Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 08 Jan 2017 21:27:57 +0000
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/Jan/08/t1483910903r99bfwe1xkdyt6a.htm/, Retrieved Tue, 14 May 2024 14:33:53 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 14 May 2024 14:33:53 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
98.98
98.97
98.91
98.98
98.95
98.96
98.96
99.04
99.33
100.04
100.14
100.21
100.21
100.27
100.44
100.57
100.51
100.47
100.47
100.49
101
101.61
101.65
101.74
101.74
101.73
101.77
101.82
101.97
102.09
102.09
102.08
102.42
102.78
103.04
103.08
99.16
99.19
99.23
99.31
99.46
99.49
99.95
100.14
100.43
101.1
101.26
101.28
101.04
101.12
101.07
100.97
101.01
100.99
101.19
101.25
101.33
101.79
102.06
102.09
102.27
102.26
102.46
102.46
102.51
102.56
102.59
102.26
102.33
102.84
102.93
102.95




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 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]1 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 time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.00164594862076607
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.00164594862076607 \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]0.00164594862076607[/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
beta0.00164594862076607
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
398.9198.96-0.0499999999999972
498.9898.8999177025690.0800822974310478
598.9598.970049513916-0.0200495139159642
698.9698.94001651344620.0199834865538122
798.9698.95004940523830.00995059476169047
899.0498.9500657834060.0899342165939743
999.3399.03021381050580.299786189494185
10100.0499.32070724317090.719292756829077
11100.14100.0318911620920.108108837908034
12100.21100.1320691036850.0779308963153937
13100.21100.2021973739360.0078026260640911
14100.27100.2022102166580.0677897833424908
15100.44100.2623217951580.177678204842096
16100.57100.4326142443540.13738575564588
17100.51100.562840374249-0.052840374249115
18100.47100.502753401708-0.0327534017080211
19100.47100.4626994912920.00730050870835441
20100.49100.4627115075540.0272884924461181
21101100.482756423010.517243576989614
22101.61100.9936077793630.616392220637465
23101.65101.6046223292880.0453776707120568
24101.74101.6446970186020.0953029813975235
25101.74101.7348538824130.00514611758674732
26101.73101.734862352658-0.00486235265839241
27101.77101.7248543494760.0451456505242476
28101.82101.7649286568970.0550713431030374
29101.97101.8150193014980.154980698501817
30102.09101.9652743917650.124725608234883
31102.09102.0854796837080.0045203162920302
32102.08102.085487123916-0.0054871239163532
33102.42102.0754780923920.3445219076077
34102.78102.4160451577510.363954842249044
35103.04102.7766442087220.263355791278428
36103.08103.0370776788230.042922321176988
3799.16103.077148326758-3.91714832675834
3899.1999.15070090187260.0392990981274295
3999.2399.18076558616890.0492344138310727
4099.3199.22084662348450.0891533765155259
4199.4699.30099336536160.159006634638402
4299.4999.45125508211260.0387449178874419
4399.9599.48131885425670.46868114574329
44100.1499.94209027934210.197909720657861
45100.43100.1324160285740.297583971426121
46101.1100.4229058365010.677094163498765
47101.26101.0940202987060.165979701294248
48101.28101.2542934927660.0257065072338207
49101.04101.274335804356-0.234335804356306
50101.12101.0339500996620.0860499003376702
51101.07101.114091733377-0.0440917333771154
52100.97101.064019160649-0.094019160649367
53101.01100.9638644099420.0461355900584408
54100.99101.003940346752-0.0139403467524062
55101.19100.9839174016580.206082598342121
56101.25101.1842566030260.0657433969736161
57101.33101.244364813280.085635186720026
58101.79101.3245057643970.465494235602577
59102.06101.7852719439930.27472805600749
60102.09102.0557241322570.0342758677426218
61102.27102.0857805485750.184219451425378
62102.26102.266083764327-0.00608376432658986
63102.46102.2560737507630.203926249236886
64102.46102.4564094028920.00359059710822862
65102.51102.456415312830.053584687169888
66102.56102.5065035104720.0534964895279302
67102.59102.5565915629450.0334084370547743
68102.26102.586646551516-0.326646551516106
69102.33102.2561089080750.0738910919248212
70102.84102.3262305290160.513769470984002
71102.93102.8370761671680.0929238328318434
72102.95102.9272291150230.0227708849773478

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 98.91 & 98.96 & -0.0499999999999972 \tabularnewline
4 & 98.98 & 98.899917702569 & 0.0800822974310478 \tabularnewline
5 & 98.95 & 98.970049513916 & -0.0200495139159642 \tabularnewline
6 & 98.96 & 98.9400165134462 & 0.0199834865538122 \tabularnewline
7 & 98.96 & 98.9500494052383 & 0.00995059476169047 \tabularnewline
8 & 99.04 & 98.950065783406 & 0.0899342165939743 \tabularnewline
9 & 99.33 & 99.0302138105058 & 0.299786189494185 \tabularnewline
10 & 100.04 & 99.3207072431709 & 0.719292756829077 \tabularnewline
11 & 100.14 & 100.031891162092 & 0.108108837908034 \tabularnewline
12 & 100.21 & 100.132069103685 & 0.0779308963153937 \tabularnewline
13 & 100.21 & 100.202197373936 & 0.0078026260640911 \tabularnewline
14 & 100.27 & 100.202210216658 & 0.0677897833424908 \tabularnewline
15 & 100.44 & 100.262321795158 & 0.177678204842096 \tabularnewline
16 & 100.57 & 100.432614244354 & 0.13738575564588 \tabularnewline
17 & 100.51 & 100.562840374249 & -0.052840374249115 \tabularnewline
18 & 100.47 & 100.502753401708 & -0.0327534017080211 \tabularnewline
19 & 100.47 & 100.462699491292 & 0.00730050870835441 \tabularnewline
20 & 100.49 & 100.462711507554 & 0.0272884924461181 \tabularnewline
21 & 101 & 100.48275642301 & 0.517243576989614 \tabularnewline
22 & 101.61 & 100.993607779363 & 0.616392220637465 \tabularnewline
23 & 101.65 & 101.604622329288 & 0.0453776707120568 \tabularnewline
24 & 101.74 & 101.644697018602 & 0.0953029813975235 \tabularnewline
25 & 101.74 & 101.734853882413 & 0.00514611758674732 \tabularnewline
26 & 101.73 & 101.734862352658 & -0.00486235265839241 \tabularnewline
27 & 101.77 & 101.724854349476 & 0.0451456505242476 \tabularnewline
28 & 101.82 & 101.764928656897 & 0.0550713431030374 \tabularnewline
29 & 101.97 & 101.815019301498 & 0.154980698501817 \tabularnewline
30 & 102.09 & 101.965274391765 & 0.124725608234883 \tabularnewline
31 & 102.09 & 102.085479683708 & 0.0045203162920302 \tabularnewline
32 & 102.08 & 102.085487123916 & -0.0054871239163532 \tabularnewline
33 & 102.42 & 102.075478092392 & 0.3445219076077 \tabularnewline
34 & 102.78 & 102.416045157751 & 0.363954842249044 \tabularnewline
35 & 103.04 & 102.776644208722 & 0.263355791278428 \tabularnewline
36 & 103.08 & 103.037077678823 & 0.042922321176988 \tabularnewline
37 & 99.16 & 103.077148326758 & -3.91714832675834 \tabularnewline
38 & 99.19 & 99.1507009018726 & 0.0392990981274295 \tabularnewline
39 & 99.23 & 99.1807655861689 & 0.0492344138310727 \tabularnewline
40 & 99.31 & 99.2208466234845 & 0.0891533765155259 \tabularnewline
41 & 99.46 & 99.3009933653616 & 0.159006634638402 \tabularnewline
42 & 99.49 & 99.4512550821126 & 0.0387449178874419 \tabularnewline
43 & 99.95 & 99.4813188542567 & 0.46868114574329 \tabularnewline
44 & 100.14 & 99.9420902793421 & 0.197909720657861 \tabularnewline
45 & 100.43 & 100.132416028574 & 0.297583971426121 \tabularnewline
46 & 101.1 & 100.422905836501 & 0.677094163498765 \tabularnewline
47 & 101.26 & 101.094020298706 & 0.165979701294248 \tabularnewline
48 & 101.28 & 101.254293492766 & 0.0257065072338207 \tabularnewline
49 & 101.04 & 101.274335804356 & -0.234335804356306 \tabularnewline
50 & 101.12 & 101.033950099662 & 0.0860499003376702 \tabularnewline
51 & 101.07 & 101.114091733377 & -0.0440917333771154 \tabularnewline
52 & 100.97 & 101.064019160649 & -0.094019160649367 \tabularnewline
53 & 101.01 & 100.963864409942 & 0.0461355900584408 \tabularnewline
54 & 100.99 & 101.003940346752 & -0.0139403467524062 \tabularnewline
55 & 101.19 & 100.983917401658 & 0.206082598342121 \tabularnewline
56 & 101.25 & 101.184256603026 & 0.0657433969736161 \tabularnewline
57 & 101.33 & 101.24436481328 & 0.085635186720026 \tabularnewline
58 & 101.79 & 101.324505764397 & 0.465494235602577 \tabularnewline
59 & 102.06 & 101.785271943993 & 0.27472805600749 \tabularnewline
60 & 102.09 & 102.055724132257 & 0.0342758677426218 \tabularnewline
61 & 102.27 & 102.085780548575 & 0.184219451425378 \tabularnewline
62 & 102.26 & 102.266083764327 & -0.00608376432658986 \tabularnewline
63 & 102.46 & 102.256073750763 & 0.203926249236886 \tabularnewline
64 & 102.46 & 102.456409402892 & 0.00359059710822862 \tabularnewline
65 & 102.51 & 102.45641531283 & 0.053584687169888 \tabularnewline
66 & 102.56 & 102.506503510472 & 0.0534964895279302 \tabularnewline
67 & 102.59 & 102.556591562945 & 0.0334084370547743 \tabularnewline
68 & 102.26 & 102.586646551516 & -0.326646551516106 \tabularnewline
69 & 102.33 & 102.256108908075 & 0.0738910919248212 \tabularnewline
70 & 102.84 & 102.326230529016 & 0.513769470984002 \tabularnewline
71 & 102.93 & 102.837076167168 & 0.0929238328318434 \tabularnewline
72 & 102.95 & 102.927229115023 & 0.0227708849773478 \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]98.91[/C][C]98.96[/C][C]-0.0499999999999972[/C][/ROW]
[ROW][C]4[/C][C]98.98[/C][C]98.899917702569[/C][C]0.0800822974310478[/C][/ROW]
[ROW][C]5[/C][C]98.95[/C][C]98.970049513916[/C][C]-0.0200495139159642[/C][/ROW]
[ROW][C]6[/C][C]98.96[/C][C]98.9400165134462[/C][C]0.0199834865538122[/C][/ROW]
[ROW][C]7[/C][C]98.96[/C][C]98.9500494052383[/C][C]0.00995059476169047[/C][/ROW]
[ROW][C]8[/C][C]99.04[/C][C]98.950065783406[/C][C]0.0899342165939743[/C][/ROW]
[ROW][C]9[/C][C]99.33[/C][C]99.0302138105058[/C][C]0.299786189494185[/C][/ROW]
[ROW][C]10[/C][C]100.04[/C][C]99.3207072431709[/C][C]0.719292756829077[/C][/ROW]
[ROW][C]11[/C][C]100.14[/C][C]100.031891162092[/C][C]0.108108837908034[/C][/ROW]
[ROW][C]12[/C][C]100.21[/C][C]100.132069103685[/C][C]0.0779308963153937[/C][/ROW]
[ROW][C]13[/C][C]100.21[/C][C]100.202197373936[/C][C]0.0078026260640911[/C][/ROW]
[ROW][C]14[/C][C]100.27[/C][C]100.202210216658[/C][C]0.0677897833424908[/C][/ROW]
[ROW][C]15[/C][C]100.44[/C][C]100.262321795158[/C][C]0.177678204842096[/C][/ROW]
[ROW][C]16[/C][C]100.57[/C][C]100.432614244354[/C][C]0.13738575564588[/C][/ROW]
[ROW][C]17[/C][C]100.51[/C][C]100.562840374249[/C][C]-0.052840374249115[/C][/ROW]
[ROW][C]18[/C][C]100.47[/C][C]100.502753401708[/C][C]-0.0327534017080211[/C][/ROW]
[ROW][C]19[/C][C]100.47[/C][C]100.462699491292[/C][C]0.00730050870835441[/C][/ROW]
[ROW][C]20[/C][C]100.49[/C][C]100.462711507554[/C][C]0.0272884924461181[/C][/ROW]
[ROW][C]21[/C][C]101[/C][C]100.48275642301[/C][C]0.517243576989614[/C][/ROW]
[ROW][C]22[/C][C]101.61[/C][C]100.993607779363[/C][C]0.616392220637465[/C][/ROW]
[ROW][C]23[/C][C]101.65[/C][C]101.604622329288[/C][C]0.0453776707120568[/C][/ROW]
[ROW][C]24[/C][C]101.74[/C][C]101.644697018602[/C][C]0.0953029813975235[/C][/ROW]
[ROW][C]25[/C][C]101.74[/C][C]101.734853882413[/C][C]0.00514611758674732[/C][/ROW]
[ROW][C]26[/C][C]101.73[/C][C]101.734862352658[/C][C]-0.00486235265839241[/C][/ROW]
[ROW][C]27[/C][C]101.77[/C][C]101.724854349476[/C][C]0.0451456505242476[/C][/ROW]
[ROW][C]28[/C][C]101.82[/C][C]101.764928656897[/C][C]0.0550713431030374[/C][/ROW]
[ROW][C]29[/C][C]101.97[/C][C]101.815019301498[/C][C]0.154980698501817[/C][/ROW]
[ROW][C]30[/C][C]102.09[/C][C]101.965274391765[/C][C]0.124725608234883[/C][/ROW]
[ROW][C]31[/C][C]102.09[/C][C]102.085479683708[/C][C]0.0045203162920302[/C][/ROW]
[ROW][C]32[/C][C]102.08[/C][C]102.085487123916[/C][C]-0.0054871239163532[/C][/ROW]
[ROW][C]33[/C][C]102.42[/C][C]102.075478092392[/C][C]0.3445219076077[/C][/ROW]
[ROW][C]34[/C][C]102.78[/C][C]102.416045157751[/C][C]0.363954842249044[/C][/ROW]
[ROW][C]35[/C][C]103.04[/C][C]102.776644208722[/C][C]0.263355791278428[/C][/ROW]
[ROW][C]36[/C][C]103.08[/C][C]103.037077678823[/C][C]0.042922321176988[/C][/ROW]
[ROW][C]37[/C][C]99.16[/C][C]103.077148326758[/C][C]-3.91714832675834[/C][/ROW]
[ROW][C]38[/C][C]99.19[/C][C]99.1507009018726[/C][C]0.0392990981274295[/C][/ROW]
[ROW][C]39[/C][C]99.23[/C][C]99.1807655861689[/C][C]0.0492344138310727[/C][/ROW]
[ROW][C]40[/C][C]99.31[/C][C]99.2208466234845[/C][C]0.0891533765155259[/C][/ROW]
[ROW][C]41[/C][C]99.46[/C][C]99.3009933653616[/C][C]0.159006634638402[/C][/ROW]
[ROW][C]42[/C][C]99.49[/C][C]99.4512550821126[/C][C]0.0387449178874419[/C][/ROW]
[ROW][C]43[/C][C]99.95[/C][C]99.4813188542567[/C][C]0.46868114574329[/C][/ROW]
[ROW][C]44[/C][C]100.14[/C][C]99.9420902793421[/C][C]0.197909720657861[/C][/ROW]
[ROW][C]45[/C][C]100.43[/C][C]100.132416028574[/C][C]0.297583971426121[/C][/ROW]
[ROW][C]46[/C][C]101.1[/C][C]100.422905836501[/C][C]0.677094163498765[/C][/ROW]
[ROW][C]47[/C][C]101.26[/C][C]101.094020298706[/C][C]0.165979701294248[/C][/ROW]
[ROW][C]48[/C][C]101.28[/C][C]101.254293492766[/C][C]0.0257065072338207[/C][/ROW]
[ROW][C]49[/C][C]101.04[/C][C]101.274335804356[/C][C]-0.234335804356306[/C][/ROW]
[ROW][C]50[/C][C]101.12[/C][C]101.033950099662[/C][C]0.0860499003376702[/C][/ROW]
[ROW][C]51[/C][C]101.07[/C][C]101.114091733377[/C][C]-0.0440917333771154[/C][/ROW]
[ROW][C]52[/C][C]100.97[/C][C]101.064019160649[/C][C]-0.094019160649367[/C][/ROW]
[ROW][C]53[/C][C]101.01[/C][C]100.963864409942[/C][C]0.0461355900584408[/C][/ROW]
[ROW][C]54[/C][C]100.99[/C][C]101.003940346752[/C][C]-0.0139403467524062[/C][/ROW]
[ROW][C]55[/C][C]101.19[/C][C]100.983917401658[/C][C]0.206082598342121[/C][/ROW]
[ROW][C]56[/C][C]101.25[/C][C]101.184256603026[/C][C]0.0657433969736161[/C][/ROW]
[ROW][C]57[/C][C]101.33[/C][C]101.24436481328[/C][C]0.085635186720026[/C][/ROW]
[ROW][C]58[/C][C]101.79[/C][C]101.324505764397[/C][C]0.465494235602577[/C][/ROW]
[ROW][C]59[/C][C]102.06[/C][C]101.785271943993[/C][C]0.27472805600749[/C][/ROW]
[ROW][C]60[/C][C]102.09[/C][C]102.055724132257[/C][C]0.0342758677426218[/C][/ROW]
[ROW][C]61[/C][C]102.27[/C][C]102.085780548575[/C][C]0.184219451425378[/C][/ROW]
[ROW][C]62[/C][C]102.26[/C][C]102.266083764327[/C][C]-0.00608376432658986[/C][/ROW]
[ROW][C]63[/C][C]102.46[/C][C]102.256073750763[/C][C]0.203926249236886[/C][/ROW]
[ROW][C]64[/C][C]102.46[/C][C]102.456409402892[/C][C]0.00359059710822862[/C][/ROW]
[ROW][C]65[/C][C]102.51[/C][C]102.45641531283[/C][C]0.053584687169888[/C][/ROW]
[ROW][C]66[/C][C]102.56[/C][C]102.506503510472[/C][C]0.0534964895279302[/C][/ROW]
[ROW][C]67[/C][C]102.59[/C][C]102.556591562945[/C][C]0.0334084370547743[/C][/ROW]
[ROW][C]68[/C][C]102.26[/C][C]102.586646551516[/C][C]-0.326646551516106[/C][/ROW]
[ROW][C]69[/C][C]102.33[/C][C]102.256108908075[/C][C]0.0738910919248212[/C][/ROW]
[ROW][C]70[/C][C]102.84[/C][C]102.326230529016[/C][C]0.513769470984002[/C][/ROW]
[ROW][C]71[/C][C]102.93[/C][C]102.837076167168[/C][C]0.0929238328318434[/C][/ROW]
[ROW][C]72[/C][C]102.95[/C][C]102.927229115023[/C][C]0.0227708849773478[/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
398.9198.96-0.0499999999999972
498.9898.8999177025690.0800822974310478
598.9598.970049513916-0.0200495139159642
698.9698.94001651344620.0199834865538122
798.9698.95004940523830.00995059476169047
899.0498.9500657834060.0899342165939743
999.3399.03021381050580.299786189494185
10100.0499.32070724317090.719292756829077
11100.14100.0318911620920.108108837908034
12100.21100.1320691036850.0779308963153937
13100.21100.2021973739360.0078026260640911
14100.27100.2022102166580.0677897833424908
15100.44100.2623217951580.177678204842096
16100.57100.4326142443540.13738575564588
17100.51100.562840374249-0.052840374249115
18100.47100.502753401708-0.0327534017080211
19100.47100.4626994912920.00730050870835441
20100.49100.4627115075540.0272884924461181
21101100.482756423010.517243576989614
22101.61100.9936077793630.616392220637465
23101.65101.6046223292880.0453776707120568
24101.74101.6446970186020.0953029813975235
25101.74101.7348538824130.00514611758674732
26101.73101.734862352658-0.00486235265839241
27101.77101.7248543494760.0451456505242476
28101.82101.7649286568970.0550713431030374
29101.97101.8150193014980.154980698501817
30102.09101.9652743917650.124725608234883
31102.09102.0854796837080.0045203162920302
32102.08102.085487123916-0.0054871239163532
33102.42102.0754780923920.3445219076077
34102.78102.4160451577510.363954842249044
35103.04102.7766442087220.263355791278428
36103.08103.0370776788230.042922321176988
3799.16103.077148326758-3.91714832675834
3899.1999.15070090187260.0392990981274295
3999.2399.18076558616890.0492344138310727
4099.3199.22084662348450.0891533765155259
4199.4699.30099336536160.159006634638402
4299.4999.45125508211260.0387449178874419
4399.9599.48131885425670.46868114574329
44100.1499.94209027934210.197909720657861
45100.43100.1324160285740.297583971426121
46101.1100.4229058365010.677094163498765
47101.26101.0940202987060.165979701294248
48101.28101.2542934927660.0257065072338207
49101.04101.274335804356-0.234335804356306
50101.12101.0339500996620.0860499003376702
51101.07101.114091733377-0.0440917333771154
52100.97101.064019160649-0.094019160649367
53101.01100.9638644099420.0461355900584408
54100.99101.003940346752-0.0139403467524062
55101.19100.9839174016580.206082598342121
56101.25101.1842566030260.0657433969736161
57101.33101.244364813280.085635186720026
58101.79101.3245057643970.465494235602577
59102.06101.7852719439930.27472805600749
60102.09102.0557241322570.0342758677426218
61102.27102.0857805485750.184219451425378
62102.26102.266083764327-0.00608376432658986
63102.46102.2560737507630.203926249236886
64102.46102.4564094028920.00359059710822862
65102.51102.456415312830.053584687169888
66102.56102.5065035104720.0534964895279302
67102.59102.5565915629450.0334084370547743
68102.26102.586646551516-0.326646551516106
69102.33102.2561089080750.0738910919248212
70102.84102.3262305290160.513769470984002
71102.93102.8370761671680.0929238328318434
72102.95102.9272291150230.0227708849773478







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73102.947266594729101.930827145143103.963706044316
74102.944533189459101.505887253463104.383179125454
75102.941799784188101.178375694144104.705223874232
76102.939066378918100.90116502479104.976967733045
77102.936332973647100.656017216896105.216648730397
78102.933599568376100.433586731761105.433612404992
79102.930866163106100.22832657499105.633405751221
80102.928132757835100.036625594665105.819639921005
81102.92539935256499.855977561879105.99482114325
82102.92266594729499.6845592185621106.160772676025
83102.91993254202399.5209952897139106.318869794332
84102.91719913675299.3642182048483106.470180068657

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 102.947266594729 & 101.930827145143 & 103.963706044316 \tabularnewline
74 & 102.944533189459 & 101.505887253463 & 104.383179125454 \tabularnewline
75 & 102.941799784188 & 101.178375694144 & 104.705223874232 \tabularnewline
76 & 102.939066378918 & 100.90116502479 & 104.976967733045 \tabularnewline
77 & 102.936332973647 & 100.656017216896 & 105.216648730397 \tabularnewline
78 & 102.933599568376 & 100.433586731761 & 105.433612404992 \tabularnewline
79 & 102.930866163106 & 100.22832657499 & 105.633405751221 \tabularnewline
80 & 102.928132757835 & 100.036625594665 & 105.819639921005 \tabularnewline
81 & 102.925399352564 & 99.855977561879 & 105.99482114325 \tabularnewline
82 & 102.922665947294 & 99.6845592185621 & 106.160772676025 \tabularnewline
83 & 102.919932542023 & 99.5209952897139 & 106.318869794332 \tabularnewline
84 & 102.917199136752 & 99.3642182048483 & 106.470180068657 \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]73[/C][C]102.947266594729[/C][C]101.930827145143[/C][C]103.963706044316[/C][/ROW]
[ROW][C]74[/C][C]102.944533189459[/C][C]101.505887253463[/C][C]104.383179125454[/C][/ROW]
[ROW][C]75[/C][C]102.941799784188[/C][C]101.178375694144[/C][C]104.705223874232[/C][/ROW]
[ROW][C]76[/C][C]102.939066378918[/C][C]100.90116502479[/C][C]104.976967733045[/C][/ROW]
[ROW][C]77[/C][C]102.936332973647[/C][C]100.656017216896[/C][C]105.216648730397[/C][/ROW]
[ROW][C]78[/C][C]102.933599568376[/C][C]100.433586731761[/C][C]105.433612404992[/C][/ROW]
[ROW][C]79[/C][C]102.930866163106[/C][C]100.22832657499[/C][C]105.633405751221[/C][/ROW]
[ROW][C]80[/C][C]102.928132757835[/C][C]100.036625594665[/C][C]105.819639921005[/C][/ROW]
[ROW][C]81[/C][C]102.925399352564[/C][C]99.855977561879[/C][C]105.99482114325[/C][/ROW]
[ROW][C]82[/C][C]102.922665947294[/C][C]99.6845592185621[/C][C]106.160772676025[/C][/ROW]
[ROW][C]83[/C][C]102.919932542023[/C][C]99.5209952897139[/C][C]106.318869794332[/C][/ROW]
[ROW][C]84[/C][C]102.917199136752[/C][C]99.3642182048483[/C][C]106.470180068657[/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
73102.947266594729101.930827145143103.963706044316
74102.944533189459101.505887253463104.383179125454
75102.941799784188101.178375694144104.705223874232
76102.939066378918100.90116502479104.976967733045
77102.936332973647100.656017216896105.216648730397
78102.933599568376100.433586731761105.433612404992
79102.930866163106100.22832657499105.633405751221
80102.928132757835100.036625594665105.819639921005
81102.92539935256499.855977561879105.99482114325
82102.92266594729499.6845592185621106.160772676025
83102.91993254202399.5209952897139106.318869794332
84102.91719913675299.3642182048483106.470180068657



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):
par3 <- 'additive'
par2 <- 'Double'
par1 <- '12'
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')