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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 04 Dec 2009 08:34:14 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/04/t1259940896757ftczxhxqw1lo.htm/, Retrieved Sun, 28 Apr 2024 11:27:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=63772, Retrieved Sun, 28 Apr 2024 11:27:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact131
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [] [2009-11-27 15:04:36] [b98453cac15ba1066b407e146608df68]
-   PD      [Exponential Smoothing] [] [2009-12-04 15:34:14] [612b7913d2a3b4fa79d126829bd148db] [Current]
-   P         [Exponential Smoothing] [] [2009-12-29 11:09:00] [eea7474c6df699240a34279975905c82]
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Dataseries X:
8
8,1
7,7
7,5
7,6
7,8
7,8
7,8
7,5
7,5
7,1
7,5
7,5
7,6
7,7
7,7
7,9
8,1
8,2
8,2
8,2
7,9
7,3
6,9
6,6
6,7
6,9
7
7,1
7,2
7,1
6,9
7
6,8
6,4
6,7
6,6
6,4
6,3
6,2
6,5
6,8
6,8
6,4
6,1
5,8
6,1
7,2
7,3
6,9
6,1
5,8
6,2
7,1
7,7
7,9
7,7
7,4
7,5
8
8,1




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63772&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63772&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63772&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

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







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.92852853543084
beta1
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.92852853543084 \tabularnewline
beta & 1 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63772&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]0.92852853543084[/C][/ROW]
[ROW][C]beta[/C][C]1[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63772&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63772&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
alpha0.92852853543084
beta1
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
137.57.433256880142390.0667431198576134
147.67.64604691568444-0.0460469156844354
157.77.699037092973510.000962907026494264
167.77.696568095672210.00343190432778773
177.97.92064617861872-0.0206461786187218
188.18.14660566968208-0.04660566968208
198.27.945480715867160.254519284132838
208.28.44899290291657-0.248992902916571
218.27.91488304083960.285116959160407
227.98.42651571563598-0.526515715635977
237.37.273731747191670.0262682528083253
246.97.47809936117529-0.578099361175288
256.66.178935999457080.421064000542922
266.76.269445703611160.430554296388845
276.96.76794437845950.132055621540500
2877.01977935011743-0.0197793501174273
297.17.31337398152559-0.213373981525590
307.27.26470807925219-0.0647080792521857
317.16.993331653084930.106668346915072
326.97.0959413772399-0.1959413772399
3376.517254682403610.482745317596389
346.87.1734434987627-0.373443498762699
356.46.40044617609966-0.000446176099661244
366.76.615803616372850.0841963836271464
376.66.74078965616378-0.140789656163782
386.46.52783593537739-0.127835935377389
396.36.182772784006920.117227215993077
406.26.100599540295920.0994004597040838
416.56.266658970195140.233341029804856
426.86.83851412014025-0.0385141201402517
436.86.84293848398286-0.042938483982863
446.46.88007070462229-0.480070704622288
456.15.930077594197890.169922405802114
465.85.798727860024590.00127213997541276
476.15.349207418109440.75079258189056
487.26.878649835074750.321350164925254
497.38.06153427409026-0.76153427409026
506.97.55622209466666-0.656222094666664
516.16.52672261166944-0.426722611669438
525.85.224569960801170.575430039198834
536.25.553075990087050.646924009912953
547.16.587847946441360.512152053558637
557.77.71001599648092-0.0100159964809237
567.98.3743139653839-0.47431396538390
577.78.077476478256-0.377476478256004
587.47.51232643982913-0.112326439829127
597.56.95343464941560.546565350584396
6088.12597042012929-0.125970420129287
618.18.201469492428-0.101469492427995

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 7.5 & 7.43325688014239 & 0.0667431198576134 \tabularnewline
14 & 7.6 & 7.64604691568444 & -0.0460469156844354 \tabularnewline
15 & 7.7 & 7.69903709297351 & 0.000962907026494264 \tabularnewline
16 & 7.7 & 7.69656809567221 & 0.00343190432778773 \tabularnewline
17 & 7.9 & 7.92064617861872 & -0.0206461786187218 \tabularnewline
18 & 8.1 & 8.14660566968208 & -0.04660566968208 \tabularnewline
19 & 8.2 & 7.94548071586716 & 0.254519284132838 \tabularnewline
20 & 8.2 & 8.44899290291657 & -0.248992902916571 \tabularnewline
21 & 8.2 & 7.9148830408396 & 0.285116959160407 \tabularnewline
22 & 7.9 & 8.42651571563598 & -0.526515715635977 \tabularnewline
23 & 7.3 & 7.27373174719167 & 0.0262682528083253 \tabularnewline
24 & 6.9 & 7.47809936117529 & -0.578099361175288 \tabularnewline
25 & 6.6 & 6.17893599945708 & 0.421064000542922 \tabularnewline
26 & 6.7 & 6.26944570361116 & 0.430554296388845 \tabularnewline
27 & 6.9 & 6.7679443784595 & 0.132055621540500 \tabularnewline
28 & 7 & 7.01977935011743 & -0.0197793501174273 \tabularnewline
29 & 7.1 & 7.31337398152559 & -0.213373981525590 \tabularnewline
30 & 7.2 & 7.26470807925219 & -0.0647080792521857 \tabularnewline
31 & 7.1 & 6.99333165308493 & 0.106668346915072 \tabularnewline
32 & 6.9 & 7.0959413772399 & -0.1959413772399 \tabularnewline
33 & 7 & 6.51725468240361 & 0.482745317596389 \tabularnewline
34 & 6.8 & 7.1734434987627 & -0.373443498762699 \tabularnewline
35 & 6.4 & 6.40044617609966 & -0.000446176099661244 \tabularnewline
36 & 6.7 & 6.61580361637285 & 0.0841963836271464 \tabularnewline
37 & 6.6 & 6.74078965616378 & -0.140789656163782 \tabularnewline
38 & 6.4 & 6.52783593537739 & -0.127835935377389 \tabularnewline
39 & 6.3 & 6.18277278400692 & 0.117227215993077 \tabularnewline
40 & 6.2 & 6.10059954029592 & 0.0994004597040838 \tabularnewline
41 & 6.5 & 6.26665897019514 & 0.233341029804856 \tabularnewline
42 & 6.8 & 6.83851412014025 & -0.0385141201402517 \tabularnewline
43 & 6.8 & 6.84293848398286 & -0.042938483982863 \tabularnewline
44 & 6.4 & 6.88007070462229 & -0.480070704622288 \tabularnewline
45 & 6.1 & 5.93007759419789 & 0.169922405802114 \tabularnewline
46 & 5.8 & 5.79872786002459 & 0.00127213997541276 \tabularnewline
47 & 6.1 & 5.34920741810944 & 0.75079258189056 \tabularnewline
48 & 7.2 & 6.87864983507475 & 0.321350164925254 \tabularnewline
49 & 7.3 & 8.06153427409026 & -0.76153427409026 \tabularnewline
50 & 6.9 & 7.55622209466666 & -0.656222094666664 \tabularnewline
51 & 6.1 & 6.52672261166944 & -0.426722611669438 \tabularnewline
52 & 5.8 & 5.22456996080117 & 0.575430039198834 \tabularnewline
53 & 6.2 & 5.55307599008705 & 0.646924009912953 \tabularnewline
54 & 7.1 & 6.58784794644136 & 0.512152053558637 \tabularnewline
55 & 7.7 & 7.71001599648092 & -0.0100159964809237 \tabularnewline
56 & 7.9 & 8.3743139653839 & -0.47431396538390 \tabularnewline
57 & 7.7 & 8.077476478256 & -0.377476478256004 \tabularnewline
58 & 7.4 & 7.51232643982913 & -0.112326439829127 \tabularnewline
59 & 7.5 & 6.9534346494156 & 0.546565350584396 \tabularnewline
60 & 8 & 8.12597042012929 & -0.125970420129287 \tabularnewline
61 & 8.1 & 8.201469492428 & -0.101469492427995 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63772&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]7.5[/C][C]7.43325688014239[/C][C]0.0667431198576134[/C][/ROW]
[ROW][C]14[/C][C]7.6[/C][C]7.64604691568444[/C][C]-0.0460469156844354[/C][/ROW]
[ROW][C]15[/C][C]7.7[/C][C]7.69903709297351[/C][C]0.000962907026494264[/C][/ROW]
[ROW][C]16[/C][C]7.7[/C][C]7.69656809567221[/C][C]0.00343190432778773[/C][/ROW]
[ROW][C]17[/C][C]7.9[/C][C]7.92064617861872[/C][C]-0.0206461786187218[/C][/ROW]
[ROW][C]18[/C][C]8.1[/C][C]8.14660566968208[/C][C]-0.04660566968208[/C][/ROW]
[ROW][C]19[/C][C]8.2[/C][C]7.94548071586716[/C][C]0.254519284132838[/C][/ROW]
[ROW][C]20[/C][C]8.2[/C][C]8.44899290291657[/C][C]-0.248992902916571[/C][/ROW]
[ROW][C]21[/C][C]8.2[/C][C]7.9148830408396[/C][C]0.285116959160407[/C][/ROW]
[ROW][C]22[/C][C]7.9[/C][C]8.42651571563598[/C][C]-0.526515715635977[/C][/ROW]
[ROW][C]23[/C][C]7.3[/C][C]7.27373174719167[/C][C]0.0262682528083253[/C][/ROW]
[ROW][C]24[/C][C]6.9[/C][C]7.47809936117529[/C][C]-0.578099361175288[/C][/ROW]
[ROW][C]25[/C][C]6.6[/C][C]6.17893599945708[/C][C]0.421064000542922[/C][/ROW]
[ROW][C]26[/C][C]6.7[/C][C]6.26944570361116[/C][C]0.430554296388845[/C][/ROW]
[ROW][C]27[/C][C]6.9[/C][C]6.7679443784595[/C][C]0.132055621540500[/C][/ROW]
[ROW][C]28[/C][C]7[/C][C]7.01977935011743[/C][C]-0.0197793501174273[/C][/ROW]
[ROW][C]29[/C][C]7.1[/C][C]7.31337398152559[/C][C]-0.213373981525590[/C][/ROW]
[ROW][C]30[/C][C]7.2[/C][C]7.26470807925219[/C][C]-0.0647080792521857[/C][/ROW]
[ROW][C]31[/C][C]7.1[/C][C]6.99333165308493[/C][C]0.106668346915072[/C][/ROW]
[ROW][C]32[/C][C]6.9[/C][C]7.0959413772399[/C][C]-0.1959413772399[/C][/ROW]
[ROW][C]33[/C][C]7[/C][C]6.51725468240361[/C][C]0.482745317596389[/C][/ROW]
[ROW][C]34[/C][C]6.8[/C][C]7.1734434987627[/C][C]-0.373443498762699[/C][/ROW]
[ROW][C]35[/C][C]6.4[/C][C]6.40044617609966[/C][C]-0.000446176099661244[/C][/ROW]
[ROW][C]36[/C][C]6.7[/C][C]6.61580361637285[/C][C]0.0841963836271464[/C][/ROW]
[ROW][C]37[/C][C]6.6[/C][C]6.74078965616378[/C][C]-0.140789656163782[/C][/ROW]
[ROW][C]38[/C][C]6.4[/C][C]6.52783593537739[/C][C]-0.127835935377389[/C][/ROW]
[ROW][C]39[/C][C]6.3[/C][C]6.18277278400692[/C][C]0.117227215993077[/C][/ROW]
[ROW][C]40[/C][C]6.2[/C][C]6.10059954029592[/C][C]0.0994004597040838[/C][/ROW]
[ROW][C]41[/C][C]6.5[/C][C]6.26665897019514[/C][C]0.233341029804856[/C][/ROW]
[ROW][C]42[/C][C]6.8[/C][C]6.83851412014025[/C][C]-0.0385141201402517[/C][/ROW]
[ROW][C]43[/C][C]6.8[/C][C]6.84293848398286[/C][C]-0.042938483982863[/C][/ROW]
[ROW][C]44[/C][C]6.4[/C][C]6.88007070462229[/C][C]-0.480070704622288[/C][/ROW]
[ROW][C]45[/C][C]6.1[/C][C]5.93007759419789[/C][C]0.169922405802114[/C][/ROW]
[ROW][C]46[/C][C]5.8[/C][C]5.79872786002459[/C][C]0.00127213997541276[/C][/ROW]
[ROW][C]47[/C][C]6.1[/C][C]5.34920741810944[/C][C]0.75079258189056[/C][/ROW]
[ROW][C]48[/C][C]7.2[/C][C]6.87864983507475[/C][C]0.321350164925254[/C][/ROW]
[ROW][C]49[/C][C]7.3[/C][C]8.06153427409026[/C][C]-0.76153427409026[/C][/ROW]
[ROW][C]50[/C][C]6.9[/C][C]7.55622209466666[/C][C]-0.656222094666664[/C][/ROW]
[ROW][C]51[/C][C]6.1[/C][C]6.52672261166944[/C][C]-0.426722611669438[/C][/ROW]
[ROW][C]52[/C][C]5.8[/C][C]5.22456996080117[/C][C]0.575430039198834[/C][/ROW]
[ROW][C]53[/C][C]6.2[/C][C]5.55307599008705[/C][C]0.646924009912953[/C][/ROW]
[ROW][C]54[/C][C]7.1[/C][C]6.58784794644136[/C][C]0.512152053558637[/C][/ROW]
[ROW][C]55[/C][C]7.7[/C][C]7.71001599648092[/C][C]-0.0100159964809237[/C][/ROW]
[ROW][C]56[/C][C]7.9[/C][C]8.3743139653839[/C][C]-0.47431396538390[/C][/ROW]
[ROW][C]57[/C][C]7.7[/C][C]8.077476478256[/C][C]-0.377476478256004[/C][/ROW]
[ROW][C]58[/C][C]7.4[/C][C]7.51232643982913[/C][C]-0.112326439829127[/C][/ROW]
[ROW][C]59[/C][C]7.5[/C][C]6.9534346494156[/C][C]0.546565350584396[/C][/ROW]
[ROW][C]60[/C][C]8[/C][C]8.12597042012929[/C][C]-0.125970420129287[/C][/ROW]
[ROW][C]61[/C][C]8.1[/C][C]8.201469492428[/C][C]-0.101469492427995[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63772&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63772&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
137.57.433256880142390.0667431198576134
147.67.64604691568444-0.0460469156844354
157.77.699037092973510.000962907026494264
167.77.696568095672210.00343190432778773
177.97.92064617861872-0.0206461786187218
188.18.14660566968208-0.04660566968208
198.27.945480715867160.254519284132838
208.28.44899290291657-0.248992902916571
218.27.91488304083960.285116959160407
227.98.42651571563598-0.526515715635977
237.37.273731747191670.0262682528083253
246.97.47809936117529-0.578099361175288
256.66.178935999457080.421064000542922
266.76.269445703611160.430554296388845
276.96.76794437845950.132055621540500
2877.01977935011743-0.0197793501174273
297.17.31337398152559-0.213373981525590
307.27.26470807925219-0.0647080792521857
317.16.993331653084930.106668346915072
326.97.0959413772399-0.1959413772399
3376.517254682403610.482745317596389
346.87.1734434987627-0.373443498762699
356.46.40044617609966-0.000446176099661244
366.76.615803616372850.0841963836271464
376.66.74078965616378-0.140789656163782
386.46.52783593537739-0.127835935377389
396.36.182772784006920.117227215993077
406.26.100599540295920.0994004597040838
416.56.266658970195140.233341029804856
426.86.83851412014025-0.0385141201402517
436.86.84293848398286-0.042938483982863
446.46.88007070462229-0.480070704622288
456.15.930077594197890.169922405802114
465.85.798727860024590.00127213997541276
476.15.349207418109440.75079258189056
487.26.878649835074750.321350164925254
497.38.06153427409026-0.76153427409026
506.97.55622209466666-0.656222094666664
516.16.52672261166944-0.426722611669438
525.85.224569960801170.575430039198834
536.25.553075990087050.646924009912953
547.16.587847946441360.512152053558637
557.77.71001599648092-0.0100159964809237
567.98.3743139653839-0.47431396538390
577.78.077476478256-0.377476478256004
587.47.51232643982913-0.112326439829127
597.56.95343464941560.546565350584396
6088.12597042012929-0.125970420129287
618.18.201469492428-0.101469492427995







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
628.322304692291237.650320093445528.99428929113694
638.542738997304067.115586445882849.96989154872528
648.727806212345046.3568318970166611.0987805276734
659.072639620951495.5427254582197412.6025537836832
669.438530492528064.5662136728976914.3108473121584
679.414300686766923.2835220238521915.5450793496817
689.459446490774111.9596892699214216.9592037116268
699.449186753299870.56492798377686718.3334455228229
709.43631804412498-0.87485285304107519.7474889412910
719.26485419615837-2.3150639936903220.8447723860071
729.73163480068307-4.0012519845209923.4645215858871
739.82221515550887-6.2817192808073225.9261495918251

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
62 & 8.32230469229123 & 7.65032009344552 & 8.99428929113694 \tabularnewline
63 & 8.54273899730406 & 7.11558644588284 & 9.96989154872528 \tabularnewline
64 & 8.72780621234504 & 6.35683189701666 & 11.0987805276734 \tabularnewline
65 & 9.07263962095149 & 5.54272545821974 & 12.6025537836832 \tabularnewline
66 & 9.43853049252806 & 4.56621367289769 & 14.3108473121584 \tabularnewline
67 & 9.41430068676692 & 3.28352202385219 & 15.5450793496817 \tabularnewline
68 & 9.45944649077411 & 1.95968926992142 & 16.9592037116268 \tabularnewline
69 & 9.44918675329987 & 0.564927983776867 & 18.3334455228229 \tabularnewline
70 & 9.43631804412498 & -0.874852853041075 & 19.7474889412910 \tabularnewline
71 & 9.26485419615837 & -2.31506399369032 & 20.8447723860071 \tabularnewline
72 & 9.73163480068307 & -4.00125198452099 & 23.4645215858871 \tabularnewline
73 & 9.82221515550887 & -6.28171928080732 & 25.9261495918251 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63772&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]62[/C][C]8.32230469229123[/C][C]7.65032009344552[/C][C]8.99428929113694[/C][/ROW]
[ROW][C]63[/C][C]8.54273899730406[/C][C]7.11558644588284[/C][C]9.96989154872528[/C][/ROW]
[ROW][C]64[/C][C]8.72780621234504[/C][C]6.35683189701666[/C][C]11.0987805276734[/C][/ROW]
[ROW][C]65[/C][C]9.07263962095149[/C][C]5.54272545821974[/C][C]12.6025537836832[/C][/ROW]
[ROW][C]66[/C][C]9.43853049252806[/C][C]4.56621367289769[/C][C]14.3108473121584[/C][/ROW]
[ROW][C]67[/C][C]9.41430068676692[/C][C]3.28352202385219[/C][C]15.5450793496817[/C][/ROW]
[ROW][C]68[/C][C]9.45944649077411[/C][C]1.95968926992142[/C][C]16.9592037116268[/C][/ROW]
[ROW][C]69[/C][C]9.44918675329987[/C][C]0.564927983776867[/C][C]18.3334455228229[/C][/ROW]
[ROW][C]70[/C][C]9.43631804412498[/C][C]-0.874852853041075[/C][C]19.7474889412910[/C][/ROW]
[ROW][C]71[/C][C]9.26485419615837[/C][C]-2.31506399369032[/C][C]20.8447723860071[/C][/ROW]
[ROW][C]72[/C][C]9.73163480068307[/C][C]-4.00125198452099[/C][C]23.4645215858871[/C][/ROW]
[ROW][C]73[/C][C]9.82221515550887[/C][C]-6.28171928080732[/C][C]25.9261495918251[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63772&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63772&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
628.322304692291237.650320093445528.99428929113694
638.542738997304067.115586445882849.96989154872528
648.727806212345046.3568318970166611.0987805276734
659.072639620951495.5427254582197412.6025537836832
669.438530492528064.5662136728976914.3108473121584
679.414300686766923.2835220238521915.5450793496817
689.459446490774111.9596892699214216.9592037116268
699.449186753299870.56492798377686718.3334455228229
709.43631804412498-0.87485285304107519.7474889412910
719.26485419615837-2.3150639936903220.8447723860071
729.73163480068307-4.0012519845209923.4645215858871
739.82221515550887-6.2817192808073225.9261495918251



Parameters (Session):
par1 = 12 ;
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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')