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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 07 Dec 2010 13:27:14 +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/2010/Dec/07/t1291728779yl68l164sx6axsg.htm/, Retrieved Fri, 03 May 2024 20:35:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=106295, Retrieved Fri, 03 May 2024 20:35:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsExponential Smoothing
Estimated Impact159
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Workshop 5] [2010-12-07 13:27:14] [0b94335bf72158573fe52322b9537409] [Current]
-    D    [Exponential Smoothing] [] [2010-12-09 18:58:12] [94f4aa1c01e87d8321fffb341ed4df07]
- R  D    [Exponential Smoothing] [Exponential Smoot...] [2011-12-22 12:22:45] [74be16979710d4c4e7c6647856088456]
-    D    [Exponential Smoothing] [Berekening 6] [2012-08-11 13:16:22] [eb6e95800005ec22b7fd76eead8d8a59]
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Post a new message
Dataseries X:
-5
-1
-2
-5
-4
-6
-2
-2
-2
-2
2
1
-8
-1
1
-1
2
2
1
-1
-2
-2
-1
-8
-4
-6
-3
-3
-7
-9
-11
-13
-11
-9
-17
-22
-25
-20
-24
-24
-22
-19
-18
-17
-11
-11
-12
-10
-15
-15
-15
-13
-8
-13
-9
-7
-4
-4
-2
0




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106295&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106295&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106295&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' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.81736044436888
beta0.186444348831529
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.81736044436888 \tabularnewline
beta & 0.186444348831529 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106295&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]0.81736044436888[/C][/ROW]
[ROW][C]beta[/C][C]0.186444348831529[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106295&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106295&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
alpha0.81736044436888
beta0.186444348831529
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3-23-5
4-52.15123659910057-7.15123659910057
5-4-1.54565543853273-2.45434456146727
6-6-1.77751676830599-4.22248323169401
7-2-4.098058367633912.09805836763391
8-2-0.93271147117745-1.06728852882255
9-2-0.517240405753006-1.48275959424699
10-2-0.667320004723815-1.33267999527618
112-0.8978205600898792.89782056008988
1212.77112805251206-1.77112805251206
13-82.3539565885523-10.3539565885523
14-1-6.656342015586795.65634201558679
151-1.718473231901292.71847323190129
16-11.23237203105538-2.23237203105538
172-0.2036039550942692.20360395509427
1822.32202349556383-0.322023495563832
1912.73422909036914-1.73422909036914
20-11.72787064417432-2.72787064417432
21-2-0.506357410451018-1.49364258954898
22-2-1.95939580761916-0.0406041923808396
23-1-2.230965858453121.23096585845312
24-8-1.27561520811459-6.72438479188541
25-4-7.847397533335963.84739753333596
26-6-5.1919096472845-0.808090352715497
27-3-6.464780104117623.46478010411762
28-3-3.717169678962990.71716967896299
29-7-3.10605624103229-3.89394375896771
30-9-6.85729132731534-2.14270867268466
31-11-9.50366829060175-1.49633170939825
32-13-11.8497516266567-1.15024837334333
33-11-14.08824905471683.08824905471684
34-9-12.39174116333193.39174116333187
35-17-9.9302958080145-7.0697041919855
36-22-17.0969901053992-4.90300989460079
37-25-23.2398948291037-1.76010517089627
38-20-27.08213991348757.08213991348746
39-24-22.6178204907380-1.38217950926195
40-24-25.28253437835581.28253437835582
41-22-25.57376825725233.57376825725229
42-19-23.44762365974784.44762365974783
43-18-19.92944090859061.92944090859057
44-17-18.17548931599591.17548931599592
45-11-16.85865248712055.85865248712049
46-11-10.8211701762907-0.178829823709291
47-12-9.74573936657476-2.25426063342524
48-10-10.71021542377350.710215423773509
49-15-9.14341469720308-5.85658530279692
50-15-13.8365552590952-1.16344474090476
51-15-14.8710083111426-0.128991688857363
52-13-15.07959768875582.07959768875584
53-8-13.16605892987785.16605892987782
54-13-7.94250156877353-5.05749843122647
55-9-11.84599908891742.84599908891743
56-7-8.855782199651961.85578219965196
57-4-6.392122628434852.39212262843485
58-4-3.12553869033348-0.87446130966652
59-2-2.662192365557190.662192365557194
600-0.841933134834740.84193313483474

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & -2 & 3 & -5 \tabularnewline
4 & -5 & 2.15123659910057 & -7.15123659910057 \tabularnewline
5 & -4 & -1.54565543853273 & -2.45434456146727 \tabularnewline
6 & -6 & -1.77751676830599 & -4.22248323169401 \tabularnewline
7 & -2 & -4.09805836763391 & 2.09805836763391 \tabularnewline
8 & -2 & -0.93271147117745 & -1.06728852882255 \tabularnewline
9 & -2 & -0.517240405753006 & -1.48275959424699 \tabularnewline
10 & -2 & -0.667320004723815 & -1.33267999527618 \tabularnewline
11 & 2 & -0.897820560089879 & 2.89782056008988 \tabularnewline
12 & 1 & 2.77112805251206 & -1.77112805251206 \tabularnewline
13 & -8 & 2.3539565885523 & -10.3539565885523 \tabularnewline
14 & -1 & -6.65634201558679 & 5.65634201558679 \tabularnewline
15 & 1 & -1.71847323190129 & 2.71847323190129 \tabularnewline
16 & -1 & 1.23237203105538 & -2.23237203105538 \tabularnewline
17 & 2 & -0.203603955094269 & 2.20360395509427 \tabularnewline
18 & 2 & 2.32202349556383 & -0.322023495563832 \tabularnewline
19 & 1 & 2.73422909036914 & -1.73422909036914 \tabularnewline
20 & -1 & 1.72787064417432 & -2.72787064417432 \tabularnewline
21 & -2 & -0.506357410451018 & -1.49364258954898 \tabularnewline
22 & -2 & -1.95939580761916 & -0.0406041923808396 \tabularnewline
23 & -1 & -2.23096585845312 & 1.23096585845312 \tabularnewline
24 & -8 & -1.27561520811459 & -6.72438479188541 \tabularnewline
25 & -4 & -7.84739753333596 & 3.84739753333596 \tabularnewline
26 & -6 & -5.1919096472845 & -0.808090352715497 \tabularnewline
27 & -3 & -6.46478010411762 & 3.46478010411762 \tabularnewline
28 & -3 & -3.71716967896299 & 0.71716967896299 \tabularnewline
29 & -7 & -3.10605624103229 & -3.89394375896771 \tabularnewline
30 & -9 & -6.85729132731534 & -2.14270867268466 \tabularnewline
31 & -11 & -9.50366829060175 & -1.49633170939825 \tabularnewline
32 & -13 & -11.8497516266567 & -1.15024837334333 \tabularnewline
33 & -11 & -14.0882490547168 & 3.08824905471684 \tabularnewline
34 & -9 & -12.3917411633319 & 3.39174116333187 \tabularnewline
35 & -17 & -9.9302958080145 & -7.0697041919855 \tabularnewline
36 & -22 & -17.0969901053992 & -4.90300989460079 \tabularnewline
37 & -25 & -23.2398948291037 & -1.76010517089627 \tabularnewline
38 & -20 & -27.0821399134875 & 7.08213991348746 \tabularnewline
39 & -24 & -22.6178204907380 & -1.38217950926195 \tabularnewline
40 & -24 & -25.2825343783558 & 1.28253437835582 \tabularnewline
41 & -22 & -25.5737682572523 & 3.57376825725229 \tabularnewline
42 & -19 & -23.4476236597478 & 4.44762365974783 \tabularnewline
43 & -18 & -19.9294409085906 & 1.92944090859057 \tabularnewline
44 & -17 & -18.1754893159959 & 1.17548931599592 \tabularnewline
45 & -11 & -16.8586524871205 & 5.85865248712049 \tabularnewline
46 & -11 & -10.8211701762907 & -0.178829823709291 \tabularnewline
47 & -12 & -9.74573936657476 & -2.25426063342524 \tabularnewline
48 & -10 & -10.7102154237735 & 0.710215423773509 \tabularnewline
49 & -15 & -9.14341469720308 & -5.85658530279692 \tabularnewline
50 & -15 & -13.8365552590952 & -1.16344474090476 \tabularnewline
51 & -15 & -14.8710083111426 & -0.128991688857363 \tabularnewline
52 & -13 & -15.0795976887558 & 2.07959768875584 \tabularnewline
53 & -8 & -13.1660589298778 & 5.16605892987782 \tabularnewline
54 & -13 & -7.94250156877353 & -5.05749843122647 \tabularnewline
55 & -9 & -11.8459990889174 & 2.84599908891743 \tabularnewline
56 & -7 & -8.85578219965196 & 1.85578219965196 \tabularnewline
57 & -4 & -6.39212262843485 & 2.39212262843485 \tabularnewline
58 & -4 & -3.12553869033348 & -0.87446130966652 \tabularnewline
59 & -2 & -2.66219236555719 & 0.662192365557194 \tabularnewline
60 & 0 & -0.84193313483474 & 0.84193313483474 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106295&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]-2[/C][C]3[/C][C]-5[/C][/ROW]
[ROW][C]4[/C][C]-5[/C][C]2.15123659910057[/C][C]-7.15123659910057[/C][/ROW]
[ROW][C]5[/C][C]-4[/C][C]-1.54565543853273[/C][C]-2.45434456146727[/C][/ROW]
[ROW][C]6[/C][C]-6[/C][C]-1.77751676830599[/C][C]-4.22248323169401[/C][/ROW]
[ROW][C]7[/C][C]-2[/C][C]-4.09805836763391[/C][C]2.09805836763391[/C][/ROW]
[ROW][C]8[/C][C]-2[/C][C]-0.93271147117745[/C][C]-1.06728852882255[/C][/ROW]
[ROW][C]9[/C][C]-2[/C][C]-0.517240405753006[/C][C]-1.48275959424699[/C][/ROW]
[ROW][C]10[/C][C]-2[/C][C]-0.667320004723815[/C][C]-1.33267999527618[/C][/ROW]
[ROW][C]11[/C][C]2[/C][C]-0.897820560089879[/C][C]2.89782056008988[/C][/ROW]
[ROW][C]12[/C][C]1[/C][C]2.77112805251206[/C][C]-1.77112805251206[/C][/ROW]
[ROW][C]13[/C][C]-8[/C][C]2.3539565885523[/C][C]-10.3539565885523[/C][/ROW]
[ROW][C]14[/C][C]-1[/C][C]-6.65634201558679[/C][C]5.65634201558679[/C][/ROW]
[ROW][C]15[/C][C]1[/C][C]-1.71847323190129[/C][C]2.71847323190129[/C][/ROW]
[ROW][C]16[/C][C]-1[/C][C]1.23237203105538[/C][C]-2.23237203105538[/C][/ROW]
[ROW][C]17[/C][C]2[/C][C]-0.203603955094269[/C][C]2.20360395509427[/C][/ROW]
[ROW][C]18[/C][C]2[/C][C]2.32202349556383[/C][C]-0.322023495563832[/C][/ROW]
[ROW][C]19[/C][C]1[/C][C]2.73422909036914[/C][C]-1.73422909036914[/C][/ROW]
[ROW][C]20[/C][C]-1[/C][C]1.72787064417432[/C][C]-2.72787064417432[/C][/ROW]
[ROW][C]21[/C][C]-2[/C][C]-0.506357410451018[/C][C]-1.49364258954898[/C][/ROW]
[ROW][C]22[/C][C]-2[/C][C]-1.95939580761916[/C][C]-0.0406041923808396[/C][/ROW]
[ROW][C]23[/C][C]-1[/C][C]-2.23096585845312[/C][C]1.23096585845312[/C][/ROW]
[ROW][C]24[/C][C]-8[/C][C]-1.27561520811459[/C][C]-6.72438479188541[/C][/ROW]
[ROW][C]25[/C][C]-4[/C][C]-7.84739753333596[/C][C]3.84739753333596[/C][/ROW]
[ROW][C]26[/C][C]-6[/C][C]-5.1919096472845[/C][C]-0.808090352715497[/C][/ROW]
[ROW][C]27[/C][C]-3[/C][C]-6.46478010411762[/C][C]3.46478010411762[/C][/ROW]
[ROW][C]28[/C][C]-3[/C][C]-3.71716967896299[/C][C]0.71716967896299[/C][/ROW]
[ROW][C]29[/C][C]-7[/C][C]-3.10605624103229[/C][C]-3.89394375896771[/C][/ROW]
[ROW][C]30[/C][C]-9[/C][C]-6.85729132731534[/C][C]-2.14270867268466[/C][/ROW]
[ROW][C]31[/C][C]-11[/C][C]-9.50366829060175[/C][C]-1.49633170939825[/C][/ROW]
[ROW][C]32[/C][C]-13[/C][C]-11.8497516266567[/C][C]-1.15024837334333[/C][/ROW]
[ROW][C]33[/C][C]-11[/C][C]-14.0882490547168[/C][C]3.08824905471684[/C][/ROW]
[ROW][C]34[/C][C]-9[/C][C]-12.3917411633319[/C][C]3.39174116333187[/C][/ROW]
[ROW][C]35[/C][C]-17[/C][C]-9.9302958080145[/C][C]-7.0697041919855[/C][/ROW]
[ROW][C]36[/C][C]-22[/C][C]-17.0969901053992[/C][C]-4.90300989460079[/C][/ROW]
[ROW][C]37[/C][C]-25[/C][C]-23.2398948291037[/C][C]-1.76010517089627[/C][/ROW]
[ROW][C]38[/C][C]-20[/C][C]-27.0821399134875[/C][C]7.08213991348746[/C][/ROW]
[ROW][C]39[/C][C]-24[/C][C]-22.6178204907380[/C][C]-1.38217950926195[/C][/ROW]
[ROW][C]40[/C][C]-24[/C][C]-25.2825343783558[/C][C]1.28253437835582[/C][/ROW]
[ROW][C]41[/C][C]-22[/C][C]-25.5737682572523[/C][C]3.57376825725229[/C][/ROW]
[ROW][C]42[/C][C]-19[/C][C]-23.4476236597478[/C][C]4.44762365974783[/C][/ROW]
[ROW][C]43[/C][C]-18[/C][C]-19.9294409085906[/C][C]1.92944090859057[/C][/ROW]
[ROW][C]44[/C][C]-17[/C][C]-18.1754893159959[/C][C]1.17548931599592[/C][/ROW]
[ROW][C]45[/C][C]-11[/C][C]-16.8586524871205[/C][C]5.85865248712049[/C][/ROW]
[ROW][C]46[/C][C]-11[/C][C]-10.8211701762907[/C][C]-0.178829823709291[/C][/ROW]
[ROW][C]47[/C][C]-12[/C][C]-9.74573936657476[/C][C]-2.25426063342524[/C][/ROW]
[ROW][C]48[/C][C]-10[/C][C]-10.7102154237735[/C][C]0.710215423773509[/C][/ROW]
[ROW][C]49[/C][C]-15[/C][C]-9.14341469720308[/C][C]-5.85658530279692[/C][/ROW]
[ROW][C]50[/C][C]-15[/C][C]-13.8365552590952[/C][C]-1.16344474090476[/C][/ROW]
[ROW][C]51[/C][C]-15[/C][C]-14.8710083111426[/C][C]-0.128991688857363[/C][/ROW]
[ROW][C]52[/C][C]-13[/C][C]-15.0795976887558[/C][C]2.07959768875584[/C][/ROW]
[ROW][C]53[/C][C]-8[/C][C]-13.1660589298778[/C][C]5.16605892987782[/C][/ROW]
[ROW][C]54[/C][C]-13[/C][C]-7.94250156877353[/C][C]-5.05749843122647[/C][/ROW]
[ROW][C]55[/C][C]-9[/C][C]-11.8459990889174[/C][C]2.84599908891743[/C][/ROW]
[ROW][C]56[/C][C]-7[/C][C]-8.85578219965196[/C][C]1.85578219965196[/C][/ROW]
[ROW][C]57[/C][C]-4[/C][C]-6.39212262843485[/C][C]2.39212262843485[/C][/ROW]
[ROW][C]58[/C][C]-4[/C][C]-3.12553869033348[/C][C]-0.87446130966652[/C][/ROW]
[ROW][C]59[/C][C]-2[/C][C]-2.66219236555719[/C][C]0.662192365557194[/C][/ROW]
[ROW][C]60[/C][C]0[/C][C]-0.84193313483474[/C][C]0.84193313483474[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106295&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106295&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
3-23-5
4-52.15123659910057-7.15123659910057
5-4-1.54565543853273-2.45434456146727
6-6-1.77751676830599-4.22248323169401
7-2-4.098058367633912.09805836763391
8-2-0.93271147117745-1.06728852882255
9-2-0.517240405753006-1.48275959424699
10-2-0.667320004723815-1.33267999527618
112-0.8978205600898792.89782056008988
1212.77112805251206-1.77112805251206
13-82.3539565885523-10.3539565885523
14-1-6.656342015586795.65634201558679
151-1.718473231901292.71847323190129
16-11.23237203105538-2.23237203105538
172-0.2036039550942692.20360395509427
1822.32202349556383-0.322023495563832
1912.73422909036914-1.73422909036914
20-11.72787064417432-2.72787064417432
21-2-0.506357410451018-1.49364258954898
22-2-1.95939580761916-0.0406041923808396
23-1-2.230965858453121.23096585845312
24-8-1.27561520811459-6.72438479188541
25-4-7.847397533335963.84739753333596
26-6-5.1919096472845-0.808090352715497
27-3-6.464780104117623.46478010411762
28-3-3.717169678962990.71716967896299
29-7-3.10605624103229-3.89394375896771
30-9-6.85729132731534-2.14270867268466
31-11-9.50366829060175-1.49633170939825
32-13-11.8497516266567-1.15024837334333
33-11-14.08824905471683.08824905471684
34-9-12.39174116333193.39174116333187
35-17-9.9302958080145-7.0697041919855
36-22-17.0969901053992-4.90300989460079
37-25-23.2398948291037-1.76010517089627
38-20-27.08213991348757.08213991348746
39-24-22.6178204907380-1.38217950926195
40-24-25.28253437835581.28253437835582
41-22-25.57376825725233.57376825725229
42-19-23.44762365974784.44762365974783
43-18-19.92944090859061.92944090859057
44-17-18.17548931599591.17548931599592
45-11-16.85865248712055.85865248712049
46-11-10.8211701762907-0.178829823709291
47-12-9.74573936657476-2.25426063342524
48-10-10.71021542377350.710215423773509
49-15-9.14341469720308-5.85658530279692
50-15-13.8365552590952-1.16344474090476
51-15-14.8710083111426-0.128991688857363
52-13-15.07959768875582.07959768875584
53-8-13.16605892987785.16605892987782
54-13-7.94250156877353-5.05749843122647
55-9-11.84599908891742.84599908891743
56-7-8.855782199651961.85578219965196
57-4-6.392122628434852.39212262843485
58-4-3.12553869033348-0.87446130966652
59-2-2.662192365557190.662192365557194
600-0.841933134834740.84193313483474







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
611.25354316375645-5.732634520719788.23972084823267
622.66085662113023-7.070816826407812.3925300686683
634.06817007850401-8.4283609386460816.5647010956541
645.47548353587779-9.8688004216321120.8197674933877
656.88279699325157-11.415390611487125.1809845979902
668.29011045062535-13.077155617393929.6573765186446
679.69742390799913-14.857069212182334.2519170281806
6811.1047373653729-16.755266269428238.964741000174
6912.5120508227467-18.770483969980643.794585615474
7013.9193642801205-20.900767646404748.7394962066457
7115.3266777374943-23.143837321558453.7971927965469
7216.7339911948680-25.497285378935858.9652677686719

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 1.25354316375645 & -5.73263452071978 & 8.23972084823267 \tabularnewline
62 & 2.66085662113023 & -7.0708168264078 & 12.3925300686683 \tabularnewline
63 & 4.06817007850401 & -8.42836093864608 & 16.5647010956541 \tabularnewline
64 & 5.47548353587779 & -9.86880042163211 & 20.8197674933877 \tabularnewline
65 & 6.88279699325157 & -11.4153906114871 & 25.1809845979902 \tabularnewline
66 & 8.29011045062535 & -13.0771556173939 & 29.6573765186446 \tabularnewline
67 & 9.69742390799913 & -14.8570692121823 & 34.2519170281806 \tabularnewline
68 & 11.1047373653729 & -16.7552662694282 & 38.964741000174 \tabularnewline
69 & 12.5120508227467 & -18.7704839699806 & 43.794585615474 \tabularnewline
70 & 13.9193642801205 & -20.9007676464047 & 48.7394962066457 \tabularnewline
71 & 15.3266777374943 & -23.1438373215584 & 53.7971927965469 \tabularnewline
72 & 16.7339911948680 & -25.4972853789358 & 58.9652677686719 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106295&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]61[/C][C]1.25354316375645[/C][C]-5.73263452071978[/C][C]8.23972084823267[/C][/ROW]
[ROW][C]62[/C][C]2.66085662113023[/C][C]-7.0708168264078[/C][C]12.3925300686683[/C][/ROW]
[ROW][C]63[/C][C]4.06817007850401[/C][C]-8.42836093864608[/C][C]16.5647010956541[/C][/ROW]
[ROW][C]64[/C][C]5.47548353587779[/C][C]-9.86880042163211[/C][C]20.8197674933877[/C][/ROW]
[ROW][C]65[/C][C]6.88279699325157[/C][C]-11.4153906114871[/C][C]25.1809845979902[/C][/ROW]
[ROW][C]66[/C][C]8.29011045062535[/C][C]-13.0771556173939[/C][C]29.6573765186446[/C][/ROW]
[ROW][C]67[/C][C]9.69742390799913[/C][C]-14.8570692121823[/C][C]34.2519170281806[/C][/ROW]
[ROW][C]68[/C][C]11.1047373653729[/C][C]-16.7552662694282[/C][C]38.964741000174[/C][/ROW]
[ROW][C]69[/C][C]12.5120508227467[/C][C]-18.7704839699806[/C][C]43.794585615474[/C][/ROW]
[ROW][C]70[/C][C]13.9193642801205[/C][C]-20.9007676464047[/C][C]48.7394962066457[/C][/ROW]
[ROW][C]71[/C][C]15.3266777374943[/C][C]-23.1438373215584[/C][C]53.7971927965469[/C][/ROW]
[ROW][C]72[/C][C]16.7339911948680[/C][C]-25.4972853789358[/C][C]58.9652677686719[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106295&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106295&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
611.25354316375645-5.732634520719788.23972084823267
622.66085662113023-7.070816826407812.3925300686683
634.06817007850401-8.4283609386460816.5647010956541
645.47548353587779-9.8688004216321120.8197674933877
656.88279699325157-11.415390611487125.1809845979902
668.29011045062535-13.077155617393929.6573765186446
679.69742390799913-14.857069212182334.2519170281806
6811.1047373653729-16.755266269428238.964741000174
6912.5120508227467-18.770483969980643.794585615474
7013.9193642801205-20.900767646404748.7394962066457
7115.3266777374943-23.143837321558453.7971927965469
7216.7339911948680-25.497285378935858.9652677686719



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')