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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 08:08:40 -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/t1259939380q926p21kykfbmts.htm/, Retrieved Sun, 28 Apr 2024 17:53:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=63719, Retrieved Sun, 28 Apr 2024 17:53:35 +0000
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Original text written by user:WS 9 Estimation of Box-Jenkins ARIMA models
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact97
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 Estimation o...] [2009-12-04 15:08:40] [9b6f46453e60f88d91cef176fe926003] [Current]
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Dataseries X:
14,5
14,3
15,3
14,4
13,7
14,2
13,5
11,9
14,6
15,6
14,1
14,9
14,2
14,6
17,2
15,4
14,3
17,5
14,5
14,4
16,6
16,7
16,6
16,9
15,7
16,4
18,4
16,9
16,5
18,3
15,1
15,7
18,1
16,8
18,9
19
18,1
17,8
21,5
17,1
18,7
19
16,4
16,9
18,6
19,3
19,4
17,6
18,6
18,1
20,4
18,1
19,6
19,9
19,2
17,8
19,2
22
21,1
19,5
22,2
20,9
22,2
23,5
21,5
24,3
22,8
20,3
23,7
23,3
19,6
18
17,3
16,8
18,2
16,5
16
18,4




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=63719&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=63719&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63719&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
alpha0.597126235287043
beta0
gamma0.901410325583061

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.597126235287043 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.901410325583061 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63719&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]0.597126235287043[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.901410325583061[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63719&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63719&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
alpha0.597126235287043
beta0
gamma0.901410325583061







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1314.213.48124933461880.718750665381153
1414.614.29628340915340.303716590846596
1517.217.00011340243040.199886597569616
1615.415.33607807945040.0639219205496122
1714.314.26402498196810.0359750180319054
1817.517.42570034121200.0742996587880462
1914.514.9514570741622-0.451457074162191
2014.413.05606186322431.34393813677572
2116.617.033454253127-0.433454253127014
2216.717.9212732352252-1.22127323522519
2316.615.60035473860590.999645261394079
2416.917.0655402785585-0.165540278558492
2515.716.4074650629215-0.707465062921482
2616.416.23152604485300.168473955147029
2718.419.0948308769003-0.694830876900333
2816.916.67657282704870.223427172951286
2916.515.57521179240120.924788207598825
3018.319.6653161652278-1.36531616522776
3115.115.9178336435388-0.81783364353884
3215.714.35706484297231.34293515702767
3318.117.82123443869970.278765561300325
3416.818.8869887133395-2.08698871333949
3518.916.79251394429582.10748605570420
361918.52331806598210.476681934017947
3718.117.94462089744220.155379102557834
3817.818.6647243046389-0.864724304638944
3921.520.83715667016040.662843329839617
4017.119.2870598574822-2.18705985748221
4118.716.91721966035001.78278033965004
421920.9004375180540-1.90043751805396
4316.416.8022581308116-0.40225813081161
4416.916.20738236589340.69261763410659
4518.619.0288496196914-0.428849619691373
4619.318.75368616633170.546313833668307
4719.419.7639881593884-0.363988159388381
4817.619.4139860794003-1.81398607940025
4918.617.38858217036841.21141782963165
5018.118.3600001031061-0.260000103106115
5120.421.5078361206708-1.10783612067084
5218.117.90041220778390.199587792216132
5319.618.36900533320611.23099466679392
5419.920.681164758908-0.781164758907984
5519.217.64123096182061.55876903817939
5617.818.5972258934997-0.797225893499718
5719.220.2573983934826-1.05739839348260
582219.96809477258642.03190522741363
5921.121.5543092064775-0.454309206477525
6019.520.5047320951071-1.00473209510708
6122.220.04422198446672.15577801553334
6220.920.9816621659555-0.0816621659554997
6322.224.3564489374252-2.15644893742518
6423.520.26282759724123.23717240275884
6521.523.0318681203166-1.53186812031663
6624.323.04859786704481.25140213295523
6722.821.67910658304581.12089341695419
6820.321.3494133167639-1.04941331676385
6923.723.05931917341650.640680826583509
7023.325.1425232705637-1.84252327056371
7119.623.4451898225841-3.84518982258406
721820.1582924440604-2.15829244406035
7317.320.0717158947412-2.77171589474115
7416.817.4705444768559-0.670544476855923
7518.219.2418463363559-1.0418463363559
7616.517.8493142704545-1.34931427045453
771616.4096486766431-0.409648676643094
7818.417.64664394087790.753356059122133

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 14.2 & 13.4812493346188 & 0.718750665381153 \tabularnewline
14 & 14.6 & 14.2962834091534 & 0.303716590846596 \tabularnewline
15 & 17.2 & 17.0001134024304 & 0.199886597569616 \tabularnewline
16 & 15.4 & 15.3360780794504 & 0.0639219205496122 \tabularnewline
17 & 14.3 & 14.2640249819681 & 0.0359750180319054 \tabularnewline
18 & 17.5 & 17.4257003412120 & 0.0742996587880462 \tabularnewline
19 & 14.5 & 14.9514570741622 & -0.451457074162191 \tabularnewline
20 & 14.4 & 13.0560618632243 & 1.34393813677572 \tabularnewline
21 & 16.6 & 17.033454253127 & -0.433454253127014 \tabularnewline
22 & 16.7 & 17.9212732352252 & -1.22127323522519 \tabularnewline
23 & 16.6 & 15.6003547386059 & 0.999645261394079 \tabularnewline
24 & 16.9 & 17.0655402785585 & -0.165540278558492 \tabularnewline
25 & 15.7 & 16.4074650629215 & -0.707465062921482 \tabularnewline
26 & 16.4 & 16.2315260448530 & 0.168473955147029 \tabularnewline
27 & 18.4 & 19.0948308769003 & -0.694830876900333 \tabularnewline
28 & 16.9 & 16.6765728270487 & 0.223427172951286 \tabularnewline
29 & 16.5 & 15.5752117924012 & 0.924788207598825 \tabularnewline
30 & 18.3 & 19.6653161652278 & -1.36531616522776 \tabularnewline
31 & 15.1 & 15.9178336435388 & -0.81783364353884 \tabularnewline
32 & 15.7 & 14.3570648429723 & 1.34293515702767 \tabularnewline
33 & 18.1 & 17.8212344386997 & 0.278765561300325 \tabularnewline
34 & 16.8 & 18.8869887133395 & -2.08698871333949 \tabularnewline
35 & 18.9 & 16.7925139442958 & 2.10748605570420 \tabularnewline
36 & 19 & 18.5233180659821 & 0.476681934017947 \tabularnewline
37 & 18.1 & 17.9446208974422 & 0.155379102557834 \tabularnewline
38 & 17.8 & 18.6647243046389 & -0.864724304638944 \tabularnewline
39 & 21.5 & 20.8371566701604 & 0.662843329839617 \tabularnewline
40 & 17.1 & 19.2870598574822 & -2.18705985748221 \tabularnewline
41 & 18.7 & 16.9172196603500 & 1.78278033965004 \tabularnewline
42 & 19 & 20.9004375180540 & -1.90043751805396 \tabularnewline
43 & 16.4 & 16.8022581308116 & -0.40225813081161 \tabularnewline
44 & 16.9 & 16.2073823658934 & 0.69261763410659 \tabularnewline
45 & 18.6 & 19.0288496196914 & -0.428849619691373 \tabularnewline
46 & 19.3 & 18.7536861663317 & 0.546313833668307 \tabularnewline
47 & 19.4 & 19.7639881593884 & -0.363988159388381 \tabularnewline
48 & 17.6 & 19.4139860794003 & -1.81398607940025 \tabularnewline
49 & 18.6 & 17.3885821703684 & 1.21141782963165 \tabularnewline
50 & 18.1 & 18.3600001031061 & -0.260000103106115 \tabularnewline
51 & 20.4 & 21.5078361206708 & -1.10783612067084 \tabularnewline
52 & 18.1 & 17.9004122077839 & 0.199587792216132 \tabularnewline
53 & 19.6 & 18.3690053332061 & 1.23099466679392 \tabularnewline
54 & 19.9 & 20.681164758908 & -0.781164758907984 \tabularnewline
55 & 19.2 & 17.6412309618206 & 1.55876903817939 \tabularnewline
56 & 17.8 & 18.5972258934997 & -0.797225893499718 \tabularnewline
57 & 19.2 & 20.2573983934826 & -1.05739839348260 \tabularnewline
58 & 22 & 19.9680947725864 & 2.03190522741363 \tabularnewline
59 & 21.1 & 21.5543092064775 & -0.454309206477525 \tabularnewline
60 & 19.5 & 20.5047320951071 & -1.00473209510708 \tabularnewline
61 & 22.2 & 20.0442219844667 & 2.15577801553334 \tabularnewline
62 & 20.9 & 20.9816621659555 & -0.0816621659554997 \tabularnewline
63 & 22.2 & 24.3564489374252 & -2.15644893742518 \tabularnewline
64 & 23.5 & 20.2628275972412 & 3.23717240275884 \tabularnewline
65 & 21.5 & 23.0318681203166 & -1.53186812031663 \tabularnewline
66 & 24.3 & 23.0485978670448 & 1.25140213295523 \tabularnewline
67 & 22.8 & 21.6791065830458 & 1.12089341695419 \tabularnewline
68 & 20.3 & 21.3494133167639 & -1.04941331676385 \tabularnewline
69 & 23.7 & 23.0593191734165 & 0.640680826583509 \tabularnewline
70 & 23.3 & 25.1425232705637 & -1.84252327056371 \tabularnewline
71 & 19.6 & 23.4451898225841 & -3.84518982258406 \tabularnewline
72 & 18 & 20.1582924440604 & -2.15829244406035 \tabularnewline
73 & 17.3 & 20.0717158947412 & -2.77171589474115 \tabularnewline
74 & 16.8 & 17.4705444768559 & -0.670544476855923 \tabularnewline
75 & 18.2 & 19.2418463363559 & -1.0418463363559 \tabularnewline
76 & 16.5 & 17.8493142704545 & -1.34931427045453 \tabularnewline
77 & 16 & 16.4096486766431 & -0.409648676643094 \tabularnewline
78 & 18.4 & 17.6466439408779 & 0.753356059122133 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63719&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]14.2[/C][C]13.4812493346188[/C][C]0.718750665381153[/C][/ROW]
[ROW][C]14[/C][C]14.6[/C][C]14.2962834091534[/C][C]0.303716590846596[/C][/ROW]
[ROW][C]15[/C][C]17.2[/C][C]17.0001134024304[/C][C]0.199886597569616[/C][/ROW]
[ROW][C]16[/C][C]15.4[/C][C]15.3360780794504[/C][C]0.0639219205496122[/C][/ROW]
[ROW][C]17[/C][C]14.3[/C][C]14.2640249819681[/C][C]0.0359750180319054[/C][/ROW]
[ROW][C]18[/C][C]17.5[/C][C]17.4257003412120[/C][C]0.0742996587880462[/C][/ROW]
[ROW][C]19[/C][C]14.5[/C][C]14.9514570741622[/C][C]-0.451457074162191[/C][/ROW]
[ROW][C]20[/C][C]14.4[/C][C]13.0560618632243[/C][C]1.34393813677572[/C][/ROW]
[ROW][C]21[/C][C]16.6[/C][C]17.033454253127[/C][C]-0.433454253127014[/C][/ROW]
[ROW][C]22[/C][C]16.7[/C][C]17.9212732352252[/C][C]-1.22127323522519[/C][/ROW]
[ROW][C]23[/C][C]16.6[/C][C]15.6003547386059[/C][C]0.999645261394079[/C][/ROW]
[ROW][C]24[/C][C]16.9[/C][C]17.0655402785585[/C][C]-0.165540278558492[/C][/ROW]
[ROW][C]25[/C][C]15.7[/C][C]16.4074650629215[/C][C]-0.707465062921482[/C][/ROW]
[ROW][C]26[/C][C]16.4[/C][C]16.2315260448530[/C][C]0.168473955147029[/C][/ROW]
[ROW][C]27[/C][C]18.4[/C][C]19.0948308769003[/C][C]-0.694830876900333[/C][/ROW]
[ROW][C]28[/C][C]16.9[/C][C]16.6765728270487[/C][C]0.223427172951286[/C][/ROW]
[ROW][C]29[/C][C]16.5[/C][C]15.5752117924012[/C][C]0.924788207598825[/C][/ROW]
[ROW][C]30[/C][C]18.3[/C][C]19.6653161652278[/C][C]-1.36531616522776[/C][/ROW]
[ROW][C]31[/C][C]15.1[/C][C]15.9178336435388[/C][C]-0.81783364353884[/C][/ROW]
[ROW][C]32[/C][C]15.7[/C][C]14.3570648429723[/C][C]1.34293515702767[/C][/ROW]
[ROW][C]33[/C][C]18.1[/C][C]17.8212344386997[/C][C]0.278765561300325[/C][/ROW]
[ROW][C]34[/C][C]16.8[/C][C]18.8869887133395[/C][C]-2.08698871333949[/C][/ROW]
[ROW][C]35[/C][C]18.9[/C][C]16.7925139442958[/C][C]2.10748605570420[/C][/ROW]
[ROW][C]36[/C][C]19[/C][C]18.5233180659821[/C][C]0.476681934017947[/C][/ROW]
[ROW][C]37[/C][C]18.1[/C][C]17.9446208974422[/C][C]0.155379102557834[/C][/ROW]
[ROW][C]38[/C][C]17.8[/C][C]18.6647243046389[/C][C]-0.864724304638944[/C][/ROW]
[ROW][C]39[/C][C]21.5[/C][C]20.8371566701604[/C][C]0.662843329839617[/C][/ROW]
[ROW][C]40[/C][C]17.1[/C][C]19.2870598574822[/C][C]-2.18705985748221[/C][/ROW]
[ROW][C]41[/C][C]18.7[/C][C]16.9172196603500[/C][C]1.78278033965004[/C][/ROW]
[ROW][C]42[/C][C]19[/C][C]20.9004375180540[/C][C]-1.90043751805396[/C][/ROW]
[ROW][C]43[/C][C]16.4[/C][C]16.8022581308116[/C][C]-0.40225813081161[/C][/ROW]
[ROW][C]44[/C][C]16.9[/C][C]16.2073823658934[/C][C]0.69261763410659[/C][/ROW]
[ROW][C]45[/C][C]18.6[/C][C]19.0288496196914[/C][C]-0.428849619691373[/C][/ROW]
[ROW][C]46[/C][C]19.3[/C][C]18.7536861663317[/C][C]0.546313833668307[/C][/ROW]
[ROW][C]47[/C][C]19.4[/C][C]19.7639881593884[/C][C]-0.363988159388381[/C][/ROW]
[ROW][C]48[/C][C]17.6[/C][C]19.4139860794003[/C][C]-1.81398607940025[/C][/ROW]
[ROW][C]49[/C][C]18.6[/C][C]17.3885821703684[/C][C]1.21141782963165[/C][/ROW]
[ROW][C]50[/C][C]18.1[/C][C]18.3600001031061[/C][C]-0.260000103106115[/C][/ROW]
[ROW][C]51[/C][C]20.4[/C][C]21.5078361206708[/C][C]-1.10783612067084[/C][/ROW]
[ROW][C]52[/C][C]18.1[/C][C]17.9004122077839[/C][C]0.199587792216132[/C][/ROW]
[ROW][C]53[/C][C]19.6[/C][C]18.3690053332061[/C][C]1.23099466679392[/C][/ROW]
[ROW][C]54[/C][C]19.9[/C][C]20.681164758908[/C][C]-0.781164758907984[/C][/ROW]
[ROW][C]55[/C][C]19.2[/C][C]17.6412309618206[/C][C]1.55876903817939[/C][/ROW]
[ROW][C]56[/C][C]17.8[/C][C]18.5972258934997[/C][C]-0.797225893499718[/C][/ROW]
[ROW][C]57[/C][C]19.2[/C][C]20.2573983934826[/C][C]-1.05739839348260[/C][/ROW]
[ROW][C]58[/C][C]22[/C][C]19.9680947725864[/C][C]2.03190522741363[/C][/ROW]
[ROW][C]59[/C][C]21.1[/C][C]21.5543092064775[/C][C]-0.454309206477525[/C][/ROW]
[ROW][C]60[/C][C]19.5[/C][C]20.5047320951071[/C][C]-1.00473209510708[/C][/ROW]
[ROW][C]61[/C][C]22.2[/C][C]20.0442219844667[/C][C]2.15577801553334[/C][/ROW]
[ROW][C]62[/C][C]20.9[/C][C]20.9816621659555[/C][C]-0.0816621659554997[/C][/ROW]
[ROW][C]63[/C][C]22.2[/C][C]24.3564489374252[/C][C]-2.15644893742518[/C][/ROW]
[ROW][C]64[/C][C]23.5[/C][C]20.2628275972412[/C][C]3.23717240275884[/C][/ROW]
[ROW][C]65[/C][C]21.5[/C][C]23.0318681203166[/C][C]-1.53186812031663[/C][/ROW]
[ROW][C]66[/C][C]24.3[/C][C]23.0485978670448[/C][C]1.25140213295523[/C][/ROW]
[ROW][C]67[/C][C]22.8[/C][C]21.6791065830458[/C][C]1.12089341695419[/C][/ROW]
[ROW][C]68[/C][C]20.3[/C][C]21.3494133167639[/C][C]-1.04941331676385[/C][/ROW]
[ROW][C]69[/C][C]23.7[/C][C]23.0593191734165[/C][C]0.640680826583509[/C][/ROW]
[ROW][C]70[/C][C]23.3[/C][C]25.1425232705637[/C][C]-1.84252327056371[/C][/ROW]
[ROW][C]71[/C][C]19.6[/C][C]23.4451898225841[/C][C]-3.84518982258406[/C][/ROW]
[ROW][C]72[/C][C]18[/C][C]20.1582924440604[/C][C]-2.15829244406035[/C][/ROW]
[ROW][C]73[/C][C]17.3[/C][C]20.0717158947412[/C][C]-2.77171589474115[/C][/ROW]
[ROW][C]74[/C][C]16.8[/C][C]17.4705444768559[/C][C]-0.670544476855923[/C][/ROW]
[ROW][C]75[/C][C]18.2[/C][C]19.2418463363559[/C][C]-1.0418463363559[/C][/ROW]
[ROW][C]76[/C][C]16.5[/C][C]17.8493142704545[/C][C]-1.34931427045453[/C][/ROW]
[ROW][C]77[/C][C]16[/C][C]16.4096486766431[/C][C]-0.409648676643094[/C][/ROW]
[ROW][C]78[/C][C]18.4[/C][C]17.6466439408779[/C][C]0.753356059122133[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63719&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63719&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
1314.213.48124933461880.718750665381153
1414.614.29628340915340.303716590846596
1517.217.00011340243040.199886597569616
1615.415.33607807945040.0639219205496122
1714.314.26402498196810.0359750180319054
1817.517.42570034121200.0742996587880462
1914.514.9514570741622-0.451457074162191
2014.413.05606186322431.34393813677572
2116.617.033454253127-0.433454253127014
2216.717.9212732352252-1.22127323522519
2316.615.60035473860590.999645261394079
2416.917.0655402785585-0.165540278558492
2515.716.4074650629215-0.707465062921482
2616.416.23152604485300.168473955147029
2718.419.0948308769003-0.694830876900333
2816.916.67657282704870.223427172951286
2916.515.57521179240120.924788207598825
3018.319.6653161652278-1.36531616522776
3115.115.9178336435388-0.81783364353884
3215.714.35706484297231.34293515702767
3318.117.82123443869970.278765561300325
3416.818.8869887133395-2.08698871333949
3518.916.79251394429582.10748605570420
361918.52331806598210.476681934017947
3718.117.94462089744220.155379102557834
3817.818.6647243046389-0.864724304638944
3921.520.83715667016040.662843329839617
4017.119.2870598574822-2.18705985748221
4118.716.91721966035001.78278033965004
421920.9004375180540-1.90043751805396
4316.416.8022581308116-0.40225813081161
4416.916.20738236589340.69261763410659
4518.619.0288496196914-0.428849619691373
4619.318.75368616633170.546313833668307
4719.419.7639881593884-0.363988159388381
4817.619.4139860794003-1.81398607940025
4918.617.38858217036841.21141782963165
5018.118.3600001031061-0.260000103106115
5120.421.5078361206708-1.10783612067084
5218.117.90041220778390.199587792216132
5319.618.36900533320611.23099466679392
5419.920.681164758908-0.781164758907984
5519.217.64123096182061.55876903817939
5617.818.5972258934997-0.797225893499718
5719.220.2573983934826-1.05739839348260
582219.96809477258642.03190522741363
5921.121.5543092064775-0.454309206477525
6019.520.5047320951071-1.00473209510708
6122.220.04422198446672.15577801553334
6220.920.9816621659555-0.0816621659554997
6322.224.3564489374252-2.15644893742518
6423.520.26282759724123.23717240275884
6521.523.0318681203166-1.53186812031663
6624.323.04859786704481.25140213295523
6722.821.67910658304581.12089341695419
6820.321.3494133167639-1.04941331676385
6923.723.05931917341650.640680826583509
7023.325.1425232705637-1.84252327056371
7119.623.4451898225841-3.84518982258406
721820.1582924440604-2.15829244406035
7317.320.0717158947412-2.77171589474115
7416.817.4705444768559-0.670544476855923
7518.219.2418463363559-1.0418463363559
7616.517.8493142704545-1.34931427045453
771616.4096486766431-0.409648676643094
7818.417.64664394087790.753356059122133







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7916.505612912401914.040650971610818.970574853193
8015.233818510149712.397271306980118.0703657133193
8117.474659892236414.058331721550520.8909880629224
8218.078333329684414.277277972399421.8793886869694
8316.966212033204913.045183087572820.887240978837
8416.613214360807012.481060831112120.7453678905019
8517.440543823409312.905675773334821.9754118734839
8617.251218213052812.528454932407621.9739814936979
8719.322883787982613.934206814970724.7115607609946
8818.355926147873613.009818415290523.7020338804567
8918.014454267228812.567981332051923.4609272024057
9020.1300023440808-0.09561815155130340.3556228397129

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
79 & 16.5056129124019 & 14.0406509716108 & 18.970574853193 \tabularnewline
80 & 15.2338185101497 & 12.3972713069801 & 18.0703657133193 \tabularnewline
81 & 17.4746598922364 & 14.0583317215505 & 20.8909880629224 \tabularnewline
82 & 18.0783333296844 & 14.2772779723994 & 21.8793886869694 \tabularnewline
83 & 16.9662120332049 & 13.0451830875728 & 20.887240978837 \tabularnewline
84 & 16.6132143608070 & 12.4810608311121 & 20.7453678905019 \tabularnewline
85 & 17.4405438234093 & 12.9056757733348 & 21.9754118734839 \tabularnewline
86 & 17.2512182130528 & 12.5284549324076 & 21.9739814936979 \tabularnewline
87 & 19.3228837879826 & 13.9342068149707 & 24.7115607609946 \tabularnewline
88 & 18.3559261478736 & 13.0098184152905 & 23.7020338804567 \tabularnewline
89 & 18.0144542672288 & 12.5679813320519 & 23.4609272024057 \tabularnewline
90 & 20.1300023440808 & -0.095618151551303 & 40.3556228397129 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63719&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]79[/C][C]16.5056129124019[/C][C]14.0406509716108[/C][C]18.970574853193[/C][/ROW]
[ROW][C]80[/C][C]15.2338185101497[/C][C]12.3972713069801[/C][C]18.0703657133193[/C][/ROW]
[ROW][C]81[/C][C]17.4746598922364[/C][C]14.0583317215505[/C][C]20.8909880629224[/C][/ROW]
[ROW][C]82[/C][C]18.0783333296844[/C][C]14.2772779723994[/C][C]21.8793886869694[/C][/ROW]
[ROW][C]83[/C][C]16.9662120332049[/C][C]13.0451830875728[/C][C]20.887240978837[/C][/ROW]
[ROW][C]84[/C][C]16.6132143608070[/C][C]12.4810608311121[/C][C]20.7453678905019[/C][/ROW]
[ROW][C]85[/C][C]17.4405438234093[/C][C]12.9056757733348[/C][C]21.9754118734839[/C][/ROW]
[ROW][C]86[/C][C]17.2512182130528[/C][C]12.5284549324076[/C][C]21.9739814936979[/C][/ROW]
[ROW][C]87[/C][C]19.3228837879826[/C][C]13.9342068149707[/C][C]24.7115607609946[/C][/ROW]
[ROW][C]88[/C][C]18.3559261478736[/C][C]13.0098184152905[/C][C]23.7020338804567[/C][/ROW]
[ROW][C]89[/C][C]18.0144542672288[/C][C]12.5679813320519[/C][C]23.4609272024057[/C][/ROW]
[ROW][C]90[/C][C]20.1300023440808[/C][C]-0.095618151551303[/C][C]40.3556228397129[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63719&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63719&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
7916.505612912401914.040650971610818.970574853193
8015.233818510149712.397271306980118.0703657133193
8117.474659892236414.058331721550520.8909880629224
8218.078333329684414.277277972399421.8793886869694
8316.966212033204913.045183087572820.887240978837
8416.613214360807012.481060831112120.7453678905019
8517.440543823409312.905675773334821.9754118734839
8617.251218213052812.528454932407621.9739814936979
8719.322883787982613.934206814970724.7115607609946
8818.355926147873613.009818415290523.7020338804567
8918.014454267228812.567981332051923.4609272024057
9020.1300023440808-0.09561815155130340.3556228397129



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')