Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 16 May 2013 07:58:24 -0400
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/May/16/t1368705657kbd96sv2vh1sxov.htm/, Retrieved Sun, 28 Apr 2024 22:28:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=208982, Retrieved Sun, 28 Apr 2024 22:28:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsyasmien.naciri@student.kdg.be
Estimated Impact143
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-05-16 11:58:24] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
557
561
549
532
526
511
499
555
565
542
527
510
514
517
508
493
490
469
478
528
534
518
506
502
516
528
533
536
537
524
536
587
597
581
564
558
575
580
575
563
552
537
545
601
604
586
564
549
551
556
548
540
531
521
519
572
581
563
548
539
541
562
559
546
536
528
530
582
599
584
571
563
565




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208982&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208982&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208982&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.832763480172306
beta0.24730359976672
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.832763480172306 \tabularnewline
beta & 0.24730359976672 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208982&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]0.832763480172306[/C][/ROW]
[ROW][C]beta[/C][C]0.24730359976672[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208982&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208982&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
alpha0.832763480172306
beta0.24730359976672
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13514533.730891379087-19.7308913790873
14517515.5235472169641.47645278303582
15508503.7240394862754.2759605137249
16493489.1093059147733.89069408522664
17490486.5610790085993.43892099140101
18469465.8320330901583.16796690984222
19478468.0114326582699.98856734173074
20528532.232351603279-4.23235160327943
21534539.755960533725-5.75596053372544
22518513.2849021164494.71509788355092
23506503.7685646509182.23143534908201
24502490.74621107005811.2537889299425
25516504.05766620136911.9423337986307
26528525.7914162320732.20858376792694
27533524.9878781224778.01212187752265
28536523.36282873722212.6371712627783
29537540.228078320548-3.22807832054775
30524522.4629432933751.53705670662475
31536535.0751195258260.924880474174188
32587605.306573204061-18.3065732040614
33597608.939639495367-11.9396394953675
34581582.161919705784-1.1619197057837
35564569.74329515312-5.74329515312013
36558552.3270793713095.67292062869103
37575562.42530162924112.5746983707593
38580584.952497062059-4.95249706205868
39575578.265057088727-3.26505708872742
40563564.359588084106-1.35958808410589
41552561.250698107948-9.25069810794776
42537532.1811418775944.81885812240603
43545541.7126848111243.28731518887628
44601605.635258606133-4.63525860613345
45604618.891716080579-14.8917160805794
46586587.497740382745-1.49774038274506
47564570.230457196768-6.23045719676759
48549550.592728443555-1.59272844355507
49551550.4415547069830.558445293016689
50556552.0356538219323.96434617806779
51548547.3932089502070.606791049792605
52540532.6813218206287.31867817937155
53531532.534918486278-1.53491848627766
54521511.4414132286459.55858677135456
55519523.979747255182-4.97974725518202
56572574.5318491999-2.53184919990042
57581584.994653235604-3.99465323560446
58563565.58864395149-2.5886439514901
59548547.0794303268650.920569673135446
60539535.8127857168413.18721428315882
61541542.250925172943-1.25092517294331
62562544.80469891476717.1953010852333
63559555.252664698763.74733530124024
64546549.244619523082-3.24461952308229
65536541.721559699757-5.72155969975677
66528520.8383316412587.16166835874162
67530530.516510940078-0.516510940078206
68582589.116842543579-7.11684254357874
69599597.6071711850121.39282881498775
70584585.359008856418-1.35900885641774
71571570.9948087704570.00519122954324303
72563561.7416951369981.25830486300242
73565568.450328334038-3.45032833403843

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 514 & 533.730891379087 & -19.7308913790873 \tabularnewline
14 & 517 & 515.523547216964 & 1.47645278303582 \tabularnewline
15 & 508 & 503.724039486275 & 4.2759605137249 \tabularnewline
16 & 493 & 489.109305914773 & 3.89069408522664 \tabularnewline
17 & 490 & 486.561079008599 & 3.43892099140101 \tabularnewline
18 & 469 & 465.832033090158 & 3.16796690984222 \tabularnewline
19 & 478 & 468.011432658269 & 9.98856734173074 \tabularnewline
20 & 528 & 532.232351603279 & -4.23235160327943 \tabularnewline
21 & 534 & 539.755960533725 & -5.75596053372544 \tabularnewline
22 & 518 & 513.284902116449 & 4.71509788355092 \tabularnewline
23 & 506 & 503.768564650918 & 2.23143534908201 \tabularnewline
24 & 502 & 490.746211070058 & 11.2537889299425 \tabularnewline
25 & 516 & 504.057666201369 & 11.9423337986307 \tabularnewline
26 & 528 & 525.791416232073 & 2.20858376792694 \tabularnewline
27 & 533 & 524.987878122477 & 8.01212187752265 \tabularnewline
28 & 536 & 523.362828737222 & 12.6371712627783 \tabularnewline
29 & 537 & 540.228078320548 & -3.22807832054775 \tabularnewline
30 & 524 & 522.462943293375 & 1.53705670662475 \tabularnewline
31 & 536 & 535.075119525826 & 0.924880474174188 \tabularnewline
32 & 587 & 605.306573204061 & -18.3065732040614 \tabularnewline
33 & 597 & 608.939639495367 & -11.9396394953675 \tabularnewline
34 & 581 & 582.161919705784 & -1.1619197057837 \tabularnewline
35 & 564 & 569.74329515312 & -5.74329515312013 \tabularnewline
36 & 558 & 552.327079371309 & 5.67292062869103 \tabularnewline
37 & 575 & 562.425301629241 & 12.5746983707593 \tabularnewline
38 & 580 & 584.952497062059 & -4.95249706205868 \tabularnewline
39 & 575 & 578.265057088727 & -3.26505708872742 \tabularnewline
40 & 563 & 564.359588084106 & -1.35958808410589 \tabularnewline
41 & 552 & 561.250698107948 & -9.25069810794776 \tabularnewline
42 & 537 & 532.181141877594 & 4.81885812240603 \tabularnewline
43 & 545 & 541.712684811124 & 3.28731518887628 \tabularnewline
44 & 601 & 605.635258606133 & -4.63525860613345 \tabularnewline
45 & 604 & 618.891716080579 & -14.8917160805794 \tabularnewline
46 & 586 & 587.497740382745 & -1.49774038274506 \tabularnewline
47 & 564 & 570.230457196768 & -6.23045719676759 \tabularnewline
48 & 549 & 550.592728443555 & -1.59272844355507 \tabularnewline
49 & 551 & 550.441554706983 & 0.558445293016689 \tabularnewline
50 & 556 & 552.035653821932 & 3.96434617806779 \tabularnewline
51 & 548 & 547.393208950207 & 0.606791049792605 \tabularnewline
52 & 540 & 532.681321820628 & 7.31867817937155 \tabularnewline
53 & 531 & 532.534918486278 & -1.53491848627766 \tabularnewline
54 & 521 & 511.441413228645 & 9.55858677135456 \tabularnewline
55 & 519 & 523.979747255182 & -4.97974725518202 \tabularnewline
56 & 572 & 574.5318491999 & -2.53184919990042 \tabularnewline
57 & 581 & 584.994653235604 & -3.99465323560446 \tabularnewline
58 & 563 & 565.58864395149 & -2.5886439514901 \tabularnewline
59 & 548 & 547.079430326865 & 0.920569673135446 \tabularnewline
60 & 539 & 535.812785716841 & 3.18721428315882 \tabularnewline
61 & 541 & 542.250925172943 & -1.25092517294331 \tabularnewline
62 & 562 & 544.804698914767 & 17.1953010852333 \tabularnewline
63 & 559 & 555.25266469876 & 3.74733530124024 \tabularnewline
64 & 546 & 549.244619523082 & -3.24461952308229 \tabularnewline
65 & 536 & 541.721559699757 & -5.72155969975677 \tabularnewline
66 & 528 & 520.838331641258 & 7.16166835874162 \tabularnewline
67 & 530 & 530.516510940078 & -0.516510940078206 \tabularnewline
68 & 582 & 589.116842543579 & -7.11684254357874 \tabularnewline
69 & 599 & 597.607171185012 & 1.39282881498775 \tabularnewline
70 & 584 & 585.359008856418 & -1.35900885641774 \tabularnewline
71 & 571 & 570.994808770457 & 0.00519122954324303 \tabularnewline
72 & 563 & 561.741695136998 & 1.25830486300242 \tabularnewline
73 & 565 & 568.450328334038 & -3.45032833403843 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208982&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]514[/C][C]533.730891379087[/C][C]-19.7308913790873[/C][/ROW]
[ROW][C]14[/C][C]517[/C][C]515.523547216964[/C][C]1.47645278303582[/C][/ROW]
[ROW][C]15[/C][C]508[/C][C]503.724039486275[/C][C]4.2759605137249[/C][/ROW]
[ROW][C]16[/C][C]493[/C][C]489.109305914773[/C][C]3.89069408522664[/C][/ROW]
[ROW][C]17[/C][C]490[/C][C]486.561079008599[/C][C]3.43892099140101[/C][/ROW]
[ROW][C]18[/C][C]469[/C][C]465.832033090158[/C][C]3.16796690984222[/C][/ROW]
[ROW][C]19[/C][C]478[/C][C]468.011432658269[/C][C]9.98856734173074[/C][/ROW]
[ROW][C]20[/C][C]528[/C][C]532.232351603279[/C][C]-4.23235160327943[/C][/ROW]
[ROW][C]21[/C][C]534[/C][C]539.755960533725[/C][C]-5.75596053372544[/C][/ROW]
[ROW][C]22[/C][C]518[/C][C]513.284902116449[/C][C]4.71509788355092[/C][/ROW]
[ROW][C]23[/C][C]506[/C][C]503.768564650918[/C][C]2.23143534908201[/C][/ROW]
[ROW][C]24[/C][C]502[/C][C]490.746211070058[/C][C]11.2537889299425[/C][/ROW]
[ROW][C]25[/C][C]516[/C][C]504.057666201369[/C][C]11.9423337986307[/C][/ROW]
[ROW][C]26[/C][C]528[/C][C]525.791416232073[/C][C]2.20858376792694[/C][/ROW]
[ROW][C]27[/C][C]533[/C][C]524.987878122477[/C][C]8.01212187752265[/C][/ROW]
[ROW][C]28[/C][C]536[/C][C]523.362828737222[/C][C]12.6371712627783[/C][/ROW]
[ROW][C]29[/C][C]537[/C][C]540.228078320548[/C][C]-3.22807832054775[/C][/ROW]
[ROW][C]30[/C][C]524[/C][C]522.462943293375[/C][C]1.53705670662475[/C][/ROW]
[ROW][C]31[/C][C]536[/C][C]535.075119525826[/C][C]0.924880474174188[/C][/ROW]
[ROW][C]32[/C][C]587[/C][C]605.306573204061[/C][C]-18.3065732040614[/C][/ROW]
[ROW][C]33[/C][C]597[/C][C]608.939639495367[/C][C]-11.9396394953675[/C][/ROW]
[ROW][C]34[/C][C]581[/C][C]582.161919705784[/C][C]-1.1619197057837[/C][/ROW]
[ROW][C]35[/C][C]564[/C][C]569.74329515312[/C][C]-5.74329515312013[/C][/ROW]
[ROW][C]36[/C][C]558[/C][C]552.327079371309[/C][C]5.67292062869103[/C][/ROW]
[ROW][C]37[/C][C]575[/C][C]562.425301629241[/C][C]12.5746983707593[/C][/ROW]
[ROW][C]38[/C][C]580[/C][C]584.952497062059[/C][C]-4.95249706205868[/C][/ROW]
[ROW][C]39[/C][C]575[/C][C]578.265057088727[/C][C]-3.26505708872742[/C][/ROW]
[ROW][C]40[/C][C]563[/C][C]564.359588084106[/C][C]-1.35958808410589[/C][/ROW]
[ROW][C]41[/C][C]552[/C][C]561.250698107948[/C][C]-9.25069810794776[/C][/ROW]
[ROW][C]42[/C][C]537[/C][C]532.181141877594[/C][C]4.81885812240603[/C][/ROW]
[ROW][C]43[/C][C]545[/C][C]541.712684811124[/C][C]3.28731518887628[/C][/ROW]
[ROW][C]44[/C][C]601[/C][C]605.635258606133[/C][C]-4.63525860613345[/C][/ROW]
[ROW][C]45[/C][C]604[/C][C]618.891716080579[/C][C]-14.8917160805794[/C][/ROW]
[ROW][C]46[/C][C]586[/C][C]587.497740382745[/C][C]-1.49774038274506[/C][/ROW]
[ROW][C]47[/C][C]564[/C][C]570.230457196768[/C][C]-6.23045719676759[/C][/ROW]
[ROW][C]48[/C][C]549[/C][C]550.592728443555[/C][C]-1.59272844355507[/C][/ROW]
[ROW][C]49[/C][C]551[/C][C]550.441554706983[/C][C]0.558445293016689[/C][/ROW]
[ROW][C]50[/C][C]556[/C][C]552.035653821932[/C][C]3.96434617806779[/C][/ROW]
[ROW][C]51[/C][C]548[/C][C]547.393208950207[/C][C]0.606791049792605[/C][/ROW]
[ROW][C]52[/C][C]540[/C][C]532.681321820628[/C][C]7.31867817937155[/C][/ROW]
[ROW][C]53[/C][C]531[/C][C]532.534918486278[/C][C]-1.53491848627766[/C][/ROW]
[ROW][C]54[/C][C]521[/C][C]511.441413228645[/C][C]9.55858677135456[/C][/ROW]
[ROW][C]55[/C][C]519[/C][C]523.979747255182[/C][C]-4.97974725518202[/C][/ROW]
[ROW][C]56[/C][C]572[/C][C]574.5318491999[/C][C]-2.53184919990042[/C][/ROW]
[ROW][C]57[/C][C]581[/C][C]584.994653235604[/C][C]-3.99465323560446[/C][/ROW]
[ROW][C]58[/C][C]563[/C][C]565.58864395149[/C][C]-2.5886439514901[/C][/ROW]
[ROW][C]59[/C][C]548[/C][C]547.079430326865[/C][C]0.920569673135446[/C][/ROW]
[ROW][C]60[/C][C]539[/C][C]535.812785716841[/C][C]3.18721428315882[/C][/ROW]
[ROW][C]61[/C][C]541[/C][C]542.250925172943[/C][C]-1.25092517294331[/C][/ROW]
[ROW][C]62[/C][C]562[/C][C]544.804698914767[/C][C]17.1953010852333[/C][/ROW]
[ROW][C]63[/C][C]559[/C][C]555.25266469876[/C][C]3.74733530124024[/C][/ROW]
[ROW][C]64[/C][C]546[/C][C]549.244619523082[/C][C]-3.24461952308229[/C][/ROW]
[ROW][C]65[/C][C]536[/C][C]541.721559699757[/C][C]-5.72155969975677[/C][/ROW]
[ROW][C]66[/C][C]528[/C][C]520.838331641258[/C][C]7.16166835874162[/C][/ROW]
[ROW][C]67[/C][C]530[/C][C]530.516510940078[/C][C]-0.516510940078206[/C][/ROW]
[ROW][C]68[/C][C]582[/C][C]589.116842543579[/C][C]-7.11684254357874[/C][/ROW]
[ROW][C]69[/C][C]599[/C][C]597.607171185012[/C][C]1.39282881498775[/C][/ROW]
[ROW][C]70[/C][C]584[/C][C]585.359008856418[/C][C]-1.35900885641774[/C][/ROW]
[ROW][C]71[/C][C]571[/C][C]570.994808770457[/C][C]0.00519122954324303[/C][/ROW]
[ROW][C]72[/C][C]563[/C][C]561.741695136998[/C][C]1.25830486300242[/C][/ROW]
[ROW][C]73[/C][C]565[/C][C]568.450328334038[/C][C]-3.45032833403843[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208982&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208982&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
13514533.730891379087-19.7308913790873
14517515.5235472169641.47645278303582
15508503.7240394862754.2759605137249
16493489.1093059147733.89069408522664
17490486.5610790085993.43892099140101
18469465.8320330901583.16796690984222
19478468.0114326582699.98856734173074
20528532.232351603279-4.23235160327943
21534539.755960533725-5.75596053372544
22518513.2849021164494.71509788355092
23506503.7685646509182.23143534908201
24502490.74621107005811.2537889299425
25516504.05766620136911.9423337986307
26528525.7914162320732.20858376792694
27533524.9878781224778.01212187752265
28536523.36282873722212.6371712627783
29537540.228078320548-3.22807832054775
30524522.4629432933751.53705670662475
31536535.0751195258260.924880474174188
32587605.306573204061-18.3065732040614
33597608.939639495367-11.9396394953675
34581582.161919705784-1.1619197057837
35564569.74329515312-5.74329515312013
36558552.3270793713095.67292062869103
37575562.42530162924112.5746983707593
38580584.952497062059-4.95249706205868
39575578.265057088727-3.26505708872742
40563564.359588084106-1.35958808410589
41552561.250698107948-9.25069810794776
42537532.1811418775944.81885812240603
43545541.7126848111243.28731518887628
44601605.635258606133-4.63525860613345
45604618.891716080579-14.8917160805794
46586587.497740382745-1.49774038274506
47564570.230457196768-6.23045719676759
48549550.592728443555-1.59272844355507
49551550.4415547069830.558445293016689
50556552.0356538219323.96434617806779
51548547.3932089502070.606791049792605
52540532.6813218206287.31867817937155
53531532.534918486278-1.53491848627766
54521511.4414132286459.55858677135456
55519523.979747255182-4.97974725518202
56572574.5318491999-2.53184919990042
57581584.994653235604-3.99465323560446
58563565.58864395149-2.5886439514901
59548547.0794303268650.920569673135446
60539535.8127857168413.18721428315882
61541542.250925172943-1.25092517294331
62562544.80469891476717.1953010852333
63559555.252664698763.74733530124024
64546549.244619523082-3.24461952308229
65536541.721559699757-5.72155969975677
66528520.8383316412587.16166835874162
67530530.516510940078-0.516510940078206
68582589.116842543579-7.11684254357874
69599597.6071711850121.39282881498775
70584585.359008856418-1.35900885641774
71571570.9948087704570.00519122954324303
72563561.7416951369981.25830486300242
73565568.450328334038-3.45032833403843







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
74574.5599280751560.738863305916588.380992844284
75566.724652562858546.946483412471586.502821713244
76553.996064589159528.271627951709579.720501226609
77547.086492821294515.009832090377579.16315355221
78532.430128090011494.245994916798570.614261263224
79533.010255782625487.483198686596578.537312878655
80589.312826652019530.855288863942647.770364440095
81604.862617974308536.123968686118673.601267262498
82590.101949949686514.119878342458666.084021556914
83576.498732079339493.218586433754659.778877724923
84566.908141307183475.798912660009658.017369954356
85571.094018602271467.046965121546675.141072082996

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
74 & 574.5599280751 & 560.738863305916 & 588.380992844284 \tabularnewline
75 & 566.724652562858 & 546.946483412471 & 586.502821713244 \tabularnewline
76 & 553.996064589159 & 528.271627951709 & 579.720501226609 \tabularnewline
77 & 547.086492821294 & 515.009832090377 & 579.16315355221 \tabularnewline
78 & 532.430128090011 & 494.245994916798 & 570.614261263224 \tabularnewline
79 & 533.010255782625 & 487.483198686596 & 578.537312878655 \tabularnewline
80 & 589.312826652019 & 530.855288863942 & 647.770364440095 \tabularnewline
81 & 604.862617974308 & 536.123968686118 & 673.601267262498 \tabularnewline
82 & 590.101949949686 & 514.119878342458 & 666.084021556914 \tabularnewline
83 & 576.498732079339 & 493.218586433754 & 659.778877724923 \tabularnewline
84 & 566.908141307183 & 475.798912660009 & 658.017369954356 \tabularnewline
85 & 571.094018602271 & 467.046965121546 & 675.141072082996 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208982&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]574.5599280751[/C][C]560.738863305916[/C][C]588.380992844284[/C][/ROW]
[ROW][C]75[/C][C]566.724652562858[/C][C]546.946483412471[/C][C]586.502821713244[/C][/ROW]
[ROW][C]76[/C][C]553.996064589159[/C][C]528.271627951709[/C][C]579.720501226609[/C][/ROW]
[ROW][C]77[/C][C]547.086492821294[/C][C]515.009832090377[/C][C]579.16315355221[/C][/ROW]
[ROW][C]78[/C][C]532.430128090011[/C][C]494.245994916798[/C][C]570.614261263224[/C][/ROW]
[ROW][C]79[/C][C]533.010255782625[/C][C]487.483198686596[/C][C]578.537312878655[/C][/ROW]
[ROW][C]80[/C][C]589.312826652019[/C][C]530.855288863942[/C][C]647.770364440095[/C][/ROW]
[ROW][C]81[/C][C]604.862617974308[/C][C]536.123968686118[/C][C]673.601267262498[/C][/ROW]
[ROW][C]82[/C][C]590.101949949686[/C][C]514.119878342458[/C][C]666.084021556914[/C][/ROW]
[ROW][C]83[/C][C]576.498732079339[/C][C]493.218586433754[/C][C]659.778877724923[/C][/ROW]
[ROW][C]84[/C][C]566.908141307183[/C][C]475.798912660009[/C][C]658.017369954356[/C][/ROW]
[ROW][C]85[/C][C]571.094018602271[/C][C]467.046965121546[/C][C]675.141072082996[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208982&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208982&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
74574.5599280751560.738863305916588.380992844284
75566.724652562858546.946483412471586.502821713244
76553.996064589159528.271627951709579.720501226609
77547.086492821294515.009832090377579.16315355221
78532.430128090011494.245994916798570.614261263224
79533.010255782625487.483198686596578.537312878655
80589.312826652019530.855288863942647.770364440095
81604.862617974308536.123968686118673.601267262498
82590.101949949686514.119878342458666.084021556914
83576.498732079339493.218586433754659.778877724923
84566.908141307183475.798912660009658.017369954356
85571.094018602271467.046965121546675.141072082996



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')