Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 24 May 2008 04:27:10 -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/May/24/t1211624891yheg3vwzy440xog.htm/, Retrieved Tue, 14 May 2024 00:22:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13056, Retrieved Tue, 14 May 2024 00:22:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact202
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Nietje van Santfo...] [2008-05-24 10:27:10] [934a640f32b984cc814aae4d8bf2ca79] [Current]
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Dataseries X:
71,42
71,47
71,64
71,55
71,62
71,65
71,65
71,65
71,6
71,7
71,73
71,83
71,83
71,87
71,91
71,99
72,1
72,12
72,12
72,12
72,25
72,59
72,72
72,76
72,76
72,91
73
73,16
73,16
73,11
73,11
73,33
73,51
73,66
73,65
73,65
73,65
73,65
73,71
73,73
73,85
73,77
73,77
73,78
73,88
74,3
74,53
74,71
74,71
74,78
74,9
74,65
74,65
74,53
74,53
74,53
74,65
74,85
74,96
74,96
74,96
75,19
74,98
75,54
75,61
75,59
75,58
75,44
75,37
75,22
75,33
75,33




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 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 & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13056&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]5 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=13056&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13056&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 time5 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.986964904484443
beta0.00068148021869358
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.986964904484443 \tabularnewline
beta & 0.00068148021869358 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13056&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]0.986964904484443[/C][/ROW]
[ROW][C]beta[/C][C]0.00068148021869358[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13056&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13056&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
alpha0.986964904484443
beta0.00068148021869358
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
371.6471.520.120000000000005
471.5571.6885165001852-0.138516500185204
571.6271.60179312166680.0182068783331886
671.6571.6697624633511-0.0197624633511282
771.6571.7002441051719-0.0502441051719131
871.6571.7006076422472-0.050607642247158
971.671.7005783424363-0.100578342436336
1071.771.6511620665890.0488379334110363
1171.7371.7492472594121-0.0192472594120829
1271.8371.78012181075370.0498781892463427
1371.8371.8792543018512-0.0492543018512208
1471.8771.8805133750428-0.0105133750428053
1571.9171.9200013120964-0.0100013120963922
1671.9971.95998791045380.0300120895461475
1772.172.03948651798470.0605134820152955
1872.1272.1491296306105-0.0291296306105409
1972.1272.170278544642-0.0502785446420546
2072.1272.1705204055553-0.0505204055552468
2172.2572.17048957835920.0795104216408333
2272.5972.29884809258240.291151907417557
2372.7272.6362851535170.0837148464830619
2472.7672.7690454217792-0.00904542177919154
2572.7672.810248476812-0.0502484768119729
2672.9172.81075176559210.0992482344078525
277372.95886981575270.041130184247308
2873.1673.04965505412870.110344945871319
2973.1673.2088270507859-0.0488270507858886
3073.1173.210869032035-0.100869032034950
3173.1173.161479560017-0.0514795600170714
3273.3373.16080113853120.169198861468814
3373.5173.37803837688550.131961623114506
3473.6673.55861252484380.101387475156201
3573.6573.7090792547003-0.0590792547003076
3673.6573.7011312173181-0.0511312173181153
3773.6573.7009932231853-0.0509932231852872
3873.6573.7009571265267-0.0509571265266686
3973.7173.70092238238980.0090776176101599
4073.7373.7601459293447-0.0301459293446555
4173.8573.78063693596230.0693630640377307
4273.7773.8993864801217-0.129386480121724
4373.7773.8218901744475-0.0518901744475215
4473.7873.8208451015222-0.0408451015222369
4573.8873.83067365564650.0493263443534744
4674.373.92953143899090.370468561009105
4774.5374.34559449558730.184405504412723
4874.7174.57814387590190.131856124098135
4974.7174.7589175481348-0.0489175481348099
5074.7874.761241048420.0187589515799544
5174.974.83037149599780.0696285040022246
5274.6574.9497552384501-0.299755238450132
5374.6574.7043685763231-0.0543685763230997
5474.5374.7011333695995-0.171133369599517
5574.5374.5825403060316-0.0525403060316307
5674.5374.5809590956652-0.0509590956652346
5774.6574.58090420949920.0690957905007963
5874.8574.69938575621640.150614243783593
5974.9674.8984244580890.0615755419110116
6074.9675.0096265016009-0.0496265016008692
6174.9675.0110426522206-0.0510426522205591
6275.1975.01102678074140.178973219258623
6374.9875.2381488787475-0.258148878747448
6475.5475.03367317687030.506326823129697
6575.6175.58404871700910.0259512829908743
6675.5975.6603279128148-0.0703279128147756
6775.5875.641535618981-0.0615356189809546
6875.4475.6313796219147-0.191379621914663
6975.3775.4929434295242-0.122943429524170
7075.2275.4219686658305-0.201968665830549
7175.3375.27286292380330.057137076196696
7275.3375.3795238859368-0.0495238859367646

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 71.64 & 71.52 & 0.120000000000005 \tabularnewline
4 & 71.55 & 71.6885165001852 & -0.138516500185204 \tabularnewline
5 & 71.62 & 71.6017931216668 & 0.0182068783331886 \tabularnewline
6 & 71.65 & 71.6697624633511 & -0.0197624633511282 \tabularnewline
7 & 71.65 & 71.7002441051719 & -0.0502441051719131 \tabularnewline
8 & 71.65 & 71.7006076422472 & -0.050607642247158 \tabularnewline
9 & 71.6 & 71.7005783424363 & -0.100578342436336 \tabularnewline
10 & 71.7 & 71.651162066589 & 0.0488379334110363 \tabularnewline
11 & 71.73 & 71.7492472594121 & -0.0192472594120829 \tabularnewline
12 & 71.83 & 71.7801218107537 & 0.0498781892463427 \tabularnewline
13 & 71.83 & 71.8792543018512 & -0.0492543018512208 \tabularnewline
14 & 71.87 & 71.8805133750428 & -0.0105133750428053 \tabularnewline
15 & 71.91 & 71.9200013120964 & -0.0100013120963922 \tabularnewline
16 & 71.99 & 71.9599879104538 & 0.0300120895461475 \tabularnewline
17 & 72.1 & 72.0394865179847 & 0.0605134820152955 \tabularnewline
18 & 72.12 & 72.1491296306105 & -0.0291296306105409 \tabularnewline
19 & 72.12 & 72.170278544642 & -0.0502785446420546 \tabularnewline
20 & 72.12 & 72.1705204055553 & -0.0505204055552468 \tabularnewline
21 & 72.25 & 72.1704895783592 & 0.0795104216408333 \tabularnewline
22 & 72.59 & 72.2988480925824 & 0.291151907417557 \tabularnewline
23 & 72.72 & 72.636285153517 & 0.0837148464830619 \tabularnewline
24 & 72.76 & 72.7690454217792 & -0.00904542177919154 \tabularnewline
25 & 72.76 & 72.810248476812 & -0.0502484768119729 \tabularnewline
26 & 72.91 & 72.8107517655921 & 0.0992482344078525 \tabularnewline
27 & 73 & 72.9588698157527 & 0.041130184247308 \tabularnewline
28 & 73.16 & 73.0496550541287 & 0.110344945871319 \tabularnewline
29 & 73.16 & 73.2088270507859 & -0.0488270507858886 \tabularnewline
30 & 73.11 & 73.210869032035 & -0.100869032034950 \tabularnewline
31 & 73.11 & 73.161479560017 & -0.0514795600170714 \tabularnewline
32 & 73.33 & 73.1608011385312 & 0.169198861468814 \tabularnewline
33 & 73.51 & 73.3780383768855 & 0.131961623114506 \tabularnewline
34 & 73.66 & 73.5586125248438 & 0.101387475156201 \tabularnewline
35 & 73.65 & 73.7090792547003 & -0.0590792547003076 \tabularnewline
36 & 73.65 & 73.7011312173181 & -0.0511312173181153 \tabularnewline
37 & 73.65 & 73.7009932231853 & -0.0509932231852872 \tabularnewline
38 & 73.65 & 73.7009571265267 & -0.0509571265266686 \tabularnewline
39 & 73.71 & 73.7009223823898 & 0.0090776176101599 \tabularnewline
40 & 73.73 & 73.7601459293447 & -0.0301459293446555 \tabularnewline
41 & 73.85 & 73.7806369359623 & 0.0693630640377307 \tabularnewline
42 & 73.77 & 73.8993864801217 & -0.129386480121724 \tabularnewline
43 & 73.77 & 73.8218901744475 & -0.0518901744475215 \tabularnewline
44 & 73.78 & 73.8208451015222 & -0.0408451015222369 \tabularnewline
45 & 73.88 & 73.8306736556465 & 0.0493263443534744 \tabularnewline
46 & 74.3 & 73.9295314389909 & 0.370468561009105 \tabularnewline
47 & 74.53 & 74.3455944955873 & 0.184405504412723 \tabularnewline
48 & 74.71 & 74.5781438759019 & 0.131856124098135 \tabularnewline
49 & 74.71 & 74.7589175481348 & -0.0489175481348099 \tabularnewline
50 & 74.78 & 74.76124104842 & 0.0187589515799544 \tabularnewline
51 & 74.9 & 74.8303714959978 & 0.0696285040022246 \tabularnewline
52 & 74.65 & 74.9497552384501 & -0.299755238450132 \tabularnewline
53 & 74.65 & 74.7043685763231 & -0.0543685763230997 \tabularnewline
54 & 74.53 & 74.7011333695995 & -0.171133369599517 \tabularnewline
55 & 74.53 & 74.5825403060316 & -0.0525403060316307 \tabularnewline
56 & 74.53 & 74.5809590956652 & -0.0509590956652346 \tabularnewline
57 & 74.65 & 74.5809042094992 & 0.0690957905007963 \tabularnewline
58 & 74.85 & 74.6993857562164 & 0.150614243783593 \tabularnewline
59 & 74.96 & 74.898424458089 & 0.0615755419110116 \tabularnewline
60 & 74.96 & 75.0096265016009 & -0.0496265016008692 \tabularnewline
61 & 74.96 & 75.0110426522206 & -0.0510426522205591 \tabularnewline
62 & 75.19 & 75.0110267807414 & 0.178973219258623 \tabularnewline
63 & 74.98 & 75.2381488787475 & -0.258148878747448 \tabularnewline
64 & 75.54 & 75.0336731768703 & 0.506326823129697 \tabularnewline
65 & 75.61 & 75.5840487170091 & 0.0259512829908743 \tabularnewline
66 & 75.59 & 75.6603279128148 & -0.0703279128147756 \tabularnewline
67 & 75.58 & 75.641535618981 & -0.0615356189809546 \tabularnewline
68 & 75.44 & 75.6313796219147 & -0.191379621914663 \tabularnewline
69 & 75.37 & 75.4929434295242 & -0.122943429524170 \tabularnewline
70 & 75.22 & 75.4219686658305 & -0.201968665830549 \tabularnewline
71 & 75.33 & 75.2728629238033 & 0.057137076196696 \tabularnewline
72 & 75.33 & 75.3795238859368 & -0.0495238859367646 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13056&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]71.64[/C][C]71.52[/C][C]0.120000000000005[/C][/ROW]
[ROW][C]4[/C][C]71.55[/C][C]71.6885165001852[/C][C]-0.138516500185204[/C][/ROW]
[ROW][C]5[/C][C]71.62[/C][C]71.6017931216668[/C][C]0.0182068783331886[/C][/ROW]
[ROW][C]6[/C][C]71.65[/C][C]71.6697624633511[/C][C]-0.0197624633511282[/C][/ROW]
[ROW][C]7[/C][C]71.65[/C][C]71.7002441051719[/C][C]-0.0502441051719131[/C][/ROW]
[ROW][C]8[/C][C]71.65[/C][C]71.7006076422472[/C][C]-0.050607642247158[/C][/ROW]
[ROW][C]9[/C][C]71.6[/C][C]71.7005783424363[/C][C]-0.100578342436336[/C][/ROW]
[ROW][C]10[/C][C]71.7[/C][C]71.651162066589[/C][C]0.0488379334110363[/C][/ROW]
[ROW][C]11[/C][C]71.73[/C][C]71.7492472594121[/C][C]-0.0192472594120829[/C][/ROW]
[ROW][C]12[/C][C]71.83[/C][C]71.7801218107537[/C][C]0.0498781892463427[/C][/ROW]
[ROW][C]13[/C][C]71.83[/C][C]71.8792543018512[/C][C]-0.0492543018512208[/C][/ROW]
[ROW][C]14[/C][C]71.87[/C][C]71.8805133750428[/C][C]-0.0105133750428053[/C][/ROW]
[ROW][C]15[/C][C]71.91[/C][C]71.9200013120964[/C][C]-0.0100013120963922[/C][/ROW]
[ROW][C]16[/C][C]71.99[/C][C]71.9599879104538[/C][C]0.0300120895461475[/C][/ROW]
[ROW][C]17[/C][C]72.1[/C][C]72.0394865179847[/C][C]0.0605134820152955[/C][/ROW]
[ROW][C]18[/C][C]72.12[/C][C]72.1491296306105[/C][C]-0.0291296306105409[/C][/ROW]
[ROW][C]19[/C][C]72.12[/C][C]72.170278544642[/C][C]-0.0502785446420546[/C][/ROW]
[ROW][C]20[/C][C]72.12[/C][C]72.1705204055553[/C][C]-0.0505204055552468[/C][/ROW]
[ROW][C]21[/C][C]72.25[/C][C]72.1704895783592[/C][C]0.0795104216408333[/C][/ROW]
[ROW][C]22[/C][C]72.59[/C][C]72.2988480925824[/C][C]0.291151907417557[/C][/ROW]
[ROW][C]23[/C][C]72.72[/C][C]72.636285153517[/C][C]0.0837148464830619[/C][/ROW]
[ROW][C]24[/C][C]72.76[/C][C]72.7690454217792[/C][C]-0.00904542177919154[/C][/ROW]
[ROW][C]25[/C][C]72.76[/C][C]72.810248476812[/C][C]-0.0502484768119729[/C][/ROW]
[ROW][C]26[/C][C]72.91[/C][C]72.8107517655921[/C][C]0.0992482344078525[/C][/ROW]
[ROW][C]27[/C][C]73[/C][C]72.9588698157527[/C][C]0.041130184247308[/C][/ROW]
[ROW][C]28[/C][C]73.16[/C][C]73.0496550541287[/C][C]0.110344945871319[/C][/ROW]
[ROW][C]29[/C][C]73.16[/C][C]73.2088270507859[/C][C]-0.0488270507858886[/C][/ROW]
[ROW][C]30[/C][C]73.11[/C][C]73.210869032035[/C][C]-0.100869032034950[/C][/ROW]
[ROW][C]31[/C][C]73.11[/C][C]73.161479560017[/C][C]-0.0514795600170714[/C][/ROW]
[ROW][C]32[/C][C]73.33[/C][C]73.1608011385312[/C][C]0.169198861468814[/C][/ROW]
[ROW][C]33[/C][C]73.51[/C][C]73.3780383768855[/C][C]0.131961623114506[/C][/ROW]
[ROW][C]34[/C][C]73.66[/C][C]73.5586125248438[/C][C]0.101387475156201[/C][/ROW]
[ROW][C]35[/C][C]73.65[/C][C]73.7090792547003[/C][C]-0.0590792547003076[/C][/ROW]
[ROW][C]36[/C][C]73.65[/C][C]73.7011312173181[/C][C]-0.0511312173181153[/C][/ROW]
[ROW][C]37[/C][C]73.65[/C][C]73.7009932231853[/C][C]-0.0509932231852872[/C][/ROW]
[ROW][C]38[/C][C]73.65[/C][C]73.7009571265267[/C][C]-0.0509571265266686[/C][/ROW]
[ROW][C]39[/C][C]73.71[/C][C]73.7009223823898[/C][C]0.0090776176101599[/C][/ROW]
[ROW][C]40[/C][C]73.73[/C][C]73.7601459293447[/C][C]-0.0301459293446555[/C][/ROW]
[ROW][C]41[/C][C]73.85[/C][C]73.7806369359623[/C][C]0.0693630640377307[/C][/ROW]
[ROW][C]42[/C][C]73.77[/C][C]73.8993864801217[/C][C]-0.129386480121724[/C][/ROW]
[ROW][C]43[/C][C]73.77[/C][C]73.8218901744475[/C][C]-0.0518901744475215[/C][/ROW]
[ROW][C]44[/C][C]73.78[/C][C]73.8208451015222[/C][C]-0.0408451015222369[/C][/ROW]
[ROW][C]45[/C][C]73.88[/C][C]73.8306736556465[/C][C]0.0493263443534744[/C][/ROW]
[ROW][C]46[/C][C]74.3[/C][C]73.9295314389909[/C][C]0.370468561009105[/C][/ROW]
[ROW][C]47[/C][C]74.53[/C][C]74.3455944955873[/C][C]0.184405504412723[/C][/ROW]
[ROW][C]48[/C][C]74.71[/C][C]74.5781438759019[/C][C]0.131856124098135[/C][/ROW]
[ROW][C]49[/C][C]74.71[/C][C]74.7589175481348[/C][C]-0.0489175481348099[/C][/ROW]
[ROW][C]50[/C][C]74.78[/C][C]74.76124104842[/C][C]0.0187589515799544[/C][/ROW]
[ROW][C]51[/C][C]74.9[/C][C]74.8303714959978[/C][C]0.0696285040022246[/C][/ROW]
[ROW][C]52[/C][C]74.65[/C][C]74.9497552384501[/C][C]-0.299755238450132[/C][/ROW]
[ROW][C]53[/C][C]74.65[/C][C]74.7043685763231[/C][C]-0.0543685763230997[/C][/ROW]
[ROW][C]54[/C][C]74.53[/C][C]74.7011333695995[/C][C]-0.171133369599517[/C][/ROW]
[ROW][C]55[/C][C]74.53[/C][C]74.5825403060316[/C][C]-0.0525403060316307[/C][/ROW]
[ROW][C]56[/C][C]74.53[/C][C]74.5809590956652[/C][C]-0.0509590956652346[/C][/ROW]
[ROW][C]57[/C][C]74.65[/C][C]74.5809042094992[/C][C]0.0690957905007963[/C][/ROW]
[ROW][C]58[/C][C]74.85[/C][C]74.6993857562164[/C][C]0.150614243783593[/C][/ROW]
[ROW][C]59[/C][C]74.96[/C][C]74.898424458089[/C][C]0.0615755419110116[/C][/ROW]
[ROW][C]60[/C][C]74.96[/C][C]75.0096265016009[/C][C]-0.0496265016008692[/C][/ROW]
[ROW][C]61[/C][C]74.96[/C][C]75.0110426522206[/C][C]-0.0510426522205591[/C][/ROW]
[ROW][C]62[/C][C]75.19[/C][C]75.0110267807414[/C][C]0.178973219258623[/C][/ROW]
[ROW][C]63[/C][C]74.98[/C][C]75.2381488787475[/C][C]-0.258148878747448[/C][/ROW]
[ROW][C]64[/C][C]75.54[/C][C]75.0336731768703[/C][C]0.506326823129697[/C][/ROW]
[ROW][C]65[/C][C]75.61[/C][C]75.5840487170091[/C][C]0.0259512829908743[/C][/ROW]
[ROW][C]66[/C][C]75.59[/C][C]75.6603279128148[/C][C]-0.0703279128147756[/C][/ROW]
[ROW][C]67[/C][C]75.58[/C][C]75.641535618981[/C][C]-0.0615356189809546[/C][/ROW]
[ROW][C]68[/C][C]75.44[/C][C]75.6313796219147[/C][C]-0.191379621914663[/C][/ROW]
[ROW][C]69[/C][C]75.37[/C][C]75.4929434295242[/C][C]-0.122943429524170[/C][/ROW]
[ROW][C]70[/C][C]75.22[/C][C]75.4219686658305[/C][C]-0.201968665830549[/C][/ROW]
[ROW][C]71[/C][C]75.33[/C][C]75.2728629238033[/C][C]0.057137076196696[/C][/ROW]
[ROW][C]72[/C][C]75.33[/C][C]75.3795238859368[/C][C]-0.0495238859367646[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13056&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13056&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
371.6471.520.120000000000005
471.5571.6885165001852-0.138516500185204
571.6271.60179312166680.0182068783331886
671.6571.6697624633511-0.0197624633511282
771.6571.7002441051719-0.0502441051719131
871.6571.7006076422472-0.050607642247158
971.671.7005783424363-0.100578342436336
1071.771.6511620665890.0488379334110363
1171.7371.7492472594121-0.0192472594120829
1271.8371.78012181075370.0498781892463427
1371.8371.8792543018512-0.0492543018512208
1471.8771.8805133750428-0.0105133750428053
1571.9171.9200013120964-0.0100013120963922
1671.9971.95998791045380.0300120895461475
1772.172.03948651798470.0605134820152955
1872.1272.1491296306105-0.0291296306105409
1972.1272.170278544642-0.0502785446420546
2072.1272.1705204055553-0.0505204055552468
2172.2572.17048957835920.0795104216408333
2272.5972.29884809258240.291151907417557
2372.7272.6362851535170.0837148464830619
2472.7672.7690454217792-0.00904542177919154
2572.7672.810248476812-0.0502484768119729
2672.9172.81075176559210.0992482344078525
277372.95886981575270.041130184247308
2873.1673.04965505412870.110344945871319
2973.1673.2088270507859-0.0488270507858886
3073.1173.210869032035-0.100869032034950
3173.1173.161479560017-0.0514795600170714
3273.3373.16080113853120.169198861468814
3373.5173.37803837688550.131961623114506
3473.6673.55861252484380.101387475156201
3573.6573.7090792547003-0.0590792547003076
3673.6573.7011312173181-0.0511312173181153
3773.6573.7009932231853-0.0509932231852872
3873.6573.7009571265267-0.0509571265266686
3973.7173.70092238238980.0090776176101599
4073.7373.7601459293447-0.0301459293446555
4173.8573.78063693596230.0693630640377307
4273.7773.8993864801217-0.129386480121724
4373.7773.8218901744475-0.0518901744475215
4473.7873.8208451015222-0.0408451015222369
4573.8873.83067365564650.0493263443534744
4674.373.92953143899090.370468561009105
4774.5374.34559449558730.184405504412723
4874.7174.57814387590190.131856124098135
4974.7174.7589175481348-0.0489175481348099
5074.7874.761241048420.0187589515799544
5174.974.83037149599780.0696285040022246
5274.6574.9497552384501-0.299755238450132
5374.6574.7043685763231-0.0543685763230997
5474.5374.7011333695995-0.171133369599517
5574.5374.5825403060316-0.0525403060316307
5674.5374.5809590956652-0.0509590956652346
5774.6574.58090420949920.0690957905007963
5874.8574.69938575621640.150614243783593
5974.9674.8984244580890.0615755419110116
6074.9675.0096265016009-0.0496265016008692
6174.9675.0110426522206-0.0510426522205591
6275.1975.01102678074140.178973219258623
6374.9875.2381488787475-0.258148878747448
6475.5475.03367317687030.506326823129697
6575.6175.58404871700910.0259512829908743
6675.5975.6603279128148-0.0703279128147756
6775.5875.641535618981-0.0615356189809546
6875.4475.6313796219147-0.191379621914663
6975.3775.4929434295242-0.122943429524170
7075.2275.4219686658305-0.201968665830549
7175.3375.27286292380330.057137076196696
7275.3375.3795238859368-0.0495238859367646







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7375.38088091214675.130568929715875.6311928945761
7475.431116275708475.079302999500775.7829295519161
7575.481351639270875.051267525332475.9114357532092
7675.531587002833275.035345694117176.0278283115493
7775.581822366395775.027185627396476.1364591053949
7875.63205772995875.024544907816676.2395705520996
7975.682293093520575.026087909434576.3384982776066
8075.73252845708375.030942957943676.4341139562223
8175.782763820645475.038503924708776.5270237165821
8275.832999184207875.04832916400776.6176692044087
8375.883234547770375.060085100221876.7063839953187
8475.933469911332775.073512489955976.7934273327095

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 75.380880912146 & 75.1305689297158 & 75.6311928945761 \tabularnewline
74 & 75.4311162757084 & 75.0793029995007 & 75.7829295519161 \tabularnewline
75 & 75.4813516392708 & 75.0512675253324 & 75.9114357532092 \tabularnewline
76 & 75.5315870028332 & 75.0353456941171 & 76.0278283115493 \tabularnewline
77 & 75.5818223663957 & 75.0271856273964 & 76.1364591053949 \tabularnewline
78 & 75.632057729958 & 75.0245449078166 & 76.2395705520996 \tabularnewline
79 & 75.6822930935205 & 75.0260879094345 & 76.3384982776066 \tabularnewline
80 & 75.732528457083 & 75.0309429579436 & 76.4341139562223 \tabularnewline
81 & 75.7827638206454 & 75.0385039247087 & 76.5270237165821 \tabularnewline
82 & 75.8329991842078 & 75.048329164007 & 76.6176692044087 \tabularnewline
83 & 75.8832345477703 & 75.0600851002218 & 76.7063839953187 \tabularnewline
84 & 75.9334699113327 & 75.0735124899559 & 76.7934273327095 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13056&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]75.380880912146[/C][C]75.1305689297158[/C][C]75.6311928945761[/C][/ROW]
[ROW][C]74[/C][C]75.4311162757084[/C][C]75.0793029995007[/C][C]75.7829295519161[/C][/ROW]
[ROW][C]75[/C][C]75.4813516392708[/C][C]75.0512675253324[/C][C]75.9114357532092[/C][/ROW]
[ROW][C]76[/C][C]75.5315870028332[/C][C]75.0353456941171[/C][C]76.0278283115493[/C][/ROW]
[ROW][C]77[/C][C]75.5818223663957[/C][C]75.0271856273964[/C][C]76.1364591053949[/C][/ROW]
[ROW][C]78[/C][C]75.632057729958[/C][C]75.0245449078166[/C][C]76.2395705520996[/C][/ROW]
[ROW][C]79[/C][C]75.6822930935205[/C][C]75.0260879094345[/C][C]76.3384982776066[/C][/ROW]
[ROW][C]80[/C][C]75.732528457083[/C][C]75.0309429579436[/C][C]76.4341139562223[/C][/ROW]
[ROW][C]81[/C][C]75.7827638206454[/C][C]75.0385039247087[/C][C]76.5270237165821[/C][/ROW]
[ROW][C]82[/C][C]75.8329991842078[/C][C]75.048329164007[/C][C]76.6176692044087[/C][/ROW]
[ROW][C]83[/C][C]75.8832345477703[/C][C]75.0600851002218[/C][C]76.7063839953187[/C][/ROW]
[ROW][C]84[/C][C]75.9334699113327[/C][C]75.0735124899559[/C][C]76.7934273327095[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13056&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13056&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
7375.38088091214675.130568929715875.6311928945761
7475.431116275708475.079302999500775.7829295519161
7575.481351639270875.051267525332475.9114357532092
7675.531587002833275.035345694117176.0278283115493
7775.581822366395775.027185627396476.1364591053949
7875.63205772995875.024544907816676.2395705520996
7975.682293093520575.026087909434576.3384982776066
8075.73252845708375.030942957943676.4341139562223
8175.782763820645475.038503924708776.5270237165821
8275.832999184207875.04832916400776.6176692044087
8375.883234547770375.060085100221876.7063839953187
8475.933469911332775.073512489955976.7934273327095



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=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')