Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 15 Aug 2016 14:00:34 +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/15/t1471266708e9mq1ow3fswi2po.htm/, Retrieved Sun, 28 Apr 2024 09:53:44 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sun, 28 Apr 2024 09:53:44 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
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'Sir Ronald Aylmer Fisher' @ fisher.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 Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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 Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.548594506058367
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.548594506058367 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.548594506058367[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
alpha0.548594506058367
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2520540-20
3550529.02810987883320.9718901211673
4440540.533173580965-100.533173580965
5570485.38122687783584.6187731221647
6560531.80262092205428.1973790779457
7600547.2715481694652.7284518305396
8620576.19808715665843.8019128433423
9690600.22757589736389.7724241026373
10600649.476234555611-49.4762345556112
11570622.333844097948-52.3338440979478
12710593.623784744899116.376215255101
13600657.467137069713-57.4671370697131
14450625.940981394365-175.940981394365
15530529.4207256108990.579274389100988
16400529.73851235826-129.73851235826
17560458.564677254333101.435322745667
18460514.211538032863-54.2115380328632
19610484.47138610306125.52861389694
20550553.335694040043-3.33569404004334
21580551.50575061578428.4942493842161
22650567.13753928222282.8624607177782
23640612.59542999047227.4045700095278
24760627.629426538591132.370573461409
25550700.247195903316-150.247195903316
26460617.822409680081-157.822409680081
27510531.241902796696-21.2419027966959
28370519.588711624203-149.588711624203
29530437.52516625881692.4748337411843
30410488.25635199789-78.2563519978903
31580445.325347227678134.674652772322
32550519.20712184389230.7928781561079
33490536.099925626058-46.0999256260576
34700510.809759697903189.190240302097
35630614.59848612749615.4015138725042
36720623.04767202293396.9523279770667
37540676.235186500721-136.235186500721
38500601.497311654588-101.497311654588
39450545.816444101187-95.8164441011872
40370493.252069277227-123.252069277227
41490425.63666121141564.3633387885849
42440460.946035262406-20.9460352624062
43600449.455155393745150.544844606255
44580532.04323006014747.9567699398527
45500558.352050577456-58.3520505774555
46670526.340436213423143.659563786577
47620605.15128364948114.8487163505191
48800613.297207861395186.702792138605
49640715.721333894391-75.7213338943909
50390674.181026128517-284.181026128517
51390518.280876468383-128.280876468383
52390447.906692405476-57.9066924054761
53460416.1393990878243.8606009121799
54460440.20108378066119.7989162193394
55620451.0626604445168.9373395555
56570543.74075679276426.2592432072357
57510558.146433349504-48.1464333495043
58640531.733564527661108.266435472339
59590591.127936218309-1.12793621830883
60850590.50915660576259.49084339424
61670732.864407664292-62.8644076642925
62390698.377338993048-308.377338993048
63410529.203225028563-119.203225028563
64340463.808990673454-123.808990673454
65470395.88805858936674.1119414106345
66540436.545462480559103.454537519441
67680493.300053390534186.699946609466
68670595.72261838187774.2773816181226
69540636.47078186198-96.4707818619802
70630583.54744093734346.4525590626574
71560609.031059631468-49.0310596314682
72800582.132889691425217.867110308575
73610701.653589457521-91.6535894575213
74490651.372933820596-161.372933820596
75440562.844628900096-122.844628900096
76330495.452740386725-165.452740386725
77490404.68627599826685.3137240017339
78590451.488916276997138.511083723003
79690527.475335835627162.524664164373
80650616.63547369518333.3645263048168
81480634.939069523246-154.939069523246
82690549.940347208998140.059652791002
83540626.776303250584-86.776303250584
84830579.171300031259250.828699968741
85690716.774546795873-26.7745467958728
86500702.086177521454-202.086177521454
87460591.222810782849-131.222810782849
88310519.234697717841-209.234697717841
89490404.4496920730585.5503079269497
90470451.38212099337618.6178790066235
91710461.59578713087248.40421286913
92710597.868973592628112.131026407372
93540659.383438638398-119.383438638398
94700593.890340087017106.109659912983
95520652.101516555001-132.101516555001
96810579.631350330949230.368649669051
97690706.010325907475-16.0103259074751
98510697.22714907443-187.22714907443
99390594.515363707227-204.515363707227
100270482.319358772913-212.319358772913
101530365.842125020258164.157874979742
102510455.89823336036154.1017666396394
103670485.578165306919184.421834693081
104770586.750970616748183.249029383252
105570687.280381376928-117.280381376928
106640622.94100848511517.0589915148847
107480632.299477509077-152.299477509077
108830548.748820872038281.251179127962

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 520 & 540 & -20 \tabularnewline
3 & 550 & 529.028109878833 & 20.9718901211673 \tabularnewline
4 & 440 & 540.533173580965 & -100.533173580965 \tabularnewline
5 & 570 & 485.381226877835 & 84.6187731221647 \tabularnewline
6 & 560 & 531.802620922054 & 28.1973790779457 \tabularnewline
7 & 600 & 547.27154816946 & 52.7284518305396 \tabularnewline
8 & 620 & 576.198087156658 & 43.8019128433423 \tabularnewline
9 & 690 & 600.227575897363 & 89.7724241026373 \tabularnewline
10 & 600 & 649.476234555611 & -49.4762345556112 \tabularnewline
11 & 570 & 622.333844097948 & -52.3338440979478 \tabularnewline
12 & 710 & 593.623784744899 & 116.376215255101 \tabularnewline
13 & 600 & 657.467137069713 & -57.4671370697131 \tabularnewline
14 & 450 & 625.940981394365 & -175.940981394365 \tabularnewline
15 & 530 & 529.420725610899 & 0.579274389100988 \tabularnewline
16 & 400 & 529.73851235826 & -129.73851235826 \tabularnewline
17 & 560 & 458.564677254333 & 101.435322745667 \tabularnewline
18 & 460 & 514.211538032863 & -54.2115380328632 \tabularnewline
19 & 610 & 484.47138610306 & 125.52861389694 \tabularnewline
20 & 550 & 553.335694040043 & -3.33569404004334 \tabularnewline
21 & 580 & 551.505750615784 & 28.4942493842161 \tabularnewline
22 & 650 & 567.137539282222 & 82.8624607177782 \tabularnewline
23 & 640 & 612.595429990472 & 27.4045700095278 \tabularnewline
24 & 760 & 627.629426538591 & 132.370573461409 \tabularnewline
25 & 550 & 700.247195903316 & -150.247195903316 \tabularnewline
26 & 460 & 617.822409680081 & -157.822409680081 \tabularnewline
27 & 510 & 531.241902796696 & -21.2419027966959 \tabularnewline
28 & 370 & 519.588711624203 & -149.588711624203 \tabularnewline
29 & 530 & 437.525166258816 & 92.4748337411843 \tabularnewline
30 & 410 & 488.25635199789 & -78.2563519978903 \tabularnewline
31 & 580 & 445.325347227678 & 134.674652772322 \tabularnewline
32 & 550 & 519.207121843892 & 30.7928781561079 \tabularnewline
33 & 490 & 536.099925626058 & -46.0999256260576 \tabularnewline
34 & 700 & 510.809759697903 & 189.190240302097 \tabularnewline
35 & 630 & 614.598486127496 & 15.4015138725042 \tabularnewline
36 & 720 & 623.047672022933 & 96.9523279770667 \tabularnewline
37 & 540 & 676.235186500721 & -136.235186500721 \tabularnewline
38 & 500 & 601.497311654588 & -101.497311654588 \tabularnewline
39 & 450 & 545.816444101187 & -95.8164441011872 \tabularnewline
40 & 370 & 493.252069277227 & -123.252069277227 \tabularnewline
41 & 490 & 425.636661211415 & 64.3633387885849 \tabularnewline
42 & 440 & 460.946035262406 & -20.9460352624062 \tabularnewline
43 & 600 & 449.455155393745 & 150.544844606255 \tabularnewline
44 & 580 & 532.043230060147 & 47.9567699398527 \tabularnewline
45 & 500 & 558.352050577456 & -58.3520505774555 \tabularnewline
46 & 670 & 526.340436213423 & 143.659563786577 \tabularnewline
47 & 620 & 605.151283649481 & 14.8487163505191 \tabularnewline
48 & 800 & 613.297207861395 & 186.702792138605 \tabularnewline
49 & 640 & 715.721333894391 & -75.7213338943909 \tabularnewline
50 & 390 & 674.181026128517 & -284.181026128517 \tabularnewline
51 & 390 & 518.280876468383 & -128.280876468383 \tabularnewline
52 & 390 & 447.906692405476 & -57.9066924054761 \tabularnewline
53 & 460 & 416.13939908782 & 43.8606009121799 \tabularnewline
54 & 460 & 440.201083780661 & 19.7989162193394 \tabularnewline
55 & 620 & 451.0626604445 & 168.9373395555 \tabularnewline
56 & 570 & 543.740756792764 & 26.2592432072357 \tabularnewline
57 & 510 & 558.146433349504 & -48.1464333495043 \tabularnewline
58 & 640 & 531.733564527661 & 108.266435472339 \tabularnewline
59 & 590 & 591.127936218309 & -1.12793621830883 \tabularnewline
60 & 850 & 590.50915660576 & 259.49084339424 \tabularnewline
61 & 670 & 732.864407664292 & -62.8644076642925 \tabularnewline
62 & 390 & 698.377338993048 & -308.377338993048 \tabularnewline
63 & 410 & 529.203225028563 & -119.203225028563 \tabularnewline
64 & 340 & 463.808990673454 & -123.808990673454 \tabularnewline
65 & 470 & 395.888058589366 & 74.1119414106345 \tabularnewline
66 & 540 & 436.545462480559 & 103.454537519441 \tabularnewline
67 & 680 & 493.300053390534 & 186.699946609466 \tabularnewline
68 & 670 & 595.722618381877 & 74.2773816181226 \tabularnewline
69 & 540 & 636.47078186198 & -96.4707818619802 \tabularnewline
70 & 630 & 583.547440937343 & 46.4525590626574 \tabularnewline
71 & 560 & 609.031059631468 & -49.0310596314682 \tabularnewline
72 & 800 & 582.132889691425 & 217.867110308575 \tabularnewline
73 & 610 & 701.653589457521 & -91.6535894575213 \tabularnewline
74 & 490 & 651.372933820596 & -161.372933820596 \tabularnewline
75 & 440 & 562.844628900096 & -122.844628900096 \tabularnewline
76 & 330 & 495.452740386725 & -165.452740386725 \tabularnewline
77 & 490 & 404.686275998266 & 85.3137240017339 \tabularnewline
78 & 590 & 451.488916276997 & 138.511083723003 \tabularnewline
79 & 690 & 527.475335835627 & 162.524664164373 \tabularnewline
80 & 650 & 616.635473695183 & 33.3645263048168 \tabularnewline
81 & 480 & 634.939069523246 & -154.939069523246 \tabularnewline
82 & 690 & 549.940347208998 & 140.059652791002 \tabularnewline
83 & 540 & 626.776303250584 & -86.776303250584 \tabularnewline
84 & 830 & 579.171300031259 & 250.828699968741 \tabularnewline
85 & 690 & 716.774546795873 & -26.7745467958728 \tabularnewline
86 & 500 & 702.086177521454 & -202.086177521454 \tabularnewline
87 & 460 & 591.222810782849 & -131.222810782849 \tabularnewline
88 & 310 & 519.234697717841 & -209.234697717841 \tabularnewline
89 & 490 & 404.44969207305 & 85.5503079269497 \tabularnewline
90 & 470 & 451.382120993376 & 18.6178790066235 \tabularnewline
91 & 710 & 461.59578713087 & 248.40421286913 \tabularnewline
92 & 710 & 597.868973592628 & 112.131026407372 \tabularnewline
93 & 540 & 659.383438638398 & -119.383438638398 \tabularnewline
94 & 700 & 593.890340087017 & 106.109659912983 \tabularnewline
95 & 520 & 652.101516555001 & -132.101516555001 \tabularnewline
96 & 810 & 579.631350330949 & 230.368649669051 \tabularnewline
97 & 690 & 706.010325907475 & -16.0103259074751 \tabularnewline
98 & 510 & 697.22714907443 & -187.22714907443 \tabularnewline
99 & 390 & 594.515363707227 & -204.515363707227 \tabularnewline
100 & 270 & 482.319358772913 & -212.319358772913 \tabularnewline
101 & 530 & 365.842125020258 & 164.157874979742 \tabularnewline
102 & 510 & 455.898233360361 & 54.1017666396394 \tabularnewline
103 & 670 & 485.578165306919 & 184.421834693081 \tabularnewline
104 & 770 & 586.750970616748 & 183.249029383252 \tabularnewline
105 & 570 & 687.280381376928 & -117.280381376928 \tabularnewline
106 & 640 & 622.941008485115 & 17.0589915148847 \tabularnewline
107 & 480 & 632.299477509077 & -152.299477509077 \tabularnewline
108 & 830 & 548.748820872038 & 281.251179127962 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]2[/C][C]520[/C][C]540[/C][C]-20[/C][/ROW]
[ROW][C]3[/C][C]550[/C][C]529.028109878833[/C][C]20.9718901211673[/C][/ROW]
[ROW][C]4[/C][C]440[/C][C]540.533173580965[/C][C]-100.533173580965[/C][/ROW]
[ROW][C]5[/C][C]570[/C][C]485.381226877835[/C][C]84.6187731221647[/C][/ROW]
[ROW][C]6[/C][C]560[/C][C]531.802620922054[/C][C]28.1973790779457[/C][/ROW]
[ROW][C]7[/C][C]600[/C][C]547.27154816946[/C][C]52.7284518305396[/C][/ROW]
[ROW][C]8[/C][C]620[/C][C]576.198087156658[/C][C]43.8019128433423[/C][/ROW]
[ROW][C]9[/C][C]690[/C][C]600.227575897363[/C][C]89.7724241026373[/C][/ROW]
[ROW][C]10[/C][C]600[/C][C]649.476234555611[/C][C]-49.4762345556112[/C][/ROW]
[ROW][C]11[/C][C]570[/C][C]622.333844097948[/C][C]-52.3338440979478[/C][/ROW]
[ROW][C]12[/C][C]710[/C][C]593.623784744899[/C][C]116.376215255101[/C][/ROW]
[ROW][C]13[/C][C]600[/C][C]657.467137069713[/C][C]-57.4671370697131[/C][/ROW]
[ROW][C]14[/C][C]450[/C][C]625.940981394365[/C][C]-175.940981394365[/C][/ROW]
[ROW][C]15[/C][C]530[/C][C]529.420725610899[/C][C]0.579274389100988[/C][/ROW]
[ROW][C]16[/C][C]400[/C][C]529.73851235826[/C][C]-129.73851235826[/C][/ROW]
[ROW][C]17[/C][C]560[/C][C]458.564677254333[/C][C]101.435322745667[/C][/ROW]
[ROW][C]18[/C][C]460[/C][C]514.211538032863[/C][C]-54.2115380328632[/C][/ROW]
[ROW][C]19[/C][C]610[/C][C]484.47138610306[/C][C]125.52861389694[/C][/ROW]
[ROW][C]20[/C][C]550[/C][C]553.335694040043[/C][C]-3.33569404004334[/C][/ROW]
[ROW][C]21[/C][C]580[/C][C]551.505750615784[/C][C]28.4942493842161[/C][/ROW]
[ROW][C]22[/C][C]650[/C][C]567.137539282222[/C][C]82.8624607177782[/C][/ROW]
[ROW][C]23[/C][C]640[/C][C]612.595429990472[/C][C]27.4045700095278[/C][/ROW]
[ROW][C]24[/C][C]760[/C][C]627.629426538591[/C][C]132.370573461409[/C][/ROW]
[ROW][C]25[/C][C]550[/C][C]700.247195903316[/C][C]-150.247195903316[/C][/ROW]
[ROW][C]26[/C][C]460[/C][C]617.822409680081[/C][C]-157.822409680081[/C][/ROW]
[ROW][C]27[/C][C]510[/C][C]531.241902796696[/C][C]-21.2419027966959[/C][/ROW]
[ROW][C]28[/C][C]370[/C][C]519.588711624203[/C][C]-149.588711624203[/C][/ROW]
[ROW][C]29[/C][C]530[/C][C]437.525166258816[/C][C]92.4748337411843[/C][/ROW]
[ROW][C]30[/C][C]410[/C][C]488.25635199789[/C][C]-78.2563519978903[/C][/ROW]
[ROW][C]31[/C][C]580[/C][C]445.325347227678[/C][C]134.674652772322[/C][/ROW]
[ROW][C]32[/C][C]550[/C][C]519.207121843892[/C][C]30.7928781561079[/C][/ROW]
[ROW][C]33[/C][C]490[/C][C]536.099925626058[/C][C]-46.0999256260576[/C][/ROW]
[ROW][C]34[/C][C]700[/C][C]510.809759697903[/C][C]189.190240302097[/C][/ROW]
[ROW][C]35[/C][C]630[/C][C]614.598486127496[/C][C]15.4015138725042[/C][/ROW]
[ROW][C]36[/C][C]720[/C][C]623.047672022933[/C][C]96.9523279770667[/C][/ROW]
[ROW][C]37[/C][C]540[/C][C]676.235186500721[/C][C]-136.235186500721[/C][/ROW]
[ROW][C]38[/C][C]500[/C][C]601.497311654588[/C][C]-101.497311654588[/C][/ROW]
[ROW][C]39[/C][C]450[/C][C]545.816444101187[/C][C]-95.8164441011872[/C][/ROW]
[ROW][C]40[/C][C]370[/C][C]493.252069277227[/C][C]-123.252069277227[/C][/ROW]
[ROW][C]41[/C][C]490[/C][C]425.636661211415[/C][C]64.3633387885849[/C][/ROW]
[ROW][C]42[/C][C]440[/C][C]460.946035262406[/C][C]-20.9460352624062[/C][/ROW]
[ROW][C]43[/C][C]600[/C][C]449.455155393745[/C][C]150.544844606255[/C][/ROW]
[ROW][C]44[/C][C]580[/C][C]532.043230060147[/C][C]47.9567699398527[/C][/ROW]
[ROW][C]45[/C][C]500[/C][C]558.352050577456[/C][C]-58.3520505774555[/C][/ROW]
[ROW][C]46[/C][C]670[/C][C]526.340436213423[/C][C]143.659563786577[/C][/ROW]
[ROW][C]47[/C][C]620[/C][C]605.151283649481[/C][C]14.8487163505191[/C][/ROW]
[ROW][C]48[/C][C]800[/C][C]613.297207861395[/C][C]186.702792138605[/C][/ROW]
[ROW][C]49[/C][C]640[/C][C]715.721333894391[/C][C]-75.7213338943909[/C][/ROW]
[ROW][C]50[/C][C]390[/C][C]674.181026128517[/C][C]-284.181026128517[/C][/ROW]
[ROW][C]51[/C][C]390[/C][C]518.280876468383[/C][C]-128.280876468383[/C][/ROW]
[ROW][C]52[/C][C]390[/C][C]447.906692405476[/C][C]-57.9066924054761[/C][/ROW]
[ROW][C]53[/C][C]460[/C][C]416.13939908782[/C][C]43.8606009121799[/C][/ROW]
[ROW][C]54[/C][C]460[/C][C]440.201083780661[/C][C]19.7989162193394[/C][/ROW]
[ROW][C]55[/C][C]620[/C][C]451.0626604445[/C][C]168.9373395555[/C][/ROW]
[ROW][C]56[/C][C]570[/C][C]543.740756792764[/C][C]26.2592432072357[/C][/ROW]
[ROW][C]57[/C][C]510[/C][C]558.146433349504[/C][C]-48.1464333495043[/C][/ROW]
[ROW][C]58[/C][C]640[/C][C]531.733564527661[/C][C]108.266435472339[/C][/ROW]
[ROW][C]59[/C][C]590[/C][C]591.127936218309[/C][C]-1.12793621830883[/C][/ROW]
[ROW][C]60[/C][C]850[/C][C]590.50915660576[/C][C]259.49084339424[/C][/ROW]
[ROW][C]61[/C][C]670[/C][C]732.864407664292[/C][C]-62.8644076642925[/C][/ROW]
[ROW][C]62[/C][C]390[/C][C]698.377338993048[/C][C]-308.377338993048[/C][/ROW]
[ROW][C]63[/C][C]410[/C][C]529.203225028563[/C][C]-119.203225028563[/C][/ROW]
[ROW][C]64[/C][C]340[/C][C]463.808990673454[/C][C]-123.808990673454[/C][/ROW]
[ROW][C]65[/C][C]470[/C][C]395.888058589366[/C][C]74.1119414106345[/C][/ROW]
[ROW][C]66[/C][C]540[/C][C]436.545462480559[/C][C]103.454537519441[/C][/ROW]
[ROW][C]67[/C][C]680[/C][C]493.300053390534[/C][C]186.699946609466[/C][/ROW]
[ROW][C]68[/C][C]670[/C][C]595.722618381877[/C][C]74.2773816181226[/C][/ROW]
[ROW][C]69[/C][C]540[/C][C]636.47078186198[/C][C]-96.4707818619802[/C][/ROW]
[ROW][C]70[/C][C]630[/C][C]583.547440937343[/C][C]46.4525590626574[/C][/ROW]
[ROW][C]71[/C][C]560[/C][C]609.031059631468[/C][C]-49.0310596314682[/C][/ROW]
[ROW][C]72[/C][C]800[/C][C]582.132889691425[/C][C]217.867110308575[/C][/ROW]
[ROW][C]73[/C][C]610[/C][C]701.653589457521[/C][C]-91.6535894575213[/C][/ROW]
[ROW][C]74[/C][C]490[/C][C]651.372933820596[/C][C]-161.372933820596[/C][/ROW]
[ROW][C]75[/C][C]440[/C][C]562.844628900096[/C][C]-122.844628900096[/C][/ROW]
[ROW][C]76[/C][C]330[/C][C]495.452740386725[/C][C]-165.452740386725[/C][/ROW]
[ROW][C]77[/C][C]490[/C][C]404.686275998266[/C][C]85.3137240017339[/C][/ROW]
[ROW][C]78[/C][C]590[/C][C]451.488916276997[/C][C]138.511083723003[/C][/ROW]
[ROW][C]79[/C][C]690[/C][C]527.475335835627[/C][C]162.524664164373[/C][/ROW]
[ROW][C]80[/C][C]650[/C][C]616.635473695183[/C][C]33.3645263048168[/C][/ROW]
[ROW][C]81[/C][C]480[/C][C]634.939069523246[/C][C]-154.939069523246[/C][/ROW]
[ROW][C]82[/C][C]690[/C][C]549.940347208998[/C][C]140.059652791002[/C][/ROW]
[ROW][C]83[/C][C]540[/C][C]626.776303250584[/C][C]-86.776303250584[/C][/ROW]
[ROW][C]84[/C][C]830[/C][C]579.171300031259[/C][C]250.828699968741[/C][/ROW]
[ROW][C]85[/C][C]690[/C][C]716.774546795873[/C][C]-26.7745467958728[/C][/ROW]
[ROW][C]86[/C][C]500[/C][C]702.086177521454[/C][C]-202.086177521454[/C][/ROW]
[ROW][C]87[/C][C]460[/C][C]591.222810782849[/C][C]-131.222810782849[/C][/ROW]
[ROW][C]88[/C][C]310[/C][C]519.234697717841[/C][C]-209.234697717841[/C][/ROW]
[ROW][C]89[/C][C]490[/C][C]404.44969207305[/C][C]85.5503079269497[/C][/ROW]
[ROW][C]90[/C][C]470[/C][C]451.382120993376[/C][C]18.6178790066235[/C][/ROW]
[ROW][C]91[/C][C]710[/C][C]461.59578713087[/C][C]248.40421286913[/C][/ROW]
[ROW][C]92[/C][C]710[/C][C]597.868973592628[/C][C]112.131026407372[/C][/ROW]
[ROW][C]93[/C][C]540[/C][C]659.383438638398[/C][C]-119.383438638398[/C][/ROW]
[ROW][C]94[/C][C]700[/C][C]593.890340087017[/C][C]106.109659912983[/C][/ROW]
[ROW][C]95[/C][C]520[/C][C]652.101516555001[/C][C]-132.101516555001[/C][/ROW]
[ROW][C]96[/C][C]810[/C][C]579.631350330949[/C][C]230.368649669051[/C][/ROW]
[ROW][C]97[/C][C]690[/C][C]706.010325907475[/C][C]-16.0103259074751[/C][/ROW]
[ROW][C]98[/C][C]510[/C][C]697.22714907443[/C][C]-187.22714907443[/C][/ROW]
[ROW][C]99[/C][C]390[/C][C]594.515363707227[/C][C]-204.515363707227[/C][/ROW]
[ROW][C]100[/C][C]270[/C][C]482.319358772913[/C][C]-212.319358772913[/C][/ROW]
[ROW][C]101[/C][C]530[/C][C]365.842125020258[/C][C]164.157874979742[/C][/ROW]
[ROW][C]102[/C][C]510[/C][C]455.898233360361[/C][C]54.1017666396394[/C][/ROW]
[ROW][C]103[/C][C]670[/C][C]485.578165306919[/C][C]184.421834693081[/C][/ROW]
[ROW][C]104[/C][C]770[/C][C]586.750970616748[/C][C]183.249029383252[/C][/ROW]
[ROW][C]105[/C][C]570[/C][C]687.280381376928[/C][C]-117.280381376928[/C][/ROW]
[ROW][C]106[/C][C]640[/C][C]622.941008485115[/C][C]17.0589915148847[/C][/ROW]
[ROW][C]107[/C][C]480[/C][C]632.299477509077[/C][C]-152.299477509077[/C][/ROW]
[ROW][C]108[/C][C]830[/C][C]548.748820872038[/C][C]281.251179127962[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
2520540-20
3550529.02810987883320.9718901211673
4440540.533173580965-100.533173580965
5570485.38122687783584.6187731221647
6560531.80262092205428.1973790779457
7600547.2715481694652.7284518305396
8620576.19808715665843.8019128433423
9690600.22757589736389.7724241026373
10600649.476234555611-49.4762345556112
11570622.333844097948-52.3338440979478
12710593.623784744899116.376215255101
13600657.467137069713-57.4671370697131
14450625.940981394365-175.940981394365
15530529.4207256108990.579274389100988
16400529.73851235826-129.73851235826
17560458.564677254333101.435322745667
18460514.211538032863-54.2115380328632
19610484.47138610306125.52861389694
20550553.335694040043-3.33569404004334
21580551.50575061578428.4942493842161
22650567.13753928222282.8624607177782
23640612.59542999047227.4045700095278
24760627.629426538591132.370573461409
25550700.247195903316-150.247195903316
26460617.822409680081-157.822409680081
27510531.241902796696-21.2419027966959
28370519.588711624203-149.588711624203
29530437.52516625881692.4748337411843
30410488.25635199789-78.2563519978903
31580445.325347227678134.674652772322
32550519.20712184389230.7928781561079
33490536.099925626058-46.0999256260576
34700510.809759697903189.190240302097
35630614.59848612749615.4015138725042
36720623.04767202293396.9523279770667
37540676.235186500721-136.235186500721
38500601.497311654588-101.497311654588
39450545.816444101187-95.8164441011872
40370493.252069277227-123.252069277227
41490425.63666121141564.3633387885849
42440460.946035262406-20.9460352624062
43600449.455155393745150.544844606255
44580532.04323006014747.9567699398527
45500558.352050577456-58.3520505774555
46670526.340436213423143.659563786577
47620605.15128364948114.8487163505191
48800613.297207861395186.702792138605
49640715.721333894391-75.7213338943909
50390674.181026128517-284.181026128517
51390518.280876468383-128.280876468383
52390447.906692405476-57.9066924054761
53460416.1393990878243.8606009121799
54460440.20108378066119.7989162193394
55620451.0626604445168.9373395555
56570543.74075679276426.2592432072357
57510558.146433349504-48.1464333495043
58640531.733564527661108.266435472339
59590591.127936218309-1.12793621830883
60850590.50915660576259.49084339424
61670732.864407664292-62.8644076642925
62390698.377338993048-308.377338993048
63410529.203225028563-119.203225028563
64340463.808990673454-123.808990673454
65470395.88805858936674.1119414106345
66540436.545462480559103.454537519441
67680493.300053390534186.699946609466
68670595.72261838187774.2773816181226
69540636.47078186198-96.4707818619802
70630583.54744093734346.4525590626574
71560609.031059631468-49.0310596314682
72800582.132889691425217.867110308575
73610701.653589457521-91.6535894575213
74490651.372933820596-161.372933820596
75440562.844628900096-122.844628900096
76330495.452740386725-165.452740386725
77490404.68627599826685.3137240017339
78590451.488916276997138.511083723003
79690527.475335835627162.524664164373
80650616.63547369518333.3645263048168
81480634.939069523246-154.939069523246
82690549.940347208998140.059652791002
83540626.776303250584-86.776303250584
84830579.171300031259250.828699968741
85690716.774546795873-26.7745467958728
86500702.086177521454-202.086177521454
87460591.222810782849-131.222810782849
88310519.234697717841-209.234697717841
89490404.4496920730585.5503079269497
90470451.38212099337618.6178790066235
91710461.59578713087248.40421286913
92710597.868973592628112.131026407372
93540659.383438638398-119.383438638398
94700593.890340087017106.109659912983
95520652.101516555001-132.101516555001
96810579.631350330949230.368649669051
97690706.010325907475-16.0103259074751
98510697.22714907443-187.22714907443
99390594.515363707227-204.515363707227
100270482.319358772913-212.319358772913
101530365.842125020258164.157874979742
102510455.89823336036154.1017666396394
103670485.578165306919184.421834693081
104770586.750970616748183.249029383252
105570687.280381376928-117.280381376928
106640622.94100848511517.0589915148847
107480632.299477509077-152.299477509077
108830548.748820872038281.251179127962







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109703.041672564075449.317843696247956.765501431904
110703.041672564075413.645655642032992.437689486119
111703.041672564075381.9119045802641024.17144054789
112703.041672564075353.0436709121661053.03967421598
113703.041672564075326.3815148153131079.70183031284
114703.041672564075301.4857639905421104.59758113761
115703.041672564075278.0458831904531128.0374619377
116703.041672564075255.8328910533571150.25045407479
117703.041672564075234.6721949768881171.41115015126
118703.041672564075214.4270587729121191.65628635524
119703.041672564075194.9880198016131211.09532532654
120703.041672564075176.265830900591229.81751422756

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 703.041672564075 & 449.317843696247 & 956.765501431904 \tabularnewline
110 & 703.041672564075 & 413.645655642032 & 992.437689486119 \tabularnewline
111 & 703.041672564075 & 381.911904580264 & 1024.17144054789 \tabularnewline
112 & 703.041672564075 & 353.043670912166 & 1053.03967421598 \tabularnewline
113 & 703.041672564075 & 326.381514815313 & 1079.70183031284 \tabularnewline
114 & 703.041672564075 & 301.485763990542 & 1104.59758113761 \tabularnewline
115 & 703.041672564075 & 278.045883190453 & 1128.0374619377 \tabularnewline
116 & 703.041672564075 & 255.832891053357 & 1150.25045407479 \tabularnewline
117 & 703.041672564075 & 234.672194976888 & 1171.41115015126 \tabularnewline
118 & 703.041672564075 & 214.427058772912 & 1191.65628635524 \tabularnewline
119 & 703.041672564075 & 194.988019801613 & 1211.09532532654 \tabularnewline
120 & 703.041672564075 & 176.26583090059 & 1229.81751422756 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]703.041672564075[/C][C]449.317843696247[/C][C]956.765501431904[/C][/ROW]
[ROW][C]110[/C][C]703.041672564075[/C][C]413.645655642032[/C][C]992.437689486119[/C][/ROW]
[ROW][C]111[/C][C]703.041672564075[/C][C]381.911904580264[/C][C]1024.17144054789[/C][/ROW]
[ROW][C]112[/C][C]703.041672564075[/C][C]353.043670912166[/C][C]1053.03967421598[/C][/ROW]
[ROW][C]113[/C][C]703.041672564075[/C][C]326.381514815313[/C][C]1079.70183031284[/C][/ROW]
[ROW][C]114[/C][C]703.041672564075[/C][C]301.485763990542[/C][C]1104.59758113761[/C][/ROW]
[ROW][C]115[/C][C]703.041672564075[/C][C]278.045883190453[/C][C]1128.0374619377[/C][/ROW]
[ROW][C]116[/C][C]703.041672564075[/C][C]255.832891053357[/C][C]1150.25045407479[/C][/ROW]
[ROW][C]117[/C][C]703.041672564075[/C][C]234.672194976888[/C][C]1171.41115015126[/C][/ROW]
[ROW][C]118[/C][C]703.041672564075[/C][C]214.427058772912[/C][C]1191.65628635524[/C][/ROW]
[ROW][C]119[/C][C]703.041672564075[/C][C]194.988019801613[/C][C]1211.09532532654[/C][/ROW]
[ROW][C]120[/C][C]703.041672564075[/C][C]176.26583090059[/C][C]1229.81751422756[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
109703.041672564075449.317843696247956.765501431904
110703.041672564075413.645655642032992.437689486119
111703.041672564075381.9119045802641024.17144054789
112703.041672564075353.0436709121661053.03967421598
113703.041672564075326.3815148153131079.70183031284
114703.041672564075301.4857639905421104.59758113761
115703.041672564075278.0458831904531128.0374619377
116703.041672564075255.8328910533571150.25045407479
117703.041672564075234.6721949768881171.41115015126
118703.041672564075214.4270587729121191.65628635524
119703.041672564075194.9880198016131211.09532532654
120703.041672564075176.265830900591229.81751422756



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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')