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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 26 Apr 2016 21:56:44 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Apr/26/t1461704257p598okuh2fxvjvd.htm/, Retrieved Fri, 03 May 2024 20:53:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294985, Retrieved Fri, 03 May 2024 20:53:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact68
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-04-26 20:56:44] [0b2c3ebb4286059f748822350b46c363] [Current]
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Dataseries X:
105,95
108,55
110,81
111,54
110,38
106,67
106,45
105,44
105,37
103,72
106,57
108,54
110,36
106,64
103,45
101,36
101,9
100,86
100,37
100,16
99,5
99,52
99,2
99,35
99,37
99,85
99,76
100,07
99,77
99,93
99,16
99,4
99,81
99,67
99,37
99,49
99,28
99,33
99,19
98,11
99,12
99,06
97,41
98,45
100,33
103,18
103,06
103,48
102,8
103,92
103,9
103,96
103,62
103,83
104,09
104,07
103,22
104,01
104,01
104,24
102,93
104,73
106,48
119,5
122,45
125,29
126,56
126,38
127,95
128,23
128,7
127,86




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294985&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294985&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294985&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'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999938458061159
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999938458061159 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294985&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]0.999938458061159[/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=294985&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294985&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
alpha0.999938458061159
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2108.55105.952.59999999999999
3110.81108.5498399909592.26016000904099
4111.54110.8098609053710.730139094629038
5110.38111.539955065825-1.15995506582451
6106.67110.380071385884-3.71007138588371
7106.45106.670228324986-0.220228324986323
8105.44106.450013553278-1.01001355327811
9105.37105.440062158192-0.0700621581923286
10103.72105.370004311761-1.65000431176105
11106.57103.7201015444642.84989845553555
12108.54106.5698246117241.97017538827646
13110.36108.5398787515871.82012124841324
14106.64110.359887986209-3.71988798620944
15103.45106.640228929119-3.19022892911894
16101.36103.450196332874-2.09019633287365
17101.9101.3601286347350.539871365265128
18100.86101.899966775269-1.03996677526946
19100.37100.860064001572-0.490064001571682
20100.16100.370030159489-0.210030159488809
2199.5100.160012925663-0.660012925663224
2299.5299.50004061847510.0199593815248988
2399.299.519998771661-0.319998771660948
2499.3599.20001969334480.149980306655166
2599.3799.34999076992110.0200092300788697
2699.8599.36999876859320.480001231406803
2799.7699.8499704597936-0.0899704597935624
28100.0799.76000553695650.309994463043452
2999.77100.06998092234-0.299980922339714
3099.9399.77001846140760.159981538592433
3199.1699.929990154426-0.769990154425955
3299.499.1600473866870.239952613313008
3399.8199.3999852328510.41001476714905
3499.6799.8099747668963-0.139974766896287
3599.3799.6700086143185-0.300008614318543
3699.4999.37001846311180.11998153688819
3799.2899.4899926161036-0.209992616103591
3899.3399.28001292335270.0499870766472696
3999.1999.3299969236984-0.139996923698391
4098.1199.1900086156821-1.08000861568212
4199.1298.11006646582421.00993353417583
4299.0699.1199378467322-0.0599378467322111
4397.4199.0600036886913-1.65000368869131
4498.4597.41010154442611.0398984555739
45100.3398.44993600263281.88006399736716
46103.18100.3298842972162.85011570278355
47103.06103.179824598354-0.119824598353745
48103.48103.0600073742380.419992625761893
49102.8103.47997415284-0.679974152839506
50103.92102.8000418469281.11995815307228
51103.9103.919931075604-0.0199310756038358
52103.96103.9000012265970.0599987734029526
53103.62103.959996307559-0.339996307559147
54103.83103.6200209240320.209979075968036
55104.09103.8299870774810.260012922519451
56104.07104.089983998301-0.0199839983006456
57103.22104.070001229854-0.850001229854001
58104.01103.2200523107240.789947689276303
59104.01104.0099513850884.86149123730684e-05
60104.24104.0099999970080.230000002991844
61102.93104.239985845354-1.30998584535386
62104.73102.9300806190691.79991938093123
63106.48104.7298892294721.75011077052847
64119.5106.4798922947913.02010770521
65122.45119.4991987173282.95080128267209
66125.29122.4498184019682.84018159803207
67126.56125.2898252097181.2701747902822
68126.38126.559921830981-0.179921830980746
69127.95126.3800110727381.56998892726169
70128.23127.9499033798370.280096620162524
71128.7128.2299827623110.470017237689063
72127.86128.699971074228-0.839971074227876

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 108.55 & 105.95 & 2.59999999999999 \tabularnewline
3 & 110.81 & 108.549839990959 & 2.26016000904099 \tabularnewline
4 & 111.54 & 110.809860905371 & 0.730139094629038 \tabularnewline
5 & 110.38 & 111.539955065825 & -1.15995506582451 \tabularnewline
6 & 106.67 & 110.380071385884 & -3.71007138588371 \tabularnewline
7 & 106.45 & 106.670228324986 & -0.220228324986323 \tabularnewline
8 & 105.44 & 106.450013553278 & -1.01001355327811 \tabularnewline
9 & 105.37 & 105.440062158192 & -0.0700621581923286 \tabularnewline
10 & 103.72 & 105.370004311761 & -1.65000431176105 \tabularnewline
11 & 106.57 & 103.720101544464 & 2.84989845553555 \tabularnewline
12 & 108.54 & 106.569824611724 & 1.97017538827646 \tabularnewline
13 & 110.36 & 108.539878751587 & 1.82012124841324 \tabularnewline
14 & 106.64 & 110.359887986209 & -3.71988798620944 \tabularnewline
15 & 103.45 & 106.640228929119 & -3.19022892911894 \tabularnewline
16 & 101.36 & 103.450196332874 & -2.09019633287365 \tabularnewline
17 & 101.9 & 101.360128634735 & 0.539871365265128 \tabularnewline
18 & 100.86 & 101.899966775269 & -1.03996677526946 \tabularnewline
19 & 100.37 & 100.860064001572 & -0.490064001571682 \tabularnewline
20 & 100.16 & 100.370030159489 & -0.210030159488809 \tabularnewline
21 & 99.5 & 100.160012925663 & -0.660012925663224 \tabularnewline
22 & 99.52 & 99.5000406184751 & 0.0199593815248988 \tabularnewline
23 & 99.2 & 99.519998771661 & -0.319998771660948 \tabularnewline
24 & 99.35 & 99.2000196933448 & 0.149980306655166 \tabularnewline
25 & 99.37 & 99.3499907699211 & 0.0200092300788697 \tabularnewline
26 & 99.85 & 99.3699987685932 & 0.480001231406803 \tabularnewline
27 & 99.76 & 99.8499704597936 & -0.0899704597935624 \tabularnewline
28 & 100.07 & 99.7600055369565 & 0.309994463043452 \tabularnewline
29 & 99.77 & 100.06998092234 & -0.299980922339714 \tabularnewline
30 & 99.93 & 99.7700184614076 & 0.159981538592433 \tabularnewline
31 & 99.16 & 99.929990154426 & -0.769990154425955 \tabularnewline
32 & 99.4 & 99.160047386687 & 0.239952613313008 \tabularnewline
33 & 99.81 & 99.399985232851 & 0.41001476714905 \tabularnewline
34 & 99.67 & 99.8099747668963 & -0.139974766896287 \tabularnewline
35 & 99.37 & 99.6700086143185 & -0.300008614318543 \tabularnewline
36 & 99.49 & 99.3700184631118 & 0.11998153688819 \tabularnewline
37 & 99.28 & 99.4899926161036 & -0.209992616103591 \tabularnewline
38 & 99.33 & 99.2800129233527 & 0.0499870766472696 \tabularnewline
39 & 99.19 & 99.3299969236984 & -0.139996923698391 \tabularnewline
40 & 98.11 & 99.1900086156821 & -1.08000861568212 \tabularnewline
41 & 99.12 & 98.1100664658242 & 1.00993353417583 \tabularnewline
42 & 99.06 & 99.1199378467322 & -0.0599378467322111 \tabularnewline
43 & 97.41 & 99.0600036886913 & -1.65000368869131 \tabularnewline
44 & 98.45 & 97.4101015444261 & 1.0398984555739 \tabularnewline
45 & 100.33 & 98.4499360026328 & 1.88006399736716 \tabularnewline
46 & 103.18 & 100.329884297216 & 2.85011570278355 \tabularnewline
47 & 103.06 & 103.179824598354 & -0.119824598353745 \tabularnewline
48 & 103.48 & 103.060007374238 & 0.419992625761893 \tabularnewline
49 & 102.8 & 103.47997415284 & -0.679974152839506 \tabularnewline
50 & 103.92 & 102.800041846928 & 1.11995815307228 \tabularnewline
51 & 103.9 & 103.919931075604 & -0.0199310756038358 \tabularnewline
52 & 103.96 & 103.900001226597 & 0.0599987734029526 \tabularnewline
53 & 103.62 & 103.959996307559 & -0.339996307559147 \tabularnewline
54 & 103.83 & 103.620020924032 & 0.209979075968036 \tabularnewline
55 & 104.09 & 103.829987077481 & 0.260012922519451 \tabularnewline
56 & 104.07 & 104.089983998301 & -0.0199839983006456 \tabularnewline
57 & 103.22 & 104.070001229854 & -0.850001229854001 \tabularnewline
58 & 104.01 & 103.220052310724 & 0.789947689276303 \tabularnewline
59 & 104.01 & 104.009951385088 & 4.86149123730684e-05 \tabularnewline
60 & 104.24 & 104.009999997008 & 0.230000002991844 \tabularnewline
61 & 102.93 & 104.239985845354 & -1.30998584535386 \tabularnewline
62 & 104.73 & 102.930080619069 & 1.79991938093123 \tabularnewline
63 & 106.48 & 104.729889229472 & 1.75011077052847 \tabularnewline
64 & 119.5 & 106.47989229479 & 13.02010770521 \tabularnewline
65 & 122.45 & 119.499198717328 & 2.95080128267209 \tabularnewline
66 & 125.29 & 122.449818401968 & 2.84018159803207 \tabularnewline
67 & 126.56 & 125.289825209718 & 1.2701747902822 \tabularnewline
68 & 126.38 & 126.559921830981 & -0.179921830980746 \tabularnewline
69 & 127.95 & 126.380011072738 & 1.56998892726169 \tabularnewline
70 & 128.23 & 127.949903379837 & 0.280096620162524 \tabularnewline
71 & 128.7 & 128.229982762311 & 0.470017237689063 \tabularnewline
72 & 127.86 & 128.699971074228 & -0.839971074227876 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294985&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]108.55[/C][C]105.95[/C][C]2.59999999999999[/C][/ROW]
[ROW][C]3[/C][C]110.81[/C][C]108.549839990959[/C][C]2.26016000904099[/C][/ROW]
[ROW][C]4[/C][C]111.54[/C][C]110.809860905371[/C][C]0.730139094629038[/C][/ROW]
[ROW][C]5[/C][C]110.38[/C][C]111.539955065825[/C][C]-1.15995506582451[/C][/ROW]
[ROW][C]6[/C][C]106.67[/C][C]110.380071385884[/C][C]-3.71007138588371[/C][/ROW]
[ROW][C]7[/C][C]106.45[/C][C]106.670228324986[/C][C]-0.220228324986323[/C][/ROW]
[ROW][C]8[/C][C]105.44[/C][C]106.450013553278[/C][C]-1.01001355327811[/C][/ROW]
[ROW][C]9[/C][C]105.37[/C][C]105.440062158192[/C][C]-0.0700621581923286[/C][/ROW]
[ROW][C]10[/C][C]103.72[/C][C]105.370004311761[/C][C]-1.65000431176105[/C][/ROW]
[ROW][C]11[/C][C]106.57[/C][C]103.720101544464[/C][C]2.84989845553555[/C][/ROW]
[ROW][C]12[/C][C]108.54[/C][C]106.569824611724[/C][C]1.97017538827646[/C][/ROW]
[ROW][C]13[/C][C]110.36[/C][C]108.539878751587[/C][C]1.82012124841324[/C][/ROW]
[ROW][C]14[/C][C]106.64[/C][C]110.359887986209[/C][C]-3.71988798620944[/C][/ROW]
[ROW][C]15[/C][C]103.45[/C][C]106.640228929119[/C][C]-3.19022892911894[/C][/ROW]
[ROW][C]16[/C][C]101.36[/C][C]103.450196332874[/C][C]-2.09019633287365[/C][/ROW]
[ROW][C]17[/C][C]101.9[/C][C]101.360128634735[/C][C]0.539871365265128[/C][/ROW]
[ROW][C]18[/C][C]100.86[/C][C]101.899966775269[/C][C]-1.03996677526946[/C][/ROW]
[ROW][C]19[/C][C]100.37[/C][C]100.860064001572[/C][C]-0.490064001571682[/C][/ROW]
[ROW][C]20[/C][C]100.16[/C][C]100.370030159489[/C][C]-0.210030159488809[/C][/ROW]
[ROW][C]21[/C][C]99.5[/C][C]100.160012925663[/C][C]-0.660012925663224[/C][/ROW]
[ROW][C]22[/C][C]99.52[/C][C]99.5000406184751[/C][C]0.0199593815248988[/C][/ROW]
[ROW][C]23[/C][C]99.2[/C][C]99.519998771661[/C][C]-0.319998771660948[/C][/ROW]
[ROW][C]24[/C][C]99.35[/C][C]99.2000196933448[/C][C]0.149980306655166[/C][/ROW]
[ROW][C]25[/C][C]99.37[/C][C]99.3499907699211[/C][C]0.0200092300788697[/C][/ROW]
[ROW][C]26[/C][C]99.85[/C][C]99.3699987685932[/C][C]0.480001231406803[/C][/ROW]
[ROW][C]27[/C][C]99.76[/C][C]99.8499704597936[/C][C]-0.0899704597935624[/C][/ROW]
[ROW][C]28[/C][C]100.07[/C][C]99.7600055369565[/C][C]0.309994463043452[/C][/ROW]
[ROW][C]29[/C][C]99.77[/C][C]100.06998092234[/C][C]-0.299980922339714[/C][/ROW]
[ROW][C]30[/C][C]99.93[/C][C]99.7700184614076[/C][C]0.159981538592433[/C][/ROW]
[ROW][C]31[/C][C]99.16[/C][C]99.929990154426[/C][C]-0.769990154425955[/C][/ROW]
[ROW][C]32[/C][C]99.4[/C][C]99.160047386687[/C][C]0.239952613313008[/C][/ROW]
[ROW][C]33[/C][C]99.81[/C][C]99.399985232851[/C][C]0.41001476714905[/C][/ROW]
[ROW][C]34[/C][C]99.67[/C][C]99.8099747668963[/C][C]-0.139974766896287[/C][/ROW]
[ROW][C]35[/C][C]99.37[/C][C]99.6700086143185[/C][C]-0.300008614318543[/C][/ROW]
[ROW][C]36[/C][C]99.49[/C][C]99.3700184631118[/C][C]0.11998153688819[/C][/ROW]
[ROW][C]37[/C][C]99.28[/C][C]99.4899926161036[/C][C]-0.209992616103591[/C][/ROW]
[ROW][C]38[/C][C]99.33[/C][C]99.2800129233527[/C][C]0.0499870766472696[/C][/ROW]
[ROW][C]39[/C][C]99.19[/C][C]99.3299969236984[/C][C]-0.139996923698391[/C][/ROW]
[ROW][C]40[/C][C]98.11[/C][C]99.1900086156821[/C][C]-1.08000861568212[/C][/ROW]
[ROW][C]41[/C][C]99.12[/C][C]98.1100664658242[/C][C]1.00993353417583[/C][/ROW]
[ROW][C]42[/C][C]99.06[/C][C]99.1199378467322[/C][C]-0.0599378467322111[/C][/ROW]
[ROW][C]43[/C][C]97.41[/C][C]99.0600036886913[/C][C]-1.65000368869131[/C][/ROW]
[ROW][C]44[/C][C]98.45[/C][C]97.4101015444261[/C][C]1.0398984555739[/C][/ROW]
[ROW][C]45[/C][C]100.33[/C][C]98.4499360026328[/C][C]1.88006399736716[/C][/ROW]
[ROW][C]46[/C][C]103.18[/C][C]100.329884297216[/C][C]2.85011570278355[/C][/ROW]
[ROW][C]47[/C][C]103.06[/C][C]103.179824598354[/C][C]-0.119824598353745[/C][/ROW]
[ROW][C]48[/C][C]103.48[/C][C]103.060007374238[/C][C]0.419992625761893[/C][/ROW]
[ROW][C]49[/C][C]102.8[/C][C]103.47997415284[/C][C]-0.679974152839506[/C][/ROW]
[ROW][C]50[/C][C]103.92[/C][C]102.800041846928[/C][C]1.11995815307228[/C][/ROW]
[ROW][C]51[/C][C]103.9[/C][C]103.919931075604[/C][C]-0.0199310756038358[/C][/ROW]
[ROW][C]52[/C][C]103.96[/C][C]103.900001226597[/C][C]0.0599987734029526[/C][/ROW]
[ROW][C]53[/C][C]103.62[/C][C]103.959996307559[/C][C]-0.339996307559147[/C][/ROW]
[ROW][C]54[/C][C]103.83[/C][C]103.620020924032[/C][C]0.209979075968036[/C][/ROW]
[ROW][C]55[/C][C]104.09[/C][C]103.829987077481[/C][C]0.260012922519451[/C][/ROW]
[ROW][C]56[/C][C]104.07[/C][C]104.089983998301[/C][C]-0.0199839983006456[/C][/ROW]
[ROW][C]57[/C][C]103.22[/C][C]104.070001229854[/C][C]-0.850001229854001[/C][/ROW]
[ROW][C]58[/C][C]104.01[/C][C]103.220052310724[/C][C]0.789947689276303[/C][/ROW]
[ROW][C]59[/C][C]104.01[/C][C]104.009951385088[/C][C]4.86149123730684e-05[/C][/ROW]
[ROW][C]60[/C][C]104.24[/C][C]104.009999997008[/C][C]0.230000002991844[/C][/ROW]
[ROW][C]61[/C][C]102.93[/C][C]104.239985845354[/C][C]-1.30998584535386[/C][/ROW]
[ROW][C]62[/C][C]104.73[/C][C]102.930080619069[/C][C]1.79991938093123[/C][/ROW]
[ROW][C]63[/C][C]106.48[/C][C]104.729889229472[/C][C]1.75011077052847[/C][/ROW]
[ROW][C]64[/C][C]119.5[/C][C]106.47989229479[/C][C]13.02010770521[/C][/ROW]
[ROW][C]65[/C][C]122.45[/C][C]119.499198717328[/C][C]2.95080128267209[/C][/ROW]
[ROW][C]66[/C][C]125.29[/C][C]122.449818401968[/C][C]2.84018159803207[/C][/ROW]
[ROW][C]67[/C][C]126.56[/C][C]125.289825209718[/C][C]1.2701747902822[/C][/ROW]
[ROW][C]68[/C][C]126.38[/C][C]126.559921830981[/C][C]-0.179921830980746[/C][/ROW]
[ROW][C]69[/C][C]127.95[/C][C]126.380011072738[/C][C]1.56998892726169[/C][/ROW]
[ROW][C]70[/C][C]128.23[/C][C]127.949903379837[/C][C]0.280096620162524[/C][/ROW]
[ROW][C]71[/C][C]128.7[/C][C]128.229982762311[/C][C]0.470017237689063[/C][/ROW]
[ROW][C]72[/C][C]127.86[/C][C]128.699971074228[/C][C]-0.839971074227876[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294985&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294985&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
2108.55105.952.59999999999999
3110.81108.5498399909592.26016000904099
4111.54110.8098609053710.730139094629038
5110.38111.539955065825-1.15995506582451
6106.67110.380071385884-3.71007138588371
7106.45106.670228324986-0.220228324986323
8105.44106.450013553278-1.01001355327811
9105.37105.440062158192-0.0700621581923286
10103.72105.370004311761-1.65000431176105
11106.57103.7201015444642.84989845553555
12108.54106.5698246117241.97017538827646
13110.36108.5398787515871.82012124841324
14106.64110.359887986209-3.71988798620944
15103.45106.640228929119-3.19022892911894
16101.36103.450196332874-2.09019633287365
17101.9101.3601286347350.539871365265128
18100.86101.899966775269-1.03996677526946
19100.37100.860064001572-0.490064001571682
20100.16100.370030159489-0.210030159488809
2199.5100.160012925663-0.660012925663224
2299.5299.50004061847510.0199593815248988
2399.299.519998771661-0.319998771660948
2499.3599.20001969334480.149980306655166
2599.3799.34999076992110.0200092300788697
2699.8599.36999876859320.480001231406803
2799.7699.8499704597936-0.0899704597935624
28100.0799.76000553695650.309994463043452
2999.77100.06998092234-0.299980922339714
3099.9399.77001846140760.159981538592433
3199.1699.929990154426-0.769990154425955
3299.499.1600473866870.239952613313008
3399.8199.3999852328510.41001476714905
3499.6799.8099747668963-0.139974766896287
3599.3799.6700086143185-0.300008614318543
3699.4999.37001846311180.11998153688819
3799.2899.4899926161036-0.209992616103591
3899.3399.28001292335270.0499870766472696
3999.1999.3299969236984-0.139996923698391
4098.1199.1900086156821-1.08000861568212
4199.1298.11006646582421.00993353417583
4299.0699.1199378467322-0.0599378467322111
4397.4199.0600036886913-1.65000368869131
4498.4597.41010154442611.0398984555739
45100.3398.44993600263281.88006399736716
46103.18100.3298842972162.85011570278355
47103.06103.179824598354-0.119824598353745
48103.48103.0600073742380.419992625761893
49102.8103.47997415284-0.679974152839506
50103.92102.8000418469281.11995815307228
51103.9103.919931075604-0.0199310756038358
52103.96103.9000012265970.0599987734029526
53103.62103.959996307559-0.339996307559147
54103.83103.6200209240320.209979075968036
55104.09103.8299870774810.260012922519451
56104.07104.089983998301-0.0199839983006456
57103.22104.070001229854-0.850001229854001
58104.01103.2200523107240.789947689276303
59104.01104.0099513850884.86149123730684e-05
60104.24104.0099999970080.230000002991844
61102.93104.239985845354-1.30998584535386
62104.73102.9300806190691.79991938093123
63106.48104.7298892294721.75011077052847
64119.5106.4798922947913.02010770521
65122.45119.4991987173282.95080128267209
66125.29122.4498184019682.84018159803207
67126.56125.2898252097181.2701747902822
68126.38126.559921830981-0.179921830980746
69127.95126.3800110727381.56998892726169
70128.23127.9499033798370.280096620162524
71128.7128.2299827623110.470017237689063
72127.86128.699971074228-0.839971074227876







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73127.860051693448123.853273495859131.866829891038
74127.860051693448122.193785984167133.52631740273
75127.860051693448120.920393009358134.799710377539
76127.860051693448119.846865172771135.873238214126
77127.860051693448118.901064374635136.819039012262
78127.860051693448118.04599293358137.674110453317
79127.860051693448117.25967222356138.460431163337
80127.860051693448116.527781820685139.192321566212
81127.860051693448115.840374658161139.879728728736
82127.860051693448115.190208300726140.529895086171
83127.860051693448114.57181527323141.148288113667
84127.860051693448113.980947877888141.739155509009

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 127.860051693448 & 123.853273495859 & 131.866829891038 \tabularnewline
74 & 127.860051693448 & 122.193785984167 & 133.52631740273 \tabularnewline
75 & 127.860051693448 & 120.920393009358 & 134.799710377539 \tabularnewline
76 & 127.860051693448 & 119.846865172771 & 135.873238214126 \tabularnewline
77 & 127.860051693448 & 118.901064374635 & 136.819039012262 \tabularnewline
78 & 127.860051693448 & 118.04599293358 & 137.674110453317 \tabularnewline
79 & 127.860051693448 & 117.25967222356 & 138.460431163337 \tabularnewline
80 & 127.860051693448 & 116.527781820685 & 139.192321566212 \tabularnewline
81 & 127.860051693448 & 115.840374658161 & 139.879728728736 \tabularnewline
82 & 127.860051693448 & 115.190208300726 & 140.529895086171 \tabularnewline
83 & 127.860051693448 & 114.57181527323 & 141.148288113667 \tabularnewline
84 & 127.860051693448 & 113.980947877888 & 141.739155509009 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294985&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]127.860051693448[/C][C]123.853273495859[/C][C]131.866829891038[/C][/ROW]
[ROW][C]74[/C][C]127.860051693448[/C][C]122.193785984167[/C][C]133.52631740273[/C][/ROW]
[ROW][C]75[/C][C]127.860051693448[/C][C]120.920393009358[/C][C]134.799710377539[/C][/ROW]
[ROW][C]76[/C][C]127.860051693448[/C][C]119.846865172771[/C][C]135.873238214126[/C][/ROW]
[ROW][C]77[/C][C]127.860051693448[/C][C]118.901064374635[/C][C]136.819039012262[/C][/ROW]
[ROW][C]78[/C][C]127.860051693448[/C][C]118.04599293358[/C][C]137.674110453317[/C][/ROW]
[ROW][C]79[/C][C]127.860051693448[/C][C]117.25967222356[/C][C]138.460431163337[/C][/ROW]
[ROW][C]80[/C][C]127.860051693448[/C][C]116.527781820685[/C][C]139.192321566212[/C][/ROW]
[ROW][C]81[/C][C]127.860051693448[/C][C]115.840374658161[/C][C]139.879728728736[/C][/ROW]
[ROW][C]82[/C][C]127.860051693448[/C][C]115.190208300726[/C][C]140.529895086171[/C][/ROW]
[ROW][C]83[/C][C]127.860051693448[/C][C]114.57181527323[/C][C]141.148288113667[/C][/ROW]
[ROW][C]84[/C][C]127.860051693448[/C][C]113.980947877888[/C][C]141.739155509009[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294985&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294985&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
73127.860051693448123.853273495859131.866829891038
74127.860051693448122.193785984167133.52631740273
75127.860051693448120.920393009358134.799710377539
76127.860051693448119.846865172771135.873238214126
77127.860051693448118.901064374635136.819039012262
78127.860051693448118.04599293358137.674110453317
79127.860051693448117.25967222356138.460431163337
80127.860051693448116.527781820685139.192321566212
81127.860051693448115.840374658161139.879728728736
82127.860051693448115.190208300726140.529895086171
83127.860051693448114.57181527323141.148288113667
84127.860051693448113.980947877888141.739155509009



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')