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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 computationWed, 10 Aug 2016 23:48:28 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Aug/10/t1470869324v5ap72dzy5jxx06.htm/, Retrieved Tue, 30 Apr 2024 00:21:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=296275, Retrieved Tue, 30 Apr 2024 00:21:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact76
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-08-10 22:48:28] [3e69b53d94b342798d3f1a806941de01] [Current]
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Dataseries X:
615
680
680
625
710
695
640
665
700
685
645
750
630
680
660
650
720
680
665
710
755
640
655
730
640
685
695
695
730
705
615
630
795
625
700
725
610
645
700
700
730
725
635
630
775
615
690
745
590
595
700
690
755
700
645
600
800
610
690
725
630
565
695
690
785
660
605
595
790
575
665
710
630
520
725
680
750
620
630
610
840
605
675
740
635
520
725
655
755
580
645
615
840
595
655
740
660
525
690
660
740
575
625
630
840
575
655
735




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296275&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]2 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=296275&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296275&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 time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0158751338414481
beta0.26613735251105
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0158751338414481 \tabularnewline
beta & 0.26613735251105 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296275&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]0.0158751338414481[/C][/ROW]
[ROW][C]beta[/C][C]0.26613735251105[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296275&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296275&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
alpha0.0158751338414481
beta0.26613735251105
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13630629.6968482905990.303151709401163
14680677.7062924861032.29370751389683
15660654.5070278578935.49297214210731
16650645.131759604894.86824039510986
17720717.6421418023832.35785819761713
18680679.0809665507630.919033449236622
19665647.37583264884917.624167351151
20710673.09368982624736.9063101737535
21755710.73191484407644.2680851559243
22640697.632373517103-57.6323735171028
23655656.421653946318-1.42165394631809
24730762.763947298994-32.7639472989938
25640643.143590118882-3.14359011888178
26685693.140794841018-8.14079484101831
27695672.96379409656122.0362059034386
28695663.34566957963731.6543304203627
29730734.033257052177-4.03325705217731
30705694.15013858735110.8498614126489
31615679.280052795004-64.2800527950039
32630722.565120408202-92.5651204082018
33795764.73727722016930.2627227798308
34625650.417853721007-25.4178537210067
35700664.45824617480135.5417538251993
36725740.120112803639-15.1201128036389
37610649.582032986885-39.5820329868849
38645693.580997021462-48.5809970214621
39700701.787178888866-1.78717888886558
40700700.482876875139-0.4828768751388
41730734.630047446961-4.63004744696116
42725708.47258821410416.5274117858963
43635618.86769137966416.1323086203356
44630635.045290963968-5.04529096396766
45775799.306553182083-24.3065531820831
46615628.915423548284-13.9154235482836
47690702.770109936914-12.7701099369139
48745727.24312625960217.7568737403981
49590612.728002944204-22.7280029442044
50595647.7842442568-52.7842442567998
51700701.602722012937-1.60272201293674
52690701.213786639913-11.2137866399128
53755730.69277348758224.3072265124175
54700725.522042677416-25.5220426774164
55645634.38888034600810.6111196539915
56600629.142207194401-29.1422071944013
57800773.46841112012226.5315888798782
58610613.72827286264-3.72827286264032
59690688.5326136093151.46738639068451
60725742.994969129588-17.9949691295883
61630587.64000966320242.3599903367983
62565593.995334674512-28.9953346745118
63695698.505878171472-3.50587817147152
64690688.5656063690391.43439363096138
65785753.19329933746731.8067006625332
66660699.125888086692-39.1258880866918
67605643.301317922111-38.3013179221107
68595597.914273913412-2.91427391341233
69790797.315987129222-7.31598712922221
70575606.985197052874-31.9851970528738
71665686.060913634635-21.0609136346346
72710720.523840872834-10.5238408728339
73630624.2274677554495.77253224455137
74520559.167996307479-39.1679963074791
75725687.94746026985137.0525397301485
76680683.029865907563-3.02986590756325
77750776.974932206716-26.9749322067163
78620651.417581307977-31.4175813079773
79630595.80917993318234.1908200668177
80610585.98682347633524.0131765236649
81840781.18654091750558.8134590824955
82605567.60973917919937.390260820801
83675658.81252579687716.1874742031232
84740704.66881107436835.3311889256324
85635625.7640342269479.23596577305295
86520517.1730620142432.82693798575679
87725722.4477615899542.55223841004556
88655678.208651224103-23.2086512241032
89755748.855459736056.14454026395015
90580620.178710388787-40.1787103887873
91645629.68801561120515.3119843887951
92615610.1600520530274.83994794697344
93840839.8323781308020.167621869197546
94595604.522849872836-9.52284987283554
95655674.197874852425-19.1978748524255
96740738.2658965822131.73410341778663
97660632.93853488173927.0614651182609
98525518.1903047423226.80969525767819
99690723.141762952796-33.1417629527961
100660652.7171380424137.28286195758665
101740752.597099228692-12.5970992286924
102575577.817668383108-2.81766838310762
103625642.470414240151-17.4704142401511
104630611.91828625307618.0817137469239
105840837.0606728694742.93932713052595
106575592.128219968293-17.1282199682935
107655651.9986519567553.00134804324534
108735736.950136538952-1.95013653895171

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 630 & 629.696848290599 & 0.303151709401163 \tabularnewline
14 & 680 & 677.706292486103 & 2.29370751389683 \tabularnewline
15 & 660 & 654.507027857893 & 5.49297214210731 \tabularnewline
16 & 650 & 645.13175960489 & 4.86824039510986 \tabularnewline
17 & 720 & 717.642141802383 & 2.35785819761713 \tabularnewline
18 & 680 & 679.080966550763 & 0.919033449236622 \tabularnewline
19 & 665 & 647.375832648849 & 17.624167351151 \tabularnewline
20 & 710 & 673.093689826247 & 36.9063101737535 \tabularnewline
21 & 755 & 710.731914844076 & 44.2680851559243 \tabularnewline
22 & 640 & 697.632373517103 & -57.6323735171028 \tabularnewline
23 & 655 & 656.421653946318 & -1.42165394631809 \tabularnewline
24 & 730 & 762.763947298994 & -32.7639472989938 \tabularnewline
25 & 640 & 643.143590118882 & -3.14359011888178 \tabularnewline
26 & 685 & 693.140794841018 & -8.14079484101831 \tabularnewline
27 & 695 & 672.963794096561 & 22.0362059034386 \tabularnewline
28 & 695 & 663.345669579637 & 31.6543304203627 \tabularnewline
29 & 730 & 734.033257052177 & -4.03325705217731 \tabularnewline
30 & 705 & 694.150138587351 & 10.8498614126489 \tabularnewline
31 & 615 & 679.280052795004 & -64.2800527950039 \tabularnewline
32 & 630 & 722.565120408202 & -92.5651204082018 \tabularnewline
33 & 795 & 764.737277220169 & 30.2627227798308 \tabularnewline
34 & 625 & 650.417853721007 & -25.4178537210067 \tabularnewline
35 & 700 & 664.458246174801 & 35.5417538251993 \tabularnewline
36 & 725 & 740.120112803639 & -15.1201128036389 \tabularnewline
37 & 610 & 649.582032986885 & -39.5820329868849 \tabularnewline
38 & 645 & 693.580997021462 & -48.5809970214621 \tabularnewline
39 & 700 & 701.787178888866 & -1.78717888886558 \tabularnewline
40 & 700 & 700.482876875139 & -0.4828768751388 \tabularnewline
41 & 730 & 734.630047446961 & -4.63004744696116 \tabularnewline
42 & 725 & 708.472588214104 & 16.5274117858963 \tabularnewline
43 & 635 & 618.867691379664 & 16.1323086203356 \tabularnewline
44 & 630 & 635.045290963968 & -5.04529096396766 \tabularnewline
45 & 775 & 799.306553182083 & -24.3065531820831 \tabularnewline
46 & 615 & 628.915423548284 & -13.9154235482836 \tabularnewline
47 & 690 & 702.770109936914 & -12.7701099369139 \tabularnewline
48 & 745 & 727.243126259602 & 17.7568737403981 \tabularnewline
49 & 590 & 612.728002944204 & -22.7280029442044 \tabularnewline
50 & 595 & 647.7842442568 & -52.7842442567998 \tabularnewline
51 & 700 & 701.602722012937 & -1.60272201293674 \tabularnewline
52 & 690 & 701.213786639913 & -11.2137866399128 \tabularnewline
53 & 755 & 730.692773487582 & 24.3072265124175 \tabularnewline
54 & 700 & 725.522042677416 & -25.5220426774164 \tabularnewline
55 & 645 & 634.388880346008 & 10.6111196539915 \tabularnewline
56 & 600 & 629.142207194401 & -29.1422071944013 \tabularnewline
57 & 800 & 773.468411120122 & 26.5315888798782 \tabularnewline
58 & 610 & 613.72827286264 & -3.72827286264032 \tabularnewline
59 & 690 & 688.532613609315 & 1.46738639068451 \tabularnewline
60 & 725 & 742.994969129588 & -17.9949691295883 \tabularnewline
61 & 630 & 587.640009663202 & 42.3599903367983 \tabularnewline
62 & 565 & 593.995334674512 & -28.9953346745118 \tabularnewline
63 & 695 & 698.505878171472 & -3.50587817147152 \tabularnewline
64 & 690 & 688.565606369039 & 1.43439363096138 \tabularnewline
65 & 785 & 753.193299337467 & 31.8067006625332 \tabularnewline
66 & 660 & 699.125888086692 & -39.1258880866918 \tabularnewline
67 & 605 & 643.301317922111 & -38.3013179221107 \tabularnewline
68 & 595 & 597.914273913412 & -2.91427391341233 \tabularnewline
69 & 790 & 797.315987129222 & -7.31598712922221 \tabularnewline
70 & 575 & 606.985197052874 & -31.9851970528738 \tabularnewline
71 & 665 & 686.060913634635 & -21.0609136346346 \tabularnewline
72 & 710 & 720.523840872834 & -10.5238408728339 \tabularnewline
73 & 630 & 624.227467755449 & 5.77253224455137 \tabularnewline
74 & 520 & 559.167996307479 & -39.1679963074791 \tabularnewline
75 & 725 & 687.947460269851 & 37.0525397301485 \tabularnewline
76 & 680 & 683.029865907563 & -3.02986590756325 \tabularnewline
77 & 750 & 776.974932206716 & -26.9749322067163 \tabularnewline
78 & 620 & 651.417581307977 & -31.4175813079773 \tabularnewline
79 & 630 & 595.809179933182 & 34.1908200668177 \tabularnewline
80 & 610 & 585.986823476335 & 24.0131765236649 \tabularnewline
81 & 840 & 781.186540917505 & 58.8134590824955 \tabularnewline
82 & 605 & 567.609739179199 & 37.390260820801 \tabularnewline
83 & 675 & 658.812525796877 & 16.1874742031232 \tabularnewline
84 & 740 & 704.668811074368 & 35.3311889256324 \tabularnewline
85 & 635 & 625.764034226947 & 9.23596577305295 \tabularnewline
86 & 520 & 517.173062014243 & 2.82693798575679 \tabularnewline
87 & 725 & 722.447761589954 & 2.55223841004556 \tabularnewline
88 & 655 & 678.208651224103 & -23.2086512241032 \tabularnewline
89 & 755 & 748.85545973605 & 6.14454026395015 \tabularnewline
90 & 580 & 620.178710388787 & -40.1787103887873 \tabularnewline
91 & 645 & 629.688015611205 & 15.3119843887951 \tabularnewline
92 & 615 & 610.160052053027 & 4.83994794697344 \tabularnewline
93 & 840 & 839.832378130802 & 0.167621869197546 \tabularnewline
94 & 595 & 604.522849872836 & -9.52284987283554 \tabularnewline
95 & 655 & 674.197874852425 & -19.1978748524255 \tabularnewline
96 & 740 & 738.265896582213 & 1.73410341778663 \tabularnewline
97 & 660 & 632.938534881739 & 27.0614651182609 \tabularnewline
98 & 525 & 518.190304742322 & 6.80969525767819 \tabularnewline
99 & 690 & 723.141762952796 & -33.1417629527961 \tabularnewline
100 & 660 & 652.717138042413 & 7.28286195758665 \tabularnewline
101 & 740 & 752.597099228692 & -12.5970992286924 \tabularnewline
102 & 575 & 577.817668383108 & -2.81766838310762 \tabularnewline
103 & 625 & 642.470414240151 & -17.4704142401511 \tabularnewline
104 & 630 & 611.918286253076 & 18.0817137469239 \tabularnewline
105 & 840 & 837.060672869474 & 2.93932713052595 \tabularnewline
106 & 575 & 592.128219968293 & -17.1282199682935 \tabularnewline
107 & 655 & 651.998651956755 & 3.00134804324534 \tabularnewline
108 & 735 & 736.950136538952 & -1.95013653895171 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296275&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]630[/C][C]629.696848290599[/C][C]0.303151709401163[/C][/ROW]
[ROW][C]14[/C][C]680[/C][C]677.706292486103[/C][C]2.29370751389683[/C][/ROW]
[ROW][C]15[/C][C]660[/C][C]654.507027857893[/C][C]5.49297214210731[/C][/ROW]
[ROW][C]16[/C][C]650[/C][C]645.13175960489[/C][C]4.86824039510986[/C][/ROW]
[ROW][C]17[/C][C]720[/C][C]717.642141802383[/C][C]2.35785819761713[/C][/ROW]
[ROW][C]18[/C][C]680[/C][C]679.080966550763[/C][C]0.919033449236622[/C][/ROW]
[ROW][C]19[/C][C]665[/C][C]647.375832648849[/C][C]17.624167351151[/C][/ROW]
[ROW][C]20[/C][C]710[/C][C]673.093689826247[/C][C]36.9063101737535[/C][/ROW]
[ROW][C]21[/C][C]755[/C][C]710.731914844076[/C][C]44.2680851559243[/C][/ROW]
[ROW][C]22[/C][C]640[/C][C]697.632373517103[/C][C]-57.6323735171028[/C][/ROW]
[ROW][C]23[/C][C]655[/C][C]656.421653946318[/C][C]-1.42165394631809[/C][/ROW]
[ROW][C]24[/C][C]730[/C][C]762.763947298994[/C][C]-32.7639472989938[/C][/ROW]
[ROW][C]25[/C][C]640[/C][C]643.143590118882[/C][C]-3.14359011888178[/C][/ROW]
[ROW][C]26[/C][C]685[/C][C]693.140794841018[/C][C]-8.14079484101831[/C][/ROW]
[ROW][C]27[/C][C]695[/C][C]672.963794096561[/C][C]22.0362059034386[/C][/ROW]
[ROW][C]28[/C][C]695[/C][C]663.345669579637[/C][C]31.6543304203627[/C][/ROW]
[ROW][C]29[/C][C]730[/C][C]734.033257052177[/C][C]-4.03325705217731[/C][/ROW]
[ROW][C]30[/C][C]705[/C][C]694.150138587351[/C][C]10.8498614126489[/C][/ROW]
[ROW][C]31[/C][C]615[/C][C]679.280052795004[/C][C]-64.2800527950039[/C][/ROW]
[ROW][C]32[/C][C]630[/C][C]722.565120408202[/C][C]-92.5651204082018[/C][/ROW]
[ROW][C]33[/C][C]795[/C][C]764.737277220169[/C][C]30.2627227798308[/C][/ROW]
[ROW][C]34[/C][C]625[/C][C]650.417853721007[/C][C]-25.4178537210067[/C][/ROW]
[ROW][C]35[/C][C]700[/C][C]664.458246174801[/C][C]35.5417538251993[/C][/ROW]
[ROW][C]36[/C][C]725[/C][C]740.120112803639[/C][C]-15.1201128036389[/C][/ROW]
[ROW][C]37[/C][C]610[/C][C]649.582032986885[/C][C]-39.5820329868849[/C][/ROW]
[ROW][C]38[/C][C]645[/C][C]693.580997021462[/C][C]-48.5809970214621[/C][/ROW]
[ROW][C]39[/C][C]700[/C][C]701.787178888866[/C][C]-1.78717888886558[/C][/ROW]
[ROW][C]40[/C][C]700[/C][C]700.482876875139[/C][C]-0.4828768751388[/C][/ROW]
[ROW][C]41[/C][C]730[/C][C]734.630047446961[/C][C]-4.63004744696116[/C][/ROW]
[ROW][C]42[/C][C]725[/C][C]708.472588214104[/C][C]16.5274117858963[/C][/ROW]
[ROW][C]43[/C][C]635[/C][C]618.867691379664[/C][C]16.1323086203356[/C][/ROW]
[ROW][C]44[/C][C]630[/C][C]635.045290963968[/C][C]-5.04529096396766[/C][/ROW]
[ROW][C]45[/C][C]775[/C][C]799.306553182083[/C][C]-24.3065531820831[/C][/ROW]
[ROW][C]46[/C][C]615[/C][C]628.915423548284[/C][C]-13.9154235482836[/C][/ROW]
[ROW][C]47[/C][C]690[/C][C]702.770109936914[/C][C]-12.7701099369139[/C][/ROW]
[ROW][C]48[/C][C]745[/C][C]727.243126259602[/C][C]17.7568737403981[/C][/ROW]
[ROW][C]49[/C][C]590[/C][C]612.728002944204[/C][C]-22.7280029442044[/C][/ROW]
[ROW][C]50[/C][C]595[/C][C]647.7842442568[/C][C]-52.7842442567998[/C][/ROW]
[ROW][C]51[/C][C]700[/C][C]701.602722012937[/C][C]-1.60272201293674[/C][/ROW]
[ROW][C]52[/C][C]690[/C][C]701.213786639913[/C][C]-11.2137866399128[/C][/ROW]
[ROW][C]53[/C][C]755[/C][C]730.692773487582[/C][C]24.3072265124175[/C][/ROW]
[ROW][C]54[/C][C]700[/C][C]725.522042677416[/C][C]-25.5220426774164[/C][/ROW]
[ROW][C]55[/C][C]645[/C][C]634.388880346008[/C][C]10.6111196539915[/C][/ROW]
[ROW][C]56[/C][C]600[/C][C]629.142207194401[/C][C]-29.1422071944013[/C][/ROW]
[ROW][C]57[/C][C]800[/C][C]773.468411120122[/C][C]26.5315888798782[/C][/ROW]
[ROW][C]58[/C][C]610[/C][C]613.72827286264[/C][C]-3.72827286264032[/C][/ROW]
[ROW][C]59[/C][C]690[/C][C]688.532613609315[/C][C]1.46738639068451[/C][/ROW]
[ROW][C]60[/C][C]725[/C][C]742.994969129588[/C][C]-17.9949691295883[/C][/ROW]
[ROW][C]61[/C][C]630[/C][C]587.640009663202[/C][C]42.3599903367983[/C][/ROW]
[ROW][C]62[/C][C]565[/C][C]593.995334674512[/C][C]-28.9953346745118[/C][/ROW]
[ROW][C]63[/C][C]695[/C][C]698.505878171472[/C][C]-3.50587817147152[/C][/ROW]
[ROW][C]64[/C][C]690[/C][C]688.565606369039[/C][C]1.43439363096138[/C][/ROW]
[ROW][C]65[/C][C]785[/C][C]753.193299337467[/C][C]31.8067006625332[/C][/ROW]
[ROW][C]66[/C][C]660[/C][C]699.125888086692[/C][C]-39.1258880866918[/C][/ROW]
[ROW][C]67[/C][C]605[/C][C]643.301317922111[/C][C]-38.3013179221107[/C][/ROW]
[ROW][C]68[/C][C]595[/C][C]597.914273913412[/C][C]-2.91427391341233[/C][/ROW]
[ROW][C]69[/C][C]790[/C][C]797.315987129222[/C][C]-7.31598712922221[/C][/ROW]
[ROW][C]70[/C][C]575[/C][C]606.985197052874[/C][C]-31.9851970528738[/C][/ROW]
[ROW][C]71[/C][C]665[/C][C]686.060913634635[/C][C]-21.0609136346346[/C][/ROW]
[ROW][C]72[/C][C]710[/C][C]720.523840872834[/C][C]-10.5238408728339[/C][/ROW]
[ROW][C]73[/C][C]630[/C][C]624.227467755449[/C][C]5.77253224455137[/C][/ROW]
[ROW][C]74[/C][C]520[/C][C]559.167996307479[/C][C]-39.1679963074791[/C][/ROW]
[ROW][C]75[/C][C]725[/C][C]687.947460269851[/C][C]37.0525397301485[/C][/ROW]
[ROW][C]76[/C][C]680[/C][C]683.029865907563[/C][C]-3.02986590756325[/C][/ROW]
[ROW][C]77[/C][C]750[/C][C]776.974932206716[/C][C]-26.9749322067163[/C][/ROW]
[ROW][C]78[/C][C]620[/C][C]651.417581307977[/C][C]-31.4175813079773[/C][/ROW]
[ROW][C]79[/C][C]630[/C][C]595.809179933182[/C][C]34.1908200668177[/C][/ROW]
[ROW][C]80[/C][C]610[/C][C]585.986823476335[/C][C]24.0131765236649[/C][/ROW]
[ROW][C]81[/C][C]840[/C][C]781.186540917505[/C][C]58.8134590824955[/C][/ROW]
[ROW][C]82[/C][C]605[/C][C]567.609739179199[/C][C]37.390260820801[/C][/ROW]
[ROW][C]83[/C][C]675[/C][C]658.812525796877[/C][C]16.1874742031232[/C][/ROW]
[ROW][C]84[/C][C]740[/C][C]704.668811074368[/C][C]35.3311889256324[/C][/ROW]
[ROW][C]85[/C][C]635[/C][C]625.764034226947[/C][C]9.23596577305295[/C][/ROW]
[ROW][C]86[/C][C]520[/C][C]517.173062014243[/C][C]2.82693798575679[/C][/ROW]
[ROW][C]87[/C][C]725[/C][C]722.447761589954[/C][C]2.55223841004556[/C][/ROW]
[ROW][C]88[/C][C]655[/C][C]678.208651224103[/C][C]-23.2086512241032[/C][/ROW]
[ROW][C]89[/C][C]755[/C][C]748.85545973605[/C][C]6.14454026395015[/C][/ROW]
[ROW][C]90[/C][C]580[/C][C]620.178710388787[/C][C]-40.1787103887873[/C][/ROW]
[ROW][C]91[/C][C]645[/C][C]629.688015611205[/C][C]15.3119843887951[/C][/ROW]
[ROW][C]92[/C][C]615[/C][C]610.160052053027[/C][C]4.83994794697344[/C][/ROW]
[ROW][C]93[/C][C]840[/C][C]839.832378130802[/C][C]0.167621869197546[/C][/ROW]
[ROW][C]94[/C][C]595[/C][C]604.522849872836[/C][C]-9.52284987283554[/C][/ROW]
[ROW][C]95[/C][C]655[/C][C]674.197874852425[/C][C]-19.1978748524255[/C][/ROW]
[ROW][C]96[/C][C]740[/C][C]738.265896582213[/C][C]1.73410341778663[/C][/ROW]
[ROW][C]97[/C][C]660[/C][C]632.938534881739[/C][C]27.0614651182609[/C][/ROW]
[ROW][C]98[/C][C]525[/C][C]518.190304742322[/C][C]6.80969525767819[/C][/ROW]
[ROW][C]99[/C][C]690[/C][C]723.141762952796[/C][C]-33.1417629527961[/C][/ROW]
[ROW][C]100[/C][C]660[/C][C]652.717138042413[/C][C]7.28286195758665[/C][/ROW]
[ROW][C]101[/C][C]740[/C][C]752.597099228692[/C][C]-12.5970992286924[/C][/ROW]
[ROW][C]102[/C][C]575[/C][C]577.817668383108[/C][C]-2.81766838310762[/C][/ROW]
[ROW][C]103[/C][C]625[/C][C]642.470414240151[/C][C]-17.4704142401511[/C][/ROW]
[ROW][C]104[/C][C]630[/C][C]611.918286253076[/C][C]18.0817137469239[/C][/ROW]
[ROW][C]105[/C][C]840[/C][C]837.060672869474[/C][C]2.93932713052595[/C][/ROW]
[ROW][C]106[/C][C]575[/C][C]592.128219968293[/C][C]-17.1282199682935[/C][/ROW]
[ROW][C]107[/C][C]655[/C][C]651.998651956755[/C][C]3.00134804324534[/C][/ROW]
[ROW][C]108[/C][C]735[/C][C]736.950136538952[/C][C]-1.95013653895171[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296275&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296275&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
13630629.6968482905990.303151709401163
14680677.7062924861032.29370751389683
15660654.5070278578935.49297214210731
16650645.131759604894.86824039510986
17720717.6421418023832.35785819761713
18680679.0809665507630.919033449236622
19665647.37583264884917.624167351151
20710673.09368982624736.9063101737535
21755710.73191484407644.2680851559243
22640697.632373517103-57.6323735171028
23655656.421653946318-1.42165394631809
24730762.763947298994-32.7639472989938
25640643.143590118882-3.14359011888178
26685693.140794841018-8.14079484101831
27695672.96379409656122.0362059034386
28695663.34566957963731.6543304203627
29730734.033257052177-4.03325705217731
30705694.15013858735110.8498614126489
31615679.280052795004-64.2800527950039
32630722.565120408202-92.5651204082018
33795764.73727722016930.2627227798308
34625650.417853721007-25.4178537210067
35700664.45824617480135.5417538251993
36725740.120112803639-15.1201128036389
37610649.582032986885-39.5820329868849
38645693.580997021462-48.5809970214621
39700701.787178888866-1.78717888886558
40700700.482876875139-0.4828768751388
41730734.630047446961-4.63004744696116
42725708.47258821410416.5274117858963
43635618.86769137966416.1323086203356
44630635.045290963968-5.04529096396766
45775799.306553182083-24.3065531820831
46615628.915423548284-13.9154235482836
47690702.770109936914-12.7701099369139
48745727.24312625960217.7568737403981
49590612.728002944204-22.7280029442044
50595647.7842442568-52.7842442567998
51700701.602722012937-1.60272201293674
52690701.213786639913-11.2137866399128
53755730.69277348758224.3072265124175
54700725.522042677416-25.5220426774164
55645634.38888034600810.6111196539915
56600629.142207194401-29.1422071944013
57800773.46841112012226.5315888798782
58610613.72827286264-3.72827286264032
59690688.5326136093151.46738639068451
60725742.994969129588-17.9949691295883
61630587.64000966320242.3599903367983
62565593.995334674512-28.9953346745118
63695698.505878171472-3.50587817147152
64690688.5656063690391.43439363096138
65785753.19329933746731.8067006625332
66660699.125888086692-39.1258880866918
67605643.301317922111-38.3013179221107
68595597.914273913412-2.91427391341233
69790797.315987129222-7.31598712922221
70575606.985197052874-31.9851970528738
71665686.060913634635-21.0609136346346
72710720.523840872834-10.5238408728339
73630624.2274677554495.77253224455137
74520559.167996307479-39.1679963074791
75725687.94746026985137.0525397301485
76680683.029865907563-3.02986590756325
77750776.974932206716-26.9749322067163
78620651.417581307977-31.4175813079773
79630595.80917993318234.1908200668177
80610585.98682347633524.0131765236649
81840781.18654091750558.8134590824955
82605567.60973917919937.390260820801
83675658.81252579687716.1874742031232
84740704.66881107436835.3311889256324
85635625.7640342269479.23596577305295
86520517.1730620142432.82693798575679
87725722.4477615899542.55223841004556
88655678.208651224103-23.2086512241032
89755748.855459736056.14454026395015
90580620.178710388787-40.1787103887873
91645629.68801561120515.3119843887951
92615610.1600520530274.83994794697344
93840839.8323781308020.167621869197546
94595604.522849872836-9.52284987283554
95655674.197874852425-19.1978748524255
96740738.2658965822131.73410341778663
97660632.93853488173927.0614651182609
98525518.1903047423226.80969525767819
99690723.141762952796-33.1417629527961
100660652.7171380424137.28286195758665
101740752.597099228692-12.5970992286924
102575577.817668383108-2.81766838310762
103625642.470414240151-17.4704142401511
104630611.91828625307618.0817137469239
105840837.0606728694742.93932713052595
106575592.128219968293-17.1282199682935
107655651.9986519567553.00134804324534
108735736.950136538952-1.95013653895171







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109656.405374594957605.435184903185707.375564286729
110521.098737114084470.118252126518572.07922210165
111686.397563647908635.402004178497737.393123117318
112656.194666675471605.178348754176707.210984596765
113736.27659690281685.232934960785787.320258844835
114571.256499673673520.178010804553622.334988542792
115621.480921299536570.359230743677672.602611855394
116626.214760043022575.040608034421677.388912051622
117836.112591573268784.875841680022887.349341466515
118571.316579542121520.006228620505622.626930463737
119651.27337407319599.87756394272702.66918420366
120731.296093491004679.802124423102782.790062558906

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 656.405374594957 & 605.435184903185 & 707.375564286729 \tabularnewline
110 & 521.098737114084 & 470.118252126518 & 572.07922210165 \tabularnewline
111 & 686.397563647908 & 635.402004178497 & 737.393123117318 \tabularnewline
112 & 656.194666675471 & 605.178348754176 & 707.210984596765 \tabularnewline
113 & 736.27659690281 & 685.232934960785 & 787.320258844835 \tabularnewline
114 & 571.256499673673 & 520.178010804553 & 622.334988542792 \tabularnewline
115 & 621.480921299536 & 570.359230743677 & 672.602611855394 \tabularnewline
116 & 626.214760043022 & 575.040608034421 & 677.388912051622 \tabularnewline
117 & 836.112591573268 & 784.875841680022 & 887.349341466515 \tabularnewline
118 & 571.316579542121 & 520.006228620505 & 622.626930463737 \tabularnewline
119 & 651.27337407319 & 599.87756394272 & 702.66918420366 \tabularnewline
120 & 731.296093491004 & 679.802124423102 & 782.790062558906 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296275&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]109[/C][C]656.405374594957[/C][C]605.435184903185[/C][C]707.375564286729[/C][/ROW]
[ROW][C]110[/C][C]521.098737114084[/C][C]470.118252126518[/C][C]572.07922210165[/C][/ROW]
[ROW][C]111[/C][C]686.397563647908[/C][C]635.402004178497[/C][C]737.393123117318[/C][/ROW]
[ROW][C]112[/C][C]656.194666675471[/C][C]605.178348754176[/C][C]707.210984596765[/C][/ROW]
[ROW][C]113[/C][C]736.27659690281[/C][C]685.232934960785[/C][C]787.320258844835[/C][/ROW]
[ROW][C]114[/C][C]571.256499673673[/C][C]520.178010804553[/C][C]622.334988542792[/C][/ROW]
[ROW][C]115[/C][C]621.480921299536[/C][C]570.359230743677[/C][C]672.602611855394[/C][/ROW]
[ROW][C]116[/C][C]626.214760043022[/C][C]575.040608034421[/C][C]677.388912051622[/C][/ROW]
[ROW][C]117[/C][C]836.112591573268[/C][C]784.875841680022[/C][C]887.349341466515[/C][/ROW]
[ROW][C]118[/C][C]571.316579542121[/C][C]520.006228620505[/C][C]622.626930463737[/C][/ROW]
[ROW][C]119[/C][C]651.27337407319[/C][C]599.87756394272[/C][C]702.66918420366[/C][/ROW]
[ROW][C]120[/C][C]731.296093491004[/C][C]679.802124423102[/C][C]782.790062558906[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296275&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296275&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
109656.405374594957605.435184903185707.375564286729
110521.098737114084470.118252126518572.07922210165
111686.397563647908635.402004178497737.393123117318
112656.194666675471605.178348754176707.210984596765
113736.27659690281685.232934960785787.320258844835
114571.256499673673520.178010804553622.334988542792
115621.480921299536570.359230743677672.602611855394
116626.214760043022575.040608034421677.388912051622
117836.112591573268784.875841680022887.349341466515
118571.316579542121520.006228620505622.626930463737
119651.27337407319599.87756394272702.66918420366
120731.296093491004679.802124423102782.790062558906



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')