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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 06 Aug 2010 07:52:42 +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/Aug/06/t1281081221vp8qubzqqu2f4ez.htm/, Retrieved Tue, 07 May 2024 03:22:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78445, Retrieved Tue, 07 May 2024 03:22:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsVan de Walle Mathias
Estimated Impact187
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Variability] [Spreidingsmaten -...] [2010-05-21 12:27:10] [251b004ef89b028696de15eeefcf9b4b]
- RMPD    [Exponential Smoothing] [tijdreeks 2 - sta...] [2010-08-06 07:52:42] [589929edeb20bd59f78e9be1ffd92c80] [Current]
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Dataseries X:
239
238
237
235
233
232
233
235
236
236
237
239
238
237
244
230
237
244
239
240
230
228
231
228
225
227
238
214
222
233
228
218
203
209
207
203
195
199
207
182
181
189
186
174
153
158
153
147
143
156
168
142
146
150
145
133
111
115
109
105
96
112
127
107
116
125
120
107
86
87
79
83
75
89
104
86
98
98
85
74
49
54
47
56




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78445&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78445&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78445&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 time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.346185870041599
beta0.111603919487912
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.346185870041599 \tabularnewline
beta & 0.111603919487912 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78445&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]0.346185870041599[/C][/ROW]
[ROW][C]beta[/C][C]0.111603919487912[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78445&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78445&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
alpha0.346185870041599
beta0.111603919487912
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13238235.9412393162392.0587606837606
14237235.39695637331.60304362670033
15244243.2568453370650.74315466293453
16230230.389431859024-0.389431859024484
17237238.114886958018-1.11488695801847
18244245.671125314383-1.67112531438292
19239234.4285700484774.57142995152327
20240238.4403862712791.55961372872056
21230240.136477709341-10.1364777093412
22228236.558584311988-8.55858431198797
23231234.321268417602-3.32126841760171
24228234.060384419367-6.06038441936744
25225230.879823462712-5.87982346271187
26227226.1822646530140.81773534698624
27238232.0706465409895.92935345901117
28214219.321056263557-5.3210562635569
29222223.737338651766-1.73733865176635
30233229.5627664418613.43723355813876
31228223.2158386092524.78416139074776
32218224.386065407814-6.38606540781421
33203214.431352238965-11.4313522389646
34209210.133759276445-1.1337592764454
35207212.874826045797-5.87482604579728
36203208.824187260518-5.82418726051802
37195204.737696897866-9.73769689786576
38199201.828752932247-2.82875293224694
39207208.40113315391-1.40113315390957
40182184.07924956736-2.07924956736014
41181190.407228731678-9.4072287316782
42189195.110669698856-6.11066969885616
43186184.120155513781.87984448622038
44174174.65060880023-0.650608800230458
45153161.273255306033-8.27325530603287
46158162.814183405711-4.81418340571108
47153159.051687882799-6.05168788279883
48147152.836422182996-5.83642218299565
49143144.050007460696-1.05000746069641
50156146.8644580681199.13554193188074
51168157.1730290655110.8269709344904
52142135.7743445650986.22565543490157
53146139.6404583157026.35954168429771
54150152.020859648375-2.02085964837457
55145147.891894023194-2.89189402319386
56133135.153036320324-2.15303632032445
57111116.250765887901-5.2507658879006
58115121.195399428938-6.1953994289378
59109116.188056501917-7.1880565019172
60105109.718643381837-4.71864338183654
6196104.490303212596-8.49030321259619
62112111.1427133906790.857286609321037
63127119.1257420742717.87425792572856
6410793.016777353754413.9832226462456
6511699.27601941158816.7239805884119
66125109.78568702068915.2143129793113
67120111.7401617864828.25983821351832
68107104.4621685389122.53783146108769
698686.4569225710658-0.456922571065846
708793.9271673493949-6.92716734939488
717989.4728762963973-10.4728762963973
728384.8093236651718-1.80932366517177
737579.5630694829347-4.56306948293468
748995.2792353176928-6.27923531769282
75104106.696387949595-2.69638794959508
768681.83063014551624.16936985448385
779887.013723935562510.9862760644375
789894.85767969713063.14232030286936
798587.9272998192283-2.92729981922825
807472.44435819597611.55564180402391
814951.5121415641949-2.51214156419486
825453.3322183015270.667781698472979
834748.7740500496292-1.77405004962918
845652.70743988517113.29256011482893

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 238 & 235.941239316239 & 2.0587606837606 \tabularnewline
14 & 237 & 235.3969563733 & 1.60304362670033 \tabularnewline
15 & 244 & 243.256845337065 & 0.74315466293453 \tabularnewline
16 & 230 & 230.389431859024 & -0.389431859024484 \tabularnewline
17 & 237 & 238.114886958018 & -1.11488695801847 \tabularnewline
18 & 244 & 245.671125314383 & -1.67112531438292 \tabularnewline
19 & 239 & 234.428570048477 & 4.57142995152327 \tabularnewline
20 & 240 & 238.440386271279 & 1.55961372872056 \tabularnewline
21 & 230 & 240.136477709341 & -10.1364777093412 \tabularnewline
22 & 228 & 236.558584311988 & -8.55858431198797 \tabularnewline
23 & 231 & 234.321268417602 & -3.32126841760171 \tabularnewline
24 & 228 & 234.060384419367 & -6.06038441936744 \tabularnewline
25 & 225 & 230.879823462712 & -5.87982346271187 \tabularnewline
26 & 227 & 226.182264653014 & 0.81773534698624 \tabularnewline
27 & 238 & 232.070646540989 & 5.92935345901117 \tabularnewline
28 & 214 & 219.321056263557 & -5.3210562635569 \tabularnewline
29 & 222 & 223.737338651766 & -1.73733865176635 \tabularnewline
30 & 233 & 229.562766441861 & 3.43723355813876 \tabularnewline
31 & 228 & 223.215838609252 & 4.78416139074776 \tabularnewline
32 & 218 & 224.386065407814 & -6.38606540781421 \tabularnewline
33 & 203 & 214.431352238965 & -11.4313522389646 \tabularnewline
34 & 209 & 210.133759276445 & -1.1337592764454 \tabularnewline
35 & 207 & 212.874826045797 & -5.87482604579728 \tabularnewline
36 & 203 & 208.824187260518 & -5.82418726051802 \tabularnewline
37 & 195 & 204.737696897866 & -9.73769689786576 \tabularnewline
38 & 199 & 201.828752932247 & -2.82875293224694 \tabularnewline
39 & 207 & 208.40113315391 & -1.40113315390957 \tabularnewline
40 & 182 & 184.07924956736 & -2.07924956736014 \tabularnewline
41 & 181 & 190.407228731678 & -9.4072287316782 \tabularnewline
42 & 189 & 195.110669698856 & -6.11066969885616 \tabularnewline
43 & 186 & 184.12015551378 & 1.87984448622038 \tabularnewline
44 & 174 & 174.65060880023 & -0.650608800230458 \tabularnewline
45 & 153 & 161.273255306033 & -8.27325530603287 \tabularnewline
46 & 158 & 162.814183405711 & -4.81418340571108 \tabularnewline
47 & 153 & 159.051687882799 & -6.05168788279883 \tabularnewline
48 & 147 & 152.836422182996 & -5.83642218299565 \tabularnewline
49 & 143 & 144.050007460696 & -1.05000746069641 \tabularnewline
50 & 156 & 146.864458068119 & 9.13554193188074 \tabularnewline
51 & 168 & 157.17302906551 & 10.8269709344904 \tabularnewline
52 & 142 & 135.774344565098 & 6.22565543490157 \tabularnewline
53 & 146 & 139.640458315702 & 6.35954168429771 \tabularnewline
54 & 150 & 152.020859648375 & -2.02085964837457 \tabularnewline
55 & 145 & 147.891894023194 & -2.89189402319386 \tabularnewline
56 & 133 & 135.153036320324 & -2.15303632032445 \tabularnewline
57 & 111 & 116.250765887901 & -5.2507658879006 \tabularnewline
58 & 115 & 121.195399428938 & -6.1953994289378 \tabularnewline
59 & 109 & 116.188056501917 & -7.1880565019172 \tabularnewline
60 & 105 & 109.718643381837 & -4.71864338183654 \tabularnewline
61 & 96 & 104.490303212596 & -8.49030321259619 \tabularnewline
62 & 112 & 111.142713390679 & 0.857286609321037 \tabularnewline
63 & 127 & 119.125742074271 & 7.87425792572856 \tabularnewline
64 & 107 & 93.0167773537544 & 13.9832226462456 \tabularnewline
65 & 116 & 99.276019411588 & 16.7239805884119 \tabularnewline
66 & 125 & 109.785687020689 & 15.2143129793113 \tabularnewline
67 & 120 & 111.740161786482 & 8.25983821351832 \tabularnewline
68 & 107 & 104.462168538912 & 2.53783146108769 \tabularnewline
69 & 86 & 86.4569225710658 & -0.456922571065846 \tabularnewline
70 & 87 & 93.9271673493949 & -6.92716734939488 \tabularnewline
71 & 79 & 89.4728762963973 & -10.4728762963973 \tabularnewline
72 & 83 & 84.8093236651718 & -1.80932366517177 \tabularnewline
73 & 75 & 79.5630694829347 & -4.56306948293468 \tabularnewline
74 & 89 & 95.2792353176928 & -6.27923531769282 \tabularnewline
75 & 104 & 106.696387949595 & -2.69638794959508 \tabularnewline
76 & 86 & 81.8306301455162 & 4.16936985448385 \tabularnewline
77 & 98 & 87.0137239355625 & 10.9862760644375 \tabularnewline
78 & 98 & 94.8576796971306 & 3.14232030286936 \tabularnewline
79 & 85 & 87.9272998192283 & -2.92729981922825 \tabularnewline
80 & 74 & 72.4443581959761 & 1.55564180402391 \tabularnewline
81 & 49 & 51.5121415641949 & -2.51214156419486 \tabularnewline
82 & 54 & 53.332218301527 & 0.667781698472979 \tabularnewline
83 & 47 & 48.7740500496292 & -1.77405004962918 \tabularnewline
84 & 56 & 52.7074398851711 & 3.29256011482893 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78445&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]238[/C][C]235.941239316239[/C][C]2.0587606837606[/C][/ROW]
[ROW][C]14[/C][C]237[/C][C]235.3969563733[/C][C]1.60304362670033[/C][/ROW]
[ROW][C]15[/C][C]244[/C][C]243.256845337065[/C][C]0.74315466293453[/C][/ROW]
[ROW][C]16[/C][C]230[/C][C]230.389431859024[/C][C]-0.389431859024484[/C][/ROW]
[ROW][C]17[/C][C]237[/C][C]238.114886958018[/C][C]-1.11488695801847[/C][/ROW]
[ROW][C]18[/C][C]244[/C][C]245.671125314383[/C][C]-1.67112531438292[/C][/ROW]
[ROW][C]19[/C][C]239[/C][C]234.428570048477[/C][C]4.57142995152327[/C][/ROW]
[ROW][C]20[/C][C]240[/C][C]238.440386271279[/C][C]1.55961372872056[/C][/ROW]
[ROW][C]21[/C][C]230[/C][C]240.136477709341[/C][C]-10.1364777093412[/C][/ROW]
[ROW][C]22[/C][C]228[/C][C]236.558584311988[/C][C]-8.55858431198797[/C][/ROW]
[ROW][C]23[/C][C]231[/C][C]234.321268417602[/C][C]-3.32126841760171[/C][/ROW]
[ROW][C]24[/C][C]228[/C][C]234.060384419367[/C][C]-6.06038441936744[/C][/ROW]
[ROW][C]25[/C][C]225[/C][C]230.879823462712[/C][C]-5.87982346271187[/C][/ROW]
[ROW][C]26[/C][C]227[/C][C]226.182264653014[/C][C]0.81773534698624[/C][/ROW]
[ROW][C]27[/C][C]238[/C][C]232.070646540989[/C][C]5.92935345901117[/C][/ROW]
[ROW][C]28[/C][C]214[/C][C]219.321056263557[/C][C]-5.3210562635569[/C][/ROW]
[ROW][C]29[/C][C]222[/C][C]223.737338651766[/C][C]-1.73733865176635[/C][/ROW]
[ROW][C]30[/C][C]233[/C][C]229.562766441861[/C][C]3.43723355813876[/C][/ROW]
[ROW][C]31[/C][C]228[/C][C]223.215838609252[/C][C]4.78416139074776[/C][/ROW]
[ROW][C]32[/C][C]218[/C][C]224.386065407814[/C][C]-6.38606540781421[/C][/ROW]
[ROW][C]33[/C][C]203[/C][C]214.431352238965[/C][C]-11.4313522389646[/C][/ROW]
[ROW][C]34[/C][C]209[/C][C]210.133759276445[/C][C]-1.1337592764454[/C][/ROW]
[ROW][C]35[/C][C]207[/C][C]212.874826045797[/C][C]-5.87482604579728[/C][/ROW]
[ROW][C]36[/C][C]203[/C][C]208.824187260518[/C][C]-5.82418726051802[/C][/ROW]
[ROW][C]37[/C][C]195[/C][C]204.737696897866[/C][C]-9.73769689786576[/C][/ROW]
[ROW][C]38[/C][C]199[/C][C]201.828752932247[/C][C]-2.82875293224694[/C][/ROW]
[ROW][C]39[/C][C]207[/C][C]208.40113315391[/C][C]-1.40113315390957[/C][/ROW]
[ROW][C]40[/C][C]182[/C][C]184.07924956736[/C][C]-2.07924956736014[/C][/ROW]
[ROW][C]41[/C][C]181[/C][C]190.407228731678[/C][C]-9.4072287316782[/C][/ROW]
[ROW][C]42[/C][C]189[/C][C]195.110669698856[/C][C]-6.11066969885616[/C][/ROW]
[ROW][C]43[/C][C]186[/C][C]184.12015551378[/C][C]1.87984448622038[/C][/ROW]
[ROW][C]44[/C][C]174[/C][C]174.65060880023[/C][C]-0.650608800230458[/C][/ROW]
[ROW][C]45[/C][C]153[/C][C]161.273255306033[/C][C]-8.27325530603287[/C][/ROW]
[ROW][C]46[/C][C]158[/C][C]162.814183405711[/C][C]-4.81418340571108[/C][/ROW]
[ROW][C]47[/C][C]153[/C][C]159.051687882799[/C][C]-6.05168788279883[/C][/ROW]
[ROW][C]48[/C][C]147[/C][C]152.836422182996[/C][C]-5.83642218299565[/C][/ROW]
[ROW][C]49[/C][C]143[/C][C]144.050007460696[/C][C]-1.05000746069641[/C][/ROW]
[ROW][C]50[/C][C]156[/C][C]146.864458068119[/C][C]9.13554193188074[/C][/ROW]
[ROW][C]51[/C][C]168[/C][C]157.17302906551[/C][C]10.8269709344904[/C][/ROW]
[ROW][C]52[/C][C]142[/C][C]135.774344565098[/C][C]6.22565543490157[/C][/ROW]
[ROW][C]53[/C][C]146[/C][C]139.640458315702[/C][C]6.35954168429771[/C][/ROW]
[ROW][C]54[/C][C]150[/C][C]152.020859648375[/C][C]-2.02085964837457[/C][/ROW]
[ROW][C]55[/C][C]145[/C][C]147.891894023194[/C][C]-2.89189402319386[/C][/ROW]
[ROW][C]56[/C][C]133[/C][C]135.153036320324[/C][C]-2.15303632032445[/C][/ROW]
[ROW][C]57[/C][C]111[/C][C]116.250765887901[/C][C]-5.2507658879006[/C][/ROW]
[ROW][C]58[/C][C]115[/C][C]121.195399428938[/C][C]-6.1953994289378[/C][/ROW]
[ROW][C]59[/C][C]109[/C][C]116.188056501917[/C][C]-7.1880565019172[/C][/ROW]
[ROW][C]60[/C][C]105[/C][C]109.718643381837[/C][C]-4.71864338183654[/C][/ROW]
[ROW][C]61[/C][C]96[/C][C]104.490303212596[/C][C]-8.49030321259619[/C][/ROW]
[ROW][C]62[/C][C]112[/C][C]111.142713390679[/C][C]0.857286609321037[/C][/ROW]
[ROW][C]63[/C][C]127[/C][C]119.125742074271[/C][C]7.87425792572856[/C][/ROW]
[ROW][C]64[/C][C]107[/C][C]93.0167773537544[/C][C]13.9832226462456[/C][/ROW]
[ROW][C]65[/C][C]116[/C][C]99.276019411588[/C][C]16.7239805884119[/C][/ROW]
[ROW][C]66[/C][C]125[/C][C]109.785687020689[/C][C]15.2143129793113[/C][/ROW]
[ROW][C]67[/C][C]120[/C][C]111.740161786482[/C][C]8.25983821351832[/C][/ROW]
[ROW][C]68[/C][C]107[/C][C]104.462168538912[/C][C]2.53783146108769[/C][/ROW]
[ROW][C]69[/C][C]86[/C][C]86.4569225710658[/C][C]-0.456922571065846[/C][/ROW]
[ROW][C]70[/C][C]87[/C][C]93.9271673493949[/C][C]-6.92716734939488[/C][/ROW]
[ROW][C]71[/C][C]79[/C][C]89.4728762963973[/C][C]-10.4728762963973[/C][/ROW]
[ROW][C]72[/C][C]83[/C][C]84.8093236651718[/C][C]-1.80932366517177[/C][/ROW]
[ROW][C]73[/C][C]75[/C][C]79.5630694829347[/C][C]-4.56306948293468[/C][/ROW]
[ROW][C]74[/C][C]89[/C][C]95.2792353176928[/C][C]-6.27923531769282[/C][/ROW]
[ROW][C]75[/C][C]104[/C][C]106.696387949595[/C][C]-2.69638794959508[/C][/ROW]
[ROW][C]76[/C][C]86[/C][C]81.8306301455162[/C][C]4.16936985448385[/C][/ROW]
[ROW][C]77[/C][C]98[/C][C]87.0137239355625[/C][C]10.9862760644375[/C][/ROW]
[ROW][C]78[/C][C]98[/C][C]94.8576796971306[/C][C]3.14232030286936[/C][/ROW]
[ROW][C]79[/C][C]85[/C][C]87.9272998192283[/C][C]-2.92729981922825[/C][/ROW]
[ROW][C]80[/C][C]74[/C][C]72.4443581959761[/C][C]1.55564180402391[/C][/ROW]
[ROW][C]81[/C][C]49[/C][C]51.5121415641949[/C][C]-2.51214156419486[/C][/ROW]
[ROW][C]82[/C][C]54[/C][C]53.332218301527[/C][C]0.667781698472979[/C][/ROW]
[ROW][C]83[/C][C]47[/C][C]48.7740500496292[/C][C]-1.77405004962918[/C][/ROW]
[ROW][C]84[/C][C]56[/C][C]52.7074398851711[/C][C]3.29256011482893[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78445&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78445&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
13238235.9412393162392.0587606837606
14237235.39695637331.60304362670033
15244243.2568453370650.74315466293453
16230230.389431859024-0.389431859024484
17237238.114886958018-1.11488695801847
18244245.671125314383-1.67112531438292
19239234.4285700484774.57142995152327
20240238.4403862712791.55961372872056
21230240.136477709341-10.1364777093412
22228236.558584311988-8.55858431198797
23231234.321268417602-3.32126841760171
24228234.060384419367-6.06038441936744
25225230.879823462712-5.87982346271187
26227226.1822646530140.81773534698624
27238232.0706465409895.92935345901117
28214219.321056263557-5.3210562635569
29222223.737338651766-1.73733865176635
30233229.5627664418613.43723355813876
31228223.2158386092524.78416139074776
32218224.386065407814-6.38606540781421
33203214.431352238965-11.4313522389646
34209210.133759276445-1.1337592764454
35207212.874826045797-5.87482604579728
36203208.824187260518-5.82418726051802
37195204.737696897866-9.73769689786576
38199201.828752932247-2.82875293224694
39207208.40113315391-1.40113315390957
40182184.07924956736-2.07924956736014
41181190.407228731678-9.4072287316782
42189195.110669698856-6.11066969885616
43186184.120155513781.87984448622038
44174174.65060880023-0.650608800230458
45153161.273255306033-8.27325530603287
46158162.814183405711-4.81418340571108
47153159.051687882799-6.05168788279883
48147152.836422182996-5.83642218299565
49143144.050007460696-1.05000746069641
50156146.8644580681199.13554193188074
51168157.1730290655110.8269709344904
52142135.7743445650986.22565543490157
53146139.6404583157026.35954168429771
54150152.020859648375-2.02085964837457
55145147.891894023194-2.89189402319386
56133135.153036320324-2.15303632032445
57111116.250765887901-5.2507658879006
58115121.195399428938-6.1953994289378
59109116.188056501917-7.1880565019172
60105109.718643381837-4.71864338183654
6196104.490303212596-8.49030321259619
62112111.1427133906790.857286609321037
63127119.1257420742717.87425792572856
6410793.016777353754413.9832226462456
6511699.27601941158816.7239805884119
66125109.78568702068915.2143129793113
67120111.7401617864828.25983821351832
68107104.4621685389122.53783146108769
698686.4569225710658-0.456922571065846
708793.9271673493949-6.92716734939488
717989.4728762963973-10.4728762963973
728384.8093236651718-1.80932366517177
737579.5630694829347-4.56306948293468
748995.2792353176928-6.27923531769282
75104106.696387949595-2.69638794959508
768681.83063014551624.16936985448385
779887.013723935562510.9862760644375
789894.85767969713063.14232030286936
798587.9272998192283-2.92729981922825
807472.44435819597611.55564180402391
814951.5121415641949-2.51214156419486
825453.3322183015270.667781698472979
834748.7740500496292-1.77405004962918
845652.70743988517113.29256011482893







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8547.545241311448735.359614237733759.7308683851638
8664.013614695827250.956855221393177.0703741702614
8780.484259598617266.444832214378694.5236869828558
8861.68225299832546.55570438973876.8088016069121
8970.359243267994854.04841470899286.6700718269975
9069.327237721759851.741994094984486.9124813485352
9157.275043153890238.331738956375476.2183473514051
9245.784015817361425.404850586252766.1631810484702
9321.6410942953023-0.24654842658154143.5287370171862
9426.49438661964233.0302082865449.9585649527446
9520.1672063788479-4.9375733256874445.2719860833833
9628.15457895555471.3486261253763754.9605317857329

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 47.5452413114487 & 35.3596142377337 & 59.7308683851638 \tabularnewline
86 & 64.0136146958272 & 50.9568552213931 & 77.0703741702614 \tabularnewline
87 & 80.4842595986172 & 66.4448322143786 & 94.5236869828558 \tabularnewline
88 & 61.682252998325 & 46.555704389738 & 76.8088016069121 \tabularnewline
89 & 70.3592432679948 & 54.048414708992 & 86.6700718269975 \tabularnewline
90 & 69.3272377217598 & 51.7419940949844 & 86.9124813485352 \tabularnewline
91 & 57.2750431538902 & 38.3317389563754 & 76.2183473514051 \tabularnewline
92 & 45.7840158173614 & 25.4048505862527 & 66.1631810484702 \tabularnewline
93 & 21.6410942953023 & -0.246548426581541 & 43.5287370171862 \tabularnewline
94 & 26.4943866196423 & 3.03020828654 & 49.9585649527446 \tabularnewline
95 & 20.1672063788479 & -4.93757332568744 & 45.2719860833833 \tabularnewline
96 & 28.1545789555547 & 1.34862612537637 & 54.9605317857329 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78445&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]85[/C][C]47.5452413114487[/C][C]35.3596142377337[/C][C]59.7308683851638[/C][/ROW]
[ROW][C]86[/C][C]64.0136146958272[/C][C]50.9568552213931[/C][C]77.0703741702614[/C][/ROW]
[ROW][C]87[/C][C]80.4842595986172[/C][C]66.4448322143786[/C][C]94.5236869828558[/C][/ROW]
[ROW][C]88[/C][C]61.682252998325[/C][C]46.555704389738[/C][C]76.8088016069121[/C][/ROW]
[ROW][C]89[/C][C]70.3592432679948[/C][C]54.048414708992[/C][C]86.6700718269975[/C][/ROW]
[ROW][C]90[/C][C]69.3272377217598[/C][C]51.7419940949844[/C][C]86.9124813485352[/C][/ROW]
[ROW][C]91[/C][C]57.2750431538902[/C][C]38.3317389563754[/C][C]76.2183473514051[/C][/ROW]
[ROW][C]92[/C][C]45.7840158173614[/C][C]25.4048505862527[/C][C]66.1631810484702[/C][/ROW]
[ROW][C]93[/C][C]21.6410942953023[/C][C]-0.246548426581541[/C][C]43.5287370171862[/C][/ROW]
[ROW][C]94[/C][C]26.4943866196423[/C][C]3.03020828654[/C][C]49.9585649527446[/C][/ROW]
[ROW][C]95[/C][C]20.1672063788479[/C][C]-4.93757332568744[/C][C]45.2719860833833[/C][/ROW]
[ROW][C]96[/C][C]28.1545789555547[/C][C]1.34862612537637[/C][C]54.9605317857329[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78445&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78445&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
8547.545241311448735.359614237733759.7308683851638
8664.013614695827250.956855221393177.0703741702614
8780.484259598617266.444832214378694.5236869828558
8861.68225299832546.55570438973876.8088016069121
8970.359243267994854.04841470899286.6700718269975
9069.327237721759851.741994094984486.9124813485352
9157.275043153890238.331738956375476.2183473514051
9245.784015817361425.404850586252766.1631810484702
9321.6410942953023-0.24654842658154143.5287370171862
9426.49438661964233.0302082865449.9585649527446
9520.1672063788479-4.9375733256874445.2719860833833
9628.15457895555471.3486261253763754.9605317857329



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