Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 17 Aug 2012 02:08:12 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Aug/17/t1345183732mp6jgeij6rexh64.htm/, Retrieved Sat, 04 May 2024 16:29:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=169455, Retrieved Sat, 04 May 2024 16:29:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsOcak Akif
Estimated Impact168
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks B - Sta...] [2012-08-17 06:08:12] [919141dca056cde38faaf6352f12d0de] [Current]
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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=169455&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=169455&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169455&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
alpha0.0413348347616346
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0413348347616346 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169455&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]0.0413348347616346[/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=169455&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169455&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
alpha0.0413348347616346
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
272063090
3740633.720135128547106.279864871453
4720638.11319578149781.8868042185026
5720641.49797330302878.5020266969724
6690644.74284160545.2571583949996
7790646.613538769039143.386461230961
8760652.540394451076107.459605548924
9840656.982219489991183.017780510009
10840664.547229205814175.452770794186
11640671.799540495062-31.7995404950623
12840670.485111743203169.514888256797
13590677.491981638935-87.4919816389346
14770673.87551503492196.1244849650788
15750677.848804737572.1511952625
16590680.83116247153-90.8311624715299
17730677.07667137956252.923328620438
18740679.26424842312360.7357515768765
19770681.77475067867788.2252493213226
20660685.421526781178-25.4215267811783
21830684.37073217229145.62926782771
22900690.390293894406209.609706105594
23630699.054476460715-69.0544764607155
24770696.20012108666173.7998789133394
25640699.250626886972-59.2506268869721
26700696.8015120150763.1984879849241
27760696.9337209874263.0662790125801
28500699.540555209436-199.540555209436
29740691.29257933160948.7074206683909
30740693.30589251660246.6941074833976
31680695.235985733771-15.2359857337707
32580694.606208781035-114.606208781035
33780689.86898007841390.1310199215868
34990693.59453089377296.40546910623
35630705.84640198172-75.8464019817204
36780702.71130348854177.2886965114585
37630705.906018987785-75.9060189877847
38780702.76845623551177.2315437644888
39730705.96080933540224.0391906645978
40490706.954465309327-216.954465309327
41710697.98668833496712.013311665033
42700698.4832565875811.51674341241892
43740698.54595092590941.4540490740908
44520700.259447194587-180.259447194587
45730692.80845273057637.1915472694244
461110694.345759191487415.654240808513
47510711.526758553279-201.526758553279
48750703.19668328843246.8033167115683
49690705.131290651001-15.1312906510009
50740704.50584125221135.4941587477886
51690705.972986439054-15.9729864390545
52640705.312745683946-65.3127456839463
53660702.613054133272-42.6130541332717
54580700.851650581984-120.851650581984
55760695.85626757450764.1437324254928
56510698.507638155309-188.507638155309
57810690.715706080854119.284293919146
581050695.64630265966354.35369734034
59510710.293454186397-200.293454186397
60740702.01435735376537.9856426462346
61690703.584487615862-13.584487615862
62800703.02297506493996.9770249350611
63670707.031504366305-37.0315043663046
64670705.500813252349-35.5008132523486
65640704.033393002659-64.0333930026592
66540701.386583283668-161.386583283668
67740694.71569553089245.2843044691076
68600696.587514773419-96.5875147734185
69860692.595085810222167.404914189778
701080699.514740276542380.485259723458
71480715.242035616449-235.242035616449
72680705.518344945253-25.5183449452527
73650704.46354837355-54.4635483735502
74860702.212306600997157.787693399003
75650708.734434835064-58.7344348350645
76630706.306656676339-76.3066566763391
77600703.15253363141-103.15253363141
78500698.888740698512-198.888740698512
79760690.66770746578969.332292534211
80590693.533546321336-103.533546321336
81800689.254004291858110.745995708142
821120693.831671724966426.168328275034
83520711.447269154857-191.447269154857
84710703.5338279187756.46617208122541
85600703.801106073292-103.801106073292
86880699.510504505678180.489495494322
87700706.971007978147-6.97100797814653
88590706.682862515248-116.682862515248
89680701.859795673666-21.8597956736655
90530700.956224631571-170.956224631571
91730693.88977733495336.1102226650474
92600695.382387422018-95.3823874220182
93880691.439772198759188.560227801241
941120699.233878057539420.766121942461
95540716.626176181325-176.626176181325
96740709.3253623742930.6746376257097
97580710.593293451922-130.593293451922
98850705.195241246109144.804758753891
99670711.1807220219-41.1807220218996
100530709.478523681759-179.478523681759
101680702.059808562112-22.0598085621118
102540701.147970020324-161.147970020324
103760694.48694530736165.5130546926392
104620697.194916597811-77.1949165978109
105910694.004077475802215.995922524198
1061230702.932233242527527.067766757473
107530724.718492289631-194.718492289631
108720716.6698355858043.33016441419579

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 720 & 630 & 90 \tabularnewline
3 & 740 & 633.720135128547 & 106.279864871453 \tabularnewline
4 & 720 & 638.113195781497 & 81.8868042185026 \tabularnewline
5 & 720 & 641.497973303028 & 78.5020266969724 \tabularnewline
6 & 690 & 644.742841605 & 45.2571583949996 \tabularnewline
7 & 790 & 646.613538769039 & 143.386461230961 \tabularnewline
8 & 760 & 652.540394451076 & 107.459605548924 \tabularnewline
9 & 840 & 656.982219489991 & 183.017780510009 \tabularnewline
10 & 840 & 664.547229205814 & 175.452770794186 \tabularnewline
11 & 640 & 671.799540495062 & -31.7995404950623 \tabularnewline
12 & 840 & 670.485111743203 & 169.514888256797 \tabularnewline
13 & 590 & 677.491981638935 & -87.4919816389346 \tabularnewline
14 & 770 & 673.875515034921 & 96.1244849650788 \tabularnewline
15 & 750 & 677.8488047375 & 72.1511952625 \tabularnewline
16 & 590 & 680.83116247153 & -90.8311624715299 \tabularnewline
17 & 730 & 677.076671379562 & 52.923328620438 \tabularnewline
18 & 740 & 679.264248423123 & 60.7357515768765 \tabularnewline
19 & 770 & 681.774750678677 & 88.2252493213226 \tabularnewline
20 & 660 & 685.421526781178 & -25.4215267811783 \tabularnewline
21 & 830 & 684.37073217229 & 145.62926782771 \tabularnewline
22 & 900 & 690.390293894406 & 209.609706105594 \tabularnewline
23 & 630 & 699.054476460715 & -69.0544764607155 \tabularnewline
24 & 770 & 696.200121086661 & 73.7998789133394 \tabularnewline
25 & 640 & 699.250626886972 & -59.2506268869721 \tabularnewline
26 & 700 & 696.801512015076 & 3.1984879849241 \tabularnewline
27 & 760 & 696.93372098742 & 63.0662790125801 \tabularnewline
28 & 500 & 699.540555209436 & -199.540555209436 \tabularnewline
29 & 740 & 691.292579331609 & 48.7074206683909 \tabularnewline
30 & 740 & 693.305892516602 & 46.6941074833976 \tabularnewline
31 & 680 & 695.235985733771 & -15.2359857337707 \tabularnewline
32 & 580 & 694.606208781035 & -114.606208781035 \tabularnewline
33 & 780 & 689.868980078413 & 90.1310199215868 \tabularnewline
34 & 990 & 693.59453089377 & 296.40546910623 \tabularnewline
35 & 630 & 705.84640198172 & -75.8464019817204 \tabularnewline
36 & 780 & 702.711303488541 & 77.2886965114585 \tabularnewline
37 & 630 & 705.906018987785 & -75.9060189877847 \tabularnewline
38 & 780 & 702.768456235511 & 77.2315437644888 \tabularnewline
39 & 730 & 705.960809335402 & 24.0391906645978 \tabularnewline
40 & 490 & 706.954465309327 & -216.954465309327 \tabularnewline
41 & 710 & 697.986688334967 & 12.013311665033 \tabularnewline
42 & 700 & 698.483256587581 & 1.51674341241892 \tabularnewline
43 & 740 & 698.545950925909 & 41.4540490740908 \tabularnewline
44 & 520 & 700.259447194587 & -180.259447194587 \tabularnewline
45 & 730 & 692.808452730576 & 37.1915472694244 \tabularnewline
46 & 1110 & 694.345759191487 & 415.654240808513 \tabularnewline
47 & 510 & 711.526758553279 & -201.526758553279 \tabularnewline
48 & 750 & 703.196683288432 & 46.8033167115683 \tabularnewline
49 & 690 & 705.131290651001 & -15.1312906510009 \tabularnewline
50 & 740 & 704.505841252211 & 35.4941587477886 \tabularnewline
51 & 690 & 705.972986439054 & -15.9729864390545 \tabularnewline
52 & 640 & 705.312745683946 & -65.3127456839463 \tabularnewline
53 & 660 & 702.613054133272 & -42.6130541332717 \tabularnewline
54 & 580 & 700.851650581984 & -120.851650581984 \tabularnewline
55 & 760 & 695.856267574507 & 64.1437324254928 \tabularnewline
56 & 510 & 698.507638155309 & -188.507638155309 \tabularnewline
57 & 810 & 690.715706080854 & 119.284293919146 \tabularnewline
58 & 1050 & 695.64630265966 & 354.35369734034 \tabularnewline
59 & 510 & 710.293454186397 & -200.293454186397 \tabularnewline
60 & 740 & 702.014357353765 & 37.9856426462346 \tabularnewline
61 & 690 & 703.584487615862 & -13.584487615862 \tabularnewline
62 & 800 & 703.022975064939 & 96.9770249350611 \tabularnewline
63 & 670 & 707.031504366305 & -37.0315043663046 \tabularnewline
64 & 670 & 705.500813252349 & -35.5008132523486 \tabularnewline
65 & 640 & 704.033393002659 & -64.0333930026592 \tabularnewline
66 & 540 & 701.386583283668 & -161.386583283668 \tabularnewline
67 & 740 & 694.715695530892 & 45.2843044691076 \tabularnewline
68 & 600 & 696.587514773419 & -96.5875147734185 \tabularnewline
69 & 860 & 692.595085810222 & 167.404914189778 \tabularnewline
70 & 1080 & 699.514740276542 & 380.485259723458 \tabularnewline
71 & 480 & 715.242035616449 & -235.242035616449 \tabularnewline
72 & 680 & 705.518344945253 & -25.5183449452527 \tabularnewline
73 & 650 & 704.46354837355 & -54.4635483735502 \tabularnewline
74 & 860 & 702.212306600997 & 157.787693399003 \tabularnewline
75 & 650 & 708.734434835064 & -58.7344348350645 \tabularnewline
76 & 630 & 706.306656676339 & -76.3066566763391 \tabularnewline
77 & 600 & 703.15253363141 & -103.15253363141 \tabularnewline
78 & 500 & 698.888740698512 & -198.888740698512 \tabularnewline
79 & 760 & 690.667707465789 & 69.332292534211 \tabularnewline
80 & 590 & 693.533546321336 & -103.533546321336 \tabularnewline
81 & 800 & 689.254004291858 & 110.745995708142 \tabularnewline
82 & 1120 & 693.831671724966 & 426.168328275034 \tabularnewline
83 & 520 & 711.447269154857 & -191.447269154857 \tabularnewline
84 & 710 & 703.533827918775 & 6.46617208122541 \tabularnewline
85 & 600 & 703.801106073292 & -103.801106073292 \tabularnewline
86 & 880 & 699.510504505678 & 180.489495494322 \tabularnewline
87 & 700 & 706.971007978147 & -6.97100797814653 \tabularnewline
88 & 590 & 706.682862515248 & -116.682862515248 \tabularnewline
89 & 680 & 701.859795673666 & -21.8597956736655 \tabularnewline
90 & 530 & 700.956224631571 & -170.956224631571 \tabularnewline
91 & 730 & 693.889777334953 & 36.1102226650474 \tabularnewline
92 & 600 & 695.382387422018 & -95.3823874220182 \tabularnewline
93 & 880 & 691.439772198759 & 188.560227801241 \tabularnewline
94 & 1120 & 699.233878057539 & 420.766121942461 \tabularnewline
95 & 540 & 716.626176181325 & -176.626176181325 \tabularnewline
96 & 740 & 709.32536237429 & 30.6746376257097 \tabularnewline
97 & 580 & 710.593293451922 & -130.593293451922 \tabularnewline
98 & 850 & 705.195241246109 & 144.804758753891 \tabularnewline
99 & 670 & 711.1807220219 & -41.1807220218996 \tabularnewline
100 & 530 & 709.478523681759 & -179.478523681759 \tabularnewline
101 & 680 & 702.059808562112 & -22.0598085621118 \tabularnewline
102 & 540 & 701.147970020324 & -161.147970020324 \tabularnewline
103 & 760 & 694.486945307361 & 65.5130546926392 \tabularnewline
104 & 620 & 697.194916597811 & -77.1949165978109 \tabularnewline
105 & 910 & 694.004077475802 & 215.995922524198 \tabularnewline
106 & 1230 & 702.932233242527 & 527.067766757473 \tabularnewline
107 & 530 & 724.718492289631 & -194.718492289631 \tabularnewline
108 & 720 & 716.669835585804 & 3.33016441419579 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169455&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]633.720135128547[/C][C]106.279864871453[/C][/ROW]
[ROW][C]4[/C][C]720[/C][C]638.113195781497[/C][C]81.8868042185026[/C][/ROW]
[ROW][C]5[/C][C]720[/C][C]641.497973303028[/C][C]78.5020266969724[/C][/ROW]
[ROW][C]6[/C][C]690[/C][C]644.742841605[/C][C]45.2571583949996[/C][/ROW]
[ROW][C]7[/C][C]790[/C][C]646.613538769039[/C][C]143.386461230961[/C][/ROW]
[ROW][C]8[/C][C]760[/C][C]652.540394451076[/C][C]107.459605548924[/C][/ROW]
[ROW][C]9[/C][C]840[/C][C]656.982219489991[/C][C]183.017780510009[/C][/ROW]
[ROW][C]10[/C][C]840[/C][C]664.547229205814[/C][C]175.452770794186[/C][/ROW]
[ROW][C]11[/C][C]640[/C][C]671.799540495062[/C][C]-31.7995404950623[/C][/ROW]
[ROW][C]12[/C][C]840[/C][C]670.485111743203[/C][C]169.514888256797[/C][/ROW]
[ROW][C]13[/C][C]590[/C][C]677.491981638935[/C][C]-87.4919816389346[/C][/ROW]
[ROW][C]14[/C][C]770[/C][C]673.875515034921[/C][C]96.1244849650788[/C][/ROW]
[ROW][C]15[/C][C]750[/C][C]677.8488047375[/C][C]72.1511952625[/C][/ROW]
[ROW][C]16[/C][C]590[/C][C]680.83116247153[/C][C]-90.8311624715299[/C][/ROW]
[ROW][C]17[/C][C]730[/C][C]677.076671379562[/C][C]52.923328620438[/C][/ROW]
[ROW][C]18[/C][C]740[/C][C]679.264248423123[/C][C]60.7357515768765[/C][/ROW]
[ROW][C]19[/C][C]770[/C][C]681.774750678677[/C][C]88.2252493213226[/C][/ROW]
[ROW][C]20[/C][C]660[/C][C]685.421526781178[/C][C]-25.4215267811783[/C][/ROW]
[ROW][C]21[/C][C]830[/C][C]684.37073217229[/C][C]145.62926782771[/C][/ROW]
[ROW][C]22[/C][C]900[/C][C]690.390293894406[/C][C]209.609706105594[/C][/ROW]
[ROW][C]23[/C][C]630[/C][C]699.054476460715[/C][C]-69.0544764607155[/C][/ROW]
[ROW][C]24[/C][C]770[/C][C]696.200121086661[/C][C]73.7998789133394[/C][/ROW]
[ROW][C]25[/C][C]640[/C][C]699.250626886972[/C][C]-59.2506268869721[/C][/ROW]
[ROW][C]26[/C][C]700[/C][C]696.801512015076[/C][C]3.1984879849241[/C][/ROW]
[ROW][C]27[/C][C]760[/C][C]696.93372098742[/C][C]63.0662790125801[/C][/ROW]
[ROW][C]28[/C][C]500[/C][C]699.540555209436[/C][C]-199.540555209436[/C][/ROW]
[ROW][C]29[/C][C]740[/C][C]691.292579331609[/C][C]48.7074206683909[/C][/ROW]
[ROW][C]30[/C][C]740[/C][C]693.305892516602[/C][C]46.6941074833976[/C][/ROW]
[ROW][C]31[/C][C]680[/C][C]695.235985733771[/C][C]-15.2359857337707[/C][/ROW]
[ROW][C]32[/C][C]580[/C][C]694.606208781035[/C][C]-114.606208781035[/C][/ROW]
[ROW][C]33[/C][C]780[/C][C]689.868980078413[/C][C]90.1310199215868[/C][/ROW]
[ROW][C]34[/C][C]990[/C][C]693.59453089377[/C][C]296.40546910623[/C][/ROW]
[ROW][C]35[/C][C]630[/C][C]705.84640198172[/C][C]-75.8464019817204[/C][/ROW]
[ROW][C]36[/C][C]780[/C][C]702.711303488541[/C][C]77.2886965114585[/C][/ROW]
[ROW][C]37[/C][C]630[/C][C]705.906018987785[/C][C]-75.9060189877847[/C][/ROW]
[ROW][C]38[/C][C]780[/C][C]702.768456235511[/C][C]77.2315437644888[/C][/ROW]
[ROW][C]39[/C][C]730[/C][C]705.960809335402[/C][C]24.0391906645978[/C][/ROW]
[ROW][C]40[/C][C]490[/C][C]706.954465309327[/C][C]-216.954465309327[/C][/ROW]
[ROW][C]41[/C][C]710[/C][C]697.986688334967[/C][C]12.013311665033[/C][/ROW]
[ROW][C]42[/C][C]700[/C][C]698.483256587581[/C][C]1.51674341241892[/C][/ROW]
[ROW][C]43[/C][C]740[/C][C]698.545950925909[/C][C]41.4540490740908[/C][/ROW]
[ROW][C]44[/C][C]520[/C][C]700.259447194587[/C][C]-180.259447194587[/C][/ROW]
[ROW][C]45[/C][C]730[/C][C]692.808452730576[/C][C]37.1915472694244[/C][/ROW]
[ROW][C]46[/C][C]1110[/C][C]694.345759191487[/C][C]415.654240808513[/C][/ROW]
[ROW][C]47[/C][C]510[/C][C]711.526758553279[/C][C]-201.526758553279[/C][/ROW]
[ROW][C]48[/C][C]750[/C][C]703.196683288432[/C][C]46.8033167115683[/C][/ROW]
[ROW][C]49[/C][C]690[/C][C]705.131290651001[/C][C]-15.1312906510009[/C][/ROW]
[ROW][C]50[/C][C]740[/C][C]704.505841252211[/C][C]35.4941587477886[/C][/ROW]
[ROW][C]51[/C][C]690[/C][C]705.972986439054[/C][C]-15.9729864390545[/C][/ROW]
[ROW][C]52[/C][C]640[/C][C]705.312745683946[/C][C]-65.3127456839463[/C][/ROW]
[ROW][C]53[/C][C]660[/C][C]702.613054133272[/C][C]-42.6130541332717[/C][/ROW]
[ROW][C]54[/C][C]580[/C][C]700.851650581984[/C][C]-120.851650581984[/C][/ROW]
[ROW][C]55[/C][C]760[/C][C]695.856267574507[/C][C]64.1437324254928[/C][/ROW]
[ROW][C]56[/C][C]510[/C][C]698.507638155309[/C][C]-188.507638155309[/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]695.64630265966[/C][C]354.35369734034[/C][/ROW]
[ROW][C]59[/C][C]510[/C][C]710.293454186397[/C][C]-200.293454186397[/C][/ROW]
[ROW][C]60[/C][C]740[/C][C]702.014357353765[/C][C]37.9856426462346[/C][/ROW]
[ROW][C]61[/C][C]690[/C][C]703.584487615862[/C][C]-13.584487615862[/C][/ROW]
[ROW][C]62[/C][C]800[/C][C]703.022975064939[/C][C]96.9770249350611[/C][/ROW]
[ROW][C]63[/C][C]670[/C][C]707.031504366305[/C][C]-37.0315043663046[/C][/ROW]
[ROW][C]64[/C][C]670[/C][C]705.500813252349[/C][C]-35.5008132523486[/C][/ROW]
[ROW][C]65[/C][C]640[/C][C]704.033393002659[/C][C]-64.0333930026592[/C][/ROW]
[ROW][C]66[/C][C]540[/C][C]701.386583283668[/C][C]-161.386583283668[/C][/ROW]
[ROW][C]67[/C][C]740[/C][C]694.715695530892[/C][C]45.2843044691076[/C][/ROW]
[ROW][C]68[/C][C]600[/C][C]696.587514773419[/C][C]-96.5875147734185[/C][/ROW]
[ROW][C]69[/C][C]860[/C][C]692.595085810222[/C][C]167.404914189778[/C][/ROW]
[ROW][C]70[/C][C]1080[/C][C]699.514740276542[/C][C]380.485259723458[/C][/ROW]
[ROW][C]71[/C][C]480[/C][C]715.242035616449[/C][C]-235.242035616449[/C][/ROW]
[ROW][C]72[/C][C]680[/C][C]705.518344945253[/C][C]-25.5183449452527[/C][/ROW]
[ROW][C]73[/C][C]650[/C][C]704.46354837355[/C][C]-54.4635483735502[/C][/ROW]
[ROW][C]74[/C][C]860[/C][C]702.212306600997[/C][C]157.787693399003[/C][/ROW]
[ROW][C]75[/C][C]650[/C][C]708.734434835064[/C][C]-58.7344348350645[/C][/ROW]
[ROW][C]76[/C][C]630[/C][C]706.306656676339[/C][C]-76.3066566763391[/C][/ROW]
[ROW][C]77[/C][C]600[/C][C]703.15253363141[/C][C]-103.15253363141[/C][/ROW]
[ROW][C]78[/C][C]500[/C][C]698.888740698512[/C][C]-198.888740698512[/C][/ROW]
[ROW][C]79[/C][C]760[/C][C]690.667707465789[/C][C]69.332292534211[/C][/ROW]
[ROW][C]80[/C][C]590[/C][C]693.533546321336[/C][C]-103.533546321336[/C][/ROW]
[ROW][C]81[/C][C]800[/C][C]689.254004291858[/C][C]110.745995708142[/C][/ROW]
[ROW][C]82[/C][C]1120[/C][C]693.831671724966[/C][C]426.168328275034[/C][/ROW]
[ROW][C]83[/C][C]520[/C][C]711.447269154857[/C][C]-191.447269154857[/C][/ROW]
[ROW][C]84[/C][C]710[/C][C]703.533827918775[/C][C]6.46617208122541[/C][/ROW]
[ROW][C]85[/C][C]600[/C][C]703.801106073292[/C][C]-103.801106073292[/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]706.971007978147[/C][C]-6.97100797814653[/C][/ROW]
[ROW][C]88[/C][C]590[/C][C]706.682862515248[/C][C]-116.682862515248[/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]693.889777334953[/C][C]36.1102226650474[/C][/ROW]
[ROW][C]92[/C][C]600[/C][C]695.382387422018[/C][C]-95.3823874220182[/C][/ROW]
[ROW][C]93[/C][C]880[/C][C]691.439772198759[/C][C]188.560227801241[/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]716.626176181325[/C][C]-176.626176181325[/C][/ROW]
[ROW][C]96[/C][C]740[/C][C]709.32536237429[/C][C]30.6746376257097[/C][/ROW]
[ROW][C]97[/C][C]580[/C][C]710.593293451922[/C][C]-130.593293451922[/C][/ROW]
[ROW][C]98[/C][C]850[/C][C]705.195241246109[/C][C]144.804758753891[/C][/ROW]
[ROW][C]99[/C][C]670[/C][C]711.1807220219[/C][C]-41.1807220218996[/C][/ROW]
[ROW][C]100[/C][C]530[/C][C]709.478523681759[/C][C]-179.478523681759[/C][/ROW]
[ROW][C]101[/C][C]680[/C][C]702.059808562112[/C][C]-22.0598085621118[/C][/ROW]
[ROW][C]102[/C][C]540[/C][C]701.147970020324[/C][C]-161.147970020324[/C][/ROW]
[ROW][C]103[/C][C]760[/C][C]694.486945307361[/C][C]65.5130546926392[/C][/ROW]
[ROW][C]104[/C][C]620[/C][C]697.194916597811[/C][C]-77.1949165978109[/C][/ROW]
[ROW][C]105[/C][C]910[/C][C]694.004077475802[/C][C]215.995922524198[/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]724.718492289631[/C][C]-194.718492289631[/C][/ROW]
[ROW][C]108[/C][C]720[/C][C]716.669835585804[/C][C]3.33016441419579[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169455&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169455&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
3740633.720135128547106.279864871453
4720638.11319578149781.8868042185026
5720641.49797330302878.5020266969724
6690644.74284160545.2571583949996
7790646.613538769039143.386461230961
8760652.540394451076107.459605548924
9840656.982219489991183.017780510009
10840664.547229205814175.452770794186
11640671.799540495062-31.7995404950623
12840670.485111743203169.514888256797
13590677.491981638935-87.4919816389346
14770673.87551503492196.1244849650788
15750677.848804737572.1511952625
16590680.83116247153-90.8311624715299
17730677.07667137956252.923328620438
18740679.26424842312360.7357515768765
19770681.77475067867788.2252493213226
20660685.421526781178-25.4215267811783
21830684.37073217229145.62926782771
22900690.390293894406209.609706105594
23630699.054476460715-69.0544764607155
24770696.20012108666173.7998789133394
25640699.250626886972-59.2506268869721
26700696.8015120150763.1984879849241
27760696.9337209874263.0662790125801
28500699.540555209436-199.540555209436
29740691.29257933160948.7074206683909
30740693.30589251660246.6941074833976
31680695.235985733771-15.2359857337707
32580694.606208781035-114.606208781035
33780689.86898007841390.1310199215868
34990693.59453089377296.40546910623
35630705.84640198172-75.8464019817204
36780702.71130348854177.2886965114585
37630705.906018987785-75.9060189877847
38780702.76845623551177.2315437644888
39730705.96080933540224.0391906645978
40490706.954465309327-216.954465309327
41710697.98668833496712.013311665033
42700698.4832565875811.51674341241892
43740698.54595092590941.4540490740908
44520700.259447194587-180.259447194587
45730692.80845273057637.1915472694244
461110694.345759191487415.654240808513
47510711.526758553279-201.526758553279
48750703.19668328843246.8033167115683
49690705.131290651001-15.1312906510009
50740704.50584125221135.4941587477886
51690705.972986439054-15.9729864390545
52640705.312745683946-65.3127456839463
53660702.613054133272-42.6130541332717
54580700.851650581984-120.851650581984
55760695.85626757450764.1437324254928
56510698.507638155309-188.507638155309
57810690.715706080854119.284293919146
581050695.64630265966354.35369734034
59510710.293454186397-200.293454186397
60740702.01435735376537.9856426462346
61690703.584487615862-13.584487615862
62800703.02297506493996.9770249350611
63670707.031504366305-37.0315043663046
64670705.500813252349-35.5008132523486
65640704.033393002659-64.0333930026592
66540701.386583283668-161.386583283668
67740694.71569553089245.2843044691076
68600696.587514773419-96.5875147734185
69860692.595085810222167.404914189778
701080699.514740276542380.485259723458
71480715.242035616449-235.242035616449
72680705.518344945253-25.5183449452527
73650704.46354837355-54.4635483735502
74860702.212306600997157.787693399003
75650708.734434835064-58.7344348350645
76630706.306656676339-76.3066566763391
77600703.15253363141-103.15253363141
78500698.888740698512-198.888740698512
79760690.66770746578969.332292534211
80590693.533546321336-103.533546321336
81800689.254004291858110.745995708142
821120693.831671724966426.168328275034
83520711.447269154857-191.447269154857
84710703.5338279187756.46617208122541
85600703.801106073292-103.801106073292
86880699.510504505678180.489495494322
87700706.971007978147-6.97100797814653
88590706.682862515248-116.682862515248
89680701.859795673666-21.8597956736655
90530700.956224631571-170.956224631571
91730693.88977733495336.1102226650474
92600695.382387422018-95.3823874220182
93880691.439772198759188.560227801241
941120699.233878057539420.766121942461
95540716.626176181325-176.626176181325
96740709.3253623742930.6746376257097
97580710.593293451922-130.593293451922
98850705.195241246109144.804758753891
99670711.1807220219-41.1807220218996
100530709.478523681759-179.478523681759
101680702.059808562112-22.0598085621118
102540701.147970020324-161.147970020324
103760694.48694530736165.5130546926392
104620697.194916597811-77.1949165978109
105910694.004077475802215.995922524198
1061230702.932233242527527.067766757473
107530724.718492289631-194.718492289631
108720716.6698355858043.33016441419579







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109716.807487381594422.1503806380691011.46459412512
110716.807487381594421.8987671319481011.71620763124
111716.807487381594421.6473681173171011.96760664587
112716.807487381594421.3961830465691012.21879171662
113716.807487381594421.1452113744251012.46976338876
114716.807487381594420.8944525579191012.72052220527
115716.807487381594420.6439060563811012.97106870681
116716.807487381594420.3935713314281013.22140343176
117716.807487381594420.1434478469491013.47152691624
118716.807487381594419.893535069091013.7214396941
119716.807487381594419.6438324662421013.97114229695
120716.807487381594419.3943395090281014.22063525416

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 716.807487381594 & 422.150380638069 & 1011.46459412512 \tabularnewline
110 & 716.807487381594 & 421.898767131948 & 1011.71620763124 \tabularnewline
111 & 716.807487381594 & 421.647368117317 & 1011.96760664587 \tabularnewline
112 & 716.807487381594 & 421.396183046569 & 1012.21879171662 \tabularnewline
113 & 716.807487381594 & 421.145211374425 & 1012.46976338876 \tabularnewline
114 & 716.807487381594 & 420.894452557919 & 1012.72052220527 \tabularnewline
115 & 716.807487381594 & 420.643906056381 & 1012.97106870681 \tabularnewline
116 & 716.807487381594 & 420.393571331428 & 1013.22140343176 \tabularnewline
117 & 716.807487381594 & 420.143447846949 & 1013.47152691624 \tabularnewline
118 & 716.807487381594 & 419.89353506909 & 1013.7214396941 \tabularnewline
119 & 716.807487381594 & 419.643832466242 & 1013.97114229695 \tabularnewline
120 & 716.807487381594 & 419.394339509028 & 1014.22063525416 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169455&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]716.807487381594[/C][C]422.150380638069[/C][C]1011.46459412512[/C][/ROW]
[ROW][C]110[/C][C]716.807487381594[/C][C]421.898767131948[/C][C]1011.71620763124[/C][/ROW]
[ROW][C]111[/C][C]716.807487381594[/C][C]421.647368117317[/C][C]1011.96760664587[/C][/ROW]
[ROW][C]112[/C][C]716.807487381594[/C][C]421.396183046569[/C][C]1012.21879171662[/C][/ROW]
[ROW][C]113[/C][C]716.807487381594[/C][C]421.145211374425[/C][C]1012.46976338876[/C][/ROW]
[ROW][C]114[/C][C]716.807487381594[/C][C]420.894452557919[/C][C]1012.72052220527[/C][/ROW]
[ROW][C]115[/C][C]716.807487381594[/C][C]420.643906056381[/C][C]1012.97106870681[/C][/ROW]
[ROW][C]116[/C][C]716.807487381594[/C][C]420.393571331428[/C][C]1013.22140343176[/C][/ROW]
[ROW][C]117[/C][C]716.807487381594[/C][C]420.143447846949[/C][C]1013.47152691624[/C][/ROW]
[ROW][C]118[/C][C]716.807487381594[/C][C]419.89353506909[/C][C]1013.7214396941[/C][/ROW]
[ROW][C]119[/C][C]716.807487381594[/C][C]419.643832466242[/C][C]1013.97114229695[/C][/ROW]
[ROW][C]120[/C][C]716.807487381594[/C][C]419.394339509028[/C][C]1014.22063525416[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169455&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169455&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
109716.807487381594422.1503806380691011.46459412512
110716.807487381594421.8987671319481011.71620763124
111716.807487381594421.6473681173171011.96760664587
112716.807487381594421.3961830465691012.21879171662
113716.807487381594421.1452113744251012.46976338876
114716.807487381594420.8944525579191012.72052220527
115716.807487381594420.6439060563811012.97106870681
116716.807487381594420.3935713314281013.22140343176
117716.807487381594420.1434478469491013.47152691624
118716.807487381594419.893535069091013.7214396941
119716.807487381594419.6438324662421013.97114229695
120716.807487381594419.3943395090281014.22063525416



Parameters (Session):
par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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')