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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 02 Jun 2010 11:54:57 +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/2010/Jun/02/t1275479910076ssvw7qlm8sym.htm/, Retrieved Thu, 25 Apr 2024 21:58:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=77273, Retrieved Thu, 25 Apr 2024 21:58:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact132
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2010-06-02 11:54:57] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
2.17
2.18
2.18
2.18
2.17
2.17
2.18
2.17
2.18
2.17
2.17
2.17
2.17
2.17
2.17
2.17
2.17
2.17
2.18
2.18
2.18
2.18
2.18
2.18
2.18
2.18
2.18
2.18
2.18
2.18
2.18
2.19
2.19
2.19
2.20
2.20
2.21
2.21
2.21
2.20
2.21
2.20
2.21
2.21
2.22
2.22
2.23
2.24
2.24
2.25
2.25
2.32
2.36
2.37
2.37
2.37
2.38
2.38
2.41
2.42
2.43
2.44
2.44
2.44
2.43
2.43
2.43
2.42
2.42
2.42
2.42
2.42




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77273&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77273&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77273&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.217390091297997
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.217390091297997 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77273&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]0.217390091297997[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77273&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77273&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
beta0.217390091297997
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
32.182.19-0.0100000000000002
42.182.18782609908702-0.00782609908702003
52.172.18612478269199-0.0161247826919859
62.172.17261941471041-0.0026194147104146
72.182.172049979907370.0079500200926299
82.172.18377823550113-0.0137782355011282
92.182.170782983627610.00921701637238792
102.172.1827866716583-0.0127866716583012
112.172.17000697593911-6.97593910548022e-06
122.172.17000545943907-5.45943906615776e-06
132.172.17000427261111-4.27261110935717e-06
142.172.17000334378779-3.34378779021094e-06
152.172.17000261688146-2.61688145730687e-06
162.172.17000204799736-2.04799735836758e-06
172.172.17000160278303-1.60278302541172e-06
182.172.17000125435388-1.2543538772114e-06
192.182.170000981669770.00999901833022676
202.182.18217466917747-0.00217466917747178
212.182.18170191764644-0.00170191764643812
222.182.1813319376139-0.00133193761389716
232.182.18104238757441-0.001042387574409
242.182.18081578284444-0.000815782844440172
252.182.18063843973741-0.00063843973740818
262.182.1804996492646-0.000499649264604773
272.182.18039103046536-0.000391030465355158
282.182.18030602431679-0.000306024316791387
292.182.18023949766262-0.000239497662624544
302.182.18018743324388-0.000187433243881152
312.182.18014668711388-0.000146687113881327
322.192.18011479878880.00988520121119718
332.192.1922637435826-0.00226374358260362
342.192.19177162815851-0.00177162815850629
352.22.191386493751380.00861350624861767
362.22.20325898466117-0.00325898466116525
372.212.202550513688140.00744948631186393
382.212.2141699581976-0.00416995819759514
392.212.21326345060431-0.00326345060431121
402.22.21255400877949-0.0125540087794933
412.212.199824891664760.0101751083352362
422.22.21203685939473-0.0120368593947275
432.212.199420165431970.0105798345680332
442.212.21172011663463-0.00172011663462923
452.222.211346180322380.00865381967761625
462.222.22322743497218-0.00322743497217726
472.232.222525822588920.00747417741108247
482.242.234150634698690.00584936530131008
492.242.24542222875558-0.00542222875557696
502.252.244243489951360.00575651004863609
512.252.25549489819639-0.00549489819639426
522.322.254300361775810.0656996382241926
532.362.338582812127610.0214171878723906
542.372.38323869655453-0.0132386965545348
552.372.39036073510188-0.0203607351018782
562.372.38593451303919-0.0159345130391864
572.382.38247050779481-0.00247050779480906
582.382.39193344387974-0.0119334438797427
592.412.389339231425230.0206607685747744
602.422.42383067779198-0.00383067779198321
612.432.43299792639705-0.00299792639705032
622.442.44234620690389-0.00234620690389109
632.442.45183616477085-0.01183616477085
642.442.4492630998307-0.00926309983069684
652.432.4472493937128-0.0172493937127989
662.432.43349954643874-0.00349954643873884
672.432.43273877971892-0.00273877971891956
682.422.43214339614578-0.0121433961457789
692.422.419503542148980.000496457851019816
702.422.419611467166540.000388532833460964
712.422.419695930354680.000304069645322702
722.422.419762032082630.000237967917365189

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 2.18 & 2.19 & -0.0100000000000002 \tabularnewline
4 & 2.18 & 2.18782609908702 & -0.00782609908702003 \tabularnewline
5 & 2.17 & 2.18612478269199 & -0.0161247826919859 \tabularnewline
6 & 2.17 & 2.17261941471041 & -0.0026194147104146 \tabularnewline
7 & 2.18 & 2.17204997990737 & 0.0079500200926299 \tabularnewline
8 & 2.17 & 2.18377823550113 & -0.0137782355011282 \tabularnewline
9 & 2.18 & 2.17078298362761 & 0.00921701637238792 \tabularnewline
10 & 2.17 & 2.1827866716583 & -0.0127866716583012 \tabularnewline
11 & 2.17 & 2.17000697593911 & -6.97593910548022e-06 \tabularnewline
12 & 2.17 & 2.17000545943907 & -5.45943906615776e-06 \tabularnewline
13 & 2.17 & 2.17000427261111 & -4.27261110935717e-06 \tabularnewline
14 & 2.17 & 2.17000334378779 & -3.34378779021094e-06 \tabularnewline
15 & 2.17 & 2.17000261688146 & -2.61688145730687e-06 \tabularnewline
16 & 2.17 & 2.17000204799736 & -2.04799735836758e-06 \tabularnewline
17 & 2.17 & 2.17000160278303 & -1.60278302541172e-06 \tabularnewline
18 & 2.17 & 2.17000125435388 & -1.2543538772114e-06 \tabularnewline
19 & 2.18 & 2.17000098166977 & 0.00999901833022676 \tabularnewline
20 & 2.18 & 2.18217466917747 & -0.00217466917747178 \tabularnewline
21 & 2.18 & 2.18170191764644 & -0.00170191764643812 \tabularnewline
22 & 2.18 & 2.1813319376139 & -0.00133193761389716 \tabularnewline
23 & 2.18 & 2.18104238757441 & -0.001042387574409 \tabularnewline
24 & 2.18 & 2.18081578284444 & -0.000815782844440172 \tabularnewline
25 & 2.18 & 2.18063843973741 & -0.00063843973740818 \tabularnewline
26 & 2.18 & 2.1804996492646 & -0.000499649264604773 \tabularnewline
27 & 2.18 & 2.18039103046536 & -0.000391030465355158 \tabularnewline
28 & 2.18 & 2.18030602431679 & -0.000306024316791387 \tabularnewline
29 & 2.18 & 2.18023949766262 & -0.000239497662624544 \tabularnewline
30 & 2.18 & 2.18018743324388 & -0.000187433243881152 \tabularnewline
31 & 2.18 & 2.18014668711388 & -0.000146687113881327 \tabularnewline
32 & 2.19 & 2.1801147987888 & 0.00988520121119718 \tabularnewline
33 & 2.19 & 2.1922637435826 & -0.00226374358260362 \tabularnewline
34 & 2.19 & 2.19177162815851 & -0.00177162815850629 \tabularnewline
35 & 2.2 & 2.19138649375138 & 0.00861350624861767 \tabularnewline
36 & 2.2 & 2.20325898466117 & -0.00325898466116525 \tabularnewline
37 & 2.21 & 2.20255051368814 & 0.00744948631186393 \tabularnewline
38 & 2.21 & 2.2141699581976 & -0.00416995819759514 \tabularnewline
39 & 2.21 & 2.21326345060431 & -0.00326345060431121 \tabularnewline
40 & 2.2 & 2.21255400877949 & -0.0125540087794933 \tabularnewline
41 & 2.21 & 2.19982489166476 & 0.0101751083352362 \tabularnewline
42 & 2.2 & 2.21203685939473 & -0.0120368593947275 \tabularnewline
43 & 2.21 & 2.19942016543197 & 0.0105798345680332 \tabularnewline
44 & 2.21 & 2.21172011663463 & -0.00172011663462923 \tabularnewline
45 & 2.22 & 2.21134618032238 & 0.00865381967761625 \tabularnewline
46 & 2.22 & 2.22322743497218 & -0.00322743497217726 \tabularnewline
47 & 2.23 & 2.22252582258892 & 0.00747417741108247 \tabularnewline
48 & 2.24 & 2.23415063469869 & 0.00584936530131008 \tabularnewline
49 & 2.24 & 2.24542222875558 & -0.00542222875557696 \tabularnewline
50 & 2.25 & 2.24424348995136 & 0.00575651004863609 \tabularnewline
51 & 2.25 & 2.25549489819639 & -0.00549489819639426 \tabularnewline
52 & 2.32 & 2.25430036177581 & 0.0656996382241926 \tabularnewline
53 & 2.36 & 2.33858281212761 & 0.0214171878723906 \tabularnewline
54 & 2.37 & 2.38323869655453 & -0.0132386965545348 \tabularnewline
55 & 2.37 & 2.39036073510188 & -0.0203607351018782 \tabularnewline
56 & 2.37 & 2.38593451303919 & -0.0159345130391864 \tabularnewline
57 & 2.38 & 2.38247050779481 & -0.00247050779480906 \tabularnewline
58 & 2.38 & 2.39193344387974 & -0.0119334438797427 \tabularnewline
59 & 2.41 & 2.38933923142523 & 0.0206607685747744 \tabularnewline
60 & 2.42 & 2.42383067779198 & -0.00383067779198321 \tabularnewline
61 & 2.43 & 2.43299792639705 & -0.00299792639705032 \tabularnewline
62 & 2.44 & 2.44234620690389 & -0.00234620690389109 \tabularnewline
63 & 2.44 & 2.45183616477085 & -0.01183616477085 \tabularnewline
64 & 2.44 & 2.4492630998307 & -0.00926309983069684 \tabularnewline
65 & 2.43 & 2.4472493937128 & -0.0172493937127989 \tabularnewline
66 & 2.43 & 2.43349954643874 & -0.00349954643873884 \tabularnewline
67 & 2.43 & 2.43273877971892 & -0.00273877971891956 \tabularnewline
68 & 2.42 & 2.43214339614578 & -0.0121433961457789 \tabularnewline
69 & 2.42 & 2.41950354214898 & 0.000496457851019816 \tabularnewline
70 & 2.42 & 2.41961146716654 & 0.000388532833460964 \tabularnewline
71 & 2.42 & 2.41969593035468 & 0.000304069645322702 \tabularnewline
72 & 2.42 & 2.41976203208263 & 0.000237967917365189 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77273&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]2.18[/C][C]2.19[/C][C]-0.0100000000000002[/C][/ROW]
[ROW][C]4[/C][C]2.18[/C][C]2.18782609908702[/C][C]-0.00782609908702003[/C][/ROW]
[ROW][C]5[/C][C]2.17[/C][C]2.18612478269199[/C][C]-0.0161247826919859[/C][/ROW]
[ROW][C]6[/C][C]2.17[/C][C]2.17261941471041[/C][C]-0.0026194147104146[/C][/ROW]
[ROW][C]7[/C][C]2.18[/C][C]2.17204997990737[/C][C]0.0079500200926299[/C][/ROW]
[ROW][C]8[/C][C]2.17[/C][C]2.18377823550113[/C][C]-0.0137782355011282[/C][/ROW]
[ROW][C]9[/C][C]2.18[/C][C]2.17078298362761[/C][C]0.00921701637238792[/C][/ROW]
[ROW][C]10[/C][C]2.17[/C][C]2.1827866716583[/C][C]-0.0127866716583012[/C][/ROW]
[ROW][C]11[/C][C]2.17[/C][C]2.17000697593911[/C][C]-6.97593910548022e-06[/C][/ROW]
[ROW][C]12[/C][C]2.17[/C][C]2.17000545943907[/C][C]-5.45943906615776e-06[/C][/ROW]
[ROW][C]13[/C][C]2.17[/C][C]2.17000427261111[/C][C]-4.27261110935717e-06[/C][/ROW]
[ROW][C]14[/C][C]2.17[/C][C]2.17000334378779[/C][C]-3.34378779021094e-06[/C][/ROW]
[ROW][C]15[/C][C]2.17[/C][C]2.17000261688146[/C][C]-2.61688145730687e-06[/C][/ROW]
[ROW][C]16[/C][C]2.17[/C][C]2.17000204799736[/C][C]-2.04799735836758e-06[/C][/ROW]
[ROW][C]17[/C][C]2.17[/C][C]2.17000160278303[/C][C]-1.60278302541172e-06[/C][/ROW]
[ROW][C]18[/C][C]2.17[/C][C]2.17000125435388[/C][C]-1.2543538772114e-06[/C][/ROW]
[ROW][C]19[/C][C]2.18[/C][C]2.17000098166977[/C][C]0.00999901833022676[/C][/ROW]
[ROW][C]20[/C][C]2.18[/C][C]2.18217466917747[/C][C]-0.00217466917747178[/C][/ROW]
[ROW][C]21[/C][C]2.18[/C][C]2.18170191764644[/C][C]-0.00170191764643812[/C][/ROW]
[ROW][C]22[/C][C]2.18[/C][C]2.1813319376139[/C][C]-0.00133193761389716[/C][/ROW]
[ROW][C]23[/C][C]2.18[/C][C]2.18104238757441[/C][C]-0.001042387574409[/C][/ROW]
[ROW][C]24[/C][C]2.18[/C][C]2.18081578284444[/C][C]-0.000815782844440172[/C][/ROW]
[ROW][C]25[/C][C]2.18[/C][C]2.18063843973741[/C][C]-0.00063843973740818[/C][/ROW]
[ROW][C]26[/C][C]2.18[/C][C]2.1804996492646[/C][C]-0.000499649264604773[/C][/ROW]
[ROW][C]27[/C][C]2.18[/C][C]2.18039103046536[/C][C]-0.000391030465355158[/C][/ROW]
[ROW][C]28[/C][C]2.18[/C][C]2.18030602431679[/C][C]-0.000306024316791387[/C][/ROW]
[ROW][C]29[/C][C]2.18[/C][C]2.18023949766262[/C][C]-0.000239497662624544[/C][/ROW]
[ROW][C]30[/C][C]2.18[/C][C]2.18018743324388[/C][C]-0.000187433243881152[/C][/ROW]
[ROW][C]31[/C][C]2.18[/C][C]2.18014668711388[/C][C]-0.000146687113881327[/C][/ROW]
[ROW][C]32[/C][C]2.19[/C][C]2.1801147987888[/C][C]0.00988520121119718[/C][/ROW]
[ROW][C]33[/C][C]2.19[/C][C]2.1922637435826[/C][C]-0.00226374358260362[/C][/ROW]
[ROW][C]34[/C][C]2.19[/C][C]2.19177162815851[/C][C]-0.00177162815850629[/C][/ROW]
[ROW][C]35[/C][C]2.2[/C][C]2.19138649375138[/C][C]0.00861350624861767[/C][/ROW]
[ROW][C]36[/C][C]2.2[/C][C]2.20325898466117[/C][C]-0.00325898466116525[/C][/ROW]
[ROW][C]37[/C][C]2.21[/C][C]2.20255051368814[/C][C]0.00744948631186393[/C][/ROW]
[ROW][C]38[/C][C]2.21[/C][C]2.2141699581976[/C][C]-0.00416995819759514[/C][/ROW]
[ROW][C]39[/C][C]2.21[/C][C]2.21326345060431[/C][C]-0.00326345060431121[/C][/ROW]
[ROW][C]40[/C][C]2.2[/C][C]2.21255400877949[/C][C]-0.0125540087794933[/C][/ROW]
[ROW][C]41[/C][C]2.21[/C][C]2.19982489166476[/C][C]0.0101751083352362[/C][/ROW]
[ROW][C]42[/C][C]2.2[/C][C]2.21203685939473[/C][C]-0.0120368593947275[/C][/ROW]
[ROW][C]43[/C][C]2.21[/C][C]2.19942016543197[/C][C]0.0105798345680332[/C][/ROW]
[ROW][C]44[/C][C]2.21[/C][C]2.21172011663463[/C][C]-0.00172011663462923[/C][/ROW]
[ROW][C]45[/C][C]2.22[/C][C]2.21134618032238[/C][C]0.00865381967761625[/C][/ROW]
[ROW][C]46[/C][C]2.22[/C][C]2.22322743497218[/C][C]-0.00322743497217726[/C][/ROW]
[ROW][C]47[/C][C]2.23[/C][C]2.22252582258892[/C][C]0.00747417741108247[/C][/ROW]
[ROW][C]48[/C][C]2.24[/C][C]2.23415063469869[/C][C]0.00584936530131008[/C][/ROW]
[ROW][C]49[/C][C]2.24[/C][C]2.24542222875558[/C][C]-0.00542222875557696[/C][/ROW]
[ROW][C]50[/C][C]2.25[/C][C]2.24424348995136[/C][C]0.00575651004863609[/C][/ROW]
[ROW][C]51[/C][C]2.25[/C][C]2.25549489819639[/C][C]-0.00549489819639426[/C][/ROW]
[ROW][C]52[/C][C]2.32[/C][C]2.25430036177581[/C][C]0.0656996382241926[/C][/ROW]
[ROW][C]53[/C][C]2.36[/C][C]2.33858281212761[/C][C]0.0214171878723906[/C][/ROW]
[ROW][C]54[/C][C]2.37[/C][C]2.38323869655453[/C][C]-0.0132386965545348[/C][/ROW]
[ROW][C]55[/C][C]2.37[/C][C]2.39036073510188[/C][C]-0.0203607351018782[/C][/ROW]
[ROW][C]56[/C][C]2.37[/C][C]2.38593451303919[/C][C]-0.0159345130391864[/C][/ROW]
[ROW][C]57[/C][C]2.38[/C][C]2.38247050779481[/C][C]-0.00247050779480906[/C][/ROW]
[ROW][C]58[/C][C]2.38[/C][C]2.39193344387974[/C][C]-0.0119334438797427[/C][/ROW]
[ROW][C]59[/C][C]2.41[/C][C]2.38933923142523[/C][C]0.0206607685747744[/C][/ROW]
[ROW][C]60[/C][C]2.42[/C][C]2.42383067779198[/C][C]-0.00383067779198321[/C][/ROW]
[ROW][C]61[/C][C]2.43[/C][C]2.43299792639705[/C][C]-0.00299792639705032[/C][/ROW]
[ROW][C]62[/C][C]2.44[/C][C]2.44234620690389[/C][C]-0.00234620690389109[/C][/ROW]
[ROW][C]63[/C][C]2.44[/C][C]2.45183616477085[/C][C]-0.01183616477085[/C][/ROW]
[ROW][C]64[/C][C]2.44[/C][C]2.4492630998307[/C][C]-0.00926309983069684[/C][/ROW]
[ROW][C]65[/C][C]2.43[/C][C]2.4472493937128[/C][C]-0.0172493937127989[/C][/ROW]
[ROW][C]66[/C][C]2.43[/C][C]2.43349954643874[/C][C]-0.00349954643873884[/C][/ROW]
[ROW][C]67[/C][C]2.43[/C][C]2.43273877971892[/C][C]-0.00273877971891956[/C][/ROW]
[ROW][C]68[/C][C]2.42[/C][C]2.43214339614578[/C][C]-0.0121433961457789[/C][/ROW]
[ROW][C]69[/C][C]2.42[/C][C]2.41950354214898[/C][C]0.000496457851019816[/C][/ROW]
[ROW][C]70[/C][C]2.42[/C][C]2.41961146716654[/C][C]0.000388532833460964[/C][/ROW]
[ROW][C]71[/C][C]2.42[/C][C]2.41969593035468[/C][C]0.000304069645322702[/C][/ROW]
[ROW][C]72[/C][C]2.42[/C][C]2.41976203208263[/C][C]0.000237967917365189[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77273&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77273&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
32.182.19-0.0100000000000002
42.182.18782609908702-0.00782609908702003
52.172.18612478269199-0.0161247826919859
62.172.17261941471041-0.0026194147104146
72.182.172049979907370.0079500200926299
82.172.18377823550113-0.0137782355011282
92.182.170782983627610.00921701637238792
102.172.1827866716583-0.0127866716583012
112.172.17000697593911-6.97593910548022e-06
122.172.17000545943907-5.45943906615776e-06
132.172.17000427261111-4.27261110935717e-06
142.172.17000334378779-3.34378779021094e-06
152.172.17000261688146-2.61688145730687e-06
162.172.17000204799736-2.04799735836758e-06
172.172.17000160278303-1.60278302541172e-06
182.172.17000125435388-1.2543538772114e-06
192.182.170000981669770.00999901833022676
202.182.18217466917747-0.00217466917747178
212.182.18170191764644-0.00170191764643812
222.182.1813319376139-0.00133193761389716
232.182.18104238757441-0.001042387574409
242.182.18081578284444-0.000815782844440172
252.182.18063843973741-0.00063843973740818
262.182.1804996492646-0.000499649264604773
272.182.18039103046536-0.000391030465355158
282.182.18030602431679-0.000306024316791387
292.182.18023949766262-0.000239497662624544
302.182.18018743324388-0.000187433243881152
312.182.18014668711388-0.000146687113881327
322.192.18011479878880.00988520121119718
332.192.1922637435826-0.00226374358260362
342.192.19177162815851-0.00177162815850629
352.22.191386493751380.00861350624861767
362.22.20325898466117-0.00325898466116525
372.212.202550513688140.00744948631186393
382.212.2141699581976-0.00416995819759514
392.212.21326345060431-0.00326345060431121
402.22.21255400877949-0.0125540087794933
412.212.199824891664760.0101751083352362
422.22.21203685939473-0.0120368593947275
432.212.199420165431970.0105798345680332
442.212.21172011663463-0.00172011663462923
452.222.211346180322380.00865381967761625
462.222.22322743497218-0.00322743497217726
472.232.222525822588920.00747417741108247
482.242.234150634698690.00584936530131008
492.242.24542222875558-0.00542222875557696
502.252.244243489951360.00575651004863609
512.252.25549489819639-0.00549489819639426
522.322.254300361775810.0656996382241926
532.362.338582812127610.0214171878723906
542.372.38323869655453-0.0132386965545348
552.372.39036073510188-0.0203607351018782
562.372.38593451303919-0.0159345130391864
572.382.38247050779481-0.00247050779480906
582.382.39193344387974-0.0119334438797427
592.412.389339231425230.0206607685747744
602.422.42383067779198-0.00383067779198321
612.432.43299792639705-0.00299792639705032
622.442.44234620690389-0.00234620690389109
632.442.45183616477085-0.01183616477085
642.442.4492630998307-0.00926309983069684
652.432.4472493937128-0.0172493937127989
662.432.43349954643874-0.00349954643873884
672.432.43273877971892-0.00273877971891956
682.422.43214339614578-0.0121433961457789
692.422.419503542148980.000496457851019816
702.422.419611467166540.000388532833460964
712.422.419695930354680.000304069645322702
722.422.419762032082630.000237967917365189







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
732.419813763949922.397443870984962.44218365691487
742.419627527899832.384384908909852.45487014688982
752.419441291849752.371773822341672.46710876135784
762.419255055799672.358938011088982.47957210051036
772.419068819749582.345671174715632.49246646478354
782.41888258369952.331895858883152.50586930851585
792.418696347649422.317583186888112.51980950841073
802.418510111599342.302725593401072.53429462979761
812.418323875549252.287325639594182.54932211150433
822.418137639499172.271390856947652.56488442205069
832.417951403449092.254931180300762.58097162659741
842.4177651673992.237957603250742.59757273154726

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 2.41981376394992 & 2.39744387098496 & 2.44218365691487 \tabularnewline
74 & 2.41962752789983 & 2.38438490890985 & 2.45487014688982 \tabularnewline
75 & 2.41944129184975 & 2.37177382234167 & 2.46710876135784 \tabularnewline
76 & 2.41925505579967 & 2.35893801108898 & 2.47957210051036 \tabularnewline
77 & 2.41906881974958 & 2.34567117471563 & 2.49246646478354 \tabularnewline
78 & 2.4188825836995 & 2.33189585888315 & 2.50586930851585 \tabularnewline
79 & 2.41869634764942 & 2.31758318688811 & 2.51980950841073 \tabularnewline
80 & 2.41851011159934 & 2.30272559340107 & 2.53429462979761 \tabularnewline
81 & 2.41832387554925 & 2.28732563959418 & 2.54932211150433 \tabularnewline
82 & 2.41813763949917 & 2.27139085694765 & 2.56488442205069 \tabularnewline
83 & 2.41795140344909 & 2.25493118030076 & 2.58097162659741 \tabularnewline
84 & 2.417765167399 & 2.23795760325074 & 2.59757273154726 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77273&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]2.41981376394992[/C][C]2.39744387098496[/C][C]2.44218365691487[/C][/ROW]
[ROW][C]74[/C][C]2.41962752789983[/C][C]2.38438490890985[/C][C]2.45487014688982[/C][/ROW]
[ROW][C]75[/C][C]2.41944129184975[/C][C]2.37177382234167[/C][C]2.46710876135784[/C][/ROW]
[ROW][C]76[/C][C]2.41925505579967[/C][C]2.35893801108898[/C][C]2.47957210051036[/C][/ROW]
[ROW][C]77[/C][C]2.41906881974958[/C][C]2.34567117471563[/C][C]2.49246646478354[/C][/ROW]
[ROW][C]78[/C][C]2.4188825836995[/C][C]2.33189585888315[/C][C]2.50586930851585[/C][/ROW]
[ROW][C]79[/C][C]2.41869634764942[/C][C]2.31758318688811[/C][C]2.51980950841073[/C][/ROW]
[ROW][C]80[/C][C]2.41851011159934[/C][C]2.30272559340107[/C][C]2.53429462979761[/C][/ROW]
[ROW][C]81[/C][C]2.41832387554925[/C][C]2.28732563959418[/C][C]2.54932211150433[/C][/ROW]
[ROW][C]82[/C][C]2.41813763949917[/C][C]2.27139085694765[/C][C]2.56488442205069[/C][/ROW]
[ROW][C]83[/C][C]2.41795140344909[/C][C]2.25493118030076[/C][C]2.58097162659741[/C][/ROW]
[ROW][C]84[/C][C]2.417765167399[/C][C]2.23795760325074[/C][C]2.59757273154726[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77273&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77273&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
732.419813763949922.397443870984962.44218365691487
742.419627527899832.384384908909852.45487014688982
752.419441291849752.371773822341672.46710876135784
762.419255055799672.358938011088982.47957210051036
772.419068819749582.345671174715632.49246646478354
782.41888258369952.331895858883152.50586930851585
792.418696347649422.317583186888112.51980950841073
802.418510111599342.302725593401072.53429462979761
812.418323875549252.287325639594182.54932211150433
822.418137639499172.271390856947652.56488442205069
832.417951403449092.254931180300762.58097162659741
842.4177651673992.237957603250742.59757273154726



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=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')