Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 27 Jan 2010 03:13:03 -0700
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/Jan/27/t1264587208uynzc2t7lg2ad2g.htm/, Retrieved Mon, 06 May 2024 04:21:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72692, Retrieved Mon, 06 May 2024 04:21:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact207
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Variability] [] [2010-01-26 17:24:45] [9f4a7874cbf3ce9f943189309f9ce114]
- RMPD    [Exponential Smoothing] [] [2010-01-27 10:13:03] [a0577a728571d1f3a39246738c9fa77a] [Current]
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Dataseries X:
1.61
1.58
1.69
1.78
1.76
1.83
1.8
1.57
1.45
1.4
1.55
1.58
1.58
1.59
1.8
1.99
2.06
2.06
2.08
2
1.85
1.77
1.7
1.66
1.67
1.73
1.91
2.02
2.07
2.15
2.1
1.68
1.68
1.65
1.72
1.73
1.76
1.84
1.99
2.05
2.12
2.13
2.08
1.88
1.81
1.81
1.88
1.87
1.87
1.9
2.01
2.05
2.16
2.18
2.15
2.12
2.04
2.04
2.06
1.93
1.86
1.94
2.35
2.46
2.59
2.66
2.41
2.18
2.13
2.11
2.12
2.16
2.07
2.2
2.29
2.32
2.37
2.38
2.38
2.28
2.22
2.25
2.3
2.3
2.23
2.27
2.3
2.32
2.41
2.43
2.45
2.47
2.46
2.5
2.46
2.43
2.37
2.45
2.53
2.56
2.62
2.67
2.62
2.6
2.53
2.49
2.48
2.44




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72692&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72692&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72692&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.836733274783946
beta0.00571230996515615
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.836733274783946 \tabularnewline
beta & 0.00571230996515615 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72692&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]0.836733274783946[/C][/ROW]
[ROW][C]beta[/C][C]0.00571230996515615[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72692&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72692&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
alpha0.836733274783946
beta0.00571230996515615
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131.581.482686965811970.0973130341880326
141.591.566727494383730.0232725056162744
151.81.783927084142440.0160729158575561
161.991.977679360976880.0123206390231181
172.062.058767538304160.00123246169583524
182.062.07266709281064-0.0126670928106405
192.082.034042549575610.0459574504243911
2021.865940774282880.134059225717118
211.851.87636411278813-0.0263641127881282
221.771.81409656056281-0.0440965605628096
231.71.92886424513356-0.228864245133563
241.661.76710342877101-0.107103428771011
251.671.69343333267237-0.0234333326723666
261.731.663351117877220.0666488821227764
271.911.91487515117494-0.0048751511749392
282.022.08959217569594-0.0695921756959352
292.072.09904464225383-0.0290446422538309
302.152.083910084150520.0660899158494783
312.12.11970110363563-0.0197011036356267
321.681.90967640861885-0.229676408618849
331.681.586451394546360.0935486054536363
341.651.619089978487270.0309100215127311
351.721.76427655219160-0.0442765521915973
361.731.77555296131678-0.0455529613167778
371.761.76604599447201-0.00604599447200727
381.841.764304140696300.075695859303704
391.992.01084819617850-0.0208481961784972
402.052.16068516977695-0.110685169776952
412.122.14122867646356-0.0212286764635632
422.132.14705851521806-0.0170585152180607
432.082.09776444445036-0.0177644444503615
441.881.853582280377560.0264177196224447
451.811.797139726557200.0128602734427978
461.811.751379329473430.0586206705265735
471.881.90695173536237-0.0269517353623734
481.871.93207368290545-0.0620736829054451
491.871.91467217075956-0.0446721707595563
501.91.893250333105560.00674966689444045
512.012.06530694104696-0.0553069410469638
522.052.17044360355169-0.120443603551688
532.162.156180386340510.00381961365948635
542.182.18252274793323-0.00252274793322771
552.152.144218395332530.00578160466747102
562.121.926006426622590.193993573377411
572.042.007422600111590.0325773998884089
582.041.985581484798180.0544185152018208
592.062.12359675187947-0.0635967518794693
601.932.11207726879975-0.182077268799748
611.861.99628719183693-0.136287191836930
621.941.905346942840390.0346530571596109
632.352.089496286235370.260503713764634
642.462.448633875884560.0113661241154368
652.592.565964593898420.0240354061015844
662.662.609299611718290.0507003882817103
672.412.61825196880358-0.208251968803575
682.182.25202404324695-0.0720240432469472
692.132.083573360369950.0464266396300488
702.112.076025312267660.0339746877323392
712.122.1767078876263-0.0567078876263016
722.162.150682852225540.00931714777445602
732.072.20250388389495-0.132503883894955
742.22.142645227967760.0573547720322414
752.292.38277937437592-0.0927793743759198
762.322.40406441601359-0.0840644160135908
772.372.44158461606873-0.0715846160687259
782.382.40677856904803-0.0267785690480333
792.382.305766961628970.0742330383710317
802.282.196638876898120.0833611231018758
812.222.176779627957060.0432203720429358
822.252.16373691448650.0862630855135018
832.32.292836521659310.00716347834068687
842.32.33081079607892-0.0308107960789186
852.232.32548530904424-0.0954853090442436
862.272.32736038699631-0.0573603869963124
872.32.44620979007434-0.146209790074337
882.322.42316846522228-0.103168465222284
892.412.44560767394966-0.0356076739496585
902.432.44725849261619-0.0172584926161896
912.452.369788411719780.0802115882802243
922.472.266265594130310.203734405869694
932.462.340260876049810.119739123950191
942.52.398324975199220.101675024800781
952.462.52753317899041-0.0675331789904101
962.432.49657656118980-0.0665765611898044
972.372.45036474545687-0.080364745456869
982.452.47078777772548-0.0207877777254817
992.532.60557889866838-0.0755788986683825
1002.562.64884794990773-0.0888479499077328
1012.622.69455242979988-0.0745524297998825
1022.672.666678932996080.00332106700392165
1032.622.62250668591578-0.00250668591578318
1042.62.469707145511950.130292854488054
1052.532.467956019645560.0620439803544404
1062.492.473937858348570.0160621416514268
1072.482.5026180948813-0.0226180948812997
1082.442.50834753620686-0.0683475362068608

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1.58 & 1.48268696581197 & 0.0973130341880326 \tabularnewline
14 & 1.59 & 1.56672749438373 & 0.0232725056162744 \tabularnewline
15 & 1.8 & 1.78392708414244 & 0.0160729158575561 \tabularnewline
16 & 1.99 & 1.97767936097688 & 0.0123206390231181 \tabularnewline
17 & 2.06 & 2.05876753830416 & 0.00123246169583524 \tabularnewline
18 & 2.06 & 2.07266709281064 & -0.0126670928106405 \tabularnewline
19 & 2.08 & 2.03404254957561 & 0.0459574504243911 \tabularnewline
20 & 2 & 1.86594077428288 & 0.134059225717118 \tabularnewline
21 & 1.85 & 1.87636411278813 & -0.0263641127881282 \tabularnewline
22 & 1.77 & 1.81409656056281 & -0.0440965605628096 \tabularnewline
23 & 1.7 & 1.92886424513356 & -0.228864245133563 \tabularnewline
24 & 1.66 & 1.76710342877101 & -0.107103428771011 \tabularnewline
25 & 1.67 & 1.69343333267237 & -0.0234333326723666 \tabularnewline
26 & 1.73 & 1.66335111787722 & 0.0666488821227764 \tabularnewline
27 & 1.91 & 1.91487515117494 & -0.0048751511749392 \tabularnewline
28 & 2.02 & 2.08959217569594 & -0.0695921756959352 \tabularnewline
29 & 2.07 & 2.09904464225383 & -0.0290446422538309 \tabularnewline
30 & 2.15 & 2.08391008415052 & 0.0660899158494783 \tabularnewline
31 & 2.1 & 2.11970110363563 & -0.0197011036356267 \tabularnewline
32 & 1.68 & 1.90967640861885 & -0.229676408618849 \tabularnewline
33 & 1.68 & 1.58645139454636 & 0.0935486054536363 \tabularnewline
34 & 1.65 & 1.61908997848727 & 0.0309100215127311 \tabularnewline
35 & 1.72 & 1.76427655219160 & -0.0442765521915973 \tabularnewline
36 & 1.73 & 1.77555296131678 & -0.0455529613167778 \tabularnewline
37 & 1.76 & 1.76604599447201 & -0.00604599447200727 \tabularnewline
38 & 1.84 & 1.76430414069630 & 0.075695859303704 \tabularnewline
39 & 1.99 & 2.01084819617850 & -0.0208481961784972 \tabularnewline
40 & 2.05 & 2.16068516977695 & -0.110685169776952 \tabularnewline
41 & 2.12 & 2.14122867646356 & -0.0212286764635632 \tabularnewline
42 & 2.13 & 2.14705851521806 & -0.0170585152180607 \tabularnewline
43 & 2.08 & 2.09776444445036 & -0.0177644444503615 \tabularnewline
44 & 1.88 & 1.85358228037756 & 0.0264177196224447 \tabularnewline
45 & 1.81 & 1.79713972655720 & 0.0128602734427978 \tabularnewline
46 & 1.81 & 1.75137932947343 & 0.0586206705265735 \tabularnewline
47 & 1.88 & 1.90695173536237 & -0.0269517353623734 \tabularnewline
48 & 1.87 & 1.93207368290545 & -0.0620736829054451 \tabularnewline
49 & 1.87 & 1.91467217075956 & -0.0446721707595563 \tabularnewline
50 & 1.9 & 1.89325033310556 & 0.00674966689444045 \tabularnewline
51 & 2.01 & 2.06530694104696 & -0.0553069410469638 \tabularnewline
52 & 2.05 & 2.17044360355169 & -0.120443603551688 \tabularnewline
53 & 2.16 & 2.15618038634051 & 0.00381961365948635 \tabularnewline
54 & 2.18 & 2.18252274793323 & -0.00252274793322771 \tabularnewline
55 & 2.15 & 2.14421839533253 & 0.00578160466747102 \tabularnewline
56 & 2.12 & 1.92600642662259 & 0.193993573377411 \tabularnewline
57 & 2.04 & 2.00742260011159 & 0.0325773998884089 \tabularnewline
58 & 2.04 & 1.98558148479818 & 0.0544185152018208 \tabularnewline
59 & 2.06 & 2.12359675187947 & -0.0635967518794693 \tabularnewline
60 & 1.93 & 2.11207726879975 & -0.182077268799748 \tabularnewline
61 & 1.86 & 1.99628719183693 & -0.136287191836930 \tabularnewline
62 & 1.94 & 1.90534694284039 & 0.0346530571596109 \tabularnewline
63 & 2.35 & 2.08949628623537 & 0.260503713764634 \tabularnewline
64 & 2.46 & 2.44863387588456 & 0.0113661241154368 \tabularnewline
65 & 2.59 & 2.56596459389842 & 0.0240354061015844 \tabularnewline
66 & 2.66 & 2.60929961171829 & 0.0507003882817103 \tabularnewline
67 & 2.41 & 2.61825196880358 & -0.208251968803575 \tabularnewline
68 & 2.18 & 2.25202404324695 & -0.0720240432469472 \tabularnewline
69 & 2.13 & 2.08357336036995 & 0.0464266396300488 \tabularnewline
70 & 2.11 & 2.07602531226766 & 0.0339746877323392 \tabularnewline
71 & 2.12 & 2.1767078876263 & -0.0567078876263016 \tabularnewline
72 & 2.16 & 2.15068285222554 & 0.00931714777445602 \tabularnewline
73 & 2.07 & 2.20250388389495 & -0.132503883894955 \tabularnewline
74 & 2.2 & 2.14264522796776 & 0.0573547720322414 \tabularnewline
75 & 2.29 & 2.38277937437592 & -0.0927793743759198 \tabularnewline
76 & 2.32 & 2.40406441601359 & -0.0840644160135908 \tabularnewline
77 & 2.37 & 2.44158461606873 & -0.0715846160687259 \tabularnewline
78 & 2.38 & 2.40677856904803 & -0.0267785690480333 \tabularnewline
79 & 2.38 & 2.30576696162897 & 0.0742330383710317 \tabularnewline
80 & 2.28 & 2.19663887689812 & 0.0833611231018758 \tabularnewline
81 & 2.22 & 2.17677962795706 & 0.0432203720429358 \tabularnewline
82 & 2.25 & 2.1637369144865 & 0.0862630855135018 \tabularnewline
83 & 2.3 & 2.29283652165931 & 0.00716347834068687 \tabularnewline
84 & 2.3 & 2.33081079607892 & -0.0308107960789186 \tabularnewline
85 & 2.23 & 2.32548530904424 & -0.0954853090442436 \tabularnewline
86 & 2.27 & 2.32736038699631 & -0.0573603869963124 \tabularnewline
87 & 2.3 & 2.44620979007434 & -0.146209790074337 \tabularnewline
88 & 2.32 & 2.42316846522228 & -0.103168465222284 \tabularnewline
89 & 2.41 & 2.44560767394966 & -0.0356076739496585 \tabularnewline
90 & 2.43 & 2.44725849261619 & -0.0172584926161896 \tabularnewline
91 & 2.45 & 2.36978841171978 & 0.0802115882802243 \tabularnewline
92 & 2.47 & 2.26626559413031 & 0.203734405869694 \tabularnewline
93 & 2.46 & 2.34026087604981 & 0.119739123950191 \tabularnewline
94 & 2.5 & 2.39832497519922 & 0.101675024800781 \tabularnewline
95 & 2.46 & 2.52753317899041 & -0.0675331789904101 \tabularnewline
96 & 2.43 & 2.49657656118980 & -0.0665765611898044 \tabularnewline
97 & 2.37 & 2.45036474545687 & -0.080364745456869 \tabularnewline
98 & 2.45 & 2.47078777772548 & -0.0207877777254817 \tabularnewline
99 & 2.53 & 2.60557889866838 & -0.0755788986683825 \tabularnewline
100 & 2.56 & 2.64884794990773 & -0.0888479499077328 \tabularnewline
101 & 2.62 & 2.69455242979988 & -0.0745524297998825 \tabularnewline
102 & 2.67 & 2.66667893299608 & 0.00332106700392165 \tabularnewline
103 & 2.62 & 2.62250668591578 & -0.00250668591578318 \tabularnewline
104 & 2.6 & 2.46970714551195 & 0.130292854488054 \tabularnewline
105 & 2.53 & 2.46795601964556 & 0.0620439803544404 \tabularnewline
106 & 2.49 & 2.47393785834857 & 0.0160621416514268 \tabularnewline
107 & 2.48 & 2.5026180948813 & -0.0226180948812997 \tabularnewline
108 & 2.44 & 2.50834753620686 & -0.0683475362068608 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72692&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]1.58[/C][C]1.48268696581197[/C][C]0.0973130341880326[/C][/ROW]
[ROW][C]14[/C][C]1.59[/C][C]1.56672749438373[/C][C]0.0232725056162744[/C][/ROW]
[ROW][C]15[/C][C]1.8[/C][C]1.78392708414244[/C][C]0.0160729158575561[/C][/ROW]
[ROW][C]16[/C][C]1.99[/C][C]1.97767936097688[/C][C]0.0123206390231181[/C][/ROW]
[ROW][C]17[/C][C]2.06[/C][C]2.05876753830416[/C][C]0.00123246169583524[/C][/ROW]
[ROW][C]18[/C][C]2.06[/C][C]2.07266709281064[/C][C]-0.0126670928106405[/C][/ROW]
[ROW][C]19[/C][C]2.08[/C][C]2.03404254957561[/C][C]0.0459574504243911[/C][/ROW]
[ROW][C]20[/C][C]2[/C][C]1.86594077428288[/C][C]0.134059225717118[/C][/ROW]
[ROW][C]21[/C][C]1.85[/C][C]1.87636411278813[/C][C]-0.0263641127881282[/C][/ROW]
[ROW][C]22[/C][C]1.77[/C][C]1.81409656056281[/C][C]-0.0440965605628096[/C][/ROW]
[ROW][C]23[/C][C]1.7[/C][C]1.92886424513356[/C][C]-0.228864245133563[/C][/ROW]
[ROW][C]24[/C][C]1.66[/C][C]1.76710342877101[/C][C]-0.107103428771011[/C][/ROW]
[ROW][C]25[/C][C]1.67[/C][C]1.69343333267237[/C][C]-0.0234333326723666[/C][/ROW]
[ROW][C]26[/C][C]1.73[/C][C]1.66335111787722[/C][C]0.0666488821227764[/C][/ROW]
[ROW][C]27[/C][C]1.91[/C][C]1.91487515117494[/C][C]-0.0048751511749392[/C][/ROW]
[ROW][C]28[/C][C]2.02[/C][C]2.08959217569594[/C][C]-0.0695921756959352[/C][/ROW]
[ROW][C]29[/C][C]2.07[/C][C]2.09904464225383[/C][C]-0.0290446422538309[/C][/ROW]
[ROW][C]30[/C][C]2.15[/C][C]2.08391008415052[/C][C]0.0660899158494783[/C][/ROW]
[ROW][C]31[/C][C]2.1[/C][C]2.11970110363563[/C][C]-0.0197011036356267[/C][/ROW]
[ROW][C]32[/C][C]1.68[/C][C]1.90967640861885[/C][C]-0.229676408618849[/C][/ROW]
[ROW][C]33[/C][C]1.68[/C][C]1.58645139454636[/C][C]0.0935486054536363[/C][/ROW]
[ROW][C]34[/C][C]1.65[/C][C]1.61908997848727[/C][C]0.0309100215127311[/C][/ROW]
[ROW][C]35[/C][C]1.72[/C][C]1.76427655219160[/C][C]-0.0442765521915973[/C][/ROW]
[ROW][C]36[/C][C]1.73[/C][C]1.77555296131678[/C][C]-0.0455529613167778[/C][/ROW]
[ROW][C]37[/C][C]1.76[/C][C]1.76604599447201[/C][C]-0.00604599447200727[/C][/ROW]
[ROW][C]38[/C][C]1.84[/C][C]1.76430414069630[/C][C]0.075695859303704[/C][/ROW]
[ROW][C]39[/C][C]1.99[/C][C]2.01084819617850[/C][C]-0.0208481961784972[/C][/ROW]
[ROW][C]40[/C][C]2.05[/C][C]2.16068516977695[/C][C]-0.110685169776952[/C][/ROW]
[ROW][C]41[/C][C]2.12[/C][C]2.14122867646356[/C][C]-0.0212286764635632[/C][/ROW]
[ROW][C]42[/C][C]2.13[/C][C]2.14705851521806[/C][C]-0.0170585152180607[/C][/ROW]
[ROW][C]43[/C][C]2.08[/C][C]2.09776444445036[/C][C]-0.0177644444503615[/C][/ROW]
[ROW][C]44[/C][C]1.88[/C][C]1.85358228037756[/C][C]0.0264177196224447[/C][/ROW]
[ROW][C]45[/C][C]1.81[/C][C]1.79713972655720[/C][C]0.0128602734427978[/C][/ROW]
[ROW][C]46[/C][C]1.81[/C][C]1.75137932947343[/C][C]0.0586206705265735[/C][/ROW]
[ROW][C]47[/C][C]1.88[/C][C]1.90695173536237[/C][C]-0.0269517353623734[/C][/ROW]
[ROW][C]48[/C][C]1.87[/C][C]1.93207368290545[/C][C]-0.0620736829054451[/C][/ROW]
[ROW][C]49[/C][C]1.87[/C][C]1.91467217075956[/C][C]-0.0446721707595563[/C][/ROW]
[ROW][C]50[/C][C]1.9[/C][C]1.89325033310556[/C][C]0.00674966689444045[/C][/ROW]
[ROW][C]51[/C][C]2.01[/C][C]2.06530694104696[/C][C]-0.0553069410469638[/C][/ROW]
[ROW][C]52[/C][C]2.05[/C][C]2.17044360355169[/C][C]-0.120443603551688[/C][/ROW]
[ROW][C]53[/C][C]2.16[/C][C]2.15618038634051[/C][C]0.00381961365948635[/C][/ROW]
[ROW][C]54[/C][C]2.18[/C][C]2.18252274793323[/C][C]-0.00252274793322771[/C][/ROW]
[ROW][C]55[/C][C]2.15[/C][C]2.14421839533253[/C][C]0.00578160466747102[/C][/ROW]
[ROW][C]56[/C][C]2.12[/C][C]1.92600642662259[/C][C]0.193993573377411[/C][/ROW]
[ROW][C]57[/C][C]2.04[/C][C]2.00742260011159[/C][C]0.0325773998884089[/C][/ROW]
[ROW][C]58[/C][C]2.04[/C][C]1.98558148479818[/C][C]0.0544185152018208[/C][/ROW]
[ROW][C]59[/C][C]2.06[/C][C]2.12359675187947[/C][C]-0.0635967518794693[/C][/ROW]
[ROW][C]60[/C][C]1.93[/C][C]2.11207726879975[/C][C]-0.182077268799748[/C][/ROW]
[ROW][C]61[/C][C]1.86[/C][C]1.99628719183693[/C][C]-0.136287191836930[/C][/ROW]
[ROW][C]62[/C][C]1.94[/C][C]1.90534694284039[/C][C]0.0346530571596109[/C][/ROW]
[ROW][C]63[/C][C]2.35[/C][C]2.08949628623537[/C][C]0.260503713764634[/C][/ROW]
[ROW][C]64[/C][C]2.46[/C][C]2.44863387588456[/C][C]0.0113661241154368[/C][/ROW]
[ROW][C]65[/C][C]2.59[/C][C]2.56596459389842[/C][C]0.0240354061015844[/C][/ROW]
[ROW][C]66[/C][C]2.66[/C][C]2.60929961171829[/C][C]0.0507003882817103[/C][/ROW]
[ROW][C]67[/C][C]2.41[/C][C]2.61825196880358[/C][C]-0.208251968803575[/C][/ROW]
[ROW][C]68[/C][C]2.18[/C][C]2.25202404324695[/C][C]-0.0720240432469472[/C][/ROW]
[ROW][C]69[/C][C]2.13[/C][C]2.08357336036995[/C][C]0.0464266396300488[/C][/ROW]
[ROW][C]70[/C][C]2.11[/C][C]2.07602531226766[/C][C]0.0339746877323392[/C][/ROW]
[ROW][C]71[/C][C]2.12[/C][C]2.1767078876263[/C][C]-0.0567078876263016[/C][/ROW]
[ROW][C]72[/C][C]2.16[/C][C]2.15068285222554[/C][C]0.00931714777445602[/C][/ROW]
[ROW][C]73[/C][C]2.07[/C][C]2.20250388389495[/C][C]-0.132503883894955[/C][/ROW]
[ROW][C]74[/C][C]2.2[/C][C]2.14264522796776[/C][C]0.0573547720322414[/C][/ROW]
[ROW][C]75[/C][C]2.29[/C][C]2.38277937437592[/C][C]-0.0927793743759198[/C][/ROW]
[ROW][C]76[/C][C]2.32[/C][C]2.40406441601359[/C][C]-0.0840644160135908[/C][/ROW]
[ROW][C]77[/C][C]2.37[/C][C]2.44158461606873[/C][C]-0.0715846160687259[/C][/ROW]
[ROW][C]78[/C][C]2.38[/C][C]2.40677856904803[/C][C]-0.0267785690480333[/C][/ROW]
[ROW][C]79[/C][C]2.38[/C][C]2.30576696162897[/C][C]0.0742330383710317[/C][/ROW]
[ROW][C]80[/C][C]2.28[/C][C]2.19663887689812[/C][C]0.0833611231018758[/C][/ROW]
[ROW][C]81[/C][C]2.22[/C][C]2.17677962795706[/C][C]0.0432203720429358[/C][/ROW]
[ROW][C]82[/C][C]2.25[/C][C]2.1637369144865[/C][C]0.0862630855135018[/C][/ROW]
[ROW][C]83[/C][C]2.3[/C][C]2.29283652165931[/C][C]0.00716347834068687[/C][/ROW]
[ROW][C]84[/C][C]2.3[/C][C]2.33081079607892[/C][C]-0.0308107960789186[/C][/ROW]
[ROW][C]85[/C][C]2.23[/C][C]2.32548530904424[/C][C]-0.0954853090442436[/C][/ROW]
[ROW][C]86[/C][C]2.27[/C][C]2.32736038699631[/C][C]-0.0573603869963124[/C][/ROW]
[ROW][C]87[/C][C]2.3[/C][C]2.44620979007434[/C][C]-0.146209790074337[/C][/ROW]
[ROW][C]88[/C][C]2.32[/C][C]2.42316846522228[/C][C]-0.103168465222284[/C][/ROW]
[ROW][C]89[/C][C]2.41[/C][C]2.44560767394966[/C][C]-0.0356076739496585[/C][/ROW]
[ROW][C]90[/C][C]2.43[/C][C]2.44725849261619[/C][C]-0.0172584926161896[/C][/ROW]
[ROW][C]91[/C][C]2.45[/C][C]2.36978841171978[/C][C]0.0802115882802243[/C][/ROW]
[ROW][C]92[/C][C]2.47[/C][C]2.26626559413031[/C][C]0.203734405869694[/C][/ROW]
[ROW][C]93[/C][C]2.46[/C][C]2.34026087604981[/C][C]0.119739123950191[/C][/ROW]
[ROW][C]94[/C][C]2.5[/C][C]2.39832497519922[/C][C]0.101675024800781[/C][/ROW]
[ROW][C]95[/C][C]2.46[/C][C]2.52753317899041[/C][C]-0.0675331789904101[/C][/ROW]
[ROW][C]96[/C][C]2.43[/C][C]2.49657656118980[/C][C]-0.0665765611898044[/C][/ROW]
[ROW][C]97[/C][C]2.37[/C][C]2.45036474545687[/C][C]-0.080364745456869[/C][/ROW]
[ROW][C]98[/C][C]2.45[/C][C]2.47078777772548[/C][C]-0.0207877777254817[/C][/ROW]
[ROW][C]99[/C][C]2.53[/C][C]2.60557889866838[/C][C]-0.0755788986683825[/C][/ROW]
[ROW][C]100[/C][C]2.56[/C][C]2.64884794990773[/C][C]-0.0888479499077328[/C][/ROW]
[ROW][C]101[/C][C]2.62[/C][C]2.69455242979988[/C][C]-0.0745524297998825[/C][/ROW]
[ROW][C]102[/C][C]2.67[/C][C]2.66667893299608[/C][C]0.00332106700392165[/C][/ROW]
[ROW][C]103[/C][C]2.62[/C][C]2.62250668591578[/C][C]-0.00250668591578318[/C][/ROW]
[ROW][C]104[/C][C]2.6[/C][C]2.46970714551195[/C][C]0.130292854488054[/C][/ROW]
[ROW][C]105[/C][C]2.53[/C][C]2.46795601964556[/C][C]0.0620439803544404[/C][/ROW]
[ROW][C]106[/C][C]2.49[/C][C]2.47393785834857[/C][C]0.0160621416514268[/C][/ROW]
[ROW][C]107[/C][C]2.48[/C][C]2.5026180948813[/C][C]-0.0226180948812997[/C][/ROW]
[ROW][C]108[/C][C]2.44[/C][C]2.50834753620686[/C][C]-0.0683475362068608[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72692&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72692&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
131.581.482686965811970.0973130341880326
141.591.566727494383730.0232725056162744
151.81.783927084142440.0160729158575561
161.991.977679360976880.0123206390231181
172.062.058767538304160.00123246169583524
182.062.07266709281064-0.0126670928106405
192.082.034042549575610.0459574504243911
2021.865940774282880.134059225717118
211.851.87636411278813-0.0263641127881282
221.771.81409656056281-0.0440965605628096
231.71.92886424513356-0.228864245133563
241.661.76710342877101-0.107103428771011
251.671.69343333267237-0.0234333326723666
261.731.663351117877220.0666488821227764
271.911.91487515117494-0.0048751511749392
282.022.08959217569594-0.0695921756959352
292.072.09904464225383-0.0290446422538309
302.152.083910084150520.0660899158494783
312.12.11970110363563-0.0197011036356267
321.681.90967640861885-0.229676408618849
331.681.586451394546360.0935486054536363
341.651.619089978487270.0309100215127311
351.721.76427655219160-0.0442765521915973
361.731.77555296131678-0.0455529613167778
371.761.76604599447201-0.00604599447200727
381.841.764304140696300.075695859303704
391.992.01084819617850-0.0208481961784972
402.052.16068516977695-0.110685169776952
412.122.14122867646356-0.0212286764635632
422.132.14705851521806-0.0170585152180607
432.082.09776444445036-0.0177644444503615
441.881.853582280377560.0264177196224447
451.811.797139726557200.0128602734427978
461.811.751379329473430.0586206705265735
471.881.90695173536237-0.0269517353623734
481.871.93207368290545-0.0620736829054451
491.871.91467217075956-0.0446721707595563
501.91.893250333105560.00674966689444045
512.012.06530694104696-0.0553069410469638
522.052.17044360355169-0.120443603551688
532.162.156180386340510.00381961365948635
542.182.18252274793323-0.00252274793322771
552.152.144218395332530.00578160466747102
562.121.926006426622590.193993573377411
572.042.007422600111590.0325773998884089
582.041.985581484798180.0544185152018208
592.062.12359675187947-0.0635967518794693
601.932.11207726879975-0.182077268799748
611.861.99628719183693-0.136287191836930
621.941.905346942840390.0346530571596109
632.352.089496286235370.260503713764634
642.462.448633875884560.0113661241154368
652.592.565964593898420.0240354061015844
662.662.609299611718290.0507003882817103
672.412.61825196880358-0.208251968803575
682.182.25202404324695-0.0720240432469472
692.132.083573360369950.0464266396300488
702.112.076025312267660.0339746877323392
712.122.1767078876263-0.0567078876263016
722.162.150682852225540.00931714777445602
732.072.20250388389495-0.132503883894955
742.22.142645227967760.0573547720322414
752.292.38277937437592-0.0927793743759198
762.322.40406441601359-0.0840644160135908
772.372.44158461606873-0.0715846160687259
782.382.40677856904803-0.0267785690480333
792.382.305766961628970.0742330383710317
802.282.196638876898120.0833611231018758
812.222.176779627957060.0432203720429358
822.252.16373691448650.0862630855135018
832.32.292836521659310.00716347834068687
842.32.33081079607892-0.0308107960789186
852.232.32548530904424-0.0954853090442436
862.272.32736038699631-0.0573603869963124
872.32.44620979007434-0.146209790074337
882.322.42316846522228-0.103168465222284
892.412.44560767394966-0.0356076739496585
902.432.44725849261619-0.0172584926161896
912.452.369788411719780.0802115882802243
922.472.266265594130310.203734405869694
932.462.340260876049810.119739123950191
942.52.398324975199220.101675024800781
952.462.52753317899041-0.0675331789904101
962.432.49657656118980-0.0665765611898044
972.372.45036474545687-0.080364745456869
982.452.47078777772548-0.0207877777254817
992.532.60557889866838-0.0755788986683825
1002.562.64884794990773-0.0888479499077328
1012.622.69455242979988-0.0745524297998825
1022.672.666678932996080.00332106700392165
1032.622.62250668591578-0.00250668591578318
1042.62.469707145511950.130292854488054
1052.532.467956019645560.0620439803544404
1062.492.473937858348570.0160621416514268
1072.482.5026180948813-0.0226180948812997
1082.442.50834753620686-0.0683475362068608







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1092.457342200219592.290632294771042.62405210566815
1102.554059608466922.336176455240422.77194276169343
1112.696721929691662.437148917426802.95629494195653
1122.800848150550252.505029450790083.09666685031042
1132.923437498807812.595007899656513.2518670979591
1142.971223837810362.612822785980093.32962488964063
1152.92387057796112.537521111758533.31022004416367
1162.795411504936032.382723899490073.208099110382
1172.673435777737332.235728075316733.11114348015793
1182.61963803465612.158012538081313.08126353123089
1192.628128560663942.143523021568823.11273409975906
1202.644990539117912.138213871439043.15176720679678

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 2.45734220021959 & 2.29063229477104 & 2.62405210566815 \tabularnewline
110 & 2.55405960846692 & 2.33617645524042 & 2.77194276169343 \tabularnewline
111 & 2.69672192969166 & 2.43714891742680 & 2.95629494195653 \tabularnewline
112 & 2.80084815055025 & 2.50502945079008 & 3.09666685031042 \tabularnewline
113 & 2.92343749880781 & 2.59500789965651 & 3.2518670979591 \tabularnewline
114 & 2.97122383781036 & 2.61282278598009 & 3.32962488964063 \tabularnewline
115 & 2.9238705779611 & 2.53752111175853 & 3.31022004416367 \tabularnewline
116 & 2.79541150493603 & 2.38272389949007 & 3.208099110382 \tabularnewline
117 & 2.67343577773733 & 2.23572807531673 & 3.11114348015793 \tabularnewline
118 & 2.6196380346561 & 2.15801253808131 & 3.08126353123089 \tabularnewline
119 & 2.62812856066394 & 2.14352302156882 & 3.11273409975906 \tabularnewline
120 & 2.64499053911791 & 2.13821387143904 & 3.15176720679678 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72692&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]109[/C][C]2.45734220021959[/C][C]2.29063229477104[/C][C]2.62405210566815[/C][/ROW]
[ROW][C]110[/C][C]2.55405960846692[/C][C]2.33617645524042[/C][C]2.77194276169343[/C][/ROW]
[ROW][C]111[/C][C]2.69672192969166[/C][C]2.43714891742680[/C][C]2.95629494195653[/C][/ROW]
[ROW][C]112[/C][C]2.80084815055025[/C][C]2.50502945079008[/C][C]3.09666685031042[/C][/ROW]
[ROW][C]113[/C][C]2.92343749880781[/C][C]2.59500789965651[/C][C]3.2518670979591[/C][/ROW]
[ROW][C]114[/C][C]2.97122383781036[/C][C]2.61282278598009[/C][C]3.32962488964063[/C][/ROW]
[ROW][C]115[/C][C]2.9238705779611[/C][C]2.53752111175853[/C][C]3.31022004416367[/C][/ROW]
[ROW][C]116[/C][C]2.79541150493603[/C][C]2.38272389949007[/C][C]3.208099110382[/C][/ROW]
[ROW][C]117[/C][C]2.67343577773733[/C][C]2.23572807531673[/C][C]3.11114348015793[/C][/ROW]
[ROW][C]118[/C][C]2.6196380346561[/C][C]2.15801253808131[/C][C]3.08126353123089[/C][/ROW]
[ROW][C]119[/C][C]2.62812856066394[/C][C]2.14352302156882[/C][C]3.11273409975906[/C][/ROW]
[ROW][C]120[/C][C]2.64499053911791[/C][C]2.13821387143904[/C][C]3.15176720679678[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72692&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72692&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
1092.457342200219592.290632294771042.62405210566815
1102.554059608466922.336176455240422.77194276169343
1112.696721929691662.437148917426802.95629494195653
1122.800848150550252.505029450790083.09666685031042
1132.923437498807812.595007899656513.2518670979591
1142.971223837810362.612822785980093.32962488964063
1152.92387057796112.537521111758533.31022004416367
1162.795411504936032.382723899490073.208099110382
1172.673435777737332.235728075316733.11114348015793
1182.61963803465612.158012538081313.08126353123089
1192.628128560663942.143523021568823.11273409975906
1202.644990539117912.138213871439043.15176720679678



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')