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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 10 Jan 2013 12:04:27 -0500
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/Jan/10/t1357837508ka3lm88sfzi2t88.htm/, Retrieved Mon, 29 Apr 2024 22:52:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=205143, Retrieved Mon, 29 Apr 2024 22:52:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact138
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Opgave 10 oef 2 m...] [2013-01-10 17:04:27] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
101.81
101.72
101.78
102.04
102.36
102.56
102.69
102.77
102.85
102.9
102.72
102.79
102.9
102.91
103.29
103.35
102.97
103.05
103.18
103.21
103.32
103.31
103.6
103.68
103.77
103.82
103.86
103.9
103.63
103.65
103.7
103.77
103.94
104.03
104.03
104.29
104.35
104.67
104.73
104.86
104.05
104.15
104.27
104.33
104.41
104.4
104.41
104.6
104.61
104.65
104.55
104.51
104.74
104.89
104.91
104.93
104.95
104.97
105.16
105.29
105.35
105.36
105.45
105.3
105.73
105.86
105.85
105.95
105.97
106.15
105.37
105.39




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205143&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205143&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205143&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.740373466602422
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.740373466602422 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205143&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]0.740373466602422[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205143&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205143&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
alpha0.740373466602422
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13102.9102.4448701623930.45512983760743
14102.91102.81442702620.0955729738000883
15103.29103.2885724933420.00142750665771985
16103.35103.374356249935-0.0243562499350531
17102.97102.983861704607-0.0138617046067395
18103.05103.0411921255920.00880787440763697
19103.18103.483302926548-0.303302926547971
20103.21103.304916859164-0.0949168591639022
21103.32103.2632304861720.0567695138280726
22103.31103.2987253304480.0112746695516108
23103.6103.1073969658140.49260303418562
24103.68103.5577585446260.122241455373882
25103.77103.898632981152-0.128632981151924
26103.82103.741548090620.0784519093795666
27103.86104.181319293605-0.321319293604702
28103.9104.02155927111-0.121559271110343
29103.63103.559397372990.0706026270101319
30103.65103.685224680268-0.0352246802675609
31103.7104.015263248144-0.315263248144277
32103.77103.882334280978-0.112334280978118
33103.94103.8671655438370.0728344561634344
34104.03103.9022786146190.127721385380724
35104.03103.920771803070.109228196929564
36104.29103.9908310470140.299168952986193
37104.35104.398169550859-0.0481695508594413
38104.67104.3540147292470.315985270752662
39104.73104.867266975668-0.137266975668027
40104.86104.89620738305-0.0362073830503533
41104.05104.543540483666-0.493540483665939
42104.15104.224133140537-0.0741331405368868
43104.27104.45358682585-0.183586825849886
44104.33104.471356297581-0.141356297580671
45104.41104.483079362608-0.0730793626077855
46104.4104.424071145224-0.0240711452238713
47104.41104.3248434156810.0851565843191224
48104.6104.4261501942530.173849805747125
49104.61104.650610327421-0.0406103274207226
50104.65104.706476466661-0.0564764666606266
51104.55104.826251936341-0.276251936341438
52104.51104.778428347848-0.268428347848044
53104.74104.1359991633260.604000836674274
54104.89104.7385413239580.151458676042083
55104.91105.107846676982-0.197846676981584
56104.93105.126670298978-0.196670298978049
57104.95105.115610404951-0.165610404951295
58104.97105.000518190197-0.0305181901970428
59105.16104.9242289956820.235771004318082
60105.29105.1600174958450.129982504154967
61105.35105.2961834402660.0538165597336189
62105.36105.417977642561-0.0579776425613261
63105.45105.479739988245-0.0297399882447422
64105.3105.617169805603-0.317169805603342
65105.73105.1621591791040.56784082089635
66105.86105.6202069678340.23979303216619
67105.85105.965061667634-0.115061667634222
68105.95106.046374729209-0.0963747292089465
69105.97106.118392922129-0.148392922129148
70106.15106.0509301402190.0990698597808262
71105.37106.13911230456-0.769112304559584
72105.39105.60330786866-0.213307868660081

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 102.9 & 102.444870162393 & 0.45512983760743 \tabularnewline
14 & 102.91 & 102.8144270262 & 0.0955729738000883 \tabularnewline
15 & 103.29 & 103.288572493342 & 0.00142750665771985 \tabularnewline
16 & 103.35 & 103.374356249935 & -0.0243562499350531 \tabularnewline
17 & 102.97 & 102.983861704607 & -0.0138617046067395 \tabularnewline
18 & 103.05 & 103.041192125592 & 0.00880787440763697 \tabularnewline
19 & 103.18 & 103.483302926548 & -0.303302926547971 \tabularnewline
20 & 103.21 & 103.304916859164 & -0.0949168591639022 \tabularnewline
21 & 103.32 & 103.263230486172 & 0.0567695138280726 \tabularnewline
22 & 103.31 & 103.298725330448 & 0.0112746695516108 \tabularnewline
23 & 103.6 & 103.107396965814 & 0.49260303418562 \tabularnewline
24 & 103.68 & 103.557758544626 & 0.122241455373882 \tabularnewline
25 & 103.77 & 103.898632981152 & -0.128632981151924 \tabularnewline
26 & 103.82 & 103.74154809062 & 0.0784519093795666 \tabularnewline
27 & 103.86 & 104.181319293605 & -0.321319293604702 \tabularnewline
28 & 103.9 & 104.02155927111 & -0.121559271110343 \tabularnewline
29 & 103.63 & 103.55939737299 & 0.0706026270101319 \tabularnewline
30 & 103.65 & 103.685224680268 & -0.0352246802675609 \tabularnewline
31 & 103.7 & 104.015263248144 & -0.315263248144277 \tabularnewline
32 & 103.77 & 103.882334280978 & -0.112334280978118 \tabularnewline
33 & 103.94 & 103.867165543837 & 0.0728344561634344 \tabularnewline
34 & 104.03 & 103.902278614619 & 0.127721385380724 \tabularnewline
35 & 104.03 & 103.92077180307 & 0.109228196929564 \tabularnewline
36 & 104.29 & 103.990831047014 & 0.299168952986193 \tabularnewline
37 & 104.35 & 104.398169550859 & -0.0481695508594413 \tabularnewline
38 & 104.67 & 104.354014729247 & 0.315985270752662 \tabularnewline
39 & 104.73 & 104.867266975668 & -0.137266975668027 \tabularnewline
40 & 104.86 & 104.89620738305 & -0.0362073830503533 \tabularnewline
41 & 104.05 & 104.543540483666 & -0.493540483665939 \tabularnewline
42 & 104.15 & 104.224133140537 & -0.0741331405368868 \tabularnewline
43 & 104.27 & 104.45358682585 & -0.183586825849886 \tabularnewline
44 & 104.33 & 104.471356297581 & -0.141356297580671 \tabularnewline
45 & 104.41 & 104.483079362608 & -0.0730793626077855 \tabularnewline
46 & 104.4 & 104.424071145224 & -0.0240711452238713 \tabularnewline
47 & 104.41 & 104.324843415681 & 0.0851565843191224 \tabularnewline
48 & 104.6 & 104.426150194253 & 0.173849805747125 \tabularnewline
49 & 104.61 & 104.650610327421 & -0.0406103274207226 \tabularnewline
50 & 104.65 & 104.706476466661 & -0.0564764666606266 \tabularnewline
51 & 104.55 & 104.826251936341 & -0.276251936341438 \tabularnewline
52 & 104.51 & 104.778428347848 & -0.268428347848044 \tabularnewline
53 & 104.74 & 104.135999163326 & 0.604000836674274 \tabularnewline
54 & 104.89 & 104.738541323958 & 0.151458676042083 \tabularnewline
55 & 104.91 & 105.107846676982 & -0.197846676981584 \tabularnewline
56 & 104.93 & 105.126670298978 & -0.196670298978049 \tabularnewline
57 & 104.95 & 105.115610404951 & -0.165610404951295 \tabularnewline
58 & 104.97 & 105.000518190197 & -0.0305181901970428 \tabularnewline
59 & 105.16 & 104.924228995682 & 0.235771004318082 \tabularnewline
60 & 105.29 & 105.160017495845 & 0.129982504154967 \tabularnewline
61 & 105.35 & 105.296183440266 & 0.0538165597336189 \tabularnewline
62 & 105.36 & 105.417977642561 & -0.0579776425613261 \tabularnewline
63 & 105.45 & 105.479739988245 & -0.0297399882447422 \tabularnewline
64 & 105.3 & 105.617169805603 & -0.317169805603342 \tabularnewline
65 & 105.73 & 105.162159179104 & 0.56784082089635 \tabularnewline
66 & 105.86 & 105.620206967834 & 0.23979303216619 \tabularnewline
67 & 105.85 & 105.965061667634 & -0.115061667634222 \tabularnewline
68 & 105.95 & 106.046374729209 & -0.0963747292089465 \tabularnewline
69 & 105.97 & 106.118392922129 & -0.148392922129148 \tabularnewline
70 & 106.15 & 106.050930140219 & 0.0990698597808262 \tabularnewline
71 & 105.37 & 106.13911230456 & -0.769112304559584 \tabularnewline
72 & 105.39 & 105.60330786866 & -0.213307868660081 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205143&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]102.9[/C][C]102.444870162393[/C][C]0.45512983760743[/C][/ROW]
[ROW][C]14[/C][C]102.91[/C][C]102.8144270262[/C][C]0.0955729738000883[/C][/ROW]
[ROW][C]15[/C][C]103.29[/C][C]103.288572493342[/C][C]0.00142750665771985[/C][/ROW]
[ROW][C]16[/C][C]103.35[/C][C]103.374356249935[/C][C]-0.0243562499350531[/C][/ROW]
[ROW][C]17[/C][C]102.97[/C][C]102.983861704607[/C][C]-0.0138617046067395[/C][/ROW]
[ROW][C]18[/C][C]103.05[/C][C]103.041192125592[/C][C]0.00880787440763697[/C][/ROW]
[ROW][C]19[/C][C]103.18[/C][C]103.483302926548[/C][C]-0.303302926547971[/C][/ROW]
[ROW][C]20[/C][C]103.21[/C][C]103.304916859164[/C][C]-0.0949168591639022[/C][/ROW]
[ROW][C]21[/C][C]103.32[/C][C]103.263230486172[/C][C]0.0567695138280726[/C][/ROW]
[ROW][C]22[/C][C]103.31[/C][C]103.298725330448[/C][C]0.0112746695516108[/C][/ROW]
[ROW][C]23[/C][C]103.6[/C][C]103.107396965814[/C][C]0.49260303418562[/C][/ROW]
[ROW][C]24[/C][C]103.68[/C][C]103.557758544626[/C][C]0.122241455373882[/C][/ROW]
[ROW][C]25[/C][C]103.77[/C][C]103.898632981152[/C][C]-0.128632981151924[/C][/ROW]
[ROW][C]26[/C][C]103.82[/C][C]103.74154809062[/C][C]0.0784519093795666[/C][/ROW]
[ROW][C]27[/C][C]103.86[/C][C]104.181319293605[/C][C]-0.321319293604702[/C][/ROW]
[ROW][C]28[/C][C]103.9[/C][C]104.02155927111[/C][C]-0.121559271110343[/C][/ROW]
[ROW][C]29[/C][C]103.63[/C][C]103.55939737299[/C][C]0.0706026270101319[/C][/ROW]
[ROW][C]30[/C][C]103.65[/C][C]103.685224680268[/C][C]-0.0352246802675609[/C][/ROW]
[ROW][C]31[/C][C]103.7[/C][C]104.015263248144[/C][C]-0.315263248144277[/C][/ROW]
[ROW][C]32[/C][C]103.77[/C][C]103.882334280978[/C][C]-0.112334280978118[/C][/ROW]
[ROW][C]33[/C][C]103.94[/C][C]103.867165543837[/C][C]0.0728344561634344[/C][/ROW]
[ROW][C]34[/C][C]104.03[/C][C]103.902278614619[/C][C]0.127721385380724[/C][/ROW]
[ROW][C]35[/C][C]104.03[/C][C]103.92077180307[/C][C]0.109228196929564[/C][/ROW]
[ROW][C]36[/C][C]104.29[/C][C]103.990831047014[/C][C]0.299168952986193[/C][/ROW]
[ROW][C]37[/C][C]104.35[/C][C]104.398169550859[/C][C]-0.0481695508594413[/C][/ROW]
[ROW][C]38[/C][C]104.67[/C][C]104.354014729247[/C][C]0.315985270752662[/C][/ROW]
[ROW][C]39[/C][C]104.73[/C][C]104.867266975668[/C][C]-0.137266975668027[/C][/ROW]
[ROW][C]40[/C][C]104.86[/C][C]104.89620738305[/C][C]-0.0362073830503533[/C][/ROW]
[ROW][C]41[/C][C]104.05[/C][C]104.543540483666[/C][C]-0.493540483665939[/C][/ROW]
[ROW][C]42[/C][C]104.15[/C][C]104.224133140537[/C][C]-0.0741331405368868[/C][/ROW]
[ROW][C]43[/C][C]104.27[/C][C]104.45358682585[/C][C]-0.183586825849886[/C][/ROW]
[ROW][C]44[/C][C]104.33[/C][C]104.471356297581[/C][C]-0.141356297580671[/C][/ROW]
[ROW][C]45[/C][C]104.41[/C][C]104.483079362608[/C][C]-0.0730793626077855[/C][/ROW]
[ROW][C]46[/C][C]104.4[/C][C]104.424071145224[/C][C]-0.0240711452238713[/C][/ROW]
[ROW][C]47[/C][C]104.41[/C][C]104.324843415681[/C][C]0.0851565843191224[/C][/ROW]
[ROW][C]48[/C][C]104.6[/C][C]104.426150194253[/C][C]0.173849805747125[/C][/ROW]
[ROW][C]49[/C][C]104.61[/C][C]104.650610327421[/C][C]-0.0406103274207226[/C][/ROW]
[ROW][C]50[/C][C]104.65[/C][C]104.706476466661[/C][C]-0.0564764666606266[/C][/ROW]
[ROW][C]51[/C][C]104.55[/C][C]104.826251936341[/C][C]-0.276251936341438[/C][/ROW]
[ROW][C]52[/C][C]104.51[/C][C]104.778428347848[/C][C]-0.268428347848044[/C][/ROW]
[ROW][C]53[/C][C]104.74[/C][C]104.135999163326[/C][C]0.604000836674274[/C][/ROW]
[ROW][C]54[/C][C]104.89[/C][C]104.738541323958[/C][C]0.151458676042083[/C][/ROW]
[ROW][C]55[/C][C]104.91[/C][C]105.107846676982[/C][C]-0.197846676981584[/C][/ROW]
[ROW][C]56[/C][C]104.93[/C][C]105.126670298978[/C][C]-0.196670298978049[/C][/ROW]
[ROW][C]57[/C][C]104.95[/C][C]105.115610404951[/C][C]-0.165610404951295[/C][/ROW]
[ROW][C]58[/C][C]104.97[/C][C]105.000518190197[/C][C]-0.0305181901970428[/C][/ROW]
[ROW][C]59[/C][C]105.16[/C][C]104.924228995682[/C][C]0.235771004318082[/C][/ROW]
[ROW][C]60[/C][C]105.29[/C][C]105.160017495845[/C][C]0.129982504154967[/C][/ROW]
[ROW][C]61[/C][C]105.35[/C][C]105.296183440266[/C][C]0.0538165597336189[/C][/ROW]
[ROW][C]62[/C][C]105.36[/C][C]105.417977642561[/C][C]-0.0579776425613261[/C][/ROW]
[ROW][C]63[/C][C]105.45[/C][C]105.479739988245[/C][C]-0.0297399882447422[/C][/ROW]
[ROW][C]64[/C][C]105.3[/C][C]105.617169805603[/C][C]-0.317169805603342[/C][/ROW]
[ROW][C]65[/C][C]105.73[/C][C]105.162159179104[/C][C]0.56784082089635[/C][/ROW]
[ROW][C]66[/C][C]105.86[/C][C]105.620206967834[/C][C]0.23979303216619[/C][/ROW]
[ROW][C]67[/C][C]105.85[/C][C]105.965061667634[/C][C]-0.115061667634222[/C][/ROW]
[ROW][C]68[/C][C]105.95[/C][C]106.046374729209[/C][C]-0.0963747292089465[/C][/ROW]
[ROW][C]69[/C][C]105.97[/C][C]106.118392922129[/C][C]-0.148392922129148[/C][/ROW]
[ROW][C]70[/C][C]106.15[/C][C]106.050930140219[/C][C]0.0990698597808262[/C][/ROW]
[ROW][C]71[/C][C]105.37[/C][C]106.13911230456[/C][C]-0.769112304559584[/C][/ROW]
[ROW][C]72[/C][C]105.39[/C][C]105.60330786866[/C][C]-0.213307868660081[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205143&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205143&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
13102.9102.4448701623930.45512983760743
14102.91102.81442702620.0955729738000883
15103.29103.2885724933420.00142750665771985
16103.35103.374356249935-0.0243562499350531
17102.97102.983861704607-0.0138617046067395
18103.05103.0411921255920.00880787440763697
19103.18103.483302926548-0.303302926547971
20103.21103.304916859164-0.0949168591639022
21103.32103.2632304861720.0567695138280726
22103.31103.2987253304480.0112746695516108
23103.6103.1073969658140.49260303418562
24103.68103.5577585446260.122241455373882
25103.77103.898632981152-0.128632981151924
26103.82103.741548090620.0784519093795666
27103.86104.181319293605-0.321319293604702
28103.9104.02155927111-0.121559271110343
29103.63103.559397372990.0706026270101319
30103.65103.685224680268-0.0352246802675609
31103.7104.015263248144-0.315263248144277
32103.77103.882334280978-0.112334280978118
33103.94103.8671655438370.0728344561634344
34104.03103.9022786146190.127721385380724
35104.03103.920771803070.109228196929564
36104.29103.9908310470140.299168952986193
37104.35104.398169550859-0.0481695508594413
38104.67104.3540147292470.315985270752662
39104.73104.867266975668-0.137266975668027
40104.86104.89620738305-0.0362073830503533
41104.05104.543540483666-0.493540483665939
42104.15104.224133140537-0.0741331405368868
43104.27104.45358682585-0.183586825849886
44104.33104.471356297581-0.141356297580671
45104.41104.483079362608-0.0730793626077855
46104.4104.424071145224-0.0240711452238713
47104.41104.3248434156810.0851565843191224
48104.6104.4261501942530.173849805747125
49104.61104.650610327421-0.0406103274207226
50104.65104.706476466661-0.0564764666606266
51104.55104.826251936341-0.276251936341438
52104.51104.778428347848-0.268428347848044
53104.74104.1359991633260.604000836674274
54104.89104.7385413239580.151458676042083
55104.91105.107846676982-0.197846676981584
56104.93105.126670298978-0.196670298978049
57104.95105.115610404951-0.165610404951295
58104.97105.000518190197-0.0305181901970428
59105.16104.9242289956820.235771004318082
60105.29105.1600174958450.129982504154967
61105.35105.2961834402660.0538165597336189
62105.36105.417977642561-0.0579776425613261
63105.45105.479739988245-0.0297399882447422
64105.3105.617169805603-0.317169805603342
65105.73105.1621591791040.56784082089635
66105.86105.6202069678340.23979303216619
67105.85105.965061667634-0.115061667634222
68105.95106.046374729209-0.0963747292089465
69105.97106.118392922129-0.148392922129148
70106.15106.0509301402190.0990698597808262
71105.37106.13911230456-0.769112304559584
72105.39105.60330786866-0.213307868660081







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73105.465469960074105.001130368587105.929809551562
74105.518379712479104.940642485437106.09611693952
75105.630472941295104.958018073359106.30292780923
76105.715153371868104.959812372247106.47049437149
77105.723945676186104.894332715493106.553558636879
78105.676311043747104.77896559985106.573656487645
79105.751451542469104.79040924488106.712493840059
80105.922685593521104.901163220003106.944207967039
81106.052494205144104.974107262969107.130881147319
82106.159162928329105.026901604388107.29142425227
83105.947492652875104.76676392827107.12822137748
84106.12597575925698.4753818076871113.776569710825

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 105.465469960074 & 105.001130368587 & 105.929809551562 \tabularnewline
74 & 105.518379712479 & 104.940642485437 & 106.09611693952 \tabularnewline
75 & 105.630472941295 & 104.958018073359 & 106.30292780923 \tabularnewline
76 & 105.715153371868 & 104.959812372247 & 106.47049437149 \tabularnewline
77 & 105.723945676186 & 104.894332715493 & 106.553558636879 \tabularnewline
78 & 105.676311043747 & 104.77896559985 & 106.573656487645 \tabularnewline
79 & 105.751451542469 & 104.79040924488 & 106.712493840059 \tabularnewline
80 & 105.922685593521 & 104.901163220003 & 106.944207967039 \tabularnewline
81 & 106.052494205144 & 104.974107262969 & 107.130881147319 \tabularnewline
82 & 106.159162928329 & 105.026901604388 & 107.29142425227 \tabularnewline
83 & 105.947492652875 & 104.76676392827 & 107.12822137748 \tabularnewline
84 & 106.125975759256 & 98.4753818076871 & 113.776569710825 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205143&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]105.465469960074[/C][C]105.001130368587[/C][C]105.929809551562[/C][/ROW]
[ROW][C]74[/C][C]105.518379712479[/C][C]104.940642485437[/C][C]106.09611693952[/C][/ROW]
[ROW][C]75[/C][C]105.630472941295[/C][C]104.958018073359[/C][C]106.30292780923[/C][/ROW]
[ROW][C]76[/C][C]105.715153371868[/C][C]104.959812372247[/C][C]106.47049437149[/C][/ROW]
[ROW][C]77[/C][C]105.723945676186[/C][C]104.894332715493[/C][C]106.553558636879[/C][/ROW]
[ROW][C]78[/C][C]105.676311043747[/C][C]104.77896559985[/C][C]106.573656487645[/C][/ROW]
[ROW][C]79[/C][C]105.751451542469[/C][C]104.79040924488[/C][C]106.712493840059[/C][/ROW]
[ROW][C]80[/C][C]105.922685593521[/C][C]104.901163220003[/C][C]106.944207967039[/C][/ROW]
[ROW][C]81[/C][C]106.052494205144[/C][C]104.974107262969[/C][C]107.130881147319[/C][/ROW]
[ROW][C]82[/C][C]106.159162928329[/C][C]105.026901604388[/C][C]107.29142425227[/C][/ROW]
[ROW][C]83[/C][C]105.947492652875[/C][C]104.76676392827[/C][C]107.12822137748[/C][/ROW]
[ROW][C]84[/C][C]106.125975759256[/C][C]98.4753818076871[/C][C]113.776569710825[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205143&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205143&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
73105.465469960074105.001130368587105.929809551562
74105.518379712479104.940642485437106.09611693952
75105.630472941295104.958018073359106.30292780923
76105.715153371868104.959812372247106.47049437149
77105.723945676186104.894332715493106.553558636879
78105.676311043747104.77896559985106.573656487645
79105.751451542469104.79040924488106.712493840059
80105.922685593521104.901163220003106.944207967039
81106.052494205144104.974107262969107.130881147319
82106.159162928329105.026901604388107.29142425227
83105.947492652875104.76676392827107.12822137748
84106.12597575925698.4753818076871113.776569710825



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