Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 19 Aug 2010 21:31:31 +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/Aug/19/t1282253459xtg13qwgwiitdy4.htm/, Retrieved Fri, 03 May 2024 09:34:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79393, Retrieved Fri, 03 May 2024 09:34:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsgilian keirsebelik
Estimated Impact130
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [tijdreeks B-Stap 27] [2010-08-19 21:31:31] [46199ea7e385a69efb178ac615a86e3a] [Current]
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Dataseries X:
51
50
49
47
45
44
45
47
48
48
49
51
45
42
40
37
28
33
32
38
38
34
38
48
41
41
43
37
22
30
32
41
44
37
53
67
62
63
68
62
50
64
71
76
73
68
78
89
74
74
73
65
55
69
80
81
80
86
90
100
90
89
83
63
48
62
69
73
76
77
75
77
78
73
74
55
36
41
52
53
49
47
44
55




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=79393&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=79393&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79393&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
alpha0.623952021814807
beta0.100724002028723
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.623952021814807 \tabularnewline
beta & 0.100724002028723 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79393&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]0.623952021814807[/C][/ROW]
[ROW][C]beta[/C][C]0.100724002028723[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79393&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79393&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
alpha0.623952021814807
beta0.100724002028723
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
134550.7978098290599-5.79780982905986
144243.800874202842-1.80087420284197
154040.0596552002087-0.0596552002087094
163736.60945750095490.390542499045083
172827.50637263587840.493627364121593
183332.04029741911240.95970258088763
193233.6336784845388-1.63367848453877
203833.79790915612934.20209084387073
213836.99246846996151.00753153003851
223437.3404296528171-3.34042965281712
233836.09886920048911.90113079951090
244839.28893791876788.71106208123223
254136.92861933490374.07138066509633
264138.52919687838462.47080312161540
274339.31311557905773.68688442094231
283739.8103674688996-2.81036746889963
292229.988158484071-7.98815848407097
303030.1113934267199-0.111393426719928
313230.70018209980191.29981790019806
324135.71262014731825.28737985268179
334439.27456437820374.72543562179625
343741.432460453792-4.43246045379204
355342.537155716380810.4628442836192
366755.224813627743111.7751863722569
376254.81881948870417.18118051129586
386359.74051111781253.25948888218755
396863.50604543098734.49395456901267
406264.1465224511985-2.14652245119845
415054.916074212409-4.916074212409
426462.2359061801661.76409381983397
437166.96118298035584.03881701964418
447677.7898683039958-1.78986830399580
457378.887576450827-5.88757645082707
466872.4756037036228-4.47560370362275
477880.6479672788918-2.64796727889183
488986.31787534760922.68212465239080
497478.6084731513218-4.6084731513218
507474.0560914241881-0.056091424188125
517375.3655560264167-2.36555602641674
526567.9462653002144-2.94626530021442
535555.8424458748523-0.842445874852302
546967.13921957860151.86078042139850
558071.70943511323158.29056488676846
568182.1955570202008-1.19555702020075
578081.356917915551-1.35691791555102
588677.82133215011158.17866784988851
599094.890419264536-4.89041926453596
60100101.338370157700-1.33837015769979
619088.29893669748351.70106330251646
628989.71203119589-0.71203119589002
638390.0192418004899-7.0192418004899
646379.4609203892645-16.4609203892645
654858.8494073680886-10.8494073680886
666263.4236187732553-1.42361877325534
676966.66077855777062.33922144222939
687367.79063129312315.2093687068769
697669.21452968710266.78547031289736
707773.18381607001933.81618392998067
717581.1807247535695-6.18072475356946
727786.6426420725949-9.64264207259485
737867.526130310483810.4738696895162
747372.01835600327920.981643996720848
757469.62972740347294.37027259652714
765561.9623910960823-6.96239109608229
773649.3196550154634-13.3196550154634
784155.6738038908738-14.6738038908738
795251.00246342591710.997536574082872
805351.23413254520721.76586745479281
814949.7453779544746-0.745377954474598
824746.06912815063730.930871849362731
834446.4950361371652-2.49503613716519
845551.17504648820663.82495351179342

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 45 & 50.7978098290599 & -5.79780982905986 \tabularnewline
14 & 42 & 43.800874202842 & -1.80087420284197 \tabularnewline
15 & 40 & 40.0596552002087 & -0.0596552002087094 \tabularnewline
16 & 37 & 36.6094575009549 & 0.390542499045083 \tabularnewline
17 & 28 & 27.5063726358784 & 0.493627364121593 \tabularnewline
18 & 33 & 32.0402974191124 & 0.95970258088763 \tabularnewline
19 & 32 & 33.6336784845388 & -1.63367848453877 \tabularnewline
20 & 38 & 33.7979091561293 & 4.20209084387073 \tabularnewline
21 & 38 & 36.9924684699615 & 1.00753153003851 \tabularnewline
22 & 34 & 37.3404296528171 & -3.34042965281712 \tabularnewline
23 & 38 & 36.0988692004891 & 1.90113079951090 \tabularnewline
24 & 48 & 39.2889379187678 & 8.71106208123223 \tabularnewline
25 & 41 & 36.9286193349037 & 4.07138066509633 \tabularnewline
26 & 41 & 38.5291968783846 & 2.47080312161540 \tabularnewline
27 & 43 & 39.3131155790577 & 3.68688442094231 \tabularnewline
28 & 37 & 39.8103674688996 & -2.81036746889963 \tabularnewline
29 & 22 & 29.988158484071 & -7.98815848407097 \tabularnewline
30 & 30 & 30.1113934267199 & -0.111393426719928 \tabularnewline
31 & 32 & 30.7001820998019 & 1.29981790019806 \tabularnewline
32 & 41 & 35.7126201473182 & 5.28737985268179 \tabularnewline
33 & 44 & 39.2745643782037 & 4.72543562179625 \tabularnewline
34 & 37 & 41.432460453792 & -4.43246045379204 \tabularnewline
35 & 53 & 42.5371557163808 & 10.4628442836192 \tabularnewline
36 & 67 & 55.2248136277431 & 11.7751863722569 \tabularnewline
37 & 62 & 54.8188194887041 & 7.18118051129586 \tabularnewline
38 & 63 & 59.7405111178125 & 3.25948888218755 \tabularnewline
39 & 68 & 63.5060454309873 & 4.49395456901267 \tabularnewline
40 & 62 & 64.1465224511985 & -2.14652245119845 \tabularnewline
41 & 50 & 54.916074212409 & -4.916074212409 \tabularnewline
42 & 64 & 62.235906180166 & 1.76409381983397 \tabularnewline
43 & 71 & 66.9611829803558 & 4.03881701964418 \tabularnewline
44 & 76 & 77.7898683039958 & -1.78986830399580 \tabularnewline
45 & 73 & 78.887576450827 & -5.88757645082707 \tabularnewline
46 & 68 & 72.4756037036228 & -4.47560370362275 \tabularnewline
47 & 78 & 80.6479672788918 & -2.64796727889183 \tabularnewline
48 & 89 & 86.3178753476092 & 2.68212465239080 \tabularnewline
49 & 74 & 78.6084731513218 & -4.6084731513218 \tabularnewline
50 & 74 & 74.0560914241881 & -0.056091424188125 \tabularnewline
51 & 73 & 75.3655560264167 & -2.36555602641674 \tabularnewline
52 & 65 & 67.9462653002144 & -2.94626530021442 \tabularnewline
53 & 55 & 55.8424458748523 & -0.842445874852302 \tabularnewline
54 & 69 & 67.1392195786015 & 1.86078042139850 \tabularnewline
55 & 80 & 71.7094351132315 & 8.29056488676846 \tabularnewline
56 & 81 & 82.1955570202008 & -1.19555702020075 \tabularnewline
57 & 80 & 81.356917915551 & -1.35691791555102 \tabularnewline
58 & 86 & 77.8213321501115 & 8.17866784988851 \tabularnewline
59 & 90 & 94.890419264536 & -4.89041926453596 \tabularnewline
60 & 100 & 101.338370157700 & -1.33837015769979 \tabularnewline
61 & 90 & 88.2989366974835 & 1.70106330251646 \tabularnewline
62 & 89 & 89.71203119589 & -0.71203119589002 \tabularnewline
63 & 83 & 90.0192418004899 & -7.0192418004899 \tabularnewline
64 & 63 & 79.4609203892645 & -16.4609203892645 \tabularnewline
65 & 48 & 58.8494073680886 & -10.8494073680886 \tabularnewline
66 & 62 & 63.4236187732553 & -1.42361877325534 \tabularnewline
67 & 69 & 66.6607785577706 & 2.33922144222939 \tabularnewline
68 & 73 & 67.7906312931231 & 5.2093687068769 \tabularnewline
69 & 76 & 69.2145296871026 & 6.78547031289736 \tabularnewline
70 & 77 & 73.1838160700193 & 3.81618392998067 \tabularnewline
71 & 75 & 81.1807247535695 & -6.18072475356946 \tabularnewline
72 & 77 & 86.6426420725949 & -9.64264207259485 \tabularnewline
73 & 78 & 67.5261303104838 & 10.4738696895162 \tabularnewline
74 & 73 & 72.0183560032792 & 0.981643996720848 \tabularnewline
75 & 74 & 69.6297274034729 & 4.37027259652714 \tabularnewline
76 & 55 & 61.9623910960823 & -6.96239109608229 \tabularnewline
77 & 36 & 49.3196550154634 & -13.3196550154634 \tabularnewline
78 & 41 & 55.6738038908738 & -14.6738038908738 \tabularnewline
79 & 52 & 51.0024634259171 & 0.997536574082872 \tabularnewline
80 & 53 & 51.2341325452072 & 1.76586745479281 \tabularnewline
81 & 49 & 49.7453779544746 & -0.745377954474598 \tabularnewline
82 & 47 & 46.0691281506373 & 0.930871849362731 \tabularnewline
83 & 44 & 46.4950361371652 & -2.49503613716519 \tabularnewline
84 & 55 & 51.1750464882066 & 3.82495351179342 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79393&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]45[/C][C]50.7978098290599[/C][C]-5.79780982905986[/C][/ROW]
[ROW][C]14[/C][C]42[/C][C]43.800874202842[/C][C]-1.80087420284197[/C][/ROW]
[ROW][C]15[/C][C]40[/C][C]40.0596552002087[/C][C]-0.0596552002087094[/C][/ROW]
[ROW][C]16[/C][C]37[/C][C]36.6094575009549[/C][C]0.390542499045083[/C][/ROW]
[ROW][C]17[/C][C]28[/C][C]27.5063726358784[/C][C]0.493627364121593[/C][/ROW]
[ROW][C]18[/C][C]33[/C][C]32.0402974191124[/C][C]0.95970258088763[/C][/ROW]
[ROW][C]19[/C][C]32[/C][C]33.6336784845388[/C][C]-1.63367848453877[/C][/ROW]
[ROW][C]20[/C][C]38[/C][C]33.7979091561293[/C][C]4.20209084387073[/C][/ROW]
[ROW][C]21[/C][C]38[/C][C]36.9924684699615[/C][C]1.00753153003851[/C][/ROW]
[ROW][C]22[/C][C]34[/C][C]37.3404296528171[/C][C]-3.34042965281712[/C][/ROW]
[ROW][C]23[/C][C]38[/C][C]36.0988692004891[/C][C]1.90113079951090[/C][/ROW]
[ROW][C]24[/C][C]48[/C][C]39.2889379187678[/C][C]8.71106208123223[/C][/ROW]
[ROW][C]25[/C][C]41[/C][C]36.9286193349037[/C][C]4.07138066509633[/C][/ROW]
[ROW][C]26[/C][C]41[/C][C]38.5291968783846[/C][C]2.47080312161540[/C][/ROW]
[ROW][C]27[/C][C]43[/C][C]39.3131155790577[/C][C]3.68688442094231[/C][/ROW]
[ROW][C]28[/C][C]37[/C][C]39.8103674688996[/C][C]-2.81036746889963[/C][/ROW]
[ROW][C]29[/C][C]22[/C][C]29.988158484071[/C][C]-7.98815848407097[/C][/ROW]
[ROW][C]30[/C][C]30[/C][C]30.1113934267199[/C][C]-0.111393426719928[/C][/ROW]
[ROW][C]31[/C][C]32[/C][C]30.7001820998019[/C][C]1.29981790019806[/C][/ROW]
[ROW][C]32[/C][C]41[/C][C]35.7126201473182[/C][C]5.28737985268179[/C][/ROW]
[ROW][C]33[/C][C]44[/C][C]39.2745643782037[/C][C]4.72543562179625[/C][/ROW]
[ROW][C]34[/C][C]37[/C][C]41.432460453792[/C][C]-4.43246045379204[/C][/ROW]
[ROW][C]35[/C][C]53[/C][C]42.5371557163808[/C][C]10.4628442836192[/C][/ROW]
[ROW][C]36[/C][C]67[/C][C]55.2248136277431[/C][C]11.7751863722569[/C][/ROW]
[ROW][C]37[/C][C]62[/C][C]54.8188194887041[/C][C]7.18118051129586[/C][/ROW]
[ROW][C]38[/C][C]63[/C][C]59.7405111178125[/C][C]3.25948888218755[/C][/ROW]
[ROW][C]39[/C][C]68[/C][C]63.5060454309873[/C][C]4.49395456901267[/C][/ROW]
[ROW][C]40[/C][C]62[/C][C]64.1465224511985[/C][C]-2.14652245119845[/C][/ROW]
[ROW][C]41[/C][C]50[/C][C]54.916074212409[/C][C]-4.916074212409[/C][/ROW]
[ROW][C]42[/C][C]64[/C][C]62.235906180166[/C][C]1.76409381983397[/C][/ROW]
[ROW][C]43[/C][C]71[/C][C]66.9611829803558[/C][C]4.03881701964418[/C][/ROW]
[ROW][C]44[/C][C]76[/C][C]77.7898683039958[/C][C]-1.78986830399580[/C][/ROW]
[ROW][C]45[/C][C]73[/C][C]78.887576450827[/C][C]-5.88757645082707[/C][/ROW]
[ROW][C]46[/C][C]68[/C][C]72.4756037036228[/C][C]-4.47560370362275[/C][/ROW]
[ROW][C]47[/C][C]78[/C][C]80.6479672788918[/C][C]-2.64796727889183[/C][/ROW]
[ROW][C]48[/C][C]89[/C][C]86.3178753476092[/C][C]2.68212465239080[/C][/ROW]
[ROW][C]49[/C][C]74[/C][C]78.6084731513218[/C][C]-4.6084731513218[/C][/ROW]
[ROW][C]50[/C][C]74[/C][C]74.0560914241881[/C][C]-0.056091424188125[/C][/ROW]
[ROW][C]51[/C][C]73[/C][C]75.3655560264167[/C][C]-2.36555602641674[/C][/ROW]
[ROW][C]52[/C][C]65[/C][C]67.9462653002144[/C][C]-2.94626530021442[/C][/ROW]
[ROW][C]53[/C][C]55[/C][C]55.8424458748523[/C][C]-0.842445874852302[/C][/ROW]
[ROW][C]54[/C][C]69[/C][C]67.1392195786015[/C][C]1.86078042139850[/C][/ROW]
[ROW][C]55[/C][C]80[/C][C]71.7094351132315[/C][C]8.29056488676846[/C][/ROW]
[ROW][C]56[/C][C]81[/C][C]82.1955570202008[/C][C]-1.19555702020075[/C][/ROW]
[ROW][C]57[/C][C]80[/C][C]81.356917915551[/C][C]-1.35691791555102[/C][/ROW]
[ROW][C]58[/C][C]86[/C][C]77.8213321501115[/C][C]8.17866784988851[/C][/ROW]
[ROW][C]59[/C][C]90[/C][C]94.890419264536[/C][C]-4.89041926453596[/C][/ROW]
[ROW][C]60[/C][C]100[/C][C]101.338370157700[/C][C]-1.33837015769979[/C][/ROW]
[ROW][C]61[/C][C]90[/C][C]88.2989366974835[/C][C]1.70106330251646[/C][/ROW]
[ROW][C]62[/C][C]89[/C][C]89.71203119589[/C][C]-0.71203119589002[/C][/ROW]
[ROW][C]63[/C][C]83[/C][C]90.0192418004899[/C][C]-7.0192418004899[/C][/ROW]
[ROW][C]64[/C][C]63[/C][C]79.4609203892645[/C][C]-16.4609203892645[/C][/ROW]
[ROW][C]65[/C][C]48[/C][C]58.8494073680886[/C][C]-10.8494073680886[/C][/ROW]
[ROW][C]66[/C][C]62[/C][C]63.4236187732553[/C][C]-1.42361877325534[/C][/ROW]
[ROW][C]67[/C][C]69[/C][C]66.6607785577706[/C][C]2.33922144222939[/C][/ROW]
[ROW][C]68[/C][C]73[/C][C]67.7906312931231[/C][C]5.2093687068769[/C][/ROW]
[ROW][C]69[/C][C]76[/C][C]69.2145296871026[/C][C]6.78547031289736[/C][/ROW]
[ROW][C]70[/C][C]77[/C][C]73.1838160700193[/C][C]3.81618392998067[/C][/ROW]
[ROW][C]71[/C][C]75[/C][C]81.1807247535695[/C][C]-6.18072475356946[/C][/ROW]
[ROW][C]72[/C][C]77[/C][C]86.6426420725949[/C][C]-9.64264207259485[/C][/ROW]
[ROW][C]73[/C][C]78[/C][C]67.5261303104838[/C][C]10.4738696895162[/C][/ROW]
[ROW][C]74[/C][C]73[/C][C]72.0183560032792[/C][C]0.981643996720848[/C][/ROW]
[ROW][C]75[/C][C]74[/C][C]69.6297274034729[/C][C]4.37027259652714[/C][/ROW]
[ROW][C]76[/C][C]55[/C][C]61.9623910960823[/C][C]-6.96239109608229[/C][/ROW]
[ROW][C]77[/C][C]36[/C][C]49.3196550154634[/C][C]-13.3196550154634[/C][/ROW]
[ROW][C]78[/C][C]41[/C][C]55.6738038908738[/C][C]-14.6738038908738[/C][/ROW]
[ROW][C]79[/C][C]52[/C][C]51.0024634259171[/C][C]0.997536574082872[/C][/ROW]
[ROW][C]80[/C][C]53[/C][C]51.2341325452072[/C][C]1.76586745479281[/C][/ROW]
[ROW][C]81[/C][C]49[/C][C]49.7453779544746[/C][C]-0.745377954474598[/C][/ROW]
[ROW][C]82[/C][C]47[/C][C]46.0691281506373[/C][C]0.930871849362731[/C][/ROW]
[ROW][C]83[/C][C]44[/C][C]46.4950361371652[/C][C]-2.49503613716519[/C][/ROW]
[ROW][C]84[/C][C]55[/C][C]51.1750464882066[/C][C]3.82495351179342[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79393&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79393&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
134550.7978098290599-5.79780982905986
144243.800874202842-1.80087420284197
154040.0596552002087-0.0596552002087094
163736.60945750095490.390542499045083
172827.50637263587840.493627364121593
183332.04029741911240.95970258088763
193233.6336784845388-1.63367848453877
203833.79790915612934.20209084387073
213836.99246846996151.00753153003851
223437.3404296528171-3.34042965281712
233836.09886920048911.90113079951090
244839.28893791876788.71106208123223
254136.92861933490374.07138066509633
264138.52919687838462.47080312161540
274339.31311557905773.68688442094231
283739.8103674688996-2.81036746889963
292229.988158484071-7.98815848407097
303030.1113934267199-0.111393426719928
313230.70018209980191.29981790019806
324135.71262014731825.28737985268179
334439.27456437820374.72543562179625
343741.432460453792-4.43246045379204
355342.537155716380810.4628442836192
366755.224813627743111.7751863722569
376254.81881948870417.18118051129586
386359.74051111781253.25948888218755
396863.50604543098734.49395456901267
406264.1465224511985-2.14652245119845
415054.916074212409-4.916074212409
426462.2359061801661.76409381983397
437166.96118298035584.03881701964418
447677.7898683039958-1.78986830399580
457378.887576450827-5.88757645082707
466872.4756037036228-4.47560370362275
477880.6479672788918-2.64796727889183
488986.31787534760922.68212465239080
497478.6084731513218-4.6084731513218
507474.0560914241881-0.056091424188125
517375.3655560264167-2.36555602641674
526567.9462653002144-2.94626530021442
535555.8424458748523-0.842445874852302
546967.13921957860151.86078042139850
558071.70943511323158.29056488676846
568182.1955570202008-1.19555702020075
578081.356917915551-1.35691791555102
588677.82133215011158.17866784988851
599094.890419264536-4.89041926453596
60100101.338370157700-1.33837015769979
619088.29893669748351.70106330251646
628989.71203119589-0.71203119589002
638390.0192418004899-7.0192418004899
646379.4609203892645-16.4609203892645
654858.8494073680886-10.8494073680886
666263.4236187732553-1.42361877325534
676966.66077855777062.33922144222939
687367.79063129312315.2093687068769
697669.21452968710266.78547031289736
707773.18381607001933.81618392998067
717581.1807247535695-6.18072475356946
727786.6426420725949-9.64264207259485
737867.526130310483810.4738696895162
747372.01835600327920.981643996720848
757469.62972740347294.37027259652714
765561.9623910960823-6.96239109608229
773649.3196550154634-13.3196550154634
784155.6738038908738-14.6738038908738
795251.00246342591710.997536574082872
805351.23413254520721.76586745479281
814949.7453779544746-0.745377954474598
824746.06912815063730.930871849362731
834446.4950361371652-2.49503613716519
845551.17504648820663.82495351179342







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8547.093086207817336.065820053907858.1203523617269
8639.888981153650826.51143547980753.2665268274945
8736.508841107467720.783241143240852.2344410716946
8819.92508120458911.8262282605402338.0239341486379
897.74551398569121-12.766464474364928.2574924457473
9021.2479703177717-1.7253494842330944.2212901197765
9131.89446582402556.4067129581442957.3822186899068
9231.9988675979193.9407455696941560.0569896261438
9328.5591866478995-2.1268362394759759.2452095352749
9426.1204509708027-7.2518053802046659.4927073218101
9524.7608150568015-11.356289932566360.8779200461693
9633.6146142216486-5.3058934617734672.5351219050707

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 47.0930862078173 & 36.0658200539078 & 58.1203523617269 \tabularnewline
86 & 39.8889811536508 & 26.511435479807 & 53.2665268274945 \tabularnewline
87 & 36.5088411074677 & 20.7832411432408 & 52.2344410716946 \tabularnewline
88 & 19.9250812045891 & 1.82622826054023 & 38.0239341486379 \tabularnewline
89 & 7.74551398569121 & -12.7664644743649 & 28.2574924457473 \tabularnewline
90 & 21.2479703177717 & -1.72534948423309 & 44.2212901197765 \tabularnewline
91 & 31.8944658240255 & 6.40671295814429 & 57.3822186899068 \tabularnewline
92 & 31.998867597919 & 3.94074556969415 & 60.0569896261438 \tabularnewline
93 & 28.5591866478995 & -2.12683623947597 & 59.2452095352749 \tabularnewline
94 & 26.1204509708027 & -7.25180538020466 & 59.4927073218101 \tabularnewline
95 & 24.7608150568015 & -11.3562899325663 & 60.8779200461693 \tabularnewline
96 & 33.6146142216486 & -5.30589346177346 & 72.5351219050707 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79393&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]85[/C][C]47.0930862078173[/C][C]36.0658200539078[/C][C]58.1203523617269[/C][/ROW]
[ROW][C]86[/C][C]39.8889811536508[/C][C]26.511435479807[/C][C]53.2665268274945[/C][/ROW]
[ROW][C]87[/C][C]36.5088411074677[/C][C]20.7832411432408[/C][C]52.2344410716946[/C][/ROW]
[ROW][C]88[/C][C]19.9250812045891[/C][C]1.82622826054023[/C][C]38.0239341486379[/C][/ROW]
[ROW][C]89[/C][C]7.74551398569121[/C][C]-12.7664644743649[/C][C]28.2574924457473[/C][/ROW]
[ROW][C]90[/C][C]21.2479703177717[/C][C]-1.72534948423309[/C][C]44.2212901197765[/C][/ROW]
[ROW][C]91[/C][C]31.8944658240255[/C][C]6.40671295814429[/C][C]57.3822186899068[/C][/ROW]
[ROW][C]92[/C][C]31.998867597919[/C][C]3.94074556969415[/C][C]60.0569896261438[/C][/ROW]
[ROW][C]93[/C][C]28.5591866478995[/C][C]-2.12683623947597[/C][C]59.2452095352749[/C][/ROW]
[ROW][C]94[/C][C]26.1204509708027[/C][C]-7.25180538020466[/C][C]59.4927073218101[/C][/ROW]
[ROW][C]95[/C][C]24.7608150568015[/C][C]-11.3562899325663[/C][C]60.8779200461693[/C][/ROW]
[ROW][C]96[/C][C]33.6146142216486[/C][C]-5.30589346177346[/C][C]72.5351219050707[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79393&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79393&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
8547.093086207817336.065820053907858.1203523617269
8639.888981153650826.51143547980753.2665268274945
8736.508841107467720.783241143240852.2344410716946
8819.92508120458911.8262282605402338.0239341486379
897.74551398569121-12.766464474364928.2574924457473
9021.2479703177717-1.7253494842330944.2212901197765
9131.89446582402556.4067129581442957.3822186899068
9231.9988675979193.9407455696941560.0569896261438
9328.5591866478995-2.1268362394759759.2452095352749
9426.1204509708027-7.2518053802046659.4927073218101
9524.7608150568015-11.356289932566360.8779200461693
9633.6146142216486-5.3058934617734672.5351219050707



Parameters (Session):
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')