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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 28 Dec 2010 11:59:51 +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/Dec/28/t1293537462ypx8bhbmhfvwhta.htm/, Retrieved Sat, 04 May 2024 20:33:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116305, Retrieved Sat, 04 May 2024 20:33:58 +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)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [Unemployment] [2010-11-30 13:37:23] [b98453cac15ba1066b407e146608df68]
- R PD      [Exponential Smoothing] [Exponential smoot...] [2010-12-28 11:59:51] [062de5fc17e30860c0960288bdb996a8] [Current]
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Dataseries X:
621
587
655
517
646
657
382
345
625
654
606
510
614
647
580
614
636
388
356
639
753
611
639
630
586
695
552
619
681
421
307
754
690
644
643
608
651
691
627
634
731
475
337
803
722
590
724
627
696
825
677
656
785
412
352
839
729
696
641
695
638
762
635
721
854
418
367
824
687
601
676
740
691
683
594
729
731
386
331
706
715
657
653
642
643
718
654
632
731
392
344
792
852
649
629
685
617
715
715
629
916
531
357
917
828
708
858
775
785
1006
789
734
906
532
387
991
841
892
782
813
793
978
775
797
946
594
438
1022
868
795




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116305&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116305&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116305&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'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.121313434871579
beta0
gamma0.727613202056801

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.121313434871579 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.727613202056801 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116305&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]0.121313434871579[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.727613202056801[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116305&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116305&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
alpha0.121313434871579
beta0
gamma0.727613202056801







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13614647.620192307693-33.6201923076928
14647666.82278845398-19.8227884539805
15580581.282528387406-1.28252838740593
16614613.0331176195860.966882380413608
17636637.014923931782-1.01492393178171
18388383.9646438463284.03535615367218
19356400.360363918437-44.3603639184371
20639357.218366288849281.781633711151
21753673.47510798091779.5248920190827
22611712.653722945721-101.653722945721
23639650.144604470535-11.1446044705352
24630565.86545804477364.1345419552268
25586669.890483722475-83.8904837224753
26695691.8159047593823.18409524061758
27552620.920291796552-68.920291796552
28619645.90365877734-26.9036587773400
29681665.23733814358315.7626618564166
30421417.4512706134373.54872938656263
31307402.846445716454-95.8464457164538
32754561.975406134494192.024593865506
33690738.031789830672-48.0317898306716
34644645.900615091595-1.90061509159455
35643653.359345657001-10.3593456570012
36608617.304728146627-9.3047281466271
37651617.78167980020433.2183201997957
38691709.584576940514-18.5845769405137
39627589.94862830408837.0513716959123
40634654.650861703136-20.6508617031362
41731702.02154312360928.9784568763912
42475448.02982530951126.9701746904890
43337372.718633002093-35.7186330020926
44803723.19051108350179.809488916499
45722732.155099517306-10.1550995173059
46590674.11256343875-84.1125634387495
47724666.18984199112257.8101580088784
48627639.079364443766-12.0793644437661
49696666.4065689317929.5934310682096
50825724.649849687071100.350150312929
51677655.01278823862421.9872117613761
52656680.995963101049-24.9959631010490
53785759.56972968714625.4302703128540
54412503.863586117536-91.8635861175355
55352374.056552474132-22.0565524741315
56839800.04802972748738.9519702725128
57729746.537737331535-17.5377373315350
58696640.31533133655555.6846686634447
59641740.089324952775-99.089324952775
60695649.26138918073845.7386108192617
61638710.245940337771-72.2459403377711
62762801.372617178017-39.3726171780174
63635664.684436579969-29.6844365799691
64721654.36073791936966.639262080631
65854776.290795442877.7092045571995
66418451.935672033139-33.9356720331388
67367373.786776918547-6.78677691854745
68824840.636112721433-16.6361127214334
69687744.265886513551-57.2658865135514
70601680.038224210279-79.038224210279
71676664.51470523431711.4852947656833
72740679.69582022992260.3041797700785
73691667.01466217107823.9853378289220
74683790.832846030486-107.832846030486
75594652.033599524172-58.0335995241725
76729699.85474005452829.1452599454718
77731824.313772088603-93.313772088603
78386407.831788073037-21.8317880730366
79331348.508738408874-17.5087384088740
80706807.760243024426-101.760243024426
81715675.08691630786439.9130836921358
82657608.72835639702548.2716436029752
83653666.524898539208-13.5248985392084
84642709.883999619971-67.883999619971
85643658.431661515548-15.4316615155482
86718693.19087606681124.8091239331891
87654602.32172927711551.678270722885
88632719.189669589688-87.1896695896876
89731751.242271053243-20.2422710532435
90392389.3264154948362.67358450516389
91344335.7401123787728.25988762122779
92792744.2520081751847.7479918248206
93852720.294022610471131.705977389529
94649670.41516860093-21.4151686009303
95629680.24851913296-51.2485191329597
96685684.2770760780830.7229239219173
97617674.682764306154-57.6827643061538
98715730.044054979828-15.0440549798276
99715651.51880847986663.4811915201341
100629681.034224826663-52.0342248266631
101916760.154067953868155.845932046132
102531434.25119065547196.7488093445294
103357395.649045274614-38.6490452746141
104917823.71673762752693.283262372474
105828858.960821867563-30.9608218675631
106708691.45122212070716.5487778792930
107858686.816337372139171.183662627861
108775751.05653375607123.9434662439289
109785706.93786259559978.0621374044014
1101006806.02763420346199.972365796539
111789803.791409161267-14.7914091612669
112734749.957225437861-15.9572254378614
113906966.360612916558-60.360612916558
114532576.445589425618-44.445589425618
115387434.148867993739-47.1488679937387
116991945.53553973479445.4644602652058
117841895.543857846838-54.5438578468385
118892755.54829394039136.451706059609
119782864.324122550107-82.324122550107
120813803.6732906908389.32670930916152
121793792.381855271750.618144728250172
122978960.01919650535717.9808034946434
123775798.397030742782-23.3970307427824
124797742.77351192839554.2264880716049
125946939.3020898315466.6979101684542
126594567.69734002102526.3026599789748
127438432.2550069506965.74499304930379
12810221009.2701853309912.7298146690063
129868891.36763848615-23.3676384861495
130795877.266026191264-82.2660261912636

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 614 & 647.620192307693 & -33.6201923076928 \tabularnewline
14 & 647 & 666.82278845398 & -19.8227884539805 \tabularnewline
15 & 580 & 581.282528387406 & -1.28252838740593 \tabularnewline
16 & 614 & 613.033117619586 & 0.966882380413608 \tabularnewline
17 & 636 & 637.014923931782 & -1.01492393178171 \tabularnewline
18 & 388 & 383.964643846328 & 4.03535615367218 \tabularnewline
19 & 356 & 400.360363918437 & -44.3603639184371 \tabularnewline
20 & 639 & 357.218366288849 & 281.781633711151 \tabularnewline
21 & 753 & 673.475107980917 & 79.5248920190827 \tabularnewline
22 & 611 & 712.653722945721 & -101.653722945721 \tabularnewline
23 & 639 & 650.144604470535 & -11.1446044705352 \tabularnewline
24 & 630 & 565.865458044773 & 64.1345419552268 \tabularnewline
25 & 586 & 669.890483722475 & -83.8904837224753 \tabularnewline
26 & 695 & 691.815904759382 & 3.18409524061758 \tabularnewline
27 & 552 & 620.920291796552 & -68.920291796552 \tabularnewline
28 & 619 & 645.90365877734 & -26.9036587773400 \tabularnewline
29 & 681 & 665.237338143583 & 15.7626618564166 \tabularnewline
30 & 421 & 417.451270613437 & 3.54872938656263 \tabularnewline
31 & 307 & 402.846445716454 & -95.8464457164538 \tabularnewline
32 & 754 & 561.975406134494 & 192.024593865506 \tabularnewline
33 & 690 & 738.031789830672 & -48.0317898306716 \tabularnewline
34 & 644 & 645.900615091595 & -1.90061509159455 \tabularnewline
35 & 643 & 653.359345657001 & -10.3593456570012 \tabularnewline
36 & 608 & 617.304728146627 & -9.3047281466271 \tabularnewline
37 & 651 & 617.781679800204 & 33.2183201997957 \tabularnewline
38 & 691 & 709.584576940514 & -18.5845769405137 \tabularnewline
39 & 627 & 589.948628304088 & 37.0513716959123 \tabularnewline
40 & 634 & 654.650861703136 & -20.6508617031362 \tabularnewline
41 & 731 & 702.021543123609 & 28.9784568763912 \tabularnewline
42 & 475 & 448.029825309511 & 26.9701746904890 \tabularnewline
43 & 337 & 372.718633002093 & -35.7186330020926 \tabularnewline
44 & 803 & 723.190511083501 & 79.809488916499 \tabularnewline
45 & 722 & 732.155099517306 & -10.1550995173059 \tabularnewline
46 & 590 & 674.11256343875 & -84.1125634387495 \tabularnewline
47 & 724 & 666.189841991122 & 57.8101580088784 \tabularnewline
48 & 627 & 639.079364443766 & -12.0793644437661 \tabularnewline
49 & 696 & 666.40656893179 & 29.5934310682096 \tabularnewline
50 & 825 & 724.649849687071 & 100.350150312929 \tabularnewline
51 & 677 & 655.012788238624 & 21.9872117613761 \tabularnewline
52 & 656 & 680.995963101049 & -24.9959631010490 \tabularnewline
53 & 785 & 759.569729687146 & 25.4302703128540 \tabularnewline
54 & 412 & 503.863586117536 & -91.8635861175355 \tabularnewline
55 & 352 & 374.056552474132 & -22.0565524741315 \tabularnewline
56 & 839 & 800.048029727487 & 38.9519702725128 \tabularnewline
57 & 729 & 746.537737331535 & -17.5377373315350 \tabularnewline
58 & 696 & 640.315331336555 & 55.6846686634447 \tabularnewline
59 & 641 & 740.089324952775 & -99.089324952775 \tabularnewline
60 & 695 & 649.261389180738 & 45.7386108192617 \tabularnewline
61 & 638 & 710.245940337771 & -72.2459403377711 \tabularnewline
62 & 762 & 801.372617178017 & -39.3726171780174 \tabularnewline
63 & 635 & 664.684436579969 & -29.6844365799691 \tabularnewline
64 & 721 & 654.360737919369 & 66.639262080631 \tabularnewline
65 & 854 & 776.2907954428 & 77.7092045571995 \tabularnewline
66 & 418 & 451.935672033139 & -33.9356720331388 \tabularnewline
67 & 367 & 373.786776918547 & -6.78677691854745 \tabularnewline
68 & 824 & 840.636112721433 & -16.6361127214334 \tabularnewline
69 & 687 & 744.265886513551 & -57.2658865135514 \tabularnewline
70 & 601 & 680.038224210279 & -79.038224210279 \tabularnewline
71 & 676 & 664.514705234317 & 11.4852947656833 \tabularnewline
72 & 740 & 679.695820229922 & 60.3041797700785 \tabularnewline
73 & 691 & 667.014662171078 & 23.9853378289220 \tabularnewline
74 & 683 & 790.832846030486 & -107.832846030486 \tabularnewline
75 & 594 & 652.033599524172 & -58.0335995241725 \tabularnewline
76 & 729 & 699.854740054528 & 29.1452599454718 \tabularnewline
77 & 731 & 824.313772088603 & -93.313772088603 \tabularnewline
78 & 386 & 407.831788073037 & -21.8317880730366 \tabularnewline
79 & 331 & 348.508738408874 & -17.5087384088740 \tabularnewline
80 & 706 & 807.760243024426 & -101.760243024426 \tabularnewline
81 & 715 & 675.086916307864 & 39.9130836921358 \tabularnewline
82 & 657 & 608.728356397025 & 48.2716436029752 \tabularnewline
83 & 653 & 666.524898539208 & -13.5248985392084 \tabularnewline
84 & 642 & 709.883999619971 & -67.883999619971 \tabularnewline
85 & 643 & 658.431661515548 & -15.4316615155482 \tabularnewline
86 & 718 & 693.190876066811 & 24.8091239331891 \tabularnewline
87 & 654 & 602.321729277115 & 51.678270722885 \tabularnewline
88 & 632 & 719.189669589688 & -87.1896695896876 \tabularnewline
89 & 731 & 751.242271053243 & -20.2422710532435 \tabularnewline
90 & 392 & 389.326415494836 & 2.67358450516389 \tabularnewline
91 & 344 & 335.740112378772 & 8.25988762122779 \tabularnewline
92 & 792 & 744.25200817518 & 47.7479918248206 \tabularnewline
93 & 852 & 720.294022610471 & 131.705977389529 \tabularnewline
94 & 649 & 670.41516860093 & -21.4151686009303 \tabularnewline
95 & 629 & 680.24851913296 & -51.2485191329597 \tabularnewline
96 & 685 & 684.277076078083 & 0.7229239219173 \tabularnewline
97 & 617 & 674.682764306154 & -57.6827643061538 \tabularnewline
98 & 715 & 730.044054979828 & -15.0440549798276 \tabularnewline
99 & 715 & 651.518808479866 & 63.4811915201341 \tabularnewline
100 & 629 & 681.034224826663 & -52.0342248266631 \tabularnewline
101 & 916 & 760.154067953868 & 155.845932046132 \tabularnewline
102 & 531 & 434.251190655471 & 96.7488093445294 \tabularnewline
103 & 357 & 395.649045274614 & -38.6490452746141 \tabularnewline
104 & 917 & 823.716737627526 & 93.283262372474 \tabularnewline
105 & 828 & 858.960821867563 & -30.9608218675631 \tabularnewline
106 & 708 & 691.451222120707 & 16.5487778792930 \tabularnewline
107 & 858 & 686.816337372139 & 171.183662627861 \tabularnewline
108 & 775 & 751.056533756071 & 23.9434662439289 \tabularnewline
109 & 785 & 706.937862595599 & 78.0621374044014 \tabularnewline
110 & 1006 & 806.02763420346 & 199.972365796539 \tabularnewline
111 & 789 & 803.791409161267 & -14.7914091612669 \tabularnewline
112 & 734 & 749.957225437861 & -15.9572254378614 \tabularnewline
113 & 906 & 966.360612916558 & -60.360612916558 \tabularnewline
114 & 532 & 576.445589425618 & -44.445589425618 \tabularnewline
115 & 387 & 434.148867993739 & -47.1488679937387 \tabularnewline
116 & 991 & 945.535539734794 & 45.4644602652058 \tabularnewline
117 & 841 & 895.543857846838 & -54.5438578468385 \tabularnewline
118 & 892 & 755.54829394039 & 136.451706059609 \tabularnewline
119 & 782 & 864.324122550107 & -82.324122550107 \tabularnewline
120 & 813 & 803.673290690838 & 9.32670930916152 \tabularnewline
121 & 793 & 792.38185527175 & 0.618144728250172 \tabularnewline
122 & 978 & 960.019196505357 & 17.9808034946434 \tabularnewline
123 & 775 & 798.397030742782 & -23.3970307427824 \tabularnewline
124 & 797 & 742.773511928395 & 54.2264880716049 \tabularnewline
125 & 946 & 939.302089831546 & 6.6979101684542 \tabularnewline
126 & 594 & 567.697340021025 & 26.3026599789748 \tabularnewline
127 & 438 & 432.255006950696 & 5.74499304930379 \tabularnewline
128 & 1022 & 1009.27018533099 & 12.7298146690063 \tabularnewline
129 & 868 & 891.36763848615 & -23.3676384861495 \tabularnewline
130 & 795 & 877.266026191264 & -82.2660261912636 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116305&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]614[/C][C]647.620192307693[/C][C]-33.6201923076928[/C][/ROW]
[ROW][C]14[/C][C]647[/C][C]666.82278845398[/C][C]-19.8227884539805[/C][/ROW]
[ROW][C]15[/C][C]580[/C][C]581.282528387406[/C][C]-1.28252838740593[/C][/ROW]
[ROW][C]16[/C][C]614[/C][C]613.033117619586[/C][C]0.966882380413608[/C][/ROW]
[ROW][C]17[/C][C]636[/C][C]637.014923931782[/C][C]-1.01492393178171[/C][/ROW]
[ROW][C]18[/C][C]388[/C][C]383.964643846328[/C][C]4.03535615367218[/C][/ROW]
[ROW][C]19[/C][C]356[/C][C]400.360363918437[/C][C]-44.3603639184371[/C][/ROW]
[ROW][C]20[/C][C]639[/C][C]357.218366288849[/C][C]281.781633711151[/C][/ROW]
[ROW][C]21[/C][C]753[/C][C]673.475107980917[/C][C]79.5248920190827[/C][/ROW]
[ROW][C]22[/C][C]611[/C][C]712.653722945721[/C][C]-101.653722945721[/C][/ROW]
[ROW][C]23[/C][C]639[/C][C]650.144604470535[/C][C]-11.1446044705352[/C][/ROW]
[ROW][C]24[/C][C]630[/C][C]565.865458044773[/C][C]64.1345419552268[/C][/ROW]
[ROW][C]25[/C][C]586[/C][C]669.890483722475[/C][C]-83.8904837224753[/C][/ROW]
[ROW][C]26[/C][C]695[/C][C]691.815904759382[/C][C]3.18409524061758[/C][/ROW]
[ROW][C]27[/C][C]552[/C][C]620.920291796552[/C][C]-68.920291796552[/C][/ROW]
[ROW][C]28[/C][C]619[/C][C]645.90365877734[/C][C]-26.9036587773400[/C][/ROW]
[ROW][C]29[/C][C]681[/C][C]665.237338143583[/C][C]15.7626618564166[/C][/ROW]
[ROW][C]30[/C][C]421[/C][C]417.451270613437[/C][C]3.54872938656263[/C][/ROW]
[ROW][C]31[/C][C]307[/C][C]402.846445716454[/C][C]-95.8464457164538[/C][/ROW]
[ROW][C]32[/C][C]754[/C][C]561.975406134494[/C][C]192.024593865506[/C][/ROW]
[ROW][C]33[/C][C]690[/C][C]738.031789830672[/C][C]-48.0317898306716[/C][/ROW]
[ROW][C]34[/C][C]644[/C][C]645.900615091595[/C][C]-1.90061509159455[/C][/ROW]
[ROW][C]35[/C][C]643[/C][C]653.359345657001[/C][C]-10.3593456570012[/C][/ROW]
[ROW][C]36[/C][C]608[/C][C]617.304728146627[/C][C]-9.3047281466271[/C][/ROW]
[ROW][C]37[/C][C]651[/C][C]617.781679800204[/C][C]33.2183201997957[/C][/ROW]
[ROW][C]38[/C][C]691[/C][C]709.584576940514[/C][C]-18.5845769405137[/C][/ROW]
[ROW][C]39[/C][C]627[/C][C]589.948628304088[/C][C]37.0513716959123[/C][/ROW]
[ROW][C]40[/C][C]634[/C][C]654.650861703136[/C][C]-20.6508617031362[/C][/ROW]
[ROW][C]41[/C][C]731[/C][C]702.021543123609[/C][C]28.9784568763912[/C][/ROW]
[ROW][C]42[/C][C]475[/C][C]448.029825309511[/C][C]26.9701746904890[/C][/ROW]
[ROW][C]43[/C][C]337[/C][C]372.718633002093[/C][C]-35.7186330020926[/C][/ROW]
[ROW][C]44[/C][C]803[/C][C]723.190511083501[/C][C]79.809488916499[/C][/ROW]
[ROW][C]45[/C][C]722[/C][C]732.155099517306[/C][C]-10.1550995173059[/C][/ROW]
[ROW][C]46[/C][C]590[/C][C]674.11256343875[/C][C]-84.1125634387495[/C][/ROW]
[ROW][C]47[/C][C]724[/C][C]666.189841991122[/C][C]57.8101580088784[/C][/ROW]
[ROW][C]48[/C][C]627[/C][C]639.079364443766[/C][C]-12.0793644437661[/C][/ROW]
[ROW][C]49[/C][C]696[/C][C]666.40656893179[/C][C]29.5934310682096[/C][/ROW]
[ROW][C]50[/C][C]825[/C][C]724.649849687071[/C][C]100.350150312929[/C][/ROW]
[ROW][C]51[/C][C]677[/C][C]655.012788238624[/C][C]21.9872117613761[/C][/ROW]
[ROW][C]52[/C][C]656[/C][C]680.995963101049[/C][C]-24.9959631010490[/C][/ROW]
[ROW][C]53[/C][C]785[/C][C]759.569729687146[/C][C]25.4302703128540[/C][/ROW]
[ROW][C]54[/C][C]412[/C][C]503.863586117536[/C][C]-91.8635861175355[/C][/ROW]
[ROW][C]55[/C][C]352[/C][C]374.056552474132[/C][C]-22.0565524741315[/C][/ROW]
[ROW][C]56[/C][C]839[/C][C]800.048029727487[/C][C]38.9519702725128[/C][/ROW]
[ROW][C]57[/C][C]729[/C][C]746.537737331535[/C][C]-17.5377373315350[/C][/ROW]
[ROW][C]58[/C][C]696[/C][C]640.315331336555[/C][C]55.6846686634447[/C][/ROW]
[ROW][C]59[/C][C]641[/C][C]740.089324952775[/C][C]-99.089324952775[/C][/ROW]
[ROW][C]60[/C][C]695[/C][C]649.261389180738[/C][C]45.7386108192617[/C][/ROW]
[ROW][C]61[/C][C]638[/C][C]710.245940337771[/C][C]-72.2459403377711[/C][/ROW]
[ROW][C]62[/C][C]762[/C][C]801.372617178017[/C][C]-39.3726171780174[/C][/ROW]
[ROW][C]63[/C][C]635[/C][C]664.684436579969[/C][C]-29.6844365799691[/C][/ROW]
[ROW][C]64[/C][C]721[/C][C]654.360737919369[/C][C]66.639262080631[/C][/ROW]
[ROW][C]65[/C][C]854[/C][C]776.2907954428[/C][C]77.7092045571995[/C][/ROW]
[ROW][C]66[/C][C]418[/C][C]451.935672033139[/C][C]-33.9356720331388[/C][/ROW]
[ROW][C]67[/C][C]367[/C][C]373.786776918547[/C][C]-6.78677691854745[/C][/ROW]
[ROW][C]68[/C][C]824[/C][C]840.636112721433[/C][C]-16.6361127214334[/C][/ROW]
[ROW][C]69[/C][C]687[/C][C]744.265886513551[/C][C]-57.2658865135514[/C][/ROW]
[ROW][C]70[/C][C]601[/C][C]680.038224210279[/C][C]-79.038224210279[/C][/ROW]
[ROW][C]71[/C][C]676[/C][C]664.514705234317[/C][C]11.4852947656833[/C][/ROW]
[ROW][C]72[/C][C]740[/C][C]679.695820229922[/C][C]60.3041797700785[/C][/ROW]
[ROW][C]73[/C][C]691[/C][C]667.014662171078[/C][C]23.9853378289220[/C][/ROW]
[ROW][C]74[/C][C]683[/C][C]790.832846030486[/C][C]-107.832846030486[/C][/ROW]
[ROW][C]75[/C][C]594[/C][C]652.033599524172[/C][C]-58.0335995241725[/C][/ROW]
[ROW][C]76[/C][C]729[/C][C]699.854740054528[/C][C]29.1452599454718[/C][/ROW]
[ROW][C]77[/C][C]731[/C][C]824.313772088603[/C][C]-93.313772088603[/C][/ROW]
[ROW][C]78[/C][C]386[/C][C]407.831788073037[/C][C]-21.8317880730366[/C][/ROW]
[ROW][C]79[/C][C]331[/C][C]348.508738408874[/C][C]-17.5087384088740[/C][/ROW]
[ROW][C]80[/C][C]706[/C][C]807.760243024426[/C][C]-101.760243024426[/C][/ROW]
[ROW][C]81[/C][C]715[/C][C]675.086916307864[/C][C]39.9130836921358[/C][/ROW]
[ROW][C]82[/C][C]657[/C][C]608.728356397025[/C][C]48.2716436029752[/C][/ROW]
[ROW][C]83[/C][C]653[/C][C]666.524898539208[/C][C]-13.5248985392084[/C][/ROW]
[ROW][C]84[/C][C]642[/C][C]709.883999619971[/C][C]-67.883999619971[/C][/ROW]
[ROW][C]85[/C][C]643[/C][C]658.431661515548[/C][C]-15.4316615155482[/C][/ROW]
[ROW][C]86[/C][C]718[/C][C]693.190876066811[/C][C]24.8091239331891[/C][/ROW]
[ROW][C]87[/C][C]654[/C][C]602.321729277115[/C][C]51.678270722885[/C][/ROW]
[ROW][C]88[/C][C]632[/C][C]719.189669589688[/C][C]-87.1896695896876[/C][/ROW]
[ROW][C]89[/C][C]731[/C][C]751.242271053243[/C][C]-20.2422710532435[/C][/ROW]
[ROW][C]90[/C][C]392[/C][C]389.326415494836[/C][C]2.67358450516389[/C][/ROW]
[ROW][C]91[/C][C]344[/C][C]335.740112378772[/C][C]8.25988762122779[/C][/ROW]
[ROW][C]92[/C][C]792[/C][C]744.25200817518[/C][C]47.7479918248206[/C][/ROW]
[ROW][C]93[/C][C]852[/C][C]720.294022610471[/C][C]131.705977389529[/C][/ROW]
[ROW][C]94[/C][C]649[/C][C]670.41516860093[/C][C]-21.4151686009303[/C][/ROW]
[ROW][C]95[/C][C]629[/C][C]680.24851913296[/C][C]-51.2485191329597[/C][/ROW]
[ROW][C]96[/C][C]685[/C][C]684.277076078083[/C][C]0.7229239219173[/C][/ROW]
[ROW][C]97[/C][C]617[/C][C]674.682764306154[/C][C]-57.6827643061538[/C][/ROW]
[ROW][C]98[/C][C]715[/C][C]730.044054979828[/C][C]-15.0440549798276[/C][/ROW]
[ROW][C]99[/C][C]715[/C][C]651.518808479866[/C][C]63.4811915201341[/C][/ROW]
[ROW][C]100[/C][C]629[/C][C]681.034224826663[/C][C]-52.0342248266631[/C][/ROW]
[ROW][C]101[/C][C]916[/C][C]760.154067953868[/C][C]155.845932046132[/C][/ROW]
[ROW][C]102[/C][C]531[/C][C]434.251190655471[/C][C]96.7488093445294[/C][/ROW]
[ROW][C]103[/C][C]357[/C][C]395.649045274614[/C][C]-38.6490452746141[/C][/ROW]
[ROW][C]104[/C][C]917[/C][C]823.716737627526[/C][C]93.283262372474[/C][/ROW]
[ROW][C]105[/C][C]828[/C][C]858.960821867563[/C][C]-30.9608218675631[/C][/ROW]
[ROW][C]106[/C][C]708[/C][C]691.451222120707[/C][C]16.5487778792930[/C][/ROW]
[ROW][C]107[/C][C]858[/C][C]686.816337372139[/C][C]171.183662627861[/C][/ROW]
[ROW][C]108[/C][C]775[/C][C]751.056533756071[/C][C]23.9434662439289[/C][/ROW]
[ROW][C]109[/C][C]785[/C][C]706.937862595599[/C][C]78.0621374044014[/C][/ROW]
[ROW][C]110[/C][C]1006[/C][C]806.02763420346[/C][C]199.972365796539[/C][/ROW]
[ROW][C]111[/C][C]789[/C][C]803.791409161267[/C][C]-14.7914091612669[/C][/ROW]
[ROW][C]112[/C][C]734[/C][C]749.957225437861[/C][C]-15.9572254378614[/C][/ROW]
[ROW][C]113[/C][C]906[/C][C]966.360612916558[/C][C]-60.360612916558[/C][/ROW]
[ROW][C]114[/C][C]532[/C][C]576.445589425618[/C][C]-44.445589425618[/C][/ROW]
[ROW][C]115[/C][C]387[/C][C]434.148867993739[/C][C]-47.1488679937387[/C][/ROW]
[ROW][C]116[/C][C]991[/C][C]945.535539734794[/C][C]45.4644602652058[/C][/ROW]
[ROW][C]117[/C][C]841[/C][C]895.543857846838[/C][C]-54.5438578468385[/C][/ROW]
[ROW][C]118[/C][C]892[/C][C]755.54829394039[/C][C]136.451706059609[/C][/ROW]
[ROW][C]119[/C][C]782[/C][C]864.324122550107[/C][C]-82.324122550107[/C][/ROW]
[ROW][C]120[/C][C]813[/C][C]803.673290690838[/C][C]9.32670930916152[/C][/ROW]
[ROW][C]121[/C][C]793[/C][C]792.38185527175[/C][C]0.618144728250172[/C][/ROW]
[ROW][C]122[/C][C]978[/C][C]960.019196505357[/C][C]17.9808034946434[/C][/ROW]
[ROW][C]123[/C][C]775[/C][C]798.397030742782[/C][C]-23.3970307427824[/C][/ROW]
[ROW][C]124[/C][C]797[/C][C]742.773511928395[/C][C]54.2264880716049[/C][/ROW]
[ROW][C]125[/C][C]946[/C][C]939.302089831546[/C][C]6.6979101684542[/C][/ROW]
[ROW][C]126[/C][C]594[/C][C]567.697340021025[/C][C]26.3026599789748[/C][/ROW]
[ROW][C]127[/C][C]438[/C][C]432.255006950696[/C][C]5.74499304930379[/C][/ROW]
[ROW][C]128[/C][C]1022[/C][C]1009.27018533099[/C][C]12.7298146690063[/C][/ROW]
[ROW][C]129[/C][C]868[/C][C]891.36763848615[/C][C]-23.3676384861495[/C][/ROW]
[ROW][C]130[/C][C]795[/C][C]877.266026191264[/C][C]-82.2660261912636[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116305&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116305&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
13614647.620192307693-33.6201923076928
14647666.82278845398-19.8227884539805
15580581.282528387406-1.28252838740593
16614613.0331176195860.966882380413608
17636637.014923931782-1.01492393178171
18388383.9646438463284.03535615367218
19356400.360363918437-44.3603639184371
20639357.218366288849281.781633711151
21753673.47510798091779.5248920190827
22611712.653722945721-101.653722945721
23639650.144604470535-11.1446044705352
24630565.86545804477364.1345419552268
25586669.890483722475-83.8904837224753
26695691.8159047593823.18409524061758
27552620.920291796552-68.920291796552
28619645.90365877734-26.9036587773400
29681665.23733814358315.7626618564166
30421417.4512706134373.54872938656263
31307402.846445716454-95.8464457164538
32754561.975406134494192.024593865506
33690738.031789830672-48.0317898306716
34644645.900615091595-1.90061509159455
35643653.359345657001-10.3593456570012
36608617.304728146627-9.3047281466271
37651617.78167980020433.2183201997957
38691709.584576940514-18.5845769405137
39627589.94862830408837.0513716959123
40634654.650861703136-20.6508617031362
41731702.02154312360928.9784568763912
42475448.02982530951126.9701746904890
43337372.718633002093-35.7186330020926
44803723.19051108350179.809488916499
45722732.155099517306-10.1550995173059
46590674.11256343875-84.1125634387495
47724666.18984199112257.8101580088784
48627639.079364443766-12.0793644437661
49696666.4065689317929.5934310682096
50825724.649849687071100.350150312929
51677655.01278823862421.9872117613761
52656680.995963101049-24.9959631010490
53785759.56972968714625.4302703128540
54412503.863586117536-91.8635861175355
55352374.056552474132-22.0565524741315
56839800.04802972748738.9519702725128
57729746.537737331535-17.5377373315350
58696640.31533133655555.6846686634447
59641740.089324952775-99.089324952775
60695649.26138918073845.7386108192617
61638710.245940337771-72.2459403377711
62762801.372617178017-39.3726171780174
63635664.684436579969-29.6844365799691
64721654.36073791936966.639262080631
65854776.290795442877.7092045571995
66418451.935672033139-33.9356720331388
67367373.786776918547-6.78677691854745
68824840.636112721433-16.6361127214334
69687744.265886513551-57.2658865135514
70601680.038224210279-79.038224210279
71676664.51470523431711.4852947656833
72740679.69582022992260.3041797700785
73691667.01466217107823.9853378289220
74683790.832846030486-107.832846030486
75594652.033599524172-58.0335995241725
76729699.85474005452829.1452599454718
77731824.313772088603-93.313772088603
78386407.831788073037-21.8317880730366
79331348.508738408874-17.5087384088740
80706807.760243024426-101.760243024426
81715675.08691630786439.9130836921358
82657608.72835639702548.2716436029752
83653666.524898539208-13.5248985392084
84642709.883999619971-67.883999619971
85643658.431661515548-15.4316615155482
86718693.19087606681124.8091239331891
87654602.32172927711551.678270722885
88632719.189669589688-87.1896695896876
89731751.242271053243-20.2422710532435
90392389.3264154948362.67358450516389
91344335.7401123787728.25988762122779
92792744.2520081751847.7479918248206
93852720.294022610471131.705977389529
94649670.41516860093-21.4151686009303
95629680.24851913296-51.2485191329597
96685684.2770760780830.7229239219173
97617674.682764306154-57.6827643061538
98715730.044054979828-15.0440549798276
99715651.51880847986663.4811915201341
100629681.034224826663-52.0342248266631
101916760.154067953868155.845932046132
102531434.25119065547196.7488093445294
103357395.649045274614-38.6490452746141
104917823.71673762752693.283262372474
105828858.960821867563-30.9608218675631
106708691.45122212070716.5487778792930
107858686.816337372139171.183662627861
108775751.05653375607123.9434662439289
109785706.93786259559978.0621374044014
1101006806.02763420346199.972365796539
111789803.791409161267-14.7914091612669
112734749.957225437861-15.9572254378614
113906966.360612916558-60.360612916558
114532576.445589425618-44.445589425618
115387434.148867993739-47.1488679937387
116991945.53553973479445.4644602652058
117841895.543857846838-54.5438578468385
118892755.54829394039136.451706059609
119782864.324122550107-82.324122550107
120813803.6732906908389.32670930916152
121793792.381855271750.618144728250172
122978960.01919650535717.9808034946434
123775798.397030742782-23.3970307427824
124797742.77351192839554.2264880716049
125946939.3020898315466.6979101684542
126594567.69734002102526.3026599789748
127438432.2550069506965.74499304930379
12810221009.2701853309912.7298146690063
129868891.36763848615-23.3676384861495
130795877.266026191264-82.2660261912636







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
131819.635454044015689.008340930445950.262567157586
132827.568048691115695.983230021659959.15286736057
133809.577390092995677.041786091045942.112994094944
134988.240452822233854.7608358312881121.72006981318
135797.982306238411663.565305915024932.399306561798
136794.825288352778659.477396607744930.17318009781
137954.388356217866818.1159319211171090.66078051461
138594.505238007991457.314511471533731.695964544449
139442.728619029250304.625696281435580.831541777066
1401023.51255598068884.5034228441261162.52168911724
141880.987023479102741.0775494637061020.8964974945
142832.063892109122691.259834130835972.86795008741

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
131 & 819.635454044015 & 689.008340930445 & 950.262567157586 \tabularnewline
132 & 827.568048691115 & 695.983230021659 & 959.15286736057 \tabularnewline
133 & 809.577390092995 & 677.041786091045 & 942.112994094944 \tabularnewline
134 & 988.240452822233 & 854.760835831288 & 1121.72006981318 \tabularnewline
135 & 797.982306238411 & 663.565305915024 & 932.399306561798 \tabularnewline
136 & 794.825288352778 & 659.477396607744 & 930.17318009781 \tabularnewline
137 & 954.388356217866 & 818.115931921117 & 1090.66078051461 \tabularnewline
138 & 594.505238007991 & 457.314511471533 & 731.695964544449 \tabularnewline
139 & 442.728619029250 & 304.625696281435 & 580.831541777066 \tabularnewline
140 & 1023.51255598068 & 884.503422844126 & 1162.52168911724 \tabularnewline
141 & 880.987023479102 & 741.077549463706 & 1020.8964974945 \tabularnewline
142 & 832.063892109122 & 691.259834130835 & 972.86795008741 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116305&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]131[/C][C]819.635454044015[/C][C]689.008340930445[/C][C]950.262567157586[/C][/ROW]
[ROW][C]132[/C][C]827.568048691115[/C][C]695.983230021659[/C][C]959.15286736057[/C][/ROW]
[ROW][C]133[/C][C]809.577390092995[/C][C]677.041786091045[/C][C]942.112994094944[/C][/ROW]
[ROW][C]134[/C][C]988.240452822233[/C][C]854.760835831288[/C][C]1121.72006981318[/C][/ROW]
[ROW][C]135[/C][C]797.982306238411[/C][C]663.565305915024[/C][C]932.399306561798[/C][/ROW]
[ROW][C]136[/C][C]794.825288352778[/C][C]659.477396607744[/C][C]930.17318009781[/C][/ROW]
[ROW][C]137[/C][C]954.388356217866[/C][C]818.115931921117[/C][C]1090.66078051461[/C][/ROW]
[ROW][C]138[/C][C]594.505238007991[/C][C]457.314511471533[/C][C]731.695964544449[/C][/ROW]
[ROW][C]139[/C][C]442.728619029250[/C][C]304.625696281435[/C][C]580.831541777066[/C][/ROW]
[ROW][C]140[/C][C]1023.51255598068[/C][C]884.503422844126[/C][C]1162.52168911724[/C][/ROW]
[ROW][C]141[/C][C]880.987023479102[/C][C]741.077549463706[/C][C]1020.8964974945[/C][/ROW]
[ROW][C]142[/C][C]832.063892109122[/C][C]691.259834130835[/C][C]972.86795008741[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116305&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116305&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
131819.635454044015689.008340930445950.262567157586
132827.568048691115695.983230021659959.15286736057
133809.577390092995677.041786091045942.112994094944
134988.240452822233854.7608358312881121.72006981318
135797.982306238411663.565305915024932.399306561798
136794.825288352778659.477396607744930.17318009781
137954.388356217866818.1159319211171090.66078051461
138594.505238007991457.314511471533731.695964544449
139442.728619029250304.625696281435580.831541777066
1401023.51255598068884.5034228441261162.52168911724
141880.987023479102741.0775494637061020.8964974945
142832.063892109122691.259834130835972.86795008741



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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')