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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 computationFri, 04 Dec 2009 08:14:43 -0700
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/Dec/04/t125993972548a6kdg5gcbylmf.htm/, Retrieved Sat, 27 Apr 2024 16:56:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=63736, Retrieved Sat, 27 Apr 2024 16:56:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact94
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [] [2009-11-27 15:04:36] [b98453cac15ba1066b407e146608df68]
-    D      [Exponential Smoothing] [ws 9] [2009-12-04 15:14:43] [dd4f17965cad1d38de7a1c062d32d75d] [Current]
-    D        [Exponential Smoothing] [ws9 exp] [2009-12-09 19:00:27] [626f1d98f4a7f05bcb9f17666b672c60]
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Dataseries X:
8.2
8
7.5
6.8
6.5
6.6
7.6
8
8.1
7.7
7.5
7.6
7.8
7.8
7.8
7.5
7.5
7.1
7.5
7.5
7.6
7.7
7.7
7.9
8.1
8.2
8.2
8.2
7.9
7.3
6.9
6.6
6.7
6.9
7
7.1
7.2
7.1
6.9
7
6.8
6.4
6.7
6.6
6.4
6.3
6.2
6.5
6.8
6.8
6.4
6.1
5.8
6.1
7.2
7.3
6.9
6.1
5.8
6.2
7.1
7.7
7.9
7.7
7.4
7.5
8
8.1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63736&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63736&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63736&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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0
gamma0.668258580403658

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.668258580403658 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63736&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[/C][/ROW]
[ROW][C]gamma[/C][C]0.668258580403658[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63736&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63736&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
gamma0.668258580403658







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
137.87.535619351761540.264380648238461
147.87.838265199013-0.0382651990129999
157.87.85558974755393-0.0555897475539346
167.57.53297162445567-0.0329716244556737
177.57.50408923805517-0.0040892380551707
187.17.092189306604490.00781069339551177
197.57.726775108697-0.226775108697007
207.57.93452869210363-0.434528692103629
217.67.60303279772518-0.00303279772517673
227.77.197400156712310.50259984328769
237.77.442276051241980.257723948758016
247.97.751277917586130.148722082413871
258.18.10295103420125-0.00295103420124754
268.28.139247195739680.0607528042603231
278.28.2577839329626-0.057783932962602
288.27.918644807158560.281355192841441
297.98.20332000728594-0.303320007285938
307.37.46981853034878-0.169818530348782
316.97.94407445538895-1.04407445538895
326.67.30083508308107-0.700835083081073
336.76.692291024161320.00770897583868368
346.96.346589778946860.553410221053142
3576.670333707871070.32966629212893
367.17.047742949375410.0522570506245881
377.27.2836842702277-0.0836842702276916
387.17.23630120555964-0.136301205559645
396.97.15174992308877-0.251749923088767
4076.665206963374180.334793036625819
416.87.00463868860462-0.204638688604619
426.46.43133816505198-0.0313381650519773
436.76.96622739527521-0.266227395275208
446.67.08960388007355-0.489603880073554
456.46.69229102416132-0.292291024161316
466.36.062986319691710.237013680308293
476.26.091376950342880.108623049657117
486.56.243702985706020.256297014293979
496.86.669234197247530.130765802752474
506.86.83499187659074-0.0349918765907411
516.46.85010428403227-0.450104284032268
526.16.18311548499557-0.0831154849955738
535.86.10562769959363-0.305627699593630
546.15.487265105691250.612734894308752
557.26.64027837523730.559721624762706
567.37.61768188759235-0.317681887592351
576.97.40064573693321-0.500645736933206
586.16.53565875178363-0.435658751783627
595.85.89839136450015-0.098391364500154
606.25.841683003871320.358316996128676
617.16.362009160757440.737990839242557
627.77.135973873317420.564026126682581
637.97.755041201201770.144958798798232
647.77.62938992013140.0706100798686062
657.47.70386945783539-0.303869457835389
667.56.997782000668420.502217999331584
6788.1613738020809-0.161373802080893
688.18.46260669962242-0.362606699622425

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 7.8 & 7.53561935176154 & 0.264380648238461 \tabularnewline
14 & 7.8 & 7.838265199013 & -0.0382651990129999 \tabularnewline
15 & 7.8 & 7.85558974755393 & -0.0555897475539346 \tabularnewline
16 & 7.5 & 7.53297162445567 & -0.0329716244556737 \tabularnewline
17 & 7.5 & 7.50408923805517 & -0.0040892380551707 \tabularnewline
18 & 7.1 & 7.09218930660449 & 0.00781069339551177 \tabularnewline
19 & 7.5 & 7.726775108697 & -0.226775108697007 \tabularnewline
20 & 7.5 & 7.93452869210363 & -0.434528692103629 \tabularnewline
21 & 7.6 & 7.60303279772518 & -0.00303279772517673 \tabularnewline
22 & 7.7 & 7.19740015671231 & 0.50259984328769 \tabularnewline
23 & 7.7 & 7.44227605124198 & 0.257723948758016 \tabularnewline
24 & 7.9 & 7.75127791758613 & 0.148722082413871 \tabularnewline
25 & 8.1 & 8.10295103420125 & -0.00295103420124754 \tabularnewline
26 & 8.2 & 8.13924719573968 & 0.0607528042603231 \tabularnewline
27 & 8.2 & 8.2577839329626 & -0.057783932962602 \tabularnewline
28 & 8.2 & 7.91864480715856 & 0.281355192841441 \tabularnewline
29 & 7.9 & 8.20332000728594 & -0.303320007285938 \tabularnewline
30 & 7.3 & 7.46981853034878 & -0.169818530348782 \tabularnewline
31 & 6.9 & 7.94407445538895 & -1.04407445538895 \tabularnewline
32 & 6.6 & 7.30083508308107 & -0.700835083081073 \tabularnewline
33 & 6.7 & 6.69229102416132 & 0.00770897583868368 \tabularnewline
34 & 6.9 & 6.34658977894686 & 0.553410221053142 \tabularnewline
35 & 7 & 6.67033370787107 & 0.32966629212893 \tabularnewline
36 & 7.1 & 7.04774294937541 & 0.0522570506245881 \tabularnewline
37 & 7.2 & 7.2836842702277 & -0.0836842702276916 \tabularnewline
38 & 7.1 & 7.23630120555964 & -0.136301205559645 \tabularnewline
39 & 6.9 & 7.15174992308877 & -0.251749923088767 \tabularnewline
40 & 7 & 6.66520696337418 & 0.334793036625819 \tabularnewline
41 & 6.8 & 7.00463868860462 & -0.204638688604619 \tabularnewline
42 & 6.4 & 6.43133816505198 & -0.0313381650519773 \tabularnewline
43 & 6.7 & 6.96622739527521 & -0.266227395275208 \tabularnewline
44 & 6.6 & 7.08960388007355 & -0.489603880073554 \tabularnewline
45 & 6.4 & 6.69229102416132 & -0.292291024161316 \tabularnewline
46 & 6.3 & 6.06298631969171 & 0.237013680308293 \tabularnewline
47 & 6.2 & 6.09137695034288 & 0.108623049657117 \tabularnewline
48 & 6.5 & 6.24370298570602 & 0.256297014293979 \tabularnewline
49 & 6.8 & 6.66923419724753 & 0.130765802752474 \tabularnewline
50 & 6.8 & 6.83499187659074 & -0.0349918765907411 \tabularnewline
51 & 6.4 & 6.85010428403227 & -0.450104284032268 \tabularnewline
52 & 6.1 & 6.18311548499557 & -0.0831154849955738 \tabularnewline
53 & 5.8 & 6.10562769959363 & -0.305627699593630 \tabularnewline
54 & 6.1 & 5.48726510569125 & 0.612734894308752 \tabularnewline
55 & 7.2 & 6.6402783752373 & 0.559721624762706 \tabularnewline
56 & 7.3 & 7.61768188759235 & -0.317681887592351 \tabularnewline
57 & 6.9 & 7.40064573693321 & -0.500645736933206 \tabularnewline
58 & 6.1 & 6.53565875178363 & -0.435658751783627 \tabularnewline
59 & 5.8 & 5.89839136450015 & -0.098391364500154 \tabularnewline
60 & 6.2 & 5.84168300387132 & 0.358316996128676 \tabularnewline
61 & 7.1 & 6.36200916075744 & 0.737990839242557 \tabularnewline
62 & 7.7 & 7.13597387331742 & 0.564026126682581 \tabularnewline
63 & 7.9 & 7.75504120120177 & 0.144958798798232 \tabularnewline
64 & 7.7 & 7.6293899201314 & 0.0706100798686062 \tabularnewline
65 & 7.4 & 7.70386945783539 & -0.303869457835389 \tabularnewline
66 & 7.5 & 6.99778200066842 & 0.502217999331584 \tabularnewline
67 & 8 & 8.1613738020809 & -0.161373802080893 \tabularnewline
68 & 8.1 & 8.46260669962242 & -0.362606699622425 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63736&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]7.8[/C][C]7.53561935176154[/C][C]0.264380648238461[/C][/ROW]
[ROW][C]14[/C][C]7.8[/C][C]7.838265199013[/C][C]-0.0382651990129999[/C][/ROW]
[ROW][C]15[/C][C]7.8[/C][C]7.85558974755393[/C][C]-0.0555897475539346[/C][/ROW]
[ROW][C]16[/C][C]7.5[/C][C]7.53297162445567[/C][C]-0.0329716244556737[/C][/ROW]
[ROW][C]17[/C][C]7.5[/C][C]7.50408923805517[/C][C]-0.0040892380551707[/C][/ROW]
[ROW][C]18[/C][C]7.1[/C][C]7.09218930660449[/C][C]0.00781069339551177[/C][/ROW]
[ROW][C]19[/C][C]7.5[/C][C]7.726775108697[/C][C]-0.226775108697007[/C][/ROW]
[ROW][C]20[/C][C]7.5[/C][C]7.93452869210363[/C][C]-0.434528692103629[/C][/ROW]
[ROW][C]21[/C][C]7.6[/C][C]7.60303279772518[/C][C]-0.00303279772517673[/C][/ROW]
[ROW][C]22[/C][C]7.7[/C][C]7.19740015671231[/C][C]0.50259984328769[/C][/ROW]
[ROW][C]23[/C][C]7.7[/C][C]7.44227605124198[/C][C]0.257723948758016[/C][/ROW]
[ROW][C]24[/C][C]7.9[/C][C]7.75127791758613[/C][C]0.148722082413871[/C][/ROW]
[ROW][C]25[/C][C]8.1[/C][C]8.10295103420125[/C][C]-0.00295103420124754[/C][/ROW]
[ROW][C]26[/C][C]8.2[/C][C]8.13924719573968[/C][C]0.0607528042603231[/C][/ROW]
[ROW][C]27[/C][C]8.2[/C][C]8.2577839329626[/C][C]-0.057783932962602[/C][/ROW]
[ROW][C]28[/C][C]8.2[/C][C]7.91864480715856[/C][C]0.281355192841441[/C][/ROW]
[ROW][C]29[/C][C]7.9[/C][C]8.20332000728594[/C][C]-0.303320007285938[/C][/ROW]
[ROW][C]30[/C][C]7.3[/C][C]7.46981853034878[/C][C]-0.169818530348782[/C][/ROW]
[ROW][C]31[/C][C]6.9[/C][C]7.94407445538895[/C][C]-1.04407445538895[/C][/ROW]
[ROW][C]32[/C][C]6.6[/C][C]7.30083508308107[/C][C]-0.700835083081073[/C][/ROW]
[ROW][C]33[/C][C]6.7[/C][C]6.69229102416132[/C][C]0.00770897583868368[/C][/ROW]
[ROW][C]34[/C][C]6.9[/C][C]6.34658977894686[/C][C]0.553410221053142[/C][/ROW]
[ROW][C]35[/C][C]7[/C][C]6.67033370787107[/C][C]0.32966629212893[/C][/ROW]
[ROW][C]36[/C][C]7.1[/C][C]7.04774294937541[/C][C]0.0522570506245881[/C][/ROW]
[ROW][C]37[/C][C]7.2[/C][C]7.2836842702277[/C][C]-0.0836842702276916[/C][/ROW]
[ROW][C]38[/C][C]7.1[/C][C]7.23630120555964[/C][C]-0.136301205559645[/C][/ROW]
[ROW][C]39[/C][C]6.9[/C][C]7.15174992308877[/C][C]-0.251749923088767[/C][/ROW]
[ROW][C]40[/C][C]7[/C][C]6.66520696337418[/C][C]0.334793036625819[/C][/ROW]
[ROW][C]41[/C][C]6.8[/C][C]7.00463868860462[/C][C]-0.204638688604619[/C][/ROW]
[ROW][C]42[/C][C]6.4[/C][C]6.43133816505198[/C][C]-0.0313381650519773[/C][/ROW]
[ROW][C]43[/C][C]6.7[/C][C]6.96622739527521[/C][C]-0.266227395275208[/C][/ROW]
[ROW][C]44[/C][C]6.6[/C][C]7.08960388007355[/C][C]-0.489603880073554[/C][/ROW]
[ROW][C]45[/C][C]6.4[/C][C]6.69229102416132[/C][C]-0.292291024161316[/C][/ROW]
[ROW][C]46[/C][C]6.3[/C][C]6.06298631969171[/C][C]0.237013680308293[/C][/ROW]
[ROW][C]47[/C][C]6.2[/C][C]6.09137695034288[/C][C]0.108623049657117[/C][/ROW]
[ROW][C]48[/C][C]6.5[/C][C]6.24370298570602[/C][C]0.256297014293979[/C][/ROW]
[ROW][C]49[/C][C]6.8[/C][C]6.66923419724753[/C][C]0.130765802752474[/C][/ROW]
[ROW][C]50[/C][C]6.8[/C][C]6.83499187659074[/C][C]-0.0349918765907411[/C][/ROW]
[ROW][C]51[/C][C]6.4[/C][C]6.85010428403227[/C][C]-0.450104284032268[/C][/ROW]
[ROW][C]52[/C][C]6.1[/C][C]6.18311548499557[/C][C]-0.0831154849955738[/C][/ROW]
[ROW][C]53[/C][C]5.8[/C][C]6.10562769959363[/C][C]-0.305627699593630[/C][/ROW]
[ROW][C]54[/C][C]6.1[/C][C]5.48726510569125[/C][C]0.612734894308752[/C][/ROW]
[ROW][C]55[/C][C]7.2[/C][C]6.6402783752373[/C][C]0.559721624762706[/C][/ROW]
[ROW][C]56[/C][C]7.3[/C][C]7.61768188759235[/C][C]-0.317681887592351[/C][/ROW]
[ROW][C]57[/C][C]6.9[/C][C]7.40064573693321[/C][C]-0.500645736933206[/C][/ROW]
[ROW][C]58[/C][C]6.1[/C][C]6.53565875178363[/C][C]-0.435658751783627[/C][/ROW]
[ROW][C]59[/C][C]5.8[/C][C]5.89839136450015[/C][C]-0.098391364500154[/C][/ROW]
[ROW][C]60[/C][C]6.2[/C][C]5.84168300387132[/C][C]0.358316996128676[/C][/ROW]
[ROW][C]61[/C][C]7.1[/C][C]6.36200916075744[/C][C]0.737990839242557[/C][/ROW]
[ROW][C]62[/C][C]7.7[/C][C]7.13597387331742[/C][C]0.564026126682581[/C][/ROW]
[ROW][C]63[/C][C]7.9[/C][C]7.75504120120177[/C][C]0.144958798798232[/C][/ROW]
[ROW][C]64[/C][C]7.7[/C][C]7.6293899201314[/C][C]0.0706100798686062[/C][/ROW]
[ROW][C]65[/C][C]7.4[/C][C]7.70386945783539[/C][C]-0.303869457835389[/C][/ROW]
[ROW][C]66[/C][C]7.5[/C][C]6.99778200066842[/C][C]0.502217999331584[/C][/ROW]
[ROW][C]67[/C][C]8[/C][C]8.1613738020809[/C][C]-0.161373802080893[/C][/ROW]
[ROW][C]68[/C][C]8.1[/C][C]8.46260669962242[/C][C]-0.362606699622425[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63736&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63736&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
137.87.535619351761540.264380648238461
147.87.838265199013-0.0382651990129999
157.87.85558974755393-0.0555897475539346
167.57.53297162445567-0.0329716244556737
177.57.50408923805517-0.0040892380551707
187.17.092189306604490.00781069339551177
197.57.726775108697-0.226775108697007
207.57.93452869210363-0.434528692103629
217.67.60303279772518-0.00303279772517673
227.77.197400156712310.50259984328769
237.77.442276051241980.257723948758016
247.97.751277917586130.148722082413871
258.18.10295103420125-0.00295103420124754
268.28.139247195739680.0607528042603231
278.28.2577839329626-0.057783932962602
288.27.918644807158560.281355192841441
297.98.20332000728594-0.303320007285938
307.37.46981853034878-0.169818530348782
316.97.94407445538895-1.04407445538895
326.67.30083508308107-0.700835083081073
336.76.692291024161320.00770897583868368
346.96.346589778946860.553410221053142
3576.670333707871070.32966629212893
367.17.047742949375410.0522570506245881
377.27.2836842702277-0.0836842702276916
387.17.23630120555964-0.136301205559645
396.97.15174992308877-0.251749923088767
4076.665206963374180.334793036625819
416.87.00463868860462-0.204638688604619
426.46.43133816505198-0.0313381650519773
436.76.96622739527521-0.266227395275208
446.67.08960388007355-0.489603880073554
456.46.69229102416132-0.292291024161316
466.36.062986319691710.237013680308293
476.26.091376950342880.108623049657117
486.56.243702985706020.256297014293979
496.86.669234197247530.130765802752474
506.86.83499187659074-0.0349918765907411
516.46.85010428403227-0.450104284032268
526.16.18311548499557-0.0831154849955738
535.86.10562769959363-0.305627699593630
546.15.487265105691250.612734894308752
557.26.64027837523730.559721624762706
567.37.61768188759235-0.317681887592351
576.97.40064573693321-0.500645736933206
586.16.53565875178363-0.435658751783627
595.85.89839136450015-0.098391364500154
606.25.841683003871320.358316996128676
617.16.362009160757440.737990839242557
627.77.135973873317420.564026126682581
637.97.755041201201770.144958798798232
647.77.62938992013140.0706100798686062
657.47.70386945783539-0.303869457835389
667.56.997782000668420.502217999331584
6788.1613738020809-0.161373802080893
688.18.46260669962242-0.362606699622425







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
698.210193980101087.52583909608818.89454886411406
707.774243901956766.832496755036448.71599104887708
717.513916065813866.376326404845868.65150572678187
727.564254267983036.231754646100158.8967538898659
737.75911938496696.232538334448129.28570043548569
747.797250768546086.119730900543589.47477063654858
757.852825435291166.032558372548699.67309249803363
767.583905008846695.70012848487269.46768153282078
777.587902043595435.58561317003979.59019091715117
787.175175257825695.164801636911029.18554887874037
797.808452780761615.5194895974079710.0974159641153
808.26030295186008-49.091117114819765.6117230185399

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
69 & 8.21019398010108 & 7.5258390960881 & 8.89454886411406 \tabularnewline
70 & 7.77424390195676 & 6.83249675503644 & 8.71599104887708 \tabularnewline
71 & 7.51391606581386 & 6.37632640484586 & 8.65150572678187 \tabularnewline
72 & 7.56425426798303 & 6.23175464610015 & 8.8967538898659 \tabularnewline
73 & 7.7591193849669 & 6.23253833444812 & 9.28570043548569 \tabularnewline
74 & 7.79725076854608 & 6.11973090054358 & 9.47477063654858 \tabularnewline
75 & 7.85282543529116 & 6.03255837254869 & 9.67309249803363 \tabularnewline
76 & 7.58390500884669 & 5.7001284848726 & 9.46768153282078 \tabularnewline
77 & 7.58790204359543 & 5.5856131700397 & 9.59019091715117 \tabularnewline
78 & 7.17517525782569 & 5.16480163691102 & 9.18554887874037 \tabularnewline
79 & 7.80845278076161 & 5.51948959740797 & 10.0974159641153 \tabularnewline
80 & 8.26030295186008 & -49.0911171148197 & 65.6117230185399 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63736&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]69[/C][C]8.21019398010108[/C][C]7.5258390960881[/C][C]8.89454886411406[/C][/ROW]
[ROW][C]70[/C][C]7.77424390195676[/C][C]6.83249675503644[/C][C]8.71599104887708[/C][/ROW]
[ROW][C]71[/C][C]7.51391606581386[/C][C]6.37632640484586[/C][C]8.65150572678187[/C][/ROW]
[ROW][C]72[/C][C]7.56425426798303[/C][C]6.23175464610015[/C][C]8.8967538898659[/C][/ROW]
[ROW][C]73[/C][C]7.7591193849669[/C][C]6.23253833444812[/C][C]9.28570043548569[/C][/ROW]
[ROW][C]74[/C][C]7.79725076854608[/C][C]6.11973090054358[/C][C]9.47477063654858[/C][/ROW]
[ROW][C]75[/C][C]7.85282543529116[/C][C]6.03255837254869[/C][C]9.67309249803363[/C][/ROW]
[ROW][C]76[/C][C]7.58390500884669[/C][C]5.7001284848726[/C][C]9.46768153282078[/C][/ROW]
[ROW][C]77[/C][C]7.58790204359543[/C][C]5.5856131700397[/C][C]9.59019091715117[/C][/ROW]
[ROW][C]78[/C][C]7.17517525782569[/C][C]5.16480163691102[/C][C]9.18554887874037[/C][/ROW]
[ROW][C]79[/C][C]7.80845278076161[/C][C]5.51948959740797[/C][C]10.0974159641153[/C][/ROW]
[ROW][C]80[/C][C]8.26030295186008[/C][C]-49.0911171148197[/C][C]65.6117230185399[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63736&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63736&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
698.210193980101087.52583909608818.89454886411406
707.774243901956766.832496755036448.71599104887708
717.513916065813866.376326404845868.65150572678187
727.564254267983036.231754646100158.8967538898659
737.75911938496696.232538334448129.28570043548569
747.797250768546086.119730900543589.47477063654858
757.852825435291166.032558372548699.67309249803363
767.583905008846695.70012848487269.46768153282078
777.587902043595435.58561317003979.59019091715117
787.175175257825695.164801636911029.18554887874037
797.808452780761615.5194895974079710.0974159641153
808.26030295186008-49.091117114819765.6117230185399



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')