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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 01 Jun 2008 14:44:19 -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/Jun/01/t1212353115fhr8odz2asweioo.htm/, Retrieved Sat, 18 May 2024 16:48:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13747, Retrieved Sat, 18 May 2024 16:48:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact197
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [cijferreeks - oli...] [2008-06-01 20:44:19] [e744b461908af7c125bdbb2f3548f5e0] [Current]
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Dataseries X:
90.2
94.3
96
99
103.3
113.1
112.8
112.1
107.4
111
110.5
110.8
112.4
111.5
116.2
122.5
121.3
113.9
110.7
120.8
141.1
147.4
148
158.1
165
187
190.3
182.4
168.8
151.2
120.1
112.5
106.2
107.1
108.5
106.5
108.3
125.6
124
127.2
136.9
135.8
124.3
115.4
113.6
114.4
118.4
117
116.5
115.4
113.6
117.4
116.9
116.4
111.1
110.2
118.9
131.8
130.6
138.3
148.4
148.7
144.3
152.5
162.9
167.2
166.5
185.6
193.2
207.8
223.4
246.4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13747&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13747&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13747&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 time5 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.572958262964854
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.572958262964854 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13747&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]0.572958262964854[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13747&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13747&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
beta0.572958262964854
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
39698.4-2.39999999999999
49998.72490016888430.275099831115654
5103.3101.8825208902621.4174791097377
6113.1106.9946772587676.10532274123342
7112.8120.292772371423-7.4927723714235
8112.1115.699726528702-3.59972652870165
9107.4112.937233469668-5.53723346966824
10111105.0646297992565.9353702007437
11110.5112.065349199528-1.56534919952776
12110.8110.6684694412330.131530558767082
13112.4111.0438309617111.35616903828911
14111.5113.420859218176-1.92085921817575
15116.2111.4202870571304.77971294287026
16122.5118.8588630823473.64113691765269
17121.3127.245082565903-5.94508256590279
18113.9122.638798385760-8.73879838576049
19110.7110.2318316422550.468168357744901
20120.8107.30007257128413.4999274287163
21141.1125.13496754099315.9650324590074
22147.4154.582264806883-7.18226480688296
23148156.767126838978-8.76712683897773
24158.1152.3439290741255.75607092587549
25165165.741917473317-0.741917473316619
26187172.21682972654214.7831702734582
27190.3202.686969287536-12.3869692875361
28182.4198.889752881150-16.4897528811504
29168.8181.541812713647-12.7418127136468
30151.2160.641285834212-9.44128583421227
31120.1137.631823102487-17.5318231024873
32112.596.48682019107916.0131798089209
33106.298.06170387894238.13829612105772
34107.196.424607887957110.6753921120429
35108.5103.4411620089425.0588379910581
36106.5107.739665036919-1.23966503691916
37108.3105.0293887107083.27061128929230
38125.6108.70331247385416.8966875261461
39124135.684409208694-11.6844092086945
40127.2127.389730404710-0.189730404710346
41136.9130.4810228015966.41897719840412
42135.8143.858828827205-8.0588288272045
43124.3138.141456260838-13.8414562608383
44115.4118.710879524724-3.31087952472438
45113.6107.9138837433525.68611625664758
46114.4109.3717910367775.0282089632226
47118.4113.0527449101705.34725508983026
48117120.116498898069-3.11649889806887
49116.5116.930875102899-0.430875102899449
50115.4116.184001652387-0.784001652387374
51113.6114.634801427474-1.03480142747395
52117.4112.2419033990755.1580966009251
53116.9118.997277467746-2.09727746774587
54116.4117.295625012871-0.895625012870866
55111.1116.282469261229-5.18246926122852
56110.2108.0131306754462.18686932455374
57118.9108.36611552497410.5338844750263
58131.8123.1015916760578.6984083239428
59130.6140.985416599903-10.3854165999025
60138.3133.8350063446564.46499365534402
61148.4144.0932613535714.30673864642898
62148.7156.660842847473-7.96084284747258
63144.3152.399612157848-8.09961215784847
64152.5143.3588724451999.14112755480136
65162.9156.7963570105386.10364298946223
66167.2170.693489695538-3.49348969553768
67166.5172.991865907897-6.49186590789677
68185.6168.57229769390817.0277023060925
69193.2197.428460429489-4.22846042948890
70207.8202.6057290867935.19427091320671
71223.4220.1818295265933.2181704734069
72246.4237.6257068909618.7742931090389

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 96 & 98.4 & -2.39999999999999 \tabularnewline
4 & 99 & 98.7249001688843 & 0.275099831115654 \tabularnewline
5 & 103.3 & 101.882520890262 & 1.4174791097377 \tabularnewline
6 & 113.1 & 106.994677258767 & 6.10532274123342 \tabularnewline
7 & 112.8 & 120.292772371423 & -7.4927723714235 \tabularnewline
8 & 112.1 & 115.699726528702 & -3.59972652870165 \tabularnewline
9 & 107.4 & 112.937233469668 & -5.53723346966824 \tabularnewline
10 & 111 & 105.064629799256 & 5.9353702007437 \tabularnewline
11 & 110.5 & 112.065349199528 & -1.56534919952776 \tabularnewline
12 & 110.8 & 110.668469441233 & 0.131530558767082 \tabularnewline
13 & 112.4 & 111.043830961711 & 1.35616903828911 \tabularnewline
14 & 111.5 & 113.420859218176 & -1.92085921817575 \tabularnewline
15 & 116.2 & 111.420287057130 & 4.77971294287026 \tabularnewline
16 & 122.5 & 118.858863082347 & 3.64113691765269 \tabularnewline
17 & 121.3 & 127.245082565903 & -5.94508256590279 \tabularnewline
18 & 113.9 & 122.638798385760 & -8.73879838576049 \tabularnewline
19 & 110.7 & 110.231831642255 & 0.468168357744901 \tabularnewline
20 & 120.8 & 107.300072571284 & 13.4999274287163 \tabularnewline
21 & 141.1 & 125.134967540993 & 15.9650324590074 \tabularnewline
22 & 147.4 & 154.582264806883 & -7.18226480688296 \tabularnewline
23 & 148 & 156.767126838978 & -8.76712683897773 \tabularnewline
24 & 158.1 & 152.343929074125 & 5.75607092587549 \tabularnewline
25 & 165 & 165.741917473317 & -0.741917473316619 \tabularnewline
26 & 187 & 172.216829726542 & 14.7831702734582 \tabularnewline
27 & 190.3 & 202.686969287536 & -12.3869692875361 \tabularnewline
28 & 182.4 & 198.889752881150 & -16.4897528811504 \tabularnewline
29 & 168.8 & 181.541812713647 & -12.7418127136468 \tabularnewline
30 & 151.2 & 160.641285834212 & -9.44128583421227 \tabularnewline
31 & 120.1 & 137.631823102487 & -17.5318231024873 \tabularnewline
32 & 112.5 & 96.486820191079 & 16.0131798089209 \tabularnewline
33 & 106.2 & 98.0617038789423 & 8.13829612105772 \tabularnewline
34 & 107.1 & 96.4246078879571 & 10.6753921120429 \tabularnewline
35 & 108.5 & 103.441162008942 & 5.0588379910581 \tabularnewline
36 & 106.5 & 107.739665036919 & -1.23966503691916 \tabularnewline
37 & 108.3 & 105.029388710708 & 3.27061128929230 \tabularnewline
38 & 125.6 & 108.703312473854 & 16.8966875261461 \tabularnewline
39 & 124 & 135.684409208694 & -11.6844092086945 \tabularnewline
40 & 127.2 & 127.389730404710 & -0.189730404710346 \tabularnewline
41 & 136.9 & 130.481022801596 & 6.41897719840412 \tabularnewline
42 & 135.8 & 143.858828827205 & -8.0588288272045 \tabularnewline
43 & 124.3 & 138.141456260838 & -13.8414562608383 \tabularnewline
44 & 115.4 & 118.710879524724 & -3.31087952472438 \tabularnewline
45 & 113.6 & 107.913883743352 & 5.68611625664758 \tabularnewline
46 & 114.4 & 109.371791036777 & 5.0282089632226 \tabularnewline
47 & 118.4 & 113.052744910170 & 5.34725508983026 \tabularnewline
48 & 117 & 120.116498898069 & -3.11649889806887 \tabularnewline
49 & 116.5 & 116.930875102899 & -0.430875102899449 \tabularnewline
50 & 115.4 & 116.184001652387 & -0.784001652387374 \tabularnewline
51 & 113.6 & 114.634801427474 & -1.03480142747395 \tabularnewline
52 & 117.4 & 112.241903399075 & 5.1580966009251 \tabularnewline
53 & 116.9 & 118.997277467746 & -2.09727746774587 \tabularnewline
54 & 116.4 & 117.295625012871 & -0.895625012870866 \tabularnewline
55 & 111.1 & 116.282469261229 & -5.18246926122852 \tabularnewline
56 & 110.2 & 108.013130675446 & 2.18686932455374 \tabularnewline
57 & 118.9 & 108.366115524974 & 10.5338844750263 \tabularnewline
58 & 131.8 & 123.101591676057 & 8.6984083239428 \tabularnewline
59 & 130.6 & 140.985416599903 & -10.3854165999025 \tabularnewline
60 & 138.3 & 133.835006344656 & 4.46499365534402 \tabularnewline
61 & 148.4 & 144.093261353571 & 4.30673864642898 \tabularnewline
62 & 148.7 & 156.660842847473 & -7.96084284747258 \tabularnewline
63 & 144.3 & 152.399612157848 & -8.09961215784847 \tabularnewline
64 & 152.5 & 143.358872445199 & 9.14112755480136 \tabularnewline
65 & 162.9 & 156.796357010538 & 6.10364298946223 \tabularnewline
66 & 167.2 & 170.693489695538 & -3.49348969553768 \tabularnewline
67 & 166.5 & 172.991865907897 & -6.49186590789677 \tabularnewline
68 & 185.6 & 168.572297693908 & 17.0277023060925 \tabularnewline
69 & 193.2 & 197.428460429489 & -4.22846042948890 \tabularnewline
70 & 207.8 & 202.605729086793 & 5.19427091320671 \tabularnewline
71 & 223.4 & 220.181829526593 & 3.2181704734069 \tabularnewline
72 & 246.4 & 237.625706890961 & 8.7742931090389 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13747&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]96[/C][C]98.4[/C][C]-2.39999999999999[/C][/ROW]
[ROW][C]4[/C][C]99[/C][C]98.7249001688843[/C][C]0.275099831115654[/C][/ROW]
[ROW][C]5[/C][C]103.3[/C][C]101.882520890262[/C][C]1.4174791097377[/C][/ROW]
[ROW][C]6[/C][C]113.1[/C][C]106.994677258767[/C][C]6.10532274123342[/C][/ROW]
[ROW][C]7[/C][C]112.8[/C][C]120.292772371423[/C][C]-7.4927723714235[/C][/ROW]
[ROW][C]8[/C][C]112.1[/C][C]115.699726528702[/C][C]-3.59972652870165[/C][/ROW]
[ROW][C]9[/C][C]107.4[/C][C]112.937233469668[/C][C]-5.53723346966824[/C][/ROW]
[ROW][C]10[/C][C]111[/C][C]105.064629799256[/C][C]5.9353702007437[/C][/ROW]
[ROW][C]11[/C][C]110.5[/C][C]112.065349199528[/C][C]-1.56534919952776[/C][/ROW]
[ROW][C]12[/C][C]110.8[/C][C]110.668469441233[/C][C]0.131530558767082[/C][/ROW]
[ROW][C]13[/C][C]112.4[/C][C]111.043830961711[/C][C]1.35616903828911[/C][/ROW]
[ROW][C]14[/C][C]111.5[/C][C]113.420859218176[/C][C]-1.92085921817575[/C][/ROW]
[ROW][C]15[/C][C]116.2[/C][C]111.420287057130[/C][C]4.77971294287026[/C][/ROW]
[ROW][C]16[/C][C]122.5[/C][C]118.858863082347[/C][C]3.64113691765269[/C][/ROW]
[ROW][C]17[/C][C]121.3[/C][C]127.245082565903[/C][C]-5.94508256590279[/C][/ROW]
[ROW][C]18[/C][C]113.9[/C][C]122.638798385760[/C][C]-8.73879838576049[/C][/ROW]
[ROW][C]19[/C][C]110.7[/C][C]110.231831642255[/C][C]0.468168357744901[/C][/ROW]
[ROW][C]20[/C][C]120.8[/C][C]107.300072571284[/C][C]13.4999274287163[/C][/ROW]
[ROW][C]21[/C][C]141.1[/C][C]125.134967540993[/C][C]15.9650324590074[/C][/ROW]
[ROW][C]22[/C][C]147.4[/C][C]154.582264806883[/C][C]-7.18226480688296[/C][/ROW]
[ROW][C]23[/C][C]148[/C][C]156.767126838978[/C][C]-8.76712683897773[/C][/ROW]
[ROW][C]24[/C][C]158.1[/C][C]152.343929074125[/C][C]5.75607092587549[/C][/ROW]
[ROW][C]25[/C][C]165[/C][C]165.741917473317[/C][C]-0.741917473316619[/C][/ROW]
[ROW][C]26[/C][C]187[/C][C]172.216829726542[/C][C]14.7831702734582[/C][/ROW]
[ROW][C]27[/C][C]190.3[/C][C]202.686969287536[/C][C]-12.3869692875361[/C][/ROW]
[ROW][C]28[/C][C]182.4[/C][C]198.889752881150[/C][C]-16.4897528811504[/C][/ROW]
[ROW][C]29[/C][C]168.8[/C][C]181.541812713647[/C][C]-12.7418127136468[/C][/ROW]
[ROW][C]30[/C][C]151.2[/C][C]160.641285834212[/C][C]-9.44128583421227[/C][/ROW]
[ROW][C]31[/C][C]120.1[/C][C]137.631823102487[/C][C]-17.5318231024873[/C][/ROW]
[ROW][C]32[/C][C]112.5[/C][C]96.486820191079[/C][C]16.0131798089209[/C][/ROW]
[ROW][C]33[/C][C]106.2[/C][C]98.0617038789423[/C][C]8.13829612105772[/C][/ROW]
[ROW][C]34[/C][C]107.1[/C][C]96.4246078879571[/C][C]10.6753921120429[/C][/ROW]
[ROW][C]35[/C][C]108.5[/C][C]103.441162008942[/C][C]5.0588379910581[/C][/ROW]
[ROW][C]36[/C][C]106.5[/C][C]107.739665036919[/C][C]-1.23966503691916[/C][/ROW]
[ROW][C]37[/C][C]108.3[/C][C]105.029388710708[/C][C]3.27061128929230[/C][/ROW]
[ROW][C]38[/C][C]125.6[/C][C]108.703312473854[/C][C]16.8966875261461[/C][/ROW]
[ROW][C]39[/C][C]124[/C][C]135.684409208694[/C][C]-11.6844092086945[/C][/ROW]
[ROW][C]40[/C][C]127.2[/C][C]127.389730404710[/C][C]-0.189730404710346[/C][/ROW]
[ROW][C]41[/C][C]136.9[/C][C]130.481022801596[/C][C]6.41897719840412[/C][/ROW]
[ROW][C]42[/C][C]135.8[/C][C]143.858828827205[/C][C]-8.0588288272045[/C][/ROW]
[ROW][C]43[/C][C]124.3[/C][C]138.141456260838[/C][C]-13.8414562608383[/C][/ROW]
[ROW][C]44[/C][C]115.4[/C][C]118.710879524724[/C][C]-3.31087952472438[/C][/ROW]
[ROW][C]45[/C][C]113.6[/C][C]107.913883743352[/C][C]5.68611625664758[/C][/ROW]
[ROW][C]46[/C][C]114.4[/C][C]109.371791036777[/C][C]5.0282089632226[/C][/ROW]
[ROW][C]47[/C][C]118.4[/C][C]113.052744910170[/C][C]5.34725508983026[/C][/ROW]
[ROW][C]48[/C][C]117[/C][C]120.116498898069[/C][C]-3.11649889806887[/C][/ROW]
[ROW][C]49[/C][C]116.5[/C][C]116.930875102899[/C][C]-0.430875102899449[/C][/ROW]
[ROW][C]50[/C][C]115.4[/C][C]116.184001652387[/C][C]-0.784001652387374[/C][/ROW]
[ROW][C]51[/C][C]113.6[/C][C]114.634801427474[/C][C]-1.03480142747395[/C][/ROW]
[ROW][C]52[/C][C]117.4[/C][C]112.241903399075[/C][C]5.1580966009251[/C][/ROW]
[ROW][C]53[/C][C]116.9[/C][C]118.997277467746[/C][C]-2.09727746774587[/C][/ROW]
[ROW][C]54[/C][C]116.4[/C][C]117.295625012871[/C][C]-0.895625012870866[/C][/ROW]
[ROW][C]55[/C][C]111.1[/C][C]116.282469261229[/C][C]-5.18246926122852[/C][/ROW]
[ROW][C]56[/C][C]110.2[/C][C]108.013130675446[/C][C]2.18686932455374[/C][/ROW]
[ROW][C]57[/C][C]118.9[/C][C]108.366115524974[/C][C]10.5338844750263[/C][/ROW]
[ROW][C]58[/C][C]131.8[/C][C]123.101591676057[/C][C]8.6984083239428[/C][/ROW]
[ROW][C]59[/C][C]130.6[/C][C]140.985416599903[/C][C]-10.3854165999025[/C][/ROW]
[ROW][C]60[/C][C]138.3[/C][C]133.835006344656[/C][C]4.46499365534402[/C][/ROW]
[ROW][C]61[/C][C]148.4[/C][C]144.093261353571[/C][C]4.30673864642898[/C][/ROW]
[ROW][C]62[/C][C]148.7[/C][C]156.660842847473[/C][C]-7.96084284747258[/C][/ROW]
[ROW][C]63[/C][C]144.3[/C][C]152.399612157848[/C][C]-8.09961215784847[/C][/ROW]
[ROW][C]64[/C][C]152.5[/C][C]143.358872445199[/C][C]9.14112755480136[/C][/ROW]
[ROW][C]65[/C][C]162.9[/C][C]156.796357010538[/C][C]6.10364298946223[/C][/ROW]
[ROW][C]66[/C][C]167.2[/C][C]170.693489695538[/C][C]-3.49348969553768[/C][/ROW]
[ROW][C]67[/C][C]166.5[/C][C]172.991865907897[/C][C]-6.49186590789677[/C][/ROW]
[ROW][C]68[/C][C]185.6[/C][C]168.572297693908[/C][C]17.0277023060925[/C][/ROW]
[ROW][C]69[/C][C]193.2[/C][C]197.428460429489[/C][C]-4.22846042948890[/C][/ROW]
[ROW][C]70[/C][C]207.8[/C][C]202.605729086793[/C][C]5.19427091320671[/C][/ROW]
[ROW][C]71[/C][C]223.4[/C][C]220.181829526593[/C][C]3.2181704734069[/C][/ROW]
[ROW][C]72[/C][C]246.4[/C][C]237.625706890961[/C][C]8.7742931090389[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13747&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13747&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
39698.4-2.39999999999999
49998.72490016888430.275099831115654
5103.3101.8825208902621.4174791097377
6113.1106.9946772587676.10532274123342
7112.8120.292772371423-7.4927723714235
8112.1115.699726528702-3.59972652870165
9107.4112.937233469668-5.53723346966824
10111105.0646297992565.9353702007437
11110.5112.065349199528-1.56534919952776
12110.8110.6684694412330.131530558767082
13112.4111.0438309617111.35616903828911
14111.5113.420859218176-1.92085921817575
15116.2111.4202870571304.77971294287026
16122.5118.8588630823473.64113691765269
17121.3127.245082565903-5.94508256590279
18113.9122.638798385760-8.73879838576049
19110.7110.2318316422550.468168357744901
20120.8107.30007257128413.4999274287163
21141.1125.13496754099315.9650324590074
22147.4154.582264806883-7.18226480688296
23148156.767126838978-8.76712683897773
24158.1152.3439290741255.75607092587549
25165165.741917473317-0.741917473316619
26187172.21682972654214.7831702734582
27190.3202.686969287536-12.3869692875361
28182.4198.889752881150-16.4897528811504
29168.8181.541812713647-12.7418127136468
30151.2160.641285834212-9.44128583421227
31120.1137.631823102487-17.5318231024873
32112.596.48682019107916.0131798089209
33106.298.06170387894238.13829612105772
34107.196.424607887957110.6753921120429
35108.5103.4411620089425.0588379910581
36106.5107.739665036919-1.23966503691916
37108.3105.0293887107083.27061128929230
38125.6108.70331247385416.8966875261461
39124135.684409208694-11.6844092086945
40127.2127.389730404710-0.189730404710346
41136.9130.4810228015966.41897719840412
42135.8143.858828827205-8.0588288272045
43124.3138.141456260838-13.8414562608383
44115.4118.710879524724-3.31087952472438
45113.6107.9138837433525.68611625664758
46114.4109.3717910367775.0282089632226
47118.4113.0527449101705.34725508983026
48117120.116498898069-3.11649889806887
49116.5116.930875102899-0.430875102899449
50115.4116.184001652387-0.784001652387374
51113.6114.634801427474-1.03480142747395
52117.4112.2419033990755.1580966009251
53116.9118.997277467746-2.09727746774587
54116.4117.295625012871-0.895625012870866
55111.1116.282469261229-5.18246926122852
56110.2108.0131306754462.18686932455374
57118.9108.36611552497410.5338844750263
58131.8123.1015916760578.6984083239428
59130.6140.985416599903-10.3854165999025
60138.3133.8350063446564.46499365534402
61148.4144.0932613535714.30673864642898
62148.7156.660842847473-7.96084284747258
63144.3152.399612157848-8.09961215784847
64152.5143.3588724451999.14112755480136
65162.9156.7963570105386.10364298946223
66167.2170.693489695538-3.49348969553768
67166.5172.991865907897-6.49186590789677
68185.6168.57229769390817.0277023060925
69193.2197.428460429489-4.22846042948890
70207.8202.6057290867935.19427091320671
71223.4220.1818295265933.2181704734069
72246.4237.6257068909618.7742931090389







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73265.653010629461249.730452954411281.57556830451
74284.906021258921255.227647853542314.5843946643
75304.159031888382258.900984542316349.417079234447
76323.412042517842260.782658982306386.041426053378
77342.665053147303260.996765668416424.333340626189
78361.918063776763259.660759993541464.175367559985
79381.171074406224256.875308153954505.466840658494
80400.424085035684252.725709933703548.122460137666
81419.677095665145247.284721965055592.069469365234
82438.930106294605240.615064381105637.245148208105
83458.183116924066232.771398373923683.594835474209
84477.436127553526223.801846794724731.070408312329

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 265.653010629461 & 249.730452954411 & 281.57556830451 \tabularnewline
74 & 284.906021258921 & 255.227647853542 & 314.5843946643 \tabularnewline
75 & 304.159031888382 & 258.900984542316 & 349.417079234447 \tabularnewline
76 & 323.412042517842 & 260.782658982306 & 386.041426053378 \tabularnewline
77 & 342.665053147303 & 260.996765668416 & 424.333340626189 \tabularnewline
78 & 361.918063776763 & 259.660759993541 & 464.175367559985 \tabularnewline
79 & 381.171074406224 & 256.875308153954 & 505.466840658494 \tabularnewline
80 & 400.424085035684 & 252.725709933703 & 548.122460137666 \tabularnewline
81 & 419.677095665145 & 247.284721965055 & 592.069469365234 \tabularnewline
82 & 438.930106294605 & 240.615064381105 & 637.245148208105 \tabularnewline
83 & 458.183116924066 & 232.771398373923 & 683.594835474209 \tabularnewline
84 & 477.436127553526 & 223.801846794724 & 731.070408312329 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13747&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]265.653010629461[/C][C]249.730452954411[/C][C]281.57556830451[/C][/ROW]
[ROW][C]74[/C][C]284.906021258921[/C][C]255.227647853542[/C][C]314.5843946643[/C][/ROW]
[ROW][C]75[/C][C]304.159031888382[/C][C]258.900984542316[/C][C]349.417079234447[/C][/ROW]
[ROW][C]76[/C][C]323.412042517842[/C][C]260.782658982306[/C][C]386.041426053378[/C][/ROW]
[ROW][C]77[/C][C]342.665053147303[/C][C]260.996765668416[/C][C]424.333340626189[/C][/ROW]
[ROW][C]78[/C][C]361.918063776763[/C][C]259.660759993541[/C][C]464.175367559985[/C][/ROW]
[ROW][C]79[/C][C]381.171074406224[/C][C]256.875308153954[/C][C]505.466840658494[/C][/ROW]
[ROW][C]80[/C][C]400.424085035684[/C][C]252.725709933703[/C][C]548.122460137666[/C][/ROW]
[ROW][C]81[/C][C]419.677095665145[/C][C]247.284721965055[/C][C]592.069469365234[/C][/ROW]
[ROW][C]82[/C][C]438.930106294605[/C][C]240.615064381105[/C][C]637.245148208105[/C][/ROW]
[ROW][C]83[/C][C]458.183116924066[/C][C]232.771398373923[/C][C]683.594835474209[/C][/ROW]
[ROW][C]84[/C][C]477.436127553526[/C][C]223.801846794724[/C][C]731.070408312329[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13747&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13747&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
73265.653010629461249.730452954411281.57556830451
74284.906021258921255.227647853542314.5843946643
75304.159031888382258.900984542316349.417079234447
76323.412042517842260.782658982306386.041426053378
77342.665053147303260.996765668416424.333340626189
78361.918063776763259.660759993541464.175367559985
79381.171074406224256.875308153954505.466840658494
80400.424085035684252.725709933703548.122460137666
81419.677095665145247.284721965055592.069469365234
82438.930106294605240.615064381105637.245148208105
83458.183116924066232.771398373923683.594835474209
84477.436127553526223.801846794724731.070408312329



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')