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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 22 Nov 2012 07:55:09 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Nov/22/t135358895237yisy2zjs68f0j.htm/, Retrieved Thu, 02 May 2024 00:42:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=191637, Retrieved Thu, 02 May 2024 00:42:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact93
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [WS 8 Exponential ...] [2012-11-22 12:53:26] [64c86865dff7d646747b84f713e71815]
- R P     [Exponential Smoothing] [WS 8 Exponential ...] [2012-11-22 12:55:09] [46cc0db4bd6f6541b375e62191991224] [Current]
-   P       [Exponential Smoothing] [WS 8 Exponential ...] [2012-11-22 12:56:26] [64c86865dff7d646747b84f713e71815]
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Dataseries X:
3.06
3.07
3.08
3.07
3.08
3.06
3.07
3.04
3.05
3.06
3.05
3.06
3.07
3.07
3.1
3.1
3.1
3.1
3.09
3.08
3.1
3.08
3.08
3.09
3.11
3.19
3.24
3.25
3.22
3.21
3.21
3.19
3.21
3.21
3.19
3.18
3.16
3.15
3.15
3.14
3.14
3.12
3.12
3.12
3.12
3.13
3.14
3.14
3.16
3.19
3.18
3.18
3.19
3.18
3.17
3.17
3.16
3.15
3.14
3.15
3.15
3.16
3.18
3.18
3.19
3.18
3.19
3.2
3.2
3.18
3.2
3.21
3.24
3.29
3.28
3.27
3.29
3.27
3.27
3.25
3.25
3.23
3.23
3.25




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 3 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=191637&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=191637&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=191637&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 time3 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.039686617033814
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.039686617033814 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=191637&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]0.039686617033814[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=191637&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=191637&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
alpha1
beta0.039686617033814
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
33.083.084.44089209850063e-16
43.073.09-0.02
53.083.079206267659320.000793732340676812
63.063.08923776821076-0.0292377682107552
73.073.068077420100850.00192257989914824
83.043.07815372079303-0.038153720793026
93.053.04663952868750.00336047131250172
103.063.056772894425530.00322710557446992
113.053.06690096732859-0.0169009673285925
123.063.056230225110720.0037697748892791
133.073.066379834723060.00362016527694387
143.073.076523506836-0.00652350683600122
153.13.076264610918480.0237353890815171
163.13.10720658821511-0.00720658821511
173.13.1069205831085-0.00692058310849664
183.13.10664592857702-0.00664592857701907
193.093.10638217415475-0.016382174154749
203.083.09573202108289-0.0157320210828877
213.13.0851076703870.0148923296129966
223.083.1056986965691-0.025698696569096
233.083.08467880224009-0.00467880224008965
243.093.084493116407410.00550688359258933
253.113.09471166598760.0152883340124008
263.193.115318408244630.0746815917553656
273.243.198282267976110.0417177320238951
283.253.249937903630466.20963695427967e-05
293.223.25994036802529-0.0399403680252939
303.213.22835526993528-0.0183552699352849
313.213.21762681136681-0.00762681136681076
323.193.21732412902491-0.0273241290249069
333.213.196239726780510.013760273219487
343.213.21678582547406-0.0067858254740556
353.193.21651651901721-0.0265165190172083
363.183.1954641680819-0.0154641680819023
373.163.18485044756549-0.0248504475654894
383.153.16386421736984-0.0138642173698393
393.153.15331399348461-0.0033139934846087
403.143.15318247229433-0.0131824722943321
413.143.14265930456483-0.00265930456482844
423.123.14255376576299-0.022553765762988
433.123.12165868309848-0.00165868309848172
443.123.12159285557757-0.00159285557757194
453.123.12152964052827-0.00152964052827453
463.133.121468934270430.0085310657295703
473.143.131807503408930.00819249659107069
483.143.14213263588369-0.00213263588369017
493.163.14204799878010.0179520012198986
503.193.162760452977510.0272395470224938
513.183.19384149844836-0.0138414984483624
523.183.18329217620027-0.00329217620026823
533.193.18316152086420.0068384791357996
543.183.19343291696676-0.0134329169667562
553.173.18289980993545-0.0128998099354498
563.173.17238786011873-0.00238786011873238
573.163.17229309402867-0.0122930940286698
583.153.16180522271379-0.0118052227137939
593.143.15133671336095-0.0113367133609521
603.153.140886797559370.00911320244062575
613.153.15124846973459-0.0012484697345867
623.163.151198922194350.00880107780564821
633.183.161548207198710.0184517928012906
643.183.1822804964332-0.0022804964332015
653.193.182189991244610.0078100087553894
663.183.19249994407112-0.012499944071116
673.193.182003863577820.00799613642217833
683.23.192321203181760.00767879681824146
693.23.20262594865036-0.00262594865036458
703.183.20252173363193-0.0225217336319274
713.23.181627922214340.0183720777856604
723.213.202357047829530.00764295217046529
733.243.212660370745330.0273396292546688
743.293.243745388141410.046254611858592
753.283.29558107720829-0.0155810772082878
763.273.28496271696415-0.0149627169641477
773.293.274368897346210.0156311026537934
783.273.29498924293104-0.0249892429310439
793.273.27399750441687-0.00399750441687452
803.253.27383885698999-0.023838856989991
813.253.25289277340211-0.00289277340210559
823.233.25277796901193-0.0227779690119303
833.233.23187398847895-0.00187398847894604
843.253.231799616215860.0182003837841438

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 3.08 & 3.08 & 4.44089209850063e-16 \tabularnewline
4 & 3.07 & 3.09 & -0.02 \tabularnewline
5 & 3.08 & 3.07920626765932 & 0.000793732340676812 \tabularnewline
6 & 3.06 & 3.08923776821076 & -0.0292377682107552 \tabularnewline
7 & 3.07 & 3.06807742010085 & 0.00192257989914824 \tabularnewline
8 & 3.04 & 3.07815372079303 & -0.038153720793026 \tabularnewline
9 & 3.05 & 3.0466395286875 & 0.00336047131250172 \tabularnewline
10 & 3.06 & 3.05677289442553 & 0.00322710557446992 \tabularnewline
11 & 3.05 & 3.06690096732859 & -0.0169009673285925 \tabularnewline
12 & 3.06 & 3.05623022511072 & 0.0037697748892791 \tabularnewline
13 & 3.07 & 3.06637983472306 & 0.00362016527694387 \tabularnewline
14 & 3.07 & 3.076523506836 & -0.00652350683600122 \tabularnewline
15 & 3.1 & 3.07626461091848 & 0.0237353890815171 \tabularnewline
16 & 3.1 & 3.10720658821511 & -0.00720658821511 \tabularnewline
17 & 3.1 & 3.1069205831085 & -0.00692058310849664 \tabularnewline
18 & 3.1 & 3.10664592857702 & -0.00664592857701907 \tabularnewline
19 & 3.09 & 3.10638217415475 & -0.016382174154749 \tabularnewline
20 & 3.08 & 3.09573202108289 & -0.0157320210828877 \tabularnewline
21 & 3.1 & 3.085107670387 & 0.0148923296129966 \tabularnewline
22 & 3.08 & 3.1056986965691 & -0.025698696569096 \tabularnewline
23 & 3.08 & 3.08467880224009 & -0.00467880224008965 \tabularnewline
24 & 3.09 & 3.08449311640741 & 0.00550688359258933 \tabularnewline
25 & 3.11 & 3.0947116659876 & 0.0152883340124008 \tabularnewline
26 & 3.19 & 3.11531840824463 & 0.0746815917553656 \tabularnewline
27 & 3.24 & 3.19828226797611 & 0.0417177320238951 \tabularnewline
28 & 3.25 & 3.24993790363046 & 6.20963695427967e-05 \tabularnewline
29 & 3.22 & 3.25994036802529 & -0.0399403680252939 \tabularnewline
30 & 3.21 & 3.22835526993528 & -0.0183552699352849 \tabularnewline
31 & 3.21 & 3.21762681136681 & -0.00762681136681076 \tabularnewline
32 & 3.19 & 3.21732412902491 & -0.0273241290249069 \tabularnewline
33 & 3.21 & 3.19623972678051 & 0.013760273219487 \tabularnewline
34 & 3.21 & 3.21678582547406 & -0.0067858254740556 \tabularnewline
35 & 3.19 & 3.21651651901721 & -0.0265165190172083 \tabularnewline
36 & 3.18 & 3.1954641680819 & -0.0154641680819023 \tabularnewline
37 & 3.16 & 3.18485044756549 & -0.0248504475654894 \tabularnewline
38 & 3.15 & 3.16386421736984 & -0.0138642173698393 \tabularnewline
39 & 3.15 & 3.15331399348461 & -0.0033139934846087 \tabularnewline
40 & 3.14 & 3.15318247229433 & -0.0131824722943321 \tabularnewline
41 & 3.14 & 3.14265930456483 & -0.00265930456482844 \tabularnewline
42 & 3.12 & 3.14255376576299 & -0.022553765762988 \tabularnewline
43 & 3.12 & 3.12165868309848 & -0.00165868309848172 \tabularnewline
44 & 3.12 & 3.12159285557757 & -0.00159285557757194 \tabularnewline
45 & 3.12 & 3.12152964052827 & -0.00152964052827453 \tabularnewline
46 & 3.13 & 3.12146893427043 & 0.0085310657295703 \tabularnewline
47 & 3.14 & 3.13180750340893 & 0.00819249659107069 \tabularnewline
48 & 3.14 & 3.14213263588369 & -0.00213263588369017 \tabularnewline
49 & 3.16 & 3.1420479987801 & 0.0179520012198986 \tabularnewline
50 & 3.19 & 3.16276045297751 & 0.0272395470224938 \tabularnewline
51 & 3.18 & 3.19384149844836 & -0.0138414984483624 \tabularnewline
52 & 3.18 & 3.18329217620027 & -0.00329217620026823 \tabularnewline
53 & 3.19 & 3.1831615208642 & 0.0068384791357996 \tabularnewline
54 & 3.18 & 3.19343291696676 & -0.0134329169667562 \tabularnewline
55 & 3.17 & 3.18289980993545 & -0.0128998099354498 \tabularnewline
56 & 3.17 & 3.17238786011873 & -0.00238786011873238 \tabularnewline
57 & 3.16 & 3.17229309402867 & -0.0122930940286698 \tabularnewline
58 & 3.15 & 3.16180522271379 & -0.0118052227137939 \tabularnewline
59 & 3.14 & 3.15133671336095 & -0.0113367133609521 \tabularnewline
60 & 3.15 & 3.14088679755937 & 0.00911320244062575 \tabularnewline
61 & 3.15 & 3.15124846973459 & -0.0012484697345867 \tabularnewline
62 & 3.16 & 3.15119892219435 & 0.00880107780564821 \tabularnewline
63 & 3.18 & 3.16154820719871 & 0.0184517928012906 \tabularnewline
64 & 3.18 & 3.1822804964332 & -0.0022804964332015 \tabularnewline
65 & 3.19 & 3.18218999124461 & 0.0078100087553894 \tabularnewline
66 & 3.18 & 3.19249994407112 & -0.012499944071116 \tabularnewline
67 & 3.19 & 3.18200386357782 & 0.00799613642217833 \tabularnewline
68 & 3.2 & 3.19232120318176 & 0.00767879681824146 \tabularnewline
69 & 3.2 & 3.20262594865036 & -0.00262594865036458 \tabularnewline
70 & 3.18 & 3.20252173363193 & -0.0225217336319274 \tabularnewline
71 & 3.2 & 3.18162792221434 & 0.0183720777856604 \tabularnewline
72 & 3.21 & 3.20235704782953 & 0.00764295217046529 \tabularnewline
73 & 3.24 & 3.21266037074533 & 0.0273396292546688 \tabularnewline
74 & 3.29 & 3.24374538814141 & 0.046254611858592 \tabularnewline
75 & 3.28 & 3.29558107720829 & -0.0155810772082878 \tabularnewline
76 & 3.27 & 3.28496271696415 & -0.0149627169641477 \tabularnewline
77 & 3.29 & 3.27436889734621 & 0.0156311026537934 \tabularnewline
78 & 3.27 & 3.29498924293104 & -0.0249892429310439 \tabularnewline
79 & 3.27 & 3.27399750441687 & -0.00399750441687452 \tabularnewline
80 & 3.25 & 3.27383885698999 & -0.023838856989991 \tabularnewline
81 & 3.25 & 3.25289277340211 & -0.00289277340210559 \tabularnewline
82 & 3.23 & 3.25277796901193 & -0.0227779690119303 \tabularnewline
83 & 3.23 & 3.23187398847895 & -0.00187398847894604 \tabularnewline
84 & 3.25 & 3.23179961621586 & 0.0182003837841438 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=191637&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]3[/C][C]3.08[/C][C]3.08[/C][C]4.44089209850063e-16[/C][/ROW]
[ROW][C]4[/C][C]3.07[/C][C]3.09[/C][C]-0.02[/C][/ROW]
[ROW][C]5[/C][C]3.08[/C][C]3.07920626765932[/C][C]0.000793732340676812[/C][/ROW]
[ROW][C]6[/C][C]3.06[/C][C]3.08923776821076[/C][C]-0.0292377682107552[/C][/ROW]
[ROW][C]7[/C][C]3.07[/C][C]3.06807742010085[/C][C]0.00192257989914824[/C][/ROW]
[ROW][C]8[/C][C]3.04[/C][C]3.07815372079303[/C][C]-0.038153720793026[/C][/ROW]
[ROW][C]9[/C][C]3.05[/C][C]3.0466395286875[/C][C]0.00336047131250172[/C][/ROW]
[ROW][C]10[/C][C]3.06[/C][C]3.05677289442553[/C][C]0.00322710557446992[/C][/ROW]
[ROW][C]11[/C][C]3.05[/C][C]3.06690096732859[/C][C]-0.0169009673285925[/C][/ROW]
[ROW][C]12[/C][C]3.06[/C][C]3.05623022511072[/C][C]0.0037697748892791[/C][/ROW]
[ROW][C]13[/C][C]3.07[/C][C]3.06637983472306[/C][C]0.00362016527694387[/C][/ROW]
[ROW][C]14[/C][C]3.07[/C][C]3.076523506836[/C][C]-0.00652350683600122[/C][/ROW]
[ROW][C]15[/C][C]3.1[/C][C]3.07626461091848[/C][C]0.0237353890815171[/C][/ROW]
[ROW][C]16[/C][C]3.1[/C][C]3.10720658821511[/C][C]-0.00720658821511[/C][/ROW]
[ROW][C]17[/C][C]3.1[/C][C]3.1069205831085[/C][C]-0.00692058310849664[/C][/ROW]
[ROW][C]18[/C][C]3.1[/C][C]3.10664592857702[/C][C]-0.00664592857701907[/C][/ROW]
[ROW][C]19[/C][C]3.09[/C][C]3.10638217415475[/C][C]-0.016382174154749[/C][/ROW]
[ROW][C]20[/C][C]3.08[/C][C]3.09573202108289[/C][C]-0.0157320210828877[/C][/ROW]
[ROW][C]21[/C][C]3.1[/C][C]3.085107670387[/C][C]0.0148923296129966[/C][/ROW]
[ROW][C]22[/C][C]3.08[/C][C]3.1056986965691[/C][C]-0.025698696569096[/C][/ROW]
[ROW][C]23[/C][C]3.08[/C][C]3.08467880224009[/C][C]-0.00467880224008965[/C][/ROW]
[ROW][C]24[/C][C]3.09[/C][C]3.08449311640741[/C][C]0.00550688359258933[/C][/ROW]
[ROW][C]25[/C][C]3.11[/C][C]3.0947116659876[/C][C]0.0152883340124008[/C][/ROW]
[ROW][C]26[/C][C]3.19[/C][C]3.11531840824463[/C][C]0.0746815917553656[/C][/ROW]
[ROW][C]27[/C][C]3.24[/C][C]3.19828226797611[/C][C]0.0417177320238951[/C][/ROW]
[ROW][C]28[/C][C]3.25[/C][C]3.24993790363046[/C][C]6.20963695427967e-05[/C][/ROW]
[ROW][C]29[/C][C]3.22[/C][C]3.25994036802529[/C][C]-0.0399403680252939[/C][/ROW]
[ROW][C]30[/C][C]3.21[/C][C]3.22835526993528[/C][C]-0.0183552699352849[/C][/ROW]
[ROW][C]31[/C][C]3.21[/C][C]3.21762681136681[/C][C]-0.00762681136681076[/C][/ROW]
[ROW][C]32[/C][C]3.19[/C][C]3.21732412902491[/C][C]-0.0273241290249069[/C][/ROW]
[ROW][C]33[/C][C]3.21[/C][C]3.19623972678051[/C][C]0.013760273219487[/C][/ROW]
[ROW][C]34[/C][C]3.21[/C][C]3.21678582547406[/C][C]-0.0067858254740556[/C][/ROW]
[ROW][C]35[/C][C]3.19[/C][C]3.21651651901721[/C][C]-0.0265165190172083[/C][/ROW]
[ROW][C]36[/C][C]3.18[/C][C]3.1954641680819[/C][C]-0.0154641680819023[/C][/ROW]
[ROW][C]37[/C][C]3.16[/C][C]3.18485044756549[/C][C]-0.0248504475654894[/C][/ROW]
[ROW][C]38[/C][C]3.15[/C][C]3.16386421736984[/C][C]-0.0138642173698393[/C][/ROW]
[ROW][C]39[/C][C]3.15[/C][C]3.15331399348461[/C][C]-0.0033139934846087[/C][/ROW]
[ROW][C]40[/C][C]3.14[/C][C]3.15318247229433[/C][C]-0.0131824722943321[/C][/ROW]
[ROW][C]41[/C][C]3.14[/C][C]3.14265930456483[/C][C]-0.00265930456482844[/C][/ROW]
[ROW][C]42[/C][C]3.12[/C][C]3.14255376576299[/C][C]-0.022553765762988[/C][/ROW]
[ROW][C]43[/C][C]3.12[/C][C]3.12165868309848[/C][C]-0.00165868309848172[/C][/ROW]
[ROW][C]44[/C][C]3.12[/C][C]3.12159285557757[/C][C]-0.00159285557757194[/C][/ROW]
[ROW][C]45[/C][C]3.12[/C][C]3.12152964052827[/C][C]-0.00152964052827453[/C][/ROW]
[ROW][C]46[/C][C]3.13[/C][C]3.12146893427043[/C][C]0.0085310657295703[/C][/ROW]
[ROW][C]47[/C][C]3.14[/C][C]3.13180750340893[/C][C]0.00819249659107069[/C][/ROW]
[ROW][C]48[/C][C]3.14[/C][C]3.14213263588369[/C][C]-0.00213263588369017[/C][/ROW]
[ROW][C]49[/C][C]3.16[/C][C]3.1420479987801[/C][C]0.0179520012198986[/C][/ROW]
[ROW][C]50[/C][C]3.19[/C][C]3.16276045297751[/C][C]0.0272395470224938[/C][/ROW]
[ROW][C]51[/C][C]3.18[/C][C]3.19384149844836[/C][C]-0.0138414984483624[/C][/ROW]
[ROW][C]52[/C][C]3.18[/C][C]3.18329217620027[/C][C]-0.00329217620026823[/C][/ROW]
[ROW][C]53[/C][C]3.19[/C][C]3.1831615208642[/C][C]0.0068384791357996[/C][/ROW]
[ROW][C]54[/C][C]3.18[/C][C]3.19343291696676[/C][C]-0.0134329169667562[/C][/ROW]
[ROW][C]55[/C][C]3.17[/C][C]3.18289980993545[/C][C]-0.0128998099354498[/C][/ROW]
[ROW][C]56[/C][C]3.17[/C][C]3.17238786011873[/C][C]-0.00238786011873238[/C][/ROW]
[ROW][C]57[/C][C]3.16[/C][C]3.17229309402867[/C][C]-0.0122930940286698[/C][/ROW]
[ROW][C]58[/C][C]3.15[/C][C]3.16180522271379[/C][C]-0.0118052227137939[/C][/ROW]
[ROW][C]59[/C][C]3.14[/C][C]3.15133671336095[/C][C]-0.0113367133609521[/C][/ROW]
[ROW][C]60[/C][C]3.15[/C][C]3.14088679755937[/C][C]0.00911320244062575[/C][/ROW]
[ROW][C]61[/C][C]3.15[/C][C]3.15124846973459[/C][C]-0.0012484697345867[/C][/ROW]
[ROW][C]62[/C][C]3.16[/C][C]3.15119892219435[/C][C]0.00880107780564821[/C][/ROW]
[ROW][C]63[/C][C]3.18[/C][C]3.16154820719871[/C][C]0.0184517928012906[/C][/ROW]
[ROW][C]64[/C][C]3.18[/C][C]3.1822804964332[/C][C]-0.0022804964332015[/C][/ROW]
[ROW][C]65[/C][C]3.19[/C][C]3.18218999124461[/C][C]0.0078100087553894[/C][/ROW]
[ROW][C]66[/C][C]3.18[/C][C]3.19249994407112[/C][C]-0.012499944071116[/C][/ROW]
[ROW][C]67[/C][C]3.19[/C][C]3.18200386357782[/C][C]0.00799613642217833[/C][/ROW]
[ROW][C]68[/C][C]3.2[/C][C]3.19232120318176[/C][C]0.00767879681824146[/C][/ROW]
[ROW][C]69[/C][C]3.2[/C][C]3.20262594865036[/C][C]-0.00262594865036458[/C][/ROW]
[ROW][C]70[/C][C]3.18[/C][C]3.20252173363193[/C][C]-0.0225217336319274[/C][/ROW]
[ROW][C]71[/C][C]3.2[/C][C]3.18162792221434[/C][C]0.0183720777856604[/C][/ROW]
[ROW][C]72[/C][C]3.21[/C][C]3.20235704782953[/C][C]0.00764295217046529[/C][/ROW]
[ROW][C]73[/C][C]3.24[/C][C]3.21266037074533[/C][C]0.0273396292546688[/C][/ROW]
[ROW][C]74[/C][C]3.29[/C][C]3.24374538814141[/C][C]0.046254611858592[/C][/ROW]
[ROW][C]75[/C][C]3.28[/C][C]3.29558107720829[/C][C]-0.0155810772082878[/C][/ROW]
[ROW][C]76[/C][C]3.27[/C][C]3.28496271696415[/C][C]-0.0149627169641477[/C][/ROW]
[ROW][C]77[/C][C]3.29[/C][C]3.27436889734621[/C][C]0.0156311026537934[/C][/ROW]
[ROW][C]78[/C][C]3.27[/C][C]3.29498924293104[/C][C]-0.0249892429310439[/C][/ROW]
[ROW][C]79[/C][C]3.27[/C][C]3.27399750441687[/C][C]-0.00399750441687452[/C][/ROW]
[ROW][C]80[/C][C]3.25[/C][C]3.27383885698999[/C][C]-0.023838856989991[/C][/ROW]
[ROW][C]81[/C][C]3.25[/C][C]3.25289277340211[/C][C]-0.00289277340210559[/C][/ROW]
[ROW][C]82[/C][C]3.23[/C][C]3.25277796901193[/C][C]-0.0227779690119303[/C][/ROW]
[ROW][C]83[/C][C]3.23[/C][C]3.23187398847895[/C][C]-0.00187398847894604[/C][/ROW]
[ROW][C]84[/C][C]3.25[/C][C]3.23179961621586[/C][C]0.0182003837841438[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=191637&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=191637&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
33.083.084.44089209850063e-16
43.073.09-0.02
53.083.079206267659320.000793732340676812
63.063.08923776821076-0.0292377682107552
73.073.068077420100850.00192257989914824
83.043.07815372079303-0.038153720793026
93.053.04663952868750.00336047131250172
103.063.056772894425530.00322710557446992
113.053.06690096732859-0.0169009673285925
123.063.056230225110720.0037697748892791
133.073.066379834723060.00362016527694387
143.073.076523506836-0.00652350683600122
153.13.076264610918480.0237353890815171
163.13.10720658821511-0.00720658821511
173.13.1069205831085-0.00692058310849664
183.13.10664592857702-0.00664592857701907
193.093.10638217415475-0.016382174154749
203.083.09573202108289-0.0157320210828877
213.13.0851076703870.0148923296129966
223.083.1056986965691-0.025698696569096
233.083.08467880224009-0.00467880224008965
243.093.084493116407410.00550688359258933
253.113.09471166598760.0152883340124008
263.193.115318408244630.0746815917553656
273.243.198282267976110.0417177320238951
283.253.249937903630466.20963695427967e-05
293.223.25994036802529-0.0399403680252939
303.213.22835526993528-0.0183552699352849
313.213.21762681136681-0.00762681136681076
323.193.21732412902491-0.0273241290249069
333.213.196239726780510.013760273219487
343.213.21678582547406-0.0067858254740556
353.193.21651651901721-0.0265165190172083
363.183.1954641680819-0.0154641680819023
373.163.18485044756549-0.0248504475654894
383.153.16386421736984-0.0138642173698393
393.153.15331399348461-0.0033139934846087
403.143.15318247229433-0.0131824722943321
413.143.14265930456483-0.00265930456482844
423.123.14255376576299-0.022553765762988
433.123.12165868309848-0.00165868309848172
443.123.12159285557757-0.00159285557757194
453.123.12152964052827-0.00152964052827453
463.133.121468934270430.0085310657295703
473.143.131807503408930.00819249659107069
483.143.14213263588369-0.00213263588369017
493.163.14204799878010.0179520012198986
503.193.162760452977510.0272395470224938
513.183.19384149844836-0.0138414984483624
523.183.18329217620027-0.00329217620026823
533.193.18316152086420.0068384791357996
543.183.19343291696676-0.0134329169667562
553.173.18289980993545-0.0128998099354498
563.173.17238786011873-0.00238786011873238
573.163.17229309402867-0.0122930940286698
583.153.16180522271379-0.0118052227137939
593.143.15133671336095-0.0113367133609521
603.153.140886797559370.00911320244062575
613.153.15124846973459-0.0012484697345867
623.163.151198922194350.00880107780564821
633.183.161548207198710.0184517928012906
643.183.1822804964332-0.0022804964332015
653.193.182189991244610.0078100087553894
663.183.19249994407112-0.012499944071116
673.193.182003863577820.00799613642217833
683.23.192321203181760.00767879681824146
693.23.20262594865036-0.00262594865036458
703.183.20252173363193-0.0225217336319274
713.23.181627922214340.0183720777856604
723.213.202357047829530.00764295217046529
733.243.212660370745330.0273396292546688
743.293.243745388141410.046254611858592
753.283.29558107720829-0.0155810772082878
763.273.28496271696415-0.0149627169641477
773.293.274368897346210.0156311026537934
783.273.29498924293104-0.0249892429310439
793.273.27399750441687-0.00399750441687452
803.253.27383885698999-0.023838856989991
813.253.25289277340211-0.00289277340210559
823.233.25277796901193-0.0227779690119303
833.233.23187398847895-0.00187398847894604
843.253.231799616215860.0182003837841438







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
853.252521927876973.216436647507473.28860720824646
863.255043855753933.202989062584413.30709864892345
873.25756578363093.192552216323513.32257935093828
883.260087711507863.183553819525443.33662160349028
893.262609639384833.175398278931863.3498209998378
903.26513156726183.167786715931193.3624764185924
913.267653495138763.160545444443053.37476154583448
923.270175423015733.153563817426343.38678702860512
933.272697350892693.146766742938253.39862795884714
943.275219278769663.140100846477613.41033771106171
953.277741206646633.133526829519063.42195558377419
963.280263134523593.127014945849893.43351132319729

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 3.25252192787697 & 3.21643664750747 & 3.28860720824646 \tabularnewline
86 & 3.25504385575393 & 3.20298906258441 & 3.30709864892345 \tabularnewline
87 & 3.2575657836309 & 3.19255221632351 & 3.32257935093828 \tabularnewline
88 & 3.26008771150786 & 3.18355381952544 & 3.33662160349028 \tabularnewline
89 & 3.26260963938483 & 3.17539827893186 & 3.3498209998378 \tabularnewline
90 & 3.2651315672618 & 3.16778671593119 & 3.3624764185924 \tabularnewline
91 & 3.26765349513876 & 3.16054544444305 & 3.37476154583448 \tabularnewline
92 & 3.27017542301573 & 3.15356381742634 & 3.38678702860512 \tabularnewline
93 & 3.27269735089269 & 3.14676674293825 & 3.39862795884714 \tabularnewline
94 & 3.27521927876966 & 3.14010084647761 & 3.41033771106171 \tabularnewline
95 & 3.27774120664663 & 3.13352682951906 & 3.42195558377419 \tabularnewline
96 & 3.28026313452359 & 3.12701494584989 & 3.43351132319729 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=191637&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]3.25252192787697[/C][C]3.21643664750747[/C][C]3.28860720824646[/C][/ROW]
[ROW][C]86[/C][C]3.25504385575393[/C][C]3.20298906258441[/C][C]3.30709864892345[/C][/ROW]
[ROW][C]87[/C][C]3.2575657836309[/C][C]3.19255221632351[/C][C]3.32257935093828[/C][/ROW]
[ROW][C]88[/C][C]3.26008771150786[/C][C]3.18355381952544[/C][C]3.33662160349028[/C][/ROW]
[ROW][C]89[/C][C]3.26260963938483[/C][C]3.17539827893186[/C][C]3.3498209998378[/C][/ROW]
[ROW][C]90[/C][C]3.2651315672618[/C][C]3.16778671593119[/C][C]3.3624764185924[/C][/ROW]
[ROW][C]91[/C][C]3.26765349513876[/C][C]3.16054544444305[/C][C]3.37476154583448[/C][/ROW]
[ROW][C]92[/C][C]3.27017542301573[/C][C]3.15356381742634[/C][C]3.38678702860512[/C][/ROW]
[ROW][C]93[/C][C]3.27269735089269[/C][C]3.14676674293825[/C][C]3.39862795884714[/C][/ROW]
[ROW][C]94[/C][C]3.27521927876966[/C][C]3.14010084647761[/C][C]3.41033771106171[/C][/ROW]
[ROW][C]95[/C][C]3.27774120664663[/C][C]3.13352682951906[/C][C]3.42195558377419[/C][/ROW]
[ROW][C]96[/C][C]3.28026313452359[/C][C]3.12701494584989[/C][C]3.43351132319729[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=191637&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=191637&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
853.252521927876973.216436647507473.28860720824646
863.255043855753933.202989062584413.30709864892345
873.25756578363093.192552216323513.32257935093828
883.260087711507863.183553819525443.33662160349028
893.262609639384833.175398278931863.3498209998378
903.26513156726183.167786715931193.3624764185924
913.267653495138763.160545444443053.37476154583448
923.270175423015733.153563817426343.38678702860512
933.272697350892693.146766742938253.39862795884714
943.275219278769663.140100846477613.41033771106171
953.277741206646633.133526829519063.42195558377419
963.280263134523593.127014945849893.43351132319729



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')