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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 computationSat, 14 Aug 2010 11:49:27 +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/14/t12817865605vas2ug2ze3kquu.htm/, Retrieved Mon, 06 May 2024 00:17:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78795, Retrieved Mon, 06 May 2024 00:17:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsmattias debbaut
Estimated Impact166
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2010-08-14 11:49:27] [59fa324537f53fb6459bc6951db20f7b] [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'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 & 3 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78795&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78795&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78795&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999933983418648
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999933983418648 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78795&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]0.999933983418648[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78795&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78795&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
alpha0.999933983418648
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2375376-1
3374375.000066016581-1.00006601658134
4372374.00006602094-2.00006602093953
5370372.000132037521-2.00013203752115
6369370.000132041879-1.0001320418794
7370369.0000660252980.999933974701719
8372369.9999339877772.00006601222259
9373371.9998679624791.00013203752059
10373372.9999339747026.602529799693e-05
11374372.9999999956411.00000000435875
12376373.9999339834182.00006601658163
13371375.999867962479-4.99986796247913
14374371.000330074192.99966992580988
15369373.999801972046-4.99980197204633
16363369.000330069834-6.00033006983364
17357363.000396121278-6.00039612127819
18366357.0003961256398.9996038743613
19362365.999405876919-3.99940587691867
20366362.0002640271033.99973597289659
21361365.999735951105-4.99973595110475
22362361.0003300654750.999669934524832
23358361.999934005208-3.99993400520844
24363358.0002640619694.99973593803134
25360362.999669934526-2.99966993452568
26360360.000198027954-0.000198027954240843
27348360.000000013073-12.0000000130731
28345348.000792198977-3.00079219897708
29332345.000198102042-13.0001981020423
30333332.0008582286360.999141771364407
31323332.999934040076-9.99993404007597
32327323.0006601614593.99933983854095
33332326.9997359772565.00026402274381
34337331.9996698996635.00033010033661
35336336.999669895301-0.999669895301167
36337336.0000659947890.99993400521106
37343336.9999339877756.00006601222458
38337342.999603896154-5.99960389615399
39326337.000396073339-11.0003960733387
40321326.000726208542-5.00072620854229
41309321.000330130849-12.0003301308486
42302309.00079222077-7.00079222077034
43293302.000462168369-9.00046216836915
44287293.000594179743-6.00059417974296
45292287.0003961387144.99960386128618
46292291.9996699432450.000330056755046826
47289291.999999978211-2.99999997821078
48302289.00019804974312.9998019502574
49310301.9991417975178.00085820248302
50295309.999471810694-14.9994718106936
51276295.000990213851-19.000990213851
52264276.001254380416-12.0012543804162
53257264.000792281786-7.00079228178612
54243257.000462168373-14.0004621683732
55227243.00092426265-16.0009242626497
56226227.001056326318-1.00105632631829
57226226.000066086316-6.60863163943759e-05
58229226.0000000043632.99999999563721
59224228.999801950256-4.99980195025623
60240224.00033006983215.9996699301678
61244239.9989437564884.00105624351156
62226243.999735863945-17.999735863945
63208226.001188281027-18.001188281027
64199208.001188376911-9.00118837691059
65193199.000594227685-6.00059422768476
66180193.000396138717-13.000396138717
67167180.000858241709-13.0008582417093
68164167.000858272216-3.00085827221577
69166164.0001981064041.99980189359576
70173165.9998679799167.00013202008441
71169172.999537875215-3.99953787521503
72191169.00026403581821.9997359641825
73193190.9985476526412.00145234735899
74166192.999867870958-26.9998678709583
75143166.001782438974-23.0017824389738
76147143.0015184990423.99848150095838
77139146.999736033921-7.9997360339207
78129139.000528115225-10.0005281152247
79115129.000660200678-14.0006602006779
80108115.000924275723-7.00092427572312
81106108.000462177087-2.00046217708699
82116106.0001320636749.99986793632594
83108115.999339842905-7.99933984290487
84135108.0005280890726.9994719109305

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 375 & 376 & -1 \tabularnewline
3 & 374 & 375.000066016581 & -1.00006601658134 \tabularnewline
4 & 372 & 374.00006602094 & -2.00006602093953 \tabularnewline
5 & 370 & 372.000132037521 & -2.00013203752115 \tabularnewline
6 & 369 & 370.000132041879 & -1.0001320418794 \tabularnewline
7 & 370 & 369.000066025298 & 0.999933974701719 \tabularnewline
8 & 372 & 369.999933987777 & 2.00006601222259 \tabularnewline
9 & 373 & 371.999867962479 & 1.00013203752059 \tabularnewline
10 & 373 & 372.999933974702 & 6.602529799693e-05 \tabularnewline
11 & 374 & 372.999999995641 & 1.00000000435875 \tabularnewline
12 & 376 & 373.999933983418 & 2.00006601658163 \tabularnewline
13 & 371 & 375.999867962479 & -4.99986796247913 \tabularnewline
14 & 374 & 371.00033007419 & 2.99966992580988 \tabularnewline
15 & 369 & 373.999801972046 & -4.99980197204633 \tabularnewline
16 & 363 & 369.000330069834 & -6.00033006983364 \tabularnewline
17 & 357 & 363.000396121278 & -6.00039612127819 \tabularnewline
18 & 366 & 357.000396125639 & 8.9996038743613 \tabularnewline
19 & 362 & 365.999405876919 & -3.99940587691867 \tabularnewline
20 & 366 & 362.000264027103 & 3.99973597289659 \tabularnewline
21 & 361 & 365.999735951105 & -4.99973595110475 \tabularnewline
22 & 362 & 361.000330065475 & 0.999669934524832 \tabularnewline
23 & 358 & 361.999934005208 & -3.99993400520844 \tabularnewline
24 & 363 & 358.000264061969 & 4.99973593803134 \tabularnewline
25 & 360 & 362.999669934526 & -2.99966993452568 \tabularnewline
26 & 360 & 360.000198027954 & -0.000198027954240843 \tabularnewline
27 & 348 & 360.000000013073 & -12.0000000130731 \tabularnewline
28 & 345 & 348.000792198977 & -3.00079219897708 \tabularnewline
29 & 332 & 345.000198102042 & -13.0001981020423 \tabularnewline
30 & 333 & 332.000858228636 & 0.999141771364407 \tabularnewline
31 & 323 & 332.999934040076 & -9.99993404007597 \tabularnewline
32 & 327 & 323.000660161459 & 3.99933983854095 \tabularnewline
33 & 332 & 326.999735977256 & 5.00026402274381 \tabularnewline
34 & 337 & 331.999669899663 & 5.00033010033661 \tabularnewline
35 & 336 & 336.999669895301 & -0.999669895301167 \tabularnewline
36 & 337 & 336.000065994789 & 0.99993400521106 \tabularnewline
37 & 343 & 336.999933987775 & 6.00006601222458 \tabularnewline
38 & 337 & 342.999603896154 & -5.99960389615399 \tabularnewline
39 & 326 & 337.000396073339 & -11.0003960733387 \tabularnewline
40 & 321 & 326.000726208542 & -5.00072620854229 \tabularnewline
41 & 309 & 321.000330130849 & -12.0003301308486 \tabularnewline
42 & 302 & 309.00079222077 & -7.00079222077034 \tabularnewline
43 & 293 & 302.000462168369 & -9.00046216836915 \tabularnewline
44 & 287 & 293.000594179743 & -6.00059417974296 \tabularnewline
45 & 292 & 287.000396138714 & 4.99960386128618 \tabularnewline
46 & 292 & 291.999669943245 & 0.000330056755046826 \tabularnewline
47 & 289 & 291.999999978211 & -2.99999997821078 \tabularnewline
48 & 302 & 289.000198049743 & 12.9998019502574 \tabularnewline
49 & 310 & 301.999141797517 & 8.00085820248302 \tabularnewline
50 & 295 & 309.999471810694 & -14.9994718106936 \tabularnewline
51 & 276 & 295.000990213851 & -19.000990213851 \tabularnewline
52 & 264 & 276.001254380416 & -12.0012543804162 \tabularnewline
53 & 257 & 264.000792281786 & -7.00079228178612 \tabularnewline
54 & 243 & 257.000462168373 & -14.0004621683732 \tabularnewline
55 & 227 & 243.00092426265 & -16.0009242626497 \tabularnewline
56 & 226 & 227.001056326318 & -1.00105632631829 \tabularnewline
57 & 226 & 226.000066086316 & -6.60863163943759e-05 \tabularnewline
58 & 229 & 226.000000004363 & 2.99999999563721 \tabularnewline
59 & 224 & 228.999801950256 & -4.99980195025623 \tabularnewline
60 & 240 & 224.000330069832 & 15.9996699301678 \tabularnewline
61 & 244 & 239.998943756488 & 4.00105624351156 \tabularnewline
62 & 226 & 243.999735863945 & -17.999735863945 \tabularnewline
63 & 208 & 226.001188281027 & -18.001188281027 \tabularnewline
64 & 199 & 208.001188376911 & -9.00118837691059 \tabularnewline
65 & 193 & 199.000594227685 & -6.00059422768476 \tabularnewline
66 & 180 & 193.000396138717 & -13.000396138717 \tabularnewline
67 & 167 & 180.000858241709 & -13.0008582417093 \tabularnewline
68 & 164 & 167.000858272216 & -3.00085827221577 \tabularnewline
69 & 166 & 164.000198106404 & 1.99980189359576 \tabularnewline
70 & 173 & 165.999867979916 & 7.00013202008441 \tabularnewline
71 & 169 & 172.999537875215 & -3.99953787521503 \tabularnewline
72 & 191 & 169.000264035818 & 21.9997359641825 \tabularnewline
73 & 193 & 190.998547652641 & 2.00145234735899 \tabularnewline
74 & 166 & 192.999867870958 & -26.9998678709583 \tabularnewline
75 & 143 & 166.001782438974 & -23.0017824389738 \tabularnewline
76 & 147 & 143.001518499042 & 3.99848150095838 \tabularnewline
77 & 139 & 146.999736033921 & -7.9997360339207 \tabularnewline
78 & 129 & 139.000528115225 & -10.0005281152247 \tabularnewline
79 & 115 & 129.000660200678 & -14.0006602006779 \tabularnewline
80 & 108 & 115.000924275723 & -7.00092427572312 \tabularnewline
81 & 106 & 108.000462177087 & -2.00046217708699 \tabularnewline
82 & 116 & 106.000132063674 & 9.99986793632594 \tabularnewline
83 & 108 & 115.999339842905 & -7.99933984290487 \tabularnewline
84 & 135 & 108.00052808907 & 26.9994719109305 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78795&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]2[/C][C]375[/C][C]376[/C][C]-1[/C][/ROW]
[ROW][C]3[/C][C]374[/C][C]375.000066016581[/C][C]-1.00006601658134[/C][/ROW]
[ROW][C]4[/C][C]372[/C][C]374.00006602094[/C][C]-2.00006602093953[/C][/ROW]
[ROW][C]5[/C][C]370[/C][C]372.000132037521[/C][C]-2.00013203752115[/C][/ROW]
[ROW][C]6[/C][C]369[/C][C]370.000132041879[/C][C]-1.0001320418794[/C][/ROW]
[ROW][C]7[/C][C]370[/C][C]369.000066025298[/C][C]0.999933974701719[/C][/ROW]
[ROW][C]8[/C][C]372[/C][C]369.999933987777[/C][C]2.00006601222259[/C][/ROW]
[ROW][C]9[/C][C]373[/C][C]371.999867962479[/C][C]1.00013203752059[/C][/ROW]
[ROW][C]10[/C][C]373[/C][C]372.999933974702[/C][C]6.602529799693e-05[/C][/ROW]
[ROW][C]11[/C][C]374[/C][C]372.999999995641[/C][C]1.00000000435875[/C][/ROW]
[ROW][C]12[/C][C]376[/C][C]373.999933983418[/C][C]2.00006601658163[/C][/ROW]
[ROW][C]13[/C][C]371[/C][C]375.999867962479[/C][C]-4.99986796247913[/C][/ROW]
[ROW][C]14[/C][C]374[/C][C]371.00033007419[/C][C]2.99966992580988[/C][/ROW]
[ROW][C]15[/C][C]369[/C][C]373.999801972046[/C][C]-4.99980197204633[/C][/ROW]
[ROW][C]16[/C][C]363[/C][C]369.000330069834[/C][C]-6.00033006983364[/C][/ROW]
[ROW][C]17[/C][C]357[/C][C]363.000396121278[/C][C]-6.00039612127819[/C][/ROW]
[ROW][C]18[/C][C]366[/C][C]357.000396125639[/C][C]8.9996038743613[/C][/ROW]
[ROW][C]19[/C][C]362[/C][C]365.999405876919[/C][C]-3.99940587691867[/C][/ROW]
[ROW][C]20[/C][C]366[/C][C]362.000264027103[/C][C]3.99973597289659[/C][/ROW]
[ROW][C]21[/C][C]361[/C][C]365.999735951105[/C][C]-4.99973595110475[/C][/ROW]
[ROW][C]22[/C][C]362[/C][C]361.000330065475[/C][C]0.999669934524832[/C][/ROW]
[ROW][C]23[/C][C]358[/C][C]361.999934005208[/C][C]-3.99993400520844[/C][/ROW]
[ROW][C]24[/C][C]363[/C][C]358.000264061969[/C][C]4.99973593803134[/C][/ROW]
[ROW][C]25[/C][C]360[/C][C]362.999669934526[/C][C]-2.99966993452568[/C][/ROW]
[ROW][C]26[/C][C]360[/C][C]360.000198027954[/C][C]-0.000198027954240843[/C][/ROW]
[ROW][C]27[/C][C]348[/C][C]360.000000013073[/C][C]-12.0000000130731[/C][/ROW]
[ROW][C]28[/C][C]345[/C][C]348.000792198977[/C][C]-3.00079219897708[/C][/ROW]
[ROW][C]29[/C][C]332[/C][C]345.000198102042[/C][C]-13.0001981020423[/C][/ROW]
[ROW][C]30[/C][C]333[/C][C]332.000858228636[/C][C]0.999141771364407[/C][/ROW]
[ROW][C]31[/C][C]323[/C][C]332.999934040076[/C][C]-9.99993404007597[/C][/ROW]
[ROW][C]32[/C][C]327[/C][C]323.000660161459[/C][C]3.99933983854095[/C][/ROW]
[ROW][C]33[/C][C]332[/C][C]326.999735977256[/C][C]5.00026402274381[/C][/ROW]
[ROW][C]34[/C][C]337[/C][C]331.999669899663[/C][C]5.00033010033661[/C][/ROW]
[ROW][C]35[/C][C]336[/C][C]336.999669895301[/C][C]-0.999669895301167[/C][/ROW]
[ROW][C]36[/C][C]337[/C][C]336.000065994789[/C][C]0.99993400521106[/C][/ROW]
[ROW][C]37[/C][C]343[/C][C]336.999933987775[/C][C]6.00006601222458[/C][/ROW]
[ROW][C]38[/C][C]337[/C][C]342.999603896154[/C][C]-5.99960389615399[/C][/ROW]
[ROW][C]39[/C][C]326[/C][C]337.000396073339[/C][C]-11.0003960733387[/C][/ROW]
[ROW][C]40[/C][C]321[/C][C]326.000726208542[/C][C]-5.00072620854229[/C][/ROW]
[ROW][C]41[/C][C]309[/C][C]321.000330130849[/C][C]-12.0003301308486[/C][/ROW]
[ROW][C]42[/C][C]302[/C][C]309.00079222077[/C][C]-7.00079222077034[/C][/ROW]
[ROW][C]43[/C][C]293[/C][C]302.000462168369[/C][C]-9.00046216836915[/C][/ROW]
[ROW][C]44[/C][C]287[/C][C]293.000594179743[/C][C]-6.00059417974296[/C][/ROW]
[ROW][C]45[/C][C]292[/C][C]287.000396138714[/C][C]4.99960386128618[/C][/ROW]
[ROW][C]46[/C][C]292[/C][C]291.999669943245[/C][C]0.000330056755046826[/C][/ROW]
[ROW][C]47[/C][C]289[/C][C]291.999999978211[/C][C]-2.99999997821078[/C][/ROW]
[ROW][C]48[/C][C]302[/C][C]289.000198049743[/C][C]12.9998019502574[/C][/ROW]
[ROW][C]49[/C][C]310[/C][C]301.999141797517[/C][C]8.00085820248302[/C][/ROW]
[ROW][C]50[/C][C]295[/C][C]309.999471810694[/C][C]-14.9994718106936[/C][/ROW]
[ROW][C]51[/C][C]276[/C][C]295.000990213851[/C][C]-19.000990213851[/C][/ROW]
[ROW][C]52[/C][C]264[/C][C]276.001254380416[/C][C]-12.0012543804162[/C][/ROW]
[ROW][C]53[/C][C]257[/C][C]264.000792281786[/C][C]-7.00079228178612[/C][/ROW]
[ROW][C]54[/C][C]243[/C][C]257.000462168373[/C][C]-14.0004621683732[/C][/ROW]
[ROW][C]55[/C][C]227[/C][C]243.00092426265[/C][C]-16.0009242626497[/C][/ROW]
[ROW][C]56[/C][C]226[/C][C]227.001056326318[/C][C]-1.00105632631829[/C][/ROW]
[ROW][C]57[/C][C]226[/C][C]226.000066086316[/C][C]-6.60863163943759e-05[/C][/ROW]
[ROW][C]58[/C][C]229[/C][C]226.000000004363[/C][C]2.99999999563721[/C][/ROW]
[ROW][C]59[/C][C]224[/C][C]228.999801950256[/C][C]-4.99980195025623[/C][/ROW]
[ROW][C]60[/C][C]240[/C][C]224.000330069832[/C][C]15.9996699301678[/C][/ROW]
[ROW][C]61[/C][C]244[/C][C]239.998943756488[/C][C]4.00105624351156[/C][/ROW]
[ROW][C]62[/C][C]226[/C][C]243.999735863945[/C][C]-17.999735863945[/C][/ROW]
[ROW][C]63[/C][C]208[/C][C]226.001188281027[/C][C]-18.001188281027[/C][/ROW]
[ROW][C]64[/C][C]199[/C][C]208.001188376911[/C][C]-9.00118837691059[/C][/ROW]
[ROW][C]65[/C][C]193[/C][C]199.000594227685[/C][C]-6.00059422768476[/C][/ROW]
[ROW][C]66[/C][C]180[/C][C]193.000396138717[/C][C]-13.000396138717[/C][/ROW]
[ROW][C]67[/C][C]167[/C][C]180.000858241709[/C][C]-13.0008582417093[/C][/ROW]
[ROW][C]68[/C][C]164[/C][C]167.000858272216[/C][C]-3.00085827221577[/C][/ROW]
[ROW][C]69[/C][C]166[/C][C]164.000198106404[/C][C]1.99980189359576[/C][/ROW]
[ROW][C]70[/C][C]173[/C][C]165.999867979916[/C][C]7.00013202008441[/C][/ROW]
[ROW][C]71[/C][C]169[/C][C]172.999537875215[/C][C]-3.99953787521503[/C][/ROW]
[ROW][C]72[/C][C]191[/C][C]169.000264035818[/C][C]21.9997359641825[/C][/ROW]
[ROW][C]73[/C][C]193[/C][C]190.998547652641[/C][C]2.00145234735899[/C][/ROW]
[ROW][C]74[/C][C]166[/C][C]192.999867870958[/C][C]-26.9998678709583[/C][/ROW]
[ROW][C]75[/C][C]143[/C][C]166.001782438974[/C][C]-23.0017824389738[/C][/ROW]
[ROW][C]76[/C][C]147[/C][C]143.001518499042[/C][C]3.99848150095838[/C][/ROW]
[ROW][C]77[/C][C]139[/C][C]146.999736033921[/C][C]-7.9997360339207[/C][/ROW]
[ROW][C]78[/C][C]129[/C][C]139.000528115225[/C][C]-10.0005281152247[/C][/ROW]
[ROW][C]79[/C][C]115[/C][C]129.000660200678[/C][C]-14.0006602006779[/C][/ROW]
[ROW][C]80[/C][C]108[/C][C]115.000924275723[/C][C]-7.00092427572312[/C][/ROW]
[ROW][C]81[/C][C]106[/C][C]108.000462177087[/C][C]-2.00046217708699[/C][/ROW]
[ROW][C]82[/C][C]116[/C][C]106.000132063674[/C][C]9.99986793632594[/C][/ROW]
[ROW][C]83[/C][C]108[/C][C]115.999339842905[/C][C]-7.99933984290487[/C][/ROW]
[ROW][C]84[/C][C]135[/C][C]108.00052808907[/C][C]26.9994719109305[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78795&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78795&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
2375376-1
3374375.000066016581-1.00006601658134
4372374.00006602094-2.00006602093953
5370372.000132037521-2.00013203752115
6369370.000132041879-1.0001320418794
7370369.0000660252980.999933974701719
8372369.9999339877772.00006601222259
9373371.9998679624791.00013203752059
10373372.9999339747026.602529799693e-05
11374372.9999999956411.00000000435875
12376373.9999339834182.00006601658163
13371375.999867962479-4.99986796247913
14374371.000330074192.99966992580988
15369373.999801972046-4.99980197204633
16363369.000330069834-6.00033006983364
17357363.000396121278-6.00039612127819
18366357.0003961256398.9996038743613
19362365.999405876919-3.99940587691867
20366362.0002640271033.99973597289659
21361365.999735951105-4.99973595110475
22362361.0003300654750.999669934524832
23358361.999934005208-3.99993400520844
24363358.0002640619694.99973593803134
25360362.999669934526-2.99966993452568
26360360.000198027954-0.000198027954240843
27348360.000000013073-12.0000000130731
28345348.000792198977-3.00079219897708
29332345.000198102042-13.0001981020423
30333332.0008582286360.999141771364407
31323332.999934040076-9.99993404007597
32327323.0006601614593.99933983854095
33332326.9997359772565.00026402274381
34337331.9996698996635.00033010033661
35336336.999669895301-0.999669895301167
36337336.0000659947890.99993400521106
37343336.9999339877756.00006601222458
38337342.999603896154-5.99960389615399
39326337.000396073339-11.0003960733387
40321326.000726208542-5.00072620854229
41309321.000330130849-12.0003301308486
42302309.00079222077-7.00079222077034
43293302.000462168369-9.00046216836915
44287293.000594179743-6.00059417974296
45292287.0003961387144.99960386128618
46292291.9996699432450.000330056755046826
47289291.999999978211-2.99999997821078
48302289.00019804974312.9998019502574
49310301.9991417975178.00085820248302
50295309.999471810694-14.9994718106936
51276295.000990213851-19.000990213851
52264276.001254380416-12.0012543804162
53257264.000792281786-7.00079228178612
54243257.000462168373-14.0004621683732
55227243.00092426265-16.0009242626497
56226227.001056326318-1.00105632631829
57226226.000066086316-6.60863163943759e-05
58229226.0000000043632.99999999563721
59224228.999801950256-4.99980195025623
60240224.00033006983215.9996699301678
61244239.9989437564884.00105624351156
62226243.999735863945-17.999735863945
63208226.001188281027-18.001188281027
64199208.001188376911-9.00118837691059
65193199.000594227685-6.00059422768476
66180193.000396138717-13.000396138717
67167180.000858241709-13.0008582417093
68164167.000858272216-3.00085827221577
69166164.0001981064041.99980189359576
70173165.9998679799167.00013202008441
71169172.999537875215-3.99953787521503
72191169.00026403581821.9997359641825
73193190.9985476526412.00145234735899
74166192.999867870958-26.9998678709583
75143166.001782438974-23.0017824389738
76147143.0015184990423.99848150095838
77139146.999736033921-7.9997360339207
78129139.000528115225-10.0005281152247
79115129.000660200678-14.0006602006779
80108115.000924275723-7.00092427572312
81106108.000462177087-2.00046217708699
82116106.0001320636749.99986793632594
83108115.999339842905-7.99933984290487
84135108.0005280890726.9994719109305







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85134.998217587166117.2613133139152.735121860432
86134.998217587166109.915274968125160.081160206207
87134.998217587166104.278350275259165.718084899073
88134.99821758716699.5261654208157170.470269753517
89134.99821758716695.3393885307834174.657046643549
90134.99821758716691.5542426383371178.442192535995
91134.99821758716688.0734352585758181.922999915756
92134.99821758716684.8335743230435185.162860851289
93134.99821758716681.7906272353397188.205807938993
94134.99821758716678.9125339568592191.083901217473
95134.99821758716676.1750916458327193.8213435285
96134.99821758716673.5594970378166196.436938136516

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 134.998217587166 & 117.2613133139 & 152.735121860432 \tabularnewline
86 & 134.998217587166 & 109.915274968125 & 160.081160206207 \tabularnewline
87 & 134.998217587166 & 104.278350275259 & 165.718084899073 \tabularnewline
88 & 134.998217587166 & 99.5261654208157 & 170.470269753517 \tabularnewline
89 & 134.998217587166 & 95.3393885307834 & 174.657046643549 \tabularnewline
90 & 134.998217587166 & 91.5542426383371 & 178.442192535995 \tabularnewline
91 & 134.998217587166 & 88.0734352585758 & 181.922999915756 \tabularnewline
92 & 134.998217587166 & 84.8335743230435 & 185.162860851289 \tabularnewline
93 & 134.998217587166 & 81.7906272353397 & 188.205807938993 \tabularnewline
94 & 134.998217587166 & 78.9125339568592 & 191.083901217473 \tabularnewline
95 & 134.998217587166 & 76.1750916458327 & 193.8213435285 \tabularnewline
96 & 134.998217587166 & 73.5594970378166 & 196.436938136516 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78795&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]134.998217587166[/C][C]117.2613133139[/C][C]152.735121860432[/C][/ROW]
[ROW][C]86[/C][C]134.998217587166[/C][C]109.915274968125[/C][C]160.081160206207[/C][/ROW]
[ROW][C]87[/C][C]134.998217587166[/C][C]104.278350275259[/C][C]165.718084899073[/C][/ROW]
[ROW][C]88[/C][C]134.998217587166[/C][C]99.5261654208157[/C][C]170.470269753517[/C][/ROW]
[ROW][C]89[/C][C]134.998217587166[/C][C]95.3393885307834[/C][C]174.657046643549[/C][/ROW]
[ROW][C]90[/C][C]134.998217587166[/C][C]91.5542426383371[/C][C]178.442192535995[/C][/ROW]
[ROW][C]91[/C][C]134.998217587166[/C][C]88.0734352585758[/C][C]181.922999915756[/C][/ROW]
[ROW][C]92[/C][C]134.998217587166[/C][C]84.8335743230435[/C][C]185.162860851289[/C][/ROW]
[ROW][C]93[/C][C]134.998217587166[/C][C]81.7906272353397[/C][C]188.205807938993[/C][/ROW]
[ROW][C]94[/C][C]134.998217587166[/C][C]78.9125339568592[/C][C]191.083901217473[/C][/ROW]
[ROW][C]95[/C][C]134.998217587166[/C][C]76.1750916458327[/C][C]193.8213435285[/C][/ROW]
[ROW][C]96[/C][C]134.998217587166[/C][C]73.5594970378166[/C][C]196.436938136516[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78795&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78795&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
85134.998217587166117.2613133139152.735121860432
86134.998217587166109.915274968125160.081160206207
87134.998217587166104.278350275259165.718084899073
88134.99821758716699.5261654208157170.470269753517
89134.99821758716695.3393885307834174.657046643549
90134.99821758716691.5542426383371178.442192535995
91134.99821758716688.0734352585758181.922999915756
92134.99821758716684.8335743230435185.162860851289
93134.99821758716681.7906272353397188.205807938993
94134.99821758716678.9125339568592191.083901217473
95134.99821758716676.1750916458327193.8213435285
96134.99821758716673.5594970378166196.436938136516



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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')