Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 29 Jul 2010 14:34:16 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Jul/29/t1280414120g9tg96bd55q01d4.htm/, Retrieved Sun, 28 Apr 2024 20:29:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78193, Retrieved Sun, 28 Apr 2024 20:29:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsPatrick Fieremans
Estimated Impact154
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks 2 - Sta...] [2010-07-29 14:34:16] [c9c054077df6495a4b48ba74c2b1bb38] [Current]
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Dataseries X:
259
258
257
255
253
252
253
255
256
256
257
259
267
263
266
257
249
249
251
252
252
252
256
257
259
260
261
253
243
233
241
239
233
228
228
227
225
230
222
207
190
184
192
187
173
167
163
156
153
157
152
128
115
114
136
132
126
124
123
119
105
107
108
92
74
73
100
97
99
102
99
103
92
99
97
87
69
66
95
91
93
99
91
91




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78193&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78193&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78193&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.703339343785154
beta0.111780621846133
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.703339343785154 \tabularnewline
beta & 0.111780621846133 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78193&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]0.703339343785154[/C][/ROW]
[ROW][C]beta[/C][C]0.111780621846133[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78193&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78193&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
alpha0.703339343785154
beta0.111780621846133
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13267266.6989850427350.30101495726484
14263263.06737923417-0.0673792341703461
15266266.254703294283-0.25470329428282
16257257.331916940614-0.331916940614121
17249249.203727978248-0.203727978248168
18249249.066348988811-0.0663489888105175
19251252.72871104278-1.72871104277996
20252252.710957701073-0.710957701073482
21252252.311468372467-0.311468372467147
22252251.2934680532180.706531946781695
23256252.5886814133583.41131858664176
24257257.262807842518-0.262807842518498
25259265.33808068527-6.33808068526997
26260256.4434896956853.55651030431545
27261261.924815363002-0.924815363002153
28253252.2558717555370.744128244462729
29243244.755199868646-1.75519986864552
30233243.278051869614-10.2780518696139
31241238.1728102621152.82718973788542
32239240.927358314087-1.92735831408686
33233238.961236034472-5.96123603447214
34228232.997746078847-4.99774607884723
35228229.361064976328-1.36106497632835
36227227.491159037687-0.491159037686742
37225231.488117681057-6.48811768105722
38230223.2961283688756.70387163112531
39222227.781921449197-5.78192144919723
40207212.930267047946-5.93026704794619
41190197.207412128505-7.20741212850544
42184186.152096617264-2.15209661726439
43192188.0738116070133.92618839298657
44187187.701087248775-0.70108724877477
45173183.007411860488-10.0074118604882
46167171.772462666732-4.77246266673185
47163166.679350019811-3.67935001981115
48156160.560964536619-4.56096453661883
49153156.720434909742-3.72043490974195
50157151.41023214775.58976785230041
51152148.3424202834413.65757971655884
52128137.762092616605-9.76209261660503
53115116.34019078805-1.3401907880498
54114108.747420806415.25257919359026
55136116.09866180603119.9013381939695
56132125.2634579936886.73654200631194
57126123.2991835644072.70081643559263
58124123.8135960431380.186403956862137
59123124.180558819298-1.18055881929804
60119121.402611306797-2.40261130679667
61105121.343657746784-16.343657746784
62107110.938751721999-3.93875172199904
63108100.8685586576637.13144134233664
649289.29616544227112.70383455772891
657480.6662748405034-6.66627484050345
667372.39032795130470.609672048695259
6710081.563768220323218.4362317796768
689786.419462183905510.5805378160945
699986.890635917568612.1093640824314
7010294.94527581710437.05472418289565
7199101.946212647575-2.94621264757464
7210399.63379953453623.36620046546376
7392102.019983676966-10.0199836769657
7499102.763444802236-3.76344480223604
759799.1350561276357-2.13505612763575
768782.037557988734.96244201127006
776974.6999471899395-5.69994718993945
786671.8215712556196-5.82157125561956
799583.813909029130311.1860909708697
809182.72361946749078.27638053250928
819383.33038023697699.66961976302308
829989.28037609364219.71962390635794
839196.5091078205981-5.5091078205981
849195.3856107981544-4.38561079815436

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 267 & 266.698985042735 & 0.30101495726484 \tabularnewline
14 & 263 & 263.06737923417 & -0.0673792341703461 \tabularnewline
15 & 266 & 266.254703294283 & -0.25470329428282 \tabularnewline
16 & 257 & 257.331916940614 & -0.331916940614121 \tabularnewline
17 & 249 & 249.203727978248 & -0.203727978248168 \tabularnewline
18 & 249 & 249.066348988811 & -0.0663489888105175 \tabularnewline
19 & 251 & 252.72871104278 & -1.72871104277996 \tabularnewline
20 & 252 & 252.710957701073 & -0.710957701073482 \tabularnewline
21 & 252 & 252.311468372467 & -0.311468372467147 \tabularnewline
22 & 252 & 251.293468053218 & 0.706531946781695 \tabularnewline
23 & 256 & 252.588681413358 & 3.41131858664176 \tabularnewline
24 & 257 & 257.262807842518 & -0.262807842518498 \tabularnewline
25 & 259 & 265.33808068527 & -6.33808068526997 \tabularnewline
26 & 260 & 256.443489695685 & 3.55651030431545 \tabularnewline
27 & 261 & 261.924815363002 & -0.924815363002153 \tabularnewline
28 & 253 & 252.255871755537 & 0.744128244462729 \tabularnewline
29 & 243 & 244.755199868646 & -1.75519986864552 \tabularnewline
30 & 233 & 243.278051869614 & -10.2780518696139 \tabularnewline
31 & 241 & 238.172810262115 & 2.82718973788542 \tabularnewline
32 & 239 & 240.927358314087 & -1.92735831408686 \tabularnewline
33 & 233 & 238.961236034472 & -5.96123603447214 \tabularnewline
34 & 228 & 232.997746078847 & -4.99774607884723 \tabularnewline
35 & 228 & 229.361064976328 & -1.36106497632835 \tabularnewline
36 & 227 & 227.491159037687 & -0.491159037686742 \tabularnewline
37 & 225 & 231.488117681057 & -6.48811768105722 \tabularnewline
38 & 230 & 223.296128368875 & 6.70387163112531 \tabularnewline
39 & 222 & 227.781921449197 & -5.78192144919723 \tabularnewline
40 & 207 & 212.930267047946 & -5.93026704794619 \tabularnewline
41 & 190 & 197.207412128505 & -7.20741212850544 \tabularnewline
42 & 184 & 186.152096617264 & -2.15209661726439 \tabularnewline
43 & 192 & 188.073811607013 & 3.92618839298657 \tabularnewline
44 & 187 & 187.701087248775 & -0.70108724877477 \tabularnewline
45 & 173 & 183.007411860488 & -10.0074118604882 \tabularnewline
46 & 167 & 171.772462666732 & -4.77246266673185 \tabularnewline
47 & 163 & 166.679350019811 & -3.67935001981115 \tabularnewline
48 & 156 & 160.560964536619 & -4.56096453661883 \tabularnewline
49 & 153 & 156.720434909742 & -3.72043490974195 \tabularnewline
50 & 157 & 151.4102321477 & 5.58976785230041 \tabularnewline
51 & 152 & 148.342420283441 & 3.65757971655884 \tabularnewline
52 & 128 & 137.762092616605 & -9.76209261660503 \tabularnewline
53 & 115 & 116.34019078805 & -1.3401907880498 \tabularnewline
54 & 114 & 108.74742080641 & 5.25257919359026 \tabularnewline
55 & 136 & 116.098661806031 & 19.9013381939695 \tabularnewline
56 & 132 & 125.263457993688 & 6.73654200631194 \tabularnewline
57 & 126 & 123.299183564407 & 2.70081643559263 \tabularnewline
58 & 124 & 123.813596043138 & 0.186403956862137 \tabularnewline
59 & 123 & 124.180558819298 & -1.18055881929804 \tabularnewline
60 & 119 & 121.402611306797 & -2.40261130679667 \tabularnewline
61 & 105 & 121.343657746784 & -16.343657746784 \tabularnewline
62 & 107 & 110.938751721999 & -3.93875172199904 \tabularnewline
63 & 108 & 100.868558657663 & 7.13144134233664 \tabularnewline
64 & 92 & 89.2961654422711 & 2.70383455772891 \tabularnewline
65 & 74 & 80.6662748405034 & -6.66627484050345 \tabularnewline
66 & 73 & 72.3903279513047 & 0.609672048695259 \tabularnewline
67 & 100 & 81.5637682203232 & 18.4362317796768 \tabularnewline
68 & 97 & 86.4194621839055 & 10.5805378160945 \tabularnewline
69 & 99 & 86.8906359175686 & 12.1093640824314 \tabularnewline
70 & 102 & 94.9452758171043 & 7.05472418289565 \tabularnewline
71 & 99 & 101.946212647575 & -2.94621264757464 \tabularnewline
72 & 103 & 99.6337995345362 & 3.36620046546376 \tabularnewline
73 & 92 & 102.019983676966 & -10.0199836769657 \tabularnewline
74 & 99 & 102.763444802236 & -3.76344480223604 \tabularnewline
75 & 97 & 99.1350561276357 & -2.13505612763575 \tabularnewline
76 & 87 & 82.03755798873 & 4.96244201127006 \tabularnewline
77 & 69 & 74.6999471899395 & -5.69994718993945 \tabularnewline
78 & 66 & 71.8215712556196 & -5.82157125561956 \tabularnewline
79 & 95 & 83.8139090291303 & 11.1860909708697 \tabularnewline
80 & 91 & 82.7236194674907 & 8.27638053250928 \tabularnewline
81 & 93 & 83.3303802369769 & 9.66961976302308 \tabularnewline
82 & 99 & 89.2803760936421 & 9.71962390635794 \tabularnewline
83 & 91 & 96.5091078205981 & -5.5091078205981 \tabularnewline
84 & 91 & 95.3856107981544 & -4.38561079815436 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78193&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]267[/C][C]266.698985042735[/C][C]0.30101495726484[/C][/ROW]
[ROW][C]14[/C][C]263[/C][C]263.06737923417[/C][C]-0.0673792341703461[/C][/ROW]
[ROW][C]15[/C][C]266[/C][C]266.254703294283[/C][C]-0.25470329428282[/C][/ROW]
[ROW][C]16[/C][C]257[/C][C]257.331916940614[/C][C]-0.331916940614121[/C][/ROW]
[ROW][C]17[/C][C]249[/C][C]249.203727978248[/C][C]-0.203727978248168[/C][/ROW]
[ROW][C]18[/C][C]249[/C][C]249.066348988811[/C][C]-0.0663489888105175[/C][/ROW]
[ROW][C]19[/C][C]251[/C][C]252.72871104278[/C][C]-1.72871104277996[/C][/ROW]
[ROW][C]20[/C][C]252[/C][C]252.710957701073[/C][C]-0.710957701073482[/C][/ROW]
[ROW][C]21[/C][C]252[/C][C]252.311468372467[/C][C]-0.311468372467147[/C][/ROW]
[ROW][C]22[/C][C]252[/C][C]251.293468053218[/C][C]0.706531946781695[/C][/ROW]
[ROW][C]23[/C][C]256[/C][C]252.588681413358[/C][C]3.41131858664176[/C][/ROW]
[ROW][C]24[/C][C]257[/C][C]257.262807842518[/C][C]-0.262807842518498[/C][/ROW]
[ROW][C]25[/C][C]259[/C][C]265.33808068527[/C][C]-6.33808068526997[/C][/ROW]
[ROW][C]26[/C][C]260[/C][C]256.443489695685[/C][C]3.55651030431545[/C][/ROW]
[ROW][C]27[/C][C]261[/C][C]261.924815363002[/C][C]-0.924815363002153[/C][/ROW]
[ROW][C]28[/C][C]253[/C][C]252.255871755537[/C][C]0.744128244462729[/C][/ROW]
[ROW][C]29[/C][C]243[/C][C]244.755199868646[/C][C]-1.75519986864552[/C][/ROW]
[ROW][C]30[/C][C]233[/C][C]243.278051869614[/C][C]-10.2780518696139[/C][/ROW]
[ROW][C]31[/C][C]241[/C][C]238.172810262115[/C][C]2.82718973788542[/C][/ROW]
[ROW][C]32[/C][C]239[/C][C]240.927358314087[/C][C]-1.92735831408686[/C][/ROW]
[ROW][C]33[/C][C]233[/C][C]238.961236034472[/C][C]-5.96123603447214[/C][/ROW]
[ROW][C]34[/C][C]228[/C][C]232.997746078847[/C][C]-4.99774607884723[/C][/ROW]
[ROW][C]35[/C][C]228[/C][C]229.361064976328[/C][C]-1.36106497632835[/C][/ROW]
[ROW][C]36[/C][C]227[/C][C]227.491159037687[/C][C]-0.491159037686742[/C][/ROW]
[ROW][C]37[/C][C]225[/C][C]231.488117681057[/C][C]-6.48811768105722[/C][/ROW]
[ROW][C]38[/C][C]230[/C][C]223.296128368875[/C][C]6.70387163112531[/C][/ROW]
[ROW][C]39[/C][C]222[/C][C]227.781921449197[/C][C]-5.78192144919723[/C][/ROW]
[ROW][C]40[/C][C]207[/C][C]212.930267047946[/C][C]-5.93026704794619[/C][/ROW]
[ROW][C]41[/C][C]190[/C][C]197.207412128505[/C][C]-7.20741212850544[/C][/ROW]
[ROW][C]42[/C][C]184[/C][C]186.152096617264[/C][C]-2.15209661726439[/C][/ROW]
[ROW][C]43[/C][C]192[/C][C]188.073811607013[/C][C]3.92618839298657[/C][/ROW]
[ROW][C]44[/C][C]187[/C][C]187.701087248775[/C][C]-0.70108724877477[/C][/ROW]
[ROW][C]45[/C][C]173[/C][C]183.007411860488[/C][C]-10.0074118604882[/C][/ROW]
[ROW][C]46[/C][C]167[/C][C]171.772462666732[/C][C]-4.77246266673185[/C][/ROW]
[ROW][C]47[/C][C]163[/C][C]166.679350019811[/C][C]-3.67935001981115[/C][/ROW]
[ROW][C]48[/C][C]156[/C][C]160.560964536619[/C][C]-4.56096453661883[/C][/ROW]
[ROW][C]49[/C][C]153[/C][C]156.720434909742[/C][C]-3.72043490974195[/C][/ROW]
[ROW][C]50[/C][C]157[/C][C]151.4102321477[/C][C]5.58976785230041[/C][/ROW]
[ROW][C]51[/C][C]152[/C][C]148.342420283441[/C][C]3.65757971655884[/C][/ROW]
[ROW][C]52[/C][C]128[/C][C]137.762092616605[/C][C]-9.76209261660503[/C][/ROW]
[ROW][C]53[/C][C]115[/C][C]116.34019078805[/C][C]-1.3401907880498[/C][/ROW]
[ROW][C]54[/C][C]114[/C][C]108.74742080641[/C][C]5.25257919359026[/C][/ROW]
[ROW][C]55[/C][C]136[/C][C]116.098661806031[/C][C]19.9013381939695[/C][/ROW]
[ROW][C]56[/C][C]132[/C][C]125.263457993688[/C][C]6.73654200631194[/C][/ROW]
[ROW][C]57[/C][C]126[/C][C]123.299183564407[/C][C]2.70081643559263[/C][/ROW]
[ROW][C]58[/C][C]124[/C][C]123.813596043138[/C][C]0.186403956862137[/C][/ROW]
[ROW][C]59[/C][C]123[/C][C]124.180558819298[/C][C]-1.18055881929804[/C][/ROW]
[ROW][C]60[/C][C]119[/C][C]121.402611306797[/C][C]-2.40261130679667[/C][/ROW]
[ROW][C]61[/C][C]105[/C][C]121.343657746784[/C][C]-16.343657746784[/C][/ROW]
[ROW][C]62[/C][C]107[/C][C]110.938751721999[/C][C]-3.93875172199904[/C][/ROW]
[ROW][C]63[/C][C]108[/C][C]100.868558657663[/C][C]7.13144134233664[/C][/ROW]
[ROW][C]64[/C][C]92[/C][C]89.2961654422711[/C][C]2.70383455772891[/C][/ROW]
[ROW][C]65[/C][C]74[/C][C]80.6662748405034[/C][C]-6.66627484050345[/C][/ROW]
[ROW][C]66[/C][C]73[/C][C]72.3903279513047[/C][C]0.609672048695259[/C][/ROW]
[ROW][C]67[/C][C]100[/C][C]81.5637682203232[/C][C]18.4362317796768[/C][/ROW]
[ROW][C]68[/C][C]97[/C][C]86.4194621839055[/C][C]10.5805378160945[/C][/ROW]
[ROW][C]69[/C][C]99[/C][C]86.8906359175686[/C][C]12.1093640824314[/C][/ROW]
[ROW][C]70[/C][C]102[/C][C]94.9452758171043[/C][C]7.05472418289565[/C][/ROW]
[ROW][C]71[/C][C]99[/C][C]101.946212647575[/C][C]-2.94621264757464[/C][/ROW]
[ROW][C]72[/C][C]103[/C][C]99.6337995345362[/C][C]3.36620046546376[/C][/ROW]
[ROW][C]73[/C][C]92[/C][C]102.019983676966[/C][C]-10.0199836769657[/C][/ROW]
[ROW][C]74[/C][C]99[/C][C]102.763444802236[/C][C]-3.76344480223604[/C][/ROW]
[ROW][C]75[/C][C]97[/C][C]99.1350561276357[/C][C]-2.13505612763575[/C][/ROW]
[ROW][C]76[/C][C]87[/C][C]82.03755798873[/C][C]4.96244201127006[/C][/ROW]
[ROW][C]77[/C][C]69[/C][C]74.6999471899395[/C][C]-5.69994718993945[/C][/ROW]
[ROW][C]78[/C][C]66[/C][C]71.8215712556196[/C][C]-5.82157125561956[/C][/ROW]
[ROW][C]79[/C][C]95[/C][C]83.8139090291303[/C][C]11.1860909708697[/C][/ROW]
[ROW][C]80[/C][C]91[/C][C]82.7236194674907[/C][C]8.27638053250928[/C][/ROW]
[ROW][C]81[/C][C]93[/C][C]83.3303802369769[/C][C]9.66961976302308[/C][/ROW]
[ROW][C]82[/C][C]99[/C][C]89.2803760936421[/C][C]9.71962390635794[/C][/ROW]
[ROW][C]83[/C][C]91[/C][C]96.5091078205981[/C][C]-5.5091078205981[/C][/ROW]
[ROW][C]84[/C][C]91[/C][C]95.3856107981544[/C][C]-4.38561079815436[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78193&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78193&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
13267266.6989850427350.30101495726484
14263263.06737923417-0.0673792341703461
15266266.254703294283-0.25470329428282
16257257.331916940614-0.331916940614121
17249249.203727978248-0.203727978248168
18249249.066348988811-0.0663489888105175
19251252.72871104278-1.72871104277996
20252252.710957701073-0.710957701073482
21252252.311468372467-0.311468372467147
22252251.2934680532180.706531946781695
23256252.5886814133583.41131858664176
24257257.262807842518-0.262807842518498
25259265.33808068527-6.33808068526997
26260256.4434896956853.55651030431545
27261261.924815363002-0.924815363002153
28253252.2558717555370.744128244462729
29243244.755199868646-1.75519986864552
30233243.278051869614-10.2780518696139
31241238.1728102621152.82718973788542
32239240.927358314087-1.92735831408686
33233238.961236034472-5.96123603447214
34228232.997746078847-4.99774607884723
35228229.361064976328-1.36106497632835
36227227.491159037687-0.491159037686742
37225231.488117681057-6.48811768105722
38230223.2961283688756.70387163112531
39222227.781921449197-5.78192144919723
40207212.930267047946-5.93026704794619
41190197.207412128505-7.20741212850544
42184186.152096617264-2.15209661726439
43192188.0738116070133.92618839298657
44187187.701087248775-0.70108724877477
45173183.007411860488-10.0074118604882
46167171.772462666732-4.77246266673185
47163166.679350019811-3.67935001981115
48156160.560964536619-4.56096453661883
49153156.720434909742-3.72043490974195
50157151.41023214775.58976785230041
51152148.3424202834413.65757971655884
52128137.762092616605-9.76209261660503
53115116.34019078805-1.3401907880498
54114108.747420806415.25257919359026
55136116.09866180603119.9013381939695
56132125.2634579936886.73654200631194
57126123.2991835644072.70081643559263
58124123.8135960431380.186403956862137
59123124.180558819298-1.18055881929804
60119121.402611306797-2.40261130679667
61105121.343657746784-16.343657746784
62107110.938751721999-3.93875172199904
63108100.8685586576637.13144134233664
649289.29616544227112.70383455772891
657480.6662748405034-6.66627484050345
667372.39032795130470.609672048695259
6710081.563768220323218.4362317796768
689786.419462183905510.5805378160945
699986.890635917568612.1093640824314
7010294.94527581710437.05472418289565
7199101.946212647575-2.94621264757464
7210399.63379953453623.36620046546376
7392102.019983676966-10.0199836769657
7499102.763444802236-3.76344480223604
759799.1350561276357-2.13505612763575
768782.037557988734.96244201127006
776974.6999471899395-5.69994718993945
786671.8215712556196-5.82157125561956
799583.813909029130311.1860909708697
809182.72361946749078.27638053250928
819383.33038023697699.66961976302308
829989.28037609364219.71962390635794
839196.5091078205981-5.5091078205981
849195.3856107981544-4.38561079815436







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8588.857898257292476.1752451530761101.540551361509
8699.802056593826483.7022791195334115.901834068119
87100.89678604454781.4461449149307120.347427174162
8889.167423303649466.3592679771602111.975578630139
8976.547192638779750.3394684988334102.754916778726
9079.460633155080149.7922248949589109.129041415201
91102.86960592098669.6685618949362136.070649947036
9294.445645297806457.633719587132131.257571008481
9390.391078077665249.886404992253130.895751163077
9489.54111828215545.2598607475646133.822375816745
9584.637970660944336.4953699985855132.780571323303
9687.377747836124735.2888078049693139.46668786728

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 88.8578982572924 & 76.1752451530761 & 101.540551361509 \tabularnewline
86 & 99.8020565938264 & 83.7022791195334 & 115.901834068119 \tabularnewline
87 & 100.896786044547 & 81.4461449149307 & 120.347427174162 \tabularnewline
88 & 89.1674233036494 & 66.3592679771602 & 111.975578630139 \tabularnewline
89 & 76.5471926387797 & 50.3394684988334 & 102.754916778726 \tabularnewline
90 & 79.4606331550801 & 49.7922248949589 & 109.129041415201 \tabularnewline
91 & 102.869605920986 & 69.6685618949362 & 136.070649947036 \tabularnewline
92 & 94.4456452978064 & 57.633719587132 & 131.257571008481 \tabularnewline
93 & 90.3910780776652 & 49.886404992253 & 130.895751163077 \tabularnewline
94 & 89.541118282155 & 45.2598607475646 & 133.822375816745 \tabularnewline
95 & 84.6379706609443 & 36.4953699985855 & 132.780571323303 \tabularnewline
96 & 87.3777478361247 & 35.2888078049693 & 139.46668786728 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78193&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]88.8578982572924[/C][C]76.1752451530761[/C][C]101.540551361509[/C][/ROW]
[ROW][C]86[/C][C]99.8020565938264[/C][C]83.7022791195334[/C][C]115.901834068119[/C][/ROW]
[ROW][C]87[/C][C]100.896786044547[/C][C]81.4461449149307[/C][C]120.347427174162[/C][/ROW]
[ROW][C]88[/C][C]89.1674233036494[/C][C]66.3592679771602[/C][C]111.975578630139[/C][/ROW]
[ROW][C]89[/C][C]76.5471926387797[/C][C]50.3394684988334[/C][C]102.754916778726[/C][/ROW]
[ROW][C]90[/C][C]79.4606331550801[/C][C]49.7922248949589[/C][C]109.129041415201[/C][/ROW]
[ROW][C]91[/C][C]102.869605920986[/C][C]69.6685618949362[/C][C]136.070649947036[/C][/ROW]
[ROW][C]92[/C][C]94.4456452978064[/C][C]57.633719587132[/C][C]131.257571008481[/C][/ROW]
[ROW][C]93[/C][C]90.3910780776652[/C][C]49.886404992253[/C][C]130.895751163077[/C][/ROW]
[ROW][C]94[/C][C]89.541118282155[/C][C]45.2598607475646[/C][C]133.822375816745[/C][/ROW]
[ROW][C]95[/C][C]84.6379706609443[/C][C]36.4953699985855[/C][C]132.780571323303[/C][/ROW]
[ROW][C]96[/C][C]87.3777478361247[/C][C]35.2888078049693[/C][C]139.46668786728[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78193&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78193&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
8588.857898257292476.1752451530761101.540551361509
8699.802056593826483.7022791195334115.901834068119
87100.89678604454781.4461449149307120.347427174162
8889.167423303649466.3592679771602111.975578630139
8976.547192638779750.3394684988334102.754916778726
9079.460633155080149.7922248949589109.129041415201
91102.86960592098669.6685618949362136.070649947036
9294.445645297806457.633719587132131.257571008481
9390.391078077665249.886404992253130.895751163077
9489.54111828215545.2598607475646133.822375816745
9584.637970660944336.4953699985855132.780571323303
9687.377747836124735.2888078049693139.46668786728



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')