Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 19 Dec 2011 12:52:32 -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/2011/Dec/19/t1324317207cq85tzh0q4h7has.htm/, Retrieved Wed, 15 May 2024 19:06:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=157560, Retrieved Wed, 15 May 2024 19:06:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact87
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Opdracht 10 oefen...] [2011-12-19 17:52:32] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
6
6
5
3
2
3
3
2
0
4
4
5
6
6
5
5
3
5
5
5
3
6
6
4
6
5
4
5
5
4
3
2
3
2
-1
0
-2
1
-2
-2
-2
-6
-4
-2
0
-5
-4
-5
-1
-2
-4
-1
1
1
-2
1
1
3
3
1
1
0
2
2
-1
1
0
1
1
3
2
0





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=157560&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=157560&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157560&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 time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.54129218387642
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.54129218387642 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157560&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]0.54129218387642[/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=157560&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157560&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
alpha0.54129218387642
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2660
356-1
435.45870781612358-2.45870781612358
524.12782849282002-2.12782849282002
632.9760515610270.0239484389729983
732.989014663859130.0109853361408727
822.99496094044944-0.994960940449437
902.45639636012182-2.45639636012182
1041.126768209885392.87323179011461
1142.682026120339681.31797387966032
1253.395435079953091.60456492004691
1364.263973529696781.73602647030322
1465.203671089074480.796328910925518
1555.63471770435329-0.634717704353287
1655.29114997201887-0.291149972018869
1735.13355276782922-2.13355276782922
1853.978677330715361.02132266928464
1954.531511308814940.468488691185063
2054.785100575587910.214899424412095
2134.90142395434171-1.90142395434171
2263.872198029621152.12780197037885
2365.023960605024070.976039394975933
2445.55228310068001-1.55228310068001
2564.712044391118471.28795560888153
2655.40920469538584-0.409204695385836
2745.18770539216795-1.18770539216795
2854.544809746639560.455190253360438
2954.791200672960290.208799327039705
3044.90422211668554-0.904222116685544
3134.41477375243547-1.41477375243547
3223.64896777828864-1.64896777828864
3332.756394408436930.243605591563068
3422.88825621109861-0.888256211098612
35-12.40745006675125-3.40745006675125
3600.563023978669613-0.563023978669613
37-20.258263499680747-2.25826349968075
381-0.9641168818298511.96411688182985
39-20.0990442345243732-2.09904423452437
40-2-1.03715200323453-0.962847996765467
41-2-1.55833409814475-0.441665901855251
42-6-1.79740439870373-4.20259560129627
43-4-4.072236549678820.0722365496788226
44-2-4.033135469947482.03313546994748
450-2.932615131302992.93261513130299
46-5-1.34521348241096-3.65478651758904
47-4-3.32352085811883-0.676479141881171
48-5-3.68969373017453-1.31030626982547
49-1-4.398952272515333.39895227251533
50-2-2.559125974033780.559125974033785
51-4-2.25647545448701-1.74352454551299
52-1-3.200231663369882.20023166336988
531-2.009263461270353.00926346127035
541-0.3803726704598071.38037267045981
55-20.366812266896708-2.36681226689671
561-0.9143247138773111.91432471387731
5710.1218842911459410.878115708854059
5830.5972014608877452.40279853911225
5931.897817529538891.10218247046111
6012.49442028600509-1.49442028600509
6111.68550226576417-0.685502265764171
6201.31444524727645-1.31444524727645
6320.6029463087921991.3970536912078
6421.359160552298680.640839447701317
65-11.70604193645909-2.70604193645909
6610.2412825870119720.758717412988028
6700.651970392433329-0.651970392433329
6810.2990639148903260.700936085109674
6910.678475139157130.32152486084287
7030.8525140332533292.14748596674667
7122.0149314020376-0.0149314020375995
7202.00684915082033-2.00684915082033

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 6 & 6 & 0 \tabularnewline
3 & 5 & 6 & -1 \tabularnewline
4 & 3 & 5.45870781612358 & -2.45870781612358 \tabularnewline
5 & 2 & 4.12782849282002 & -2.12782849282002 \tabularnewline
6 & 3 & 2.976051561027 & 0.0239484389729983 \tabularnewline
7 & 3 & 2.98901466385913 & 0.0109853361408727 \tabularnewline
8 & 2 & 2.99496094044944 & -0.994960940449437 \tabularnewline
9 & 0 & 2.45639636012182 & -2.45639636012182 \tabularnewline
10 & 4 & 1.12676820988539 & 2.87323179011461 \tabularnewline
11 & 4 & 2.68202612033968 & 1.31797387966032 \tabularnewline
12 & 5 & 3.39543507995309 & 1.60456492004691 \tabularnewline
13 & 6 & 4.26397352969678 & 1.73602647030322 \tabularnewline
14 & 6 & 5.20367108907448 & 0.796328910925518 \tabularnewline
15 & 5 & 5.63471770435329 & -0.634717704353287 \tabularnewline
16 & 5 & 5.29114997201887 & -0.291149972018869 \tabularnewline
17 & 3 & 5.13355276782922 & -2.13355276782922 \tabularnewline
18 & 5 & 3.97867733071536 & 1.02132266928464 \tabularnewline
19 & 5 & 4.53151130881494 & 0.468488691185063 \tabularnewline
20 & 5 & 4.78510057558791 & 0.214899424412095 \tabularnewline
21 & 3 & 4.90142395434171 & -1.90142395434171 \tabularnewline
22 & 6 & 3.87219802962115 & 2.12780197037885 \tabularnewline
23 & 6 & 5.02396060502407 & 0.976039394975933 \tabularnewline
24 & 4 & 5.55228310068001 & -1.55228310068001 \tabularnewline
25 & 6 & 4.71204439111847 & 1.28795560888153 \tabularnewline
26 & 5 & 5.40920469538584 & -0.409204695385836 \tabularnewline
27 & 4 & 5.18770539216795 & -1.18770539216795 \tabularnewline
28 & 5 & 4.54480974663956 & 0.455190253360438 \tabularnewline
29 & 5 & 4.79120067296029 & 0.208799327039705 \tabularnewline
30 & 4 & 4.90422211668554 & -0.904222116685544 \tabularnewline
31 & 3 & 4.41477375243547 & -1.41477375243547 \tabularnewline
32 & 2 & 3.64896777828864 & -1.64896777828864 \tabularnewline
33 & 3 & 2.75639440843693 & 0.243605591563068 \tabularnewline
34 & 2 & 2.88825621109861 & -0.888256211098612 \tabularnewline
35 & -1 & 2.40745006675125 & -3.40745006675125 \tabularnewline
36 & 0 & 0.563023978669613 & -0.563023978669613 \tabularnewline
37 & -2 & 0.258263499680747 & -2.25826349968075 \tabularnewline
38 & 1 & -0.964116881829851 & 1.96411688182985 \tabularnewline
39 & -2 & 0.0990442345243732 & -2.09904423452437 \tabularnewline
40 & -2 & -1.03715200323453 & -0.962847996765467 \tabularnewline
41 & -2 & -1.55833409814475 & -0.441665901855251 \tabularnewline
42 & -6 & -1.79740439870373 & -4.20259560129627 \tabularnewline
43 & -4 & -4.07223654967882 & 0.0722365496788226 \tabularnewline
44 & -2 & -4.03313546994748 & 2.03313546994748 \tabularnewline
45 & 0 & -2.93261513130299 & 2.93261513130299 \tabularnewline
46 & -5 & -1.34521348241096 & -3.65478651758904 \tabularnewline
47 & -4 & -3.32352085811883 & -0.676479141881171 \tabularnewline
48 & -5 & -3.68969373017453 & -1.31030626982547 \tabularnewline
49 & -1 & -4.39895227251533 & 3.39895227251533 \tabularnewline
50 & -2 & -2.55912597403378 & 0.559125974033785 \tabularnewline
51 & -4 & -2.25647545448701 & -1.74352454551299 \tabularnewline
52 & -1 & -3.20023166336988 & 2.20023166336988 \tabularnewline
53 & 1 & -2.00926346127035 & 3.00926346127035 \tabularnewline
54 & 1 & -0.380372670459807 & 1.38037267045981 \tabularnewline
55 & -2 & 0.366812266896708 & -2.36681226689671 \tabularnewline
56 & 1 & -0.914324713877311 & 1.91432471387731 \tabularnewline
57 & 1 & 0.121884291145941 & 0.878115708854059 \tabularnewline
58 & 3 & 0.597201460887745 & 2.40279853911225 \tabularnewline
59 & 3 & 1.89781752953889 & 1.10218247046111 \tabularnewline
60 & 1 & 2.49442028600509 & -1.49442028600509 \tabularnewline
61 & 1 & 1.68550226576417 & -0.685502265764171 \tabularnewline
62 & 0 & 1.31444524727645 & -1.31444524727645 \tabularnewline
63 & 2 & 0.602946308792199 & 1.3970536912078 \tabularnewline
64 & 2 & 1.35916055229868 & 0.640839447701317 \tabularnewline
65 & -1 & 1.70604193645909 & -2.70604193645909 \tabularnewline
66 & 1 & 0.241282587011972 & 0.758717412988028 \tabularnewline
67 & 0 & 0.651970392433329 & -0.651970392433329 \tabularnewline
68 & 1 & 0.299063914890326 & 0.700936085109674 \tabularnewline
69 & 1 & 0.67847513915713 & 0.32152486084287 \tabularnewline
70 & 3 & 0.852514033253329 & 2.14748596674667 \tabularnewline
71 & 2 & 2.0149314020376 & -0.0149314020375995 \tabularnewline
72 & 0 & 2.00684915082033 & -2.00684915082033 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157560&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]6[/C][C]6[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]5[/C][C]6[/C][C]-1[/C][/ROW]
[ROW][C]4[/C][C]3[/C][C]5.45870781612358[/C][C]-2.45870781612358[/C][/ROW]
[ROW][C]5[/C][C]2[/C][C]4.12782849282002[/C][C]-2.12782849282002[/C][/ROW]
[ROW][C]6[/C][C]3[/C][C]2.976051561027[/C][C]0.0239484389729983[/C][/ROW]
[ROW][C]7[/C][C]3[/C][C]2.98901466385913[/C][C]0.0109853361408727[/C][/ROW]
[ROW][C]8[/C][C]2[/C][C]2.99496094044944[/C][C]-0.994960940449437[/C][/ROW]
[ROW][C]9[/C][C]0[/C][C]2.45639636012182[/C][C]-2.45639636012182[/C][/ROW]
[ROW][C]10[/C][C]4[/C][C]1.12676820988539[/C][C]2.87323179011461[/C][/ROW]
[ROW][C]11[/C][C]4[/C][C]2.68202612033968[/C][C]1.31797387966032[/C][/ROW]
[ROW][C]12[/C][C]5[/C][C]3.39543507995309[/C][C]1.60456492004691[/C][/ROW]
[ROW][C]13[/C][C]6[/C][C]4.26397352969678[/C][C]1.73602647030322[/C][/ROW]
[ROW][C]14[/C][C]6[/C][C]5.20367108907448[/C][C]0.796328910925518[/C][/ROW]
[ROW][C]15[/C][C]5[/C][C]5.63471770435329[/C][C]-0.634717704353287[/C][/ROW]
[ROW][C]16[/C][C]5[/C][C]5.29114997201887[/C][C]-0.291149972018869[/C][/ROW]
[ROW][C]17[/C][C]3[/C][C]5.13355276782922[/C][C]-2.13355276782922[/C][/ROW]
[ROW][C]18[/C][C]5[/C][C]3.97867733071536[/C][C]1.02132266928464[/C][/ROW]
[ROW][C]19[/C][C]5[/C][C]4.53151130881494[/C][C]0.468488691185063[/C][/ROW]
[ROW][C]20[/C][C]5[/C][C]4.78510057558791[/C][C]0.214899424412095[/C][/ROW]
[ROW][C]21[/C][C]3[/C][C]4.90142395434171[/C][C]-1.90142395434171[/C][/ROW]
[ROW][C]22[/C][C]6[/C][C]3.87219802962115[/C][C]2.12780197037885[/C][/ROW]
[ROW][C]23[/C][C]6[/C][C]5.02396060502407[/C][C]0.976039394975933[/C][/ROW]
[ROW][C]24[/C][C]4[/C][C]5.55228310068001[/C][C]-1.55228310068001[/C][/ROW]
[ROW][C]25[/C][C]6[/C][C]4.71204439111847[/C][C]1.28795560888153[/C][/ROW]
[ROW][C]26[/C][C]5[/C][C]5.40920469538584[/C][C]-0.409204695385836[/C][/ROW]
[ROW][C]27[/C][C]4[/C][C]5.18770539216795[/C][C]-1.18770539216795[/C][/ROW]
[ROW][C]28[/C][C]5[/C][C]4.54480974663956[/C][C]0.455190253360438[/C][/ROW]
[ROW][C]29[/C][C]5[/C][C]4.79120067296029[/C][C]0.208799327039705[/C][/ROW]
[ROW][C]30[/C][C]4[/C][C]4.90422211668554[/C][C]-0.904222116685544[/C][/ROW]
[ROW][C]31[/C][C]3[/C][C]4.41477375243547[/C][C]-1.41477375243547[/C][/ROW]
[ROW][C]32[/C][C]2[/C][C]3.64896777828864[/C][C]-1.64896777828864[/C][/ROW]
[ROW][C]33[/C][C]3[/C][C]2.75639440843693[/C][C]0.243605591563068[/C][/ROW]
[ROW][C]34[/C][C]2[/C][C]2.88825621109861[/C][C]-0.888256211098612[/C][/ROW]
[ROW][C]35[/C][C]-1[/C][C]2.40745006675125[/C][C]-3.40745006675125[/C][/ROW]
[ROW][C]36[/C][C]0[/C][C]0.563023978669613[/C][C]-0.563023978669613[/C][/ROW]
[ROW][C]37[/C][C]-2[/C][C]0.258263499680747[/C][C]-2.25826349968075[/C][/ROW]
[ROW][C]38[/C][C]1[/C][C]-0.964116881829851[/C][C]1.96411688182985[/C][/ROW]
[ROW][C]39[/C][C]-2[/C][C]0.0990442345243732[/C][C]-2.09904423452437[/C][/ROW]
[ROW][C]40[/C][C]-2[/C][C]-1.03715200323453[/C][C]-0.962847996765467[/C][/ROW]
[ROW][C]41[/C][C]-2[/C][C]-1.55833409814475[/C][C]-0.441665901855251[/C][/ROW]
[ROW][C]42[/C][C]-6[/C][C]-1.79740439870373[/C][C]-4.20259560129627[/C][/ROW]
[ROW][C]43[/C][C]-4[/C][C]-4.07223654967882[/C][C]0.0722365496788226[/C][/ROW]
[ROW][C]44[/C][C]-2[/C][C]-4.03313546994748[/C][C]2.03313546994748[/C][/ROW]
[ROW][C]45[/C][C]0[/C][C]-2.93261513130299[/C][C]2.93261513130299[/C][/ROW]
[ROW][C]46[/C][C]-5[/C][C]-1.34521348241096[/C][C]-3.65478651758904[/C][/ROW]
[ROW][C]47[/C][C]-4[/C][C]-3.32352085811883[/C][C]-0.676479141881171[/C][/ROW]
[ROW][C]48[/C][C]-5[/C][C]-3.68969373017453[/C][C]-1.31030626982547[/C][/ROW]
[ROW][C]49[/C][C]-1[/C][C]-4.39895227251533[/C][C]3.39895227251533[/C][/ROW]
[ROW][C]50[/C][C]-2[/C][C]-2.55912597403378[/C][C]0.559125974033785[/C][/ROW]
[ROW][C]51[/C][C]-4[/C][C]-2.25647545448701[/C][C]-1.74352454551299[/C][/ROW]
[ROW][C]52[/C][C]-1[/C][C]-3.20023166336988[/C][C]2.20023166336988[/C][/ROW]
[ROW][C]53[/C][C]1[/C][C]-2.00926346127035[/C][C]3.00926346127035[/C][/ROW]
[ROW][C]54[/C][C]1[/C][C]-0.380372670459807[/C][C]1.38037267045981[/C][/ROW]
[ROW][C]55[/C][C]-2[/C][C]0.366812266896708[/C][C]-2.36681226689671[/C][/ROW]
[ROW][C]56[/C][C]1[/C][C]-0.914324713877311[/C][C]1.91432471387731[/C][/ROW]
[ROW][C]57[/C][C]1[/C][C]0.121884291145941[/C][C]0.878115708854059[/C][/ROW]
[ROW][C]58[/C][C]3[/C][C]0.597201460887745[/C][C]2.40279853911225[/C][/ROW]
[ROW][C]59[/C][C]3[/C][C]1.89781752953889[/C][C]1.10218247046111[/C][/ROW]
[ROW][C]60[/C][C]1[/C][C]2.49442028600509[/C][C]-1.49442028600509[/C][/ROW]
[ROW][C]61[/C][C]1[/C][C]1.68550226576417[/C][C]-0.685502265764171[/C][/ROW]
[ROW][C]62[/C][C]0[/C][C]1.31444524727645[/C][C]-1.31444524727645[/C][/ROW]
[ROW][C]63[/C][C]2[/C][C]0.602946308792199[/C][C]1.3970536912078[/C][/ROW]
[ROW][C]64[/C][C]2[/C][C]1.35916055229868[/C][C]0.640839447701317[/C][/ROW]
[ROW][C]65[/C][C]-1[/C][C]1.70604193645909[/C][C]-2.70604193645909[/C][/ROW]
[ROW][C]66[/C][C]1[/C][C]0.241282587011972[/C][C]0.758717412988028[/C][/ROW]
[ROW][C]67[/C][C]0[/C][C]0.651970392433329[/C][C]-0.651970392433329[/C][/ROW]
[ROW][C]68[/C][C]1[/C][C]0.299063914890326[/C][C]0.700936085109674[/C][/ROW]
[ROW][C]69[/C][C]1[/C][C]0.67847513915713[/C][C]0.32152486084287[/C][/ROW]
[ROW][C]70[/C][C]3[/C][C]0.852514033253329[/C][C]2.14748596674667[/C][/ROW]
[ROW][C]71[/C][C]2[/C][C]2.0149314020376[/C][C]-0.0149314020375995[/C][/ROW]
[ROW][C]72[/C][C]0[/C][C]2.00684915082033[/C][C]-2.00684915082033[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157560&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157560&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
2660
356-1
435.45870781612358-2.45870781612358
524.12782849282002-2.12782849282002
632.9760515610270.0239484389729983
732.989014663859130.0109853361408727
822.99496094044944-0.994960940449437
902.45639636012182-2.45639636012182
1041.126768209885392.87323179011461
1142.682026120339681.31797387966032
1253.395435079953091.60456492004691
1364.263973529696781.73602647030322
1465.203671089074480.796328910925518
1555.63471770435329-0.634717704353287
1655.29114997201887-0.291149972018869
1735.13355276782922-2.13355276782922
1853.978677330715361.02132266928464
1954.531511308814940.468488691185063
2054.785100575587910.214899424412095
2134.90142395434171-1.90142395434171
2263.872198029621152.12780197037885
2365.023960605024070.976039394975933
2445.55228310068001-1.55228310068001
2564.712044391118471.28795560888153
2655.40920469538584-0.409204695385836
2745.18770539216795-1.18770539216795
2854.544809746639560.455190253360438
2954.791200672960290.208799327039705
3044.90422211668554-0.904222116685544
3134.41477375243547-1.41477375243547
3223.64896777828864-1.64896777828864
3332.756394408436930.243605591563068
3422.88825621109861-0.888256211098612
35-12.40745006675125-3.40745006675125
3600.563023978669613-0.563023978669613
37-20.258263499680747-2.25826349968075
381-0.9641168818298511.96411688182985
39-20.0990442345243732-2.09904423452437
40-2-1.03715200323453-0.962847996765467
41-2-1.55833409814475-0.441665901855251
42-6-1.79740439870373-4.20259560129627
43-4-4.072236549678820.0722365496788226
44-2-4.033135469947482.03313546994748
450-2.932615131302992.93261513130299
46-5-1.34521348241096-3.65478651758904
47-4-3.32352085811883-0.676479141881171
48-5-3.68969373017453-1.31030626982547
49-1-4.398952272515333.39895227251533
50-2-2.559125974033780.559125974033785
51-4-2.25647545448701-1.74352454551299
52-1-3.200231663369882.20023166336988
531-2.009263461270353.00926346127035
541-0.3803726704598071.38037267045981
55-20.366812266896708-2.36681226689671
561-0.9143247138773111.91432471387731
5710.1218842911459410.878115708854059
5830.5972014608877452.40279853911225
5931.897817529538891.10218247046111
6012.49442028600509-1.49442028600509
6111.68550226576417-0.685502265764171
6201.31444524727645-1.31444524727645
6320.6029463087921991.3970536912078
6421.359160552298680.640839447701317
65-11.70604193645909-2.70604193645909
6610.2412825870119720.758717412988028
6700.651970392433329-0.651970392433329
6810.2990639148903260.700936085109674
6910.678475139157130.32152486084287
7030.8525140332533292.14748596674667
7122.0149314020376-0.0149314020375995
7202.00684915082033-2.00684915082033







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
730.920557391262255-2.439513944507274.28062872703178
740.920557391262255-2.900180933696024.74129571622053
750.920557391262255-3.310991180377915.15210596290242
760.920557391262255-3.685304664910825.52641944743533
770.920557391262255-4.031404568086775.87251935061128
780.920557391262255-4.354846784076816.19596156660132
790.920557391262255-4.65957264123076.50068742375521
800.920557391262255-4.948498166991966.78961294951647
810.920557391262255-5.223852679055297.0649674615798
820.920557391262255-5.487385888649387.32850067117389
830.920557391262255-5.740501011492497.581615794017
840.920557391262255-5.984343839838357.82545862236286

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 0.920557391262255 & -2.43951394450727 & 4.28062872703178 \tabularnewline
74 & 0.920557391262255 & -2.90018093369602 & 4.74129571622053 \tabularnewline
75 & 0.920557391262255 & -3.31099118037791 & 5.15210596290242 \tabularnewline
76 & 0.920557391262255 & -3.68530466491082 & 5.52641944743533 \tabularnewline
77 & 0.920557391262255 & -4.03140456808677 & 5.87251935061128 \tabularnewline
78 & 0.920557391262255 & -4.35484678407681 & 6.19596156660132 \tabularnewline
79 & 0.920557391262255 & -4.6595726412307 & 6.50068742375521 \tabularnewline
80 & 0.920557391262255 & -4.94849816699196 & 6.78961294951647 \tabularnewline
81 & 0.920557391262255 & -5.22385267905529 & 7.0649674615798 \tabularnewline
82 & 0.920557391262255 & -5.48738588864938 & 7.32850067117389 \tabularnewline
83 & 0.920557391262255 & -5.74050101149249 & 7.581615794017 \tabularnewline
84 & 0.920557391262255 & -5.98434383983835 & 7.82545862236286 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157560&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]0.920557391262255[/C][C]-2.43951394450727[/C][C]4.28062872703178[/C][/ROW]
[ROW][C]74[/C][C]0.920557391262255[/C][C]-2.90018093369602[/C][C]4.74129571622053[/C][/ROW]
[ROW][C]75[/C][C]0.920557391262255[/C][C]-3.31099118037791[/C][C]5.15210596290242[/C][/ROW]
[ROW][C]76[/C][C]0.920557391262255[/C][C]-3.68530466491082[/C][C]5.52641944743533[/C][/ROW]
[ROW][C]77[/C][C]0.920557391262255[/C][C]-4.03140456808677[/C][C]5.87251935061128[/C][/ROW]
[ROW][C]78[/C][C]0.920557391262255[/C][C]-4.35484678407681[/C][C]6.19596156660132[/C][/ROW]
[ROW][C]79[/C][C]0.920557391262255[/C][C]-4.6595726412307[/C][C]6.50068742375521[/C][/ROW]
[ROW][C]80[/C][C]0.920557391262255[/C][C]-4.94849816699196[/C][C]6.78961294951647[/C][/ROW]
[ROW][C]81[/C][C]0.920557391262255[/C][C]-5.22385267905529[/C][C]7.0649674615798[/C][/ROW]
[ROW][C]82[/C][C]0.920557391262255[/C][C]-5.48738588864938[/C][C]7.32850067117389[/C][/ROW]
[ROW][C]83[/C][C]0.920557391262255[/C][C]-5.74050101149249[/C][C]7.581615794017[/C][/ROW]
[ROW][C]84[/C][C]0.920557391262255[/C][C]-5.98434383983835[/C][C]7.82545862236286[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157560&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157560&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
730.920557391262255-2.439513944507274.28062872703178
740.920557391262255-2.900180933696024.74129571622053
750.920557391262255-3.310991180377915.15210596290242
760.920557391262255-3.685304664910825.52641944743533
770.920557391262255-4.031404568086775.87251935061128
780.920557391262255-4.354846784076816.19596156660132
790.920557391262255-4.65957264123076.50068742375521
800.920557391262255-4.948498166991966.78961294951647
810.920557391262255-5.223852679055297.0649674615798
820.920557391262255-5.487385888649387.32850067117389
830.920557391262255-5.740501011492497.581615794017
840.920557391262255-5.984343839838357.82545862236286



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')