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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 16 Jan 2012 04:30:50 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Jan/16/t1326706278v8uz4e9t79d4dk3.htm/, Retrieved Sun, 28 Apr 2024 03:39:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=161202, Retrieved Sun, 28 Apr 2024 03:39:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact200

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-01-16 09:30:50] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
14,14
14,16
14,21
14,26
14,29
14,32
14,33
14,39
14,48
14,44
14,46
14,48
14,53
14,58
14,62
14,62
14,61
14,65
14,68
14,7
14,78
14,84
14,89
14,89
15,13
15,25
15,33
15,36
15,4
15,4
15,41
15,47
15,54
15,55
15,59
15,65
15,75
15,86
15,89
15,94
15,93
15,95
15,99
15,99
16,06
16,08
16,07
16,11
16,15
16,18
16,3
16,42
16,49
16,5
16,58
16,64
16,66
16,81
16,91
16,92
16,95
17,11
17,16
17,16
17,27
17,34
17,39
17,43
17,45
17,5
17,56
17,65
17,62
17,7
17,72
17,71
17,74
17,75
17,78
17,8
17,86
17,88
17,89
17,94

Tables (Output of Computation)





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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161202&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161202&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161202&T=0

As an alternative you can also use a QR Code:  
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' @ jenkins.wessa.net






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0796336282309531
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0796336282309531 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161202&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]0.0796336282309531[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161202&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161202&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0796336282309531
gammaFALSE






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
314.2114.180.0300000000000011
414.2614.23238900884690.02761099115307
514.2914.28458777225150.00541222774849892
614.3214.31501876758390.00498123241607651
714.3314.3454154411943-0.0154154411942784
814.3914.35418785368120.0358121463188024
914.4814.41703970482730.0629602951726973
1014.4414.5120534615664-0.0720534615663961
1114.4614.4663155829953-0.00631558299526169
1214.4814.485812650207-0.00581265020695731
1314.5314.50534976778130.0246502322186597
1414.5814.55731275520960.0226872447903528
1514.6214.60911942282690.0108805771731326
1614.6214.6499858826644-0.0299858826644108
1714.6114.6475979980321-0.037597998032135
1814.6514.63460393303460.0153960669653852
1914.6814.67582997770760.0041700222924419
2014.714.7061620517125-0.00616205171250783
2114.7814.72567134517730.0543286548227062
2214.8414.80999773307770.030002266922267
2314.8914.87238692244790.0176130775520935
2414.8914.9237895157177-0.0337895157176931
2515.1314.92109873398490.208901266015074
2615.2515.17773429973970.0722657002602531
2715.3315.30348907964810.0265109203518801
2815.3615.3856002404235-0.0256002404234827
2915.415.413561600395-0.0135616003949757
3015.415.4524816409509-0.052481640950905
3115.4115.4483023374665-0.0383023374664706
3215.4715.45525218336430.01474781663571
3315.5415.51642660551150.0235733944885226
3415.5515.5883038404443-0.0383038404443159
3515.5915.5952535666546-0.00525356665455767
3615.6515.63483520608070.0151647939193005
3715.7515.69604283364190.0539571663581295
3815.8615.8003396385680.0596603614319715
3915.8915.9150906096104-0.0250906096104249
4015.9415.9430925533326-0.00309255333262293
4115.9315.9928462820902-0.0628462820902467
4215.9515.9778416046266-0.027841604626575
4315.9915.9956244766344-0.00562447663438803
4415.9916.0351765791531-0.0451765791530914
4516.0616.03157900424410.0284209957559298
4616.0816.103842271254-0.0238422712540505
4716.0716.1219436246888-0.0519436246888212
4816.1116.10780716539140.00219283460861419
4916.1516.14798178876740.00201821123262036
5016.1816.1881425062504-0.00814250625036905
5116.316.21749408893480.0825059110652404
5216.4216.34406433398340.0759356660166155
5316.4916.47011136658040.0198886334195727
5416.516.5416951706202-0.0416951706201765
5516.5816.5483748329040.0316251670960135
5616.6416.63089325970320.00910674029675107
5716.6616.6916184624744-0.0316184624744373
5816.8116.70910056958850.100899430411484
5916.9116.86713555731860.0428644426813847
6016.9216.9705490084114-0.0505490084114335
6116.9516.9765236074682-0.0265236074681567
6217.1117.00441143637170.105588563628309
6317.1617.1728198367931-0.0128198367931063
6417.1617.2217989466759-0.0617989466759461
6517.2717.21687767233130.0531223276687101
6617.3417.33110799602360.00889200397637779
6717.3917.4018160985625-0.0118160985625018
6817.4317.4508751397624-0.0208751397624383
6917.4517.4892127766433-0.0392127766433283
7017.517.5060901209662-0.00609012096620631
7117.5617.55560514253730.00439485746269597
7217.6517.61595512098260.0340448790173831
7317.6217.7086662382215-0.0886662382214531
7417.717.67160542397030.028394576029708
7517.7217.7538665870816-0.0338665870816151
7617.7117.7711696678765-0.0611696678765057
7717.7417.7562985052858-0.0162985052858211
7817.7517.7850005961752-0.0350005961751663
7917.7817.7922133717115-0.0122133717114927
8017.817.8212407766092-0.0212407766091722
8117.8617.83954929650130.020450703498657
8217.8817.9011778602208-0.0211778602208135
8317.8917.9194913903733-0.0294913903732628
8417.9417.92714288395630.0128571160437367

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 14.21 & 14.18 & 0.0300000000000011 \tabularnewline
4 & 14.26 & 14.2323890088469 & 0.02761099115307 \tabularnewline
5 & 14.29 & 14.2845877722515 & 0.00541222774849892 \tabularnewline
6 & 14.32 & 14.3150187675839 & 0.00498123241607651 \tabularnewline
7 & 14.33 & 14.3454154411943 & -0.0154154411942784 \tabularnewline
8 & 14.39 & 14.3541878536812 & 0.0358121463188024 \tabularnewline
9 & 14.48 & 14.4170397048273 & 0.0629602951726973 \tabularnewline
10 & 14.44 & 14.5120534615664 & -0.0720534615663961 \tabularnewline
11 & 14.46 & 14.4663155829953 & -0.00631558299526169 \tabularnewline
12 & 14.48 & 14.485812650207 & -0.00581265020695731 \tabularnewline
13 & 14.53 & 14.5053497677813 & 0.0246502322186597 \tabularnewline
14 & 14.58 & 14.5573127552096 & 0.0226872447903528 \tabularnewline
15 & 14.62 & 14.6091194228269 & 0.0108805771731326 \tabularnewline
16 & 14.62 & 14.6499858826644 & -0.0299858826644108 \tabularnewline
17 & 14.61 & 14.6475979980321 & -0.037597998032135 \tabularnewline
18 & 14.65 & 14.6346039330346 & 0.0153960669653852 \tabularnewline
19 & 14.68 & 14.6758299777076 & 0.0041700222924419 \tabularnewline
20 & 14.7 & 14.7061620517125 & -0.00616205171250783 \tabularnewline
21 & 14.78 & 14.7256713451773 & 0.0543286548227062 \tabularnewline
22 & 14.84 & 14.8099977330777 & 0.030002266922267 \tabularnewline
23 & 14.89 & 14.8723869224479 & 0.0176130775520935 \tabularnewline
24 & 14.89 & 14.9237895157177 & -0.0337895157176931 \tabularnewline
25 & 15.13 & 14.9210987339849 & 0.208901266015074 \tabularnewline
26 & 15.25 & 15.1777342997397 & 0.0722657002602531 \tabularnewline
27 & 15.33 & 15.3034890796481 & 0.0265109203518801 \tabularnewline
28 & 15.36 & 15.3856002404235 & -0.0256002404234827 \tabularnewline
29 & 15.4 & 15.413561600395 & -0.0135616003949757 \tabularnewline
30 & 15.4 & 15.4524816409509 & -0.052481640950905 \tabularnewline
31 & 15.41 & 15.4483023374665 & -0.0383023374664706 \tabularnewline
32 & 15.47 & 15.4552521833643 & 0.01474781663571 \tabularnewline
33 & 15.54 & 15.5164266055115 & 0.0235733944885226 \tabularnewline
34 & 15.55 & 15.5883038404443 & -0.0383038404443159 \tabularnewline
35 & 15.59 & 15.5952535666546 & -0.00525356665455767 \tabularnewline
36 & 15.65 & 15.6348352060807 & 0.0151647939193005 \tabularnewline
37 & 15.75 & 15.6960428336419 & 0.0539571663581295 \tabularnewline
38 & 15.86 & 15.800339638568 & 0.0596603614319715 \tabularnewline
39 & 15.89 & 15.9150906096104 & -0.0250906096104249 \tabularnewline
40 & 15.94 & 15.9430925533326 & -0.00309255333262293 \tabularnewline
41 & 15.93 & 15.9928462820902 & -0.0628462820902467 \tabularnewline
42 & 15.95 & 15.9778416046266 & -0.027841604626575 \tabularnewline
43 & 15.99 & 15.9956244766344 & -0.00562447663438803 \tabularnewline
44 & 15.99 & 16.0351765791531 & -0.0451765791530914 \tabularnewline
45 & 16.06 & 16.0315790042441 & 0.0284209957559298 \tabularnewline
46 & 16.08 & 16.103842271254 & -0.0238422712540505 \tabularnewline
47 & 16.07 & 16.1219436246888 & -0.0519436246888212 \tabularnewline
48 & 16.11 & 16.1078071653914 & 0.00219283460861419 \tabularnewline
49 & 16.15 & 16.1479817887674 & 0.00201821123262036 \tabularnewline
50 & 16.18 & 16.1881425062504 & -0.00814250625036905 \tabularnewline
51 & 16.3 & 16.2174940889348 & 0.0825059110652404 \tabularnewline
52 & 16.42 & 16.3440643339834 & 0.0759356660166155 \tabularnewline
53 & 16.49 & 16.4701113665804 & 0.0198886334195727 \tabularnewline
54 & 16.5 & 16.5416951706202 & -0.0416951706201765 \tabularnewline
55 & 16.58 & 16.548374832904 & 0.0316251670960135 \tabularnewline
56 & 16.64 & 16.6308932597032 & 0.00910674029675107 \tabularnewline
57 & 16.66 & 16.6916184624744 & -0.0316184624744373 \tabularnewline
58 & 16.81 & 16.7091005695885 & 0.100899430411484 \tabularnewline
59 & 16.91 & 16.8671355573186 & 0.0428644426813847 \tabularnewline
60 & 16.92 & 16.9705490084114 & -0.0505490084114335 \tabularnewline
61 & 16.95 & 16.9765236074682 & -0.0265236074681567 \tabularnewline
62 & 17.11 & 17.0044114363717 & 0.105588563628309 \tabularnewline
63 & 17.16 & 17.1728198367931 & -0.0128198367931063 \tabularnewline
64 & 17.16 & 17.2217989466759 & -0.0617989466759461 \tabularnewline
65 & 17.27 & 17.2168776723313 & 0.0531223276687101 \tabularnewline
66 & 17.34 & 17.3311079960236 & 0.00889200397637779 \tabularnewline
67 & 17.39 & 17.4018160985625 & -0.0118160985625018 \tabularnewline
68 & 17.43 & 17.4508751397624 & -0.0208751397624383 \tabularnewline
69 & 17.45 & 17.4892127766433 & -0.0392127766433283 \tabularnewline
70 & 17.5 & 17.5060901209662 & -0.00609012096620631 \tabularnewline
71 & 17.56 & 17.5556051425373 & 0.00439485746269597 \tabularnewline
72 & 17.65 & 17.6159551209826 & 0.0340448790173831 \tabularnewline
73 & 17.62 & 17.7086662382215 & -0.0886662382214531 \tabularnewline
74 & 17.7 & 17.6716054239703 & 0.028394576029708 \tabularnewline
75 & 17.72 & 17.7538665870816 & -0.0338665870816151 \tabularnewline
76 & 17.71 & 17.7711696678765 & -0.0611696678765057 \tabularnewline
77 & 17.74 & 17.7562985052858 & -0.0162985052858211 \tabularnewline
78 & 17.75 & 17.7850005961752 & -0.0350005961751663 \tabularnewline
79 & 17.78 & 17.7922133717115 & -0.0122133717114927 \tabularnewline
80 & 17.8 & 17.8212407766092 & -0.0212407766091722 \tabularnewline
81 & 17.86 & 17.8395492965013 & 0.020450703498657 \tabularnewline
82 & 17.88 & 17.9011778602208 & -0.0211778602208135 \tabularnewline
83 & 17.89 & 17.9194913903733 & -0.0294913903732628 \tabularnewline
84 & 17.94 & 17.9271428839563 & 0.0128571160437367 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161202&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]14.21[/C][C]14.18[/C][C]0.0300000000000011[/C][/ROW]
[ROW][C]4[/C][C]14.26[/C][C]14.2323890088469[/C][C]0.02761099115307[/C][/ROW]
[ROW][C]5[/C][C]14.29[/C][C]14.2845877722515[/C][C]0.00541222774849892[/C][/ROW]
[ROW][C]6[/C][C]14.32[/C][C]14.3150187675839[/C][C]0.00498123241607651[/C][/ROW]
[ROW][C]7[/C][C]14.33[/C][C]14.3454154411943[/C][C]-0.0154154411942784[/C][/ROW]
[ROW][C]8[/C][C]14.39[/C][C]14.3541878536812[/C][C]0.0358121463188024[/C][/ROW]
[ROW][C]9[/C][C]14.48[/C][C]14.4170397048273[/C][C]0.0629602951726973[/C][/ROW]
[ROW][C]10[/C][C]14.44[/C][C]14.5120534615664[/C][C]-0.0720534615663961[/C][/ROW]
[ROW][C]11[/C][C]14.46[/C][C]14.4663155829953[/C][C]-0.00631558299526169[/C][/ROW]
[ROW][C]12[/C][C]14.48[/C][C]14.485812650207[/C][C]-0.00581265020695731[/C][/ROW]
[ROW][C]13[/C][C]14.53[/C][C]14.5053497677813[/C][C]0.0246502322186597[/C][/ROW]
[ROW][C]14[/C][C]14.58[/C][C]14.5573127552096[/C][C]0.0226872447903528[/C][/ROW]
[ROW][C]15[/C][C]14.62[/C][C]14.6091194228269[/C][C]0.0108805771731326[/C][/ROW]
[ROW][C]16[/C][C]14.62[/C][C]14.6499858826644[/C][C]-0.0299858826644108[/C][/ROW]
[ROW][C]17[/C][C]14.61[/C][C]14.6475979980321[/C][C]-0.037597998032135[/C][/ROW]
[ROW][C]18[/C][C]14.65[/C][C]14.6346039330346[/C][C]0.0153960669653852[/C][/ROW]
[ROW][C]19[/C][C]14.68[/C][C]14.6758299777076[/C][C]0.0041700222924419[/C][/ROW]
[ROW][C]20[/C][C]14.7[/C][C]14.7061620517125[/C][C]-0.00616205171250783[/C][/ROW]
[ROW][C]21[/C][C]14.78[/C][C]14.7256713451773[/C][C]0.0543286548227062[/C][/ROW]
[ROW][C]22[/C][C]14.84[/C][C]14.8099977330777[/C][C]0.030002266922267[/C][/ROW]
[ROW][C]23[/C][C]14.89[/C][C]14.8723869224479[/C][C]0.0176130775520935[/C][/ROW]
[ROW][C]24[/C][C]14.89[/C][C]14.9237895157177[/C][C]-0.0337895157176931[/C][/ROW]
[ROW][C]25[/C][C]15.13[/C][C]14.9210987339849[/C][C]0.208901266015074[/C][/ROW]
[ROW][C]26[/C][C]15.25[/C][C]15.1777342997397[/C][C]0.0722657002602531[/C][/ROW]
[ROW][C]27[/C][C]15.33[/C][C]15.3034890796481[/C][C]0.0265109203518801[/C][/ROW]
[ROW][C]28[/C][C]15.36[/C][C]15.3856002404235[/C][C]-0.0256002404234827[/C][/ROW]
[ROW][C]29[/C][C]15.4[/C][C]15.413561600395[/C][C]-0.0135616003949757[/C][/ROW]
[ROW][C]30[/C][C]15.4[/C][C]15.4524816409509[/C][C]-0.052481640950905[/C][/ROW]
[ROW][C]31[/C][C]15.41[/C][C]15.4483023374665[/C][C]-0.0383023374664706[/C][/ROW]
[ROW][C]32[/C][C]15.47[/C][C]15.4552521833643[/C][C]0.01474781663571[/C][/ROW]
[ROW][C]33[/C][C]15.54[/C][C]15.5164266055115[/C][C]0.0235733944885226[/C][/ROW]
[ROW][C]34[/C][C]15.55[/C][C]15.5883038404443[/C][C]-0.0383038404443159[/C][/ROW]
[ROW][C]35[/C][C]15.59[/C][C]15.5952535666546[/C][C]-0.00525356665455767[/C][/ROW]
[ROW][C]36[/C][C]15.65[/C][C]15.6348352060807[/C][C]0.0151647939193005[/C][/ROW]
[ROW][C]37[/C][C]15.75[/C][C]15.6960428336419[/C][C]0.0539571663581295[/C][/ROW]
[ROW][C]38[/C][C]15.86[/C][C]15.800339638568[/C][C]0.0596603614319715[/C][/ROW]
[ROW][C]39[/C][C]15.89[/C][C]15.9150906096104[/C][C]-0.0250906096104249[/C][/ROW]
[ROW][C]40[/C][C]15.94[/C][C]15.9430925533326[/C][C]-0.00309255333262293[/C][/ROW]
[ROW][C]41[/C][C]15.93[/C][C]15.9928462820902[/C][C]-0.0628462820902467[/C][/ROW]
[ROW][C]42[/C][C]15.95[/C][C]15.9778416046266[/C][C]-0.027841604626575[/C][/ROW]
[ROW][C]43[/C][C]15.99[/C][C]15.9956244766344[/C][C]-0.00562447663438803[/C][/ROW]
[ROW][C]44[/C][C]15.99[/C][C]16.0351765791531[/C][C]-0.0451765791530914[/C][/ROW]
[ROW][C]45[/C][C]16.06[/C][C]16.0315790042441[/C][C]0.0284209957559298[/C][/ROW]
[ROW][C]46[/C][C]16.08[/C][C]16.103842271254[/C][C]-0.0238422712540505[/C][/ROW]
[ROW][C]47[/C][C]16.07[/C][C]16.1219436246888[/C][C]-0.0519436246888212[/C][/ROW]
[ROW][C]48[/C][C]16.11[/C][C]16.1078071653914[/C][C]0.00219283460861419[/C][/ROW]
[ROW][C]49[/C][C]16.15[/C][C]16.1479817887674[/C][C]0.00201821123262036[/C][/ROW]
[ROW][C]50[/C][C]16.18[/C][C]16.1881425062504[/C][C]-0.00814250625036905[/C][/ROW]
[ROW][C]51[/C][C]16.3[/C][C]16.2174940889348[/C][C]0.0825059110652404[/C][/ROW]
[ROW][C]52[/C][C]16.42[/C][C]16.3440643339834[/C][C]0.0759356660166155[/C][/ROW]
[ROW][C]53[/C][C]16.49[/C][C]16.4701113665804[/C][C]0.0198886334195727[/C][/ROW]
[ROW][C]54[/C][C]16.5[/C][C]16.5416951706202[/C][C]-0.0416951706201765[/C][/ROW]
[ROW][C]55[/C][C]16.58[/C][C]16.548374832904[/C][C]0.0316251670960135[/C][/ROW]
[ROW][C]56[/C][C]16.64[/C][C]16.6308932597032[/C][C]0.00910674029675107[/C][/ROW]
[ROW][C]57[/C][C]16.66[/C][C]16.6916184624744[/C][C]-0.0316184624744373[/C][/ROW]
[ROW][C]58[/C][C]16.81[/C][C]16.7091005695885[/C][C]0.100899430411484[/C][/ROW]
[ROW][C]59[/C][C]16.91[/C][C]16.8671355573186[/C][C]0.0428644426813847[/C][/ROW]
[ROW][C]60[/C][C]16.92[/C][C]16.9705490084114[/C][C]-0.0505490084114335[/C][/ROW]
[ROW][C]61[/C][C]16.95[/C][C]16.9765236074682[/C][C]-0.0265236074681567[/C][/ROW]
[ROW][C]62[/C][C]17.11[/C][C]17.0044114363717[/C][C]0.105588563628309[/C][/ROW]
[ROW][C]63[/C][C]17.16[/C][C]17.1728198367931[/C][C]-0.0128198367931063[/C][/ROW]
[ROW][C]64[/C][C]17.16[/C][C]17.2217989466759[/C][C]-0.0617989466759461[/C][/ROW]
[ROW][C]65[/C][C]17.27[/C][C]17.2168776723313[/C][C]0.0531223276687101[/C][/ROW]
[ROW][C]66[/C][C]17.34[/C][C]17.3311079960236[/C][C]0.00889200397637779[/C][/ROW]
[ROW][C]67[/C][C]17.39[/C][C]17.4018160985625[/C][C]-0.0118160985625018[/C][/ROW]
[ROW][C]68[/C][C]17.43[/C][C]17.4508751397624[/C][C]-0.0208751397624383[/C][/ROW]
[ROW][C]69[/C][C]17.45[/C][C]17.4892127766433[/C][C]-0.0392127766433283[/C][/ROW]
[ROW][C]70[/C][C]17.5[/C][C]17.5060901209662[/C][C]-0.00609012096620631[/C][/ROW]
[ROW][C]71[/C][C]17.56[/C][C]17.5556051425373[/C][C]0.00439485746269597[/C][/ROW]
[ROW][C]72[/C][C]17.65[/C][C]17.6159551209826[/C][C]0.0340448790173831[/C][/ROW]
[ROW][C]73[/C][C]17.62[/C][C]17.7086662382215[/C][C]-0.0886662382214531[/C][/ROW]
[ROW][C]74[/C][C]17.7[/C][C]17.6716054239703[/C][C]0.028394576029708[/C][/ROW]
[ROW][C]75[/C][C]17.72[/C][C]17.7538665870816[/C][C]-0.0338665870816151[/C][/ROW]
[ROW][C]76[/C][C]17.71[/C][C]17.7711696678765[/C][C]-0.0611696678765057[/C][/ROW]
[ROW][C]77[/C][C]17.74[/C][C]17.7562985052858[/C][C]-0.0162985052858211[/C][/ROW]
[ROW][C]78[/C][C]17.75[/C][C]17.7850005961752[/C][C]-0.0350005961751663[/C][/ROW]
[ROW][C]79[/C][C]17.78[/C][C]17.7922133717115[/C][C]-0.0122133717114927[/C][/ROW]
[ROW][C]80[/C][C]17.8[/C][C]17.8212407766092[/C][C]-0.0212407766091722[/C][/ROW]
[ROW][C]81[/C][C]17.86[/C][C]17.8395492965013[/C][C]0.020450703498657[/C][/ROW]
[ROW][C]82[/C][C]17.88[/C][C]17.9011778602208[/C][C]-0.0211778602208135[/C][/ROW]
[ROW][C]83[/C][C]17.89[/C][C]17.9194913903733[/C][C]-0.0294913903732628[/C][/ROW]
[ROW][C]84[/C][C]17.94[/C][C]17.9271428839563[/C][C]0.0128571160437367[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161202&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161202&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
314.2114.180.0300000000000011
414.2614.23238900884690.02761099115307
514.2914.28458777225150.00541222774849892
614.3214.31501876758390.00498123241607651
714.3314.3454154411943-0.0154154411942784
814.3914.35418785368120.0358121463188024
914.4814.41703970482730.0629602951726973
1014.4414.5120534615664-0.0720534615663961
1114.4614.4663155829953-0.00631558299526169
1214.4814.485812650207-0.00581265020695731
1314.5314.50534976778130.0246502322186597
1414.5814.55731275520960.0226872447903528
1514.6214.60911942282690.0108805771731326
1614.6214.6499858826644-0.0299858826644108
1714.6114.6475979980321-0.037597998032135
1814.6514.63460393303460.0153960669653852
1914.6814.67582997770760.0041700222924419
2014.714.7061620517125-0.00616205171250783
2114.7814.72567134517730.0543286548227062
2214.8414.80999773307770.030002266922267
2314.8914.87238692244790.0176130775520935
2414.8914.9237895157177-0.0337895157176931
2515.1314.92109873398490.208901266015074
2615.2515.17773429973970.0722657002602531
2715.3315.30348907964810.0265109203518801
2815.3615.3856002404235-0.0256002404234827
2915.415.413561600395-0.0135616003949757
3015.415.4524816409509-0.052481640950905
3115.4115.4483023374665-0.0383023374664706
3215.4715.45525218336430.01474781663571
3315.5415.51642660551150.0235733944885226
3415.5515.5883038404443-0.0383038404443159
3515.5915.5952535666546-0.00525356665455767
3615.6515.63483520608070.0151647939193005
3715.7515.69604283364190.0539571663581295
3815.8615.8003396385680.0596603614319715
3915.8915.9150906096104-0.0250906096104249
4015.9415.9430925533326-0.00309255333262293
4115.9315.9928462820902-0.0628462820902467
4215.9515.9778416046266-0.027841604626575
4315.9915.9956244766344-0.00562447663438803
4415.9916.0351765791531-0.0451765791530914
4516.0616.03157900424410.0284209957559298
4616.0816.103842271254-0.0238422712540505
4716.0716.1219436246888-0.0519436246888212
4816.1116.10780716539140.00219283460861419
4916.1516.14798178876740.00201821123262036
5016.1816.1881425062504-0.00814250625036905
5116.316.21749408893480.0825059110652404
5216.4216.34406433398340.0759356660166155
5316.4916.47011136658040.0198886334195727
5416.516.5416951706202-0.0416951706201765
5516.5816.5483748329040.0316251670960135
5616.6416.63089325970320.00910674029675107
5716.6616.6916184624744-0.0316184624744373
5816.8116.70910056958850.100899430411484
5916.9116.86713555731860.0428644426813847
6016.9216.9705490084114-0.0505490084114335
6116.9516.9765236074682-0.0265236074681567
6217.1117.00441143637170.105588563628309
6317.1617.1728198367931-0.0128198367931063
6417.1617.2217989466759-0.0617989466759461
6517.2717.21687767233130.0531223276687101
6617.3417.33110799602360.00889200397637779
6717.3917.4018160985625-0.0118160985625018
6817.4317.4508751397624-0.0208751397624383
6917.4517.4892127766433-0.0392127766433283
7017.517.5060901209662-0.00609012096620631
7117.5617.55560514253730.00439485746269597
7217.6517.61595512098260.0340448790173831
7317.6217.7086662382215-0.0886662382214531
7417.717.67160542397030.028394576029708
7517.7217.7538665870816-0.0338665870816151
7617.7117.7711696678765-0.0611696678765057
7717.7417.7562985052858-0.0162985052858211
7817.7517.7850005961752-0.0350005961751663
7917.7817.7922133717115-0.0122133717114927
8017.817.8212407766092-0.0212407766091722
8117.8617.83954929650130.020450703498657
8217.8817.9011778602208-0.0211778602208135
8317.8917.9194913903733-0.0294913903732628
8417.9417.92714288395630.0128571160437367






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8517.978166742755417.889134916176418.0671985693344
8618.016333485510817.885314182628118.1473527883935
8718.054500228266217.88771081345818.2212896430745
8818.092666971021717.892704090023418.2926298520199
8918.130833713777117.8989589059118.3627085216442
9018.169000456532517.905824543365218.4321763696998
9118.207167199287917.912934991394718.5013994071811
9218.245333942043317.920065509307218.5706023747794
9318.283500684798717.927069795381718.6399315742158
9418.321667427554117.933848651461118.7094862036471
9518.359834170309617.940332847362918.7793354932562
9618.39800091306517.946473080409918.8495287457201

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 17.9781667427554 & 17.8891349161764 & 18.0671985693344 \tabularnewline
86 & 18.0163334855108 & 17.8853141826281 & 18.1473527883935 \tabularnewline
87 & 18.0545002282662 & 17.887710813458 & 18.2212896430745 \tabularnewline
88 & 18.0926669710217 & 17.8927040900234 & 18.2926298520199 \tabularnewline
89 & 18.1308337137771 & 17.89895890591 & 18.3627085216442 \tabularnewline
90 & 18.1690004565325 & 17.9058245433652 & 18.4321763696998 \tabularnewline
91 & 18.2071671992879 & 17.9129349913947 & 18.5013994071811 \tabularnewline
92 & 18.2453339420433 & 17.9200655093072 & 18.5706023747794 \tabularnewline
93 & 18.2835006847987 & 17.9270697953817 & 18.6399315742158 \tabularnewline
94 & 18.3216674275541 & 17.9338486514611 & 18.7094862036471 \tabularnewline
95 & 18.3598341703096 & 17.9403328473629 & 18.7793354932562 \tabularnewline
96 & 18.398000913065 & 17.9464730804099 & 18.8495287457201 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161202&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]85[/C][C]17.9781667427554[/C][C]17.8891349161764[/C][C]18.0671985693344[/C][/ROW]
[ROW][C]86[/C][C]18.0163334855108[/C][C]17.8853141826281[/C][C]18.1473527883935[/C][/ROW]
[ROW][C]87[/C][C]18.0545002282662[/C][C]17.887710813458[/C][C]18.2212896430745[/C][/ROW]
[ROW][C]88[/C][C]18.0926669710217[/C][C]17.8927040900234[/C][C]18.2926298520199[/C][/ROW]
[ROW][C]89[/C][C]18.1308337137771[/C][C]17.89895890591[/C][C]18.3627085216442[/C][/ROW]
[ROW][C]90[/C][C]18.1690004565325[/C][C]17.9058245433652[/C][C]18.4321763696998[/C][/ROW]
[ROW][C]91[/C][C]18.2071671992879[/C][C]17.9129349913947[/C][C]18.5013994071811[/C][/ROW]
[ROW][C]92[/C][C]18.2453339420433[/C][C]17.9200655093072[/C][C]18.5706023747794[/C][/ROW]
[ROW][C]93[/C][C]18.2835006847987[/C][C]17.9270697953817[/C][C]18.6399315742158[/C][/ROW]
[ROW][C]94[/C][C]18.3216674275541[/C][C]17.9338486514611[/C][C]18.7094862036471[/C][/ROW]
[ROW][C]95[/C][C]18.3598341703096[/C][C]17.9403328473629[/C][C]18.7793354932562[/C][/ROW]
[ROW][C]96[/C][C]18.398000913065[/C][C]17.9464730804099[/C][C]18.8495287457201[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161202&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161202&T=3

As an alternative you can also use a QR Code:  
QR Code


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

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8517.978166742755417.889134916176418.0671985693344
8618.016333485510817.885314182628118.1473527883935
8718.054500228266217.88771081345818.2212896430745
8818.092666971021717.892704090023418.2926298520199
8918.130833713777117.8989589059118.3627085216442
9018.169000456532517.905824543365218.4321763696998
9118.207167199287917.912934991394718.5013994071811
9218.245333942043317.920065509307218.5706023747794
9318.283500684798717.927069795381718.6399315742158
9418.321667427554117.933848651461118.7094862036471
9518.359834170309617.940332847362918.7793354932562
9618.39800091306517.946473080409918.8495287457201


Figures (Output of Computation)

Input Parameters & R Code

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')