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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 22 May 2015 21:47:19 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/May/22/t1432327708zcn4tsn45vfod1d.htm/, Retrieved Fri, 03 May 2024 13:53:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279254, Retrieved Fri, 03 May 2024 13:53:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact89
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-05-22 20:47:19] [70e23d918d09c907c02097a361cd6415] [Current]
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Dataseries X:
3.5
4.8
6
5.9
3.6
6.8
8.7
8.4
8.1
8.9
8.7
7.8
6.3
7.5
6.8
7
8.8
8.4
7.6
7.9
7.4
8.7
8.7
8
9.4
8.5
5.8
2.8
3.3
4.8
1.8
4.8
-0.9
-6
-9
-21.1
-20.9
-23.5
-20.8
-17.3
-16.1
-13.9
-14.6
-9.2
-9.7
-7.2
-5
-8.1
-6.2
-4.8
-3.1
-1.4
0.6
-0.8
-2
0.2
-0.1
0.3
0.2
2.6
2.5
1.5
5.7
4.3
2.7
1.7
-2.2
-3.2
-0.5
-3.1
-4.8
-1.3
-1.8
-1.7
-2.8
-3.4
-4.9
-4.8
-5.4
-4.7
-6.6
-7.6
-6.8
-5.6
-5.6
-3.7
-5.1
-5.6
-4.1
-3.8
-3.1
-1.4
-2.4
-0.3
-0.3
0.1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279254&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279254&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279254&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999922263945937
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999922263945937 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279254&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]0.999922263945937[/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=279254&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279254&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
alpha0.999922263945937
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
24.83.51.3
364.799898943129721.20010105687028
45.95.99990670887936-0.0999067088793621
53.65.90000776635332-2.30000776635332
66.83.600178793528073.19982120647193
78.76.79975125852571.9002487414743
88.48.6998522821611-0.299852282161099
98.18.40002330933322-0.300023309333218
108.98.100023322628190.799976677371806
118.78.89993781296976-0.199937812969759
127.88.70001554237664-0.900015542376638
136.37.80006996365686-1.50006996365686
147.56.300116609519791.19988339048021
156.87.49990672579989-0.699906725799889
1676.800054407987080.199945592012925
178.86.999984457018651.80001554298135
188.48.79986007389444-0.399860073894439
197.68.40003108354432-0.800031083544322
207.97.600062191259560.299937808740439
217.47.89997668401829-0.499976684018285
228.77.400038866214541.29996113378546
238.78.699898946151020.000101053848975852
2488.69999999214447-0.699999992144472
259.48.000054415237231.39994558476277
268.59.39989117375434-0.899891173754337
275.88.50006995398893-2.70006995398893
282.85.80020989278392-3.00020989278392
293.32.800233224478420.499766775521575
304.83.299961150102921.50003884989708
311.84.79988339289887-2.99988339289887
324.81.800233199097612.99976680090239
33-0.94.79976680996579-5.69976680996579
34-6-0.899556922619116-5.10044307738088
35-9-5.99960351168119-3.00039648831881
36-21.1-8.99976676101637-12.1002332389836
37-20.9-21.09905937561480.19905937561477
38-23.5-20.9000154740904-2.59998452590962
39-20.8-23.49979788746232.69979788746233
40-17.3-20.80020987163453.50020987163454
41-16.1-17.30027209250381.20027209250381
42-13.9-16.10009330441632.20009330441628
43-14.6-13.9001710265721-0.699828973427945
44-9.2-14.59994559805715.39994559805709
45-9.7-9.20041977046295-0.499580229537054
46-7.2-9.699961164604272.49996116460427
47-5-7.200194337116252.20019433711625
48-8.1-5.00017103442594-3.09982896557406
49-6.2-8.099759031527951.89975903152795
50-4.8-6.200147679770781.40014767977078
51-3.1-4.800108841955731.70010884195573
52-1.4-3.100132159752851.70013215975285
530.6-1.400132161565482.00013216156548
54-0.80.599844517618156-1.39984451761816
55-2-0.799891181610899-1.2001088183891
560.2-1.999906708276012.19990670827601
57-0.10.199828987933193-0.299828987933193
580.3-0.09997669247758450.399976692477584
590.20.29996890739021-0.0999689073902098
602.60.2000077711883892.39999222881161
612.52.59981343407435-0.0998134340743517
621.52.50000775910251-1.00000775910251
635.71.500077736657224.19992226334278
644.35.69967351461588-1.39967351461588
652.74.300108805096-1.600108805096
661.72.70012438614458-1.00012438614458
67-2.21.70007774572335-3.90007774572335
68-3.2-2.19969682334551-1.00030317665449
69-0.5-3.199922240378182.69992224037818
70-3.1-0.500209881301243-2.59979011869876
71-4.8-3.09979790257478-1.70020209742522
72-1.3-4.799867832997843.49986783299784
73-1.8-1.30027206591508-0.499727934084922
74-1.7-1.79996115312230.0999611531222995
75-2.8-1.7000077705856-1.0999922294144
76-3.4-2.79991449094459-0.600085509055414
77-4.9-3.39995335172043-1.50004664827957
78-4.8-4.899883392292650.0998833922926536
79-5.4-4.80000776454078-0.599992235459217
80-4.7-5.399953358971150.699953358971147
81-6.6-4.70005441161215-1.89994558838785
82-7.6-6.59985230572702-1.00014769427298
83-6.8-7.599922252464770.799922252464767
84-5.6-6.800062182799461.20006218279946
85-5.6-5.600093288098729.32880987205564e-05
86-3.7-5.600000007251851.90000000725185
87-5.1-3.70014769850328-1.39985230149672
88-5.6-5.09989118100581-0.500108818994189
89-4.1-5.599961123513811.49996112351381
90-3.8-4.100116601058990.300116601058989
91-3.1-3.800023329880320.700023329880325
92-1.4-3.100054417051421.70005441705142
93-2.4-1.40013215552207-0.999867844477927
94-0.3-2.399922274219192.09992227421919
95-0.3-0.3001632396714360.000163239671435944
960.1-0.3000000126896080.400000012689608

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 4.8 & 3.5 & 1.3 \tabularnewline
3 & 6 & 4.79989894312972 & 1.20010105687028 \tabularnewline
4 & 5.9 & 5.99990670887936 & -0.0999067088793621 \tabularnewline
5 & 3.6 & 5.90000776635332 & -2.30000776635332 \tabularnewline
6 & 6.8 & 3.60017879352807 & 3.19982120647193 \tabularnewline
7 & 8.7 & 6.7997512585257 & 1.9002487414743 \tabularnewline
8 & 8.4 & 8.6998522821611 & -0.299852282161099 \tabularnewline
9 & 8.1 & 8.40002330933322 & -0.300023309333218 \tabularnewline
10 & 8.9 & 8.10002332262819 & 0.799976677371806 \tabularnewline
11 & 8.7 & 8.89993781296976 & -0.199937812969759 \tabularnewline
12 & 7.8 & 8.70001554237664 & -0.900015542376638 \tabularnewline
13 & 6.3 & 7.80006996365686 & -1.50006996365686 \tabularnewline
14 & 7.5 & 6.30011660951979 & 1.19988339048021 \tabularnewline
15 & 6.8 & 7.49990672579989 & -0.699906725799889 \tabularnewline
16 & 7 & 6.80005440798708 & 0.199945592012925 \tabularnewline
17 & 8.8 & 6.99998445701865 & 1.80001554298135 \tabularnewline
18 & 8.4 & 8.79986007389444 & -0.399860073894439 \tabularnewline
19 & 7.6 & 8.40003108354432 & -0.800031083544322 \tabularnewline
20 & 7.9 & 7.60006219125956 & 0.299937808740439 \tabularnewline
21 & 7.4 & 7.89997668401829 & -0.499976684018285 \tabularnewline
22 & 8.7 & 7.40003886621454 & 1.29996113378546 \tabularnewline
23 & 8.7 & 8.69989894615102 & 0.000101053848975852 \tabularnewline
24 & 8 & 8.69999999214447 & -0.699999992144472 \tabularnewline
25 & 9.4 & 8.00005441523723 & 1.39994558476277 \tabularnewline
26 & 8.5 & 9.39989117375434 & -0.899891173754337 \tabularnewline
27 & 5.8 & 8.50006995398893 & -2.70006995398893 \tabularnewline
28 & 2.8 & 5.80020989278392 & -3.00020989278392 \tabularnewline
29 & 3.3 & 2.80023322447842 & 0.499766775521575 \tabularnewline
30 & 4.8 & 3.29996115010292 & 1.50003884989708 \tabularnewline
31 & 1.8 & 4.79988339289887 & -2.99988339289887 \tabularnewline
32 & 4.8 & 1.80023319909761 & 2.99976680090239 \tabularnewline
33 & -0.9 & 4.79976680996579 & -5.69976680996579 \tabularnewline
34 & -6 & -0.899556922619116 & -5.10044307738088 \tabularnewline
35 & -9 & -5.99960351168119 & -3.00039648831881 \tabularnewline
36 & -21.1 & -8.99976676101637 & -12.1002332389836 \tabularnewline
37 & -20.9 & -21.0990593756148 & 0.19905937561477 \tabularnewline
38 & -23.5 & -20.9000154740904 & -2.59998452590962 \tabularnewline
39 & -20.8 & -23.4997978874623 & 2.69979788746233 \tabularnewline
40 & -17.3 & -20.8002098716345 & 3.50020987163454 \tabularnewline
41 & -16.1 & -17.3002720925038 & 1.20027209250381 \tabularnewline
42 & -13.9 & -16.1000933044163 & 2.20009330441628 \tabularnewline
43 & -14.6 & -13.9001710265721 & -0.699828973427945 \tabularnewline
44 & -9.2 & -14.5999455980571 & 5.39994559805709 \tabularnewline
45 & -9.7 & -9.20041977046295 & -0.499580229537054 \tabularnewline
46 & -7.2 & -9.69996116460427 & 2.49996116460427 \tabularnewline
47 & -5 & -7.20019433711625 & 2.20019433711625 \tabularnewline
48 & -8.1 & -5.00017103442594 & -3.09982896557406 \tabularnewline
49 & -6.2 & -8.09975903152795 & 1.89975903152795 \tabularnewline
50 & -4.8 & -6.20014767977078 & 1.40014767977078 \tabularnewline
51 & -3.1 & -4.80010884195573 & 1.70010884195573 \tabularnewline
52 & -1.4 & -3.10013215975285 & 1.70013215975285 \tabularnewline
53 & 0.6 & -1.40013216156548 & 2.00013216156548 \tabularnewline
54 & -0.8 & 0.599844517618156 & -1.39984451761816 \tabularnewline
55 & -2 & -0.799891181610899 & -1.2001088183891 \tabularnewline
56 & 0.2 & -1.99990670827601 & 2.19990670827601 \tabularnewline
57 & -0.1 & 0.199828987933193 & -0.299828987933193 \tabularnewline
58 & 0.3 & -0.0999766924775845 & 0.399976692477584 \tabularnewline
59 & 0.2 & 0.29996890739021 & -0.0999689073902098 \tabularnewline
60 & 2.6 & 0.200007771188389 & 2.39999222881161 \tabularnewline
61 & 2.5 & 2.59981343407435 & -0.0998134340743517 \tabularnewline
62 & 1.5 & 2.50000775910251 & -1.00000775910251 \tabularnewline
63 & 5.7 & 1.50007773665722 & 4.19992226334278 \tabularnewline
64 & 4.3 & 5.69967351461588 & -1.39967351461588 \tabularnewline
65 & 2.7 & 4.300108805096 & -1.600108805096 \tabularnewline
66 & 1.7 & 2.70012438614458 & -1.00012438614458 \tabularnewline
67 & -2.2 & 1.70007774572335 & -3.90007774572335 \tabularnewline
68 & -3.2 & -2.19969682334551 & -1.00030317665449 \tabularnewline
69 & -0.5 & -3.19992224037818 & 2.69992224037818 \tabularnewline
70 & -3.1 & -0.500209881301243 & -2.59979011869876 \tabularnewline
71 & -4.8 & -3.09979790257478 & -1.70020209742522 \tabularnewline
72 & -1.3 & -4.79986783299784 & 3.49986783299784 \tabularnewline
73 & -1.8 & -1.30027206591508 & -0.499727934084922 \tabularnewline
74 & -1.7 & -1.7999611531223 & 0.0999611531222995 \tabularnewline
75 & -2.8 & -1.7000077705856 & -1.0999922294144 \tabularnewline
76 & -3.4 & -2.79991449094459 & -0.600085509055414 \tabularnewline
77 & -4.9 & -3.39995335172043 & -1.50004664827957 \tabularnewline
78 & -4.8 & -4.89988339229265 & 0.0998833922926536 \tabularnewline
79 & -5.4 & -4.80000776454078 & -0.599992235459217 \tabularnewline
80 & -4.7 & -5.39995335897115 & 0.699953358971147 \tabularnewline
81 & -6.6 & -4.70005441161215 & -1.89994558838785 \tabularnewline
82 & -7.6 & -6.59985230572702 & -1.00014769427298 \tabularnewline
83 & -6.8 & -7.59992225246477 & 0.799922252464767 \tabularnewline
84 & -5.6 & -6.80006218279946 & 1.20006218279946 \tabularnewline
85 & -5.6 & -5.60009328809872 & 9.32880987205564e-05 \tabularnewline
86 & -3.7 & -5.60000000725185 & 1.90000000725185 \tabularnewline
87 & -5.1 & -3.70014769850328 & -1.39985230149672 \tabularnewline
88 & -5.6 & -5.09989118100581 & -0.500108818994189 \tabularnewline
89 & -4.1 & -5.59996112351381 & 1.49996112351381 \tabularnewline
90 & -3.8 & -4.10011660105899 & 0.300116601058989 \tabularnewline
91 & -3.1 & -3.80002332988032 & 0.700023329880325 \tabularnewline
92 & -1.4 & -3.10005441705142 & 1.70005441705142 \tabularnewline
93 & -2.4 & -1.40013215552207 & -0.999867844477927 \tabularnewline
94 & -0.3 & -2.39992227421919 & 2.09992227421919 \tabularnewline
95 & -0.3 & -0.300163239671436 & 0.000163239671435944 \tabularnewline
96 & 0.1 & -0.300000012689608 & 0.400000012689608 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279254&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]4.8[/C][C]3.5[/C][C]1.3[/C][/ROW]
[ROW][C]3[/C][C]6[/C][C]4.79989894312972[/C][C]1.20010105687028[/C][/ROW]
[ROW][C]4[/C][C]5.9[/C][C]5.99990670887936[/C][C]-0.0999067088793621[/C][/ROW]
[ROW][C]5[/C][C]3.6[/C][C]5.90000776635332[/C][C]-2.30000776635332[/C][/ROW]
[ROW][C]6[/C][C]6.8[/C][C]3.60017879352807[/C][C]3.19982120647193[/C][/ROW]
[ROW][C]7[/C][C]8.7[/C][C]6.7997512585257[/C][C]1.9002487414743[/C][/ROW]
[ROW][C]8[/C][C]8.4[/C][C]8.6998522821611[/C][C]-0.299852282161099[/C][/ROW]
[ROW][C]9[/C][C]8.1[/C][C]8.40002330933322[/C][C]-0.300023309333218[/C][/ROW]
[ROW][C]10[/C][C]8.9[/C][C]8.10002332262819[/C][C]0.799976677371806[/C][/ROW]
[ROW][C]11[/C][C]8.7[/C][C]8.89993781296976[/C][C]-0.199937812969759[/C][/ROW]
[ROW][C]12[/C][C]7.8[/C][C]8.70001554237664[/C][C]-0.900015542376638[/C][/ROW]
[ROW][C]13[/C][C]6.3[/C][C]7.80006996365686[/C][C]-1.50006996365686[/C][/ROW]
[ROW][C]14[/C][C]7.5[/C][C]6.30011660951979[/C][C]1.19988339048021[/C][/ROW]
[ROW][C]15[/C][C]6.8[/C][C]7.49990672579989[/C][C]-0.699906725799889[/C][/ROW]
[ROW][C]16[/C][C]7[/C][C]6.80005440798708[/C][C]0.199945592012925[/C][/ROW]
[ROW][C]17[/C][C]8.8[/C][C]6.99998445701865[/C][C]1.80001554298135[/C][/ROW]
[ROW][C]18[/C][C]8.4[/C][C]8.79986007389444[/C][C]-0.399860073894439[/C][/ROW]
[ROW][C]19[/C][C]7.6[/C][C]8.40003108354432[/C][C]-0.800031083544322[/C][/ROW]
[ROW][C]20[/C][C]7.9[/C][C]7.60006219125956[/C][C]0.299937808740439[/C][/ROW]
[ROW][C]21[/C][C]7.4[/C][C]7.89997668401829[/C][C]-0.499976684018285[/C][/ROW]
[ROW][C]22[/C][C]8.7[/C][C]7.40003886621454[/C][C]1.29996113378546[/C][/ROW]
[ROW][C]23[/C][C]8.7[/C][C]8.69989894615102[/C][C]0.000101053848975852[/C][/ROW]
[ROW][C]24[/C][C]8[/C][C]8.69999999214447[/C][C]-0.699999992144472[/C][/ROW]
[ROW][C]25[/C][C]9.4[/C][C]8.00005441523723[/C][C]1.39994558476277[/C][/ROW]
[ROW][C]26[/C][C]8.5[/C][C]9.39989117375434[/C][C]-0.899891173754337[/C][/ROW]
[ROW][C]27[/C][C]5.8[/C][C]8.50006995398893[/C][C]-2.70006995398893[/C][/ROW]
[ROW][C]28[/C][C]2.8[/C][C]5.80020989278392[/C][C]-3.00020989278392[/C][/ROW]
[ROW][C]29[/C][C]3.3[/C][C]2.80023322447842[/C][C]0.499766775521575[/C][/ROW]
[ROW][C]30[/C][C]4.8[/C][C]3.29996115010292[/C][C]1.50003884989708[/C][/ROW]
[ROW][C]31[/C][C]1.8[/C][C]4.79988339289887[/C][C]-2.99988339289887[/C][/ROW]
[ROW][C]32[/C][C]4.8[/C][C]1.80023319909761[/C][C]2.99976680090239[/C][/ROW]
[ROW][C]33[/C][C]-0.9[/C][C]4.79976680996579[/C][C]-5.69976680996579[/C][/ROW]
[ROW][C]34[/C][C]-6[/C][C]-0.899556922619116[/C][C]-5.10044307738088[/C][/ROW]
[ROW][C]35[/C][C]-9[/C][C]-5.99960351168119[/C][C]-3.00039648831881[/C][/ROW]
[ROW][C]36[/C][C]-21.1[/C][C]-8.99976676101637[/C][C]-12.1002332389836[/C][/ROW]
[ROW][C]37[/C][C]-20.9[/C][C]-21.0990593756148[/C][C]0.19905937561477[/C][/ROW]
[ROW][C]38[/C][C]-23.5[/C][C]-20.9000154740904[/C][C]-2.59998452590962[/C][/ROW]
[ROW][C]39[/C][C]-20.8[/C][C]-23.4997978874623[/C][C]2.69979788746233[/C][/ROW]
[ROW][C]40[/C][C]-17.3[/C][C]-20.8002098716345[/C][C]3.50020987163454[/C][/ROW]
[ROW][C]41[/C][C]-16.1[/C][C]-17.3002720925038[/C][C]1.20027209250381[/C][/ROW]
[ROW][C]42[/C][C]-13.9[/C][C]-16.1000933044163[/C][C]2.20009330441628[/C][/ROW]
[ROW][C]43[/C][C]-14.6[/C][C]-13.9001710265721[/C][C]-0.699828973427945[/C][/ROW]
[ROW][C]44[/C][C]-9.2[/C][C]-14.5999455980571[/C][C]5.39994559805709[/C][/ROW]
[ROW][C]45[/C][C]-9.7[/C][C]-9.20041977046295[/C][C]-0.499580229537054[/C][/ROW]
[ROW][C]46[/C][C]-7.2[/C][C]-9.69996116460427[/C][C]2.49996116460427[/C][/ROW]
[ROW][C]47[/C][C]-5[/C][C]-7.20019433711625[/C][C]2.20019433711625[/C][/ROW]
[ROW][C]48[/C][C]-8.1[/C][C]-5.00017103442594[/C][C]-3.09982896557406[/C][/ROW]
[ROW][C]49[/C][C]-6.2[/C][C]-8.09975903152795[/C][C]1.89975903152795[/C][/ROW]
[ROW][C]50[/C][C]-4.8[/C][C]-6.20014767977078[/C][C]1.40014767977078[/C][/ROW]
[ROW][C]51[/C][C]-3.1[/C][C]-4.80010884195573[/C][C]1.70010884195573[/C][/ROW]
[ROW][C]52[/C][C]-1.4[/C][C]-3.10013215975285[/C][C]1.70013215975285[/C][/ROW]
[ROW][C]53[/C][C]0.6[/C][C]-1.40013216156548[/C][C]2.00013216156548[/C][/ROW]
[ROW][C]54[/C][C]-0.8[/C][C]0.599844517618156[/C][C]-1.39984451761816[/C][/ROW]
[ROW][C]55[/C][C]-2[/C][C]-0.799891181610899[/C][C]-1.2001088183891[/C][/ROW]
[ROW][C]56[/C][C]0.2[/C][C]-1.99990670827601[/C][C]2.19990670827601[/C][/ROW]
[ROW][C]57[/C][C]-0.1[/C][C]0.199828987933193[/C][C]-0.299828987933193[/C][/ROW]
[ROW][C]58[/C][C]0.3[/C][C]-0.0999766924775845[/C][C]0.399976692477584[/C][/ROW]
[ROW][C]59[/C][C]0.2[/C][C]0.29996890739021[/C][C]-0.0999689073902098[/C][/ROW]
[ROW][C]60[/C][C]2.6[/C][C]0.200007771188389[/C][C]2.39999222881161[/C][/ROW]
[ROW][C]61[/C][C]2.5[/C][C]2.59981343407435[/C][C]-0.0998134340743517[/C][/ROW]
[ROW][C]62[/C][C]1.5[/C][C]2.50000775910251[/C][C]-1.00000775910251[/C][/ROW]
[ROW][C]63[/C][C]5.7[/C][C]1.50007773665722[/C][C]4.19992226334278[/C][/ROW]
[ROW][C]64[/C][C]4.3[/C][C]5.69967351461588[/C][C]-1.39967351461588[/C][/ROW]
[ROW][C]65[/C][C]2.7[/C][C]4.300108805096[/C][C]-1.600108805096[/C][/ROW]
[ROW][C]66[/C][C]1.7[/C][C]2.70012438614458[/C][C]-1.00012438614458[/C][/ROW]
[ROW][C]67[/C][C]-2.2[/C][C]1.70007774572335[/C][C]-3.90007774572335[/C][/ROW]
[ROW][C]68[/C][C]-3.2[/C][C]-2.19969682334551[/C][C]-1.00030317665449[/C][/ROW]
[ROW][C]69[/C][C]-0.5[/C][C]-3.19992224037818[/C][C]2.69992224037818[/C][/ROW]
[ROW][C]70[/C][C]-3.1[/C][C]-0.500209881301243[/C][C]-2.59979011869876[/C][/ROW]
[ROW][C]71[/C][C]-4.8[/C][C]-3.09979790257478[/C][C]-1.70020209742522[/C][/ROW]
[ROW][C]72[/C][C]-1.3[/C][C]-4.79986783299784[/C][C]3.49986783299784[/C][/ROW]
[ROW][C]73[/C][C]-1.8[/C][C]-1.30027206591508[/C][C]-0.499727934084922[/C][/ROW]
[ROW][C]74[/C][C]-1.7[/C][C]-1.7999611531223[/C][C]0.0999611531222995[/C][/ROW]
[ROW][C]75[/C][C]-2.8[/C][C]-1.7000077705856[/C][C]-1.0999922294144[/C][/ROW]
[ROW][C]76[/C][C]-3.4[/C][C]-2.79991449094459[/C][C]-0.600085509055414[/C][/ROW]
[ROW][C]77[/C][C]-4.9[/C][C]-3.39995335172043[/C][C]-1.50004664827957[/C][/ROW]
[ROW][C]78[/C][C]-4.8[/C][C]-4.89988339229265[/C][C]0.0998833922926536[/C][/ROW]
[ROW][C]79[/C][C]-5.4[/C][C]-4.80000776454078[/C][C]-0.599992235459217[/C][/ROW]
[ROW][C]80[/C][C]-4.7[/C][C]-5.39995335897115[/C][C]0.699953358971147[/C][/ROW]
[ROW][C]81[/C][C]-6.6[/C][C]-4.70005441161215[/C][C]-1.89994558838785[/C][/ROW]
[ROW][C]82[/C][C]-7.6[/C][C]-6.59985230572702[/C][C]-1.00014769427298[/C][/ROW]
[ROW][C]83[/C][C]-6.8[/C][C]-7.59992225246477[/C][C]0.799922252464767[/C][/ROW]
[ROW][C]84[/C][C]-5.6[/C][C]-6.80006218279946[/C][C]1.20006218279946[/C][/ROW]
[ROW][C]85[/C][C]-5.6[/C][C]-5.60009328809872[/C][C]9.32880987205564e-05[/C][/ROW]
[ROW][C]86[/C][C]-3.7[/C][C]-5.60000000725185[/C][C]1.90000000725185[/C][/ROW]
[ROW][C]87[/C][C]-5.1[/C][C]-3.70014769850328[/C][C]-1.39985230149672[/C][/ROW]
[ROW][C]88[/C][C]-5.6[/C][C]-5.09989118100581[/C][C]-0.500108818994189[/C][/ROW]
[ROW][C]89[/C][C]-4.1[/C][C]-5.59996112351381[/C][C]1.49996112351381[/C][/ROW]
[ROW][C]90[/C][C]-3.8[/C][C]-4.10011660105899[/C][C]0.300116601058989[/C][/ROW]
[ROW][C]91[/C][C]-3.1[/C][C]-3.80002332988032[/C][C]0.700023329880325[/C][/ROW]
[ROW][C]92[/C][C]-1.4[/C][C]-3.10005441705142[/C][C]1.70005441705142[/C][/ROW]
[ROW][C]93[/C][C]-2.4[/C][C]-1.40013215552207[/C][C]-0.999867844477927[/C][/ROW]
[ROW][C]94[/C][C]-0.3[/C][C]-2.39992227421919[/C][C]2.09992227421919[/C][/ROW]
[ROW][C]95[/C][C]-0.3[/C][C]-0.300163239671436[/C][C]0.000163239671435944[/C][/ROW]
[ROW][C]96[/C][C]0.1[/C][C]-0.300000012689608[/C][C]0.400000012689608[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279254&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279254&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
24.83.51.3
364.799898943129721.20010105687028
45.95.99990670887936-0.0999067088793621
53.65.90000776635332-2.30000776635332
66.83.600178793528073.19982120647193
78.76.79975125852571.9002487414743
88.48.6998522821611-0.299852282161099
98.18.40002330933322-0.300023309333218
108.98.100023322628190.799976677371806
118.78.89993781296976-0.199937812969759
127.88.70001554237664-0.900015542376638
136.37.80006996365686-1.50006996365686
147.56.300116609519791.19988339048021
156.87.49990672579989-0.699906725799889
1676.800054407987080.199945592012925
178.86.999984457018651.80001554298135
188.48.79986007389444-0.399860073894439
197.68.40003108354432-0.800031083544322
207.97.600062191259560.299937808740439
217.47.89997668401829-0.499976684018285
228.77.400038866214541.29996113378546
238.78.699898946151020.000101053848975852
2488.69999999214447-0.699999992144472
259.48.000054415237231.39994558476277
268.59.39989117375434-0.899891173754337
275.88.50006995398893-2.70006995398893
282.85.80020989278392-3.00020989278392
293.32.800233224478420.499766775521575
304.83.299961150102921.50003884989708
311.84.79988339289887-2.99988339289887
324.81.800233199097612.99976680090239
33-0.94.79976680996579-5.69976680996579
34-6-0.899556922619116-5.10044307738088
35-9-5.99960351168119-3.00039648831881
36-21.1-8.99976676101637-12.1002332389836
37-20.9-21.09905937561480.19905937561477
38-23.5-20.9000154740904-2.59998452590962
39-20.8-23.49979788746232.69979788746233
40-17.3-20.80020987163453.50020987163454
41-16.1-17.30027209250381.20027209250381
42-13.9-16.10009330441632.20009330441628
43-14.6-13.9001710265721-0.699828973427945
44-9.2-14.59994559805715.39994559805709
45-9.7-9.20041977046295-0.499580229537054
46-7.2-9.699961164604272.49996116460427
47-5-7.200194337116252.20019433711625
48-8.1-5.00017103442594-3.09982896557406
49-6.2-8.099759031527951.89975903152795
50-4.8-6.200147679770781.40014767977078
51-3.1-4.800108841955731.70010884195573
52-1.4-3.100132159752851.70013215975285
530.6-1.400132161565482.00013216156548
54-0.80.599844517618156-1.39984451761816
55-2-0.799891181610899-1.2001088183891
560.2-1.999906708276012.19990670827601
57-0.10.199828987933193-0.299828987933193
580.3-0.09997669247758450.399976692477584
590.20.29996890739021-0.0999689073902098
602.60.2000077711883892.39999222881161
612.52.59981343407435-0.0998134340743517
621.52.50000775910251-1.00000775910251
635.71.500077736657224.19992226334278
644.35.69967351461588-1.39967351461588
652.74.300108805096-1.600108805096
661.72.70012438614458-1.00012438614458
67-2.21.70007774572335-3.90007774572335
68-3.2-2.19969682334551-1.00030317665449
69-0.5-3.199922240378182.69992224037818
70-3.1-0.500209881301243-2.59979011869876
71-4.8-3.09979790257478-1.70020209742522
72-1.3-4.799867832997843.49986783299784
73-1.8-1.30027206591508-0.499727934084922
74-1.7-1.79996115312230.0999611531222995
75-2.8-1.7000077705856-1.0999922294144
76-3.4-2.79991449094459-0.600085509055414
77-4.9-3.39995335172043-1.50004664827957
78-4.8-4.899883392292650.0998833922926536
79-5.4-4.80000776454078-0.599992235459217
80-4.7-5.399953358971150.699953358971147
81-6.6-4.70005441161215-1.89994558838785
82-7.6-6.59985230572702-1.00014769427298
83-6.8-7.599922252464770.799922252464767
84-5.6-6.800062182799461.20006218279946
85-5.6-5.600093288098729.32880987205564e-05
86-3.7-5.600000007251851.90000000725185
87-5.1-3.70014769850328-1.39985230149672
88-5.6-5.09989118100581-0.500108818994189
89-4.1-5.599961123513811.49996112351381
90-3.8-4.100116601058990.300116601058989
91-3.1-3.800023329880320.700023329880325
92-1.4-3.100054417051421.70005441705142
93-2.4-1.40013215552207-0.999867844477927
94-0.3-2.399922274219192.09992227421919
95-0.3-0.3001632396714360.000163239671435944
960.1-0.3000000126896080.400000012689608







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
970.0999689055773885-4.416841637427544.61677944858231
980.0999689055773885-6.28751754918916.48745536034388
990.0999689055773885-7.722971010991727.9229088221465
1000.0999689055773885-8.933125507007669.13306331816243
1010.0999689055773885-9.9992984141394310.1992362252942
1020.0999689055773885-10.963195475535511.1631332866903
1030.0999689055773885-11.849592251718312.0495300628731
1040.0999689055773885-12.674631580558212.8745693917129
1050.0999689055773885-13.449526410071813.6494642212266
1060.0999689055773885-14.182440871390414.3823786825452
1070.0999689055773885-14.879538254728315.0794760658831
1080.0999689055773885-15.545606842667715.7455446538225

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 0.0999689055773885 & -4.41684163742754 & 4.61677944858231 \tabularnewline
98 & 0.0999689055773885 & -6.2875175491891 & 6.48745536034388 \tabularnewline
99 & 0.0999689055773885 & -7.72297101099172 & 7.9229088221465 \tabularnewline
100 & 0.0999689055773885 & -8.93312550700766 & 9.13306331816243 \tabularnewline
101 & 0.0999689055773885 & -9.99929841413943 & 10.1992362252942 \tabularnewline
102 & 0.0999689055773885 & -10.9631954755355 & 11.1631332866903 \tabularnewline
103 & 0.0999689055773885 & -11.8495922517183 & 12.0495300628731 \tabularnewline
104 & 0.0999689055773885 & -12.6746315805582 & 12.8745693917129 \tabularnewline
105 & 0.0999689055773885 & -13.4495264100718 & 13.6494642212266 \tabularnewline
106 & 0.0999689055773885 & -14.1824408713904 & 14.3823786825452 \tabularnewline
107 & 0.0999689055773885 & -14.8795382547283 & 15.0794760658831 \tabularnewline
108 & 0.0999689055773885 & -15.5456068426677 & 15.7455446538225 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279254&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]97[/C][C]0.0999689055773885[/C][C]-4.41684163742754[/C][C]4.61677944858231[/C][/ROW]
[ROW][C]98[/C][C]0.0999689055773885[/C][C]-6.2875175491891[/C][C]6.48745536034388[/C][/ROW]
[ROW][C]99[/C][C]0.0999689055773885[/C][C]-7.72297101099172[/C][C]7.9229088221465[/C][/ROW]
[ROW][C]100[/C][C]0.0999689055773885[/C][C]-8.93312550700766[/C][C]9.13306331816243[/C][/ROW]
[ROW][C]101[/C][C]0.0999689055773885[/C][C]-9.99929841413943[/C][C]10.1992362252942[/C][/ROW]
[ROW][C]102[/C][C]0.0999689055773885[/C][C]-10.9631954755355[/C][C]11.1631332866903[/C][/ROW]
[ROW][C]103[/C][C]0.0999689055773885[/C][C]-11.8495922517183[/C][C]12.0495300628731[/C][/ROW]
[ROW][C]104[/C][C]0.0999689055773885[/C][C]-12.6746315805582[/C][C]12.8745693917129[/C][/ROW]
[ROW][C]105[/C][C]0.0999689055773885[/C][C]-13.4495264100718[/C][C]13.6494642212266[/C][/ROW]
[ROW][C]106[/C][C]0.0999689055773885[/C][C]-14.1824408713904[/C][C]14.3823786825452[/C][/ROW]
[ROW][C]107[/C][C]0.0999689055773885[/C][C]-14.8795382547283[/C][C]15.0794760658831[/C][/ROW]
[ROW][C]108[/C][C]0.0999689055773885[/C][C]-15.5456068426677[/C][C]15.7455446538225[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279254&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279254&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
970.0999689055773885-4.416841637427544.61677944858231
980.0999689055773885-6.28751754918916.48745536034388
990.0999689055773885-7.722971010991727.9229088221465
1000.0999689055773885-8.933125507007669.13306331816243
1010.0999689055773885-9.9992984141394310.1992362252942
1020.0999689055773885-10.963195475535511.1631332866903
1030.0999689055773885-11.849592251718312.0495300628731
1040.0999689055773885-12.674631580558212.8745693917129
1050.0999689055773885-13.449526410071813.6494642212266
1060.0999689055773885-14.182440871390414.3823786825452
1070.0999689055773885-14.879538254728315.0794760658831
1080.0999689055773885-15.545606842667715.7455446538225



Parameters (Session):
par1 = 0.01 ; par2 = 0.09 ; par3 = 0.01 ;
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = additive ;
R code (references can be found in the software module):
par3 <- 'additive'
par2 <- 'Double'
par1 <- '12'
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')