Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 16 Jan 2011 18:29:05 +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/2011/Jan/16/t1295202407lzf39qcs74ys4y0.htm/, Retrieved Thu, 16 May 2024 04:49:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=117454, Retrieved Thu, 16 May 2024 04:49:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact114
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Classical Decomposition] [Opdracht 9 deel 1] [2010-12-15 20:03:56] [ca9acc7ddfad525f2136abf1b3000808]
- RMPD    [Exponential Smoothing] [opdracht 10 deel 2] [2011-01-16 18:29:05] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum

Post a new message
Dataseries X:
110.04
111.73
110.99
115.83
125.33
123.03
123.46
130.34
131.21
132.97
133.91
133.14
135.31
133.09
135.39
131.85
130.25
127.65
118.3
119.73
122.51
123.28
133.52
153.2
163.63
168.45
166.26
162.31
161.56
156.59
157.97
158.68
163.55
162.89
164.95
159.82
159.05
166.76
164.55
163.22
160.68
155.24
157.6
156.56
154.82
151.11
149.65
148.99
148.53
146.7
145.11
142.7
143.59
140.96
140.77
139.81
140.58
139.59
138.05
136.06
135.98
134.75
132.22
135.37
138.84
138.83
136.55
135.63
139.14
136.09
135.97
134.51
134.54
134.08
132.86
134.48
129.08
133.13
134.78
134.13
132.43
127.84
128.12




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ www.yougetit.org

\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 & 'Herman Ole Andreas Wold' @ www.yougetit.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117454&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]'Herman Ole Andreas Wold' @ www.yougetit.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117454&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117454&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'Herman Ole Andreas Wold' @ www.yougetit.org







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0586130494653002
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0586130494653002 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117454&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0586130494653002[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117454&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117454&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
alpha1
beta0.0586130494653002
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3110.99113.42-2.43000000000001
4115.83112.5375702897993.29242971020068
5125.33117.5705496352647.75945036473567
6123.03127.525354683316-4.49535468331612
7123.46124.961868236899-1.50186823689886
8130.34125.3038391596395.03616084036088
9131.21132.47902390409-1.2690239040904
10132.97133.274642543227-0.304642543227317
11133.91135.016786514772-1.1067865147719
12133.14135.891914382034-2.75191438203404
13135.31134.9606162882360.349383711764403
14133.09137.151094733016-4.06109473301564
15135.39134.6930615865460.696938413453864
16131.85137.033911272248-5.18391127224814
17130.25133.190066424424-2.94006642442415
18127.65131.417740165658-3.7677401656581
19118.3128.596901424956-10.296901424956
20119.73118.6433686323961.08663136760428
21122.51120.1370594104962.37294058950434
22123.28123.0561446946470.223855305353496
23133.52123.8392655367329.68073446326775
24153.2134.64668290468818.5533170953118
25163.63155.4141493973418.21585060265889
26168.45166.3257054551142.12429454488571
27166.26171.270216836353-5.01021683635253
28162.31168.786552749091-6.4765527490915
29161.56164.456942242444-2.8969422424444
30156.59163.53714362349-6.94714362348986
31157.97158.159950350644-0.189950350643727
32158.68159.528816781345-0.848816781345477
33163.55160.1890650413543.36093495864651
34162.89165.256059688334-2.36605968833433
35164.95164.4573777147840.492622285215873
36159.82166.546251809155-6.72625180915517
37159.05161.022005679149-1.97200567914908
38166.76160.1364204127316.6235795872687
39164.55168.234648610717-3.6846486107172
40163.22165.808680119435-2.58868011943503
41160.68164.326949683545-3.6469496835447
42155.24161.573190841346-6.33319084134564
43157.6155.7619832132891.83801678671131
44156.56158.229714982126-1.66971498212624
45154.82157.091847895286-2.27184789528593
46151.11155.218687962222-4.10868796222186
47149.65151.267865231455-1.61786523145472
48148.99149.713037216615-0.723037216615239
49148.53149.010657800473-0.480657800472528
50146.7148.522484981038-1.82248498103755
51145.11146.585663578694-1.4756635786942
52142.7144.909170436362-2.20917043636211
53143.59142.3696842202981.22031577970171
54140.96143.331210649457-2.37121064945725
55140.77140.5622267623680.20777323763204
56139.81140.384404985423-0.574404985422859
57140.58139.3907373575991.18926264240085
58139.59140.230443667685-0.640443667685446
59138.05139.202905311312-1.15290531131163
60136.06137.595330015271-1.53533001527094
61135.98135.515339641140.464660358859703
62134.75135.462574801739-0.712574801738697
63132.22134.190808619637-1.97080861963667
64135.37131.5452935165273.82470648347274
65138.84134.9194712268333.92052877316669
66138.83138.6192653737450.210734626254947
67136.55138.621617172818-2.07161717281778
68135.63136.220193372994-0.590193372994264
69139.14135.2656003396293.87439966037115
70136.09139.002690718571-2.9126907185705
71135.97135.7819690334060.18803096659417
72134.51135.672990101752-1.16299010175183
73134.54134.144823705390.395176294609826
74134.08134.197986193094-0.117986193093657
75132.86133.731070662522-0.871070662521646
76134.48132.4600145546912.01998544530849
77129.08134.198412061517-5.11841206151652
78133.13128.4984063221714.6315936778289
79134.78132.8198781515131.96012184848715
80134.13134.584766870376-0.454766870376233
81132.43133.908111597308-1.47811159730767
82127.84132.121474969139-4.28147496913948
83128.12127.2805246649890.839475335011144

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 110.99 & 113.42 & -2.43000000000001 \tabularnewline
4 & 115.83 & 112.537570289799 & 3.29242971020068 \tabularnewline
5 & 125.33 & 117.570549635264 & 7.75945036473567 \tabularnewline
6 & 123.03 & 127.525354683316 & -4.49535468331612 \tabularnewline
7 & 123.46 & 124.961868236899 & -1.50186823689886 \tabularnewline
8 & 130.34 & 125.303839159639 & 5.03616084036088 \tabularnewline
9 & 131.21 & 132.47902390409 & -1.2690239040904 \tabularnewline
10 & 132.97 & 133.274642543227 & -0.304642543227317 \tabularnewline
11 & 133.91 & 135.016786514772 & -1.1067865147719 \tabularnewline
12 & 133.14 & 135.891914382034 & -2.75191438203404 \tabularnewline
13 & 135.31 & 134.960616288236 & 0.349383711764403 \tabularnewline
14 & 133.09 & 137.151094733016 & -4.06109473301564 \tabularnewline
15 & 135.39 & 134.693061586546 & 0.696938413453864 \tabularnewline
16 & 131.85 & 137.033911272248 & -5.18391127224814 \tabularnewline
17 & 130.25 & 133.190066424424 & -2.94006642442415 \tabularnewline
18 & 127.65 & 131.417740165658 & -3.7677401656581 \tabularnewline
19 & 118.3 & 128.596901424956 & -10.296901424956 \tabularnewline
20 & 119.73 & 118.643368632396 & 1.08663136760428 \tabularnewline
21 & 122.51 & 120.137059410496 & 2.37294058950434 \tabularnewline
22 & 123.28 & 123.056144694647 & 0.223855305353496 \tabularnewline
23 & 133.52 & 123.839265536732 & 9.68073446326775 \tabularnewline
24 & 153.2 & 134.646682904688 & 18.5533170953118 \tabularnewline
25 & 163.63 & 155.414149397341 & 8.21585060265889 \tabularnewline
26 & 168.45 & 166.325705455114 & 2.12429454488571 \tabularnewline
27 & 166.26 & 171.270216836353 & -5.01021683635253 \tabularnewline
28 & 162.31 & 168.786552749091 & -6.4765527490915 \tabularnewline
29 & 161.56 & 164.456942242444 & -2.8969422424444 \tabularnewline
30 & 156.59 & 163.53714362349 & -6.94714362348986 \tabularnewline
31 & 157.97 & 158.159950350644 & -0.189950350643727 \tabularnewline
32 & 158.68 & 159.528816781345 & -0.848816781345477 \tabularnewline
33 & 163.55 & 160.189065041354 & 3.36093495864651 \tabularnewline
34 & 162.89 & 165.256059688334 & -2.36605968833433 \tabularnewline
35 & 164.95 & 164.457377714784 & 0.492622285215873 \tabularnewline
36 & 159.82 & 166.546251809155 & -6.72625180915517 \tabularnewline
37 & 159.05 & 161.022005679149 & -1.97200567914908 \tabularnewline
38 & 166.76 & 160.136420412731 & 6.6235795872687 \tabularnewline
39 & 164.55 & 168.234648610717 & -3.6846486107172 \tabularnewline
40 & 163.22 & 165.808680119435 & -2.58868011943503 \tabularnewline
41 & 160.68 & 164.326949683545 & -3.6469496835447 \tabularnewline
42 & 155.24 & 161.573190841346 & -6.33319084134564 \tabularnewline
43 & 157.6 & 155.761983213289 & 1.83801678671131 \tabularnewline
44 & 156.56 & 158.229714982126 & -1.66971498212624 \tabularnewline
45 & 154.82 & 157.091847895286 & -2.27184789528593 \tabularnewline
46 & 151.11 & 155.218687962222 & -4.10868796222186 \tabularnewline
47 & 149.65 & 151.267865231455 & -1.61786523145472 \tabularnewline
48 & 148.99 & 149.713037216615 & -0.723037216615239 \tabularnewline
49 & 148.53 & 149.010657800473 & -0.480657800472528 \tabularnewline
50 & 146.7 & 148.522484981038 & -1.82248498103755 \tabularnewline
51 & 145.11 & 146.585663578694 & -1.4756635786942 \tabularnewline
52 & 142.7 & 144.909170436362 & -2.20917043636211 \tabularnewline
53 & 143.59 & 142.369684220298 & 1.22031577970171 \tabularnewline
54 & 140.96 & 143.331210649457 & -2.37121064945725 \tabularnewline
55 & 140.77 & 140.562226762368 & 0.20777323763204 \tabularnewline
56 & 139.81 & 140.384404985423 & -0.574404985422859 \tabularnewline
57 & 140.58 & 139.390737357599 & 1.18926264240085 \tabularnewline
58 & 139.59 & 140.230443667685 & -0.640443667685446 \tabularnewline
59 & 138.05 & 139.202905311312 & -1.15290531131163 \tabularnewline
60 & 136.06 & 137.595330015271 & -1.53533001527094 \tabularnewline
61 & 135.98 & 135.51533964114 & 0.464660358859703 \tabularnewline
62 & 134.75 & 135.462574801739 & -0.712574801738697 \tabularnewline
63 & 132.22 & 134.190808619637 & -1.97080861963667 \tabularnewline
64 & 135.37 & 131.545293516527 & 3.82470648347274 \tabularnewline
65 & 138.84 & 134.919471226833 & 3.92052877316669 \tabularnewline
66 & 138.83 & 138.619265373745 & 0.210734626254947 \tabularnewline
67 & 136.55 & 138.621617172818 & -2.07161717281778 \tabularnewline
68 & 135.63 & 136.220193372994 & -0.590193372994264 \tabularnewline
69 & 139.14 & 135.265600339629 & 3.87439966037115 \tabularnewline
70 & 136.09 & 139.002690718571 & -2.9126907185705 \tabularnewline
71 & 135.97 & 135.781969033406 & 0.18803096659417 \tabularnewline
72 & 134.51 & 135.672990101752 & -1.16299010175183 \tabularnewline
73 & 134.54 & 134.14482370539 & 0.395176294609826 \tabularnewline
74 & 134.08 & 134.197986193094 & -0.117986193093657 \tabularnewline
75 & 132.86 & 133.731070662522 & -0.871070662521646 \tabularnewline
76 & 134.48 & 132.460014554691 & 2.01998544530849 \tabularnewline
77 & 129.08 & 134.198412061517 & -5.11841206151652 \tabularnewline
78 & 133.13 & 128.498406322171 & 4.6315936778289 \tabularnewline
79 & 134.78 & 132.819878151513 & 1.96012184848715 \tabularnewline
80 & 134.13 & 134.584766870376 & -0.454766870376233 \tabularnewline
81 & 132.43 & 133.908111597308 & -1.47811159730767 \tabularnewline
82 & 127.84 & 132.121474969139 & -4.28147496913948 \tabularnewline
83 & 128.12 & 127.280524664989 & 0.839475335011144 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117454&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]110.99[/C][C]113.42[/C][C]-2.43000000000001[/C][/ROW]
[ROW][C]4[/C][C]115.83[/C][C]112.537570289799[/C][C]3.29242971020068[/C][/ROW]
[ROW][C]5[/C][C]125.33[/C][C]117.570549635264[/C][C]7.75945036473567[/C][/ROW]
[ROW][C]6[/C][C]123.03[/C][C]127.525354683316[/C][C]-4.49535468331612[/C][/ROW]
[ROW][C]7[/C][C]123.46[/C][C]124.961868236899[/C][C]-1.50186823689886[/C][/ROW]
[ROW][C]8[/C][C]130.34[/C][C]125.303839159639[/C][C]5.03616084036088[/C][/ROW]
[ROW][C]9[/C][C]131.21[/C][C]132.47902390409[/C][C]-1.2690239040904[/C][/ROW]
[ROW][C]10[/C][C]132.97[/C][C]133.274642543227[/C][C]-0.304642543227317[/C][/ROW]
[ROW][C]11[/C][C]133.91[/C][C]135.016786514772[/C][C]-1.1067865147719[/C][/ROW]
[ROW][C]12[/C][C]133.14[/C][C]135.891914382034[/C][C]-2.75191438203404[/C][/ROW]
[ROW][C]13[/C][C]135.31[/C][C]134.960616288236[/C][C]0.349383711764403[/C][/ROW]
[ROW][C]14[/C][C]133.09[/C][C]137.151094733016[/C][C]-4.06109473301564[/C][/ROW]
[ROW][C]15[/C][C]135.39[/C][C]134.693061586546[/C][C]0.696938413453864[/C][/ROW]
[ROW][C]16[/C][C]131.85[/C][C]137.033911272248[/C][C]-5.18391127224814[/C][/ROW]
[ROW][C]17[/C][C]130.25[/C][C]133.190066424424[/C][C]-2.94006642442415[/C][/ROW]
[ROW][C]18[/C][C]127.65[/C][C]131.417740165658[/C][C]-3.7677401656581[/C][/ROW]
[ROW][C]19[/C][C]118.3[/C][C]128.596901424956[/C][C]-10.296901424956[/C][/ROW]
[ROW][C]20[/C][C]119.73[/C][C]118.643368632396[/C][C]1.08663136760428[/C][/ROW]
[ROW][C]21[/C][C]122.51[/C][C]120.137059410496[/C][C]2.37294058950434[/C][/ROW]
[ROW][C]22[/C][C]123.28[/C][C]123.056144694647[/C][C]0.223855305353496[/C][/ROW]
[ROW][C]23[/C][C]133.52[/C][C]123.839265536732[/C][C]9.68073446326775[/C][/ROW]
[ROW][C]24[/C][C]153.2[/C][C]134.646682904688[/C][C]18.5533170953118[/C][/ROW]
[ROW][C]25[/C][C]163.63[/C][C]155.414149397341[/C][C]8.21585060265889[/C][/ROW]
[ROW][C]26[/C][C]168.45[/C][C]166.325705455114[/C][C]2.12429454488571[/C][/ROW]
[ROW][C]27[/C][C]166.26[/C][C]171.270216836353[/C][C]-5.01021683635253[/C][/ROW]
[ROW][C]28[/C][C]162.31[/C][C]168.786552749091[/C][C]-6.4765527490915[/C][/ROW]
[ROW][C]29[/C][C]161.56[/C][C]164.456942242444[/C][C]-2.8969422424444[/C][/ROW]
[ROW][C]30[/C][C]156.59[/C][C]163.53714362349[/C][C]-6.94714362348986[/C][/ROW]
[ROW][C]31[/C][C]157.97[/C][C]158.159950350644[/C][C]-0.189950350643727[/C][/ROW]
[ROW][C]32[/C][C]158.68[/C][C]159.528816781345[/C][C]-0.848816781345477[/C][/ROW]
[ROW][C]33[/C][C]163.55[/C][C]160.189065041354[/C][C]3.36093495864651[/C][/ROW]
[ROW][C]34[/C][C]162.89[/C][C]165.256059688334[/C][C]-2.36605968833433[/C][/ROW]
[ROW][C]35[/C][C]164.95[/C][C]164.457377714784[/C][C]0.492622285215873[/C][/ROW]
[ROW][C]36[/C][C]159.82[/C][C]166.546251809155[/C][C]-6.72625180915517[/C][/ROW]
[ROW][C]37[/C][C]159.05[/C][C]161.022005679149[/C][C]-1.97200567914908[/C][/ROW]
[ROW][C]38[/C][C]166.76[/C][C]160.136420412731[/C][C]6.6235795872687[/C][/ROW]
[ROW][C]39[/C][C]164.55[/C][C]168.234648610717[/C][C]-3.6846486107172[/C][/ROW]
[ROW][C]40[/C][C]163.22[/C][C]165.808680119435[/C][C]-2.58868011943503[/C][/ROW]
[ROW][C]41[/C][C]160.68[/C][C]164.326949683545[/C][C]-3.6469496835447[/C][/ROW]
[ROW][C]42[/C][C]155.24[/C][C]161.573190841346[/C][C]-6.33319084134564[/C][/ROW]
[ROW][C]43[/C][C]157.6[/C][C]155.761983213289[/C][C]1.83801678671131[/C][/ROW]
[ROW][C]44[/C][C]156.56[/C][C]158.229714982126[/C][C]-1.66971498212624[/C][/ROW]
[ROW][C]45[/C][C]154.82[/C][C]157.091847895286[/C][C]-2.27184789528593[/C][/ROW]
[ROW][C]46[/C][C]151.11[/C][C]155.218687962222[/C][C]-4.10868796222186[/C][/ROW]
[ROW][C]47[/C][C]149.65[/C][C]151.267865231455[/C][C]-1.61786523145472[/C][/ROW]
[ROW][C]48[/C][C]148.99[/C][C]149.713037216615[/C][C]-0.723037216615239[/C][/ROW]
[ROW][C]49[/C][C]148.53[/C][C]149.010657800473[/C][C]-0.480657800472528[/C][/ROW]
[ROW][C]50[/C][C]146.7[/C][C]148.522484981038[/C][C]-1.82248498103755[/C][/ROW]
[ROW][C]51[/C][C]145.11[/C][C]146.585663578694[/C][C]-1.4756635786942[/C][/ROW]
[ROW][C]52[/C][C]142.7[/C][C]144.909170436362[/C][C]-2.20917043636211[/C][/ROW]
[ROW][C]53[/C][C]143.59[/C][C]142.369684220298[/C][C]1.22031577970171[/C][/ROW]
[ROW][C]54[/C][C]140.96[/C][C]143.331210649457[/C][C]-2.37121064945725[/C][/ROW]
[ROW][C]55[/C][C]140.77[/C][C]140.562226762368[/C][C]0.20777323763204[/C][/ROW]
[ROW][C]56[/C][C]139.81[/C][C]140.384404985423[/C][C]-0.574404985422859[/C][/ROW]
[ROW][C]57[/C][C]140.58[/C][C]139.390737357599[/C][C]1.18926264240085[/C][/ROW]
[ROW][C]58[/C][C]139.59[/C][C]140.230443667685[/C][C]-0.640443667685446[/C][/ROW]
[ROW][C]59[/C][C]138.05[/C][C]139.202905311312[/C][C]-1.15290531131163[/C][/ROW]
[ROW][C]60[/C][C]136.06[/C][C]137.595330015271[/C][C]-1.53533001527094[/C][/ROW]
[ROW][C]61[/C][C]135.98[/C][C]135.51533964114[/C][C]0.464660358859703[/C][/ROW]
[ROW][C]62[/C][C]134.75[/C][C]135.462574801739[/C][C]-0.712574801738697[/C][/ROW]
[ROW][C]63[/C][C]132.22[/C][C]134.190808619637[/C][C]-1.97080861963667[/C][/ROW]
[ROW][C]64[/C][C]135.37[/C][C]131.545293516527[/C][C]3.82470648347274[/C][/ROW]
[ROW][C]65[/C][C]138.84[/C][C]134.919471226833[/C][C]3.92052877316669[/C][/ROW]
[ROW][C]66[/C][C]138.83[/C][C]138.619265373745[/C][C]0.210734626254947[/C][/ROW]
[ROW][C]67[/C][C]136.55[/C][C]138.621617172818[/C][C]-2.07161717281778[/C][/ROW]
[ROW][C]68[/C][C]135.63[/C][C]136.220193372994[/C][C]-0.590193372994264[/C][/ROW]
[ROW][C]69[/C][C]139.14[/C][C]135.265600339629[/C][C]3.87439966037115[/C][/ROW]
[ROW][C]70[/C][C]136.09[/C][C]139.002690718571[/C][C]-2.9126907185705[/C][/ROW]
[ROW][C]71[/C][C]135.97[/C][C]135.781969033406[/C][C]0.18803096659417[/C][/ROW]
[ROW][C]72[/C][C]134.51[/C][C]135.672990101752[/C][C]-1.16299010175183[/C][/ROW]
[ROW][C]73[/C][C]134.54[/C][C]134.14482370539[/C][C]0.395176294609826[/C][/ROW]
[ROW][C]74[/C][C]134.08[/C][C]134.197986193094[/C][C]-0.117986193093657[/C][/ROW]
[ROW][C]75[/C][C]132.86[/C][C]133.731070662522[/C][C]-0.871070662521646[/C][/ROW]
[ROW][C]76[/C][C]134.48[/C][C]132.460014554691[/C][C]2.01998544530849[/C][/ROW]
[ROW][C]77[/C][C]129.08[/C][C]134.198412061517[/C][C]-5.11841206151652[/C][/ROW]
[ROW][C]78[/C][C]133.13[/C][C]128.498406322171[/C][C]4.6315936778289[/C][/ROW]
[ROW][C]79[/C][C]134.78[/C][C]132.819878151513[/C][C]1.96012184848715[/C][/ROW]
[ROW][C]80[/C][C]134.13[/C][C]134.584766870376[/C][C]-0.454766870376233[/C][/ROW]
[ROW][C]81[/C][C]132.43[/C][C]133.908111597308[/C][C]-1.47811159730767[/C][/ROW]
[ROW][C]82[/C][C]127.84[/C][C]132.121474969139[/C][C]-4.28147496913948[/C][/ROW]
[ROW][C]83[/C][C]128.12[/C][C]127.280524664989[/C][C]0.839475335011144[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117454&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117454&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
3110.99113.42-2.43000000000001
4115.83112.5375702897993.29242971020068
5125.33117.5705496352647.75945036473567
6123.03127.525354683316-4.49535468331612
7123.46124.961868236899-1.50186823689886
8130.34125.3038391596395.03616084036088
9131.21132.47902390409-1.2690239040904
10132.97133.274642543227-0.304642543227317
11133.91135.016786514772-1.1067865147719
12133.14135.891914382034-2.75191438203404
13135.31134.9606162882360.349383711764403
14133.09137.151094733016-4.06109473301564
15135.39134.6930615865460.696938413453864
16131.85137.033911272248-5.18391127224814
17130.25133.190066424424-2.94006642442415
18127.65131.417740165658-3.7677401656581
19118.3128.596901424956-10.296901424956
20119.73118.6433686323961.08663136760428
21122.51120.1370594104962.37294058950434
22123.28123.0561446946470.223855305353496
23133.52123.8392655367329.68073446326775
24153.2134.64668290468818.5533170953118
25163.63155.4141493973418.21585060265889
26168.45166.3257054551142.12429454488571
27166.26171.270216836353-5.01021683635253
28162.31168.786552749091-6.4765527490915
29161.56164.456942242444-2.8969422424444
30156.59163.53714362349-6.94714362348986
31157.97158.159950350644-0.189950350643727
32158.68159.528816781345-0.848816781345477
33163.55160.1890650413543.36093495864651
34162.89165.256059688334-2.36605968833433
35164.95164.4573777147840.492622285215873
36159.82166.546251809155-6.72625180915517
37159.05161.022005679149-1.97200567914908
38166.76160.1364204127316.6235795872687
39164.55168.234648610717-3.6846486107172
40163.22165.808680119435-2.58868011943503
41160.68164.326949683545-3.6469496835447
42155.24161.573190841346-6.33319084134564
43157.6155.7619832132891.83801678671131
44156.56158.229714982126-1.66971498212624
45154.82157.091847895286-2.27184789528593
46151.11155.218687962222-4.10868796222186
47149.65151.267865231455-1.61786523145472
48148.99149.713037216615-0.723037216615239
49148.53149.010657800473-0.480657800472528
50146.7148.522484981038-1.82248498103755
51145.11146.585663578694-1.4756635786942
52142.7144.909170436362-2.20917043636211
53143.59142.3696842202981.22031577970171
54140.96143.331210649457-2.37121064945725
55140.77140.5622267623680.20777323763204
56139.81140.384404985423-0.574404985422859
57140.58139.3907373575991.18926264240085
58139.59140.230443667685-0.640443667685446
59138.05139.202905311312-1.15290531131163
60136.06137.595330015271-1.53533001527094
61135.98135.515339641140.464660358859703
62134.75135.462574801739-0.712574801738697
63132.22134.190808619637-1.97080861963667
64135.37131.5452935165273.82470648347274
65138.84134.9194712268333.92052877316669
66138.83138.6192653737450.210734626254947
67136.55138.621617172818-2.07161717281778
68135.63136.220193372994-0.590193372994264
69139.14135.2656003396293.87439966037115
70136.09139.002690718571-2.9126907185705
71135.97135.7819690334060.18803096659417
72134.51135.672990101752-1.16299010175183
73134.54134.144823705390.395176294609826
74134.08134.197986193094-0.117986193093657
75132.86133.731070662522-0.871070662521646
76134.48132.4600145546912.01998544530849
77129.08134.198412061517-5.11841206151652
78133.13128.4984063221714.6315936778289
79134.78132.8198781515131.96012184848715
80134.13134.584766870376-0.454766870376233
81132.43133.908111597308-1.47811159730767
82127.84132.121474969139-4.28147496913948
83128.12127.2805246649890.839475335011144







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
84127.609728874325119.669801764698135.549655983952
85127.09945774865115.53694563977138.661969857529
86126.589186622974112.015892740242141.162480505706
87126.078915497299108.771598235899143.386232758699
88125.568644371624105.678650451113145.458638292134
89125.058373245949102.674898537738147.441847954159
90124.54810212027399.7247131562471149.3714910843
91124.03783099459896.8057337488157151.26992824038
92123.52755986892393.9030337874236153.152085950422
93123.01728874324891.006195690753155.028381795742
94122.50701761757288.1077024747243156.90633276042
95121.99674649189785.2019897933534158.791503190441

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
84 & 127.609728874325 & 119.669801764698 & 135.549655983952 \tabularnewline
85 & 127.09945774865 & 115.53694563977 & 138.661969857529 \tabularnewline
86 & 126.589186622974 & 112.015892740242 & 141.162480505706 \tabularnewline
87 & 126.078915497299 & 108.771598235899 & 143.386232758699 \tabularnewline
88 & 125.568644371624 & 105.678650451113 & 145.458638292134 \tabularnewline
89 & 125.058373245949 & 102.674898537738 & 147.441847954159 \tabularnewline
90 & 124.548102120273 & 99.7247131562471 & 149.3714910843 \tabularnewline
91 & 124.037830994598 & 96.8057337488157 & 151.26992824038 \tabularnewline
92 & 123.527559868923 & 93.9030337874236 & 153.152085950422 \tabularnewline
93 & 123.017288743248 & 91.006195690753 & 155.028381795742 \tabularnewline
94 & 122.507017617572 & 88.1077024747243 & 156.90633276042 \tabularnewline
95 & 121.996746491897 & 85.2019897933534 & 158.791503190441 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117454&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]84[/C][C]127.609728874325[/C][C]119.669801764698[/C][C]135.549655983952[/C][/ROW]
[ROW][C]85[/C][C]127.09945774865[/C][C]115.53694563977[/C][C]138.661969857529[/C][/ROW]
[ROW][C]86[/C][C]126.589186622974[/C][C]112.015892740242[/C][C]141.162480505706[/C][/ROW]
[ROW][C]87[/C][C]126.078915497299[/C][C]108.771598235899[/C][C]143.386232758699[/C][/ROW]
[ROW][C]88[/C][C]125.568644371624[/C][C]105.678650451113[/C][C]145.458638292134[/C][/ROW]
[ROW][C]89[/C][C]125.058373245949[/C][C]102.674898537738[/C][C]147.441847954159[/C][/ROW]
[ROW][C]90[/C][C]124.548102120273[/C][C]99.7247131562471[/C][C]149.3714910843[/C][/ROW]
[ROW][C]91[/C][C]124.037830994598[/C][C]96.8057337488157[/C][C]151.26992824038[/C][/ROW]
[ROW][C]92[/C][C]123.527559868923[/C][C]93.9030337874236[/C][C]153.152085950422[/C][/ROW]
[ROW][C]93[/C][C]123.017288743248[/C][C]91.006195690753[/C][C]155.028381795742[/C][/ROW]
[ROW][C]94[/C][C]122.507017617572[/C][C]88.1077024747243[/C][C]156.90633276042[/C][/ROW]
[ROW][C]95[/C][C]121.996746491897[/C][C]85.2019897933534[/C][C]158.791503190441[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117454&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117454&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
84127.609728874325119.669801764698135.549655983952
85127.09945774865115.53694563977138.661969857529
86126.589186622974112.015892740242141.162480505706
87126.078915497299108.771598235899143.386232758699
88125.568644371624105.678650451113145.458638292134
89125.058373245949102.674898537738147.441847954159
90124.54810212027399.7247131562471149.3714910843
91124.03783099459896.8057337488157151.26992824038
92123.52755986892393.9030337874236153.152085950422
93123.01728874324891.006195690753155.028381795742
94122.50701761757288.1077024747243156.90633276042
95121.99674649189785.2019897933534158.791503190441



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