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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 07 Jun 2009 14:09:25 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jun/07/t1244405469ww49rupy9dg9gdg.htm/, Retrieved Mon, 13 May 2024 08:12:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=42254, Retrieved Mon, 13 May 2024 08:12:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact100
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [huishoudbroodprij...] [2009-06-07 20:09:25] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
40.04
40.04
40.03
40.03
41.63
42.03
42.03
42.03
42.03
42.03
42.03
42.03
42.03
42.03
42.03
42.03
42.03
42.03
42.03
42.03
42.03
42.38
42.06
42.06
42.05
42.05
42.05
42.05
44.36
44.48
44.49
44.49
44.49
44.49
44.49
44.48
44.48
44.48
44.48
44.48
44.48
44.49
44.49
44.49
44.49
44.49
44.49
44.49
44.49
45.5
45.94
45.95
45.96
45.96
45.96
45.96
45.96
45.96
45.96
45.96
45.97
46.06
47.9
47.93
47.94
47.94
47.94
47.94
47.94
47.94
47.94
47.94




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42254&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42254&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42254&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'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.894925705383375
beta0.00194398841394829
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.894925705383375 \tabularnewline
beta & 0.00194398841394829 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42254&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]0.894925705383375[/C][/ROW]
[ROW][C]beta[/C][C]0.00194398841394829[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42254&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42254&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
alpha0.894925705383375
beta0.00194398841394829
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1342.0341.52360002392990.5063999760701
1442.0342.02707917659290.0029208234071163
1542.0342.0799869748432-0.0499869748432147
1642.0342.0708617495105-0.0408617495104835
1742.0342.0685695653491-0.0385695653491140
1842.0342.0815838565958-0.0515838565958262
1942.0342.7441940129195-0.714194012919492
2042.0341.98639943829880.0436005617012256
2142.0341.90721959148540.122780408514600
2242.3841.89919789596440.480802104035611
2342.0642.2786232324901-0.218623232490089
2442.0642.1157796963423-0.0557796963422987
2542.0542.1686448008874-0.118644800887367
2642.0542.0587154064800-0.00871540647995772
2742.0542.0945256342213-0.0445256342213227
2842.0542.090128442476-0.0401284424760178
2944.3642.08761618134832.27238381865168
3044.4844.17011159432610.309888405673917
3144.4945.1228281182427-0.632828118242664
3244.4944.5158871038238-0.0258871038238340
3344.4944.37707587343330.112924126566696
3444.4944.39332716547440.096672834525613
3544.4944.34963070340710.140369296592922
3644.4844.5286923503892-0.048692350389203
3744.4844.5874775530088-0.107477553008820
3844.4844.5002271325712-0.0202271325712289
3944.4844.5249456558405-0.044945655840543
4044.4844.5233837679123-0.0433837679122959
4144.4844.7659788994564-0.285978899456438
4244.4944.3508663230730.139133676927010
4344.4945.0495630977604-0.55956309776036
4444.4944.5707960839758-0.0807960839757627
4544.4944.39615746955610.0938425304439363
4644.4944.39238925288130.0976107471187504
4744.4944.35288315708480.137116842915226
4844.4944.5079248156548-0.0179248156548297
4944.4944.5868623097427-0.09686230974269
5045.544.51708960041010.982910399589876
5145.9445.43725505010440.502744949895551
5245.9545.92708437369820.0229156263017884
5345.9646.2116943006226-0.251694300622589
5445.9645.86794842437490.092051575625149
5545.9646.4667498236828-0.506749823682789
5645.9646.0879636217293-0.127963621729272
5745.9645.88656275726640.0734372427336112
5845.9645.86193990525310.0980600947468773
5945.9645.82282106159240.137178938407622
6045.9645.9620497300195-0.00204973001952879
6145.9746.0496538079115-0.0796538079114981
6246.0646.1109550520416-0.0509550520416227
6347.946.05397498652531.8460250134747
6447.9347.69522049381990.234779506180089
6547.9448.1507024651347-0.210702465134716
6647.9447.87643626608070.0635637339193451
6747.9448.4060110834942-0.466011083494195
6847.9448.1088100038075-0.168810003807515
6947.9447.88942845469060.05057154530936
7047.9447.84339925732080.0966007426791649
7147.9447.80203816693980.137961833060182
7247.9447.92766763590480.0123323640952293

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 42.03 & 41.5236000239299 & 0.5063999760701 \tabularnewline
14 & 42.03 & 42.0270791765929 & 0.0029208234071163 \tabularnewline
15 & 42.03 & 42.0799869748432 & -0.0499869748432147 \tabularnewline
16 & 42.03 & 42.0708617495105 & -0.0408617495104835 \tabularnewline
17 & 42.03 & 42.0685695653491 & -0.0385695653491140 \tabularnewline
18 & 42.03 & 42.0815838565958 & -0.0515838565958262 \tabularnewline
19 & 42.03 & 42.7441940129195 & -0.714194012919492 \tabularnewline
20 & 42.03 & 41.9863994382988 & 0.0436005617012256 \tabularnewline
21 & 42.03 & 41.9072195914854 & 0.122780408514600 \tabularnewline
22 & 42.38 & 41.8991978959644 & 0.480802104035611 \tabularnewline
23 & 42.06 & 42.2786232324901 & -0.218623232490089 \tabularnewline
24 & 42.06 & 42.1157796963423 & -0.0557796963422987 \tabularnewline
25 & 42.05 & 42.1686448008874 & -0.118644800887367 \tabularnewline
26 & 42.05 & 42.0587154064800 & -0.00871540647995772 \tabularnewline
27 & 42.05 & 42.0945256342213 & -0.0445256342213227 \tabularnewline
28 & 42.05 & 42.090128442476 & -0.0401284424760178 \tabularnewline
29 & 44.36 & 42.0876161813483 & 2.27238381865168 \tabularnewline
30 & 44.48 & 44.1701115943261 & 0.309888405673917 \tabularnewline
31 & 44.49 & 45.1228281182427 & -0.632828118242664 \tabularnewline
32 & 44.49 & 44.5158871038238 & -0.0258871038238340 \tabularnewline
33 & 44.49 & 44.3770758734333 & 0.112924126566696 \tabularnewline
34 & 44.49 & 44.3933271654744 & 0.096672834525613 \tabularnewline
35 & 44.49 & 44.3496307034071 & 0.140369296592922 \tabularnewline
36 & 44.48 & 44.5286923503892 & -0.048692350389203 \tabularnewline
37 & 44.48 & 44.5874775530088 & -0.107477553008820 \tabularnewline
38 & 44.48 & 44.5002271325712 & -0.0202271325712289 \tabularnewline
39 & 44.48 & 44.5249456558405 & -0.044945655840543 \tabularnewline
40 & 44.48 & 44.5233837679123 & -0.0433837679122959 \tabularnewline
41 & 44.48 & 44.7659788994564 & -0.285978899456438 \tabularnewline
42 & 44.49 & 44.350866323073 & 0.139133676927010 \tabularnewline
43 & 44.49 & 45.0495630977604 & -0.55956309776036 \tabularnewline
44 & 44.49 & 44.5707960839758 & -0.0807960839757627 \tabularnewline
45 & 44.49 & 44.3961574695561 & 0.0938425304439363 \tabularnewline
46 & 44.49 & 44.3923892528813 & 0.0976107471187504 \tabularnewline
47 & 44.49 & 44.3528831570848 & 0.137116842915226 \tabularnewline
48 & 44.49 & 44.5079248156548 & -0.0179248156548297 \tabularnewline
49 & 44.49 & 44.5868623097427 & -0.09686230974269 \tabularnewline
50 & 45.5 & 44.5170896004101 & 0.982910399589876 \tabularnewline
51 & 45.94 & 45.4372550501044 & 0.502744949895551 \tabularnewline
52 & 45.95 & 45.9270843736982 & 0.0229156263017884 \tabularnewline
53 & 45.96 & 46.2116943006226 & -0.251694300622589 \tabularnewline
54 & 45.96 & 45.8679484243749 & 0.092051575625149 \tabularnewline
55 & 45.96 & 46.4667498236828 & -0.506749823682789 \tabularnewline
56 & 45.96 & 46.0879636217293 & -0.127963621729272 \tabularnewline
57 & 45.96 & 45.8865627572664 & 0.0734372427336112 \tabularnewline
58 & 45.96 & 45.8619399052531 & 0.0980600947468773 \tabularnewline
59 & 45.96 & 45.8228210615924 & 0.137178938407622 \tabularnewline
60 & 45.96 & 45.9620497300195 & -0.00204973001952879 \tabularnewline
61 & 45.97 & 46.0496538079115 & -0.0796538079114981 \tabularnewline
62 & 46.06 & 46.1109550520416 & -0.0509550520416227 \tabularnewline
63 & 47.9 & 46.0539749865253 & 1.8460250134747 \tabularnewline
64 & 47.93 & 47.6952204938199 & 0.234779506180089 \tabularnewline
65 & 47.94 & 48.1507024651347 & -0.210702465134716 \tabularnewline
66 & 47.94 & 47.8764362660807 & 0.0635637339193451 \tabularnewline
67 & 47.94 & 48.4060110834942 & -0.466011083494195 \tabularnewline
68 & 47.94 & 48.1088100038075 & -0.168810003807515 \tabularnewline
69 & 47.94 & 47.8894284546906 & 0.05057154530936 \tabularnewline
70 & 47.94 & 47.8433992573208 & 0.0966007426791649 \tabularnewline
71 & 47.94 & 47.8020381669398 & 0.137961833060182 \tabularnewline
72 & 47.94 & 47.9276676359048 & 0.0123323640952293 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42254&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]13[/C][C]42.03[/C][C]41.5236000239299[/C][C]0.5063999760701[/C][/ROW]
[ROW][C]14[/C][C]42.03[/C][C]42.0270791765929[/C][C]0.0029208234071163[/C][/ROW]
[ROW][C]15[/C][C]42.03[/C][C]42.0799869748432[/C][C]-0.0499869748432147[/C][/ROW]
[ROW][C]16[/C][C]42.03[/C][C]42.0708617495105[/C][C]-0.0408617495104835[/C][/ROW]
[ROW][C]17[/C][C]42.03[/C][C]42.0685695653491[/C][C]-0.0385695653491140[/C][/ROW]
[ROW][C]18[/C][C]42.03[/C][C]42.0815838565958[/C][C]-0.0515838565958262[/C][/ROW]
[ROW][C]19[/C][C]42.03[/C][C]42.7441940129195[/C][C]-0.714194012919492[/C][/ROW]
[ROW][C]20[/C][C]42.03[/C][C]41.9863994382988[/C][C]0.0436005617012256[/C][/ROW]
[ROW][C]21[/C][C]42.03[/C][C]41.9072195914854[/C][C]0.122780408514600[/C][/ROW]
[ROW][C]22[/C][C]42.38[/C][C]41.8991978959644[/C][C]0.480802104035611[/C][/ROW]
[ROW][C]23[/C][C]42.06[/C][C]42.2786232324901[/C][C]-0.218623232490089[/C][/ROW]
[ROW][C]24[/C][C]42.06[/C][C]42.1157796963423[/C][C]-0.0557796963422987[/C][/ROW]
[ROW][C]25[/C][C]42.05[/C][C]42.1686448008874[/C][C]-0.118644800887367[/C][/ROW]
[ROW][C]26[/C][C]42.05[/C][C]42.0587154064800[/C][C]-0.00871540647995772[/C][/ROW]
[ROW][C]27[/C][C]42.05[/C][C]42.0945256342213[/C][C]-0.0445256342213227[/C][/ROW]
[ROW][C]28[/C][C]42.05[/C][C]42.090128442476[/C][C]-0.0401284424760178[/C][/ROW]
[ROW][C]29[/C][C]44.36[/C][C]42.0876161813483[/C][C]2.27238381865168[/C][/ROW]
[ROW][C]30[/C][C]44.48[/C][C]44.1701115943261[/C][C]0.309888405673917[/C][/ROW]
[ROW][C]31[/C][C]44.49[/C][C]45.1228281182427[/C][C]-0.632828118242664[/C][/ROW]
[ROW][C]32[/C][C]44.49[/C][C]44.5158871038238[/C][C]-0.0258871038238340[/C][/ROW]
[ROW][C]33[/C][C]44.49[/C][C]44.3770758734333[/C][C]0.112924126566696[/C][/ROW]
[ROW][C]34[/C][C]44.49[/C][C]44.3933271654744[/C][C]0.096672834525613[/C][/ROW]
[ROW][C]35[/C][C]44.49[/C][C]44.3496307034071[/C][C]0.140369296592922[/C][/ROW]
[ROW][C]36[/C][C]44.48[/C][C]44.5286923503892[/C][C]-0.048692350389203[/C][/ROW]
[ROW][C]37[/C][C]44.48[/C][C]44.5874775530088[/C][C]-0.107477553008820[/C][/ROW]
[ROW][C]38[/C][C]44.48[/C][C]44.5002271325712[/C][C]-0.0202271325712289[/C][/ROW]
[ROW][C]39[/C][C]44.48[/C][C]44.5249456558405[/C][C]-0.044945655840543[/C][/ROW]
[ROW][C]40[/C][C]44.48[/C][C]44.5233837679123[/C][C]-0.0433837679122959[/C][/ROW]
[ROW][C]41[/C][C]44.48[/C][C]44.7659788994564[/C][C]-0.285978899456438[/C][/ROW]
[ROW][C]42[/C][C]44.49[/C][C]44.350866323073[/C][C]0.139133676927010[/C][/ROW]
[ROW][C]43[/C][C]44.49[/C][C]45.0495630977604[/C][C]-0.55956309776036[/C][/ROW]
[ROW][C]44[/C][C]44.49[/C][C]44.5707960839758[/C][C]-0.0807960839757627[/C][/ROW]
[ROW][C]45[/C][C]44.49[/C][C]44.3961574695561[/C][C]0.0938425304439363[/C][/ROW]
[ROW][C]46[/C][C]44.49[/C][C]44.3923892528813[/C][C]0.0976107471187504[/C][/ROW]
[ROW][C]47[/C][C]44.49[/C][C]44.3528831570848[/C][C]0.137116842915226[/C][/ROW]
[ROW][C]48[/C][C]44.49[/C][C]44.5079248156548[/C][C]-0.0179248156548297[/C][/ROW]
[ROW][C]49[/C][C]44.49[/C][C]44.5868623097427[/C][C]-0.09686230974269[/C][/ROW]
[ROW][C]50[/C][C]45.5[/C][C]44.5170896004101[/C][C]0.982910399589876[/C][/ROW]
[ROW][C]51[/C][C]45.94[/C][C]45.4372550501044[/C][C]0.502744949895551[/C][/ROW]
[ROW][C]52[/C][C]45.95[/C][C]45.9270843736982[/C][C]0.0229156263017884[/C][/ROW]
[ROW][C]53[/C][C]45.96[/C][C]46.2116943006226[/C][C]-0.251694300622589[/C][/ROW]
[ROW][C]54[/C][C]45.96[/C][C]45.8679484243749[/C][C]0.092051575625149[/C][/ROW]
[ROW][C]55[/C][C]45.96[/C][C]46.4667498236828[/C][C]-0.506749823682789[/C][/ROW]
[ROW][C]56[/C][C]45.96[/C][C]46.0879636217293[/C][C]-0.127963621729272[/C][/ROW]
[ROW][C]57[/C][C]45.96[/C][C]45.8865627572664[/C][C]0.0734372427336112[/C][/ROW]
[ROW][C]58[/C][C]45.96[/C][C]45.8619399052531[/C][C]0.0980600947468773[/C][/ROW]
[ROW][C]59[/C][C]45.96[/C][C]45.8228210615924[/C][C]0.137178938407622[/C][/ROW]
[ROW][C]60[/C][C]45.96[/C][C]45.9620497300195[/C][C]-0.00204973001952879[/C][/ROW]
[ROW][C]61[/C][C]45.97[/C][C]46.0496538079115[/C][C]-0.0796538079114981[/C][/ROW]
[ROW][C]62[/C][C]46.06[/C][C]46.1109550520416[/C][C]-0.0509550520416227[/C][/ROW]
[ROW][C]63[/C][C]47.9[/C][C]46.0539749865253[/C][C]1.8460250134747[/C][/ROW]
[ROW][C]64[/C][C]47.93[/C][C]47.6952204938199[/C][C]0.234779506180089[/C][/ROW]
[ROW][C]65[/C][C]47.94[/C][C]48.1507024651347[/C][C]-0.210702465134716[/C][/ROW]
[ROW][C]66[/C][C]47.94[/C][C]47.8764362660807[/C][C]0.0635637339193451[/C][/ROW]
[ROW][C]67[/C][C]47.94[/C][C]48.4060110834942[/C][C]-0.466011083494195[/C][/ROW]
[ROW][C]68[/C][C]47.94[/C][C]48.1088100038075[/C][C]-0.168810003807515[/C][/ROW]
[ROW][C]69[/C][C]47.94[/C][C]47.8894284546906[/C][C]0.05057154530936[/C][/ROW]
[ROW][C]70[/C][C]47.94[/C][C]47.8433992573208[/C][C]0.0966007426791649[/C][/ROW]
[ROW][C]71[/C][C]47.94[/C][C]47.8020381669398[/C][C]0.137961833060182[/C][/ROW]
[ROW][C]72[/C][C]47.94[/C][C]47.9276676359048[/C][C]0.0123323640952293[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42254&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42254&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
1342.0341.52360002392990.5063999760701
1442.0342.02707917659290.0029208234071163
1542.0342.0799869748432-0.0499869748432147
1642.0342.0708617495105-0.0408617495104835
1742.0342.0685695653491-0.0385695653491140
1842.0342.0815838565958-0.0515838565958262
1942.0342.7441940129195-0.714194012919492
2042.0341.98639943829880.0436005617012256
2142.0341.90721959148540.122780408514600
2242.3841.89919789596440.480802104035611
2342.0642.2786232324901-0.218623232490089
2442.0642.1157796963423-0.0557796963422987
2542.0542.1686448008874-0.118644800887367
2642.0542.0587154064800-0.00871540647995772
2742.0542.0945256342213-0.0445256342213227
2842.0542.090128442476-0.0401284424760178
2944.3642.08761618134832.27238381865168
3044.4844.17011159432610.309888405673917
3144.4945.1228281182427-0.632828118242664
3244.4944.5158871038238-0.0258871038238340
3344.4944.37707587343330.112924126566696
3444.4944.39332716547440.096672834525613
3544.4944.34963070340710.140369296592922
3644.4844.5286923503892-0.048692350389203
3744.4844.5874775530088-0.107477553008820
3844.4844.5002271325712-0.0202271325712289
3944.4844.5249456558405-0.044945655840543
4044.4844.5233837679123-0.0433837679122959
4144.4844.7659788994564-0.285978899456438
4244.4944.3508663230730.139133676927010
4344.4945.0495630977604-0.55956309776036
4444.4944.5707960839758-0.0807960839757627
4544.4944.39615746955610.0938425304439363
4644.4944.39238925288130.0976107471187504
4744.4944.35288315708480.137116842915226
4844.4944.5079248156548-0.0179248156548297
4944.4944.5868623097427-0.09686230974269
5045.544.51708960041010.982910399589876
5145.9445.43725505010440.502744949895551
5245.9545.92708437369820.0229156263017884
5345.9646.2116943006226-0.251694300622589
5445.9645.86794842437490.092051575625149
5545.9646.4667498236828-0.506749823682789
5645.9646.0879636217293-0.127963621729272
5745.9645.88656275726640.0734372427336112
5845.9645.86193990525310.0980600947468773
5945.9645.82282106159240.137178938407622
6045.9645.9620497300195-0.00204973001952879
6145.9746.0496538079115-0.0796538079114981
6246.0646.1109550520416-0.0509550520416227
6347.946.05397498652531.8460250134747
6447.9347.69522049381990.234779506180089
6547.9448.1507024651347-0.210702465134716
6647.9447.87643626608070.0635637339193451
6747.9448.4060110834942-0.466011083494195
6847.9448.1088100038075-0.168810003807515
6947.9447.88942845469060.05057154530936
7047.9447.84339925732080.0966007426791649
7147.9447.80203816693980.137961833060182
7247.9447.92766763590480.0123323640952293







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7348.0237354997847.123478916118348.9239920834416
7448.165708815180546.955578589403849.3758390409573
7548.3555795309646.897551442451649.8136076194685
7648.172687024526246.51041764236349.8349564066894
7748.371044426497846.516919069023950.2251697839718
7848.312665080535146.291762401264950.3335677598053
7948.731497992690846.538863854801450.9241321305802
8048.884306860640246.540554415845151.2280593054353
8148.837572855032846.359604162067151.3155415479985
8248.748872081276646.145614110893251.35213005166
8348.622607048427445.901943889583551.3432702072713
8448.610639053481932.376324719407564.8449533875563

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 48.02373549978 & 47.1234789161183 & 48.9239920834416 \tabularnewline
74 & 48.1657088151805 & 46.9555785894038 & 49.3758390409573 \tabularnewline
75 & 48.35557953096 & 46.8975514424516 & 49.8136076194685 \tabularnewline
76 & 48.1726870245262 & 46.510417642363 & 49.8349564066894 \tabularnewline
77 & 48.3710444264978 & 46.5169190690239 & 50.2251697839718 \tabularnewline
78 & 48.3126650805351 & 46.2917624012649 & 50.3335677598053 \tabularnewline
79 & 48.7314979926908 & 46.5388638548014 & 50.9241321305802 \tabularnewline
80 & 48.8843068606402 & 46.5405544158451 & 51.2280593054353 \tabularnewline
81 & 48.8375728550328 & 46.3596041620671 & 51.3155415479985 \tabularnewline
82 & 48.7488720812766 & 46.1456141108932 & 51.35213005166 \tabularnewline
83 & 48.6226070484274 & 45.9019438895835 & 51.3432702072713 \tabularnewline
84 & 48.6106390534819 & 32.3763247194075 & 64.8449533875563 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42254&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]48.02373549978[/C][C]47.1234789161183[/C][C]48.9239920834416[/C][/ROW]
[ROW][C]74[/C][C]48.1657088151805[/C][C]46.9555785894038[/C][C]49.3758390409573[/C][/ROW]
[ROW][C]75[/C][C]48.35557953096[/C][C]46.8975514424516[/C][C]49.8136076194685[/C][/ROW]
[ROW][C]76[/C][C]48.1726870245262[/C][C]46.510417642363[/C][C]49.8349564066894[/C][/ROW]
[ROW][C]77[/C][C]48.3710444264978[/C][C]46.5169190690239[/C][C]50.2251697839718[/C][/ROW]
[ROW][C]78[/C][C]48.3126650805351[/C][C]46.2917624012649[/C][C]50.3335677598053[/C][/ROW]
[ROW][C]79[/C][C]48.7314979926908[/C][C]46.5388638548014[/C][C]50.9241321305802[/C][/ROW]
[ROW][C]80[/C][C]48.8843068606402[/C][C]46.5405544158451[/C][C]51.2280593054353[/C][/ROW]
[ROW][C]81[/C][C]48.8375728550328[/C][C]46.3596041620671[/C][C]51.3155415479985[/C][/ROW]
[ROW][C]82[/C][C]48.7488720812766[/C][C]46.1456141108932[/C][C]51.35213005166[/C][/ROW]
[ROW][C]83[/C][C]48.6226070484274[/C][C]45.9019438895835[/C][C]51.3432702072713[/C][/ROW]
[ROW][C]84[/C][C]48.6106390534819[/C][C]32.3763247194075[/C][C]64.8449533875563[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42254&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42254&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
7348.0237354997847.123478916118348.9239920834416
7448.165708815180546.955578589403849.3758390409573
7548.3555795309646.897551442451649.8136076194685
7648.172687024526246.51041764236349.8349564066894
7748.371044426497846.516919069023950.2251697839718
7848.312665080535146.291762401264950.3335677598053
7948.731497992690846.538863854801450.9241321305802
8048.884306860640246.540554415845151.2280593054353
8148.837572855032846.359604162067151.3155415479985
8248.748872081276646.145614110893251.35213005166
8348.622607048427445.901943889583551.3432702072713
8448.610639053481932.376324719407564.8449533875563



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; 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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')