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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 23 May 2014 03:38:17 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/May/23/t1400830818x52kj1362n6s4fu.htm/, Retrieved Tue, 14 May 2024 16:34:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235210, Retrieved Tue, 14 May 2024 16:34:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact159
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [gemiddelde prijs ...] [2014-05-23 07:38:17] [f824ea295e177f9d3dd7528a75f4b680] [Current]
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Dataseries X:
2,9
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3,1
3,1
3,1
3,1
3,1
3,1
3,1
3,1
3,1
3,1
3,1
3,1
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,5
3,5
3,5
3,5
3,5
3,5
3,5
3,5
3,5
3,5
3,5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235210&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235210&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235210&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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.277760302369149
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.277760302369149 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235210&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]0.277760302369149[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235210&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235210&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
beta0.277760302369149
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
333.1-0.1
433.07222396976309-0.0722239697630851
533.05216301808339-0.0521630180833905
633.03767420240806-0.0376742024080605
733.02720980455568-0.0272098045556812
833.01965200101489-0.0196520010148897
933.01419345527083-0.0141934552708349
1033.01025107684314-0.010251076843145
1133.00740373463958-0.00740373463958344
1233.00534727106743-0.00534727106743205
1333.00386201143889-0.00386201143889231
1433.00278929797387-0.00278929797387262
1533.00201454172525-0.00201454172525217
1633.00145498200651-0.00145498200651062
1733.00105084576444-0.00105084576444048
1833.00075896252717-0.000758962527166229
1933.00054815286613-0.000548152866133744
2033.00039589776029-0.00039589776029203
2133.00028593307869-0.000285933078685741
2233.00020651222029-0.000206512220292776
2333.00014915132354-0.000149151323541208
2433.00010772300682-0.000107723006815608
2533.00007780183187-7.78018318703388e-05
263.13.000056191571530.0999438084284749
273.13.12781661402054-0.0278166140205425
283.13.12009026289931-0.0200902628993109
293.13.11450998540172-0.0145099854017228
303.13.11047968746917-0.0104796874691684
313.13.107568846309-0.00756884630899801
323.13.10546652126963-0.00546652126962499
333.13.10394813866887-0.00394813866886645
343.13.10285150247841-0.00285150247840704
353.13.1020594682878-0.00205946828779835
363.13.10148742975346-0.0014874297534595
373.13.10107428081539-0.00107428081538608
383.33.100775888251270.199224111748725
393.33.35611243776983-0.0561124377698259
403.33.34052663008821-0.040526630088209
413.33.32926994106091-0.0292699410609054
423.33.3211399133815-0.0211399133815013
433.33.3152680846486-0.0152680846485977
443.33.31102721684001-0.0110272168400054
453.33.30796429375624-0.0079642937562352
463.33.30575212911435-0.00575212911434653
473.33.30415441599228-0.0041544159922795
483.33.3030004841501-0.00300048415009657
493.33.30216706876531-0.00216706876531214
503.33.3015651430898-0.00156514308980427
513.33.30113040847193-0.00113040847192902
523.33.30081642587297-0.000816425872965709
533.33.30058965517563-0.000589655175628589
543.33.30042587237575-0.000425872375752423
553.33.30030758193589-0.000307581935892642
563.33.30022214788438-0.000222147884375801
573.33.30016044402084-0.000160444020841144
583.33.3001158790411-0.000115879041098665
593.33.3000836924436-8.36924436051767e-05
603.33.30006044600516-6.0446005163417e-05
613.33.30004365650449-4.36565044918957e-05
623.33.3000315304606-3.15304606042233e-05
633.33.30002277255033-2.27725503330056e-05
643.33.30001644723987-1.64472398664905e-05
653.33.30001187884955-1.18788495480082e-05
663.33.30000857937671-8.57937670595277e-06
673.33.30000619636644-6.19636643772736e-06
683.33.30000447526182-4.47526182245639e-06
693.33.30000323221175-3.23221174536314e-06
703.33.30000233443163-2.334431633777e-06
713.33.3000016860192-1.68601919714462e-06
723.33.30000121770999-1.21770999506055e-06
733.33.3000008794785-8.79478498916342e-07
743.53.300000635194280.199999364805715
753.53.55555251923636-0.055552519236358
763.53.5401222346959-0.0401222346958994
773.53.52897787065504-0.0289778706550403
783.53.52092896853988-0.0209289685398821
793.53.51511573190997-0.0151157319099702
803.53.51091718164413-0.010917181644126
813.53.50788482196963-0.00788482196963436
823.53.50569473143522-0.00569473143522181
833.53.50411296110986-0.00411296110986381
843.53.50297054378836-0.00297054378835515

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 3 & 3.1 & -0.1 \tabularnewline
4 & 3 & 3.07222396976309 & -0.0722239697630851 \tabularnewline
5 & 3 & 3.05216301808339 & -0.0521630180833905 \tabularnewline
6 & 3 & 3.03767420240806 & -0.0376742024080605 \tabularnewline
7 & 3 & 3.02720980455568 & -0.0272098045556812 \tabularnewline
8 & 3 & 3.01965200101489 & -0.0196520010148897 \tabularnewline
9 & 3 & 3.01419345527083 & -0.0141934552708349 \tabularnewline
10 & 3 & 3.01025107684314 & -0.010251076843145 \tabularnewline
11 & 3 & 3.00740373463958 & -0.00740373463958344 \tabularnewline
12 & 3 & 3.00534727106743 & -0.00534727106743205 \tabularnewline
13 & 3 & 3.00386201143889 & -0.00386201143889231 \tabularnewline
14 & 3 & 3.00278929797387 & -0.00278929797387262 \tabularnewline
15 & 3 & 3.00201454172525 & -0.00201454172525217 \tabularnewline
16 & 3 & 3.00145498200651 & -0.00145498200651062 \tabularnewline
17 & 3 & 3.00105084576444 & -0.00105084576444048 \tabularnewline
18 & 3 & 3.00075896252717 & -0.000758962527166229 \tabularnewline
19 & 3 & 3.00054815286613 & -0.000548152866133744 \tabularnewline
20 & 3 & 3.00039589776029 & -0.00039589776029203 \tabularnewline
21 & 3 & 3.00028593307869 & -0.000285933078685741 \tabularnewline
22 & 3 & 3.00020651222029 & -0.000206512220292776 \tabularnewline
23 & 3 & 3.00014915132354 & -0.000149151323541208 \tabularnewline
24 & 3 & 3.00010772300682 & -0.000107723006815608 \tabularnewline
25 & 3 & 3.00007780183187 & -7.78018318703388e-05 \tabularnewline
26 & 3.1 & 3.00005619157153 & 0.0999438084284749 \tabularnewline
27 & 3.1 & 3.12781661402054 & -0.0278166140205425 \tabularnewline
28 & 3.1 & 3.12009026289931 & -0.0200902628993109 \tabularnewline
29 & 3.1 & 3.11450998540172 & -0.0145099854017228 \tabularnewline
30 & 3.1 & 3.11047968746917 & -0.0104796874691684 \tabularnewline
31 & 3.1 & 3.107568846309 & -0.00756884630899801 \tabularnewline
32 & 3.1 & 3.10546652126963 & -0.00546652126962499 \tabularnewline
33 & 3.1 & 3.10394813866887 & -0.00394813866886645 \tabularnewline
34 & 3.1 & 3.10285150247841 & -0.00285150247840704 \tabularnewline
35 & 3.1 & 3.1020594682878 & -0.00205946828779835 \tabularnewline
36 & 3.1 & 3.10148742975346 & -0.0014874297534595 \tabularnewline
37 & 3.1 & 3.10107428081539 & -0.00107428081538608 \tabularnewline
38 & 3.3 & 3.10077588825127 & 0.199224111748725 \tabularnewline
39 & 3.3 & 3.35611243776983 & -0.0561124377698259 \tabularnewline
40 & 3.3 & 3.34052663008821 & -0.040526630088209 \tabularnewline
41 & 3.3 & 3.32926994106091 & -0.0292699410609054 \tabularnewline
42 & 3.3 & 3.3211399133815 & -0.0211399133815013 \tabularnewline
43 & 3.3 & 3.3152680846486 & -0.0152680846485977 \tabularnewline
44 & 3.3 & 3.31102721684001 & -0.0110272168400054 \tabularnewline
45 & 3.3 & 3.30796429375624 & -0.0079642937562352 \tabularnewline
46 & 3.3 & 3.30575212911435 & -0.00575212911434653 \tabularnewline
47 & 3.3 & 3.30415441599228 & -0.0041544159922795 \tabularnewline
48 & 3.3 & 3.3030004841501 & -0.00300048415009657 \tabularnewline
49 & 3.3 & 3.30216706876531 & -0.00216706876531214 \tabularnewline
50 & 3.3 & 3.3015651430898 & -0.00156514308980427 \tabularnewline
51 & 3.3 & 3.30113040847193 & -0.00113040847192902 \tabularnewline
52 & 3.3 & 3.30081642587297 & -0.000816425872965709 \tabularnewline
53 & 3.3 & 3.30058965517563 & -0.000589655175628589 \tabularnewline
54 & 3.3 & 3.30042587237575 & -0.000425872375752423 \tabularnewline
55 & 3.3 & 3.30030758193589 & -0.000307581935892642 \tabularnewline
56 & 3.3 & 3.30022214788438 & -0.000222147884375801 \tabularnewline
57 & 3.3 & 3.30016044402084 & -0.000160444020841144 \tabularnewline
58 & 3.3 & 3.3001158790411 & -0.000115879041098665 \tabularnewline
59 & 3.3 & 3.3000836924436 & -8.36924436051767e-05 \tabularnewline
60 & 3.3 & 3.30006044600516 & -6.0446005163417e-05 \tabularnewline
61 & 3.3 & 3.30004365650449 & -4.36565044918957e-05 \tabularnewline
62 & 3.3 & 3.3000315304606 & -3.15304606042233e-05 \tabularnewline
63 & 3.3 & 3.30002277255033 & -2.27725503330056e-05 \tabularnewline
64 & 3.3 & 3.30001644723987 & -1.64472398664905e-05 \tabularnewline
65 & 3.3 & 3.30001187884955 & -1.18788495480082e-05 \tabularnewline
66 & 3.3 & 3.30000857937671 & -8.57937670595277e-06 \tabularnewline
67 & 3.3 & 3.30000619636644 & -6.19636643772736e-06 \tabularnewline
68 & 3.3 & 3.30000447526182 & -4.47526182245639e-06 \tabularnewline
69 & 3.3 & 3.30000323221175 & -3.23221174536314e-06 \tabularnewline
70 & 3.3 & 3.30000233443163 & -2.334431633777e-06 \tabularnewline
71 & 3.3 & 3.3000016860192 & -1.68601919714462e-06 \tabularnewline
72 & 3.3 & 3.30000121770999 & -1.21770999506055e-06 \tabularnewline
73 & 3.3 & 3.3000008794785 & -8.79478498916342e-07 \tabularnewline
74 & 3.5 & 3.30000063519428 & 0.199999364805715 \tabularnewline
75 & 3.5 & 3.55555251923636 & -0.055552519236358 \tabularnewline
76 & 3.5 & 3.5401222346959 & -0.0401222346958994 \tabularnewline
77 & 3.5 & 3.52897787065504 & -0.0289778706550403 \tabularnewline
78 & 3.5 & 3.52092896853988 & -0.0209289685398821 \tabularnewline
79 & 3.5 & 3.51511573190997 & -0.0151157319099702 \tabularnewline
80 & 3.5 & 3.51091718164413 & -0.010917181644126 \tabularnewline
81 & 3.5 & 3.50788482196963 & -0.00788482196963436 \tabularnewline
82 & 3.5 & 3.50569473143522 & -0.00569473143522181 \tabularnewline
83 & 3.5 & 3.50411296110986 & -0.00411296110986381 \tabularnewline
84 & 3.5 & 3.50297054378836 & -0.00297054378835515 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235210&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]3[/C][C]3.1[/C][C]-0.1[/C][/ROW]
[ROW][C]4[/C][C]3[/C][C]3.07222396976309[/C][C]-0.0722239697630851[/C][/ROW]
[ROW][C]5[/C][C]3[/C][C]3.05216301808339[/C][C]-0.0521630180833905[/C][/ROW]
[ROW][C]6[/C][C]3[/C][C]3.03767420240806[/C][C]-0.0376742024080605[/C][/ROW]
[ROW][C]7[/C][C]3[/C][C]3.02720980455568[/C][C]-0.0272098045556812[/C][/ROW]
[ROW][C]8[/C][C]3[/C][C]3.01965200101489[/C][C]-0.0196520010148897[/C][/ROW]
[ROW][C]9[/C][C]3[/C][C]3.01419345527083[/C][C]-0.0141934552708349[/C][/ROW]
[ROW][C]10[/C][C]3[/C][C]3.01025107684314[/C][C]-0.010251076843145[/C][/ROW]
[ROW][C]11[/C][C]3[/C][C]3.00740373463958[/C][C]-0.00740373463958344[/C][/ROW]
[ROW][C]12[/C][C]3[/C][C]3.00534727106743[/C][C]-0.00534727106743205[/C][/ROW]
[ROW][C]13[/C][C]3[/C][C]3.00386201143889[/C][C]-0.00386201143889231[/C][/ROW]
[ROW][C]14[/C][C]3[/C][C]3.00278929797387[/C][C]-0.00278929797387262[/C][/ROW]
[ROW][C]15[/C][C]3[/C][C]3.00201454172525[/C][C]-0.00201454172525217[/C][/ROW]
[ROW][C]16[/C][C]3[/C][C]3.00145498200651[/C][C]-0.00145498200651062[/C][/ROW]
[ROW][C]17[/C][C]3[/C][C]3.00105084576444[/C][C]-0.00105084576444048[/C][/ROW]
[ROW][C]18[/C][C]3[/C][C]3.00075896252717[/C][C]-0.000758962527166229[/C][/ROW]
[ROW][C]19[/C][C]3[/C][C]3.00054815286613[/C][C]-0.000548152866133744[/C][/ROW]
[ROW][C]20[/C][C]3[/C][C]3.00039589776029[/C][C]-0.00039589776029203[/C][/ROW]
[ROW][C]21[/C][C]3[/C][C]3.00028593307869[/C][C]-0.000285933078685741[/C][/ROW]
[ROW][C]22[/C][C]3[/C][C]3.00020651222029[/C][C]-0.000206512220292776[/C][/ROW]
[ROW][C]23[/C][C]3[/C][C]3.00014915132354[/C][C]-0.000149151323541208[/C][/ROW]
[ROW][C]24[/C][C]3[/C][C]3.00010772300682[/C][C]-0.000107723006815608[/C][/ROW]
[ROW][C]25[/C][C]3[/C][C]3.00007780183187[/C][C]-7.78018318703388e-05[/C][/ROW]
[ROW][C]26[/C][C]3.1[/C][C]3.00005619157153[/C][C]0.0999438084284749[/C][/ROW]
[ROW][C]27[/C][C]3.1[/C][C]3.12781661402054[/C][C]-0.0278166140205425[/C][/ROW]
[ROW][C]28[/C][C]3.1[/C][C]3.12009026289931[/C][C]-0.0200902628993109[/C][/ROW]
[ROW][C]29[/C][C]3.1[/C][C]3.11450998540172[/C][C]-0.0145099854017228[/C][/ROW]
[ROW][C]30[/C][C]3.1[/C][C]3.11047968746917[/C][C]-0.0104796874691684[/C][/ROW]
[ROW][C]31[/C][C]3.1[/C][C]3.107568846309[/C][C]-0.00756884630899801[/C][/ROW]
[ROW][C]32[/C][C]3.1[/C][C]3.10546652126963[/C][C]-0.00546652126962499[/C][/ROW]
[ROW][C]33[/C][C]3.1[/C][C]3.10394813866887[/C][C]-0.00394813866886645[/C][/ROW]
[ROW][C]34[/C][C]3.1[/C][C]3.10285150247841[/C][C]-0.00285150247840704[/C][/ROW]
[ROW][C]35[/C][C]3.1[/C][C]3.1020594682878[/C][C]-0.00205946828779835[/C][/ROW]
[ROW][C]36[/C][C]3.1[/C][C]3.10148742975346[/C][C]-0.0014874297534595[/C][/ROW]
[ROW][C]37[/C][C]3.1[/C][C]3.10107428081539[/C][C]-0.00107428081538608[/C][/ROW]
[ROW][C]38[/C][C]3.3[/C][C]3.10077588825127[/C][C]0.199224111748725[/C][/ROW]
[ROW][C]39[/C][C]3.3[/C][C]3.35611243776983[/C][C]-0.0561124377698259[/C][/ROW]
[ROW][C]40[/C][C]3.3[/C][C]3.34052663008821[/C][C]-0.040526630088209[/C][/ROW]
[ROW][C]41[/C][C]3.3[/C][C]3.32926994106091[/C][C]-0.0292699410609054[/C][/ROW]
[ROW][C]42[/C][C]3.3[/C][C]3.3211399133815[/C][C]-0.0211399133815013[/C][/ROW]
[ROW][C]43[/C][C]3.3[/C][C]3.3152680846486[/C][C]-0.0152680846485977[/C][/ROW]
[ROW][C]44[/C][C]3.3[/C][C]3.31102721684001[/C][C]-0.0110272168400054[/C][/ROW]
[ROW][C]45[/C][C]3.3[/C][C]3.30796429375624[/C][C]-0.0079642937562352[/C][/ROW]
[ROW][C]46[/C][C]3.3[/C][C]3.30575212911435[/C][C]-0.00575212911434653[/C][/ROW]
[ROW][C]47[/C][C]3.3[/C][C]3.30415441599228[/C][C]-0.0041544159922795[/C][/ROW]
[ROW][C]48[/C][C]3.3[/C][C]3.3030004841501[/C][C]-0.00300048415009657[/C][/ROW]
[ROW][C]49[/C][C]3.3[/C][C]3.30216706876531[/C][C]-0.00216706876531214[/C][/ROW]
[ROW][C]50[/C][C]3.3[/C][C]3.3015651430898[/C][C]-0.00156514308980427[/C][/ROW]
[ROW][C]51[/C][C]3.3[/C][C]3.30113040847193[/C][C]-0.00113040847192902[/C][/ROW]
[ROW][C]52[/C][C]3.3[/C][C]3.30081642587297[/C][C]-0.000816425872965709[/C][/ROW]
[ROW][C]53[/C][C]3.3[/C][C]3.30058965517563[/C][C]-0.000589655175628589[/C][/ROW]
[ROW][C]54[/C][C]3.3[/C][C]3.30042587237575[/C][C]-0.000425872375752423[/C][/ROW]
[ROW][C]55[/C][C]3.3[/C][C]3.30030758193589[/C][C]-0.000307581935892642[/C][/ROW]
[ROW][C]56[/C][C]3.3[/C][C]3.30022214788438[/C][C]-0.000222147884375801[/C][/ROW]
[ROW][C]57[/C][C]3.3[/C][C]3.30016044402084[/C][C]-0.000160444020841144[/C][/ROW]
[ROW][C]58[/C][C]3.3[/C][C]3.3001158790411[/C][C]-0.000115879041098665[/C][/ROW]
[ROW][C]59[/C][C]3.3[/C][C]3.3000836924436[/C][C]-8.36924436051767e-05[/C][/ROW]
[ROW][C]60[/C][C]3.3[/C][C]3.30006044600516[/C][C]-6.0446005163417e-05[/C][/ROW]
[ROW][C]61[/C][C]3.3[/C][C]3.30004365650449[/C][C]-4.36565044918957e-05[/C][/ROW]
[ROW][C]62[/C][C]3.3[/C][C]3.3000315304606[/C][C]-3.15304606042233e-05[/C][/ROW]
[ROW][C]63[/C][C]3.3[/C][C]3.30002277255033[/C][C]-2.27725503330056e-05[/C][/ROW]
[ROW][C]64[/C][C]3.3[/C][C]3.30001644723987[/C][C]-1.64472398664905e-05[/C][/ROW]
[ROW][C]65[/C][C]3.3[/C][C]3.30001187884955[/C][C]-1.18788495480082e-05[/C][/ROW]
[ROW][C]66[/C][C]3.3[/C][C]3.30000857937671[/C][C]-8.57937670595277e-06[/C][/ROW]
[ROW][C]67[/C][C]3.3[/C][C]3.30000619636644[/C][C]-6.19636643772736e-06[/C][/ROW]
[ROW][C]68[/C][C]3.3[/C][C]3.30000447526182[/C][C]-4.47526182245639e-06[/C][/ROW]
[ROW][C]69[/C][C]3.3[/C][C]3.30000323221175[/C][C]-3.23221174536314e-06[/C][/ROW]
[ROW][C]70[/C][C]3.3[/C][C]3.30000233443163[/C][C]-2.334431633777e-06[/C][/ROW]
[ROW][C]71[/C][C]3.3[/C][C]3.3000016860192[/C][C]-1.68601919714462e-06[/C][/ROW]
[ROW][C]72[/C][C]3.3[/C][C]3.30000121770999[/C][C]-1.21770999506055e-06[/C][/ROW]
[ROW][C]73[/C][C]3.3[/C][C]3.3000008794785[/C][C]-8.79478498916342e-07[/C][/ROW]
[ROW][C]74[/C][C]3.5[/C][C]3.30000063519428[/C][C]0.199999364805715[/C][/ROW]
[ROW][C]75[/C][C]3.5[/C][C]3.55555251923636[/C][C]-0.055552519236358[/C][/ROW]
[ROW][C]76[/C][C]3.5[/C][C]3.5401222346959[/C][C]-0.0401222346958994[/C][/ROW]
[ROW][C]77[/C][C]3.5[/C][C]3.52897787065504[/C][C]-0.0289778706550403[/C][/ROW]
[ROW][C]78[/C][C]3.5[/C][C]3.52092896853988[/C][C]-0.0209289685398821[/C][/ROW]
[ROW][C]79[/C][C]3.5[/C][C]3.51511573190997[/C][C]-0.0151157319099702[/C][/ROW]
[ROW][C]80[/C][C]3.5[/C][C]3.51091718164413[/C][C]-0.010917181644126[/C][/ROW]
[ROW][C]81[/C][C]3.5[/C][C]3.50788482196963[/C][C]-0.00788482196963436[/C][/ROW]
[ROW][C]82[/C][C]3.5[/C][C]3.50569473143522[/C][C]-0.00569473143522181[/C][/ROW]
[ROW][C]83[/C][C]3.5[/C][C]3.50411296110986[/C][C]-0.00411296110986381[/C][/ROW]
[ROW][C]84[/C][C]3.5[/C][C]3.50297054378836[/C][C]-0.00297054378835515[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235210&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235210&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
333.1-0.1
433.07222396976309-0.0722239697630851
533.05216301808339-0.0521630180833905
633.03767420240806-0.0376742024080605
733.02720980455568-0.0272098045556812
833.01965200101489-0.0196520010148897
933.01419345527083-0.0141934552708349
1033.01025107684314-0.010251076843145
1133.00740373463958-0.00740373463958344
1233.00534727106743-0.00534727106743205
1333.00386201143889-0.00386201143889231
1433.00278929797387-0.00278929797387262
1533.00201454172525-0.00201454172525217
1633.00145498200651-0.00145498200651062
1733.00105084576444-0.00105084576444048
1833.00075896252717-0.000758962527166229
1933.00054815286613-0.000548152866133744
2033.00039589776029-0.00039589776029203
2133.00028593307869-0.000285933078685741
2233.00020651222029-0.000206512220292776
2333.00014915132354-0.000149151323541208
2433.00010772300682-0.000107723006815608
2533.00007780183187-7.78018318703388e-05
263.13.000056191571530.0999438084284749
273.13.12781661402054-0.0278166140205425
283.13.12009026289931-0.0200902628993109
293.13.11450998540172-0.0145099854017228
303.13.11047968746917-0.0104796874691684
313.13.107568846309-0.00756884630899801
323.13.10546652126963-0.00546652126962499
333.13.10394813866887-0.00394813866886645
343.13.10285150247841-0.00285150247840704
353.13.1020594682878-0.00205946828779835
363.13.10148742975346-0.0014874297534595
373.13.10107428081539-0.00107428081538608
383.33.100775888251270.199224111748725
393.33.35611243776983-0.0561124377698259
403.33.34052663008821-0.040526630088209
413.33.32926994106091-0.0292699410609054
423.33.3211399133815-0.0211399133815013
433.33.3152680846486-0.0152680846485977
443.33.31102721684001-0.0110272168400054
453.33.30796429375624-0.0079642937562352
463.33.30575212911435-0.00575212911434653
473.33.30415441599228-0.0041544159922795
483.33.3030004841501-0.00300048415009657
493.33.30216706876531-0.00216706876531214
503.33.3015651430898-0.00156514308980427
513.33.30113040847193-0.00113040847192902
523.33.30081642587297-0.000816425872965709
533.33.30058965517563-0.000589655175628589
543.33.30042587237575-0.000425872375752423
553.33.30030758193589-0.000307581935892642
563.33.30022214788438-0.000222147884375801
573.33.30016044402084-0.000160444020841144
583.33.3001158790411-0.000115879041098665
593.33.3000836924436-8.36924436051767e-05
603.33.30006044600516-6.0446005163417e-05
613.33.30004365650449-4.36565044918957e-05
623.33.3000315304606-3.15304606042233e-05
633.33.30002277255033-2.27725503330056e-05
643.33.30001644723987-1.64472398664905e-05
653.33.30001187884955-1.18788495480082e-05
663.33.30000857937671-8.57937670595277e-06
673.33.30000619636644-6.19636643772736e-06
683.33.30000447526182-4.47526182245639e-06
693.33.30000323221175-3.23221174536314e-06
703.33.30000233443163-2.334431633777e-06
713.33.3000016860192-1.68601919714462e-06
723.33.30000121770999-1.21770999506055e-06
733.33.3000008794785-8.79478498916342e-07
743.53.300000635194280.199999364805715
753.53.55555251923636-0.055552519236358
763.53.5401222346959-0.0401222346958994
773.53.52897787065504-0.0289778706550403
783.53.52092896853988-0.0209289685398821
793.53.51511573190997-0.0151157319099702
803.53.51091718164413-0.010917181644126
813.53.50788482196963-0.00788482196963436
823.53.50569473143522-0.00569473143522181
833.53.50411296110986-0.00411296110986381
843.53.50297054378836-0.00297054378835515







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
853.50214544464753.425549324407743.57874156488726
863.5042908892953.38000978623723.6285719923528
873.50643633394253.334268500594083.67860416729092
883.508581778593.286410316788283.73075324039173
893.51072722323753.235943196426653.78551125004836
903.512872667885013.182743369413693.84300196635632
913.515018112532513.126813633667443.90322259139757
923.517163557180013.068205168784123.96612194557589
933.519309001827513.006987435792054.03163056786297
943.521454446475012.943235407556084.09967348539393
953.523599891122512.877023889127094.17017589311793
963.525745335770012.808424990871964.24306568066806

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 3.5021454446475 & 3.42554932440774 & 3.57874156488726 \tabularnewline
86 & 3.504290889295 & 3.3800097862372 & 3.6285719923528 \tabularnewline
87 & 3.5064363339425 & 3.33426850059408 & 3.67860416729092 \tabularnewline
88 & 3.50858177859 & 3.28641031678828 & 3.73075324039173 \tabularnewline
89 & 3.5107272232375 & 3.23594319642665 & 3.78551125004836 \tabularnewline
90 & 3.51287266788501 & 3.18274336941369 & 3.84300196635632 \tabularnewline
91 & 3.51501811253251 & 3.12681363366744 & 3.90322259139757 \tabularnewline
92 & 3.51716355718001 & 3.06820516878412 & 3.96612194557589 \tabularnewline
93 & 3.51930900182751 & 3.00698743579205 & 4.03163056786297 \tabularnewline
94 & 3.52145444647501 & 2.94323540755608 & 4.09967348539393 \tabularnewline
95 & 3.52359989112251 & 2.87702388912709 & 4.17017589311793 \tabularnewline
96 & 3.52574533577001 & 2.80842499087196 & 4.24306568066806 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235210&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]85[/C][C]3.5021454446475[/C][C]3.42554932440774[/C][C]3.57874156488726[/C][/ROW]
[ROW][C]86[/C][C]3.504290889295[/C][C]3.3800097862372[/C][C]3.6285719923528[/C][/ROW]
[ROW][C]87[/C][C]3.5064363339425[/C][C]3.33426850059408[/C][C]3.67860416729092[/C][/ROW]
[ROW][C]88[/C][C]3.50858177859[/C][C]3.28641031678828[/C][C]3.73075324039173[/C][/ROW]
[ROW][C]89[/C][C]3.5107272232375[/C][C]3.23594319642665[/C][C]3.78551125004836[/C][/ROW]
[ROW][C]90[/C][C]3.51287266788501[/C][C]3.18274336941369[/C][C]3.84300196635632[/C][/ROW]
[ROW][C]91[/C][C]3.51501811253251[/C][C]3.12681363366744[/C][C]3.90322259139757[/C][/ROW]
[ROW][C]92[/C][C]3.51716355718001[/C][C]3.06820516878412[/C][C]3.96612194557589[/C][/ROW]
[ROW][C]93[/C][C]3.51930900182751[/C][C]3.00698743579205[/C][C]4.03163056786297[/C][/ROW]
[ROW][C]94[/C][C]3.52145444647501[/C][C]2.94323540755608[/C][C]4.09967348539393[/C][/ROW]
[ROW][C]95[/C][C]3.52359989112251[/C][C]2.87702388912709[/C][C]4.17017589311793[/C][/ROW]
[ROW][C]96[/C][C]3.52574533577001[/C][C]2.80842499087196[/C][C]4.24306568066806[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235210&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235210&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
853.50214544464753.425549324407743.57874156488726
863.5042908892953.38000978623723.6285719923528
873.50643633394253.334268500594083.67860416729092
883.508581778593.286410316788283.73075324039173
893.51072722323753.235943196426653.78551125004836
903.512872667885013.182743369413693.84300196635632
913.515018112532513.126813633667443.90322259139757
923.517163557180013.068205168784123.96612194557589
933.519309001827513.006987435792054.03163056786297
943.521454446475012.943235407556084.09967348539393
953.523599891122512.877023889127094.17017589311793
963.525745335770012.808424990871964.24306568066806



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')