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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 computationThu, 29 Jul 2010 12:58:25 +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/t1280408287beok07dnsz0w69u.htm/, Retrieved Sun, 28 Apr 2024 22:49:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78177, Retrieved Sun, 28 Apr 2024 22:49:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsHabimana Christelle
Estimated Impact159
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Standard Deviation-Mean Plot] [] [2010-05-26 18:42:57] [5a3034bcadf7735f2909fd8cdba599d5]
- RMPD    [Exponential Smoothing] [Tijdreeks 2 - Sta...] [2010-07-29 12:58:25] [ac302f869d0778eba7cafda3b14e71eb] [Current]
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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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78177&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78177&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78177&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.17405321302253
beta0.155374088159449
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.17405321302253 \tabularnewline
beta & 0.155374088159449 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78177&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]0.17405321302253[/C][/ROW]
[ROW][C]beta[/C][C]0.155374088159449[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78177&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78177&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
alpha0.17405321302253
beta0.155374088159449
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13371374.488782051282-3.48878205128227
14374376.675603202716-2.67560320271582
15369371.098270113510-2.09827011351041
16363364.773012764285-1.77301276428483
17357358.623085947253-1.62308594725272
18366367.538694011388-1.53869401138763
19362362.469045974832-0.469045974831545
20366363.5728890370322.42711096296767
21361364.246454753421-3.24645475342118
22362363.178056418678-1.17805641867830
23358363.771144190277-5.77114419027686
24363364.158719151829-1.15871915182885
25360355.2278841937844.77211580621605
26360359.1365749412260.86342505877434
27348354.360166038926-6.36016603892637
28345347.15459982716-2.15459982716004
29332340.644611286876-8.64461128687589
30333347.80044107954-14.8004410795398
31323340.340011049965-17.3400110499645
32327339.477227717233-12.4772277172326
33332331.0452664044970.954733595502944
34337330.7047839853236.29521601467667
35336327.2953737659368.70462623406428
36337332.8939951991724.10600480082832
37343328.80230673740514.1976932625948
38337330.4023285379646.59767146203558
39326320.0919046508065.90809534919407
40321318.2612405141182.73875948588221
41309307.1408835083031.85911649169736
42302311.222919851203-9.22291985120336
43293302.968947385222-9.96894738522155
44287307.938081689494-20.9380816894941
45292309.431316986699-17.4313169866991
46292310.108167252241-18.1081672522406
47289303.587894503197-14.5878945031967
48302299.8508333662932.14916663370724
49310302.2175012176537.78249878234749
50295294.7139884338530.28601156614684
51276280.855022415635-4.85502241563495
52264272.361805144265-8.36180514426519
53257256.1111292037230.88887079627699
54243248.373188462661-5.37318846266055
55227237.779274345754-10.7792743457542
56226231.131712717639-5.13171271763855
57226236.284220987578-10.2842209875784
58229235.851008086266-6.85100808626552
59224232.707073538354-8.70707353835397
60240242.485982721617-2.48598272161672
61244247.241843180283-3.2418431802825
62226229.872796143532-3.8727961435317
63208209.176275068043-1.17627506804314
64199196.6589446371812.34105536281902
65193188.4331483008434.56685169915735
66180174.7841554614585.21584453854172
67167160.4754315525426.5245684474582
68164160.8794730351303.1205269648697
69166162.8110090623923.18899093760788
70173167.5212606381625.47873936183774
71169165.286542229583.71345777042015
72191182.9976629334048.00233706659606
73193189.8704762005353.12952379946466
74166174.177283218823-8.17728321882322
75143155.930358198954-12.9303581989537
76147144.9260726513672.07392734863311
77139139.138700169714-0.138700169714326
78129125.7259995406203.27400045938026
79115112.6269888327282.37301116727181
80108109.851370345917-1.85137034591713
81106111.194111504069-5.1941115040689
82116116.329792502009-0.329792502009028
83108111.462294570306-3.46229457030607
84135131.1090249185073.89097508149294

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 371 & 374.488782051282 & -3.48878205128227 \tabularnewline
14 & 374 & 376.675603202716 & -2.67560320271582 \tabularnewline
15 & 369 & 371.098270113510 & -2.09827011351041 \tabularnewline
16 & 363 & 364.773012764285 & -1.77301276428483 \tabularnewline
17 & 357 & 358.623085947253 & -1.62308594725272 \tabularnewline
18 & 366 & 367.538694011388 & -1.53869401138763 \tabularnewline
19 & 362 & 362.469045974832 & -0.469045974831545 \tabularnewline
20 & 366 & 363.572889037032 & 2.42711096296767 \tabularnewline
21 & 361 & 364.246454753421 & -3.24645475342118 \tabularnewline
22 & 362 & 363.178056418678 & -1.17805641867830 \tabularnewline
23 & 358 & 363.771144190277 & -5.77114419027686 \tabularnewline
24 & 363 & 364.158719151829 & -1.15871915182885 \tabularnewline
25 & 360 & 355.227884193784 & 4.77211580621605 \tabularnewline
26 & 360 & 359.136574941226 & 0.86342505877434 \tabularnewline
27 & 348 & 354.360166038926 & -6.36016603892637 \tabularnewline
28 & 345 & 347.15459982716 & -2.15459982716004 \tabularnewline
29 & 332 & 340.644611286876 & -8.64461128687589 \tabularnewline
30 & 333 & 347.80044107954 & -14.8004410795398 \tabularnewline
31 & 323 & 340.340011049965 & -17.3400110499645 \tabularnewline
32 & 327 & 339.477227717233 & -12.4772277172326 \tabularnewline
33 & 332 & 331.045266404497 & 0.954733595502944 \tabularnewline
34 & 337 & 330.704783985323 & 6.29521601467667 \tabularnewline
35 & 336 & 327.295373765936 & 8.70462623406428 \tabularnewline
36 & 337 & 332.893995199172 & 4.10600480082832 \tabularnewline
37 & 343 & 328.802306737405 & 14.1976932625948 \tabularnewline
38 & 337 & 330.402328537964 & 6.59767146203558 \tabularnewline
39 & 326 & 320.091904650806 & 5.90809534919407 \tabularnewline
40 & 321 & 318.261240514118 & 2.73875948588221 \tabularnewline
41 & 309 & 307.140883508303 & 1.85911649169736 \tabularnewline
42 & 302 & 311.222919851203 & -9.22291985120336 \tabularnewline
43 & 293 & 302.968947385222 & -9.96894738522155 \tabularnewline
44 & 287 & 307.938081689494 & -20.9380816894941 \tabularnewline
45 & 292 & 309.431316986699 & -17.4313169866991 \tabularnewline
46 & 292 & 310.108167252241 & -18.1081672522406 \tabularnewline
47 & 289 & 303.587894503197 & -14.5878945031967 \tabularnewline
48 & 302 & 299.850833366293 & 2.14916663370724 \tabularnewline
49 & 310 & 302.217501217653 & 7.78249878234749 \tabularnewline
50 & 295 & 294.713988433853 & 0.28601156614684 \tabularnewline
51 & 276 & 280.855022415635 & -4.85502241563495 \tabularnewline
52 & 264 & 272.361805144265 & -8.36180514426519 \tabularnewline
53 & 257 & 256.111129203723 & 0.88887079627699 \tabularnewline
54 & 243 & 248.373188462661 & -5.37318846266055 \tabularnewline
55 & 227 & 237.779274345754 & -10.7792743457542 \tabularnewline
56 & 226 & 231.131712717639 & -5.13171271763855 \tabularnewline
57 & 226 & 236.284220987578 & -10.2842209875784 \tabularnewline
58 & 229 & 235.851008086266 & -6.85100808626552 \tabularnewline
59 & 224 & 232.707073538354 & -8.70707353835397 \tabularnewline
60 & 240 & 242.485982721617 & -2.48598272161672 \tabularnewline
61 & 244 & 247.241843180283 & -3.2418431802825 \tabularnewline
62 & 226 & 229.872796143532 & -3.8727961435317 \tabularnewline
63 & 208 & 209.176275068043 & -1.17627506804314 \tabularnewline
64 & 199 & 196.658944637181 & 2.34105536281902 \tabularnewline
65 & 193 & 188.433148300843 & 4.56685169915735 \tabularnewline
66 & 180 & 174.784155461458 & 5.21584453854172 \tabularnewline
67 & 167 & 160.475431552542 & 6.5245684474582 \tabularnewline
68 & 164 & 160.879473035130 & 3.1205269648697 \tabularnewline
69 & 166 & 162.811009062392 & 3.18899093760788 \tabularnewline
70 & 173 & 167.521260638162 & 5.47873936183774 \tabularnewline
71 & 169 & 165.28654222958 & 3.71345777042015 \tabularnewline
72 & 191 & 182.997662933404 & 8.00233706659606 \tabularnewline
73 & 193 & 189.870476200535 & 3.12952379946466 \tabularnewline
74 & 166 & 174.177283218823 & -8.17728321882322 \tabularnewline
75 & 143 & 155.930358198954 & -12.9303581989537 \tabularnewline
76 & 147 & 144.926072651367 & 2.07392734863311 \tabularnewline
77 & 139 & 139.138700169714 & -0.138700169714326 \tabularnewline
78 & 129 & 125.725999540620 & 3.27400045938026 \tabularnewline
79 & 115 & 112.626988832728 & 2.37301116727181 \tabularnewline
80 & 108 & 109.851370345917 & -1.85137034591713 \tabularnewline
81 & 106 & 111.194111504069 & -5.1941115040689 \tabularnewline
82 & 116 & 116.329792502009 & -0.329792502009028 \tabularnewline
83 & 108 & 111.462294570306 & -3.46229457030607 \tabularnewline
84 & 135 & 131.109024918507 & 3.89097508149294 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78177&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]374.488782051282[/C][C]-3.48878205128227[/C][/ROW]
[ROW][C]14[/C][C]374[/C][C]376.675603202716[/C][C]-2.67560320271582[/C][/ROW]
[ROW][C]15[/C][C]369[/C][C]371.098270113510[/C][C]-2.09827011351041[/C][/ROW]
[ROW][C]16[/C][C]363[/C][C]364.773012764285[/C][C]-1.77301276428483[/C][/ROW]
[ROW][C]17[/C][C]357[/C][C]358.623085947253[/C][C]-1.62308594725272[/C][/ROW]
[ROW][C]18[/C][C]366[/C][C]367.538694011388[/C][C]-1.53869401138763[/C][/ROW]
[ROW][C]19[/C][C]362[/C][C]362.469045974832[/C][C]-0.469045974831545[/C][/ROW]
[ROW][C]20[/C][C]366[/C][C]363.572889037032[/C][C]2.42711096296767[/C][/ROW]
[ROW][C]21[/C][C]361[/C][C]364.246454753421[/C][C]-3.24645475342118[/C][/ROW]
[ROW][C]22[/C][C]362[/C][C]363.178056418678[/C][C]-1.17805641867830[/C][/ROW]
[ROW][C]23[/C][C]358[/C][C]363.771144190277[/C][C]-5.77114419027686[/C][/ROW]
[ROW][C]24[/C][C]363[/C][C]364.158719151829[/C][C]-1.15871915182885[/C][/ROW]
[ROW][C]25[/C][C]360[/C][C]355.227884193784[/C][C]4.77211580621605[/C][/ROW]
[ROW][C]26[/C][C]360[/C][C]359.136574941226[/C][C]0.86342505877434[/C][/ROW]
[ROW][C]27[/C][C]348[/C][C]354.360166038926[/C][C]-6.36016603892637[/C][/ROW]
[ROW][C]28[/C][C]345[/C][C]347.15459982716[/C][C]-2.15459982716004[/C][/ROW]
[ROW][C]29[/C][C]332[/C][C]340.644611286876[/C][C]-8.64461128687589[/C][/ROW]
[ROW][C]30[/C][C]333[/C][C]347.80044107954[/C][C]-14.8004410795398[/C][/ROW]
[ROW][C]31[/C][C]323[/C][C]340.340011049965[/C][C]-17.3400110499645[/C][/ROW]
[ROW][C]32[/C][C]327[/C][C]339.477227717233[/C][C]-12.4772277172326[/C][/ROW]
[ROW][C]33[/C][C]332[/C][C]331.045266404497[/C][C]0.954733595502944[/C][/ROW]
[ROW][C]34[/C][C]337[/C][C]330.704783985323[/C][C]6.29521601467667[/C][/ROW]
[ROW][C]35[/C][C]336[/C][C]327.295373765936[/C][C]8.70462623406428[/C][/ROW]
[ROW][C]36[/C][C]337[/C][C]332.893995199172[/C][C]4.10600480082832[/C][/ROW]
[ROW][C]37[/C][C]343[/C][C]328.802306737405[/C][C]14.1976932625948[/C][/ROW]
[ROW][C]38[/C][C]337[/C][C]330.402328537964[/C][C]6.59767146203558[/C][/ROW]
[ROW][C]39[/C][C]326[/C][C]320.091904650806[/C][C]5.90809534919407[/C][/ROW]
[ROW][C]40[/C][C]321[/C][C]318.261240514118[/C][C]2.73875948588221[/C][/ROW]
[ROW][C]41[/C][C]309[/C][C]307.140883508303[/C][C]1.85911649169736[/C][/ROW]
[ROW][C]42[/C][C]302[/C][C]311.222919851203[/C][C]-9.22291985120336[/C][/ROW]
[ROW][C]43[/C][C]293[/C][C]302.968947385222[/C][C]-9.96894738522155[/C][/ROW]
[ROW][C]44[/C][C]287[/C][C]307.938081689494[/C][C]-20.9380816894941[/C][/ROW]
[ROW][C]45[/C][C]292[/C][C]309.431316986699[/C][C]-17.4313169866991[/C][/ROW]
[ROW][C]46[/C][C]292[/C][C]310.108167252241[/C][C]-18.1081672522406[/C][/ROW]
[ROW][C]47[/C][C]289[/C][C]303.587894503197[/C][C]-14.5878945031967[/C][/ROW]
[ROW][C]48[/C][C]302[/C][C]299.850833366293[/C][C]2.14916663370724[/C][/ROW]
[ROW][C]49[/C][C]310[/C][C]302.217501217653[/C][C]7.78249878234749[/C][/ROW]
[ROW][C]50[/C][C]295[/C][C]294.713988433853[/C][C]0.28601156614684[/C][/ROW]
[ROW][C]51[/C][C]276[/C][C]280.855022415635[/C][C]-4.85502241563495[/C][/ROW]
[ROW][C]52[/C][C]264[/C][C]272.361805144265[/C][C]-8.36180514426519[/C][/ROW]
[ROW][C]53[/C][C]257[/C][C]256.111129203723[/C][C]0.88887079627699[/C][/ROW]
[ROW][C]54[/C][C]243[/C][C]248.373188462661[/C][C]-5.37318846266055[/C][/ROW]
[ROW][C]55[/C][C]227[/C][C]237.779274345754[/C][C]-10.7792743457542[/C][/ROW]
[ROW][C]56[/C][C]226[/C][C]231.131712717639[/C][C]-5.13171271763855[/C][/ROW]
[ROW][C]57[/C][C]226[/C][C]236.284220987578[/C][C]-10.2842209875784[/C][/ROW]
[ROW][C]58[/C][C]229[/C][C]235.851008086266[/C][C]-6.85100808626552[/C][/ROW]
[ROW][C]59[/C][C]224[/C][C]232.707073538354[/C][C]-8.70707353835397[/C][/ROW]
[ROW][C]60[/C][C]240[/C][C]242.485982721617[/C][C]-2.48598272161672[/C][/ROW]
[ROW][C]61[/C][C]244[/C][C]247.241843180283[/C][C]-3.2418431802825[/C][/ROW]
[ROW][C]62[/C][C]226[/C][C]229.872796143532[/C][C]-3.8727961435317[/C][/ROW]
[ROW][C]63[/C][C]208[/C][C]209.176275068043[/C][C]-1.17627506804314[/C][/ROW]
[ROW][C]64[/C][C]199[/C][C]196.658944637181[/C][C]2.34105536281902[/C][/ROW]
[ROW][C]65[/C][C]193[/C][C]188.433148300843[/C][C]4.56685169915735[/C][/ROW]
[ROW][C]66[/C][C]180[/C][C]174.784155461458[/C][C]5.21584453854172[/C][/ROW]
[ROW][C]67[/C][C]167[/C][C]160.475431552542[/C][C]6.5245684474582[/C][/ROW]
[ROW][C]68[/C][C]164[/C][C]160.879473035130[/C][C]3.1205269648697[/C][/ROW]
[ROW][C]69[/C][C]166[/C][C]162.811009062392[/C][C]3.18899093760788[/C][/ROW]
[ROW][C]70[/C][C]173[/C][C]167.521260638162[/C][C]5.47873936183774[/C][/ROW]
[ROW][C]71[/C][C]169[/C][C]165.28654222958[/C][C]3.71345777042015[/C][/ROW]
[ROW][C]72[/C][C]191[/C][C]182.997662933404[/C][C]8.00233706659606[/C][/ROW]
[ROW][C]73[/C][C]193[/C][C]189.870476200535[/C][C]3.12952379946466[/C][/ROW]
[ROW][C]74[/C][C]166[/C][C]174.177283218823[/C][C]-8.17728321882322[/C][/ROW]
[ROW][C]75[/C][C]143[/C][C]155.930358198954[/C][C]-12.9303581989537[/C][/ROW]
[ROW][C]76[/C][C]147[/C][C]144.926072651367[/C][C]2.07392734863311[/C][/ROW]
[ROW][C]77[/C][C]139[/C][C]139.138700169714[/C][C]-0.138700169714326[/C][/ROW]
[ROW][C]78[/C][C]129[/C][C]125.725999540620[/C][C]3.27400045938026[/C][/ROW]
[ROW][C]79[/C][C]115[/C][C]112.626988832728[/C][C]2.37301116727181[/C][/ROW]
[ROW][C]80[/C][C]108[/C][C]109.851370345917[/C][C]-1.85137034591713[/C][/ROW]
[ROW][C]81[/C][C]106[/C][C]111.194111504069[/C][C]-5.1941115040689[/C][/ROW]
[ROW][C]82[/C][C]116[/C][C]116.329792502009[/C][C]-0.329792502009028[/C][/ROW]
[ROW][C]83[/C][C]108[/C][C]111.462294570306[/C][C]-3.46229457030607[/C][/ROW]
[ROW][C]84[/C][C]135[/C][C]131.109024918507[/C][C]3.89097508149294[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78177&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78177&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
13371374.488782051282-3.48878205128227
14374376.675603202716-2.67560320271582
15369371.098270113510-2.09827011351041
16363364.773012764285-1.77301276428483
17357358.623085947253-1.62308594725272
18366367.538694011388-1.53869401138763
19362362.469045974832-0.469045974831545
20366363.5728890370322.42711096296767
21361364.246454753421-3.24645475342118
22362363.178056418678-1.17805641867830
23358363.771144190277-5.77114419027686
24363364.158719151829-1.15871915182885
25360355.2278841937844.77211580621605
26360359.1365749412260.86342505877434
27348354.360166038926-6.36016603892637
28345347.15459982716-2.15459982716004
29332340.644611286876-8.64461128687589
30333347.80044107954-14.8004410795398
31323340.340011049965-17.3400110499645
32327339.477227717233-12.4772277172326
33332331.0452664044970.954733595502944
34337330.7047839853236.29521601467667
35336327.2953737659368.70462623406428
36337332.8939951991724.10600480082832
37343328.80230673740514.1976932625948
38337330.4023285379646.59767146203558
39326320.0919046508065.90809534919407
40321318.2612405141182.73875948588221
41309307.1408835083031.85911649169736
42302311.222919851203-9.22291985120336
43293302.968947385222-9.96894738522155
44287307.938081689494-20.9380816894941
45292309.431316986699-17.4313169866991
46292310.108167252241-18.1081672522406
47289303.587894503197-14.5878945031967
48302299.8508333662932.14916663370724
49310302.2175012176537.78249878234749
50295294.7139884338530.28601156614684
51276280.855022415635-4.85502241563495
52264272.361805144265-8.36180514426519
53257256.1111292037230.88887079627699
54243248.373188462661-5.37318846266055
55227237.779274345754-10.7792743457542
56226231.131712717639-5.13171271763855
57226236.284220987578-10.2842209875784
58229235.851008086266-6.85100808626552
59224232.707073538354-8.70707353835397
60240242.485982721617-2.48598272161672
61244247.241843180283-3.2418431802825
62226229.872796143532-3.8727961435317
63208209.176275068043-1.17627506804314
64199196.6589446371812.34105536281902
65193188.4331483008434.56685169915735
66180174.7841554614585.21584453854172
67167160.4754315525426.5245684474582
68164160.8794730351303.1205269648697
69166162.8110090623923.18899093760788
70173167.5212606381625.47873936183774
71169165.286542229583.71345777042015
72191182.9976629334048.00233706659606
73193189.8704762005353.12952379946466
74166174.177283218823-8.17728321882322
75143155.930358198954-12.9303581989537
76147144.9260726513672.07392734863311
77139139.138700169714-0.138700169714326
78129125.7259995406203.27400045938026
79115112.6269888327282.37301116727181
80108109.851370345917-1.85137034591713
81106111.194111504069-5.1941115040689
82116116.329792502009-0.329792502009028
83108111.462294570306-3.46229457030607
84135131.1090249185073.89097508149294







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85132.772559242198118.798813406849146.746305077547
86106.64221010528792.3887165158134120.895703694760
8785.560290148299570.9546327335236100.165947563075
8889.216506404841474.1818586857312104.251154123951
8981.20175162779665.65846039350896.745042862084
9070.596756259692354.463850386442186.7296621329425
9156.060041002123539.256574308300772.8635076959463
9249.194418726422831.640586160040766.7482512928049
9347.960678562997529.578679249578366.3426778764167
9458.020754271562138.735405215109677.3061033280146
9550.634970727028130.374096646439170.895844807617
9677.06295904932255.757595829506998.3683222691372

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 132.772559242198 & 118.798813406849 & 146.746305077547 \tabularnewline
86 & 106.642210105287 & 92.3887165158134 & 120.895703694760 \tabularnewline
87 & 85.5602901482995 & 70.9546327335236 & 100.165947563075 \tabularnewline
88 & 89.2165064048414 & 74.1818586857312 & 104.251154123951 \tabularnewline
89 & 81.201751627796 & 65.658460393508 & 96.745042862084 \tabularnewline
90 & 70.5967562596923 & 54.4638503864421 & 86.7296621329425 \tabularnewline
91 & 56.0600410021235 & 39.2565743083007 & 72.8635076959463 \tabularnewline
92 & 49.1944187264228 & 31.6405861600407 & 66.7482512928049 \tabularnewline
93 & 47.9606785629975 & 29.5786792495783 & 66.3426778764167 \tabularnewline
94 & 58.0207542715621 & 38.7354052151096 & 77.3061033280146 \tabularnewline
95 & 50.6349707270281 & 30.3740966464391 & 70.895844807617 \tabularnewline
96 & 77.062959049322 & 55.7575958295069 & 98.3683222691372 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78177&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]132.772559242198[/C][C]118.798813406849[/C][C]146.746305077547[/C][/ROW]
[ROW][C]86[/C][C]106.642210105287[/C][C]92.3887165158134[/C][C]120.895703694760[/C][/ROW]
[ROW][C]87[/C][C]85.5602901482995[/C][C]70.9546327335236[/C][C]100.165947563075[/C][/ROW]
[ROW][C]88[/C][C]89.2165064048414[/C][C]74.1818586857312[/C][C]104.251154123951[/C][/ROW]
[ROW][C]89[/C][C]81.201751627796[/C][C]65.658460393508[/C][C]96.745042862084[/C][/ROW]
[ROW][C]90[/C][C]70.5967562596923[/C][C]54.4638503864421[/C][C]86.7296621329425[/C][/ROW]
[ROW][C]91[/C][C]56.0600410021235[/C][C]39.2565743083007[/C][C]72.8635076959463[/C][/ROW]
[ROW][C]92[/C][C]49.1944187264228[/C][C]31.6405861600407[/C][C]66.7482512928049[/C][/ROW]
[ROW][C]93[/C][C]47.9606785629975[/C][C]29.5786792495783[/C][C]66.3426778764167[/C][/ROW]
[ROW][C]94[/C][C]58.0207542715621[/C][C]38.7354052151096[/C][C]77.3061033280146[/C][/ROW]
[ROW][C]95[/C][C]50.6349707270281[/C][C]30.3740966464391[/C][C]70.895844807617[/C][/ROW]
[ROW][C]96[/C][C]77.062959049322[/C][C]55.7575958295069[/C][C]98.3683222691372[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78177&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78177&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
85132.772559242198118.798813406849146.746305077547
86106.64221010528792.3887165158134120.895703694760
8785.560290148299570.9546327335236100.165947563075
8889.216506404841474.1818586857312104.251154123951
8981.20175162779665.65846039350896.745042862084
9070.596756259692354.463850386442186.7296621329425
9156.060041002123539.256574308300772.8635076959463
9249.194418726422831.640586160040766.7482512928049
9347.960678562997529.578679249578366.3426778764167
9458.020754271562138.735405215109677.3061033280146
9550.634970727028130.374096646439170.895844807617
9677.06295904932255.757595829506998.3683222691372



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')