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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 28 Dec 2011 13:05:32 -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/28/t1325095613m8u6e37iqqyspos.htm/, Retrieved Fri, 03 May 2024 05:03:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160880, Retrieved Fri, 03 May 2024 05:03:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact150
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [opgave 10 oefening 2] [2011-12-28 18:05:32] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
14.5
15.1
17.4
16.2
15.6
17.2
14.9
13.8
17.5
16.2
17.5
16.6
16.2
16.6
19.6
15.9
18
18.3
16.3
14.9
18.2
18.4
18.5
16
17.4
17.2
19.6
17.2
18.3
19.3
18.1
16.2
18.4
20.5
19
16.5
18.7
19
19.2
20.5
19.3
20.6
20.1
16.1
20.4
19.7
15.6
14.4
13.7
14.1
15
14.2
13.6
15.4
14.8
12.5
16.2
16.1
16
15.8
14.9
15.4
18.6
17.1
16.8
19.5
17.3
15.8
19.3
18.8
18.5
17.3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160880&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160880&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160880&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 time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.429323441142746
beta0.102747475630242
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.429323441142746 \tabularnewline
beta & 0.102747475630242 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160880&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]0.429323441142746[/C][/ROW]
[ROW][C]beta[/C][C]0.102747475630242[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160880&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160880&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
alpha0.429323441142746
beta0.102747475630242
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
317.415.71.7
416.217.1048400796134-0.904840079613386
515.617.351447037688-1.75144703768797
617.217.1573261269840.042673873015957
714.917.7353458051005-2.83534580510051
813.816.9526916812607-3.15269168126065
917.515.89472231427131.60527768572868
1016.216.9502725772038-0.750272577203784
1117.516.96143394671630.538566053283652
1216.617.549681123929-0.949681123929007
1316.217.4570966631631-1.25709666316306
1416.617.1770785831801-0.5770785831801
1519.617.16355217269312.4364478273069
1615.918.5512796331724-2.65127963317239
171817.63777345118530.362226548814743
1818.318.03401461438230.265985385617721
1916.318.4006703108963-2.10067031089629
2014.917.6586006815025-2.75860068150248
2118.216.51237900449971.68762099550034
2218.417.34946868621571.05053131378432
2318.517.95938176551790.540618234482107
241618.3742249043233-2.37422490432332
2517.417.4329259852883-0.0329259852883332
2617.217.4953491471532-0.295349147153171
2719.617.43207948214352.16792051785646
2817.218.5219803188501-1.32198031885011
2918.318.05526985572380.244730144276168
3019.318.27198043150521.02801956849483
3118.118.8703234145072-0.77032341450715
3216.218.6626151704126-2.46261517041262
3318.417.61973577259650.780264227403482
3420.518.00351945448342.49648054551659
351919.2342395315002-0.23423953150018
3616.519.2822647175103-2.78226471751031
3718.718.11363198009070.586368019909251
381918.41709804879010.582901951209877
3919.218.74478896541690.455211034583087
4020.519.03773940186311.46226059813693
4119.319.8275429153312-0.527542915331196
4220.619.73980621697460.860193783025363
4320.120.2858021953274-0.185802195327412
4416.120.3745314930082-4.27453149300823
4520.418.51931575376911.88068424623092
4619.719.38963897171310.310361028286898
4715.619.5994762366066-3.99947623660662
4814.417.7825748411439-3.38257484114392
4913.716.0813118731472-2.38131187314716
5014.114.7048703773037-0.604870377303731
511514.06441487596510.935585124034853
5214.214.12658346864020.0734165313597863
5313.613.8218414169383-0.221841416938291
5415.413.38055236049142.01944763950858
5514.813.9905829062920.809417093708017
5612.514.1168239000208-1.61682390002077
5716.213.13010158739823.06989841260184
5816.114.29091807690341.80908192309659
591614.99023853301781.00976146698221
6015.815.39093447699710.409065523002862
6114.915.5517822285917-0.651782228591699
6215.415.228431820580.17156817942003
6318.615.26613324134263.33386675865735
6417.116.80854676648980.291453233510225
6516.817.0576374034763-0.257637403476334
6619.517.05962568336412.44037431663594
6717.318.3275831865192-1.02758318651917
6815.818.0613365941165-2.26133659411654
6919.317.16565888997462.13434111002538
7018.818.25129850512730.548701494872727
7118.518.6803901296557-0.180390129655727
7217.318.7885082777078-1.48850827770785

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 17.4 & 15.7 & 1.7 \tabularnewline
4 & 16.2 & 17.1048400796134 & -0.904840079613386 \tabularnewline
5 & 15.6 & 17.351447037688 & -1.75144703768797 \tabularnewline
6 & 17.2 & 17.157326126984 & 0.042673873015957 \tabularnewline
7 & 14.9 & 17.7353458051005 & -2.83534580510051 \tabularnewline
8 & 13.8 & 16.9526916812607 & -3.15269168126065 \tabularnewline
9 & 17.5 & 15.8947223142713 & 1.60527768572868 \tabularnewline
10 & 16.2 & 16.9502725772038 & -0.750272577203784 \tabularnewline
11 & 17.5 & 16.9614339467163 & 0.538566053283652 \tabularnewline
12 & 16.6 & 17.549681123929 & -0.949681123929007 \tabularnewline
13 & 16.2 & 17.4570966631631 & -1.25709666316306 \tabularnewline
14 & 16.6 & 17.1770785831801 & -0.5770785831801 \tabularnewline
15 & 19.6 & 17.1635521726931 & 2.4364478273069 \tabularnewline
16 & 15.9 & 18.5512796331724 & -2.65127963317239 \tabularnewline
17 & 18 & 17.6377734511853 & 0.362226548814743 \tabularnewline
18 & 18.3 & 18.0340146143823 & 0.265985385617721 \tabularnewline
19 & 16.3 & 18.4006703108963 & -2.10067031089629 \tabularnewline
20 & 14.9 & 17.6586006815025 & -2.75860068150248 \tabularnewline
21 & 18.2 & 16.5123790044997 & 1.68762099550034 \tabularnewline
22 & 18.4 & 17.3494686862157 & 1.05053131378432 \tabularnewline
23 & 18.5 & 17.9593817655179 & 0.540618234482107 \tabularnewline
24 & 16 & 18.3742249043233 & -2.37422490432332 \tabularnewline
25 & 17.4 & 17.4329259852883 & -0.0329259852883332 \tabularnewline
26 & 17.2 & 17.4953491471532 & -0.295349147153171 \tabularnewline
27 & 19.6 & 17.4320794821435 & 2.16792051785646 \tabularnewline
28 & 17.2 & 18.5219803188501 & -1.32198031885011 \tabularnewline
29 & 18.3 & 18.0552698557238 & 0.244730144276168 \tabularnewline
30 & 19.3 & 18.2719804315052 & 1.02801956849483 \tabularnewline
31 & 18.1 & 18.8703234145072 & -0.77032341450715 \tabularnewline
32 & 16.2 & 18.6626151704126 & -2.46261517041262 \tabularnewline
33 & 18.4 & 17.6197357725965 & 0.780264227403482 \tabularnewline
34 & 20.5 & 18.0035194544834 & 2.49648054551659 \tabularnewline
35 & 19 & 19.2342395315002 & -0.23423953150018 \tabularnewline
36 & 16.5 & 19.2822647175103 & -2.78226471751031 \tabularnewline
37 & 18.7 & 18.1136319800907 & 0.586368019909251 \tabularnewline
38 & 19 & 18.4170980487901 & 0.582901951209877 \tabularnewline
39 & 19.2 & 18.7447889654169 & 0.455211034583087 \tabularnewline
40 & 20.5 & 19.0377394018631 & 1.46226059813693 \tabularnewline
41 & 19.3 & 19.8275429153312 & -0.527542915331196 \tabularnewline
42 & 20.6 & 19.7398062169746 & 0.860193783025363 \tabularnewline
43 & 20.1 & 20.2858021953274 & -0.185802195327412 \tabularnewline
44 & 16.1 & 20.3745314930082 & -4.27453149300823 \tabularnewline
45 & 20.4 & 18.5193157537691 & 1.88068424623092 \tabularnewline
46 & 19.7 & 19.3896389717131 & 0.310361028286898 \tabularnewline
47 & 15.6 & 19.5994762366066 & -3.99947623660662 \tabularnewline
48 & 14.4 & 17.7825748411439 & -3.38257484114392 \tabularnewline
49 & 13.7 & 16.0813118731472 & -2.38131187314716 \tabularnewline
50 & 14.1 & 14.7048703773037 & -0.604870377303731 \tabularnewline
51 & 15 & 14.0644148759651 & 0.935585124034853 \tabularnewline
52 & 14.2 & 14.1265834686402 & 0.0734165313597863 \tabularnewline
53 & 13.6 & 13.8218414169383 & -0.221841416938291 \tabularnewline
54 & 15.4 & 13.3805523604914 & 2.01944763950858 \tabularnewline
55 & 14.8 & 13.990582906292 & 0.809417093708017 \tabularnewline
56 & 12.5 & 14.1168239000208 & -1.61682390002077 \tabularnewline
57 & 16.2 & 13.1301015873982 & 3.06989841260184 \tabularnewline
58 & 16.1 & 14.2909180769034 & 1.80908192309659 \tabularnewline
59 & 16 & 14.9902385330178 & 1.00976146698221 \tabularnewline
60 & 15.8 & 15.3909344769971 & 0.409065523002862 \tabularnewline
61 & 14.9 & 15.5517822285917 & -0.651782228591699 \tabularnewline
62 & 15.4 & 15.22843182058 & 0.17156817942003 \tabularnewline
63 & 18.6 & 15.2661332413426 & 3.33386675865735 \tabularnewline
64 & 17.1 & 16.8085467664898 & 0.291453233510225 \tabularnewline
65 & 16.8 & 17.0576374034763 & -0.257637403476334 \tabularnewline
66 & 19.5 & 17.0596256833641 & 2.44037431663594 \tabularnewline
67 & 17.3 & 18.3275831865192 & -1.02758318651917 \tabularnewline
68 & 15.8 & 18.0613365941165 & -2.26133659411654 \tabularnewline
69 & 19.3 & 17.1656588899746 & 2.13434111002538 \tabularnewline
70 & 18.8 & 18.2512985051273 & 0.548701494872727 \tabularnewline
71 & 18.5 & 18.6803901296557 & -0.180390129655727 \tabularnewline
72 & 17.3 & 18.7885082777078 & -1.48850827770785 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160880&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]17.4[/C][C]15.7[/C][C]1.7[/C][/ROW]
[ROW][C]4[/C][C]16.2[/C][C]17.1048400796134[/C][C]-0.904840079613386[/C][/ROW]
[ROW][C]5[/C][C]15.6[/C][C]17.351447037688[/C][C]-1.75144703768797[/C][/ROW]
[ROW][C]6[/C][C]17.2[/C][C]17.157326126984[/C][C]0.042673873015957[/C][/ROW]
[ROW][C]7[/C][C]14.9[/C][C]17.7353458051005[/C][C]-2.83534580510051[/C][/ROW]
[ROW][C]8[/C][C]13.8[/C][C]16.9526916812607[/C][C]-3.15269168126065[/C][/ROW]
[ROW][C]9[/C][C]17.5[/C][C]15.8947223142713[/C][C]1.60527768572868[/C][/ROW]
[ROW][C]10[/C][C]16.2[/C][C]16.9502725772038[/C][C]-0.750272577203784[/C][/ROW]
[ROW][C]11[/C][C]17.5[/C][C]16.9614339467163[/C][C]0.538566053283652[/C][/ROW]
[ROW][C]12[/C][C]16.6[/C][C]17.549681123929[/C][C]-0.949681123929007[/C][/ROW]
[ROW][C]13[/C][C]16.2[/C][C]17.4570966631631[/C][C]-1.25709666316306[/C][/ROW]
[ROW][C]14[/C][C]16.6[/C][C]17.1770785831801[/C][C]-0.5770785831801[/C][/ROW]
[ROW][C]15[/C][C]19.6[/C][C]17.1635521726931[/C][C]2.4364478273069[/C][/ROW]
[ROW][C]16[/C][C]15.9[/C][C]18.5512796331724[/C][C]-2.65127963317239[/C][/ROW]
[ROW][C]17[/C][C]18[/C][C]17.6377734511853[/C][C]0.362226548814743[/C][/ROW]
[ROW][C]18[/C][C]18.3[/C][C]18.0340146143823[/C][C]0.265985385617721[/C][/ROW]
[ROW][C]19[/C][C]16.3[/C][C]18.4006703108963[/C][C]-2.10067031089629[/C][/ROW]
[ROW][C]20[/C][C]14.9[/C][C]17.6586006815025[/C][C]-2.75860068150248[/C][/ROW]
[ROW][C]21[/C][C]18.2[/C][C]16.5123790044997[/C][C]1.68762099550034[/C][/ROW]
[ROW][C]22[/C][C]18.4[/C][C]17.3494686862157[/C][C]1.05053131378432[/C][/ROW]
[ROW][C]23[/C][C]18.5[/C][C]17.9593817655179[/C][C]0.540618234482107[/C][/ROW]
[ROW][C]24[/C][C]16[/C][C]18.3742249043233[/C][C]-2.37422490432332[/C][/ROW]
[ROW][C]25[/C][C]17.4[/C][C]17.4329259852883[/C][C]-0.0329259852883332[/C][/ROW]
[ROW][C]26[/C][C]17.2[/C][C]17.4953491471532[/C][C]-0.295349147153171[/C][/ROW]
[ROW][C]27[/C][C]19.6[/C][C]17.4320794821435[/C][C]2.16792051785646[/C][/ROW]
[ROW][C]28[/C][C]17.2[/C][C]18.5219803188501[/C][C]-1.32198031885011[/C][/ROW]
[ROW][C]29[/C][C]18.3[/C][C]18.0552698557238[/C][C]0.244730144276168[/C][/ROW]
[ROW][C]30[/C][C]19.3[/C][C]18.2719804315052[/C][C]1.02801956849483[/C][/ROW]
[ROW][C]31[/C][C]18.1[/C][C]18.8703234145072[/C][C]-0.77032341450715[/C][/ROW]
[ROW][C]32[/C][C]16.2[/C][C]18.6626151704126[/C][C]-2.46261517041262[/C][/ROW]
[ROW][C]33[/C][C]18.4[/C][C]17.6197357725965[/C][C]0.780264227403482[/C][/ROW]
[ROW][C]34[/C][C]20.5[/C][C]18.0035194544834[/C][C]2.49648054551659[/C][/ROW]
[ROW][C]35[/C][C]19[/C][C]19.2342395315002[/C][C]-0.23423953150018[/C][/ROW]
[ROW][C]36[/C][C]16.5[/C][C]19.2822647175103[/C][C]-2.78226471751031[/C][/ROW]
[ROW][C]37[/C][C]18.7[/C][C]18.1136319800907[/C][C]0.586368019909251[/C][/ROW]
[ROW][C]38[/C][C]19[/C][C]18.4170980487901[/C][C]0.582901951209877[/C][/ROW]
[ROW][C]39[/C][C]19.2[/C][C]18.7447889654169[/C][C]0.455211034583087[/C][/ROW]
[ROW][C]40[/C][C]20.5[/C][C]19.0377394018631[/C][C]1.46226059813693[/C][/ROW]
[ROW][C]41[/C][C]19.3[/C][C]19.8275429153312[/C][C]-0.527542915331196[/C][/ROW]
[ROW][C]42[/C][C]20.6[/C][C]19.7398062169746[/C][C]0.860193783025363[/C][/ROW]
[ROW][C]43[/C][C]20.1[/C][C]20.2858021953274[/C][C]-0.185802195327412[/C][/ROW]
[ROW][C]44[/C][C]16.1[/C][C]20.3745314930082[/C][C]-4.27453149300823[/C][/ROW]
[ROW][C]45[/C][C]20.4[/C][C]18.5193157537691[/C][C]1.88068424623092[/C][/ROW]
[ROW][C]46[/C][C]19.7[/C][C]19.3896389717131[/C][C]0.310361028286898[/C][/ROW]
[ROW][C]47[/C][C]15.6[/C][C]19.5994762366066[/C][C]-3.99947623660662[/C][/ROW]
[ROW][C]48[/C][C]14.4[/C][C]17.7825748411439[/C][C]-3.38257484114392[/C][/ROW]
[ROW][C]49[/C][C]13.7[/C][C]16.0813118731472[/C][C]-2.38131187314716[/C][/ROW]
[ROW][C]50[/C][C]14.1[/C][C]14.7048703773037[/C][C]-0.604870377303731[/C][/ROW]
[ROW][C]51[/C][C]15[/C][C]14.0644148759651[/C][C]0.935585124034853[/C][/ROW]
[ROW][C]52[/C][C]14.2[/C][C]14.1265834686402[/C][C]0.0734165313597863[/C][/ROW]
[ROW][C]53[/C][C]13.6[/C][C]13.8218414169383[/C][C]-0.221841416938291[/C][/ROW]
[ROW][C]54[/C][C]15.4[/C][C]13.3805523604914[/C][C]2.01944763950858[/C][/ROW]
[ROW][C]55[/C][C]14.8[/C][C]13.990582906292[/C][C]0.809417093708017[/C][/ROW]
[ROW][C]56[/C][C]12.5[/C][C]14.1168239000208[/C][C]-1.61682390002077[/C][/ROW]
[ROW][C]57[/C][C]16.2[/C][C]13.1301015873982[/C][C]3.06989841260184[/C][/ROW]
[ROW][C]58[/C][C]16.1[/C][C]14.2909180769034[/C][C]1.80908192309659[/C][/ROW]
[ROW][C]59[/C][C]16[/C][C]14.9902385330178[/C][C]1.00976146698221[/C][/ROW]
[ROW][C]60[/C][C]15.8[/C][C]15.3909344769971[/C][C]0.409065523002862[/C][/ROW]
[ROW][C]61[/C][C]14.9[/C][C]15.5517822285917[/C][C]-0.651782228591699[/C][/ROW]
[ROW][C]62[/C][C]15.4[/C][C]15.22843182058[/C][C]0.17156817942003[/C][/ROW]
[ROW][C]63[/C][C]18.6[/C][C]15.2661332413426[/C][C]3.33386675865735[/C][/ROW]
[ROW][C]64[/C][C]17.1[/C][C]16.8085467664898[/C][C]0.291453233510225[/C][/ROW]
[ROW][C]65[/C][C]16.8[/C][C]17.0576374034763[/C][C]-0.257637403476334[/C][/ROW]
[ROW][C]66[/C][C]19.5[/C][C]17.0596256833641[/C][C]2.44037431663594[/C][/ROW]
[ROW][C]67[/C][C]17.3[/C][C]18.3275831865192[/C][C]-1.02758318651917[/C][/ROW]
[ROW][C]68[/C][C]15.8[/C][C]18.0613365941165[/C][C]-2.26133659411654[/C][/ROW]
[ROW][C]69[/C][C]19.3[/C][C]17.1656588899746[/C][C]2.13434111002538[/C][/ROW]
[ROW][C]70[/C][C]18.8[/C][C]18.2512985051273[/C][C]0.548701494872727[/C][/ROW]
[ROW][C]71[/C][C]18.5[/C][C]18.6803901296557[/C][C]-0.180390129655727[/C][/ROW]
[ROW][C]72[/C][C]17.3[/C][C]18.7885082777078[/C][C]-1.48850827770785[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160880&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160880&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
317.415.71.7
416.217.1048400796134-0.904840079613386
515.617.351447037688-1.75144703768797
617.217.1573261269840.042673873015957
714.917.7353458051005-2.83534580510051
813.816.9526916812607-3.15269168126065
917.515.89472231427131.60527768572868
1016.216.9502725772038-0.750272577203784
1117.516.96143394671630.538566053283652
1216.617.549681123929-0.949681123929007
1316.217.4570966631631-1.25709666316306
1416.617.1770785831801-0.5770785831801
1519.617.16355217269312.4364478273069
1615.918.5512796331724-2.65127963317239
171817.63777345118530.362226548814743
1818.318.03401461438230.265985385617721
1916.318.4006703108963-2.10067031089629
2014.917.6586006815025-2.75860068150248
2118.216.51237900449971.68762099550034
2218.417.34946868621571.05053131378432
2318.517.95938176551790.540618234482107
241618.3742249043233-2.37422490432332
2517.417.4329259852883-0.0329259852883332
2617.217.4953491471532-0.295349147153171
2719.617.43207948214352.16792051785646
2817.218.5219803188501-1.32198031885011
2918.318.05526985572380.244730144276168
3019.318.27198043150521.02801956849483
3118.118.8703234145072-0.77032341450715
3216.218.6626151704126-2.46261517041262
3318.417.61973577259650.780264227403482
3420.518.00351945448342.49648054551659
351919.2342395315002-0.23423953150018
3616.519.2822647175103-2.78226471751031
3718.718.11363198009070.586368019909251
381918.41709804879010.582901951209877
3919.218.74478896541690.455211034583087
4020.519.03773940186311.46226059813693
4119.319.8275429153312-0.527542915331196
4220.619.73980621697460.860193783025363
4320.120.2858021953274-0.185802195327412
4416.120.3745314930082-4.27453149300823
4520.418.51931575376911.88068424623092
4619.719.38963897171310.310361028286898
4715.619.5994762366066-3.99947623660662
4814.417.7825748411439-3.38257484114392
4913.716.0813118731472-2.38131187314716
5014.114.7048703773037-0.604870377303731
511514.06441487596510.935585124034853
5214.214.12658346864020.0734165313597863
5313.613.8218414169383-0.221841416938291
5415.413.38055236049142.01944763950858
5514.813.9905829062920.809417093708017
5612.514.1168239000208-1.61682390002077
5716.213.13010158739823.06989841260184
5816.114.29091807690341.80908192309659
591614.99023853301781.00976146698221
6015.815.39093447699710.409065523002862
6114.915.5517822285917-0.651782228591699
6215.415.228431820580.17156817942003
6318.615.26613324134263.33386675865735
6417.116.80854676648980.291453233510225
6516.817.0576374034763-0.257637403476334
6619.517.05962568336412.44037431663594
6717.318.3275831865192-1.02758318651917
6815.818.0613365941165-2.26133659411654
6919.317.16565888997462.13434111002538
7018.818.25129850512730.548701494872727
7118.518.6803901296557-0.180390129655727
7217.318.7885082777078-1.48850827770785







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7318.269359713009914.883630970403421.6550884556163
7418.389262644266914.643261667309522.1352636212242
7518.509165575523914.373589499157322.6447416518904
7618.629068506780914.077237116066623.1808998974951
7718.748971438037913.756409641081923.7415332349938
7818.868874369294913.412949723275324.3247990153144
7918.988777300551813.048398377605924.9291562234977
8019.108680231808912.664050784690525.5533096789272
8119.228583163065812.261003523813226.1961628023185
8219.348486094322811.840193005810726.856779182835
8319.468389025579811.402426136345227.5343519148145
8419.588291956836810.948404566905728.228179346768

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 18.2693597130099 & 14.8836309704034 & 21.6550884556163 \tabularnewline
74 & 18.3892626442669 & 14.6432616673095 & 22.1352636212242 \tabularnewline
75 & 18.5091655755239 & 14.3735894991573 & 22.6447416518904 \tabularnewline
76 & 18.6290685067809 & 14.0772371160666 & 23.1808998974951 \tabularnewline
77 & 18.7489714380379 & 13.7564096410819 & 23.7415332349938 \tabularnewline
78 & 18.8688743692949 & 13.4129497232753 & 24.3247990153144 \tabularnewline
79 & 18.9887773005518 & 13.0483983776059 & 24.9291562234977 \tabularnewline
80 & 19.1086802318089 & 12.6640507846905 & 25.5533096789272 \tabularnewline
81 & 19.2285831630658 & 12.2610035238132 & 26.1961628023185 \tabularnewline
82 & 19.3484860943228 & 11.8401930058107 & 26.856779182835 \tabularnewline
83 & 19.4683890255798 & 11.4024261363452 & 27.5343519148145 \tabularnewline
84 & 19.5882919568368 & 10.9484045669057 & 28.228179346768 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160880&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]18.2693597130099[/C][C]14.8836309704034[/C][C]21.6550884556163[/C][/ROW]
[ROW][C]74[/C][C]18.3892626442669[/C][C]14.6432616673095[/C][C]22.1352636212242[/C][/ROW]
[ROW][C]75[/C][C]18.5091655755239[/C][C]14.3735894991573[/C][C]22.6447416518904[/C][/ROW]
[ROW][C]76[/C][C]18.6290685067809[/C][C]14.0772371160666[/C][C]23.1808998974951[/C][/ROW]
[ROW][C]77[/C][C]18.7489714380379[/C][C]13.7564096410819[/C][C]23.7415332349938[/C][/ROW]
[ROW][C]78[/C][C]18.8688743692949[/C][C]13.4129497232753[/C][C]24.3247990153144[/C][/ROW]
[ROW][C]79[/C][C]18.9887773005518[/C][C]13.0483983776059[/C][C]24.9291562234977[/C][/ROW]
[ROW][C]80[/C][C]19.1086802318089[/C][C]12.6640507846905[/C][C]25.5533096789272[/C][/ROW]
[ROW][C]81[/C][C]19.2285831630658[/C][C]12.2610035238132[/C][C]26.1961628023185[/C][/ROW]
[ROW][C]82[/C][C]19.3484860943228[/C][C]11.8401930058107[/C][C]26.856779182835[/C][/ROW]
[ROW][C]83[/C][C]19.4683890255798[/C][C]11.4024261363452[/C][C]27.5343519148145[/C][/ROW]
[ROW][C]84[/C][C]19.5882919568368[/C][C]10.9484045669057[/C][C]28.228179346768[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160880&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160880&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
7318.269359713009914.883630970403421.6550884556163
7418.389262644266914.643261667309522.1352636212242
7518.509165575523914.373589499157322.6447416518904
7618.629068506780914.077237116066623.1808998974951
7718.748971438037913.756409641081923.7415332349938
7818.868874369294913.412949723275324.3247990153144
7918.988777300551813.048398377605924.9291562234977
8019.108680231808912.664050784690525.5533096789272
8119.228583163065812.261003523813226.1961628023185
8219.348486094322811.840193005810726.856779182835
8319.468389025579811.402426136345227.5343519148145
8419.588291956836810.948404566905728.228179346768



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
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')