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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 19 May 2011 14:47:31 +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/2011/May/19/t1305816251pwmovhiymncxehy.htm/, Retrieved Sat, 11 May 2024 15:20:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=122058, Retrieved Sat, 11 May 2024 15:20:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact78

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Opgave 10 Eigen r...] [2011-05-19 14:47:31] [ee335b92128d1ec04d3c346475765c6a] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
0,8833
0,87
0,8758
0,8858
0,917
0,9554
0,9922
0,9778
0,9808
0,9811
1,0014
1,0183
1,0622
1,0773
1,0807
1,0848
1,1582
1,1663
1,1372
1,1139
1,1222
1,1692
1,1702
1,2286
1,2613
1,2646
1,2262
1,1985
1,2007
1,2138
1,2266
1,2176
1,2218
1,249
1,2991
1,3408
1,3119
1,3014
1,3201
1,2938
1,2694
1,2165
1,2037
1,2292
1,2256
1,2015
1,1786
1,1856
1,2103
1,1938
1,202
1,2271
1,277
1,265
1,2684
1,2811
1,2727
1,2611
1,2881
1,3213
1,2999
1,3074
1,3242
1,3516
1,3511
1,3419
1,3716
1,3622
1,3896
1,4227
1,4684
1,457
1,4718
1,4748
1,5527
1,575
1,5557
1,5553
1,577
1,4975
1,4369
1,3322
1,2732
1,3449
1,3239
1,2785
1,305
1,319
1,365
1,4016
1,4088
1,4268
1,4562
1,4816
1,4914
1,4614
1,4272

Tables (Output of Computation)





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

\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' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122058&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' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122058&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122058&T=0

As an alternative you can also use a QR Code:  
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' @ www.wessa.org






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.026516277171168
gamma0.0783163830565602

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.026516277171168 \tabularnewline
gamma & 0.0783163830565602 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122058&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.026516277171168[/C][/ROW]
[ROW][C]gamma[/C][C]0.0783163830565602[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122058&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122058&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.026516277171168
gamma0.0783163830565602






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131.06220.956419204059830.10578079594017
141.07731.08369586570174-0.00639586570173889
151.08071.08707627115404-0.00637627115404249
161.08481.08884052951414-0.00404052951413636
171.15821.16099172304695-0.00279172304695452
181.16631.16809269694486-0.00179269694485651
191.13721.17951599462912-0.0423159946291161
201.11391.12312726532009-0.00922726532009022
211.12221.1158992592620.0063007407380029
221.16921.122012164783120.0471878352168769
231.17021.18875091050084-0.0185509105008419
241.22861.185363176082890.0432368239171099
251.26131.27591798902321-0.0146179890232103
261.26461.28254704104125-0.0179470410412526
271.22621.2738211523266-0.0476211523266008
281.19851.23269174998563-0.0341917499856312
291.20071.27224344539938-0.071543445399378
301.21381.206321379571390.0074786204286117
311.22661.222990518076860.00360948192313537
321.21761.209719561433320.00788043856668397
331.22181.217245187993250.0045548120067529
341.2491.219211797984210.0297882020157862
351.29911.26568917020530.033410829794704
361.34081.312779267695320.028020732304683
371.31191.38623060653298-0.0743306065329805
381.30141.32967630223452-0.0282763022345176
391.32011.306876519967090.0132234800329083
401.29381.32446049076214-0.0306604907621448
411.26941.36550582202423-0.096105822024225
421.21651.27233245340967-0.0558324534096681
431.20371.22132281793324-0.0176228179332441
441.22921.181888859741720.0473111402582775
451.22561.224960041716760.000639958283238373
461.20151.21902284436131-0.0175228443613111
471.17861.2129457037634-0.0343457037633998
481.18561.185239150229440.000360849770562943
491.21031.2232570519553-0.0129570519553039
501.19381.221930145841-0.0281301458410022
511.2021.193134239097020.00886576090298252
521.22711.200102659403790.0269973405962129
531.2771.29407686170325-0.0170768617032542
541.2651.27729904690512-0.012299046905117
551.26841.268343755301775.62446982270703e-05
561.28111.245578580035110.0355214199648859
571.27271.27553714251908-0.00283714251908296
581.26111.26470774539501-0.00360774539500586
591.28811.271499581418150.0166004185818502
601.32131.295043929385090.0262560706149104
611.29991.35994847596427-0.0600484759642737
621.30741.31127288059857-0.00387288059856528
631.32421.307120186223160.0170798137768366
641.35161.322906412632630.028693587367365
651.35111.41922559308164-0.0681255930816362
661.34191.35069415597303-0.00879415597303357
671.37161.34463180102910.0269681989709003
681.36221.348880230601150.0133197693988476
691.38961.356150087965050.033449912034945
701.42271.382082888437260.0406171115627423
711.46841.434747403025350.0336525969746515
721.4571.47744391128092-0.0204439112809238
731.47181.49651014819627-0.0247101481962699
741.47481.48497159372442-0.0101715937244231
751.55271.476151880925950.0765481190740454
761.5751.554614985401590.0203850145984137
771.55571.64561385343215-0.0899138534321493
781.55531.55770467277302-0.00240467277301515
791.5771.560611743136590.0163882568634068
801.49751.55657963203127-0.0590796320312688
811.43691.49182972679982-0.0549297267998237
821.33221.4274190282724-0.0952190282723961
831.27321.33868167412676-0.0654816741267565
841.34491.274049510572650.0708504894273543
851.32391.37863653512135-0.0547365351213476
861.27851.33050179265135-0.0520017926513472
871.3051.272172898704010.0328271012959929
881.3191.298076684554030.0209233154459696
891.3651.38078982631907-0.0157898263190688
901.40161.360146138907910.041453861092092
911.40881.401216174311770.00758382568822569
921.42681.382450602469070.0443493975309255
931.45621.417943250053050.0382567499469544
941.48161.446003509971640.0355964900283601
951.49141.490834896367550.000565103632446551
961.46141.49675404747877-0.0353540474787679
971.42721.49682492309003-0.0696249230900319

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1.0622 & 0.95641920405983 & 0.10578079594017 \tabularnewline
14 & 1.0773 & 1.08369586570174 & -0.00639586570173889 \tabularnewline
15 & 1.0807 & 1.08707627115404 & -0.00637627115404249 \tabularnewline
16 & 1.0848 & 1.08884052951414 & -0.00404052951413636 \tabularnewline
17 & 1.1582 & 1.16099172304695 & -0.00279172304695452 \tabularnewline
18 & 1.1663 & 1.16809269694486 & -0.00179269694485651 \tabularnewline
19 & 1.1372 & 1.17951599462912 & -0.0423159946291161 \tabularnewline
20 & 1.1139 & 1.12312726532009 & -0.00922726532009022 \tabularnewline
21 & 1.1222 & 1.115899259262 & 0.0063007407380029 \tabularnewline
22 & 1.1692 & 1.12201216478312 & 0.0471878352168769 \tabularnewline
23 & 1.1702 & 1.18875091050084 & -0.0185509105008419 \tabularnewline
24 & 1.2286 & 1.18536317608289 & 0.0432368239171099 \tabularnewline
25 & 1.2613 & 1.27591798902321 & -0.0146179890232103 \tabularnewline
26 & 1.2646 & 1.28254704104125 & -0.0179470410412526 \tabularnewline
27 & 1.2262 & 1.2738211523266 & -0.0476211523266008 \tabularnewline
28 & 1.1985 & 1.23269174998563 & -0.0341917499856312 \tabularnewline
29 & 1.2007 & 1.27224344539938 & -0.071543445399378 \tabularnewline
30 & 1.2138 & 1.20632137957139 & 0.0074786204286117 \tabularnewline
31 & 1.2266 & 1.22299051807686 & 0.00360948192313537 \tabularnewline
32 & 1.2176 & 1.20971956143332 & 0.00788043856668397 \tabularnewline
33 & 1.2218 & 1.21724518799325 & 0.0045548120067529 \tabularnewline
34 & 1.249 & 1.21921179798421 & 0.0297882020157862 \tabularnewline
35 & 1.2991 & 1.2656891702053 & 0.033410829794704 \tabularnewline
36 & 1.3408 & 1.31277926769532 & 0.028020732304683 \tabularnewline
37 & 1.3119 & 1.38623060653298 & -0.0743306065329805 \tabularnewline
38 & 1.3014 & 1.32967630223452 & -0.0282763022345176 \tabularnewline
39 & 1.3201 & 1.30687651996709 & 0.0132234800329083 \tabularnewline
40 & 1.2938 & 1.32446049076214 & -0.0306604907621448 \tabularnewline
41 & 1.2694 & 1.36550582202423 & -0.096105822024225 \tabularnewline
42 & 1.2165 & 1.27233245340967 & -0.0558324534096681 \tabularnewline
43 & 1.2037 & 1.22132281793324 & -0.0176228179332441 \tabularnewline
44 & 1.2292 & 1.18188885974172 & 0.0473111402582775 \tabularnewline
45 & 1.2256 & 1.22496004171676 & 0.000639958283238373 \tabularnewline
46 & 1.2015 & 1.21902284436131 & -0.0175228443613111 \tabularnewline
47 & 1.1786 & 1.2129457037634 & -0.0343457037633998 \tabularnewline
48 & 1.1856 & 1.18523915022944 & 0.000360849770562943 \tabularnewline
49 & 1.2103 & 1.2232570519553 & -0.0129570519553039 \tabularnewline
50 & 1.1938 & 1.221930145841 & -0.0281301458410022 \tabularnewline
51 & 1.202 & 1.19313423909702 & 0.00886576090298252 \tabularnewline
52 & 1.2271 & 1.20010265940379 & 0.0269973405962129 \tabularnewline
53 & 1.277 & 1.29407686170325 & -0.0170768617032542 \tabularnewline
54 & 1.265 & 1.27729904690512 & -0.012299046905117 \tabularnewline
55 & 1.2684 & 1.26834375530177 & 5.62446982270703e-05 \tabularnewline
56 & 1.2811 & 1.24557858003511 & 0.0355214199648859 \tabularnewline
57 & 1.2727 & 1.27553714251908 & -0.00283714251908296 \tabularnewline
58 & 1.2611 & 1.26470774539501 & -0.00360774539500586 \tabularnewline
59 & 1.2881 & 1.27149958141815 & 0.0166004185818502 \tabularnewline
60 & 1.3213 & 1.29504392938509 & 0.0262560706149104 \tabularnewline
61 & 1.2999 & 1.35994847596427 & -0.0600484759642737 \tabularnewline
62 & 1.3074 & 1.31127288059857 & -0.00387288059856528 \tabularnewline
63 & 1.3242 & 1.30712018622316 & 0.0170798137768366 \tabularnewline
64 & 1.3516 & 1.32290641263263 & 0.028693587367365 \tabularnewline
65 & 1.3511 & 1.41922559308164 & -0.0681255930816362 \tabularnewline
66 & 1.3419 & 1.35069415597303 & -0.00879415597303357 \tabularnewline
67 & 1.3716 & 1.3446318010291 & 0.0269681989709003 \tabularnewline
68 & 1.3622 & 1.34888023060115 & 0.0133197693988476 \tabularnewline
69 & 1.3896 & 1.35615008796505 & 0.033449912034945 \tabularnewline
70 & 1.4227 & 1.38208288843726 & 0.0406171115627423 \tabularnewline
71 & 1.4684 & 1.43474740302535 & 0.0336525969746515 \tabularnewline
72 & 1.457 & 1.47744391128092 & -0.0204439112809238 \tabularnewline
73 & 1.4718 & 1.49651014819627 & -0.0247101481962699 \tabularnewline
74 & 1.4748 & 1.48497159372442 & -0.0101715937244231 \tabularnewline
75 & 1.5527 & 1.47615188092595 & 0.0765481190740454 \tabularnewline
76 & 1.575 & 1.55461498540159 & 0.0203850145984137 \tabularnewline
77 & 1.5557 & 1.64561385343215 & -0.0899138534321493 \tabularnewline
78 & 1.5553 & 1.55770467277302 & -0.00240467277301515 \tabularnewline
79 & 1.577 & 1.56061174313659 & 0.0163882568634068 \tabularnewline
80 & 1.4975 & 1.55657963203127 & -0.0590796320312688 \tabularnewline
81 & 1.4369 & 1.49182972679982 & -0.0549297267998237 \tabularnewline
82 & 1.3322 & 1.4274190282724 & -0.0952190282723961 \tabularnewline
83 & 1.2732 & 1.33868167412676 & -0.0654816741267565 \tabularnewline
84 & 1.3449 & 1.27404951057265 & 0.0708504894273543 \tabularnewline
85 & 1.3239 & 1.37863653512135 & -0.0547365351213476 \tabularnewline
86 & 1.2785 & 1.33050179265135 & -0.0520017926513472 \tabularnewline
87 & 1.305 & 1.27217289870401 & 0.0328271012959929 \tabularnewline
88 & 1.319 & 1.29807668455403 & 0.0209233154459696 \tabularnewline
89 & 1.365 & 1.38078982631907 & -0.0157898263190688 \tabularnewline
90 & 1.4016 & 1.36014613890791 & 0.041453861092092 \tabularnewline
91 & 1.4088 & 1.40121617431177 & 0.00758382568822569 \tabularnewline
92 & 1.4268 & 1.38245060246907 & 0.0443493975309255 \tabularnewline
93 & 1.4562 & 1.41794325005305 & 0.0382567499469544 \tabularnewline
94 & 1.4816 & 1.44600350997164 & 0.0355964900283601 \tabularnewline
95 & 1.4914 & 1.49083489636755 & 0.000565103632446551 \tabularnewline
96 & 1.4614 & 1.49675404747877 & -0.0353540474787679 \tabularnewline
97 & 1.4272 & 1.49682492309003 & -0.0696249230900319 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122058&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]1.0622[/C][C]0.95641920405983[/C][C]0.10578079594017[/C][/ROW]
[ROW][C]14[/C][C]1.0773[/C][C]1.08369586570174[/C][C]-0.00639586570173889[/C][/ROW]
[ROW][C]15[/C][C]1.0807[/C][C]1.08707627115404[/C][C]-0.00637627115404249[/C][/ROW]
[ROW][C]16[/C][C]1.0848[/C][C]1.08884052951414[/C][C]-0.00404052951413636[/C][/ROW]
[ROW][C]17[/C][C]1.1582[/C][C]1.16099172304695[/C][C]-0.00279172304695452[/C][/ROW]
[ROW][C]18[/C][C]1.1663[/C][C]1.16809269694486[/C][C]-0.00179269694485651[/C][/ROW]
[ROW][C]19[/C][C]1.1372[/C][C]1.17951599462912[/C][C]-0.0423159946291161[/C][/ROW]
[ROW][C]20[/C][C]1.1139[/C][C]1.12312726532009[/C][C]-0.00922726532009022[/C][/ROW]
[ROW][C]21[/C][C]1.1222[/C][C]1.115899259262[/C][C]0.0063007407380029[/C][/ROW]
[ROW][C]22[/C][C]1.1692[/C][C]1.12201216478312[/C][C]0.0471878352168769[/C][/ROW]
[ROW][C]23[/C][C]1.1702[/C][C]1.18875091050084[/C][C]-0.0185509105008419[/C][/ROW]
[ROW][C]24[/C][C]1.2286[/C][C]1.18536317608289[/C][C]0.0432368239171099[/C][/ROW]
[ROW][C]25[/C][C]1.2613[/C][C]1.27591798902321[/C][C]-0.0146179890232103[/C][/ROW]
[ROW][C]26[/C][C]1.2646[/C][C]1.28254704104125[/C][C]-0.0179470410412526[/C][/ROW]
[ROW][C]27[/C][C]1.2262[/C][C]1.2738211523266[/C][C]-0.0476211523266008[/C][/ROW]
[ROW][C]28[/C][C]1.1985[/C][C]1.23269174998563[/C][C]-0.0341917499856312[/C][/ROW]
[ROW][C]29[/C][C]1.2007[/C][C]1.27224344539938[/C][C]-0.071543445399378[/C][/ROW]
[ROW][C]30[/C][C]1.2138[/C][C]1.20632137957139[/C][C]0.0074786204286117[/C][/ROW]
[ROW][C]31[/C][C]1.2266[/C][C]1.22299051807686[/C][C]0.00360948192313537[/C][/ROW]
[ROW][C]32[/C][C]1.2176[/C][C]1.20971956143332[/C][C]0.00788043856668397[/C][/ROW]
[ROW][C]33[/C][C]1.2218[/C][C]1.21724518799325[/C][C]0.0045548120067529[/C][/ROW]
[ROW][C]34[/C][C]1.249[/C][C]1.21921179798421[/C][C]0.0297882020157862[/C][/ROW]
[ROW][C]35[/C][C]1.2991[/C][C]1.2656891702053[/C][C]0.033410829794704[/C][/ROW]
[ROW][C]36[/C][C]1.3408[/C][C]1.31277926769532[/C][C]0.028020732304683[/C][/ROW]
[ROW][C]37[/C][C]1.3119[/C][C]1.38623060653298[/C][C]-0.0743306065329805[/C][/ROW]
[ROW][C]38[/C][C]1.3014[/C][C]1.32967630223452[/C][C]-0.0282763022345176[/C][/ROW]
[ROW][C]39[/C][C]1.3201[/C][C]1.30687651996709[/C][C]0.0132234800329083[/C][/ROW]
[ROW][C]40[/C][C]1.2938[/C][C]1.32446049076214[/C][C]-0.0306604907621448[/C][/ROW]
[ROW][C]41[/C][C]1.2694[/C][C]1.36550582202423[/C][C]-0.096105822024225[/C][/ROW]
[ROW][C]42[/C][C]1.2165[/C][C]1.27233245340967[/C][C]-0.0558324534096681[/C][/ROW]
[ROW][C]43[/C][C]1.2037[/C][C]1.22132281793324[/C][C]-0.0176228179332441[/C][/ROW]
[ROW][C]44[/C][C]1.2292[/C][C]1.18188885974172[/C][C]0.0473111402582775[/C][/ROW]
[ROW][C]45[/C][C]1.2256[/C][C]1.22496004171676[/C][C]0.000639958283238373[/C][/ROW]
[ROW][C]46[/C][C]1.2015[/C][C]1.21902284436131[/C][C]-0.0175228443613111[/C][/ROW]
[ROW][C]47[/C][C]1.1786[/C][C]1.2129457037634[/C][C]-0.0343457037633998[/C][/ROW]
[ROW][C]48[/C][C]1.1856[/C][C]1.18523915022944[/C][C]0.000360849770562943[/C][/ROW]
[ROW][C]49[/C][C]1.2103[/C][C]1.2232570519553[/C][C]-0.0129570519553039[/C][/ROW]
[ROW][C]50[/C][C]1.1938[/C][C]1.221930145841[/C][C]-0.0281301458410022[/C][/ROW]
[ROW][C]51[/C][C]1.202[/C][C]1.19313423909702[/C][C]0.00886576090298252[/C][/ROW]
[ROW][C]52[/C][C]1.2271[/C][C]1.20010265940379[/C][C]0.0269973405962129[/C][/ROW]
[ROW][C]53[/C][C]1.277[/C][C]1.29407686170325[/C][C]-0.0170768617032542[/C][/ROW]
[ROW][C]54[/C][C]1.265[/C][C]1.27729904690512[/C][C]-0.012299046905117[/C][/ROW]
[ROW][C]55[/C][C]1.2684[/C][C]1.26834375530177[/C][C]5.62446982270703e-05[/C][/ROW]
[ROW][C]56[/C][C]1.2811[/C][C]1.24557858003511[/C][C]0.0355214199648859[/C][/ROW]
[ROW][C]57[/C][C]1.2727[/C][C]1.27553714251908[/C][C]-0.00283714251908296[/C][/ROW]
[ROW][C]58[/C][C]1.2611[/C][C]1.26470774539501[/C][C]-0.00360774539500586[/C][/ROW]
[ROW][C]59[/C][C]1.2881[/C][C]1.27149958141815[/C][C]0.0166004185818502[/C][/ROW]
[ROW][C]60[/C][C]1.3213[/C][C]1.29504392938509[/C][C]0.0262560706149104[/C][/ROW]
[ROW][C]61[/C][C]1.2999[/C][C]1.35994847596427[/C][C]-0.0600484759642737[/C][/ROW]
[ROW][C]62[/C][C]1.3074[/C][C]1.31127288059857[/C][C]-0.00387288059856528[/C][/ROW]
[ROW][C]63[/C][C]1.3242[/C][C]1.30712018622316[/C][C]0.0170798137768366[/C][/ROW]
[ROW][C]64[/C][C]1.3516[/C][C]1.32290641263263[/C][C]0.028693587367365[/C][/ROW]
[ROW][C]65[/C][C]1.3511[/C][C]1.41922559308164[/C][C]-0.0681255930816362[/C][/ROW]
[ROW][C]66[/C][C]1.3419[/C][C]1.35069415597303[/C][C]-0.00879415597303357[/C][/ROW]
[ROW][C]67[/C][C]1.3716[/C][C]1.3446318010291[/C][C]0.0269681989709003[/C][/ROW]
[ROW][C]68[/C][C]1.3622[/C][C]1.34888023060115[/C][C]0.0133197693988476[/C][/ROW]
[ROW][C]69[/C][C]1.3896[/C][C]1.35615008796505[/C][C]0.033449912034945[/C][/ROW]
[ROW][C]70[/C][C]1.4227[/C][C]1.38208288843726[/C][C]0.0406171115627423[/C][/ROW]
[ROW][C]71[/C][C]1.4684[/C][C]1.43474740302535[/C][C]0.0336525969746515[/C][/ROW]
[ROW][C]72[/C][C]1.457[/C][C]1.47744391128092[/C][C]-0.0204439112809238[/C][/ROW]
[ROW][C]73[/C][C]1.4718[/C][C]1.49651014819627[/C][C]-0.0247101481962699[/C][/ROW]
[ROW][C]74[/C][C]1.4748[/C][C]1.48497159372442[/C][C]-0.0101715937244231[/C][/ROW]
[ROW][C]75[/C][C]1.5527[/C][C]1.47615188092595[/C][C]0.0765481190740454[/C][/ROW]
[ROW][C]76[/C][C]1.575[/C][C]1.55461498540159[/C][C]0.0203850145984137[/C][/ROW]
[ROW][C]77[/C][C]1.5557[/C][C]1.64561385343215[/C][C]-0.0899138534321493[/C][/ROW]
[ROW][C]78[/C][C]1.5553[/C][C]1.55770467277302[/C][C]-0.00240467277301515[/C][/ROW]
[ROW][C]79[/C][C]1.577[/C][C]1.56061174313659[/C][C]0.0163882568634068[/C][/ROW]
[ROW][C]80[/C][C]1.4975[/C][C]1.55657963203127[/C][C]-0.0590796320312688[/C][/ROW]
[ROW][C]81[/C][C]1.4369[/C][C]1.49182972679982[/C][C]-0.0549297267998237[/C][/ROW]
[ROW][C]82[/C][C]1.3322[/C][C]1.4274190282724[/C][C]-0.0952190282723961[/C][/ROW]
[ROW][C]83[/C][C]1.2732[/C][C]1.33868167412676[/C][C]-0.0654816741267565[/C][/ROW]
[ROW][C]84[/C][C]1.3449[/C][C]1.27404951057265[/C][C]0.0708504894273543[/C][/ROW]
[ROW][C]85[/C][C]1.3239[/C][C]1.37863653512135[/C][C]-0.0547365351213476[/C][/ROW]
[ROW][C]86[/C][C]1.2785[/C][C]1.33050179265135[/C][C]-0.0520017926513472[/C][/ROW]
[ROW][C]87[/C][C]1.305[/C][C]1.27217289870401[/C][C]0.0328271012959929[/C][/ROW]
[ROW][C]88[/C][C]1.319[/C][C]1.29807668455403[/C][C]0.0209233154459696[/C][/ROW]
[ROW][C]89[/C][C]1.365[/C][C]1.38078982631907[/C][C]-0.0157898263190688[/C][/ROW]
[ROW][C]90[/C][C]1.4016[/C][C]1.36014613890791[/C][C]0.041453861092092[/C][/ROW]
[ROW][C]91[/C][C]1.4088[/C][C]1.40121617431177[/C][C]0.00758382568822569[/C][/ROW]
[ROW][C]92[/C][C]1.4268[/C][C]1.38245060246907[/C][C]0.0443493975309255[/C][/ROW]
[ROW][C]93[/C][C]1.4562[/C][C]1.41794325005305[/C][C]0.0382567499469544[/C][/ROW]
[ROW][C]94[/C][C]1.4816[/C][C]1.44600350997164[/C][C]0.0355964900283601[/C][/ROW]
[ROW][C]95[/C][C]1.4914[/C][C]1.49083489636755[/C][C]0.000565103632446551[/C][/ROW]
[ROW][C]96[/C][C]1.4614[/C][C]1.49675404747877[/C][C]-0.0353540474787679[/C][/ROW]
[ROW][C]97[/C][C]1.4272[/C][C]1.49682492309003[/C][C]-0.0696249230900319[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122058&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122058&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131.06220.956419204059830.10578079594017
141.07731.08369586570174-0.00639586570173889
151.08071.08707627115404-0.00637627115404249
161.08481.08884052951414-0.00404052951413636
171.15821.16099172304695-0.00279172304695452
181.16631.16809269694486-0.00179269694485651
191.13721.17951599462912-0.0423159946291161
201.11391.12312726532009-0.00922726532009022
211.12221.1158992592620.0063007407380029
221.16921.122012164783120.0471878352168769
231.17021.18875091050084-0.0185509105008419
241.22861.185363176082890.0432368239171099
251.26131.27591798902321-0.0146179890232103
261.26461.28254704104125-0.0179470410412526
271.22621.2738211523266-0.0476211523266008
281.19851.23269174998563-0.0341917499856312
291.20071.27224344539938-0.071543445399378
301.21381.206321379571390.0074786204286117
311.22661.222990518076860.00360948192313537
321.21761.209719561433320.00788043856668397
331.22181.217245187993250.0045548120067529
341.2491.219211797984210.0297882020157862
351.29911.26568917020530.033410829794704
361.34081.312779267695320.028020732304683
371.31191.38623060653298-0.0743306065329805
381.30141.32967630223452-0.0282763022345176
391.32011.306876519967090.0132234800329083
401.29381.32446049076214-0.0306604907621448
411.26941.36550582202423-0.096105822024225
421.21651.27233245340967-0.0558324534096681
431.20371.22132281793324-0.0176228179332441
441.22921.181888859741720.0473111402582775
451.22561.224960041716760.000639958283238373
461.20151.21902284436131-0.0175228443613111
471.17861.2129457037634-0.0343457037633998
481.18561.185239150229440.000360849770562943
491.21031.2232570519553-0.0129570519553039
501.19381.221930145841-0.0281301458410022
511.2021.193134239097020.00886576090298252
521.22711.200102659403790.0269973405962129
531.2771.29407686170325-0.0170768617032542
541.2651.27729904690512-0.012299046905117
551.26841.268343755301775.62446982270703e-05
561.28111.245578580035110.0355214199648859
571.27271.27553714251908-0.00283714251908296
581.26111.26470774539501-0.00360774539500586
591.28811.271499581418150.0166004185818502
601.32131.295043929385090.0262560706149104
611.29991.35994847596427-0.0600484759642737
621.30741.31127288059857-0.00387288059856528
631.32421.307120186223160.0170798137768366
641.35161.322906412632630.028693587367365
651.35111.41922559308164-0.0681255930816362
661.34191.35069415597303-0.00879415597303357
671.37161.34463180102910.0269681989709003
681.36221.348880230601150.0133197693988476
691.38961.356150087965050.033449912034945
701.42271.382082888437260.0406171115627423
711.46841.434747403025350.0336525969746515
721.4571.47744391128092-0.0204439112809238
731.47181.49651014819627-0.0247101481962699
741.47481.48497159372442-0.0101715937244231
751.55271.476151880925950.0765481190740454
761.5751.554614985401590.0203850145984137
771.55571.64561385343215-0.0899138534321493
781.55531.55770467277302-0.00240467277301515
791.5771.560611743136590.0163882568634068
801.49751.55657963203127-0.0590796320312688
811.43691.49182972679982-0.0549297267998237
821.33221.4274190282724-0.0952190282723961
831.27321.33868167412676-0.0654816741267565
841.34491.274049510572650.0708504894273543
851.32391.37863653512135-0.0547365351213476
861.27851.33050179265135-0.0520017926513472
871.3051.272172898704010.0328271012959929
881.3191.298076684554030.0209233154459696
891.3651.38078982631907-0.0157898263190688
901.40161.360146138907910.041453861092092
911.40881.401216174311770.00758382568822569
921.42681.382450602469070.0443493975309255
931.45621.417943250053050.0382567499469544
941.48161.446003509971640.0355964900283601
951.49141.490834896367550.000565103632446551
961.46141.49675404747877-0.0353540474787679
971.42721.49682492309003-0.0696249230900319






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
981.435095395998021.357704615799071.51248617619698
991.431440791996041.320533143398241.54234844059385
1001.42631952132741.288689788609061.56394925404574
1011.489356583992091.328353274564171.65035989342
1021.486168646656781.303824752247331.66851254106622
1031.48635154265481.284034820092981.68866826521662
1041.460367771986151.239056296456631.68167924751567
1051.450700667984171.211122169153111.69027916681524
1061.438679397315531.181390178173951.69596861645711
1071.445145626646891.170578973338221.71971227995555
1081.447716022644911.156213717465161.73921832782465
1091.481294751976261.173128554787971.78946094916455

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
98 & 1.43509539599802 & 1.35770461579907 & 1.51248617619698 \tabularnewline
99 & 1.43144079199604 & 1.32053314339824 & 1.54234844059385 \tabularnewline
100 & 1.4263195213274 & 1.28868978860906 & 1.56394925404574 \tabularnewline
101 & 1.48935658399209 & 1.32835327456417 & 1.65035989342 \tabularnewline
102 & 1.48616864665678 & 1.30382475224733 & 1.66851254106622 \tabularnewline
103 & 1.4863515426548 & 1.28403482009298 & 1.68866826521662 \tabularnewline
104 & 1.46036777198615 & 1.23905629645663 & 1.68167924751567 \tabularnewline
105 & 1.45070066798417 & 1.21112216915311 & 1.69027916681524 \tabularnewline
106 & 1.43867939731553 & 1.18139017817395 & 1.69596861645711 \tabularnewline
107 & 1.44514562664689 & 1.17057897333822 & 1.71971227995555 \tabularnewline
108 & 1.44771602264491 & 1.15621371746516 & 1.73921832782465 \tabularnewline
109 & 1.48129475197626 & 1.17312855478797 & 1.78946094916455 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122058&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]98[/C][C]1.43509539599802[/C][C]1.35770461579907[/C][C]1.51248617619698[/C][/ROW]
[ROW][C]99[/C][C]1.43144079199604[/C][C]1.32053314339824[/C][C]1.54234844059385[/C][/ROW]
[ROW][C]100[/C][C]1.4263195213274[/C][C]1.28868978860906[/C][C]1.56394925404574[/C][/ROW]
[ROW][C]101[/C][C]1.48935658399209[/C][C]1.32835327456417[/C][C]1.65035989342[/C][/ROW]
[ROW][C]102[/C][C]1.48616864665678[/C][C]1.30382475224733[/C][C]1.66851254106622[/C][/ROW]
[ROW][C]103[/C][C]1.4863515426548[/C][C]1.28403482009298[/C][C]1.68866826521662[/C][/ROW]
[ROW][C]104[/C][C]1.46036777198615[/C][C]1.23905629645663[/C][C]1.68167924751567[/C][/ROW]
[ROW][C]105[/C][C]1.45070066798417[/C][C]1.21112216915311[/C][C]1.69027916681524[/C][/ROW]
[ROW][C]106[/C][C]1.43867939731553[/C][C]1.18139017817395[/C][C]1.69596861645711[/C][/ROW]
[ROW][C]107[/C][C]1.44514562664689[/C][C]1.17057897333822[/C][C]1.71971227995555[/C][/ROW]
[ROW][C]108[/C][C]1.44771602264491[/C][C]1.15621371746516[/C][C]1.73921832782465[/C][/ROW]
[ROW][C]109[/C][C]1.48129475197626[/C][C]1.17312855478797[/C][C]1.78946094916455[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122058&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122058&T=3

As an alternative you can also use a QR Code:  
QR Code


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

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
981.435095395998021.357704615799071.51248617619698
991.431440791996041.320533143398241.54234844059385
1001.42631952132741.288689788609061.56394925404574
1011.489356583992091.328353274564171.65035989342
1021.486168646656781.303824752247331.66851254106622
1031.48635154265481.284034820092981.68866826521662
1041.460367771986151.239056296456631.68167924751567
1051.450700667984171.211122169153111.69027916681524
1061.438679397315531.181390178173951.69596861645711
1071.445145626646891.170578973338221.71971227995555
1081.447716022644911.156213717465161.73921832782465
1091.481294751976261.173128554787971.78946094916455


Figures (Output of Computation)

Input Parameters & R Code

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')