Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 25 May 2015 13:22:57 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/May/25/t14325566065n5wodc7msdqr68.htm/, Retrieved Tue, 07 May 2024 10:15:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279336, Retrieved Tue, 07 May 2024 10:15:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact88
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [exponential smoot...] [2015-05-22 08:44:26] [25b4a943aa82de9a987df483758b2d1e]
- R PD    [Exponential Smoothing] [exponential smoot...] [2015-05-25 12:22:57] [bc7b6c6baf6d03f57c49dbed118965bb] [Current]
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Dataseries X:
6.81
6.80
6.80
6.85
6.85
6.85
6.85
6.85
6.85
6.86
6.86
6.88
6.88
6.88
6.91
6.91
6.91
6.91
6.99
6.99
6.99
7.02
7.02
7.05
7.05
7.05
7.05
7.10
7.10
7.10
7.10
7.12
7.13
7.18
7.24
7.24
7.24
7.27
7.27
7.27
7.27
7.30
7.30
7.57
7.76
7.94
7.94
7.96
7.96
7.98
7.99
8.00
8.00
8.04
8.04
8.04
8.04
8.04
8.07
8.07
8.07
8.07
8.11
8.11
8.11
8.12
8.11
8.13
8.15
8.16
8.20
8.20
8.20
8.20
8.23
8.25
8.26
8.31
8.33
8.33
8.36
8.39
8.41
8.50
8.58
8.58
8.66
8.67
8.70
8.71
8.73
8.75
8.76
8.76
8.77
8.78




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279336&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279336&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279336&T=0

As an alternative you can also use a QR Code:  

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

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







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.403340106152584
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.403340106152584 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279336&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]0.403340106152584[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279336&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279336&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
beta0.403340106152584
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
36.86.790.00999999999999979
46.856.794033401061530.0559665989384737
56.856.86660697501837-0.0166069750183695
66.856.85990871595159-0.00990871595158715
76.856.85591213340784-0.00591213340783803
86.856.85352753289153-0.00352753289153274
96.856.8521047374006-0.00210473740060468
106.866.851255812394020.00874418760597884
116.866.86478269395124-0.00478269395123565
126.886.862853641665250.0171463583347506
136.886.88976945565612-0.00976945565611764
146.886.88582904237473-0.00582904237472626
156.916.883477955804540.0265220441954641
166.916.92417535992572-0.0141753599257184
176.916.91845786874853-0.00845786874852816
186.916.91504647106967-0.00504647106967226
196.996.913011026892730.0769889731072659
206.997.0240637674784-0.0340637674783979
216.997.0103244838877-0.0203244838877037
227.027.002126804398940.0178731956010587
237.027.03933578100996-0.0193357810099579
247.057.031536885044860.018463114955142
257.057.06898379979077-0.0189837997907727
267.057.06132687196798-0.0113268719679827
277.057.05675829022604-0.00675829022604013
287.17.054032400728860.0459675992711404
297.17.12257297709846-0.0225729770984602
307.17.11346839011939-0.0134683901193879
317.17.10803604821893-0.008036048218929
327.127.104794787677260.0152052123227415
337.137.13092765962959-0.000927659629586408
347.187.140553497296120.0394465027038846
357.247.206463853884050.033536146115952
367.247.2799903266184-0.0399903266184047
377.247.26386062403506-0.023860624035061
387.277.254236677403890.0157633225961069
397.277.29059465761312-0.020594657613124
407.277.28228800622527-0.0122880062252699
417.277.27733176048997-0.00733176048996587
427.37.274374567435660.0256254325643424
437.37.31471033212637-0.0147103321263655
447.577.308777065204980.261222934795023
457.767.684138751454690.0758612485453076
467.947.904736635495820.0352633645041767
477.948.09895976467824-0.158959764678236
487.968.03484491631893-0.0748449163189262
497.968.02465695982587-0.0646569598258688
507.987.9985782147862-0.0185782147861993
517.998.01108487566221-0.0210848756622095
5288.0125804996744-0.0125804996743994
5388.01750627960027-0.0175062796002745
548.048.010445294927960.0295547050720355
558.048.06236589280902-0.0223658928090256
568.048.05334483122924-0.0133448312292366
578.048.04796232558465-0.00796232558464816
588.048.04475080033811-0.00475080033811537
598.078.042834612025430.0271653879745717
608.078.08379150249477-0.0137915024947688
618.078.07822883641453-0.00822883641452599
628.078.07490981666158-0.00490981666157886
638.118.072929490688110.0370705093118922
648.118.1278815138491-0.0178815138490958
658.118.12066918215503-0.0106691821550324
668.128.116365873092060.0036341269079383
678.118.12783166222488-0.0178316622248804
688.138.110639437690220.0193605623097817
698.158.138448328947420.0115516710525778
708.168.16310758117601-0.00310758117600862
718.28.17185416905460.0281458309453999
728.28.22320651149587-0.0232065114958697
738.28.21384639468569-0.0138463946856948
748.28.20826158838334-0.0082615883833359
758.238.204929358447810.0250706415521886
768.258.245041353672790.00495864632721421
778.268.26704137460878-0.00704137460877696
788.318.274201305826610.0357986941733888
798.338.33864035493463-0.00864035493463078
808.338.3551553532581-0.0251553532580999
818.368.345009190404670.0149908095953268
828.398.381055585138160.00894441486183695
838.418.41466322637801-0.00466322637801042
848.58.432782360155690.0672176398443103
858.588.549893930145820.0301060698541793
868.588.64203691555664-0.0620369155566429
878.668.617014939450650.042985060549352
888.678.7143525383356-0.0443525383355983
898.78.70646338081518-0.00646338081518216
908.718.73385644011108-0.0238564401110803
918.738.73423418102426-0.00423418102425543
928.758.75252636600046-0.0025263660004633
938.768.77150738126966-0.0115073812696558
948.768.77686599288681-0.0168659928868138
958.778.77006326152548-6.32615254776425e-05
968.788.78003774561508-3.77456150761901e-05

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 6.8 & 6.79 & 0.00999999999999979 \tabularnewline
4 & 6.85 & 6.79403340106153 & 0.0559665989384737 \tabularnewline
5 & 6.85 & 6.86660697501837 & -0.0166069750183695 \tabularnewline
6 & 6.85 & 6.85990871595159 & -0.00990871595158715 \tabularnewline
7 & 6.85 & 6.85591213340784 & -0.00591213340783803 \tabularnewline
8 & 6.85 & 6.85352753289153 & -0.00352753289153274 \tabularnewline
9 & 6.85 & 6.8521047374006 & -0.00210473740060468 \tabularnewline
10 & 6.86 & 6.85125581239402 & 0.00874418760597884 \tabularnewline
11 & 6.86 & 6.86478269395124 & -0.00478269395123565 \tabularnewline
12 & 6.88 & 6.86285364166525 & 0.0171463583347506 \tabularnewline
13 & 6.88 & 6.88976945565612 & -0.00976945565611764 \tabularnewline
14 & 6.88 & 6.88582904237473 & -0.00582904237472626 \tabularnewline
15 & 6.91 & 6.88347795580454 & 0.0265220441954641 \tabularnewline
16 & 6.91 & 6.92417535992572 & -0.0141753599257184 \tabularnewline
17 & 6.91 & 6.91845786874853 & -0.00845786874852816 \tabularnewline
18 & 6.91 & 6.91504647106967 & -0.00504647106967226 \tabularnewline
19 & 6.99 & 6.91301102689273 & 0.0769889731072659 \tabularnewline
20 & 6.99 & 7.0240637674784 & -0.0340637674783979 \tabularnewline
21 & 6.99 & 7.0103244838877 & -0.0203244838877037 \tabularnewline
22 & 7.02 & 7.00212680439894 & 0.0178731956010587 \tabularnewline
23 & 7.02 & 7.03933578100996 & -0.0193357810099579 \tabularnewline
24 & 7.05 & 7.03153688504486 & 0.018463114955142 \tabularnewline
25 & 7.05 & 7.06898379979077 & -0.0189837997907727 \tabularnewline
26 & 7.05 & 7.06132687196798 & -0.0113268719679827 \tabularnewline
27 & 7.05 & 7.05675829022604 & -0.00675829022604013 \tabularnewline
28 & 7.1 & 7.05403240072886 & 0.0459675992711404 \tabularnewline
29 & 7.1 & 7.12257297709846 & -0.0225729770984602 \tabularnewline
30 & 7.1 & 7.11346839011939 & -0.0134683901193879 \tabularnewline
31 & 7.1 & 7.10803604821893 & -0.008036048218929 \tabularnewline
32 & 7.12 & 7.10479478767726 & 0.0152052123227415 \tabularnewline
33 & 7.13 & 7.13092765962959 & -0.000927659629586408 \tabularnewline
34 & 7.18 & 7.14055349729612 & 0.0394465027038846 \tabularnewline
35 & 7.24 & 7.20646385388405 & 0.033536146115952 \tabularnewline
36 & 7.24 & 7.2799903266184 & -0.0399903266184047 \tabularnewline
37 & 7.24 & 7.26386062403506 & -0.023860624035061 \tabularnewline
38 & 7.27 & 7.25423667740389 & 0.0157633225961069 \tabularnewline
39 & 7.27 & 7.29059465761312 & -0.020594657613124 \tabularnewline
40 & 7.27 & 7.28228800622527 & -0.0122880062252699 \tabularnewline
41 & 7.27 & 7.27733176048997 & -0.00733176048996587 \tabularnewline
42 & 7.3 & 7.27437456743566 & 0.0256254325643424 \tabularnewline
43 & 7.3 & 7.31471033212637 & -0.0147103321263655 \tabularnewline
44 & 7.57 & 7.30877706520498 & 0.261222934795023 \tabularnewline
45 & 7.76 & 7.68413875145469 & 0.0758612485453076 \tabularnewline
46 & 7.94 & 7.90473663549582 & 0.0352633645041767 \tabularnewline
47 & 7.94 & 8.09895976467824 & -0.158959764678236 \tabularnewline
48 & 7.96 & 8.03484491631893 & -0.0748449163189262 \tabularnewline
49 & 7.96 & 8.02465695982587 & -0.0646569598258688 \tabularnewline
50 & 7.98 & 7.9985782147862 & -0.0185782147861993 \tabularnewline
51 & 7.99 & 8.01108487566221 & -0.0210848756622095 \tabularnewline
52 & 8 & 8.0125804996744 & -0.0125804996743994 \tabularnewline
53 & 8 & 8.01750627960027 & -0.0175062796002745 \tabularnewline
54 & 8.04 & 8.01044529492796 & 0.0295547050720355 \tabularnewline
55 & 8.04 & 8.06236589280902 & -0.0223658928090256 \tabularnewline
56 & 8.04 & 8.05334483122924 & -0.0133448312292366 \tabularnewline
57 & 8.04 & 8.04796232558465 & -0.00796232558464816 \tabularnewline
58 & 8.04 & 8.04475080033811 & -0.00475080033811537 \tabularnewline
59 & 8.07 & 8.04283461202543 & 0.0271653879745717 \tabularnewline
60 & 8.07 & 8.08379150249477 & -0.0137915024947688 \tabularnewline
61 & 8.07 & 8.07822883641453 & -0.00822883641452599 \tabularnewline
62 & 8.07 & 8.07490981666158 & -0.00490981666157886 \tabularnewline
63 & 8.11 & 8.07292949068811 & 0.0370705093118922 \tabularnewline
64 & 8.11 & 8.1278815138491 & -0.0178815138490958 \tabularnewline
65 & 8.11 & 8.12066918215503 & -0.0106691821550324 \tabularnewline
66 & 8.12 & 8.11636587309206 & 0.0036341269079383 \tabularnewline
67 & 8.11 & 8.12783166222488 & -0.0178316622248804 \tabularnewline
68 & 8.13 & 8.11063943769022 & 0.0193605623097817 \tabularnewline
69 & 8.15 & 8.13844832894742 & 0.0115516710525778 \tabularnewline
70 & 8.16 & 8.16310758117601 & -0.00310758117600862 \tabularnewline
71 & 8.2 & 8.1718541690546 & 0.0281458309453999 \tabularnewline
72 & 8.2 & 8.22320651149587 & -0.0232065114958697 \tabularnewline
73 & 8.2 & 8.21384639468569 & -0.0138463946856948 \tabularnewline
74 & 8.2 & 8.20826158838334 & -0.0082615883833359 \tabularnewline
75 & 8.23 & 8.20492935844781 & 0.0250706415521886 \tabularnewline
76 & 8.25 & 8.24504135367279 & 0.00495864632721421 \tabularnewline
77 & 8.26 & 8.26704137460878 & -0.00704137460877696 \tabularnewline
78 & 8.31 & 8.27420130582661 & 0.0357986941733888 \tabularnewline
79 & 8.33 & 8.33864035493463 & -0.00864035493463078 \tabularnewline
80 & 8.33 & 8.3551553532581 & -0.0251553532580999 \tabularnewline
81 & 8.36 & 8.34500919040467 & 0.0149908095953268 \tabularnewline
82 & 8.39 & 8.38105558513816 & 0.00894441486183695 \tabularnewline
83 & 8.41 & 8.41466322637801 & -0.00466322637801042 \tabularnewline
84 & 8.5 & 8.43278236015569 & 0.0672176398443103 \tabularnewline
85 & 8.58 & 8.54989393014582 & 0.0301060698541793 \tabularnewline
86 & 8.58 & 8.64203691555664 & -0.0620369155566429 \tabularnewline
87 & 8.66 & 8.61701493945065 & 0.042985060549352 \tabularnewline
88 & 8.67 & 8.7143525383356 & -0.0443525383355983 \tabularnewline
89 & 8.7 & 8.70646338081518 & -0.00646338081518216 \tabularnewline
90 & 8.71 & 8.73385644011108 & -0.0238564401110803 \tabularnewline
91 & 8.73 & 8.73423418102426 & -0.00423418102425543 \tabularnewline
92 & 8.75 & 8.75252636600046 & -0.0025263660004633 \tabularnewline
93 & 8.76 & 8.77150738126966 & -0.0115073812696558 \tabularnewline
94 & 8.76 & 8.77686599288681 & -0.0168659928868138 \tabularnewline
95 & 8.77 & 8.77006326152548 & -6.32615254776425e-05 \tabularnewline
96 & 8.78 & 8.78003774561508 & -3.77456150761901e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279336&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]6.8[/C][C]6.79[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]4[/C][C]6.85[/C][C]6.79403340106153[/C][C]0.0559665989384737[/C][/ROW]
[ROW][C]5[/C][C]6.85[/C][C]6.86660697501837[/C][C]-0.0166069750183695[/C][/ROW]
[ROW][C]6[/C][C]6.85[/C][C]6.85990871595159[/C][C]-0.00990871595158715[/C][/ROW]
[ROW][C]7[/C][C]6.85[/C][C]6.85591213340784[/C][C]-0.00591213340783803[/C][/ROW]
[ROW][C]8[/C][C]6.85[/C][C]6.85352753289153[/C][C]-0.00352753289153274[/C][/ROW]
[ROW][C]9[/C][C]6.85[/C][C]6.8521047374006[/C][C]-0.00210473740060468[/C][/ROW]
[ROW][C]10[/C][C]6.86[/C][C]6.85125581239402[/C][C]0.00874418760597884[/C][/ROW]
[ROW][C]11[/C][C]6.86[/C][C]6.86478269395124[/C][C]-0.00478269395123565[/C][/ROW]
[ROW][C]12[/C][C]6.88[/C][C]6.86285364166525[/C][C]0.0171463583347506[/C][/ROW]
[ROW][C]13[/C][C]6.88[/C][C]6.88976945565612[/C][C]-0.00976945565611764[/C][/ROW]
[ROW][C]14[/C][C]6.88[/C][C]6.88582904237473[/C][C]-0.00582904237472626[/C][/ROW]
[ROW][C]15[/C][C]6.91[/C][C]6.88347795580454[/C][C]0.0265220441954641[/C][/ROW]
[ROW][C]16[/C][C]6.91[/C][C]6.92417535992572[/C][C]-0.0141753599257184[/C][/ROW]
[ROW][C]17[/C][C]6.91[/C][C]6.91845786874853[/C][C]-0.00845786874852816[/C][/ROW]
[ROW][C]18[/C][C]6.91[/C][C]6.91504647106967[/C][C]-0.00504647106967226[/C][/ROW]
[ROW][C]19[/C][C]6.99[/C][C]6.91301102689273[/C][C]0.0769889731072659[/C][/ROW]
[ROW][C]20[/C][C]6.99[/C][C]7.0240637674784[/C][C]-0.0340637674783979[/C][/ROW]
[ROW][C]21[/C][C]6.99[/C][C]7.0103244838877[/C][C]-0.0203244838877037[/C][/ROW]
[ROW][C]22[/C][C]7.02[/C][C]7.00212680439894[/C][C]0.0178731956010587[/C][/ROW]
[ROW][C]23[/C][C]7.02[/C][C]7.03933578100996[/C][C]-0.0193357810099579[/C][/ROW]
[ROW][C]24[/C][C]7.05[/C][C]7.03153688504486[/C][C]0.018463114955142[/C][/ROW]
[ROW][C]25[/C][C]7.05[/C][C]7.06898379979077[/C][C]-0.0189837997907727[/C][/ROW]
[ROW][C]26[/C][C]7.05[/C][C]7.06132687196798[/C][C]-0.0113268719679827[/C][/ROW]
[ROW][C]27[/C][C]7.05[/C][C]7.05675829022604[/C][C]-0.00675829022604013[/C][/ROW]
[ROW][C]28[/C][C]7.1[/C][C]7.05403240072886[/C][C]0.0459675992711404[/C][/ROW]
[ROW][C]29[/C][C]7.1[/C][C]7.12257297709846[/C][C]-0.0225729770984602[/C][/ROW]
[ROW][C]30[/C][C]7.1[/C][C]7.11346839011939[/C][C]-0.0134683901193879[/C][/ROW]
[ROW][C]31[/C][C]7.1[/C][C]7.10803604821893[/C][C]-0.008036048218929[/C][/ROW]
[ROW][C]32[/C][C]7.12[/C][C]7.10479478767726[/C][C]0.0152052123227415[/C][/ROW]
[ROW][C]33[/C][C]7.13[/C][C]7.13092765962959[/C][C]-0.000927659629586408[/C][/ROW]
[ROW][C]34[/C][C]7.18[/C][C]7.14055349729612[/C][C]0.0394465027038846[/C][/ROW]
[ROW][C]35[/C][C]7.24[/C][C]7.20646385388405[/C][C]0.033536146115952[/C][/ROW]
[ROW][C]36[/C][C]7.24[/C][C]7.2799903266184[/C][C]-0.0399903266184047[/C][/ROW]
[ROW][C]37[/C][C]7.24[/C][C]7.26386062403506[/C][C]-0.023860624035061[/C][/ROW]
[ROW][C]38[/C][C]7.27[/C][C]7.25423667740389[/C][C]0.0157633225961069[/C][/ROW]
[ROW][C]39[/C][C]7.27[/C][C]7.29059465761312[/C][C]-0.020594657613124[/C][/ROW]
[ROW][C]40[/C][C]7.27[/C][C]7.28228800622527[/C][C]-0.0122880062252699[/C][/ROW]
[ROW][C]41[/C][C]7.27[/C][C]7.27733176048997[/C][C]-0.00733176048996587[/C][/ROW]
[ROW][C]42[/C][C]7.3[/C][C]7.27437456743566[/C][C]0.0256254325643424[/C][/ROW]
[ROW][C]43[/C][C]7.3[/C][C]7.31471033212637[/C][C]-0.0147103321263655[/C][/ROW]
[ROW][C]44[/C][C]7.57[/C][C]7.30877706520498[/C][C]0.261222934795023[/C][/ROW]
[ROW][C]45[/C][C]7.76[/C][C]7.68413875145469[/C][C]0.0758612485453076[/C][/ROW]
[ROW][C]46[/C][C]7.94[/C][C]7.90473663549582[/C][C]0.0352633645041767[/C][/ROW]
[ROW][C]47[/C][C]7.94[/C][C]8.09895976467824[/C][C]-0.158959764678236[/C][/ROW]
[ROW][C]48[/C][C]7.96[/C][C]8.03484491631893[/C][C]-0.0748449163189262[/C][/ROW]
[ROW][C]49[/C][C]7.96[/C][C]8.02465695982587[/C][C]-0.0646569598258688[/C][/ROW]
[ROW][C]50[/C][C]7.98[/C][C]7.9985782147862[/C][C]-0.0185782147861993[/C][/ROW]
[ROW][C]51[/C][C]7.99[/C][C]8.01108487566221[/C][C]-0.0210848756622095[/C][/ROW]
[ROW][C]52[/C][C]8[/C][C]8.0125804996744[/C][C]-0.0125804996743994[/C][/ROW]
[ROW][C]53[/C][C]8[/C][C]8.01750627960027[/C][C]-0.0175062796002745[/C][/ROW]
[ROW][C]54[/C][C]8.04[/C][C]8.01044529492796[/C][C]0.0295547050720355[/C][/ROW]
[ROW][C]55[/C][C]8.04[/C][C]8.06236589280902[/C][C]-0.0223658928090256[/C][/ROW]
[ROW][C]56[/C][C]8.04[/C][C]8.05334483122924[/C][C]-0.0133448312292366[/C][/ROW]
[ROW][C]57[/C][C]8.04[/C][C]8.04796232558465[/C][C]-0.00796232558464816[/C][/ROW]
[ROW][C]58[/C][C]8.04[/C][C]8.04475080033811[/C][C]-0.00475080033811537[/C][/ROW]
[ROW][C]59[/C][C]8.07[/C][C]8.04283461202543[/C][C]0.0271653879745717[/C][/ROW]
[ROW][C]60[/C][C]8.07[/C][C]8.08379150249477[/C][C]-0.0137915024947688[/C][/ROW]
[ROW][C]61[/C][C]8.07[/C][C]8.07822883641453[/C][C]-0.00822883641452599[/C][/ROW]
[ROW][C]62[/C][C]8.07[/C][C]8.07490981666158[/C][C]-0.00490981666157886[/C][/ROW]
[ROW][C]63[/C][C]8.11[/C][C]8.07292949068811[/C][C]0.0370705093118922[/C][/ROW]
[ROW][C]64[/C][C]8.11[/C][C]8.1278815138491[/C][C]-0.0178815138490958[/C][/ROW]
[ROW][C]65[/C][C]8.11[/C][C]8.12066918215503[/C][C]-0.0106691821550324[/C][/ROW]
[ROW][C]66[/C][C]8.12[/C][C]8.11636587309206[/C][C]0.0036341269079383[/C][/ROW]
[ROW][C]67[/C][C]8.11[/C][C]8.12783166222488[/C][C]-0.0178316622248804[/C][/ROW]
[ROW][C]68[/C][C]8.13[/C][C]8.11063943769022[/C][C]0.0193605623097817[/C][/ROW]
[ROW][C]69[/C][C]8.15[/C][C]8.13844832894742[/C][C]0.0115516710525778[/C][/ROW]
[ROW][C]70[/C][C]8.16[/C][C]8.16310758117601[/C][C]-0.00310758117600862[/C][/ROW]
[ROW][C]71[/C][C]8.2[/C][C]8.1718541690546[/C][C]0.0281458309453999[/C][/ROW]
[ROW][C]72[/C][C]8.2[/C][C]8.22320651149587[/C][C]-0.0232065114958697[/C][/ROW]
[ROW][C]73[/C][C]8.2[/C][C]8.21384639468569[/C][C]-0.0138463946856948[/C][/ROW]
[ROW][C]74[/C][C]8.2[/C][C]8.20826158838334[/C][C]-0.0082615883833359[/C][/ROW]
[ROW][C]75[/C][C]8.23[/C][C]8.20492935844781[/C][C]0.0250706415521886[/C][/ROW]
[ROW][C]76[/C][C]8.25[/C][C]8.24504135367279[/C][C]0.00495864632721421[/C][/ROW]
[ROW][C]77[/C][C]8.26[/C][C]8.26704137460878[/C][C]-0.00704137460877696[/C][/ROW]
[ROW][C]78[/C][C]8.31[/C][C]8.27420130582661[/C][C]0.0357986941733888[/C][/ROW]
[ROW][C]79[/C][C]8.33[/C][C]8.33864035493463[/C][C]-0.00864035493463078[/C][/ROW]
[ROW][C]80[/C][C]8.33[/C][C]8.3551553532581[/C][C]-0.0251553532580999[/C][/ROW]
[ROW][C]81[/C][C]8.36[/C][C]8.34500919040467[/C][C]0.0149908095953268[/C][/ROW]
[ROW][C]82[/C][C]8.39[/C][C]8.38105558513816[/C][C]0.00894441486183695[/C][/ROW]
[ROW][C]83[/C][C]8.41[/C][C]8.41466322637801[/C][C]-0.00466322637801042[/C][/ROW]
[ROW][C]84[/C][C]8.5[/C][C]8.43278236015569[/C][C]0.0672176398443103[/C][/ROW]
[ROW][C]85[/C][C]8.58[/C][C]8.54989393014582[/C][C]0.0301060698541793[/C][/ROW]
[ROW][C]86[/C][C]8.58[/C][C]8.64203691555664[/C][C]-0.0620369155566429[/C][/ROW]
[ROW][C]87[/C][C]8.66[/C][C]8.61701493945065[/C][C]0.042985060549352[/C][/ROW]
[ROW][C]88[/C][C]8.67[/C][C]8.7143525383356[/C][C]-0.0443525383355983[/C][/ROW]
[ROW][C]89[/C][C]8.7[/C][C]8.70646338081518[/C][C]-0.00646338081518216[/C][/ROW]
[ROW][C]90[/C][C]8.71[/C][C]8.73385644011108[/C][C]-0.0238564401110803[/C][/ROW]
[ROW][C]91[/C][C]8.73[/C][C]8.73423418102426[/C][C]-0.00423418102425543[/C][/ROW]
[ROW][C]92[/C][C]8.75[/C][C]8.75252636600046[/C][C]-0.0025263660004633[/C][/ROW]
[ROW][C]93[/C][C]8.76[/C][C]8.77150738126966[/C][C]-0.0115073812696558[/C][/ROW]
[ROW][C]94[/C][C]8.76[/C][C]8.77686599288681[/C][C]-0.0168659928868138[/C][/ROW]
[ROW][C]95[/C][C]8.77[/C][C]8.77006326152548[/C][C]-6.32615254776425e-05[/C][/ROW]
[ROW][C]96[/C][C]8.78[/C][C]8.78003774561508[/C][C]-3.77456150761901e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279336&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279336&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
36.86.790.00999999999999979
46.856.794033401061530.0559665989384737
56.856.86660697501837-0.0166069750183695
66.856.85990871595159-0.00990871595158715
76.856.85591213340784-0.00591213340783803
86.856.85352753289153-0.00352753289153274
96.856.8521047374006-0.00210473740060468
106.866.851255812394020.00874418760597884
116.866.86478269395124-0.00478269395123565
126.886.862853641665250.0171463583347506
136.886.88976945565612-0.00976945565611764
146.886.88582904237473-0.00582904237472626
156.916.883477955804540.0265220441954641
166.916.92417535992572-0.0141753599257184
176.916.91845786874853-0.00845786874852816
186.916.91504647106967-0.00504647106967226
196.996.913011026892730.0769889731072659
206.997.0240637674784-0.0340637674783979
216.997.0103244838877-0.0203244838877037
227.027.002126804398940.0178731956010587
237.027.03933578100996-0.0193357810099579
247.057.031536885044860.018463114955142
257.057.06898379979077-0.0189837997907727
267.057.06132687196798-0.0113268719679827
277.057.05675829022604-0.00675829022604013
287.17.054032400728860.0459675992711404
297.17.12257297709846-0.0225729770984602
307.17.11346839011939-0.0134683901193879
317.17.10803604821893-0.008036048218929
327.127.104794787677260.0152052123227415
337.137.13092765962959-0.000927659629586408
347.187.140553497296120.0394465027038846
357.247.206463853884050.033536146115952
367.247.2799903266184-0.0399903266184047
377.247.26386062403506-0.023860624035061
387.277.254236677403890.0157633225961069
397.277.29059465761312-0.020594657613124
407.277.28228800622527-0.0122880062252699
417.277.27733176048997-0.00733176048996587
427.37.274374567435660.0256254325643424
437.37.31471033212637-0.0147103321263655
447.577.308777065204980.261222934795023
457.767.684138751454690.0758612485453076
467.947.904736635495820.0352633645041767
477.948.09895976467824-0.158959764678236
487.968.03484491631893-0.0748449163189262
497.968.02465695982587-0.0646569598258688
507.987.9985782147862-0.0185782147861993
517.998.01108487566221-0.0210848756622095
5288.0125804996744-0.0125804996743994
5388.01750627960027-0.0175062796002745
548.048.010445294927960.0295547050720355
558.048.06236589280902-0.0223658928090256
568.048.05334483122924-0.0133448312292366
578.048.04796232558465-0.00796232558464816
588.048.04475080033811-0.00475080033811537
598.078.042834612025430.0271653879745717
608.078.08379150249477-0.0137915024947688
618.078.07822883641453-0.00822883641452599
628.078.07490981666158-0.00490981666157886
638.118.072929490688110.0370705093118922
648.118.1278815138491-0.0178815138490958
658.118.12066918215503-0.0106691821550324
668.128.116365873092060.0036341269079383
678.118.12783166222488-0.0178316622248804
688.138.110639437690220.0193605623097817
698.158.138448328947420.0115516710525778
708.168.16310758117601-0.00310758117600862
718.28.17185416905460.0281458309453999
728.28.22320651149587-0.0232065114958697
738.28.21384639468569-0.0138463946856948
748.28.20826158838334-0.0082615883833359
758.238.204929358447810.0250706415521886
768.258.245041353672790.00495864632721421
778.268.26704137460878-0.00704137460877696
788.318.274201305826610.0357986941733888
798.338.33864035493463-0.00864035493463078
808.338.3551553532581-0.0251553532580999
818.368.345009190404670.0149908095953268
828.398.381055585138160.00894441486183695
838.418.41466322637801-0.00466322637801042
848.58.432782360155690.0672176398443103
858.588.549893930145820.0301060698541793
868.588.64203691555664-0.0620369155566429
878.668.617014939450650.042985060549352
888.678.7143525383356-0.0443525383355983
898.78.70646338081518-0.00646338081518216
908.718.73385644011108-0.0238564401110803
918.738.73423418102426-0.00423418102425543
928.758.75252636600046-0.0025263660004633
938.768.77150738126966-0.0115073812696558
948.768.77686599288681-0.0168659928868138
958.778.77006326152548-6.32615254776425e-05
968.788.78003774561508-3.77456150761901e-05







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
978.790022521294688.708846490829048.87119855176032
988.800045042589378.660163797329748.939926287849
998.810067563884058.60739624724529.0127388805229
1008.820090085178748.549423749280039.09075642107745
1018.830112606473428.486216416895879.17400879605097
1028.840135127768118.417959036465029.26231121907119
1038.850157649062798.344877061662829.35543823646276
1048.860180170357488.267191075145499.45316926556946
1058.870202691652168.185104556194469.55530082710986
1068.880225212946858.098801733306289.66164869258741
1078.890247734241538.008448617068789.77204685141428
1088.900270255536217.914194924349369.88634558672307

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 8.79002252129468 & 8.70884649082904 & 8.87119855176032 \tabularnewline
98 & 8.80004504258937 & 8.66016379732974 & 8.939926287849 \tabularnewline
99 & 8.81006756388405 & 8.6073962472452 & 9.0127388805229 \tabularnewline
100 & 8.82009008517874 & 8.54942374928003 & 9.09075642107745 \tabularnewline
101 & 8.83011260647342 & 8.48621641689587 & 9.17400879605097 \tabularnewline
102 & 8.84013512776811 & 8.41795903646502 & 9.26231121907119 \tabularnewline
103 & 8.85015764906279 & 8.34487706166282 & 9.35543823646276 \tabularnewline
104 & 8.86018017035748 & 8.26719107514549 & 9.45316926556946 \tabularnewline
105 & 8.87020269165216 & 8.18510455619446 & 9.55530082710986 \tabularnewline
106 & 8.88022521294685 & 8.09880173330628 & 9.66164869258741 \tabularnewline
107 & 8.89024773424153 & 8.00844861706878 & 9.77204685141428 \tabularnewline
108 & 8.90027025553621 & 7.91419492434936 & 9.88634558672307 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279336&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]97[/C][C]8.79002252129468[/C][C]8.70884649082904[/C][C]8.87119855176032[/C][/ROW]
[ROW][C]98[/C][C]8.80004504258937[/C][C]8.66016379732974[/C][C]8.939926287849[/C][/ROW]
[ROW][C]99[/C][C]8.81006756388405[/C][C]8.6073962472452[/C][C]9.0127388805229[/C][/ROW]
[ROW][C]100[/C][C]8.82009008517874[/C][C]8.54942374928003[/C][C]9.09075642107745[/C][/ROW]
[ROW][C]101[/C][C]8.83011260647342[/C][C]8.48621641689587[/C][C]9.17400879605097[/C][/ROW]
[ROW][C]102[/C][C]8.84013512776811[/C][C]8.41795903646502[/C][C]9.26231121907119[/C][/ROW]
[ROW][C]103[/C][C]8.85015764906279[/C][C]8.34487706166282[/C][C]9.35543823646276[/C][/ROW]
[ROW][C]104[/C][C]8.86018017035748[/C][C]8.26719107514549[/C][C]9.45316926556946[/C][/ROW]
[ROW][C]105[/C][C]8.87020269165216[/C][C]8.18510455619446[/C][C]9.55530082710986[/C][/ROW]
[ROW][C]106[/C][C]8.88022521294685[/C][C]8.09880173330628[/C][C]9.66164869258741[/C][/ROW]
[ROW][C]107[/C][C]8.89024773424153[/C][C]8.00844861706878[/C][C]9.77204685141428[/C][/ROW]
[ROW][C]108[/C][C]8.90027025553621[/C][C]7.91419492434936[/C][C]9.88634558672307[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279336&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279336&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
978.790022521294688.708846490829048.87119855176032
988.800045042589378.660163797329748.939926287849
998.810067563884058.60739624724529.0127388805229
1008.820090085178748.549423749280039.09075642107745
1018.830112606473428.486216416895879.17400879605097
1028.840135127768118.417959036465029.26231121907119
1038.850157649062798.344877061662829.35543823646276
1048.860180170357488.267191075145499.45316926556946
1058.870202691652168.185104556194469.55530082710986
1068.880225212946858.098801733306289.66164869258741
1078.890247734241538.008448617068789.77204685141428
1088.900270255536217.914194924349369.88634558672307



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = additive ;
R code (references can be found in the software module):
par3 <- 'additive'
par2 <- 'Double'
par1 <- '12'
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')