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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 06 Jun 2010 11:46:50 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Jun/06/t1275824823gil0gazcezj36go.htm/, Retrieved Sat, 27 Apr 2024 13:46:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=77660, Retrieved Sat, 27 Apr 2024 13:46:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact114
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [opgave 10] [2010-06-06 11:46:50] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
103,6
104,7
105,5
106,6
107,2
107,5
108,3
108,7
108,8
109,8
109,5
109,2
110,6
110,1
109,9
109,7
109,4
109,4
109,4
109,5
109,5
109,9
110
110,8
112,4
112,8
113,7
114,5
114,8
115,6
115,8
115,8
116,3
116,3
116,8
116,7
116,8
117
117,2
117,1
117,3
117,4
117,7
117,9
118,8
119,9
122,4
123,5
125,6
127,4
128,9
129,5
130,8
132,7
134
132,9
133,1
131,7
128,8
125,1
123,9
121,8
119,2
118,9
119,6
120,2
119,6
121
120,4
120,4
121,4
121,7




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77660&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77660&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77660&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.696623499130001
beta1
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.696623499130001 \tabularnewline
beta & 1 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77660&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]0.696623499130001[/C][/ROW]
[ROW][C]beta[/C][C]1[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77660&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77660&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
alpha0.696623499130001
beta1
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3105.5105.8-0.300000000000011
4106.6106.4820259005220.117974099477991
5107.2107.537405910753-0.337405910753148
6107.5108.040512618647-0.540512618647227
7108.3108.0255966292650.274403370734589
8108.7108.769526104198-0.0695261041979336
9108.8109.225432706862-0.42543270686177
10109.8109.1370399857160.66296001428394
11109.5110.268680735336-0.768680735336247
12109.2109.867525832895-0.667525832895151
13110.6109.0718236310761.52817636892435
14110.1110.870262749543-0.770262749542965
15109.9110.53097203493-0.630972034930153
16109.7109.849164558501-0.149164558501042
17109.4109.399083955520.000916044480220535
18109.4109.054191165450.345808834549956
19109.4109.1904573579780.209542642022356
20109.5109.3777696471560.122230352843872
21109.5109.589406680028-0.08940668002802
22109.9109.5913295882280.308670411771516
23110110.085589415368-0.0855894153680197
24110.8110.2455749841370.554425015862932
25112.4111.237635140041.16236485996045
26112.8113.462931153409-0.662931153409204
27113.7113.954869651227-0.254869651227025
28114.5114.553525192295-0.053525192295453
29114.8115.255155108127-0.45515510812676
30115.6115.3599284425660.240071557433794
31115.8116.116252497838-0.316252497838036
32115.8116.264719221424-0.464719221423692
33116.3115.986026206380.31397379362042
34116.3116.468510566971-0.168510566970568
35116.8116.4974965632080.302503436792264
36116.7117.065332985522-0.365332985522471
37116.8116.913439319756-0.113439319755599
38117116.8579962049770.142003795023157
39117.2117.0794239472230.120576052777309
40117.1117.369920732484-0.269920732483826
41117.3117.2003551556470.0996448443532927
42117.4117.3576525842480.0423474157524879
43117.7117.5045354825860.195464517414123
44117.9117.8942485281370.00575147186279423
45118.8118.155809618520.644190381479817
46119.9119.3108804137540.589119586246341
47122.4120.8379821464891.56201785351134
48123.5124.13096601728-0.630966017279945
49125.6125.4567200356750.143279964324734
50127.4127.421644189066-0.0216441890664925
51128.9129.256600450908-0.356600450907933
52129.5130.609802055667-1.1098020556671
53130.8130.6651915316080.134808468391924
54132.7131.6815166928371.01848330716336
55134134.022929917585-0.0229299175849178
56132.9135.622896698246-2.72289669824602
57133.1133.445169346927-0.345169346926582
58131.7132.683369664812-0.983369664811988
59128.8130.791946227267-1.99194622726651
60125.1126.810288104726-1.71028810472632
61123.9121.8334127650342.06658723496645
62121.8120.9272307711350.872769228864883
63119.2119.797398654647-0.597398654646639
64118.9117.2272511016621.67274889833769
65119.6117.4038178713052.19618212869477
66120.2119.4749326086590.725067391341497
67119.6121.026333233316-1.42633323331643
68121120.0854003788760.914599621123628
69120.4121.412347949095-1.01234794909483
70120.4120.691713189672-0.291713189672151
71121.4120.2698752750211.1301247249786
72121.7121.6257945040380.0742054959616922

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 105.5 & 105.8 & -0.300000000000011 \tabularnewline
4 & 106.6 & 106.482025900522 & 0.117974099477991 \tabularnewline
5 & 107.2 & 107.537405910753 & -0.337405910753148 \tabularnewline
6 & 107.5 & 108.040512618647 & -0.540512618647227 \tabularnewline
7 & 108.3 & 108.025596629265 & 0.274403370734589 \tabularnewline
8 & 108.7 & 108.769526104198 & -0.0695261041979336 \tabularnewline
9 & 108.8 & 109.225432706862 & -0.42543270686177 \tabularnewline
10 & 109.8 & 109.137039985716 & 0.66296001428394 \tabularnewline
11 & 109.5 & 110.268680735336 & -0.768680735336247 \tabularnewline
12 & 109.2 & 109.867525832895 & -0.667525832895151 \tabularnewline
13 & 110.6 & 109.071823631076 & 1.52817636892435 \tabularnewline
14 & 110.1 & 110.870262749543 & -0.770262749542965 \tabularnewline
15 & 109.9 & 110.53097203493 & -0.630972034930153 \tabularnewline
16 & 109.7 & 109.849164558501 & -0.149164558501042 \tabularnewline
17 & 109.4 & 109.39908395552 & 0.000916044480220535 \tabularnewline
18 & 109.4 & 109.05419116545 & 0.345808834549956 \tabularnewline
19 & 109.4 & 109.190457357978 & 0.209542642022356 \tabularnewline
20 & 109.5 & 109.377769647156 & 0.122230352843872 \tabularnewline
21 & 109.5 & 109.589406680028 & -0.08940668002802 \tabularnewline
22 & 109.9 & 109.591329588228 & 0.308670411771516 \tabularnewline
23 & 110 & 110.085589415368 & -0.0855894153680197 \tabularnewline
24 & 110.8 & 110.245574984137 & 0.554425015862932 \tabularnewline
25 & 112.4 & 111.23763514004 & 1.16236485996045 \tabularnewline
26 & 112.8 & 113.462931153409 & -0.662931153409204 \tabularnewline
27 & 113.7 & 113.954869651227 & -0.254869651227025 \tabularnewline
28 & 114.5 & 114.553525192295 & -0.053525192295453 \tabularnewline
29 & 114.8 & 115.255155108127 & -0.45515510812676 \tabularnewline
30 & 115.6 & 115.359928442566 & 0.240071557433794 \tabularnewline
31 & 115.8 & 116.116252497838 & -0.316252497838036 \tabularnewline
32 & 115.8 & 116.264719221424 & -0.464719221423692 \tabularnewline
33 & 116.3 & 115.98602620638 & 0.31397379362042 \tabularnewline
34 & 116.3 & 116.468510566971 & -0.168510566970568 \tabularnewline
35 & 116.8 & 116.497496563208 & 0.302503436792264 \tabularnewline
36 & 116.7 & 117.065332985522 & -0.365332985522471 \tabularnewline
37 & 116.8 & 116.913439319756 & -0.113439319755599 \tabularnewline
38 & 117 & 116.857996204977 & 0.142003795023157 \tabularnewline
39 & 117.2 & 117.079423947223 & 0.120576052777309 \tabularnewline
40 & 117.1 & 117.369920732484 & -0.269920732483826 \tabularnewline
41 & 117.3 & 117.200355155647 & 0.0996448443532927 \tabularnewline
42 & 117.4 & 117.357652584248 & 0.0423474157524879 \tabularnewline
43 & 117.7 & 117.504535482586 & 0.195464517414123 \tabularnewline
44 & 117.9 & 117.894248528137 & 0.00575147186279423 \tabularnewline
45 & 118.8 & 118.15580961852 & 0.644190381479817 \tabularnewline
46 & 119.9 & 119.310880413754 & 0.589119586246341 \tabularnewline
47 & 122.4 & 120.837982146489 & 1.56201785351134 \tabularnewline
48 & 123.5 & 124.13096601728 & -0.630966017279945 \tabularnewline
49 & 125.6 & 125.456720035675 & 0.143279964324734 \tabularnewline
50 & 127.4 & 127.421644189066 & -0.0216441890664925 \tabularnewline
51 & 128.9 & 129.256600450908 & -0.356600450907933 \tabularnewline
52 & 129.5 & 130.609802055667 & -1.1098020556671 \tabularnewline
53 & 130.8 & 130.665191531608 & 0.134808468391924 \tabularnewline
54 & 132.7 & 131.681516692837 & 1.01848330716336 \tabularnewline
55 & 134 & 134.022929917585 & -0.0229299175849178 \tabularnewline
56 & 132.9 & 135.622896698246 & -2.72289669824602 \tabularnewline
57 & 133.1 & 133.445169346927 & -0.345169346926582 \tabularnewline
58 & 131.7 & 132.683369664812 & -0.983369664811988 \tabularnewline
59 & 128.8 & 130.791946227267 & -1.99194622726651 \tabularnewline
60 & 125.1 & 126.810288104726 & -1.71028810472632 \tabularnewline
61 & 123.9 & 121.833412765034 & 2.06658723496645 \tabularnewline
62 & 121.8 & 120.927230771135 & 0.872769228864883 \tabularnewline
63 & 119.2 & 119.797398654647 & -0.597398654646639 \tabularnewline
64 & 118.9 & 117.227251101662 & 1.67274889833769 \tabularnewline
65 & 119.6 & 117.403817871305 & 2.19618212869477 \tabularnewline
66 & 120.2 & 119.474932608659 & 0.725067391341497 \tabularnewline
67 & 119.6 & 121.026333233316 & -1.42633323331643 \tabularnewline
68 & 121 & 120.085400378876 & 0.914599621123628 \tabularnewline
69 & 120.4 & 121.412347949095 & -1.01234794909483 \tabularnewline
70 & 120.4 & 120.691713189672 & -0.291713189672151 \tabularnewline
71 & 121.4 & 120.269875275021 & 1.1301247249786 \tabularnewline
72 & 121.7 & 121.625794504038 & 0.0742054959616922 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77660&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]105.5[/C][C]105.8[/C][C]-0.300000000000011[/C][/ROW]
[ROW][C]4[/C][C]106.6[/C][C]106.482025900522[/C][C]0.117974099477991[/C][/ROW]
[ROW][C]5[/C][C]107.2[/C][C]107.537405910753[/C][C]-0.337405910753148[/C][/ROW]
[ROW][C]6[/C][C]107.5[/C][C]108.040512618647[/C][C]-0.540512618647227[/C][/ROW]
[ROW][C]7[/C][C]108.3[/C][C]108.025596629265[/C][C]0.274403370734589[/C][/ROW]
[ROW][C]8[/C][C]108.7[/C][C]108.769526104198[/C][C]-0.0695261041979336[/C][/ROW]
[ROW][C]9[/C][C]108.8[/C][C]109.225432706862[/C][C]-0.42543270686177[/C][/ROW]
[ROW][C]10[/C][C]109.8[/C][C]109.137039985716[/C][C]0.66296001428394[/C][/ROW]
[ROW][C]11[/C][C]109.5[/C][C]110.268680735336[/C][C]-0.768680735336247[/C][/ROW]
[ROW][C]12[/C][C]109.2[/C][C]109.867525832895[/C][C]-0.667525832895151[/C][/ROW]
[ROW][C]13[/C][C]110.6[/C][C]109.071823631076[/C][C]1.52817636892435[/C][/ROW]
[ROW][C]14[/C][C]110.1[/C][C]110.870262749543[/C][C]-0.770262749542965[/C][/ROW]
[ROW][C]15[/C][C]109.9[/C][C]110.53097203493[/C][C]-0.630972034930153[/C][/ROW]
[ROW][C]16[/C][C]109.7[/C][C]109.849164558501[/C][C]-0.149164558501042[/C][/ROW]
[ROW][C]17[/C][C]109.4[/C][C]109.39908395552[/C][C]0.000916044480220535[/C][/ROW]
[ROW][C]18[/C][C]109.4[/C][C]109.05419116545[/C][C]0.345808834549956[/C][/ROW]
[ROW][C]19[/C][C]109.4[/C][C]109.190457357978[/C][C]0.209542642022356[/C][/ROW]
[ROW][C]20[/C][C]109.5[/C][C]109.377769647156[/C][C]0.122230352843872[/C][/ROW]
[ROW][C]21[/C][C]109.5[/C][C]109.589406680028[/C][C]-0.08940668002802[/C][/ROW]
[ROW][C]22[/C][C]109.9[/C][C]109.591329588228[/C][C]0.308670411771516[/C][/ROW]
[ROW][C]23[/C][C]110[/C][C]110.085589415368[/C][C]-0.0855894153680197[/C][/ROW]
[ROW][C]24[/C][C]110.8[/C][C]110.245574984137[/C][C]0.554425015862932[/C][/ROW]
[ROW][C]25[/C][C]112.4[/C][C]111.23763514004[/C][C]1.16236485996045[/C][/ROW]
[ROW][C]26[/C][C]112.8[/C][C]113.462931153409[/C][C]-0.662931153409204[/C][/ROW]
[ROW][C]27[/C][C]113.7[/C][C]113.954869651227[/C][C]-0.254869651227025[/C][/ROW]
[ROW][C]28[/C][C]114.5[/C][C]114.553525192295[/C][C]-0.053525192295453[/C][/ROW]
[ROW][C]29[/C][C]114.8[/C][C]115.255155108127[/C][C]-0.45515510812676[/C][/ROW]
[ROW][C]30[/C][C]115.6[/C][C]115.359928442566[/C][C]0.240071557433794[/C][/ROW]
[ROW][C]31[/C][C]115.8[/C][C]116.116252497838[/C][C]-0.316252497838036[/C][/ROW]
[ROW][C]32[/C][C]115.8[/C][C]116.264719221424[/C][C]-0.464719221423692[/C][/ROW]
[ROW][C]33[/C][C]116.3[/C][C]115.98602620638[/C][C]0.31397379362042[/C][/ROW]
[ROW][C]34[/C][C]116.3[/C][C]116.468510566971[/C][C]-0.168510566970568[/C][/ROW]
[ROW][C]35[/C][C]116.8[/C][C]116.497496563208[/C][C]0.302503436792264[/C][/ROW]
[ROW][C]36[/C][C]116.7[/C][C]117.065332985522[/C][C]-0.365332985522471[/C][/ROW]
[ROW][C]37[/C][C]116.8[/C][C]116.913439319756[/C][C]-0.113439319755599[/C][/ROW]
[ROW][C]38[/C][C]117[/C][C]116.857996204977[/C][C]0.142003795023157[/C][/ROW]
[ROW][C]39[/C][C]117.2[/C][C]117.079423947223[/C][C]0.120576052777309[/C][/ROW]
[ROW][C]40[/C][C]117.1[/C][C]117.369920732484[/C][C]-0.269920732483826[/C][/ROW]
[ROW][C]41[/C][C]117.3[/C][C]117.200355155647[/C][C]0.0996448443532927[/C][/ROW]
[ROW][C]42[/C][C]117.4[/C][C]117.357652584248[/C][C]0.0423474157524879[/C][/ROW]
[ROW][C]43[/C][C]117.7[/C][C]117.504535482586[/C][C]0.195464517414123[/C][/ROW]
[ROW][C]44[/C][C]117.9[/C][C]117.894248528137[/C][C]0.00575147186279423[/C][/ROW]
[ROW][C]45[/C][C]118.8[/C][C]118.15580961852[/C][C]0.644190381479817[/C][/ROW]
[ROW][C]46[/C][C]119.9[/C][C]119.310880413754[/C][C]0.589119586246341[/C][/ROW]
[ROW][C]47[/C][C]122.4[/C][C]120.837982146489[/C][C]1.56201785351134[/C][/ROW]
[ROW][C]48[/C][C]123.5[/C][C]124.13096601728[/C][C]-0.630966017279945[/C][/ROW]
[ROW][C]49[/C][C]125.6[/C][C]125.456720035675[/C][C]0.143279964324734[/C][/ROW]
[ROW][C]50[/C][C]127.4[/C][C]127.421644189066[/C][C]-0.0216441890664925[/C][/ROW]
[ROW][C]51[/C][C]128.9[/C][C]129.256600450908[/C][C]-0.356600450907933[/C][/ROW]
[ROW][C]52[/C][C]129.5[/C][C]130.609802055667[/C][C]-1.1098020556671[/C][/ROW]
[ROW][C]53[/C][C]130.8[/C][C]130.665191531608[/C][C]0.134808468391924[/C][/ROW]
[ROW][C]54[/C][C]132.7[/C][C]131.681516692837[/C][C]1.01848330716336[/C][/ROW]
[ROW][C]55[/C][C]134[/C][C]134.022929917585[/C][C]-0.0229299175849178[/C][/ROW]
[ROW][C]56[/C][C]132.9[/C][C]135.622896698246[/C][C]-2.72289669824602[/C][/ROW]
[ROW][C]57[/C][C]133.1[/C][C]133.445169346927[/C][C]-0.345169346926582[/C][/ROW]
[ROW][C]58[/C][C]131.7[/C][C]132.683369664812[/C][C]-0.983369664811988[/C][/ROW]
[ROW][C]59[/C][C]128.8[/C][C]130.791946227267[/C][C]-1.99194622726651[/C][/ROW]
[ROW][C]60[/C][C]125.1[/C][C]126.810288104726[/C][C]-1.71028810472632[/C][/ROW]
[ROW][C]61[/C][C]123.9[/C][C]121.833412765034[/C][C]2.06658723496645[/C][/ROW]
[ROW][C]62[/C][C]121.8[/C][C]120.927230771135[/C][C]0.872769228864883[/C][/ROW]
[ROW][C]63[/C][C]119.2[/C][C]119.797398654647[/C][C]-0.597398654646639[/C][/ROW]
[ROW][C]64[/C][C]118.9[/C][C]117.227251101662[/C][C]1.67274889833769[/C][/ROW]
[ROW][C]65[/C][C]119.6[/C][C]117.403817871305[/C][C]2.19618212869477[/C][/ROW]
[ROW][C]66[/C][C]120.2[/C][C]119.474932608659[/C][C]0.725067391341497[/C][/ROW]
[ROW][C]67[/C][C]119.6[/C][C]121.026333233316[/C][C]-1.42633323331643[/C][/ROW]
[ROW][C]68[/C][C]121[/C][C]120.085400378876[/C][C]0.914599621123628[/C][/ROW]
[ROW][C]69[/C][C]120.4[/C][C]121.412347949095[/C][C]-1.01234794909483[/C][/ROW]
[ROW][C]70[/C][C]120.4[/C][C]120.691713189672[/C][C]-0.291713189672151[/C][/ROW]
[ROW][C]71[/C][C]121.4[/C][C]120.269875275021[/C][C]1.1301247249786[/C][/ROW]
[ROW][C]72[/C][C]121.7[/C][C]121.625794504038[/C][C]0.0742054959616922[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77660&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77660&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
3105.5105.8-0.300000000000011
4106.6106.4820259005220.117974099477991
5107.2107.537405910753-0.337405910753148
6107.5108.040512618647-0.540512618647227
7108.3108.0255966292650.274403370734589
8108.7108.769526104198-0.0695261041979336
9108.8109.225432706862-0.42543270686177
10109.8109.1370399857160.66296001428394
11109.5110.268680735336-0.768680735336247
12109.2109.867525832895-0.667525832895151
13110.6109.0718236310761.52817636892435
14110.1110.870262749543-0.770262749542965
15109.9110.53097203493-0.630972034930153
16109.7109.849164558501-0.149164558501042
17109.4109.399083955520.000916044480220535
18109.4109.054191165450.345808834549956
19109.4109.1904573579780.209542642022356
20109.5109.3777696471560.122230352843872
21109.5109.589406680028-0.08940668002802
22109.9109.5913295882280.308670411771516
23110110.085589415368-0.0855894153680197
24110.8110.2455749841370.554425015862932
25112.4111.237635140041.16236485996045
26112.8113.462931153409-0.662931153409204
27113.7113.954869651227-0.254869651227025
28114.5114.553525192295-0.053525192295453
29114.8115.255155108127-0.45515510812676
30115.6115.3599284425660.240071557433794
31115.8116.116252497838-0.316252497838036
32115.8116.264719221424-0.464719221423692
33116.3115.986026206380.31397379362042
34116.3116.468510566971-0.168510566970568
35116.8116.4974965632080.302503436792264
36116.7117.065332985522-0.365332985522471
37116.8116.913439319756-0.113439319755599
38117116.8579962049770.142003795023157
39117.2117.0794239472230.120576052777309
40117.1117.369920732484-0.269920732483826
41117.3117.2003551556470.0996448443532927
42117.4117.3576525842480.0423474157524879
43117.7117.5045354825860.195464517414123
44117.9117.8942485281370.00575147186279423
45118.8118.155809618520.644190381479817
46119.9119.3108804137540.589119586246341
47122.4120.8379821464891.56201785351134
48123.5124.13096601728-0.630966017279945
49125.6125.4567200356750.143279964324734
50127.4127.421644189066-0.0216441890664925
51128.9129.256600450908-0.356600450907933
52129.5130.609802055667-1.1098020556671
53130.8130.6651915316080.134808468391924
54132.7131.6815166928371.01848330716336
55134134.022929917585-0.0229299175849178
56132.9135.622896698246-2.72289669824602
57133.1133.445169346927-0.345169346926582
58131.7132.683369664812-0.983369664811988
59128.8130.791946227267-1.99194622726651
60125.1126.810288104726-1.71028810472632
61123.9121.8334127650342.06658723496645
62121.8120.9272307711350.872769228864883
63119.2119.797398654647-0.597398654646639
64118.9117.2272511016621.67274889833769
65119.6117.4038178713052.19618212869477
66120.2119.4749326086590.725067391341497
67119.6121.026333233316-1.42633323331643
68121120.0854003788760.914599621123628
69120.4121.412347949095-1.01234794909483
70120.4120.691713189672-0.291713189672151
71121.4120.2698752750211.1301247249786
72121.7121.6257945040380.0742054959616922







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73122.29782887719120.639835353955123.955822400425
74122.918169958091120.074753507716125.761586408466
75123.538511038991119.056191892455128.020830185528
76124.158852119892117.721812172827130.595892066956
77124.779193200792116.131306207431133.427080194153
78125.399534281693114.317538940848136.481529622538
79126.019875362593112.302093675039139.737657050148
80126.640216443494110.100726493009143.179706393979
81127.260557524394107.725710757335146.795404291453
82127.880898605295105.187020512473150.574776698116
83128.501239686195102.493003314733154.509476057657
84129.12158076709699.650797874676158.592363659515

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 122.29782887719 & 120.639835353955 & 123.955822400425 \tabularnewline
74 & 122.918169958091 & 120.074753507716 & 125.761586408466 \tabularnewline
75 & 123.538511038991 & 119.056191892455 & 128.020830185528 \tabularnewline
76 & 124.158852119892 & 117.721812172827 & 130.595892066956 \tabularnewline
77 & 124.779193200792 & 116.131306207431 & 133.427080194153 \tabularnewline
78 & 125.399534281693 & 114.317538940848 & 136.481529622538 \tabularnewline
79 & 126.019875362593 & 112.302093675039 & 139.737657050148 \tabularnewline
80 & 126.640216443494 & 110.100726493009 & 143.179706393979 \tabularnewline
81 & 127.260557524394 & 107.725710757335 & 146.795404291453 \tabularnewline
82 & 127.880898605295 & 105.187020512473 & 150.574776698116 \tabularnewline
83 & 128.501239686195 & 102.493003314733 & 154.509476057657 \tabularnewline
84 & 129.121580767096 & 99.650797874676 & 158.592363659515 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77660&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]122.29782887719[/C][C]120.639835353955[/C][C]123.955822400425[/C][/ROW]
[ROW][C]74[/C][C]122.918169958091[/C][C]120.074753507716[/C][C]125.761586408466[/C][/ROW]
[ROW][C]75[/C][C]123.538511038991[/C][C]119.056191892455[/C][C]128.020830185528[/C][/ROW]
[ROW][C]76[/C][C]124.158852119892[/C][C]117.721812172827[/C][C]130.595892066956[/C][/ROW]
[ROW][C]77[/C][C]124.779193200792[/C][C]116.131306207431[/C][C]133.427080194153[/C][/ROW]
[ROW][C]78[/C][C]125.399534281693[/C][C]114.317538940848[/C][C]136.481529622538[/C][/ROW]
[ROW][C]79[/C][C]126.019875362593[/C][C]112.302093675039[/C][C]139.737657050148[/C][/ROW]
[ROW][C]80[/C][C]126.640216443494[/C][C]110.100726493009[/C][C]143.179706393979[/C][/ROW]
[ROW][C]81[/C][C]127.260557524394[/C][C]107.725710757335[/C][C]146.795404291453[/C][/ROW]
[ROW][C]82[/C][C]127.880898605295[/C][C]105.187020512473[/C][C]150.574776698116[/C][/ROW]
[ROW][C]83[/C][C]128.501239686195[/C][C]102.493003314733[/C][C]154.509476057657[/C][/ROW]
[ROW][C]84[/C][C]129.121580767096[/C][C]99.650797874676[/C][C]158.592363659515[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77660&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77660&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
73122.29782887719120.639835353955123.955822400425
74122.918169958091120.074753507716125.761586408466
75123.538511038991119.056191892455128.020830185528
76124.158852119892117.721812172827130.595892066956
77124.779193200792116.131306207431133.427080194153
78125.399534281693114.317538940848136.481529622538
79126.019875362593112.302093675039139.737657050148
80126.640216443494110.100726493009143.179706393979
81127.260557524394107.725710757335146.795404291453
82127.880898605295105.187020512473150.574776698116
83128.501239686195102.493003314733154.509476057657
84129.12158076709699.650797874676158.592363659515



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