Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 05 Aug 2010 17:03:11 +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/05/t12810278244a62ahwuv728cua.htm/, Retrieved Thu, 31 Oct 2024 22:55:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78432, Retrieved Thu, 31 Oct 2024 22:55:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsMathias Goossenaerts
Estimated Impact146
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks 2 - Sta...] [2010-08-05 17:03:11] [f7fc4e1bbbe57039ee5ebdd2c8b864c0] [Current]
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Dataseries X:
430
429
428
426
424
423
424
426
427
427
428
430
432
435
426
411
405
403
402
399
392
387
380
379
386
385
365
356
338
338
343
338
320
316
317
315
317
321
303
303
290
285
300
291
278
273
277
269
275
278
255
254
245
240
261
247
229
213
218
206
217
219
196
193
188
171
190
180
149
135
151
134
145
151
137
124
125
109
131
133
103
85
104
82




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=78432&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=78432&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78432&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
alpha0.307424590775851
beta0.196794089031134
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.307424590775851 \tabularnewline
beta & 0.196794089031134 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78432&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]0.307424590775851[/C][/ROW]
[ROW][C]beta[/C][C]0.196794089031134[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78432&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78432&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
alpha0.307424590775851
beta0.196794089031134
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13432438.758814102564-6.7588141025642
14435439.444724495245-4.4447244952446
15426429.114806696529-3.11480669652906
16411413.546961243023-2.54696124302302
17405407.541262632317-2.54126263231717
18403405.841904530174-2.84190453017379
19402402.211521694026-0.211521694025691
20399400.58531963483-1.5853196348296
21392397.607534177317-5.60753417731712
22387392.928968930485-5.92896893048527
23380389.501221348796-9.50122134879553
24379385.608791220062-6.60879122006196
25386377.6497492749198.35025072508051
26385382.3700060213552.62999397864479
27365373.350881557889-8.35088155788901
28356354.4646171847951.53538281520508
29338347.862860828351-9.86286082835107
30338341.406476921289-3.40647692128869
31343337.0921435694245.90785643057598
32338334.4338229581133.56617704188653
33320328.603802339481-8.60380233948132
34316320.949975484108-4.94997548410754
35317313.576851551973.42314844803042
36315314.6705435416990.329456458300683
37317318.634140610284-1.63414061028442
38321315.1485781340865.85142186591372
39303298.5349470754464.46505292455373
40303290.23118694013112.7688130598685
41290279.66392239543510.3360776045649
42285285.585946458503-0.585946458502747
43300290.4574568623919.54254313760856
44291289.3825000185351.61749998146513
45278276.4946472761011.50535272389885
46273277.060638715541-4.0606387155413
47277278.395207605667-1.39520760566705
48269278.208765185761-9.20876518576063
49275279.646844913491-4.64684491349061
50278282.003858504252-4.00385850425232
51255262.388507852757-7.3885078527565
52254256.462720068085-2.46272006808482
53245238.8776255429066.12237445709434
54240235.0345726979184.96542730208247
55261248.05795353929612.9420464607039
56247242.1755641255984.8244358744015
57229230.026115936374-1.02611593637397
58213225.636034702473-12.6360347024727
59218225.338554057704-7.33855405770413
60206216.712160422525-10.7121604225253
61217219.555236335325-2.55523633532545
62219221.83482240719-2.83482240719007
63196199.139707201191-3.13970720119136
64193197.093604263142-4.09360426314203
65188184.0163133188573.98368668114301
66171177.648465039572-6.64846503957168
67190190.857190139797-0.857190139796927
68180172.5070039303287.4929960696723
69149154.683919932116-5.68391993211577
70135138.097308371729-3.09730837172867
71151142.2543956616998.74560433830081
72134135.062496105495-1.06249610549492
73145145.931504579047-0.931504579046731
74151148.0249694060482.97503059395223
75137126.76462057834510.2353794216547
76124128.838716875522-4.83871687552221
77125121.750428601123.24957139887967
78109108.3728504396210.62714956037911
79131128.8488648994792.15113510052055
80133118.40833911044214.5916608895578
8110395.2727094333967.72729056660397
828587.0429849328856-2.04298493288563
83104102.2326207663111.76737923368931
848288.1867294804112-6.1867294804112

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 432 & 438.758814102564 & -6.7588141025642 \tabularnewline
14 & 435 & 439.444724495245 & -4.4447244952446 \tabularnewline
15 & 426 & 429.114806696529 & -3.11480669652906 \tabularnewline
16 & 411 & 413.546961243023 & -2.54696124302302 \tabularnewline
17 & 405 & 407.541262632317 & -2.54126263231717 \tabularnewline
18 & 403 & 405.841904530174 & -2.84190453017379 \tabularnewline
19 & 402 & 402.211521694026 & -0.211521694025691 \tabularnewline
20 & 399 & 400.58531963483 & -1.5853196348296 \tabularnewline
21 & 392 & 397.607534177317 & -5.60753417731712 \tabularnewline
22 & 387 & 392.928968930485 & -5.92896893048527 \tabularnewline
23 & 380 & 389.501221348796 & -9.50122134879553 \tabularnewline
24 & 379 & 385.608791220062 & -6.60879122006196 \tabularnewline
25 & 386 & 377.649749274919 & 8.35025072508051 \tabularnewline
26 & 385 & 382.370006021355 & 2.62999397864479 \tabularnewline
27 & 365 & 373.350881557889 & -8.35088155788901 \tabularnewline
28 & 356 & 354.464617184795 & 1.53538281520508 \tabularnewline
29 & 338 & 347.862860828351 & -9.86286082835107 \tabularnewline
30 & 338 & 341.406476921289 & -3.40647692128869 \tabularnewline
31 & 343 & 337.092143569424 & 5.90785643057598 \tabularnewline
32 & 338 & 334.433822958113 & 3.56617704188653 \tabularnewline
33 & 320 & 328.603802339481 & -8.60380233948132 \tabularnewline
34 & 316 & 320.949975484108 & -4.94997548410754 \tabularnewline
35 & 317 & 313.57685155197 & 3.42314844803042 \tabularnewline
36 & 315 & 314.670543541699 & 0.329456458300683 \tabularnewline
37 & 317 & 318.634140610284 & -1.63414061028442 \tabularnewline
38 & 321 & 315.148578134086 & 5.85142186591372 \tabularnewline
39 & 303 & 298.534947075446 & 4.46505292455373 \tabularnewline
40 & 303 & 290.231186940131 & 12.7688130598685 \tabularnewline
41 & 290 & 279.663922395435 & 10.3360776045649 \tabularnewline
42 & 285 & 285.585946458503 & -0.585946458502747 \tabularnewline
43 & 300 & 290.457456862391 & 9.54254313760856 \tabularnewline
44 & 291 & 289.382500018535 & 1.61749998146513 \tabularnewline
45 & 278 & 276.494647276101 & 1.50535272389885 \tabularnewline
46 & 273 & 277.060638715541 & -4.0606387155413 \tabularnewline
47 & 277 & 278.395207605667 & -1.39520760566705 \tabularnewline
48 & 269 & 278.208765185761 & -9.20876518576063 \tabularnewline
49 & 275 & 279.646844913491 & -4.64684491349061 \tabularnewline
50 & 278 & 282.003858504252 & -4.00385850425232 \tabularnewline
51 & 255 & 262.388507852757 & -7.3885078527565 \tabularnewline
52 & 254 & 256.462720068085 & -2.46272006808482 \tabularnewline
53 & 245 & 238.877625542906 & 6.12237445709434 \tabularnewline
54 & 240 & 235.034572697918 & 4.96542730208247 \tabularnewline
55 & 261 & 248.057953539296 & 12.9420464607039 \tabularnewline
56 & 247 & 242.175564125598 & 4.8244358744015 \tabularnewline
57 & 229 & 230.026115936374 & -1.02611593637397 \tabularnewline
58 & 213 & 225.636034702473 & -12.6360347024727 \tabularnewline
59 & 218 & 225.338554057704 & -7.33855405770413 \tabularnewline
60 & 206 & 216.712160422525 & -10.7121604225253 \tabularnewline
61 & 217 & 219.555236335325 & -2.55523633532545 \tabularnewline
62 & 219 & 221.83482240719 & -2.83482240719007 \tabularnewline
63 & 196 & 199.139707201191 & -3.13970720119136 \tabularnewline
64 & 193 & 197.093604263142 & -4.09360426314203 \tabularnewline
65 & 188 & 184.016313318857 & 3.98368668114301 \tabularnewline
66 & 171 & 177.648465039572 & -6.64846503957168 \tabularnewline
67 & 190 & 190.857190139797 & -0.857190139796927 \tabularnewline
68 & 180 & 172.507003930328 & 7.4929960696723 \tabularnewline
69 & 149 & 154.683919932116 & -5.68391993211577 \tabularnewline
70 & 135 & 138.097308371729 & -3.09730837172867 \tabularnewline
71 & 151 & 142.254395661699 & 8.74560433830081 \tabularnewline
72 & 134 & 135.062496105495 & -1.06249610549492 \tabularnewline
73 & 145 & 145.931504579047 & -0.931504579046731 \tabularnewline
74 & 151 & 148.024969406048 & 2.97503059395223 \tabularnewline
75 & 137 & 126.764620578345 & 10.2353794216547 \tabularnewline
76 & 124 & 128.838716875522 & -4.83871687552221 \tabularnewline
77 & 125 & 121.75042860112 & 3.24957139887967 \tabularnewline
78 & 109 & 108.372850439621 & 0.62714956037911 \tabularnewline
79 & 131 & 128.848864899479 & 2.15113510052055 \tabularnewline
80 & 133 & 118.408339110442 & 14.5916608895578 \tabularnewline
81 & 103 & 95.272709433396 & 7.72729056660397 \tabularnewline
82 & 85 & 87.0429849328856 & -2.04298493288563 \tabularnewline
83 & 104 & 102.232620766311 & 1.76737923368931 \tabularnewline
84 & 82 & 88.1867294804112 & -6.1867294804112 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78432&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]432[/C][C]438.758814102564[/C][C]-6.7588141025642[/C][/ROW]
[ROW][C]14[/C][C]435[/C][C]439.444724495245[/C][C]-4.4447244952446[/C][/ROW]
[ROW][C]15[/C][C]426[/C][C]429.114806696529[/C][C]-3.11480669652906[/C][/ROW]
[ROW][C]16[/C][C]411[/C][C]413.546961243023[/C][C]-2.54696124302302[/C][/ROW]
[ROW][C]17[/C][C]405[/C][C]407.541262632317[/C][C]-2.54126263231717[/C][/ROW]
[ROW][C]18[/C][C]403[/C][C]405.841904530174[/C][C]-2.84190453017379[/C][/ROW]
[ROW][C]19[/C][C]402[/C][C]402.211521694026[/C][C]-0.211521694025691[/C][/ROW]
[ROW][C]20[/C][C]399[/C][C]400.58531963483[/C][C]-1.5853196348296[/C][/ROW]
[ROW][C]21[/C][C]392[/C][C]397.607534177317[/C][C]-5.60753417731712[/C][/ROW]
[ROW][C]22[/C][C]387[/C][C]392.928968930485[/C][C]-5.92896893048527[/C][/ROW]
[ROW][C]23[/C][C]380[/C][C]389.501221348796[/C][C]-9.50122134879553[/C][/ROW]
[ROW][C]24[/C][C]379[/C][C]385.608791220062[/C][C]-6.60879122006196[/C][/ROW]
[ROW][C]25[/C][C]386[/C][C]377.649749274919[/C][C]8.35025072508051[/C][/ROW]
[ROW][C]26[/C][C]385[/C][C]382.370006021355[/C][C]2.62999397864479[/C][/ROW]
[ROW][C]27[/C][C]365[/C][C]373.350881557889[/C][C]-8.35088155788901[/C][/ROW]
[ROW][C]28[/C][C]356[/C][C]354.464617184795[/C][C]1.53538281520508[/C][/ROW]
[ROW][C]29[/C][C]338[/C][C]347.862860828351[/C][C]-9.86286082835107[/C][/ROW]
[ROW][C]30[/C][C]338[/C][C]341.406476921289[/C][C]-3.40647692128869[/C][/ROW]
[ROW][C]31[/C][C]343[/C][C]337.092143569424[/C][C]5.90785643057598[/C][/ROW]
[ROW][C]32[/C][C]338[/C][C]334.433822958113[/C][C]3.56617704188653[/C][/ROW]
[ROW][C]33[/C][C]320[/C][C]328.603802339481[/C][C]-8.60380233948132[/C][/ROW]
[ROW][C]34[/C][C]316[/C][C]320.949975484108[/C][C]-4.94997548410754[/C][/ROW]
[ROW][C]35[/C][C]317[/C][C]313.57685155197[/C][C]3.42314844803042[/C][/ROW]
[ROW][C]36[/C][C]315[/C][C]314.670543541699[/C][C]0.329456458300683[/C][/ROW]
[ROW][C]37[/C][C]317[/C][C]318.634140610284[/C][C]-1.63414061028442[/C][/ROW]
[ROW][C]38[/C][C]321[/C][C]315.148578134086[/C][C]5.85142186591372[/C][/ROW]
[ROW][C]39[/C][C]303[/C][C]298.534947075446[/C][C]4.46505292455373[/C][/ROW]
[ROW][C]40[/C][C]303[/C][C]290.231186940131[/C][C]12.7688130598685[/C][/ROW]
[ROW][C]41[/C][C]290[/C][C]279.663922395435[/C][C]10.3360776045649[/C][/ROW]
[ROW][C]42[/C][C]285[/C][C]285.585946458503[/C][C]-0.585946458502747[/C][/ROW]
[ROW][C]43[/C][C]300[/C][C]290.457456862391[/C][C]9.54254313760856[/C][/ROW]
[ROW][C]44[/C][C]291[/C][C]289.382500018535[/C][C]1.61749998146513[/C][/ROW]
[ROW][C]45[/C][C]278[/C][C]276.494647276101[/C][C]1.50535272389885[/C][/ROW]
[ROW][C]46[/C][C]273[/C][C]277.060638715541[/C][C]-4.0606387155413[/C][/ROW]
[ROW][C]47[/C][C]277[/C][C]278.395207605667[/C][C]-1.39520760566705[/C][/ROW]
[ROW][C]48[/C][C]269[/C][C]278.208765185761[/C][C]-9.20876518576063[/C][/ROW]
[ROW][C]49[/C][C]275[/C][C]279.646844913491[/C][C]-4.64684491349061[/C][/ROW]
[ROW][C]50[/C][C]278[/C][C]282.003858504252[/C][C]-4.00385850425232[/C][/ROW]
[ROW][C]51[/C][C]255[/C][C]262.388507852757[/C][C]-7.3885078527565[/C][/ROW]
[ROW][C]52[/C][C]254[/C][C]256.462720068085[/C][C]-2.46272006808482[/C][/ROW]
[ROW][C]53[/C][C]245[/C][C]238.877625542906[/C][C]6.12237445709434[/C][/ROW]
[ROW][C]54[/C][C]240[/C][C]235.034572697918[/C][C]4.96542730208247[/C][/ROW]
[ROW][C]55[/C][C]261[/C][C]248.057953539296[/C][C]12.9420464607039[/C][/ROW]
[ROW][C]56[/C][C]247[/C][C]242.175564125598[/C][C]4.8244358744015[/C][/ROW]
[ROW][C]57[/C][C]229[/C][C]230.026115936374[/C][C]-1.02611593637397[/C][/ROW]
[ROW][C]58[/C][C]213[/C][C]225.636034702473[/C][C]-12.6360347024727[/C][/ROW]
[ROW][C]59[/C][C]218[/C][C]225.338554057704[/C][C]-7.33855405770413[/C][/ROW]
[ROW][C]60[/C][C]206[/C][C]216.712160422525[/C][C]-10.7121604225253[/C][/ROW]
[ROW][C]61[/C][C]217[/C][C]219.555236335325[/C][C]-2.55523633532545[/C][/ROW]
[ROW][C]62[/C][C]219[/C][C]221.83482240719[/C][C]-2.83482240719007[/C][/ROW]
[ROW][C]63[/C][C]196[/C][C]199.139707201191[/C][C]-3.13970720119136[/C][/ROW]
[ROW][C]64[/C][C]193[/C][C]197.093604263142[/C][C]-4.09360426314203[/C][/ROW]
[ROW][C]65[/C][C]188[/C][C]184.016313318857[/C][C]3.98368668114301[/C][/ROW]
[ROW][C]66[/C][C]171[/C][C]177.648465039572[/C][C]-6.64846503957168[/C][/ROW]
[ROW][C]67[/C][C]190[/C][C]190.857190139797[/C][C]-0.857190139796927[/C][/ROW]
[ROW][C]68[/C][C]180[/C][C]172.507003930328[/C][C]7.4929960696723[/C][/ROW]
[ROW][C]69[/C][C]149[/C][C]154.683919932116[/C][C]-5.68391993211577[/C][/ROW]
[ROW][C]70[/C][C]135[/C][C]138.097308371729[/C][C]-3.09730837172867[/C][/ROW]
[ROW][C]71[/C][C]151[/C][C]142.254395661699[/C][C]8.74560433830081[/C][/ROW]
[ROW][C]72[/C][C]134[/C][C]135.062496105495[/C][C]-1.06249610549492[/C][/ROW]
[ROW][C]73[/C][C]145[/C][C]145.931504579047[/C][C]-0.931504579046731[/C][/ROW]
[ROW][C]74[/C][C]151[/C][C]148.024969406048[/C][C]2.97503059395223[/C][/ROW]
[ROW][C]75[/C][C]137[/C][C]126.764620578345[/C][C]10.2353794216547[/C][/ROW]
[ROW][C]76[/C][C]124[/C][C]128.838716875522[/C][C]-4.83871687552221[/C][/ROW]
[ROW][C]77[/C][C]125[/C][C]121.75042860112[/C][C]3.24957139887967[/C][/ROW]
[ROW][C]78[/C][C]109[/C][C]108.372850439621[/C][C]0.62714956037911[/C][/ROW]
[ROW][C]79[/C][C]131[/C][C]128.848864899479[/C][C]2.15113510052055[/C][/ROW]
[ROW][C]80[/C][C]133[/C][C]118.408339110442[/C][C]14.5916608895578[/C][/ROW]
[ROW][C]81[/C][C]103[/C][C]95.272709433396[/C][C]7.72729056660397[/C][/ROW]
[ROW][C]82[/C][C]85[/C][C]87.0429849328856[/C][C]-2.04298493288563[/C][/ROW]
[ROW][C]83[/C][C]104[/C][C]102.232620766311[/C][C]1.76737923368931[/C][/ROW]
[ROW][C]84[/C][C]82[/C][C]88.1867294804112[/C][C]-6.1867294804112[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78432&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78432&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
13432438.758814102564-6.7588141025642
14435439.444724495245-4.4447244952446
15426429.114806696529-3.11480669652906
16411413.546961243023-2.54696124302302
17405407.541262632317-2.54126263231717
18403405.841904530174-2.84190453017379
19402402.211521694026-0.211521694025691
20399400.58531963483-1.5853196348296
21392397.607534177317-5.60753417731712
22387392.928968930485-5.92896893048527
23380389.501221348796-9.50122134879553
24379385.608791220062-6.60879122006196
25386377.6497492749198.35025072508051
26385382.3700060213552.62999397864479
27365373.350881557889-8.35088155788901
28356354.4646171847951.53538281520508
29338347.862860828351-9.86286082835107
30338341.406476921289-3.40647692128869
31343337.0921435694245.90785643057598
32338334.4338229581133.56617704188653
33320328.603802339481-8.60380233948132
34316320.949975484108-4.94997548410754
35317313.576851551973.42314844803042
36315314.6705435416990.329456458300683
37317318.634140610284-1.63414061028442
38321315.1485781340865.85142186591372
39303298.5349470754464.46505292455373
40303290.23118694013112.7688130598685
41290279.66392239543510.3360776045649
42285285.585946458503-0.585946458502747
43300290.4574568623919.54254313760856
44291289.3825000185351.61749998146513
45278276.4946472761011.50535272389885
46273277.060638715541-4.0606387155413
47277278.395207605667-1.39520760566705
48269278.208765185761-9.20876518576063
49275279.646844913491-4.64684491349061
50278282.003858504252-4.00385850425232
51255262.388507852757-7.3885078527565
52254256.462720068085-2.46272006808482
53245238.8776255429066.12237445709434
54240235.0345726979184.96542730208247
55261248.05795353929612.9420464607039
56247242.1755641255984.8244358744015
57229230.026115936374-1.02611593637397
58213225.636034702473-12.6360347024727
59218225.338554057704-7.33855405770413
60206216.712160422525-10.7121604225253
61217219.555236335325-2.55523633532545
62219221.83482240719-2.83482240719007
63196199.139707201191-3.13970720119136
64193197.093604263142-4.09360426314203
65188184.0163133188573.98368668114301
66171177.648465039572-6.64846503957168
67190190.857190139797-0.857190139796927
68180172.5070039303287.4929960696723
69149154.683919932116-5.68391993211577
70135138.097308371729-3.09730837172867
71151142.2543956616998.74560433830081
72134135.062496105495-1.06249610549492
73145145.931504579047-0.931504579046731
74151148.0249694060482.97503059395223
75137126.76462057834510.2353794216547
76124128.838716875522-4.83871687552221
77125121.750428601123.24957139887967
78109108.3728504396210.62714956037911
79131128.8488648994792.15113510052055
80133118.40833911044214.5916608895578
8110395.2727094333967.72729056660397
828587.0429849328856-2.04298493288563
83104102.2326207663111.76737923368931
848288.1867294804112-6.1867294804112







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8599.345266812769287.3595368519948111.330996773544
86106.26114736134393.4899146782371119.032380044449
8790.76503074845177.0001385637869104.529922933115
8880.283828297961465.323448489466995.2442081064558
8981.608826323121165.263241928044297.954410718198
9066.54342437647548.637576841226984.4492719117233
9188.971569662883969.345354344465108.597784981303
9287.445049140808465.9523385621415108.937759719475
9355.146018969500431.653129825562178.6389081134387
9437.383115748446311.767151035954162.9990804609386
9555.572412127518927.719698525810983.4251257292269
9635.10007184179964.9047827339876565.2953609496116

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 99.3452668127692 & 87.3595368519948 & 111.330996773544 \tabularnewline
86 & 106.261147361343 & 93.4899146782371 & 119.032380044449 \tabularnewline
87 & 90.765030748451 & 77.0001385637869 & 104.529922933115 \tabularnewline
88 & 80.2838282979614 & 65.3234484894669 & 95.2442081064558 \tabularnewline
89 & 81.6088263231211 & 65.2632419280442 & 97.954410718198 \tabularnewline
90 & 66.543424376475 & 48.6375768412269 & 84.4492719117233 \tabularnewline
91 & 88.9715696628839 & 69.345354344465 & 108.597784981303 \tabularnewline
92 & 87.4450491408084 & 65.9523385621415 & 108.937759719475 \tabularnewline
93 & 55.1460189695004 & 31.6531298255621 & 78.6389081134387 \tabularnewline
94 & 37.3831157484463 & 11.7671510359541 & 62.9990804609386 \tabularnewline
95 & 55.5724121275189 & 27.7196985258109 & 83.4251257292269 \tabularnewline
96 & 35.1000718417996 & 4.90478273398765 & 65.2953609496116 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78432&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]99.3452668127692[/C][C]87.3595368519948[/C][C]111.330996773544[/C][/ROW]
[ROW][C]86[/C][C]106.261147361343[/C][C]93.4899146782371[/C][C]119.032380044449[/C][/ROW]
[ROW][C]87[/C][C]90.765030748451[/C][C]77.0001385637869[/C][C]104.529922933115[/C][/ROW]
[ROW][C]88[/C][C]80.2838282979614[/C][C]65.3234484894669[/C][C]95.2442081064558[/C][/ROW]
[ROW][C]89[/C][C]81.6088263231211[/C][C]65.2632419280442[/C][C]97.954410718198[/C][/ROW]
[ROW][C]90[/C][C]66.543424376475[/C][C]48.6375768412269[/C][C]84.4492719117233[/C][/ROW]
[ROW][C]91[/C][C]88.9715696628839[/C][C]69.345354344465[/C][C]108.597784981303[/C][/ROW]
[ROW][C]92[/C][C]87.4450491408084[/C][C]65.9523385621415[/C][C]108.937759719475[/C][/ROW]
[ROW][C]93[/C][C]55.1460189695004[/C][C]31.6531298255621[/C][C]78.6389081134387[/C][/ROW]
[ROW][C]94[/C][C]37.3831157484463[/C][C]11.7671510359541[/C][C]62.9990804609386[/C][/ROW]
[ROW][C]95[/C][C]55.5724121275189[/C][C]27.7196985258109[/C][C]83.4251257292269[/C][/ROW]
[ROW][C]96[/C][C]35.1000718417996[/C][C]4.90478273398765[/C][C]65.2953609496116[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78432&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78432&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
8599.345266812769287.3595368519948111.330996773544
86106.26114736134393.4899146782371119.032380044449
8790.76503074845177.0001385637869104.529922933115
8880.283828297961465.323448489466995.2442081064558
8981.608826323121165.263241928044297.954410718198
9066.54342437647548.637576841226984.4492719117233
9188.971569662883969.345354344465108.597784981303
9287.445049140808465.9523385621415108.937759719475
9355.146018969500431.653129825562178.6389081134387
9437.383115748446311.767151035954162.9990804609386
9555.572412127518927.719698525810983.4251257292269
9635.10007184179964.9047827339876565.2953609496116



Parameters (Session):
par1 = additive ; par2 = 12 ;
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')