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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 25 May 2012 03:56:54 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/May/25/t13379327135zzkyuz84e5lqu1.htm/, Retrieved Fri, 03 May 2024 16:11:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167439, Retrieved Fri, 03 May 2024 16:11:05 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact116
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-05-25 07:56:54] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
101,65
101,18
102,13
102,59
103,25
103,48
104,03
103,64
103,29
103,3
104,51
104,62
105,93
105,2
106
108,05
109,36
110,05
110,23
110,45
110,64
112,31
116,13
119,08
120,55
121,13
121,16
122,23
122,49
122,94
122,56
123,3
123,75
123,32
123,66
124,01
124,42
124,63
125,36
125,84
123,79
125,66
123,23
123,44
122,98
123,34
122,85
122,72
123,18
122,7
122,24
121
121,25
120,48
120,4
120,7
121,42
121,76
121,64
120,52




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167439&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167439&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167439&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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.206826042522155
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.206826042522155 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167439&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]0.206826042522155[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167439&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167439&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
beta0.206826042522155
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3102.13100.711.41999999999999
4102.59101.9536929803810.636307019618542
5103.25102.5452978430780.704702156921769
6103.48103.3510486013510.128951398648823
7104.03103.6077191088110.422280891188578
8103.64104.245057794369-0.605057794368676
9103.29103.729916085262-0.439916085262212
10103.3103.2889299823060.0110700176943936
11104.51103.3012195502561.20878044974403
12104.62104.761226826955-0.141226826954693
13105.93104.8420174412381.08798255876231
14105.2106.3770405682-1.17704056819963
15106105.4035979255910.596402074409127
16108.05106.3269494063931.72305059360708
17109.36108.7333211417340.62667885826589
18110.05110.172934649922-0.122934649921561
19110.23110.837508562789-0.60750856278942
20110.45110.891859970949-0.441859970949366
21110.64111.020471821809-0.380471821808968
22112.31111.1317803406131.17821965938698
23116.13113.0454668499863.08453315001417
24119.08117.5034286344321.57657136556834
25120.55120.779504650726-0.229504650725914
26121.13122.202037112076-1.07203711207583
27121.16122.560311918748-1.40031191874832
28122.23122.300690946297-0.0706909462969918
29122.49123.356070217632-0.866070217632256
30122.94123.436944341973-0.496944341973062
31122.56123.784163310369-1.22416331036899
32123.3123.1509744574850.149025542515432
33123.75123.921796820678-0.171796820677741
34123.32124.336264764139-1.01626476413908
35123.66123.696074744817-0.0360747448174692
36124.01124.028613548112-0.0186135481118725
37124.42124.3747637816190.0452362183813904
38124.63124.794119809645-0.164119809645101
39125.36124.9701755589170.389824441083292
40125.84125.7808014053440.0591985946556264
41123.79126.2730452164-2.48304521639987
42125.66123.7094868008881.95051319911167
43123.23125.982903726748-2.7529037267478
44123.44122.98353154350.45646845649992
45122.98123.287941107894-0.307941107894138
46123.34122.7642508672190.575749132781482
47122.85123.243330781837-0.393330781837278
48122.72122.6719797328280.0480202671722765
49123.18122.5519115746480.628088425352189
50122.7123.141816618017-0.441816618017384
51122.24122.570437435392-0.330437435392341
52121122.042094368329-1.04209436832896
53121.25120.5865621141930.663437885807141
54120.48120.973778346574-0.493778346573606
55120.4120.1016521252690.298347874731334
56120.7120.0833582354940.616641764505758
57121.42120.5108958113010.90910418869916
58121.76121.418922232890.341077767110193
59121.64121.829465997654-0.1894659976535
60120.52121.670279495166-1.15027949516632

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 102.13 & 100.71 & 1.41999999999999 \tabularnewline
4 & 102.59 & 101.953692980381 & 0.636307019618542 \tabularnewline
5 & 103.25 & 102.545297843078 & 0.704702156921769 \tabularnewline
6 & 103.48 & 103.351048601351 & 0.128951398648823 \tabularnewline
7 & 104.03 & 103.607719108811 & 0.422280891188578 \tabularnewline
8 & 103.64 & 104.245057794369 & -0.605057794368676 \tabularnewline
9 & 103.29 & 103.729916085262 & -0.439916085262212 \tabularnewline
10 & 103.3 & 103.288929982306 & 0.0110700176943936 \tabularnewline
11 & 104.51 & 103.301219550256 & 1.20878044974403 \tabularnewline
12 & 104.62 & 104.761226826955 & -0.141226826954693 \tabularnewline
13 & 105.93 & 104.842017441238 & 1.08798255876231 \tabularnewline
14 & 105.2 & 106.3770405682 & -1.17704056819963 \tabularnewline
15 & 106 & 105.403597925591 & 0.596402074409127 \tabularnewline
16 & 108.05 & 106.326949406393 & 1.72305059360708 \tabularnewline
17 & 109.36 & 108.733321141734 & 0.62667885826589 \tabularnewline
18 & 110.05 & 110.172934649922 & -0.122934649921561 \tabularnewline
19 & 110.23 & 110.837508562789 & -0.60750856278942 \tabularnewline
20 & 110.45 & 110.891859970949 & -0.441859970949366 \tabularnewline
21 & 110.64 & 111.020471821809 & -0.380471821808968 \tabularnewline
22 & 112.31 & 111.131780340613 & 1.17821965938698 \tabularnewline
23 & 116.13 & 113.045466849986 & 3.08453315001417 \tabularnewline
24 & 119.08 & 117.503428634432 & 1.57657136556834 \tabularnewline
25 & 120.55 & 120.779504650726 & -0.229504650725914 \tabularnewline
26 & 121.13 & 122.202037112076 & -1.07203711207583 \tabularnewline
27 & 121.16 & 122.560311918748 & -1.40031191874832 \tabularnewline
28 & 122.23 & 122.300690946297 & -0.0706909462969918 \tabularnewline
29 & 122.49 & 123.356070217632 & -0.866070217632256 \tabularnewline
30 & 122.94 & 123.436944341973 & -0.496944341973062 \tabularnewline
31 & 122.56 & 123.784163310369 & -1.22416331036899 \tabularnewline
32 & 123.3 & 123.150974457485 & 0.149025542515432 \tabularnewline
33 & 123.75 & 123.921796820678 & -0.171796820677741 \tabularnewline
34 & 123.32 & 124.336264764139 & -1.01626476413908 \tabularnewline
35 & 123.66 & 123.696074744817 & -0.0360747448174692 \tabularnewline
36 & 124.01 & 124.028613548112 & -0.0186135481118725 \tabularnewline
37 & 124.42 & 124.374763781619 & 0.0452362183813904 \tabularnewline
38 & 124.63 & 124.794119809645 & -0.164119809645101 \tabularnewline
39 & 125.36 & 124.970175558917 & 0.389824441083292 \tabularnewline
40 & 125.84 & 125.780801405344 & 0.0591985946556264 \tabularnewline
41 & 123.79 & 126.2730452164 & -2.48304521639987 \tabularnewline
42 & 125.66 & 123.709486800888 & 1.95051319911167 \tabularnewline
43 & 123.23 & 125.982903726748 & -2.7529037267478 \tabularnewline
44 & 123.44 & 122.9835315435 & 0.45646845649992 \tabularnewline
45 & 122.98 & 123.287941107894 & -0.307941107894138 \tabularnewline
46 & 123.34 & 122.764250867219 & 0.575749132781482 \tabularnewline
47 & 122.85 & 123.243330781837 & -0.393330781837278 \tabularnewline
48 & 122.72 & 122.671979732828 & 0.0480202671722765 \tabularnewline
49 & 123.18 & 122.551911574648 & 0.628088425352189 \tabularnewline
50 & 122.7 & 123.141816618017 & -0.441816618017384 \tabularnewline
51 & 122.24 & 122.570437435392 & -0.330437435392341 \tabularnewline
52 & 121 & 122.042094368329 & -1.04209436832896 \tabularnewline
53 & 121.25 & 120.586562114193 & 0.663437885807141 \tabularnewline
54 & 120.48 & 120.973778346574 & -0.493778346573606 \tabularnewline
55 & 120.4 & 120.101652125269 & 0.298347874731334 \tabularnewline
56 & 120.7 & 120.083358235494 & 0.616641764505758 \tabularnewline
57 & 121.42 & 120.510895811301 & 0.90910418869916 \tabularnewline
58 & 121.76 & 121.41892223289 & 0.341077767110193 \tabularnewline
59 & 121.64 & 121.829465997654 & -0.1894659976535 \tabularnewline
60 & 120.52 & 121.670279495166 & -1.15027949516632 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167439&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]3[/C][C]102.13[/C][C]100.71[/C][C]1.41999999999999[/C][/ROW]
[ROW][C]4[/C][C]102.59[/C][C]101.953692980381[/C][C]0.636307019618542[/C][/ROW]
[ROW][C]5[/C][C]103.25[/C][C]102.545297843078[/C][C]0.704702156921769[/C][/ROW]
[ROW][C]6[/C][C]103.48[/C][C]103.351048601351[/C][C]0.128951398648823[/C][/ROW]
[ROW][C]7[/C][C]104.03[/C][C]103.607719108811[/C][C]0.422280891188578[/C][/ROW]
[ROW][C]8[/C][C]103.64[/C][C]104.245057794369[/C][C]-0.605057794368676[/C][/ROW]
[ROW][C]9[/C][C]103.29[/C][C]103.729916085262[/C][C]-0.439916085262212[/C][/ROW]
[ROW][C]10[/C][C]103.3[/C][C]103.288929982306[/C][C]0.0110700176943936[/C][/ROW]
[ROW][C]11[/C][C]104.51[/C][C]103.301219550256[/C][C]1.20878044974403[/C][/ROW]
[ROW][C]12[/C][C]104.62[/C][C]104.761226826955[/C][C]-0.141226826954693[/C][/ROW]
[ROW][C]13[/C][C]105.93[/C][C]104.842017441238[/C][C]1.08798255876231[/C][/ROW]
[ROW][C]14[/C][C]105.2[/C][C]106.3770405682[/C][C]-1.17704056819963[/C][/ROW]
[ROW][C]15[/C][C]106[/C][C]105.403597925591[/C][C]0.596402074409127[/C][/ROW]
[ROW][C]16[/C][C]108.05[/C][C]106.326949406393[/C][C]1.72305059360708[/C][/ROW]
[ROW][C]17[/C][C]109.36[/C][C]108.733321141734[/C][C]0.62667885826589[/C][/ROW]
[ROW][C]18[/C][C]110.05[/C][C]110.172934649922[/C][C]-0.122934649921561[/C][/ROW]
[ROW][C]19[/C][C]110.23[/C][C]110.837508562789[/C][C]-0.60750856278942[/C][/ROW]
[ROW][C]20[/C][C]110.45[/C][C]110.891859970949[/C][C]-0.441859970949366[/C][/ROW]
[ROW][C]21[/C][C]110.64[/C][C]111.020471821809[/C][C]-0.380471821808968[/C][/ROW]
[ROW][C]22[/C][C]112.31[/C][C]111.131780340613[/C][C]1.17821965938698[/C][/ROW]
[ROW][C]23[/C][C]116.13[/C][C]113.045466849986[/C][C]3.08453315001417[/C][/ROW]
[ROW][C]24[/C][C]119.08[/C][C]117.503428634432[/C][C]1.57657136556834[/C][/ROW]
[ROW][C]25[/C][C]120.55[/C][C]120.779504650726[/C][C]-0.229504650725914[/C][/ROW]
[ROW][C]26[/C][C]121.13[/C][C]122.202037112076[/C][C]-1.07203711207583[/C][/ROW]
[ROW][C]27[/C][C]121.16[/C][C]122.560311918748[/C][C]-1.40031191874832[/C][/ROW]
[ROW][C]28[/C][C]122.23[/C][C]122.300690946297[/C][C]-0.0706909462969918[/C][/ROW]
[ROW][C]29[/C][C]122.49[/C][C]123.356070217632[/C][C]-0.866070217632256[/C][/ROW]
[ROW][C]30[/C][C]122.94[/C][C]123.436944341973[/C][C]-0.496944341973062[/C][/ROW]
[ROW][C]31[/C][C]122.56[/C][C]123.784163310369[/C][C]-1.22416331036899[/C][/ROW]
[ROW][C]32[/C][C]123.3[/C][C]123.150974457485[/C][C]0.149025542515432[/C][/ROW]
[ROW][C]33[/C][C]123.75[/C][C]123.921796820678[/C][C]-0.171796820677741[/C][/ROW]
[ROW][C]34[/C][C]123.32[/C][C]124.336264764139[/C][C]-1.01626476413908[/C][/ROW]
[ROW][C]35[/C][C]123.66[/C][C]123.696074744817[/C][C]-0.0360747448174692[/C][/ROW]
[ROW][C]36[/C][C]124.01[/C][C]124.028613548112[/C][C]-0.0186135481118725[/C][/ROW]
[ROW][C]37[/C][C]124.42[/C][C]124.374763781619[/C][C]0.0452362183813904[/C][/ROW]
[ROW][C]38[/C][C]124.63[/C][C]124.794119809645[/C][C]-0.164119809645101[/C][/ROW]
[ROW][C]39[/C][C]125.36[/C][C]124.970175558917[/C][C]0.389824441083292[/C][/ROW]
[ROW][C]40[/C][C]125.84[/C][C]125.780801405344[/C][C]0.0591985946556264[/C][/ROW]
[ROW][C]41[/C][C]123.79[/C][C]126.2730452164[/C][C]-2.48304521639987[/C][/ROW]
[ROW][C]42[/C][C]125.66[/C][C]123.709486800888[/C][C]1.95051319911167[/C][/ROW]
[ROW][C]43[/C][C]123.23[/C][C]125.982903726748[/C][C]-2.7529037267478[/C][/ROW]
[ROW][C]44[/C][C]123.44[/C][C]122.9835315435[/C][C]0.45646845649992[/C][/ROW]
[ROW][C]45[/C][C]122.98[/C][C]123.287941107894[/C][C]-0.307941107894138[/C][/ROW]
[ROW][C]46[/C][C]123.34[/C][C]122.764250867219[/C][C]0.575749132781482[/C][/ROW]
[ROW][C]47[/C][C]122.85[/C][C]123.243330781837[/C][C]-0.393330781837278[/C][/ROW]
[ROW][C]48[/C][C]122.72[/C][C]122.671979732828[/C][C]0.0480202671722765[/C][/ROW]
[ROW][C]49[/C][C]123.18[/C][C]122.551911574648[/C][C]0.628088425352189[/C][/ROW]
[ROW][C]50[/C][C]122.7[/C][C]123.141816618017[/C][C]-0.441816618017384[/C][/ROW]
[ROW][C]51[/C][C]122.24[/C][C]122.570437435392[/C][C]-0.330437435392341[/C][/ROW]
[ROW][C]52[/C][C]121[/C][C]122.042094368329[/C][C]-1.04209436832896[/C][/ROW]
[ROW][C]53[/C][C]121.25[/C][C]120.586562114193[/C][C]0.663437885807141[/C][/ROW]
[ROW][C]54[/C][C]120.48[/C][C]120.973778346574[/C][C]-0.493778346573606[/C][/ROW]
[ROW][C]55[/C][C]120.4[/C][C]120.101652125269[/C][C]0.298347874731334[/C][/ROW]
[ROW][C]56[/C][C]120.7[/C][C]120.083358235494[/C][C]0.616641764505758[/C][/ROW]
[ROW][C]57[/C][C]121.42[/C][C]120.510895811301[/C][C]0.90910418869916[/C][/ROW]
[ROW][C]58[/C][C]121.76[/C][C]121.41892223289[/C][C]0.341077767110193[/C][/ROW]
[ROW][C]59[/C][C]121.64[/C][C]121.829465997654[/C][C]-0.1894659976535[/C][/ROW]
[ROW][C]60[/C][C]120.52[/C][C]121.670279495166[/C][C]-1.15027949516632[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167439&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167439&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
3102.13100.711.41999999999999
4102.59101.9536929803810.636307019618542
5103.25102.5452978430780.704702156921769
6103.48103.3510486013510.128951398648823
7104.03103.6077191088110.422280891188578
8103.64104.245057794369-0.605057794368676
9103.29103.729916085262-0.439916085262212
10103.3103.2889299823060.0110700176943936
11104.51103.3012195502561.20878044974403
12104.62104.761226826955-0.141226826954693
13105.93104.8420174412381.08798255876231
14105.2106.3770405682-1.17704056819963
15106105.4035979255910.596402074409127
16108.05106.3269494063931.72305059360708
17109.36108.7333211417340.62667885826589
18110.05110.172934649922-0.122934649921561
19110.23110.837508562789-0.60750856278942
20110.45110.891859970949-0.441859970949366
21110.64111.020471821809-0.380471821808968
22112.31111.1317803406131.17821965938698
23116.13113.0454668499863.08453315001417
24119.08117.5034286344321.57657136556834
25120.55120.779504650726-0.229504650725914
26121.13122.202037112076-1.07203711207583
27121.16122.560311918748-1.40031191874832
28122.23122.300690946297-0.0706909462969918
29122.49123.356070217632-0.866070217632256
30122.94123.436944341973-0.496944341973062
31122.56123.784163310369-1.22416331036899
32123.3123.1509744574850.149025542515432
33123.75123.921796820678-0.171796820677741
34123.32124.336264764139-1.01626476413908
35123.66123.696074744817-0.0360747448174692
36124.01124.028613548112-0.0186135481118725
37124.42124.3747637816190.0452362183813904
38124.63124.794119809645-0.164119809645101
39125.36124.9701755589170.389824441083292
40125.84125.7808014053440.0591985946556264
41123.79126.2730452164-2.48304521639987
42125.66123.7094868008881.95051319911167
43123.23125.982903726748-2.7529037267478
44123.44122.98353154350.45646845649992
45122.98123.287941107894-0.307941107894138
46123.34122.7642508672190.575749132781482
47122.85123.243330781837-0.393330781837278
48122.72122.6719797328280.0480202671722765
49123.18122.5519115746480.628088425352189
50122.7123.141816618017-0.441816618017384
51122.24122.570437435392-0.330437435392341
52121122.042094368329-1.04209436832896
53121.25120.5865621141930.663437885807141
54120.48120.973778346574-0.493778346573606
55120.4120.1016521252690.298347874731334
56120.7120.0833582354940.616641764505758
57121.42120.5108958113010.90910418869916
58121.76121.418922232890.341077767110193
59121.64121.829465997654-0.1894659976535
60120.52121.670279495166-1.15027949516632







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61120.312371739387118.369003186886122.255740291888
62120.104743478773117.058902066149123.150584891398
63119.89711521816115.795345353306123.998885083014
64119.689486957547114.518230828215124.860743086878
65119.481858696933113.208711003164125.755006390702
66119.27423043632111.859440998548126.689019874092
67119.066602175707110.467464922742127.665739428672
68118.858973915093109.031783597483128.686164232704
69118.65134565448107.552348545718129.750342763242
70118.443717393867106.029593436661130.857841351073
71118.236089133254104.464197823908132.007980442599
72118.02846087264102.856961377233133.199960368048

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 120.312371739387 & 118.369003186886 & 122.255740291888 \tabularnewline
62 & 120.104743478773 & 117.058902066149 & 123.150584891398 \tabularnewline
63 & 119.89711521816 & 115.795345353306 & 123.998885083014 \tabularnewline
64 & 119.689486957547 & 114.518230828215 & 124.860743086878 \tabularnewline
65 & 119.481858696933 & 113.208711003164 & 125.755006390702 \tabularnewline
66 & 119.27423043632 & 111.859440998548 & 126.689019874092 \tabularnewline
67 & 119.066602175707 & 110.467464922742 & 127.665739428672 \tabularnewline
68 & 118.858973915093 & 109.031783597483 & 128.686164232704 \tabularnewline
69 & 118.65134565448 & 107.552348545718 & 129.750342763242 \tabularnewline
70 & 118.443717393867 & 106.029593436661 & 130.857841351073 \tabularnewline
71 & 118.236089133254 & 104.464197823908 & 132.007980442599 \tabularnewline
72 & 118.02846087264 & 102.856961377233 & 133.199960368048 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167439&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]61[/C][C]120.312371739387[/C][C]118.369003186886[/C][C]122.255740291888[/C][/ROW]
[ROW][C]62[/C][C]120.104743478773[/C][C]117.058902066149[/C][C]123.150584891398[/C][/ROW]
[ROW][C]63[/C][C]119.89711521816[/C][C]115.795345353306[/C][C]123.998885083014[/C][/ROW]
[ROW][C]64[/C][C]119.689486957547[/C][C]114.518230828215[/C][C]124.860743086878[/C][/ROW]
[ROW][C]65[/C][C]119.481858696933[/C][C]113.208711003164[/C][C]125.755006390702[/C][/ROW]
[ROW][C]66[/C][C]119.27423043632[/C][C]111.859440998548[/C][C]126.689019874092[/C][/ROW]
[ROW][C]67[/C][C]119.066602175707[/C][C]110.467464922742[/C][C]127.665739428672[/C][/ROW]
[ROW][C]68[/C][C]118.858973915093[/C][C]109.031783597483[/C][C]128.686164232704[/C][/ROW]
[ROW][C]69[/C][C]118.65134565448[/C][C]107.552348545718[/C][C]129.750342763242[/C][/ROW]
[ROW][C]70[/C][C]118.443717393867[/C][C]106.029593436661[/C][C]130.857841351073[/C][/ROW]
[ROW][C]71[/C][C]118.236089133254[/C][C]104.464197823908[/C][C]132.007980442599[/C][/ROW]
[ROW][C]72[/C][C]118.02846087264[/C][C]102.856961377233[/C][C]133.199960368048[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167439&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167439&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
61120.312371739387118.369003186886122.255740291888
62120.104743478773117.058902066149123.150584891398
63119.89711521816115.795345353306123.998885083014
64119.689486957547114.518230828215124.860743086878
65119.481858696933113.208711003164125.755006390702
66119.27423043632111.859440998548126.689019874092
67119.066602175707110.467464922742127.665739428672
68118.858973915093109.031783597483128.686164232704
69118.65134565448107.552348545718129.750342763242
70118.443717393867106.029593436661130.857841351073
71118.236089133254104.464197823908132.007980442599
72118.02846087264102.856961377233133.199960368048



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')