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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 27 May 2012 16:34:43 -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/2012/May/27/t1338150995d7hst0v75z0gg9y.htm/, Retrieved Wed, 08 May 2024 19:31:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167746, Retrieved Wed, 08 May 2024 19:31:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact96
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-05-27 20:34:43] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
9,24
9,29
9,39
9,42
9,42
9,43
9,5
9,53
9,58
9,58
9,6
9,61
9,65
9,71
9,78
9,79
9,84
9,87
9,9
9,95
9,96
9,98
10,01
10
10,03
10,05
10,06
10,09
10,24
10,23
10,27
10,28
10,29
10,44
10,51
10,52
10,57
10,62
10,71
10,73
10,74
10,75
10,79
10,81
10,87
10,92
10,95
10,94
10,97
10,99
11,04
11,09
11,12
11,11
11,14
11,2
11,25
11,3
11,31
11,31




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167746&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167746&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167746&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0475528658390805
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0475528658390805 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167746&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0475528658390805[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167746&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167746&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0475528658390805
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
39.399.340.0500000000000025
49.429.44237764329195-0.0223776432919536
59.429.4713135222227-0.0513135222226957
69.439.46887341718471-0.0388734171847105
79.59.477024874792620.0229751252073811
89.539.54811740783924-0.0181174078392417
99.589.577255873174910.00274412682509073
109.589.62738636426967-0.0473863642696681
119.69.62513300684695-0.0251330068469517
129.619.64393786034423-0.033937860344226
139.659.65232401782441-0.00232401782441016
149.719.69221350411660.0177864958834011
159.789.753059302969090.0269406970309092
169.799.82434041032061-0.0343404103206115
179.849.832707425395780.00729257460422339
189.879.88305420821755-0.0130542082175538
199.99.91243344320555-0.0124334432055466
209.959.941842197348880.00815780265112132
219.969.99223012424389-0.0322301242438865
229.9810.0006974894697-0.0206974894697414
2310.0110.0197132645298-0.00971326452978083
241010.0492513709647-0.0492513709647362
2510.0310.0369093271289-0.00690932712886116
2610.0510.0665807688229-0.0165807688228607
2710.0610.0857923057475-0.0257923057475207
2810.0910.0945658076926-0.00456580769262871
2910.2410.1243486904520.115651309548026
3010.2310.279848241659-0.0498482416590242
3110.2710.26747781491110.00252218508889968
3210.2810.3075977520403-0.0275977520402524
3310.2910.31628539984-0.0262853998400221
3410.4410.32503545374790.114964546252097
3510.5110.48050234739210.0294976526079207
3610.5210.5519050453091-0.031905045309113
3710.5710.56038786896990.00961213103006209
3810.6210.61084495334720.00915504665275968
3910.7110.66128030205250.0487196979475346
4010.7310.7535970633127-0.0235970633126872
4110.7410.7724749553268-0.0324749553267836
4210.7510.780930678133-0.0309306781329983
4310.7910.78945983574540.000540164254571707
4410.8110.8294855221038-0.0194855221037553
4510.8710.84855892968540.0214410703146459
4610.9210.90957851402550.0104214859745291
4710.9510.9600740855499-0.0100740855498618
4810.9410.9895950339113-0.0495950339112579
4910.9710.9772366479174-0.00723664791738976
5010.9911.0068925245699-0.016892524569851
5111.0411.02608923661530.0139107633847022
5211.0911.07675073328020.0132492667197521
5311.1211.127380773883-0.0073807738830407
5411.1111.1570297969328-0.0470297969327902
5511.1411.1447933953088-0.00479339530880551
5611.211.17456545562480.0254345443752246
5711.2511.23577494110110.0142250588988748
5811.311.28645138341850.0135486165815024
5911.3111.3370956589651-0.0270956589651039
6011.3111.3458071827295-0.0358071827295134

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 9.39 & 9.34 & 0.0500000000000025 \tabularnewline
4 & 9.42 & 9.44237764329195 & -0.0223776432919536 \tabularnewline
5 & 9.42 & 9.4713135222227 & -0.0513135222226957 \tabularnewline
6 & 9.43 & 9.46887341718471 & -0.0388734171847105 \tabularnewline
7 & 9.5 & 9.47702487479262 & 0.0229751252073811 \tabularnewline
8 & 9.53 & 9.54811740783924 & -0.0181174078392417 \tabularnewline
9 & 9.58 & 9.57725587317491 & 0.00274412682509073 \tabularnewline
10 & 9.58 & 9.62738636426967 & -0.0473863642696681 \tabularnewline
11 & 9.6 & 9.62513300684695 & -0.0251330068469517 \tabularnewline
12 & 9.61 & 9.64393786034423 & -0.033937860344226 \tabularnewline
13 & 9.65 & 9.65232401782441 & -0.00232401782441016 \tabularnewline
14 & 9.71 & 9.6922135041166 & 0.0177864958834011 \tabularnewline
15 & 9.78 & 9.75305930296909 & 0.0269406970309092 \tabularnewline
16 & 9.79 & 9.82434041032061 & -0.0343404103206115 \tabularnewline
17 & 9.84 & 9.83270742539578 & 0.00729257460422339 \tabularnewline
18 & 9.87 & 9.88305420821755 & -0.0130542082175538 \tabularnewline
19 & 9.9 & 9.91243344320555 & -0.0124334432055466 \tabularnewline
20 & 9.95 & 9.94184219734888 & 0.00815780265112132 \tabularnewline
21 & 9.96 & 9.99223012424389 & -0.0322301242438865 \tabularnewline
22 & 9.98 & 10.0006974894697 & -0.0206974894697414 \tabularnewline
23 & 10.01 & 10.0197132645298 & -0.00971326452978083 \tabularnewline
24 & 10 & 10.0492513709647 & -0.0492513709647362 \tabularnewline
25 & 10.03 & 10.0369093271289 & -0.00690932712886116 \tabularnewline
26 & 10.05 & 10.0665807688229 & -0.0165807688228607 \tabularnewline
27 & 10.06 & 10.0857923057475 & -0.0257923057475207 \tabularnewline
28 & 10.09 & 10.0945658076926 & -0.00456580769262871 \tabularnewline
29 & 10.24 & 10.124348690452 & 0.115651309548026 \tabularnewline
30 & 10.23 & 10.279848241659 & -0.0498482416590242 \tabularnewline
31 & 10.27 & 10.2674778149111 & 0.00252218508889968 \tabularnewline
32 & 10.28 & 10.3075977520403 & -0.0275977520402524 \tabularnewline
33 & 10.29 & 10.31628539984 & -0.0262853998400221 \tabularnewline
34 & 10.44 & 10.3250354537479 & 0.114964546252097 \tabularnewline
35 & 10.51 & 10.4805023473921 & 0.0294976526079207 \tabularnewline
36 & 10.52 & 10.5519050453091 & -0.031905045309113 \tabularnewline
37 & 10.57 & 10.5603878689699 & 0.00961213103006209 \tabularnewline
38 & 10.62 & 10.6108449533472 & 0.00915504665275968 \tabularnewline
39 & 10.71 & 10.6612803020525 & 0.0487196979475346 \tabularnewline
40 & 10.73 & 10.7535970633127 & -0.0235970633126872 \tabularnewline
41 & 10.74 & 10.7724749553268 & -0.0324749553267836 \tabularnewline
42 & 10.75 & 10.780930678133 & -0.0309306781329983 \tabularnewline
43 & 10.79 & 10.7894598357454 & 0.000540164254571707 \tabularnewline
44 & 10.81 & 10.8294855221038 & -0.0194855221037553 \tabularnewline
45 & 10.87 & 10.8485589296854 & 0.0214410703146459 \tabularnewline
46 & 10.92 & 10.9095785140255 & 0.0104214859745291 \tabularnewline
47 & 10.95 & 10.9600740855499 & -0.0100740855498618 \tabularnewline
48 & 10.94 & 10.9895950339113 & -0.0495950339112579 \tabularnewline
49 & 10.97 & 10.9772366479174 & -0.00723664791738976 \tabularnewline
50 & 10.99 & 11.0068925245699 & -0.016892524569851 \tabularnewline
51 & 11.04 & 11.0260892366153 & 0.0139107633847022 \tabularnewline
52 & 11.09 & 11.0767507332802 & 0.0132492667197521 \tabularnewline
53 & 11.12 & 11.127380773883 & -0.0073807738830407 \tabularnewline
54 & 11.11 & 11.1570297969328 & -0.0470297969327902 \tabularnewline
55 & 11.14 & 11.1447933953088 & -0.00479339530880551 \tabularnewline
56 & 11.2 & 11.1745654556248 & 0.0254345443752246 \tabularnewline
57 & 11.25 & 11.2357749411011 & 0.0142250588988748 \tabularnewline
58 & 11.3 & 11.2864513834185 & 0.0135486165815024 \tabularnewline
59 & 11.31 & 11.3370956589651 & -0.0270956589651039 \tabularnewline
60 & 11.31 & 11.3458071827295 & -0.0358071827295134 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167746&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]9.39[/C][C]9.34[/C][C]0.0500000000000025[/C][/ROW]
[ROW][C]4[/C][C]9.42[/C][C]9.44237764329195[/C][C]-0.0223776432919536[/C][/ROW]
[ROW][C]5[/C][C]9.42[/C][C]9.4713135222227[/C][C]-0.0513135222226957[/C][/ROW]
[ROW][C]6[/C][C]9.43[/C][C]9.46887341718471[/C][C]-0.0388734171847105[/C][/ROW]
[ROW][C]7[/C][C]9.5[/C][C]9.47702487479262[/C][C]0.0229751252073811[/C][/ROW]
[ROW][C]8[/C][C]9.53[/C][C]9.54811740783924[/C][C]-0.0181174078392417[/C][/ROW]
[ROW][C]9[/C][C]9.58[/C][C]9.57725587317491[/C][C]0.00274412682509073[/C][/ROW]
[ROW][C]10[/C][C]9.58[/C][C]9.62738636426967[/C][C]-0.0473863642696681[/C][/ROW]
[ROW][C]11[/C][C]9.6[/C][C]9.62513300684695[/C][C]-0.0251330068469517[/C][/ROW]
[ROW][C]12[/C][C]9.61[/C][C]9.64393786034423[/C][C]-0.033937860344226[/C][/ROW]
[ROW][C]13[/C][C]9.65[/C][C]9.65232401782441[/C][C]-0.00232401782441016[/C][/ROW]
[ROW][C]14[/C][C]9.71[/C][C]9.6922135041166[/C][C]0.0177864958834011[/C][/ROW]
[ROW][C]15[/C][C]9.78[/C][C]9.75305930296909[/C][C]0.0269406970309092[/C][/ROW]
[ROW][C]16[/C][C]9.79[/C][C]9.82434041032061[/C][C]-0.0343404103206115[/C][/ROW]
[ROW][C]17[/C][C]9.84[/C][C]9.83270742539578[/C][C]0.00729257460422339[/C][/ROW]
[ROW][C]18[/C][C]9.87[/C][C]9.88305420821755[/C][C]-0.0130542082175538[/C][/ROW]
[ROW][C]19[/C][C]9.9[/C][C]9.91243344320555[/C][C]-0.0124334432055466[/C][/ROW]
[ROW][C]20[/C][C]9.95[/C][C]9.94184219734888[/C][C]0.00815780265112132[/C][/ROW]
[ROW][C]21[/C][C]9.96[/C][C]9.99223012424389[/C][C]-0.0322301242438865[/C][/ROW]
[ROW][C]22[/C][C]9.98[/C][C]10.0006974894697[/C][C]-0.0206974894697414[/C][/ROW]
[ROW][C]23[/C][C]10.01[/C][C]10.0197132645298[/C][C]-0.00971326452978083[/C][/ROW]
[ROW][C]24[/C][C]10[/C][C]10.0492513709647[/C][C]-0.0492513709647362[/C][/ROW]
[ROW][C]25[/C][C]10.03[/C][C]10.0369093271289[/C][C]-0.00690932712886116[/C][/ROW]
[ROW][C]26[/C][C]10.05[/C][C]10.0665807688229[/C][C]-0.0165807688228607[/C][/ROW]
[ROW][C]27[/C][C]10.06[/C][C]10.0857923057475[/C][C]-0.0257923057475207[/C][/ROW]
[ROW][C]28[/C][C]10.09[/C][C]10.0945658076926[/C][C]-0.00456580769262871[/C][/ROW]
[ROW][C]29[/C][C]10.24[/C][C]10.124348690452[/C][C]0.115651309548026[/C][/ROW]
[ROW][C]30[/C][C]10.23[/C][C]10.279848241659[/C][C]-0.0498482416590242[/C][/ROW]
[ROW][C]31[/C][C]10.27[/C][C]10.2674778149111[/C][C]0.00252218508889968[/C][/ROW]
[ROW][C]32[/C][C]10.28[/C][C]10.3075977520403[/C][C]-0.0275977520402524[/C][/ROW]
[ROW][C]33[/C][C]10.29[/C][C]10.31628539984[/C][C]-0.0262853998400221[/C][/ROW]
[ROW][C]34[/C][C]10.44[/C][C]10.3250354537479[/C][C]0.114964546252097[/C][/ROW]
[ROW][C]35[/C][C]10.51[/C][C]10.4805023473921[/C][C]0.0294976526079207[/C][/ROW]
[ROW][C]36[/C][C]10.52[/C][C]10.5519050453091[/C][C]-0.031905045309113[/C][/ROW]
[ROW][C]37[/C][C]10.57[/C][C]10.5603878689699[/C][C]0.00961213103006209[/C][/ROW]
[ROW][C]38[/C][C]10.62[/C][C]10.6108449533472[/C][C]0.00915504665275968[/C][/ROW]
[ROW][C]39[/C][C]10.71[/C][C]10.6612803020525[/C][C]0.0487196979475346[/C][/ROW]
[ROW][C]40[/C][C]10.73[/C][C]10.7535970633127[/C][C]-0.0235970633126872[/C][/ROW]
[ROW][C]41[/C][C]10.74[/C][C]10.7724749553268[/C][C]-0.0324749553267836[/C][/ROW]
[ROW][C]42[/C][C]10.75[/C][C]10.780930678133[/C][C]-0.0309306781329983[/C][/ROW]
[ROW][C]43[/C][C]10.79[/C][C]10.7894598357454[/C][C]0.000540164254571707[/C][/ROW]
[ROW][C]44[/C][C]10.81[/C][C]10.8294855221038[/C][C]-0.0194855221037553[/C][/ROW]
[ROW][C]45[/C][C]10.87[/C][C]10.8485589296854[/C][C]0.0214410703146459[/C][/ROW]
[ROW][C]46[/C][C]10.92[/C][C]10.9095785140255[/C][C]0.0104214859745291[/C][/ROW]
[ROW][C]47[/C][C]10.95[/C][C]10.9600740855499[/C][C]-0.0100740855498618[/C][/ROW]
[ROW][C]48[/C][C]10.94[/C][C]10.9895950339113[/C][C]-0.0495950339112579[/C][/ROW]
[ROW][C]49[/C][C]10.97[/C][C]10.9772366479174[/C][C]-0.00723664791738976[/C][/ROW]
[ROW][C]50[/C][C]10.99[/C][C]11.0068925245699[/C][C]-0.016892524569851[/C][/ROW]
[ROW][C]51[/C][C]11.04[/C][C]11.0260892366153[/C][C]0.0139107633847022[/C][/ROW]
[ROW][C]52[/C][C]11.09[/C][C]11.0767507332802[/C][C]0.0132492667197521[/C][/ROW]
[ROW][C]53[/C][C]11.12[/C][C]11.127380773883[/C][C]-0.0073807738830407[/C][/ROW]
[ROW][C]54[/C][C]11.11[/C][C]11.1570297969328[/C][C]-0.0470297969327902[/C][/ROW]
[ROW][C]55[/C][C]11.14[/C][C]11.1447933953088[/C][C]-0.00479339530880551[/C][/ROW]
[ROW][C]56[/C][C]11.2[/C][C]11.1745654556248[/C][C]0.0254345443752246[/C][/ROW]
[ROW][C]57[/C][C]11.25[/C][C]11.2357749411011[/C][C]0.0142250588988748[/C][/ROW]
[ROW][C]58[/C][C]11.3[/C][C]11.2864513834185[/C][C]0.0135486165815024[/C][/ROW]
[ROW][C]59[/C][C]11.31[/C][C]11.3370956589651[/C][C]-0.0270956589651039[/C][/ROW]
[ROW][C]60[/C][C]11.31[/C][C]11.3458071827295[/C][C]-0.0358071827295134[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167746&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167746&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
39.399.340.0500000000000025
49.429.44237764329195-0.0223776432919536
59.429.4713135222227-0.0513135222226957
69.439.46887341718471-0.0388734171847105
79.59.477024874792620.0229751252073811
89.539.54811740783924-0.0181174078392417
99.589.577255873174910.00274412682509073
109.589.62738636426967-0.0473863642696681
119.69.62513300684695-0.0251330068469517
129.619.64393786034423-0.033937860344226
139.659.65232401782441-0.00232401782441016
149.719.69221350411660.0177864958834011
159.789.753059302969090.0269406970309092
169.799.82434041032061-0.0343404103206115
179.849.832707425395780.00729257460422339
189.879.88305420821755-0.0130542082175538
199.99.91243344320555-0.0124334432055466
209.959.941842197348880.00815780265112132
219.969.99223012424389-0.0322301242438865
229.9810.0006974894697-0.0206974894697414
2310.0110.0197132645298-0.00971326452978083
241010.0492513709647-0.0492513709647362
2510.0310.0369093271289-0.00690932712886116
2610.0510.0665807688229-0.0165807688228607
2710.0610.0857923057475-0.0257923057475207
2810.0910.0945658076926-0.00456580769262871
2910.2410.1243486904520.115651309548026
3010.2310.279848241659-0.0498482416590242
3110.2710.26747781491110.00252218508889968
3210.2810.3075977520403-0.0275977520402524
3310.2910.31628539984-0.0262853998400221
3410.4410.32503545374790.114964546252097
3510.5110.48050234739210.0294976526079207
3610.5210.5519050453091-0.031905045309113
3710.5710.56038786896990.00961213103006209
3810.6210.61084495334720.00915504665275968
3910.7110.66128030205250.0487196979475346
4010.7310.7535970633127-0.0235970633126872
4110.7410.7724749553268-0.0324749553267836
4210.7510.780930678133-0.0309306781329983
4310.7910.78945983574540.000540164254571707
4410.8110.8294855221038-0.0194855221037553
4510.8710.84855892968540.0214410703146459
4610.9210.90957851402550.0104214859745291
4710.9510.9600740855499-0.0100740855498618
4810.9410.9895950339113-0.0495950339112579
4910.9710.9772366479174-0.00723664791738976
5010.9911.0068925245699-0.016892524569851
5111.0411.02608923661530.0139107633847022
5211.0911.07675073328020.0132492667197521
5311.1211.127380773883-0.0073807738830407
5411.1111.1570297969328-0.0470297969327902
5511.1411.1447933953088-0.00479339530880551
5611.211.17456545562480.0254345443752246
5711.2511.23577494110110.0142250588988748
5811.311.28645138341850.0135486165815024
5911.3111.3370956589651-0.0270956589651039
6011.3111.3458071827295-0.0358071827295134







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6111.344104448573111.277981913831911.4102269833143
6211.378208897146211.282448330024611.4739694642678
6311.412313345719311.292257261779111.5323694296596
6411.446417794292411.304565426409611.5882701621752
6511.480522242865511.318300935354311.6427435503767
6611.514626691438611.332928557855411.6963248250219
6711.548731140011711.348138904041711.7493233759817
6811.582835588584811.363736008008911.8019351691608
6911.616940037157911.379587707433711.8542923668821
7011.65104448573111.395600704775611.9064882666865
7111.685148934304111.411706819652811.9585910489554
7211.719253382877211.427854864726412.010651901028

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 11.3441044485731 & 11.2779819138319 & 11.4102269833143 \tabularnewline
62 & 11.3782088971462 & 11.2824483300246 & 11.4739694642678 \tabularnewline
63 & 11.4123133457193 & 11.2922572617791 & 11.5323694296596 \tabularnewline
64 & 11.4464177942924 & 11.3045654264096 & 11.5882701621752 \tabularnewline
65 & 11.4805222428655 & 11.3183009353543 & 11.6427435503767 \tabularnewline
66 & 11.5146266914386 & 11.3329285578554 & 11.6963248250219 \tabularnewline
67 & 11.5487311400117 & 11.3481389040417 & 11.7493233759817 \tabularnewline
68 & 11.5828355885848 & 11.3637360080089 & 11.8019351691608 \tabularnewline
69 & 11.6169400371579 & 11.3795877074337 & 11.8542923668821 \tabularnewline
70 & 11.651044485731 & 11.3956007047756 & 11.9064882666865 \tabularnewline
71 & 11.6851489343041 & 11.4117068196528 & 11.9585910489554 \tabularnewline
72 & 11.7192533828772 & 11.4278548647264 & 12.010651901028 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167746&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]11.3441044485731[/C][C]11.2779819138319[/C][C]11.4102269833143[/C][/ROW]
[ROW][C]62[/C][C]11.3782088971462[/C][C]11.2824483300246[/C][C]11.4739694642678[/C][/ROW]
[ROW][C]63[/C][C]11.4123133457193[/C][C]11.2922572617791[/C][C]11.5323694296596[/C][/ROW]
[ROW][C]64[/C][C]11.4464177942924[/C][C]11.3045654264096[/C][C]11.5882701621752[/C][/ROW]
[ROW][C]65[/C][C]11.4805222428655[/C][C]11.3183009353543[/C][C]11.6427435503767[/C][/ROW]
[ROW][C]66[/C][C]11.5146266914386[/C][C]11.3329285578554[/C][C]11.6963248250219[/C][/ROW]
[ROW][C]67[/C][C]11.5487311400117[/C][C]11.3481389040417[/C][C]11.7493233759817[/C][/ROW]
[ROW][C]68[/C][C]11.5828355885848[/C][C]11.3637360080089[/C][C]11.8019351691608[/C][/ROW]
[ROW][C]69[/C][C]11.6169400371579[/C][C]11.3795877074337[/C][C]11.8542923668821[/C][/ROW]
[ROW][C]70[/C][C]11.651044485731[/C][C]11.3956007047756[/C][C]11.9064882666865[/C][/ROW]
[ROW][C]71[/C][C]11.6851489343041[/C][C]11.4117068196528[/C][C]11.9585910489554[/C][/ROW]
[ROW][C]72[/C][C]11.7192533828772[/C][C]11.4278548647264[/C][C]12.010651901028[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167746&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167746&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
6111.344104448573111.277981913831911.4102269833143
6211.378208897146211.282448330024611.4739694642678
6311.412313345719311.292257261779111.5323694296596
6411.446417794292411.304565426409611.5882701621752
6511.480522242865511.318300935354311.6427435503767
6611.514626691438611.332928557855411.6963248250219
6711.548731140011711.348138904041711.7493233759817
6811.582835588584811.363736008008911.8019351691608
6911.616940037157911.379587707433711.8542923668821
7011.65104448573111.395600704775611.9064882666865
7111.685148934304111.411706819652811.9585910489554
7211.719253382877211.427854864726412.010651901028



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')