Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 28 Apr 2017 13:25:23 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Apr/28/t1493382460xnbenkaxk7x1p9v.htm/, Retrieved Fri, 10 May 2024 02:22:22 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Fri, 10 May 2024 02:22:22 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
100.57
100.27
100.27
100.18
100.16
100.18
100.18
100.59
100.69
101.06
101.15
101.16
101.16
100.81
100.94
101.13
101.29
101.34
101.35
101.7
102.05
102.48
102.66
102.72
102.73
102.18
102.22
102.37
102.53
102.61
102.62
103
103.17
103.52
103.69
103.73
99.57
99.09
99.14
99.36
99.6
99.65
99.8
100.15
100.45
100.89
101.13
101.17
101.21
101.1
101.17
101.11
101.2
101.15
100.92
101.1
101.22
101.25
101.39
101.43
101.95
101.92
102.05
102.07
102.1
102.16
101.63
101.43
101.4
101.6
101.72
101.73
102.67
102.59
102.69
102.93
103.02
103.06
102.47
102.4
102.42
102.51
102.61
102.78




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

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0594162856861059
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0594162856861059 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.0594162856861059[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
beta0.0594162856861059
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3100.2799.970.299999999999997
4100.1899.98782488570580.192175114294173
5100.1699.90924321719850.250756782801488
6100.1899.90414225384320.275857746156845
7100.1899.94053269649750.239467303502465
8100.5999.95476095421490.63523904578507
9100.69100.4025044988380.287495501161729
10101.06100.5195864136690.540413586331255
11101.15100.9216957817030.22830421829714
12101.16101.0252607703610.134739229639436
13101.16101.0432664749220.116733525078061
14100.81101.050202347397-0.240202347397116
15100.94100.6859304161020.2540695838983
16101.13100.8310262870830.298973712917245
17101.29101.0387901946220.25120980537794
18101.34101.2137161481860.126283851814435
19101.35101.2712194656030.078780534397481
20101.7101.2859003123410.414099687659231
21102.05101.6605045776850.389495422314724
22102.48102.0336469489710.446353051029064
23102.66102.4901675893680.169832410632239
24102.72102.6802584003970.0397415996033601
25102.73102.742619698632-0.0126196986322924
26102.18102.751869883013-0.571869883013079
27102.22102.1678914986690.0521085013312899
28102.37102.210987592270.159012407729534
29102.53102.3704355189160.159564481084232
30102.61102.5399162477090.0700837522907705
31102.62102.624080363957-0.00408036395728573
32103102.6338379238870.366162076113298
33103.17103.0355939144080.134406085591536
34103.52103.2135798247880.306420175212068
35103.69103.5817861734580.108213826541686
36103.73103.758215837091-0.0282158370912953
3799.57103.796539356854-4.22653935685382
3899.0999.3854140869634-0.295414086963405
3999.1498.88786167917670.252138320823306
4099.3698.95284280167920.407157198320846
4199.699.19703457009370.40296542990626
4299.6599.46097727919870.189022720801347
4399.899.5222083071790.277791692821026
44100.1599.68871365776080.461286342239163
45100.45100.0661215788540.383878421145567
46100.89100.3889302087940.501069791206049
47101.13100.8587019146570.271298085343076
48101.17101.1148214392020.0551785607982538
49101.21101.1580999443340.0519000556660956
50101.1101.201183652868-0.101183652868471
51101.17101.0851716960430.0848283039571243
52101.11101.160211878785-0.0502118787850634
53101.2101.097228475450.102771524549667
54101.15101.193334777713-0.043334777713369
55100.92101.140759986181-0.22075998618061
56101.1100.8976432477740.202356752226351
57101.22101.0896665343740.130333465625569
58101.25101.2174104648030.0325895351974879
59101.39101.2493468139360.14065318606383
60101.43101.3977039038220.0322960961780012
61101.95101.4396228178990.510377182100925
62101.92101.989947534358-0.0699475343584481
63102.05101.9557915116740.0942084883260321
64102.07102.09138903013-0.0213890301304076
65102.1102.110118173406-0.0101181734056155
66102.16102.1395169891240.0204830108760632
67101.63102.20073401355-0.570734013549853
68101.43101.63682311835-0.206823118349988
69101.4101.424534456864-0.0245344568636341
70101.6101.3930767105650.206923289434528
71101.72101.6053713238460.114628676154396
72101.73101.732182134016-0.00218213401582545
73102.67101.7420524797180.92794752028226
74102.59102.737187674685-0.147187674684531
75102.69102.6484423297560.0415576702439893
76102.93102.7509115321640.179088467836337
77103.02103.0015523037320.018447696268268
78103.06103.092648397323-0.0326483973234417
79102.47103.130708550821-0.660708550820885
80102.4102.50145170281-0.101451702810053
81102.42102.425423819453-0.00542381945255954
82102.51102.4451015562460.0648984437535489
83102.61102.5389575807210.0710424192788963
84102.78102.6431786574010.136821342599191

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 100.27 & 99.97 & 0.299999999999997 \tabularnewline
4 & 100.18 & 99.9878248857058 & 0.192175114294173 \tabularnewline
5 & 100.16 & 99.9092432171985 & 0.250756782801488 \tabularnewline
6 & 100.18 & 99.9041422538432 & 0.275857746156845 \tabularnewline
7 & 100.18 & 99.9405326964975 & 0.239467303502465 \tabularnewline
8 & 100.59 & 99.9547609542149 & 0.63523904578507 \tabularnewline
9 & 100.69 & 100.402504498838 & 0.287495501161729 \tabularnewline
10 & 101.06 & 100.519586413669 & 0.540413586331255 \tabularnewline
11 & 101.15 & 100.921695781703 & 0.22830421829714 \tabularnewline
12 & 101.16 & 101.025260770361 & 0.134739229639436 \tabularnewline
13 & 101.16 & 101.043266474922 & 0.116733525078061 \tabularnewline
14 & 100.81 & 101.050202347397 & -0.240202347397116 \tabularnewline
15 & 100.94 & 100.685930416102 & 0.2540695838983 \tabularnewline
16 & 101.13 & 100.831026287083 & 0.298973712917245 \tabularnewline
17 & 101.29 & 101.038790194622 & 0.25120980537794 \tabularnewline
18 & 101.34 & 101.213716148186 & 0.126283851814435 \tabularnewline
19 & 101.35 & 101.271219465603 & 0.078780534397481 \tabularnewline
20 & 101.7 & 101.285900312341 & 0.414099687659231 \tabularnewline
21 & 102.05 & 101.660504577685 & 0.389495422314724 \tabularnewline
22 & 102.48 & 102.033646948971 & 0.446353051029064 \tabularnewline
23 & 102.66 & 102.490167589368 & 0.169832410632239 \tabularnewline
24 & 102.72 & 102.680258400397 & 0.0397415996033601 \tabularnewline
25 & 102.73 & 102.742619698632 & -0.0126196986322924 \tabularnewline
26 & 102.18 & 102.751869883013 & -0.571869883013079 \tabularnewline
27 & 102.22 & 102.167891498669 & 0.0521085013312899 \tabularnewline
28 & 102.37 & 102.21098759227 & 0.159012407729534 \tabularnewline
29 & 102.53 & 102.370435518916 & 0.159564481084232 \tabularnewline
30 & 102.61 & 102.539916247709 & 0.0700837522907705 \tabularnewline
31 & 102.62 & 102.624080363957 & -0.00408036395728573 \tabularnewline
32 & 103 & 102.633837923887 & 0.366162076113298 \tabularnewline
33 & 103.17 & 103.035593914408 & 0.134406085591536 \tabularnewline
34 & 103.52 & 103.213579824788 & 0.306420175212068 \tabularnewline
35 & 103.69 & 103.581786173458 & 0.108213826541686 \tabularnewline
36 & 103.73 & 103.758215837091 & -0.0282158370912953 \tabularnewline
37 & 99.57 & 103.796539356854 & -4.22653935685382 \tabularnewline
38 & 99.09 & 99.3854140869634 & -0.295414086963405 \tabularnewline
39 & 99.14 & 98.8878616791767 & 0.252138320823306 \tabularnewline
40 & 99.36 & 98.9528428016792 & 0.407157198320846 \tabularnewline
41 & 99.6 & 99.1970345700937 & 0.40296542990626 \tabularnewline
42 & 99.65 & 99.4609772791987 & 0.189022720801347 \tabularnewline
43 & 99.8 & 99.522208307179 & 0.277791692821026 \tabularnewline
44 & 100.15 & 99.6887136577608 & 0.461286342239163 \tabularnewline
45 & 100.45 & 100.066121578854 & 0.383878421145567 \tabularnewline
46 & 100.89 & 100.388930208794 & 0.501069791206049 \tabularnewline
47 & 101.13 & 100.858701914657 & 0.271298085343076 \tabularnewline
48 & 101.17 & 101.114821439202 & 0.0551785607982538 \tabularnewline
49 & 101.21 & 101.158099944334 & 0.0519000556660956 \tabularnewline
50 & 101.1 & 101.201183652868 & -0.101183652868471 \tabularnewline
51 & 101.17 & 101.085171696043 & 0.0848283039571243 \tabularnewline
52 & 101.11 & 101.160211878785 & -0.0502118787850634 \tabularnewline
53 & 101.2 & 101.09722847545 & 0.102771524549667 \tabularnewline
54 & 101.15 & 101.193334777713 & -0.043334777713369 \tabularnewline
55 & 100.92 & 101.140759986181 & -0.22075998618061 \tabularnewline
56 & 101.1 & 100.897643247774 & 0.202356752226351 \tabularnewline
57 & 101.22 & 101.089666534374 & 0.130333465625569 \tabularnewline
58 & 101.25 & 101.217410464803 & 0.0325895351974879 \tabularnewline
59 & 101.39 & 101.249346813936 & 0.14065318606383 \tabularnewline
60 & 101.43 & 101.397703903822 & 0.0322960961780012 \tabularnewline
61 & 101.95 & 101.439622817899 & 0.510377182100925 \tabularnewline
62 & 101.92 & 101.989947534358 & -0.0699475343584481 \tabularnewline
63 & 102.05 & 101.955791511674 & 0.0942084883260321 \tabularnewline
64 & 102.07 & 102.09138903013 & -0.0213890301304076 \tabularnewline
65 & 102.1 & 102.110118173406 & -0.0101181734056155 \tabularnewline
66 & 102.16 & 102.139516989124 & 0.0204830108760632 \tabularnewline
67 & 101.63 & 102.20073401355 & -0.570734013549853 \tabularnewline
68 & 101.43 & 101.63682311835 & -0.206823118349988 \tabularnewline
69 & 101.4 & 101.424534456864 & -0.0245344568636341 \tabularnewline
70 & 101.6 & 101.393076710565 & 0.206923289434528 \tabularnewline
71 & 101.72 & 101.605371323846 & 0.114628676154396 \tabularnewline
72 & 101.73 & 101.732182134016 & -0.00218213401582545 \tabularnewline
73 & 102.67 & 101.742052479718 & 0.92794752028226 \tabularnewline
74 & 102.59 & 102.737187674685 & -0.147187674684531 \tabularnewline
75 & 102.69 & 102.648442329756 & 0.0415576702439893 \tabularnewline
76 & 102.93 & 102.750911532164 & 0.179088467836337 \tabularnewline
77 & 103.02 & 103.001552303732 & 0.018447696268268 \tabularnewline
78 & 103.06 & 103.092648397323 & -0.0326483973234417 \tabularnewline
79 & 102.47 & 103.130708550821 & -0.660708550820885 \tabularnewline
80 & 102.4 & 102.50145170281 & -0.101451702810053 \tabularnewline
81 & 102.42 & 102.425423819453 & -0.00542381945255954 \tabularnewline
82 & 102.51 & 102.445101556246 & 0.0648984437535489 \tabularnewline
83 & 102.61 & 102.538957580721 & 0.0710424192788963 \tabularnewline
84 & 102.78 & 102.643178657401 & 0.136821342599191 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]100.27[/C][C]99.97[/C][C]0.299999999999997[/C][/ROW]
[ROW][C]4[/C][C]100.18[/C][C]99.9878248857058[/C][C]0.192175114294173[/C][/ROW]
[ROW][C]5[/C][C]100.16[/C][C]99.9092432171985[/C][C]0.250756782801488[/C][/ROW]
[ROW][C]6[/C][C]100.18[/C][C]99.9041422538432[/C][C]0.275857746156845[/C][/ROW]
[ROW][C]7[/C][C]100.18[/C][C]99.9405326964975[/C][C]0.239467303502465[/C][/ROW]
[ROW][C]8[/C][C]100.59[/C][C]99.9547609542149[/C][C]0.63523904578507[/C][/ROW]
[ROW][C]9[/C][C]100.69[/C][C]100.402504498838[/C][C]0.287495501161729[/C][/ROW]
[ROW][C]10[/C][C]101.06[/C][C]100.519586413669[/C][C]0.540413586331255[/C][/ROW]
[ROW][C]11[/C][C]101.15[/C][C]100.921695781703[/C][C]0.22830421829714[/C][/ROW]
[ROW][C]12[/C][C]101.16[/C][C]101.025260770361[/C][C]0.134739229639436[/C][/ROW]
[ROW][C]13[/C][C]101.16[/C][C]101.043266474922[/C][C]0.116733525078061[/C][/ROW]
[ROW][C]14[/C][C]100.81[/C][C]101.050202347397[/C][C]-0.240202347397116[/C][/ROW]
[ROW][C]15[/C][C]100.94[/C][C]100.685930416102[/C][C]0.2540695838983[/C][/ROW]
[ROW][C]16[/C][C]101.13[/C][C]100.831026287083[/C][C]0.298973712917245[/C][/ROW]
[ROW][C]17[/C][C]101.29[/C][C]101.038790194622[/C][C]0.25120980537794[/C][/ROW]
[ROW][C]18[/C][C]101.34[/C][C]101.213716148186[/C][C]0.126283851814435[/C][/ROW]
[ROW][C]19[/C][C]101.35[/C][C]101.271219465603[/C][C]0.078780534397481[/C][/ROW]
[ROW][C]20[/C][C]101.7[/C][C]101.285900312341[/C][C]0.414099687659231[/C][/ROW]
[ROW][C]21[/C][C]102.05[/C][C]101.660504577685[/C][C]0.389495422314724[/C][/ROW]
[ROW][C]22[/C][C]102.48[/C][C]102.033646948971[/C][C]0.446353051029064[/C][/ROW]
[ROW][C]23[/C][C]102.66[/C][C]102.490167589368[/C][C]0.169832410632239[/C][/ROW]
[ROW][C]24[/C][C]102.72[/C][C]102.680258400397[/C][C]0.0397415996033601[/C][/ROW]
[ROW][C]25[/C][C]102.73[/C][C]102.742619698632[/C][C]-0.0126196986322924[/C][/ROW]
[ROW][C]26[/C][C]102.18[/C][C]102.751869883013[/C][C]-0.571869883013079[/C][/ROW]
[ROW][C]27[/C][C]102.22[/C][C]102.167891498669[/C][C]0.0521085013312899[/C][/ROW]
[ROW][C]28[/C][C]102.37[/C][C]102.21098759227[/C][C]0.159012407729534[/C][/ROW]
[ROW][C]29[/C][C]102.53[/C][C]102.370435518916[/C][C]0.159564481084232[/C][/ROW]
[ROW][C]30[/C][C]102.61[/C][C]102.539916247709[/C][C]0.0700837522907705[/C][/ROW]
[ROW][C]31[/C][C]102.62[/C][C]102.624080363957[/C][C]-0.00408036395728573[/C][/ROW]
[ROW][C]32[/C][C]103[/C][C]102.633837923887[/C][C]0.366162076113298[/C][/ROW]
[ROW][C]33[/C][C]103.17[/C][C]103.035593914408[/C][C]0.134406085591536[/C][/ROW]
[ROW][C]34[/C][C]103.52[/C][C]103.213579824788[/C][C]0.306420175212068[/C][/ROW]
[ROW][C]35[/C][C]103.69[/C][C]103.581786173458[/C][C]0.108213826541686[/C][/ROW]
[ROW][C]36[/C][C]103.73[/C][C]103.758215837091[/C][C]-0.0282158370912953[/C][/ROW]
[ROW][C]37[/C][C]99.57[/C][C]103.796539356854[/C][C]-4.22653935685382[/C][/ROW]
[ROW][C]38[/C][C]99.09[/C][C]99.3854140869634[/C][C]-0.295414086963405[/C][/ROW]
[ROW][C]39[/C][C]99.14[/C][C]98.8878616791767[/C][C]0.252138320823306[/C][/ROW]
[ROW][C]40[/C][C]99.36[/C][C]98.9528428016792[/C][C]0.407157198320846[/C][/ROW]
[ROW][C]41[/C][C]99.6[/C][C]99.1970345700937[/C][C]0.40296542990626[/C][/ROW]
[ROW][C]42[/C][C]99.65[/C][C]99.4609772791987[/C][C]0.189022720801347[/C][/ROW]
[ROW][C]43[/C][C]99.8[/C][C]99.522208307179[/C][C]0.277791692821026[/C][/ROW]
[ROW][C]44[/C][C]100.15[/C][C]99.6887136577608[/C][C]0.461286342239163[/C][/ROW]
[ROW][C]45[/C][C]100.45[/C][C]100.066121578854[/C][C]0.383878421145567[/C][/ROW]
[ROW][C]46[/C][C]100.89[/C][C]100.388930208794[/C][C]0.501069791206049[/C][/ROW]
[ROW][C]47[/C][C]101.13[/C][C]100.858701914657[/C][C]0.271298085343076[/C][/ROW]
[ROW][C]48[/C][C]101.17[/C][C]101.114821439202[/C][C]0.0551785607982538[/C][/ROW]
[ROW][C]49[/C][C]101.21[/C][C]101.158099944334[/C][C]0.0519000556660956[/C][/ROW]
[ROW][C]50[/C][C]101.1[/C][C]101.201183652868[/C][C]-0.101183652868471[/C][/ROW]
[ROW][C]51[/C][C]101.17[/C][C]101.085171696043[/C][C]0.0848283039571243[/C][/ROW]
[ROW][C]52[/C][C]101.11[/C][C]101.160211878785[/C][C]-0.0502118787850634[/C][/ROW]
[ROW][C]53[/C][C]101.2[/C][C]101.09722847545[/C][C]0.102771524549667[/C][/ROW]
[ROW][C]54[/C][C]101.15[/C][C]101.193334777713[/C][C]-0.043334777713369[/C][/ROW]
[ROW][C]55[/C][C]100.92[/C][C]101.140759986181[/C][C]-0.22075998618061[/C][/ROW]
[ROW][C]56[/C][C]101.1[/C][C]100.897643247774[/C][C]0.202356752226351[/C][/ROW]
[ROW][C]57[/C][C]101.22[/C][C]101.089666534374[/C][C]0.130333465625569[/C][/ROW]
[ROW][C]58[/C][C]101.25[/C][C]101.217410464803[/C][C]0.0325895351974879[/C][/ROW]
[ROW][C]59[/C][C]101.39[/C][C]101.249346813936[/C][C]0.14065318606383[/C][/ROW]
[ROW][C]60[/C][C]101.43[/C][C]101.397703903822[/C][C]0.0322960961780012[/C][/ROW]
[ROW][C]61[/C][C]101.95[/C][C]101.439622817899[/C][C]0.510377182100925[/C][/ROW]
[ROW][C]62[/C][C]101.92[/C][C]101.989947534358[/C][C]-0.0699475343584481[/C][/ROW]
[ROW][C]63[/C][C]102.05[/C][C]101.955791511674[/C][C]0.0942084883260321[/C][/ROW]
[ROW][C]64[/C][C]102.07[/C][C]102.09138903013[/C][C]-0.0213890301304076[/C][/ROW]
[ROW][C]65[/C][C]102.1[/C][C]102.110118173406[/C][C]-0.0101181734056155[/C][/ROW]
[ROW][C]66[/C][C]102.16[/C][C]102.139516989124[/C][C]0.0204830108760632[/C][/ROW]
[ROW][C]67[/C][C]101.63[/C][C]102.20073401355[/C][C]-0.570734013549853[/C][/ROW]
[ROW][C]68[/C][C]101.43[/C][C]101.63682311835[/C][C]-0.206823118349988[/C][/ROW]
[ROW][C]69[/C][C]101.4[/C][C]101.424534456864[/C][C]-0.0245344568636341[/C][/ROW]
[ROW][C]70[/C][C]101.6[/C][C]101.393076710565[/C][C]0.206923289434528[/C][/ROW]
[ROW][C]71[/C][C]101.72[/C][C]101.605371323846[/C][C]0.114628676154396[/C][/ROW]
[ROW][C]72[/C][C]101.73[/C][C]101.732182134016[/C][C]-0.00218213401582545[/C][/ROW]
[ROW][C]73[/C][C]102.67[/C][C]101.742052479718[/C][C]0.92794752028226[/C][/ROW]
[ROW][C]74[/C][C]102.59[/C][C]102.737187674685[/C][C]-0.147187674684531[/C][/ROW]
[ROW][C]75[/C][C]102.69[/C][C]102.648442329756[/C][C]0.0415576702439893[/C][/ROW]
[ROW][C]76[/C][C]102.93[/C][C]102.750911532164[/C][C]0.179088467836337[/C][/ROW]
[ROW][C]77[/C][C]103.02[/C][C]103.001552303732[/C][C]0.018447696268268[/C][/ROW]
[ROW][C]78[/C][C]103.06[/C][C]103.092648397323[/C][C]-0.0326483973234417[/C][/ROW]
[ROW][C]79[/C][C]102.47[/C][C]103.130708550821[/C][C]-0.660708550820885[/C][/ROW]
[ROW][C]80[/C][C]102.4[/C][C]102.50145170281[/C][C]-0.101451702810053[/C][/ROW]
[ROW][C]81[/C][C]102.42[/C][C]102.425423819453[/C][C]-0.00542381945255954[/C][/ROW]
[ROW][C]82[/C][C]102.51[/C][C]102.445101556246[/C][C]0.0648984437535489[/C][/ROW]
[ROW][C]83[/C][C]102.61[/C][C]102.538957580721[/C][C]0.0710424192788963[/C][/ROW]
[ROW][C]84[/C][C]102.78[/C][C]102.643178657401[/C][C]0.136821342599191[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
3100.2799.970.299999999999997
4100.1899.98782488570580.192175114294173
5100.1699.90924321719850.250756782801488
6100.1899.90414225384320.275857746156845
7100.1899.94053269649750.239467303502465
8100.5999.95476095421490.63523904578507
9100.69100.4025044988380.287495501161729
10101.06100.5195864136690.540413586331255
11101.15100.9216957817030.22830421829714
12101.16101.0252607703610.134739229639436
13101.16101.0432664749220.116733525078061
14100.81101.050202347397-0.240202347397116
15100.94100.6859304161020.2540695838983
16101.13100.8310262870830.298973712917245
17101.29101.0387901946220.25120980537794
18101.34101.2137161481860.126283851814435
19101.35101.2712194656030.078780534397481
20101.7101.2859003123410.414099687659231
21102.05101.6605045776850.389495422314724
22102.48102.0336469489710.446353051029064
23102.66102.4901675893680.169832410632239
24102.72102.6802584003970.0397415996033601
25102.73102.742619698632-0.0126196986322924
26102.18102.751869883013-0.571869883013079
27102.22102.1678914986690.0521085013312899
28102.37102.210987592270.159012407729534
29102.53102.3704355189160.159564481084232
30102.61102.5399162477090.0700837522907705
31102.62102.624080363957-0.00408036395728573
32103102.6338379238870.366162076113298
33103.17103.0355939144080.134406085591536
34103.52103.2135798247880.306420175212068
35103.69103.5817861734580.108213826541686
36103.73103.758215837091-0.0282158370912953
3799.57103.796539356854-4.22653935685382
3899.0999.3854140869634-0.295414086963405
3999.1498.88786167917670.252138320823306
4099.3698.95284280167920.407157198320846
4199.699.19703457009370.40296542990626
4299.6599.46097727919870.189022720801347
4399.899.5222083071790.277791692821026
44100.1599.68871365776080.461286342239163
45100.45100.0661215788540.383878421145567
46100.89100.3889302087940.501069791206049
47101.13100.8587019146570.271298085343076
48101.17101.1148214392020.0551785607982538
49101.21101.1580999443340.0519000556660956
50101.1101.201183652868-0.101183652868471
51101.17101.0851716960430.0848283039571243
52101.11101.160211878785-0.0502118787850634
53101.2101.097228475450.102771524549667
54101.15101.193334777713-0.043334777713369
55100.92101.140759986181-0.22075998618061
56101.1100.8976432477740.202356752226351
57101.22101.0896665343740.130333465625569
58101.25101.2174104648030.0325895351974879
59101.39101.2493468139360.14065318606383
60101.43101.3977039038220.0322960961780012
61101.95101.4396228178990.510377182100925
62101.92101.989947534358-0.0699475343584481
63102.05101.9557915116740.0942084883260321
64102.07102.09138903013-0.0213890301304076
65102.1102.110118173406-0.0101181734056155
66102.16102.1395169891240.0204830108760632
67101.63102.20073401355-0.570734013549853
68101.43101.63682311835-0.206823118349988
69101.4101.424534456864-0.0245344568636341
70101.6101.3930767105650.206923289434528
71101.72101.6053713238460.114628676154396
72101.73101.732182134016-0.00218213401582545
73102.67101.7420524797180.92794752028226
74102.59102.737187674685-0.147187674684531
75102.69102.6484423297560.0415576702439893
76102.93102.7509115321640.179088467836337
77103.02103.0015523037320.018447696268268
78103.06103.092648397323-0.0326483973234417
79102.47103.130708550821-0.660708550820885
80102.4102.50145170281-0.101451702810053
81102.42102.425423819453-0.00542381945255954
82102.51102.4451015562460.0648984437535489
83102.61102.5389575807210.0710424192788963
84102.78102.6431786574010.136821342599191







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85102.821308073381101.761642679007103.880973467755
86102.862616146761101.318860457986104.406371835536
87102.903924220142100.95743997747104.850408462814
88102.945232293523100.632727837252105.257736749793
89102.986540366903100.328018642764105.645062091042
90103.027848440284100.035038411145106.020658469422
91103.06915651366499.7490469567597106.389266070569
92103.11046458704599.4670715493768106.753857624713
93103.15177266042699.1871293961523107.116415924699
94103.19308073380698.9078379286549107.478323538958
95103.23438880718798.6282005612954107.840577053079
96103.27569688056898.3474804428888108.203913318246

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 102.821308073381 & 101.761642679007 & 103.880973467755 \tabularnewline
86 & 102.862616146761 & 101.318860457986 & 104.406371835536 \tabularnewline
87 & 102.903924220142 & 100.95743997747 & 104.850408462814 \tabularnewline
88 & 102.945232293523 & 100.632727837252 & 105.257736749793 \tabularnewline
89 & 102.986540366903 & 100.328018642764 & 105.645062091042 \tabularnewline
90 & 103.027848440284 & 100.035038411145 & 106.020658469422 \tabularnewline
91 & 103.069156513664 & 99.7490469567597 & 106.389266070569 \tabularnewline
92 & 103.110464587045 & 99.4670715493768 & 106.753857624713 \tabularnewline
93 & 103.151772660426 & 99.1871293961523 & 107.116415924699 \tabularnewline
94 & 103.193080733806 & 98.9078379286549 & 107.478323538958 \tabularnewline
95 & 103.234388807187 & 98.6282005612954 & 107.840577053079 \tabularnewline
96 & 103.275696880568 & 98.3474804428888 & 108.203913318246 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]102.821308073381[/C][C]101.761642679007[/C][C]103.880973467755[/C][/ROW]
[ROW][C]86[/C][C]102.862616146761[/C][C]101.318860457986[/C][C]104.406371835536[/C][/ROW]
[ROW][C]87[/C][C]102.903924220142[/C][C]100.95743997747[/C][C]104.850408462814[/C][/ROW]
[ROW][C]88[/C][C]102.945232293523[/C][C]100.632727837252[/C][C]105.257736749793[/C][/ROW]
[ROW][C]89[/C][C]102.986540366903[/C][C]100.328018642764[/C][C]105.645062091042[/C][/ROW]
[ROW][C]90[/C][C]103.027848440284[/C][C]100.035038411145[/C][C]106.020658469422[/C][/ROW]
[ROW][C]91[/C][C]103.069156513664[/C][C]99.7490469567597[/C][C]106.389266070569[/C][/ROW]
[ROW][C]92[/C][C]103.110464587045[/C][C]99.4670715493768[/C][C]106.753857624713[/C][/ROW]
[ROW][C]93[/C][C]103.151772660426[/C][C]99.1871293961523[/C][C]107.116415924699[/C][/ROW]
[ROW][C]94[/C][C]103.193080733806[/C][C]98.9078379286549[/C][C]107.478323538958[/C][/ROW]
[ROW][C]95[/C][C]103.234388807187[/C][C]98.6282005612954[/C][C]107.840577053079[/C][/ROW]
[ROW][C]96[/C][C]103.275696880568[/C][C]98.3474804428888[/C][C]108.203913318246[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
85102.821308073381101.761642679007103.880973467755
86102.862616146761101.318860457986104.406371835536
87102.903924220142100.95743997747104.850408462814
88102.945232293523100.632727837252105.257736749793
89102.986540366903100.328018642764105.645062091042
90103.027848440284100.035038411145106.020658469422
91103.06915651366499.7490469567597106.389266070569
92103.11046458704599.4670715493768106.753857624713
93103.15177266042699.1871293961523107.116415924699
94103.19308073380698.9078379286549107.478323538958
95103.23438880718798.6282005612954107.840577053079
96103.27569688056898.3474804428888108.203913318246



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')