Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 01 Aug 2016 13:48:26 +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/01/t1470055777loq9l5nppkth4tq.htm/, Retrieved Mon, 29 Apr 2024 09:08:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=295995, Retrieved Mon, 29 Apr 2024 09:08:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact152
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-08-01 12:48:26] [b94c13d84d922b33c8d74b1e5b1d38c1] [Current]
Feedback Forum

Post a new message
Dataseries X:
630
720
740
720
720
690
790
760
840
840
640
840
590
770
750
590
730
740
770
660
830
900
630
770
640
700
760
500
740
740
680
580
780
990
630
780
630
780
730
490
710
700
740
520
730
1110
510
750
690
740
690
640
660
580
760
510
810
1050
510
740
690
800
670
670
640
540
740
600
860
1080
480
680
650
860
650
630
600
500
760
590
800
1120
520
710
600
880
700
590
680
530
730
600
880
1120
540
740
580
850
670
530
680
540
760
620
910
1230
530
720




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295995&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295995&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295995&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0413348347616464
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0413348347616464 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295995&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]0.0413348347616464[/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=295995&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295995&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
alpha0.0413348347616464
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
272063090
3740633.720135128548106.279864871452
4720638.113195781581.8868042185003
5720641.49797330303178.5020266969693
6690644.74284160500445.2571583949957
7790646.613538769043143.386461230957
8760652.540394451082107.459605548918
9840656.982219489998183.017780510002
10840664.547229205822175.452770794178
11640671.799540495073-31.7995404950727
12840670.485111743213169.514888256787
13590677.491981638946-87.4919816389458
14770673.87551503493196.124484965069
15750677.8488047375172.1511952624895
16590680.831162471541-90.8311624715408
17730677.07667137957152.9233286204286
18740679.26424842313360.735751576867
19770681.77475067868788.2252493213127
20660685.421526781189-25.4215267811887
21830684.3707321723145.6292678277
22900690.390293894417209.609706105583
23630699.054476460729-69.0544764607286
24770696.20012108667273.7998789133277
25640699.250626886984-59.2506268869843
26700696.8015120150873.19848798491319
27760696.9337209874363.0662790125697
28500699.540555209447-199.540555209447
29740691.29257933161748.7074206683831
30740693.30589251661146.6941074833894
31680695.235985733779-15.2359857337791
32580694.606208781042-114.606208781042
33780689.86898007841990.1310199215808
34990693.594530893776296.405469106224
35630705.84640198173-75.8464019817303
36780702.7113034885577.28869651145
37630705.906018987794-75.9060189877938
38780702.76845623551977.2315437644811
39730705.96080933541124.0391906645895
40490706.954465309335-216.954465309335
41710697.98668833497212.0133116650278
42700698.4832565875861.5167434124138
43740698.54595092591441.4540490740859
44520700.259447194593-180.259447194593
45730692.80845273057837.1915472694216
461110694.34575919149415.65424080851
47510711.526758553287-201.526758553287
48750703.19668328843746.8033167115632
49690705.131290651006-15.1312906510062
50740704.50584125221635.4941587477836
51690705.97298643906-15.9729864390597
52640705.312745683951-65.3127456839511
53660702.613054133276-42.6130541332756
54580700.851650581988-120.851650581988
55760695.85626757450964.1437324254912
56510698.507638155312-188.507638155312
57810690.715706080854119.284293919146
581050695.646302659661354.353697340339
59510710.293454186403-200.293454186403
60740702.01435735376837.9856426462318
61690703.584487615865-13.5844876158652
62800703.02297506494296.9770249350582
63670707.031504366308-37.0315043663085
64670705.500813252352-35.5008132523519
65640704.033393002662-64.0333930026619
66540701.386583283669-161.386583283669
67740694.71569553089245.2843044691078
68600696.587514773419-96.5875147734189
69860692.595085810221167.404914189779
701080699.514740276544380.485259723456
71480715.242035616455-235.242035616455
72680705.518344945255-25.5183449452552
73650704.463548373552-54.4635483735523
74860702.212306600999157.787693399001
75650708.734434835068-58.7344348350675
76630706.306656676341-76.3066566763413
77600703.152533631411-103.152533631411
78500698.888740698511-198.888740698511
79760690.66770746578669.3322925342136
80590693.533546321334-103.533546321334
81800689.254004291854110.745995708146
821120693.831671724965426.168328275035
83520711.44726915486-191.44726915486
84710703.5338279187766.46617208122439
85600703.801106073293-103.801106073293
86880699.510504505678180.489495494322
87700706.971007978148-6.97100797814824
88590706.682862515249-116.682862515249
89680701.859795673666-21.8597956736655
90530700.956224631571-170.956224631571
91730693.8897773349536.1102226650498
92600695.382387422016-95.3823874220162
93880691.439772198756188.560227801244
941120699.233878057539420.766121942461
95540716.626176181329-176.626176181329
96740709.32536237429230.6746376257078
97580710.593293451924-130.593293451924
98850705.19524124611144.80475875389
99670711.180722021902-41.1807220219018
100530709.478523681761-179.478523681761
101680702.059808562111-22.0598085621114
102540701.147970020323-161.147970020323
103760694.48694530735865.513054692642
104620697.194916597809-77.194916597809
105910694.004077475799215.995922524201
1061230702.932233242527527.067766757473
107530724.718492289637-194.718492289637
108720716.6698355858083.33016441419227

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 720 & 630 & 90 \tabularnewline
3 & 740 & 633.720135128548 & 106.279864871452 \tabularnewline
4 & 720 & 638.1131957815 & 81.8868042185003 \tabularnewline
5 & 720 & 641.497973303031 & 78.5020266969693 \tabularnewline
6 & 690 & 644.742841605004 & 45.2571583949957 \tabularnewline
7 & 790 & 646.613538769043 & 143.386461230957 \tabularnewline
8 & 760 & 652.540394451082 & 107.459605548918 \tabularnewline
9 & 840 & 656.982219489998 & 183.017780510002 \tabularnewline
10 & 840 & 664.547229205822 & 175.452770794178 \tabularnewline
11 & 640 & 671.799540495073 & -31.7995404950727 \tabularnewline
12 & 840 & 670.485111743213 & 169.514888256787 \tabularnewline
13 & 590 & 677.491981638946 & -87.4919816389458 \tabularnewline
14 & 770 & 673.875515034931 & 96.124484965069 \tabularnewline
15 & 750 & 677.84880473751 & 72.1511952624895 \tabularnewline
16 & 590 & 680.831162471541 & -90.8311624715408 \tabularnewline
17 & 730 & 677.076671379571 & 52.9233286204286 \tabularnewline
18 & 740 & 679.264248423133 & 60.735751576867 \tabularnewline
19 & 770 & 681.774750678687 & 88.2252493213127 \tabularnewline
20 & 660 & 685.421526781189 & -25.4215267811887 \tabularnewline
21 & 830 & 684.3707321723 & 145.6292678277 \tabularnewline
22 & 900 & 690.390293894417 & 209.609706105583 \tabularnewline
23 & 630 & 699.054476460729 & -69.0544764607286 \tabularnewline
24 & 770 & 696.200121086672 & 73.7998789133277 \tabularnewline
25 & 640 & 699.250626886984 & -59.2506268869843 \tabularnewline
26 & 700 & 696.801512015087 & 3.19848798491319 \tabularnewline
27 & 760 & 696.93372098743 & 63.0662790125697 \tabularnewline
28 & 500 & 699.540555209447 & -199.540555209447 \tabularnewline
29 & 740 & 691.292579331617 & 48.7074206683831 \tabularnewline
30 & 740 & 693.305892516611 & 46.6941074833894 \tabularnewline
31 & 680 & 695.235985733779 & -15.2359857337791 \tabularnewline
32 & 580 & 694.606208781042 & -114.606208781042 \tabularnewline
33 & 780 & 689.868980078419 & 90.1310199215808 \tabularnewline
34 & 990 & 693.594530893776 & 296.405469106224 \tabularnewline
35 & 630 & 705.84640198173 & -75.8464019817303 \tabularnewline
36 & 780 & 702.71130348855 & 77.28869651145 \tabularnewline
37 & 630 & 705.906018987794 & -75.9060189877938 \tabularnewline
38 & 780 & 702.768456235519 & 77.2315437644811 \tabularnewline
39 & 730 & 705.960809335411 & 24.0391906645895 \tabularnewline
40 & 490 & 706.954465309335 & -216.954465309335 \tabularnewline
41 & 710 & 697.986688334972 & 12.0133116650278 \tabularnewline
42 & 700 & 698.483256587586 & 1.5167434124138 \tabularnewline
43 & 740 & 698.545950925914 & 41.4540490740859 \tabularnewline
44 & 520 & 700.259447194593 & -180.259447194593 \tabularnewline
45 & 730 & 692.808452730578 & 37.1915472694216 \tabularnewline
46 & 1110 & 694.34575919149 & 415.65424080851 \tabularnewline
47 & 510 & 711.526758553287 & -201.526758553287 \tabularnewline
48 & 750 & 703.196683288437 & 46.8033167115632 \tabularnewline
49 & 690 & 705.131290651006 & -15.1312906510062 \tabularnewline
50 & 740 & 704.505841252216 & 35.4941587477836 \tabularnewline
51 & 690 & 705.97298643906 & -15.9729864390597 \tabularnewline
52 & 640 & 705.312745683951 & -65.3127456839511 \tabularnewline
53 & 660 & 702.613054133276 & -42.6130541332756 \tabularnewline
54 & 580 & 700.851650581988 & -120.851650581988 \tabularnewline
55 & 760 & 695.856267574509 & 64.1437324254912 \tabularnewline
56 & 510 & 698.507638155312 & -188.507638155312 \tabularnewline
57 & 810 & 690.715706080854 & 119.284293919146 \tabularnewline
58 & 1050 & 695.646302659661 & 354.353697340339 \tabularnewline
59 & 510 & 710.293454186403 & -200.293454186403 \tabularnewline
60 & 740 & 702.014357353768 & 37.9856426462318 \tabularnewline
61 & 690 & 703.584487615865 & -13.5844876158652 \tabularnewline
62 & 800 & 703.022975064942 & 96.9770249350582 \tabularnewline
63 & 670 & 707.031504366308 & -37.0315043663085 \tabularnewline
64 & 670 & 705.500813252352 & -35.5008132523519 \tabularnewline
65 & 640 & 704.033393002662 & -64.0333930026619 \tabularnewline
66 & 540 & 701.386583283669 & -161.386583283669 \tabularnewline
67 & 740 & 694.715695530892 & 45.2843044691078 \tabularnewline
68 & 600 & 696.587514773419 & -96.5875147734189 \tabularnewline
69 & 860 & 692.595085810221 & 167.404914189779 \tabularnewline
70 & 1080 & 699.514740276544 & 380.485259723456 \tabularnewline
71 & 480 & 715.242035616455 & -235.242035616455 \tabularnewline
72 & 680 & 705.518344945255 & -25.5183449452552 \tabularnewline
73 & 650 & 704.463548373552 & -54.4635483735523 \tabularnewline
74 & 860 & 702.212306600999 & 157.787693399001 \tabularnewline
75 & 650 & 708.734434835068 & -58.7344348350675 \tabularnewline
76 & 630 & 706.306656676341 & -76.3066566763413 \tabularnewline
77 & 600 & 703.152533631411 & -103.152533631411 \tabularnewline
78 & 500 & 698.888740698511 & -198.888740698511 \tabularnewline
79 & 760 & 690.667707465786 & 69.3322925342136 \tabularnewline
80 & 590 & 693.533546321334 & -103.533546321334 \tabularnewline
81 & 800 & 689.254004291854 & 110.745995708146 \tabularnewline
82 & 1120 & 693.831671724965 & 426.168328275035 \tabularnewline
83 & 520 & 711.44726915486 & -191.44726915486 \tabularnewline
84 & 710 & 703.533827918776 & 6.46617208122439 \tabularnewline
85 & 600 & 703.801106073293 & -103.801106073293 \tabularnewline
86 & 880 & 699.510504505678 & 180.489495494322 \tabularnewline
87 & 700 & 706.971007978148 & -6.97100797814824 \tabularnewline
88 & 590 & 706.682862515249 & -116.682862515249 \tabularnewline
89 & 680 & 701.859795673666 & -21.8597956736655 \tabularnewline
90 & 530 & 700.956224631571 & -170.956224631571 \tabularnewline
91 & 730 & 693.88977733495 & 36.1102226650498 \tabularnewline
92 & 600 & 695.382387422016 & -95.3823874220162 \tabularnewline
93 & 880 & 691.439772198756 & 188.560227801244 \tabularnewline
94 & 1120 & 699.233878057539 & 420.766121942461 \tabularnewline
95 & 540 & 716.626176181329 & -176.626176181329 \tabularnewline
96 & 740 & 709.325362374292 & 30.6746376257078 \tabularnewline
97 & 580 & 710.593293451924 & -130.593293451924 \tabularnewline
98 & 850 & 705.19524124611 & 144.80475875389 \tabularnewline
99 & 670 & 711.180722021902 & -41.1807220219018 \tabularnewline
100 & 530 & 709.478523681761 & -179.478523681761 \tabularnewline
101 & 680 & 702.059808562111 & -22.0598085621114 \tabularnewline
102 & 540 & 701.147970020323 & -161.147970020323 \tabularnewline
103 & 760 & 694.486945307358 & 65.513054692642 \tabularnewline
104 & 620 & 697.194916597809 & -77.194916597809 \tabularnewline
105 & 910 & 694.004077475799 & 215.995922524201 \tabularnewline
106 & 1230 & 702.932233242527 & 527.067766757473 \tabularnewline
107 & 530 & 724.718492289637 & -194.718492289637 \tabularnewline
108 & 720 & 716.669835585808 & 3.33016441419227 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295995&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]720[/C][C]630[/C][C]90[/C][/ROW]
[ROW][C]3[/C][C]740[/C][C]633.720135128548[/C][C]106.279864871452[/C][/ROW]
[ROW][C]4[/C][C]720[/C][C]638.1131957815[/C][C]81.8868042185003[/C][/ROW]
[ROW][C]5[/C][C]720[/C][C]641.497973303031[/C][C]78.5020266969693[/C][/ROW]
[ROW][C]6[/C][C]690[/C][C]644.742841605004[/C][C]45.2571583949957[/C][/ROW]
[ROW][C]7[/C][C]790[/C][C]646.613538769043[/C][C]143.386461230957[/C][/ROW]
[ROW][C]8[/C][C]760[/C][C]652.540394451082[/C][C]107.459605548918[/C][/ROW]
[ROW][C]9[/C][C]840[/C][C]656.982219489998[/C][C]183.017780510002[/C][/ROW]
[ROW][C]10[/C][C]840[/C][C]664.547229205822[/C][C]175.452770794178[/C][/ROW]
[ROW][C]11[/C][C]640[/C][C]671.799540495073[/C][C]-31.7995404950727[/C][/ROW]
[ROW][C]12[/C][C]840[/C][C]670.485111743213[/C][C]169.514888256787[/C][/ROW]
[ROW][C]13[/C][C]590[/C][C]677.491981638946[/C][C]-87.4919816389458[/C][/ROW]
[ROW][C]14[/C][C]770[/C][C]673.875515034931[/C][C]96.124484965069[/C][/ROW]
[ROW][C]15[/C][C]750[/C][C]677.84880473751[/C][C]72.1511952624895[/C][/ROW]
[ROW][C]16[/C][C]590[/C][C]680.831162471541[/C][C]-90.8311624715408[/C][/ROW]
[ROW][C]17[/C][C]730[/C][C]677.076671379571[/C][C]52.9233286204286[/C][/ROW]
[ROW][C]18[/C][C]740[/C][C]679.264248423133[/C][C]60.735751576867[/C][/ROW]
[ROW][C]19[/C][C]770[/C][C]681.774750678687[/C][C]88.2252493213127[/C][/ROW]
[ROW][C]20[/C][C]660[/C][C]685.421526781189[/C][C]-25.4215267811887[/C][/ROW]
[ROW][C]21[/C][C]830[/C][C]684.3707321723[/C][C]145.6292678277[/C][/ROW]
[ROW][C]22[/C][C]900[/C][C]690.390293894417[/C][C]209.609706105583[/C][/ROW]
[ROW][C]23[/C][C]630[/C][C]699.054476460729[/C][C]-69.0544764607286[/C][/ROW]
[ROW][C]24[/C][C]770[/C][C]696.200121086672[/C][C]73.7998789133277[/C][/ROW]
[ROW][C]25[/C][C]640[/C][C]699.250626886984[/C][C]-59.2506268869843[/C][/ROW]
[ROW][C]26[/C][C]700[/C][C]696.801512015087[/C][C]3.19848798491319[/C][/ROW]
[ROW][C]27[/C][C]760[/C][C]696.93372098743[/C][C]63.0662790125697[/C][/ROW]
[ROW][C]28[/C][C]500[/C][C]699.540555209447[/C][C]-199.540555209447[/C][/ROW]
[ROW][C]29[/C][C]740[/C][C]691.292579331617[/C][C]48.7074206683831[/C][/ROW]
[ROW][C]30[/C][C]740[/C][C]693.305892516611[/C][C]46.6941074833894[/C][/ROW]
[ROW][C]31[/C][C]680[/C][C]695.235985733779[/C][C]-15.2359857337791[/C][/ROW]
[ROW][C]32[/C][C]580[/C][C]694.606208781042[/C][C]-114.606208781042[/C][/ROW]
[ROW][C]33[/C][C]780[/C][C]689.868980078419[/C][C]90.1310199215808[/C][/ROW]
[ROW][C]34[/C][C]990[/C][C]693.594530893776[/C][C]296.405469106224[/C][/ROW]
[ROW][C]35[/C][C]630[/C][C]705.84640198173[/C][C]-75.8464019817303[/C][/ROW]
[ROW][C]36[/C][C]780[/C][C]702.71130348855[/C][C]77.28869651145[/C][/ROW]
[ROW][C]37[/C][C]630[/C][C]705.906018987794[/C][C]-75.9060189877938[/C][/ROW]
[ROW][C]38[/C][C]780[/C][C]702.768456235519[/C][C]77.2315437644811[/C][/ROW]
[ROW][C]39[/C][C]730[/C][C]705.960809335411[/C][C]24.0391906645895[/C][/ROW]
[ROW][C]40[/C][C]490[/C][C]706.954465309335[/C][C]-216.954465309335[/C][/ROW]
[ROW][C]41[/C][C]710[/C][C]697.986688334972[/C][C]12.0133116650278[/C][/ROW]
[ROW][C]42[/C][C]700[/C][C]698.483256587586[/C][C]1.5167434124138[/C][/ROW]
[ROW][C]43[/C][C]740[/C][C]698.545950925914[/C][C]41.4540490740859[/C][/ROW]
[ROW][C]44[/C][C]520[/C][C]700.259447194593[/C][C]-180.259447194593[/C][/ROW]
[ROW][C]45[/C][C]730[/C][C]692.808452730578[/C][C]37.1915472694216[/C][/ROW]
[ROW][C]46[/C][C]1110[/C][C]694.34575919149[/C][C]415.65424080851[/C][/ROW]
[ROW][C]47[/C][C]510[/C][C]711.526758553287[/C][C]-201.526758553287[/C][/ROW]
[ROW][C]48[/C][C]750[/C][C]703.196683288437[/C][C]46.8033167115632[/C][/ROW]
[ROW][C]49[/C][C]690[/C][C]705.131290651006[/C][C]-15.1312906510062[/C][/ROW]
[ROW][C]50[/C][C]740[/C][C]704.505841252216[/C][C]35.4941587477836[/C][/ROW]
[ROW][C]51[/C][C]690[/C][C]705.97298643906[/C][C]-15.9729864390597[/C][/ROW]
[ROW][C]52[/C][C]640[/C][C]705.312745683951[/C][C]-65.3127456839511[/C][/ROW]
[ROW][C]53[/C][C]660[/C][C]702.613054133276[/C][C]-42.6130541332756[/C][/ROW]
[ROW][C]54[/C][C]580[/C][C]700.851650581988[/C][C]-120.851650581988[/C][/ROW]
[ROW][C]55[/C][C]760[/C][C]695.856267574509[/C][C]64.1437324254912[/C][/ROW]
[ROW][C]56[/C][C]510[/C][C]698.507638155312[/C][C]-188.507638155312[/C][/ROW]
[ROW][C]57[/C][C]810[/C][C]690.715706080854[/C][C]119.284293919146[/C][/ROW]
[ROW][C]58[/C][C]1050[/C][C]695.646302659661[/C][C]354.353697340339[/C][/ROW]
[ROW][C]59[/C][C]510[/C][C]710.293454186403[/C][C]-200.293454186403[/C][/ROW]
[ROW][C]60[/C][C]740[/C][C]702.014357353768[/C][C]37.9856426462318[/C][/ROW]
[ROW][C]61[/C][C]690[/C][C]703.584487615865[/C][C]-13.5844876158652[/C][/ROW]
[ROW][C]62[/C][C]800[/C][C]703.022975064942[/C][C]96.9770249350582[/C][/ROW]
[ROW][C]63[/C][C]670[/C][C]707.031504366308[/C][C]-37.0315043663085[/C][/ROW]
[ROW][C]64[/C][C]670[/C][C]705.500813252352[/C][C]-35.5008132523519[/C][/ROW]
[ROW][C]65[/C][C]640[/C][C]704.033393002662[/C][C]-64.0333930026619[/C][/ROW]
[ROW][C]66[/C][C]540[/C][C]701.386583283669[/C][C]-161.386583283669[/C][/ROW]
[ROW][C]67[/C][C]740[/C][C]694.715695530892[/C][C]45.2843044691078[/C][/ROW]
[ROW][C]68[/C][C]600[/C][C]696.587514773419[/C][C]-96.5875147734189[/C][/ROW]
[ROW][C]69[/C][C]860[/C][C]692.595085810221[/C][C]167.404914189779[/C][/ROW]
[ROW][C]70[/C][C]1080[/C][C]699.514740276544[/C][C]380.485259723456[/C][/ROW]
[ROW][C]71[/C][C]480[/C][C]715.242035616455[/C][C]-235.242035616455[/C][/ROW]
[ROW][C]72[/C][C]680[/C][C]705.518344945255[/C][C]-25.5183449452552[/C][/ROW]
[ROW][C]73[/C][C]650[/C][C]704.463548373552[/C][C]-54.4635483735523[/C][/ROW]
[ROW][C]74[/C][C]860[/C][C]702.212306600999[/C][C]157.787693399001[/C][/ROW]
[ROW][C]75[/C][C]650[/C][C]708.734434835068[/C][C]-58.7344348350675[/C][/ROW]
[ROW][C]76[/C][C]630[/C][C]706.306656676341[/C][C]-76.3066566763413[/C][/ROW]
[ROW][C]77[/C][C]600[/C][C]703.152533631411[/C][C]-103.152533631411[/C][/ROW]
[ROW][C]78[/C][C]500[/C][C]698.888740698511[/C][C]-198.888740698511[/C][/ROW]
[ROW][C]79[/C][C]760[/C][C]690.667707465786[/C][C]69.3322925342136[/C][/ROW]
[ROW][C]80[/C][C]590[/C][C]693.533546321334[/C][C]-103.533546321334[/C][/ROW]
[ROW][C]81[/C][C]800[/C][C]689.254004291854[/C][C]110.745995708146[/C][/ROW]
[ROW][C]82[/C][C]1120[/C][C]693.831671724965[/C][C]426.168328275035[/C][/ROW]
[ROW][C]83[/C][C]520[/C][C]711.44726915486[/C][C]-191.44726915486[/C][/ROW]
[ROW][C]84[/C][C]710[/C][C]703.533827918776[/C][C]6.46617208122439[/C][/ROW]
[ROW][C]85[/C][C]600[/C][C]703.801106073293[/C][C]-103.801106073293[/C][/ROW]
[ROW][C]86[/C][C]880[/C][C]699.510504505678[/C][C]180.489495494322[/C][/ROW]
[ROW][C]87[/C][C]700[/C][C]706.971007978148[/C][C]-6.97100797814824[/C][/ROW]
[ROW][C]88[/C][C]590[/C][C]706.682862515249[/C][C]-116.682862515249[/C][/ROW]
[ROW][C]89[/C][C]680[/C][C]701.859795673666[/C][C]-21.8597956736655[/C][/ROW]
[ROW][C]90[/C][C]530[/C][C]700.956224631571[/C][C]-170.956224631571[/C][/ROW]
[ROW][C]91[/C][C]730[/C][C]693.88977733495[/C][C]36.1102226650498[/C][/ROW]
[ROW][C]92[/C][C]600[/C][C]695.382387422016[/C][C]-95.3823874220162[/C][/ROW]
[ROW][C]93[/C][C]880[/C][C]691.439772198756[/C][C]188.560227801244[/C][/ROW]
[ROW][C]94[/C][C]1120[/C][C]699.233878057539[/C][C]420.766121942461[/C][/ROW]
[ROW][C]95[/C][C]540[/C][C]716.626176181329[/C][C]-176.626176181329[/C][/ROW]
[ROW][C]96[/C][C]740[/C][C]709.325362374292[/C][C]30.6746376257078[/C][/ROW]
[ROW][C]97[/C][C]580[/C][C]710.593293451924[/C][C]-130.593293451924[/C][/ROW]
[ROW][C]98[/C][C]850[/C][C]705.19524124611[/C][C]144.80475875389[/C][/ROW]
[ROW][C]99[/C][C]670[/C][C]711.180722021902[/C][C]-41.1807220219018[/C][/ROW]
[ROW][C]100[/C][C]530[/C][C]709.478523681761[/C][C]-179.478523681761[/C][/ROW]
[ROW][C]101[/C][C]680[/C][C]702.059808562111[/C][C]-22.0598085621114[/C][/ROW]
[ROW][C]102[/C][C]540[/C][C]701.147970020323[/C][C]-161.147970020323[/C][/ROW]
[ROW][C]103[/C][C]760[/C][C]694.486945307358[/C][C]65.513054692642[/C][/ROW]
[ROW][C]104[/C][C]620[/C][C]697.194916597809[/C][C]-77.194916597809[/C][/ROW]
[ROW][C]105[/C][C]910[/C][C]694.004077475799[/C][C]215.995922524201[/C][/ROW]
[ROW][C]106[/C][C]1230[/C][C]702.932233242527[/C][C]527.067766757473[/C][/ROW]
[ROW][C]107[/C][C]530[/C][C]724.718492289637[/C][C]-194.718492289637[/C][/ROW]
[ROW][C]108[/C][C]720[/C][C]716.669835585808[/C][C]3.33016441419227[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295995&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295995&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
272063090
3740633.720135128548106.279864871452
4720638.113195781581.8868042185003
5720641.49797330303178.5020266969693
6690644.74284160500445.2571583949957
7790646.613538769043143.386461230957
8760652.540394451082107.459605548918
9840656.982219489998183.017780510002
10840664.547229205822175.452770794178
11640671.799540495073-31.7995404950727
12840670.485111743213169.514888256787
13590677.491981638946-87.4919816389458
14770673.87551503493196.124484965069
15750677.8488047375172.1511952624895
16590680.831162471541-90.8311624715408
17730677.07667137957152.9233286204286
18740679.26424842313360.735751576867
19770681.77475067868788.2252493213127
20660685.421526781189-25.4215267811887
21830684.3707321723145.6292678277
22900690.390293894417209.609706105583
23630699.054476460729-69.0544764607286
24770696.20012108667273.7998789133277
25640699.250626886984-59.2506268869843
26700696.8015120150873.19848798491319
27760696.9337209874363.0662790125697
28500699.540555209447-199.540555209447
29740691.29257933161748.7074206683831
30740693.30589251661146.6941074833894
31680695.235985733779-15.2359857337791
32580694.606208781042-114.606208781042
33780689.86898007841990.1310199215808
34990693.594530893776296.405469106224
35630705.84640198173-75.8464019817303
36780702.7113034885577.28869651145
37630705.906018987794-75.9060189877938
38780702.76845623551977.2315437644811
39730705.96080933541124.0391906645895
40490706.954465309335-216.954465309335
41710697.98668833497212.0133116650278
42700698.4832565875861.5167434124138
43740698.54595092591441.4540490740859
44520700.259447194593-180.259447194593
45730692.80845273057837.1915472694216
461110694.34575919149415.65424080851
47510711.526758553287-201.526758553287
48750703.19668328843746.8033167115632
49690705.131290651006-15.1312906510062
50740704.50584125221635.4941587477836
51690705.97298643906-15.9729864390597
52640705.312745683951-65.3127456839511
53660702.613054133276-42.6130541332756
54580700.851650581988-120.851650581988
55760695.85626757450964.1437324254912
56510698.507638155312-188.507638155312
57810690.715706080854119.284293919146
581050695.646302659661354.353697340339
59510710.293454186403-200.293454186403
60740702.01435735376837.9856426462318
61690703.584487615865-13.5844876158652
62800703.02297506494296.9770249350582
63670707.031504366308-37.0315043663085
64670705.500813252352-35.5008132523519
65640704.033393002662-64.0333930026619
66540701.386583283669-161.386583283669
67740694.71569553089245.2843044691078
68600696.587514773419-96.5875147734189
69860692.595085810221167.404914189779
701080699.514740276544380.485259723456
71480715.242035616455-235.242035616455
72680705.518344945255-25.5183449452552
73650704.463548373552-54.4635483735523
74860702.212306600999157.787693399001
75650708.734434835068-58.7344348350675
76630706.306656676341-76.3066566763413
77600703.152533631411-103.152533631411
78500698.888740698511-198.888740698511
79760690.66770746578669.3322925342136
80590693.533546321334-103.533546321334
81800689.254004291854110.745995708146
821120693.831671724965426.168328275035
83520711.44726915486-191.44726915486
84710703.5338279187766.46617208122439
85600703.801106073293-103.801106073293
86880699.510504505678180.489495494322
87700706.971007978148-6.97100797814824
88590706.682862515249-116.682862515249
89680701.859795673666-21.8597956736655
90530700.956224631571-170.956224631571
91730693.8897773349536.1102226650498
92600695.382387422016-95.3823874220162
93880691.439772198756188.560227801244
941120699.233878057539420.766121942461
95540716.626176181329-176.626176181329
96740709.32536237429230.6746376257078
97580710.593293451924-130.593293451924
98850705.19524124611144.80475875389
99670711.180722021902-41.1807220219018
100530709.478523681761-179.478523681761
101680702.059808562111-22.0598085621114
102540701.147970020323-161.147970020323
103760694.48694530735865.513054692642
104620697.194916597809-77.194916597809
105910694.004077475799215.995922524201
1061230702.932233242527527.067766757473
107530724.718492289637-194.718492289637
108720716.6698355858083.33016441419227







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109716.807487381598422.1503806380711011.46459412512
110716.807487381598421.898767131951011.71620763124
111716.807487381598421.6473681173191011.96760664588
112716.807487381598421.3961830465711012.21879171662
113716.807487381598421.1452113744271012.46976338877
114716.807487381598420.894452557921012.72052220527
115716.807487381598420.6439060563821012.97106870681
116716.807487381598420.393571331431013.22140343177
117716.807487381598420.143447846951013.47152691624
118716.807487381598419.8935350690911013.7214396941
119716.807487381598419.6438324662431013.97114229695
120716.807487381598419.3943395090291014.22063525417

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 716.807487381598 & 422.150380638071 & 1011.46459412512 \tabularnewline
110 & 716.807487381598 & 421.89876713195 & 1011.71620763124 \tabularnewline
111 & 716.807487381598 & 421.647368117319 & 1011.96760664588 \tabularnewline
112 & 716.807487381598 & 421.396183046571 & 1012.21879171662 \tabularnewline
113 & 716.807487381598 & 421.145211374427 & 1012.46976338877 \tabularnewline
114 & 716.807487381598 & 420.89445255792 & 1012.72052220527 \tabularnewline
115 & 716.807487381598 & 420.643906056382 & 1012.97106870681 \tabularnewline
116 & 716.807487381598 & 420.39357133143 & 1013.22140343177 \tabularnewline
117 & 716.807487381598 & 420.14344784695 & 1013.47152691624 \tabularnewline
118 & 716.807487381598 & 419.893535069091 & 1013.7214396941 \tabularnewline
119 & 716.807487381598 & 419.643832466243 & 1013.97114229695 \tabularnewline
120 & 716.807487381598 & 419.394339509029 & 1014.22063525417 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295995&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]716.807487381598[/C][C]422.150380638071[/C][C]1011.46459412512[/C][/ROW]
[ROW][C]110[/C][C]716.807487381598[/C][C]421.89876713195[/C][C]1011.71620763124[/C][/ROW]
[ROW][C]111[/C][C]716.807487381598[/C][C]421.647368117319[/C][C]1011.96760664588[/C][/ROW]
[ROW][C]112[/C][C]716.807487381598[/C][C]421.396183046571[/C][C]1012.21879171662[/C][/ROW]
[ROW][C]113[/C][C]716.807487381598[/C][C]421.145211374427[/C][C]1012.46976338877[/C][/ROW]
[ROW][C]114[/C][C]716.807487381598[/C][C]420.89445255792[/C][C]1012.72052220527[/C][/ROW]
[ROW][C]115[/C][C]716.807487381598[/C][C]420.643906056382[/C][C]1012.97106870681[/C][/ROW]
[ROW][C]116[/C][C]716.807487381598[/C][C]420.39357133143[/C][C]1013.22140343177[/C][/ROW]
[ROW][C]117[/C][C]716.807487381598[/C][C]420.14344784695[/C][C]1013.47152691624[/C][/ROW]
[ROW][C]118[/C][C]716.807487381598[/C][C]419.893535069091[/C][C]1013.7214396941[/C][/ROW]
[ROW][C]119[/C][C]716.807487381598[/C][C]419.643832466243[/C][C]1013.97114229695[/C][/ROW]
[ROW][C]120[/C][C]716.807487381598[/C][C]419.394339509029[/C][C]1014.22063525417[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295995&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295995&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
109716.807487381598422.1503806380711011.46459412512
110716.807487381598421.898767131951011.71620763124
111716.807487381598421.6473681173191011.96760664588
112716.807487381598421.3961830465711012.21879171662
113716.807487381598421.1452113744271012.46976338877
114716.807487381598420.894452557921012.72052220527
115716.807487381598420.6439060563821012.97106870681
116716.807487381598420.393571331431013.22140343177
117716.807487381598420.143447846951013.47152691624
118716.807487381598419.8935350690911013.7214396941
119716.807487381598419.6438324662431013.97114229695
120716.807487381598419.3943395090291014.22063525417



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')