Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 23 Apr 2015 12:15:24 +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/2015/Apr/23/t1429787754ycmuav3yvhuppnf.htm/, Retrieved Thu, 09 May 2024 12:36:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278843, Retrieved Thu, 09 May 2024 12:36:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact102
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-04-23 11:15:24] [57f5dbee1b697c074ab0c7d81efd3c32] [Current]
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Dataseries X:
732
768
902
739
744
848
745
752
833
703
824
759
797
840
988
819
831
904
814
798
828
789
930
744
832
826
907
776
835
715
729
733
736
712
711
667
799
661
692
649
729
622
671
635
648
744
624
476
710
515
461
590
415
554
585
513
591
561
684
668
795
776
1043
964
762
1030
939
779
918
839
874
840
794
820
1003
780
607
1001
743
810
716
775
883
633
755
782
882
694
896
674
702
799
791
797
1021
738
1023
955
912
850
1011
872
1074
811
878
1081
956
812
1125
1051
1090
1028
1178
1041
1146
866
875
1116
903
887




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278843&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278843&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278843&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.325934913160014
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.325934913160014 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278843&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]0.325934913160014[/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=278843&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278843&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
alpha0.325934913160014
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
276873236
3902743.733656873761158.266343126239
4739795.318183676764-56.3181836767644
5744776.962121370748-32.9621213707484
6848766.21861520420481.7813847957964
7745792.874023755727-47.8740237557272
8752777.270207980284-25.2702079802838
9833769.03376493669463.9662350633056
10703789.882594207226-86.8825942072259
11824761.56452340917762.4354765908231
12759781.914425049911-22.914425049911
13797774.44581391115722.5541860888434
14840781.79701059541958.2029894045814
15988800.767396892654187.232603107346
16819861.79303912717-42.7930391271702
17831847.845293635403-16.8452936354029
18904842.35482431719361.6451756828071
19814862.447139300102-48.4471393001024
20798846.656525159472-48.6565251594724
21828830.797664856952-2.79766485695166
22789829.88580820475-40.8858082047502
23930816.559695858058113.440304141942
24744853.533851537407-109.533851537407
25832817.83294514848114.1670548515194
26826822.4504829412443.54951705875635
27907823.60739447554983.3926055244506
28776850.787956115348-74.7879561153485
29835826.4119501334778.58804986652262
30715829.211095420936-114.211095420936
31729791.985711953003-62.9857119530033
32733771.45646939728-38.4564693972795
33736758.922163383837-22.9221633838365
34712751.451030051886-39.4510300518861
35711738.592561997851-27.5925619978514
36667729.599182699219-62.5991826992193
37799709.19592352226189.8040764777386
38661738.466207390448-77.4662073904484
39692713.217265811807-21.2172658118069
40649706.301818121943-57.3018181219427
41729687.62515500845641.3748449915437
42622701.110661517784-79.1106615177841
43671675.325734925954-4.32573492595384
44635673.91582688851-38.9158268885099
45648661.231800231053-13.2318002310532
46744656.91909457179487.0809054282058
47624685.301801920432-61.3018019204319
48476665.321404434943-189.321404434943
49710603.614948921108106.385051078892
50515638.28955130603-123.28955130603
51461598.105182107562-137.105182107562
52590553.41781648354636.5821835164541
53415565.341227291185-150.341227291185
54554516.33977242966337.6602275703374
55585528.61455543238756.3854445676131
56513546.992540411021-33.9925404110206
57591535.91318470406655.0868152959338
58561553.8679010638087.13209893619194
59684556.192501111224127.807498888776
60668597.84942716273670.1505728372639
61795620.713948028575174.286051971425
62776677.51985724288398.4801427571169
631043709.61797402041333.38202597959
64964818.278815707177145.721184292823
65762865.774437255233-103.774437255233
661030831.950725060219198.049274939781
67939896.5018982891242.4981017108797
68779910.353513379721-131.353513379721
69918867.54081740303950.459182596961
70839883.987226700905-44.9872267009048
71874869.3243188728354.67568112716458
72840870.848286594982-30.8482865949816
73794860.793752982511-66.793752982511
74820839.023336904525-19.0233369045247
751003832.822967242535170.177032757465
76780888.289603636168-108.289603636168
77607852.994241078881-245.994241078881
781001772.816129474972228.183870525028
79743847.189219499063-104.189219499063
80810813.230315289426-3.23031528942636
81716812.177442756088-96.1774427560877
82775780.82985630343-5.82985630343001
83883778.929702595436104.070297404564
84633812.84984594253-179.84984594253
85755754.2305020234090.769497976590856
86782754.48130827958627.5186917204139
87882763.450610675756118.549389324244
88694802.089995590326-108.089995590326
89896766.859692264127129.140307735873
90674808.951027251476-134.951027251476
91702764.965775903412-62.9657759034116
92799744.4430312022854.5569687977199
93791762.22505208963828.7749479103616
94797771.60381223798625.3961877620141
951021779.881316490793241.118683509207
96738858.470313661624-120.470313661624
971023819.204832439963203.795167560037
98955885.62879268107469.3712073189261
99912908.2392911143733.76070888562663
100850909.46503743843-59.4650374384302
1011011890.083305624878120.916694375122
102872929.49427790563-57.4942779056296
1031074910.75488542926163.24511457074
104811963.962167670671-152.962167670671
105878914.106456834163-36.1064568341633
1061081902.338101961404178.661898038596
107956960.570252183617-4.57025218361741
108812959.080647435031-147.080647435031
1091125911.141929385775213.858070614225
1101051980.84574105999170.1542589400092
11110901003.7114633554186.2885366445921
11210281031.83591005337-3.83591005336757
11311781030.58565304323147.414346956766
11410411078.63313541713-37.6331354171275
11511461066.3671826930179.632817306993
1168661092.32229808665-226.322298086649
1178751018.5559595136-143.555959513602
1181116971.766060315934144.233939684066
1199031018.77693692159-115.776936921586
120887981.041191040117-94.0411910401166

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 768 & 732 & 36 \tabularnewline
3 & 902 & 743.733656873761 & 158.266343126239 \tabularnewline
4 & 739 & 795.318183676764 & -56.3181836767644 \tabularnewline
5 & 744 & 776.962121370748 & -32.9621213707484 \tabularnewline
6 & 848 & 766.218615204204 & 81.7813847957964 \tabularnewline
7 & 745 & 792.874023755727 & -47.8740237557272 \tabularnewline
8 & 752 & 777.270207980284 & -25.2702079802838 \tabularnewline
9 & 833 & 769.033764936694 & 63.9662350633056 \tabularnewline
10 & 703 & 789.882594207226 & -86.8825942072259 \tabularnewline
11 & 824 & 761.564523409177 & 62.4354765908231 \tabularnewline
12 & 759 & 781.914425049911 & -22.914425049911 \tabularnewline
13 & 797 & 774.445813911157 & 22.5541860888434 \tabularnewline
14 & 840 & 781.797010595419 & 58.2029894045814 \tabularnewline
15 & 988 & 800.767396892654 & 187.232603107346 \tabularnewline
16 & 819 & 861.79303912717 & -42.7930391271702 \tabularnewline
17 & 831 & 847.845293635403 & -16.8452936354029 \tabularnewline
18 & 904 & 842.354824317193 & 61.6451756828071 \tabularnewline
19 & 814 & 862.447139300102 & -48.4471393001024 \tabularnewline
20 & 798 & 846.656525159472 & -48.6565251594724 \tabularnewline
21 & 828 & 830.797664856952 & -2.79766485695166 \tabularnewline
22 & 789 & 829.88580820475 & -40.8858082047502 \tabularnewline
23 & 930 & 816.559695858058 & 113.440304141942 \tabularnewline
24 & 744 & 853.533851537407 & -109.533851537407 \tabularnewline
25 & 832 & 817.832945148481 & 14.1670548515194 \tabularnewline
26 & 826 & 822.450482941244 & 3.54951705875635 \tabularnewline
27 & 907 & 823.607394475549 & 83.3926055244506 \tabularnewline
28 & 776 & 850.787956115348 & -74.7879561153485 \tabularnewline
29 & 835 & 826.411950133477 & 8.58804986652262 \tabularnewline
30 & 715 & 829.211095420936 & -114.211095420936 \tabularnewline
31 & 729 & 791.985711953003 & -62.9857119530033 \tabularnewline
32 & 733 & 771.45646939728 & -38.4564693972795 \tabularnewline
33 & 736 & 758.922163383837 & -22.9221633838365 \tabularnewline
34 & 712 & 751.451030051886 & -39.4510300518861 \tabularnewline
35 & 711 & 738.592561997851 & -27.5925619978514 \tabularnewline
36 & 667 & 729.599182699219 & -62.5991826992193 \tabularnewline
37 & 799 & 709.195923522261 & 89.8040764777386 \tabularnewline
38 & 661 & 738.466207390448 & -77.4662073904484 \tabularnewline
39 & 692 & 713.217265811807 & -21.2172658118069 \tabularnewline
40 & 649 & 706.301818121943 & -57.3018181219427 \tabularnewline
41 & 729 & 687.625155008456 & 41.3748449915437 \tabularnewline
42 & 622 & 701.110661517784 & -79.1106615177841 \tabularnewline
43 & 671 & 675.325734925954 & -4.32573492595384 \tabularnewline
44 & 635 & 673.91582688851 & -38.9158268885099 \tabularnewline
45 & 648 & 661.231800231053 & -13.2318002310532 \tabularnewline
46 & 744 & 656.919094571794 & 87.0809054282058 \tabularnewline
47 & 624 & 685.301801920432 & -61.3018019204319 \tabularnewline
48 & 476 & 665.321404434943 & -189.321404434943 \tabularnewline
49 & 710 & 603.614948921108 & 106.385051078892 \tabularnewline
50 & 515 & 638.28955130603 & -123.28955130603 \tabularnewline
51 & 461 & 598.105182107562 & -137.105182107562 \tabularnewline
52 & 590 & 553.417816483546 & 36.5821835164541 \tabularnewline
53 & 415 & 565.341227291185 & -150.341227291185 \tabularnewline
54 & 554 & 516.339772429663 & 37.6602275703374 \tabularnewline
55 & 585 & 528.614555432387 & 56.3854445676131 \tabularnewline
56 & 513 & 546.992540411021 & -33.9925404110206 \tabularnewline
57 & 591 & 535.913184704066 & 55.0868152959338 \tabularnewline
58 & 561 & 553.867901063808 & 7.13209893619194 \tabularnewline
59 & 684 & 556.192501111224 & 127.807498888776 \tabularnewline
60 & 668 & 597.849427162736 & 70.1505728372639 \tabularnewline
61 & 795 & 620.713948028575 & 174.286051971425 \tabularnewline
62 & 776 & 677.519857242883 & 98.4801427571169 \tabularnewline
63 & 1043 & 709.61797402041 & 333.38202597959 \tabularnewline
64 & 964 & 818.278815707177 & 145.721184292823 \tabularnewline
65 & 762 & 865.774437255233 & -103.774437255233 \tabularnewline
66 & 1030 & 831.950725060219 & 198.049274939781 \tabularnewline
67 & 939 & 896.50189828912 & 42.4981017108797 \tabularnewline
68 & 779 & 910.353513379721 & -131.353513379721 \tabularnewline
69 & 918 & 867.540817403039 & 50.459182596961 \tabularnewline
70 & 839 & 883.987226700905 & -44.9872267009048 \tabularnewline
71 & 874 & 869.324318872835 & 4.67568112716458 \tabularnewline
72 & 840 & 870.848286594982 & -30.8482865949816 \tabularnewline
73 & 794 & 860.793752982511 & -66.793752982511 \tabularnewline
74 & 820 & 839.023336904525 & -19.0233369045247 \tabularnewline
75 & 1003 & 832.822967242535 & 170.177032757465 \tabularnewline
76 & 780 & 888.289603636168 & -108.289603636168 \tabularnewline
77 & 607 & 852.994241078881 & -245.994241078881 \tabularnewline
78 & 1001 & 772.816129474972 & 228.183870525028 \tabularnewline
79 & 743 & 847.189219499063 & -104.189219499063 \tabularnewline
80 & 810 & 813.230315289426 & -3.23031528942636 \tabularnewline
81 & 716 & 812.177442756088 & -96.1774427560877 \tabularnewline
82 & 775 & 780.82985630343 & -5.82985630343001 \tabularnewline
83 & 883 & 778.929702595436 & 104.070297404564 \tabularnewline
84 & 633 & 812.84984594253 & -179.84984594253 \tabularnewline
85 & 755 & 754.230502023409 & 0.769497976590856 \tabularnewline
86 & 782 & 754.481308279586 & 27.5186917204139 \tabularnewline
87 & 882 & 763.450610675756 & 118.549389324244 \tabularnewline
88 & 694 & 802.089995590326 & -108.089995590326 \tabularnewline
89 & 896 & 766.859692264127 & 129.140307735873 \tabularnewline
90 & 674 & 808.951027251476 & -134.951027251476 \tabularnewline
91 & 702 & 764.965775903412 & -62.9657759034116 \tabularnewline
92 & 799 & 744.44303120228 & 54.5569687977199 \tabularnewline
93 & 791 & 762.225052089638 & 28.7749479103616 \tabularnewline
94 & 797 & 771.603812237986 & 25.3961877620141 \tabularnewline
95 & 1021 & 779.881316490793 & 241.118683509207 \tabularnewline
96 & 738 & 858.470313661624 & -120.470313661624 \tabularnewline
97 & 1023 & 819.204832439963 & 203.795167560037 \tabularnewline
98 & 955 & 885.628792681074 & 69.3712073189261 \tabularnewline
99 & 912 & 908.239291114373 & 3.76070888562663 \tabularnewline
100 & 850 & 909.46503743843 & -59.4650374384302 \tabularnewline
101 & 1011 & 890.083305624878 & 120.916694375122 \tabularnewline
102 & 872 & 929.49427790563 & -57.4942779056296 \tabularnewline
103 & 1074 & 910.75488542926 & 163.24511457074 \tabularnewline
104 & 811 & 963.962167670671 & -152.962167670671 \tabularnewline
105 & 878 & 914.106456834163 & -36.1064568341633 \tabularnewline
106 & 1081 & 902.338101961404 & 178.661898038596 \tabularnewline
107 & 956 & 960.570252183617 & -4.57025218361741 \tabularnewline
108 & 812 & 959.080647435031 & -147.080647435031 \tabularnewline
109 & 1125 & 911.141929385775 & 213.858070614225 \tabularnewline
110 & 1051 & 980.845741059991 & 70.1542589400092 \tabularnewline
111 & 1090 & 1003.71146335541 & 86.2885366445921 \tabularnewline
112 & 1028 & 1031.83591005337 & -3.83591005336757 \tabularnewline
113 & 1178 & 1030.58565304323 & 147.414346956766 \tabularnewline
114 & 1041 & 1078.63313541713 & -37.6331354171275 \tabularnewline
115 & 1146 & 1066.36718269301 & 79.632817306993 \tabularnewline
116 & 866 & 1092.32229808665 & -226.322298086649 \tabularnewline
117 & 875 & 1018.5559595136 & -143.555959513602 \tabularnewline
118 & 1116 & 971.766060315934 & 144.233939684066 \tabularnewline
119 & 903 & 1018.77693692159 & -115.776936921586 \tabularnewline
120 & 887 & 981.041191040117 & -94.0411910401166 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278843&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]768[/C][C]732[/C][C]36[/C][/ROW]
[ROW][C]3[/C][C]902[/C][C]743.733656873761[/C][C]158.266343126239[/C][/ROW]
[ROW][C]4[/C][C]739[/C][C]795.318183676764[/C][C]-56.3181836767644[/C][/ROW]
[ROW][C]5[/C][C]744[/C][C]776.962121370748[/C][C]-32.9621213707484[/C][/ROW]
[ROW][C]6[/C][C]848[/C][C]766.218615204204[/C][C]81.7813847957964[/C][/ROW]
[ROW][C]7[/C][C]745[/C][C]792.874023755727[/C][C]-47.8740237557272[/C][/ROW]
[ROW][C]8[/C][C]752[/C][C]777.270207980284[/C][C]-25.2702079802838[/C][/ROW]
[ROW][C]9[/C][C]833[/C][C]769.033764936694[/C][C]63.9662350633056[/C][/ROW]
[ROW][C]10[/C][C]703[/C][C]789.882594207226[/C][C]-86.8825942072259[/C][/ROW]
[ROW][C]11[/C][C]824[/C][C]761.564523409177[/C][C]62.4354765908231[/C][/ROW]
[ROW][C]12[/C][C]759[/C][C]781.914425049911[/C][C]-22.914425049911[/C][/ROW]
[ROW][C]13[/C][C]797[/C][C]774.445813911157[/C][C]22.5541860888434[/C][/ROW]
[ROW][C]14[/C][C]840[/C][C]781.797010595419[/C][C]58.2029894045814[/C][/ROW]
[ROW][C]15[/C][C]988[/C][C]800.767396892654[/C][C]187.232603107346[/C][/ROW]
[ROW][C]16[/C][C]819[/C][C]861.79303912717[/C][C]-42.7930391271702[/C][/ROW]
[ROW][C]17[/C][C]831[/C][C]847.845293635403[/C][C]-16.8452936354029[/C][/ROW]
[ROW][C]18[/C][C]904[/C][C]842.354824317193[/C][C]61.6451756828071[/C][/ROW]
[ROW][C]19[/C][C]814[/C][C]862.447139300102[/C][C]-48.4471393001024[/C][/ROW]
[ROW][C]20[/C][C]798[/C][C]846.656525159472[/C][C]-48.6565251594724[/C][/ROW]
[ROW][C]21[/C][C]828[/C][C]830.797664856952[/C][C]-2.79766485695166[/C][/ROW]
[ROW][C]22[/C][C]789[/C][C]829.88580820475[/C][C]-40.8858082047502[/C][/ROW]
[ROW][C]23[/C][C]930[/C][C]816.559695858058[/C][C]113.440304141942[/C][/ROW]
[ROW][C]24[/C][C]744[/C][C]853.533851537407[/C][C]-109.533851537407[/C][/ROW]
[ROW][C]25[/C][C]832[/C][C]817.832945148481[/C][C]14.1670548515194[/C][/ROW]
[ROW][C]26[/C][C]826[/C][C]822.450482941244[/C][C]3.54951705875635[/C][/ROW]
[ROW][C]27[/C][C]907[/C][C]823.607394475549[/C][C]83.3926055244506[/C][/ROW]
[ROW][C]28[/C][C]776[/C][C]850.787956115348[/C][C]-74.7879561153485[/C][/ROW]
[ROW][C]29[/C][C]835[/C][C]826.411950133477[/C][C]8.58804986652262[/C][/ROW]
[ROW][C]30[/C][C]715[/C][C]829.211095420936[/C][C]-114.211095420936[/C][/ROW]
[ROW][C]31[/C][C]729[/C][C]791.985711953003[/C][C]-62.9857119530033[/C][/ROW]
[ROW][C]32[/C][C]733[/C][C]771.45646939728[/C][C]-38.4564693972795[/C][/ROW]
[ROW][C]33[/C][C]736[/C][C]758.922163383837[/C][C]-22.9221633838365[/C][/ROW]
[ROW][C]34[/C][C]712[/C][C]751.451030051886[/C][C]-39.4510300518861[/C][/ROW]
[ROW][C]35[/C][C]711[/C][C]738.592561997851[/C][C]-27.5925619978514[/C][/ROW]
[ROW][C]36[/C][C]667[/C][C]729.599182699219[/C][C]-62.5991826992193[/C][/ROW]
[ROW][C]37[/C][C]799[/C][C]709.195923522261[/C][C]89.8040764777386[/C][/ROW]
[ROW][C]38[/C][C]661[/C][C]738.466207390448[/C][C]-77.4662073904484[/C][/ROW]
[ROW][C]39[/C][C]692[/C][C]713.217265811807[/C][C]-21.2172658118069[/C][/ROW]
[ROW][C]40[/C][C]649[/C][C]706.301818121943[/C][C]-57.3018181219427[/C][/ROW]
[ROW][C]41[/C][C]729[/C][C]687.625155008456[/C][C]41.3748449915437[/C][/ROW]
[ROW][C]42[/C][C]622[/C][C]701.110661517784[/C][C]-79.1106615177841[/C][/ROW]
[ROW][C]43[/C][C]671[/C][C]675.325734925954[/C][C]-4.32573492595384[/C][/ROW]
[ROW][C]44[/C][C]635[/C][C]673.91582688851[/C][C]-38.9158268885099[/C][/ROW]
[ROW][C]45[/C][C]648[/C][C]661.231800231053[/C][C]-13.2318002310532[/C][/ROW]
[ROW][C]46[/C][C]744[/C][C]656.919094571794[/C][C]87.0809054282058[/C][/ROW]
[ROW][C]47[/C][C]624[/C][C]685.301801920432[/C][C]-61.3018019204319[/C][/ROW]
[ROW][C]48[/C][C]476[/C][C]665.321404434943[/C][C]-189.321404434943[/C][/ROW]
[ROW][C]49[/C][C]710[/C][C]603.614948921108[/C][C]106.385051078892[/C][/ROW]
[ROW][C]50[/C][C]515[/C][C]638.28955130603[/C][C]-123.28955130603[/C][/ROW]
[ROW][C]51[/C][C]461[/C][C]598.105182107562[/C][C]-137.105182107562[/C][/ROW]
[ROW][C]52[/C][C]590[/C][C]553.417816483546[/C][C]36.5821835164541[/C][/ROW]
[ROW][C]53[/C][C]415[/C][C]565.341227291185[/C][C]-150.341227291185[/C][/ROW]
[ROW][C]54[/C][C]554[/C][C]516.339772429663[/C][C]37.6602275703374[/C][/ROW]
[ROW][C]55[/C][C]585[/C][C]528.614555432387[/C][C]56.3854445676131[/C][/ROW]
[ROW][C]56[/C][C]513[/C][C]546.992540411021[/C][C]-33.9925404110206[/C][/ROW]
[ROW][C]57[/C][C]591[/C][C]535.913184704066[/C][C]55.0868152959338[/C][/ROW]
[ROW][C]58[/C][C]561[/C][C]553.867901063808[/C][C]7.13209893619194[/C][/ROW]
[ROW][C]59[/C][C]684[/C][C]556.192501111224[/C][C]127.807498888776[/C][/ROW]
[ROW][C]60[/C][C]668[/C][C]597.849427162736[/C][C]70.1505728372639[/C][/ROW]
[ROW][C]61[/C][C]795[/C][C]620.713948028575[/C][C]174.286051971425[/C][/ROW]
[ROW][C]62[/C][C]776[/C][C]677.519857242883[/C][C]98.4801427571169[/C][/ROW]
[ROW][C]63[/C][C]1043[/C][C]709.61797402041[/C][C]333.38202597959[/C][/ROW]
[ROW][C]64[/C][C]964[/C][C]818.278815707177[/C][C]145.721184292823[/C][/ROW]
[ROW][C]65[/C][C]762[/C][C]865.774437255233[/C][C]-103.774437255233[/C][/ROW]
[ROW][C]66[/C][C]1030[/C][C]831.950725060219[/C][C]198.049274939781[/C][/ROW]
[ROW][C]67[/C][C]939[/C][C]896.50189828912[/C][C]42.4981017108797[/C][/ROW]
[ROW][C]68[/C][C]779[/C][C]910.353513379721[/C][C]-131.353513379721[/C][/ROW]
[ROW][C]69[/C][C]918[/C][C]867.540817403039[/C][C]50.459182596961[/C][/ROW]
[ROW][C]70[/C][C]839[/C][C]883.987226700905[/C][C]-44.9872267009048[/C][/ROW]
[ROW][C]71[/C][C]874[/C][C]869.324318872835[/C][C]4.67568112716458[/C][/ROW]
[ROW][C]72[/C][C]840[/C][C]870.848286594982[/C][C]-30.8482865949816[/C][/ROW]
[ROW][C]73[/C][C]794[/C][C]860.793752982511[/C][C]-66.793752982511[/C][/ROW]
[ROW][C]74[/C][C]820[/C][C]839.023336904525[/C][C]-19.0233369045247[/C][/ROW]
[ROW][C]75[/C][C]1003[/C][C]832.822967242535[/C][C]170.177032757465[/C][/ROW]
[ROW][C]76[/C][C]780[/C][C]888.289603636168[/C][C]-108.289603636168[/C][/ROW]
[ROW][C]77[/C][C]607[/C][C]852.994241078881[/C][C]-245.994241078881[/C][/ROW]
[ROW][C]78[/C][C]1001[/C][C]772.816129474972[/C][C]228.183870525028[/C][/ROW]
[ROW][C]79[/C][C]743[/C][C]847.189219499063[/C][C]-104.189219499063[/C][/ROW]
[ROW][C]80[/C][C]810[/C][C]813.230315289426[/C][C]-3.23031528942636[/C][/ROW]
[ROW][C]81[/C][C]716[/C][C]812.177442756088[/C][C]-96.1774427560877[/C][/ROW]
[ROW][C]82[/C][C]775[/C][C]780.82985630343[/C][C]-5.82985630343001[/C][/ROW]
[ROW][C]83[/C][C]883[/C][C]778.929702595436[/C][C]104.070297404564[/C][/ROW]
[ROW][C]84[/C][C]633[/C][C]812.84984594253[/C][C]-179.84984594253[/C][/ROW]
[ROW][C]85[/C][C]755[/C][C]754.230502023409[/C][C]0.769497976590856[/C][/ROW]
[ROW][C]86[/C][C]782[/C][C]754.481308279586[/C][C]27.5186917204139[/C][/ROW]
[ROW][C]87[/C][C]882[/C][C]763.450610675756[/C][C]118.549389324244[/C][/ROW]
[ROW][C]88[/C][C]694[/C][C]802.089995590326[/C][C]-108.089995590326[/C][/ROW]
[ROW][C]89[/C][C]896[/C][C]766.859692264127[/C][C]129.140307735873[/C][/ROW]
[ROW][C]90[/C][C]674[/C][C]808.951027251476[/C][C]-134.951027251476[/C][/ROW]
[ROW][C]91[/C][C]702[/C][C]764.965775903412[/C][C]-62.9657759034116[/C][/ROW]
[ROW][C]92[/C][C]799[/C][C]744.44303120228[/C][C]54.5569687977199[/C][/ROW]
[ROW][C]93[/C][C]791[/C][C]762.225052089638[/C][C]28.7749479103616[/C][/ROW]
[ROW][C]94[/C][C]797[/C][C]771.603812237986[/C][C]25.3961877620141[/C][/ROW]
[ROW][C]95[/C][C]1021[/C][C]779.881316490793[/C][C]241.118683509207[/C][/ROW]
[ROW][C]96[/C][C]738[/C][C]858.470313661624[/C][C]-120.470313661624[/C][/ROW]
[ROW][C]97[/C][C]1023[/C][C]819.204832439963[/C][C]203.795167560037[/C][/ROW]
[ROW][C]98[/C][C]955[/C][C]885.628792681074[/C][C]69.3712073189261[/C][/ROW]
[ROW][C]99[/C][C]912[/C][C]908.239291114373[/C][C]3.76070888562663[/C][/ROW]
[ROW][C]100[/C][C]850[/C][C]909.46503743843[/C][C]-59.4650374384302[/C][/ROW]
[ROW][C]101[/C][C]1011[/C][C]890.083305624878[/C][C]120.916694375122[/C][/ROW]
[ROW][C]102[/C][C]872[/C][C]929.49427790563[/C][C]-57.4942779056296[/C][/ROW]
[ROW][C]103[/C][C]1074[/C][C]910.75488542926[/C][C]163.24511457074[/C][/ROW]
[ROW][C]104[/C][C]811[/C][C]963.962167670671[/C][C]-152.962167670671[/C][/ROW]
[ROW][C]105[/C][C]878[/C][C]914.106456834163[/C][C]-36.1064568341633[/C][/ROW]
[ROW][C]106[/C][C]1081[/C][C]902.338101961404[/C][C]178.661898038596[/C][/ROW]
[ROW][C]107[/C][C]956[/C][C]960.570252183617[/C][C]-4.57025218361741[/C][/ROW]
[ROW][C]108[/C][C]812[/C][C]959.080647435031[/C][C]-147.080647435031[/C][/ROW]
[ROW][C]109[/C][C]1125[/C][C]911.141929385775[/C][C]213.858070614225[/C][/ROW]
[ROW][C]110[/C][C]1051[/C][C]980.845741059991[/C][C]70.1542589400092[/C][/ROW]
[ROW][C]111[/C][C]1090[/C][C]1003.71146335541[/C][C]86.2885366445921[/C][/ROW]
[ROW][C]112[/C][C]1028[/C][C]1031.83591005337[/C][C]-3.83591005336757[/C][/ROW]
[ROW][C]113[/C][C]1178[/C][C]1030.58565304323[/C][C]147.414346956766[/C][/ROW]
[ROW][C]114[/C][C]1041[/C][C]1078.63313541713[/C][C]-37.6331354171275[/C][/ROW]
[ROW][C]115[/C][C]1146[/C][C]1066.36718269301[/C][C]79.632817306993[/C][/ROW]
[ROW][C]116[/C][C]866[/C][C]1092.32229808665[/C][C]-226.322298086649[/C][/ROW]
[ROW][C]117[/C][C]875[/C][C]1018.5559595136[/C][C]-143.555959513602[/C][/ROW]
[ROW][C]118[/C][C]1116[/C][C]971.766060315934[/C][C]144.233939684066[/C][/ROW]
[ROW][C]119[/C][C]903[/C][C]1018.77693692159[/C][C]-115.776936921586[/C][/ROW]
[ROW][C]120[/C][C]887[/C][C]981.041191040117[/C][C]-94.0411910401166[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278843&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278843&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
276873236
3902743.733656873761158.266343126239
4739795.318183676764-56.3181836767644
5744776.962121370748-32.9621213707484
6848766.21861520420481.7813847957964
7745792.874023755727-47.8740237557272
8752777.270207980284-25.2702079802838
9833769.03376493669463.9662350633056
10703789.882594207226-86.8825942072259
11824761.56452340917762.4354765908231
12759781.914425049911-22.914425049911
13797774.44581391115722.5541860888434
14840781.79701059541958.2029894045814
15988800.767396892654187.232603107346
16819861.79303912717-42.7930391271702
17831847.845293635403-16.8452936354029
18904842.35482431719361.6451756828071
19814862.447139300102-48.4471393001024
20798846.656525159472-48.6565251594724
21828830.797664856952-2.79766485695166
22789829.88580820475-40.8858082047502
23930816.559695858058113.440304141942
24744853.533851537407-109.533851537407
25832817.83294514848114.1670548515194
26826822.4504829412443.54951705875635
27907823.60739447554983.3926055244506
28776850.787956115348-74.7879561153485
29835826.4119501334778.58804986652262
30715829.211095420936-114.211095420936
31729791.985711953003-62.9857119530033
32733771.45646939728-38.4564693972795
33736758.922163383837-22.9221633838365
34712751.451030051886-39.4510300518861
35711738.592561997851-27.5925619978514
36667729.599182699219-62.5991826992193
37799709.19592352226189.8040764777386
38661738.466207390448-77.4662073904484
39692713.217265811807-21.2172658118069
40649706.301818121943-57.3018181219427
41729687.62515500845641.3748449915437
42622701.110661517784-79.1106615177841
43671675.325734925954-4.32573492595384
44635673.91582688851-38.9158268885099
45648661.231800231053-13.2318002310532
46744656.91909457179487.0809054282058
47624685.301801920432-61.3018019204319
48476665.321404434943-189.321404434943
49710603.614948921108106.385051078892
50515638.28955130603-123.28955130603
51461598.105182107562-137.105182107562
52590553.41781648354636.5821835164541
53415565.341227291185-150.341227291185
54554516.33977242966337.6602275703374
55585528.61455543238756.3854445676131
56513546.992540411021-33.9925404110206
57591535.91318470406655.0868152959338
58561553.8679010638087.13209893619194
59684556.192501111224127.807498888776
60668597.84942716273670.1505728372639
61795620.713948028575174.286051971425
62776677.51985724288398.4801427571169
631043709.61797402041333.38202597959
64964818.278815707177145.721184292823
65762865.774437255233-103.774437255233
661030831.950725060219198.049274939781
67939896.5018982891242.4981017108797
68779910.353513379721-131.353513379721
69918867.54081740303950.459182596961
70839883.987226700905-44.9872267009048
71874869.3243188728354.67568112716458
72840870.848286594982-30.8482865949816
73794860.793752982511-66.793752982511
74820839.023336904525-19.0233369045247
751003832.822967242535170.177032757465
76780888.289603636168-108.289603636168
77607852.994241078881-245.994241078881
781001772.816129474972228.183870525028
79743847.189219499063-104.189219499063
80810813.230315289426-3.23031528942636
81716812.177442756088-96.1774427560877
82775780.82985630343-5.82985630343001
83883778.929702595436104.070297404564
84633812.84984594253-179.84984594253
85755754.2305020234090.769497976590856
86782754.48130827958627.5186917204139
87882763.450610675756118.549389324244
88694802.089995590326-108.089995590326
89896766.859692264127129.140307735873
90674808.951027251476-134.951027251476
91702764.965775903412-62.9657759034116
92799744.4430312022854.5569687977199
93791762.22505208963828.7749479103616
94797771.60381223798625.3961877620141
951021779.881316490793241.118683509207
96738858.470313661624-120.470313661624
971023819.204832439963203.795167560037
98955885.62879268107469.3712073189261
99912908.2392911143733.76070888562663
100850909.46503743843-59.4650374384302
1011011890.083305624878120.916694375122
102872929.49427790563-57.4942779056296
1031074910.75488542926163.24511457074
104811963.962167670671-152.962167670671
105878914.106456834163-36.1064568341633
1061081902.338101961404178.661898038596
107956960.570252183617-4.57025218361741
108812959.080647435031-147.080647435031
1091125911.141929385775213.858070614225
1101051980.84574105999170.1542589400092
11110901003.7114633554186.2885366445921
11210281031.83591005337-3.83591005336757
11311781030.58565304323147.414346956766
11410411078.63313541713-37.6331354171275
11511461066.3671826930179.632817306993
1168661092.32229808665-226.322298086649
1178751018.5559595136-143.555959513602
1181116971.766060315934144.233939684066
1199031018.77693692159-115.776936921586
120887981.041191040117-94.0411910401166







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121950.389883604992742.5522655760621158.22750163392
122950.389883604992731.7911846944941168.98858251549
123950.389883604992721.5355481363671179.24421907362
124950.389883604992711.7201901786811189.0595770313
125950.389883604992702.2928496492581198.48691756073
126950.389883604992693.2108526653451207.56891454464
127950.389883604992684.4388173306131216.34094987937
128950.389883604992675.947020061591224.83274714839
129950.389883604992667.7102043789721233.06956283101
130950.389883604992659.7066939555921241.07307325439
131950.389883604992651.9177200081631248.86204720182
132950.389883604992644.3269029301061256.45286427988

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 950.389883604992 & 742.552265576062 & 1158.22750163392 \tabularnewline
122 & 950.389883604992 & 731.791184694494 & 1168.98858251549 \tabularnewline
123 & 950.389883604992 & 721.535548136367 & 1179.24421907362 \tabularnewline
124 & 950.389883604992 & 711.720190178681 & 1189.0595770313 \tabularnewline
125 & 950.389883604992 & 702.292849649258 & 1198.48691756073 \tabularnewline
126 & 950.389883604992 & 693.210852665345 & 1207.56891454464 \tabularnewline
127 & 950.389883604992 & 684.438817330613 & 1216.34094987937 \tabularnewline
128 & 950.389883604992 & 675.94702006159 & 1224.83274714839 \tabularnewline
129 & 950.389883604992 & 667.710204378972 & 1233.06956283101 \tabularnewline
130 & 950.389883604992 & 659.706693955592 & 1241.07307325439 \tabularnewline
131 & 950.389883604992 & 651.917720008163 & 1248.86204720182 \tabularnewline
132 & 950.389883604992 & 644.326902930106 & 1256.45286427988 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278843&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]121[/C][C]950.389883604992[/C][C]742.552265576062[/C][C]1158.22750163392[/C][/ROW]
[ROW][C]122[/C][C]950.389883604992[/C][C]731.791184694494[/C][C]1168.98858251549[/C][/ROW]
[ROW][C]123[/C][C]950.389883604992[/C][C]721.535548136367[/C][C]1179.24421907362[/C][/ROW]
[ROW][C]124[/C][C]950.389883604992[/C][C]711.720190178681[/C][C]1189.0595770313[/C][/ROW]
[ROW][C]125[/C][C]950.389883604992[/C][C]702.292849649258[/C][C]1198.48691756073[/C][/ROW]
[ROW][C]126[/C][C]950.389883604992[/C][C]693.210852665345[/C][C]1207.56891454464[/C][/ROW]
[ROW][C]127[/C][C]950.389883604992[/C][C]684.438817330613[/C][C]1216.34094987937[/C][/ROW]
[ROW][C]128[/C][C]950.389883604992[/C][C]675.94702006159[/C][C]1224.83274714839[/C][/ROW]
[ROW][C]129[/C][C]950.389883604992[/C][C]667.710204378972[/C][C]1233.06956283101[/C][/ROW]
[ROW][C]130[/C][C]950.389883604992[/C][C]659.706693955592[/C][C]1241.07307325439[/C][/ROW]
[ROW][C]131[/C][C]950.389883604992[/C][C]651.917720008163[/C][C]1248.86204720182[/C][/ROW]
[ROW][C]132[/C][C]950.389883604992[/C][C]644.326902930106[/C][C]1256.45286427988[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278843&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278843&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
121950.389883604992742.5522655760621158.22750163392
122950.389883604992731.7911846944941168.98858251549
123950.389883604992721.5355481363671179.24421907362
124950.389883604992711.7201901786811189.0595770313
125950.389883604992702.2928496492581198.48691756073
126950.389883604992693.2108526653451207.56891454464
127950.389883604992684.4388173306131216.34094987937
128950.389883604992675.947020061591224.83274714839
129950.389883604992667.7102043789721233.06956283101
130950.389883604992659.7066939555921241.07307325439
131950.389883604992651.9177200081631248.86204720182
132950.389883604992644.3269029301061256.45286427988



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')