Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 17 Aug 2010 11:00:50 +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/17/t1282042824xkhpngemztvwc4l.htm/, Retrieved Sat, 27 Apr 2024 11:19:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79082, Retrieved Sat, 27 Apr 2024 11:19:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsmattias debbaut
Estimated Impact146
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2010-08-17 11:00:50] [59fa324537f53fb6459bc6951db20f7b] [Current]
Feedback Forum

Post a new message
Dataseries X:
376
375
374
372
370
369
370
372
373
373
374
376
371
374
369
363
357
366
362
366
361
362
358
363
360
360
348
345
332
333
323
327
332
337
336
337
343
337
326
321
309
302
293
287
292
292
289
302
310
295
276
264
257
243
227
226
226
229
224
240
244
226
208
199
193
180
167
164
166
173
169
191
193
166
143
147
139
129
115
108
106
116
108
135




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79082&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79082&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79082&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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.208492559269248
beta0.141775183847602
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.208492559269248 \tabularnewline
beta & 0.141775183847602 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79082&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]0.208492559269248[/C][/ROW]
[ROW][C]beta[/C][C]0.141775183847602[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79082&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79082&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
alpha0.208492559269248
beta0.141775183847602
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13371374.507612695369-3.50761269536900
14374376.585977222432-2.58597722243223
15369370.900310874623-1.90031087462319
16363364.512486632936-1.51248663293580
17357358.327983093222-1.32798309322249
18366367.275602408463-1.27560240846304
19362362.259368067115-0.259368067115133
20366363.3488973112182.65110268878215
21361364.141315833245-3.14131583324479
22362362.978837078825-0.978837078824654
23358363.534128010580-5.53412801057959
24363363.689075557080-0.689075557079548
25360355.2076617745654.79233822543478
26360359.2218744258340.778125574165642
27348354.678026407921-6.67802640792121
28345347.420129010354-2.42012901035366
29332340.998648946626-8.99864894662642
30333347.223273111413-14.2232731114133
31323339.459966416589-16.4599664165887
32327337.626876307825-10.6268763078251
33332329.4463950541162.55360494588433
34337329.2461571137177.75384288628317
35336326.6789730670719.32102693292939
36337332.1817431784184.81825682158205
37343328.51235391042314.4876460895769
38337330.6882180385436.31178196145709
39326321.6879742435314.31202575646864
40321320.0706179905640.92938200943621
41309309.799136350361-0.799136350361437
42302313.364980153577-11.3649801535774
43293304.905156915081-11.9051569150807
44287308.456452468431-21.4564524684312
45292308.030175139126-16.0301751391261
46292307.072034845111-15.0720348451113
47289299.842156329827-10.8421563298269
48302295.5471346782716.45286532172884
49310297.42783679095412.5721632090459
50295291.6372504166873.36274958331285
51276279.99921544962-3.99921544962001
52264272.489107781961-8.48910778196102
53257258.300935615494-1.30093561549421
54243251.664688011571-8.66468801157131
55227242.004060005047-15.0040600050474
56226234.842887633332-8.84288763333197
57226237.202346754043-11.2023467540430
58229234.800738038305-5.80073803830547
59224230.587396995002-6.58739699500185
60240235.9784093476714.02159065232914
61244238.3560469615525.64395303844844
62226224.7171770269881.28282297301206
63208208.508337883012-0.508337883012217
64199198.1427493860380.857250613961867
65193190.9880799453072.01192005469309
66180180.152171035643-0.152171035642596
67167168.571679084693-1.57167908469299
68164167.166604134288-3.16660413428838
69166166.528754607842-0.528754607841677
70173168.0271578485564.97284215144413
71169165.1626751688693.83732483113073
72191176.16734159284414.8326584071559
73193180.69238089551812.3076191044825
74166169.159491556411-3.15949155641064
75143154.659252026973-11.6592520269731
76147144.6243330530092.37566694699055
77139139.594335045257-0.594335045256713
78129129.203786698198-0.203786698197518
79115119.18633660126-4.1863366012599
80108115.623060155510-7.6230601555096
81106114.199953626781-8.19995362678145
82116114.7864715222821.21352847771753
83108109.975515644333-1.97551564433303
84135119.30880994794115.6911900520593

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 371 & 374.507612695369 & -3.50761269536900 \tabularnewline
14 & 374 & 376.585977222432 & -2.58597722243223 \tabularnewline
15 & 369 & 370.900310874623 & -1.90031087462319 \tabularnewline
16 & 363 & 364.512486632936 & -1.51248663293580 \tabularnewline
17 & 357 & 358.327983093222 & -1.32798309322249 \tabularnewline
18 & 366 & 367.275602408463 & -1.27560240846304 \tabularnewline
19 & 362 & 362.259368067115 & -0.259368067115133 \tabularnewline
20 & 366 & 363.348897311218 & 2.65110268878215 \tabularnewline
21 & 361 & 364.141315833245 & -3.14131583324479 \tabularnewline
22 & 362 & 362.978837078825 & -0.978837078824654 \tabularnewline
23 & 358 & 363.534128010580 & -5.53412801057959 \tabularnewline
24 & 363 & 363.689075557080 & -0.689075557079548 \tabularnewline
25 & 360 & 355.207661774565 & 4.79233822543478 \tabularnewline
26 & 360 & 359.221874425834 & 0.778125574165642 \tabularnewline
27 & 348 & 354.678026407921 & -6.67802640792121 \tabularnewline
28 & 345 & 347.420129010354 & -2.42012901035366 \tabularnewline
29 & 332 & 340.998648946626 & -8.99864894662642 \tabularnewline
30 & 333 & 347.223273111413 & -14.2232731114133 \tabularnewline
31 & 323 & 339.459966416589 & -16.4599664165887 \tabularnewline
32 & 327 & 337.626876307825 & -10.6268763078251 \tabularnewline
33 & 332 & 329.446395054116 & 2.55360494588433 \tabularnewline
34 & 337 & 329.246157113717 & 7.75384288628317 \tabularnewline
35 & 336 & 326.678973067071 & 9.32102693292939 \tabularnewline
36 & 337 & 332.181743178418 & 4.81825682158205 \tabularnewline
37 & 343 & 328.512353910423 & 14.4876460895769 \tabularnewline
38 & 337 & 330.688218038543 & 6.31178196145709 \tabularnewline
39 & 326 & 321.687974243531 & 4.31202575646864 \tabularnewline
40 & 321 & 320.070617990564 & 0.92938200943621 \tabularnewline
41 & 309 & 309.799136350361 & -0.799136350361437 \tabularnewline
42 & 302 & 313.364980153577 & -11.3649801535774 \tabularnewline
43 & 293 & 304.905156915081 & -11.9051569150807 \tabularnewline
44 & 287 & 308.456452468431 & -21.4564524684312 \tabularnewline
45 & 292 & 308.030175139126 & -16.0301751391261 \tabularnewline
46 & 292 & 307.072034845111 & -15.0720348451113 \tabularnewline
47 & 289 & 299.842156329827 & -10.8421563298269 \tabularnewline
48 & 302 & 295.547134678271 & 6.45286532172884 \tabularnewline
49 & 310 & 297.427836790954 & 12.5721632090459 \tabularnewline
50 & 295 & 291.637250416687 & 3.36274958331285 \tabularnewline
51 & 276 & 279.99921544962 & -3.99921544962001 \tabularnewline
52 & 264 & 272.489107781961 & -8.48910778196102 \tabularnewline
53 & 257 & 258.300935615494 & -1.30093561549421 \tabularnewline
54 & 243 & 251.664688011571 & -8.66468801157131 \tabularnewline
55 & 227 & 242.004060005047 & -15.0040600050474 \tabularnewline
56 & 226 & 234.842887633332 & -8.84288763333197 \tabularnewline
57 & 226 & 237.202346754043 & -11.2023467540430 \tabularnewline
58 & 229 & 234.800738038305 & -5.80073803830547 \tabularnewline
59 & 224 & 230.587396995002 & -6.58739699500185 \tabularnewline
60 & 240 & 235.978409347671 & 4.02159065232914 \tabularnewline
61 & 244 & 238.356046961552 & 5.64395303844844 \tabularnewline
62 & 226 & 224.717177026988 & 1.28282297301206 \tabularnewline
63 & 208 & 208.508337883012 & -0.508337883012217 \tabularnewline
64 & 199 & 198.142749386038 & 0.857250613961867 \tabularnewline
65 & 193 & 190.988079945307 & 2.01192005469309 \tabularnewline
66 & 180 & 180.152171035643 & -0.152171035642596 \tabularnewline
67 & 167 & 168.571679084693 & -1.57167908469299 \tabularnewline
68 & 164 & 167.166604134288 & -3.16660413428838 \tabularnewline
69 & 166 & 166.528754607842 & -0.528754607841677 \tabularnewline
70 & 173 & 168.027157848556 & 4.97284215144413 \tabularnewline
71 & 169 & 165.162675168869 & 3.83732483113073 \tabularnewline
72 & 191 & 176.167341592844 & 14.8326584071559 \tabularnewline
73 & 193 & 180.692380895518 & 12.3076191044825 \tabularnewline
74 & 166 & 169.159491556411 & -3.15949155641064 \tabularnewline
75 & 143 & 154.659252026973 & -11.6592520269731 \tabularnewline
76 & 147 & 144.624333053009 & 2.37566694699055 \tabularnewline
77 & 139 & 139.594335045257 & -0.594335045256713 \tabularnewline
78 & 129 & 129.203786698198 & -0.203786698197518 \tabularnewline
79 & 115 & 119.18633660126 & -4.1863366012599 \tabularnewline
80 & 108 & 115.623060155510 & -7.6230601555096 \tabularnewline
81 & 106 & 114.199953626781 & -8.19995362678145 \tabularnewline
82 & 116 & 114.786471522282 & 1.21352847771753 \tabularnewline
83 & 108 & 109.975515644333 & -1.97551564433303 \tabularnewline
84 & 135 & 119.308809947941 & 15.6911900520593 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79082&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]371[/C][C]374.507612695369[/C][C]-3.50761269536900[/C][/ROW]
[ROW][C]14[/C][C]374[/C][C]376.585977222432[/C][C]-2.58597722243223[/C][/ROW]
[ROW][C]15[/C][C]369[/C][C]370.900310874623[/C][C]-1.90031087462319[/C][/ROW]
[ROW][C]16[/C][C]363[/C][C]364.512486632936[/C][C]-1.51248663293580[/C][/ROW]
[ROW][C]17[/C][C]357[/C][C]358.327983093222[/C][C]-1.32798309322249[/C][/ROW]
[ROW][C]18[/C][C]366[/C][C]367.275602408463[/C][C]-1.27560240846304[/C][/ROW]
[ROW][C]19[/C][C]362[/C][C]362.259368067115[/C][C]-0.259368067115133[/C][/ROW]
[ROW][C]20[/C][C]366[/C][C]363.348897311218[/C][C]2.65110268878215[/C][/ROW]
[ROW][C]21[/C][C]361[/C][C]364.141315833245[/C][C]-3.14131583324479[/C][/ROW]
[ROW][C]22[/C][C]362[/C][C]362.978837078825[/C][C]-0.978837078824654[/C][/ROW]
[ROW][C]23[/C][C]358[/C][C]363.534128010580[/C][C]-5.53412801057959[/C][/ROW]
[ROW][C]24[/C][C]363[/C][C]363.689075557080[/C][C]-0.689075557079548[/C][/ROW]
[ROW][C]25[/C][C]360[/C][C]355.207661774565[/C][C]4.79233822543478[/C][/ROW]
[ROW][C]26[/C][C]360[/C][C]359.221874425834[/C][C]0.778125574165642[/C][/ROW]
[ROW][C]27[/C][C]348[/C][C]354.678026407921[/C][C]-6.67802640792121[/C][/ROW]
[ROW][C]28[/C][C]345[/C][C]347.420129010354[/C][C]-2.42012901035366[/C][/ROW]
[ROW][C]29[/C][C]332[/C][C]340.998648946626[/C][C]-8.99864894662642[/C][/ROW]
[ROW][C]30[/C][C]333[/C][C]347.223273111413[/C][C]-14.2232731114133[/C][/ROW]
[ROW][C]31[/C][C]323[/C][C]339.459966416589[/C][C]-16.4599664165887[/C][/ROW]
[ROW][C]32[/C][C]327[/C][C]337.626876307825[/C][C]-10.6268763078251[/C][/ROW]
[ROW][C]33[/C][C]332[/C][C]329.446395054116[/C][C]2.55360494588433[/C][/ROW]
[ROW][C]34[/C][C]337[/C][C]329.246157113717[/C][C]7.75384288628317[/C][/ROW]
[ROW][C]35[/C][C]336[/C][C]326.678973067071[/C][C]9.32102693292939[/C][/ROW]
[ROW][C]36[/C][C]337[/C][C]332.181743178418[/C][C]4.81825682158205[/C][/ROW]
[ROW][C]37[/C][C]343[/C][C]328.512353910423[/C][C]14.4876460895769[/C][/ROW]
[ROW][C]38[/C][C]337[/C][C]330.688218038543[/C][C]6.31178196145709[/C][/ROW]
[ROW][C]39[/C][C]326[/C][C]321.687974243531[/C][C]4.31202575646864[/C][/ROW]
[ROW][C]40[/C][C]321[/C][C]320.070617990564[/C][C]0.92938200943621[/C][/ROW]
[ROW][C]41[/C][C]309[/C][C]309.799136350361[/C][C]-0.799136350361437[/C][/ROW]
[ROW][C]42[/C][C]302[/C][C]313.364980153577[/C][C]-11.3649801535774[/C][/ROW]
[ROW][C]43[/C][C]293[/C][C]304.905156915081[/C][C]-11.9051569150807[/C][/ROW]
[ROW][C]44[/C][C]287[/C][C]308.456452468431[/C][C]-21.4564524684312[/C][/ROW]
[ROW][C]45[/C][C]292[/C][C]308.030175139126[/C][C]-16.0301751391261[/C][/ROW]
[ROW][C]46[/C][C]292[/C][C]307.072034845111[/C][C]-15.0720348451113[/C][/ROW]
[ROW][C]47[/C][C]289[/C][C]299.842156329827[/C][C]-10.8421563298269[/C][/ROW]
[ROW][C]48[/C][C]302[/C][C]295.547134678271[/C][C]6.45286532172884[/C][/ROW]
[ROW][C]49[/C][C]310[/C][C]297.427836790954[/C][C]12.5721632090459[/C][/ROW]
[ROW][C]50[/C][C]295[/C][C]291.637250416687[/C][C]3.36274958331285[/C][/ROW]
[ROW][C]51[/C][C]276[/C][C]279.99921544962[/C][C]-3.99921544962001[/C][/ROW]
[ROW][C]52[/C][C]264[/C][C]272.489107781961[/C][C]-8.48910778196102[/C][/ROW]
[ROW][C]53[/C][C]257[/C][C]258.300935615494[/C][C]-1.30093561549421[/C][/ROW]
[ROW][C]54[/C][C]243[/C][C]251.664688011571[/C][C]-8.66468801157131[/C][/ROW]
[ROW][C]55[/C][C]227[/C][C]242.004060005047[/C][C]-15.0040600050474[/C][/ROW]
[ROW][C]56[/C][C]226[/C][C]234.842887633332[/C][C]-8.84288763333197[/C][/ROW]
[ROW][C]57[/C][C]226[/C][C]237.202346754043[/C][C]-11.2023467540430[/C][/ROW]
[ROW][C]58[/C][C]229[/C][C]234.800738038305[/C][C]-5.80073803830547[/C][/ROW]
[ROW][C]59[/C][C]224[/C][C]230.587396995002[/C][C]-6.58739699500185[/C][/ROW]
[ROW][C]60[/C][C]240[/C][C]235.978409347671[/C][C]4.02159065232914[/C][/ROW]
[ROW][C]61[/C][C]244[/C][C]238.356046961552[/C][C]5.64395303844844[/C][/ROW]
[ROW][C]62[/C][C]226[/C][C]224.717177026988[/C][C]1.28282297301206[/C][/ROW]
[ROW][C]63[/C][C]208[/C][C]208.508337883012[/C][C]-0.508337883012217[/C][/ROW]
[ROW][C]64[/C][C]199[/C][C]198.142749386038[/C][C]0.857250613961867[/C][/ROW]
[ROW][C]65[/C][C]193[/C][C]190.988079945307[/C][C]2.01192005469309[/C][/ROW]
[ROW][C]66[/C][C]180[/C][C]180.152171035643[/C][C]-0.152171035642596[/C][/ROW]
[ROW][C]67[/C][C]167[/C][C]168.571679084693[/C][C]-1.57167908469299[/C][/ROW]
[ROW][C]68[/C][C]164[/C][C]167.166604134288[/C][C]-3.16660413428838[/C][/ROW]
[ROW][C]69[/C][C]166[/C][C]166.528754607842[/C][C]-0.528754607841677[/C][/ROW]
[ROW][C]70[/C][C]173[/C][C]168.027157848556[/C][C]4.97284215144413[/C][/ROW]
[ROW][C]71[/C][C]169[/C][C]165.162675168869[/C][C]3.83732483113073[/C][/ROW]
[ROW][C]72[/C][C]191[/C][C]176.167341592844[/C][C]14.8326584071559[/C][/ROW]
[ROW][C]73[/C][C]193[/C][C]180.692380895518[/C][C]12.3076191044825[/C][/ROW]
[ROW][C]74[/C][C]166[/C][C]169.159491556411[/C][C]-3.15949155641064[/C][/ROW]
[ROW][C]75[/C][C]143[/C][C]154.659252026973[/C][C]-11.6592520269731[/C][/ROW]
[ROW][C]76[/C][C]147[/C][C]144.624333053009[/C][C]2.37566694699055[/C][/ROW]
[ROW][C]77[/C][C]139[/C][C]139.594335045257[/C][C]-0.594335045256713[/C][/ROW]
[ROW][C]78[/C][C]129[/C][C]129.203786698198[/C][C]-0.203786698197518[/C][/ROW]
[ROW][C]79[/C][C]115[/C][C]119.18633660126[/C][C]-4.1863366012599[/C][/ROW]
[ROW][C]80[/C][C]108[/C][C]115.623060155510[/C][C]-7.6230601555096[/C][/ROW]
[ROW][C]81[/C][C]106[/C][C]114.199953626781[/C][C]-8.19995362678145[/C][/ROW]
[ROW][C]82[/C][C]116[/C][C]114.786471522282[/C][C]1.21352847771753[/C][/ROW]
[ROW][C]83[/C][C]108[/C][C]109.975515644333[/C][C]-1.97551564433303[/C][/ROW]
[ROW][C]84[/C][C]135[/C][C]119.308809947941[/C][C]15.6911900520593[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79082&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79082&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
13371374.507612695369-3.50761269536900
14374376.585977222432-2.58597722243223
15369370.900310874623-1.90031087462319
16363364.512486632936-1.51248663293580
17357358.327983093222-1.32798309322249
18366367.275602408463-1.27560240846304
19362362.259368067115-0.259368067115133
20366363.3488973112182.65110268878215
21361364.141315833245-3.14131583324479
22362362.978837078825-0.978837078824654
23358363.534128010580-5.53412801057959
24363363.689075557080-0.689075557079548
25360355.2076617745654.79233822543478
26360359.2218744258340.778125574165642
27348354.678026407921-6.67802640792121
28345347.420129010354-2.42012901035366
29332340.998648946626-8.99864894662642
30333347.223273111413-14.2232731114133
31323339.459966416589-16.4599664165887
32327337.626876307825-10.6268763078251
33332329.4463950541162.55360494588433
34337329.2461571137177.75384288628317
35336326.6789730670719.32102693292939
36337332.1817431784184.81825682158205
37343328.51235391042314.4876460895769
38337330.6882180385436.31178196145709
39326321.6879742435314.31202575646864
40321320.0706179905640.92938200943621
41309309.799136350361-0.799136350361437
42302313.364980153577-11.3649801535774
43293304.905156915081-11.9051569150807
44287308.456452468431-21.4564524684312
45292308.030175139126-16.0301751391261
46292307.072034845111-15.0720348451113
47289299.842156329827-10.8421563298269
48302295.5471346782716.45286532172884
49310297.42783679095412.5721632090459
50295291.6372504166873.36274958331285
51276279.99921544962-3.99921544962001
52264272.489107781961-8.48910778196102
53257258.300935615494-1.30093561549421
54243251.664688011571-8.66468801157131
55227242.004060005047-15.0040600050474
56226234.842887633332-8.84288763333197
57226237.202346754043-11.2023467540430
58229234.800738038305-5.80073803830547
59224230.587396995002-6.58739699500185
60240235.9784093476714.02159065232914
61244238.3560469615525.64395303844844
62226224.7171770269881.28282297301206
63208208.508337883012-0.508337883012217
64199198.1427493860380.857250613961867
65193190.9880799453072.01192005469309
66180180.152171035643-0.152171035642596
67167168.571679084693-1.57167908469299
68164167.166604134288-3.16660413428838
69166166.528754607842-0.528754607841677
70173168.0271578485564.97284215144413
71169165.1626751688693.83732483113073
72191176.16734159284414.8326584071559
73193180.69238089551812.3076191044825
74166169.159491556411-3.15949155641064
75143154.659252026973-11.6592520269731
76147144.6243330530092.37566694699055
77139139.594335045257-0.594335045256713
78129129.203786698198-0.203786698197518
79115119.18633660126-4.1863366012599
80108115.623060155510-7.6230601555096
81106114.199953626781-8.19995362678145
82116114.7864715222821.21352847771753
83108109.975515644333-1.97551564433303
84135119.30880994794115.6911900520593







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85119.819716647760104.639012598616135.000420696903
86101.10225256807585.5872789328358116.617226203313
8786.366966031275970.5075809733362102.226351089216
8886.426231519952869.8606126703296102.991850369576
8979.676100465976662.508453302623396.8437476293298
9071.882057790694454.142682754190589.6214328271982
9162.554806860640844.400501771904880.7091119493768
9257.604208695657838.657792952693976.5506244386217
9355.434950134177535.21335206352375.656548204832
9458.374192450921335.522551810247081.2258330915955
9552.319601073566428.431756147734176.2074459993987
9660.709787265677834.594956609599486.8246179217563

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 119.819716647760 & 104.639012598616 & 135.000420696903 \tabularnewline
86 & 101.102252568075 & 85.5872789328358 & 116.617226203313 \tabularnewline
87 & 86.3669660312759 & 70.5075809733362 & 102.226351089216 \tabularnewline
88 & 86.4262315199528 & 69.8606126703296 & 102.991850369576 \tabularnewline
89 & 79.6761004659766 & 62.5084533026233 & 96.8437476293298 \tabularnewline
90 & 71.8820577906944 & 54.1426827541905 & 89.6214328271982 \tabularnewline
91 & 62.5548068606408 & 44.4005017719048 & 80.7091119493768 \tabularnewline
92 & 57.6042086956578 & 38.6577929526939 & 76.5506244386217 \tabularnewline
93 & 55.4349501341775 & 35.213352063523 & 75.656548204832 \tabularnewline
94 & 58.3741924509213 & 35.5225518102470 & 81.2258330915955 \tabularnewline
95 & 52.3196010735664 & 28.4317561477341 & 76.2074459993987 \tabularnewline
96 & 60.7097872656778 & 34.5949566095994 & 86.8246179217563 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79082&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]119.819716647760[/C][C]104.639012598616[/C][C]135.000420696903[/C][/ROW]
[ROW][C]86[/C][C]101.102252568075[/C][C]85.5872789328358[/C][C]116.617226203313[/C][/ROW]
[ROW][C]87[/C][C]86.3669660312759[/C][C]70.5075809733362[/C][C]102.226351089216[/C][/ROW]
[ROW][C]88[/C][C]86.4262315199528[/C][C]69.8606126703296[/C][C]102.991850369576[/C][/ROW]
[ROW][C]89[/C][C]79.6761004659766[/C][C]62.5084533026233[/C][C]96.8437476293298[/C][/ROW]
[ROW][C]90[/C][C]71.8820577906944[/C][C]54.1426827541905[/C][C]89.6214328271982[/C][/ROW]
[ROW][C]91[/C][C]62.5548068606408[/C][C]44.4005017719048[/C][C]80.7091119493768[/C][/ROW]
[ROW][C]92[/C][C]57.6042086956578[/C][C]38.6577929526939[/C][C]76.5506244386217[/C][/ROW]
[ROW][C]93[/C][C]55.4349501341775[/C][C]35.213352063523[/C][C]75.656548204832[/C][/ROW]
[ROW][C]94[/C][C]58.3741924509213[/C][C]35.5225518102470[/C][C]81.2258330915955[/C][/ROW]
[ROW][C]95[/C][C]52.3196010735664[/C][C]28.4317561477341[/C][C]76.2074459993987[/C][/ROW]
[ROW][C]96[/C][C]60.7097872656778[/C][C]34.5949566095994[/C][C]86.8246179217563[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79082&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79082&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
85119.819716647760104.639012598616135.000420696903
86101.10225256807585.5872789328358116.617226203313
8786.366966031275970.5075809733362102.226351089216
8886.426231519952869.8606126703296102.991850369576
8979.676100465976662.508453302623396.8437476293298
9071.882057790694454.142682754190589.6214328271982
9162.554806860640844.400501771904880.7091119493768
9257.604208695657838.657792952693976.5506244386217
9355.434950134177535.21335206352375.656548204832
9458.374192450921335.522551810247081.2258330915955
9552.319601073566428.431756147734176.2074459993987
9660.709787265677834.594956609599486.8246179217563



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; 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=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')