Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 02 Aug 2016 13:53:09 +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/02/t1470142412q40z93rqywsby72.htm/, Retrieved Mon, 06 May 2024 04:00:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=296004, Retrieved Mon, 06 May 2024 04:00:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact136
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-08-02 12:53:09] [1b498ae19017f51f703ef2d779b672b0] [Current]
Feedback Forum

Post a new message
Dataseries X:
540
520
550
440
570
560
600
620
690
600
570
710
600
450
530
400
560
460
610
550
580
650
640
760
550
460
510
370
530
410
580
550
490
700
630
720
540
500
450
370
490
440
600
580
500
670
620
800
640
390
390
390
460
460
620
570
510
640
590
850
670
390
410
340
470
540
680
670
540
630
560
800
610
490
440
330
490
590
690
650
480
690
540
830
690
500
460
310
490
470
710
710
540
700
520
810
690
510
390
270
530
510
670
770
570
640
480
830




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296004&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296004&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296004&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.00926118605788256
beta1
gamma0.929768627342304

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.00926118605788256 \tabularnewline
beta & 1 \tabularnewline
gamma & 0.929768627342304 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296004&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]0.00926118605788256[/C][/ROW]
[ROW][C]beta[/C][C]1[/C][/ROW]
[ROW][C]gamma[/C][C]0.929768627342304[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296004&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296004&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
alpha0.00926118605788256
beta1
gamma0.929768627342304







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13600620.518162393162-20.5181623931624
14450470.018653484721-20.0186534847205
15530554.338374146667-24.3383741466672
16400423.392686860527-23.3926868605269
17560574.739113734887-14.7391137348869
18460466.029181285402-6.02918128540216
19610582.76074243788927.2392575621107
20550600.05267662476-50.0526766247601
21580669.498582010769-89.4985820107689
22650576.50030850785873.4996914921421
23640545.2756199944194.7243800055898
24760687.62475737775572.3752426222445
25550560.703395789369-10.7033957893685
26460411.02409460082248.9759053991783
27510492.91179826454817.0882017354524
28370364.512712942195.48728705781025
29530525.6571878566714.34281214332862
30410426.883199001849-16.8831990018491
31580575.7952017006174.20479829938267
32550523.0978882759326.9021117240701
33490559.055424857411-69.0554248574113
34700618.71779373189981.2822062681013
35630609.51271718939620.4872828106037
36720732.295971563106-12.2959715631065
37540528.98648116110611.0135188388944
38500435.60805495398964.3919450460115
39450489.53338394918-39.53338394918
40370350.66772233960819.3322776603916
41490511.758477824301-21.7584778243009
42440393.82082561803546.1791743819654
43600563.95684038309836.0431596169025
44580533.97166283518746.0283371648131
45500483.40088881828316.5991111817171
46670684.821072112374-14.8210721123742
47620620.314073057076-0.314073057076484
48800714.10331415290885.8966858470919
49640535.481489776589104.518510223411
50390495.311520142483-105.311520142483
51390453.534436228588-63.5344362285879
52390370.04966234177419.9503376582261
53460494.679391724357-34.6793917243573
54460440.46803895324119.5319610467591
55620602.03827399638317.9617260036166
56570581.933985079803-11.9339850798029
57510504.0310676244145.96893237558641
58640676.625025213099-36.6250252130986
59590625.292572917807-35.2925729178073
60850797.86088893462152.1391110653785
61670635.45673274387834.5432672561216
62390400.080735739196-10.0807357391957
63410397.27945096045612.720549039544
64340391.720316145678-51.7203161456783
65470465.0167012280084.983298771992
66540461.13022561776578.8697743822353
67680622.3734428705957.6265571294102
68670576.0350493024793.9649506975304
69540517.52226602447522.4777339755251
70630653.104217827974-23.1042178279745
71560605.320464127788-45.3204641277885
72800860.437504314361-60.4375043143613
73610681.842823010633-71.8428230106326
74490404.451169654685.5488303453998
75440424.50011058285915.4998894171405
76330360.593245466174-30.5932454661744
77490487.500674624842.49932537516003
78590552.81169958506937.1883004149314
79690694.873917201977-4.87391720197729
80650681.624640648183-31.6246406481825
81480555.129176568301-75.1291765683011
82690645.94648320296544.0535167970349
83540577.069464089116-37.0694640891159
84830817.16359624081312.8364037591872
85690628.24588089865361.7541191013471
86500497.8157812312352.18421876876545
87460452.5362066320937.46379336790682
88310345.991112805951-35.9911128059511
89490503.17729151798-13.1772915179797
90470599.997228840161-129.997228840161
91710699.91690537506910.0830946249309
92710660.45476668299149.5452333170088
93540493.67847324144346.3215267585569
94700695.5733974620694.42660253793099
95520551.402086261838-31.4020862618382
96810837.372146662018-27.3721466620179
97690692.622870739762-2.62287073976245
98510505.6069541362614.3930458637393
99390464.115286609446-74.115286609446
100270314.934455057957-44.9344550579567
101530491.11872281334238.8812771866581
102510479.35908806121130.640911938789
103670709.83816413324-39.8381641332395
104770705.8378326609864.1621673390204
105570535.9360146299334.06398537007
106640698.720708993054-58.720708993054
107480519.97100978601-39.9710097860097
108830808.5048735122221.4951264877802

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 600 & 620.518162393162 & -20.5181623931624 \tabularnewline
14 & 450 & 470.018653484721 & -20.0186534847205 \tabularnewline
15 & 530 & 554.338374146667 & -24.3383741466672 \tabularnewline
16 & 400 & 423.392686860527 & -23.3926868605269 \tabularnewline
17 & 560 & 574.739113734887 & -14.7391137348869 \tabularnewline
18 & 460 & 466.029181285402 & -6.02918128540216 \tabularnewline
19 & 610 & 582.760742437889 & 27.2392575621107 \tabularnewline
20 & 550 & 600.05267662476 & -50.0526766247601 \tabularnewline
21 & 580 & 669.498582010769 & -89.4985820107689 \tabularnewline
22 & 650 & 576.500308507858 & 73.4996914921421 \tabularnewline
23 & 640 & 545.27561999441 & 94.7243800055898 \tabularnewline
24 & 760 & 687.624757377755 & 72.3752426222445 \tabularnewline
25 & 550 & 560.703395789369 & -10.7033957893685 \tabularnewline
26 & 460 & 411.024094600822 & 48.9759053991783 \tabularnewline
27 & 510 & 492.911798264548 & 17.0882017354524 \tabularnewline
28 & 370 & 364.51271294219 & 5.48728705781025 \tabularnewline
29 & 530 & 525.657187856671 & 4.34281214332862 \tabularnewline
30 & 410 & 426.883199001849 & -16.8831990018491 \tabularnewline
31 & 580 & 575.795201700617 & 4.20479829938267 \tabularnewline
32 & 550 & 523.09788827593 & 26.9021117240701 \tabularnewline
33 & 490 & 559.055424857411 & -69.0554248574113 \tabularnewline
34 & 700 & 618.717793731899 & 81.2822062681013 \tabularnewline
35 & 630 & 609.512717189396 & 20.4872828106037 \tabularnewline
36 & 720 & 732.295971563106 & -12.2959715631065 \tabularnewline
37 & 540 & 528.986481161106 & 11.0135188388944 \tabularnewline
38 & 500 & 435.608054953989 & 64.3919450460115 \tabularnewline
39 & 450 & 489.53338394918 & -39.53338394918 \tabularnewline
40 & 370 & 350.667722339608 & 19.3322776603916 \tabularnewline
41 & 490 & 511.758477824301 & -21.7584778243009 \tabularnewline
42 & 440 & 393.820825618035 & 46.1791743819654 \tabularnewline
43 & 600 & 563.956840383098 & 36.0431596169025 \tabularnewline
44 & 580 & 533.971662835187 & 46.0283371648131 \tabularnewline
45 & 500 & 483.400888818283 & 16.5991111817171 \tabularnewline
46 & 670 & 684.821072112374 & -14.8210721123742 \tabularnewline
47 & 620 & 620.314073057076 & -0.314073057076484 \tabularnewline
48 & 800 & 714.103314152908 & 85.8966858470919 \tabularnewline
49 & 640 & 535.481489776589 & 104.518510223411 \tabularnewline
50 & 390 & 495.311520142483 & -105.311520142483 \tabularnewline
51 & 390 & 453.534436228588 & -63.5344362285879 \tabularnewline
52 & 390 & 370.049662341774 & 19.9503376582261 \tabularnewline
53 & 460 & 494.679391724357 & -34.6793917243573 \tabularnewline
54 & 460 & 440.468038953241 & 19.5319610467591 \tabularnewline
55 & 620 & 602.038273996383 & 17.9617260036166 \tabularnewline
56 & 570 & 581.933985079803 & -11.9339850798029 \tabularnewline
57 & 510 & 504.031067624414 & 5.96893237558641 \tabularnewline
58 & 640 & 676.625025213099 & -36.6250252130986 \tabularnewline
59 & 590 & 625.292572917807 & -35.2925729178073 \tabularnewline
60 & 850 & 797.860888934621 & 52.1391110653785 \tabularnewline
61 & 670 & 635.456732743878 & 34.5432672561216 \tabularnewline
62 & 390 & 400.080735739196 & -10.0807357391957 \tabularnewline
63 & 410 & 397.279450960456 & 12.720549039544 \tabularnewline
64 & 340 & 391.720316145678 & -51.7203161456783 \tabularnewline
65 & 470 & 465.016701228008 & 4.983298771992 \tabularnewline
66 & 540 & 461.130225617765 & 78.8697743822353 \tabularnewline
67 & 680 & 622.37344287059 & 57.6265571294102 \tabularnewline
68 & 670 & 576.03504930247 & 93.9649506975304 \tabularnewline
69 & 540 & 517.522266024475 & 22.4777339755251 \tabularnewline
70 & 630 & 653.104217827974 & -23.1042178279745 \tabularnewline
71 & 560 & 605.320464127788 & -45.3204641277885 \tabularnewline
72 & 800 & 860.437504314361 & -60.4375043143613 \tabularnewline
73 & 610 & 681.842823010633 & -71.8428230106326 \tabularnewline
74 & 490 & 404.4511696546 & 85.5488303453998 \tabularnewline
75 & 440 & 424.500110582859 & 15.4998894171405 \tabularnewline
76 & 330 & 360.593245466174 & -30.5932454661744 \tabularnewline
77 & 490 & 487.50067462484 & 2.49932537516003 \tabularnewline
78 & 590 & 552.811699585069 & 37.1883004149314 \tabularnewline
79 & 690 & 694.873917201977 & -4.87391720197729 \tabularnewline
80 & 650 & 681.624640648183 & -31.6246406481825 \tabularnewline
81 & 480 & 555.129176568301 & -75.1291765683011 \tabularnewline
82 & 690 & 645.946483202965 & 44.0535167970349 \tabularnewline
83 & 540 & 577.069464089116 & -37.0694640891159 \tabularnewline
84 & 830 & 817.163596240813 & 12.8364037591872 \tabularnewline
85 & 690 & 628.245880898653 & 61.7541191013471 \tabularnewline
86 & 500 & 497.815781231235 & 2.18421876876545 \tabularnewline
87 & 460 & 452.536206632093 & 7.46379336790682 \tabularnewline
88 & 310 & 345.991112805951 & -35.9911128059511 \tabularnewline
89 & 490 & 503.17729151798 & -13.1772915179797 \tabularnewline
90 & 470 & 599.997228840161 & -129.997228840161 \tabularnewline
91 & 710 & 699.916905375069 & 10.0830946249309 \tabularnewline
92 & 710 & 660.454766682991 & 49.5452333170088 \tabularnewline
93 & 540 & 493.678473241443 & 46.3215267585569 \tabularnewline
94 & 700 & 695.573397462069 & 4.42660253793099 \tabularnewline
95 & 520 & 551.402086261838 & -31.4020862618382 \tabularnewline
96 & 810 & 837.372146662018 & -27.3721466620179 \tabularnewline
97 & 690 & 692.622870739762 & -2.62287073976245 \tabularnewline
98 & 510 & 505.606954136261 & 4.3930458637393 \tabularnewline
99 & 390 & 464.115286609446 & -74.115286609446 \tabularnewline
100 & 270 & 314.934455057957 & -44.9344550579567 \tabularnewline
101 & 530 & 491.118722813342 & 38.8812771866581 \tabularnewline
102 & 510 & 479.359088061211 & 30.640911938789 \tabularnewline
103 & 670 & 709.83816413324 & -39.8381641332395 \tabularnewline
104 & 770 & 705.83783266098 & 64.1621673390204 \tabularnewline
105 & 570 & 535.93601462993 & 34.06398537007 \tabularnewline
106 & 640 & 698.720708993054 & -58.720708993054 \tabularnewline
107 & 480 & 519.97100978601 & -39.9710097860097 \tabularnewline
108 & 830 & 808.50487351222 & 21.4951264877802 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296004&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]600[/C][C]620.518162393162[/C][C]-20.5181623931624[/C][/ROW]
[ROW][C]14[/C][C]450[/C][C]470.018653484721[/C][C]-20.0186534847205[/C][/ROW]
[ROW][C]15[/C][C]530[/C][C]554.338374146667[/C][C]-24.3383741466672[/C][/ROW]
[ROW][C]16[/C][C]400[/C][C]423.392686860527[/C][C]-23.3926868605269[/C][/ROW]
[ROW][C]17[/C][C]560[/C][C]574.739113734887[/C][C]-14.7391137348869[/C][/ROW]
[ROW][C]18[/C][C]460[/C][C]466.029181285402[/C][C]-6.02918128540216[/C][/ROW]
[ROW][C]19[/C][C]610[/C][C]582.760742437889[/C][C]27.2392575621107[/C][/ROW]
[ROW][C]20[/C][C]550[/C][C]600.05267662476[/C][C]-50.0526766247601[/C][/ROW]
[ROW][C]21[/C][C]580[/C][C]669.498582010769[/C][C]-89.4985820107689[/C][/ROW]
[ROW][C]22[/C][C]650[/C][C]576.500308507858[/C][C]73.4996914921421[/C][/ROW]
[ROW][C]23[/C][C]640[/C][C]545.27561999441[/C][C]94.7243800055898[/C][/ROW]
[ROW][C]24[/C][C]760[/C][C]687.624757377755[/C][C]72.3752426222445[/C][/ROW]
[ROW][C]25[/C][C]550[/C][C]560.703395789369[/C][C]-10.7033957893685[/C][/ROW]
[ROW][C]26[/C][C]460[/C][C]411.024094600822[/C][C]48.9759053991783[/C][/ROW]
[ROW][C]27[/C][C]510[/C][C]492.911798264548[/C][C]17.0882017354524[/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]525.657187856671[/C][C]4.34281214332862[/C][/ROW]
[ROW][C]30[/C][C]410[/C][C]426.883199001849[/C][C]-16.8831990018491[/C][/ROW]
[ROW][C]31[/C][C]580[/C][C]575.795201700617[/C][C]4.20479829938267[/C][/ROW]
[ROW][C]32[/C][C]550[/C][C]523.09788827593[/C][C]26.9021117240701[/C][/ROW]
[ROW][C]33[/C][C]490[/C][C]559.055424857411[/C][C]-69.0554248574113[/C][/ROW]
[ROW][C]34[/C][C]700[/C][C]618.717793731899[/C][C]81.2822062681013[/C][/ROW]
[ROW][C]35[/C][C]630[/C][C]609.512717189396[/C][C]20.4872828106037[/C][/ROW]
[ROW][C]36[/C][C]720[/C][C]732.295971563106[/C][C]-12.2959715631065[/C][/ROW]
[ROW][C]37[/C][C]540[/C][C]528.986481161106[/C][C]11.0135188388944[/C][/ROW]
[ROW][C]38[/C][C]500[/C][C]435.608054953989[/C][C]64.3919450460115[/C][/ROW]
[ROW][C]39[/C][C]450[/C][C]489.53338394918[/C][C]-39.53338394918[/C][/ROW]
[ROW][C]40[/C][C]370[/C][C]350.667722339608[/C][C]19.3322776603916[/C][/ROW]
[ROW][C]41[/C][C]490[/C][C]511.758477824301[/C][C]-21.7584778243009[/C][/ROW]
[ROW][C]42[/C][C]440[/C][C]393.820825618035[/C][C]46.1791743819654[/C][/ROW]
[ROW][C]43[/C][C]600[/C][C]563.956840383098[/C][C]36.0431596169025[/C][/ROW]
[ROW][C]44[/C][C]580[/C][C]533.971662835187[/C][C]46.0283371648131[/C][/ROW]
[ROW][C]45[/C][C]500[/C][C]483.400888818283[/C][C]16.5991111817171[/C][/ROW]
[ROW][C]46[/C][C]670[/C][C]684.821072112374[/C][C]-14.8210721123742[/C][/ROW]
[ROW][C]47[/C][C]620[/C][C]620.314073057076[/C][C]-0.314073057076484[/C][/ROW]
[ROW][C]48[/C][C]800[/C][C]714.103314152908[/C][C]85.8966858470919[/C][/ROW]
[ROW][C]49[/C][C]640[/C][C]535.481489776589[/C][C]104.518510223411[/C][/ROW]
[ROW][C]50[/C][C]390[/C][C]495.311520142483[/C][C]-105.311520142483[/C][/ROW]
[ROW][C]51[/C][C]390[/C][C]453.534436228588[/C][C]-63.5344362285879[/C][/ROW]
[ROW][C]52[/C][C]390[/C][C]370.049662341774[/C][C]19.9503376582261[/C][/ROW]
[ROW][C]53[/C][C]460[/C][C]494.679391724357[/C][C]-34.6793917243573[/C][/ROW]
[ROW][C]54[/C][C]460[/C][C]440.468038953241[/C][C]19.5319610467591[/C][/ROW]
[ROW][C]55[/C][C]620[/C][C]602.038273996383[/C][C]17.9617260036166[/C][/ROW]
[ROW][C]56[/C][C]570[/C][C]581.933985079803[/C][C]-11.9339850798029[/C][/ROW]
[ROW][C]57[/C][C]510[/C][C]504.031067624414[/C][C]5.96893237558641[/C][/ROW]
[ROW][C]58[/C][C]640[/C][C]676.625025213099[/C][C]-36.6250252130986[/C][/ROW]
[ROW][C]59[/C][C]590[/C][C]625.292572917807[/C][C]-35.2925729178073[/C][/ROW]
[ROW][C]60[/C][C]850[/C][C]797.860888934621[/C][C]52.1391110653785[/C][/ROW]
[ROW][C]61[/C][C]670[/C][C]635.456732743878[/C][C]34.5432672561216[/C][/ROW]
[ROW][C]62[/C][C]390[/C][C]400.080735739196[/C][C]-10.0807357391957[/C][/ROW]
[ROW][C]63[/C][C]410[/C][C]397.279450960456[/C][C]12.720549039544[/C][/ROW]
[ROW][C]64[/C][C]340[/C][C]391.720316145678[/C][C]-51.7203161456783[/C][/ROW]
[ROW][C]65[/C][C]470[/C][C]465.016701228008[/C][C]4.983298771992[/C][/ROW]
[ROW][C]66[/C][C]540[/C][C]461.130225617765[/C][C]78.8697743822353[/C][/ROW]
[ROW][C]67[/C][C]680[/C][C]622.37344287059[/C][C]57.6265571294102[/C][/ROW]
[ROW][C]68[/C][C]670[/C][C]576.03504930247[/C][C]93.9649506975304[/C][/ROW]
[ROW][C]69[/C][C]540[/C][C]517.522266024475[/C][C]22.4777339755251[/C][/ROW]
[ROW][C]70[/C][C]630[/C][C]653.104217827974[/C][C]-23.1042178279745[/C][/ROW]
[ROW][C]71[/C][C]560[/C][C]605.320464127788[/C][C]-45.3204641277885[/C][/ROW]
[ROW][C]72[/C][C]800[/C][C]860.437504314361[/C][C]-60.4375043143613[/C][/ROW]
[ROW][C]73[/C][C]610[/C][C]681.842823010633[/C][C]-71.8428230106326[/C][/ROW]
[ROW][C]74[/C][C]490[/C][C]404.4511696546[/C][C]85.5488303453998[/C][/ROW]
[ROW][C]75[/C][C]440[/C][C]424.500110582859[/C][C]15.4998894171405[/C][/ROW]
[ROW][C]76[/C][C]330[/C][C]360.593245466174[/C][C]-30.5932454661744[/C][/ROW]
[ROW][C]77[/C][C]490[/C][C]487.50067462484[/C][C]2.49932537516003[/C][/ROW]
[ROW][C]78[/C][C]590[/C][C]552.811699585069[/C][C]37.1883004149314[/C][/ROW]
[ROW][C]79[/C][C]690[/C][C]694.873917201977[/C][C]-4.87391720197729[/C][/ROW]
[ROW][C]80[/C][C]650[/C][C]681.624640648183[/C][C]-31.6246406481825[/C][/ROW]
[ROW][C]81[/C][C]480[/C][C]555.129176568301[/C][C]-75.1291765683011[/C][/ROW]
[ROW][C]82[/C][C]690[/C][C]645.946483202965[/C][C]44.0535167970349[/C][/ROW]
[ROW][C]83[/C][C]540[/C][C]577.069464089116[/C][C]-37.0694640891159[/C][/ROW]
[ROW][C]84[/C][C]830[/C][C]817.163596240813[/C][C]12.8364037591872[/C][/ROW]
[ROW][C]85[/C][C]690[/C][C]628.245880898653[/C][C]61.7541191013471[/C][/ROW]
[ROW][C]86[/C][C]500[/C][C]497.815781231235[/C][C]2.18421876876545[/C][/ROW]
[ROW][C]87[/C][C]460[/C][C]452.536206632093[/C][C]7.46379336790682[/C][/ROW]
[ROW][C]88[/C][C]310[/C][C]345.991112805951[/C][C]-35.9911128059511[/C][/ROW]
[ROW][C]89[/C][C]490[/C][C]503.17729151798[/C][C]-13.1772915179797[/C][/ROW]
[ROW][C]90[/C][C]470[/C][C]599.997228840161[/C][C]-129.997228840161[/C][/ROW]
[ROW][C]91[/C][C]710[/C][C]699.916905375069[/C][C]10.0830946249309[/C][/ROW]
[ROW][C]92[/C][C]710[/C][C]660.454766682991[/C][C]49.5452333170088[/C][/ROW]
[ROW][C]93[/C][C]540[/C][C]493.678473241443[/C][C]46.3215267585569[/C][/ROW]
[ROW][C]94[/C][C]700[/C][C]695.573397462069[/C][C]4.42660253793099[/C][/ROW]
[ROW][C]95[/C][C]520[/C][C]551.402086261838[/C][C]-31.4020862618382[/C][/ROW]
[ROW][C]96[/C][C]810[/C][C]837.372146662018[/C][C]-27.3721466620179[/C][/ROW]
[ROW][C]97[/C][C]690[/C][C]692.622870739762[/C][C]-2.62287073976245[/C][/ROW]
[ROW][C]98[/C][C]510[/C][C]505.606954136261[/C][C]4.3930458637393[/C][/ROW]
[ROW][C]99[/C][C]390[/C][C]464.115286609446[/C][C]-74.115286609446[/C][/ROW]
[ROW][C]100[/C][C]270[/C][C]314.934455057957[/C][C]-44.9344550579567[/C][/ROW]
[ROW][C]101[/C][C]530[/C][C]491.118722813342[/C][C]38.8812771866581[/C][/ROW]
[ROW][C]102[/C][C]510[/C][C]479.359088061211[/C][C]30.640911938789[/C][/ROW]
[ROW][C]103[/C][C]670[/C][C]709.83816413324[/C][C]-39.8381641332395[/C][/ROW]
[ROW][C]104[/C][C]770[/C][C]705.83783266098[/C][C]64.1621673390204[/C][/ROW]
[ROW][C]105[/C][C]570[/C][C]535.93601462993[/C][C]34.06398537007[/C][/ROW]
[ROW][C]106[/C][C]640[/C][C]698.720708993054[/C][C]-58.720708993054[/C][/ROW]
[ROW][C]107[/C][C]480[/C][C]519.97100978601[/C][C]-39.9710097860097[/C][/ROW]
[ROW][C]108[/C][C]830[/C][C]808.50487351222[/C][C]21.4951264877802[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296004&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296004&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13600620.518162393162-20.5181623931624
14450470.018653484721-20.0186534847205
15530554.338374146667-24.3383741466672
16400423.392686860527-23.3926868605269
17560574.739113734887-14.7391137348869
18460466.029181285402-6.02918128540216
19610582.76074243788927.2392575621107
20550600.05267662476-50.0526766247601
21580669.498582010769-89.4985820107689
22650576.50030850785873.4996914921421
23640545.2756199944194.7243800055898
24760687.62475737775572.3752426222445
25550560.703395789369-10.7033957893685
26460411.02409460082248.9759053991783
27510492.91179826454817.0882017354524
28370364.512712942195.48728705781025
29530525.6571878566714.34281214332862
30410426.883199001849-16.8831990018491
31580575.7952017006174.20479829938267
32550523.0978882759326.9021117240701
33490559.055424857411-69.0554248574113
34700618.71779373189981.2822062681013
35630609.51271718939620.4872828106037
36720732.295971563106-12.2959715631065
37540528.98648116110611.0135188388944
38500435.60805495398964.3919450460115
39450489.53338394918-39.53338394918
40370350.66772233960819.3322776603916
41490511.758477824301-21.7584778243009
42440393.82082561803546.1791743819654
43600563.95684038309836.0431596169025
44580533.97166283518746.0283371648131
45500483.40088881828316.5991111817171
46670684.821072112374-14.8210721123742
47620620.314073057076-0.314073057076484
48800714.10331415290885.8966858470919
49640535.481489776589104.518510223411
50390495.311520142483-105.311520142483
51390453.534436228588-63.5344362285879
52390370.04966234177419.9503376582261
53460494.679391724357-34.6793917243573
54460440.46803895324119.5319610467591
55620602.03827399638317.9617260036166
56570581.933985079803-11.9339850798029
57510504.0310676244145.96893237558641
58640676.625025213099-36.6250252130986
59590625.292572917807-35.2925729178073
60850797.86088893462152.1391110653785
61670635.45673274387834.5432672561216
62390400.080735739196-10.0807357391957
63410397.27945096045612.720549039544
64340391.720316145678-51.7203161456783
65470465.0167012280084.983298771992
66540461.13022561776578.8697743822353
67680622.3734428705957.6265571294102
68670576.0350493024793.9649506975304
69540517.52226602447522.4777339755251
70630653.104217827974-23.1042178279745
71560605.320464127788-45.3204641277885
72800860.437504314361-60.4375043143613
73610681.842823010633-71.8428230106326
74490404.451169654685.5488303453998
75440424.50011058285915.4998894171405
76330360.593245466174-30.5932454661744
77490487.500674624842.49932537516003
78590552.81169958506937.1883004149314
79690694.873917201977-4.87391720197729
80650681.624640648183-31.6246406481825
81480555.129176568301-75.1291765683011
82690645.94648320296544.0535167970349
83540577.069464089116-37.0694640891159
84830817.16359624081312.8364037591872
85690628.24588089865361.7541191013471
86500497.8157812312352.18421876876545
87460452.5362066320937.46379336790682
88310345.991112805951-35.9911128059511
89490503.17729151798-13.1772915179797
90470599.997228840161-129.997228840161
91710699.91690537506910.0830946249309
92710660.45476668299149.5452333170088
93540493.67847324144346.3215267585569
94700695.5733974620694.42660253793099
95520551.402086261838-31.4020862618382
96810837.372146662018-27.3721466620179
97690692.622870739762-2.62287073976245
98510505.6069541362614.3930458637393
99390464.115286609446-74.115286609446
100270314.934455057957-44.9344550579567
101530491.11872281334238.8812771866581
102510479.35908806121130.640911938789
103670709.83816413324-39.8381641332395
104770705.8378326609864.1621673390204
105570535.9360146299334.06398537007
106640698.720708993054-58.720708993054
107480519.97100978601-39.9710097860097
108830808.5048735122221.4951264877802







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109686.389676783002594.727011022744778.05234254326
110505.268628805141413.590240658929596.947016951354
111390.784834515559299.071080855533482.498588175585
112269.224072576527177.447480541002361.000664612052
113523.501675774104431.626984818309615.376366729899
114503.90085821193411.885088544333595.916627879526
115668.999617729767576.792171105578761.207064353957
116761.36371709552668.90651535371853.82091883733
117562.743045091091469.970711015437655.515379166746
118639.027983385109545.868067433476732.187899336742
119477.922431926901384.295687114628571.549176739175
120823.645559965857729.466265737603917.824854194111

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 686.389676783002 & 594.727011022744 & 778.05234254326 \tabularnewline
110 & 505.268628805141 & 413.590240658929 & 596.947016951354 \tabularnewline
111 & 390.784834515559 & 299.071080855533 & 482.498588175585 \tabularnewline
112 & 269.224072576527 & 177.447480541002 & 361.000664612052 \tabularnewline
113 & 523.501675774104 & 431.626984818309 & 615.376366729899 \tabularnewline
114 & 503.90085821193 & 411.885088544333 & 595.916627879526 \tabularnewline
115 & 668.999617729767 & 576.792171105578 & 761.207064353957 \tabularnewline
116 & 761.36371709552 & 668.90651535371 & 853.82091883733 \tabularnewline
117 & 562.743045091091 & 469.970711015437 & 655.515379166746 \tabularnewline
118 & 639.027983385109 & 545.868067433476 & 732.187899336742 \tabularnewline
119 & 477.922431926901 & 384.295687114628 & 571.549176739175 \tabularnewline
120 & 823.645559965857 & 729.466265737603 & 917.824854194111 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296004&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]109[/C][C]686.389676783002[/C][C]594.727011022744[/C][C]778.05234254326[/C][/ROW]
[ROW][C]110[/C][C]505.268628805141[/C][C]413.590240658929[/C][C]596.947016951354[/C][/ROW]
[ROW][C]111[/C][C]390.784834515559[/C][C]299.071080855533[/C][C]482.498588175585[/C][/ROW]
[ROW][C]112[/C][C]269.224072576527[/C][C]177.447480541002[/C][C]361.000664612052[/C][/ROW]
[ROW][C]113[/C][C]523.501675774104[/C][C]431.626984818309[/C][C]615.376366729899[/C][/ROW]
[ROW][C]114[/C][C]503.90085821193[/C][C]411.885088544333[/C][C]595.916627879526[/C][/ROW]
[ROW][C]115[/C][C]668.999617729767[/C][C]576.792171105578[/C][C]761.207064353957[/C][/ROW]
[ROW][C]116[/C][C]761.36371709552[/C][C]668.90651535371[/C][C]853.82091883733[/C][/ROW]
[ROW][C]117[/C][C]562.743045091091[/C][C]469.970711015437[/C][C]655.515379166746[/C][/ROW]
[ROW][C]118[/C][C]639.027983385109[/C][C]545.868067433476[/C][C]732.187899336742[/C][/ROW]
[ROW][C]119[/C][C]477.922431926901[/C][C]384.295687114628[/C][C]571.549176739175[/C][/ROW]
[ROW][C]120[/C][C]823.645559965857[/C][C]729.466265737603[/C][C]917.824854194111[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296004&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296004&T=3

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109686.389676783002594.727011022744778.05234254326
110505.268628805141413.590240658929596.947016951354
111390.784834515559299.071080855533482.498588175585
112269.224072576527177.447480541002361.000664612052
113523.501675774104431.626984818309615.376366729899
114503.90085821193411.885088544333595.916627879526
115668.999617729767576.792171105578761.207064353957
116761.36371709552668.90651535371853.82091883733
117562.743045091091469.970711015437655.515379166746
118639.027983385109545.868067433476732.187899336742
119477.922431926901384.295687114628571.549176739175
120823.645559965857729.466265737603917.824854194111



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')