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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 11 Aug 2008 13:26:29 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Aug/11/t1218482821vrhl6orspatfn34.htm/, Retrieved Tue, 14 May 2024 15:40:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13979, Retrieved Tue, 14 May 2024 15:40:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact192
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Michaël Mertens o...] [2008-08-11 19:26:29] [8ef116c437494d1794893d3b8a73922a] [Current]
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Dataseries X:
15.14
15.09
15.17
15.18
15.21
15.27
15.28
15.3
15.34
15.33
15.27
15.35
15.38
15.38
15.39
15.4
15.39
15.43
15.43
15.47
15.48
15.47
15.58
15.56
15.61
15.56
15.62
15.63
15.58
15.65
15.79
15.76
15.77
15.79
15.87
15.79
15.9
15.96
16.05
16.18
16.29
16.43
16.38
16.39
16.35
16.48
16.52
16.44
16.46
16.52
16.47
16.59
16.59
16.59
16.54
16.48
16.47
16.56
16.61
16.57
16.72
16.69
16.72
16.81
16.75
16.85
16.84
16.92
17.02
17.11
17.2
17.3
17.37
17.42
17.51
17.56
17.62
17.59
17.78
17.73
17.79
17.85
17.86
17.79
17.97
17.96
18.03
18.02
18.03
18.14
18.16
18.24
18.28
18.18
18.19
18.32




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13979&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13979&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13979&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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.862499742878666
beta0.0338568524640709
gamma0.871697167846424

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.862499742878666 \tabularnewline
beta & 0.0338568524640709 \tabularnewline
gamma & 0.871697167846424 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13979&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]0.862499742878666[/C][/ROW]
[ROW][C]beta[/C][C]0.0338568524640709[/C][/ROW]
[ROW][C]gamma[/C][C]0.871697167846424[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13979&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13979&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
alpha0.862499742878666
beta0.0338568524640709
gamma0.871697167846424







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1315.3815.26961250.110387499999995
1415.3815.37292035503790.00707964496207936
1515.3915.3977486147752-0.00774861477524169
1615.415.4108112329217-0.0108112329217409
1715.3915.3938333058659-0.00383330586586617
1815.4315.42984523405190.00015476594814956
1915.4315.4326347258873-0.00263472588727609
2015.4715.4741913437140-0.00419134371395025
2115.4815.4842829854306-0.00428298543063832
2215.4715.4720871831442-0.00208718314416600
2315.5815.5833909774979-0.00339097749786887
2415.5615.5638878945040-0.00388789450397908
2515.6115.59874024445200.0112597555480356
2615.5615.6034563512448-0.0434563512447621
2715.6215.58073254393820.039267456061788
2815.6315.6331648819733-0.00316488197333697
2915.5815.6230270321828-0.0430270321828186
3015.6515.62397660657920.0260233934208483
3115.7915.64776306226460.142236937735401
3215.7615.8173349762871-0.0573349762871356
3315.7715.7832774869106-0.0132774869106083
3415.7915.76502268437420.0249773156257653
3515.8715.9017392249009-0.0317392249009423
3615.7915.8591243078315-0.0691243078315171
3715.915.83901892288940.0609810771106343
3815.9615.88100647905010.0789935209498509
3916.0515.97833155411170.0716684458883297
4016.1816.05909075654190.120909243458112
4116.2916.16027903997710.129720960022883
4216.4316.33263455745110.0973654425489379
4316.3816.4481005577839-0.0681005577839251
4416.3916.4224117075540-0.0324117075539618
4516.3516.425934675581-0.0759346755809993
4616.4816.36719702106610.112802978933946
4716.5216.5844036434241-0.06440364342415
4816.4416.5197193338504-0.0797193338503988
4916.4616.5163451812626-0.056345181262639
5016.5216.46614690219000.0538530978099523
5116.4716.5470253433148-0.0770253433148369
5216.5916.5072109851510.0827890148490056
5316.5916.57723643427570.0127635657243275
5416.5916.6420825014401-0.0520825014400614
5516.5416.6016974185202-0.061697418520243
5616.4816.5788761214078-0.098876121407752
5716.4716.5109833179501-0.0409833179501504
5816.5616.49716003127950.0628399687205139
5916.6116.6407218417714-0.0307218417714203
6016.5716.5949239270631-0.0249239270631172
6116.7216.63488406769280.0851159323072146
6216.6916.7173067290362-0.0273067290361944
6316.7216.70753050138120.0124694986188345
6416.8116.76170649589190.0482935041081305
6516.7516.7902250548055-0.0402250548054681
6616.8516.79668737410330.0533126258967407
6716.8416.8442221112176-0.00422211121762572
6816.9216.86636441203680.0536355879632175
6917.0216.94125278978540.0787472102146474
7017.1117.05093840086870.0590615991312760
7117.217.18771408400980.0122859159901552
7217.317.18864807298080.111351927019246
7317.3717.3722575813102-0.00225758131021436
7417.4217.37621660535620.0437833946438069
7517.5117.44496987039200.065030129607976
7617.5617.5627548178179-0.00275481781785203
7717.6217.54912542168090.070874578319092
7817.5917.6783576375715-0.088357637571498
7917.7817.60840398631230.171596013687729
8017.7317.8058564838392-0.0758564838392033
8117.7917.78501882752920.00498117247082774
8217.8517.83951868070540.0104813192946338
8317.8617.9381657196307-0.0781657196306895
8417.7917.8796960840044-0.0896960840044052
8517.9717.87715072680480.092849273195231
8617.9617.9723011271238-0.0123011271238163
8718.0317.99723368898660.0327663110134502
8818.0218.0801299194004-0.0601299194004454
8918.0318.02522761365640.0047723863436353
9018.1418.07581905855510.0641809414448531
9118.1618.1704996291990-0.0104996291989750
9218.2418.17782996466260.0621700353373811
9318.2818.2863544070357-0.0063544070356798
9418.1818.3320307236965-0.152030723696477
9518.1918.2754346170459-0.0854346170459372
9618.3218.20464984155520.115350158444805

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 15.38 & 15.2696125 & 0.110387499999995 \tabularnewline
14 & 15.38 & 15.3729203550379 & 0.00707964496207936 \tabularnewline
15 & 15.39 & 15.3977486147752 & -0.00774861477524169 \tabularnewline
16 & 15.4 & 15.4108112329217 & -0.0108112329217409 \tabularnewline
17 & 15.39 & 15.3938333058659 & -0.00383330586586617 \tabularnewline
18 & 15.43 & 15.4298452340519 & 0.00015476594814956 \tabularnewline
19 & 15.43 & 15.4326347258873 & -0.00263472588727609 \tabularnewline
20 & 15.47 & 15.4741913437140 & -0.00419134371395025 \tabularnewline
21 & 15.48 & 15.4842829854306 & -0.00428298543063832 \tabularnewline
22 & 15.47 & 15.4720871831442 & -0.00208718314416600 \tabularnewline
23 & 15.58 & 15.5833909774979 & -0.00339097749786887 \tabularnewline
24 & 15.56 & 15.5638878945040 & -0.00388789450397908 \tabularnewline
25 & 15.61 & 15.5987402444520 & 0.0112597555480356 \tabularnewline
26 & 15.56 & 15.6034563512448 & -0.0434563512447621 \tabularnewline
27 & 15.62 & 15.5807325439382 & 0.039267456061788 \tabularnewline
28 & 15.63 & 15.6331648819733 & -0.00316488197333697 \tabularnewline
29 & 15.58 & 15.6230270321828 & -0.0430270321828186 \tabularnewline
30 & 15.65 & 15.6239766065792 & 0.0260233934208483 \tabularnewline
31 & 15.79 & 15.6477630622646 & 0.142236937735401 \tabularnewline
32 & 15.76 & 15.8173349762871 & -0.0573349762871356 \tabularnewline
33 & 15.77 & 15.7832774869106 & -0.0132774869106083 \tabularnewline
34 & 15.79 & 15.7650226843742 & 0.0249773156257653 \tabularnewline
35 & 15.87 & 15.9017392249009 & -0.0317392249009423 \tabularnewline
36 & 15.79 & 15.8591243078315 & -0.0691243078315171 \tabularnewline
37 & 15.9 & 15.8390189228894 & 0.0609810771106343 \tabularnewline
38 & 15.96 & 15.8810064790501 & 0.0789935209498509 \tabularnewline
39 & 16.05 & 15.9783315541117 & 0.0716684458883297 \tabularnewline
40 & 16.18 & 16.0590907565419 & 0.120909243458112 \tabularnewline
41 & 16.29 & 16.1602790399771 & 0.129720960022883 \tabularnewline
42 & 16.43 & 16.3326345574511 & 0.0973654425489379 \tabularnewline
43 & 16.38 & 16.4481005577839 & -0.0681005577839251 \tabularnewline
44 & 16.39 & 16.4224117075540 & -0.0324117075539618 \tabularnewline
45 & 16.35 & 16.425934675581 & -0.0759346755809993 \tabularnewline
46 & 16.48 & 16.3671970210661 & 0.112802978933946 \tabularnewline
47 & 16.52 & 16.5844036434241 & -0.06440364342415 \tabularnewline
48 & 16.44 & 16.5197193338504 & -0.0797193338503988 \tabularnewline
49 & 16.46 & 16.5163451812626 & -0.056345181262639 \tabularnewline
50 & 16.52 & 16.4661469021900 & 0.0538530978099523 \tabularnewline
51 & 16.47 & 16.5470253433148 & -0.0770253433148369 \tabularnewline
52 & 16.59 & 16.507210985151 & 0.0827890148490056 \tabularnewline
53 & 16.59 & 16.5772364342757 & 0.0127635657243275 \tabularnewline
54 & 16.59 & 16.6420825014401 & -0.0520825014400614 \tabularnewline
55 & 16.54 & 16.6016974185202 & -0.061697418520243 \tabularnewline
56 & 16.48 & 16.5788761214078 & -0.098876121407752 \tabularnewline
57 & 16.47 & 16.5109833179501 & -0.0409833179501504 \tabularnewline
58 & 16.56 & 16.4971600312795 & 0.0628399687205139 \tabularnewline
59 & 16.61 & 16.6407218417714 & -0.0307218417714203 \tabularnewline
60 & 16.57 & 16.5949239270631 & -0.0249239270631172 \tabularnewline
61 & 16.72 & 16.6348840676928 & 0.0851159323072146 \tabularnewline
62 & 16.69 & 16.7173067290362 & -0.0273067290361944 \tabularnewline
63 & 16.72 & 16.7075305013812 & 0.0124694986188345 \tabularnewline
64 & 16.81 & 16.7617064958919 & 0.0482935041081305 \tabularnewline
65 & 16.75 & 16.7902250548055 & -0.0402250548054681 \tabularnewline
66 & 16.85 & 16.7966873741033 & 0.0533126258967407 \tabularnewline
67 & 16.84 & 16.8442221112176 & -0.00422211121762572 \tabularnewline
68 & 16.92 & 16.8663644120368 & 0.0536355879632175 \tabularnewline
69 & 17.02 & 16.9412527897854 & 0.0787472102146474 \tabularnewline
70 & 17.11 & 17.0509384008687 & 0.0590615991312760 \tabularnewline
71 & 17.2 & 17.1877140840098 & 0.0122859159901552 \tabularnewline
72 & 17.3 & 17.1886480729808 & 0.111351927019246 \tabularnewline
73 & 17.37 & 17.3722575813102 & -0.00225758131021436 \tabularnewline
74 & 17.42 & 17.3762166053562 & 0.0437833946438069 \tabularnewline
75 & 17.51 & 17.4449698703920 & 0.065030129607976 \tabularnewline
76 & 17.56 & 17.5627548178179 & -0.00275481781785203 \tabularnewline
77 & 17.62 & 17.5491254216809 & 0.070874578319092 \tabularnewline
78 & 17.59 & 17.6783576375715 & -0.088357637571498 \tabularnewline
79 & 17.78 & 17.6084039863123 & 0.171596013687729 \tabularnewline
80 & 17.73 & 17.8058564838392 & -0.0758564838392033 \tabularnewline
81 & 17.79 & 17.7850188275292 & 0.00498117247082774 \tabularnewline
82 & 17.85 & 17.8395186807054 & 0.0104813192946338 \tabularnewline
83 & 17.86 & 17.9381657196307 & -0.0781657196306895 \tabularnewline
84 & 17.79 & 17.8796960840044 & -0.0896960840044052 \tabularnewline
85 & 17.97 & 17.8771507268048 & 0.092849273195231 \tabularnewline
86 & 17.96 & 17.9723011271238 & -0.0123011271238163 \tabularnewline
87 & 18.03 & 17.9972336889866 & 0.0327663110134502 \tabularnewline
88 & 18.02 & 18.0801299194004 & -0.0601299194004454 \tabularnewline
89 & 18.03 & 18.0252276136564 & 0.0047723863436353 \tabularnewline
90 & 18.14 & 18.0758190585551 & 0.0641809414448531 \tabularnewline
91 & 18.16 & 18.1704996291990 & -0.0104996291989750 \tabularnewline
92 & 18.24 & 18.1778299646626 & 0.0621700353373811 \tabularnewline
93 & 18.28 & 18.2863544070357 & -0.0063544070356798 \tabularnewline
94 & 18.18 & 18.3320307236965 & -0.152030723696477 \tabularnewline
95 & 18.19 & 18.2754346170459 & -0.0854346170459372 \tabularnewline
96 & 18.32 & 18.2046498415552 & 0.115350158444805 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13979&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]15.38[/C][C]15.2696125[/C][C]0.110387499999995[/C][/ROW]
[ROW][C]14[/C][C]15.38[/C][C]15.3729203550379[/C][C]0.00707964496207936[/C][/ROW]
[ROW][C]15[/C][C]15.39[/C][C]15.3977486147752[/C][C]-0.00774861477524169[/C][/ROW]
[ROW][C]16[/C][C]15.4[/C][C]15.4108112329217[/C][C]-0.0108112329217409[/C][/ROW]
[ROW][C]17[/C][C]15.39[/C][C]15.3938333058659[/C][C]-0.00383330586586617[/C][/ROW]
[ROW][C]18[/C][C]15.43[/C][C]15.4298452340519[/C][C]0.00015476594814956[/C][/ROW]
[ROW][C]19[/C][C]15.43[/C][C]15.4326347258873[/C][C]-0.00263472588727609[/C][/ROW]
[ROW][C]20[/C][C]15.47[/C][C]15.4741913437140[/C][C]-0.00419134371395025[/C][/ROW]
[ROW][C]21[/C][C]15.48[/C][C]15.4842829854306[/C][C]-0.00428298543063832[/C][/ROW]
[ROW][C]22[/C][C]15.47[/C][C]15.4720871831442[/C][C]-0.00208718314416600[/C][/ROW]
[ROW][C]23[/C][C]15.58[/C][C]15.5833909774979[/C][C]-0.00339097749786887[/C][/ROW]
[ROW][C]24[/C][C]15.56[/C][C]15.5638878945040[/C][C]-0.00388789450397908[/C][/ROW]
[ROW][C]25[/C][C]15.61[/C][C]15.5987402444520[/C][C]0.0112597555480356[/C][/ROW]
[ROW][C]26[/C][C]15.56[/C][C]15.6034563512448[/C][C]-0.0434563512447621[/C][/ROW]
[ROW][C]27[/C][C]15.62[/C][C]15.5807325439382[/C][C]0.039267456061788[/C][/ROW]
[ROW][C]28[/C][C]15.63[/C][C]15.6331648819733[/C][C]-0.00316488197333697[/C][/ROW]
[ROW][C]29[/C][C]15.58[/C][C]15.6230270321828[/C][C]-0.0430270321828186[/C][/ROW]
[ROW][C]30[/C][C]15.65[/C][C]15.6239766065792[/C][C]0.0260233934208483[/C][/ROW]
[ROW][C]31[/C][C]15.79[/C][C]15.6477630622646[/C][C]0.142236937735401[/C][/ROW]
[ROW][C]32[/C][C]15.76[/C][C]15.8173349762871[/C][C]-0.0573349762871356[/C][/ROW]
[ROW][C]33[/C][C]15.77[/C][C]15.7832774869106[/C][C]-0.0132774869106083[/C][/ROW]
[ROW][C]34[/C][C]15.79[/C][C]15.7650226843742[/C][C]0.0249773156257653[/C][/ROW]
[ROW][C]35[/C][C]15.87[/C][C]15.9017392249009[/C][C]-0.0317392249009423[/C][/ROW]
[ROW][C]36[/C][C]15.79[/C][C]15.8591243078315[/C][C]-0.0691243078315171[/C][/ROW]
[ROW][C]37[/C][C]15.9[/C][C]15.8390189228894[/C][C]0.0609810771106343[/C][/ROW]
[ROW][C]38[/C][C]15.96[/C][C]15.8810064790501[/C][C]0.0789935209498509[/C][/ROW]
[ROW][C]39[/C][C]16.05[/C][C]15.9783315541117[/C][C]0.0716684458883297[/C][/ROW]
[ROW][C]40[/C][C]16.18[/C][C]16.0590907565419[/C][C]0.120909243458112[/C][/ROW]
[ROW][C]41[/C][C]16.29[/C][C]16.1602790399771[/C][C]0.129720960022883[/C][/ROW]
[ROW][C]42[/C][C]16.43[/C][C]16.3326345574511[/C][C]0.0973654425489379[/C][/ROW]
[ROW][C]43[/C][C]16.38[/C][C]16.4481005577839[/C][C]-0.0681005577839251[/C][/ROW]
[ROW][C]44[/C][C]16.39[/C][C]16.4224117075540[/C][C]-0.0324117075539618[/C][/ROW]
[ROW][C]45[/C][C]16.35[/C][C]16.425934675581[/C][C]-0.0759346755809993[/C][/ROW]
[ROW][C]46[/C][C]16.48[/C][C]16.3671970210661[/C][C]0.112802978933946[/C][/ROW]
[ROW][C]47[/C][C]16.52[/C][C]16.5844036434241[/C][C]-0.06440364342415[/C][/ROW]
[ROW][C]48[/C][C]16.44[/C][C]16.5197193338504[/C][C]-0.0797193338503988[/C][/ROW]
[ROW][C]49[/C][C]16.46[/C][C]16.5163451812626[/C][C]-0.056345181262639[/C][/ROW]
[ROW][C]50[/C][C]16.52[/C][C]16.4661469021900[/C][C]0.0538530978099523[/C][/ROW]
[ROW][C]51[/C][C]16.47[/C][C]16.5470253433148[/C][C]-0.0770253433148369[/C][/ROW]
[ROW][C]52[/C][C]16.59[/C][C]16.507210985151[/C][C]0.0827890148490056[/C][/ROW]
[ROW][C]53[/C][C]16.59[/C][C]16.5772364342757[/C][C]0.0127635657243275[/C][/ROW]
[ROW][C]54[/C][C]16.59[/C][C]16.6420825014401[/C][C]-0.0520825014400614[/C][/ROW]
[ROW][C]55[/C][C]16.54[/C][C]16.6016974185202[/C][C]-0.061697418520243[/C][/ROW]
[ROW][C]56[/C][C]16.48[/C][C]16.5788761214078[/C][C]-0.098876121407752[/C][/ROW]
[ROW][C]57[/C][C]16.47[/C][C]16.5109833179501[/C][C]-0.0409833179501504[/C][/ROW]
[ROW][C]58[/C][C]16.56[/C][C]16.4971600312795[/C][C]0.0628399687205139[/C][/ROW]
[ROW][C]59[/C][C]16.61[/C][C]16.6407218417714[/C][C]-0.0307218417714203[/C][/ROW]
[ROW][C]60[/C][C]16.57[/C][C]16.5949239270631[/C][C]-0.0249239270631172[/C][/ROW]
[ROW][C]61[/C][C]16.72[/C][C]16.6348840676928[/C][C]0.0851159323072146[/C][/ROW]
[ROW][C]62[/C][C]16.69[/C][C]16.7173067290362[/C][C]-0.0273067290361944[/C][/ROW]
[ROW][C]63[/C][C]16.72[/C][C]16.7075305013812[/C][C]0.0124694986188345[/C][/ROW]
[ROW][C]64[/C][C]16.81[/C][C]16.7617064958919[/C][C]0.0482935041081305[/C][/ROW]
[ROW][C]65[/C][C]16.75[/C][C]16.7902250548055[/C][C]-0.0402250548054681[/C][/ROW]
[ROW][C]66[/C][C]16.85[/C][C]16.7966873741033[/C][C]0.0533126258967407[/C][/ROW]
[ROW][C]67[/C][C]16.84[/C][C]16.8442221112176[/C][C]-0.00422211121762572[/C][/ROW]
[ROW][C]68[/C][C]16.92[/C][C]16.8663644120368[/C][C]0.0536355879632175[/C][/ROW]
[ROW][C]69[/C][C]17.02[/C][C]16.9412527897854[/C][C]0.0787472102146474[/C][/ROW]
[ROW][C]70[/C][C]17.11[/C][C]17.0509384008687[/C][C]0.0590615991312760[/C][/ROW]
[ROW][C]71[/C][C]17.2[/C][C]17.1877140840098[/C][C]0.0122859159901552[/C][/ROW]
[ROW][C]72[/C][C]17.3[/C][C]17.1886480729808[/C][C]0.111351927019246[/C][/ROW]
[ROW][C]73[/C][C]17.37[/C][C]17.3722575813102[/C][C]-0.00225758131021436[/C][/ROW]
[ROW][C]74[/C][C]17.42[/C][C]17.3762166053562[/C][C]0.0437833946438069[/C][/ROW]
[ROW][C]75[/C][C]17.51[/C][C]17.4449698703920[/C][C]0.065030129607976[/C][/ROW]
[ROW][C]76[/C][C]17.56[/C][C]17.5627548178179[/C][C]-0.00275481781785203[/C][/ROW]
[ROW][C]77[/C][C]17.62[/C][C]17.5491254216809[/C][C]0.070874578319092[/C][/ROW]
[ROW][C]78[/C][C]17.59[/C][C]17.6783576375715[/C][C]-0.088357637571498[/C][/ROW]
[ROW][C]79[/C][C]17.78[/C][C]17.6084039863123[/C][C]0.171596013687729[/C][/ROW]
[ROW][C]80[/C][C]17.73[/C][C]17.8058564838392[/C][C]-0.0758564838392033[/C][/ROW]
[ROW][C]81[/C][C]17.79[/C][C]17.7850188275292[/C][C]0.00498117247082774[/C][/ROW]
[ROW][C]82[/C][C]17.85[/C][C]17.8395186807054[/C][C]0.0104813192946338[/C][/ROW]
[ROW][C]83[/C][C]17.86[/C][C]17.9381657196307[/C][C]-0.0781657196306895[/C][/ROW]
[ROW][C]84[/C][C]17.79[/C][C]17.8796960840044[/C][C]-0.0896960840044052[/C][/ROW]
[ROW][C]85[/C][C]17.97[/C][C]17.8771507268048[/C][C]0.092849273195231[/C][/ROW]
[ROW][C]86[/C][C]17.96[/C][C]17.9723011271238[/C][C]-0.0123011271238163[/C][/ROW]
[ROW][C]87[/C][C]18.03[/C][C]17.9972336889866[/C][C]0.0327663110134502[/C][/ROW]
[ROW][C]88[/C][C]18.02[/C][C]18.0801299194004[/C][C]-0.0601299194004454[/C][/ROW]
[ROW][C]89[/C][C]18.03[/C][C]18.0252276136564[/C][C]0.0047723863436353[/C][/ROW]
[ROW][C]90[/C][C]18.14[/C][C]18.0758190585551[/C][C]0.0641809414448531[/C][/ROW]
[ROW][C]91[/C][C]18.16[/C][C]18.1704996291990[/C][C]-0.0104996291989750[/C][/ROW]
[ROW][C]92[/C][C]18.24[/C][C]18.1778299646626[/C][C]0.0621700353373811[/C][/ROW]
[ROW][C]93[/C][C]18.28[/C][C]18.2863544070357[/C][C]-0.0063544070356798[/C][/ROW]
[ROW][C]94[/C][C]18.18[/C][C]18.3320307236965[/C][C]-0.152030723696477[/C][/ROW]
[ROW][C]95[/C][C]18.19[/C][C]18.2754346170459[/C][C]-0.0854346170459372[/C][/ROW]
[ROW][C]96[/C][C]18.32[/C][C]18.2046498415552[/C][C]0.115350158444805[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13979&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13979&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
1315.3815.26961250.110387499999995
1415.3815.37292035503790.00707964496207936
1515.3915.3977486147752-0.00774861477524169
1615.415.4108112329217-0.0108112329217409
1715.3915.3938333058659-0.00383330586586617
1815.4315.42984523405190.00015476594814956
1915.4315.4326347258873-0.00263472588727609
2015.4715.4741913437140-0.00419134371395025
2115.4815.4842829854306-0.00428298543063832
2215.4715.4720871831442-0.00208718314416600
2315.5815.5833909774979-0.00339097749786887
2415.5615.5638878945040-0.00388789450397908
2515.6115.59874024445200.0112597555480356
2615.5615.6034563512448-0.0434563512447621
2715.6215.58073254393820.039267456061788
2815.6315.6331648819733-0.00316488197333697
2915.5815.6230270321828-0.0430270321828186
3015.6515.62397660657920.0260233934208483
3115.7915.64776306226460.142236937735401
3215.7615.8173349762871-0.0573349762871356
3315.7715.7832774869106-0.0132774869106083
3415.7915.76502268437420.0249773156257653
3515.8715.9017392249009-0.0317392249009423
3615.7915.8591243078315-0.0691243078315171
3715.915.83901892288940.0609810771106343
3815.9615.88100647905010.0789935209498509
3916.0515.97833155411170.0716684458883297
4016.1816.05909075654190.120909243458112
4116.2916.16027903997710.129720960022883
4216.4316.33263455745110.0973654425489379
4316.3816.4481005577839-0.0681005577839251
4416.3916.4224117075540-0.0324117075539618
4516.3516.425934675581-0.0759346755809993
4616.4816.36719702106610.112802978933946
4716.5216.5844036434241-0.06440364342415
4816.4416.5197193338504-0.0797193338503988
4916.4616.5163451812626-0.056345181262639
5016.5216.46614690219000.0538530978099523
5116.4716.5470253433148-0.0770253433148369
5216.5916.5072109851510.0827890148490056
5316.5916.57723643427570.0127635657243275
5416.5916.6420825014401-0.0520825014400614
5516.5416.6016974185202-0.061697418520243
5616.4816.5788761214078-0.098876121407752
5716.4716.5109833179501-0.0409833179501504
5816.5616.49716003127950.0628399687205139
5916.6116.6407218417714-0.0307218417714203
6016.5716.5949239270631-0.0249239270631172
6116.7216.63488406769280.0851159323072146
6216.6916.7173067290362-0.0273067290361944
6316.7216.70753050138120.0124694986188345
6416.8116.76170649589190.0482935041081305
6516.7516.7902250548055-0.0402250548054681
6616.8516.79668737410330.0533126258967407
6716.8416.8442221112176-0.00422211121762572
6816.9216.86636441203680.0536355879632175
6917.0216.94125278978540.0787472102146474
7017.1117.05093840086870.0590615991312760
7117.217.18771408400980.0122859159901552
7217.317.18864807298080.111351927019246
7317.3717.3722575813102-0.00225758131021436
7417.4217.37621660535620.0437833946438069
7517.5117.44496987039200.065030129607976
7617.5617.5627548178179-0.00275481781785203
7717.6217.54912542168090.070874578319092
7817.5917.6783576375715-0.088357637571498
7917.7817.60840398631230.171596013687729
8017.7317.8058564838392-0.0758564838392033
8117.7917.78501882752920.00498117247082774
8217.8517.83951868070540.0104813192946338
8317.8617.9381657196307-0.0781657196306895
8417.7917.8796960840044-0.0896960840044052
8517.9717.87715072680480.092849273195231
8617.9617.9723011271238-0.0123011271238163
8718.0317.99723368898660.0327663110134502
8818.0218.0801299194004-0.0601299194004454
8918.0318.02522761365640.0047723863436353
9018.1418.07581905855510.0641809414448531
9118.1618.1704996291990-0.0104996291989750
9218.2418.17782996466260.0621700353373811
9318.2818.2863544070357-0.0063544070356798
9418.1818.3320307236965-0.152030723696477
9518.1918.2754346170459-0.0854346170459372
9618.3218.20464984155520.115350158444805







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
9718.402160402639818.274879315820818.5294414894587
9818.403237768755618.232703380753318.5737721567579
9918.443153598859818.236221281134818.6500859165849
10018.484669487354718.244992362497618.7243466122119
10118.489179209188918.219027350212818.759331068165
10218.542406625506118.243309113749218.8415041372630
10318.570537389766618.243574643712318.8975001358208
10418.593697687671518.239655877361718.9477394979812
10518.636635739747218.256096846604619.0171746328898
10618.666766223964218.260164448534719.0733679993937
10718.750152271978218.317811322672119.1824932212842
10818.780489011458118.322647820189619.2383302027265

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 18.4021604026398 & 18.2748793158208 & 18.5294414894587 \tabularnewline
98 & 18.4032377687556 & 18.2327033807533 & 18.5737721567579 \tabularnewline
99 & 18.4431535988598 & 18.2362212811348 & 18.6500859165849 \tabularnewline
100 & 18.4846694873547 & 18.2449923624976 & 18.7243466122119 \tabularnewline
101 & 18.4891792091889 & 18.2190273502128 & 18.759331068165 \tabularnewline
102 & 18.5424066255061 & 18.2433091137492 & 18.8415041372630 \tabularnewline
103 & 18.5705373897666 & 18.2435746437123 & 18.8975001358208 \tabularnewline
104 & 18.5936976876715 & 18.2396558773617 & 18.9477394979812 \tabularnewline
105 & 18.6366357397472 & 18.2560968466046 & 19.0171746328898 \tabularnewline
106 & 18.6667662239642 & 18.2601644485347 & 19.0733679993937 \tabularnewline
107 & 18.7501522719782 & 18.3178113226721 & 19.1824932212842 \tabularnewline
108 & 18.7804890114581 & 18.3226478201896 & 19.2383302027265 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13979&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]18.4021604026398[/C][C]18.2748793158208[/C][C]18.5294414894587[/C][/ROW]
[ROW][C]98[/C][C]18.4032377687556[/C][C]18.2327033807533[/C][C]18.5737721567579[/C][/ROW]
[ROW][C]99[/C][C]18.4431535988598[/C][C]18.2362212811348[/C][C]18.6500859165849[/C][/ROW]
[ROW][C]100[/C][C]18.4846694873547[/C][C]18.2449923624976[/C][C]18.7243466122119[/C][/ROW]
[ROW][C]101[/C][C]18.4891792091889[/C][C]18.2190273502128[/C][C]18.759331068165[/C][/ROW]
[ROW][C]102[/C][C]18.5424066255061[/C][C]18.2433091137492[/C][C]18.8415041372630[/C][/ROW]
[ROW][C]103[/C][C]18.5705373897666[/C][C]18.2435746437123[/C][C]18.8975001358208[/C][/ROW]
[ROW][C]104[/C][C]18.5936976876715[/C][C]18.2396558773617[/C][C]18.9477394979812[/C][/ROW]
[ROW][C]105[/C][C]18.6366357397472[/C][C]18.2560968466046[/C][C]19.0171746328898[/C][/ROW]
[ROW][C]106[/C][C]18.6667662239642[/C][C]18.2601644485347[/C][C]19.0733679993937[/C][/ROW]
[ROW][C]107[/C][C]18.7501522719782[/C][C]18.3178113226721[/C][C]19.1824932212842[/C][/ROW]
[ROW][C]108[/C][C]18.7804890114581[/C][C]18.3226478201896[/C][C]19.2383302027265[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13979&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13979&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
9718.402160402639818.274879315820818.5294414894587
9818.403237768755618.232703380753318.5737721567579
9918.443153598859818.236221281134818.6500859165849
10018.484669487354718.244992362497618.7243466122119
10118.489179209188918.219027350212818.759331068165
10218.542406625506118.243309113749218.8415041372630
10318.570537389766618.243574643712318.8975001358208
10418.593697687671518.239655877361718.9477394979812
10518.636635739747218.256096846604619.0171746328898
10618.666766223964218.260164448534719.0733679993937
10718.750152271978218.317811322672119.1824932212842
10818.780489011458118.322647820189619.2383302027265



Parameters (Session):
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')