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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 25 Apr 2016 23:14:29 +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/2016/Apr/25/t14616225345bafw8reyxal98m.htm/, Retrieved Mon, 06 May 2024 02:51:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294813, Retrieved Mon, 06 May 2024 02:51:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact56
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-04-25 22:14:29] [809417a83781bff5791db815734e4daf] [Current]
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Dataseries X:
90,18
90,5
90,63
90,75
90,76
90,67
90,5
90,8
91,22
92,19
92,51
92,67
93,75
94,1
94,96
95,21
95,33
95,43
95,44
95,64
95,8
95,87
95,98
96,07
96,23
96,32
96,55
96,73
96,61
96,64
96,86
97,02
97,22
98,1
98,46
98,6
98,78
99,13
99,48
99,62
99,68
99,95
100,12
100,25
100,47
100,7
100,88
100,95
100,92
101,12
101,19
101,28
101,28
101,3
101,3
101,36
101,45
101,58
101,73
101,84
102,01
102,14
102,16
102,32
102,41
102,4
102,43
102,42
102,3
102,65
102,72
102,86




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ yule.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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294813&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294813&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294813&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 time1 seconds
R Server'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.848082601775169
beta0.0746158879217505
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.848082601775169 \tabularnewline
beta & 0.0746158879217505 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294813&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]0.848082601775169[/C][/ROW]
[ROW][C]beta[/C][C]0.0746158879217505[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294813&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294813&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
alpha0.848082601775169
beta0.0746158879217505
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1393.7591.53105769230772.21894230769226
1494.193.86365769063620.236342309363778
1594.9695.0548049685703-0.0948049685703012
1695.2195.3974460350161-0.187446035016151
1795.3395.5659081579091-0.235908157909137
1895.4395.6700086930242-0.240008693024237
1995.4494.90461044749150.535389552508448
2095.6495.8690269812821-0.229026981282075
2195.896.2589955582746-0.458995558274594
2295.8796.9390530136154-1.06905301361542
2395.9896.3740812138023-0.394081213802295
2496.0796.1841036229279-0.114103622927914
2596.2397.4660289042405-1.23602890424051
2696.3296.3466317165677-0.0266317165677208
2796.5597.0271023763242-0.477102376324183
2896.7396.7699120368107-0.0399120368107333
2996.6196.8039311169582-0.193931116958197
3096.6496.6934632128488-0.0534632128488397
3196.8695.96632661222610.893673387773873
3297.0296.90340080435020.116599195649755
3397.2297.3583556182423-0.138355618242272
3498.198.04475703951190.0552429604880729
3598.4698.43406014686260.0259398531374018
3698.698.56764679138110.0323532086189289
3798.7899.7374256548839-0.957425654883906
3899.1398.98975170633540.140248293664641
3999.4899.70559250499-0.225592504990004
4099.6299.7063122210881-0.0863122210880647
4199.6899.65283780103980.0271621989602409
4299.9599.74046155830610.209538441693866
43100.1299.38614822098290.733851779017087
44100.25100.0654054244090.184594575591106
45100.47100.539372668924-0.0693726689235774
46100.7101.318132396729-0.618132396729422
47100.88101.09373851591-0.213738515909895
48100.95100.971698042695-0.0216980426948936
49100.92101.888517600623-0.968517600622704
50101.12101.240735883099-0.12073588309913
51101.19101.60569111408-0.415691114079621
52101.28101.38034923688-0.100349236880348
53101.28101.2453193694710.0346806305291523
54101.3101.2806116345220.019388365477738
55101.3100.7462409965820.553759003417952
56101.36101.0794799282780.280520071721952
57101.45101.492445084622-0.0424450846221447
58101.58102.108606677883-0.528606677883033
59101.73101.925168894215-0.195168894214916
60101.84101.7528228032440.0871771967561443
61102.01102.529800386465-0.519800386465121
62102.14102.331416938069-0.191416938069338
63102.16102.527203450665-0.367203450664974
64102.32102.329540841137-0.00954084113679698
65102.41102.2364355816930.173564418307009
66102.4102.3403764377030.0596235622969346
67102.43101.8770416959750.552958304025097
68102.42102.123774081050.296225918950299
69102.3102.457671199971-0.157671199971389
70102.65102.851639699376-0.201639699375889
71102.72102.966227109382-0.246227109381948
72102.86102.7603169191360.0996830808637839

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 93.75 & 91.5310576923077 & 2.21894230769226 \tabularnewline
14 & 94.1 & 93.8636576906362 & 0.236342309363778 \tabularnewline
15 & 94.96 & 95.0548049685703 & -0.0948049685703012 \tabularnewline
16 & 95.21 & 95.3974460350161 & -0.187446035016151 \tabularnewline
17 & 95.33 & 95.5659081579091 & -0.235908157909137 \tabularnewline
18 & 95.43 & 95.6700086930242 & -0.240008693024237 \tabularnewline
19 & 95.44 & 94.9046104474915 & 0.535389552508448 \tabularnewline
20 & 95.64 & 95.8690269812821 & -0.229026981282075 \tabularnewline
21 & 95.8 & 96.2589955582746 & -0.458995558274594 \tabularnewline
22 & 95.87 & 96.9390530136154 & -1.06905301361542 \tabularnewline
23 & 95.98 & 96.3740812138023 & -0.394081213802295 \tabularnewline
24 & 96.07 & 96.1841036229279 & -0.114103622927914 \tabularnewline
25 & 96.23 & 97.4660289042405 & -1.23602890424051 \tabularnewline
26 & 96.32 & 96.3466317165677 & -0.0266317165677208 \tabularnewline
27 & 96.55 & 97.0271023763242 & -0.477102376324183 \tabularnewline
28 & 96.73 & 96.7699120368107 & -0.0399120368107333 \tabularnewline
29 & 96.61 & 96.8039311169582 & -0.193931116958197 \tabularnewline
30 & 96.64 & 96.6934632128488 & -0.0534632128488397 \tabularnewline
31 & 96.86 & 95.9663266122261 & 0.893673387773873 \tabularnewline
32 & 97.02 & 96.9034008043502 & 0.116599195649755 \tabularnewline
33 & 97.22 & 97.3583556182423 & -0.138355618242272 \tabularnewline
34 & 98.1 & 98.0447570395119 & 0.0552429604880729 \tabularnewline
35 & 98.46 & 98.4340601468626 & 0.0259398531374018 \tabularnewline
36 & 98.6 & 98.5676467913811 & 0.0323532086189289 \tabularnewline
37 & 98.78 & 99.7374256548839 & -0.957425654883906 \tabularnewline
38 & 99.13 & 98.9897517063354 & 0.140248293664641 \tabularnewline
39 & 99.48 & 99.70559250499 & -0.225592504990004 \tabularnewline
40 & 99.62 & 99.7063122210881 & -0.0863122210880647 \tabularnewline
41 & 99.68 & 99.6528378010398 & 0.0271621989602409 \tabularnewline
42 & 99.95 & 99.7404615583061 & 0.209538441693866 \tabularnewline
43 & 100.12 & 99.3861482209829 & 0.733851779017087 \tabularnewline
44 & 100.25 & 100.065405424409 & 0.184594575591106 \tabularnewline
45 & 100.47 & 100.539372668924 & -0.0693726689235774 \tabularnewline
46 & 100.7 & 101.318132396729 & -0.618132396729422 \tabularnewline
47 & 100.88 & 101.09373851591 & -0.213738515909895 \tabularnewline
48 & 100.95 & 100.971698042695 & -0.0216980426948936 \tabularnewline
49 & 100.92 & 101.888517600623 & -0.968517600622704 \tabularnewline
50 & 101.12 & 101.240735883099 & -0.12073588309913 \tabularnewline
51 & 101.19 & 101.60569111408 & -0.415691114079621 \tabularnewline
52 & 101.28 & 101.38034923688 & -0.100349236880348 \tabularnewline
53 & 101.28 & 101.245319369471 & 0.0346806305291523 \tabularnewline
54 & 101.3 & 101.280611634522 & 0.019388365477738 \tabularnewline
55 & 101.3 & 100.746240996582 & 0.553759003417952 \tabularnewline
56 & 101.36 & 101.079479928278 & 0.280520071721952 \tabularnewline
57 & 101.45 & 101.492445084622 & -0.0424450846221447 \tabularnewline
58 & 101.58 & 102.108606677883 & -0.528606677883033 \tabularnewline
59 & 101.73 & 101.925168894215 & -0.195168894214916 \tabularnewline
60 & 101.84 & 101.752822803244 & 0.0871771967561443 \tabularnewline
61 & 102.01 & 102.529800386465 & -0.519800386465121 \tabularnewline
62 & 102.14 & 102.331416938069 & -0.191416938069338 \tabularnewline
63 & 102.16 & 102.527203450665 & -0.367203450664974 \tabularnewline
64 & 102.32 & 102.329540841137 & -0.00954084113679698 \tabularnewline
65 & 102.41 & 102.236435581693 & 0.173564418307009 \tabularnewline
66 & 102.4 & 102.340376437703 & 0.0596235622969346 \tabularnewline
67 & 102.43 & 101.877041695975 & 0.552958304025097 \tabularnewline
68 & 102.42 & 102.12377408105 & 0.296225918950299 \tabularnewline
69 & 102.3 & 102.457671199971 & -0.157671199971389 \tabularnewline
70 & 102.65 & 102.851639699376 & -0.201639699375889 \tabularnewline
71 & 102.72 & 102.966227109382 & -0.246227109381948 \tabularnewline
72 & 102.86 & 102.760316919136 & 0.0996830808637839 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294813&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]93.75[/C][C]91.5310576923077[/C][C]2.21894230769226[/C][/ROW]
[ROW][C]14[/C][C]94.1[/C][C]93.8636576906362[/C][C]0.236342309363778[/C][/ROW]
[ROW][C]15[/C][C]94.96[/C][C]95.0548049685703[/C][C]-0.0948049685703012[/C][/ROW]
[ROW][C]16[/C][C]95.21[/C][C]95.3974460350161[/C][C]-0.187446035016151[/C][/ROW]
[ROW][C]17[/C][C]95.33[/C][C]95.5659081579091[/C][C]-0.235908157909137[/C][/ROW]
[ROW][C]18[/C][C]95.43[/C][C]95.6700086930242[/C][C]-0.240008693024237[/C][/ROW]
[ROW][C]19[/C][C]95.44[/C][C]94.9046104474915[/C][C]0.535389552508448[/C][/ROW]
[ROW][C]20[/C][C]95.64[/C][C]95.8690269812821[/C][C]-0.229026981282075[/C][/ROW]
[ROW][C]21[/C][C]95.8[/C][C]96.2589955582746[/C][C]-0.458995558274594[/C][/ROW]
[ROW][C]22[/C][C]95.87[/C][C]96.9390530136154[/C][C]-1.06905301361542[/C][/ROW]
[ROW][C]23[/C][C]95.98[/C][C]96.3740812138023[/C][C]-0.394081213802295[/C][/ROW]
[ROW][C]24[/C][C]96.07[/C][C]96.1841036229279[/C][C]-0.114103622927914[/C][/ROW]
[ROW][C]25[/C][C]96.23[/C][C]97.4660289042405[/C][C]-1.23602890424051[/C][/ROW]
[ROW][C]26[/C][C]96.32[/C][C]96.3466317165677[/C][C]-0.0266317165677208[/C][/ROW]
[ROW][C]27[/C][C]96.55[/C][C]97.0271023763242[/C][C]-0.477102376324183[/C][/ROW]
[ROW][C]28[/C][C]96.73[/C][C]96.7699120368107[/C][C]-0.0399120368107333[/C][/ROW]
[ROW][C]29[/C][C]96.61[/C][C]96.8039311169582[/C][C]-0.193931116958197[/C][/ROW]
[ROW][C]30[/C][C]96.64[/C][C]96.6934632128488[/C][C]-0.0534632128488397[/C][/ROW]
[ROW][C]31[/C][C]96.86[/C][C]95.9663266122261[/C][C]0.893673387773873[/C][/ROW]
[ROW][C]32[/C][C]97.02[/C][C]96.9034008043502[/C][C]0.116599195649755[/C][/ROW]
[ROW][C]33[/C][C]97.22[/C][C]97.3583556182423[/C][C]-0.138355618242272[/C][/ROW]
[ROW][C]34[/C][C]98.1[/C][C]98.0447570395119[/C][C]0.0552429604880729[/C][/ROW]
[ROW][C]35[/C][C]98.46[/C][C]98.4340601468626[/C][C]0.0259398531374018[/C][/ROW]
[ROW][C]36[/C][C]98.6[/C][C]98.5676467913811[/C][C]0.0323532086189289[/C][/ROW]
[ROW][C]37[/C][C]98.78[/C][C]99.7374256548839[/C][C]-0.957425654883906[/C][/ROW]
[ROW][C]38[/C][C]99.13[/C][C]98.9897517063354[/C][C]0.140248293664641[/C][/ROW]
[ROW][C]39[/C][C]99.48[/C][C]99.70559250499[/C][C]-0.225592504990004[/C][/ROW]
[ROW][C]40[/C][C]99.62[/C][C]99.7063122210881[/C][C]-0.0863122210880647[/C][/ROW]
[ROW][C]41[/C][C]99.68[/C][C]99.6528378010398[/C][C]0.0271621989602409[/C][/ROW]
[ROW][C]42[/C][C]99.95[/C][C]99.7404615583061[/C][C]0.209538441693866[/C][/ROW]
[ROW][C]43[/C][C]100.12[/C][C]99.3861482209829[/C][C]0.733851779017087[/C][/ROW]
[ROW][C]44[/C][C]100.25[/C][C]100.065405424409[/C][C]0.184594575591106[/C][/ROW]
[ROW][C]45[/C][C]100.47[/C][C]100.539372668924[/C][C]-0.0693726689235774[/C][/ROW]
[ROW][C]46[/C][C]100.7[/C][C]101.318132396729[/C][C]-0.618132396729422[/C][/ROW]
[ROW][C]47[/C][C]100.88[/C][C]101.09373851591[/C][C]-0.213738515909895[/C][/ROW]
[ROW][C]48[/C][C]100.95[/C][C]100.971698042695[/C][C]-0.0216980426948936[/C][/ROW]
[ROW][C]49[/C][C]100.92[/C][C]101.888517600623[/C][C]-0.968517600622704[/C][/ROW]
[ROW][C]50[/C][C]101.12[/C][C]101.240735883099[/C][C]-0.12073588309913[/C][/ROW]
[ROW][C]51[/C][C]101.19[/C][C]101.60569111408[/C][C]-0.415691114079621[/C][/ROW]
[ROW][C]52[/C][C]101.28[/C][C]101.38034923688[/C][C]-0.100349236880348[/C][/ROW]
[ROW][C]53[/C][C]101.28[/C][C]101.245319369471[/C][C]0.0346806305291523[/C][/ROW]
[ROW][C]54[/C][C]101.3[/C][C]101.280611634522[/C][C]0.019388365477738[/C][/ROW]
[ROW][C]55[/C][C]101.3[/C][C]100.746240996582[/C][C]0.553759003417952[/C][/ROW]
[ROW][C]56[/C][C]101.36[/C][C]101.079479928278[/C][C]0.280520071721952[/C][/ROW]
[ROW][C]57[/C][C]101.45[/C][C]101.492445084622[/C][C]-0.0424450846221447[/C][/ROW]
[ROW][C]58[/C][C]101.58[/C][C]102.108606677883[/C][C]-0.528606677883033[/C][/ROW]
[ROW][C]59[/C][C]101.73[/C][C]101.925168894215[/C][C]-0.195168894214916[/C][/ROW]
[ROW][C]60[/C][C]101.84[/C][C]101.752822803244[/C][C]0.0871771967561443[/C][/ROW]
[ROW][C]61[/C][C]102.01[/C][C]102.529800386465[/C][C]-0.519800386465121[/C][/ROW]
[ROW][C]62[/C][C]102.14[/C][C]102.331416938069[/C][C]-0.191416938069338[/C][/ROW]
[ROW][C]63[/C][C]102.16[/C][C]102.527203450665[/C][C]-0.367203450664974[/C][/ROW]
[ROW][C]64[/C][C]102.32[/C][C]102.329540841137[/C][C]-0.00954084113679698[/C][/ROW]
[ROW][C]65[/C][C]102.41[/C][C]102.236435581693[/C][C]0.173564418307009[/C][/ROW]
[ROW][C]66[/C][C]102.4[/C][C]102.340376437703[/C][C]0.0596235622969346[/C][/ROW]
[ROW][C]67[/C][C]102.43[/C][C]101.877041695975[/C][C]0.552958304025097[/C][/ROW]
[ROW][C]68[/C][C]102.42[/C][C]102.12377408105[/C][C]0.296225918950299[/C][/ROW]
[ROW][C]69[/C][C]102.3[/C][C]102.457671199971[/C][C]-0.157671199971389[/C][/ROW]
[ROW][C]70[/C][C]102.65[/C][C]102.851639699376[/C][C]-0.201639699375889[/C][/ROW]
[ROW][C]71[/C][C]102.72[/C][C]102.966227109382[/C][C]-0.246227109381948[/C][/ROW]
[ROW][C]72[/C][C]102.86[/C][C]102.760316919136[/C][C]0.0996830808637839[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294813&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294813&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
1393.7591.53105769230772.21894230769226
1494.193.86365769063620.236342309363778
1594.9695.0548049685703-0.0948049685703012
1695.2195.3974460350161-0.187446035016151
1795.3395.5659081579091-0.235908157909137
1895.4395.6700086930242-0.240008693024237
1995.4494.90461044749150.535389552508448
2095.6495.8690269812821-0.229026981282075
2195.896.2589955582746-0.458995558274594
2295.8796.9390530136154-1.06905301361542
2395.9896.3740812138023-0.394081213802295
2496.0796.1841036229279-0.114103622927914
2596.2397.4660289042405-1.23602890424051
2696.3296.3466317165677-0.0266317165677208
2796.5597.0271023763242-0.477102376324183
2896.7396.7699120368107-0.0399120368107333
2996.6196.8039311169582-0.193931116958197
3096.6496.6934632128488-0.0534632128488397
3196.8695.96632661222610.893673387773873
3297.0296.90340080435020.116599195649755
3397.2297.3583556182423-0.138355618242272
3498.198.04475703951190.0552429604880729
3598.4698.43406014686260.0259398531374018
3698.698.56764679138110.0323532086189289
3798.7899.7374256548839-0.957425654883906
3899.1398.98975170633540.140248293664641
3999.4899.70559250499-0.225592504990004
4099.6299.7063122210881-0.0863122210880647
4199.6899.65283780103980.0271621989602409
4299.9599.74046155830610.209538441693866
43100.1299.38614822098290.733851779017087
44100.25100.0654054244090.184594575591106
45100.47100.539372668924-0.0693726689235774
46100.7101.318132396729-0.618132396729422
47100.88101.09373851591-0.213738515909895
48100.95100.971698042695-0.0216980426948936
49100.92101.888517600623-0.968517600622704
50101.12101.240735883099-0.12073588309913
51101.19101.60569111408-0.415691114079621
52101.28101.38034923688-0.100349236880348
53101.28101.2453193694710.0346806305291523
54101.3101.2806116345220.019388365477738
55101.3100.7462409965820.553759003417952
56101.36101.0794799282780.280520071721952
57101.45101.492445084622-0.0424450846221447
58101.58102.108606677883-0.528606677883033
59101.73101.925168894215-0.195168894214916
60101.84101.7528228032440.0871771967561443
61102.01102.529800386465-0.519800386465121
62102.14102.331416938069-0.191416938069338
63102.16102.527203450665-0.367203450664974
64102.32102.329540841137-0.00954084113679698
65102.41102.2364355816930.173564418307009
66102.4102.3403764377030.0596235622969346
67102.43101.8770416959750.552958304025097
68102.42102.123774081050.296225918950299
69102.3102.457671199971-0.157671199971389
70102.65102.851639699376-0.201639699375889
71102.72102.966227109382-0.246227109381948
72102.86102.7603169191360.0996830808637839







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73103.423325648816102.459055174694104.387596122937
74103.716191797904102.4115432585105.020840337309
75104.060252377321102.452344014484105.668160740157
76104.264222314882102.370271742375106.158172887389
77104.243507616207102.07219626982106.414818962593
78104.208440943017101.763967865454106.65291402058
79103.791212653477101.075137818137106.507287488816
80103.516723190262100.528934482244106.50451189828
81103.498430671187100.237701928585106.759159413789
82103.997404573819100.461740425956107.533068721683
83104.266952131301100.453812321007108.080091941594
84104.328720633584100.235171877307108.422269389861

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 103.423325648816 & 102.459055174694 & 104.387596122937 \tabularnewline
74 & 103.716191797904 & 102.4115432585 & 105.020840337309 \tabularnewline
75 & 104.060252377321 & 102.452344014484 & 105.668160740157 \tabularnewline
76 & 104.264222314882 & 102.370271742375 & 106.158172887389 \tabularnewline
77 & 104.243507616207 & 102.07219626982 & 106.414818962593 \tabularnewline
78 & 104.208440943017 & 101.763967865454 & 106.65291402058 \tabularnewline
79 & 103.791212653477 & 101.075137818137 & 106.507287488816 \tabularnewline
80 & 103.516723190262 & 100.528934482244 & 106.50451189828 \tabularnewline
81 & 103.498430671187 & 100.237701928585 & 106.759159413789 \tabularnewline
82 & 103.997404573819 & 100.461740425956 & 107.533068721683 \tabularnewline
83 & 104.266952131301 & 100.453812321007 & 108.080091941594 \tabularnewline
84 & 104.328720633584 & 100.235171877307 & 108.422269389861 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294813&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]73[/C][C]103.423325648816[/C][C]102.459055174694[/C][C]104.387596122937[/C][/ROW]
[ROW][C]74[/C][C]103.716191797904[/C][C]102.4115432585[/C][C]105.020840337309[/C][/ROW]
[ROW][C]75[/C][C]104.060252377321[/C][C]102.452344014484[/C][C]105.668160740157[/C][/ROW]
[ROW][C]76[/C][C]104.264222314882[/C][C]102.370271742375[/C][C]106.158172887389[/C][/ROW]
[ROW][C]77[/C][C]104.243507616207[/C][C]102.07219626982[/C][C]106.414818962593[/C][/ROW]
[ROW][C]78[/C][C]104.208440943017[/C][C]101.763967865454[/C][C]106.65291402058[/C][/ROW]
[ROW][C]79[/C][C]103.791212653477[/C][C]101.075137818137[/C][C]106.507287488816[/C][/ROW]
[ROW][C]80[/C][C]103.516723190262[/C][C]100.528934482244[/C][C]106.50451189828[/C][/ROW]
[ROW][C]81[/C][C]103.498430671187[/C][C]100.237701928585[/C][C]106.759159413789[/C][/ROW]
[ROW][C]82[/C][C]103.997404573819[/C][C]100.461740425956[/C][C]107.533068721683[/C][/ROW]
[ROW][C]83[/C][C]104.266952131301[/C][C]100.453812321007[/C][C]108.080091941594[/C][/ROW]
[ROW][C]84[/C][C]104.328720633584[/C][C]100.235171877307[/C][C]108.422269389861[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294813&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294813&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
73103.423325648816102.459055174694104.387596122937
74103.716191797904102.4115432585105.020840337309
75104.060252377321102.452344014484105.668160740157
76104.264222314882102.370271742375106.158172887389
77104.243507616207102.07219626982106.414818962593
78104.208440943017101.763967865454106.65291402058
79103.791212653477101.075137818137106.507287488816
80103.516723190262100.528934482244106.50451189828
81103.498430671187100.237701928585106.759159413789
82103.997404573819100.461740425956107.533068721683
83104.266952131301100.453812321007108.080091941594
84104.328720633584100.235171877307108.422269389861



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