Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 02 Jun 2010 17:32:32 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Jun/02/t1275499992ay55j5k2caom6i5.htm/, Retrieved Thu, 25 Apr 2024 11:25:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=77316, Retrieved Thu, 25 Apr 2024 11:25:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact160
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2010-06-02 17:32:32] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
562674
599000
668516
597798
579889
668233
499232
215187
555813
586935
546136
571111
634712
639283
712182
621557
621000
675989
501322
220286
560727
602530
626379
605508
646783
658442
712906
687714
723916
707183
629000
237530
613296
730444
734925
651812
676155
748183
810681
729363
701108
790079
594621
230716
617189
691389
701067
705777
747636
773392
813788
766713
728875
749197
680954
241424
680234
708326
694238
772071
795337
788421
889968
797393
751000
821255
691605
290655
727147
868355
812390
799556
843038
847000
941952
804309
840307
871528
656330
370508
742000
847152
731675
898527
778139
856075
938833
813023
783417
828110
657311
310032
780000
860000
780000
807993
895217
856075
893268
875000
835088
934595
832500
300000
791443
900000
781729
880000
875024
992968
976804
968697
871675
1006852
832037
345587
849528
913871
868746
993733




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 4 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77316&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77316&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77316&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 time4 seconds
R Server'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.175227912761956
beta0
gamma0.28039163452554

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.175227912761956 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.28039163452554 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77316&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]0.175227912761956[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.28039163452554[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77316&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77316&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
alpha0.175227912761956
beta0
gamma0.28039163452554







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13634712619554.40676292115157.5932370792
14639283628499.91973341110783.0802665888
15712182704141.4406566748040.55934332637
16621557616925.9233113474631.07668865321
17621000614982.4062419766017.59375802369
18675989667318.1108558198670.88914418127
19501322519139.232379148-17817.2323791476
20220286221303.387136167-1017.38713616732
21560727569501.226683812-8774.22668381152
22602530598780.3168981443749.68310185627
23626379556961.89879649769417.1012035034
24605508594947.33379770310560.6662022970
25646783668652.31125539-21869.3112553904
26658442670285.927135215-11843.9271352155
27712906745272.76983353-32366.7698335300
28687714646023.5428825241690.4571174798
29723916650641.24870413773274.7512958628
30707183719075.658912477-11892.6589124774
31629000550304.49802957478695.5019704263
32237530243535.140489665-6005.14048966489
33613296622755.681361663-9459.68136166257
34730444657902.74280984772541.2571901528
35734925639524.44739917695400.5526008242
36651812669693.193506365-17881.1935063653
37676155737874.078085287-61719.0780852865
38748183735410.17125237312772.8287476272
39810681817488.285284563-6807.28528456332
40729363730691.404920605-1328.40492060478
41701108734968.695528562-33860.6955285618
42790079767331.82167004722747.1783299531
43594621613312.747193763-18691.7471937635
44230716253642.775494520-22926.7754945197
45617189642454.913711632-25265.9137116324
46691389695127.772412943-3738.77241294342
47701067667815.76293469533251.2370653052
48705777660978.150150744798.8498492998
49747636730361.35630919217274.6436908082
50773392759634.40421290213757.5957870976
51813788839466.974308982-25678.9743089821
52766713748482.06920527118230.9307947287
53728875748447.241538165-19572.2415381655
54749197798000.115042067-48803.1150420669
55680954619030.34311081461923.6568891864
56241424258131.639720939-16707.6397209391
57680234664837.82199144915396.1780085505
58708326732971.165874855-24645.165874855
59694238709465.977862678-15227.9778626784
60772071696231.92433437275839.0756656277
61795337767042.40260039228294.5973996082
62788421798515.457734531-10094.4577345313
63889968867732.145024722235.8549752998
64797393791247.9448676126145.05513238837
65751000779654.019083943-28654.0190839426
66821255822757.408468614-1502.40846861433
67691605669070.25051826722534.7494817328
68290655265564.4209158625090.5790841401
69727147717763.7817659359383.21823406534
70868355779446.42736307188908.5726369286
71812390776111.0921282836278.9078717206
72799556793555.4457556486000.55424435192
73843038845214.216072039-2176.21607203863
74847000863783.437214284-16783.4372142840
75941952945644.270329026-3692.27032902581
76804309854184.040582017-49875.040582017
77840307823196.8715784317110.1284215699
78871528884553.590219084-13025.5902190842
79656330723428.13446402-67098.1344640201
80370508284612.11693595385895.8830640467
81742000782162.077508625-40162.0775086255
82847152858787.930539864-11635.930539864
83731675823922.787155937-92247.7871559366
84898527811886.48689002386640.5131099772
85778139877604.094570184-99465.094570184
86856075875986.169298653-19911.1692986527
87938833961875.459262197-23042.4592621974
88813023854720.928859736-41697.9288597363
89783417840500.032015401-57083.0320154008
90828110881899.559526141-53789.5595261412
91657311702207.740221743-44896.7402217428
92310032302690.2271032697341.7728967308
93780000735269.14835494744730.8516450532
94860000830743.59159113529256.4084088654
95780000785121.037605322-5121.03760532173
96807993829232.905936562-21239.9059365618
97895217832415.10072453962801.8992754614
98856075877849.309781133-21774.3097811330
99893268963276.153969898-70008.1539698981
100875000843667.12416250431332.8758374964
101835088838354.149920531-3266.1499205312
102934595891061.09207404943533.9079259512
103832500722718.484718449109781.515281551
1043e+05330126.176007452-30126.1760074521
105791443792146.906842533-703.906842533033
1069e+05880234.62584880719765.3741511930
107781729822043.126160688-40314.1261606885
108880000857838.81832930322161.1816706973
109875024889078.137458024-14054.1374580237
110992968901889.62079442691078.3792055736
111976804999976.874470696-23172.8744706957
112968697906340.6262092262356.37379078
113871675896980.881478231-25305.8814782314
1141006852960664.61867395446187.3813260460
115832037796680.26300526335356.7369947374
116345587337970.0547336467616.94526635355
117849528845236.0426947024291.95730529772
118913871945124.313741886-31253.3137418862
119868746859533.4650107639212.5349892372
120993733922237.97267841471495.0273215859

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 634712 & 619554.406762921 & 15157.5932370792 \tabularnewline
14 & 639283 & 628499.919733411 & 10783.0802665888 \tabularnewline
15 & 712182 & 704141.440656674 & 8040.55934332637 \tabularnewline
16 & 621557 & 616925.923311347 & 4631.07668865321 \tabularnewline
17 & 621000 & 614982.406241976 & 6017.59375802369 \tabularnewline
18 & 675989 & 667318.110855819 & 8670.88914418127 \tabularnewline
19 & 501322 & 519139.232379148 & -17817.2323791476 \tabularnewline
20 & 220286 & 221303.387136167 & -1017.38713616732 \tabularnewline
21 & 560727 & 569501.226683812 & -8774.22668381152 \tabularnewline
22 & 602530 & 598780.316898144 & 3749.68310185627 \tabularnewline
23 & 626379 & 556961.898796497 & 69417.1012035034 \tabularnewline
24 & 605508 & 594947.333797703 & 10560.6662022970 \tabularnewline
25 & 646783 & 668652.31125539 & -21869.3112553904 \tabularnewline
26 & 658442 & 670285.927135215 & -11843.9271352155 \tabularnewline
27 & 712906 & 745272.76983353 & -32366.7698335300 \tabularnewline
28 & 687714 & 646023.54288252 & 41690.4571174798 \tabularnewline
29 & 723916 & 650641.248704137 & 73274.7512958628 \tabularnewline
30 & 707183 & 719075.658912477 & -11892.6589124774 \tabularnewline
31 & 629000 & 550304.498029574 & 78695.5019704263 \tabularnewline
32 & 237530 & 243535.140489665 & -6005.14048966489 \tabularnewline
33 & 613296 & 622755.681361663 & -9459.68136166257 \tabularnewline
34 & 730444 & 657902.742809847 & 72541.2571901528 \tabularnewline
35 & 734925 & 639524.447399176 & 95400.5526008242 \tabularnewline
36 & 651812 & 669693.193506365 & -17881.1935063653 \tabularnewline
37 & 676155 & 737874.078085287 & -61719.0780852865 \tabularnewline
38 & 748183 & 735410.171252373 & 12772.8287476272 \tabularnewline
39 & 810681 & 817488.285284563 & -6807.28528456332 \tabularnewline
40 & 729363 & 730691.404920605 & -1328.40492060478 \tabularnewline
41 & 701108 & 734968.695528562 & -33860.6955285618 \tabularnewline
42 & 790079 & 767331.821670047 & 22747.1783299531 \tabularnewline
43 & 594621 & 613312.747193763 & -18691.7471937635 \tabularnewline
44 & 230716 & 253642.775494520 & -22926.7754945197 \tabularnewline
45 & 617189 & 642454.913711632 & -25265.9137116324 \tabularnewline
46 & 691389 & 695127.772412943 & -3738.77241294342 \tabularnewline
47 & 701067 & 667815.762934695 & 33251.2370653052 \tabularnewline
48 & 705777 & 660978.1501507 & 44798.8498492998 \tabularnewline
49 & 747636 & 730361.356309192 & 17274.6436908082 \tabularnewline
50 & 773392 & 759634.404212902 & 13757.5957870976 \tabularnewline
51 & 813788 & 839466.974308982 & -25678.9743089821 \tabularnewline
52 & 766713 & 748482.069205271 & 18230.9307947287 \tabularnewline
53 & 728875 & 748447.241538165 & -19572.2415381655 \tabularnewline
54 & 749197 & 798000.115042067 & -48803.1150420669 \tabularnewline
55 & 680954 & 619030.343110814 & 61923.6568891864 \tabularnewline
56 & 241424 & 258131.639720939 & -16707.6397209391 \tabularnewline
57 & 680234 & 664837.821991449 & 15396.1780085505 \tabularnewline
58 & 708326 & 732971.165874855 & -24645.165874855 \tabularnewline
59 & 694238 & 709465.977862678 & -15227.9778626784 \tabularnewline
60 & 772071 & 696231.924334372 & 75839.0756656277 \tabularnewline
61 & 795337 & 767042.402600392 & 28294.5973996082 \tabularnewline
62 & 788421 & 798515.457734531 & -10094.4577345313 \tabularnewline
63 & 889968 & 867732.1450247 & 22235.8549752998 \tabularnewline
64 & 797393 & 791247.944867612 & 6145.05513238837 \tabularnewline
65 & 751000 & 779654.019083943 & -28654.0190839426 \tabularnewline
66 & 821255 & 822757.408468614 & -1502.40846861433 \tabularnewline
67 & 691605 & 669070.250518267 & 22534.7494817328 \tabularnewline
68 & 290655 & 265564.42091586 & 25090.5790841401 \tabularnewline
69 & 727147 & 717763.781765935 & 9383.21823406534 \tabularnewline
70 & 868355 & 779446.427363071 & 88908.5726369286 \tabularnewline
71 & 812390 & 776111.09212828 & 36278.9078717206 \tabularnewline
72 & 799556 & 793555.445755648 & 6000.55424435192 \tabularnewline
73 & 843038 & 845214.216072039 & -2176.21607203863 \tabularnewline
74 & 847000 & 863783.437214284 & -16783.4372142840 \tabularnewline
75 & 941952 & 945644.270329026 & -3692.27032902581 \tabularnewline
76 & 804309 & 854184.040582017 & -49875.040582017 \tabularnewline
77 & 840307 & 823196.87157843 & 17110.1284215699 \tabularnewline
78 & 871528 & 884553.590219084 & -13025.5902190842 \tabularnewline
79 & 656330 & 723428.13446402 & -67098.1344640201 \tabularnewline
80 & 370508 & 284612.116935953 & 85895.8830640467 \tabularnewline
81 & 742000 & 782162.077508625 & -40162.0775086255 \tabularnewline
82 & 847152 & 858787.930539864 & -11635.930539864 \tabularnewline
83 & 731675 & 823922.787155937 & -92247.7871559366 \tabularnewline
84 & 898527 & 811886.486890023 & 86640.5131099772 \tabularnewline
85 & 778139 & 877604.094570184 & -99465.094570184 \tabularnewline
86 & 856075 & 875986.169298653 & -19911.1692986527 \tabularnewline
87 & 938833 & 961875.459262197 & -23042.4592621974 \tabularnewline
88 & 813023 & 854720.928859736 & -41697.9288597363 \tabularnewline
89 & 783417 & 840500.032015401 & -57083.0320154008 \tabularnewline
90 & 828110 & 881899.559526141 & -53789.5595261412 \tabularnewline
91 & 657311 & 702207.740221743 & -44896.7402217428 \tabularnewline
92 & 310032 & 302690.227103269 & 7341.7728967308 \tabularnewline
93 & 780000 & 735269.148354947 & 44730.8516450532 \tabularnewline
94 & 860000 & 830743.591591135 & 29256.4084088654 \tabularnewline
95 & 780000 & 785121.037605322 & -5121.03760532173 \tabularnewline
96 & 807993 & 829232.905936562 & -21239.9059365618 \tabularnewline
97 & 895217 & 832415.100724539 & 62801.8992754614 \tabularnewline
98 & 856075 & 877849.309781133 & -21774.3097811330 \tabularnewline
99 & 893268 & 963276.153969898 & -70008.1539698981 \tabularnewline
100 & 875000 & 843667.124162504 & 31332.8758374964 \tabularnewline
101 & 835088 & 838354.149920531 & -3266.1499205312 \tabularnewline
102 & 934595 & 891061.092074049 & 43533.9079259512 \tabularnewline
103 & 832500 & 722718.484718449 & 109781.515281551 \tabularnewline
104 & 3e+05 & 330126.176007452 & -30126.1760074521 \tabularnewline
105 & 791443 & 792146.906842533 & -703.906842533033 \tabularnewline
106 & 9e+05 & 880234.625848807 & 19765.3741511930 \tabularnewline
107 & 781729 & 822043.126160688 & -40314.1261606885 \tabularnewline
108 & 880000 & 857838.818329303 & 22161.1816706973 \tabularnewline
109 & 875024 & 889078.137458024 & -14054.1374580237 \tabularnewline
110 & 992968 & 901889.620794426 & 91078.3792055736 \tabularnewline
111 & 976804 & 999976.874470696 & -23172.8744706957 \tabularnewline
112 & 968697 & 906340.62620922 & 62356.37379078 \tabularnewline
113 & 871675 & 896980.881478231 & -25305.8814782314 \tabularnewline
114 & 1006852 & 960664.618673954 & 46187.3813260460 \tabularnewline
115 & 832037 & 796680.263005263 & 35356.7369947374 \tabularnewline
116 & 345587 & 337970.054733646 & 7616.94526635355 \tabularnewline
117 & 849528 & 845236.042694702 & 4291.95730529772 \tabularnewline
118 & 913871 & 945124.313741886 & -31253.3137418862 \tabularnewline
119 & 868746 & 859533.465010763 & 9212.5349892372 \tabularnewline
120 & 993733 & 922237.972678414 & 71495.0273215859 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77316&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]634712[/C][C]619554.406762921[/C][C]15157.5932370792[/C][/ROW]
[ROW][C]14[/C][C]639283[/C][C]628499.919733411[/C][C]10783.0802665888[/C][/ROW]
[ROW][C]15[/C][C]712182[/C][C]704141.440656674[/C][C]8040.55934332637[/C][/ROW]
[ROW][C]16[/C][C]621557[/C][C]616925.923311347[/C][C]4631.07668865321[/C][/ROW]
[ROW][C]17[/C][C]621000[/C][C]614982.406241976[/C][C]6017.59375802369[/C][/ROW]
[ROW][C]18[/C][C]675989[/C][C]667318.110855819[/C][C]8670.88914418127[/C][/ROW]
[ROW][C]19[/C][C]501322[/C][C]519139.232379148[/C][C]-17817.2323791476[/C][/ROW]
[ROW][C]20[/C][C]220286[/C][C]221303.387136167[/C][C]-1017.38713616732[/C][/ROW]
[ROW][C]21[/C][C]560727[/C][C]569501.226683812[/C][C]-8774.22668381152[/C][/ROW]
[ROW][C]22[/C][C]602530[/C][C]598780.316898144[/C][C]3749.68310185627[/C][/ROW]
[ROW][C]23[/C][C]626379[/C][C]556961.898796497[/C][C]69417.1012035034[/C][/ROW]
[ROW][C]24[/C][C]605508[/C][C]594947.333797703[/C][C]10560.6662022970[/C][/ROW]
[ROW][C]25[/C][C]646783[/C][C]668652.31125539[/C][C]-21869.3112553904[/C][/ROW]
[ROW][C]26[/C][C]658442[/C][C]670285.927135215[/C][C]-11843.9271352155[/C][/ROW]
[ROW][C]27[/C][C]712906[/C][C]745272.76983353[/C][C]-32366.7698335300[/C][/ROW]
[ROW][C]28[/C][C]687714[/C][C]646023.54288252[/C][C]41690.4571174798[/C][/ROW]
[ROW][C]29[/C][C]723916[/C][C]650641.248704137[/C][C]73274.7512958628[/C][/ROW]
[ROW][C]30[/C][C]707183[/C][C]719075.658912477[/C][C]-11892.6589124774[/C][/ROW]
[ROW][C]31[/C][C]629000[/C][C]550304.498029574[/C][C]78695.5019704263[/C][/ROW]
[ROW][C]32[/C][C]237530[/C][C]243535.140489665[/C][C]-6005.14048966489[/C][/ROW]
[ROW][C]33[/C][C]613296[/C][C]622755.681361663[/C][C]-9459.68136166257[/C][/ROW]
[ROW][C]34[/C][C]730444[/C][C]657902.742809847[/C][C]72541.2571901528[/C][/ROW]
[ROW][C]35[/C][C]734925[/C][C]639524.447399176[/C][C]95400.5526008242[/C][/ROW]
[ROW][C]36[/C][C]651812[/C][C]669693.193506365[/C][C]-17881.1935063653[/C][/ROW]
[ROW][C]37[/C][C]676155[/C][C]737874.078085287[/C][C]-61719.0780852865[/C][/ROW]
[ROW][C]38[/C][C]748183[/C][C]735410.171252373[/C][C]12772.8287476272[/C][/ROW]
[ROW][C]39[/C][C]810681[/C][C]817488.285284563[/C][C]-6807.28528456332[/C][/ROW]
[ROW][C]40[/C][C]729363[/C][C]730691.404920605[/C][C]-1328.40492060478[/C][/ROW]
[ROW][C]41[/C][C]701108[/C][C]734968.695528562[/C][C]-33860.6955285618[/C][/ROW]
[ROW][C]42[/C][C]790079[/C][C]767331.821670047[/C][C]22747.1783299531[/C][/ROW]
[ROW][C]43[/C][C]594621[/C][C]613312.747193763[/C][C]-18691.7471937635[/C][/ROW]
[ROW][C]44[/C][C]230716[/C][C]253642.775494520[/C][C]-22926.7754945197[/C][/ROW]
[ROW][C]45[/C][C]617189[/C][C]642454.913711632[/C][C]-25265.9137116324[/C][/ROW]
[ROW][C]46[/C][C]691389[/C][C]695127.772412943[/C][C]-3738.77241294342[/C][/ROW]
[ROW][C]47[/C][C]701067[/C][C]667815.762934695[/C][C]33251.2370653052[/C][/ROW]
[ROW][C]48[/C][C]705777[/C][C]660978.1501507[/C][C]44798.8498492998[/C][/ROW]
[ROW][C]49[/C][C]747636[/C][C]730361.356309192[/C][C]17274.6436908082[/C][/ROW]
[ROW][C]50[/C][C]773392[/C][C]759634.404212902[/C][C]13757.5957870976[/C][/ROW]
[ROW][C]51[/C][C]813788[/C][C]839466.974308982[/C][C]-25678.9743089821[/C][/ROW]
[ROW][C]52[/C][C]766713[/C][C]748482.069205271[/C][C]18230.9307947287[/C][/ROW]
[ROW][C]53[/C][C]728875[/C][C]748447.241538165[/C][C]-19572.2415381655[/C][/ROW]
[ROW][C]54[/C][C]749197[/C][C]798000.115042067[/C][C]-48803.1150420669[/C][/ROW]
[ROW][C]55[/C][C]680954[/C][C]619030.343110814[/C][C]61923.6568891864[/C][/ROW]
[ROW][C]56[/C][C]241424[/C][C]258131.639720939[/C][C]-16707.6397209391[/C][/ROW]
[ROW][C]57[/C][C]680234[/C][C]664837.821991449[/C][C]15396.1780085505[/C][/ROW]
[ROW][C]58[/C][C]708326[/C][C]732971.165874855[/C][C]-24645.165874855[/C][/ROW]
[ROW][C]59[/C][C]694238[/C][C]709465.977862678[/C][C]-15227.9778626784[/C][/ROW]
[ROW][C]60[/C][C]772071[/C][C]696231.924334372[/C][C]75839.0756656277[/C][/ROW]
[ROW][C]61[/C][C]795337[/C][C]767042.402600392[/C][C]28294.5973996082[/C][/ROW]
[ROW][C]62[/C][C]788421[/C][C]798515.457734531[/C][C]-10094.4577345313[/C][/ROW]
[ROW][C]63[/C][C]889968[/C][C]867732.1450247[/C][C]22235.8549752998[/C][/ROW]
[ROW][C]64[/C][C]797393[/C][C]791247.944867612[/C][C]6145.05513238837[/C][/ROW]
[ROW][C]65[/C][C]751000[/C][C]779654.019083943[/C][C]-28654.0190839426[/C][/ROW]
[ROW][C]66[/C][C]821255[/C][C]822757.408468614[/C][C]-1502.40846861433[/C][/ROW]
[ROW][C]67[/C][C]691605[/C][C]669070.250518267[/C][C]22534.7494817328[/C][/ROW]
[ROW][C]68[/C][C]290655[/C][C]265564.42091586[/C][C]25090.5790841401[/C][/ROW]
[ROW][C]69[/C][C]727147[/C][C]717763.781765935[/C][C]9383.21823406534[/C][/ROW]
[ROW][C]70[/C][C]868355[/C][C]779446.427363071[/C][C]88908.5726369286[/C][/ROW]
[ROW][C]71[/C][C]812390[/C][C]776111.09212828[/C][C]36278.9078717206[/C][/ROW]
[ROW][C]72[/C][C]799556[/C][C]793555.445755648[/C][C]6000.55424435192[/C][/ROW]
[ROW][C]73[/C][C]843038[/C][C]845214.216072039[/C][C]-2176.21607203863[/C][/ROW]
[ROW][C]74[/C][C]847000[/C][C]863783.437214284[/C][C]-16783.4372142840[/C][/ROW]
[ROW][C]75[/C][C]941952[/C][C]945644.270329026[/C][C]-3692.27032902581[/C][/ROW]
[ROW][C]76[/C][C]804309[/C][C]854184.040582017[/C][C]-49875.040582017[/C][/ROW]
[ROW][C]77[/C][C]840307[/C][C]823196.87157843[/C][C]17110.1284215699[/C][/ROW]
[ROW][C]78[/C][C]871528[/C][C]884553.590219084[/C][C]-13025.5902190842[/C][/ROW]
[ROW][C]79[/C][C]656330[/C][C]723428.13446402[/C][C]-67098.1344640201[/C][/ROW]
[ROW][C]80[/C][C]370508[/C][C]284612.116935953[/C][C]85895.8830640467[/C][/ROW]
[ROW][C]81[/C][C]742000[/C][C]782162.077508625[/C][C]-40162.0775086255[/C][/ROW]
[ROW][C]82[/C][C]847152[/C][C]858787.930539864[/C][C]-11635.930539864[/C][/ROW]
[ROW][C]83[/C][C]731675[/C][C]823922.787155937[/C][C]-92247.7871559366[/C][/ROW]
[ROW][C]84[/C][C]898527[/C][C]811886.486890023[/C][C]86640.5131099772[/C][/ROW]
[ROW][C]85[/C][C]778139[/C][C]877604.094570184[/C][C]-99465.094570184[/C][/ROW]
[ROW][C]86[/C][C]856075[/C][C]875986.169298653[/C][C]-19911.1692986527[/C][/ROW]
[ROW][C]87[/C][C]938833[/C][C]961875.459262197[/C][C]-23042.4592621974[/C][/ROW]
[ROW][C]88[/C][C]813023[/C][C]854720.928859736[/C][C]-41697.9288597363[/C][/ROW]
[ROW][C]89[/C][C]783417[/C][C]840500.032015401[/C][C]-57083.0320154008[/C][/ROW]
[ROW][C]90[/C][C]828110[/C][C]881899.559526141[/C][C]-53789.5595261412[/C][/ROW]
[ROW][C]91[/C][C]657311[/C][C]702207.740221743[/C][C]-44896.7402217428[/C][/ROW]
[ROW][C]92[/C][C]310032[/C][C]302690.227103269[/C][C]7341.7728967308[/C][/ROW]
[ROW][C]93[/C][C]780000[/C][C]735269.148354947[/C][C]44730.8516450532[/C][/ROW]
[ROW][C]94[/C][C]860000[/C][C]830743.591591135[/C][C]29256.4084088654[/C][/ROW]
[ROW][C]95[/C][C]780000[/C][C]785121.037605322[/C][C]-5121.03760532173[/C][/ROW]
[ROW][C]96[/C][C]807993[/C][C]829232.905936562[/C][C]-21239.9059365618[/C][/ROW]
[ROW][C]97[/C][C]895217[/C][C]832415.100724539[/C][C]62801.8992754614[/C][/ROW]
[ROW][C]98[/C][C]856075[/C][C]877849.309781133[/C][C]-21774.3097811330[/C][/ROW]
[ROW][C]99[/C][C]893268[/C][C]963276.153969898[/C][C]-70008.1539698981[/C][/ROW]
[ROW][C]100[/C][C]875000[/C][C]843667.124162504[/C][C]31332.8758374964[/C][/ROW]
[ROW][C]101[/C][C]835088[/C][C]838354.149920531[/C][C]-3266.1499205312[/C][/ROW]
[ROW][C]102[/C][C]934595[/C][C]891061.092074049[/C][C]43533.9079259512[/C][/ROW]
[ROW][C]103[/C][C]832500[/C][C]722718.484718449[/C][C]109781.515281551[/C][/ROW]
[ROW][C]104[/C][C]3e+05[/C][C]330126.176007452[/C][C]-30126.1760074521[/C][/ROW]
[ROW][C]105[/C][C]791443[/C][C]792146.906842533[/C][C]-703.906842533033[/C][/ROW]
[ROW][C]106[/C][C]9e+05[/C][C]880234.625848807[/C][C]19765.3741511930[/C][/ROW]
[ROW][C]107[/C][C]781729[/C][C]822043.126160688[/C][C]-40314.1261606885[/C][/ROW]
[ROW][C]108[/C][C]880000[/C][C]857838.818329303[/C][C]22161.1816706973[/C][/ROW]
[ROW][C]109[/C][C]875024[/C][C]889078.137458024[/C][C]-14054.1374580237[/C][/ROW]
[ROW][C]110[/C][C]992968[/C][C]901889.620794426[/C][C]91078.3792055736[/C][/ROW]
[ROW][C]111[/C][C]976804[/C][C]999976.874470696[/C][C]-23172.8744706957[/C][/ROW]
[ROW][C]112[/C][C]968697[/C][C]906340.62620922[/C][C]62356.37379078[/C][/ROW]
[ROW][C]113[/C][C]871675[/C][C]896980.881478231[/C][C]-25305.8814782314[/C][/ROW]
[ROW][C]114[/C][C]1006852[/C][C]960664.618673954[/C][C]46187.3813260460[/C][/ROW]
[ROW][C]115[/C][C]832037[/C][C]796680.263005263[/C][C]35356.7369947374[/C][/ROW]
[ROW][C]116[/C][C]345587[/C][C]337970.054733646[/C][C]7616.94526635355[/C][/ROW]
[ROW][C]117[/C][C]849528[/C][C]845236.042694702[/C][C]4291.95730529772[/C][/ROW]
[ROW][C]118[/C][C]913871[/C][C]945124.313741886[/C][C]-31253.3137418862[/C][/ROW]
[ROW][C]119[/C][C]868746[/C][C]859533.465010763[/C][C]9212.5349892372[/C][/ROW]
[ROW][C]120[/C][C]993733[/C][C]922237.972678414[/C][C]71495.0273215859[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77316&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77316&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
13634712619554.40676292115157.5932370792
14639283628499.91973341110783.0802665888
15712182704141.4406566748040.55934332637
16621557616925.9233113474631.07668865321
17621000614982.4062419766017.59375802369
18675989667318.1108558198670.88914418127
19501322519139.232379148-17817.2323791476
20220286221303.387136167-1017.38713616732
21560727569501.226683812-8774.22668381152
22602530598780.3168981443749.68310185627
23626379556961.89879649769417.1012035034
24605508594947.33379770310560.6662022970
25646783668652.31125539-21869.3112553904
26658442670285.927135215-11843.9271352155
27712906745272.76983353-32366.7698335300
28687714646023.5428825241690.4571174798
29723916650641.24870413773274.7512958628
30707183719075.658912477-11892.6589124774
31629000550304.49802957478695.5019704263
32237530243535.140489665-6005.14048966489
33613296622755.681361663-9459.68136166257
34730444657902.74280984772541.2571901528
35734925639524.44739917695400.5526008242
36651812669693.193506365-17881.1935063653
37676155737874.078085287-61719.0780852865
38748183735410.17125237312772.8287476272
39810681817488.285284563-6807.28528456332
40729363730691.404920605-1328.40492060478
41701108734968.695528562-33860.6955285618
42790079767331.82167004722747.1783299531
43594621613312.747193763-18691.7471937635
44230716253642.775494520-22926.7754945197
45617189642454.913711632-25265.9137116324
46691389695127.772412943-3738.77241294342
47701067667815.76293469533251.2370653052
48705777660978.150150744798.8498492998
49747636730361.35630919217274.6436908082
50773392759634.40421290213757.5957870976
51813788839466.974308982-25678.9743089821
52766713748482.06920527118230.9307947287
53728875748447.241538165-19572.2415381655
54749197798000.115042067-48803.1150420669
55680954619030.34311081461923.6568891864
56241424258131.639720939-16707.6397209391
57680234664837.82199144915396.1780085505
58708326732971.165874855-24645.165874855
59694238709465.977862678-15227.9778626784
60772071696231.92433437275839.0756656277
61795337767042.40260039228294.5973996082
62788421798515.457734531-10094.4577345313
63889968867732.145024722235.8549752998
64797393791247.9448676126145.05513238837
65751000779654.019083943-28654.0190839426
66821255822757.408468614-1502.40846861433
67691605669070.25051826722534.7494817328
68290655265564.4209158625090.5790841401
69727147717763.7817659359383.21823406534
70868355779446.42736307188908.5726369286
71812390776111.0921282836278.9078717206
72799556793555.4457556486000.55424435192
73843038845214.216072039-2176.21607203863
74847000863783.437214284-16783.4372142840
75941952945644.270329026-3692.27032902581
76804309854184.040582017-49875.040582017
77840307823196.8715784317110.1284215699
78871528884553.590219084-13025.5902190842
79656330723428.13446402-67098.1344640201
80370508284612.11693595385895.8830640467
81742000782162.077508625-40162.0775086255
82847152858787.930539864-11635.930539864
83731675823922.787155937-92247.7871559366
84898527811886.48689002386640.5131099772
85778139877604.094570184-99465.094570184
86856075875986.169298653-19911.1692986527
87938833961875.459262197-23042.4592621974
88813023854720.928859736-41697.9288597363
89783417840500.032015401-57083.0320154008
90828110881899.559526141-53789.5595261412
91657311702207.740221743-44896.7402217428
92310032302690.2271032697341.7728967308
93780000735269.14835494744730.8516450532
94860000830743.59159113529256.4084088654
95780000785121.037605322-5121.03760532173
96807993829232.905936562-21239.9059365618
97895217832415.10072453962801.8992754614
98856075877849.309781133-21774.3097811330
99893268963276.153969898-70008.1539698981
100875000843667.12416250431332.8758374964
101835088838354.149920531-3266.1499205312
102934595891061.09207404943533.9079259512
103832500722718.484718449109781.515281551
1043e+05330126.176007452-30126.1760074521
105791443792146.906842533-703.906842533033
1069e+05880234.62584880719765.3741511930
107781729822043.126160688-40314.1261606885
108880000857838.81832930322161.1816706973
109875024889078.137458024-14054.1374580237
110992968901889.62079442691078.3792055736
111976804999976.874470696-23172.8744706957
112968697906340.6262092262356.37379078
113871675896980.881478231-25305.8814782314
1141006852960664.61867395446187.3813260460
115832037796680.26300526335356.7369947374
116345587337970.0547336467616.94526635355
117849528845236.0426947024291.95730529772
118913871945124.313741886-31253.3137418862
119868746859533.4650107639212.5349892372
120993733922237.97267841471495.0273215859







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121955061.71633301922437.751567954987685.681098066
122997290.304336678961526.5277764441033054.08089691
1231056294.784697961017242.441983191095347.12741273
124981542.757045696941163.239233551021922.27485784
125938674.58725364896722.14997822980627.02452906
1261028064.58716711981896.8565111241074232.3178231
127844658.726667276800903.499963127888413.953371425
128353769.924801058318451.748058775389088.101543340
129877677.315879882819381.982782185935972.648977579
130971769.667736124907311.4417410261036227.89373122
131897942.62113054835813.258045257960071.984215824
132976153.976366589916801.5962854731035506.35644770

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 955061.71633301 & 922437.751567954 & 987685.681098066 \tabularnewline
122 & 997290.304336678 & 961526.527776444 & 1033054.08089691 \tabularnewline
123 & 1056294.78469796 & 1017242.44198319 & 1095347.12741273 \tabularnewline
124 & 981542.757045696 & 941163.23923355 & 1021922.27485784 \tabularnewline
125 & 938674.58725364 & 896722.14997822 & 980627.02452906 \tabularnewline
126 & 1028064.58716711 & 981896.856511124 & 1074232.3178231 \tabularnewline
127 & 844658.726667276 & 800903.499963127 & 888413.953371425 \tabularnewline
128 & 353769.924801058 & 318451.748058775 & 389088.101543340 \tabularnewline
129 & 877677.315879882 & 819381.982782185 & 935972.648977579 \tabularnewline
130 & 971769.667736124 & 907311.441741026 & 1036227.89373122 \tabularnewline
131 & 897942.62113054 & 835813.258045257 & 960071.984215824 \tabularnewline
132 & 976153.976366589 & 916801.596285473 & 1035506.35644770 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77316&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]955061.71633301[/C][C]922437.751567954[/C][C]987685.681098066[/C][/ROW]
[ROW][C]122[/C][C]997290.304336678[/C][C]961526.527776444[/C][C]1033054.08089691[/C][/ROW]
[ROW][C]123[/C][C]1056294.78469796[/C][C]1017242.44198319[/C][C]1095347.12741273[/C][/ROW]
[ROW][C]124[/C][C]981542.757045696[/C][C]941163.23923355[/C][C]1021922.27485784[/C][/ROW]
[ROW][C]125[/C][C]938674.58725364[/C][C]896722.14997822[/C][C]980627.02452906[/C][/ROW]
[ROW][C]126[/C][C]1028064.58716711[/C][C]981896.856511124[/C][C]1074232.3178231[/C][/ROW]
[ROW][C]127[/C][C]844658.726667276[/C][C]800903.499963127[/C][C]888413.953371425[/C][/ROW]
[ROW][C]128[/C][C]353769.924801058[/C][C]318451.748058775[/C][C]389088.101543340[/C][/ROW]
[ROW][C]129[/C][C]877677.315879882[/C][C]819381.982782185[/C][C]935972.648977579[/C][/ROW]
[ROW][C]130[/C][C]971769.667736124[/C][C]907311.441741026[/C][C]1036227.89373122[/C][/ROW]
[ROW][C]131[/C][C]897942.62113054[/C][C]835813.258045257[/C][C]960071.984215824[/C][/ROW]
[ROW][C]132[/C][C]976153.976366589[/C][C]916801.596285473[/C][C]1035506.35644770[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77316&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77316&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
121955061.71633301922437.751567954987685.681098066
122997290.304336678961526.5277764441033054.08089691
1231056294.784697961017242.441983191095347.12741273
124981542.757045696941163.239233551021922.27485784
125938674.58725364896722.14997822980627.02452906
1261028064.58716711981896.8565111241074232.3178231
127844658.726667276800903.499963127888413.953371425
128353769.924801058318451.748058775389088.101543340
129877677.315879882819381.982782185935972.648977579
130971769.667736124907311.4417410261036227.89373122
131897942.62113054835813.258045257960071.984215824
132976153.976366589916801.5962854731035506.35644770



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')