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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 02 Jan 2013 13:26:09 -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/Jan/02/t1357151234uhn4ciu0zy53tlq.htm/, Retrieved Mon, 29 Apr 2024 10:43:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=204976, Retrieved Mon, 29 Apr 2024 10:43:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact173
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-01-02 18:26:09] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
7,66
7,53
7,54
7,56
7,57
7,56
7,57
7,61
7,61
7,6
7,61
7,61
7,62
7,7
7,73
7,75
7,76
7,76
7,77
7,79
7,79
7,79
7,83
7,83
7,88
7,95
8,01
8,05
8,1
8,1
8,16
8,18
8,2
7,99
8,01
8,02
8,03
8,04
8,07
8,08
8,08
8,1
8,11
8,15
8,16
8,17
8,18
8,15
8,15
8,17
8,16
8,15
8,16
8,15
8,18
8,19
8,18
8,2
8,21
8,22
8,23
8,25
8,28
8,28
8,29
8,3
8,34
8,38
8,39
8,44
8,46
8,46





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=204976&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=204976&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204976&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.422981882109855
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.422981882109855 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204976&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]0.422981882109855[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204976&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204976&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
beta0.422981882109855
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
37.547.40.14
47.567.469217463495380.0907825365046202
57.577.527616831648810.0423831683511899
67.567.555544143967780.00445585603222387
77.577.54742889033870.0225711096613042
87.617.566976060784540.0430239392154572
97.617.62517440756968-0.0151744075696767
107.67.61875590809595-0.0187559080959536
117.617.600822498788850.00917750121115368
127.617.61470441552421-0.00470441552420642
137.627.612714532991550.00728546700844923
147.77.625796153538830.0742038464611667
157.737.73718303617477-0.00718303617476845
167.757.7641447420143-0.0141447420143024
177.767.77816177241513-0.0181617724151346
187.767.78047967173653-0.0204796717365294
197.777.77181714164042-0.00181714164042024
207.797.781048523649290.00895147635070526
217.797.80483483596378-0.0148348359637787
227.797.79855996912703-0.00855996912702839
237.837.794939257274880.0350607427251246
247.837.84976931622092-0.019769316220918
257.887.841407253637770.0385927463622302
267.957.907731286129850.0422687138701461
278.017.995610186277010.0143898137229881
288.058.06169681676877-0.0116968167687705
298.18.096749275197220.00325072480277555
308.18.14812427289252-0.0481242728925224
318.168.127768577369270.0322314226307263
328.188.2014018851767-0.0214018851766973
338.28.21234927550396-0.0123492755039596
347.998.2271257557086-0.2371257557086
358.017.916825857262260.0931741427377437
368.027.976236831521440.0437631684785611
378.038.004747858891590.0252521411084086
388.048.025429057064930.0145709429350696
398.078.041592301931720.0284076980682801
408.088.08360824352705-0.0036082435270508
418.088.09208202188887-0.0120820218888671
428.18.086971545530620.0130284544693779
438.118.11248234572306-0.00248234572306139
448.158.121432358457070.0285676415429279
458.168.17351595324434-0.0135159532443403
468.178.17779894990254-0.00779894990254171
478.188.18450013539428-0.0045001353942844
488.158.19259665965546-0.0425966596554588
498.158.14457904438280.00542095561719869
508.178.14687201039260.023127989607401
518.168.17665473096615-0.0166547309661542
528.158.15961008151606-0.00961008151605647
538.168.145545191149170.0144548088508341
548.158.16165931340243-0.0116593134024292
558.188.146727635075360.0332723649246383
568.198.19080124261343-0.00080124261343073
578.188.20046233150477-0.0204623315047741
588.28.181807136012530.0181928639874691
598.218.209502387862920.000497612137083436
608.228.219712868781220.000287131218776437
618.238.229834320084550.000165679915445693
628.258.239904399687020.0100956003129831
638.288.264174655708430.015825344291569
648.288.30086848962191-0.0208684896219147
658.298.29204149660485-0.00204149660484809
668.38.30117798052861-0.00117798052860607
678.348.310679716107530.0293202838924707
688.388.363081664972360.0169183350276398
698.398.41023781416452-0.020237814164517
708.448.411677585439420.0283224145605789
718.468.47365745365615-0.0136574536561476
728.468.48788059820384-0.0278805982038435

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 7.54 & 7.4 & 0.14 \tabularnewline
4 & 7.56 & 7.46921746349538 & 0.0907825365046202 \tabularnewline
5 & 7.57 & 7.52761683164881 & 0.0423831683511899 \tabularnewline
6 & 7.56 & 7.55554414396778 & 0.00445585603222387 \tabularnewline
7 & 7.57 & 7.5474288903387 & 0.0225711096613042 \tabularnewline
8 & 7.61 & 7.56697606078454 & 0.0430239392154572 \tabularnewline
9 & 7.61 & 7.62517440756968 & -0.0151744075696767 \tabularnewline
10 & 7.6 & 7.61875590809595 & -0.0187559080959536 \tabularnewline
11 & 7.61 & 7.60082249878885 & 0.00917750121115368 \tabularnewline
12 & 7.61 & 7.61470441552421 & -0.00470441552420642 \tabularnewline
13 & 7.62 & 7.61271453299155 & 0.00728546700844923 \tabularnewline
14 & 7.7 & 7.62579615353883 & 0.0742038464611667 \tabularnewline
15 & 7.73 & 7.73718303617477 & -0.00718303617476845 \tabularnewline
16 & 7.75 & 7.7641447420143 & -0.0141447420143024 \tabularnewline
17 & 7.76 & 7.77816177241513 & -0.0181617724151346 \tabularnewline
18 & 7.76 & 7.78047967173653 & -0.0204796717365294 \tabularnewline
19 & 7.77 & 7.77181714164042 & -0.00181714164042024 \tabularnewline
20 & 7.79 & 7.78104852364929 & 0.00895147635070526 \tabularnewline
21 & 7.79 & 7.80483483596378 & -0.0148348359637787 \tabularnewline
22 & 7.79 & 7.79855996912703 & -0.00855996912702839 \tabularnewline
23 & 7.83 & 7.79493925727488 & 0.0350607427251246 \tabularnewline
24 & 7.83 & 7.84976931622092 & -0.019769316220918 \tabularnewline
25 & 7.88 & 7.84140725363777 & 0.0385927463622302 \tabularnewline
26 & 7.95 & 7.90773128612985 & 0.0422687138701461 \tabularnewline
27 & 8.01 & 7.99561018627701 & 0.0143898137229881 \tabularnewline
28 & 8.05 & 8.06169681676877 & -0.0116968167687705 \tabularnewline
29 & 8.1 & 8.09674927519722 & 0.00325072480277555 \tabularnewline
30 & 8.1 & 8.14812427289252 & -0.0481242728925224 \tabularnewline
31 & 8.16 & 8.12776857736927 & 0.0322314226307263 \tabularnewline
32 & 8.18 & 8.2014018851767 & -0.0214018851766973 \tabularnewline
33 & 8.2 & 8.21234927550396 & -0.0123492755039596 \tabularnewline
34 & 7.99 & 8.2271257557086 & -0.2371257557086 \tabularnewline
35 & 8.01 & 7.91682585726226 & 0.0931741427377437 \tabularnewline
36 & 8.02 & 7.97623683152144 & 0.0437631684785611 \tabularnewline
37 & 8.03 & 8.00474785889159 & 0.0252521411084086 \tabularnewline
38 & 8.04 & 8.02542905706493 & 0.0145709429350696 \tabularnewline
39 & 8.07 & 8.04159230193172 & 0.0284076980682801 \tabularnewline
40 & 8.08 & 8.08360824352705 & -0.0036082435270508 \tabularnewline
41 & 8.08 & 8.09208202188887 & -0.0120820218888671 \tabularnewline
42 & 8.1 & 8.08697154553062 & 0.0130284544693779 \tabularnewline
43 & 8.11 & 8.11248234572306 & -0.00248234572306139 \tabularnewline
44 & 8.15 & 8.12143235845707 & 0.0285676415429279 \tabularnewline
45 & 8.16 & 8.17351595324434 & -0.0135159532443403 \tabularnewline
46 & 8.17 & 8.17779894990254 & -0.00779894990254171 \tabularnewline
47 & 8.18 & 8.18450013539428 & -0.0045001353942844 \tabularnewline
48 & 8.15 & 8.19259665965546 & -0.0425966596554588 \tabularnewline
49 & 8.15 & 8.1445790443828 & 0.00542095561719869 \tabularnewline
50 & 8.17 & 8.1468720103926 & 0.023127989607401 \tabularnewline
51 & 8.16 & 8.17665473096615 & -0.0166547309661542 \tabularnewline
52 & 8.15 & 8.15961008151606 & -0.00961008151605647 \tabularnewline
53 & 8.16 & 8.14554519114917 & 0.0144548088508341 \tabularnewline
54 & 8.15 & 8.16165931340243 & -0.0116593134024292 \tabularnewline
55 & 8.18 & 8.14672763507536 & 0.0332723649246383 \tabularnewline
56 & 8.19 & 8.19080124261343 & -0.00080124261343073 \tabularnewline
57 & 8.18 & 8.20046233150477 & -0.0204623315047741 \tabularnewline
58 & 8.2 & 8.18180713601253 & 0.0181928639874691 \tabularnewline
59 & 8.21 & 8.20950238786292 & 0.000497612137083436 \tabularnewline
60 & 8.22 & 8.21971286878122 & 0.000287131218776437 \tabularnewline
61 & 8.23 & 8.22983432008455 & 0.000165679915445693 \tabularnewline
62 & 8.25 & 8.23990439968702 & 0.0100956003129831 \tabularnewline
63 & 8.28 & 8.26417465570843 & 0.015825344291569 \tabularnewline
64 & 8.28 & 8.30086848962191 & -0.0208684896219147 \tabularnewline
65 & 8.29 & 8.29204149660485 & -0.00204149660484809 \tabularnewline
66 & 8.3 & 8.30117798052861 & -0.00117798052860607 \tabularnewline
67 & 8.34 & 8.31067971610753 & 0.0293202838924707 \tabularnewline
68 & 8.38 & 8.36308166497236 & 0.0169183350276398 \tabularnewline
69 & 8.39 & 8.41023781416452 & -0.020237814164517 \tabularnewline
70 & 8.44 & 8.41167758543942 & 0.0283224145605789 \tabularnewline
71 & 8.46 & 8.47365745365615 & -0.0136574536561476 \tabularnewline
72 & 8.46 & 8.48788059820384 & -0.0278805982038435 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204976&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]7.54[/C][C]7.4[/C][C]0.14[/C][/ROW]
[ROW][C]4[/C][C]7.56[/C][C]7.46921746349538[/C][C]0.0907825365046202[/C][/ROW]
[ROW][C]5[/C][C]7.57[/C][C]7.52761683164881[/C][C]0.0423831683511899[/C][/ROW]
[ROW][C]6[/C][C]7.56[/C][C]7.55554414396778[/C][C]0.00445585603222387[/C][/ROW]
[ROW][C]7[/C][C]7.57[/C][C]7.5474288903387[/C][C]0.0225711096613042[/C][/ROW]
[ROW][C]8[/C][C]7.61[/C][C]7.56697606078454[/C][C]0.0430239392154572[/C][/ROW]
[ROW][C]9[/C][C]7.61[/C][C]7.62517440756968[/C][C]-0.0151744075696767[/C][/ROW]
[ROW][C]10[/C][C]7.6[/C][C]7.61875590809595[/C][C]-0.0187559080959536[/C][/ROW]
[ROW][C]11[/C][C]7.61[/C][C]7.60082249878885[/C][C]0.00917750121115368[/C][/ROW]
[ROW][C]12[/C][C]7.61[/C][C]7.61470441552421[/C][C]-0.00470441552420642[/C][/ROW]
[ROW][C]13[/C][C]7.62[/C][C]7.61271453299155[/C][C]0.00728546700844923[/C][/ROW]
[ROW][C]14[/C][C]7.7[/C][C]7.62579615353883[/C][C]0.0742038464611667[/C][/ROW]
[ROW][C]15[/C][C]7.73[/C][C]7.73718303617477[/C][C]-0.00718303617476845[/C][/ROW]
[ROW][C]16[/C][C]7.75[/C][C]7.7641447420143[/C][C]-0.0141447420143024[/C][/ROW]
[ROW][C]17[/C][C]7.76[/C][C]7.77816177241513[/C][C]-0.0181617724151346[/C][/ROW]
[ROW][C]18[/C][C]7.76[/C][C]7.78047967173653[/C][C]-0.0204796717365294[/C][/ROW]
[ROW][C]19[/C][C]7.77[/C][C]7.77181714164042[/C][C]-0.00181714164042024[/C][/ROW]
[ROW][C]20[/C][C]7.79[/C][C]7.78104852364929[/C][C]0.00895147635070526[/C][/ROW]
[ROW][C]21[/C][C]7.79[/C][C]7.80483483596378[/C][C]-0.0148348359637787[/C][/ROW]
[ROW][C]22[/C][C]7.79[/C][C]7.79855996912703[/C][C]-0.00855996912702839[/C][/ROW]
[ROW][C]23[/C][C]7.83[/C][C]7.79493925727488[/C][C]0.0350607427251246[/C][/ROW]
[ROW][C]24[/C][C]7.83[/C][C]7.84976931622092[/C][C]-0.019769316220918[/C][/ROW]
[ROW][C]25[/C][C]7.88[/C][C]7.84140725363777[/C][C]0.0385927463622302[/C][/ROW]
[ROW][C]26[/C][C]7.95[/C][C]7.90773128612985[/C][C]0.0422687138701461[/C][/ROW]
[ROW][C]27[/C][C]8.01[/C][C]7.99561018627701[/C][C]0.0143898137229881[/C][/ROW]
[ROW][C]28[/C][C]8.05[/C][C]8.06169681676877[/C][C]-0.0116968167687705[/C][/ROW]
[ROW][C]29[/C][C]8.1[/C][C]8.09674927519722[/C][C]0.00325072480277555[/C][/ROW]
[ROW][C]30[/C][C]8.1[/C][C]8.14812427289252[/C][C]-0.0481242728925224[/C][/ROW]
[ROW][C]31[/C][C]8.16[/C][C]8.12776857736927[/C][C]0.0322314226307263[/C][/ROW]
[ROW][C]32[/C][C]8.18[/C][C]8.2014018851767[/C][C]-0.0214018851766973[/C][/ROW]
[ROW][C]33[/C][C]8.2[/C][C]8.21234927550396[/C][C]-0.0123492755039596[/C][/ROW]
[ROW][C]34[/C][C]7.99[/C][C]8.2271257557086[/C][C]-0.2371257557086[/C][/ROW]
[ROW][C]35[/C][C]8.01[/C][C]7.91682585726226[/C][C]0.0931741427377437[/C][/ROW]
[ROW][C]36[/C][C]8.02[/C][C]7.97623683152144[/C][C]0.0437631684785611[/C][/ROW]
[ROW][C]37[/C][C]8.03[/C][C]8.00474785889159[/C][C]0.0252521411084086[/C][/ROW]
[ROW][C]38[/C][C]8.04[/C][C]8.02542905706493[/C][C]0.0145709429350696[/C][/ROW]
[ROW][C]39[/C][C]8.07[/C][C]8.04159230193172[/C][C]0.0284076980682801[/C][/ROW]
[ROW][C]40[/C][C]8.08[/C][C]8.08360824352705[/C][C]-0.0036082435270508[/C][/ROW]
[ROW][C]41[/C][C]8.08[/C][C]8.09208202188887[/C][C]-0.0120820218888671[/C][/ROW]
[ROW][C]42[/C][C]8.1[/C][C]8.08697154553062[/C][C]0.0130284544693779[/C][/ROW]
[ROW][C]43[/C][C]8.11[/C][C]8.11248234572306[/C][C]-0.00248234572306139[/C][/ROW]
[ROW][C]44[/C][C]8.15[/C][C]8.12143235845707[/C][C]0.0285676415429279[/C][/ROW]
[ROW][C]45[/C][C]8.16[/C][C]8.17351595324434[/C][C]-0.0135159532443403[/C][/ROW]
[ROW][C]46[/C][C]8.17[/C][C]8.17779894990254[/C][C]-0.00779894990254171[/C][/ROW]
[ROW][C]47[/C][C]8.18[/C][C]8.18450013539428[/C][C]-0.0045001353942844[/C][/ROW]
[ROW][C]48[/C][C]8.15[/C][C]8.19259665965546[/C][C]-0.0425966596554588[/C][/ROW]
[ROW][C]49[/C][C]8.15[/C][C]8.1445790443828[/C][C]0.00542095561719869[/C][/ROW]
[ROW][C]50[/C][C]8.17[/C][C]8.1468720103926[/C][C]0.023127989607401[/C][/ROW]
[ROW][C]51[/C][C]8.16[/C][C]8.17665473096615[/C][C]-0.0166547309661542[/C][/ROW]
[ROW][C]52[/C][C]8.15[/C][C]8.15961008151606[/C][C]-0.00961008151605647[/C][/ROW]
[ROW][C]53[/C][C]8.16[/C][C]8.14554519114917[/C][C]0.0144548088508341[/C][/ROW]
[ROW][C]54[/C][C]8.15[/C][C]8.16165931340243[/C][C]-0.0116593134024292[/C][/ROW]
[ROW][C]55[/C][C]8.18[/C][C]8.14672763507536[/C][C]0.0332723649246383[/C][/ROW]
[ROW][C]56[/C][C]8.19[/C][C]8.19080124261343[/C][C]-0.00080124261343073[/C][/ROW]
[ROW][C]57[/C][C]8.18[/C][C]8.20046233150477[/C][C]-0.0204623315047741[/C][/ROW]
[ROW][C]58[/C][C]8.2[/C][C]8.18180713601253[/C][C]0.0181928639874691[/C][/ROW]
[ROW][C]59[/C][C]8.21[/C][C]8.20950238786292[/C][C]0.000497612137083436[/C][/ROW]
[ROW][C]60[/C][C]8.22[/C][C]8.21971286878122[/C][C]0.000287131218776437[/C][/ROW]
[ROW][C]61[/C][C]8.23[/C][C]8.22983432008455[/C][C]0.000165679915445693[/C][/ROW]
[ROW][C]62[/C][C]8.25[/C][C]8.23990439968702[/C][C]0.0100956003129831[/C][/ROW]
[ROW][C]63[/C][C]8.28[/C][C]8.26417465570843[/C][C]0.015825344291569[/C][/ROW]
[ROW][C]64[/C][C]8.28[/C][C]8.30086848962191[/C][C]-0.0208684896219147[/C][/ROW]
[ROW][C]65[/C][C]8.29[/C][C]8.29204149660485[/C][C]-0.00204149660484809[/C][/ROW]
[ROW][C]66[/C][C]8.3[/C][C]8.30117798052861[/C][C]-0.00117798052860607[/C][/ROW]
[ROW][C]67[/C][C]8.34[/C][C]8.31067971610753[/C][C]0.0293202838924707[/C][/ROW]
[ROW][C]68[/C][C]8.38[/C][C]8.36308166497236[/C][C]0.0169183350276398[/C][/ROW]
[ROW][C]69[/C][C]8.39[/C][C]8.41023781416452[/C][C]-0.020237814164517[/C][/ROW]
[ROW][C]70[/C][C]8.44[/C][C]8.41167758543942[/C][C]0.0283224145605789[/C][/ROW]
[ROW][C]71[/C][C]8.46[/C][C]8.47365745365615[/C][C]-0.0136574536561476[/C][/ROW]
[ROW][C]72[/C][C]8.46[/C][C]8.48788059820384[/C][C]-0.0278805982038435[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204976&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204976&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
37.547.40.14
47.567.469217463495380.0907825365046202
57.577.527616831648810.0423831683511899
67.567.555544143967780.00445585603222387
77.577.54742889033870.0225711096613042
87.617.566976060784540.0430239392154572
97.617.62517440756968-0.0151744075696767
107.67.61875590809595-0.0187559080959536
117.617.600822498788850.00917750121115368
127.617.61470441552421-0.00470441552420642
137.627.612714532991550.00728546700844923
147.77.625796153538830.0742038464611667
157.737.73718303617477-0.00718303617476845
167.757.7641447420143-0.0141447420143024
177.767.77816177241513-0.0181617724151346
187.767.78047967173653-0.0204796717365294
197.777.77181714164042-0.00181714164042024
207.797.781048523649290.00895147635070526
217.797.80483483596378-0.0148348359637787
227.797.79855996912703-0.00855996912702839
237.837.794939257274880.0350607427251246
247.837.84976931622092-0.019769316220918
257.887.841407253637770.0385927463622302
267.957.907731286129850.0422687138701461
278.017.995610186277010.0143898137229881
288.058.06169681676877-0.0116968167687705
298.18.096749275197220.00325072480277555
308.18.14812427289252-0.0481242728925224
318.168.127768577369270.0322314226307263
328.188.2014018851767-0.0214018851766973
338.28.21234927550396-0.0123492755039596
347.998.2271257557086-0.2371257557086
358.017.916825857262260.0931741427377437
368.027.976236831521440.0437631684785611
378.038.004747858891590.0252521411084086
388.048.025429057064930.0145709429350696
398.078.041592301931720.0284076980682801
408.088.08360824352705-0.0036082435270508
418.088.09208202188887-0.0120820218888671
428.18.086971545530620.0130284544693779
438.118.11248234572306-0.00248234572306139
448.158.121432358457070.0285676415429279
458.168.17351595324434-0.0135159532443403
468.178.17779894990254-0.00779894990254171
478.188.18450013539428-0.0045001353942844
488.158.19259665965546-0.0425966596554588
498.158.14457904438280.00542095561719869
508.178.14687201039260.023127989607401
518.168.17665473096615-0.0166547309661542
528.158.15961008151606-0.00961008151605647
538.168.145545191149170.0144548088508341
548.158.16165931340243-0.0116593134024292
558.188.146727635075360.0332723649246383
568.198.19080124261343-0.00080124261343073
578.188.20046233150477-0.0204623315047741
588.28.181807136012530.0181928639874691
598.218.209502387862920.000497612137083436
608.228.219712868781220.000287131218776437
618.238.229834320084550.000165679915445693
628.258.239904399687020.0100956003129831
638.288.264174655708430.015825344291569
648.288.30086848962191-0.0208684896219147
658.298.29204149660485-0.00204149660484809
668.38.30117798052861-0.00117798052860607
678.348.310679716107530.0293202838924707
688.388.363081664972360.0169183350276398
698.398.41023781416452-0.020237814164517
708.448.411677585439420.0283224145605789
718.468.47365745365615-0.0136574536561476
728.468.48788059820384-0.0278805982038435







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
738.476087610301248.392293615567468.55988160503501
748.492175220602478.346439240385178.63791120081976
758.50826283090378.295742036492468.72078362531494
768.524350441204938.239197445668958.80950343674092
778.540438051506178.176854683795818.90402141921653
788.55652566180748.108955050370059.00409627324475
798.572613272108638.035766503811249.10946004040603
808.588700882409877.957542956506759.21985880831298
818.60478849271117.874514888130539.33506209729168
828.620876103012337.786888966475119.45486323954955
838.636963713313577.694850234243519.57907719238363
848.65305132361487.598564818683259.70753782854635

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 8.47608761030124 & 8.39229361556746 & 8.55988160503501 \tabularnewline
74 & 8.49217522060247 & 8.34643924038517 & 8.63791120081976 \tabularnewline
75 & 8.5082628309037 & 8.29574203649246 & 8.72078362531494 \tabularnewline
76 & 8.52435044120493 & 8.23919744566895 & 8.80950343674092 \tabularnewline
77 & 8.54043805150617 & 8.17685468379581 & 8.90402141921653 \tabularnewline
78 & 8.5565256618074 & 8.10895505037005 & 9.00409627324475 \tabularnewline
79 & 8.57261327210863 & 8.03576650381124 & 9.10946004040603 \tabularnewline
80 & 8.58870088240987 & 7.95754295650675 & 9.21985880831298 \tabularnewline
81 & 8.6047884927111 & 7.87451488813053 & 9.33506209729168 \tabularnewline
82 & 8.62087610301233 & 7.78688896647511 & 9.45486323954955 \tabularnewline
83 & 8.63696371331357 & 7.69485023424351 & 9.57907719238363 \tabularnewline
84 & 8.6530513236148 & 7.59856481868325 & 9.70753782854635 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204976&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]8.47608761030124[/C][C]8.39229361556746[/C][C]8.55988160503501[/C][/ROW]
[ROW][C]74[/C][C]8.49217522060247[/C][C]8.34643924038517[/C][C]8.63791120081976[/C][/ROW]
[ROW][C]75[/C][C]8.5082628309037[/C][C]8.29574203649246[/C][C]8.72078362531494[/C][/ROW]
[ROW][C]76[/C][C]8.52435044120493[/C][C]8.23919744566895[/C][C]8.80950343674092[/C][/ROW]
[ROW][C]77[/C][C]8.54043805150617[/C][C]8.17685468379581[/C][C]8.90402141921653[/C][/ROW]
[ROW][C]78[/C][C]8.5565256618074[/C][C]8.10895505037005[/C][C]9.00409627324475[/C][/ROW]
[ROW][C]79[/C][C]8.57261327210863[/C][C]8.03576650381124[/C][C]9.10946004040603[/C][/ROW]
[ROW][C]80[/C][C]8.58870088240987[/C][C]7.95754295650675[/C][C]9.21985880831298[/C][/ROW]
[ROW][C]81[/C][C]8.6047884927111[/C][C]7.87451488813053[/C][C]9.33506209729168[/C][/ROW]
[ROW][C]82[/C][C]8.62087610301233[/C][C]7.78688896647511[/C][C]9.45486323954955[/C][/ROW]
[ROW][C]83[/C][C]8.63696371331357[/C][C]7.69485023424351[/C][C]9.57907719238363[/C][/ROW]
[ROW][C]84[/C][C]8.6530513236148[/C][C]7.59856481868325[/C][C]9.70753782854635[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204976&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204976&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
738.476087610301248.392293615567468.55988160503501
748.492175220602478.346439240385178.63791120081976
758.50826283090378.295742036492468.72078362531494
768.524350441204938.239197445668958.80950343674092
778.540438051506178.176854683795818.90402141921653
788.55652566180748.108955050370059.00409627324475
798.572613272108638.035766503811249.10946004040603
808.588700882409877.957542956506759.21985880831298
818.60478849271117.874514888130539.33506209729168
828.620876103012337.786888966475119.45486323954955
838.636963713313577.694850234243519.57907719238363
848.65305132361487.598564818683259.70753782854635



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')