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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 06 Jun 2009 10:50:56 -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/2009/Jun/06/t12443071771tw8n2yh49m7qwo.htm/, Retrieved Fri, 10 May 2024 04:04:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=42036, Retrieved Fri, 10 May 2024 04:04:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact121
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Vincent Van Roy, ...] [2009-06-06 16:50:56] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
4.73
4.73
4.73
4.73
4.74
4.74
4.74
4.74
4.74
4.76
4.76
4.76
4.76
4.76
4.76
4.77
4.77
4.78
4.78
4.79
4.83
4.84
4.85
4.85
4.86
4.87
4.87
4.9
4.9
4.92
4.92
4.95
4.96
4.95
4.95
4.95
4.96
4.96
4.96
4.96
4.97
4.97
4.97
5.03
5.08
5.1
5.11
5.13
5.13
5.13
5.15
5.15
5.15
5.17
5.17
5.18
5.2
5.22
5.23
5.23
5.26
5.27
5.28
5.31
5.31
5.32
5.33
5.34
5.38
5.39
5.41
5.44
5.44
5.44
5.46
5.47
5.47
5.49
5.49
5.5
5.52
5.59
5.6
5.6




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42036&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42036&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42036&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0719407104710672
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0719407104710672 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42036&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]0.0719407104710672[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42036&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42036&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
beta0.0719407104710672
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
34.734.730
44.734.730
54.744.730.00999999999999979
64.744.74071940710471-0.000719407104710967
74.744.74066765244648-0.000667652446479927
84.744.74061962105513-0.000619621055132136
94.744.7405750450762-0.000575045076203651
104.764.740533675924870.0194663240751316
114.764.76193409710909-0.00193409710909354
124.764.76179495678895-0.00179495678894526
134.764.76166582632228-0.00166582632228351
144.764.76154598559314-0.00154598559313701
154.764.76143476629119-0.00143476629118844
164.774.761331548184840.00866845181515874
174.774.77195516276711-0.00195516276710705
184.784.771814506968560.00818549303144511
194.784.78240337715279-0.00240337715279360
204.794.782230476492890.00776952350710847
214.834.792789421534010.0372105784659853
224.844.83546637698590.00453362301410287
234.854.845792529046540.0042074709534603
244.854.85609521749622-0.00609521749621766
254.864.855656723219060.00434327678093638
264.874.865969181636460.00403081836354247
274.874.87625916157331-0.0062591615733103
284.94.875808873042770.0241911269572270
294.94.90754919990317-0.00754919990317227
304.924.907006105098650.0129938949013502
314.924.92794089512964-0.00794089512963936
324.954.927369621492240.0226303785077633
334.964.958997667000310.00100233299968533
344.954.96906977554844-0.0190697755484397
354.954.95769788234696-0.007697882346962
364.954.9571440912218-0.00714409122179838
374.964.956630140223630.00336985977636761
384.964.96687257033013-0.006872570330132
394.964.96637815273782-0.0063781527378195
404.964.96591930389837-0.00591930389836826
414.974.965493464970430.00450653502957454
424.974.97581766830222-0.00581766830221575
434.974.97539914111127-0.00539914111126905
445.034.975010723063790.054989276936209
455.085.038966690714870.0410333092851278
465.15.091918656137820.00808134386217585
475.115.11250003375683-0.00250003375682883
485.135.122320179552160.0076798204478381
495.135.14287267129147-0.0128726712914693
505.135.1419466021731-0.0119466021731007
515.155.141087155125050.00891284487494826
525.155.16172835151767-0.0117283515176743
535.155.16088460557684-0.0108846055768383
545.175.160101559318440.00989844068155588
555.175.18081366017363-0.0108136601736302
565.185.18003571777795-3.57177779468643e-05
575.25.190033148215620.00996685178437584
585.225.210750170614150.00924982938584673
595.235.23141560991191-0.00141560991190559
605.235.24131376992909-0.0113137699290942
615.265.240499849282290.0195001507177102
625.275.27190270397921-0.00190270397921388
635.285.28176582210313-0.00176582210313203
645.315.291638787606470.0183612123935308
655.315.32295970627117-0.0129597062711690
665.325.32202737579452-0.00202737579452439
675.335.33188152493948-0.00188152493947502
685.345.34174616669856-0.00174616669856054
695.385.351620546225660.0283794537743356
705.395.39366218429297-0.00366218429297138
715.415.403398724153060.00660127584694159
725.445.42387362462750.0161263753724974
735.445.45503376752912-0.0150337675291237
745.445.45395222761202-0.0139522276120214
755.465.452948494444960.00705150555504108
765.475.47345578476448-0.00345578476447983
775.475.48320717315329-0.0132071731532877
785.495.482257039733330.00774296026667454
795.495.50281407379606-0.0128140737960596
805.55.50189222022314-0.00189222022314262
815.525.511756092555920.00824390744407832
825.595.532349165114510.0576508348854938
835.65.60649660713542-0.00649660713541955
845.65.61602923660245-0.0160292366024457

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 4.73 & 4.73 & 0 \tabularnewline
4 & 4.73 & 4.73 & 0 \tabularnewline
5 & 4.74 & 4.73 & 0.00999999999999979 \tabularnewline
6 & 4.74 & 4.74071940710471 & -0.000719407104710967 \tabularnewline
7 & 4.74 & 4.74066765244648 & -0.000667652446479927 \tabularnewline
8 & 4.74 & 4.74061962105513 & -0.000619621055132136 \tabularnewline
9 & 4.74 & 4.7405750450762 & -0.000575045076203651 \tabularnewline
10 & 4.76 & 4.74053367592487 & 0.0194663240751316 \tabularnewline
11 & 4.76 & 4.76193409710909 & -0.00193409710909354 \tabularnewline
12 & 4.76 & 4.76179495678895 & -0.00179495678894526 \tabularnewline
13 & 4.76 & 4.76166582632228 & -0.00166582632228351 \tabularnewline
14 & 4.76 & 4.76154598559314 & -0.00154598559313701 \tabularnewline
15 & 4.76 & 4.76143476629119 & -0.00143476629118844 \tabularnewline
16 & 4.77 & 4.76133154818484 & 0.00866845181515874 \tabularnewline
17 & 4.77 & 4.77195516276711 & -0.00195516276710705 \tabularnewline
18 & 4.78 & 4.77181450696856 & 0.00818549303144511 \tabularnewline
19 & 4.78 & 4.78240337715279 & -0.00240337715279360 \tabularnewline
20 & 4.79 & 4.78223047649289 & 0.00776952350710847 \tabularnewline
21 & 4.83 & 4.79278942153401 & 0.0372105784659853 \tabularnewline
22 & 4.84 & 4.8354663769859 & 0.00453362301410287 \tabularnewline
23 & 4.85 & 4.84579252904654 & 0.0042074709534603 \tabularnewline
24 & 4.85 & 4.85609521749622 & -0.00609521749621766 \tabularnewline
25 & 4.86 & 4.85565672321906 & 0.00434327678093638 \tabularnewline
26 & 4.87 & 4.86596918163646 & 0.00403081836354247 \tabularnewline
27 & 4.87 & 4.87625916157331 & -0.0062591615733103 \tabularnewline
28 & 4.9 & 4.87580887304277 & 0.0241911269572270 \tabularnewline
29 & 4.9 & 4.90754919990317 & -0.00754919990317227 \tabularnewline
30 & 4.92 & 4.90700610509865 & 0.0129938949013502 \tabularnewline
31 & 4.92 & 4.92794089512964 & -0.00794089512963936 \tabularnewline
32 & 4.95 & 4.92736962149224 & 0.0226303785077633 \tabularnewline
33 & 4.96 & 4.95899766700031 & 0.00100233299968533 \tabularnewline
34 & 4.95 & 4.96906977554844 & -0.0190697755484397 \tabularnewline
35 & 4.95 & 4.95769788234696 & -0.007697882346962 \tabularnewline
36 & 4.95 & 4.9571440912218 & -0.00714409122179838 \tabularnewline
37 & 4.96 & 4.95663014022363 & 0.00336985977636761 \tabularnewline
38 & 4.96 & 4.96687257033013 & -0.006872570330132 \tabularnewline
39 & 4.96 & 4.96637815273782 & -0.0063781527378195 \tabularnewline
40 & 4.96 & 4.96591930389837 & -0.00591930389836826 \tabularnewline
41 & 4.97 & 4.96549346497043 & 0.00450653502957454 \tabularnewline
42 & 4.97 & 4.97581766830222 & -0.00581766830221575 \tabularnewline
43 & 4.97 & 4.97539914111127 & -0.00539914111126905 \tabularnewline
44 & 5.03 & 4.97501072306379 & 0.054989276936209 \tabularnewline
45 & 5.08 & 5.03896669071487 & 0.0410333092851278 \tabularnewline
46 & 5.1 & 5.09191865613782 & 0.00808134386217585 \tabularnewline
47 & 5.11 & 5.11250003375683 & -0.00250003375682883 \tabularnewline
48 & 5.13 & 5.12232017955216 & 0.0076798204478381 \tabularnewline
49 & 5.13 & 5.14287267129147 & -0.0128726712914693 \tabularnewline
50 & 5.13 & 5.1419466021731 & -0.0119466021731007 \tabularnewline
51 & 5.15 & 5.14108715512505 & 0.00891284487494826 \tabularnewline
52 & 5.15 & 5.16172835151767 & -0.0117283515176743 \tabularnewline
53 & 5.15 & 5.16088460557684 & -0.0108846055768383 \tabularnewline
54 & 5.17 & 5.16010155931844 & 0.00989844068155588 \tabularnewline
55 & 5.17 & 5.18081366017363 & -0.0108136601736302 \tabularnewline
56 & 5.18 & 5.18003571777795 & -3.57177779468643e-05 \tabularnewline
57 & 5.2 & 5.19003314821562 & 0.00996685178437584 \tabularnewline
58 & 5.22 & 5.21075017061415 & 0.00924982938584673 \tabularnewline
59 & 5.23 & 5.23141560991191 & -0.00141560991190559 \tabularnewline
60 & 5.23 & 5.24131376992909 & -0.0113137699290942 \tabularnewline
61 & 5.26 & 5.24049984928229 & 0.0195001507177102 \tabularnewline
62 & 5.27 & 5.27190270397921 & -0.00190270397921388 \tabularnewline
63 & 5.28 & 5.28176582210313 & -0.00176582210313203 \tabularnewline
64 & 5.31 & 5.29163878760647 & 0.0183612123935308 \tabularnewline
65 & 5.31 & 5.32295970627117 & -0.0129597062711690 \tabularnewline
66 & 5.32 & 5.32202737579452 & -0.00202737579452439 \tabularnewline
67 & 5.33 & 5.33188152493948 & -0.00188152493947502 \tabularnewline
68 & 5.34 & 5.34174616669856 & -0.00174616669856054 \tabularnewline
69 & 5.38 & 5.35162054622566 & 0.0283794537743356 \tabularnewline
70 & 5.39 & 5.39366218429297 & -0.00366218429297138 \tabularnewline
71 & 5.41 & 5.40339872415306 & 0.00660127584694159 \tabularnewline
72 & 5.44 & 5.4238736246275 & 0.0161263753724974 \tabularnewline
73 & 5.44 & 5.45503376752912 & -0.0150337675291237 \tabularnewline
74 & 5.44 & 5.45395222761202 & -0.0139522276120214 \tabularnewline
75 & 5.46 & 5.45294849444496 & 0.00705150555504108 \tabularnewline
76 & 5.47 & 5.47345578476448 & -0.00345578476447983 \tabularnewline
77 & 5.47 & 5.48320717315329 & -0.0132071731532877 \tabularnewline
78 & 5.49 & 5.48225703973333 & 0.00774296026667454 \tabularnewline
79 & 5.49 & 5.50281407379606 & -0.0128140737960596 \tabularnewline
80 & 5.5 & 5.50189222022314 & -0.00189222022314262 \tabularnewline
81 & 5.52 & 5.51175609255592 & 0.00824390744407832 \tabularnewline
82 & 5.59 & 5.53234916511451 & 0.0576508348854938 \tabularnewline
83 & 5.6 & 5.60649660713542 & -0.00649660713541955 \tabularnewline
84 & 5.6 & 5.61602923660245 & -0.0160292366024457 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42036&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]4.73[/C][C]4.73[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]4.73[/C][C]4.73[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]4.74[/C][C]4.73[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]6[/C][C]4.74[/C][C]4.74071940710471[/C][C]-0.000719407104710967[/C][/ROW]
[ROW][C]7[/C][C]4.74[/C][C]4.74066765244648[/C][C]-0.000667652446479927[/C][/ROW]
[ROW][C]8[/C][C]4.74[/C][C]4.74061962105513[/C][C]-0.000619621055132136[/C][/ROW]
[ROW][C]9[/C][C]4.74[/C][C]4.7405750450762[/C][C]-0.000575045076203651[/C][/ROW]
[ROW][C]10[/C][C]4.76[/C][C]4.74053367592487[/C][C]0.0194663240751316[/C][/ROW]
[ROW][C]11[/C][C]4.76[/C][C]4.76193409710909[/C][C]-0.00193409710909354[/C][/ROW]
[ROW][C]12[/C][C]4.76[/C][C]4.76179495678895[/C][C]-0.00179495678894526[/C][/ROW]
[ROW][C]13[/C][C]4.76[/C][C]4.76166582632228[/C][C]-0.00166582632228351[/C][/ROW]
[ROW][C]14[/C][C]4.76[/C][C]4.76154598559314[/C][C]-0.00154598559313701[/C][/ROW]
[ROW][C]15[/C][C]4.76[/C][C]4.76143476629119[/C][C]-0.00143476629118844[/C][/ROW]
[ROW][C]16[/C][C]4.77[/C][C]4.76133154818484[/C][C]0.00866845181515874[/C][/ROW]
[ROW][C]17[/C][C]4.77[/C][C]4.77195516276711[/C][C]-0.00195516276710705[/C][/ROW]
[ROW][C]18[/C][C]4.78[/C][C]4.77181450696856[/C][C]0.00818549303144511[/C][/ROW]
[ROW][C]19[/C][C]4.78[/C][C]4.78240337715279[/C][C]-0.00240337715279360[/C][/ROW]
[ROW][C]20[/C][C]4.79[/C][C]4.78223047649289[/C][C]0.00776952350710847[/C][/ROW]
[ROW][C]21[/C][C]4.83[/C][C]4.79278942153401[/C][C]0.0372105784659853[/C][/ROW]
[ROW][C]22[/C][C]4.84[/C][C]4.8354663769859[/C][C]0.00453362301410287[/C][/ROW]
[ROW][C]23[/C][C]4.85[/C][C]4.84579252904654[/C][C]0.0042074709534603[/C][/ROW]
[ROW][C]24[/C][C]4.85[/C][C]4.85609521749622[/C][C]-0.00609521749621766[/C][/ROW]
[ROW][C]25[/C][C]4.86[/C][C]4.85565672321906[/C][C]0.00434327678093638[/C][/ROW]
[ROW][C]26[/C][C]4.87[/C][C]4.86596918163646[/C][C]0.00403081836354247[/C][/ROW]
[ROW][C]27[/C][C]4.87[/C][C]4.87625916157331[/C][C]-0.0062591615733103[/C][/ROW]
[ROW][C]28[/C][C]4.9[/C][C]4.87580887304277[/C][C]0.0241911269572270[/C][/ROW]
[ROW][C]29[/C][C]4.9[/C][C]4.90754919990317[/C][C]-0.00754919990317227[/C][/ROW]
[ROW][C]30[/C][C]4.92[/C][C]4.90700610509865[/C][C]0.0129938949013502[/C][/ROW]
[ROW][C]31[/C][C]4.92[/C][C]4.92794089512964[/C][C]-0.00794089512963936[/C][/ROW]
[ROW][C]32[/C][C]4.95[/C][C]4.92736962149224[/C][C]0.0226303785077633[/C][/ROW]
[ROW][C]33[/C][C]4.96[/C][C]4.95899766700031[/C][C]0.00100233299968533[/C][/ROW]
[ROW][C]34[/C][C]4.95[/C][C]4.96906977554844[/C][C]-0.0190697755484397[/C][/ROW]
[ROW][C]35[/C][C]4.95[/C][C]4.95769788234696[/C][C]-0.007697882346962[/C][/ROW]
[ROW][C]36[/C][C]4.95[/C][C]4.9571440912218[/C][C]-0.00714409122179838[/C][/ROW]
[ROW][C]37[/C][C]4.96[/C][C]4.95663014022363[/C][C]0.00336985977636761[/C][/ROW]
[ROW][C]38[/C][C]4.96[/C][C]4.96687257033013[/C][C]-0.006872570330132[/C][/ROW]
[ROW][C]39[/C][C]4.96[/C][C]4.96637815273782[/C][C]-0.0063781527378195[/C][/ROW]
[ROW][C]40[/C][C]4.96[/C][C]4.96591930389837[/C][C]-0.00591930389836826[/C][/ROW]
[ROW][C]41[/C][C]4.97[/C][C]4.96549346497043[/C][C]0.00450653502957454[/C][/ROW]
[ROW][C]42[/C][C]4.97[/C][C]4.97581766830222[/C][C]-0.00581766830221575[/C][/ROW]
[ROW][C]43[/C][C]4.97[/C][C]4.97539914111127[/C][C]-0.00539914111126905[/C][/ROW]
[ROW][C]44[/C][C]5.03[/C][C]4.97501072306379[/C][C]0.054989276936209[/C][/ROW]
[ROW][C]45[/C][C]5.08[/C][C]5.03896669071487[/C][C]0.0410333092851278[/C][/ROW]
[ROW][C]46[/C][C]5.1[/C][C]5.09191865613782[/C][C]0.00808134386217585[/C][/ROW]
[ROW][C]47[/C][C]5.11[/C][C]5.11250003375683[/C][C]-0.00250003375682883[/C][/ROW]
[ROW][C]48[/C][C]5.13[/C][C]5.12232017955216[/C][C]0.0076798204478381[/C][/ROW]
[ROW][C]49[/C][C]5.13[/C][C]5.14287267129147[/C][C]-0.0128726712914693[/C][/ROW]
[ROW][C]50[/C][C]5.13[/C][C]5.1419466021731[/C][C]-0.0119466021731007[/C][/ROW]
[ROW][C]51[/C][C]5.15[/C][C]5.14108715512505[/C][C]0.00891284487494826[/C][/ROW]
[ROW][C]52[/C][C]5.15[/C][C]5.16172835151767[/C][C]-0.0117283515176743[/C][/ROW]
[ROW][C]53[/C][C]5.15[/C][C]5.16088460557684[/C][C]-0.0108846055768383[/C][/ROW]
[ROW][C]54[/C][C]5.17[/C][C]5.16010155931844[/C][C]0.00989844068155588[/C][/ROW]
[ROW][C]55[/C][C]5.17[/C][C]5.18081366017363[/C][C]-0.0108136601736302[/C][/ROW]
[ROW][C]56[/C][C]5.18[/C][C]5.18003571777795[/C][C]-3.57177779468643e-05[/C][/ROW]
[ROW][C]57[/C][C]5.2[/C][C]5.19003314821562[/C][C]0.00996685178437584[/C][/ROW]
[ROW][C]58[/C][C]5.22[/C][C]5.21075017061415[/C][C]0.00924982938584673[/C][/ROW]
[ROW][C]59[/C][C]5.23[/C][C]5.23141560991191[/C][C]-0.00141560991190559[/C][/ROW]
[ROW][C]60[/C][C]5.23[/C][C]5.24131376992909[/C][C]-0.0113137699290942[/C][/ROW]
[ROW][C]61[/C][C]5.26[/C][C]5.24049984928229[/C][C]0.0195001507177102[/C][/ROW]
[ROW][C]62[/C][C]5.27[/C][C]5.27190270397921[/C][C]-0.00190270397921388[/C][/ROW]
[ROW][C]63[/C][C]5.28[/C][C]5.28176582210313[/C][C]-0.00176582210313203[/C][/ROW]
[ROW][C]64[/C][C]5.31[/C][C]5.29163878760647[/C][C]0.0183612123935308[/C][/ROW]
[ROW][C]65[/C][C]5.31[/C][C]5.32295970627117[/C][C]-0.0129597062711690[/C][/ROW]
[ROW][C]66[/C][C]5.32[/C][C]5.32202737579452[/C][C]-0.00202737579452439[/C][/ROW]
[ROW][C]67[/C][C]5.33[/C][C]5.33188152493948[/C][C]-0.00188152493947502[/C][/ROW]
[ROW][C]68[/C][C]5.34[/C][C]5.34174616669856[/C][C]-0.00174616669856054[/C][/ROW]
[ROW][C]69[/C][C]5.38[/C][C]5.35162054622566[/C][C]0.0283794537743356[/C][/ROW]
[ROW][C]70[/C][C]5.39[/C][C]5.39366218429297[/C][C]-0.00366218429297138[/C][/ROW]
[ROW][C]71[/C][C]5.41[/C][C]5.40339872415306[/C][C]0.00660127584694159[/C][/ROW]
[ROW][C]72[/C][C]5.44[/C][C]5.4238736246275[/C][C]0.0161263753724974[/C][/ROW]
[ROW][C]73[/C][C]5.44[/C][C]5.45503376752912[/C][C]-0.0150337675291237[/C][/ROW]
[ROW][C]74[/C][C]5.44[/C][C]5.45395222761202[/C][C]-0.0139522276120214[/C][/ROW]
[ROW][C]75[/C][C]5.46[/C][C]5.45294849444496[/C][C]0.00705150555504108[/C][/ROW]
[ROW][C]76[/C][C]5.47[/C][C]5.47345578476448[/C][C]-0.00345578476447983[/C][/ROW]
[ROW][C]77[/C][C]5.47[/C][C]5.48320717315329[/C][C]-0.0132071731532877[/C][/ROW]
[ROW][C]78[/C][C]5.49[/C][C]5.48225703973333[/C][C]0.00774296026667454[/C][/ROW]
[ROW][C]79[/C][C]5.49[/C][C]5.50281407379606[/C][C]-0.0128140737960596[/C][/ROW]
[ROW][C]80[/C][C]5.5[/C][C]5.50189222022314[/C][C]-0.00189222022314262[/C][/ROW]
[ROW][C]81[/C][C]5.52[/C][C]5.51175609255592[/C][C]0.00824390744407832[/C][/ROW]
[ROW][C]82[/C][C]5.59[/C][C]5.53234916511451[/C][C]0.0576508348854938[/C][/ROW]
[ROW][C]83[/C][C]5.6[/C][C]5.60649660713542[/C][C]-0.00649660713541955[/C][/ROW]
[ROW][C]84[/C][C]5.6[/C][C]5.61602923660245[/C][C]-0.0160292366024457[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42036&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42036&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
34.734.730
44.734.730
54.744.730.00999999999999979
64.744.74071940710471-0.000719407104710967
74.744.74066765244648-0.000667652446479927
84.744.74061962105513-0.000619621055132136
94.744.7405750450762-0.000575045076203651
104.764.740533675924870.0194663240751316
114.764.76193409710909-0.00193409710909354
124.764.76179495678895-0.00179495678894526
134.764.76166582632228-0.00166582632228351
144.764.76154598559314-0.00154598559313701
154.764.76143476629119-0.00143476629118844
164.774.761331548184840.00866845181515874
174.774.77195516276711-0.00195516276710705
184.784.771814506968560.00818549303144511
194.784.78240337715279-0.00240337715279360
204.794.782230476492890.00776952350710847
214.834.792789421534010.0372105784659853
224.844.83546637698590.00453362301410287
234.854.845792529046540.0042074709534603
244.854.85609521749622-0.00609521749621766
254.864.855656723219060.00434327678093638
264.874.865969181636460.00403081836354247
274.874.87625916157331-0.0062591615733103
284.94.875808873042770.0241911269572270
294.94.90754919990317-0.00754919990317227
304.924.907006105098650.0129938949013502
314.924.92794089512964-0.00794089512963936
324.954.927369621492240.0226303785077633
334.964.958997667000310.00100233299968533
344.954.96906977554844-0.0190697755484397
354.954.95769788234696-0.007697882346962
364.954.9571440912218-0.00714409122179838
374.964.956630140223630.00336985977636761
384.964.96687257033013-0.006872570330132
394.964.96637815273782-0.0063781527378195
404.964.96591930389837-0.00591930389836826
414.974.965493464970430.00450653502957454
424.974.97581766830222-0.00581766830221575
434.974.97539914111127-0.00539914111126905
445.034.975010723063790.054989276936209
455.085.038966690714870.0410333092851278
465.15.091918656137820.00808134386217585
475.115.11250003375683-0.00250003375682883
485.135.122320179552160.0076798204478381
495.135.14287267129147-0.0128726712914693
505.135.1419466021731-0.0119466021731007
515.155.141087155125050.00891284487494826
525.155.16172835151767-0.0117283515176743
535.155.16088460557684-0.0108846055768383
545.175.160101559318440.00989844068155588
555.175.18081366017363-0.0108136601736302
565.185.18003571777795-3.57177779468643e-05
575.25.190033148215620.00996685178437584
585.225.210750170614150.00924982938584673
595.235.23141560991191-0.00141560991190559
605.235.24131376992909-0.0113137699290942
615.265.240499849282290.0195001507177102
625.275.27190270397921-0.00190270397921388
635.285.28176582210313-0.00176582210313203
645.315.291638787606470.0183612123935308
655.315.32295970627117-0.0129597062711690
665.325.32202737579452-0.00202737579452439
675.335.33188152493948-0.00188152493947502
685.345.34174616669856-0.00174616669856054
695.385.351620546225660.0283794537743356
705.395.39366218429297-0.00366218429297138
715.415.403398724153060.00660127584694159
725.445.42387362462750.0161263753724974
735.445.45503376752912-0.0150337675291237
745.445.45395222761202-0.0139522276120214
755.465.452948494444960.00705150555504108
765.475.47345578476448-0.00345578476447983
775.475.48320717315329-0.0132071731532877
785.495.482257039733330.00774296026667454
795.495.50281407379606-0.0128140737960596
805.55.50189222022314-0.00189222022314262
815.525.511756092555920.00824390744407832
825.595.532349165114510.0576508348854938
835.65.60649660713542-0.00649660713541955
845.65.61602923660245-0.0160292366024457







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
855.614876081932965.586978210917685.64277395294823
865.629752163865915.588854828027145.67064949970468
875.644628245798875.592753794923135.69650269667461
885.659504327731835.59752492009415.72148373536955
895.674380409664785.602741641737185.74601917759238
905.689256491597745.608194706582045.77031827661344
915.70413257353075.613765528821635.79449961823976
925.719008655463655.619380655143325.81863665578398
935.733884737396615.62499178048875.84277769430452
945.748760819329575.630565761660055.86695587699908
955.763636901262525.63607914466985.89119465785525
965.778512983195485.641514950612375.91551101577859

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 5.61487608193296 & 5.58697821091768 & 5.64277395294823 \tabularnewline
86 & 5.62975216386591 & 5.58885482802714 & 5.67064949970468 \tabularnewline
87 & 5.64462824579887 & 5.59275379492313 & 5.69650269667461 \tabularnewline
88 & 5.65950432773183 & 5.5975249200941 & 5.72148373536955 \tabularnewline
89 & 5.67438040966478 & 5.60274164173718 & 5.74601917759238 \tabularnewline
90 & 5.68925649159774 & 5.60819470658204 & 5.77031827661344 \tabularnewline
91 & 5.7041325735307 & 5.61376552882163 & 5.79449961823976 \tabularnewline
92 & 5.71900865546365 & 5.61938065514332 & 5.81863665578398 \tabularnewline
93 & 5.73388473739661 & 5.6249917804887 & 5.84277769430452 \tabularnewline
94 & 5.74876081932957 & 5.63056576166005 & 5.86695587699908 \tabularnewline
95 & 5.76363690126252 & 5.6360791446698 & 5.89119465785525 \tabularnewline
96 & 5.77851298319548 & 5.64151495061237 & 5.91551101577859 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42036&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]5.61487608193296[/C][C]5.58697821091768[/C][C]5.64277395294823[/C][/ROW]
[ROW][C]86[/C][C]5.62975216386591[/C][C]5.58885482802714[/C][C]5.67064949970468[/C][/ROW]
[ROW][C]87[/C][C]5.64462824579887[/C][C]5.59275379492313[/C][C]5.69650269667461[/C][/ROW]
[ROW][C]88[/C][C]5.65950432773183[/C][C]5.5975249200941[/C][C]5.72148373536955[/C][/ROW]
[ROW][C]89[/C][C]5.67438040966478[/C][C]5.60274164173718[/C][C]5.74601917759238[/C][/ROW]
[ROW][C]90[/C][C]5.68925649159774[/C][C]5.60819470658204[/C][C]5.77031827661344[/C][/ROW]
[ROW][C]91[/C][C]5.7041325735307[/C][C]5.61376552882163[/C][C]5.79449961823976[/C][/ROW]
[ROW][C]92[/C][C]5.71900865546365[/C][C]5.61938065514332[/C][C]5.81863665578398[/C][/ROW]
[ROW][C]93[/C][C]5.73388473739661[/C][C]5.6249917804887[/C][C]5.84277769430452[/C][/ROW]
[ROW][C]94[/C][C]5.74876081932957[/C][C]5.63056576166005[/C][C]5.86695587699908[/C][/ROW]
[ROW][C]95[/C][C]5.76363690126252[/C][C]5.6360791446698[/C][C]5.89119465785525[/C][/ROW]
[ROW][C]96[/C][C]5.77851298319548[/C][C]5.64151495061237[/C][C]5.91551101577859[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42036&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42036&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
855.614876081932965.586978210917685.64277395294823
865.629752163865915.588854828027145.67064949970468
875.644628245798875.592753794923135.69650269667461
885.659504327731835.59752492009415.72148373536955
895.674380409664785.602741641737185.74601917759238
905.689256491597745.608194706582045.77031827661344
915.70413257353075.613765528821635.79449961823976
925.719008655463655.619380655143325.81863665578398
935.733884737396615.62499178048875.84277769430452
945.748760819329575.630565761660055.86695587699908
955.763636901262525.63607914466985.89119465785525
965.778512983195485.641514950612375.91551101577859



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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=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')