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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 02 May 2013 07:38:41 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/May/02/t1367494801co7b38bj3aji652.htm/, Retrieved Sat, 04 May 2024 23:21:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=208660, Retrieved Sat, 04 May 2024 23:21:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact116
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Opgave 10, oefeni...] [2013-05-02 11:38:41] [aebd7ed62a520371cf0fbdf4b97f0dea] [Current]
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Dataseries X:
122.27
124.69
147.56
120.03
136.01
138.16
122.87
112.22
137.35
139.08
139.64
121.12
132.37
130.69
149.41
130.72
139.14
146.55
137.35
122.73
138.97
154.73
143.4
123.88
140.25
142.39
143.81
153.58
144.71
153.84
151.3
121.92
153.05
149.29
118.81
109.19
103.68
106.94
114.43
107.87
103.14
117.02
112.44
95.85
123.86
121.83
121.95
120.34
113.32
117.31
141.69
130.35
127.28
148.1
131.21
120.37
146.91
144.04
141.77
132.15
142.04
149.77
172.31
150.24
163.23
155.92
146.96
134.51
152.83
150.54
150.98
138.82




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208660&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208660&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208660&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.402332581357443
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.402332581357443 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208660&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]0.402332581357443[/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=208660&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208660&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
alpha0.402332581357443
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2124.69122.272.42
3147.56123.24364484688524.316355153115
4120.03133.026906784842-12.9969067848421
5136.01127.7978277284358.21217227156546
6138.16131.1018521970057.05814780299451
7122.87133.941575022187-11.0715750221866
8112.22129.487119663818-17.2671196638177
9137.35122.53999483686614.8100051631339
10139.08128.49854244406710.5814575559332
11139.64132.755807577076.88419242293037
12121.12135.525542485149-14.4055424851485
13132.37129.7297233912442.64027660875558
14130.69130.791992694743-0.101992694742734
15149.41130.75095771058718.6590422894127
16130.72138.258098360544-7.53809836054438
17139.14135.225275788623.91472421137973
18146.55136.8002968858879.74970311411286
19137.35140.722920107257-3.37292010725687
20122.73139.365884453792-16.6358844537918
21138.97132.6727261183346.29727388166643
22154.73135.20632457465919.5236754253408
23143.4143.0613353061210.33866469387857
24123.88143.197591146624-19.3175911466242
25140.25135.4254948349954.82450516500478
26142.39137.3665504518045.02344954819608
27143.81139.3876478758494.4223521241515
28153.58141.1669042216312.4130957783701
29144.71146.161097088779-1.45109708877874
30153.84145.577273451258.26272654874987
31151.3148.9016375526592.39836244734067
32121.92149.866576907129-27.9465769071287
33153.05138.62275847997914.4272415200207
34149.29144.4273078025964.8626921974035
35118.81146.383727306725-27.5737273067245
36109.19135.289918421764-26.0999184217638
37103.68124.789070869917-21.1090708699169
38106.94116.296203896766-9.35620389676605
39114.43112.5318982312741.89810176872641
40107.87113.295566415564-5.42556641556442
41103.14111.112684274264-7.97268427426414
42117.02107.9050136298529.11498637014844
43112.44111.5722696251910.867730374808716
4495.85111.92138582681-16.0713858268103
45123.86105.45534368111818.4046563188817
46121.83112.8601365668918.96986343310944
47121.95116.4690048763575.48099512364278
48120.34118.674187792861.66581220714002
49113.32119.344398318215-6.02439831821538
50117.31116.9205865917220.389413408277662
51141.69117.0772602934924.6127397065101
52130.35126.9797673938893.37023260611106
53127.28128.335721778081-1.05572177808062
54148.1127.9109705099120.1890294900898
55131.21136.03367485976-4.82367485975954
56120.37134.092953301803-13.7229533018035
57146.91128.57176207604118.3382379239588
58144.04135.9498326775358.09016732246548
59141.77139.2047705799962.56522942000433
60132.15140.23684595432-8.08684595432007
61142.04136.9832443464795.05675565352149
62149.77139.01774190185410.7522580981464
63172.31143.34372565790228.9662743420977
64150.24154.997801586266-4.75780158626634
65163.23153.08358299247710.1464170075227
66155.92157.165817138643-1.24581713864296
67146.96156.664584313353-9.70458431335337
68134.51152.760113855561-18.250113855561
69152.83145.4174984379867.41250156201411
70150.54148.3997893257472.14021067425287
71150.98149.2608658109681.71913418903196
72138.82149.952529506941-11.1325295069411

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 124.69 & 122.27 & 2.42 \tabularnewline
3 & 147.56 & 123.243644846885 & 24.316355153115 \tabularnewline
4 & 120.03 & 133.026906784842 & -12.9969067848421 \tabularnewline
5 & 136.01 & 127.797827728435 & 8.21217227156546 \tabularnewline
6 & 138.16 & 131.101852197005 & 7.05814780299451 \tabularnewline
7 & 122.87 & 133.941575022187 & -11.0715750221866 \tabularnewline
8 & 112.22 & 129.487119663818 & -17.2671196638177 \tabularnewline
9 & 137.35 & 122.539994836866 & 14.8100051631339 \tabularnewline
10 & 139.08 & 128.498542444067 & 10.5814575559332 \tabularnewline
11 & 139.64 & 132.75580757707 & 6.88419242293037 \tabularnewline
12 & 121.12 & 135.525542485149 & -14.4055424851485 \tabularnewline
13 & 132.37 & 129.729723391244 & 2.64027660875558 \tabularnewline
14 & 130.69 & 130.791992694743 & -0.101992694742734 \tabularnewline
15 & 149.41 & 130.750957710587 & 18.6590422894127 \tabularnewline
16 & 130.72 & 138.258098360544 & -7.53809836054438 \tabularnewline
17 & 139.14 & 135.22527578862 & 3.91472421137973 \tabularnewline
18 & 146.55 & 136.800296885887 & 9.74970311411286 \tabularnewline
19 & 137.35 & 140.722920107257 & -3.37292010725687 \tabularnewline
20 & 122.73 & 139.365884453792 & -16.6358844537918 \tabularnewline
21 & 138.97 & 132.672726118334 & 6.29727388166643 \tabularnewline
22 & 154.73 & 135.206324574659 & 19.5236754253408 \tabularnewline
23 & 143.4 & 143.061335306121 & 0.33866469387857 \tabularnewline
24 & 123.88 & 143.197591146624 & -19.3175911466242 \tabularnewline
25 & 140.25 & 135.425494834995 & 4.82450516500478 \tabularnewline
26 & 142.39 & 137.366550451804 & 5.02344954819608 \tabularnewline
27 & 143.81 & 139.387647875849 & 4.4223521241515 \tabularnewline
28 & 153.58 & 141.16690422163 & 12.4130957783701 \tabularnewline
29 & 144.71 & 146.161097088779 & -1.45109708877874 \tabularnewline
30 & 153.84 & 145.57727345125 & 8.26272654874987 \tabularnewline
31 & 151.3 & 148.901637552659 & 2.39836244734067 \tabularnewline
32 & 121.92 & 149.866576907129 & -27.9465769071287 \tabularnewline
33 & 153.05 & 138.622758479979 & 14.4272415200207 \tabularnewline
34 & 149.29 & 144.427307802596 & 4.8626921974035 \tabularnewline
35 & 118.81 & 146.383727306725 & -27.5737273067245 \tabularnewline
36 & 109.19 & 135.289918421764 & -26.0999184217638 \tabularnewline
37 & 103.68 & 124.789070869917 & -21.1090708699169 \tabularnewline
38 & 106.94 & 116.296203896766 & -9.35620389676605 \tabularnewline
39 & 114.43 & 112.531898231274 & 1.89810176872641 \tabularnewline
40 & 107.87 & 113.295566415564 & -5.42556641556442 \tabularnewline
41 & 103.14 & 111.112684274264 & -7.97268427426414 \tabularnewline
42 & 117.02 & 107.905013629852 & 9.11498637014844 \tabularnewline
43 & 112.44 & 111.572269625191 & 0.867730374808716 \tabularnewline
44 & 95.85 & 111.92138582681 & -16.0713858268103 \tabularnewline
45 & 123.86 & 105.455343681118 & 18.4046563188817 \tabularnewline
46 & 121.83 & 112.860136566891 & 8.96986343310944 \tabularnewline
47 & 121.95 & 116.469004876357 & 5.48099512364278 \tabularnewline
48 & 120.34 & 118.67418779286 & 1.66581220714002 \tabularnewline
49 & 113.32 & 119.344398318215 & -6.02439831821538 \tabularnewline
50 & 117.31 & 116.920586591722 & 0.389413408277662 \tabularnewline
51 & 141.69 & 117.07726029349 & 24.6127397065101 \tabularnewline
52 & 130.35 & 126.979767393889 & 3.37023260611106 \tabularnewline
53 & 127.28 & 128.335721778081 & -1.05572177808062 \tabularnewline
54 & 148.1 & 127.91097050991 & 20.1890294900898 \tabularnewline
55 & 131.21 & 136.03367485976 & -4.82367485975954 \tabularnewline
56 & 120.37 & 134.092953301803 & -13.7229533018035 \tabularnewline
57 & 146.91 & 128.571762076041 & 18.3382379239588 \tabularnewline
58 & 144.04 & 135.949832677535 & 8.09016732246548 \tabularnewline
59 & 141.77 & 139.204770579996 & 2.56522942000433 \tabularnewline
60 & 132.15 & 140.23684595432 & -8.08684595432007 \tabularnewline
61 & 142.04 & 136.983244346479 & 5.05675565352149 \tabularnewline
62 & 149.77 & 139.017741901854 & 10.7522580981464 \tabularnewline
63 & 172.31 & 143.343725657902 & 28.9662743420977 \tabularnewline
64 & 150.24 & 154.997801586266 & -4.75780158626634 \tabularnewline
65 & 163.23 & 153.083582992477 & 10.1464170075227 \tabularnewline
66 & 155.92 & 157.165817138643 & -1.24581713864296 \tabularnewline
67 & 146.96 & 156.664584313353 & -9.70458431335337 \tabularnewline
68 & 134.51 & 152.760113855561 & -18.250113855561 \tabularnewline
69 & 152.83 & 145.417498437986 & 7.41250156201411 \tabularnewline
70 & 150.54 & 148.399789325747 & 2.14021067425287 \tabularnewline
71 & 150.98 & 149.260865810968 & 1.71913418903196 \tabularnewline
72 & 138.82 & 149.952529506941 & -11.1325295069411 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208660&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]124.69[/C][C]122.27[/C][C]2.42[/C][/ROW]
[ROW][C]3[/C][C]147.56[/C][C]123.243644846885[/C][C]24.316355153115[/C][/ROW]
[ROW][C]4[/C][C]120.03[/C][C]133.026906784842[/C][C]-12.9969067848421[/C][/ROW]
[ROW][C]5[/C][C]136.01[/C][C]127.797827728435[/C][C]8.21217227156546[/C][/ROW]
[ROW][C]6[/C][C]138.16[/C][C]131.101852197005[/C][C]7.05814780299451[/C][/ROW]
[ROW][C]7[/C][C]122.87[/C][C]133.941575022187[/C][C]-11.0715750221866[/C][/ROW]
[ROW][C]8[/C][C]112.22[/C][C]129.487119663818[/C][C]-17.2671196638177[/C][/ROW]
[ROW][C]9[/C][C]137.35[/C][C]122.539994836866[/C][C]14.8100051631339[/C][/ROW]
[ROW][C]10[/C][C]139.08[/C][C]128.498542444067[/C][C]10.5814575559332[/C][/ROW]
[ROW][C]11[/C][C]139.64[/C][C]132.75580757707[/C][C]6.88419242293037[/C][/ROW]
[ROW][C]12[/C][C]121.12[/C][C]135.525542485149[/C][C]-14.4055424851485[/C][/ROW]
[ROW][C]13[/C][C]132.37[/C][C]129.729723391244[/C][C]2.64027660875558[/C][/ROW]
[ROW][C]14[/C][C]130.69[/C][C]130.791992694743[/C][C]-0.101992694742734[/C][/ROW]
[ROW][C]15[/C][C]149.41[/C][C]130.750957710587[/C][C]18.6590422894127[/C][/ROW]
[ROW][C]16[/C][C]130.72[/C][C]138.258098360544[/C][C]-7.53809836054438[/C][/ROW]
[ROW][C]17[/C][C]139.14[/C][C]135.22527578862[/C][C]3.91472421137973[/C][/ROW]
[ROW][C]18[/C][C]146.55[/C][C]136.800296885887[/C][C]9.74970311411286[/C][/ROW]
[ROW][C]19[/C][C]137.35[/C][C]140.722920107257[/C][C]-3.37292010725687[/C][/ROW]
[ROW][C]20[/C][C]122.73[/C][C]139.365884453792[/C][C]-16.6358844537918[/C][/ROW]
[ROW][C]21[/C][C]138.97[/C][C]132.672726118334[/C][C]6.29727388166643[/C][/ROW]
[ROW][C]22[/C][C]154.73[/C][C]135.206324574659[/C][C]19.5236754253408[/C][/ROW]
[ROW][C]23[/C][C]143.4[/C][C]143.061335306121[/C][C]0.33866469387857[/C][/ROW]
[ROW][C]24[/C][C]123.88[/C][C]143.197591146624[/C][C]-19.3175911466242[/C][/ROW]
[ROW][C]25[/C][C]140.25[/C][C]135.425494834995[/C][C]4.82450516500478[/C][/ROW]
[ROW][C]26[/C][C]142.39[/C][C]137.366550451804[/C][C]5.02344954819608[/C][/ROW]
[ROW][C]27[/C][C]143.81[/C][C]139.387647875849[/C][C]4.4223521241515[/C][/ROW]
[ROW][C]28[/C][C]153.58[/C][C]141.16690422163[/C][C]12.4130957783701[/C][/ROW]
[ROW][C]29[/C][C]144.71[/C][C]146.161097088779[/C][C]-1.45109708877874[/C][/ROW]
[ROW][C]30[/C][C]153.84[/C][C]145.57727345125[/C][C]8.26272654874987[/C][/ROW]
[ROW][C]31[/C][C]151.3[/C][C]148.901637552659[/C][C]2.39836244734067[/C][/ROW]
[ROW][C]32[/C][C]121.92[/C][C]149.866576907129[/C][C]-27.9465769071287[/C][/ROW]
[ROW][C]33[/C][C]153.05[/C][C]138.622758479979[/C][C]14.4272415200207[/C][/ROW]
[ROW][C]34[/C][C]149.29[/C][C]144.427307802596[/C][C]4.8626921974035[/C][/ROW]
[ROW][C]35[/C][C]118.81[/C][C]146.383727306725[/C][C]-27.5737273067245[/C][/ROW]
[ROW][C]36[/C][C]109.19[/C][C]135.289918421764[/C][C]-26.0999184217638[/C][/ROW]
[ROW][C]37[/C][C]103.68[/C][C]124.789070869917[/C][C]-21.1090708699169[/C][/ROW]
[ROW][C]38[/C][C]106.94[/C][C]116.296203896766[/C][C]-9.35620389676605[/C][/ROW]
[ROW][C]39[/C][C]114.43[/C][C]112.531898231274[/C][C]1.89810176872641[/C][/ROW]
[ROW][C]40[/C][C]107.87[/C][C]113.295566415564[/C][C]-5.42556641556442[/C][/ROW]
[ROW][C]41[/C][C]103.14[/C][C]111.112684274264[/C][C]-7.97268427426414[/C][/ROW]
[ROW][C]42[/C][C]117.02[/C][C]107.905013629852[/C][C]9.11498637014844[/C][/ROW]
[ROW][C]43[/C][C]112.44[/C][C]111.572269625191[/C][C]0.867730374808716[/C][/ROW]
[ROW][C]44[/C][C]95.85[/C][C]111.92138582681[/C][C]-16.0713858268103[/C][/ROW]
[ROW][C]45[/C][C]123.86[/C][C]105.455343681118[/C][C]18.4046563188817[/C][/ROW]
[ROW][C]46[/C][C]121.83[/C][C]112.860136566891[/C][C]8.96986343310944[/C][/ROW]
[ROW][C]47[/C][C]121.95[/C][C]116.469004876357[/C][C]5.48099512364278[/C][/ROW]
[ROW][C]48[/C][C]120.34[/C][C]118.67418779286[/C][C]1.66581220714002[/C][/ROW]
[ROW][C]49[/C][C]113.32[/C][C]119.344398318215[/C][C]-6.02439831821538[/C][/ROW]
[ROW][C]50[/C][C]117.31[/C][C]116.920586591722[/C][C]0.389413408277662[/C][/ROW]
[ROW][C]51[/C][C]141.69[/C][C]117.07726029349[/C][C]24.6127397065101[/C][/ROW]
[ROW][C]52[/C][C]130.35[/C][C]126.979767393889[/C][C]3.37023260611106[/C][/ROW]
[ROW][C]53[/C][C]127.28[/C][C]128.335721778081[/C][C]-1.05572177808062[/C][/ROW]
[ROW][C]54[/C][C]148.1[/C][C]127.91097050991[/C][C]20.1890294900898[/C][/ROW]
[ROW][C]55[/C][C]131.21[/C][C]136.03367485976[/C][C]-4.82367485975954[/C][/ROW]
[ROW][C]56[/C][C]120.37[/C][C]134.092953301803[/C][C]-13.7229533018035[/C][/ROW]
[ROW][C]57[/C][C]146.91[/C][C]128.571762076041[/C][C]18.3382379239588[/C][/ROW]
[ROW][C]58[/C][C]144.04[/C][C]135.949832677535[/C][C]8.09016732246548[/C][/ROW]
[ROW][C]59[/C][C]141.77[/C][C]139.204770579996[/C][C]2.56522942000433[/C][/ROW]
[ROW][C]60[/C][C]132.15[/C][C]140.23684595432[/C][C]-8.08684595432007[/C][/ROW]
[ROW][C]61[/C][C]142.04[/C][C]136.983244346479[/C][C]5.05675565352149[/C][/ROW]
[ROW][C]62[/C][C]149.77[/C][C]139.017741901854[/C][C]10.7522580981464[/C][/ROW]
[ROW][C]63[/C][C]172.31[/C][C]143.343725657902[/C][C]28.9662743420977[/C][/ROW]
[ROW][C]64[/C][C]150.24[/C][C]154.997801586266[/C][C]-4.75780158626634[/C][/ROW]
[ROW][C]65[/C][C]163.23[/C][C]153.083582992477[/C][C]10.1464170075227[/C][/ROW]
[ROW][C]66[/C][C]155.92[/C][C]157.165817138643[/C][C]-1.24581713864296[/C][/ROW]
[ROW][C]67[/C][C]146.96[/C][C]156.664584313353[/C][C]-9.70458431335337[/C][/ROW]
[ROW][C]68[/C][C]134.51[/C][C]152.760113855561[/C][C]-18.250113855561[/C][/ROW]
[ROW][C]69[/C][C]152.83[/C][C]145.417498437986[/C][C]7.41250156201411[/C][/ROW]
[ROW][C]70[/C][C]150.54[/C][C]148.399789325747[/C][C]2.14021067425287[/C][/ROW]
[ROW][C]71[/C][C]150.98[/C][C]149.260865810968[/C][C]1.71913418903196[/C][/ROW]
[ROW][C]72[/C][C]138.82[/C][C]149.952529506941[/C][C]-11.1325295069411[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208660&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208660&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
2124.69122.272.42
3147.56123.24364484688524.316355153115
4120.03133.026906784842-12.9969067848421
5136.01127.7978277284358.21217227156546
6138.16131.1018521970057.05814780299451
7122.87133.941575022187-11.0715750221866
8112.22129.487119663818-17.2671196638177
9137.35122.53999483686614.8100051631339
10139.08128.49854244406710.5814575559332
11139.64132.755807577076.88419242293037
12121.12135.525542485149-14.4055424851485
13132.37129.7297233912442.64027660875558
14130.69130.791992694743-0.101992694742734
15149.41130.75095771058718.6590422894127
16130.72138.258098360544-7.53809836054438
17139.14135.225275788623.91472421137973
18146.55136.8002968858879.74970311411286
19137.35140.722920107257-3.37292010725687
20122.73139.365884453792-16.6358844537918
21138.97132.6727261183346.29727388166643
22154.73135.20632457465919.5236754253408
23143.4143.0613353061210.33866469387857
24123.88143.197591146624-19.3175911466242
25140.25135.4254948349954.82450516500478
26142.39137.3665504518045.02344954819608
27143.81139.3876478758494.4223521241515
28153.58141.1669042216312.4130957783701
29144.71146.161097088779-1.45109708877874
30153.84145.577273451258.26272654874987
31151.3148.9016375526592.39836244734067
32121.92149.866576907129-27.9465769071287
33153.05138.62275847997914.4272415200207
34149.29144.4273078025964.8626921974035
35118.81146.383727306725-27.5737273067245
36109.19135.289918421764-26.0999184217638
37103.68124.789070869917-21.1090708699169
38106.94116.296203896766-9.35620389676605
39114.43112.5318982312741.89810176872641
40107.87113.295566415564-5.42556641556442
41103.14111.112684274264-7.97268427426414
42117.02107.9050136298529.11498637014844
43112.44111.5722696251910.867730374808716
4495.85111.92138582681-16.0713858268103
45123.86105.45534368111818.4046563188817
46121.83112.8601365668918.96986343310944
47121.95116.4690048763575.48099512364278
48120.34118.674187792861.66581220714002
49113.32119.344398318215-6.02439831821538
50117.31116.9205865917220.389413408277662
51141.69117.0772602934924.6127397065101
52130.35126.9797673938893.37023260611106
53127.28128.335721778081-1.05572177808062
54148.1127.9109705099120.1890294900898
55131.21136.03367485976-4.82367485975954
56120.37134.092953301803-13.7229533018035
57146.91128.57176207604118.3382379239588
58144.04135.9498326775358.09016732246548
59141.77139.2047705799962.56522942000433
60132.15140.23684595432-8.08684595432007
61142.04136.9832443464795.05675565352149
62149.77139.01774190185410.7522580981464
63172.31143.34372565790228.9662743420977
64150.24154.997801586266-4.75780158626634
65163.23153.08358299247710.1464170075227
66155.92157.165817138643-1.24581713864296
67146.96156.664584313353-9.70458431335337
68134.51152.760113855561-18.250113855561
69152.83145.4174984379867.41250156201411
70150.54148.3997893257472.14021067425287
71150.98149.2608658109681.71913418903196
72138.82149.952529506941-11.1325295069411







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73145.473550173376120.800335172158170.146765174593
74145.473550173376118.878256289498172.068844057254
75145.473550173376117.086021660957173.861078685794
76145.473550173376115.400407781585175.546692565166
77145.473550173376113.80438517664177.142715170111
78145.473550173376112.285026104595178.662074242156
79145.473550173376110.832241766539180.114858580212
80145.473550173376109.437979324406181.509121022345
81145.473550173376108.095689283744182.851411063007
82145.473550173376106.799959663078184.147140683673
83145.473550173376105.546257236943185.400843109809
84145.473550173376104.330739871875186.616360474876

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 145.473550173376 & 120.800335172158 & 170.146765174593 \tabularnewline
74 & 145.473550173376 & 118.878256289498 & 172.068844057254 \tabularnewline
75 & 145.473550173376 & 117.086021660957 & 173.861078685794 \tabularnewline
76 & 145.473550173376 & 115.400407781585 & 175.546692565166 \tabularnewline
77 & 145.473550173376 & 113.80438517664 & 177.142715170111 \tabularnewline
78 & 145.473550173376 & 112.285026104595 & 178.662074242156 \tabularnewline
79 & 145.473550173376 & 110.832241766539 & 180.114858580212 \tabularnewline
80 & 145.473550173376 & 109.437979324406 & 181.509121022345 \tabularnewline
81 & 145.473550173376 & 108.095689283744 & 182.851411063007 \tabularnewline
82 & 145.473550173376 & 106.799959663078 & 184.147140683673 \tabularnewline
83 & 145.473550173376 & 105.546257236943 & 185.400843109809 \tabularnewline
84 & 145.473550173376 & 104.330739871875 & 186.616360474876 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208660&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]145.473550173376[/C][C]120.800335172158[/C][C]170.146765174593[/C][/ROW]
[ROW][C]74[/C][C]145.473550173376[/C][C]118.878256289498[/C][C]172.068844057254[/C][/ROW]
[ROW][C]75[/C][C]145.473550173376[/C][C]117.086021660957[/C][C]173.861078685794[/C][/ROW]
[ROW][C]76[/C][C]145.473550173376[/C][C]115.400407781585[/C][C]175.546692565166[/C][/ROW]
[ROW][C]77[/C][C]145.473550173376[/C][C]113.80438517664[/C][C]177.142715170111[/C][/ROW]
[ROW][C]78[/C][C]145.473550173376[/C][C]112.285026104595[/C][C]178.662074242156[/C][/ROW]
[ROW][C]79[/C][C]145.473550173376[/C][C]110.832241766539[/C][C]180.114858580212[/C][/ROW]
[ROW][C]80[/C][C]145.473550173376[/C][C]109.437979324406[/C][C]181.509121022345[/C][/ROW]
[ROW][C]81[/C][C]145.473550173376[/C][C]108.095689283744[/C][C]182.851411063007[/C][/ROW]
[ROW][C]82[/C][C]145.473550173376[/C][C]106.799959663078[/C][C]184.147140683673[/C][/ROW]
[ROW][C]83[/C][C]145.473550173376[/C][C]105.546257236943[/C][C]185.400843109809[/C][/ROW]
[ROW][C]84[/C][C]145.473550173376[/C][C]104.330739871875[/C][C]186.616360474876[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208660&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208660&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
73145.473550173376120.800335172158170.146765174593
74145.473550173376118.878256289498172.068844057254
75145.473550173376117.086021660957173.861078685794
76145.473550173376115.400407781585175.546692565166
77145.473550173376113.80438517664177.142715170111
78145.473550173376112.285026104595178.662074242156
79145.473550173376110.832241766539180.114858580212
80145.473550173376109.437979324406181.509121022345
81145.473550173376108.095689283744182.851411063007
82145.473550173376106.799959663078184.147140683673
83145.473550173376105.546257236943185.400843109809
84145.473550173376104.330739871875186.616360474876



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