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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 17 Dec 2013 12:39:08 -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/Dec/17/t1387301972ev066hz6310876m.htm/, Retrieved Thu, 18 Apr 2024 15:13:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232413, Retrieved Thu, 18 Apr 2024 15:13:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact157
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-12-17 17:39:08] [218a9c88906eff9a4c44b4631dc496db] [Current]
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Dataseries X:
2.7
3
-0.3
1.1
1.7
1.6
3
3.3
6.7
5.6
6
4.8
5.9
4.3
3.7
5.6
1.7
3.2
3.6
1.7
0.5
2.1
1.5
2.7
1.4
1.2
2.3
1.6
4.7
3.5
4.4
3.9
3.5
3
1.6
2.2
4.1
4.3
3.5
1.8
0.6
-0.4
-2.5
-1.6
-1.9
-1.6
-0.7
-1.1
0.3
1.3
3.3
2.4
2
3.9
4.2
4.9
5.8
4.8
4.4
5.3
2.1
2
-0.9
0.1
-0.5
-0.1
0.7
-0.4
-1.5
-0.3
1
0.4
0.3
1.8
3
2.2
3.4
3.4
3.1
4.5
4.6
5.7
4.3
4.5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 4 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232413&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232413&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232413&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 time4 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.803482116329661
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.803482116329661 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232413&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]0.803482116329661[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232413&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232413&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
alpha0.803482116329661
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
232.70.3
3-0.32.9410446348989-3.2410446348989
41.10.3369232325314380.763076767468562
51.70.9500417685790750.749958231420925
61.61.552619795520010.0473802044799907
731.590688942487721.40931105751228
83.32.723045173544480.57695482645552
96.73.186618058531573.51338194146843
105.66.00955761633704-0.409557616337039
1165.680485396003620.319514603996377
124.85.93720966622087-1.13720966622087
135.95.023482036895180.876517963104823
144.35.7277485448916-1.4277485448916
153.74.5805781224555-0.880578122455503
165.63.873049349031361.72695065096864
171.75.26062331286853-3.56062331286853
183.22.399726157992190.800273842007806
193.63.04273187821190.557268121788105
201.73.49048684806926-1.79048684806926
210.52.05186268612215-1.55186268612215
222.10.8049687708236921.29503122917631
231.51.84550320355527-0.345503203555274
242.71.5678975583641.132102441636
251.42.47752162407167-1.07752162407167
261.21.61175226917159-0.411752269171591
272.31.280916684534061.01908331546594
281.62.09973190356088-0.499731903560881
294.71.698206256090333.00179374390967
303.54.11009384623201-0.610093846232009
314.43.619894351501810.780105648498189
323.94.24669528891786-0.346695288917859
333.53.96813182445661-0.468131824456614
3433.59199627542095-0.591996275420948
351.63.11633785518645-1.51633785518645
362.21.897987506230460.302012493769539
374.12.140649143882411.95935085611759
384.33.71495251638810.585047483611896
393.54.18502770667393-0.685027706673933
401.83.63462019517111-1.83462019517111
410.62.16053567809389-1.56053567809389
42-0.40.906673168851069-1.30667316885107
43-2.5-0.143215354208573-2.35678464579143
44-1.6-2.036849669142320.436849669142319
45-1.9-1.68584877246194-0.214151227538063
46-1.6-1.857915453978810.257915453978814
47-0.7-1.650684999181790.950684999181791
48-1.1-0.886826604076344-0.213173395923657
490.3-1.058107615378261.35810761537826
501.30.03310756562929291.26689243437071
513.31.05103297995952.24896702004049
522.42.85803776077725-0.458037760777253
5322.49001261138905-0.490012611389047
543.92.096296241361951.80370375863805
554.23.545539954584210.654460045415786
564.94.07138689692810.828613103071905
575.84.73716270660281.0628372933972
584.85.59113346441567-0.791133464415671
594.44.95547187412775-0.55547187412775
605.34.509160157141980.790839842858017
612.15.14458582775936-3.04458582775936
6222.69831556352398-0.698315563523976
63-0.92.13723149667779-3.03723149667779
640.1-0.3031296940559840.403129694055984
65-0.50.0207778056794468-0.520777805679447
66-0.1-0.3976578477653920.297657847765392
670.7-0.1584950903007230.858495090300723
68-0.40.531290361712725-0.931290361712725
69-1.5-0.216984789033631-1.28301521096637
70-0.3-1.247864566024040.947864566024036
711-0.4862723385211481.48627233852115
720.40.707920905476058-0.307920905476058
730.30.46051196468201-0.16051196468201
741.80.3315434716030771.46845652839692
7531.511422030777541.48857796922246
762.22.70746780781011-0.507467807810112
773.42.299726499621671.10027350037833
783.43.183776580247090.216223419752905
793.13.3575082311502-0.257508231150195
804.53.150604972613331.34939502738667
814.64.234819744982690.365180255017307
825.74.52823554912581.1717644508742
834.35.46972732995407-1.16972732995407
844.54.52987233935393-0.0298723393539291

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 3 & 2.7 & 0.3 \tabularnewline
3 & -0.3 & 2.9410446348989 & -3.2410446348989 \tabularnewline
4 & 1.1 & 0.336923232531438 & 0.763076767468562 \tabularnewline
5 & 1.7 & 0.950041768579075 & 0.749958231420925 \tabularnewline
6 & 1.6 & 1.55261979552001 & 0.0473802044799907 \tabularnewline
7 & 3 & 1.59068894248772 & 1.40931105751228 \tabularnewline
8 & 3.3 & 2.72304517354448 & 0.57695482645552 \tabularnewline
9 & 6.7 & 3.18661805853157 & 3.51338194146843 \tabularnewline
10 & 5.6 & 6.00955761633704 & -0.409557616337039 \tabularnewline
11 & 6 & 5.68048539600362 & 0.319514603996377 \tabularnewline
12 & 4.8 & 5.93720966622087 & -1.13720966622087 \tabularnewline
13 & 5.9 & 5.02348203689518 & 0.876517963104823 \tabularnewline
14 & 4.3 & 5.7277485448916 & -1.4277485448916 \tabularnewline
15 & 3.7 & 4.5805781224555 & -0.880578122455503 \tabularnewline
16 & 5.6 & 3.87304934903136 & 1.72695065096864 \tabularnewline
17 & 1.7 & 5.26062331286853 & -3.56062331286853 \tabularnewline
18 & 3.2 & 2.39972615799219 & 0.800273842007806 \tabularnewline
19 & 3.6 & 3.0427318782119 & 0.557268121788105 \tabularnewline
20 & 1.7 & 3.49048684806926 & -1.79048684806926 \tabularnewline
21 & 0.5 & 2.05186268612215 & -1.55186268612215 \tabularnewline
22 & 2.1 & 0.804968770823692 & 1.29503122917631 \tabularnewline
23 & 1.5 & 1.84550320355527 & -0.345503203555274 \tabularnewline
24 & 2.7 & 1.567897558364 & 1.132102441636 \tabularnewline
25 & 1.4 & 2.47752162407167 & -1.07752162407167 \tabularnewline
26 & 1.2 & 1.61175226917159 & -0.411752269171591 \tabularnewline
27 & 2.3 & 1.28091668453406 & 1.01908331546594 \tabularnewline
28 & 1.6 & 2.09973190356088 & -0.499731903560881 \tabularnewline
29 & 4.7 & 1.69820625609033 & 3.00179374390967 \tabularnewline
30 & 3.5 & 4.11009384623201 & -0.610093846232009 \tabularnewline
31 & 4.4 & 3.61989435150181 & 0.780105648498189 \tabularnewline
32 & 3.9 & 4.24669528891786 & -0.346695288917859 \tabularnewline
33 & 3.5 & 3.96813182445661 & -0.468131824456614 \tabularnewline
34 & 3 & 3.59199627542095 & -0.591996275420948 \tabularnewline
35 & 1.6 & 3.11633785518645 & -1.51633785518645 \tabularnewline
36 & 2.2 & 1.89798750623046 & 0.302012493769539 \tabularnewline
37 & 4.1 & 2.14064914388241 & 1.95935085611759 \tabularnewline
38 & 4.3 & 3.7149525163881 & 0.585047483611896 \tabularnewline
39 & 3.5 & 4.18502770667393 & -0.685027706673933 \tabularnewline
40 & 1.8 & 3.63462019517111 & -1.83462019517111 \tabularnewline
41 & 0.6 & 2.16053567809389 & -1.56053567809389 \tabularnewline
42 & -0.4 & 0.906673168851069 & -1.30667316885107 \tabularnewline
43 & -2.5 & -0.143215354208573 & -2.35678464579143 \tabularnewline
44 & -1.6 & -2.03684966914232 & 0.436849669142319 \tabularnewline
45 & -1.9 & -1.68584877246194 & -0.214151227538063 \tabularnewline
46 & -1.6 & -1.85791545397881 & 0.257915453978814 \tabularnewline
47 & -0.7 & -1.65068499918179 & 0.950684999181791 \tabularnewline
48 & -1.1 & -0.886826604076344 & -0.213173395923657 \tabularnewline
49 & 0.3 & -1.05810761537826 & 1.35810761537826 \tabularnewline
50 & 1.3 & 0.0331075656292929 & 1.26689243437071 \tabularnewline
51 & 3.3 & 1.0510329799595 & 2.24896702004049 \tabularnewline
52 & 2.4 & 2.85803776077725 & -0.458037760777253 \tabularnewline
53 & 2 & 2.49001261138905 & -0.490012611389047 \tabularnewline
54 & 3.9 & 2.09629624136195 & 1.80370375863805 \tabularnewline
55 & 4.2 & 3.54553995458421 & 0.654460045415786 \tabularnewline
56 & 4.9 & 4.0713868969281 & 0.828613103071905 \tabularnewline
57 & 5.8 & 4.7371627066028 & 1.0628372933972 \tabularnewline
58 & 4.8 & 5.59113346441567 & -0.791133464415671 \tabularnewline
59 & 4.4 & 4.95547187412775 & -0.55547187412775 \tabularnewline
60 & 5.3 & 4.50916015714198 & 0.790839842858017 \tabularnewline
61 & 2.1 & 5.14458582775936 & -3.04458582775936 \tabularnewline
62 & 2 & 2.69831556352398 & -0.698315563523976 \tabularnewline
63 & -0.9 & 2.13723149667779 & -3.03723149667779 \tabularnewline
64 & 0.1 & -0.303129694055984 & 0.403129694055984 \tabularnewline
65 & -0.5 & 0.0207778056794468 & -0.520777805679447 \tabularnewline
66 & -0.1 & -0.397657847765392 & 0.297657847765392 \tabularnewline
67 & 0.7 & -0.158495090300723 & 0.858495090300723 \tabularnewline
68 & -0.4 & 0.531290361712725 & -0.931290361712725 \tabularnewline
69 & -1.5 & -0.216984789033631 & -1.28301521096637 \tabularnewline
70 & -0.3 & -1.24786456602404 & 0.947864566024036 \tabularnewline
71 & 1 & -0.486272338521148 & 1.48627233852115 \tabularnewline
72 & 0.4 & 0.707920905476058 & -0.307920905476058 \tabularnewline
73 & 0.3 & 0.46051196468201 & -0.16051196468201 \tabularnewline
74 & 1.8 & 0.331543471603077 & 1.46845652839692 \tabularnewline
75 & 3 & 1.51142203077754 & 1.48857796922246 \tabularnewline
76 & 2.2 & 2.70746780781011 & -0.507467807810112 \tabularnewline
77 & 3.4 & 2.29972649962167 & 1.10027350037833 \tabularnewline
78 & 3.4 & 3.18377658024709 & 0.216223419752905 \tabularnewline
79 & 3.1 & 3.3575082311502 & -0.257508231150195 \tabularnewline
80 & 4.5 & 3.15060497261333 & 1.34939502738667 \tabularnewline
81 & 4.6 & 4.23481974498269 & 0.365180255017307 \tabularnewline
82 & 5.7 & 4.5282355491258 & 1.1717644508742 \tabularnewline
83 & 4.3 & 5.46972732995407 & -1.16972732995407 \tabularnewline
84 & 4.5 & 4.52987233935393 & -0.0298723393539291 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232413&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]2[/C][C]3[/C][C]2.7[/C][C]0.3[/C][/ROW]
[ROW][C]3[/C][C]-0.3[/C][C]2.9410446348989[/C][C]-3.2410446348989[/C][/ROW]
[ROW][C]4[/C][C]1.1[/C][C]0.336923232531438[/C][C]0.763076767468562[/C][/ROW]
[ROW][C]5[/C][C]1.7[/C][C]0.950041768579075[/C][C]0.749958231420925[/C][/ROW]
[ROW][C]6[/C][C]1.6[/C][C]1.55261979552001[/C][C]0.0473802044799907[/C][/ROW]
[ROW][C]7[/C][C]3[/C][C]1.59068894248772[/C][C]1.40931105751228[/C][/ROW]
[ROW][C]8[/C][C]3.3[/C][C]2.72304517354448[/C][C]0.57695482645552[/C][/ROW]
[ROW][C]9[/C][C]6.7[/C][C]3.18661805853157[/C][C]3.51338194146843[/C][/ROW]
[ROW][C]10[/C][C]5.6[/C][C]6.00955761633704[/C][C]-0.409557616337039[/C][/ROW]
[ROW][C]11[/C][C]6[/C][C]5.68048539600362[/C][C]0.319514603996377[/C][/ROW]
[ROW][C]12[/C][C]4.8[/C][C]5.93720966622087[/C][C]-1.13720966622087[/C][/ROW]
[ROW][C]13[/C][C]5.9[/C][C]5.02348203689518[/C][C]0.876517963104823[/C][/ROW]
[ROW][C]14[/C][C]4.3[/C][C]5.7277485448916[/C][C]-1.4277485448916[/C][/ROW]
[ROW][C]15[/C][C]3.7[/C][C]4.5805781224555[/C][C]-0.880578122455503[/C][/ROW]
[ROW][C]16[/C][C]5.6[/C][C]3.87304934903136[/C][C]1.72695065096864[/C][/ROW]
[ROW][C]17[/C][C]1.7[/C][C]5.26062331286853[/C][C]-3.56062331286853[/C][/ROW]
[ROW][C]18[/C][C]3.2[/C][C]2.39972615799219[/C][C]0.800273842007806[/C][/ROW]
[ROW][C]19[/C][C]3.6[/C][C]3.0427318782119[/C][C]0.557268121788105[/C][/ROW]
[ROW][C]20[/C][C]1.7[/C][C]3.49048684806926[/C][C]-1.79048684806926[/C][/ROW]
[ROW][C]21[/C][C]0.5[/C][C]2.05186268612215[/C][C]-1.55186268612215[/C][/ROW]
[ROW][C]22[/C][C]2.1[/C][C]0.804968770823692[/C][C]1.29503122917631[/C][/ROW]
[ROW][C]23[/C][C]1.5[/C][C]1.84550320355527[/C][C]-0.345503203555274[/C][/ROW]
[ROW][C]24[/C][C]2.7[/C][C]1.567897558364[/C][C]1.132102441636[/C][/ROW]
[ROW][C]25[/C][C]1.4[/C][C]2.47752162407167[/C][C]-1.07752162407167[/C][/ROW]
[ROW][C]26[/C][C]1.2[/C][C]1.61175226917159[/C][C]-0.411752269171591[/C][/ROW]
[ROW][C]27[/C][C]2.3[/C][C]1.28091668453406[/C][C]1.01908331546594[/C][/ROW]
[ROW][C]28[/C][C]1.6[/C][C]2.09973190356088[/C][C]-0.499731903560881[/C][/ROW]
[ROW][C]29[/C][C]4.7[/C][C]1.69820625609033[/C][C]3.00179374390967[/C][/ROW]
[ROW][C]30[/C][C]3.5[/C][C]4.11009384623201[/C][C]-0.610093846232009[/C][/ROW]
[ROW][C]31[/C][C]4.4[/C][C]3.61989435150181[/C][C]0.780105648498189[/C][/ROW]
[ROW][C]32[/C][C]3.9[/C][C]4.24669528891786[/C][C]-0.346695288917859[/C][/ROW]
[ROW][C]33[/C][C]3.5[/C][C]3.96813182445661[/C][C]-0.468131824456614[/C][/ROW]
[ROW][C]34[/C][C]3[/C][C]3.59199627542095[/C][C]-0.591996275420948[/C][/ROW]
[ROW][C]35[/C][C]1.6[/C][C]3.11633785518645[/C][C]-1.51633785518645[/C][/ROW]
[ROW][C]36[/C][C]2.2[/C][C]1.89798750623046[/C][C]0.302012493769539[/C][/ROW]
[ROW][C]37[/C][C]4.1[/C][C]2.14064914388241[/C][C]1.95935085611759[/C][/ROW]
[ROW][C]38[/C][C]4.3[/C][C]3.7149525163881[/C][C]0.585047483611896[/C][/ROW]
[ROW][C]39[/C][C]3.5[/C][C]4.18502770667393[/C][C]-0.685027706673933[/C][/ROW]
[ROW][C]40[/C][C]1.8[/C][C]3.63462019517111[/C][C]-1.83462019517111[/C][/ROW]
[ROW][C]41[/C][C]0.6[/C][C]2.16053567809389[/C][C]-1.56053567809389[/C][/ROW]
[ROW][C]42[/C][C]-0.4[/C][C]0.906673168851069[/C][C]-1.30667316885107[/C][/ROW]
[ROW][C]43[/C][C]-2.5[/C][C]-0.143215354208573[/C][C]-2.35678464579143[/C][/ROW]
[ROW][C]44[/C][C]-1.6[/C][C]-2.03684966914232[/C][C]0.436849669142319[/C][/ROW]
[ROW][C]45[/C][C]-1.9[/C][C]-1.68584877246194[/C][C]-0.214151227538063[/C][/ROW]
[ROW][C]46[/C][C]-1.6[/C][C]-1.85791545397881[/C][C]0.257915453978814[/C][/ROW]
[ROW][C]47[/C][C]-0.7[/C][C]-1.65068499918179[/C][C]0.950684999181791[/C][/ROW]
[ROW][C]48[/C][C]-1.1[/C][C]-0.886826604076344[/C][C]-0.213173395923657[/C][/ROW]
[ROW][C]49[/C][C]0.3[/C][C]-1.05810761537826[/C][C]1.35810761537826[/C][/ROW]
[ROW][C]50[/C][C]1.3[/C][C]0.0331075656292929[/C][C]1.26689243437071[/C][/ROW]
[ROW][C]51[/C][C]3.3[/C][C]1.0510329799595[/C][C]2.24896702004049[/C][/ROW]
[ROW][C]52[/C][C]2.4[/C][C]2.85803776077725[/C][C]-0.458037760777253[/C][/ROW]
[ROW][C]53[/C][C]2[/C][C]2.49001261138905[/C][C]-0.490012611389047[/C][/ROW]
[ROW][C]54[/C][C]3.9[/C][C]2.09629624136195[/C][C]1.80370375863805[/C][/ROW]
[ROW][C]55[/C][C]4.2[/C][C]3.54553995458421[/C][C]0.654460045415786[/C][/ROW]
[ROW][C]56[/C][C]4.9[/C][C]4.0713868969281[/C][C]0.828613103071905[/C][/ROW]
[ROW][C]57[/C][C]5.8[/C][C]4.7371627066028[/C][C]1.0628372933972[/C][/ROW]
[ROW][C]58[/C][C]4.8[/C][C]5.59113346441567[/C][C]-0.791133464415671[/C][/ROW]
[ROW][C]59[/C][C]4.4[/C][C]4.95547187412775[/C][C]-0.55547187412775[/C][/ROW]
[ROW][C]60[/C][C]5.3[/C][C]4.50916015714198[/C][C]0.790839842858017[/C][/ROW]
[ROW][C]61[/C][C]2.1[/C][C]5.14458582775936[/C][C]-3.04458582775936[/C][/ROW]
[ROW][C]62[/C][C]2[/C][C]2.69831556352398[/C][C]-0.698315563523976[/C][/ROW]
[ROW][C]63[/C][C]-0.9[/C][C]2.13723149667779[/C][C]-3.03723149667779[/C][/ROW]
[ROW][C]64[/C][C]0.1[/C][C]-0.303129694055984[/C][C]0.403129694055984[/C][/ROW]
[ROW][C]65[/C][C]-0.5[/C][C]0.0207778056794468[/C][C]-0.520777805679447[/C][/ROW]
[ROW][C]66[/C][C]-0.1[/C][C]-0.397657847765392[/C][C]0.297657847765392[/C][/ROW]
[ROW][C]67[/C][C]0.7[/C][C]-0.158495090300723[/C][C]0.858495090300723[/C][/ROW]
[ROW][C]68[/C][C]-0.4[/C][C]0.531290361712725[/C][C]-0.931290361712725[/C][/ROW]
[ROW][C]69[/C][C]-1.5[/C][C]-0.216984789033631[/C][C]-1.28301521096637[/C][/ROW]
[ROW][C]70[/C][C]-0.3[/C][C]-1.24786456602404[/C][C]0.947864566024036[/C][/ROW]
[ROW][C]71[/C][C]1[/C][C]-0.486272338521148[/C][C]1.48627233852115[/C][/ROW]
[ROW][C]72[/C][C]0.4[/C][C]0.707920905476058[/C][C]-0.307920905476058[/C][/ROW]
[ROW][C]73[/C][C]0.3[/C][C]0.46051196468201[/C][C]-0.16051196468201[/C][/ROW]
[ROW][C]74[/C][C]1.8[/C][C]0.331543471603077[/C][C]1.46845652839692[/C][/ROW]
[ROW][C]75[/C][C]3[/C][C]1.51142203077754[/C][C]1.48857796922246[/C][/ROW]
[ROW][C]76[/C][C]2.2[/C][C]2.70746780781011[/C][C]-0.507467807810112[/C][/ROW]
[ROW][C]77[/C][C]3.4[/C][C]2.29972649962167[/C][C]1.10027350037833[/C][/ROW]
[ROW][C]78[/C][C]3.4[/C][C]3.18377658024709[/C][C]0.216223419752905[/C][/ROW]
[ROW][C]79[/C][C]3.1[/C][C]3.3575082311502[/C][C]-0.257508231150195[/C][/ROW]
[ROW][C]80[/C][C]4.5[/C][C]3.15060497261333[/C][C]1.34939502738667[/C][/ROW]
[ROW][C]81[/C][C]4.6[/C][C]4.23481974498269[/C][C]0.365180255017307[/C][/ROW]
[ROW][C]82[/C][C]5.7[/C][C]4.5282355491258[/C][C]1.1717644508742[/C][/ROW]
[ROW][C]83[/C][C]4.3[/C][C]5.46972732995407[/C][C]-1.16972732995407[/C][/ROW]
[ROW][C]84[/C][C]4.5[/C][C]4.52987233935393[/C][C]-0.0298723393539291[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232413&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232413&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
232.70.3
3-0.32.9410446348989-3.2410446348989
41.10.3369232325314380.763076767468562
51.70.9500417685790750.749958231420925
61.61.552619795520010.0473802044799907
731.590688942487721.40931105751228
83.32.723045173544480.57695482645552
96.73.186618058531573.51338194146843
105.66.00955761633704-0.409557616337039
1165.680485396003620.319514603996377
124.85.93720966622087-1.13720966622087
135.95.023482036895180.876517963104823
144.35.7277485448916-1.4277485448916
153.74.5805781224555-0.880578122455503
165.63.873049349031361.72695065096864
171.75.26062331286853-3.56062331286853
183.22.399726157992190.800273842007806
193.63.04273187821190.557268121788105
201.73.49048684806926-1.79048684806926
210.52.05186268612215-1.55186268612215
222.10.8049687708236921.29503122917631
231.51.84550320355527-0.345503203555274
242.71.5678975583641.132102441636
251.42.47752162407167-1.07752162407167
261.21.61175226917159-0.411752269171591
272.31.280916684534061.01908331546594
281.62.09973190356088-0.499731903560881
294.71.698206256090333.00179374390967
303.54.11009384623201-0.610093846232009
314.43.619894351501810.780105648498189
323.94.24669528891786-0.346695288917859
333.53.96813182445661-0.468131824456614
3433.59199627542095-0.591996275420948
351.63.11633785518645-1.51633785518645
362.21.897987506230460.302012493769539
374.12.140649143882411.95935085611759
384.33.71495251638810.585047483611896
393.54.18502770667393-0.685027706673933
401.83.63462019517111-1.83462019517111
410.62.16053567809389-1.56053567809389
42-0.40.906673168851069-1.30667316885107
43-2.5-0.143215354208573-2.35678464579143
44-1.6-2.036849669142320.436849669142319
45-1.9-1.68584877246194-0.214151227538063
46-1.6-1.857915453978810.257915453978814
47-0.7-1.650684999181790.950684999181791
48-1.1-0.886826604076344-0.213173395923657
490.3-1.058107615378261.35810761537826
501.30.03310756562929291.26689243437071
513.31.05103297995952.24896702004049
522.42.85803776077725-0.458037760777253
5322.49001261138905-0.490012611389047
543.92.096296241361951.80370375863805
554.23.545539954584210.654460045415786
564.94.07138689692810.828613103071905
575.84.73716270660281.0628372933972
584.85.59113346441567-0.791133464415671
594.44.95547187412775-0.55547187412775
605.34.509160157141980.790839842858017
612.15.14458582775936-3.04458582775936
6222.69831556352398-0.698315563523976
63-0.92.13723149667779-3.03723149667779
640.1-0.3031296940559840.403129694055984
65-0.50.0207778056794468-0.520777805679447
66-0.1-0.3976578477653920.297657847765392
670.7-0.1584950903007230.858495090300723
68-0.40.531290361712725-0.931290361712725
69-1.5-0.216984789033631-1.28301521096637
70-0.3-1.247864566024040.947864566024036
711-0.4862723385211481.48627233852115
720.40.707920905476058-0.307920905476058
730.30.46051196468201-0.16051196468201
741.80.3315434716030771.46845652839692
7531.511422030777541.48857796922246
762.22.70746780781011-0.507467807810112
773.42.299726499621671.10027350037833
783.43.183776580247090.216223419752905
793.13.3575082311502-0.257508231150195
804.53.150604972613331.34939502738667
814.64.234819744982690.365180255017307
825.74.52823554912581.1717644508742
834.35.46972732995407-1.16972732995407
844.54.52987233935393-0.0298723393539291







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
854.505870448910121.907698763914057.10404213390618
864.505870448910121.17292804275387.83881285506644
874.505870448910120.5731215297957958.43861936802444
884.505870448910120.0533966377760588.95834426004417
894.50587044891012-0.4117033448294799.42344424264971
904.50587044891012-0.8364643398235729.8482052376438
914.50587044891012-1.2298553092615610.2415962070818
924.50587044891012-1.5979446655075710.6096855633278
934.50587044891012-1.9450649816327710.956805879453
944.50587044891012-2.2744375755879911.2861784734082
954.50587044891012-2.5885348034780811.6002757012983
964.50587044891012-2.8893033058540611.9010442036743

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 4.50587044891012 & 1.90769876391405 & 7.10404213390618 \tabularnewline
86 & 4.50587044891012 & 1.1729280427538 & 7.83881285506644 \tabularnewline
87 & 4.50587044891012 & 0.573121529795795 & 8.43861936802444 \tabularnewline
88 & 4.50587044891012 & 0.053396637776058 & 8.95834426004417 \tabularnewline
89 & 4.50587044891012 & -0.411703344829479 & 9.42344424264971 \tabularnewline
90 & 4.50587044891012 & -0.836464339823572 & 9.8482052376438 \tabularnewline
91 & 4.50587044891012 & -1.22985530926156 & 10.2415962070818 \tabularnewline
92 & 4.50587044891012 & -1.59794466550757 & 10.6096855633278 \tabularnewline
93 & 4.50587044891012 & -1.94506498163277 & 10.956805879453 \tabularnewline
94 & 4.50587044891012 & -2.27443757558799 & 11.2861784734082 \tabularnewline
95 & 4.50587044891012 & -2.58853480347808 & 11.6002757012983 \tabularnewline
96 & 4.50587044891012 & -2.88930330585406 & 11.9010442036743 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232413&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]85[/C][C]4.50587044891012[/C][C]1.90769876391405[/C][C]7.10404213390618[/C][/ROW]
[ROW][C]86[/C][C]4.50587044891012[/C][C]1.1729280427538[/C][C]7.83881285506644[/C][/ROW]
[ROW][C]87[/C][C]4.50587044891012[/C][C]0.573121529795795[/C][C]8.43861936802444[/C][/ROW]
[ROW][C]88[/C][C]4.50587044891012[/C][C]0.053396637776058[/C][C]8.95834426004417[/C][/ROW]
[ROW][C]89[/C][C]4.50587044891012[/C][C]-0.411703344829479[/C][C]9.42344424264971[/C][/ROW]
[ROW][C]90[/C][C]4.50587044891012[/C][C]-0.836464339823572[/C][C]9.8482052376438[/C][/ROW]
[ROW][C]91[/C][C]4.50587044891012[/C][C]-1.22985530926156[/C][C]10.2415962070818[/C][/ROW]
[ROW][C]92[/C][C]4.50587044891012[/C][C]-1.59794466550757[/C][C]10.6096855633278[/C][/ROW]
[ROW][C]93[/C][C]4.50587044891012[/C][C]-1.94506498163277[/C][C]10.956805879453[/C][/ROW]
[ROW][C]94[/C][C]4.50587044891012[/C][C]-2.27443757558799[/C][C]11.2861784734082[/C][/ROW]
[ROW][C]95[/C][C]4.50587044891012[/C][C]-2.58853480347808[/C][C]11.6002757012983[/C][/ROW]
[ROW][C]96[/C][C]4.50587044891012[/C][C]-2.88930330585406[/C][C]11.9010442036743[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232413&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232413&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
854.505870448910121.907698763914057.10404213390618
864.505870448910121.17292804275387.83881285506644
874.505870448910120.5731215297957958.43861936802444
884.505870448910120.0533966377760588.95834426004417
894.50587044891012-0.4117033448294799.42344424264971
904.50587044891012-0.8364643398235729.8482052376438
914.50587044891012-1.2298553092615610.2415962070818
924.50587044891012-1.5979446655075710.6096855633278
934.50587044891012-1.9450649816327710.956805879453
944.50587044891012-2.2744375755879911.2861784734082
954.50587044891012-2.5885348034780811.6002757012983
964.50587044891012-2.8893033058540611.9010442036743



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')