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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 26 Dec 2013 14:25:25 -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/2013/Dec/26/t1388085947zycc1xxtrnusvhw.htm/, Retrieved Fri, 29 Mar 2024 00:31:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232628, Retrieved Fri, 29 Mar 2024 00:31:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact138
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-12-26 19:25:25] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
27,65
28,19
28,98
28,99
29,02
29
29,04
29,19
29,23
29,26
29,02
28,47
28,53
28,48
28,68
28,89
29,2
29,21
29,15
29,22
29,34
29,13
28,84
28,76
28,75
28,89
28,82
29,12
29,21
29,3
29,32
29,52
29,64
29,54
29,54
29,34
29,34
29,54
29,94
30,17
30,23
30,34
30,34
30,36
30,3
30,28
29,89
29,58
29,68
29,73
30,07
30,32
30,55
30,62
30,67
30,79
30,8
30,5
30,07
29,41
29,42
29,99
30,14
30,41
30,78
30,88
30,92
30,93
31,62
31,48
31,3
31,11
31,16
31,22
31,66
32,11
32,27
32,36
32,42
32,52
32,41
31,87
31,04
30,58




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 4 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232628&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232628&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232628&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 time4 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.904662245210055
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.904662245210055 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232628&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]0.904662245210055[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232628&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232628&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
alpha0.904662245210055
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1328.5328.48438451095920.0456154890408484
1428.4828.47471367742330.00528632257673323
1528.6828.67854018522030.00145981477971446
1628.8928.8955535455549-0.00555354555487853
1729.229.2184864385603-0.0184864385603198
1829.2129.212054124888-0.00205412488804413
1929.1529.11256582154910.0374341784508658
2029.2229.2525160640695-0.0325160640695294
2129.3429.26849088244570.0715091175543456
2229.1329.3851511236541-0.255151123654134
2328.8428.9167489961306-0.0767489961305863
2428.7628.289485824530.470514175469994
2528.7528.7715893124228-0.0215893124228437
2628.8928.69681215271330.193187847286744
2728.8229.072926610257-0.252926610256992
2829.1229.06034004049880.0596599595012464
2929.2129.4435337486181-0.233533748618118
3029.329.24413052943420.0558694705657636
3129.3229.20051778200140.119482217998637
3229.5229.40853593515350.111464064846501
3329.6429.56516544238060.0748345576193721
3429.5429.6536552021166-0.113655202116558
3529.5429.32699254096390.213007459036096
3629.3429.00132497029230.338675029707726
3729.3429.3173311224750.0226688775250352
3829.5429.30214627197850.23785372802153
3929.9429.67928505829160.260714941708446
4030.1730.1703250985329-0.000325098532918844
4130.2330.4818197008414-0.251819700841441
4230.3430.29468987159130.0453101284086515
4330.3430.24425859765020.0957414023497734
4430.3630.4332466154967-0.0732466154967142
4530.330.420625641373-0.120625641373039
4630.2830.3142334729633-0.0342334729632618
4729.8930.0854563526378-0.195456352637827
4829.5829.39552681613690.184473183863116
4929.6829.54171166468450.138288335315522
5029.7329.65124892961460.0787510703854011
5130.0729.88742011516660.18257988483338
5230.3230.28373511076930.0362648892306972
5330.5530.6055468315375-0.0555468315374732
5430.6230.624989108218-0.00498910821798759
5530.6730.53298968378330.137010316216717
5630.7930.74403555349560.0459644465044491
5730.830.8353209901379-0.0353209901379365
5830.530.8144341748607-0.314434174860718
5930.0730.3148880877644-0.244888087764416
6029.4129.613084124808-0.203084124808043
6129.4229.40435435582130.0156456441787185
6229.9929.39747688842090.592523111579059
6330.1430.10940440378210.0305955962178608
6430.4130.35474554283880.0552544571611655
6530.7830.68574402560940.0942559743906273
6630.8830.84603071609360.0339692839064263
6730.9230.80209890438760.117901095612368
6830.9330.987743490184-0.0577434901840128
6931.6230.97763018359640.642369816403612
7031.4831.5424243152516-0.0624243152515653
7131.331.27041831699890.0295816830011333
7231.1130.80114302290860.308856977091356
7331.1631.07589051308860.0841094869114336
7431.2231.18659317964910.0334068203509403
7531.6631.34393987715550.316060122844501
7632.1131.86050698174910.249493018250877
7732.2732.3863416726684-0.116341672668405
7832.3632.35349588717790.00650411282207131
7932.4232.2892499297470.130750070252986
8032.5232.47252087204620.047479127953757
8132.4132.6284881100679-0.21848811006786
8231.8732.3450241047971-0.475024104797125
8331.0431.7055973060308-0.665597306030765
8430.5830.6367600677434-0.0567600677433546

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 28.53 & 28.4843845109592 & 0.0456154890408484 \tabularnewline
14 & 28.48 & 28.4747136774233 & 0.00528632257673323 \tabularnewline
15 & 28.68 & 28.6785401852203 & 0.00145981477971446 \tabularnewline
16 & 28.89 & 28.8955535455549 & -0.00555354555487853 \tabularnewline
17 & 29.2 & 29.2184864385603 & -0.0184864385603198 \tabularnewline
18 & 29.21 & 29.212054124888 & -0.00205412488804413 \tabularnewline
19 & 29.15 & 29.1125658215491 & 0.0374341784508658 \tabularnewline
20 & 29.22 & 29.2525160640695 & -0.0325160640695294 \tabularnewline
21 & 29.34 & 29.2684908824457 & 0.0715091175543456 \tabularnewline
22 & 29.13 & 29.3851511236541 & -0.255151123654134 \tabularnewline
23 & 28.84 & 28.9167489961306 & -0.0767489961305863 \tabularnewline
24 & 28.76 & 28.28948582453 & 0.470514175469994 \tabularnewline
25 & 28.75 & 28.7715893124228 & -0.0215893124228437 \tabularnewline
26 & 28.89 & 28.6968121527133 & 0.193187847286744 \tabularnewline
27 & 28.82 & 29.072926610257 & -0.252926610256992 \tabularnewline
28 & 29.12 & 29.0603400404988 & 0.0596599595012464 \tabularnewline
29 & 29.21 & 29.4435337486181 & -0.233533748618118 \tabularnewline
30 & 29.3 & 29.2441305294342 & 0.0558694705657636 \tabularnewline
31 & 29.32 & 29.2005177820014 & 0.119482217998637 \tabularnewline
32 & 29.52 & 29.4085359351535 & 0.111464064846501 \tabularnewline
33 & 29.64 & 29.5651654423806 & 0.0748345576193721 \tabularnewline
34 & 29.54 & 29.6536552021166 & -0.113655202116558 \tabularnewline
35 & 29.54 & 29.3269925409639 & 0.213007459036096 \tabularnewline
36 & 29.34 & 29.0013249702923 & 0.338675029707726 \tabularnewline
37 & 29.34 & 29.317331122475 & 0.0226688775250352 \tabularnewline
38 & 29.54 & 29.3021462719785 & 0.23785372802153 \tabularnewline
39 & 29.94 & 29.6792850582916 & 0.260714941708446 \tabularnewline
40 & 30.17 & 30.1703250985329 & -0.000325098532918844 \tabularnewline
41 & 30.23 & 30.4818197008414 & -0.251819700841441 \tabularnewline
42 & 30.34 & 30.2946898715913 & 0.0453101284086515 \tabularnewline
43 & 30.34 & 30.2442585976502 & 0.0957414023497734 \tabularnewline
44 & 30.36 & 30.4332466154967 & -0.0732466154967142 \tabularnewline
45 & 30.3 & 30.420625641373 & -0.120625641373039 \tabularnewline
46 & 30.28 & 30.3142334729633 & -0.0342334729632618 \tabularnewline
47 & 29.89 & 30.0854563526378 & -0.195456352637827 \tabularnewline
48 & 29.58 & 29.3955268161369 & 0.184473183863116 \tabularnewline
49 & 29.68 & 29.5417116646845 & 0.138288335315522 \tabularnewline
50 & 29.73 & 29.6512489296146 & 0.0787510703854011 \tabularnewline
51 & 30.07 & 29.8874201151666 & 0.18257988483338 \tabularnewline
52 & 30.32 & 30.2837351107693 & 0.0362648892306972 \tabularnewline
53 & 30.55 & 30.6055468315375 & -0.0555468315374732 \tabularnewline
54 & 30.62 & 30.624989108218 & -0.00498910821798759 \tabularnewline
55 & 30.67 & 30.5329896837833 & 0.137010316216717 \tabularnewline
56 & 30.79 & 30.7440355534956 & 0.0459644465044491 \tabularnewline
57 & 30.8 & 30.8353209901379 & -0.0353209901379365 \tabularnewline
58 & 30.5 & 30.8144341748607 & -0.314434174860718 \tabularnewline
59 & 30.07 & 30.3148880877644 & -0.244888087764416 \tabularnewline
60 & 29.41 & 29.613084124808 & -0.203084124808043 \tabularnewline
61 & 29.42 & 29.4043543558213 & 0.0156456441787185 \tabularnewline
62 & 29.99 & 29.3974768884209 & 0.592523111579059 \tabularnewline
63 & 30.14 & 30.1094044037821 & 0.0305955962178608 \tabularnewline
64 & 30.41 & 30.3547455428388 & 0.0552544571611655 \tabularnewline
65 & 30.78 & 30.6857440256094 & 0.0942559743906273 \tabularnewline
66 & 30.88 & 30.8460307160936 & 0.0339692839064263 \tabularnewline
67 & 30.92 & 30.8020989043876 & 0.117901095612368 \tabularnewline
68 & 30.93 & 30.987743490184 & -0.0577434901840128 \tabularnewline
69 & 31.62 & 30.9776301835964 & 0.642369816403612 \tabularnewline
70 & 31.48 & 31.5424243152516 & -0.0624243152515653 \tabularnewline
71 & 31.3 & 31.2704183169989 & 0.0295816830011333 \tabularnewline
72 & 31.11 & 30.8011430229086 & 0.308856977091356 \tabularnewline
73 & 31.16 & 31.0758905130886 & 0.0841094869114336 \tabularnewline
74 & 31.22 & 31.1865931796491 & 0.0334068203509403 \tabularnewline
75 & 31.66 & 31.3439398771555 & 0.316060122844501 \tabularnewline
76 & 32.11 & 31.8605069817491 & 0.249493018250877 \tabularnewline
77 & 32.27 & 32.3863416726684 & -0.116341672668405 \tabularnewline
78 & 32.36 & 32.3534958871779 & 0.00650411282207131 \tabularnewline
79 & 32.42 & 32.289249929747 & 0.130750070252986 \tabularnewline
80 & 32.52 & 32.4725208720462 & 0.047479127953757 \tabularnewline
81 & 32.41 & 32.6284881100679 & -0.21848811006786 \tabularnewline
82 & 31.87 & 32.3450241047971 & -0.475024104797125 \tabularnewline
83 & 31.04 & 31.7055973060308 & -0.665597306030765 \tabularnewline
84 & 30.58 & 30.6367600677434 & -0.0567600677433546 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232628&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]28.53[/C][C]28.4843845109592[/C][C]0.0456154890408484[/C][/ROW]
[ROW][C]14[/C][C]28.48[/C][C]28.4747136774233[/C][C]0.00528632257673323[/C][/ROW]
[ROW][C]15[/C][C]28.68[/C][C]28.6785401852203[/C][C]0.00145981477971446[/C][/ROW]
[ROW][C]16[/C][C]28.89[/C][C]28.8955535455549[/C][C]-0.00555354555487853[/C][/ROW]
[ROW][C]17[/C][C]29.2[/C][C]29.2184864385603[/C][C]-0.0184864385603198[/C][/ROW]
[ROW][C]18[/C][C]29.21[/C][C]29.212054124888[/C][C]-0.00205412488804413[/C][/ROW]
[ROW][C]19[/C][C]29.15[/C][C]29.1125658215491[/C][C]0.0374341784508658[/C][/ROW]
[ROW][C]20[/C][C]29.22[/C][C]29.2525160640695[/C][C]-0.0325160640695294[/C][/ROW]
[ROW][C]21[/C][C]29.34[/C][C]29.2684908824457[/C][C]0.0715091175543456[/C][/ROW]
[ROW][C]22[/C][C]29.13[/C][C]29.3851511236541[/C][C]-0.255151123654134[/C][/ROW]
[ROW][C]23[/C][C]28.84[/C][C]28.9167489961306[/C][C]-0.0767489961305863[/C][/ROW]
[ROW][C]24[/C][C]28.76[/C][C]28.28948582453[/C][C]0.470514175469994[/C][/ROW]
[ROW][C]25[/C][C]28.75[/C][C]28.7715893124228[/C][C]-0.0215893124228437[/C][/ROW]
[ROW][C]26[/C][C]28.89[/C][C]28.6968121527133[/C][C]0.193187847286744[/C][/ROW]
[ROW][C]27[/C][C]28.82[/C][C]29.072926610257[/C][C]-0.252926610256992[/C][/ROW]
[ROW][C]28[/C][C]29.12[/C][C]29.0603400404988[/C][C]0.0596599595012464[/C][/ROW]
[ROW][C]29[/C][C]29.21[/C][C]29.4435337486181[/C][C]-0.233533748618118[/C][/ROW]
[ROW][C]30[/C][C]29.3[/C][C]29.2441305294342[/C][C]0.0558694705657636[/C][/ROW]
[ROW][C]31[/C][C]29.32[/C][C]29.2005177820014[/C][C]0.119482217998637[/C][/ROW]
[ROW][C]32[/C][C]29.52[/C][C]29.4085359351535[/C][C]0.111464064846501[/C][/ROW]
[ROW][C]33[/C][C]29.64[/C][C]29.5651654423806[/C][C]0.0748345576193721[/C][/ROW]
[ROW][C]34[/C][C]29.54[/C][C]29.6536552021166[/C][C]-0.113655202116558[/C][/ROW]
[ROW][C]35[/C][C]29.54[/C][C]29.3269925409639[/C][C]0.213007459036096[/C][/ROW]
[ROW][C]36[/C][C]29.34[/C][C]29.0013249702923[/C][C]0.338675029707726[/C][/ROW]
[ROW][C]37[/C][C]29.34[/C][C]29.317331122475[/C][C]0.0226688775250352[/C][/ROW]
[ROW][C]38[/C][C]29.54[/C][C]29.3021462719785[/C][C]0.23785372802153[/C][/ROW]
[ROW][C]39[/C][C]29.94[/C][C]29.6792850582916[/C][C]0.260714941708446[/C][/ROW]
[ROW][C]40[/C][C]30.17[/C][C]30.1703250985329[/C][C]-0.000325098532918844[/C][/ROW]
[ROW][C]41[/C][C]30.23[/C][C]30.4818197008414[/C][C]-0.251819700841441[/C][/ROW]
[ROW][C]42[/C][C]30.34[/C][C]30.2946898715913[/C][C]0.0453101284086515[/C][/ROW]
[ROW][C]43[/C][C]30.34[/C][C]30.2442585976502[/C][C]0.0957414023497734[/C][/ROW]
[ROW][C]44[/C][C]30.36[/C][C]30.4332466154967[/C][C]-0.0732466154967142[/C][/ROW]
[ROW][C]45[/C][C]30.3[/C][C]30.420625641373[/C][C]-0.120625641373039[/C][/ROW]
[ROW][C]46[/C][C]30.28[/C][C]30.3142334729633[/C][C]-0.0342334729632618[/C][/ROW]
[ROW][C]47[/C][C]29.89[/C][C]30.0854563526378[/C][C]-0.195456352637827[/C][/ROW]
[ROW][C]48[/C][C]29.58[/C][C]29.3955268161369[/C][C]0.184473183863116[/C][/ROW]
[ROW][C]49[/C][C]29.68[/C][C]29.5417116646845[/C][C]0.138288335315522[/C][/ROW]
[ROW][C]50[/C][C]29.73[/C][C]29.6512489296146[/C][C]0.0787510703854011[/C][/ROW]
[ROW][C]51[/C][C]30.07[/C][C]29.8874201151666[/C][C]0.18257988483338[/C][/ROW]
[ROW][C]52[/C][C]30.32[/C][C]30.2837351107693[/C][C]0.0362648892306972[/C][/ROW]
[ROW][C]53[/C][C]30.55[/C][C]30.6055468315375[/C][C]-0.0555468315374732[/C][/ROW]
[ROW][C]54[/C][C]30.62[/C][C]30.624989108218[/C][C]-0.00498910821798759[/C][/ROW]
[ROW][C]55[/C][C]30.67[/C][C]30.5329896837833[/C][C]0.137010316216717[/C][/ROW]
[ROW][C]56[/C][C]30.79[/C][C]30.7440355534956[/C][C]0.0459644465044491[/C][/ROW]
[ROW][C]57[/C][C]30.8[/C][C]30.8353209901379[/C][C]-0.0353209901379365[/C][/ROW]
[ROW][C]58[/C][C]30.5[/C][C]30.8144341748607[/C][C]-0.314434174860718[/C][/ROW]
[ROW][C]59[/C][C]30.07[/C][C]30.3148880877644[/C][C]-0.244888087764416[/C][/ROW]
[ROW][C]60[/C][C]29.41[/C][C]29.613084124808[/C][C]-0.203084124808043[/C][/ROW]
[ROW][C]61[/C][C]29.42[/C][C]29.4043543558213[/C][C]0.0156456441787185[/C][/ROW]
[ROW][C]62[/C][C]29.99[/C][C]29.3974768884209[/C][C]0.592523111579059[/C][/ROW]
[ROW][C]63[/C][C]30.14[/C][C]30.1094044037821[/C][C]0.0305955962178608[/C][/ROW]
[ROW][C]64[/C][C]30.41[/C][C]30.3547455428388[/C][C]0.0552544571611655[/C][/ROW]
[ROW][C]65[/C][C]30.78[/C][C]30.6857440256094[/C][C]0.0942559743906273[/C][/ROW]
[ROW][C]66[/C][C]30.88[/C][C]30.8460307160936[/C][C]0.0339692839064263[/C][/ROW]
[ROW][C]67[/C][C]30.92[/C][C]30.8020989043876[/C][C]0.117901095612368[/C][/ROW]
[ROW][C]68[/C][C]30.93[/C][C]30.987743490184[/C][C]-0.0577434901840128[/C][/ROW]
[ROW][C]69[/C][C]31.62[/C][C]30.9776301835964[/C][C]0.642369816403612[/C][/ROW]
[ROW][C]70[/C][C]31.48[/C][C]31.5424243152516[/C][C]-0.0624243152515653[/C][/ROW]
[ROW][C]71[/C][C]31.3[/C][C]31.2704183169989[/C][C]0.0295816830011333[/C][/ROW]
[ROW][C]72[/C][C]31.11[/C][C]30.8011430229086[/C][C]0.308856977091356[/C][/ROW]
[ROW][C]73[/C][C]31.16[/C][C]31.0758905130886[/C][C]0.0841094869114336[/C][/ROW]
[ROW][C]74[/C][C]31.22[/C][C]31.1865931796491[/C][C]0.0334068203509403[/C][/ROW]
[ROW][C]75[/C][C]31.66[/C][C]31.3439398771555[/C][C]0.316060122844501[/C][/ROW]
[ROW][C]76[/C][C]32.11[/C][C]31.8605069817491[/C][C]0.249493018250877[/C][/ROW]
[ROW][C]77[/C][C]32.27[/C][C]32.3863416726684[/C][C]-0.116341672668405[/C][/ROW]
[ROW][C]78[/C][C]32.36[/C][C]32.3534958871779[/C][C]0.00650411282207131[/C][/ROW]
[ROW][C]79[/C][C]32.42[/C][C]32.289249929747[/C][C]0.130750070252986[/C][/ROW]
[ROW][C]80[/C][C]32.52[/C][C]32.4725208720462[/C][C]0.047479127953757[/C][/ROW]
[ROW][C]81[/C][C]32.41[/C][C]32.6284881100679[/C][C]-0.21848811006786[/C][/ROW]
[ROW][C]82[/C][C]31.87[/C][C]32.3450241047971[/C][C]-0.475024104797125[/C][/ROW]
[ROW][C]83[/C][C]31.04[/C][C]31.7055973060308[/C][C]-0.665597306030765[/C][/ROW]
[ROW][C]84[/C][C]30.58[/C][C]30.6367600677434[/C][C]-0.0567600677433546[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232628&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232628&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
1328.5328.48438451095920.0456154890408484
1428.4828.47471367742330.00528632257673323
1528.6828.67854018522030.00145981477971446
1628.8928.8955535455549-0.00555354555487853
1729.229.2184864385603-0.0184864385603198
1829.2129.212054124888-0.00205412488804413
1929.1529.11256582154910.0374341784508658
2029.2229.2525160640695-0.0325160640695294
2129.3429.26849088244570.0715091175543456
2229.1329.3851511236541-0.255151123654134
2328.8428.9167489961306-0.0767489961305863
2428.7628.289485824530.470514175469994
2528.7528.7715893124228-0.0215893124228437
2628.8928.69681215271330.193187847286744
2728.8229.072926610257-0.252926610256992
2829.1229.06034004049880.0596599595012464
2929.2129.4435337486181-0.233533748618118
3029.329.24413052943420.0558694705657636
3129.3229.20051778200140.119482217998637
3229.5229.40853593515350.111464064846501
3329.6429.56516544238060.0748345576193721
3429.5429.6536552021166-0.113655202116558
3529.5429.32699254096390.213007459036096
3629.3429.00132497029230.338675029707726
3729.3429.3173311224750.0226688775250352
3829.5429.30214627197850.23785372802153
3929.9429.67928505829160.260714941708446
4030.1730.1703250985329-0.000325098532918844
4130.2330.4818197008414-0.251819700841441
4230.3430.29468987159130.0453101284086515
4330.3430.24425859765020.0957414023497734
4430.3630.4332466154967-0.0732466154967142
4530.330.420625641373-0.120625641373039
4630.2830.3142334729633-0.0342334729632618
4729.8930.0854563526378-0.195456352637827
4829.5829.39552681613690.184473183863116
4929.6829.54171166468450.138288335315522
5029.7329.65124892961460.0787510703854011
5130.0729.88742011516660.18257988483338
5230.3230.28373511076930.0362648892306972
5330.5530.6055468315375-0.0555468315374732
5430.6230.624989108218-0.00498910821798759
5530.6730.53298968378330.137010316216717
5630.7930.74403555349560.0459644465044491
5730.830.8353209901379-0.0353209901379365
5830.530.8144341748607-0.314434174860718
5930.0730.3148880877644-0.244888087764416
6029.4129.613084124808-0.203084124808043
6129.4229.40435435582130.0156456441787185
6229.9929.39747688842090.592523111579059
6330.1430.10940440378210.0305955962178608
6430.4130.35474554283880.0552544571611655
6530.7830.68574402560940.0942559743906273
6630.8830.84603071609360.0339692839064263
6730.9230.80209890438760.117901095612368
6830.9330.987743490184-0.0577434901840128
6931.6230.97763018359640.642369816403612
7031.4831.5424243152516-0.0624243152515653
7131.331.27041831699890.0295816830011333
7231.1130.80114302290860.308856977091356
7331.1631.07589051308860.0841094869114336
7431.2231.18659317964910.0334068203509403
7531.6631.34393987715550.316060122844501
7632.1131.86050698174910.249493018250877
7732.2732.3863416726684-0.116341672668405
7832.3632.35349588717790.00650411282207131
7932.4232.2892499297470.130750070252986
8032.5232.47252087204620.047479127953757
8132.4132.6284881100679-0.21848811006786
8231.8732.3450241047971-0.475024104797125
8331.0431.7055973060308-0.665597306030765
8430.5830.6367600677434-0.0567600677433546







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8530.559822463639330.155627074844130.9640178524345
8630.589116665212830.04386837720231.1343649532236
8730.739906369008930.081451190356831.398361547661
8830.95766012826530.200768895260631.7145513612694
8931.213532202699730.367698345249232.0593660601502
9031.295055302319630.37173926524732.2183713393921
9131.238806336287430.247339246668932.2302734259059
9231.293948702005930.235750985389532.3521464186224
9331.378365523032530.256298373982932.5004326720821
9431.271177657382430.094753455870832.4476018588941
9531.046486016059829.822611084962432.2703609471572
9630.6377392236807-51.2633411824022112.538819629764

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 30.5598224636393 & 30.1556270748441 & 30.9640178524345 \tabularnewline
86 & 30.5891166652128 & 30.043868377202 & 31.1343649532236 \tabularnewline
87 & 30.7399063690089 & 30.0814511903568 & 31.398361547661 \tabularnewline
88 & 30.957660128265 & 30.2007688952606 & 31.7145513612694 \tabularnewline
89 & 31.2135322026997 & 30.3676983452492 & 32.0593660601502 \tabularnewline
90 & 31.2950553023196 & 30.371739265247 & 32.2183713393921 \tabularnewline
91 & 31.2388063362874 & 30.2473392466689 & 32.2302734259059 \tabularnewline
92 & 31.2939487020059 & 30.2357509853895 & 32.3521464186224 \tabularnewline
93 & 31.3783655230325 & 30.2562983739829 & 32.5004326720821 \tabularnewline
94 & 31.2711776573824 & 30.0947534558708 & 32.4476018588941 \tabularnewline
95 & 31.0464860160598 & 29.8226110849624 & 32.2703609471572 \tabularnewline
96 & 30.6377392236807 & -51.2633411824022 & 112.538819629764 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232628&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]30.5598224636393[/C][C]30.1556270748441[/C][C]30.9640178524345[/C][/ROW]
[ROW][C]86[/C][C]30.5891166652128[/C][C]30.043868377202[/C][C]31.1343649532236[/C][/ROW]
[ROW][C]87[/C][C]30.7399063690089[/C][C]30.0814511903568[/C][C]31.398361547661[/C][/ROW]
[ROW][C]88[/C][C]30.957660128265[/C][C]30.2007688952606[/C][C]31.7145513612694[/C][/ROW]
[ROW][C]89[/C][C]31.2135322026997[/C][C]30.3676983452492[/C][C]32.0593660601502[/C][/ROW]
[ROW][C]90[/C][C]31.2950553023196[/C][C]30.371739265247[/C][C]32.2183713393921[/C][/ROW]
[ROW][C]91[/C][C]31.2388063362874[/C][C]30.2473392466689[/C][C]32.2302734259059[/C][/ROW]
[ROW][C]92[/C][C]31.2939487020059[/C][C]30.2357509853895[/C][C]32.3521464186224[/C][/ROW]
[ROW][C]93[/C][C]31.3783655230325[/C][C]30.2562983739829[/C][C]32.5004326720821[/C][/ROW]
[ROW][C]94[/C][C]31.2711776573824[/C][C]30.0947534558708[/C][C]32.4476018588941[/C][/ROW]
[ROW][C]95[/C][C]31.0464860160598[/C][C]29.8226110849624[/C][C]32.2703609471572[/C][/ROW]
[ROW][C]96[/C][C]30.6377392236807[/C][C]-51.2633411824022[/C][C]112.538819629764[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232628&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232628&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
8530.559822463639330.155627074844130.9640178524345
8630.589116665212830.04386837720231.1343649532236
8730.739906369008930.081451190356831.398361547661
8830.95766012826530.200768895260631.7145513612694
8931.213532202699730.367698345249232.0593660601502
9031.295055302319630.37173926524732.2183713393921
9131.238806336287430.247339246668932.2302734259059
9231.293948702005930.235750985389532.3521464186224
9331.378365523032530.256298373982932.5004326720821
9431.271177657382430.094753455870832.4476018588941
9531.046486016059829.822611084962432.2703609471572
9630.6377392236807-51.2633411824022112.538819629764



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