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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 computationFri, 19 Aug 2011 03:53:16 -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/2011/Aug/19/t1313740577ypq098cgq85wqki.htm/, Retrieved Mon, 13 May 2024 23:43:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=124197, Retrieved Mon, 13 May 2024 23:43:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsVan Tongelen Caroline
Estimated Impact190
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [TIJDREEKS B - STA...] [2011-08-19 07:53:16] [7d6606cca1b3596736d7d387043cb02b] [Current]
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Dataseries X:
540
520
550
440
570
560
600
620
690
600
570
710
600
450
530
400
560
460
610
550
580
650
640
760
550
460
510
370
530
410
580
550
490
700
630
720
540
500
450
370
490
440
600
580
500
670
620
800
640
390
390
390
460
460
620
570
510
640
590
850
670
390
410
340
470
540
680
670
540
630
560
800
610
490
440
330
490
590
690
650
480
690
540
830
690
500
460
310
490
470
710
710
540
700
520
810
690
510
390
270
530
510
670
770
570
640
480
830




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124197&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124197&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124197&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.00926118605787605
beta1
gamma0.929768627341917

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.00926118605787605 \tabularnewline
beta & 1 \tabularnewline
gamma & 0.929768627341917 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124197&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]0.00926118605787605[/C][/ROW]
[ROW][C]beta[/C][C]1[/C][/ROW]
[ROW][C]gamma[/C][C]0.929768627341917[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124197&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124197&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
alpha0.00926118605787605
beta1
gamma0.929768627341917







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13600620.518162393162-20.5181623931624
14450470.018653484721-20.0186534847208
15530554.338374146668-24.338374146668
16400423.392686860528-23.3926868605282
17560574.739113734889-14.739113734889
18460466.029181285405-6.02918128540472
19610582.76074243789327.2392575621075
20550600.052676624763-50.0526766247634
21580669.498582010773-89.498582010773
22650576.50030850786473.4996914921362
23640545.27561999441694.7243800055841
24760687.6247573777672.3752426222397
25550560.70339578938-10.7033957893796
26460411.02409460083148.9759053991685
27510492.91179826455717.0882017354431
28370364.5127129421965.48728705780354
29530525.6571878566734.34281214332748
30410426.883199001845-16.8831990018446
31580575.7952017005984.20479829940177
32550523.09788827593926.9021117240612
33490559.055424857432-69.0554248574322
34700618.71779373185581.2822062681446
35630609.51271718934320.4872828106567
36720732.295971563062-12.2959715630618
37540528.98648116109311.0135188389066
38500435.60805495395364.3919450460465
39450489.533383949158-39.5333839491576
40370350.66772233959119.3322776604085
41490511.758477824285-21.7584778242851
42440393.82082561802846.1791743819718
43600563.95684038308336.0431596169174
44580533.97166283516646.0283371648341
45500483.400888818316.5991111816997
46670684.821072112329-14.8210721123295
47620620.314073057056-0.314073057055566
48800714.10331415290185.8966858470989
49640535.481489776574104.518510223426
50390495.311520142445-105.311520142445
51390453.534436228592-63.5344362285923
52390370.04966234175719.9503376582431
53460494.679391724356-34.6793917243563
54460440.46803895321519.531961046785
55620602.03827399636217.9617260036384
56570581.933985079778-11.9339850797776
57510504.0310676244045.9689323755959
58640676.625025213098-36.625025213098
59590625.292572917804-35.2925729178039
60850797.86088893458852.1391110654117
61670635.4567327438434.5432672561599
62390400.080735739238-10.0807357392381
63410397.27945096048612.7205490395142
64340391.720316145675-51.7203161456748
65470465.0167012280284.98329877197227
66540461.13022561776278.8697743822381
67680622.37344287058757.6265571294127
68670576.03504930247793.9649506975228
69540517.52226602447522.4777339755254
70630653.104217827989-23.1042178279889
71560605.3204641278-45.3204641277999
72800860.437504314335-60.4375043143352
73610681.842823010612-71.8428230106118
74490404.45116965460285.5488303453978
75440424.5001105828515.4998894171499
76330360.593245466186-30.5932454661863
77490487.5006746248312.49932537516924
78590552.81169958502937.188300414971
79690694.873917201946-4.87391720194591
80650681.624640648139-31.6246406481393
81480555.129176568287-75.1291765682872
82690645.94648320297344.0535167970274
83540577.069464089133-37.069464089133
84830817.16359624083412.8364037591656
85690628.24588089867961.7541191013206
86500497.8157812312022.18421876879847
87460452.5362066320877.46379336791313
88310345.991112805964-35.9911128059643
89490503.177291517979-13.1772915179791
90470599.997228840146-129.997228840146
91710699.91690537507210.0830946249279
92710660.45476668300449.5452333169961
93540493.67847324147346.3215267585271
94700695.5733974620534.42660253794702
95520551.402086261853-31.4020862618532
96810837.372146662013-27.3721466620133
97690692.62287073974-2.62287073973982
98510505.6069541362574.39304586374277
99390464.115286609443-74.1152866094426
100270314.934455057973-44.9344550579727
101530491.11872281334938.8812771866509
102510479.35908806126130.640911938739
103670709.838164133235-39.8381641332352
104770705.83783266096164.1621673390393
105570535.93601462991334.0639853700867
106640698.72070899305-58.72070899305
107480519.971009786022-39.9710097860225
108830808.5048735122321.49512648777

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 600 & 620.518162393162 & -20.5181623931624 \tabularnewline
14 & 450 & 470.018653484721 & -20.0186534847208 \tabularnewline
15 & 530 & 554.338374146668 & -24.338374146668 \tabularnewline
16 & 400 & 423.392686860528 & -23.3926868605282 \tabularnewline
17 & 560 & 574.739113734889 & -14.739113734889 \tabularnewline
18 & 460 & 466.029181285405 & -6.02918128540472 \tabularnewline
19 & 610 & 582.760742437893 & 27.2392575621075 \tabularnewline
20 & 550 & 600.052676624763 & -50.0526766247634 \tabularnewline
21 & 580 & 669.498582010773 & -89.498582010773 \tabularnewline
22 & 650 & 576.500308507864 & 73.4996914921362 \tabularnewline
23 & 640 & 545.275619994416 & 94.7243800055841 \tabularnewline
24 & 760 & 687.62475737776 & 72.3752426222397 \tabularnewline
25 & 550 & 560.70339578938 & -10.7033957893796 \tabularnewline
26 & 460 & 411.024094600831 & 48.9759053991685 \tabularnewline
27 & 510 & 492.911798264557 & 17.0882017354431 \tabularnewline
28 & 370 & 364.512712942196 & 5.48728705780354 \tabularnewline
29 & 530 & 525.657187856673 & 4.34281214332748 \tabularnewline
30 & 410 & 426.883199001845 & -16.8831990018446 \tabularnewline
31 & 580 & 575.795201700598 & 4.20479829940177 \tabularnewline
32 & 550 & 523.097888275939 & 26.9021117240612 \tabularnewline
33 & 490 & 559.055424857432 & -69.0554248574322 \tabularnewline
34 & 700 & 618.717793731855 & 81.2822062681446 \tabularnewline
35 & 630 & 609.512717189343 & 20.4872828106567 \tabularnewline
36 & 720 & 732.295971563062 & -12.2959715630618 \tabularnewline
37 & 540 & 528.986481161093 & 11.0135188389066 \tabularnewline
38 & 500 & 435.608054953953 & 64.3919450460465 \tabularnewline
39 & 450 & 489.533383949158 & -39.5333839491576 \tabularnewline
40 & 370 & 350.667722339591 & 19.3322776604085 \tabularnewline
41 & 490 & 511.758477824285 & -21.7584778242851 \tabularnewline
42 & 440 & 393.820825618028 & 46.1791743819718 \tabularnewline
43 & 600 & 563.956840383083 & 36.0431596169174 \tabularnewline
44 & 580 & 533.971662835166 & 46.0283371648341 \tabularnewline
45 & 500 & 483.4008888183 & 16.5991111816997 \tabularnewline
46 & 670 & 684.821072112329 & -14.8210721123295 \tabularnewline
47 & 620 & 620.314073057056 & -0.314073057055566 \tabularnewline
48 & 800 & 714.103314152901 & 85.8966858470989 \tabularnewline
49 & 640 & 535.481489776574 & 104.518510223426 \tabularnewline
50 & 390 & 495.311520142445 & -105.311520142445 \tabularnewline
51 & 390 & 453.534436228592 & -63.5344362285923 \tabularnewline
52 & 390 & 370.049662341757 & 19.9503376582431 \tabularnewline
53 & 460 & 494.679391724356 & -34.6793917243563 \tabularnewline
54 & 460 & 440.468038953215 & 19.531961046785 \tabularnewline
55 & 620 & 602.038273996362 & 17.9617260036384 \tabularnewline
56 & 570 & 581.933985079778 & -11.9339850797776 \tabularnewline
57 & 510 & 504.031067624404 & 5.9689323755959 \tabularnewline
58 & 640 & 676.625025213098 & -36.625025213098 \tabularnewline
59 & 590 & 625.292572917804 & -35.2925729178039 \tabularnewline
60 & 850 & 797.860888934588 & 52.1391110654117 \tabularnewline
61 & 670 & 635.45673274384 & 34.5432672561599 \tabularnewline
62 & 390 & 400.080735739238 & -10.0807357392381 \tabularnewline
63 & 410 & 397.279450960486 & 12.7205490395142 \tabularnewline
64 & 340 & 391.720316145675 & -51.7203161456748 \tabularnewline
65 & 470 & 465.016701228028 & 4.98329877197227 \tabularnewline
66 & 540 & 461.130225617762 & 78.8697743822381 \tabularnewline
67 & 680 & 622.373442870587 & 57.6265571294127 \tabularnewline
68 & 670 & 576.035049302477 & 93.9649506975228 \tabularnewline
69 & 540 & 517.522266024475 & 22.4777339755254 \tabularnewline
70 & 630 & 653.104217827989 & -23.1042178279889 \tabularnewline
71 & 560 & 605.3204641278 & -45.3204641277999 \tabularnewline
72 & 800 & 860.437504314335 & -60.4375043143352 \tabularnewline
73 & 610 & 681.842823010612 & -71.8428230106118 \tabularnewline
74 & 490 & 404.451169654602 & 85.5488303453978 \tabularnewline
75 & 440 & 424.50011058285 & 15.4998894171499 \tabularnewline
76 & 330 & 360.593245466186 & -30.5932454661863 \tabularnewline
77 & 490 & 487.500674624831 & 2.49932537516924 \tabularnewline
78 & 590 & 552.811699585029 & 37.188300414971 \tabularnewline
79 & 690 & 694.873917201946 & -4.87391720194591 \tabularnewline
80 & 650 & 681.624640648139 & -31.6246406481393 \tabularnewline
81 & 480 & 555.129176568287 & -75.1291765682872 \tabularnewline
82 & 690 & 645.946483202973 & 44.0535167970274 \tabularnewline
83 & 540 & 577.069464089133 & -37.069464089133 \tabularnewline
84 & 830 & 817.163596240834 & 12.8364037591656 \tabularnewline
85 & 690 & 628.245880898679 & 61.7541191013206 \tabularnewline
86 & 500 & 497.815781231202 & 2.18421876879847 \tabularnewline
87 & 460 & 452.536206632087 & 7.46379336791313 \tabularnewline
88 & 310 & 345.991112805964 & -35.9911128059643 \tabularnewline
89 & 490 & 503.177291517979 & -13.1772915179791 \tabularnewline
90 & 470 & 599.997228840146 & -129.997228840146 \tabularnewline
91 & 710 & 699.916905375072 & 10.0830946249279 \tabularnewline
92 & 710 & 660.454766683004 & 49.5452333169961 \tabularnewline
93 & 540 & 493.678473241473 & 46.3215267585271 \tabularnewline
94 & 700 & 695.573397462053 & 4.42660253794702 \tabularnewline
95 & 520 & 551.402086261853 & -31.4020862618532 \tabularnewline
96 & 810 & 837.372146662013 & -27.3721466620133 \tabularnewline
97 & 690 & 692.62287073974 & -2.62287073973982 \tabularnewline
98 & 510 & 505.606954136257 & 4.39304586374277 \tabularnewline
99 & 390 & 464.115286609443 & -74.1152866094426 \tabularnewline
100 & 270 & 314.934455057973 & -44.9344550579727 \tabularnewline
101 & 530 & 491.118722813349 & 38.8812771866509 \tabularnewline
102 & 510 & 479.359088061261 & 30.640911938739 \tabularnewline
103 & 670 & 709.838164133235 & -39.8381641332352 \tabularnewline
104 & 770 & 705.837832660961 & 64.1621673390393 \tabularnewline
105 & 570 & 535.936014629913 & 34.0639853700867 \tabularnewline
106 & 640 & 698.72070899305 & -58.72070899305 \tabularnewline
107 & 480 & 519.971009786022 & -39.9710097860225 \tabularnewline
108 & 830 & 808.50487351223 & 21.49512648777 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124197&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]600[/C][C]620.518162393162[/C][C]-20.5181623931624[/C][/ROW]
[ROW][C]14[/C][C]450[/C][C]470.018653484721[/C][C]-20.0186534847208[/C][/ROW]
[ROW][C]15[/C][C]530[/C][C]554.338374146668[/C][C]-24.338374146668[/C][/ROW]
[ROW][C]16[/C][C]400[/C][C]423.392686860528[/C][C]-23.3926868605282[/C][/ROW]
[ROW][C]17[/C][C]560[/C][C]574.739113734889[/C][C]-14.739113734889[/C][/ROW]
[ROW][C]18[/C][C]460[/C][C]466.029181285405[/C][C]-6.02918128540472[/C][/ROW]
[ROW][C]19[/C][C]610[/C][C]582.760742437893[/C][C]27.2392575621075[/C][/ROW]
[ROW][C]20[/C][C]550[/C][C]600.052676624763[/C][C]-50.0526766247634[/C][/ROW]
[ROW][C]21[/C][C]580[/C][C]669.498582010773[/C][C]-89.498582010773[/C][/ROW]
[ROW][C]22[/C][C]650[/C][C]576.500308507864[/C][C]73.4996914921362[/C][/ROW]
[ROW][C]23[/C][C]640[/C][C]545.275619994416[/C][C]94.7243800055841[/C][/ROW]
[ROW][C]24[/C][C]760[/C][C]687.62475737776[/C][C]72.3752426222397[/C][/ROW]
[ROW][C]25[/C][C]550[/C][C]560.70339578938[/C][C]-10.7033957893796[/C][/ROW]
[ROW][C]26[/C][C]460[/C][C]411.024094600831[/C][C]48.9759053991685[/C][/ROW]
[ROW][C]27[/C][C]510[/C][C]492.911798264557[/C][C]17.0882017354431[/C][/ROW]
[ROW][C]28[/C][C]370[/C][C]364.512712942196[/C][C]5.48728705780354[/C][/ROW]
[ROW][C]29[/C][C]530[/C][C]525.657187856673[/C][C]4.34281214332748[/C][/ROW]
[ROW][C]30[/C][C]410[/C][C]426.883199001845[/C][C]-16.8831990018446[/C][/ROW]
[ROW][C]31[/C][C]580[/C][C]575.795201700598[/C][C]4.20479829940177[/C][/ROW]
[ROW][C]32[/C][C]550[/C][C]523.097888275939[/C][C]26.9021117240612[/C][/ROW]
[ROW][C]33[/C][C]490[/C][C]559.055424857432[/C][C]-69.0554248574322[/C][/ROW]
[ROW][C]34[/C][C]700[/C][C]618.717793731855[/C][C]81.2822062681446[/C][/ROW]
[ROW][C]35[/C][C]630[/C][C]609.512717189343[/C][C]20.4872828106567[/C][/ROW]
[ROW][C]36[/C][C]720[/C][C]732.295971563062[/C][C]-12.2959715630618[/C][/ROW]
[ROW][C]37[/C][C]540[/C][C]528.986481161093[/C][C]11.0135188389066[/C][/ROW]
[ROW][C]38[/C][C]500[/C][C]435.608054953953[/C][C]64.3919450460465[/C][/ROW]
[ROW][C]39[/C][C]450[/C][C]489.533383949158[/C][C]-39.5333839491576[/C][/ROW]
[ROW][C]40[/C][C]370[/C][C]350.667722339591[/C][C]19.3322776604085[/C][/ROW]
[ROW][C]41[/C][C]490[/C][C]511.758477824285[/C][C]-21.7584778242851[/C][/ROW]
[ROW][C]42[/C][C]440[/C][C]393.820825618028[/C][C]46.1791743819718[/C][/ROW]
[ROW][C]43[/C][C]600[/C][C]563.956840383083[/C][C]36.0431596169174[/C][/ROW]
[ROW][C]44[/C][C]580[/C][C]533.971662835166[/C][C]46.0283371648341[/C][/ROW]
[ROW][C]45[/C][C]500[/C][C]483.4008888183[/C][C]16.5991111816997[/C][/ROW]
[ROW][C]46[/C][C]670[/C][C]684.821072112329[/C][C]-14.8210721123295[/C][/ROW]
[ROW][C]47[/C][C]620[/C][C]620.314073057056[/C][C]-0.314073057055566[/C][/ROW]
[ROW][C]48[/C][C]800[/C][C]714.103314152901[/C][C]85.8966858470989[/C][/ROW]
[ROW][C]49[/C][C]640[/C][C]535.481489776574[/C][C]104.518510223426[/C][/ROW]
[ROW][C]50[/C][C]390[/C][C]495.311520142445[/C][C]-105.311520142445[/C][/ROW]
[ROW][C]51[/C][C]390[/C][C]453.534436228592[/C][C]-63.5344362285923[/C][/ROW]
[ROW][C]52[/C][C]390[/C][C]370.049662341757[/C][C]19.9503376582431[/C][/ROW]
[ROW][C]53[/C][C]460[/C][C]494.679391724356[/C][C]-34.6793917243563[/C][/ROW]
[ROW][C]54[/C][C]460[/C][C]440.468038953215[/C][C]19.531961046785[/C][/ROW]
[ROW][C]55[/C][C]620[/C][C]602.038273996362[/C][C]17.9617260036384[/C][/ROW]
[ROW][C]56[/C][C]570[/C][C]581.933985079778[/C][C]-11.9339850797776[/C][/ROW]
[ROW][C]57[/C][C]510[/C][C]504.031067624404[/C][C]5.9689323755959[/C][/ROW]
[ROW][C]58[/C][C]640[/C][C]676.625025213098[/C][C]-36.625025213098[/C][/ROW]
[ROW][C]59[/C][C]590[/C][C]625.292572917804[/C][C]-35.2925729178039[/C][/ROW]
[ROW][C]60[/C][C]850[/C][C]797.860888934588[/C][C]52.1391110654117[/C][/ROW]
[ROW][C]61[/C][C]670[/C][C]635.45673274384[/C][C]34.5432672561599[/C][/ROW]
[ROW][C]62[/C][C]390[/C][C]400.080735739238[/C][C]-10.0807357392381[/C][/ROW]
[ROW][C]63[/C][C]410[/C][C]397.279450960486[/C][C]12.7205490395142[/C][/ROW]
[ROW][C]64[/C][C]340[/C][C]391.720316145675[/C][C]-51.7203161456748[/C][/ROW]
[ROW][C]65[/C][C]470[/C][C]465.016701228028[/C][C]4.98329877197227[/C][/ROW]
[ROW][C]66[/C][C]540[/C][C]461.130225617762[/C][C]78.8697743822381[/C][/ROW]
[ROW][C]67[/C][C]680[/C][C]622.373442870587[/C][C]57.6265571294127[/C][/ROW]
[ROW][C]68[/C][C]670[/C][C]576.035049302477[/C][C]93.9649506975228[/C][/ROW]
[ROW][C]69[/C][C]540[/C][C]517.522266024475[/C][C]22.4777339755254[/C][/ROW]
[ROW][C]70[/C][C]630[/C][C]653.104217827989[/C][C]-23.1042178279889[/C][/ROW]
[ROW][C]71[/C][C]560[/C][C]605.3204641278[/C][C]-45.3204641277999[/C][/ROW]
[ROW][C]72[/C][C]800[/C][C]860.437504314335[/C][C]-60.4375043143352[/C][/ROW]
[ROW][C]73[/C][C]610[/C][C]681.842823010612[/C][C]-71.8428230106118[/C][/ROW]
[ROW][C]74[/C][C]490[/C][C]404.451169654602[/C][C]85.5488303453978[/C][/ROW]
[ROW][C]75[/C][C]440[/C][C]424.50011058285[/C][C]15.4998894171499[/C][/ROW]
[ROW][C]76[/C][C]330[/C][C]360.593245466186[/C][C]-30.5932454661863[/C][/ROW]
[ROW][C]77[/C][C]490[/C][C]487.500674624831[/C][C]2.49932537516924[/C][/ROW]
[ROW][C]78[/C][C]590[/C][C]552.811699585029[/C][C]37.188300414971[/C][/ROW]
[ROW][C]79[/C][C]690[/C][C]694.873917201946[/C][C]-4.87391720194591[/C][/ROW]
[ROW][C]80[/C][C]650[/C][C]681.624640648139[/C][C]-31.6246406481393[/C][/ROW]
[ROW][C]81[/C][C]480[/C][C]555.129176568287[/C][C]-75.1291765682872[/C][/ROW]
[ROW][C]82[/C][C]690[/C][C]645.946483202973[/C][C]44.0535167970274[/C][/ROW]
[ROW][C]83[/C][C]540[/C][C]577.069464089133[/C][C]-37.069464089133[/C][/ROW]
[ROW][C]84[/C][C]830[/C][C]817.163596240834[/C][C]12.8364037591656[/C][/ROW]
[ROW][C]85[/C][C]690[/C][C]628.245880898679[/C][C]61.7541191013206[/C][/ROW]
[ROW][C]86[/C][C]500[/C][C]497.815781231202[/C][C]2.18421876879847[/C][/ROW]
[ROW][C]87[/C][C]460[/C][C]452.536206632087[/C][C]7.46379336791313[/C][/ROW]
[ROW][C]88[/C][C]310[/C][C]345.991112805964[/C][C]-35.9911128059643[/C][/ROW]
[ROW][C]89[/C][C]490[/C][C]503.177291517979[/C][C]-13.1772915179791[/C][/ROW]
[ROW][C]90[/C][C]470[/C][C]599.997228840146[/C][C]-129.997228840146[/C][/ROW]
[ROW][C]91[/C][C]710[/C][C]699.916905375072[/C][C]10.0830946249279[/C][/ROW]
[ROW][C]92[/C][C]710[/C][C]660.454766683004[/C][C]49.5452333169961[/C][/ROW]
[ROW][C]93[/C][C]540[/C][C]493.678473241473[/C][C]46.3215267585271[/C][/ROW]
[ROW][C]94[/C][C]700[/C][C]695.573397462053[/C][C]4.42660253794702[/C][/ROW]
[ROW][C]95[/C][C]520[/C][C]551.402086261853[/C][C]-31.4020862618532[/C][/ROW]
[ROW][C]96[/C][C]810[/C][C]837.372146662013[/C][C]-27.3721466620133[/C][/ROW]
[ROW][C]97[/C][C]690[/C][C]692.62287073974[/C][C]-2.62287073973982[/C][/ROW]
[ROW][C]98[/C][C]510[/C][C]505.606954136257[/C][C]4.39304586374277[/C][/ROW]
[ROW][C]99[/C][C]390[/C][C]464.115286609443[/C][C]-74.1152866094426[/C][/ROW]
[ROW][C]100[/C][C]270[/C][C]314.934455057973[/C][C]-44.9344550579727[/C][/ROW]
[ROW][C]101[/C][C]530[/C][C]491.118722813349[/C][C]38.8812771866509[/C][/ROW]
[ROW][C]102[/C][C]510[/C][C]479.359088061261[/C][C]30.640911938739[/C][/ROW]
[ROW][C]103[/C][C]670[/C][C]709.838164133235[/C][C]-39.8381641332352[/C][/ROW]
[ROW][C]104[/C][C]770[/C][C]705.837832660961[/C][C]64.1621673390393[/C][/ROW]
[ROW][C]105[/C][C]570[/C][C]535.936014629913[/C][C]34.0639853700867[/C][/ROW]
[ROW][C]106[/C][C]640[/C][C]698.72070899305[/C][C]-58.72070899305[/C][/ROW]
[ROW][C]107[/C][C]480[/C][C]519.971009786022[/C][C]-39.9710097860225[/C][/ROW]
[ROW][C]108[/C][C]830[/C][C]808.50487351223[/C][C]21.49512648777[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124197&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124197&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
13600620.518162393162-20.5181623931624
14450470.018653484721-20.0186534847208
15530554.338374146668-24.338374146668
16400423.392686860528-23.3926868605282
17560574.739113734889-14.739113734889
18460466.029181285405-6.02918128540472
19610582.76074243789327.2392575621075
20550600.052676624763-50.0526766247634
21580669.498582010773-89.498582010773
22650576.50030850786473.4996914921362
23640545.27561999441694.7243800055841
24760687.6247573777672.3752426222397
25550560.70339578938-10.7033957893796
26460411.02409460083148.9759053991685
27510492.91179826455717.0882017354431
28370364.5127129421965.48728705780354
29530525.6571878566734.34281214332748
30410426.883199001845-16.8831990018446
31580575.7952017005984.20479829940177
32550523.09788827593926.9021117240612
33490559.055424857432-69.0554248574322
34700618.71779373185581.2822062681446
35630609.51271718934320.4872828106567
36720732.295971563062-12.2959715630618
37540528.98648116109311.0135188389066
38500435.60805495395364.3919450460465
39450489.533383949158-39.5333839491576
40370350.66772233959119.3322776604085
41490511.758477824285-21.7584778242851
42440393.82082561802846.1791743819718
43600563.95684038308336.0431596169174
44580533.97166283516646.0283371648341
45500483.400888818316.5991111816997
46670684.821072112329-14.8210721123295
47620620.314073057056-0.314073057055566
48800714.10331415290185.8966858470989
49640535.481489776574104.518510223426
50390495.311520142445-105.311520142445
51390453.534436228592-63.5344362285923
52390370.04966234175719.9503376582431
53460494.679391724356-34.6793917243563
54460440.46803895321519.531961046785
55620602.03827399636217.9617260036384
56570581.933985079778-11.9339850797776
57510504.0310676244045.9689323755959
58640676.625025213098-36.625025213098
59590625.292572917804-35.2925729178039
60850797.86088893458852.1391110654117
61670635.4567327438434.5432672561599
62390400.080735739238-10.0807357392381
63410397.27945096048612.7205490395142
64340391.720316145675-51.7203161456748
65470465.0167012280284.98329877197227
66540461.13022561776278.8697743822381
67680622.37344287058757.6265571294127
68670576.03504930247793.9649506975228
69540517.52226602447522.4777339755254
70630653.104217827989-23.1042178279889
71560605.3204641278-45.3204641277999
72800860.437504314335-60.4375043143352
73610681.842823010612-71.8428230106118
74490404.45116965460285.5488303453978
75440424.5001105828515.4998894171499
76330360.593245466186-30.5932454661863
77490487.5006746248312.49932537516924
78590552.81169958502937.188300414971
79690694.873917201946-4.87391720194591
80650681.624640648139-31.6246406481393
81480555.129176568287-75.1291765682872
82690645.94648320297344.0535167970274
83540577.069464089133-37.069464089133
84830817.16359624083412.8364037591656
85690628.24588089867961.7541191013206
86500497.8157812312022.18421876879847
87460452.5362066320877.46379336791313
88310345.991112805964-35.9911128059643
89490503.177291517979-13.1772915179791
90470599.997228840146-129.997228840146
91710699.91690537507210.0830946249279
92710660.45476668300449.5452333169961
93540493.67847324147346.3215267585271
94700695.5733974620534.42660253794702
95520551.402086261853-31.4020862618532
96810837.372146662013-27.3721466620133
97690692.62287073974-2.62287073973982
98510505.6069541362574.39304586374277
99390464.115286609443-74.1152866094426
100270314.934455057973-44.9344550579727
101530491.11872281334938.8812771866509
102510479.35908806126130.640911938739
103670709.838164133235-39.8381641332352
104770705.83783266096164.1621673390393
105570535.93601462991334.0639853700867
106640698.72070899305-58.72070899305
107480519.971009786022-39.9710097860225
108830808.5048735122321.49512648777







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109686.389676783002594.727011022744778.052342543259
110505.268628805139413.590240658927596.947016951351
111390.784834515586299.07108085556482.498588175612
112269.224072576543177.447480541019361.000664612068
113523.501675774088431.626984818293615.376366729882
114503.90085821192411.885088544324595.916627879516
115668.999617729781576.792171105593761.207064353969
116761.363717095493668.906515353684853.820918837302
117562.743045091076469.970711015423655.515379166729
118639.027983385131545.8680674335732.187899336761
119477.922431926916384.295687114646571.549176739187
120823.645559965849729.466265737598917.824854194099

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 686.389676783002 & 594.727011022744 & 778.052342543259 \tabularnewline
110 & 505.268628805139 & 413.590240658927 & 596.947016951351 \tabularnewline
111 & 390.784834515586 & 299.07108085556 & 482.498588175612 \tabularnewline
112 & 269.224072576543 & 177.447480541019 & 361.000664612068 \tabularnewline
113 & 523.501675774088 & 431.626984818293 & 615.376366729882 \tabularnewline
114 & 503.90085821192 & 411.885088544324 & 595.916627879516 \tabularnewline
115 & 668.999617729781 & 576.792171105593 & 761.207064353969 \tabularnewline
116 & 761.363717095493 & 668.906515353684 & 853.820918837302 \tabularnewline
117 & 562.743045091076 & 469.970711015423 & 655.515379166729 \tabularnewline
118 & 639.027983385131 & 545.8680674335 & 732.187899336761 \tabularnewline
119 & 477.922431926916 & 384.295687114646 & 571.549176739187 \tabularnewline
120 & 823.645559965849 & 729.466265737598 & 917.824854194099 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124197&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]686.389676783002[/C][C]594.727011022744[/C][C]778.052342543259[/C][/ROW]
[ROW][C]110[/C][C]505.268628805139[/C][C]413.590240658927[/C][C]596.947016951351[/C][/ROW]
[ROW][C]111[/C][C]390.784834515586[/C][C]299.07108085556[/C][C]482.498588175612[/C][/ROW]
[ROW][C]112[/C][C]269.224072576543[/C][C]177.447480541019[/C][C]361.000664612068[/C][/ROW]
[ROW][C]113[/C][C]523.501675774088[/C][C]431.626984818293[/C][C]615.376366729882[/C][/ROW]
[ROW][C]114[/C][C]503.90085821192[/C][C]411.885088544324[/C][C]595.916627879516[/C][/ROW]
[ROW][C]115[/C][C]668.999617729781[/C][C]576.792171105593[/C][C]761.207064353969[/C][/ROW]
[ROW][C]116[/C][C]761.363717095493[/C][C]668.906515353684[/C][C]853.820918837302[/C][/ROW]
[ROW][C]117[/C][C]562.743045091076[/C][C]469.970711015423[/C][C]655.515379166729[/C][/ROW]
[ROW][C]118[/C][C]639.027983385131[/C][C]545.8680674335[/C][C]732.187899336761[/C][/ROW]
[ROW][C]119[/C][C]477.922431926916[/C][C]384.295687114646[/C][C]571.549176739187[/C][/ROW]
[ROW][C]120[/C][C]823.645559965849[/C][C]729.466265737598[/C][C]917.824854194099[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124197&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124197&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
109686.389676783002594.727011022744778.052342543259
110505.268628805139413.590240658927596.947016951351
111390.784834515586299.07108085556482.498588175612
112269.224072576543177.447480541019361.000664612068
113523.501675774088431.626984818293615.376366729882
114503.90085821192411.885088544324595.916627879516
115668.999617729781576.792171105593761.207064353969
116761.363717095493668.906515353684853.820918837302
117562.743045091076469.970711015423655.515379166729
118639.027983385131545.8680674335732.187899336761
119477.922431926916384.295687114646571.549176739187
120823.645559965849729.466265737598917.824854194099



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')