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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 16 Nov 2013 05:20:51 -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/Nov/16/t13845972659hp2dftfwu81z97.htm/, Retrieved Sun, 05 May 2024 22:13:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=225548, Retrieved Sun, 05 May 2024 22:13:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact110
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [ws8] [2013-11-16 10:20:51] [16986792796a040c0e2998a7aab14aa2] [Current]
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Dataseries X:
0.7869
0.7439
0.7492
0.7804
0.7678
0.7573
0.7337
0.7136
0.7107
0.7015
0.6874
0.6754
0.6713
0.6849
0.7003
0.7309
0.7364
0.7439
0.7928
0.8188
0.784
0.7746
0.7677
0.7197
0.7304
0.7567
0.749
0.7328
0.7142
0.6927
0.6974
0.6953
0.699
0.6971
0.7246
0.7301
0.736
0.7585
0.7756
0.7564
0.7568
0.7593
0.779
0.7978
0.8125
0.8075
0.7781
0.771
0.7796
0.763
0.7531
0.7473
0.7707
0.7684
0.7702
0.759
0.7649
0.7508
0.7494
0.7334




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

\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
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=225548&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]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=225548&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=225548&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







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.335904170899142
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.335904170899142 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=225548&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]0.335904170899142[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=225548&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=225548&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
beta0.335904170899142
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
30.74920.70090.0483
40.78040.7224241714544280.0579758285455715
50.76780.773098494074219-0.00529849407421945
60.75730.758718707815205-0.00141870781520481
70.73370.74774215794279-0.0140421579427902
80.71360.719425338521383-0.00582533852138256
90.71070.6973685830151510.0133314169848493
100.70150.6989466615843570.00255333841564276
110.68740.690604338607889-0.0032043386078886
120.67540.675427987904526-2.79879045257392e-05
130.67130.6634185866506610.00788141334933923
140.68490.6619659862672840.022934013732716
150.70030.6832696171355610.0170303828644386
160.73090.7043901937717360.0265098062282643
170.73640.743894948253538-0.00749494825353758
180.74390.746877363874501-0.0029773638745012
190.79280.7533772549307720.0394227450692282
200.81880.8155195194278190.00328048057218089
210.7840.842621446534568-0.0586214465345682
220.77460.788130258139466-0.0135302581394658
230.76770.774185387997077-0.0064853879970771
240.71970.76510691911896-0.0454069191189598
250.73040.7018545455992210.0285454544007788
260.75670.7221430827926540.034556917207346
270.7490.760050895416018-0.0110508954160179
280.73280.748638853553607-0.0158388535536073
290.71420.72711851658269-0.0129185165826899
300.69270.704179132980735-0.0114791329807346
310.69740.67882324433420.0185767556658001
320.69530.6897632540441170.00553674595588349
330.6990.6895230701039070.00947692989609317
340.69710.6964064103833230.000693589616676871
350.72460.6947393900284570.0298606099715427
360.73010.732269693463491-0.00216969346349105
370.7360.737040884379532-0.00104088437953176
380.75850.7425912469750230.0159087530249767
390.77560.7704350634699170.00516493653008276
400.75640.789269987192801-0.0328699871928014
410.75680.759028821397338-0.00222882139733793
420.75930.7586801509937830.000619849006217033
430.7790.7613883608602990.0176116391397011
440.79780.7870041839036950.0107958160963049
450.81250.8094305435587040.00306945644129608
460.80750.825161586779729-0.0176615867797286
470.77810.814228986115721-0.0361289861157206
480.7710.772693108989093-0.00169310898909292
490.77960.765024386617870.0145756133821302
500.7630.778520395946341-0.0155203959463406
510.75310.756707030213959-0.0036070302139587
520.74730.7455954137205310.00170458627946923
530.77070.7403679913614620.0303320086385381
540.76840.773956639574896-0.00555663957489572
550.77020.7697901411655050.000409858834495069
560.7590.771727814457492-0.0127278144574917
570.76490.756252488494790.00864751150521015
580.75080.765057223677288-0.0142572236772882
590.74940.7461681627786450.00323183722135478
600.73340.745853750380965-0.0124537503809652

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 0.7492 & 0.7009 & 0.0483 \tabularnewline
4 & 0.7804 & 0.722424171454428 & 0.0579758285455715 \tabularnewline
5 & 0.7678 & 0.773098494074219 & -0.00529849407421945 \tabularnewline
6 & 0.7573 & 0.758718707815205 & -0.00141870781520481 \tabularnewline
7 & 0.7337 & 0.74774215794279 & -0.0140421579427902 \tabularnewline
8 & 0.7136 & 0.719425338521383 & -0.00582533852138256 \tabularnewline
9 & 0.7107 & 0.697368583015151 & 0.0133314169848493 \tabularnewline
10 & 0.7015 & 0.698946661584357 & 0.00255333841564276 \tabularnewline
11 & 0.6874 & 0.690604338607889 & -0.0032043386078886 \tabularnewline
12 & 0.6754 & 0.675427987904526 & -2.79879045257392e-05 \tabularnewline
13 & 0.6713 & 0.663418586650661 & 0.00788141334933923 \tabularnewline
14 & 0.6849 & 0.661965986267284 & 0.022934013732716 \tabularnewline
15 & 0.7003 & 0.683269617135561 & 0.0170303828644386 \tabularnewline
16 & 0.7309 & 0.704390193771736 & 0.0265098062282643 \tabularnewline
17 & 0.7364 & 0.743894948253538 & -0.00749494825353758 \tabularnewline
18 & 0.7439 & 0.746877363874501 & -0.0029773638745012 \tabularnewline
19 & 0.7928 & 0.753377254930772 & 0.0394227450692282 \tabularnewline
20 & 0.8188 & 0.815519519427819 & 0.00328048057218089 \tabularnewline
21 & 0.784 & 0.842621446534568 & -0.0586214465345682 \tabularnewline
22 & 0.7746 & 0.788130258139466 & -0.0135302581394658 \tabularnewline
23 & 0.7677 & 0.774185387997077 & -0.0064853879970771 \tabularnewline
24 & 0.7197 & 0.76510691911896 & -0.0454069191189598 \tabularnewline
25 & 0.7304 & 0.701854545599221 & 0.0285454544007788 \tabularnewline
26 & 0.7567 & 0.722143082792654 & 0.034556917207346 \tabularnewline
27 & 0.749 & 0.760050895416018 & -0.0110508954160179 \tabularnewline
28 & 0.7328 & 0.748638853553607 & -0.0158388535536073 \tabularnewline
29 & 0.7142 & 0.72711851658269 & -0.0129185165826899 \tabularnewline
30 & 0.6927 & 0.704179132980735 & -0.0114791329807346 \tabularnewline
31 & 0.6974 & 0.6788232443342 & 0.0185767556658001 \tabularnewline
32 & 0.6953 & 0.689763254044117 & 0.00553674595588349 \tabularnewline
33 & 0.699 & 0.689523070103907 & 0.00947692989609317 \tabularnewline
34 & 0.6971 & 0.696406410383323 & 0.000693589616676871 \tabularnewline
35 & 0.7246 & 0.694739390028457 & 0.0298606099715427 \tabularnewline
36 & 0.7301 & 0.732269693463491 & -0.00216969346349105 \tabularnewline
37 & 0.736 & 0.737040884379532 & -0.00104088437953176 \tabularnewline
38 & 0.7585 & 0.742591246975023 & 0.0159087530249767 \tabularnewline
39 & 0.7756 & 0.770435063469917 & 0.00516493653008276 \tabularnewline
40 & 0.7564 & 0.789269987192801 & -0.0328699871928014 \tabularnewline
41 & 0.7568 & 0.759028821397338 & -0.00222882139733793 \tabularnewline
42 & 0.7593 & 0.758680150993783 & 0.000619849006217033 \tabularnewline
43 & 0.779 & 0.761388360860299 & 0.0176116391397011 \tabularnewline
44 & 0.7978 & 0.787004183903695 & 0.0107958160963049 \tabularnewline
45 & 0.8125 & 0.809430543558704 & 0.00306945644129608 \tabularnewline
46 & 0.8075 & 0.825161586779729 & -0.0176615867797286 \tabularnewline
47 & 0.7781 & 0.814228986115721 & -0.0361289861157206 \tabularnewline
48 & 0.771 & 0.772693108989093 & -0.00169310898909292 \tabularnewline
49 & 0.7796 & 0.76502438661787 & 0.0145756133821302 \tabularnewline
50 & 0.763 & 0.778520395946341 & -0.0155203959463406 \tabularnewline
51 & 0.7531 & 0.756707030213959 & -0.0036070302139587 \tabularnewline
52 & 0.7473 & 0.745595413720531 & 0.00170458627946923 \tabularnewline
53 & 0.7707 & 0.740367991361462 & 0.0303320086385381 \tabularnewline
54 & 0.7684 & 0.773956639574896 & -0.00555663957489572 \tabularnewline
55 & 0.7702 & 0.769790141165505 & 0.000409858834495069 \tabularnewline
56 & 0.759 & 0.771727814457492 & -0.0127278144574917 \tabularnewline
57 & 0.7649 & 0.75625248849479 & 0.00864751150521015 \tabularnewline
58 & 0.7508 & 0.765057223677288 & -0.0142572236772882 \tabularnewline
59 & 0.7494 & 0.746168162778645 & 0.00323183722135478 \tabularnewline
60 & 0.7334 & 0.745853750380965 & -0.0124537503809652 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=225548&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]0.7492[/C][C]0.7009[/C][C]0.0483[/C][/ROW]
[ROW][C]4[/C][C]0.7804[/C][C]0.722424171454428[/C][C]0.0579758285455715[/C][/ROW]
[ROW][C]5[/C][C]0.7678[/C][C]0.773098494074219[/C][C]-0.00529849407421945[/C][/ROW]
[ROW][C]6[/C][C]0.7573[/C][C]0.758718707815205[/C][C]-0.00141870781520481[/C][/ROW]
[ROW][C]7[/C][C]0.7337[/C][C]0.74774215794279[/C][C]-0.0140421579427902[/C][/ROW]
[ROW][C]8[/C][C]0.7136[/C][C]0.719425338521383[/C][C]-0.00582533852138256[/C][/ROW]
[ROW][C]9[/C][C]0.7107[/C][C]0.697368583015151[/C][C]0.0133314169848493[/C][/ROW]
[ROW][C]10[/C][C]0.7015[/C][C]0.698946661584357[/C][C]0.00255333841564276[/C][/ROW]
[ROW][C]11[/C][C]0.6874[/C][C]0.690604338607889[/C][C]-0.0032043386078886[/C][/ROW]
[ROW][C]12[/C][C]0.6754[/C][C]0.675427987904526[/C][C]-2.79879045257392e-05[/C][/ROW]
[ROW][C]13[/C][C]0.6713[/C][C]0.663418586650661[/C][C]0.00788141334933923[/C][/ROW]
[ROW][C]14[/C][C]0.6849[/C][C]0.661965986267284[/C][C]0.022934013732716[/C][/ROW]
[ROW][C]15[/C][C]0.7003[/C][C]0.683269617135561[/C][C]0.0170303828644386[/C][/ROW]
[ROW][C]16[/C][C]0.7309[/C][C]0.704390193771736[/C][C]0.0265098062282643[/C][/ROW]
[ROW][C]17[/C][C]0.7364[/C][C]0.743894948253538[/C][C]-0.00749494825353758[/C][/ROW]
[ROW][C]18[/C][C]0.7439[/C][C]0.746877363874501[/C][C]-0.0029773638745012[/C][/ROW]
[ROW][C]19[/C][C]0.7928[/C][C]0.753377254930772[/C][C]0.0394227450692282[/C][/ROW]
[ROW][C]20[/C][C]0.8188[/C][C]0.815519519427819[/C][C]0.00328048057218089[/C][/ROW]
[ROW][C]21[/C][C]0.784[/C][C]0.842621446534568[/C][C]-0.0586214465345682[/C][/ROW]
[ROW][C]22[/C][C]0.7746[/C][C]0.788130258139466[/C][C]-0.0135302581394658[/C][/ROW]
[ROW][C]23[/C][C]0.7677[/C][C]0.774185387997077[/C][C]-0.0064853879970771[/C][/ROW]
[ROW][C]24[/C][C]0.7197[/C][C]0.76510691911896[/C][C]-0.0454069191189598[/C][/ROW]
[ROW][C]25[/C][C]0.7304[/C][C]0.701854545599221[/C][C]0.0285454544007788[/C][/ROW]
[ROW][C]26[/C][C]0.7567[/C][C]0.722143082792654[/C][C]0.034556917207346[/C][/ROW]
[ROW][C]27[/C][C]0.749[/C][C]0.760050895416018[/C][C]-0.0110508954160179[/C][/ROW]
[ROW][C]28[/C][C]0.7328[/C][C]0.748638853553607[/C][C]-0.0158388535536073[/C][/ROW]
[ROW][C]29[/C][C]0.7142[/C][C]0.72711851658269[/C][C]-0.0129185165826899[/C][/ROW]
[ROW][C]30[/C][C]0.6927[/C][C]0.704179132980735[/C][C]-0.0114791329807346[/C][/ROW]
[ROW][C]31[/C][C]0.6974[/C][C]0.6788232443342[/C][C]0.0185767556658001[/C][/ROW]
[ROW][C]32[/C][C]0.6953[/C][C]0.689763254044117[/C][C]0.00553674595588349[/C][/ROW]
[ROW][C]33[/C][C]0.699[/C][C]0.689523070103907[/C][C]0.00947692989609317[/C][/ROW]
[ROW][C]34[/C][C]0.6971[/C][C]0.696406410383323[/C][C]0.000693589616676871[/C][/ROW]
[ROW][C]35[/C][C]0.7246[/C][C]0.694739390028457[/C][C]0.0298606099715427[/C][/ROW]
[ROW][C]36[/C][C]0.7301[/C][C]0.732269693463491[/C][C]-0.00216969346349105[/C][/ROW]
[ROW][C]37[/C][C]0.736[/C][C]0.737040884379532[/C][C]-0.00104088437953176[/C][/ROW]
[ROW][C]38[/C][C]0.7585[/C][C]0.742591246975023[/C][C]0.0159087530249767[/C][/ROW]
[ROW][C]39[/C][C]0.7756[/C][C]0.770435063469917[/C][C]0.00516493653008276[/C][/ROW]
[ROW][C]40[/C][C]0.7564[/C][C]0.789269987192801[/C][C]-0.0328699871928014[/C][/ROW]
[ROW][C]41[/C][C]0.7568[/C][C]0.759028821397338[/C][C]-0.00222882139733793[/C][/ROW]
[ROW][C]42[/C][C]0.7593[/C][C]0.758680150993783[/C][C]0.000619849006217033[/C][/ROW]
[ROW][C]43[/C][C]0.779[/C][C]0.761388360860299[/C][C]0.0176116391397011[/C][/ROW]
[ROW][C]44[/C][C]0.7978[/C][C]0.787004183903695[/C][C]0.0107958160963049[/C][/ROW]
[ROW][C]45[/C][C]0.8125[/C][C]0.809430543558704[/C][C]0.00306945644129608[/C][/ROW]
[ROW][C]46[/C][C]0.8075[/C][C]0.825161586779729[/C][C]-0.0176615867797286[/C][/ROW]
[ROW][C]47[/C][C]0.7781[/C][C]0.814228986115721[/C][C]-0.0361289861157206[/C][/ROW]
[ROW][C]48[/C][C]0.771[/C][C]0.772693108989093[/C][C]-0.00169310898909292[/C][/ROW]
[ROW][C]49[/C][C]0.7796[/C][C]0.76502438661787[/C][C]0.0145756133821302[/C][/ROW]
[ROW][C]50[/C][C]0.763[/C][C]0.778520395946341[/C][C]-0.0155203959463406[/C][/ROW]
[ROW][C]51[/C][C]0.7531[/C][C]0.756707030213959[/C][C]-0.0036070302139587[/C][/ROW]
[ROW][C]52[/C][C]0.7473[/C][C]0.745595413720531[/C][C]0.00170458627946923[/C][/ROW]
[ROW][C]53[/C][C]0.7707[/C][C]0.740367991361462[/C][C]0.0303320086385381[/C][/ROW]
[ROW][C]54[/C][C]0.7684[/C][C]0.773956639574896[/C][C]-0.00555663957489572[/C][/ROW]
[ROW][C]55[/C][C]0.7702[/C][C]0.769790141165505[/C][C]0.000409858834495069[/C][/ROW]
[ROW][C]56[/C][C]0.759[/C][C]0.771727814457492[/C][C]-0.0127278144574917[/C][/ROW]
[ROW][C]57[/C][C]0.7649[/C][C]0.75625248849479[/C][C]0.00864751150521015[/C][/ROW]
[ROW][C]58[/C][C]0.7508[/C][C]0.765057223677288[/C][C]-0.0142572236772882[/C][/ROW]
[ROW][C]59[/C][C]0.7494[/C][C]0.746168162778645[/C][C]0.00323183722135478[/C][/ROW]
[ROW][C]60[/C][C]0.7334[/C][C]0.745853750380965[/C][C]-0.0124537503809652[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=225548&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=225548&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
30.74920.70090.0483
40.78040.7224241714544280.0579758285455715
50.76780.773098494074219-0.00529849407421945
60.75730.758718707815205-0.00141870781520481
70.73370.74774215794279-0.0140421579427902
80.71360.719425338521383-0.00582533852138256
90.71070.6973685830151510.0133314169848493
100.70150.6989466615843570.00255333841564276
110.68740.690604338607889-0.0032043386078886
120.67540.675427987904526-2.79879045257392e-05
130.67130.6634185866506610.00788141334933923
140.68490.6619659862672840.022934013732716
150.70030.6832696171355610.0170303828644386
160.73090.7043901937717360.0265098062282643
170.73640.743894948253538-0.00749494825353758
180.74390.746877363874501-0.0029773638745012
190.79280.7533772549307720.0394227450692282
200.81880.8155195194278190.00328048057218089
210.7840.842621446534568-0.0586214465345682
220.77460.788130258139466-0.0135302581394658
230.76770.774185387997077-0.0064853879970771
240.71970.76510691911896-0.0454069191189598
250.73040.7018545455992210.0285454544007788
260.75670.7221430827926540.034556917207346
270.7490.760050895416018-0.0110508954160179
280.73280.748638853553607-0.0158388535536073
290.71420.72711851658269-0.0129185165826899
300.69270.704179132980735-0.0114791329807346
310.69740.67882324433420.0185767556658001
320.69530.6897632540441170.00553674595588349
330.6990.6895230701039070.00947692989609317
340.69710.6964064103833230.000693589616676871
350.72460.6947393900284570.0298606099715427
360.73010.732269693463491-0.00216969346349105
370.7360.737040884379532-0.00104088437953176
380.75850.7425912469750230.0159087530249767
390.77560.7704350634699170.00516493653008276
400.75640.789269987192801-0.0328699871928014
410.75680.759028821397338-0.00222882139733793
420.75930.7586801509937830.000619849006217033
430.7790.7613883608602990.0176116391397011
440.79780.7870041839036950.0107958160963049
450.81250.8094305435587040.00306945644129608
460.80750.825161586779729-0.0176615867797286
470.77810.814228986115721-0.0361289861157206
480.7710.772693108989093-0.00169310898909292
490.77960.765024386617870.0145756133821302
500.7630.778520395946341-0.0155203959463406
510.75310.756707030213959-0.0036070302139587
520.74730.7455954137205310.00170458627946923
530.77070.7403679913614620.0303320086385381
540.76840.773956639574896-0.00555663957489572
550.77020.7697901411655050.000409858834495069
560.7590.771727814457492-0.0127278144574917
570.76490.756252488494790.00864751150521015
580.75080.765057223677288-0.0142572236772882
590.74940.7461681627786450.00323183722135478
600.73340.745853750380965-0.0124537503809652







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
610.7256704836846620.6851308980083870.766210069360938
620.7179409673693250.650291585789140.785590348949509
630.7102114510539870.614452323569730.805970578538244
640.7024819347386490.5768059981226340.828157871354664
650.6947524184233120.5372049700025420.852299866844081
660.6870229021079740.4956568891701810.878388915045767
670.6792933857926360.4522150594641110.906371712121161
680.6715638694772990.4069454410228930.936182297931704
690.6638343531619610.3599151893886520.96775351693527
700.6561048368466230.3111885127714321.00102116092181
710.6483753205312860.2608253002439451.03592534081863
720.6406458042159480.2088808577756311.07241075065627

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 0.725670483684662 & 0.685130898008387 & 0.766210069360938 \tabularnewline
62 & 0.717940967369325 & 0.65029158578914 & 0.785590348949509 \tabularnewline
63 & 0.710211451053987 & 0.61445232356973 & 0.805970578538244 \tabularnewline
64 & 0.702481934738649 & 0.576805998122634 & 0.828157871354664 \tabularnewline
65 & 0.694752418423312 & 0.537204970002542 & 0.852299866844081 \tabularnewline
66 & 0.687022902107974 & 0.495656889170181 & 0.878388915045767 \tabularnewline
67 & 0.679293385792636 & 0.452215059464111 & 0.906371712121161 \tabularnewline
68 & 0.671563869477299 & 0.406945441022893 & 0.936182297931704 \tabularnewline
69 & 0.663834353161961 & 0.359915189388652 & 0.96775351693527 \tabularnewline
70 & 0.656104836846623 & 0.311188512771432 & 1.00102116092181 \tabularnewline
71 & 0.648375320531286 & 0.260825300243945 & 1.03592534081863 \tabularnewline
72 & 0.640645804215948 & 0.208880857775631 & 1.07241075065627 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=225548&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]61[/C][C]0.725670483684662[/C][C]0.685130898008387[/C][C]0.766210069360938[/C][/ROW]
[ROW][C]62[/C][C]0.717940967369325[/C][C]0.65029158578914[/C][C]0.785590348949509[/C][/ROW]
[ROW][C]63[/C][C]0.710211451053987[/C][C]0.61445232356973[/C][C]0.805970578538244[/C][/ROW]
[ROW][C]64[/C][C]0.702481934738649[/C][C]0.576805998122634[/C][C]0.828157871354664[/C][/ROW]
[ROW][C]65[/C][C]0.694752418423312[/C][C]0.537204970002542[/C][C]0.852299866844081[/C][/ROW]
[ROW][C]66[/C][C]0.687022902107974[/C][C]0.495656889170181[/C][C]0.878388915045767[/C][/ROW]
[ROW][C]67[/C][C]0.679293385792636[/C][C]0.452215059464111[/C][C]0.906371712121161[/C][/ROW]
[ROW][C]68[/C][C]0.671563869477299[/C][C]0.406945441022893[/C][C]0.936182297931704[/C][/ROW]
[ROW][C]69[/C][C]0.663834353161961[/C][C]0.359915189388652[/C][C]0.96775351693527[/C][/ROW]
[ROW][C]70[/C][C]0.656104836846623[/C][C]0.311188512771432[/C][C]1.00102116092181[/C][/ROW]
[ROW][C]71[/C][C]0.648375320531286[/C][C]0.260825300243945[/C][C]1.03592534081863[/C][/ROW]
[ROW][C]72[/C][C]0.640645804215948[/C][C]0.208880857775631[/C][C]1.07241075065627[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=225548&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=225548&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
610.7256704836846620.6851308980083870.766210069360938
620.7179409673693250.650291585789140.785590348949509
630.7102114510539870.614452323569730.805970578538244
640.7024819347386490.5768059981226340.828157871354664
650.6947524184233120.5372049700025420.852299866844081
660.6870229021079740.4956568891701810.878388915045767
670.6792933857926360.4522150594641110.906371712121161
680.6715638694772990.4069454410228930.936182297931704
690.6638343531619610.3599151893886520.96775351693527
700.6561048368466230.3111885127714321.00102116092181
710.6483753205312860.2608253002439451.03592534081863
720.6406458042159480.2088808577756311.07241075065627



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')