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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 18 Aug 2011 13:53:55 -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/2011/Aug/18/t1313690060s6vl4rk73a3trpa.htm/, Retrieved Wed, 15 May 2024 19:04:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=124138, Retrieved Wed, 15 May 2024 19:04:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsVan Boxel Dieter
Estimated Impact197
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [Tijdreeks B - Sta...] [2011-08-10 17:17:49] [1580052e33a81ec6e32ae46c93d1a3ad]
- R P     [Exponential Smoothing] [Tijdreeks B - sta...] [2011-08-18 17:53:55] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
500
510
590
490
540
530
550
510
390
480
530
690
570
460
540
510
520
520
580
480
410
530
540
670
570
400
510
570
470
640
650
500
340
450
600
680
630
480
400
520
470
610
670
500
290
470
660
650
570
500
400
500
340
530
680
480
340
460
630
650
550
470
240
430
390
570
700
620
280
480
560
560
560
550
140
380
390
500
750
680
280
360
590
580
490
610
170
320
440
510
770
660
300
350
580
620
490
640
150
290
370
560
780
690
310
280
590
590




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124138&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124138&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124138&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 time1 seconds
R Server'AstonUniversity' @ aston.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124138&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[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124138&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124138&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
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13570575.917036565447-5.91703656544723
14460464.741680739602-4.74168073960237
15540545.96136495399-5.96136495398991
16510512.735436718659-2.73543671865923
17520520.279777152659-0.279777152659335
18520520.652583242891-0.6525832428905
19580550.21663430242629.7833656975737
20480509.361344252978-29.361344252978
21410392.57223865251817.4277613474821
22530484.28315685436845.7168431456324
23540534.6907846054375.30921539456324
24670697.720583635073-27.7205836350727
25570569.5074057181260.492594281874403
26400459.602439141498-59.6024391414982
27510539.533264507454-29.5332645074539
28570509.55916250480160.4408374951988
29470519.55048625285-49.5504862528505
30640519.550453868689120.449546131311
31650579.4985470352370.5014529647697
32500479.58497454126120.4150254587385
33340409.645473542622-69.6454735426217
34450529.541676675473-79.5416766754735
35600539.53299541163160.4670045883692
36680669.42052661925710.579473380743
37630569.50697964969560.493020350305
38480399.65399586717280.3460041328278
39400509.55881292803-109.55881292803
40520569.506873017398-49.5068730173978
41470469.5933572063730.406642793627213
42610639.44623371629-29.4462337162897
43670649.43754056197820.5624594380224
44500499.5673076923070.43269230769323
45290339.705748010673-49.7057480106732
46470449.61052074818420.389479251816
47660599.4806568728860.5193431271199
48650679.411368664036-29.4113686640364
49570629.454611037633-59.4546110376326
50500479.58443557308420.4155644269164
51400399.6536713244660.346328675534039
52500519.54974023475-19.5497402347498
53340469.593005075409-129.593005075409
54530609.471734423862-79.4717344238622
55680669.4197319989410.5802680010597
56480499.566932922721-19.5669329227207
57340289.74880296431750.251197035683
58460469.592858174117-9.59285817411723
59630659.428227650101-29.4282276501011
60650649.4368502117820.563149788218311
61550569.50612529784-19.5061252978401
62470499.566745294372-29.5667452943716
63240399.653371205738-159.653371205738
64430499.566682715454-69.5666827154541
65390339.70532296506750.2946770349333
66570529.54061732556440.4593826744364
67700679.41056078591820.5894392140823
68620479.583895203235140.416104796765
69280339.705237808548-59.7052378085485
70480459.60117528057320.3988247194267
71560629.453744068979-69.4537440689793
72560649.436361884573-89.4363618845734
73560549.52304097511510.4769590248848
74550469.59238737653580.4076126234651
75140239.791842339846-99.7918423398459
76380429.62702390131-49.6270239013099
77390389.6616948989170.338305101082653
78500569.505518338232-69.5055183382322
79750699.3926979154150.6073020845897
80680619.4620649763860.5379350236201
81280279.7570440357680.24295596423201
82360479.583473943016-119.583473943016
83590559.51401779041930.4859822095808
84580559.51398264223620.4860173577638
85490559.513947488969-69.5139474889687
86610549.52259246756960.477407532431
87170139.87846929179430.121530708206
88320379.670107070512-59.6701070705115
89440389.66140118171950.3385988182812
90510499.56586754136210.4341324586377
91770749.34875419088620.651245809114
92660679.409494403704-19.4094944037039
93300279.75683303982820.2431669601722
94350359.687334137514-9.68733413751443
95580589.487538301927-9.48753830192663
96620579.49618762667640.5038123733241
97490489.5743345961720.42566540382802
98640609.47005164341830.5299483565821
99150169.852298781223-19.8522987812233
100290319.721954045182-29.7219540451819
101370439.617659127663-69.6176591276634
102560509.55680007724550.4431999227548
103780769.33080655674210.6691934432575
104690659.42636407532530.5736359246754
105310299.73923751116610.2607624888337
106280349.695755058675-69.6957550586752
107590579.49578614377710.5042138562229
108590619.460973724883-29.4609737248829

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 570 & 575.917036565447 & -5.91703656544723 \tabularnewline
14 & 460 & 464.741680739602 & -4.74168073960237 \tabularnewline
15 & 540 & 545.96136495399 & -5.96136495398991 \tabularnewline
16 & 510 & 512.735436718659 & -2.73543671865923 \tabularnewline
17 & 520 & 520.279777152659 & -0.279777152659335 \tabularnewline
18 & 520 & 520.652583242891 & -0.6525832428905 \tabularnewline
19 & 580 & 550.216634302426 & 29.7833656975737 \tabularnewline
20 & 480 & 509.361344252978 & -29.361344252978 \tabularnewline
21 & 410 & 392.572238652518 & 17.4277613474821 \tabularnewline
22 & 530 & 484.283156854368 & 45.7168431456324 \tabularnewline
23 & 540 & 534.690784605437 & 5.30921539456324 \tabularnewline
24 & 670 & 697.720583635073 & -27.7205836350727 \tabularnewline
25 & 570 & 569.507405718126 & 0.492594281874403 \tabularnewline
26 & 400 & 459.602439141498 & -59.6024391414982 \tabularnewline
27 & 510 & 539.533264507454 & -29.5332645074539 \tabularnewline
28 & 570 & 509.559162504801 & 60.4408374951988 \tabularnewline
29 & 470 & 519.55048625285 & -49.5504862528505 \tabularnewline
30 & 640 & 519.550453868689 & 120.449546131311 \tabularnewline
31 & 650 & 579.49854703523 & 70.5014529647697 \tabularnewline
32 & 500 & 479.584974541261 & 20.4150254587385 \tabularnewline
33 & 340 & 409.645473542622 & -69.6454735426217 \tabularnewline
34 & 450 & 529.541676675473 & -79.5416766754735 \tabularnewline
35 & 600 & 539.532995411631 & 60.4670045883692 \tabularnewline
36 & 680 & 669.420526619257 & 10.579473380743 \tabularnewline
37 & 630 & 569.506979649695 & 60.493020350305 \tabularnewline
38 & 480 & 399.653995867172 & 80.3460041328278 \tabularnewline
39 & 400 & 509.55881292803 & -109.55881292803 \tabularnewline
40 & 520 & 569.506873017398 & -49.5068730173978 \tabularnewline
41 & 470 & 469.593357206373 & 0.406642793627213 \tabularnewline
42 & 610 & 639.44623371629 & -29.4462337162897 \tabularnewline
43 & 670 & 649.437540561978 & 20.5624594380224 \tabularnewline
44 & 500 & 499.567307692307 & 0.43269230769323 \tabularnewline
45 & 290 & 339.705748010673 & -49.7057480106732 \tabularnewline
46 & 470 & 449.610520748184 & 20.389479251816 \tabularnewline
47 & 660 & 599.48065687288 & 60.5193431271199 \tabularnewline
48 & 650 & 679.411368664036 & -29.4113686640364 \tabularnewline
49 & 570 & 629.454611037633 & -59.4546110376326 \tabularnewline
50 & 500 & 479.584435573084 & 20.4155644269164 \tabularnewline
51 & 400 & 399.653671324466 & 0.346328675534039 \tabularnewline
52 & 500 & 519.54974023475 & -19.5497402347498 \tabularnewline
53 & 340 & 469.593005075409 & -129.593005075409 \tabularnewline
54 & 530 & 609.471734423862 & -79.4717344238622 \tabularnewline
55 & 680 & 669.41973199894 & 10.5802680010597 \tabularnewline
56 & 480 & 499.566932922721 & -19.5669329227207 \tabularnewline
57 & 340 & 289.748802964317 & 50.251197035683 \tabularnewline
58 & 460 & 469.592858174117 & -9.59285817411723 \tabularnewline
59 & 630 & 659.428227650101 & -29.4282276501011 \tabularnewline
60 & 650 & 649.436850211782 & 0.563149788218311 \tabularnewline
61 & 550 & 569.50612529784 & -19.5061252978401 \tabularnewline
62 & 470 & 499.566745294372 & -29.5667452943716 \tabularnewline
63 & 240 & 399.653371205738 & -159.653371205738 \tabularnewline
64 & 430 & 499.566682715454 & -69.5666827154541 \tabularnewline
65 & 390 & 339.705322965067 & 50.2946770349333 \tabularnewline
66 & 570 & 529.540617325564 & 40.4593826744364 \tabularnewline
67 & 700 & 679.410560785918 & 20.5894392140823 \tabularnewline
68 & 620 & 479.583895203235 & 140.416104796765 \tabularnewline
69 & 280 & 339.705237808548 & -59.7052378085485 \tabularnewline
70 & 480 & 459.601175280573 & 20.3988247194267 \tabularnewline
71 & 560 & 629.453744068979 & -69.4537440689793 \tabularnewline
72 & 560 & 649.436361884573 & -89.4363618845734 \tabularnewline
73 & 560 & 549.523040975115 & 10.4769590248848 \tabularnewline
74 & 550 & 469.592387376535 & 80.4076126234651 \tabularnewline
75 & 140 & 239.791842339846 & -99.7918423398459 \tabularnewline
76 & 380 & 429.62702390131 & -49.6270239013099 \tabularnewline
77 & 390 & 389.661694898917 & 0.338305101082653 \tabularnewline
78 & 500 & 569.505518338232 & -69.5055183382322 \tabularnewline
79 & 750 & 699.39269791541 & 50.6073020845897 \tabularnewline
80 & 680 & 619.46206497638 & 60.5379350236201 \tabularnewline
81 & 280 & 279.757044035768 & 0.24295596423201 \tabularnewline
82 & 360 & 479.583473943016 & -119.583473943016 \tabularnewline
83 & 590 & 559.514017790419 & 30.4859822095808 \tabularnewline
84 & 580 & 559.513982642236 & 20.4860173577638 \tabularnewline
85 & 490 & 559.513947488969 & -69.5139474889687 \tabularnewline
86 & 610 & 549.522592467569 & 60.477407532431 \tabularnewline
87 & 170 & 139.878469291794 & 30.121530708206 \tabularnewline
88 & 320 & 379.670107070512 & -59.6701070705115 \tabularnewline
89 & 440 & 389.661401181719 & 50.3385988182812 \tabularnewline
90 & 510 & 499.565867541362 & 10.4341324586377 \tabularnewline
91 & 770 & 749.348754190886 & 20.651245809114 \tabularnewline
92 & 660 & 679.409494403704 & -19.4094944037039 \tabularnewline
93 & 300 & 279.756833039828 & 20.2431669601722 \tabularnewline
94 & 350 & 359.687334137514 & -9.68733413751443 \tabularnewline
95 & 580 & 589.487538301927 & -9.48753830192663 \tabularnewline
96 & 620 & 579.496187626676 & 40.5038123733241 \tabularnewline
97 & 490 & 489.574334596172 & 0.42566540382802 \tabularnewline
98 & 640 & 609.470051643418 & 30.5299483565821 \tabularnewline
99 & 150 & 169.852298781223 & -19.8522987812233 \tabularnewline
100 & 290 & 319.721954045182 & -29.7219540451819 \tabularnewline
101 & 370 & 439.617659127663 & -69.6176591276634 \tabularnewline
102 & 560 & 509.556800077245 & 50.4431999227548 \tabularnewline
103 & 780 & 769.330806556742 & 10.6691934432575 \tabularnewline
104 & 690 & 659.426364075325 & 30.5736359246754 \tabularnewline
105 & 310 & 299.739237511166 & 10.2607624888337 \tabularnewline
106 & 280 & 349.695755058675 & -69.6957550586752 \tabularnewline
107 & 590 & 579.495786143777 & 10.5042138562229 \tabularnewline
108 & 590 & 619.460973724883 & -29.4609737248829 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124138&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]570[/C][C]575.917036565447[/C][C]-5.91703656544723[/C][/ROW]
[ROW][C]14[/C][C]460[/C][C]464.741680739602[/C][C]-4.74168073960237[/C][/ROW]
[ROW][C]15[/C][C]540[/C][C]545.96136495399[/C][C]-5.96136495398991[/C][/ROW]
[ROW][C]16[/C][C]510[/C][C]512.735436718659[/C][C]-2.73543671865923[/C][/ROW]
[ROW][C]17[/C][C]520[/C][C]520.279777152659[/C][C]-0.279777152659335[/C][/ROW]
[ROW][C]18[/C][C]520[/C][C]520.652583242891[/C][C]-0.6525832428905[/C][/ROW]
[ROW][C]19[/C][C]580[/C][C]550.216634302426[/C][C]29.7833656975737[/C][/ROW]
[ROW][C]20[/C][C]480[/C][C]509.361344252978[/C][C]-29.361344252978[/C][/ROW]
[ROW][C]21[/C][C]410[/C][C]392.572238652518[/C][C]17.4277613474821[/C][/ROW]
[ROW][C]22[/C][C]530[/C][C]484.283156854368[/C][C]45.7168431456324[/C][/ROW]
[ROW][C]23[/C][C]540[/C][C]534.690784605437[/C][C]5.30921539456324[/C][/ROW]
[ROW][C]24[/C][C]670[/C][C]697.720583635073[/C][C]-27.7205836350727[/C][/ROW]
[ROW][C]25[/C][C]570[/C][C]569.507405718126[/C][C]0.492594281874403[/C][/ROW]
[ROW][C]26[/C][C]400[/C][C]459.602439141498[/C][C]-59.6024391414982[/C][/ROW]
[ROW][C]27[/C][C]510[/C][C]539.533264507454[/C][C]-29.5332645074539[/C][/ROW]
[ROW][C]28[/C][C]570[/C][C]509.559162504801[/C][C]60.4408374951988[/C][/ROW]
[ROW][C]29[/C][C]470[/C][C]519.55048625285[/C][C]-49.5504862528505[/C][/ROW]
[ROW][C]30[/C][C]640[/C][C]519.550453868689[/C][C]120.449546131311[/C][/ROW]
[ROW][C]31[/C][C]650[/C][C]579.49854703523[/C][C]70.5014529647697[/C][/ROW]
[ROW][C]32[/C][C]500[/C][C]479.584974541261[/C][C]20.4150254587385[/C][/ROW]
[ROW][C]33[/C][C]340[/C][C]409.645473542622[/C][C]-69.6454735426217[/C][/ROW]
[ROW][C]34[/C][C]450[/C][C]529.541676675473[/C][C]-79.5416766754735[/C][/ROW]
[ROW][C]35[/C][C]600[/C][C]539.532995411631[/C][C]60.4670045883692[/C][/ROW]
[ROW][C]36[/C][C]680[/C][C]669.420526619257[/C][C]10.579473380743[/C][/ROW]
[ROW][C]37[/C][C]630[/C][C]569.506979649695[/C][C]60.493020350305[/C][/ROW]
[ROW][C]38[/C][C]480[/C][C]399.653995867172[/C][C]80.3460041328278[/C][/ROW]
[ROW][C]39[/C][C]400[/C][C]509.55881292803[/C][C]-109.55881292803[/C][/ROW]
[ROW][C]40[/C][C]520[/C][C]569.506873017398[/C][C]-49.5068730173978[/C][/ROW]
[ROW][C]41[/C][C]470[/C][C]469.593357206373[/C][C]0.406642793627213[/C][/ROW]
[ROW][C]42[/C][C]610[/C][C]639.44623371629[/C][C]-29.4462337162897[/C][/ROW]
[ROW][C]43[/C][C]670[/C][C]649.437540561978[/C][C]20.5624594380224[/C][/ROW]
[ROW][C]44[/C][C]500[/C][C]499.567307692307[/C][C]0.43269230769323[/C][/ROW]
[ROW][C]45[/C][C]290[/C][C]339.705748010673[/C][C]-49.7057480106732[/C][/ROW]
[ROW][C]46[/C][C]470[/C][C]449.610520748184[/C][C]20.389479251816[/C][/ROW]
[ROW][C]47[/C][C]660[/C][C]599.48065687288[/C][C]60.5193431271199[/C][/ROW]
[ROW][C]48[/C][C]650[/C][C]679.411368664036[/C][C]-29.4113686640364[/C][/ROW]
[ROW][C]49[/C][C]570[/C][C]629.454611037633[/C][C]-59.4546110376326[/C][/ROW]
[ROW][C]50[/C][C]500[/C][C]479.584435573084[/C][C]20.4155644269164[/C][/ROW]
[ROW][C]51[/C][C]400[/C][C]399.653671324466[/C][C]0.346328675534039[/C][/ROW]
[ROW][C]52[/C][C]500[/C][C]519.54974023475[/C][C]-19.5497402347498[/C][/ROW]
[ROW][C]53[/C][C]340[/C][C]469.593005075409[/C][C]-129.593005075409[/C][/ROW]
[ROW][C]54[/C][C]530[/C][C]609.471734423862[/C][C]-79.4717344238622[/C][/ROW]
[ROW][C]55[/C][C]680[/C][C]669.41973199894[/C][C]10.5802680010597[/C][/ROW]
[ROW][C]56[/C][C]480[/C][C]499.566932922721[/C][C]-19.5669329227207[/C][/ROW]
[ROW][C]57[/C][C]340[/C][C]289.748802964317[/C][C]50.251197035683[/C][/ROW]
[ROW][C]58[/C][C]460[/C][C]469.592858174117[/C][C]-9.59285817411723[/C][/ROW]
[ROW][C]59[/C][C]630[/C][C]659.428227650101[/C][C]-29.4282276501011[/C][/ROW]
[ROW][C]60[/C][C]650[/C][C]649.436850211782[/C][C]0.563149788218311[/C][/ROW]
[ROW][C]61[/C][C]550[/C][C]569.50612529784[/C][C]-19.5061252978401[/C][/ROW]
[ROW][C]62[/C][C]470[/C][C]499.566745294372[/C][C]-29.5667452943716[/C][/ROW]
[ROW][C]63[/C][C]240[/C][C]399.653371205738[/C][C]-159.653371205738[/C][/ROW]
[ROW][C]64[/C][C]430[/C][C]499.566682715454[/C][C]-69.5666827154541[/C][/ROW]
[ROW][C]65[/C][C]390[/C][C]339.705322965067[/C][C]50.2946770349333[/C][/ROW]
[ROW][C]66[/C][C]570[/C][C]529.540617325564[/C][C]40.4593826744364[/C][/ROW]
[ROW][C]67[/C][C]700[/C][C]679.410560785918[/C][C]20.5894392140823[/C][/ROW]
[ROW][C]68[/C][C]620[/C][C]479.583895203235[/C][C]140.416104796765[/C][/ROW]
[ROW][C]69[/C][C]280[/C][C]339.705237808548[/C][C]-59.7052378085485[/C][/ROW]
[ROW][C]70[/C][C]480[/C][C]459.601175280573[/C][C]20.3988247194267[/C][/ROW]
[ROW][C]71[/C][C]560[/C][C]629.453744068979[/C][C]-69.4537440689793[/C][/ROW]
[ROW][C]72[/C][C]560[/C][C]649.436361884573[/C][C]-89.4363618845734[/C][/ROW]
[ROW][C]73[/C][C]560[/C][C]549.523040975115[/C][C]10.4769590248848[/C][/ROW]
[ROW][C]74[/C][C]550[/C][C]469.592387376535[/C][C]80.4076126234651[/C][/ROW]
[ROW][C]75[/C][C]140[/C][C]239.791842339846[/C][C]-99.7918423398459[/C][/ROW]
[ROW][C]76[/C][C]380[/C][C]429.62702390131[/C][C]-49.6270239013099[/C][/ROW]
[ROW][C]77[/C][C]390[/C][C]389.661694898917[/C][C]0.338305101082653[/C][/ROW]
[ROW][C]78[/C][C]500[/C][C]569.505518338232[/C][C]-69.5055183382322[/C][/ROW]
[ROW][C]79[/C][C]750[/C][C]699.39269791541[/C][C]50.6073020845897[/C][/ROW]
[ROW][C]80[/C][C]680[/C][C]619.46206497638[/C][C]60.5379350236201[/C][/ROW]
[ROW][C]81[/C][C]280[/C][C]279.757044035768[/C][C]0.24295596423201[/C][/ROW]
[ROW][C]82[/C][C]360[/C][C]479.583473943016[/C][C]-119.583473943016[/C][/ROW]
[ROW][C]83[/C][C]590[/C][C]559.514017790419[/C][C]30.4859822095808[/C][/ROW]
[ROW][C]84[/C][C]580[/C][C]559.513982642236[/C][C]20.4860173577638[/C][/ROW]
[ROW][C]85[/C][C]490[/C][C]559.513947488969[/C][C]-69.5139474889687[/C][/ROW]
[ROW][C]86[/C][C]610[/C][C]549.522592467569[/C][C]60.477407532431[/C][/ROW]
[ROW][C]87[/C][C]170[/C][C]139.878469291794[/C][C]30.121530708206[/C][/ROW]
[ROW][C]88[/C][C]320[/C][C]379.670107070512[/C][C]-59.6701070705115[/C][/ROW]
[ROW][C]89[/C][C]440[/C][C]389.661401181719[/C][C]50.3385988182812[/C][/ROW]
[ROW][C]90[/C][C]510[/C][C]499.565867541362[/C][C]10.4341324586377[/C][/ROW]
[ROW][C]91[/C][C]770[/C][C]749.348754190886[/C][C]20.651245809114[/C][/ROW]
[ROW][C]92[/C][C]660[/C][C]679.409494403704[/C][C]-19.4094944037039[/C][/ROW]
[ROW][C]93[/C][C]300[/C][C]279.756833039828[/C][C]20.2431669601722[/C][/ROW]
[ROW][C]94[/C][C]350[/C][C]359.687334137514[/C][C]-9.68733413751443[/C][/ROW]
[ROW][C]95[/C][C]580[/C][C]589.487538301927[/C][C]-9.48753830192663[/C][/ROW]
[ROW][C]96[/C][C]620[/C][C]579.496187626676[/C][C]40.5038123733241[/C][/ROW]
[ROW][C]97[/C][C]490[/C][C]489.574334596172[/C][C]0.42566540382802[/C][/ROW]
[ROW][C]98[/C][C]640[/C][C]609.470051643418[/C][C]30.5299483565821[/C][/ROW]
[ROW][C]99[/C][C]150[/C][C]169.852298781223[/C][C]-19.8522987812233[/C][/ROW]
[ROW][C]100[/C][C]290[/C][C]319.721954045182[/C][C]-29.7219540451819[/C][/ROW]
[ROW][C]101[/C][C]370[/C][C]439.617659127663[/C][C]-69.6176591276634[/C][/ROW]
[ROW][C]102[/C][C]560[/C][C]509.556800077245[/C][C]50.4431999227548[/C][/ROW]
[ROW][C]103[/C][C]780[/C][C]769.330806556742[/C][C]10.6691934432575[/C][/ROW]
[ROW][C]104[/C][C]690[/C][C]659.426364075325[/C][C]30.5736359246754[/C][/ROW]
[ROW][C]105[/C][C]310[/C][C]299.739237511166[/C][C]10.2607624888337[/C][/ROW]
[ROW][C]106[/C][C]280[/C][C]349.695755058675[/C][C]-69.6957550586752[/C][/ROW]
[ROW][C]107[/C][C]590[/C][C]579.495786143777[/C][C]10.5042138562229[/C][/ROW]
[ROW][C]108[/C][C]590[/C][C]619.460973724883[/C][C]-29.4609737248829[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124138&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124138&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
13570575.917036565447-5.91703656544723
14460464.741680739602-4.74168073960237
15540545.96136495399-5.96136495398991
16510512.735436718659-2.73543671865923
17520520.279777152659-0.279777152659335
18520520.652583242891-0.6525832428905
19580550.21663430242629.7833656975737
20480509.361344252978-29.361344252978
21410392.57223865251817.4277613474821
22530484.28315685436845.7168431456324
23540534.6907846054375.30921539456324
24670697.720583635073-27.7205836350727
25570569.5074057181260.492594281874403
26400459.602439141498-59.6024391414982
27510539.533264507454-29.5332645074539
28570509.55916250480160.4408374951988
29470519.55048625285-49.5504862528505
30640519.550453868689120.449546131311
31650579.4985470352370.5014529647697
32500479.58497454126120.4150254587385
33340409.645473542622-69.6454735426217
34450529.541676675473-79.5416766754735
35600539.53299541163160.4670045883692
36680669.42052661925710.579473380743
37630569.50697964969560.493020350305
38480399.65399586717280.3460041328278
39400509.55881292803-109.55881292803
40520569.506873017398-49.5068730173978
41470469.5933572063730.406642793627213
42610639.44623371629-29.4462337162897
43670649.43754056197820.5624594380224
44500499.5673076923070.43269230769323
45290339.705748010673-49.7057480106732
46470449.61052074818420.389479251816
47660599.4806568728860.5193431271199
48650679.411368664036-29.4113686640364
49570629.454611037633-59.4546110376326
50500479.58443557308420.4155644269164
51400399.6536713244660.346328675534039
52500519.54974023475-19.5497402347498
53340469.593005075409-129.593005075409
54530609.471734423862-79.4717344238622
55680669.4197319989410.5802680010597
56480499.566932922721-19.5669329227207
57340289.74880296431750.251197035683
58460469.592858174117-9.59285817411723
59630659.428227650101-29.4282276501011
60650649.4368502117820.563149788218311
61550569.50612529784-19.5061252978401
62470499.566745294372-29.5667452943716
63240399.653371205738-159.653371205738
64430499.566682715454-69.5666827154541
65390339.70532296506750.2946770349333
66570529.54061732556440.4593826744364
67700679.41056078591820.5894392140823
68620479.583895203235140.416104796765
69280339.705237808548-59.7052378085485
70480459.60117528057320.3988247194267
71560629.453744068979-69.4537440689793
72560649.436361884573-89.4363618845734
73560549.52304097511510.4769590248848
74550469.59238737653580.4076126234651
75140239.791842339846-99.7918423398459
76380429.62702390131-49.6270239013099
77390389.6616948989170.338305101082653
78500569.505518338232-69.5055183382322
79750699.3926979154150.6073020845897
80680619.4620649763860.5379350236201
81280279.7570440357680.24295596423201
82360479.583473943016-119.583473943016
83590559.51401779041930.4859822095808
84580559.51398264223620.4860173577638
85490559.513947488969-69.5139474889687
86610549.52259246756960.477407532431
87170139.87846929179430.121530708206
88320379.670107070512-59.6701070705115
89440389.66140118171950.3385988182812
90510499.56586754136210.4341324586377
91770749.34875419088620.651245809114
92660679.409494403704-19.4094944037039
93300279.75683303982820.2431669601722
94350359.687334137514-9.68733413751443
95580589.487538301927-9.48753830192663
96620579.49618762667640.5038123733241
97490489.5743345961720.42566540382802
98640609.47005164341830.5299483565821
99150169.852298781223-19.8522987812233
100290319.721954045182-29.7219540451819
101370439.617659127663-69.6176591276634
102560509.55680007724550.4431999227548
103780769.33080655674210.6691934432575
104690659.42636407532530.5736359246754
105310299.73923751116610.2607624888337
106280349.695755058675-69.6957550586752
107590579.49578614377710.5042138562229
108590619.460973724883-29.4609737248829







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109489.57396449704385.904399871153593.243529122928
110639.443505144678535.77394051879743.113069770566
111149.86956206671646.1999974408285253.539126692604
112289.747801719973186.078237094085393.41736634586
113369.678206460029266.008641834141473.347771085917
114559.512925827494455.843361201606663.182490453382
115779.321526083069675.651961457181882.991090708957
116689.39976802629585.730203400402793.069332652178
117309.7303110123206.060746386412413.399875638188
118279.756392285755176.086827659868383.425956911643
119589.486646525679485.817081899791693.156211151567
120589.486609300976-2501.704664460443680.67788306239

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 489.57396449704 & 385.904399871153 & 593.243529122928 \tabularnewline
110 & 639.443505144678 & 535.77394051879 & 743.113069770566 \tabularnewline
111 & 149.869562066716 & 46.1999974408285 & 253.539126692604 \tabularnewline
112 & 289.747801719973 & 186.078237094085 & 393.41736634586 \tabularnewline
113 & 369.678206460029 & 266.008641834141 & 473.347771085917 \tabularnewline
114 & 559.512925827494 & 455.843361201606 & 663.182490453382 \tabularnewline
115 & 779.321526083069 & 675.651961457181 & 882.991090708957 \tabularnewline
116 & 689.39976802629 & 585.730203400402 & 793.069332652178 \tabularnewline
117 & 309.7303110123 & 206.060746386412 & 413.399875638188 \tabularnewline
118 & 279.756392285755 & 176.086827659868 & 383.425956911643 \tabularnewline
119 & 589.486646525679 & 485.817081899791 & 693.156211151567 \tabularnewline
120 & 589.486609300976 & -2501.70466446044 & 3680.67788306239 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124138&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]489.57396449704[/C][C]385.904399871153[/C][C]593.243529122928[/C][/ROW]
[ROW][C]110[/C][C]639.443505144678[/C][C]535.77394051879[/C][C]743.113069770566[/C][/ROW]
[ROW][C]111[/C][C]149.869562066716[/C][C]46.1999974408285[/C][C]253.539126692604[/C][/ROW]
[ROW][C]112[/C][C]289.747801719973[/C][C]186.078237094085[/C][C]393.41736634586[/C][/ROW]
[ROW][C]113[/C][C]369.678206460029[/C][C]266.008641834141[/C][C]473.347771085917[/C][/ROW]
[ROW][C]114[/C][C]559.512925827494[/C][C]455.843361201606[/C][C]663.182490453382[/C][/ROW]
[ROW][C]115[/C][C]779.321526083069[/C][C]675.651961457181[/C][C]882.991090708957[/C][/ROW]
[ROW][C]116[/C][C]689.39976802629[/C][C]585.730203400402[/C][C]793.069332652178[/C][/ROW]
[ROW][C]117[/C][C]309.7303110123[/C][C]206.060746386412[/C][C]413.399875638188[/C][/ROW]
[ROW][C]118[/C][C]279.756392285755[/C][C]176.086827659868[/C][C]383.425956911643[/C][/ROW]
[ROW][C]119[/C][C]589.486646525679[/C][C]485.817081899791[/C][C]693.156211151567[/C][/ROW]
[ROW][C]120[/C][C]589.486609300976[/C][C]-2501.70466446044[/C][C]3680.67788306239[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124138&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124138&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
109489.57396449704385.904399871153593.243529122928
110639.443505144678535.77394051879743.113069770566
111149.86956206671646.1999974408285253.539126692604
112289.747801719973186.078237094085393.41736634586
113369.678206460029266.008641834141473.347771085917
114559.512925827494455.843361201606663.182490453382
115779.321526083069675.651961457181882.991090708957
116689.39976802629585.730203400402793.069332652178
117309.7303110123206.060746386412413.399875638188
118279.756392285755176.086827659868383.425956911643
119589.486646525679485.817081899791693.156211151567
120589.486609300976-2501.704664460443680.67788306239



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