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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 computationTue, 15 Jan 2013 21:07:48 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Jan/15/t1358302112twrw26fodkno8vy.htm/, Retrieved Sun, 28 Apr 2024 05:05:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=205605, Retrieved Sun, 28 Apr 2024 05:05:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact108
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Standard Deviation-Mean Plot] [inschrijvingen pe...] [2011-12-07 19:29:01] [4e8d7446eb620bf0031bc115be7a2e0d]
- RM D    [Exponential Smoothing] [] [2013-01-16 02:07:48] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
435
431
434
439
455
452
426
428
433
438
442
446
442
436
444
454
469
471
443
437
444
451
457
460
454
439
441
446
459
456
433
424
430
428
424
419
409
397
397
401
413
413
390
385
397
398
406
412
409
404
412
418
434
431
406
416
424
427
438
444
442
443
453
471
476
476
461
462
460
463
467
468
465
459
465
471
472
472
456
455
456
462
463
461




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net

\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 Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205605&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 Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205605&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205605&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 Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999933893038648
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999933893038648 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205605&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]0.999933893038648[/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=205605&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205605&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
alpha0.999933893038648
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2431435-4
3434431.0002644278452.99973557215458
4439433.9998016965965.00019830340352
5455438.99966945208416.000330547916
6452454.998942266767-2.99894226676685
7426452.000198250961-26.0001982509605
8428426.0017187941011.9982812058991
9433427.9998678997025.00013210029846
10438432.999669456465.00033054353952
11442437.9996694433424.00033055665801
12446441.9997355503024.00026444969751
13442445.999735554673-3.99973555467261
14436442.000264410364-6.00026441036374
15444436.0003966592477.99960334075251
16454443.99947117053110.0005288294689
17469453.99933889542715.0006611045728
18471468.9990083518762.00099164812389
19443470.999867720522-27.9998677205224
20437443.001850986173-6.00185098617328
21444437.0003967641316.99960323586879
22451443.9995372774997.00046272250057
23457450.9995372206816.00046277931864
24460456.9996033276393.00039667236103
25454459.999801652893-5.99980165289315
26439454.000396628656-15.000396628656
27441439.000991630641.99900836935979
28446440.9998678516315.000132148369
29459445.99966945645713.0003305435427
30456458.999140587651-2.9991405876512
31433456.000198264071-23.0001982640709
32424433.001520473218-9.00152047321774
33430424.0005950631665.99940493683397
34428429.99960339757-1.99960339756973
35424428.000132187705-4.00013218770454
36419424.000264436584-5.00026443658396
37409419.000330552288-10.0003305522878
38397409.000661091465-12.0006610914653
39397397.000793327239-0.000793327238966413
40401397.0000000524443.99999994755552
41413400.99973557215812.000264427842
42413412.9992066989830.000793301016756232
43390412.999999947557-22.9999999475573
44385390.001520460108-5.0015204601076
45397385.0003306353211.9996693646802
46398396.9992067383211.00079326167895
47406397.9999338405998.00006615940146
48412405.9994711399366.00052886006443
49409411.999603323271-2.99960332327055
50404409.000198294661-5.00019829466095
51412404.0003305479157.99966945208456
52418411.9994711661616.00052883383927
53434417.99960332327216.0003966767277
54431433.998942262395-2.9989422623953
55406431.00019825096-25.0001982509602
56416406.001652687149.99834731286046
57424415.9993390396418.00066096035937
58427423.9994711006153.0005288993849
59438426.99980164415211.000198355848
60444437.9992728103126.00072718968755
61442443.99960331016-1.99960331015961
62443442.0001321876990.999867812301261
63453442.99993390177710.0000660982228
64471452.99933892601718.0006610739831
65476470.9988100309945.00118996900591
66476475.9996693865280.000330613471987817
67461475.999999978144-14.9999999781442
68462461.0009916044190.999008395581143
69460461.999933958591-1.99993395859059
70463460.0001322095572.99986779044309
71467462.9998016878564.00019831214411
72468466.9997355590451.00026444095522
73465467.999933875557-2.99993387555725
74459465.000198316513-6.00019831651275
75465459.0003966548785.99960334512178
76471464.9996033844546.00039661554644
77472470.9996033320131.00039666798716
78472471.9999338668166.61331838500701e-05
79456471.999999995628-15.9999999956281
80455456.001057711381-1.00105771138135
81456455.0000661768830.999933823116578
82462455.9999338974136.00006610258657
83463461.9996033538621.00039664613797
84461462.999933866818-1.99993386681757

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 431 & 435 & -4 \tabularnewline
3 & 434 & 431.000264427845 & 2.99973557215458 \tabularnewline
4 & 439 & 433.999801696596 & 5.00019830340352 \tabularnewline
5 & 455 & 438.999669452084 & 16.000330547916 \tabularnewline
6 & 452 & 454.998942266767 & -2.99894226676685 \tabularnewline
7 & 426 & 452.000198250961 & -26.0001982509605 \tabularnewline
8 & 428 & 426.001718794101 & 1.9982812058991 \tabularnewline
9 & 433 & 427.999867899702 & 5.00013210029846 \tabularnewline
10 & 438 & 432.99966945646 & 5.00033054353952 \tabularnewline
11 & 442 & 437.999669443342 & 4.00033055665801 \tabularnewline
12 & 446 & 441.999735550302 & 4.00026444969751 \tabularnewline
13 & 442 & 445.999735554673 & -3.99973555467261 \tabularnewline
14 & 436 & 442.000264410364 & -6.00026441036374 \tabularnewline
15 & 444 & 436.000396659247 & 7.99960334075251 \tabularnewline
16 & 454 & 443.999471170531 & 10.0005288294689 \tabularnewline
17 & 469 & 453.999338895427 & 15.0006611045728 \tabularnewline
18 & 471 & 468.999008351876 & 2.00099164812389 \tabularnewline
19 & 443 & 470.999867720522 & -27.9998677205224 \tabularnewline
20 & 437 & 443.001850986173 & -6.00185098617328 \tabularnewline
21 & 444 & 437.000396764131 & 6.99960323586879 \tabularnewline
22 & 451 & 443.999537277499 & 7.00046272250057 \tabularnewline
23 & 457 & 450.999537220681 & 6.00046277931864 \tabularnewline
24 & 460 & 456.999603327639 & 3.00039667236103 \tabularnewline
25 & 454 & 459.999801652893 & -5.99980165289315 \tabularnewline
26 & 439 & 454.000396628656 & -15.000396628656 \tabularnewline
27 & 441 & 439.00099163064 & 1.99900836935979 \tabularnewline
28 & 446 & 440.999867851631 & 5.000132148369 \tabularnewline
29 & 459 & 445.999669456457 & 13.0003305435427 \tabularnewline
30 & 456 & 458.999140587651 & -2.9991405876512 \tabularnewline
31 & 433 & 456.000198264071 & -23.0001982640709 \tabularnewline
32 & 424 & 433.001520473218 & -9.00152047321774 \tabularnewline
33 & 430 & 424.000595063166 & 5.99940493683397 \tabularnewline
34 & 428 & 429.99960339757 & -1.99960339756973 \tabularnewline
35 & 424 & 428.000132187705 & -4.00013218770454 \tabularnewline
36 & 419 & 424.000264436584 & -5.00026443658396 \tabularnewline
37 & 409 & 419.000330552288 & -10.0003305522878 \tabularnewline
38 & 397 & 409.000661091465 & -12.0006610914653 \tabularnewline
39 & 397 & 397.000793327239 & -0.000793327238966413 \tabularnewline
40 & 401 & 397.000000052444 & 3.99999994755552 \tabularnewline
41 & 413 & 400.999735572158 & 12.000264427842 \tabularnewline
42 & 413 & 412.999206698983 & 0.000793301016756232 \tabularnewline
43 & 390 & 412.999999947557 & -22.9999999475573 \tabularnewline
44 & 385 & 390.001520460108 & -5.0015204601076 \tabularnewline
45 & 397 & 385.00033063532 & 11.9996693646802 \tabularnewline
46 & 398 & 396.999206738321 & 1.00079326167895 \tabularnewline
47 & 406 & 397.999933840599 & 8.00006615940146 \tabularnewline
48 & 412 & 405.999471139936 & 6.00052886006443 \tabularnewline
49 & 409 & 411.999603323271 & -2.99960332327055 \tabularnewline
50 & 404 & 409.000198294661 & -5.00019829466095 \tabularnewline
51 & 412 & 404.000330547915 & 7.99966945208456 \tabularnewline
52 & 418 & 411.999471166161 & 6.00052883383927 \tabularnewline
53 & 434 & 417.999603323272 & 16.0003966767277 \tabularnewline
54 & 431 & 433.998942262395 & -2.9989422623953 \tabularnewline
55 & 406 & 431.00019825096 & -25.0001982509602 \tabularnewline
56 & 416 & 406.00165268714 & 9.99834731286046 \tabularnewline
57 & 424 & 415.999339039641 & 8.00066096035937 \tabularnewline
58 & 427 & 423.999471100615 & 3.0005288993849 \tabularnewline
59 & 438 & 426.999801644152 & 11.000198355848 \tabularnewline
60 & 444 & 437.999272810312 & 6.00072718968755 \tabularnewline
61 & 442 & 443.99960331016 & -1.99960331015961 \tabularnewline
62 & 443 & 442.000132187699 & 0.999867812301261 \tabularnewline
63 & 453 & 442.999933901777 & 10.0000660982228 \tabularnewline
64 & 471 & 452.999338926017 & 18.0006610739831 \tabularnewline
65 & 476 & 470.998810030994 & 5.00118996900591 \tabularnewline
66 & 476 & 475.999669386528 & 0.000330613471987817 \tabularnewline
67 & 461 & 475.999999978144 & -14.9999999781442 \tabularnewline
68 & 462 & 461.000991604419 & 0.999008395581143 \tabularnewline
69 & 460 & 461.999933958591 & -1.99993395859059 \tabularnewline
70 & 463 & 460.000132209557 & 2.99986779044309 \tabularnewline
71 & 467 & 462.999801687856 & 4.00019831214411 \tabularnewline
72 & 468 & 466.999735559045 & 1.00026444095522 \tabularnewline
73 & 465 & 467.999933875557 & -2.99993387555725 \tabularnewline
74 & 459 & 465.000198316513 & -6.00019831651275 \tabularnewline
75 & 465 & 459.000396654878 & 5.99960334512178 \tabularnewline
76 & 471 & 464.999603384454 & 6.00039661554644 \tabularnewline
77 & 472 & 470.999603332013 & 1.00039666798716 \tabularnewline
78 & 472 & 471.999933866816 & 6.61331838500701e-05 \tabularnewline
79 & 456 & 471.999999995628 & -15.9999999956281 \tabularnewline
80 & 455 & 456.001057711381 & -1.00105771138135 \tabularnewline
81 & 456 & 455.000066176883 & 0.999933823116578 \tabularnewline
82 & 462 & 455.999933897413 & 6.00006610258657 \tabularnewline
83 & 463 & 461.999603353862 & 1.00039664613797 \tabularnewline
84 & 461 & 462.999933866818 & -1.99993386681757 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205605&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]431[/C][C]435[/C][C]-4[/C][/ROW]
[ROW][C]3[/C][C]434[/C][C]431.000264427845[/C][C]2.99973557215458[/C][/ROW]
[ROW][C]4[/C][C]439[/C][C]433.999801696596[/C][C]5.00019830340352[/C][/ROW]
[ROW][C]5[/C][C]455[/C][C]438.999669452084[/C][C]16.000330547916[/C][/ROW]
[ROW][C]6[/C][C]452[/C][C]454.998942266767[/C][C]-2.99894226676685[/C][/ROW]
[ROW][C]7[/C][C]426[/C][C]452.000198250961[/C][C]-26.0001982509605[/C][/ROW]
[ROW][C]8[/C][C]428[/C][C]426.001718794101[/C][C]1.9982812058991[/C][/ROW]
[ROW][C]9[/C][C]433[/C][C]427.999867899702[/C][C]5.00013210029846[/C][/ROW]
[ROW][C]10[/C][C]438[/C][C]432.99966945646[/C][C]5.00033054353952[/C][/ROW]
[ROW][C]11[/C][C]442[/C][C]437.999669443342[/C][C]4.00033055665801[/C][/ROW]
[ROW][C]12[/C][C]446[/C][C]441.999735550302[/C][C]4.00026444969751[/C][/ROW]
[ROW][C]13[/C][C]442[/C][C]445.999735554673[/C][C]-3.99973555467261[/C][/ROW]
[ROW][C]14[/C][C]436[/C][C]442.000264410364[/C][C]-6.00026441036374[/C][/ROW]
[ROW][C]15[/C][C]444[/C][C]436.000396659247[/C][C]7.99960334075251[/C][/ROW]
[ROW][C]16[/C][C]454[/C][C]443.999471170531[/C][C]10.0005288294689[/C][/ROW]
[ROW][C]17[/C][C]469[/C][C]453.999338895427[/C][C]15.0006611045728[/C][/ROW]
[ROW][C]18[/C][C]471[/C][C]468.999008351876[/C][C]2.00099164812389[/C][/ROW]
[ROW][C]19[/C][C]443[/C][C]470.999867720522[/C][C]-27.9998677205224[/C][/ROW]
[ROW][C]20[/C][C]437[/C][C]443.001850986173[/C][C]-6.00185098617328[/C][/ROW]
[ROW][C]21[/C][C]444[/C][C]437.000396764131[/C][C]6.99960323586879[/C][/ROW]
[ROW][C]22[/C][C]451[/C][C]443.999537277499[/C][C]7.00046272250057[/C][/ROW]
[ROW][C]23[/C][C]457[/C][C]450.999537220681[/C][C]6.00046277931864[/C][/ROW]
[ROW][C]24[/C][C]460[/C][C]456.999603327639[/C][C]3.00039667236103[/C][/ROW]
[ROW][C]25[/C][C]454[/C][C]459.999801652893[/C][C]-5.99980165289315[/C][/ROW]
[ROW][C]26[/C][C]439[/C][C]454.000396628656[/C][C]-15.000396628656[/C][/ROW]
[ROW][C]27[/C][C]441[/C][C]439.00099163064[/C][C]1.99900836935979[/C][/ROW]
[ROW][C]28[/C][C]446[/C][C]440.999867851631[/C][C]5.000132148369[/C][/ROW]
[ROW][C]29[/C][C]459[/C][C]445.999669456457[/C][C]13.0003305435427[/C][/ROW]
[ROW][C]30[/C][C]456[/C][C]458.999140587651[/C][C]-2.9991405876512[/C][/ROW]
[ROW][C]31[/C][C]433[/C][C]456.000198264071[/C][C]-23.0001982640709[/C][/ROW]
[ROW][C]32[/C][C]424[/C][C]433.001520473218[/C][C]-9.00152047321774[/C][/ROW]
[ROW][C]33[/C][C]430[/C][C]424.000595063166[/C][C]5.99940493683397[/C][/ROW]
[ROW][C]34[/C][C]428[/C][C]429.99960339757[/C][C]-1.99960339756973[/C][/ROW]
[ROW][C]35[/C][C]424[/C][C]428.000132187705[/C][C]-4.00013218770454[/C][/ROW]
[ROW][C]36[/C][C]419[/C][C]424.000264436584[/C][C]-5.00026443658396[/C][/ROW]
[ROW][C]37[/C][C]409[/C][C]419.000330552288[/C][C]-10.0003305522878[/C][/ROW]
[ROW][C]38[/C][C]397[/C][C]409.000661091465[/C][C]-12.0006610914653[/C][/ROW]
[ROW][C]39[/C][C]397[/C][C]397.000793327239[/C][C]-0.000793327238966413[/C][/ROW]
[ROW][C]40[/C][C]401[/C][C]397.000000052444[/C][C]3.99999994755552[/C][/ROW]
[ROW][C]41[/C][C]413[/C][C]400.999735572158[/C][C]12.000264427842[/C][/ROW]
[ROW][C]42[/C][C]413[/C][C]412.999206698983[/C][C]0.000793301016756232[/C][/ROW]
[ROW][C]43[/C][C]390[/C][C]412.999999947557[/C][C]-22.9999999475573[/C][/ROW]
[ROW][C]44[/C][C]385[/C][C]390.001520460108[/C][C]-5.0015204601076[/C][/ROW]
[ROW][C]45[/C][C]397[/C][C]385.00033063532[/C][C]11.9996693646802[/C][/ROW]
[ROW][C]46[/C][C]398[/C][C]396.999206738321[/C][C]1.00079326167895[/C][/ROW]
[ROW][C]47[/C][C]406[/C][C]397.999933840599[/C][C]8.00006615940146[/C][/ROW]
[ROW][C]48[/C][C]412[/C][C]405.999471139936[/C][C]6.00052886006443[/C][/ROW]
[ROW][C]49[/C][C]409[/C][C]411.999603323271[/C][C]-2.99960332327055[/C][/ROW]
[ROW][C]50[/C][C]404[/C][C]409.000198294661[/C][C]-5.00019829466095[/C][/ROW]
[ROW][C]51[/C][C]412[/C][C]404.000330547915[/C][C]7.99966945208456[/C][/ROW]
[ROW][C]52[/C][C]418[/C][C]411.999471166161[/C][C]6.00052883383927[/C][/ROW]
[ROW][C]53[/C][C]434[/C][C]417.999603323272[/C][C]16.0003966767277[/C][/ROW]
[ROW][C]54[/C][C]431[/C][C]433.998942262395[/C][C]-2.9989422623953[/C][/ROW]
[ROW][C]55[/C][C]406[/C][C]431.00019825096[/C][C]-25.0001982509602[/C][/ROW]
[ROW][C]56[/C][C]416[/C][C]406.00165268714[/C][C]9.99834731286046[/C][/ROW]
[ROW][C]57[/C][C]424[/C][C]415.999339039641[/C][C]8.00066096035937[/C][/ROW]
[ROW][C]58[/C][C]427[/C][C]423.999471100615[/C][C]3.0005288993849[/C][/ROW]
[ROW][C]59[/C][C]438[/C][C]426.999801644152[/C][C]11.000198355848[/C][/ROW]
[ROW][C]60[/C][C]444[/C][C]437.999272810312[/C][C]6.00072718968755[/C][/ROW]
[ROW][C]61[/C][C]442[/C][C]443.99960331016[/C][C]-1.99960331015961[/C][/ROW]
[ROW][C]62[/C][C]443[/C][C]442.000132187699[/C][C]0.999867812301261[/C][/ROW]
[ROW][C]63[/C][C]453[/C][C]442.999933901777[/C][C]10.0000660982228[/C][/ROW]
[ROW][C]64[/C][C]471[/C][C]452.999338926017[/C][C]18.0006610739831[/C][/ROW]
[ROW][C]65[/C][C]476[/C][C]470.998810030994[/C][C]5.00118996900591[/C][/ROW]
[ROW][C]66[/C][C]476[/C][C]475.999669386528[/C][C]0.000330613471987817[/C][/ROW]
[ROW][C]67[/C][C]461[/C][C]475.999999978144[/C][C]-14.9999999781442[/C][/ROW]
[ROW][C]68[/C][C]462[/C][C]461.000991604419[/C][C]0.999008395581143[/C][/ROW]
[ROW][C]69[/C][C]460[/C][C]461.999933958591[/C][C]-1.99993395859059[/C][/ROW]
[ROW][C]70[/C][C]463[/C][C]460.000132209557[/C][C]2.99986779044309[/C][/ROW]
[ROW][C]71[/C][C]467[/C][C]462.999801687856[/C][C]4.00019831214411[/C][/ROW]
[ROW][C]72[/C][C]468[/C][C]466.999735559045[/C][C]1.00026444095522[/C][/ROW]
[ROW][C]73[/C][C]465[/C][C]467.999933875557[/C][C]-2.99993387555725[/C][/ROW]
[ROW][C]74[/C][C]459[/C][C]465.000198316513[/C][C]-6.00019831651275[/C][/ROW]
[ROW][C]75[/C][C]465[/C][C]459.000396654878[/C][C]5.99960334512178[/C][/ROW]
[ROW][C]76[/C][C]471[/C][C]464.999603384454[/C][C]6.00039661554644[/C][/ROW]
[ROW][C]77[/C][C]472[/C][C]470.999603332013[/C][C]1.00039666798716[/C][/ROW]
[ROW][C]78[/C][C]472[/C][C]471.999933866816[/C][C]6.61331838500701e-05[/C][/ROW]
[ROW][C]79[/C][C]456[/C][C]471.999999995628[/C][C]-15.9999999956281[/C][/ROW]
[ROW][C]80[/C][C]455[/C][C]456.001057711381[/C][C]-1.00105771138135[/C][/ROW]
[ROW][C]81[/C][C]456[/C][C]455.000066176883[/C][C]0.999933823116578[/C][/ROW]
[ROW][C]82[/C][C]462[/C][C]455.999933897413[/C][C]6.00006610258657[/C][/ROW]
[ROW][C]83[/C][C]463[/C][C]461.999603353862[/C][C]1.00039664613797[/C][/ROW]
[ROW][C]84[/C][C]461[/C][C]462.999933866818[/C][C]-1.99993386681757[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205605&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205605&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
2431435-4
3434431.0002644278452.99973557215458
4439433.9998016965965.00019830340352
5455438.99966945208416.000330547916
6452454.998942266767-2.99894226676685
7426452.000198250961-26.0001982509605
8428426.0017187941011.9982812058991
9433427.9998678997025.00013210029846
10438432.999669456465.00033054353952
11442437.9996694433424.00033055665801
12446441.9997355503024.00026444969751
13442445.999735554673-3.99973555467261
14436442.000264410364-6.00026441036374
15444436.0003966592477.99960334075251
16454443.99947117053110.0005288294689
17469453.99933889542715.0006611045728
18471468.9990083518762.00099164812389
19443470.999867720522-27.9998677205224
20437443.001850986173-6.00185098617328
21444437.0003967641316.99960323586879
22451443.9995372774997.00046272250057
23457450.9995372206816.00046277931864
24460456.9996033276393.00039667236103
25454459.999801652893-5.99980165289315
26439454.000396628656-15.000396628656
27441439.000991630641.99900836935979
28446440.9998678516315.000132148369
29459445.99966945645713.0003305435427
30456458.999140587651-2.9991405876512
31433456.000198264071-23.0001982640709
32424433.001520473218-9.00152047321774
33430424.0005950631665.99940493683397
34428429.99960339757-1.99960339756973
35424428.000132187705-4.00013218770454
36419424.000264436584-5.00026443658396
37409419.000330552288-10.0003305522878
38397409.000661091465-12.0006610914653
39397397.000793327239-0.000793327238966413
40401397.0000000524443.99999994755552
41413400.99973557215812.000264427842
42413412.9992066989830.000793301016756232
43390412.999999947557-22.9999999475573
44385390.001520460108-5.0015204601076
45397385.0003306353211.9996693646802
46398396.9992067383211.00079326167895
47406397.9999338405998.00006615940146
48412405.9994711399366.00052886006443
49409411.999603323271-2.99960332327055
50404409.000198294661-5.00019829466095
51412404.0003305479157.99966945208456
52418411.9994711661616.00052883383927
53434417.99960332327216.0003966767277
54431433.998942262395-2.9989422623953
55406431.00019825096-25.0001982509602
56416406.001652687149.99834731286046
57424415.9993390396418.00066096035937
58427423.9994711006153.0005288993849
59438426.99980164415211.000198355848
60444437.9992728103126.00072718968755
61442443.99960331016-1.99960331015961
62443442.0001321876990.999867812301261
63453442.99993390177710.0000660982228
64471452.99933892601718.0006610739831
65476470.9988100309945.00118996900591
66476475.9996693865280.000330613471987817
67461475.999999978144-14.9999999781442
68462461.0009916044190.999008395581143
69460461.999933958591-1.99993395859059
70463460.0001322095572.99986779044309
71467462.9998016878564.00019831214411
72468466.9997355590451.00026444095522
73465467.999933875557-2.99993387555725
74459465.000198316513-6.00019831651275
75465459.0003966548785.99960334512178
76471464.9996033844546.00039661554644
77472470.9996033320131.00039666798716
78472471.9999338668166.61331838500701e-05
79456471.999999995628-15.9999999956281
80455456.001057711381-1.00105771138135
81456455.0000661768830.999933823116578
82462455.9999338974136.00006610258657
83463461.9996033538621.00039664613797
84461462.999933866818-1.99993386681757







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85461.000132209551442.481941357531479.518323061571
86461.000132209551434.812321168622487.18794325048
87461.000132209551428.927098336857493.073166082245
88461.000132209551423.965586762326498.034677656776
89461.000132209551419.594388511772502.405875907329
90461.000132209551415.642512498529506.357751920573
91461.000132209551412.008380653465509.991883765637
92461.000132209551408.625808584163513.374455834938
93461.000132209551405.448824125039516.551440294063
94461.000132209551402.443955041092519.55630937801
95461.000132209551399.585932391695522.414332027407
96461.000132209551396.855124656733525.145139762369

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 461.000132209551 & 442.481941357531 & 479.518323061571 \tabularnewline
86 & 461.000132209551 & 434.812321168622 & 487.18794325048 \tabularnewline
87 & 461.000132209551 & 428.927098336857 & 493.073166082245 \tabularnewline
88 & 461.000132209551 & 423.965586762326 & 498.034677656776 \tabularnewline
89 & 461.000132209551 & 419.594388511772 & 502.405875907329 \tabularnewline
90 & 461.000132209551 & 415.642512498529 & 506.357751920573 \tabularnewline
91 & 461.000132209551 & 412.008380653465 & 509.991883765637 \tabularnewline
92 & 461.000132209551 & 408.625808584163 & 513.374455834938 \tabularnewline
93 & 461.000132209551 & 405.448824125039 & 516.551440294063 \tabularnewline
94 & 461.000132209551 & 402.443955041092 & 519.55630937801 \tabularnewline
95 & 461.000132209551 & 399.585932391695 & 522.414332027407 \tabularnewline
96 & 461.000132209551 & 396.855124656733 & 525.145139762369 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205605&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]461.000132209551[/C][C]442.481941357531[/C][C]479.518323061571[/C][/ROW]
[ROW][C]86[/C][C]461.000132209551[/C][C]434.812321168622[/C][C]487.18794325048[/C][/ROW]
[ROW][C]87[/C][C]461.000132209551[/C][C]428.927098336857[/C][C]493.073166082245[/C][/ROW]
[ROW][C]88[/C][C]461.000132209551[/C][C]423.965586762326[/C][C]498.034677656776[/C][/ROW]
[ROW][C]89[/C][C]461.000132209551[/C][C]419.594388511772[/C][C]502.405875907329[/C][/ROW]
[ROW][C]90[/C][C]461.000132209551[/C][C]415.642512498529[/C][C]506.357751920573[/C][/ROW]
[ROW][C]91[/C][C]461.000132209551[/C][C]412.008380653465[/C][C]509.991883765637[/C][/ROW]
[ROW][C]92[/C][C]461.000132209551[/C][C]408.625808584163[/C][C]513.374455834938[/C][/ROW]
[ROW][C]93[/C][C]461.000132209551[/C][C]405.448824125039[/C][C]516.551440294063[/C][/ROW]
[ROW][C]94[/C][C]461.000132209551[/C][C]402.443955041092[/C][C]519.55630937801[/C][/ROW]
[ROW][C]95[/C][C]461.000132209551[/C][C]399.585932391695[/C][C]522.414332027407[/C][/ROW]
[ROW][C]96[/C][C]461.000132209551[/C][C]396.855124656733[/C][C]525.145139762369[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205605&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205605&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
85461.000132209551442.481941357531479.518323061571
86461.000132209551434.812321168622487.18794325048
87461.000132209551428.927098336857493.073166082245
88461.000132209551423.965586762326498.034677656776
89461.000132209551419.594388511772502.405875907329
90461.000132209551415.642512498529506.357751920573
91461.000132209551412.008380653465509.991883765637
92461.000132209551408.625808584163513.374455834938
93461.000132209551405.448824125039516.551440294063
94461.000132209551402.443955041092519.55630937801
95461.000132209551399.585932391695522.414332027407
96461.000132209551396.855124656733525.145139762369



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