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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 12 Dec 2013 04:18:08 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Dec/12/t13868399570ke8na6ysxuk8bh.htm/, Retrieved Tue, 07 Dec 2021 12:07:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232231, Retrieved Tue, 07 Dec 2021 12:07:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact65
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-12-12 09:18:08] [17b6b1d507219cce54aa3edb43843a55] [Current]
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Dataseries X:
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
1,5751
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
1,3686
1,3569
1,3406
1,2565
1,2209
1,277
1,2894
1,3067
1,3898
1,3661
1,322
1,336
1,3649
1,3999
1,4442
1,4349
1,4388
1,4264
1,4343
1,377
1,3706
1,3556
1,3179
1,2905
1,3224
1,3201
1,3162
1,2789
1,2526
1,2288
1,24
1,2856
1,2974
1,2828
1,3119




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232231&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232231&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232231&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999949649180041
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999949649180041 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232231&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]0.999949649180041[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232231&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232231&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
alpha0.999949649180041
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
21.19381.2103-0.0165
31.2021.193800830788530.00819916921147068
41.22711.201999587165110.0251004128348928
51.2771.227098736173630.0499012638263674
61.2651.27699748743045-0.0119974874304494
71.26841.265000604083330.00339939591667049
81.28111.268399828837630.0127001711623718
91.27271.28109936053597-0.00839936053596824
101.26111.27270042291469-0.01160042291469
111.28811.261100584090810.0269994159091942
121.32131.288098640557270.0332013594427294
131.29991.32129832828433-0.0213983282843282
141.30741.299901077423380.00749892257662488
151.32421.30739962242310.0168003775769008
161.35161.324199154087210.0274008459127866
171.35111.35159862034494-0.000498620344940637
181.34191.35110002510594-0.0092000251059432
191.37161.341900463228810.0296995367711921
201.36221.37159850460397-0.00939850460397107
211.38961.362200473222410.0273995267775866
221.42271.389598620411360.0331013795886399
231.46841.42269833331840.0457016666816039
241.4571.46839769888361-0.0113976988836089
251.47181.457000573883480.0147994261165154
261.47481.471799254836760.00300074516323989
271.55271.474799848910020.0779001510899793
281.57511.552696077663520.0224039223364823
291.55571.57509887194414-0.01939887194414
301.55531.55570097674911-0.000400976749108883
311.5771.555300020189510.021699979810492
321.49751.57699890738822-0.0794989073882233
331.43691.49750400283517-0.0606040028351729
341.33221.43690305146124-0.104703051461235
351.27321.33220527188449-0.0590052718844931
361.34491.273202970963820.0716970290361787
371.32391.3448963899958-0.0209963899957992
381.27851.32390105718545-0.0454010571854526
391.3051.278502285980460.0264977140195437
401.3191.304998665818370.0140013341816279
411.3651.318999295021340.0460007049786566
421.40161.364997683826790.0366023161732143
431.40881.401598157043370.00720184295663184
441.42681.40879963738130.0180003626186982
451.45621.426799093666980.0294009063330172
461.48161.456198519640260.0254014803597415
471.49141.481598721014640.00980127898536431
481.46141.49139950649757-0.0299995064975664
491.42721.46140151049975-0.0342015104997506
501.36861.4272017220741-0.0586017220740975
511.35691.36860295064476-0.0117029506447575
521.34061.35690058925316-0.0163005892531609
531.25651.34060082074803-0.0841008207480347
541.22091.25650423454528-0.0356042345452838
551.2771.22090179270240.0560982072975964
561.28941.276997175409260.0124028245907359
571.30671.289399375507610.0173006244923879
581.38981.306699128899370.0831008711006289
591.36611.389795815803-0.0236958158030005
601.3221.36610119310376-0.0441011931037554
611.3361.322002220531230.013997779468766
621.36491.335999295200330.0289007047996739
631.39991.364898544825820.035001455174184
641.44421.399898237648030.0443017623519677
651.43491.44419776936994-0.00929776936993987
661.43881.434900468150310.00389953184968839
671.42641.43879980365537-0.0123998036553741
681.43431.426400624340280.00789937565971854
691.3771.43429960225996-0.0572996022599583
701.37061.37700288508196-0.00640288508195708
711.35561.37060032239051-0.0150003223905142
721.31791.35560075527853-0.0377007552785318
731.29051.31790189826394-0.0274018982639415
741.32241.290501379708050.031898620291954
751.32011.32239839387831-0.00229839387831277
761.31621.32010011572602-0.00390011572601634
771.27891.31620019637402-0.0373001963740249
781.25261.27890187809547-0.026301878095472
791.22881.25260132432113-0.0238013243211286
801.241.22880119841620.0111988015838045
811.28561.239999436131160.0456005638688424
821.29741.285597703974220.0118022960257813
831.28281.29739940574472-0.0145994057447179
841.31191.282800735092050.02909926490795

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 1.1938 & 1.2103 & -0.0165 \tabularnewline
3 & 1.202 & 1.19380083078853 & 0.00819916921147068 \tabularnewline
4 & 1.2271 & 1.20199958716511 & 0.0251004128348928 \tabularnewline
5 & 1.277 & 1.22709873617363 & 0.0499012638263674 \tabularnewline
6 & 1.265 & 1.27699748743045 & -0.0119974874304494 \tabularnewline
7 & 1.2684 & 1.26500060408333 & 0.00339939591667049 \tabularnewline
8 & 1.2811 & 1.26839982883763 & 0.0127001711623718 \tabularnewline
9 & 1.2727 & 1.28109936053597 & -0.00839936053596824 \tabularnewline
10 & 1.2611 & 1.27270042291469 & -0.01160042291469 \tabularnewline
11 & 1.2881 & 1.26110058409081 & 0.0269994159091942 \tabularnewline
12 & 1.3213 & 1.28809864055727 & 0.0332013594427294 \tabularnewline
13 & 1.2999 & 1.32129832828433 & -0.0213983282843282 \tabularnewline
14 & 1.3074 & 1.29990107742338 & 0.00749892257662488 \tabularnewline
15 & 1.3242 & 1.3073996224231 & 0.0168003775769008 \tabularnewline
16 & 1.3516 & 1.32419915408721 & 0.0274008459127866 \tabularnewline
17 & 1.3511 & 1.35159862034494 & -0.000498620344940637 \tabularnewline
18 & 1.3419 & 1.35110002510594 & -0.0092000251059432 \tabularnewline
19 & 1.3716 & 1.34190046322881 & 0.0296995367711921 \tabularnewline
20 & 1.3622 & 1.37159850460397 & -0.00939850460397107 \tabularnewline
21 & 1.3896 & 1.36220047322241 & 0.0273995267775866 \tabularnewline
22 & 1.4227 & 1.38959862041136 & 0.0331013795886399 \tabularnewline
23 & 1.4684 & 1.4226983333184 & 0.0457016666816039 \tabularnewline
24 & 1.457 & 1.46839769888361 & -0.0113976988836089 \tabularnewline
25 & 1.4718 & 1.45700057388348 & 0.0147994261165154 \tabularnewline
26 & 1.4748 & 1.47179925483676 & 0.00300074516323989 \tabularnewline
27 & 1.5527 & 1.47479984891002 & 0.0779001510899793 \tabularnewline
28 & 1.5751 & 1.55269607766352 & 0.0224039223364823 \tabularnewline
29 & 1.5557 & 1.57509887194414 & -0.01939887194414 \tabularnewline
30 & 1.5553 & 1.55570097674911 & -0.000400976749108883 \tabularnewline
31 & 1.577 & 1.55530002018951 & 0.021699979810492 \tabularnewline
32 & 1.4975 & 1.57699890738822 & -0.0794989073882233 \tabularnewline
33 & 1.4369 & 1.49750400283517 & -0.0606040028351729 \tabularnewline
34 & 1.3322 & 1.43690305146124 & -0.104703051461235 \tabularnewline
35 & 1.2732 & 1.33220527188449 & -0.0590052718844931 \tabularnewline
36 & 1.3449 & 1.27320297096382 & 0.0716970290361787 \tabularnewline
37 & 1.3239 & 1.3448963899958 & -0.0209963899957992 \tabularnewline
38 & 1.2785 & 1.32390105718545 & -0.0454010571854526 \tabularnewline
39 & 1.305 & 1.27850228598046 & 0.0264977140195437 \tabularnewline
40 & 1.319 & 1.30499866581837 & 0.0140013341816279 \tabularnewline
41 & 1.365 & 1.31899929502134 & 0.0460007049786566 \tabularnewline
42 & 1.4016 & 1.36499768382679 & 0.0366023161732143 \tabularnewline
43 & 1.4088 & 1.40159815704337 & 0.00720184295663184 \tabularnewline
44 & 1.4268 & 1.4087996373813 & 0.0180003626186982 \tabularnewline
45 & 1.4562 & 1.42679909366698 & 0.0294009063330172 \tabularnewline
46 & 1.4816 & 1.45619851964026 & 0.0254014803597415 \tabularnewline
47 & 1.4914 & 1.48159872101464 & 0.00980127898536431 \tabularnewline
48 & 1.4614 & 1.49139950649757 & -0.0299995064975664 \tabularnewline
49 & 1.4272 & 1.46140151049975 & -0.0342015104997506 \tabularnewline
50 & 1.3686 & 1.4272017220741 & -0.0586017220740975 \tabularnewline
51 & 1.3569 & 1.36860295064476 & -0.0117029506447575 \tabularnewline
52 & 1.3406 & 1.35690058925316 & -0.0163005892531609 \tabularnewline
53 & 1.2565 & 1.34060082074803 & -0.0841008207480347 \tabularnewline
54 & 1.2209 & 1.25650423454528 & -0.0356042345452838 \tabularnewline
55 & 1.277 & 1.2209017927024 & 0.0560982072975964 \tabularnewline
56 & 1.2894 & 1.27699717540926 & 0.0124028245907359 \tabularnewline
57 & 1.3067 & 1.28939937550761 & 0.0173006244923879 \tabularnewline
58 & 1.3898 & 1.30669912889937 & 0.0831008711006289 \tabularnewline
59 & 1.3661 & 1.389795815803 & -0.0236958158030005 \tabularnewline
60 & 1.322 & 1.36610119310376 & -0.0441011931037554 \tabularnewline
61 & 1.336 & 1.32200222053123 & 0.013997779468766 \tabularnewline
62 & 1.3649 & 1.33599929520033 & 0.0289007047996739 \tabularnewline
63 & 1.3999 & 1.36489854482582 & 0.035001455174184 \tabularnewline
64 & 1.4442 & 1.39989823764803 & 0.0443017623519677 \tabularnewline
65 & 1.4349 & 1.44419776936994 & -0.00929776936993987 \tabularnewline
66 & 1.4388 & 1.43490046815031 & 0.00389953184968839 \tabularnewline
67 & 1.4264 & 1.43879980365537 & -0.0123998036553741 \tabularnewline
68 & 1.4343 & 1.42640062434028 & 0.00789937565971854 \tabularnewline
69 & 1.377 & 1.43429960225996 & -0.0572996022599583 \tabularnewline
70 & 1.3706 & 1.37700288508196 & -0.00640288508195708 \tabularnewline
71 & 1.3556 & 1.37060032239051 & -0.0150003223905142 \tabularnewline
72 & 1.3179 & 1.35560075527853 & -0.0377007552785318 \tabularnewline
73 & 1.2905 & 1.31790189826394 & -0.0274018982639415 \tabularnewline
74 & 1.3224 & 1.29050137970805 & 0.031898620291954 \tabularnewline
75 & 1.3201 & 1.32239839387831 & -0.00229839387831277 \tabularnewline
76 & 1.3162 & 1.32010011572602 & -0.00390011572601634 \tabularnewline
77 & 1.2789 & 1.31620019637402 & -0.0373001963740249 \tabularnewline
78 & 1.2526 & 1.27890187809547 & -0.026301878095472 \tabularnewline
79 & 1.2288 & 1.25260132432113 & -0.0238013243211286 \tabularnewline
80 & 1.24 & 1.2288011984162 & 0.0111988015838045 \tabularnewline
81 & 1.2856 & 1.23999943613116 & 0.0456005638688424 \tabularnewline
82 & 1.2974 & 1.28559770397422 & 0.0118022960257813 \tabularnewline
83 & 1.2828 & 1.29739940574472 & -0.0145994057447179 \tabularnewline
84 & 1.3119 & 1.28280073509205 & 0.02909926490795 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232231&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]2[/C][C]1.1938[/C][C]1.2103[/C][C]-0.0165[/C][/ROW]
[ROW][C]3[/C][C]1.202[/C][C]1.19380083078853[/C][C]0.00819916921147068[/C][/ROW]
[ROW][C]4[/C][C]1.2271[/C][C]1.20199958716511[/C][C]0.0251004128348928[/C][/ROW]
[ROW][C]5[/C][C]1.277[/C][C]1.22709873617363[/C][C]0.0499012638263674[/C][/ROW]
[ROW][C]6[/C][C]1.265[/C][C]1.27699748743045[/C][C]-0.0119974874304494[/C][/ROW]
[ROW][C]7[/C][C]1.2684[/C][C]1.26500060408333[/C][C]0.00339939591667049[/C][/ROW]
[ROW][C]8[/C][C]1.2811[/C][C]1.26839982883763[/C][C]0.0127001711623718[/C][/ROW]
[ROW][C]9[/C][C]1.2727[/C][C]1.28109936053597[/C][C]-0.00839936053596824[/C][/ROW]
[ROW][C]10[/C][C]1.2611[/C][C]1.27270042291469[/C][C]-0.01160042291469[/C][/ROW]
[ROW][C]11[/C][C]1.2881[/C][C]1.26110058409081[/C][C]0.0269994159091942[/C][/ROW]
[ROW][C]12[/C][C]1.3213[/C][C]1.28809864055727[/C][C]0.0332013594427294[/C][/ROW]
[ROW][C]13[/C][C]1.2999[/C][C]1.32129832828433[/C][C]-0.0213983282843282[/C][/ROW]
[ROW][C]14[/C][C]1.3074[/C][C]1.29990107742338[/C][C]0.00749892257662488[/C][/ROW]
[ROW][C]15[/C][C]1.3242[/C][C]1.3073996224231[/C][C]0.0168003775769008[/C][/ROW]
[ROW][C]16[/C][C]1.3516[/C][C]1.32419915408721[/C][C]0.0274008459127866[/C][/ROW]
[ROW][C]17[/C][C]1.3511[/C][C]1.35159862034494[/C][C]-0.000498620344940637[/C][/ROW]
[ROW][C]18[/C][C]1.3419[/C][C]1.35110002510594[/C][C]-0.0092000251059432[/C][/ROW]
[ROW][C]19[/C][C]1.3716[/C][C]1.34190046322881[/C][C]0.0296995367711921[/C][/ROW]
[ROW][C]20[/C][C]1.3622[/C][C]1.37159850460397[/C][C]-0.00939850460397107[/C][/ROW]
[ROW][C]21[/C][C]1.3896[/C][C]1.36220047322241[/C][C]0.0273995267775866[/C][/ROW]
[ROW][C]22[/C][C]1.4227[/C][C]1.38959862041136[/C][C]0.0331013795886399[/C][/ROW]
[ROW][C]23[/C][C]1.4684[/C][C]1.4226983333184[/C][C]0.0457016666816039[/C][/ROW]
[ROW][C]24[/C][C]1.457[/C][C]1.46839769888361[/C][C]-0.0113976988836089[/C][/ROW]
[ROW][C]25[/C][C]1.4718[/C][C]1.45700057388348[/C][C]0.0147994261165154[/C][/ROW]
[ROW][C]26[/C][C]1.4748[/C][C]1.47179925483676[/C][C]0.00300074516323989[/C][/ROW]
[ROW][C]27[/C][C]1.5527[/C][C]1.47479984891002[/C][C]0.0779001510899793[/C][/ROW]
[ROW][C]28[/C][C]1.5751[/C][C]1.55269607766352[/C][C]0.0224039223364823[/C][/ROW]
[ROW][C]29[/C][C]1.5557[/C][C]1.57509887194414[/C][C]-0.01939887194414[/C][/ROW]
[ROW][C]30[/C][C]1.5553[/C][C]1.55570097674911[/C][C]-0.000400976749108883[/C][/ROW]
[ROW][C]31[/C][C]1.577[/C][C]1.55530002018951[/C][C]0.021699979810492[/C][/ROW]
[ROW][C]32[/C][C]1.4975[/C][C]1.57699890738822[/C][C]-0.0794989073882233[/C][/ROW]
[ROW][C]33[/C][C]1.4369[/C][C]1.49750400283517[/C][C]-0.0606040028351729[/C][/ROW]
[ROW][C]34[/C][C]1.3322[/C][C]1.43690305146124[/C][C]-0.104703051461235[/C][/ROW]
[ROW][C]35[/C][C]1.2732[/C][C]1.33220527188449[/C][C]-0.0590052718844931[/C][/ROW]
[ROW][C]36[/C][C]1.3449[/C][C]1.27320297096382[/C][C]0.0716970290361787[/C][/ROW]
[ROW][C]37[/C][C]1.3239[/C][C]1.3448963899958[/C][C]-0.0209963899957992[/C][/ROW]
[ROW][C]38[/C][C]1.2785[/C][C]1.32390105718545[/C][C]-0.0454010571854526[/C][/ROW]
[ROW][C]39[/C][C]1.305[/C][C]1.27850228598046[/C][C]0.0264977140195437[/C][/ROW]
[ROW][C]40[/C][C]1.319[/C][C]1.30499866581837[/C][C]0.0140013341816279[/C][/ROW]
[ROW][C]41[/C][C]1.365[/C][C]1.31899929502134[/C][C]0.0460007049786566[/C][/ROW]
[ROW][C]42[/C][C]1.4016[/C][C]1.36499768382679[/C][C]0.0366023161732143[/C][/ROW]
[ROW][C]43[/C][C]1.4088[/C][C]1.40159815704337[/C][C]0.00720184295663184[/C][/ROW]
[ROW][C]44[/C][C]1.4268[/C][C]1.4087996373813[/C][C]0.0180003626186982[/C][/ROW]
[ROW][C]45[/C][C]1.4562[/C][C]1.42679909366698[/C][C]0.0294009063330172[/C][/ROW]
[ROW][C]46[/C][C]1.4816[/C][C]1.45619851964026[/C][C]0.0254014803597415[/C][/ROW]
[ROW][C]47[/C][C]1.4914[/C][C]1.48159872101464[/C][C]0.00980127898536431[/C][/ROW]
[ROW][C]48[/C][C]1.4614[/C][C]1.49139950649757[/C][C]-0.0299995064975664[/C][/ROW]
[ROW][C]49[/C][C]1.4272[/C][C]1.46140151049975[/C][C]-0.0342015104997506[/C][/ROW]
[ROW][C]50[/C][C]1.3686[/C][C]1.4272017220741[/C][C]-0.0586017220740975[/C][/ROW]
[ROW][C]51[/C][C]1.3569[/C][C]1.36860295064476[/C][C]-0.0117029506447575[/C][/ROW]
[ROW][C]52[/C][C]1.3406[/C][C]1.35690058925316[/C][C]-0.0163005892531609[/C][/ROW]
[ROW][C]53[/C][C]1.2565[/C][C]1.34060082074803[/C][C]-0.0841008207480347[/C][/ROW]
[ROW][C]54[/C][C]1.2209[/C][C]1.25650423454528[/C][C]-0.0356042345452838[/C][/ROW]
[ROW][C]55[/C][C]1.277[/C][C]1.2209017927024[/C][C]0.0560982072975964[/C][/ROW]
[ROW][C]56[/C][C]1.2894[/C][C]1.27699717540926[/C][C]0.0124028245907359[/C][/ROW]
[ROW][C]57[/C][C]1.3067[/C][C]1.28939937550761[/C][C]0.0173006244923879[/C][/ROW]
[ROW][C]58[/C][C]1.3898[/C][C]1.30669912889937[/C][C]0.0831008711006289[/C][/ROW]
[ROW][C]59[/C][C]1.3661[/C][C]1.389795815803[/C][C]-0.0236958158030005[/C][/ROW]
[ROW][C]60[/C][C]1.322[/C][C]1.36610119310376[/C][C]-0.0441011931037554[/C][/ROW]
[ROW][C]61[/C][C]1.336[/C][C]1.32200222053123[/C][C]0.013997779468766[/C][/ROW]
[ROW][C]62[/C][C]1.3649[/C][C]1.33599929520033[/C][C]0.0289007047996739[/C][/ROW]
[ROW][C]63[/C][C]1.3999[/C][C]1.36489854482582[/C][C]0.035001455174184[/C][/ROW]
[ROW][C]64[/C][C]1.4442[/C][C]1.39989823764803[/C][C]0.0443017623519677[/C][/ROW]
[ROW][C]65[/C][C]1.4349[/C][C]1.44419776936994[/C][C]-0.00929776936993987[/C][/ROW]
[ROW][C]66[/C][C]1.4388[/C][C]1.43490046815031[/C][C]0.00389953184968839[/C][/ROW]
[ROW][C]67[/C][C]1.4264[/C][C]1.43879980365537[/C][C]-0.0123998036553741[/C][/ROW]
[ROW][C]68[/C][C]1.4343[/C][C]1.42640062434028[/C][C]0.00789937565971854[/C][/ROW]
[ROW][C]69[/C][C]1.377[/C][C]1.43429960225996[/C][C]-0.0572996022599583[/C][/ROW]
[ROW][C]70[/C][C]1.3706[/C][C]1.37700288508196[/C][C]-0.00640288508195708[/C][/ROW]
[ROW][C]71[/C][C]1.3556[/C][C]1.37060032239051[/C][C]-0.0150003223905142[/C][/ROW]
[ROW][C]72[/C][C]1.3179[/C][C]1.35560075527853[/C][C]-0.0377007552785318[/C][/ROW]
[ROW][C]73[/C][C]1.2905[/C][C]1.31790189826394[/C][C]-0.0274018982639415[/C][/ROW]
[ROW][C]74[/C][C]1.3224[/C][C]1.29050137970805[/C][C]0.031898620291954[/C][/ROW]
[ROW][C]75[/C][C]1.3201[/C][C]1.32239839387831[/C][C]-0.00229839387831277[/C][/ROW]
[ROW][C]76[/C][C]1.3162[/C][C]1.32010011572602[/C][C]-0.00390011572601634[/C][/ROW]
[ROW][C]77[/C][C]1.2789[/C][C]1.31620019637402[/C][C]-0.0373001963740249[/C][/ROW]
[ROW][C]78[/C][C]1.2526[/C][C]1.27890187809547[/C][C]-0.026301878095472[/C][/ROW]
[ROW][C]79[/C][C]1.2288[/C][C]1.25260132432113[/C][C]-0.0238013243211286[/C][/ROW]
[ROW][C]80[/C][C]1.24[/C][C]1.2288011984162[/C][C]0.0111988015838045[/C][/ROW]
[ROW][C]81[/C][C]1.2856[/C][C]1.23999943613116[/C][C]0.0456005638688424[/C][/ROW]
[ROW][C]82[/C][C]1.2974[/C][C]1.28559770397422[/C][C]0.0118022960257813[/C][/ROW]
[ROW][C]83[/C][C]1.2828[/C][C]1.29739940574472[/C][C]-0.0145994057447179[/C][/ROW]
[ROW][C]84[/C][C]1.3119[/C][C]1.28280073509205[/C][C]0.02909926490795[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232231&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232231&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
21.19381.2103-0.0165
31.2021.193800830788530.00819916921147068
41.22711.201999587165110.0251004128348928
51.2771.227098736173630.0499012638263674
61.2651.27699748743045-0.0119974874304494
71.26841.265000604083330.00339939591667049
81.28111.268399828837630.0127001711623718
91.27271.28109936053597-0.00839936053596824
101.26111.27270042291469-0.01160042291469
111.28811.261100584090810.0269994159091942
121.32131.288098640557270.0332013594427294
131.29991.32129832828433-0.0213983282843282
141.30741.299901077423380.00749892257662488
151.32421.30739962242310.0168003775769008
161.35161.324199154087210.0274008459127866
171.35111.35159862034494-0.000498620344940637
181.34191.35110002510594-0.0092000251059432
191.37161.341900463228810.0296995367711921
201.36221.37159850460397-0.00939850460397107
211.38961.362200473222410.0273995267775866
221.42271.389598620411360.0331013795886399
231.46841.42269833331840.0457016666816039
241.4571.46839769888361-0.0113976988836089
251.47181.457000573883480.0147994261165154
261.47481.471799254836760.00300074516323989
271.55271.474799848910020.0779001510899793
281.57511.552696077663520.0224039223364823
291.55571.57509887194414-0.01939887194414
301.55531.55570097674911-0.000400976749108883
311.5771.555300020189510.021699979810492
321.49751.57699890738822-0.0794989073882233
331.43691.49750400283517-0.0606040028351729
341.33221.43690305146124-0.104703051461235
351.27321.33220527188449-0.0590052718844931
361.34491.273202970963820.0716970290361787
371.32391.3448963899958-0.0209963899957992
381.27851.32390105718545-0.0454010571854526
391.3051.278502285980460.0264977140195437
401.3191.304998665818370.0140013341816279
411.3651.318999295021340.0460007049786566
421.40161.364997683826790.0366023161732143
431.40881.401598157043370.00720184295663184
441.42681.40879963738130.0180003626186982
451.45621.426799093666980.0294009063330172
461.48161.456198519640260.0254014803597415
471.49141.481598721014640.00980127898536431
481.46141.49139950649757-0.0299995064975664
491.42721.46140151049975-0.0342015104997506
501.36861.4272017220741-0.0586017220740975
511.35691.36860295064476-0.0117029506447575
521.34061.35690058925316-0.0163005892531609
531.25651.34060082074803-0.0841008207480347
541.22091.25650423454528-0.0356042345452838
551.2771.22090179270240.0560982072975964
561.28941.276997175409260.0124028245907359
571.30671.289399375507610.0173006244923879
581.38981.306699128899370.0831008711006289
591.36611.389795815803-0.0236958158030005
601.3221.36610119310376-0.0441011931037554
611.3361.322002220531230.013997779468766
621.36491.335999295200330.0289007047996739
631.39991.364898544825820.035001455174184
641.44421.399898237648030.0443017623519677
651.43491.44419776936994-0.00929776936993987
661.43881.434900468150310.00389953184968839
671.42641.43879980365537-0.0123998036553741
681.43431.426400624340280.00789937565971854
691.3771.43429960225996-0.0572996022599583
701.37061.37700288508196-0.00640288508195708
711.35561.37060032239051-0.0150003223905142
721.31791.35560075527853-0.0377007552785318
731.29051.31790189826394-0.0274018982639415
741.32241.290501379708050.031898620291954
751.32011.32239839387831-0.00229839387831277
761.31621.32010011572602-0.00390011572601634
771.27891.31620019637402-0.0373001963740249
781.25261.27890187809547-0.026301878095472
791.22881.25260132432113-0.0238013243211286
801.241.22880119841620.0111988015838045
811.28561.239999436131160.0456005638688424
821.29741.285597703974220.0118022960257813
831.28281.29739940574472-0.0145994057447179
841.31191.282800735092050.02909926490795







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
851.311898534828151.242425636159941.38137143349637
861.311898534828151.213651492754891.41014557690142
871.311898534828151.191571983714411.43222508594189
881.311898534828151.172957984484811.45083908517149
891.311898534828151.156558668224341.46723840143197
901.311898534828151.141732522407121.48206454724918
911.311898534828151.128098454822581.49569861483372
921.311898534828151.11540816092441.5083889087319
931.311898534828151.103489166843841.52030790281246
941.311898534828151.092215894889531.53158117476677
951.311898534828151.081493543742491.54230352591381
961.311898534828151.07124846201711.5525486076392

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 1.31189853482815 & 1.24242563615994 & 1.38137143349637 \tabularnewline
86 & 1.31189853482815 & 1.21365149275489 & 1.41014557690142 \tabularnewline
87 & 1.31189853482815 & 1.19157198371441 & 1.43222508594189 \tabularnewline
88 & 1.31189853482815 & 1.17295798448481 & 1.45083908517149 \tabularnewline
89 & 1.31189853482815 & 1.15655866822434 & 1.46723840143197 \tabularnewline
90 & 1.31189853482815 & 1.14173252240712 & 1.48206454724918 \tabularnewline
91 & 1.31189853482815 & 1.12809845482258 & 1.49569861483372 \tabularnewline
92 & 1.31189853482815 & 1.1154081609244 & 1.5083889087319 \tabularnewline
93 & 1.31189853482815 & 1.10348916684384 & 1.52030790281246 \tabularnewline
94 & 1.31189853482815 & 1.09221589488953 & 1.53158117476677 \tabularnewline
95 & 1.31189853482815 & 1.08149354374249 & 1.54230352591381 \tabularnewline
96 & 1.31189853482815 & 1.0712484620171 & 1.5525486076392 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232231&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]1.31189853482815[/C][C]1.24242563615994[/C][C]1.38137143349637[/C][/ROW]
[ROW][C]86[/C][C]1.31189853482815[/C][C]1.21365149275489[/C][C]1.41014557690142[/C][/ROW]
[ROW][C]87[/C][C]1.31189853482815[/C][C]1.19157198371441[/C][C]1.43222508594189[/C][/ROW]
[ROW][C]88[/C][C]1.31189853482815[/C][C]1.17295798448481[/C][C]1.45083908517149[/C][/ROW]
[ROW][C]89[/C][C]1.31189853482815[/C][C]1.15655866822434[/C][C]1.46723840143197[/C][/ROW]
[ROW][C]90[/C][C]1.31189853482815[/C][C]1.14173252240712[/C][C]1.48206454724918[/C][/ROW]
[ROW][C]91[/C][C]1.31189853482815[/C][C]1.12809845482258[/C][C]1.49569861483372[/C][/ROW]
[ROW][C]92[/C][C]1.31189853482815[/C][C]1.1154081609244[/C][C]1.5083889087319[/C][/ROW]
[ROW][C]93[/C][C]1.31189853482815[/C][C]1.10348916684384[/C][C]1.52030790281246[/C][/ROW]
[ROW][C]94[/C][C]1.31189853482815[/C][C]1.09221589488953[/C][C]1.53158117476677[/C][/ROW]
[ROW][C]95[/C][C]1.31189853482815[/C][C]1.08149354374249[/C][C]1.54230352591381[/C][/ROW]
[ROW][C]96[/C][C]1.31189853482815[/C][C]1.0712484620171[/C][C]1.5525486076392[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232231&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232231&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
851.311898534828151.242425636159941.38137143349637
861.311898534828151.213651492754891.41014557690142
871.311898534828151.191571983714411.43222508594189
881.311898534828151.172957984484811.45083908517149
891.311898534828151.156558668224341.46723840143197
901.311898534828151.141732522407121.48206454724918
911.311898534828151.128098454822581.49569861483372
921.311898534828151.11540816092441.5083889087319
931.311898534828151.103489166843841.52030790281246
941.311898534828151.092215894889531.53158117476677
951.311898534828151.081493543742491.54230352591381
961.311898534828151.07124846201711.5525486076392



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