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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 27 May 2008 07:24:45 -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/2008/May/27/t1211894722v9opm1lsd3kr06w.htm/, Retrieved Mon, 20 May 2024 00:41:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13350, Retrieved Mon, 20 May 2024 00:41:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact207
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2008-05-27 13:24:45] [e3a9774fc191d7d42e3eb0422143859b] [Current]
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Dataseries X:
65.05
65.84
66.6
67.55
68.07
69.06
69.06
69.11
69.29
69.38
69.28
69.75
69.9
70.21
70.48
71.55
72.18
72.64
72.77
72.74
73.13
73.44
73.34
73.34
73.81
74.26
74.72
75.11
75.26
75.89
75.91
76.43
76.56
76.76
76.76
76.56
76.82
77.09
77.51
77.76
77.86
77.89
77.94
77.99
78.17
78.91
78.87
78.88
79.08
79.41
79.51
79.73
80.38
80.56
80.46
80.45
80.58
80.68
80.52
81.49
81.66
81.95
82.3
82.4
83.14
83.17
83.11
83.21
83.33
83.88
83.8
83.73




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13350&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13350&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13350&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.91765681329827
beta0.0281982947013472
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.91765681329827 \tabularnewline
beta & 0.0281982947013472 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13350&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]0.91765681329827[/C][/ROW]
[ROW][C]beta[/C][C]0.0281982947013472[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13350&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13350&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
alpha0.91765681329827
beta0.0281982947013472
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1369.968.02802916666671.87197083333332
1470.2170.10975244512550.100247554874514
1570.4870.5228191607047-0.0428191607047381
1671.5571.58557505941-0.0355750594100357
1772.1872.2048913374113-0.0248913374112476
1872.6472.68295084189-0.0429508418899331
1972.7772.8195765077098-0.0495765077097872
2072.7472.7696725600557-0.0296725600557295
2173.1373.1435157878132-0.0135157878132333
2273.4473.4722523150126-0.0322523150125988
2373.3473.4212939012777-0.081293901277661
2473.3473.436145218406-0.0961452184060647
2573.8173.8711076123279-0.061107612327902
2674.2674.02244121058340.237558789416610
2774.7274.54268732817080.177312671829171
2875.1175.8066967965121-0.696696796512128
2975.2675.8017541088003-0.541754108800276
3075.8975.77219353574280.117806464257242
3175.9176.028123117202-0.118123117201989
3276.4375.88751158104440.542488418955642
3376.5676.7730937917569-0.21309379175689
3476.7676.8973401889136-0.137340188913640
3576.7676.72338645025410.0366135497458657
3676.5676.8257419727494-0.265741972749396
3776.8277.0840978458444-0.264097845844390
3877.0977.04463655692960.0453634430704284
3977.5177.34946647307340.160533526926628
4077.7678.4915895617186-0.731589561718593
4177.8678.4319627090602-0.571962709060188
4277.8978.3927865831474-0.50278658314744
4377.9478.0075341009755-0.067534100975493
4477.9977.91678840693220.0732115930677537
4578.1778.2464209468388-0.0764209468388088
4678.9178.44276295259030.467237047409682
4778.8778.79401084394440.0759891560555985
4878.8878.8647049446210.0152950553789708
4979.0879.3454661605704-0.265466160570440
5079.4179.29457026656860.115429733431441
5179.5179.639332533077-0.129332533077033
5279.7380.4006491909566-0.670649190956595
5380.3880.3703171754590.00968282454105918
5480.5680.8458673936501-0.285867393650108
5580.4680.6764046131194-0.216404613119437
5680.4580.4376763547750.0123236452249529
5780.5880.6745779025397-0.0945779025396547
5880.6880.8740192182473-0.194019218247334
5980.5280.5441279228942-0.0241279228942375
6081.4980.47324422195251.01675577804747
6181.6681.8310911391947-0.171091139194701
6281.9581.88181260915520.0681873908447699
6382.382.1454949542480.154505045752032
6482.483.1124748853218-0.712474885321768
6583.1483.08847116971660.0515288302834165
6683.1783.567857162711-0.397857162710949
6783.1183.2882201563354-0.178220156335357
6883.2183.09122857529460.118771424705429
6983.3383.4076267565173-0.077626756517347
7083.8883.60549044341450.274509556585457
7183.883.72271633050170.0772836694982715
7283.7383.836406681119-0.106406681118941

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 69.9 & 68.0280291666667 & 1.87197083333332 \tabularnewline
14 & 70.21 & 70.1097524451255 & 0.100247554874514 \tabularnewline
15 & 70.48 & 70.5228191607047 & -0.0428191607047381 \tabularnewline
16 & 71.55 & 71.58557505941 & -0.0355750594100357 \tabularnewline
17 & 72.18 & 72.2048913374113 & -0.0248913374112476 \tabularnewline
18 & 72.64 & 72.68295084189 & -0.0429508418899331 \tabularnewline
19 & 72.77 & 72.8195765077098 & -0.0495765077097872 \tabularnewline
20 & 72.74 & 72.7696725600557 & -0.0296725600557295 \tabularnewline
21 & 73.13 & 73.1435157878132 & -0.0135157878132333 \tabularnewline
22 & 73.44 & 73.4722523150126 & -0.0322523150125988 \tabularnewline
23 & 73.34 & 73.4212939012777 & -0.081293901277661 \tabularnewline
24 & 73.34 & 73.436145218406 & -0.0961452184060647 \tabularnewline
25 & 73.81 & 73.8711076123279 & -0.061107612327902 \tabularnewline
26 & 74.26 & 74.0224412105834 & 0.237558789416610 \tabularnewline
27 & 74.72 & 74.5426873281708 & 0.177312671829171 \tabularnewline
28 & 75.11 & 75.8066967965121 & -0.696696796512128 \tabularnewline
29 & 75.26 & 75.8017541088003 & -0.541754108800276 \tabularnewline
30 & 75.89 & 75.7721935357428 & 0.117806464257242 \tabularnewline
31 & 75.91 & 76.028123117202 & -0.118123117201989 \tabularnewline
32 & 76.43 & 75.8875115810444 & 0.542488418955642 \tabularnewline
33 & 76.56 & 76.7730937917569 & -0.21309379175689 \tabularnewline
34 & 76.76 & 76.8973401889136 & -0.137340188913640 \tabularnewline
35 & 76.76 & 76.7233864502541 & 0.0366135497458657 \tabularnewline
36 & 76.56 & 76.8257419727494 & -0.265741972749396 \tabularnewline
37 & 76.82 & 77.0840978458444 & -0.264097845844390 \tabularnewline
38 & 77.09 & 77.0446365569296 & 0.0453634430704284 \tabularnewline
39 & 77.51 & 77.3494664730734 & 0.160533526926628 \tabularnewline
40 & 77.76 & 78.4915895617186 & -0.731589561718593 \tabularnewline
41 & 77.86 & 78.4319627090602 & -0.571962709060188 \tabularnewline
42 & 77.89 & 78.3927865831474 & -0.50278658314744 \tabularnewline
43 & 77.94 & 78.0075341009755 & -0.067534100975493 \tabularnewline
44 & 77.99 & 77.9167884069322 & 0.0732115930677537 \tabularnewline
45 & 78.17 & 78.2464209468388 & -0.0764209468388088 \tabularnewline
46 & 78.91 & 78.4427629525903 & 0.467237047409682 \tabularnewline
47 & 78.87 & 78.7940108439444 & 0.0759891560555985 \tabularnewline
48 & 78.88 & 78.864704944621 & 0.0152950553789708 \tabularnewline
49 & 79.08 & 79.3454661605704 & -0.265466160570440 \tabularnewline
50 & 79.41 & 79.2945702665686 & 0.115429733431441 \tabularnewline
51 & 79.51 & 79.639332533077 & -0.129332533077033 \tabularnewline
52 & 79.73 & 80.4006491909566 & -0.670649190956595 \tabularnewline
53 & 80.38 & 80.370317175459 & 0.00968282454105918 \tabularnewline
54 & 80.56 & 80.8458673936501 & -0.285867393650108 \tabularnewline
55 & 80.46 & 80.6764046131194 & -0.216404613119437 \tabularnewline
56 & 80.45 & 80.437676354775 & 0.0123236452249529 \tabularnewline
57 & 80.58 & 80.6745779025397 & -0.0945779025396547 \tabularnewline
58 & 80.68 & 80.8740192182473 & -0.194019218247334 \tabularnewline
59 & 80.52 & 80.5441279228942 & -0.0241279228942375 \tabularnewline
60 & 81.49 & 80.4732442219525 & 1.01675577804747 \tabularnewline
61 & 81.66 & 81.8310911391947 & -0.171091139194701 \tabularnewline
62 & 81.95 & 81.8818126091552 & 0.0681873908447699 \tabularnewline
63 & 82.3 & 82.145494954248 & 0.154505045752032 \tabularnewline
64 & 82.4 & 83.1124748853218 & -0.712474885321768 \tabularnewline
65 & 83.14 & 83.0884711697166 & 0.0515288302834165 \tabularnewline
66 & 83.17 & 83.567857162711 & -0.397857162710949 \tabularnewline
67 & 83.11 & 83.2882201563354 & -0.178220156335357 \tabularnewline
68 & 83.21 & 83.0912285752946 & 0.118771424705429 \tabularnewline
69 & 83.33 & 83.4076267565173 & -0.077626756517347 \tabularnewline
70 & 83.88 & 83.6054904434145 & 0.274509556585457 \tabularnewline
71 & 83.8 & 83.7227163305017 & 0.0772836694982715 \tabularnewline
72 & 83.73 & 83.836406681119 & -0.106406681118941 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13350&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]69.9[/C][C]68.0280291666667[/C][C]1.87197083333332[/C][/ROW]
[ROW][C]14[/C][C]70.21[/C][C]70.1097524451255[/C][C]0.100247554874514[/C][/ROW]
[ROW][C]15[/C][C]70.48[/C][C]70.5228191607047[/C][C]-0.0428191607047381[/C][/ROW]
[ROW][C]16[/C][C]71.55[/C][C]71.58557505941[/C][C]-0.0355750594100357[/C][/ROW]
[ROW][C]17[/C][C]72.18[/C][C]72.2048913374113[/C][C]-0.0248913374112476[/C][/ROW]
[ROW][C]18[/C][C]72.64[/C][C]72.68295084189[/C][C]-0.0429508418899331[/C][/ROW]
[ROW][C]19[/C][C]72.77[/C][C]72.8195765077098[/C][C]-0.0495765077097872[/C][/ROW]
[ROW][C]20[/C][C]72.74[/C][C]72.7696725600557[/C][C]-0.0296725600557295[/C][/ROW]
[ROW][C]21[/C][C]73.13[/C][C]73.1435157878132[/C][C]-0.0135157878132333[/C][/ROW]
[ROW][C]22[/C][C]73.44[/C][C]73.4722523150126[/C][C]-0.0322523150125988[/C][/ROW]
[ROW][C]23[/C][C]73.34[/C][C]73.4212939012777[/C][C]-0.081293901277661[/C][/ROW]
[ROW][C]24[/C][C]73.34[/C][C]73.436145218406[/C][C]-0.0961452184060647[/C][/ROW]
[ROW][C]25[/C][C]73.81[/C][C]73.8711076123279[/C][C]-0.061107612327902[/C][/ROW]
[ROW][C]26[/C][C]74.26[/C][C]74.0224412105834[/C][C]0.237558789416610[/C][/ROW]
[ROW][C]27[/C][C]74.72[/C][C]74.5426873281708[/C][C]0.177312671829171[/C][/ROW]
[ROW][C]28[/C][C]75.11[/C][C]75.8066967965121[/C][C]-0.696696796512128[/C][/ROW]
[ROW][C]29[/C][C]75.26[/C][C]75.8017541088003[/C][C]-0.541754108800276[/C][/ROW]
[ROW][C]30[/C][C]75.89[/C][C]75.7721935357428[/C][C]0.117806464257242[/C][/ROW]
[ROW][C]31[/C][C]75.91[/C][C]76.028123117202[/C][C]-0.118123117201989[/C][/ROW]
[ROW][C]32[/C][C]76.43[/C][C]75.8875115810444[/C][C]0.542488418955642[/C][/ROW]
[ROW][C]33[/C][C]76.56[/C][C]76.7730937917569[/C][C]-0.21309379175689[/C][/ROW]
[ROW][C]34[/C][C]76.76[/C][C]76.8973401889136[/C][C]-0.137340188913640[/C][/ROW]
[ROW][C]35[/C][C]76.76[/C][C]76.7233864502541[/C][C]0.0366135497458657[/C][/ROW]
[ROW][C]36[/C][C]76.56[/C][C]76.8257419727494[/C][C]-0.265741972749396[/C][/ROW]
[ROW][C]37[/C][C]76.82[/C][C]77.0840978458444[/C][C]-0.264097845844390[/C][/ROW]
[ROW][C]38[/C][C]77.09[/C][C]77.0446365569296[/C][C]0.0453634430704284[/C][/ROW]
[ROW][C]39[/C][C]77.51[/C][C]77.3494664730734[/C][C]0.160533526926628[/C][/ROW]
[ROW][C]40[/C][C]77.76[/C][C]78.4915895617186[/C][C]-0.731589561718593[/C][/ROW]
[ROW][C]41[/C][C]77.86[/C][C]78.4319627090602[/C][C]-0.571962709060188[/C][/ROW]
[ROW][C]42[/C][C]77.89[/C][C]78.3927865831474[/C][C]-0.50278658314744[/C][/ROW]
[ROW][C]43[/C][C]77.94[/C][C]78.0075341009755[/C][C]-0.067534100975493[/C][/ROW]
[ROW][C]44[/C][C]77.99[/C][C]77.9167884069322[/C][C]0.0732115930677537[/C][/ROW]
[ROW][C]45[/C][C]78.17[/C][C]78.2464209468388[/C][C]-0.0764209468388088[/C][/ROW]
[ROW][C]46[/C][C]78.91[/C][C]78.4427629525903[/C][C]0.467237047409682[/C][/ROW]
[ROW][C]47[/C][C]78.87[/C][C]78.7940108439444[/C][C]0.0759891560555985[/C][/ROW]
[ROW][C]48[/C][C]78.88[/C][C]78.864704944621[/C][C]0.0152950553789708[/C][/ROW]
[ROW][C]49[/C][C]79.08[/C][C]79.3454661605704[/C][C]-0.265466160570440[/C][/ROW]
[ROW][C]50[/C][C]79.41[/C][C]79.2945702665686[/C][C]0.115429733431441[/C][/ROW]
[ROW][C]51[/C][C]79.51[/C][C]79.639332533077[/C][C]-0.129332533077033[/C][/ROW]
[ROW][C]52[/C][C]79.73[/C][C]80.4006491909566[/C][C]-0.670649190956595[/C][/ROW]
[ROW][C]53[/C][C]80.38[/C][C]80.370317175459[/C][C]0.00968282454105918[/C][/ROW]
[ROW][C]54[/C][C]80.56[/C][C]80.8458673936501[/C][C]-0.285867393650108[/C][/ROW]
[ROW][C]55[/C][C]80.46[/C][C]80.6764046131194[/C][C]-0.216404613119437[/C][/ROW]
[ROW][C]56[/C][C]80.45[/C][C]80.437676354775[/C][C]0.0123236452249529[/C][/ROW]
[ROW][C]57[/C][C]80.58[/C][C]80.6745779025397[/C][C]-0.0945779025396547[/C][/ROW]
[ROW][C]58[/C][C]80.68[/C][C]80.8740192182473[/C][C]-0.194019218247334[/C][/ROW]
[ROW][C]59[/C][C]80.52[/C][C]80.5441279228942[/C][C]-0.0241279228942375[/C][/ROW]
[ROW][C]60[/C][C]81.49[/C][C]80.4732442219525[/C][C]1.01675577804747[/C][/ROW]
[ROW][C]61[/C][C]81.66[/C][C]81.8310911391947[/C][C]-0.171091139194701[/C][/ROW]
[ROW][C]62[/C][C]81.95[/C][C]81.8818126091552[/C][C]0.0681873908447699[/C][/ROW]
[ROW][C]63[/C][C]82.3[/C][C]82.145494954248[/C][C]0.154505045752032[/C][/ROW]
[ROW][C]64[/C][C]82.4[/C][C]83.1124748853218[/C][C]-0.712474885321768[/C][/ROW]
[ROW][C]65[/C][C]83.14[/C][C]83.0884711697166[/C][C]0.0515288302834165[/C][/ROW]
[ROW][C]66[/C][C]83.17[/C][C]83.567857162711[/C][C]-0.397857162710949[/C][/ROW]
[ROW][C]67[/C][C]83.11[/C][C]83.2882201563354[/C][C]-0.178220156335357[/C][/ROW]
[ROW][C]68[/C][C]83.21[/C][C]83.0912285752946[/C][C]0.118771424705429[/C][/ROW]
[ROW][C]69[/C][C]83.33[/C][C]83.4076267565173[/C][C]-0.077626756517347[/C][/ROW]
[ROW][C]70[/C][C]83.88[/C][C]83.6054904434145[/C][C]0.274509556585457[/C][/ROW]
[ROW][C]71[/C][C]83.8[/C][C]83.7227163305017[/C][C]0.0772836694982715[/C][/ROW]
[ROW][C]72[/C][C]83.73[/C][C]83.836406681119[/C][C]-0.106406681118941[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13350&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13350&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
1369.968.02802916666671.87197083333332
1470.2170.10975244512550.100247554874514
1570.4870.5228191607047-0.0428191607047381
1671.5571.58557505941-0.0355750594100357
1772.1872.2048913374113-0.0248913374112476
1872.6472.68295084189-0.0429508418899331
1972.7772.8195765077098-0.0495765077097872
2072.7472.7696725600557-0.0296725600557295
2173.1373.1435157878132-0.0135157878132333
2273.4473.4722523150126-0.0322523150125988
2373.3473.4212939012777-0.081293901277661
2473.3473.436145218406-0.0961452184060647
2573.8173.8711076123279-0.061107612327902
2674.2674.02244121058340.237558789416610
2774.7274.54268732817080.177312671829171
2875.1175.8066967965121-0.696696796512128
2975.2675.8017541088003-0.541754108800276
3075.8975.77219353574280.117806464257242
3175.9176.028123117202-0.118123117201989
3276.4375.88751158104440.542488418955642
3376.5676.7730937917569-0.21309379175689
3476.7676.8973401889136-0.137340188913640
3576.7676.72338645025410.0366135497458657
3676.5676.8257419727494-0.265741972749396
3776.8277.0840978458444-0.264097845844390
3877.0977.04463655692960.0453634430704284
3977.5177.34946647307340.160533526926628
4077.7678.4915895617186-0.731589561718593
4177.8678.4319627090602-0.571962709060188
4277.8978.3927865831474-0.50278658314744
4377.9478.0075341009755-0.067534100975493
4477.9977.91678840693220.0732115930677537
4578.1778.2464209468388-0.0764209468388088
4678.9178.44276295259030.467237047409682
4778.8778.79401084394440.0759891560555985
4878.8878.8647049446210.0152950553789708
4979.0879.3454661605704-0.265466160570440
5079.4179.29457026656860.115429733431441
5179.5179.639332533077-0.129332533077033
5279.7380.4006491909566-0.670649190956595
5380.3880.3703171754590.00968282454105918
5480.5680.8458673936501-0.285867393650108
5580.4680.6764046131194-0.216404613119437
5680.4580.4376763547750.0123236452249529
5780.5880.6745779025397-0.0945779025396547
5880.6880.8740192182473-0.194019218247334
5980.5280.5441279228942-0.0241279228942375
6081.4980.47324422195251.01675577804747
6181.6681.8310911391947-0.171091139194701
6281.9581.88181260915520.0681873908447699
6382.382.1454949542480.154505045752032
6482.483.1124748853218-0.712474885321768
6583.1483.08847116971660.0515288302834165
6683.1783.567857162711-0.397857162710949
6783.1183.2882201563354-0.178220156335357
6883.2183.09122857529460.118771424705429
6983.3383.4076267565173-0.077626756517347
7083.8883.60549044341450.274509556585457
7183.883.72271633050170.0772836694982715
7283.7383.836406681119-0.106406681118941







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7384.042504793667883.283118734480284.8018908528553
7484.251099364200383.20704575285985.2951529755416
7584.438719509313383.161232241650585.7162067769761
7685.167931667407483.683607993022486.6522553417923
7785.854486865159784.179807984404887.5291657459145
7886.242090802762784.388245144312588.0959364612128
7986.348438439091984.32345149052788.3734253876569
8086.346861416022484.156700038508888.537022793536
8186.542437150253984.191645765458188.8932285350496
8286.84688129524184.338976946170889.3547856443113
8386.695207811916284.032939721788389.3574759020442
8486.720099210530483.905626991781889.534571429279

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 84.0425047936678 & 83.2831187344802 & 84.8018908528553 \tabularnewline
74 & 84.2510993642003 & 83.207045752859 & 85.2951529755416 \tabularnewline
75 & 84.4387195093133 & 83.1612322416505 & 85.7162067769761 \tabularnewline
76 & 85.1679316674074 & 83.6836079930224 & 86.6522553417923 \tabularnewline
77 & 85.8544868651597 & 84.1798079844048 & 87.5291657459145 \tabularnewline
78 & 86.2420908027627 & 84.3882451443125 & 88.0959364612128 \tabularnewline
79 & 86.3484384390919 & 84.323451490527 & 88.3734253876569 \tabularnewline
80 & 86.3468614160224 & 84.1567000385088 & 88.537022793536 \tabularnewline
81 & 86.5424371502539 & 84.1916457654581 & 88.8932285350496 \tabularnewline
82 & 86.846881295241 & 84.3389769461708 & 89.3547856443113 \tabularnewline
83 & 86.6952078119162 & 84.0329397217883 & 89.3574759020442 \tabularnewline
84 & 86.7200992105304 & 83.9056269917818 & 89.534571429279 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13350&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]84.0425047936678[/C][C]83.2831187344802[/C][C]84.8018908528553[/C][/ROW]
[ROW][C]74[/C][C]84.2510993642003[/C][C]83.207045752859[/C][C]85.2951529755416[/C][/ROW]
[ROW][C]75[/C][C]84.4387195093133[/C][C]83.1612322416505[/C][C]85.7162067769761[/C][/ROW]
[ROW][C]76[/C][C]85.1679316674074[/C][C]83.6836079930224[/C][C]86.6522553417923[/C][/ROW]
[ROW][C]77[/C][C]85.8544868651597[/C][C]84.1798079844048[/C][C]87.5291657459145[/C][/ROW]
[ROW][C]78[/C][C]86.2420908027627[/C][C]84.3882451443125[/C][C]88.0959364612128[/C][/ROW]
[ROW][C]79[/C][C]86.3484384390919[/C][C]84.323451490527[/C][C]88.3734253876569[/C][/ROW]
[ROW][C]80[/C][C]86.3468614160224[/C][C]84.1567000385088[/C][C]88.537022793536[/C][/ROW]
[ROW][C]81[/C][C]86.5424371502539[/C][C]84.1916457654581[/C][C]88.8932285350496[/C][/ROW]
[ROW][C]82[/C][C]86.846881295241[/C][C]84.3389769461708[/C][C]89.3547856443113[/C][/ROW]
[ROW][C]83[/C][C]86.6952078119162[/C][C]84.0329397217883[/C][C]89.3574759020442[/C][/ROW]
[ROW][C]84[/C][C]86.7200992105304[/C][C]83.9056269917818[/C][C]89.534571429279[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13350&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13350&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
7384.042504793667883.283118734480284.8018908528553
7484.251099364200383.20704575285985.2951529755416
7584.438719509313383.161232241650585.7162067769761
7685.167931667407483.683607993022486.6522553417923
7785.854486865159784.179807984404887.5291657459145
7886.242090802762784.388245144312588.0959364612128
7986.348438439091984.32345149052788.3734253876569
8086.346861416022484.156700038508888.537022793536
8186.542437150253984.191645765458188.8932285350496
8286.84688129524184.338976946170889.3547856443113
8386.695207811916284.032939721788389.3574759020442
8486.720099210530483.905626991781889.534571429279



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=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')