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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 21 Dec 2010 19:55:16 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/21/t1292961198l6y8u634igjwzqs.htm/, Retrieved Sun, 19 May 2024 18:21:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=113913, Retrieved Sun, 19 May 2024 18:21:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact104
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2010-12-21 19:55:16] [ca3ac3c31c98d146c448f7dbe5015da7] [Current]
-   PD    [Exponential Smoothing] [] [2011-01-05 21:32:04] [74be16979710d4c4e7c6647856088456]
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Dataseries X:
13,2
13,8
16,2
14,7
13,9
16,0
14,4
12,3
15,9
15,9
15,5
15,1
14,5
15,1
17,4
16,2
15,6
17,2
14,9
13,8
17,5
16,2
17,5
16,6
16,2
16,6
19,6
15,9
18,0
18,3
16,3
14,9
18,2
18,4
18,5
16,0
17,4
17,2
19,6
17,2
18,3
19,3
18,1
16,2
18,4
20,5
19,0
16,5
18,7
19,0
19,2
20,5
19,3
20,6
20,1
16,1
20,4
19,7
15,6
14,4
13,9
14,3
15,3
14,4
13,8
15,7
14,7
12,5
16,2
16,1
16
15,8
15,2




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 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 & 6 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113913&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]6 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=113913&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113913&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 time6 seconds
R Server'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.357744444336104
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.357744444336104 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113913&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]0.357744444336104[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113913&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113913&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
alpha0.357744444336104
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
213.813.20.600000000000001
316.213.41464666660172.78535333339834
414.714.41109134713800.288908652862034
513.914.51444681262-0.614446812619986
61614.29463187906521.70536812093484
714.414.9047178498775-0.504717849877499
812.314.7241578431266-2.42415784312656
915.913.85692884255422.04307115744576
1015.914.58782619851381.31217380148620
1115.515.05724908599890.442750914001129
1215.115.2156407657075-0.115640765707505
1314.515.1742709242369-0.674270924236872
1415.114.93305424711380.166945752886239
1517.414.99277816271432.40722183728568
1616.215.85394840128780.346051598712179
1715.615.9777464381807-0.377746438180731
1817.215.84260974855381.35739025144618
1914.916.3282085698047-1.42820856980468
2013.815.8172748886038-2.01727488860384
2117.515.09560600450712.40439399549291
2216.215.95576459838980.244235401610236
2317.516.04313845642601.45686154357398
2416.616.56432257980650.0356774201934691
2516.216.577085978669-0.377085978668990
2616.616.44218556476310.157814435236887
2719.616.49864280220523.10135719779485
2815.917.6081361096180-1.70813610961804
291816.99705990623231.00294009376770
3018.317.35585615277960.944143847220374
3116.317.6936183687768-1.39361836877683
3214.917.1950591398222-2.29505913982218
3318.216.3740144831281.82598551687200
3418.417.02725065722711.37274934277286
3518.517.51834410807020.981655891929833
361617.8695260496579-1.86952604965787
3717.417.20071349185110.199286508148855
3817.217.2720071329725-0.0720071329725371
3919.617.24624698119902.35375301880096
4017.218.0882890470144-0.888289047014418
4118.317.77050857548040.529491424519602
4219.317.95993119092591.34006880907410
4318.118.4393333624003-0.339333362400254
4416.218.3179387372237-2.11793873722367
4518.417.56025792053770.839742079462319
4620.517.86067098414062.63932901585943
471918.80487627633940.195123723660643
4816.518.8746807044371-2.37468070443713
4918.718.02515187535260.6748481246474
501918.26657504271580.733424957284157
5119.218.52895374652170.671046253478305
5220.518.76901681559611.73098318440389
5319.319.3882664330558-0.0882664330558178
5420.619.35668960700871.24331039299127
5520.119.80147699268670.298523007313307
5616.119.9082719400595-3.80827194005953
5720.418.54588381098221.85411618901784
5819.719.20918357675690.490816423243079
5915.619.3847704253611-3.78477042536105
6014.418.0307898326005-3.63078983260054
6113.916.7318949414357-2.83189494143569
6214.315.7188002591936-1.41880025919355
6315.315.21123234884440.088767651155564
6414.415.2429884828821-0.842988482882104
6513.814.9414140364917-1.14141403649171
6615.714.53307950624961.16692049375044
6714.714.9505388298707-0.250538829870720
6812.514.860909955394-2.360909955394
6916.214.0163075352742.183692464726
7016.114.79751138266831.30248861733166
711615.26346944932980.736530550670246
7215.815.52695916191580.273040838084155
7315.215.6246380048173-0.424638004817325

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 13.8 & 13.2 & 0.600000000000001 \tabularnewline
3 & 16.2 & 13.4146466666017 & 2.78535333339834 \tabularnewline
4 & 14.7 & 14.4110913471380 & 0.288908652862034 \tabularnewline
5 & 13.9 & 14.51444681262 & -0.614446812619986 \tabularnewline
6 & 16 & 14.2946318790652 & 1.70536812093484 \tabularnewline
7 & 14.4 & 14.9047178498775 & -0.504717849877499 \tabularnewline
8 & 12.3 & 14.7241578431266 & -2.42415784312656 \tabularnewline
9 & 15.9 & 13.8569288425542 & 2.04307115744576 \tabularnewline
10 & 15.9 & 14.5878261985138 & 1.31217380148620 \tabularnewline
11 & 15.5 & 15.0572490859989 & 0.442750914001129 \tabularnewline
12 & 15.1 & 15.2156407657075 & -0.115640765707505 \tabularnewline
13 & 14.5 & 15.1742709242369 & -0.674270924236872 \tabularnewline
14 & 15.1 & 14.9330542471138 & 0.166945752886239 \tabularnewline
15 & 17.4 & 14.9927781627143 & 2.40722183728568 \tabularnewline
16 & 16.2 & 15.8539484012878 & 0.346051598712179 \tabularnewline
17 & 15.6 & 15.9777464381807 & -0.377746438180731 \tabularnewline
18 & 17.2 & 15.8426097485538 & 1.35739025144618 \tabularnewline
19 & 14.9 & 16.3282085698047 & -1.42820856980468 \tabularnewline
20 & 13.8 & 15.8172748886038 & -2.01727488860384 \tabularnewline
21 & 17.5 & 15.0956060045071 & 2.40439399549291 \tabularnewline
22 & 16.2 & 15.9557645983898 & 0.244235401610236 \tabularnewline
23 & 17.5 & 16.0431384564260 & 1.45686154357398 \tabularnewline
24 & 16.6 & 16.5643225798065 & 0.0356774201934691 \tabularnewline
25 & 16.2 & 16.577085978669 & -0.377085978668990 \tabularnewline
26 & 16.6 & 16.4421855647631 & 0.157814435236887 \tabularnewline
27 & 19.6 & 16.4986428022052 & 3.10135719779485 \tabularnewline
28 & 15.9 & 17.6081361096180 & -1.70813610961804 \tabularnewline
29 & 18 & 16.9970599062323 & 1.00294009376770 \tabularnewline
30 & 18.3 & 17.3558561527796 & 0.944143847220374 \tabularnewline
31 & 16.3 & 17.6936183687768 & -1.39361836877683 \tabularnewline
32 & 14.9 & 17.1950591398222 & -2.29505913982218 \tabularnewline
33 & 18.2 & 16.374014483128 & 1.82598551687200 \tabularnewline
34 & 18.4 & 17.0272506572271 & 1.37274934277286 \tabularnewline
35 & 18.5 & 17.5183441080702 & 0.981655891929833 \tabularnewline
36 & 16 & 17.8695260496579 & -1.86952604965787 \tabularnewline
37 & 17.4 & 17.2007134918511 & 0.199286508148855 \tabularnewline
38 & 17.2 & 17.2720071329725 & -0.0720071329725371 \tabularnewline
39 & 19.6 & 17.2462469811990 & 2.35375301880096 \tabularnewline
40 & 17.2 & 18.0882890470144 & -0.888289047014418 \tabularnewline
41 & 18.3 & 17.7705085754804 & 0.529491424519602 \tabularnewline
42 & 19.3 & 17.9599311909259 & 1.34006880907410 \tabularnewline
43 & 18.1 & 18.4393333624003 & -0.339333362400254 \tabularnewline
44 & 16.2 & 18.3179387372237 & -2.11793873722367 \tabularnewline
45 & 18.4 & 17.5602579205377 & 0.839742079462319 \tabularnewline
46 & 20.5 & 17.8606709841406 & 2.63932901585943 \tabularnewline
47 & 19 & 18.8048762763394 & 0.195123723660643 \tabularnewline
48 & 16.5 & 18.8746807044371 & -2.37468070443713 \tabularnewline
49 & 18.7 & 18.0251518753526 & 0.6748481246474 \tabularnewline
50 & 19 & 18.2665750427158 & 0.733424957284157 \tabularnewline
51 & 19.2 & 18.5289537465217 & 0.671046253478305 \tabularnewline
52 & 20.5 & 18.7690168155961 & 1.73098318440389 \tabularnewline
53 & 19.3 & 19.3882664330558 & -0.0882664330558178 \tabularnewline
54 & 20.6 & 19.3566896070087 & 1.24331039299127 \tabularnewline
55 & 20.1 & 19.8014769926867 & 0.298523007313307 \tabularnewline
56 & 16.1 & 19.9082719400595 & -3.80827194005953 \tabularnewline
57 & 20.4 & 18.5458838109822 & 1.85411618901784 \tabularnewline
58 & 19.7 & 19.2091835767569 & 0.490816423243079 \tabularnewline
59 & 15.6 & 19.3847704253611 & -3.78477042536105 \tabularnewline
60 & 14.4 & 18.0307898326005 & -3.63078983260054 \tabularnewline
61 & 13.9 & 16.7318949414357 & -2.83189494143569 \tabularnewline
62 & 14.3 & 15.7188002591936 & -1.41880025919355 \tabularnewline
63 & 15.3 & 15.2112323488444 & 0.088767651155564 \tabularnewline
64 & 14.4 & 15.2429884828821 & -0.842988482882104 \tabularnewline
65 & 13.8 & 14.9414140364917 & -1.14141403649171 \tabularnewline
66 & 15.7 & 14.5330795062496 & 1.16692049375044 \tabularnewline
67 & 14.7 & 14.9505388298707 & -0.250538829870720 \tabularnewline
68 & 12.5 & 14.860909955394 & -2.360909955394 \tabularnewline
69 & 16.2 & 14.016307535274 & 2.183692464726 \tabularnewline
70 & 16.1 & 14.7975113826683 & 1.30248861733166 \tabularnewline
71 & 16 & 15.2634694493298 & 0.736530550670246 \tabularnewline
72 & 15.8 & 15.5269591619158 & 0.273040838084155 \tabularnewline
73 & 15.2 & 15.6246380048173 & -0.424638004817325 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113913&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]2[/C][C]13.8[/C][C]13.2[/C][C]0.600000000000001[/C][/ROW]
[ROW][C]3[/C][C]16.2[/C][C]13.4146466666017[/C][C]2.78535333339834[/C][/ROW]
[ROW][C]4[/C][C]14.7[/C][C]14.4110913471380[/C][C]0.288908652862034[/C][/ROW]
[ROW][C]5[/C][C]13.9[/C][C]14.51444681262[/C][C]-0.614446812619986[/C][/ROW]
[ROW][C]6[/C][C]16[/C][C]14.2946318790652[/C][C]1.70536812093484[/C][/ROW]
[ROW][C]7[/C][C]14.4[/C][C]14.9047178498775[/C][C]-0.504717849877499[/C][/ROW]
[ROW][C]8[/C][C]12.3[/C][C]14.7241578431266[/C][C]-2.42415784312656[/C][/ROW]
[ROW][C]9[/C][C]15.9[/C][C]13.8569288425542[/C][C]2.04307115744576[/C][/ROW]
[ROW][C]10[/C][C]15.9[/C][C]14.5878261985138[/C][C]1.31217380148620[/C][/ROW]
[ROW][C]11[/C][C]15.5[/C][C]15.0572490859989[/C][C]0.442750914001129[/C][/ROW]
[ROW][C]12[/C][C]15.1[/C][C]15.2156407657075[/C][C]-0.115640765707505[/C][/ROW]
[ROW][C]13[/C][C]14.5[/C][C]15.1742709242369[/C][C]-0.674270924236872[/C][/ROW]
[ROW][C]14[/C][C]15.1[/C][C]14.9330542471138[/C][C]0.166945752886239[/C][/ROW]
[ROW][C]15[/C][C]17.4[/C][C]14.9927781627143[/C][C]2.40722183728568[/C][/ROW]
[ROW][C]16[/C][C]16.2[/C][C]15.8539484012878[/C][C]0.346051598712179[/C][/ROW]
[ROW][C]17[/C][C]15.6[/C][C]15.9777464381807[/C][C]-0.377746438180731[/C][/ROW]
[ROW][C]18[/C][C]17.2[/C][C]15.8426097485538[/C][C]1.35739025144618[/C][/ROW]
[ROW][C]19[/C][C]14.9[/C][C]16.3282085698047[/C][C]-1.42820856980468[/C][/ROW]
[ROW][C]20[/C][C]13.8[/C][C]15.8172748886038[/C][C]-2.01727488860384[/C][/ROW]
[ROW][C]21[/C][C]17.5[/C][C]15.0956060045071[/C][C]2.40439399549291[/C][/ROW]
[ROW][C]22[/C][C]16.2[/C][C]15.9557645983898[/C][C]0.244235401610236[/C][/ROW]
[ROW][C]23[/C][C]17.5[/C][C]16.0431384564260[/C][C]1.45686154357398[/C][/ROW]
[ROW][C]24[/C][C]16.6[/C][C]16.5643225798065[/C][C]0.0356774201934691[/C][/ROW]
[ROW][C]25[/C][C]16.2[/C][C]16.577085978669[/C][C]-0.377085978668990[/C][/ROW]
[ROW][C]26[/C][C]16.6[/C][C]16.4421855647631[/C][C]0.157814435236887[/C][/ROW]
[ROW][C]27[/C][C]19.6[/C][C]16.4986428022052[/C][C]3.10135719779485[/C][/ROW]
[ROW][C]28[/C][C]15.9[/C][C]17.6081361096180[/C][C]-1.70813610961804[/C][/ROW]
[ROW][C]29[/C][C]18[/C][C]16.9970599062323[/C][C]1.00294009376770[/C][/ROW]
[ROW][C]30[/C][C]18.3[/C][C]17.3558561527796[/C][C]0.944143847220374[/C][/ROW]
[ROW][C]31[/C][C]16.3[/C][C]17.6936183687768[/C][C]-1.39361836877683[/C][/ROW]
[ROW][C]32[/C][C]14.9[/C][C]17.1950591398222[/C][C]-2.29505913982218[/C][/ROW]
[ROW][C]33[/C][C]18.2[/C][C]16.374014483128[/C][C]1.82598551687200[/C][/ROW]
[ROW][C]34[/C][C]18.4[/C][C]17.0272506572271[/C][C]1.37274934277286[/C][/ROW]
[ROW][C]35[/C][C]18.5[/C][C]17.5183441080702[/C][C]0.981655891929833[/C][/ROW]
[ROW][C]36[/C][C]16[/C][C]17.8695260496579[/C][C]-1.86952604965787[/C][/ROW]
[ROW][C]37[/C][C]17.4[/C][C]17.2007134918511[/C][C]0.199286508148855[/C][/ROW]
[ROW][C]38[/C][C]17.2[/C][C]17.2720071329725[/C][C]-0.0720071329725371[/C][/ROW]
[ROW][C]39[/C][C]19.6[/C][C]17.2462469811990[/C][C]2.35375301880096[/C][/ROW]
[ROW][C]40[/C][C]17.2[/C][C]18.0882890470144[/C][C]-0.888289047014418[/C][/ROW]
[ROW][C]41[/C][C]18.3[/C][C]17.7705085754804[/C][C]0.529491424519602[/C][/ROW]
[ROW][C]42[/C][C]19.3[/C][C]17.9599311909259[/C][C]1.34006880907410[/C][/ROW]
[ROW][C]43[/C][C]18.1[/C][C]18.4393333624003[/C][C]-0.339333362400254[/C][/ROW]
[ROW][C]44[/C][C]16.2[/C][C]18.3179387372237[/C][C]-2.11793873722367[/C][/ROW]
[ROW][C]45[/C][C]18.4[/C][C]17.5602579205377[/C][C]0.839742079462319[/C][/ROW]
[ROW][C]46[/C][C]20.5[/C][C]17.8606709841406[/C][C]2.63932901585943[/C][/ROW]
[ROW][C]47[/C][C]19[/C][C]18.8048762763394[/C][C]0.195123723660643[/C][/ROW]
[ROW][C]48[/C][C]16.5[/C][C]18.8746807044371[/C][C]-2.37468070443713[/C][/ROW]
[ROW][C]49[/C][C]18.7[/C][C]18.0251518753526[/C][C]0.6748481246474[/C][/ROW]
[ROW][C]50[/C][C]19[/C][C]18.2665750427158[/C][C]0.733424957284157[/C][/ROW]
[ROW][C]51[/C][C]19.2[/C][C]18.5289537465217[/C][C]0.671046253478305[/C][/ROW]
[ROW][C]52[/C][C]20.5[/C][C]18.7690168155961[/C][C]1.73098318440389[/C][/ROW]
[ROW][C]53[/C][C]19.3[/C][C]19.3882664330558[/C][C]-0.0882664330558178[/C][/ROW]
[ROW][C]54[/C][C]20.6[/C][C]19.3566896070087[/C][C]1.24331039299127[/C][/ROW]
[ROW][C]55[/C][C]20.1[/C][C]19.8014769926867[/C][C]0.298523007313307[/C][/ROW]
[ROW][C]56[/C][C]16.1[/C][C]19.9082719400595[/C][C]-3.80827194005953[/C][/ROW]
[ROW][C]57[/C][C]20.4[/C][C]18.5458838109822[/C][C]1.85411618901784[/C][/ROW]
[ROW][C]58[/C][C]19.7[/C][C]19.2091835767569[/C][C]0.490816423243079[/C][/ROW]
[ROW][C]59[/C][C]15.6[/C][C]19.3847704253611[/C][C]-3.78477042536105[/C][/ROW]
[ROW][C]60[/C][C]14.4[/C][C]18.0307898326005[/C][C]-3.63078983260054[/C][/ROW]
[ROW][C]61[/C][C]13.9[/C][C]16.7318949414357[/C][C]-2.83189494143569[/C][/ROW]
[ROW][C]62[/C][C]14.3[/C][C]15.7188002591936[/C][C]-1.41880025919355[/C][/ROW]
[ROW][C]63[/C][C]15.3[/C][C]15.2112323488444[/C][C]0.088767651155564[/C][/ROW]
[ROW][C]64[/C][C]14.4[/C][C]15.2429884828821[/C][C]-0.842988482882104[/C][/ROW]
[ROW][C]65[/C][C]13.8[/C][C]14.9414140364917[/C][C]-1.14141403649171[/C][/ROW]
[ROW][C]66[/C][C]15.7[/C][C]14.5330795062496[/C][C]1.16692049375044[/C][/ROW]
[ROW][C]67[/C][C]14.7[/C][C]14.9505388298707[/C][C]-0.250538829870720[/C][/ROW]
[ROW][C]68[/C][C]12.5[/C][C]14.860909955394[/C][C]-2.360909955394[/C][/ROW]
[ROW][C]69[/C][C]16.2[/C][C]14.016307535274[/C][C]2.183692464726[/C][/ROW]
[ROW][C]70[/C][C]16.1[/C][C]14.7975113826683[/C][C]1.30248861733166[/C][/ROW]
[ROW][C]71[/C][C]16[/C][C]15.2634694493298[/C][C]0.736530550670246[/C][/ROW]
[ROW][C]72[/C][C]15.8[/C][C]15.5269591619158[/C][C]0.273040838084155[/C][/ROW]
[ROW][C]73[/C][C]15.2[/C][C]15.6246380048173[/C][C]-0.424638004817325[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113913&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113913&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
213.813.20.600000000000001
316.213.41464666660172.78535333339834
414.714.41109134713800.288908652862034
513.914.51444681262-0.614446812619986
61614.29463187906521.70536812093484
714.414.9047178498775-0.504717849877499
812.314.7241578431266-2.42415784312656
915.913.85692884255422.04307115744576
1015.914.58782619851381.31217380148620
1115.515.05724908599890.442750914001129
1215.115.2156407657075-0.115640765707505
1314.515.1742709242369-0.674270924236872
1415.114.93305424711380.166945752886239
1517.414.99277816271432.40722183728568
1616.215.85394840128780.346051598712179
1715.615.9777464381807-0.377746438180731
1817.215.84260974855381.35739025144618
1914.916.3282085698047-1.42820856980468
2013.815.8172748886038-2.01727488860384
2117.515.09560600450712.40439399549291
2216.215.95576459838980.244235401610236
2317.516.04313845642601.45686154357398
2416.616.56432257980650.0356774201934691
2516.216.577085978669-0.377085978668990
2616.616.44218556476310.157814435236887
2719.616.49864280220523.10135719779485
2815.917.6081361096180-1.70813610961804
291816.99705990623231.00294009376770
3018.317.35585615277960.944143847220374
3116.317.6936183687768-1.39361836877683
3214.917.1950591398222-2.29505913982218
3318.216.3740144831281.82598551687200
3418.417.02725065722711.37274934277286
3518.517.51834410807020.981655891929833
361617.8695260496579-1.86952604965787
3717.417.20071349185110.199286508148855
3817.217.2720071329725-0.0720071329725371
3919.617.24624698119902.35375301880096
4017.218.0882890470144-0.888289047014418
4118.317.77050857548040.529491424519602
4219.317.95993119092591.34006880907410
4318.118.4393333624003-0.339333362400254
4416.218.3179387372237-2.11793873722367
4518.417.56025792053770.839742079462319
4620.517.86067098414062.63932901585943
471918.80487627633940.195123723660643
4816.518.8746807044371-2.37468070443713
4918.718.02515187535260.6748481246474
501918.26657504271580.733424957284157
5119.218.52895374652170.671046253478305
5220.518.76901681559611.73098318440389
5319.319.3882664330558-0.0882664330558178
5420.619.35668960700871.24331039299127
5520.119.80147699268670.298523007313307
5616.119.9082719400595-3.80827194005953
5720.418.54588381098221.85411618901784
5819.719.20918357675690.490816423243079
5915.619.3847704253611-3.78477042536105
6014.418.0307898326005-3.63078983260054
6113.916.7318949414357-2.83189494143569
6214.315.7188002591936-1.41880025919355
6315.315.21123234884440.088767651155564
6414.415.2429884828821-0.842988482882104
6513.814.9414140364917-1.14141403649171
6615.714.53307950624961.16692049375044
6714.714.9505388298707-0.250538829870720
6812.514.860909955394-2.360909955394
6916.214.0163075352742.183692464726
7016.114.79751138266831.30248861733166
711615.26346944932980.736530550670246
7215.815.52695916191580.273040838084155
7315.215.6246380048173-0.424638004817325







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7415.472726117740012.338230299862018.6072219356179
7515.472726117740012.143689258309518.8017629771704
7615.472726117740011.959905486025618.9855467494543
7715.472726117740011.785270196681419.1601820387985
7815.472726117740011.618539621356919.3269126141231
7915.472726117740011.458728617983219.4867236174967
8015.472726117740011.305041111983719.6404111234962
8115.472726117740011.156822888245919.7886293472340
8215.472726117740011.013528536839419.9319236986405
8315.472726117740010.874697687568920.070754547911
8415.472726117740010.739937529200120.2055147062798
8515.472726117740010.608909694090320.3365425413897

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
74 & 15.4727261177400 & 12.3382302998620 & 18.6072219356179 \tabularnewline
75 & 15.4727261177400 & 12.1436892583095 & 18.8017629771704 \tabularnewline
76 & 15.4727261177400 & 11.9599054860256 & 18.9855467494543 \tabularnewline
77 & 15.4727261177400 & 11.7852701966814 & 19.1601820387985 \tabularnewline
78 & 15.4727261177400 & 11.6185396213569 & 19.3269126141231 \tabularnewline
79 & 15.4727261177400 & 11.4587286179832 & 19.4867236174967 \tabularnewline
80 & 15.4727261177400 & 11.3050411119837 & 19.6404111234962 \tabularnewline
81 & 15.4727261177400 & 11.1568228882459 & 19.7886293472340 \tabularnewline
82 & 15.4727261177400 & 11.0135285368394 & 19.9319236986405 \tabularnewline
83 & 15.4727261177400 & 10.8746976875689 & 20.070754547911 \tabularnewline
84 & 15.4727261177400 & 10.7399375292001 & 20.2055147062798 \tabularnewline
85 & 15.4727261177400 & 10.6089096940903 & 20.3365425413897 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113913&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]74[/C][C]15.4727261177400[/C][C]12.3382302998620[/C][C]18.6072219356179[/C][/ROW]
[ROW][C]75[/C][C]15.4727261177400[/C][C]12.1436892583095[/C][C]18.8017629771704[/C][/ROW]
[ROW][C]76[/C][C]15.4727261177400[/C][C]11.9599054860256[/C][C]18.9855467494543[/C][/ROW]
[ROW][C]77[/C][C]15.4727261177400[/C][C]11.7852701966814[/C][C]19.1601820387985[/C][/ROW]
[ROW][C]78[/C][C]15.4727261177400[/C][C]11.6185396213569[/C][C]19.3269126141231[/C][/ROW]
[ROW][C]79[/C][C]15.4727261177400[/C][C]11.4587286179832[/C][C]19.4867236174967[/C][/ROW]
[ROW][C]80[/C][C]15.4727261177400[/C][C]11.3050411119837[/C][C]19.6404111234962[/C][/ROW]
[ROW][C]81[/C][C]15.4727261177400[/C][C]11.1568228882459[/C][C]19.7886293472340[/C][/ROW]
[ROW][C]82[/C][C]15.4727261177400[/C][C]11.0135285368394[/C][C]19.9319236986405[/C][/ROW]
[ROW][C]83[/C][C]15.4727261177400[/C][C]10.8746976875689[/C][C]20.070754547911[/C][/ROW]
[ROW][C]84[/C][C]15.4727261177400[/C][C]10.7399375292001[/C][C]20.2055147062798[/C][/ROW]
[ROW][C]85[/C][C]15.4727261177400[/C][C]10.6089096940903[/C][C]20.3365425413897[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113913&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113913&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
7415.472726117740012.338230299862018.6072219356179
7515.472726117740012.143689258309518.8017629771704
7615.472726117740011.959905486025618.9855467494543
7715.472726117740011.785270196681419.1601820387985
7815.472726117740011.618539621356919.3269126141231
7915.472726117740011.458728617983219.4867236174967
8015.472726117740011.305041111983719.6404111234962
8115.472726117740011.156822888245919.7886293472340
8215.472726117740011.013528536839419.9319236986405
8315.472726117740010.874697687568920.070754547911
8415.472726117740010.739937529200120.2055147062798
8515.472726117740010.608909694090320.3365425413897



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')