103,81 
 103,79 
 104,28 
 103,80 
 103,80 
 104,02 
 104,02 
 104,91 
 104,97 
 103,86 
 104,17 
 103,21 
 103,21 
 101,91 
 101,84 
 101,91 
 101,79 
 101,79 
 101,79 
 102,09 
 102,18 
 102,20 
 101,97 
 102,05 
 102,04 
 101,78 
 101,79 
 101,80 
 101,83 
 101,83 
 101,88 
 101,90 
 101,91 
 101,17 
 101,17 
 101,23 
 101,26 
 101,49 
 101,51 
 101,61 
 101,39 
 101,43 
 101,44 




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=208723&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=208723&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208723&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
alpha0.917973317029507
beta0.0503862068439166
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.917973317029507 \tabularnewline
beta & 0.0503862068439166 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208723&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]0.917973317029507[/C][/ROW]
[ROW][C]beta[/C][C]0.0503862068439166[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208723&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208723&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
alpha0.917973317029507
beta0.0503862068439166
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3105.82105.93-0.109999999999999
4105.72105.93393508385-0.213935083849549
5105.76105.832565353207-0.0725653532074375
6105.8105.857612883812-0.0576128838122969
7105.09105.893721602487-0.803721602486604
8105.06105.207747735072-0.147747735071917
9105.16105.1171065700440.0428934299564077
10105.2105.203452865751-0.00345286575127091
11105.21105.247094792589-0.0370947925886753
12105.23105.258138575639-0.028138575639062
13105.19105.276102427889-0.0861024278888749
14105.16105.236874498169-0.0768744981692748
15104.88105.20256187067-0.3225618706701
16104.52104.927795274287-0.407795274287139
17104.09104.555924853963-0.46592485396306
18104.35104.1091425181730.240857481827376
19104.48104.3223079352810.157692064718631
20104.47104.4664234801560.00357651984367635
21104.55104.4692304925610.0807695074392569
22104.59104.546634455490.0433655445095553
23104.59104.591708373418-0.00170837341786978
24104.72104.5953266196680.124673380332183
25104.65104.720726485596-0.0707264855956424
26104.72104.6634831626320.0565168373682212
27104.92104.725659899130.194340100870306
28105.05104.9233435642650.126656435734972
29103.74105.064753695428-1.32475369542844
30103.81103.812533965197-0.00253396519705973
31103.79103.7739594625860.0160405374143693
32104.28103.7531777838280.526822216171666
33103.8104.225647266865-0.42564726686507
34103.8103.804087633822-0.00408763382235122
35104.02103.7693194293320.250680570668266
36104.02103.9800164155150.0399835844849576
37104.91103.9991485588710.910851441129282
38104.97104.8598439451760.110156054823761
39103.86104.990617401096-1.13061740109579
40104.17103.9300992666560.239900733344427
41103.21104.13877638516-0.928776385159708
42103.21103.231680218859-0.0216802188589753
43101.91103.156271349846-1.24627134984561
44101.84101.899076468506-0.059076468506035
45101.91101.7289623350250.18103766497471
46101.79101.7876401392580.00235986074244465
47101.79101.6824056379550.107594362045432
48101.79101.6787501837180.111249816281813
49102.09101.6835959982040.406404001796147
50102.18101.9781829623070.201817037693331
51102.2102.0942992348330.105700765167271
52101.97102.127072331784-0.15707233178442
53102.05101.9113616403570.138638359643124
54102.04101.9735179400850.0664820599145912
55101.78101.972511689584-0.192511689584379
56101.79101.724851807350.0651481926498576
57101.8101.7167301338320.0832698661678819
58101.83101.729095170290.100904829709791
59101.83101.7623158033330.0676841966669457
60101.88101.7681713919080.111828608091727
61101.9101.8197228025080.0802771974916396
62101.91101.8460239368060.0639760631935218
63101.17101.860320162007-0.690320162007311
64101.17101.1502630673560.0197369326435961
65101.23101.0929323353260.13706766467422
66101.26101.1496479017740.110352098226144
67101.49101.1869434280180.303056571982168
68101.51101.4151538534860.0948461465141293
69101.61101.4566196012080.153380398792379
70101.39101.558912563907-0.168912563906645
71101.43101.3575364410910.0724635589093907
72101.44101.3810888293950.0589111706054695

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 105.82 & 105.93 & -0.109999999999999 \tabularnewline
4 & 105.72 & 105.93393508385 & -0.213935083849549 \tabularnewline
5 & 105.76 & 105.832565353207 & -0.0725653532074375 \tabularnewline
6 & 105.8 & 105.857612883812 & -0.0576128838122969 \tabularnewline
7 & 105.09 & 105.893721602487 & -0.803721602486604 \tabularnewline
8 & 105.06 & 105.207747735072 & -0.147747735071917 \tabularnewline
9 & 105.16 & 105.117106570044 & 0.0428934299564077 \tabularnewline
10 & 105.2 & 105.203452865751 & -0.00345286575127091 \tabularnewline
11 & 105.21 & 105.247094792589 & -0.0370947925886753 \tabularnewline
12 & 105.23 & 105.258138575639 & -0.028138575639062 \tabularnewline
13 & 105.19 & 105.276102427889 & -0.0861024278888749 \tabularnewline
14 & 105.16 & 105.236874498169 & -0.0768744981692748 \tabularnewline
15 & 104.88 & 105.20256187067 & -0.3225618706701 \tabularnewline
16 & 104.52 & 104.927795274287 & -0.407795274287139 \tabularnewline
17 & 104.09 & 104.555924853963 & -0.46592485396306 \tabularnewline
18 & 104.35 & 104.109142518173 & 0.240857481827376 \tabularnewline
19 & 104.48 & 104.322307935281 & 0.157692064718631 \tabularnewline
20 & 104.47 & 104.466423480156 & 0.00357651984367635 \tabularnewline
21 & 104.55 & 104.469230492561 & 0.0807695074392569 \tabularnewline
22 & 104.59 & 104.54663445549 & 0.0433655445095553 \tabularnewline
23 & 104.59 & 104.591708373418 & -0.00170837341786978 \tabularnewline
24 & 104.72 & 104.595326619668 & 0.124673380332183 \tabularnewline
25 & 104.65 & 104.720726485596 & -0.0707264855956424 \tabularnewline
26 & 104.72 & 104.663483162632 & 0.0565168373682212 \tabularnewline
27 & 104.92 & 104.72565989913 & 0.194340100870306 \tabularnewline
28 & 105.05 & 104.923343564265 & 0.126656435734972 \tabularnewline
29 & 103.74 & 105.064753695428 & -1.32475369542844 \tabularnewline
30 & 103.81 & 103.812533965197 & -0.00253396519705973 \tabularnewline
31 & 103.79 & 103.773959462586 & 0.0160405374143693 \tabularnewline
32 & 104.28 & 103.753177783828 & 0.526822216171666 \tabularnewline
33 & 103.8 & 104.225647266865 & -0.42564726686507 \tabularnewline
34 & 103.8 & 103.804087633822 & -0.00408763382235122 \tabularnewline
35 & 104.02 & 103.769319429332 & 0.250680570668266 \tabularnewline
36 & 104.02 & 103.980016415515 & 0.0399835844849576 \tabularnewline
37 & 104.91 & 103.999148558871 & 0.910851441129282 \tabularnewline
38 & 104.97 & 104.859843945176 & 0.110156054823761 \tabularnewline
39 & 103.86 & 104.990617401096 & -1.13061740109579 \tabularnewline
40 & 104.17 & 103.930099266656 & 0.239900733344427 \tabularnewline
41 & 103.21 & 104.13877638516 & -0.928776385159708 \tabularnewline
42 & 103.21 & 103.231680218859 & -0.0216802188589753 \tabularnewline
43 & 101.91 & 103.156271349846 & -1.24627134984561 \tabularnewline
44 & 101.84 & 101.899076468506 & -0.059076468506035 \tabularnewline
45 & 101.91 & 101.728962335025 & 0.18103766497471 \tabularnewline
46 & 101.79 & 101.787640139258 & 0.00235986074244465 \tabularnewline
47 & 101.79 & 101.682405637955 & 0.107594362045432 \tabularnewline
48 & 101.79 & 101.678750183718 & 0.111249816281813 \tabularnewline
49 & 102.09 & 101.683595998204 & 0.406404001796147 \tabularnewline
50 & 102.18 & 101.978182962307 & 0.201817037693331 \tabularnewline
51 & 102.2 & 102.094299234833 & 0.105700765167271 \tabularnewline
52 & 101.97 & 102.127072331784 & -0.15707233178442 \tabularnewline
53 & 102.05 & 101.911361640357 & 0.138638359643124 \tabularnewline
54 & 102.04 & 101.973517940085 & 0.0664820599145912 \tabularnewline
55 & 101.78 & 101.972511689584 & -0.192511689584379 \tabularnewline
56 & 101.79 & 101.72485180735 & 0.0651481926498576 \tabularnewline
57 & 101.8 & 101.716730133832 & 0.0832698661678819 \tabularnewline
58 & 101.83 & 101.72909517029 & 0.100904829709791 \tabularnewline
59 & 101.83 & 101.762315803333 & 0.0676841966669457 \tabularnewline
60 & 101.88 & 101.768171391908 & 0.111828608091727 \tabularnewline
61 & 101.9 & 101.819722802508 & 0.0802771974916396 \tabularnewline
62 & 101.91 & 101.846023936806 & 0.0639760631935218 \tabularnewline
63 & 101.17 & 101.860320162007 & -0.690320162007311 \tabularnewline
64 & 101.17 & 101.150263067356 & 0.0197369326435961 \tabularnewline
65 & 101.23 & 101.092932335326 & 0.13706766467422 \tabularnewline
66 & 101.26 & 101.149647901774 & 0.110352098226144 \tabularnewline
67 & 101.49 & 101.186943428018 & 0.303056571982168 \tabularnewline
68 & 101.51 & 101.415153853486 & 0.0948461465141293 \tabularnewline
69 & 101.61 & 101.456619601208 & 0.153380398792379 \tabularnewline
70 & 101.39 & 101.558912563907 & -0.168912563906645 \tabularnewline
71 & 101.43 & 101.357536441091 & 0.0724635589093907 \tabularnewline
72 & 101.44 & 101.381088829395 & 0.0589111706054695 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208723&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]105.82[/C][C]105.93[/C][C]-0.109999999999999[/C][/ROW]
[ROW][C]4[/C][C]105.72[/C][C]105.93393508385[/C][C]-0.213935083849549[/C][/ROW]
[ROW][C]5[/C][C]105.76[/C][C]105.832565353207[/C][C]-0.0725653532074375[/C][/ROW]
[ROW][C]6[/C][C]105.8[/C][C]105.857612883812[/C][C]-0.0576128838122969[/C][/ROW]
[ROW][C]7[/C][C]105.09[/C][C]105.893721602487[/C][C]-0.803721602486604[/C][/ROW]
[ROW][C]8[/C][C]105.06[/C][C]105.207747735072[/C][C]-0.147747735071917[/C][/ROW]
[ROW][C]9[/C][C]105.16[/C][C]105.117106570044[/C][C]0.0428934299564077[/C][/ROW]
[ROW][C]10[/C][C]105.2[/C][C]105.203452865751[/C][C]-0.00345286575127091[/C][/ROW]
[ROW][C]11[/C][C]105.21[/C][C]105.247094792589[/C][C]-0.0370947925886753[/C][/ROW]
[ROW][C]12[/C][C]105.23[/C][C]105.258138575639[/C][C]-0.028138575639062[/C][/ROW]
[ROW][C]13[/C][C]105.19[/C][C]105.276102427889[/C][C]-0.0861024278888749[/C][/ROW]
[ROW][C]14[/C][C]105.16[/C][C]105.236874498169[/C][C]-0.0768744981692748[/C][/ROW]
[ROW][C]15[/C][C]104.88[/C][C]105.20256187067[/C][C]-0.3225618706701[/C][/ROW]
[ROW][C]16[/C][C]104.52[/C][C]104.927795274287[/C][C]-0.407795274287139[/C][/ROW]
[ROW][C]17[/C][C]104.09[/C][C]104.555924853963[/C][C]-0.46592485396306[/C][/ROW]
[ROW][C]18[/C][C]104.35[/C][C]104.109142518173[/C][C]0.240857481827376[/C][/ROW]
[ROW][C]19[/C][C]104.48[/C][C]104.322307935281[/C][C]0.157692064718631[/C][/ROW]
[ROW][C]20[/C][C]104.47[/C][C]104.466423480156[/C][C]0.00357651984367635[/C][/ROW]
[ROW][C]21[/C][C]104.55[/C][C]104.469230492561[/C][C]0.0807695074392569[/C][/ROW]
[ROW][C]22[/C][C]104.59[/C][C]104.54663445549[/C][C]0.0433655445095553[/C][/ROW]
[ROW][C]23[/C][C]104.59[/C][C]104.591708373418[/C][C]-0.00170837341786978[/C][/ROW]
[ROW][C]24[/C][C]104.72[/C][C]104.595326619668[/C][C]0.124673380332183[/C][/ROW]
[ROW][C]25[/C][C]104.65[/C][C]104.720726485596[/C][C]-0.0707264855956424[/C][/ROW]
[ROW][C]26[/C][C]104.72[/C][C]104.663483162632[/C][C]0.0565168373682212[/C][/ROW]
[ROW][C]27[/C][C]104.92[/C][C]104.72565989913[/C][C]0.194340100870306[/C][/ROW]
[ROW][C]28[/C][C]105.05[/C][C]104.923343564265[/C][C]0.126656435734972[/C][/ROW]
[ROW][C]29[/C][C]103.74[/C][C]105.064753695428[/C][C]-1.32475369542844[/C][/ROW]
[ROW][C]30[/C][C]103.81[/C][C]103.812533965197[/C][C]-0.00253396519705973[/C][/ROW]
[ROW][C]31[/C][C]103.79[/C][C]103.773959462586[/C][C]0.0160405374143693[/C][/ROW]
[ROW][C]32[/C][C]104.28[/C][C]103.753177783828[/C][C]0.526822216171666[/C][/ROW]
[ROW][C]33[/C][C]103.8[/C][C]104.225647266865[/C][C]-0.42564726686507[/C][/ROW]
[ROW][C]34[/C][C]103.8[/C][C]103.804087633822[/C][C]-0.00408763382235122[/C][/ROW]
[ROW][C]35[/C][C]104.02[/C][C]103.769319429332[/C][C]0.250680570668266[/C][/ROW]
[ROW][C]36[/C][C]104.02[/C][C]103.980016415515[/C][C]0.0399835844849576[/C][/ROW]
[ROW][C]37[/C][C]104.91[/C][C]103.999148558871[/C][C]0.910851441129282[/C][/ROW]
[ROW][C]38[/C][C]104.97[/C][C]104.859843945176[/C][C]0.110156054823761[/C][/ROW]
[ROW][C]39[/C][C]103.86[/C][C]104.990617401096[/C][C]-1.13061740109579[/C][/ROW]
[ROW][C]40[/C][C]104.17[/C][C]103.930099266656[/C][C]0.239900733344427[/C][/ROW]
[ROW][C]41[/C][C]103.21[/C][C]104.13877638516[/C][C]-0.928776385159708[/C][/ROW]
[ROW][C]42[/C][C]103.21[/C][C]103.231680218859[/C][C]-0.0216802188589753[/C][/ROW]
[ROW][C]43[/C][C]101.91[/C][C]103.156271349846[/C][C]-1.24627134984561[/C][/ROW]
[ROW][C]44[/C][C]101.84[/C][C]101.899076468506[/C][C]-0.059076468506035[/C][/ROW]
[ROW][C]45[/C][C]101.91[/C][C]101.728962335025[/C][C]0.18103766497471[/C][/ROW]
[ROW][C]46[/C][C]101.79[/C][C]101.787640139258[/C][C]0.00235986074244465[/C][/ROW]
[ROW][C]47[/C][C]101.79[/C][C]101.682405637955[/C][C]0.107594362045432[/C][/ROW]
[ROW][C]48[/C][C]101.79[/C][C]101.678750183718[/C][C]0.111249816281813[/C][/ROW]
[ROW][C]49[/C][C]102.09[/C][C]101.683595998204[/C][C]0.406404001796147[/C][/ROW]
[ROW][C]50[/C][C]102.18[/C][C]101.978182962307[/C][C]0.201817037693331[/C][/ROW]
[ROW][C]51[/C][C]102.2[/C][C]102.094299234833[/C][C]0.105700765167271[/C][/ROW]
[ROW][C]52[/C][C]101.97[/C][C]102.127072331784[/C][C]-0.15707233178442[/C][/ROW]
[ROW][C]53[/C][C]102.05[/C][C]101.911361640357[/C][C]0.138638359643124[/C][/ROW]
[ROW][C]54[/C][C]102.04[/C][C]101.973517940085[/C][C]0.0664820599145912[/C][/ROW]
[ROW][C]55[/C][C]101.78[/C][C]101.972511689584[/C][C]-0.192511689584379[/C][/ROW]
[ROW][C]56[/C][C]101.79[/C][C]101.72485180735[/C][C]0.0651481926498576[/C][/ROW]
[ROW][C]57[/C][C]101.8[/C][C]101.716730133832[/C][C]0.0832698661678819[/C][/ROW]
[ROW][C]58[/C][C]101.83[/C][C]101.72909517029[/C][C]0.100904829709791[/C][/ROW]
[ROW][C]59[/C][C]101.83[/C][C]101.762315803333[/C][C]0.0676841966669457[/C][/ROW]
[ROW][C]60[/C][C]101.88[/C][C]101.768171391908[/C][C]0.111828608091727[/C][/ROW]
[ROW][C]61[/C][C]101.9[/C][C]101.819722802508[/C][C]0.0802771974916396[/C][/ROW]
[ROW][C]62[/C][C]101.91[/C][C]101.846023936806[/C][C]0.0639760631935218[/C][/ROW]
[ROW][C]63[/C][C]101.17[/C][C]101.860320162007[/C][C]-0.690320162007311[/C][/ROW]
[ROW][C]64[/C][C]101.17[/C][C]101.150263067356[/C][C]0.0197369326435961[/C][/ROW]
[ROW][C]65[/C][C]101.23[/C][C]101.092932335326[/C][C]0.13706766467422[/C][/ROW]
[ROW][C]66[/C][C]101.26[/C][C]101.149647901774[/C][C]0.110352098226144[/C][/ROW]
[ROW][C]67[/C][C]101.49[/C][C]101.186943428018[/C][C]0.303056571982168[/C][/ROW]
[ROW][C]68[/C][C]101.51[/C][C]101.415153853486[/C][C]0.0948461465141293[/C][/ROW]
[ROW][C]69[/C][C]101.61[/C][C]101.456619601208[/C][C]0.153380398792379[/C][/ROW]
[ROW][C]70[/C][C]101.39[/C][C]101.558912563907[/C][C]-0.168912563906645[/C][/ROW]
[ROW][C]71[/C][C]101.43[/C][C]101.357536441091[/C][C]0.0724635589093907[/C][/ROW]
[ROW][C]72[/C][C]101.44[/C][C]101.381088829395[/C][C]0.0589111706054695[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208723&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208723&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
3105.82105.93-0.109999999999999
4105.72105.93393508385-0.213935083849549
5105.76105.832565353207-0.0725653532074375
6105.8105.857612883812-0.0576128838122969
7105.09105.893721602487-0.803721602486604
8105.06105.207747735072-0.147747735071917
9105.16105.1171065700440.0428934299564077
10105.2105.203452865751-0.00345286575127091
11105.21105.247094792589-0.0370947925886753
12105.23105.258138575639-0.028138575639062
13105.19105.276102427889-0.0861024278888749
14105.16105.236874498169-0.0768744981692748
15104.88105.20256187067-0.3225618706701
16104.52104.927795274287-0.407795274287139
17104.09104.555924853963-0.46592485396306
18104.35104.1091425181730.240857481827376
19104.48104.3223079352810.157692064718631
20104.47104.4664234801560.00357651984367635
21104.55104.4692304925610.0807695074392569
22104.59104.546634455490.0433655445095553
23104.59104.591708373418-0.00170837341786978
24104.72104.5953266196680.124673380332183
25104.65104.720726485596-0.0707264855956424
26104.72104.6634831626320.0565168373682212
27104.92104.725659899130.194340100870306
28105.05104.9233435642650.126656435734972
29103.74105.064753695428-1.32475369542844
30103.81103.812533965197-0.00253396519705973
31103.79103.7739594625860.0160405374143693
32104.28103.7531777838280.526822216171666
33103.8104.225647266865-0.42564726686507
34103.8103.804087633822-0.00408763382235122
35104.02103.7693194293320.250680570668266
36104.02103.9800164155150.0399835844849576
37104.91103.9991485588710.910851441129282
38104.97104.8598439451760.110156054823761
39103.86104.990617401096-1.13061740109579
40104.17103.9300992666560.239900733344427
41103.21104.13877638516-0.928776385159708
42103.21103.231680218859-0.0216802188589753
43101.91103.156271349846-1.24627134984561
44101.84101.899076468506-0.059076468506035
45101.91101.7289623350250.18103766497471
46101.79101.7876401392580.00235986074244465
47101.79101.6824056379550.107594362045432
48101.79101.6787501837180.111249816281813
49102.09101.6835959982040.406404001796147
50102.18101.9781829623070.201817037693331
51102.2102.0942992348330.105700765167271
52101.97102.127072331784-0.15707233178442
53102.05101.9113616403570.138638359643124
54102.04101.9735179400850.0664820599145912
55101.78101.972511689584-0.192511689584379
56101.79101.724851807350.0651481926498576
57101.8101.7167301338320.0832698661678819
58101.83101.729095170290.100904829709791
59101.83101.7623158033330.0676841966669457
60101.88101.7681713919080.111828608091727
61101.9101.8197228025080.0802771974916396
62101.91101.8460239368060.0639760631935218
63101.17101.860320162007-0.690320162007311
64101.17101.1502630673560.0197369326435961
65101.23101.0929323353260.13706766467422
66101.26101.1496479017740.110352098226144
67101.49101.1869434280180.303056571982168
68101.51101.4151538534860.0948461465141293
69101.61101.4566196012080.153380398792379
70101.39101.558912563907-0.168912563906645
71101.43101.3575364410910.0724635589093907
72101.44101.3810888293950.0589111706054695







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73101.394925316623100.678834235229102.111016398016
74101.35468292116100.359926273605102.349439568715
75101.314440525697100.084346528844102.54453452255
76101.27419813023499.8299848966705102.718411363798
77101.23395573477299.5878704623732102.88004100717
78101.19371333930999.3533710101365103.034055668481
79101.15347094384699.1237578052368103.183184082455
80101.11322854838398.8972823845659103.329174712201
81101.07298615292198.6727570214296103.473215284411
82101.03274375745898.4493396193802103.616147895535
83100.99250136199598.2264133953343103.758589328656
84100.95225896653298.0035149886501103.901002944414

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 101.394925316623 & 100.678834235229 & 102.111016398016 \tabularnewline
74 & 101.35468292116 & 100.359926273605 & 102.349439568715 \tabularnewline
75 & 101.314440525697 & 100.084346528844 & 102.54453452255 \tabularnewline
76 & 101.274198130234 & 99.8299848966705 & 102.718411363798 \tabularnewline
77 & 101.233955734772 & 99.5878704623732 & 102.88004100717 \tabularnewline
78 & 101.193713339309 & 99.3533710101365 & 103.034055668481 \tabularnewline
79 & 101.153470943846 & 99.1237578052368 & 103.183184082455 \tabularnewline
80 & 101.113228548383 & 98.8972823845659 & 103.329174712201 \tabularnewline
81 & 101.072986152921 & 98.6727570214296 & 103.473215284411 \tabularnewline
82 & 101.032743757458 & 98.4493396193802 & 103.616147895535 \tabularnewline
83 & 100.992501361995 & 98.2264133953343 & 103.758589328656 \tabularnewline
84 & 100.952258966532 & 98.0035149886501 & 103.901002944414 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208723&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]101.394925316623[/C][C]100.678834235229[/C][C]102.111016398016[/C][/ROW]
[ROW][C]74[/C][C]101.35468292116[/C][C]100.359926273605[/C][C]102.349439568715[/C][/ROW]
[ROW][C]75[/C][C]101.314440525697[/C][C]100.084346528844[/C][C]102.54453452255[/C][/ROW]
[ROW][C]76[/C][C]101.274198130234[/C][C]99.8299848966705[/C][C]102.718411363798[/C][/ROW]
[ROW][C]77[/C][C]101.233955734772[/C][C]99.5878704623732[/C][C]102.88004100717[/C][/ROW]
[ROW][C]78[/C][C]101.193713339309[/C][C]99.3533710101365[/C][C]103.034055668481[/C][/ROW]
[ROW][C]79[/C][C]101.153470943846[/C][C]99.1237578052368[/C][C]103.183184082455[/C][/ROW]
[ROW][C]80[/C][C]101.113228548383[/C][C]98.8972823845659[/C][C]103.329174712201[/C][/ROW]
[ROW][C]81[/C][C]101.072986152921[/C][C]98.6727570214296[/C][C]103.473215284411[/C][/ROW]
[ROW][C]82[/C][C]101.032743757458[/C][C]98.4493396193802[/C][C]103.616147895535[/C][/ROW]
[ROW][C]83[/C][C]100.992501361995[/C][C]98.2264133953343[/C][C]103.758589328656[/C][/ROW]
[ROW][C]84[/C][C]100.952258966532[/C][C]98.0035149886501[/C][C]103.901002944414[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208723&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208723&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
73101.394925316623100.678834235229102.111016398016
74101.35468292116100.359926273605102.349439568715
75101.314440525697100.084346528844102.54453452255
76101.27419813023499.8299848966705102.718411363798
77101.23395573477299.5878704623732102.88004100717
78101.19371333930999.3533710101365103.034055668481
79101.15347094384699.1237578052368103.183184082455
80101.11322854838398.8972823845659103.329174712201
81101.07298615292198.6727570214296103.473215284411
82101.03274375745898.4493396193802103.616147895535
83100.99250136199598.2264133953343103.758589328656
84100.95225896653298.0035149886501103.901002944414



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')