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of Irreproducible Research!

Author's title

Maarten Verhaegen 2MAR03 - tweede zit - Oefening 10 - triple additief expon...

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 17 Aug 2008 13:40:03 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Aug/17/t12190022382flqf778hz8bvbv.htm/, Retrieved Tue, 14 May 2024 23:46:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=14628, Retrieved Tue, 14 May 2024 23:46:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact201
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Maarten Verhaegen...] [2008-08-17 19:40:03] [6cae5450d413d5fde7d2ce6324b75128] [Current]
-   PD    [Exponential Smoothing] [] [2009-08-16 17:12:06] [20f4bab96040345df1f930341b3cf3a9]
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Dataseries X:
0.6200		
0.6200		
0.6100		
0.6100		
0.6100		
0.6000		
0.5900		
0.5900		
0.5900		
0.5900		
0.5900		
0.5700		
0.5800		
0.5700		
0.5900		
0.6200		
0.6200		
0.6100		
0.6400		
0.6500		
0.6700		
0.6700		
0.6900		
0.7400		
0.7300		
0.7400		
0.7500		
0.7400		
0.7600		
0.7600		
0.7800		
0.7900		
0.8900		
0.8800		
0.8800		
0.8400		
0.7600		
0.7700		
0.7600		
0.7700		
0.7800		
0.7900		
0.7800		
0.7600		
0.7800		
0.7600		
0.7400		
0.7300		
0.7200		
0.7100		
0.7300		
0.7500		
0.7500		
0.7200		
0.7200		
0.7200		
0.7400		
0.7800		
0.7400		
0.7400		
0.7500		
0.7800		
0.8100		
0.7500		
0.7000		
0.7100		
0.7100		
0.7300		
0.7400		
0.7400		
0.7500		
0.7400		
0.7400		
0.7300		
0.7600		
0.8000		
0.8300		
0.8100		
0.8300		
0.8800		
0.8900		
0.9300		
0.9100		
0.9000		
0.8600		
0.8800		
0.9300		
0.9800		
0.9700		
1.0300		
1.0600		
1.0600		
1.0800		
1.0900		
1.0400		
1.0000		




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=14628&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=14628&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14628&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
alpha0.779623557136431
beta0.00737648872348067
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.779623557136431 \tabularnewline
beta & 0.00737648872348067 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14628&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]0.779623557136431[/C][/ROW]
[ROW][C]beta[/C][C]0.00737648872348067[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14628&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14628&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
alpha0.779623557136431
beta0.00737648872348067
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
130.580.5439763888888890.0360236111111109
140.570.566785260172690.00321473982731013
150.590.592784050117634-0.00278405011763394
160.620.623256698023525-0.00325669802352480
170.620.622508796260632-0.00250879626063183
180.610.6085795485332920.00142045146670833
190.640.6356384704148270.00436152958517311
200.650.645015408733250.00498459126674977
210.670.6644900997575590.00550990024244102
220.670.6664893541666520.00351064583334781
230.690.687783465393320.00221653460668014
240.740.7368314040563650.00316859594363483
250.730.7074952363368840.0225047636631156
260.740.7127776984797010.0272223015202987
270.750.756552926934541-0.00655292693454135
280.740.784343004705179-0.0443430047051790
290.760.7518516831877980.00814831681220152
300.760.7472817862056140.0127182137943862
310.780.784046726904767-0.00404672690476737
320.790.7872072164254670.00279278357453294
330.890.805277801350270.0847221986497296
340.880.8692366948935820.0107633051064182
350.880.896586121573558-0.0165861215735575
360.840.931762909591833-0.0917629095918326
370.760.832709230750218-0.0727092307502176
380.770.7642847804654770.00571521953452259
390.760.78321015808745-0.0232101580874502
400.770.788950870961858-0.0189508709618583
410.780.787234780841077-0.00723478084107665
420.790.7710015648190160.0189984351809842
430.780.808326841517319-0.0283268415173189
440.760.793284342032865-0.0332843420328651
450.780.800295280968893-0.0202952809688929
460.760.764488950178656-0.00448895017865614
470.740.772240150581619-0.0322401505816187
480.730.776875431789645-0.0468754317896447
490.720.7155041488223930.00449585117760709
500.710.723485576818818-0.0134855768188176
510.730.7198887441916450.0101112558083554
520.750.751559545173321-0.00155954517332080
530.750.765097390427123-0.0150973904271225
540.720.747583562459308-0.0275835624593085
550.720.736963233516226-0.0169632335162258
560.720.728553098183873-0.00855309818387262
570.740.756715351008665-0.0167153510086653
580.780.7262117191792690.0537882808207315
590.740.772645014778041-0.0326450147780415
600.740.773100558674985-0.0331005586749852
610.750.7332299051595720.0167700948404280
620.780.7463289205476580.0336710794523417
630.810.7844788875659010.0255211124340986
640.750.825462399986536-0.0754623999865357
650.70.777846203541177-0.0778462035411772
660.710.7077451903747230.00225480962527691
670.710.721984552422646-0.0119845524226465
680.730.718594464574930.0114055354250706
690.740.759918104592518-0.0199181045925182
700.740.741836386053711-0.00183638605371073
710.750.724917143583260.0250828564167392
720.740.769671915749024-0.0296719157490244
730.740.742877959107356-0.00287795910735567
740.730.743683802823674-0.0136838028236737
750.760.742146730048630.0178532699513699
760.80.7538817304220970.0461182695779028
770.830.8002104561268840.0297895438731163
780.810.831979286537432-0.0219792865374316
790.830.824349891840640.0056501081593604
800.880.8401269755233650.0398730244766354
810.890.89716941185198-0.0071694118519805
820.930.893512839165270.0364871608347292
830.910.91312547768583-0.00312547768583027
840.90.924381057433586-0.0243810574335855
850.860.908206513817093-0.048206513817093
860.880.871620894183320.00837910581668
870.930.8946905929892760.0353094070107237
880.980.9268201176815020.0531798823184979
890.970.975652755636756-0.00565275563675605
901.030.9687744582605150.0612255417394846
911.061.032974031352020.0270259686479786
921.061.07395274996467-0.0139527499646692
931.081.079349339947150.000650660052845087
941.091.09214037223277-0.00214037223276997
951.041.07341625367428-0.0334162536742793
9611.05670587311530-0.0567058731153010

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 0.58 & 0.543976388888889 & 0.0360236111111109 \tabularnewline
14 & 0.57 & 0.56678526017269 & 0.00321473982731013 \tabularnewline
15 & 0.59 & 0.592784050117634 & -0.00278405011763394 \tabularnewline
16 & 0.62 & 0.623256698023525 & -0.00325669802352480 \tabularnewline
17 & 0.62 & 0.622508796260632 & -0.00250879626063183 \tabularnewline
18 & 0.61 & 0.608579548533292 & 0.00142045146670833 \tabularnewline
19 & 0.64 & 0.635638470414827 & 0.00436152958517311 \tabularnewline
20 & 0.65 & 0.64501540873325 & 0.00498459126674977 \tabularnewline
21 & 0.67 & 0.664490099757559 & 0.00550990024244102 \tabularnewline
22 & 0.67 & 0.666489354166652 & 0.00351064583334781 \tabularnewline
23 & 0.69 & 0.68778346539332 & 0.00221653460668014 \tabularnewline
24 & 0.74 & 0.736831404056365 & 0.00316859594363483 \tabularnewline
25 & 0.73 & 0.707495236336884 & 0.0225047636631156 \tabularnewline
26 & 0.74 & 0.712777698479701 & 0.0272223015202987 \tabularnewline
27 & 0.75 & 0.756552926934541 & -0.00655292693454135 \tabularnewline
28 & 0.74 & 0.784343004705179 & -0.0443430047051790 \tabularnewline
29 & 0.76 & 0.751851683187798 & 0.00814831681220152 \tabularnewline
30 & 0.76 & 0.747281786205614 & 0.0127182137943862 \tabularnewline
31 & 0.78 & 0.784046726904767 & -0.00404672690476737 \tabularnewline
32 & 0.79 & 0.787207216425467 & 0.00279278357453294 \tabularnewline
33 & 0.89 & 0.80527780135027 & 0.0847221986497296 \tabularnewline
34 & 0.88 & 0.869236694893582 & 0.0107633051064182 \tabularnewline
35 & 0.88 & 0.896586121573558 & -0.0165861215735575 \tabularnewline
36 & 0.84 & 0.931762909591833 & -0.0917629095918326 \tabularnewline
37 & 0.76 & 0.832709230750218 & -0.0727092307502176 \tabularnewline
38 & 0.77 & 0.764284780465477 & 0.00571521953452259 \tabularnewline
39 & 0.76 & 0.78321015808745 & -0.0232101580874502 \tabularnewline
40 & 0.77 & 0.788950870961858 & -0.0189508709618583 \tabularnewline
41 & 0.78 & 0.787234780841077 & -0.00723478084107665 \tabularnewline
42 & 0.79 & 0.771001564819016 & 0.0189984351809842 \tabularnewline
43 & 0.78 & 0.808326841517319 & -0.0283268415173189 \tabularnewline
44 & 0.76 & 0.793284342032865 & -0.0332843420328651 \tabularnewline
45 & 0.78 & 0.800295280968893 & -0.0202952809688929 \tabularnewline
46 & 0.76 & 0.764488950178656 & -0.00448895017865614 \tabularnewline
47 & 0.74 & 0.772240150581619 & -0.0322401505816187 \tabularnewline
48 & 0.73 & 0.776875431789645 & -0.0468754317896447 \tabularnewline
49 & 0.72 & 0.715504148822393 & 0.00449585117760709 \tabularnewline
50 & 0.71 & 0.723485576818818 & -0.0134855768188176 \tabularnewline
51 & 0.73 & 0.719888744191645 & 0.0101112558083554 \tabularnewline
52 & 0.75 & 0.751559545173321 & -0.00155954517332080 \tabularnewline
53 & 0.75 & 0.765097390427123 & -0.0150973904271225 \tabularnewline
54 & 0.72 & 0.747583562459308 & -0.0275835624593085 \tabularnewline
55 & 0.72 & 0.736963233516226 & -0.0169632335162258 \tabularnewline
56 & 0.72 & 0.728553098183873 & -0.00855309818387262 \tabularnewline
57 & 0.74 & 0.756715351008665 & -0.0167153510086653 \tabularnewline
58 & 0.78 & 0.726211719179269 & 0.0537882808207315 \tabularnewline
59 & 0.74 & 0.772645014778041 & -0.0326450147780415 \tabularnewline
60 & 0.74 & 0.773100558674985 & -0.0331005586749852 \tabularnewline
61 & 0.75 & 0.733229905159572 & 0.0167700948404280 \tabularnewline
62 & 0.78 & 0.746328920547658 & 0.0336710794523417 \tabularnewline
63 & 0.81 & 0.784478887565901 & 0.0255211124340986 \tabularnewline
64 & 0.75 & 0.825462399986536 & -0.0754623999865357 \tabularnewline
65 & 0.7 & 0.777846203541177 & -0.0778462035411772 \tabularnewline
66 & 0.71 & 0.707745190374723 & 0.00225480962527691 \tabularnewline
67 & 0.71 & 0.721984552422646 & -0.0119845524226465 \tabularnewline
68 & 0.73 & 0.71859446457493 & 0.0114055354250706 \tabularnewline
69 & 0.74 & 0.759918104592518 & -0.0199181045925182 \tabularnewline
70 & 0.74 & 0.741836386053711 & -0.00183638605371073 \tabularnewline
71 & 0.75 & 0.72491714358326 & 0.0250828564167392 \tabularnewline
72 & 0.74 & 0.769671915749024 & -0.0296719157490244 \tabularnewline
73 & 0.74 & 0.742877959107356 & -0.00287795910735567 \tabularnewline
74 & 0.73 & 0.743683802823674 & -0.0136838028236737 \tabularnewline
75 & 0.76 & 0.74214673004863 & 0.0178532699513699 \tabularnewline
76 & 0.8 & 0.753881730422097 & 0.0461182695779028 \tabularnewline
77 & 0.83 & 0.800210456126884 & 0.0297895438731163 \tabularnewline
78 & 0.81 & 0.831979286537432 & -0.0219792865374316 \tabularnewline
79 & 0.83 & 0.82434989184064 & 0.0056501081593604 \tabularnewline
80 & 0.88 & 0.840126975523365 & 0.0398730244766354 \tabularnewline
81 & 0.89 & 0.89716941185198 & -0.0071694118519805 \tabularnewline
82 & 0.93 & 0.89351283916527 & 0.0364871608347292 \tabularnewline
83 & 0.91 & 0.91312547768583 & -0.00312547768583027 \tabularnewline
84 & 0.9 & 0.924381057433586 & -0.0243810574335855 \tabularnewline
85 & 0.86 & 0.908206513817093 & -0.048206513817093 \tabularnewline
86 & 0.88 & 0.87162089418332 & 0.00837910581668 \tabularnewline
87 & 0.93 & 0.894690592989276 & 0.0353094070107237 \tabularnewline
88 & 0.98 & 0.926820117681502 & 0.0531798823184979 \tabularnewline
89 & 0.97 & 0.975652755636756 & -0.00565275563675605 \tabularnewline
90 & 1.03 & 0.968774458260515 & 0.0612255417394846 \tabularnewline
91 & 1.06 & 1.03297403135202 & 0.0270259686479786 \tabularnewline
92 & 1.06 & 1.07395274996467 & -0.0139527499646692 \tabularnewline
93 & 1.08 & 1.07934933994715 & 0.000650660052845087 \tabularnewline
94 & 1.09 & 1.09214037223277 & -0.00214037223276997 \tabularnewline
95 & 1.04 & 1.07341625367428 & -0.0334162536742793 \tabularnewline
96 & 1 & 1.05670587311530 & -0.0567058731153010 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14628&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]0.58[/C][C]0.543976388888889[/C][C]0.0360236111111109[/C][/ROW]
[ROW][C]14[/C][C]0.57[/C][C]0.56678526017269[/C][C]0.00321473982731013[/C][/ROW]
[ROW][C]15[/C][C]0.59[/C][C]0.592784050117634[/C][C]-0.00278405011763394[/C][/ROW]
[ROW][C]16[/C][C]0.62[/C][C]0.623256698023525[/C][C]-0.00325669802352480[/C][/ROW]
[ROW][C]17[/C][C]0.62[/C][C]0.622508796260632[/C][C]-0.00250879626063183[/C][/ROW]
[ROW][C]18[/C][C]0.61[/C][C]0.608579548533292[/C][C]0.00142045146670833[/C][/ROW]
[ROW][C]19[/C][C]0.64[/C][C]0.635638470414827[/C][C]0.00436152958517311[/C][/ROW]
[ROW][C]20[/C][C]0.65[/C][C]0.64501540873325[/C][C]0.00498459126674977[/C][/ROW]
[ROW][C]21[/C][C]0.67[/C][C]0.664490099757559[/C][C]0.00550990024244102[/C][/ROW]
[ROW][C]22[/C][C]0.67[/C][C]0.666489354166652[/C][C]0.00351064583334781[/C][/ROW]
[ROW][C]23[/C][C]0.69[/C][C]0.68778346539332[/C][C]0.00221653460668014[/C][/ROW]
[ROW][C]24[/C][C]0.74[/C][C]0.736831404056365[/C][C]0.00316859594363483[/C][/ROW]
[ROW][C]25[/C][C]0.73[/C][C]0.707495236336884[/C][C]0.0225047636631156[/C][/ROW]
[ROW][C]26[/C][C]0.74[/C][C]0.712777698479701[/C][C]0.0272223015202987[/C][/ROW]
[ROW][C]27[/C][C]0.75[/C][C]0.756552926934541[/C][C]-0.00655292693454135[/C][/ROW]
[ROW][C]28[/C][C]0.74[/C][C]0.784343004705179[/C][C]-0.0443430047051790[/C][/ROW]
[ROW][C]29[/C][C]0.76[/C][C]0.751851683187798[/C][C]0.00814831681220152[/C][/ROW]
[ROW][C]30[/C][C]0.76[/C][C]0.747281786205614[/C][C]0.0127182137943862[/C][/ROW]
[ROW][C]31[/C][C]0.78[/C][C]0.784046726904767[/C][C]-0.00404672690476737[/C][/ROW]
[ROW][C]32[/C][C]0.79[/C][C]0.787207216425467[/C][C]0.00279278357453294[/C][/ROW]
[ROW][C]33[/C][C]0.89[/C][C]0.80527780135027[/C][C]0.0847221986497296[/C][/ROW]
[ROW][C]34[/C][C]0.88[/C][C]0.869236694893582[/C][C]0.0107633051064182[/C][/ROW]
[ROW][C]35[/C][C]0.88[/C][C]0.896586121573558[/C][C]-0.0165861215735575[/C][/ROW]
[ROW][C]36[/C][C]0.84[/C][C]0.931762909591833[/C][C]-0.0917629095918326[/C][/ROW]
[ROW][C]37[/C][C]0.76[/C][C]0.832709230750218[/C][C]-0.0727092307502176[/C][/ROW]
[ROW][C]38[/C][C]0.77[/C][C]0.764284780465477[/C][C]0.00571521953452259[/C][/ROW]
[ROW][C]39[/C][C]0.76[/C][C]0.78321015808745[/C][C]-0.0232101580874502[/C][/ROW]
[ROW][C]40[/C][C]0.77[/C][C]0.788950870961858[/C][C]-0.0189508709618583[/C][/ROW]
[ROW][C]41[/C][C]0.78[/C][C]0.787234780841077[/C][C]-0.00723478084107665[/C][/ROW]
[ROW][C]42[/C][C]0.79[/C][C]0.771001564819016[/C][C]0.0189984351809842[/C][/ROW]
[ROW][C]43[/C][C]0.78[/C][C]0.808326841517319[/C][C]-0.0283268415173189[/C][/ROW]
[ROW][C]44[/C][C]0.76[/C][C]0.793284342032865[/C][C]-0.0332843420328651[/C][/ROW]
[ROW][C]45[/C][C]0.78[/C][C]0.800295280968893[/C][C]-0.0202952809688929[/C][/ROW]
[ROW][C]46[/C][C]0.76[/C][C]0.764488950178656[/C][C]-0.00448895017865614[/C][/ROW]
[ROW][C]47[/C][C]0.74[/C][C]0.772240150581619[/C][C]-0.0322401505816187[/C][/ROW]
[ROW][C]48[/C][C]0.73[/C][C]0.776875431789645[/C][C]-0.0468754317896447[/C][/ROW]
[ROW][C]49[/C][C]0.72[/C][C]0.715504148822393[/C][C]0.00449585117760709[/C][/ROW]
[ROW][C]50[/C][C]0.71[/C][C]0.723485576818818[/C][C]-0.0134855768188176[/C][/ROW]
[ROW][C]51[/C][C]0.73[/C][C]0.719888744191645[/C][C]0.0101112558083554[/C][/ROW]
[ROW][C]52[/C][C]0.75[/C][C]0.751559545173321[/C][C]-0.00155954517332080[/C][/ROW]
[ROW][C]53[/C][C]0.75[/C][C]0.765097390427123[/C][C]-0.0150973904271225[/C][/ROW]
[ROW][C]54[/C][C]0.72[/C][C]0.747583562459308[/C][C]-0.0275835624593085[/C][/ROW]
[ROW][C]55[/C][C]0.72[/C][C]0.736963233516226[/C][C]-0.0169632335162258[/C][/ROW]
[ROW][C]56[/C][C]0.72[/C][C]0.728553098183873[/C][C]-0.00855309818387262[/C][/ROW]
[ROW][C]57[/C][C]0.74[/C][C]0.756715351008665[/C][C]-0.0167153510086653[/C][/ROW]
[ROW][C]58[/C][C]0.78[/C][C]0.726211719179269[/C][C]0.0537882808207315[/C][/ROW]
[ROW][C]59[/C][C]0.74[/C][C]0.772645014778041[/C][C]-0.0326450147780415[/C][/ROW]
[ROW][C]60[/C][C]0.74[/C][C]0.773100558674985[/C][C]-0.0331005586749852[/C][/ROW]
[ROW][C]61[/C][C]0.75[/C][C]0.733229905159572[/C][C]0.0167700948404280[/C][/ROW]
[ROW][C]62[/C][C]0.78[/C][C]0.746328920547658[/C][C]0.0336710794523417[/C][/ROW]
[ROW][C]63[/C][C]0.81[/C][C]0.784478887565901[/C][C]0.0255211124340986[/C][/ROW]
[ROW][C]64[/C][C]0.75[/C][C]0.825462399986536[/C][C]-0.0754623999865357[/C][/ROW]
[ROW][C]65[/C][C]0.7[/C][C]0.777846203541177[/C][C]-0.0778462035411772[/C][/ROW]
[ROW][C]66[/C][C]0.71[/C][C]0.707745190374723[/C][C]0.00225480962527691[/C][/ROW]
[ROW][C]67[/C][C]0.71[/C][C]0.721984552422646[/C][C]-0.0119845524226465[/C][/ROW]
[ROW][C]68[/C][C]0.73[/C][C]0.71859446457493[/C][C]0.0114055354250706[/C][/ROW]
[ROW][C]69[/C][C]0.74[/C][C]0.759918104592518[/C][C]-0.0199181045925182[/C][/ROW]
[ROW][C]70[/C][C]0.74[/C][C]0.741836386053711[/C][C]-0.00183638605371073[/C][/ROW]
[ROW][C]71[/C][C]0.75[/C][C]0.72491714358326[/C][C]0.0250828564167392[/C][/ROW]
[ROW][C]72[/C][C]0.74[/C][C]0.769671915749024[/C][C]-0.0296719157490244[/C][/ROW]
[ROW][C]73[/C][C]0.74[/C][C]0.742877959107356[/C][C]-0.00287795910735567[/C][/ROW]
[ROW][C]74[/C][C]0.73[/C][C]0.743683802823674[/C][C]-0.0136838028236737[/C][/ROW]
[ROW][C]75[/C][C]0.76[/C][C]0.74214673004863[/C][C]0.0178532699513699[/C][/ROW]
[ROW][C]76[/C][C]0.8[/C][C]0.753881730422097[/C][C]0.0461182695779028[/C][/ROW]
[ROW][C]77[/C][C]0.83[/C][C]0.800210456126884[/C][C]0.0297895438731163[/C][/ROW]
[ROW][C]78[/C][C]0.81[/C][C]0.831979286537432[/C][C]-0.0219792865374316[/C][/ROW]
[ROW][C]79[/C][C]0.83[/C][C]0.82434989184064[/C][C]0.0056501081593604[/C][/ROW]
[ROW][C]80[/C][C]0.88[/C][C]0.840126975523365[/C][C]0.0398730244766354[/C][/ROW]
[ROW][C]81[/C][C]0.89[/C][C]0.89716941185198[/C][C]-0.0071694118519805[/C][/ROW]
[ROW][C]82[/C][C]0.93[/C][C]0.89351283916527[/C][C]0.0364871608347292[/C][/ROW]
[ROW][C]83[/C][C]0.91[/C][C]0.91312547768583[/C][C]-0.00312547768583027[/C][/ROW]
[ROW][C]84[/C][C]0.9[/C][C]0.924381057433586[/C][C]-0.0243810574335855[/C][/ROW]
[ROW][C]85[/C][C]0.86[/C][C]0.908206513817093[/C][C]-0.048206513817093[/C][/ROW]
[ROW][C]86[/C][C]0.88[/C][C]0.87162089418332[/C][C]0.00837910581668[/C][/ROW]
[ROW][C]87[/C][C]0.93[/C][C]0.894690592989276[/C][C]0.0353094070107237[/C][/ROW]
[ROW][C]88[/C][C]0.98[/C][C]0.926820117681502[/C][C]0.0531798823184979[/C][/ROW]
[ROW][C]89[/C][C]0.97[/C][C]0.975652755636756[/C][C]-0.00565275563675605[/C][/ROW]
[ROW][C]90[/C][C]1.03[/C][C]0.968774458260515[/C][C]0.0612255417394846[/C][/ROW]
[ROW][C]91[/C][C]1.06[/C][C]1.03297403135202[/C][C]0.0270259686479786[/C][/ROW]
[ROW][C]92[/C][C]1.06[/C][C]1.07395274996467[/C][C]-0.0139527499646692[/C][/ROW]
[ROW][C]93[/C][C]1.08[/C][C]1.07934933994715[/C][C]0.000650660052845087[/C][/ROW]
[ROW][C]94[/C][C]1.09[/C][C]1.09214037223277[/C][C]-0.00214037223276997[/C][/ROW]
[ROW][C]95[/C][C]1.04[/C][C]1.07341625367428[/C][C]-0.0334162536742793[/C][/ROW]
[ROW][C]96[/C][C]1[/C][C]1.05670587311530[/C][C]-0.0567058731153010[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14628&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14628&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
130.580.5439763888888890.0360236111111109
140.570.566785260172690.00321473982731013
150.590.592784050117634-0.00278405011763394
160.620.623256698023525-0.00325669802352480
170.620.622508796260632-0.00250879626063183
180.610.6085795485332920.00142045146670833
190.640.6356384704148270.00436152958517311
200.650.645015408733250.00498459126674977
210.670.6644900997575590.00550990024244102
220.670.6664893541666520.00351064583334781
230.690.687783465393320.00221653460668014
240.740.7368314040563650.00316859594363483
250.730.7074952363368840.0225047636631156
260.740.7127776984797010.0272223015202987
270.750.756552926934541-0.00655292693454135
280.740.784343004705179-0.0443430047051790
290.760.7518516831877980.00814831681220152
300.760.7472817862056140.0127182137943862
310.780.784046726904767-0.00404672690476737
320.790.7872072164254670.00279278357453294
330.890.805277801350270.0847221986497296
340.880.8692366948935820.0107633051064182
350.880.896586121573558-0.0165861215735575
360.840.931762909591833-0.0917629095918326
370.760.832709230750218-0.0727092307502176
380.770.7642847804654770.00571521953452259
390.760.78321015808745-0.0232101580874502
400.770.788950870961858-0.0189508709618583
410.780.787234780841077-0.00723478084107665
420.790.7710015648190160.0189984351809842
430.780.808326841517319-0.0283268415173189
440.760.793284342032865-0.0332843420328651
450.780.800295280968893-0.0202952809688929
460.760.764488950178656-0.00448895017865614
470.740.772240150581619-0.0322401505816187
480.730.776875431789645-0.0468754317896447
490.720.7155041488223930.00449585117760709
500.710.723485576818818-0.0134855768188176
510.730.7198887441916450.0101112558083554
520.750.751559545173321-0.00155954517332080
530.750.765097390427123-0.0150973904271225
540.720.747583562459308-0.0275835624593085
550.720.736963233516226-0.0169632335162258
560.720.728553098183873-0.00855309818387262
570.740.756715351008665-0.0167153510086653
580.780.7262117191792690.0537882808207315
590.740.772645014778041-0.0326450147780415
600.740.773100558674985-0.0331005586749852
610.750.7332299051595720.0167700948404280
620.780.7463289205476580.0336710794523417
630.810.7844788875659010.0255211124340986
640.750.825462399986536-0.0754623999865357
650.70.777846203541177-0.0778462035411772
660.710.7077451903747230.00225480962527691
670.710.721984552422646-0.0119845524226465
680.730.718594464574930.0114055354250706
690.740.759918104592518-0.0199181045925182
700.740.741836386053711-0.00183638605371073
710.750.724917143583260.0250828564167392
720.740.769671915749024-0.0296719157490244
730.740.742877959107356-0.00287795910735567
740.730.743683802823674-0.0136838028236737
750.760.742146730048630.0178532699513699
760.80.7538817304220970.0461182695779028
770.830.8002104561268840.0297895438731163
780.810.831979286537432-0.0219792865374316
790.830.824349891840640.0056501081593604
800.880.8401269755233650.0398730244766354
810.890.89716941185198-0.0071694118519805
820.930.893512839165270.0364871608347292
830.910.91312547768583-0.00312547768583027
840.90.924381057433586-0.0243810574335855
850.860.908206513817093-0.048206513817093
860.880.871620894183320.00837910581668
870.930.8946905929892760.0353094070107237
880.980.9268201176815020.0531798823184979
890.970.975652755636756-0.00565275563675605
901.030.9687744582605150.0612255417394846
911.061.032974031352020.0270259686479786
921.061.07395274996467-0.0139527499646692
931.081.079349339947150.000650660052845087
941.091.09214037223277-0.00214037223276997
951.041.07341625367428-0.0334162536742793
9611.05670587311530-0.0567058731153010







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
971.010227347381950.9499930438053361.07046165095856
981.024119804182840.947529500508941.10071010785675
991.046968576503340.9567639653155261.13717318769116
1001.055682044979510.9535017968781941.15786229308082
1011.049956992579630.9369166976799881.16299728747927
1021.062124552428140.939043167267611.18520593758867
1031.070602804091290.9381120482069951.20309355997558
1041.080873606905230.9394781779730991.22226903583737
1051.099839487906800.9499533039404281.24972567187317
1061.110977581556220.9529470691710491.2690080939414
1071.086511398180890.9206312263347741.25239157002701
1081.090394523769740.9169186642631111.26387038327638

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 1.01022734738195 & 0.949993043805336 & 1.07046165095856 \tabularnewline
98 & 1.02411980418284 & 0.94752950050894 & 1.10071010785675 \tabularnewline
99 & 1.04696857650334 & 0.956763965315526 & 1.13717318769116 \tabularnewline
100 & 1.05568204497951 & 0.953501796878194 & 1.15786229308082 \tabularnewline
101 & 1.04995699257963 & 0.936916697679988 & 1.16299728747927 \tabularnewline
102 & 1.06212455242814 & 0.93904316726761 & 1.18520593758867 \tabularnewline
103 & 1.07060280409129 & 0.938112048206995 & 1.20309355997558 \tabularnewline
104 & 1.08087360690523 & 0.939478177973099 & 1.22226903583737 \tabularnewline
105 & 1.09983948790680 & 0.949953303940428 & 1.24972567187317 \tabularnewline
106 & 1.11097758155622 & 0.952947069171049 & 1.2690080939414 \tabularnewline
107 & 1.08651139818089 & 0.920631226334774 & 1.25239157002701 \tabularnewline
108 & 1.09039452376974 & 0.916918664263111 & 1.26387038327638 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14628&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]97[/C][C]1.01022734738195[/C][C]0.949993043805336[/C][C]1.07046165095856[/C][/ROW]
[ROW][C]98[/C][C]1.02411980418284[/C][C]0.94752950050894[/C][C]1.10071010785675[/C][/ROW]
[ROW][C]99[/C][C]1.04696857650334[/C][C]0.956763965315526[/C][C]1.13717318769116[/C][/ROW]
[ROW][C]100[/C][C]1.05568204497951[/C][C]0.953501796878194[/C][C]1.15786229308082[/C][/ROW]
[ROW][C]101[/C][C]1.04995699257963[/C][C]0.936916697679988[/C][C]1.16299728747927[/C][/ROW]
[ROW][C]102[/C][C]1.06212455242814[/C][C]0.93904316726761[/C][C]1.18520593758867[/C][/ROW]
[ROW][C]103[/C][C]1.07060280409129[/C][C]0.938112048206995[/C][C]1.20309355997558[/C][/ROW]
[ROW][C]104[/C][C]1.08087360690523[/C][C]0.939478177973099[/C][C]1.22226903583737[/C][/ROW]
[ROW][C]105[/C][C]1.09983948790680[/C][C]0.949953303940428[/C][C]1.24972567187317[/C][/ROW]
[ROW][C]106[/C][C]1.11097758155622[/C][C]0.952947069171049[/C][C]1.2690080939414[/C][/ROW]
[ROW][C]107[/C][C]1.08651139818089[/C][C]0.920631226334774[/C][C]1.25239157002701[/C][/ROW]
[ROW][C]108[/C][C]1.09039452376974[/C][C]0.916918664263111[/C][C]1.26387038327638[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14628&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14628&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
971.010227347381950.9499930438053361.07046165095856
981.024119804182840.947529500508941.10071010785675
991.046968576503340.9567639653155261.13717318769116
1001.055682044979510.9535017968781941.15786229308082
1011.049956992579630.9369166976799881.16299728747927
1021.062124552428140.939043167267611.18520593758867
1031.070602804091290.9381120482069951.20309355997558
1041.080873606905230.9394781779730991.22226903583737
1051.099839487906800.9499533039404281.24972567187317
1061.110977581556220.9529470691710491.2690080939414
1071.086511398180890.9206312263347741.25239157002701
1081.090394523769740.9169186642631111.26387038327638



Parameters (Session):
par1 = 4 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=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')