Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 20 Dec 2012 11:07:03 -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/2012/Dec/20/t1356024850shrh4dqubk202af.htm/, Retrieved Thu, 28 Mar 2024 11:42:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=202949, Retrieved Thu, 28 Mar 2024 11:42:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact71
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-12-20 16:07:03] [71d0353b830738bf84dffbfcdf1408fc] [Current]
Feedback Forum

Post a new message
Dataseries X:
517
514
510
527
542
565
555
499
511
526
532
549
561
557
566
588
620
626
620
573
573
574
580
590
593
597
595
612
628
629
621
569
567
573
584
589
591
595
594
611
613
611
594
543
537
544
555
561
562
555
547
565
578
580
569
507
501
509
510
517
519
512
509
519
523
525
517
456
455
461
470
475
476




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=202949&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=202949&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=202949&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
alpha0.734734057425121
beta0.142702409942763
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.734734057425121 \tabularnewline
beta & 0.142702409942763 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=202949&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]0.734734057425121[/C][/ROW]
[ROW][C]beta[/C][C]0.142702409942763[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=202949&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=202949&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
alpha0.734734057425121
beta0.142702409942763
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13561530.13167735042730.8683226495726
14557551.3600943375215.63990566247935
15566567.768668786675-1.76866878667477
16588592.63180265231-4.63180265230972
17620625.488991159498-5.48899115949826
18626631.432529238289-5.43252923828891
19620616.7646269126273.23537308737309
20573566.9712177336556.02878226634539
21573587.362329111058-14.3623291110579
22574593.515530402651-19.5155304026506
23580583.919661944338-3.91966194433837
24590596.371639225045-6.37163922504533
25593610.083990986987-17.0839909869875
26597582.71216412736514.2878358726349
27595597.740339829648-2.74033982964784
28612615.259098792603-3.25909879260269
29628643.170439162201-15.1704391622009
30629635.273544031557-6.27354403155653
31621615.4567187249125.54328127508779
32569561.5116848593117.48831514068922
33567571.130807186164-4.13080718616413
34573578.071955007427-5.07195500742739
35584579.3771783844314.6228216155688
36589594.502700597183-5.50270059718275
37591603.150493221517-12.1504932215174
38595585.3812455163429.61875448365765
39594589.6282407863034.37175921369737
40611610.1469314510260.853068548974306
41613636.263141526003-23.2631415260031
42611622.274992612593-11.2749926125929
43594598.888327503318-4.88832750331767
44543533.6713434770789.32865652292151
45537537.629983403085-0.629983403085134
46544543.3302202617630.66977973823748
47555548.4643660486796.53563395132142
48561559.5484758819061.45152411809431
49562569.510615499669-7.51061549966926
50555559.379841606558-4.37984160655787
51547548.936770751122-1.93677075112237
52565560.2125703541394.78742964586081
53578579.560381029761-1.56038102976072
54580583.711635711501-3.71163571150146
55569567.3827952128631.61720478713744
56507511.205627092877-4.20562709287708
57501501.648131090781-0.64813109078068
58509506.7475655594842.25243444051614
59510513.834240131302-3.83424013130184
60517514.0970323618682.9029676381316
61519521.046851212768-2.04685121276782
62512514.632449880433-2.63244988043255
63509505.1759929888123.82400701118792
64519522.12682369923-3.12682369923027
65523532.80479888025-9.80479888025047
66525528.292424975549-3.29242497554924
67517511.693586914055.30641308594971
68456455.0776482182270.922351781773216
69455449.1644368738865.83556312611358
70461459.4097894042481.59021059575213
71470463.9385908911296.06140910887052
72475473.8400204076441.15997959235608
73476478.594253846614-2.59425384661438

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 561 & 530.131677350427 & 30.8683226495726 \tabularnewline
14 & 557 & 551.360094337521 & 5.63990566247935 \tabularnewline
15 & 566 & 567.768668786675 & -1.76866878667477 \tabularnewline
16 & 588 & 592.63180265231 & -4.63180265230972 \tabularnewline
17 & 620 & 625.488991159498 & -5.48899115949826 \tabularnewline
18 & 626 & 631.432529238289 & -5.43252923828891 \tabularnewline
19 & 620 & 616.764626912627 & 3.23537308737309 \tabularnewline
20 & 573 & 566.971217733655 & 6.02878226634539 \tabularnewline
21 & 573 & 587.362329111058 & -14.3623291110579 \tabularnewline
22 & 574 & 593.515530402651 & -19.5155304026506 \tabularnewline
23 & 580 & 583.919661944338 & -3.91966194433837 \tabularnewline
24 & 590 & 596.371639225045 & -6.37163922504533 \tabularnewline
25 & 593 & 610.083990986987 & -17.0839909869875 \tabularnewline
26 & 597 & 582.712164127365 & 14.2878358726349 \tabularnewline
27 & 595 & 597.740339829648 & -2.74033982964784 \tabularnewline
28 & 612 & 615.259098792603 & -3.25909879260269 \tabularnewline
29 & 628 & 643.170439162201 & -15.1704391622009 \tabularnewline
30 & 629 & 635.273544031557 & -6.27354403155653 \tabularnewline
31 & 621 & 615.456718724912 & 5.54328127508779 \tabularnewline
32 & 569 & 561.511684859311 & 7.48831514068922 \tabularnewline
33 & 567 & 571.130807186164 & -4.13080718616413 \tabularnewline
34 & 573 & 578.071955007427 & -5.07195500742739 \tabularnewline
35 & 584 & 579.377178384431 & 4.6228216155688 \tabularnewline
36 & 589 & 594.502700597183 & -5.50270059718275 \tabularnewline
37 & 591 & 603.150493221517 & -12.1504932215174 \tabularnewline
38 & 595 & 585.381245516342 & 9.61875448365765 \tabularnewline
39 & 594 & 589.628240786303 & 4.37175921369737 \tabularnewline
40 & 611 & 610.146931451026 & 0.853068548974306 \tabularnewline
41 & 613 & 636.263141526003 & -23.2631415260031 \tabularnewline
42 & 611 & 622.274992612593 & -11.2749926125929 \tabularnewline
43 & 594 & 598.888327503318 & -4.88832750331767 \tabularnewline
44 & 543 & 533.671343477078 & 9.32865652292151 \tabularnewline
45 & 537 & 537.629983403085 & -0.629983403085134 \tabularnewline
46 & 544 & 543.330220261763 & 0.66977973823748 \tabularnewline
47 & 555 & 548.464366048679 & 6.53563395132142 \tabularnewline
48 & 561 & 559.548475881906 & 1.45152411809431 \tabularnewline
49 & 562 & 569.510615499669 & -7.51061549966926 \tabularnewline
50 & 555 & 559.379841606558 & -4.37984160655787 \tabularnewline
51 & 547 & 548.936770751122 & -1.93677075112237 \tabularnewline
52 & 565 & 560.212570354139 & 4.78742964586081 \tabularnewline
53 & 578 & 579.560381029761 & -1.56038102976072 \tabularnewline
54 & 580 & 583.711635711501 & -3.71163571150146 \tabularnewline
55 & 569 & 567.382795212863 & 1.61720478713744 \tabularnewline
56 & 507 & 511.205627092877 & -4.20562709287708 \tabularnewline
57 & 501 & 501.648131090781 & -0.64813109078068 \tabularnewline
58 & 509 & 506.747565559484 & 2.25243444051614 \tabularnewline
59 & 510 & 513.834240131302 & -3.83424013130184 \tabularnewline
60 & 517 & 514.097032361868 & 2.9029676381316 \tabularnewline
61 & 519 & 521.046851212768 & -2.04685121276782 \tabularnewline
62 & 512 & 514.632449880433 & -2.63244988043255 \tabularnewline
63 & 509 & 505.175992988812 & 3.82400701118792 \tabularnewline
64 & 519 & 522.12682369923 & -3.12682369923027 \tabularnewline
65 & 523 & 532.80479888025 & -9.80479888025047 \tabularnewline
66 & 525 & 528.292424975549 & -3.29242497554924 \tabularnewline
67 & 517 & 511.69358691405 & 5.30641308594971 \tabularnewline
68 & 456 & 455.077648218227 & 0.922351781773216 \tabularnewline
69 & 455 & 449.164436873886 & 5.83556312611358 \tabularnewline
70 & 461 & 459.409789404248 & 1.59021059575213 \tabularnewline
71 & 470 & 463.938590891129 & 6.06140910887052 \tabularnewline
72 & 475 & 473.840020407644 & 1.15997959235608 \tabularnewline
73 & 476 & 478.594253846614 & -2.59425384661438 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=202949&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]561[/C][C]530.131677350427[/C][C]30.8683226495726[/C][/ROW]
[ROW][C]14[/C][C]557[/C][C]551.360094337521[/C][C]5.63990566247935[/C][/ROW]
[ROW][C]15[/C][C]566[/C][C]567.768668786675[/C][C]-1.76866878667477[/C][/ROW]
[ROW][C]16[/C][C]588[/C][C]592.63180265231[/C][C]-4.63180265230972[/C][/ROW]
[ROW][C]17[/C][C]620[/C][C]625.488991159498[/C][C]-5.48899115949826[/C][/ROW]
[ROW][C]18[/C][C]626[/C][C]631.432529238289[/C][C]-5.43252923828891[/C][/ROW]
[ROW][C]19[/C][C]620[/C][C]616.764626912627[/C][C]3.23537308737309[/C][/ROW]
[ROW][C]20[/C][C]573[/C][C]566.971217733655[/C][C]6.02878226634539[/C][/ROW]
[ROW][C]21[/C][C]573[/C][C]587.362329111058[/C][C]-14.3623291110579[/C][/ROW]
[ROW][C]22[/C][C]574[/C][C]593.515530402651[/C][C]-19.5155304026506[/C][/ROW]
[ROW][C]23[/C][C]580[/C][C]583.919661944338[/C][C]-3.91966194433837[/C][/ROW]
[ROW][C]24[/C][C]590[/C][C]596.371639225045[/C][C]-6.37163922504533[/C][/ROW]
[ROW][C]25[/C][C]593[/C][C]610.083990986987[/C][C]-17.0839909869875[/C][/ROW]
[ROW][C]26[/C][C]597[/C][C]582.712164127365[/C][C]14.2878358726349[/C][/ROW]
[ROW][C]27[/C][C]595[/C][C]597.740339829648[/C][C]-2.74033982964784[/C][/ROW]
[ROW][C]28[/C][C]612[/C][C]615.259098792603[/C][C]-3.25909879260269[/C][/ROW]
[ROW][C]29[/C][C]628[/C][C]643.170439162201[/C][C]-15.1704391622009[/C][/ROW]
[ROW][C]30[/C][C]629[/C][C]635.273544031557[/C][C]-6.27354403155653[/C][/ROW]
[ROW][C]31[/C][C]621[/C][C]615.456718724912[/C][C]5.54328127508779[/C][/ROW]
[ROW][C]32[/C][C]569[/C][C]561.511684859311[/C][C]7.48831514068922[/C][/ROW]
[ROW][C]33[/C][C]567[/C][C]571.130807186164[/C][C]-4.13080718616413[/C][/ROW]
[ROW][C]34[/C][C]573[/C][C]578.071955007427[/C][C]-5.07195500742739[/C][/ROW]
[ROW][C]35[/C][C]584[/C][C]579.377178384431[/C][C]4.6228216155688[/C][/ROW]
[ROW][C]36[/C][C]589[/C][C]594.502700597183[/C][C]-5.50270059718275[/C][/ROW]
[ROW][C]37[/C][C]591[/C][C]603.150493221517[/C][C]-12.1504932215174[/C][/ROW]
[ROW][C]38[/C][C]595[/C][C]585.381245516342[/C][C]9.61875448365765[/C][/ROW]
[ROW][C]39[/C][C]594[/C][C]589.628240786303[/C][C]4.37175921369737[/C][/ROW]
[ROW][C]40[/C][C]611[/C][C]610.146931451026[/C][C]0.853068548974306[/C][/ROW]
[ROW][C]41[/C][C]613[/C][C]636.263141526003[/C][C]-23.2631415260031[/C][/ROW]
[ROW][C]42[/C][C]611[/C][C]622.274992612593[/C][C]-11.2749926125929[/C][/ROW]
[ROW][C]43[/C][C]594[/C][C]598.888327503318[/C][C]-4.88832750331767[/C][/ROW]
[ROW][C]44[/C][C]543[/C][C]533.671343477078[/C][C]9.32865652292151[/C][/ROW]
[ROW][C]45[/C][C]537[/C][C]537.629983403085[/C][C]-0.629983403085134[/C][/ROW]
[ROW][C]46[/C][C]544[/C][C]543.330220261763[/C][C]0.66977973823748[/C][/ROW]
[ROW][C]47[/C][C]555[/C][C]548.464366048679[/C][C]6.53563395132142[/C][/ROW]
[ROW][C]48[/C][C]561[/C][C]559.548475881906[/C][C]1.45152411809431[/C][/ROW]
[ROW][C]49[/C][C]562[/C][C]569.510615499669[/C][C]-7.51061549966926[/C][/ROW]
[ROW][C]50[/C][C]555[/C][C]559.379841606558[/C][C]-4.37984160655787[/C][/ROW]
[ROW][C]51[/C][C]547[/C][C]548.936770751122[/C][C]-1.93677075112237[/C][/ROW]
[ROW][C]52[/C][C]565[/C][C]560.212570354139[/C][C]4.78742964586081[/C][/ROW]
[ROW][C]53[/C][C]578[/C][C]579.560381029761[/C][C]-1.56038102976072[/C][/ROW]
[ROW][C]54[/C][C]580[/C][C]583.711635711501[/C][C]-3.71163571150146[/C][/ROW]
[ROW][C]55[/C][C]569[/C][C]567.382795212863[/C][C]1.61720478713744[/C][/ROW]
[ROW][C]56[/C][C]507[/C][C]511.205627092877[/C][C]-4.20562709287708[/C][/ROW]
[ROW][C]57[/C][C]501[/C][C]501.648131090781[/C][C]-0.64813109078068[/C][/ROW]
[ROW][C]58[/C][C]509[/C][C]506.747565559484[/C][C]2.25243444051614[/C][/ROW]
[ROW][C]59[/C][C]510[/C][C]513.834240131302[/C][C]-3.83424013130184[/C][/ROW]
[ROW][C]60[/C][C]517[/C][C]514.097032361868[/C][C]2.9029676381316[/C][/ROW]
[ROW][C]61[/C][C]519[/C][C]521.046851212768[/C][C]-2.04685121276782[/C][/ROW]
[ROW][C]62[/C][C]512[/C][C]514.632449880433[/C][C]-2.63244988043255[/C][/ROW]
[ROW][C]63[/C][C]509[/C][C]505.175992988812[/C][C]3.82400701118792[/C][/ROW]
[ROW][C]64[/C][C]519[/C][C]522.12682369923[/C][C]-3.12682369923027[/C][/ROW]
[ROW][C]65[/C][C]523[/C][C]532.80479888025[/C][C]-9.80479888025047[/C][/ROW]
[ROW][C]66[/C][C]525[/C][C]528.292424975549[/C][C]-3.29242497554924[/C][/ROW]
[ROW][C]67[/C][C]517[/C][C]511.69358691405[/C][C]5.30641308594971[/C][/ROW]
[ROW][C]68[/C][C]456[/C][C]455.077648218227[/C][C]0.922351781773216[/C][/ROW]
[ROW][C]69[/C][C]455[/C][C]449.164436873886[/C][C]5.83556312611358[/C][/ROW]
[ROW][C]70[/C][C]461[/C][C]459.409789404248[/C][C]1.59021059575213[/C][/ROW]
[ROW][C]71[/C][C]470[/C][C]463.938590891129[/C][C]6.06140910887052[/C][/ROW]
[ROW][C]72[/C][C]475[/C][C]473.840020407644[/C][C]1.15997959235608[/C][/ROW]
[ROW][C]73[/C][C]476[/C][C]478.594253846614[/C][C]-2.59425384661438[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=202949&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=202949&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
13561530.13167735042730.8683226495726
14557551.3600943375215.63990566247935
15566567.768668786675-1.76866878667477
16588592.63180265231-4.63180265230972
17620625.488991159498-5.48899115949826
18626631.432529238289-5.43252923828891
19620616.7646269126273.23537308737309
20573566.9712177336556.02878226634539
21573587.362329111058-14.3623291110579
22574593.515530402651-19.5155304026506
23580583.919661944338-3.91966194433837
24590596.371639225045-6.37163922504533
25593610.083990986987-17.0839909869875
26597582.71216412736514.2878358726349
27595597.740339829648-2.74033982964784
28612615.259098792603-3.25909879260269
29628643.170439162201-15.1704391622009
30629635.273544031557-6.27354403155653
31621615.4567187249125.54328127508779
32569561.5116848593117.48831514068922
33567571.130807186164-4.13080718616413
34573578.071955007427-5.07195500742739
35584579.3771783844314.6228216155688
36589594.502700597183-5.50270059718275
37591603.150493221517-12.1504932215174
38595585.3812455163429.61875448365765
39594589.6282407863034.37175921369737
40611610.1469314510260.853068548974306
41613636.263141526003-23.2631415260031
42611622.274992612593-11.2749926125929
43594598.888327503318-4.88832750331767
44543533.6713434770789.32865652292151
45537537.629983403085-0.629983403085134
46544543.3302202617630.66977973823748
47555548.4643660486796.53563395132142
48561559.5484758819061.45152411809431
49562569.510615499669-7.51061549966926
50555559.379841606558-4.37984160655787
51547548.936770751122-1.93677075112237
52565560.2125703541394.78742964586081
53578579.560381029761-1.56038102976072
54580583.711635711501-3.71163571150146
55569567.3827952128631.61720478713744
56507511.205627092877-4.20562709287708
57501501.648131090781-0.64813109078068
58509506.7475655594842.25243444051614
59510513.834240131302-3.83424013130184
60517514.0970323618682.9029676381316
61519521.046851212768-2.04685121276782
62512514.632449880433-2.63244988043255
63509505.1759929888123.82400701118792
64519522.12682369923-3.12682369923027
65523532.80479888025-9.80479888025047
66525528.292424975549-3.29242497554924
67517511.693586914055.30641308594971
68456455.0776482182270.922351781773216
69455449.1644368738865.83556312611358
70461459.4097894042481.59021059575213
71470463.9385908911296.06140910887052
72475473.8400204076441.15997959235608
73476478.594253846614-2.59425384661438







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
74471.962989156681455.700777404298488.225200909063
75466.770040302079445.536183463234488.003897140924
76479.283162784497453.077034079391505.489291489602
77491.030663280919459.758830191115522.302496370723
78497.02131757189460.549544063243533.493091080536
79487.039317914384445.213920925639528.864714903129
80426.722068906098379.380092253806474.06404555839
81422.69820915642369.67272923916475.723689073679
82428.181705502686369.304760677536487.058650327836
83433.213329113393368.317592850061498.109065376724
84437.210671354043366.130421794456508.290920913631
85439.84475484957362.416433117962517.273076581177

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
74 & 471.962989156681 & 455.700777404298 & 488.225200909063 \tabularnewline
75 & 466.770040302079 & 445.536183463234 & 488.003897140924 \tabularnewline
76 & 479.283162784497 & 453.077034079391 & 505.489291489602 \tabularnewline
77 & 491.030663280919 & 459.758830191115 & 522.302496370723 \tabularnewline
78 & 497.02131757189 & 460.549544063243 & 533.493091080536 \tabularnewline
79 & 487.039317914384 & 445.213920925639 & 528.864714903129 \tabularnewline
80 & 426.722068906098 & 379.380092253806 & 474.06404555839 \tabularnewline
81 & 422.69820915642 & 369.67272923916 & 475.723689073679 \tabularnewline
82 & 428.181705502686 & 369.304760677536 & 487.058650327836 \tabularnewline
83 & 433.213329113393 & 368.317592850061 & 498.109065376724 \tabularnewline
84 & 437.210671354043 & 366.130421794456 & 508.290920913631 \tabularnewline
85 & 439.84475484957 & 362.416433117962 & 517.273076581177 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=202949&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]74[/C][C]471.962989156681[/C][C]455.700777404298[/C][C]488.225200909063[/C][/ROW]
[ROW][C]75[/C][C]466.770040302079[/C][C]445.536183463234[/C][C]488.003897140924[/C][/ROW]
[ROW][C]76[/C][C]479.283162784497[/C][C]453.077034079391[/C][C]505.489291489602[/C][/ROW]
[ROW][C]77[/C][C]491.030663280919[/C][C]459.758830191115[/C][C]522.302496370723[/C][/ROW]
[ROW][C]78[/C][C]497.02131757189[/C][C]460.549544063243[/C][C]533.493091080536[/C][/ROW]
[ROW][C]79[/C][C]487.039317914384[/C][C]445.213920925639[/C][C]528.864714903129[/C][/ROW]
[ROW][C]80[/C][C]426.722068906098[/C][C]379.380092253806[/C][C]474.06404555839[/C][/ROW]
[ROW][C]81[/C][C]422.69820915642[/C][C]369.67272923916[/C][C]475.723689073679[/C][/ROW]
[ROW][C]82[/C][C]428.181705502686[/C][C]369.304760677536[/C][C]487.058650327836[/C][/ROW]
[ROW][C]83[/C][C]433.213329113393[/C][C]368.317592850061[/C][C]498.109065376724[/C][/ROW]
[ROW][C]84[/C][C]437.210671354043[/C][C]366.130421794456[/C][C]508.290920913631[/C][/ROW]
[ROW][C]85[/C][C]439.84475484957[/C][C]362.416433117962[/C][C]517.273076581177[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=202949&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=202949&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
74471.962989156681455.700777404298488.225200909063
75466.770040302079445.536183463234488.003897140924
76479.283162784497453.077034079391505.489291489602
77491.030663280919459.758830191115522.302496370723
78497.02131757189460.549544063243533.493091080536
79487.039317914384445.213920925639528.864714903129
80426.722068906098379.380092253806474.06404555839
81422.69820915642369.67272923916475.723689073679
82428.181705502686369.304760677536487.058650327836
83433.213329113393368.317592850061498.109065376724
84437.210671354043366.130421794456508.290920913631
85439.84475484957362.416433117962517.273076581177



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')