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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 03 Jan 2012 17:55:04 -0500
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/Jan/03/t1325631327irtdmf9gnm2v0d9.htm/, Retrieved Fri, 03 May 2024 17:16:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160969, Retrieved Fri, 03 May 2024 17:16:50 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact137
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-01-03 22:55:04] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
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
745
624
477
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




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160969&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160969&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160969&T=0

As an alternative you can also use a QR Code:  

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

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







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.466881677549161
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.466881677549161 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160969&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]0.466881677549161[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160969&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160969&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
alpha0.466881677549161
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13832869.23530982906-37.2353098290597
14826845.309304932985-19.3093049329846
15907917.04428994121-10.04428994121
16776781.604940691313-5.60494069131335
17835843.529908933102-8.52990893310186
18715725.089263095386-10.0892630953859
19729739.087250037156-10.0872500371564
20733710.7111768389322.2888231610701
21736748.284232341279-12.2842323412794
22712701.92409502602510.0759049739751
23711842.461829464079-131.461829464079
24667596.00152234452170.9984776554793
25799701.92373047138897.0762695286123
26661750.262022718541-89.2620227185408
27692794.276714747819-102.276714747819
28649618.14243470466430.8575652953357
29729695.53172474686233.4682752531384
30622595.86794132093326.1320586790674
31671626.77807293403444.2219270659658
32635641.018237279012-6.01823727901194
33648646.9437155651981.05628443480191
34745618.732619997012126.267380002988
35624738.061665666415-114.061665666415
36477607.660475504801-130.660475504801
37710633.33436194401576.6656380559846
38515572.802946558234-57.802946558234
39461624.56693405752-163.56693405752
40590490.79369764300399.206302356997
41415601.485578016025-186.485578016025
42554395.218299119282158.781700880718
43585497.70415849756687.295841502434
44513505.2707921380027.72920786199791
45591521.38625782184969.6137421781515
46561591.935712354926-30.9357123549263
47684509.745696884868174.254303115132
48668505.104820236473162.895179763527
49795778.36381332318616.636186676814
50776618.118080723271157.881919276729
511043714.196660614219328.803339385781
52964950.39131042253513.6086895774652
53762868.811657744554-106.811657744554
541030883.810984923671146.189015076329
55939942.307128598045-3.30712859804498
56779865.154465317583-86.1544653175831
57918870.42914329314947.5708567068514
58839877.08242195534-38.0824219553405
59874900.946295549143-26.946295549143
60840796.31278908675643.6872109132439
61794935.942416661684-141.942416661684
62820776.95992772869443.0400722713059
631003910.54229419635992.4577058036409
64780868.355455165137-88.3554551651371
65607674.972317986602-67.9723179866024
661001842.984315540016158.015684459984
67743827.302981127499-84.3029811274986
68810668.167405172121141.832594827879
69716851.176483594766-135.176483594766
70775726.84504521648948.1549547835106
71883796.90844295783886.0915570421619
72633782.706255213883-149.706255213883

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 832 & 869.23530982906 & -37.2353098290597 \tabularnewline
14 & 826 & 845.309304932985 & -19.3093049329846 \tabularnewline
15 & 907 & 917.04428994121 & -10.04428994121 \tabularnewline
16 & 776 & 781.604940691313 & -5.60494069131335 \tabularnewline
17 & 835 & 843.529908933102 & -8.52990893310186 \tabularnewline
18 & 715 & 725.089263095386 & -10.0892630953859 \tabularnewline
19 & 729 & 739.087250037156 & -10.0872500371564 \tabularnewline
20 & 733 & 710.71117683893 & 22.2888231610701 \tabularnewline
21 & 736 & 748.284232341279 & -12.2842323412794 \tabularnewline
22 & 712 & 701.924095026025 & 10.0759049739751 \tabularnewline
23 & 711 & 842.461829464079 & -131.461829464079 \tabularnewline
24 & 667 & 596.001522344521 & 70.9984776554793 \tabularnewline
25 & 799 & 701.923730471388 & 97.0762695286123 \tabularnewline
26 & 661 & 750.262022718541 & -89.2620227185408 \tabularnewline
27 & 692 & 794.276714747819 & -102.276714747819 \tabularnewline
28 & 649 & 618.142434704664 & 30.8575652953357 \tabularnewline
29 & 729 & 695.531724746862 & 33.4682752531384 \tabularnewline
30 & 622 & 595.867941320933 & 26.1320586790674 \tabularnewline
31 & 671 & 626.778072934034 & 44.2219270659658 \tabularnewline
32 & 635 & 641.018237279012 & -6.01823727901194 \tabularnewline
33 & 648 & 646.943715565198 & 1.05628443480191 \tabularnewline
34 & 745 & 618.732619997012 & 126.267380002988 \tabularnewline
35 & 624 & 738.061665666415 & -114.061665666415 \tabularnewline
36 & 477 & 607.660475504801 & -130.660475504801 \tabularnewline
37 & 710 & 633.334361944015 & 76.6656380559846 \tabularnewline
38 & 515 & 572.802946558234 & -57.802946558234 \tabularnewline
39 & 461 & 624.56693405752 & -163.56693405752 \tabularnewline
40 & 590 & 490.793697643003 & 99.206302356997 \tabularnewline
41 & 415 & 601.485578016025 & -186.485578016025 \tabularnewline
42 & 554 & 395.218299119282 & 158.781700880718 \tabularnewline
43 & 585 & 497.704158497566 & 87.295841502434 \tabularnewline
44 & 513 & 505.270792138002 & 7.72920786199791 \tabularnewline
45 & 591 & 521.386257821849 & 69.6137421781515 \tabularnewline
46 & 561 & 591.935712354926 & -30.9357123549263 \tabularnewline
47 & 684 & 509.745696884868 & 174.254303115132 \tabularnewline
48 & 668 & 505.104820236473 & 162.895179763527 \tabularnewline
49 & 795 & 778.363813323186 & 16.636186676814 \tabularnewline
50 & 776 & 618.118080723271 & 157.881919276729 \tabularnewline
51 & 1043 & 714.196660614219 & 328.803339385781 \tabularnewline
52 & 964 & 950.391310422535 & 13.6086895774652 \tabularnewline
53 & 762 & 868.811657744554 & -106.811657744554 \tabularnewline
54 & 1030 & 883.810984923671 & 146.189015076329 \tabularnewline
55 & 939 & 942.307128598045 & -3.30712859804498 \tabularnewline
56 & 779 & 865.154465317583 & -86.1544653175831 \tabularnewline
57 & 918 & 870.429143293149 & 47.5708567068514 \tabularnewline
58 & 839 & 877.08242195534 & -38.0824219553405 \tabularnewline
59 & 874 & 900.946295549143 & -26.946295549143 \tabularnewline
60 & 840 & 796.312789086756 & 43.6872109132439 \tabularnewline
61 & 794 & 935.942416661684 & -141.942416661684 \tabularnewline
62 & 820 & 776.959927728694 & 43.0400722713059 \tabularnewline
63 & 1003 & 910.542294196359 & 92.4577058036409 \tabularnewline
64 & 780 & 868.355455165137 & -88.3554551651371 \tabularnewline
65 & 607 & 674.972317986602 & -67.9723179866024 \tabularnewline
66 & 1001 & 842.984315540016 & 158.015684459984 \tabularnewline
67 & 743 & 827.302981127499 & -84.3029811274986 \tabularnewline
68 & 810 & 668.167405172121 & 141.832594827879 \tabularnewline
69 & 716 & 851.176483594766 & -135.176483594766 \tabularnewline
70 & 775 & 726.845045216489 & 48.1549547835106 \tabularnewline
71 & 883 & 796.908442957838 & 86.0915570421619 \tabularnewline
72 & 633 & 782.706255213883 & -149.706255213883 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160969&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]832[/C][C]869.23530982906[/C][C]-37.2353098290597[/C][/ROW]
[ROW][C]14[/C][C]826[/C][C]845.309304932985[/C][C]-19.3093049329846[/C][/ROW]
[ROW][C]15[/C][C]907[/C][C]917.04428994121[/C][C]-10.04428994121[/C][/ROW]
[ROW][C]16[/C][C]776[/C][C]781.604940691313[/C][C]-5.60494069131335[/C][/ROW]
[ROW][C]17[/C][C]835[/C][C]843.529908933102[/C][C]-8.52990893310186[/C][/ROW]
[ROW][C]18[/C][C]715[/C][C]725.089263095386[/C][C]-10.0892630953859[/C][/ROW]
[ROW][C]19[/C][C]729[/C][C]739.087250037156[/C][C]-10.0872500371564[/C][/ROW]
[ROW][C]20[/C][C]733[/C][C]710.71117683893[/C][C]22.2888231610701[/C][/ROW]
[ROW][C]21[/C][C]736[/C][C]748.284232341279[/C][C]-12.2842323412794[/C][/ROW]
[ROW][C]22[/C][C]712[/C][C]701.924095026025[/C][C]10.0759049739751[/C][/ROW]
[ROW][C]23[/C][C]711[/C][C]842.461829464079[/C][C]-131.461829464079[/C][/ROW]
[ROW][C]24[/C][C]667[/C][C]596.001522344521[/C][C]70.9984776554793[/C][/ROW]
[ROW][C]25[/C][C]799[/C][C]701.923730471388[/C][C]97.0762695286123[/C][/ROW]
[ROW][C]26[/C][C]661[/C][C]750.262022718541[/C][C]-89.2620227185408[/C][/ROW]
[ROW][C]27[/C][C]692[/C][C]794.276714747819[/C][C]-102.276714747819[/C][/ROW]
[ROW][C]28[/C][C]649[/C][C]618.142434704664[/C][C]30.8575652953357[/C][/ROW]
[ROW][C]29[/C][C]729[/C][C]695.531724746862[/C][C]33.4682752531384[/C][/ROW]
[ROW][C]30[/C][C]622[/C][C]595.867941320933[/C][C]26.1320586790674[/C][/ROW]
[ROW][C]31[/C][C]671[/C][C]626.778072934034[/C][C]44.2219270659658[/C][/ROW]
[ROW][C]32[/C][C]635[/C][C]641.018237279012[/C][C]-6.01823727901194[/C][/ROW]
[ROW][C]33[/C][C]648[/C][C]646.943715565198[/C][C]1.05628443480191[/C][/ROW]
[ROW][C]34[/C][C]745[/C][C]618.732619997012[/C][C]126.267380002988[/C][/ROW]
[ROW][C]35[/C][C]624[/C][C]738.061665666415[/C][C]-114.061665666415[/C][/ROW]
[ROW][C]36[/C][C]477[/C][C]607.660475504801[/C][C]-130.660475504801[/C][/ROW]
[ROW][C]37[/C][C]710[/C][C]633.334361944015[/C][C]76.6656380559846[/C][/ROW]
[ROW][C]38[/C][C]515[/C][C]572.802946558234[/C][C]-57.802946558234[/C][/ROW]
[ROW][C]39[/C][C]461[/C][C]624.56693405752[/C][C]-163.56693405752[/C][/ROW]
[ROW][C]40[/C][C]590[/C][C]490.793697643003[/C][C]99.206302356997[/C][/ROW]
[ROW][C]41[/C][C]415[/C][C]601.485578016025[/C][C]-186.485578016025[/C][/ROW]
[ROW][C]42[/C][C]554[/C][C]395.218299119282[/C][C]158.781700880718[/C][/ROW]
[ROW][C]43[/C][C]585[/C][C]497.704158497566[/C][C]87.295841502434[/C][/ROW]
[ROW][C]44[/C][C]513[/C][C]505.270792138002[/C][C]7.72920786199791[/C][/ROW]
[ROW][C]45[/C][C]591[/C][C]521.386257821849[/C][C]69.6137421781515[/C][/ROW]
[ROW][C]46[/C][C]561[/C][C]591.935712354926[/C][C]-30.9357123549263[/C][/ROW]
[ROW][C]47[/C][C]684[/C][C]509.745696884868[/C][C]174.254303115132[/C][/ROW]
[ROW][C]48[/C][C]668[/C][C]505.104820236473[/C][C]162.895179763527[/C][/ROW]
[ROW][C]49[/C][C]795[/C][C]778.363813323186[/C][C]16.636186676814[/C][/ROW]
[ROW][C]50[/C][C]776[/C][C]618.118080723271[/C][C]157.881919276729[/C][/ROW]
[ROW][C]51[/C][C]1043[/C][C]714.196660614219[/C][C]328.803339385781[/C][/ROW]
[ROW][C]52[/C][C]964[/C][C]950.391310422535[/C][C]13.6086895774652[/C][/ROW]
[ROW][C]53[/C][C]762[/C][C]868.811657744554[/C][C]-106.811657744554[/C][/ROW]
[ROW][C]54[/C][C]1030[/C][C]883.810984923671[/C][C]146.189015076329[/C][/ROW]
[ROW][C]55[/C][C]939[/C][C]942.307128598045[/C][C]-3.30712859804498[/C][/ROW]
[ROW][C]56[/C][C]779[/C][C]865.154465317583[/C][C]-86.1544653175831[/C][/ROW]
[ROW][C]57[/C][C]918[/C][C]870.429143293149[/C][C]47.5708567068514[/C][/ROW]
[ROW][C]58[/C][C]839[/C][C]877.08242195534[/C][C]-38.0824219553405[/C][/ROW]
[ROW][C]59[/C][C]874[/C][C]900.946295549143[/C][C]-26.946295549143[/C][/ROW]
[ROW][C]60[/C][C]840[/C][C]796.312789086756[/C][C]43.6872109132439[/C][/ROW]
[ROW][C]61[/C][C]794[/C][C]935.942416661684[/C][C]-141.942416661684[/C][/ROW]
[ROW][C]62[/C][C]820[/C][C]776.959927728694[/C][C]43.0400722713059[/C][/ROW]
[ROW][C]63[/C][C]1003[/C][C]910.542294196359[/C][C]92.4577058036409[/C][/ROW]
[ROW][C]64[/C][C]780[/C][C]868.355455165137[/C][C]-88.3554551651371[/C][/ROW]
[ROW][C]65[/C][C]607[/C][C]674.972317986602[/C][C]-67.9723179866024[/C][/ROW]
[ROW][C]66[/C][C]1001[/C][C]842.984315540016[/C][C]158.015684459984[/C][/ROW]
[ROW][C]67[/C][C]743[/C][C]827.302981127499[/C][C]-84.3029811274986[/C][/ROW]
[ROW][C]68[/C][C]810[/C][C]668.167405172121[/C][C]141.832594827879[/C][/ROW]
[ROW][C]69[/C][C]716[/C][C]851.176483594766[/C][C]-135.176483594766[/C][/ROW]
[ROW][C]70[/C][C]775[/C][C]726.845045216489[/C][C]48.1549547835106[/C][/ROW]
[ROW][C]71[/C][C]883[/C][C]796.908442957838[/C][C]86.0915570421619[/C][/ROW]
[ROW][C]72[/C][C]633[/C][C]782.706255213883[/C][C]-149.706255213883[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160969&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160969&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
13832869.23530982906-37.2353098290597
14826845.309304932985-19.3093049329846
15907917.04428994121-10.04428994121
16776781.604940691313-5.60494069131335
17835843.529908933102-8.52990893310186
18715725.089263095386-10.0892630953859
19729739.087250037156-10.0872500371564
20733710.7111768389322.2888231610701
21736748.284232341279-12.2842323412794
22712701.92409502602510.0759049739751
23711842.461829464079-131.461829464079
24667596.00152234452170.9984776554793
25799701.92373047138897.0762695286123
26661750.262022718541-89.2620227185408
27692794.276714747819-102.276714747819
28649618.14243470466430.8575652953357
29729695.53172474686233.4682752531384
30622595.86794132093326.1320586790674
31671626.77807293403444.2219270659658
32635641.018237279012-6.01823727901194
33648646.9437155651981.05628443480191
34745618.732619997012126.267380002988
35624738.061665666415-114.061665666415
36477607.660475504801-130.660475504801
37710633.33436194401576.6656380559846
38515572.802946558234-57.802946558234
39461624.56693405752-163.56693405752
40590490.79369764300399.206302356997
41415601.485578016025-186.485578016025
42554395.218299119282158.781700880718
43585497.70415849756687.295841502434
44513505.2707921380027.72920786199791
45591521.38625782184969.6137421781515
46561591.935712354926-30.9357123549263
47684509.745696884868174.254303115132
48668505.104820236473162.895179763527
49795778.36381332318616.636186676814
50776618.118080723271157.881919276729
511043714.196660614219328.803339385781
52964950.39131042253513.6086895774652
53762868.811657744554-106.811657744554
541030883.810984923671146.189015076329
55939942.307128598045-3.30712859804498
56779865.154465317583-86.1544653175831
57918870.42914329314947.5708567068514
58839877.08242195534-38.0824219553405
59874900.946295549143-26.946295549143
60840796.31278908675643.6872109132439
61794935.942416661684-141.942416661684
62820776.95992772869443.0400722713059
631003910.54229419635992.4577058036409
64780868.355455165137-88.3554551651371
65607674.972317986602-67.9723179866024
661001842.984315540016158.015684459984
67743827.302981127499-84.3029811274986
68810668.167405172121141.832594827879
69716851.176483594766-135.176483594766
70775726.84504521648948.1549547835106
71883796.90844295783886.0915570421619
72633782.706255213883-149.706255213883







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73733.081461246411535.379553542342930.78336895048
74738.986840102547520.798935644249957.174744560845
75878.820031314596641.9110213677841115.72904126141
76697.071574442715442.816198224131951.326950661299
77555.806604291205285.314989489325826.298219093085
78876.031976451449590.2249943460361161.83895855686
79657.391493702651357.049108478256957.733878927045
80658.17245389826343.966365949039972.378541847481
81627.283877324181299.800468513248954.767286135115
82663.801211252552323.55820928411004.044213221
83731.606640677888379.0655540928221084.14772726295
84551.501748251748187.077359560961915.926136942536

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 733.081461246411 & 535.379553542342 & 930.78336895048 \tabularnewline
74 & 738.986840102547 & 520.798935644249 & 957.174744560845 \tabularnewline
75 & 878.820031314596 & 641.911021367784 & 1115.72904126141 \tabularnewline
76 & 697.071574442715 & 442.816198224131 & 951.326950661299 \tabularnewline
77 & 555.806604291205 & 285.314989489325 & 826.298219093085 \tabularnewline
78 & 876.031976451449 & 590.224994346036 & 1161.83895855686 \tabularnewline
79 & 657.391493702651 & 357.049108478256 & 957.733878927045 \tabularnewline
80 & 658.17245389826 & 343.966365949039 & 972.378541847481 \tabularnewline
81 & 627.283877324181 & 299.800468513248 & 954.767286135115 \tabularnewline
82 & 663.801211252552 & 323.5582092841 & 1004.044213221 \tabularnewline
83 & 731.606640677888 & 379.065554092822 & 1084.14772726295 \tabularnewline
84 & 551.501748251748 & 187.077359560961 & 915.926136942536 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160969&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]73[/C][C]733.081461246411[/C][C]535.379553542342[/C][C]930.78336895048[/C][/ROW]
[ROW][C]74[/C][C]738.986840102547[/C][C]520.798935644249[/C][C]957.174744560845[/C][/ROW]
[ROW][C]75[/C][C]878.820031314596[/C][C]641.911021367784[/C][C]1115.72904126141[/C][/ROW]
[ROW][C]76[/C][C]697.071574442715[/C][C]442.816198224131[/C][C]951.326950661299[/C][/ROW]
[ROW][C]77[/C][C]555.806604291205[/C][C]285.314989489325[/C][C]826.298219093085[/C][/ROW]
[ROW][C]78[/C][C]876.031976451449[/C][C]590.224994346036[/C][C]1161.83895855686[/C][/ROW]
[ROW][C]79[/C][C]657.391493702651[/C][C]357.049108478256[/C][C]957.733878927045[/C][/ROW]
[ROW][C]80[/C][C]658.17245389826[/C][C]343.966365949039[/C][C]972.378541847481[/C][/ROW]
[ROW][C]81[/C][C]627.283877324181[/C][C]299.800468513248[/C][C]954.767286135115[/C][/ROW]
[ROW][C]82[/C][C]663.801211252552[/C][C]323.5582092841[/C][C]1004.044213221[/C][/ROW]
[ROW][C]83[/C][C]731.606640677888[/C][C]379.065554092822[/C][C]1084.14772726295[/C][/ROW]
[ROW][C]84[/C][C]551.501748251748[/C][C]187.077359560961[/C][C]915.926136942536[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160969&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160969&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
73733.081461246411535.379553542342930.78336895048
74738.986840102547520.798935644249957.174744560845
75878.820031314596641.9110213677841115.72904126141
76697.071574442715442.816198224131951.326950661299
77555.806604291205285.314989489325826.298219093085
78876.031976451449590.2249943460361161.83895855686
79657.391493702651357.049108478256957.733878927045
80658.17245389826343.966365949039972.378541847481
81627.283877324181299.800468513248954.767286135115
82663.801211252552323.55820928411004.044213221
83731.606640677888379.0655540928221084.14772726295
84551.501748251748187.077359560961915.926136942536



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