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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 computationThu, 16 Aug 2012 15:41:55 -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/2012/Aug/16/t13451461893khcy4i69whtt0n.htm/, Retrieved Fri, 03 May 2024 09:23:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=169423, Retrieved Fri, 03 May 2024 09:23:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKenneth Pijpen
Estimated Impact82
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks 2] [2012-08-16 19:41:55] [bc260e3c602952c552b9bde15a0b19a6] [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 time3 seconds
R Server'AstonUniversity' @ aston.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169423&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169423&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169423&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'AstonUniversity' @ aston.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0092611860578751
beta1
gamma0.929768627342217

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0092611860578751 \tabularnewline
beta & 1 \tabularnewline
gamma & 0.929768627342217 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169423&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]0.0092611860578751[/C][/ROW]
[ROW][C]beta[/C][C]1[/C][/ROW]
[ROW][C]gamma[/C][C]0.929768627342217[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169423&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169423&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
alpha0.0092611860578751
beta1
gamma0.929768627342217







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13600620.518162393163-20.5181623931626
14450470.018653484721-20.018653484721
15530554.338374146668-24.3383741466682
16400423.392686860528-23.3926868605284
17560574.739113734889-14.7391137348892
18460466.029181285405-6.029181285405
19610582.76074243789327.2392575621072
20550600.052676624764-50.0526766247636
21580669.498582010773-89.4985820107735
22650576.50030850786473.4996914921358
23640545.27561999441794.7243800055835
24760687.62475737776172.3752426222393
25550560.703395789374-10.7033957893736
26460411.02409460082648.9759053991743
27510492.9117982645517.0882017354501
28370364.512712942195.48728705781025
29530525.6571878566694.34281214333146
30410426.883199001843-16.8831990018433
31580575.7952017006074.20479829939279
32550523.09788827592426.9021117240756
33490559.055424857406-69.0554248574065
34700618.71779373187981.2822062681213
35630609.51271718937320.4872828106272
36720732.295971563084-12.2959715630843
37540528.98648116109111.0135188389095
38500435.60805495396864.391945046032
39450489.533383949162-39.533383949162
40370350.66772233959219.3322776604081
41490511.758477824285-21.7584778242848
42440393.82082561802146.179174381979
43600563.95684038308236.043159616918
44580533.9716628351746.0283371648302
45500483.40088881827416.5991111817263
46670684.82107211235-14.8210721123506
47620620.314073057059-0.314073057058749
48800714.10331415289485.8966858471065
49640535.481489776572104.518510223428
50390495.311520142459-105.311520142459
51390453.534436228575-63.5344362285746
52390370.04966234175719.9503376582434
53460494.679391724344-34.6793917243438
54460440.46803895322319.5319610467773
55620602.03827399636717.9617260036333
56570581.933985079786-11.933985079786
57510504.0310676244015.96893237559868
58640676.625025213089-36.625025213089
59590625.292572917798-35.2925729177985
60850797.86088893460852.1391110653922
61670635.45673274386534.5432672561346
62390400.080735739202-10.0807357392018
63410397.2794509604612.7205490395399
64340391.720316145676-51.7203161456756
65470465.0167012280114.98329877198853
66540461.13022561776478.8697743822364
67680622.37344287058957.6265571294114
68670576.0350493024793.9649506975298
69540517.52226602447222.4777339755277
70630653.104217827974-23.1042178279738
71560605.320464127786-45.3204641277857
72800860.43750431435-60.4375043143498
73610681.842823010622-71.8428230106224
74490404.45116965459585.5488303454046
75440424.50011058285115.4998894171488
76330360.59324546617-30.5932454661701
77490487.5006746248312.49932537516941
78590552.81169958505237.1883004149478
79690694.873917201963-4.87391720196274
80650681.624640648166-31.6246406481662
81480555.129176568292-75.1291765682925
82690645.94648320296344.0535167970368
83540577.069464089117-37.0694640891168
84830817.16359624081512.8364037591846
85690628.24588089865761.7541191013432
86500497.8157812312252.18421876877517
87460452.536206632097.46379336791034
88310345.991112805952-35.991112805952
89490503.177291517978-13.1772915179777
90470599.997228840156-129.997228840156
91710699.9169053750710.0830946249298
92710660.45476668299549.5452333170048
93540493.6784732414546.3215267585495
94700695.5733974620664.4266025379344
95520551.402086261842-31.4020862618415
96810837.372146662017-27.3721466620167
97690692.622870739758-2.6228707397579
98510505.6069541362614.39304586373925
99390464.115286609446-74.1152866094465
100270314.934455057963-44.9344550579627
101530491.11872281334738.8812771866529
102510479.35908806122530.6409119387748
103670709.838164133241-39.8381641332408
104770705.83783266097864.1621673390221
105570535.93601462992834.0639853700717
106640698.720708993055-58.720708993055
107480519.971009786015-39.971009786015
108830808.50487351222521.4951264877752

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 600 & 620.518162393163 & -20.5181623931626 \tabularnewline
14 & 450 & 470.018653484721 & -20.018653484721 \tabularnewline
15 & 530 & 554.338374146668 & -24.3383741466682 \tabularnewline
16 & 400 & 423.392686860528 & -23.3926868605284 \tabularnewline
17 & 560 & 574.739113734889 & -14.7391137348892 \tabularnewline
18 & 460 & 466.029181285405 & -6.029181285405 \tabularnewline
19 & 610 & 582.760742437893 & 27.2392575621072 \tabularnewline
20 & 550 & 600.052676624764 & -50.0526766247636 \tabularnewline
21 & 580 & 669.498582010773 & -89.4985820107735 \tabularnewline
22 & 650 & 576.500308507864 & 73.4996914921358 \tabularnewline
23 & 640 & 545.275619994417 & 94.7243800055835 \tabularnewline
24 & 760 & 687.624757377761 & 72.3752426222393 \tabularnewline
25 & 550 & 560.703395789374 & -10.7033957893736 \tabularnewline
26 & 460 & 411.024094600826 & 48.9759053991743 \tabularnewline
27 & 510 & 492.91179826455 & 17.0882017354501 \tabularnewline
28 & 370 & 364.51271294219 & 5.48728705781025 \tabularnewline
29 & 530 & 525.657187856669 & 4.34281214333146 \tabularnewline
30 & 410 & 426.883199001843 & -16.8831990018433 \tabularnewline
31 & 580 & 575.795201700607 & 4.20479829939279 \tabularnewline
32 & 550 & 523.097888275924 & 26.9021117240756 \tabularnewline
33 & 490 & 559.055424857406 & -69.0554248574065 \tabularnewline
34 & 700 & 618.717793731879 & 81.2822062681213 \tabularnewline
35 & 630 & 609.512717189373 & 20.4872828106272 \tabularnewline
36 & 720 & 732.295971563084 & -12.2959715630843 \tabularnewline
37 & 540 & 528.986481161091 & 11.0135188389095 \tabularnewline
38 & 500 & 435.608054953968 & 64.391945046032 \tabularnewline
39 & 450 & 489.533383949162 & -39.533383949162 \tabularnewline
40 & 370 & 350.667722339592 & 19.3322776604081 \tabularnewline
41 & 490 & 511.758477824285 & -21.7584778242848 \tabularnewline
42 & 440 & 393.820825618021 & 46.179174381979 \tabularnewline
43 & 600 & 563.956840383082 & 36.043159616918 \tabularnewline
44 & 580 & 533.97166283517 & 46.0283371648302 \tabularnewline
45 & 500 & 483.400888818274 & 16.5991111817263 \tabularnewline
46 & 670 & 684.82107211235 & -14.8210721123506 \tabularnewline
47 & 620 & 620.314073057059 & -0.314073057058749 \tabularnewline
48 & 800 & 714.103314152894 & 85.8966858471065 \tabularnewline
49 & 640 & 535.481489776572 & 104.518510223428 \tabularnewline
50 & 390 & 495.311520142459 & -105.311520142459 \tabularnewline
51 & 390 & 453.534436228575 & -63.5344362285746 \tabularnewline
52 & 390 & 370.049662341757 & 19.9503376582434 \tabularnewline
53 & 460 & 494.679391724344 & -34.6793917243438 \tabularnewline
54 & 460 & 440.468038953223 & 19.5319610467773 \tabularnewline
55 & 620 & 602.038273996367 & 17.9617260036333 \tabularnewline
56 & 570 & 581.933985079786 & -11.933985079786 \tabularnewline
57 & 510 & 504.031067624401 & 5.96893237559868 \tabularnewline
58 & 640 & 676.625025213089 & -36.625025213089 \tabularnewline
59 & 590 & 625.292572917798 & -35.2925729177985 \tabularnewline
60 & 850 & 797.860888934608 & 52.1391110653922 \tabularnewline
61 & 670 & 635.456732743865 & 34.5432672561346 \tabularnewline
62 & 390 & 400.080735739202 & -10.0807357392018 \tabularnewline
63 & 410 & 397.27945096046 & 12.7205490395399 \tabularnewline
64 & 340 & 391.720316145676 & -51.7203161456756 \tabularnewline
65 & 470 & 465.016701228011 & 4.98329877198853 \tabularnewline
66 & 540 & 461.130225617764 & 78.8697743822364 \tabularnewline
67 & 680 & 622.373442870589 & 57.6265571294114 \tabularnewline
68 & 670 & 576.03504930247 & 93.9649506975298 \tabularnewline
69 & 540 & 517.522266024472 & 22.4777339755277 \tabularnewline
70 & 630 & 653.104217827974 & -23.1042178279738 \tabularnewline
71 & 560 & 605.320464127786 & -45.3204641277857 \tabularnewline
72 & 800 & 860.43750431435 & -60.4375043143498 \tabularnewline
73 & 610 & 681.842823010622 & -71.8428230106224 \tabularnewline
74 & 490 & 404.451169654595 & 85.5488303454046 \tabularnewline
75 & 440 & 424.500110582851 & 15.4998894171488 \tabularnewline
76 & 330 & 360.59324546617 & -30.5932454661701 \tabularnewline
77 & 490 & 487.500674624831 & 2.49932537516941 \tabularnewline
78 & 590 & 552.811699585052 & 37.1883004149478 \tabularnewline
79 & 690 & 694.873917201963 & -4.87391720196274 \tabularnewline
80 & 650 & 681.624640648166 & -31.6246406481662 \tabularnewline
81 & 480 & 555.129176568292 & -75.1291765682925 \tabularnewline
82 & 690 & 645.946483202963 & 44.0535167970368 \tabularnewline
83 & 540 & 577.069464089117 & -37.0694640891168 \tabularnewline
84 & 830 & 817.163596240815 & 12.8364037591846 \tabularnewline
85 & 690 & 628.245880898657 & 61.7541191013432 \tabularnewline
86 & 500 & 497.815781231225 & 2.18421876877517 \tabularnewline
87 & 460 & 452.53620663209 & 7.46379336791034 \tabularnewline
88 & 310 & 345.991112805952 & -35.991112805952 \tabularnewline
89 & 490 & 503.177291517978 & -13.1772915179777 \tabularnewline
90 & 470 & 599.997228840156 & -129.997228840156 \tabularnewline
91 & 710 & 699.91690537507 & 10.0830946249298 \tabularnewline
92 & 710 & 660.454766682995 & 49.5452333170048 \tabularnewline
93 & 540 & 493.67847324145 & 46.3215267585495 \tabularnewline
94 & 700 & 695.573397462066 & 4.4266025379344 \tabularnewline
95 & 520 & 551.402086261842 & -31.4020862618415 \tabularnewline
96 & 810 & 837.372146662017 & -27.3721466620167 \tabularnewline
97 & 690 & 692.622870739758 & -2.6228707397579 \tabularnewline
98 & 510 & 505.606954136261 & 4.39304586373925 \tabularnewline
99 & 390 & 464.115286609446 & -74.1152866094465 \tabularnewline
100 & 270 & 314.934455057963 & -44.9344550579627 \tabularnewline
101 & 530 & 491.118722813347 & 38.8812771866529 \tabularnewline
102 & 510 & 479.359088061225 & 30.6409119387748 \tabularnewline
103 & 670 & 709.838164133241 & -39.8381641332408 \tabularnewline
104 & 770 & 705.837832660978 & 64.1621673390221 \tabularnewline
105 & 570 & 535.936014629928 & 34.0639853700717 \tabularnewline
106 & 640 & 698.720708993055 & -58.720708993055 \tabularnewline
107 & 480 & 519.971009786015 & -39.971009786015 \tabularnewline
108 & 830 & 808.504873512225 & 21.4951264877752 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169423&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]620.518162393163[/C][C]-20.5181623931626[/C][/ROW]
[ROW][C]14[/C][C]450[/C][C]470.018653484721[/C][C]-20.018653484721[/C][/ROW]
[ROW][C]15[/C][C]530[/C][C]554.338374146668[/C][C]-24.3383741466682[/C][/ROW]
[ROW][C]16[/C][C]400[/C][C]423.392686860528[/C][C]-23.3926868605284[/C][/ROW]
[ROW][C]17[/C][C]560[/C][C]574.739113734889[/C][C]-14.7391137348892[/C][/ROW]
[ROW][C]18[/C][C]460[/C][C]466.029181285405[/C][C]-6.029181285405[/C][/ROW]
[ROW][C]19[/C][C]610[/C][C]582.760742437893[/C][C]27.2392575621072[/C][/ROW]
[ROW][C]20[/C][C]550[/C][C]600.052676624764[/C][C]-50.0526766247636[/C][/ROW]
[ROW][C]21[/C][C]580[/C][C]669.498582010773[/C][C]-89.4985820107735[/C][/ROW]
[ROW][C]22[/C][C]650[/C][C]576.500308507864[/C][C]73.4996914921358[/C][/ROW]
[ROW][C]23[/C][C]640[/C][C]545.275619994417[/C][C]94.7243800055835[/C][/ROW]
[ROW][C]24[/C][C]760[/C][C]687.624757377761[/C][C]72.3752426222393[/C][/ROW]
[ROW][C]25[/C][C]550[/C][C]560.703395789374[/C][C]-10.7033957893736[/C][/ROW]
[ROW][C]26[/C][C]460[/C][C]411.024094600826[/C][C]48.9759053991743[/C][/ROW]
[ROW][C]27[/C][C]510[/C][C]492.91179826455[/C][C]17.0882017354501[/C][/ROW]
[ROW][C]28[/C][C]370[/C][C]364.51271294219[/C][C]5.48728705781025[/C][/ROW]
[ROW][C]29[/C][C]530[/C][C]525.657187856669[/C][C]4.34281214333146[/C][/ROW]
[ROW][C]30[/C][C]410[/C][C]426.883199001843[/C][C]-16.8831990018433[/C][/ROW]
[ROW][C]31[/C][C]580[/C][C]575.795201700607[/C][C]4.20479829939279[/C][/ROW]
[ROW][C]32[/C][C]550[/C][C]523.097888275924[/C][C]26.9021117240756[/C][/ROW]
[ROW][C]33[/C][C]490[/C][C]559.055424857406[/C][C]-69.0554248574065[/C][/ROW]
[ROW][C]34[/C][C]700[/C][C]618.717793731879[/C][C]81.2822062681213[/C][/ROW]
[ROW][C]35[/C][C]630[/C][C]609.512717189373[/C][C]20.4872828106272[/C][/ROW]
[ROW][C]36[/C][C]720[/C][C]732.295971563084[/C][C]-12.2959715630843[/C][/ROW]
[ROW][C]37[/C][C]540[/C][C]528.986481161091[/C][C]11.0135188389095[/C][/ROW]
[ROW][C]38[/C][C]500[/C][C]435.608054953968[/C][C]64.391945046032[/C][/ROW]
[ROW][C]39[/C][C]450[/C][C]489.533383949162[/C][C]-39.533383949162[/C][/ROW]
[ROW][C]40[/C][C]370[/C][C]350.667722339592[/C][C]19.3322776604081[/C][/ROW]
[ROW][C]41[/C][C]490[/C][C]511.758477824285[/C][C]-21.7584778242848[/C][/ROW]
[ROW][C]42[/C][C]440[/C][C]393.820825618021[/C][C]46.179174381979[/C][/ROW]
[ROW][C]43[/C][C]600[/C][C]563.956840383082[/C][C]36.043159616918[/C][/ROW]
[ROW][C]44[/C][C]580[/C][C]533.97166283517[/C][C]46.0283371648302[/C][/ROW]
[ROW][C]45[/C][C]500[/C][C]483.400888818274[/C][C]16.5991111817263[/C][/ROW]
[ROW][C]46[/C][C]670[/C][C]684.82107211235[/C][C]-14.8210721123506[/C][/ROW]
[ROW][C]47[/C][C]620[/C][C]620.314073057059[/C][C]-0.314073057058749[/C][/ROW]
[ROW][C]48[/C][C]800[/C][C]714.103314152894[/C][C]85.8966858471065[/C][/ROW]
[ROW][C]49[/C][C]640[/C][C]535.481489776572[/C][C]104.518510223428[/C][/ROW]
[ROW][C]50[/C][C]390[/C][C]495.311520142459[/C][C]-105.311520142459[/C][/ROW]
[ROW][C]51[/C][C]390[/C][C]453.534436228575[/C][C]-63.5344362285746[/C][/ROW]
[ROW][C]52[/C][C]390[/C][C]370.049662341757[/C][C]19.9503376582434[/C][/ROW]
[ROW][C]53[/C][C]460[/C][C]494.679391724344[/C][C]-34.6793917243438[/C][/ROW]
[ROW][C]54[/C][C]460[/C][C]440.468038953223[/C][C]19.5319610467773[/C][/ROW]
[ROW][C]55[/C][C]620[/C][C]602.038273996367[/C][C]17.9617260036333[/C][/ROW]
[ROW][C]56[/C][C]570[/C][C]581.933985079786[/C][C]-11.933985079786[/C][/ROW]
[ROW][C]57[/C][C]510[/C][C]504.031067624401[/C][C]5.96893237559868[/C][/ROW]
[ROW][C]58[/C][C]640[/C][C]676.625025213089[/C][C]-36.625025213089[/C][/ROW]
[ROW][C]59[/C][C]590[/C][C]625.292572917798[/C][C]-35.2925729177985[/C][/ROW]
[ROW][C]60[/C][C]850[/C][C]797.860888934608[/C][C]52.1391110653922[/C][/ROW]
[ROW][C]61[/C][C]670[/C][C]635.456732743865[/C][C]34.5432672561346[/C][/ROW]
[ROW][C]62[/C][C]390[/C][C]400.080735739202[/C][C]-10.0807357392018[/C][/ROW]
[ROW][C]63[/C][C]410[/C][C]397.27945096046[/C][C]12.7205490395399[/C][/ROW]
[ROW][C]64[/C][C]340[/C][C]391.720316145676[/C][C]-51.7203161456756[/C][/ROW]
[ROW][C]65[/C][C]470[/C][C]465.016701228011[/C][C]4.98329877198853[/C][/ROW]
[ROW][C]66[/C][C]540[/C][C]461.130225617764[/C][C]78.8697743822364[/C][/ROW]
[ROW][C]67[/C][C]680[/C][C]622.373442870589[/C][C]57.6265571294114[/C][/ROW]
[ROW][C]68[/C][C]670[/C][C]576.03504930247[/C][C]93.9649506975298[/C][/ROW]
[ROW][C]69[/C][C]540[/C][C]517.522266024472[/C][C]22.4777339755277[/C][/ROW]
[ROW][C]70[/C][C]630[/C][C]653.104217827974[/C][C]-23.1042178279738[/C][/ROW]
[ROW][C]71[/C][C]560[/C][C]605.320464127786[/C][C]-45.3204641277857[/C][/ROW]
[ROW][C]72[/C][C]800[/C][C]860.43750431435[/C][C]-60.4375043143498[/C][/ROW]
[ROW][C]73[/C][C]610[/C][C]681.842823010622[/C][C]-71.8428230106224[/C][/ROW]
[ROW][C]74[/C][C]490[/C][C]404.451169654595[/C][C]85.5488303454046[/C][/ROW]
[ROW][C]75[/C][C]440[/C][C]424.500110582851[/C][C]15.4998894171488[/C][/ROW]
[ROW][C]76[/C][C]330[/C][C]360.59324546617[/C][C]-30.5932454661701[/C][/ROW]
[ROW][C]77[/C][C]490[/C][C]487.500674624831[/C][C]2.49932537516941[/C][/ROW]
[ROW][C]78[/C][C]590[/C][C]552.811699585052[/C][C]37.1883004149478[/C][/ROW]
[ROW][C]79[/C][C]690[/C][C]694.873917201963[/C][C]-4.87391720196274[/C][/ROW]
[ROW][C]80[/C][C]650[/C][C]681.624640648166[/C][C]-31.6246406481662[/C][/ROW]
[ROW][C]81[/C][C]480[/C][C]555.129176568292[/C][C]-75.1291765682925[/C][/ROW]
[ROW][C]82[/C][C]690[/C][C]645.946483202963[/C][C]44.0535167970368[/C][/ROW]
[ROW][C]83[/C][C]540[/C][C]577.069464089117[/C][C]-37.0694640891168[/C][/ROW]
[ROW][C]84[/C][C]830[/C][C]817.163596240815[/C][C]12.8364037591846[/C][/ROW]
[ROW][C]85[/C][C]690[/C][C]628.245880898657[/C][C]61.7541191013432[/C][/ROW]
[ROW][C]86[/C][C]500[/C][C]497.815781231225[/C][C]2.18421876877517[/C][/ROW]
[ROW][C]87[/C][C]460[/C][C]452.53620663209[/C][C]7.46379336791034[/C][/ROW]
[ROW][C]88[/C][C]310[/C][C]345.991112805952[/C][C]-35.991112805952[/C][/ROW]
[ROW][C]89[/C][C]490[/C][C]503.177291517978[/C][C]-13.1772915179777[/C][/ROW]
[ROW][C]90[/C][C]470[/C][C]599.997228840156[/C][C]-129.997228840156[/C][/ROW]
[ROW][C]91[/C][C]710[/C][C]699.91690537507[/C][C]10.0830946249298[/C][/ROW]
[ROW][C]92[/C][C]710[/C][C]660.454766682995[/C][C]49.5452333170048[/C][/ROW]
[ROW][C]93[/C][C]540[/C][C]493.67847324145[/C][C]46.3215267585495[/C][/ROW]
[ROW][C]94[/C][C]700[/C][C]695.573397462066[/C][C]4.4266025379344[/C][/ROW]
[ROW][C]95[/C][C]520[/C][C]551.402086261842[/C][C]-31.4020862618415[/C][/ROW]
[ROW][C]96[/C][C]810[/C][C]837.372146662017[/C][C]-27.3721466620167[/C][/ROW]
[ROW][C]97[/C][C]690[/C][C]692.622870739758[/C][C]-2.6228707397579[/C][/ROW]
[ROW][C]98[/C][C]510[/C][C]505.606954136261[/C][C]4.39304586373925[/C][/ROW]
[ROW][C]99[/C][C]390[/C][C]464.115286609446[/C][C]-74.1152866094465[/C][/ROW]
[ROW][C]100[/C][C]270[/C][C]314.934455057963[/C][C]-44.9344550579627[/C][/ROW]
[ROW][C]101[/C][C]530[/C][C]491.118722813347[/C][C]38.8812771866529[/C][/ROW]
[ROW][C]102[/C][C]510[/C][C]479.359088061225[/C][C]30.6409119387748[/C][/ROW]
[ROW][C]103[/C][C]670[/C][C]709.838164133241[/C][C]-39.8381641332408[/C][/ROW]
[ROW][C]104[/C][C]770[/C][C]705.837832660978[/C][C]64.1621673390221[/C][/ROW]
[ROW][C]105[/C][C]570[/C][C]535.936014629928[/C][C]34.0639853700717[/C][/ROW]
[ROW][C]106[/C][C]640[/C][C]698.720708993055[/C][C]-58.720708993055[/C][/ROW]
[ROW][C]107[/C][C]480[/C][C]519.971009786015[/C][C]-39.971009786015[/C][/ROW]
[ROW][C]108[/C][C]830[/C][C]808.504873512225[/C][C]21.4951264877752[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169423&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169423&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
13600620.518162393163-20.5181623931626
14450470.018653484721-20.018653484721
15530554.338374146668-24.3383741466682
16400423.392686860528-23.3926868605284
17560574.739113734889-14.7391137348892
18460466.029181285405-6.029181285405
19610582.76074243789327.2392575621072
20550600.052676624764-50.0526766247636
21580669.498582010773-89.4985820107735
22650576.50030850786473.4996914921358
23640545.27561999441794.7243800055835
24760687.62475737776172.3752426222393
25550560.703395789374-10.7033957893736
26460411.02409460082648.9759053991743
27510492.9117982645517.0882017354501
28370364.512712942195.48728705781025
29530525.6571878566694.34281214333146
30410426.883199001843-16.8831990018433
31580575.7952017006074.20479829939279
32550523.09788827592426.9021117240756
33490559.055424857406-69.0554248574065
34700618.71779373187981.2822062681213
35630609.51271718937320.4872828106272
36720732.295971563084-12.2959715630843
37540528.98648116109111.0135188389095
38500435.60805495396864.391945046032
39450489.533383949162-39.533383949162
40370350.66772233959219.3322776604081
41490511.758477824285-21.7584778242848
42440393.82082561802146.179174381979
43600563.95684038308236.043159616918
44580533.9716628351746.0283371648302
45500483.40088881827416.5991111817263
46670684.82107211235-14.8210721123506
47620620.314073057059-0.314073057058749
48800714.10331415289485.8966858471065
49640535.481489776572104.518510223428
50390495.311520142459-105.311520142459
51390453.534436228575-63.5344362285746
52390370.04966234175719.9503376582434
53460494.679391724344-34.6793917243438
54460440.46803895322319.5319610467773
55620602.03827399636717.9617260036333
56570581.933985079786-11.933985079786
57510504.0310676244015.96893237559868
58640676.625025213089-36.625025213089
59590625.292572917798-35.2925729177985
60850797.86088893460852.1391110653922
61670635.45673274386534.5432672561346
62390400.080735739202-10.0807357392018
63410397.2794509604612.7205490395399
64340391.720316145676-51.7203161456756
65470465.0167012280114.98329877198853
66540461.13022561776478.8697743822364
67680622.37344287058957.6265571294114
68670576.0350493024793.9649506975298
69540517.52226602447222.4777339755277
70630653.104217827974-23.1042178279738
71560605.320464127786-45.3204641277857
72800860.43750431435-60.4375043143498
73610681.842823010622-71.8428230106224
74490404.45116965459585.5488303454046
75440424.50011058285115.4998894171488
76330360.59324546617-30.5932454661701
77490487.5006746248312.49932537516941
78590552.81169958505237.1883004149478
79690694.873917201963-4.87391720196274
80650681.624640648166-31.6246406481662
81480555.129176568292-75.1291765682925
82690645.94648320296344.0535167970368
83540577.069464089117-37.0694640891168
84830817.16359624081512.8364037591846
85690628.24588089865761.7541191013432
86500497.8157812312252.18421876877517
87460452.536206632097.46379336791034
88310345.991112805952-35.991112805952
89490503.177291517978-13.1772915179777
90470599.997228840156-129.997228840156
91710699.9169053750710.0830946249298
92710660.45476668299549.5452333170048
93540493.6784732414546.3215267585495
94700695.5733974620664.4266025379344
95520551.402086261842-31.4020862618415
96810837.372146662017-27.3721466620167
97690692.622870739758-2.6228707397579
98510505.6069541362614.39304586373925
99390464.115286609446-74.1152866094465
100270314.934455057963-44.9344550579627
101530491.11872281334738.8812771866529
102510479.35908806122530.6409119387748
103670709.838164133241-39.8381641332408
104770705.83783266097864.1621673390221
105570535.93601462992834.0639853700717
106640698.720708993055-58.720708993055
107480519.971009786015-39.971009786015
108830808.50487351222521.4951264877752







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109686.389676783005594.727011022747778.052342543263
110505.268628805143413.590240658931596.947016951356
111390.784834515567299.071080855542482.498588175593
112269.224072576532177.447480541008361.000664612057
113523.501675774102431.626984818308615.376366729896
114503.900858211929411.885088544334595.916627879525
115668.999617729772576.792171105584761.20706435396
116761.363717095516668.906515353707853.820918837324
117562.74304509109469.970711015437655.515379166743
118639.027983385116545.868067433486732.187899336747
119477.922431926907384.295687114637571.549176739177
120823.645559965858729.466265737608917.824854194107

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 686.389676783005 & 594.727011022747 & 778.052342543263 \tabularnewline
110 & 505.268628805143 & 413.590240658931 & 596.947016951356 \tabularnewline
111 & 390.784834515567 & 299.071080855542 & 482.498588175593 \tabularnewline
112 & 269.224072576532 & 177.447480541008 & 361.000664612057 \tabularnewline
113 & 523.501675774102 & 431.626984818308 & 615.376366729896 \tabularnewline
114 & 503.900858211929 & 411.885088544334 & 595.916627879525 \tabularnewline
115 & 668.999617729772 & 576.792171105584 & 761.20706435396 \tabularnewline
116 & 761.363717095516 & 668.906515353707 & 853.820918837324 \tabularnewline
117 & 562.74304509109 & 469.970711015437 & 655.515379166743 \tabularnewline
118 & 639.027983385116 & 545.868067433486 & 732.187899336747 \tabularnewline
119 & 477.922431926907 & 384.295687114637 & 571.549176739177 \tabularnewline
120 & 823.645559965858 & 729.466265737608 & 917.824854194107 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169423&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]686.389676783005[/C][C]594.727011022747[/C][C]778.052342543263[/C][/ROW]
[ROW][C]110[/C][C]505.268628805143[/C][C]413.590240658931[/C][C]596.947016951356[/C][/ROW]
[ROW][C]111[/C][C]390.784834515567[/C][C]299.071080855542[/C][C]482.498588175593[/C][/ROW]
[ROW][C]112[/C][C]269.224072576532[/C][C]177.447480541008[/C][C]361.000664612057[/C][/ROW]
[ROW][C]113[/C][C]523.501675774102[/C][C]431.626984818308[/C][C]615.376366729896[/C][/ROW]
[ROW][C]114[/C][C]503.900858211929[/C][C]411.885088544334[/C][C]595.916627879525[/C][/ROW]
[ROW][C]115[/C][C]668.999617729772[/C][C]576.792171105584[/C][C]761.20706435396[/C][/ROW]
[ROW][C]116[/C][C]761.363717095516[/C][C]668.906515353707[/C][C]853.820918837324[/C][/ROW]
[ROW][C]117[/C][C]562.74304509109[/C][C]469.970711015437[/C][C]655.515379166743[/C][/ROW]
[ROW][C]118[/C][C]639.027983385116[/C][C]545.868067433486[/C][C]732.187899336747[/C][/ROW]
[ROW][C]119[/C][C]477.922431926907[/C][C]384.295687114637[/C][C]571.549176739177[/C][/ROW]
[ROW][C]120[/C][C]823.645559965858[/C][C]729.466265737608[/C][C]917.824854194107[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169423&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169423&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
109686.389676783005594.727011022747778.052342543263
110505.268628805143413.590240658931596.947016951356
111390.784834515567299.071080855542482.498588175593
112269.224072576532177.447480541008361.000664612057
113523.501675774102431.626984818308615.376366729896
114503.900858211929411.885088544334595.916627879525
115668.999617729772576.792171105584761.20706435396
116761.363717095516668.906515353707853.820918837324
117562.74304509109469.970711015437655.515379166743
118639.027983385116545.868067433486732.187899336747
119477.922431926907384.295687114637571.549176739177
120823.645559965858729.466265737608917.824854194107



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')