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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 13 Dec 2013 06:48:41 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Dec/13/t1386935437m3gvgsnt2hatgqe.htm/, Retrieved Tue, 19 Nov 2019 08:32:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232289, Retrieved Tue, 19 Nov 2019 08:32:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact43
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-12-13 11:48:41] [1119827e5d0f83abb0d596f998785bb9] [Current]
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Dataseries X:
10,92
10,98
11,15
11,19
11,33
11,38
11,4
11,45
11,56
11,61
11,82
11,77
11,85
11,82
11,92
11,86
11,87
11,94
11,86
11,92
11,83
11,91
11,93
11,99
11,96
12,12
11,85
12,01
12,1
12,21
12,31
12,31
12,39
12,35
12,41
12,51
12,27
12,51
12,44
12,47
12,51
12,58
12,5
12,52
12,59
12,51
12,67
12,64
12,54
12,6
12,67
12,62
12,72
12,85
12,85
12,82
12,79
12,94
12,71
12,56
12,64
12,7
12,74
12,85
12,84
12,83
12,88
13,07
12,99
13,2
13,23
13,18
13,18
13,1
13,23
13,33
13,38
13,26
13,17
13,27
13,47
13,63
13,64
13,69




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232289&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232289&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232289&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 time5 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.884388798124206
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.884388798124206 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232289&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]0.884388798124206[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232289&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232289&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
alpha0.884388798124206
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
210.9810.920.0600000000000005
311.1510.97306332788750.176936672112548
411.1911.12954413868120.0604558613188342
511.3311.18301062521250.146989374787507
611.3811.31300638171780.0669936182821562
711.411.37225478727240.0277452127276074
811.4511.39679234261030.0532076573897378
911.5611.44384859878020.116151401219824
1011.6111.54657159690540.06342840309458
1111.8211.60266696608520.217333033914828
1211.7711.7948738667418-0.0248738667417943
1311.8511.77287569762930.0771243023706827
1411.8211.8410835667091-0.0210835667090929
1511.9211.82243749648710.0975625035129326
1611.8611.9087206817109-0.0487206817108596
1711.8711.86563265656880.00436734343120015
1811.9411.86949508617690.0705049138230862
1911.8611.9318488421748-0.071848842174763
2011.9211.86830653099720.0516934690027924
2111.8311.9140236559195-0.0840236559194576
2211.9111.83971407584680.0702859241531542
2311.9311.90187415983370.0281258401662967
2411.9911.92674833781460.063251662185392
2511.9611.9826873993141-0.0226873993141048
2612.1211.96262291750210.15737708249786
2711.8512.1018054463447-0.251805446344717
2812.0111.87911153029080.130888469709216
2912.111.99486782670520.105132173294766
3012.2112.08784554308960.122154456910424
3112.3112.19587757642210.114122423577898
3212.3112.29680616944920.0131938305508186
3312.3912.30847464539270.0815253546073258
3412.3512.3805747557705-0.0305747557704983
3512.4112.35353478426170.0564652157383136
3612.5112.40347198854430.106528011455682
3712.2712.4976841685622-0.22768416856217
3812.5112.29632284037560.213677159624437
3912.4412.4852965267624-0.0452965267624137
4012.4712.44523678589980.024763214100199
4112.5112.46713709505560.04286290494443
4212.5812.50504456804350.0749554319565142
4312.512.5713343124244-0.0713343124243888
4412.5212.50824704559440.0117529544056332
4512.5912.51864122681560.0713587731844267
4612.5112.5817501264678-0.0717501264677658
4712.6712.51829511835570.151704881644321
4812.6412.6524612163027-0.0124612163026736
4912.5412.6414406561936-0.101440656193589
5012.612.55172767618160.0482723238183898
5112.6712.5944191786260.0755808213739826
5212.6212.6612620104022-0.0412620104021943
5312.7212.62477035061440.0952296493855922
5412.8512.70899038578030.141009614219678
5512.8512.8336977090240.0163022909759789
5612.8212.8481152725469-0.0281152725469376
5712.7912.8232504404502-0.0332504404502174
5812.9412.79384412338330.146155876616652
5912.7112.9231027434431-0.213102743443137
6012.5612.7346370642925-0.17463706429249
6112.6412.58019000089490.0598099991050844
6212.712.63308529411930.0669147058807269
6312.7412.692263910430.0477360895700372
6412.8512.7344811733120.115518826688042
6512.8412.83664472960730.0033552703926869
6612.8312.8396120931573-0.0096120931572834
6712.8812.83111126564250.0488887343575453
6813.0712.87434791466270.195652085337262
6912.9913.0473804272647-0.0573804272646541
7013.212.99663382016020.203366179839787
7113.2313.17648859152780.0535114084721684
7213.1813.2238134817525-0.0438134817524674
7313.1813.1850653292838-0.00506532928376657
7413.113.1805856088064-0.080585608806393
7513.2313.1093165990880.120683400912002
7613.3313.21604764697410.113952353025894
7713.3813.31682583151010.0631741684898994
7813.2613.3726963584534-0.11269635845338
7913.1713.2730289614478-0.103028961447821
8013.2713.1819113020610.0880886979390016
8113.4713.25981595975960.210184040240403
8213.6313.44570037049270.184299629507302
8313.6413.60869289832740.0313071016726028
8413.6913.63638054834840.0536194516516169

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 10.98 & 10.92 & 0.0600000000000005 \tabularnewline
3 & 11.15 & 10.9730633278875 & 0.176936672112548 \tabularnewline
4 & 11.19 & 11.1295441386812 & 0.0604558613188342 \tabularnewline
5 & 11.33 & 11.1830106252125 & 0.146989374787507 \tabularnewline
6 & 11.38 & 11.3130063817178 & 0.0669936182821562 \tabularnewline
7 & 11.4 & 11.3722547872724 & 0.0277452127276074 \tabularnewline
8 & 11.45 & 11.3967923426103 & 0.0532076573897378 \tabularnewline
9 & 11.56 & 11.4438485987802 & 0.116151401219824 \tabularnewline
10 & 11.61 & 11.5465715969054 & 0.06342840309458 \tabularnewline
11 & 11.82 & 11.6026669660852 & 0.217333033914828 \tabularnewline
12 & 11.77 & 11.7948738667418 & -0.0248738667417943 \tabularnewline
13 & 11.85 & 11.7728756976293 & 0.0771243023706827 \tabularnewline
14 & 11.82 & 11.8410835667091 & -0.0210835667090929 \tabularnewline
15 & 11.92 & 11.8224374964871 & 0.0975625035129326 \tabularnewline
16 & 11.86 & 11.9087206817109 & -0.0487206817108596 \tabularnewline
17 & 11.87 & 11.8656326565688 & 0.00436734343120015 \tabularnewline
18 & 11.94 & 11.8694950861769 & 0.0705049138230862 \tabularnewline
19 & 11.86 & 11.9318488421748 & -0.071848842174763 \tabularnewline
20 & 11.92 & 11.8683065309972 & 0.0516934690027924 \tabularnewline
21 & 11.83 & 11.9140236559195 & -0.0840236559194576 \tabularnewline
22 & 11.91 & 11.8397140758468 & 0.0702859241531542 \tabularnewline
23 & 11.93 & 11.9018741598337 & 0.0281258401662967 \tabularnewline
24 & 11.99 & 11.9267483378146 & 0.063251662185392 \tabularnewline
25 & 11.96 & 11.9826873993141 & -0.0226873993141048 \tabularnewline
26 & 12.12 & 11.9626229175021 & 0.15737708249786 \tabularnewline
27 & 11.85 & 12.1018054463447 & -0.251805446344717 \tabularnewline
28 & 12.01 & 11.8791115302908 & 0.130888469709216 \tabularnewline
29 & 12.1 & 11.9948678267052 & 0.105132173294766 \tabularnewline
30 & 12.21 & 12.0878455430896 & 0.122154456910424 \tabularnewline
31 & 12.31 & 12.1958775764221 & 0.114122423577898 \tabularnewline
32 & 12.31 & 12.2968061694492 & 0.0131938305508186 \tabularnewline
33 & 12.39 & 12.3084746453927 & 0.0815253546073258 \tabularnewline
34 & 12.35 & 12.3805747557705 & -0.0305747557704983 \tabularnewline
35 & 12.41 & 12.3535347842617 & 0.0564652157383136 \tabularnewline
36 & 12.51 & 12.4034719885443 & 0.106528011455682 \tabularnewline
37 & 12.27 & 12.4976841685622 & -0.22768416856217 \tabularnewline
38 & 12.51 & 12.2963228403756 & 0.213677159624437 \tabularnewline
39 & 12.44 & 12.4852965267624 & -0.0452965267624137 \tabularnewline
40 & 12.47 & 12.4452367858998 & 0.024763214100199 \tabularnewline
41 & 12.51 & 12.4671370950556 & 0.04286290494443 \tabularnewline
42 & 12.58 & 12.5050445680435 & 0.0749554319565142 \tabularnewline
43 & 12.5 & 12.5713343124244 & -0.0713343124243888 \tabularnewline
44 & 12.52 & 12.5082470455944 & 0.0117529544056332 \tabularnewline
45 & 12.59 & 12.5186412268156 & 0.0713587731844267 \tabularnewline
46 & 12.51 & 12.5817501264678 & -0.0717501264677658 \tabularnewline
47 & 12.67 & 12.5182951183557 & 0.151704881644321 \tabularnewline
48 & 12.64 & 12.6524612163027 & -0.0124612163026736 \tabularnewline
49 & 12.54 & 12.6414406561936 & -0.101440656193589 \tabularnewline
50 & 12.6 & 12.5517276761816 & 0.0482723238183898 \tabularnewline
51 & 12.67 & 12.594419178626 & 0.0755808213739826 \tabularnewline
52 & 12.62 & 12.6612620104022 & -0.0412620104021943 \tabularnewline
53 & 12.72 & 12.6247703506144 & 0.0952296493855922 \tabularnewline
54 & 12.85 & 12.7089903857803 & 0.141009614219678 \tabularnewline
55 & 12.85 & 12.833697709024 & 0.0163022909759789 \tabularnewline
56 & 12.82 & 12.8481152725469 & -0.0281152725469376 \tabularnewline
57 & 12.79 & 12.8232504404502 & -0.0332504404502174 \tabularnewline
58 & 12.94 & 12.7938441233833 & 0.146155876616652 \tabularnewline
59 & 12.71 & 12.9231027434431 & -0.213102743443137 \tabularnewline
60 & 12.56 & 12.7346370642925 & -0.17463706429249 \tabularnewline
61 & 12.64 & 12.5801900008949 & 0.0598099991050844 \tabularnewline
62 & 12.7 & 12.6330852941193 & 0.0669147058807269 \tabularnewline
63 & 12.74 & 12.69226391043 & 0.0477360895700372 \tabularnewline
64 & 12.85 & 12.734481173312 & 0.115518826688042 \tabularnewline
65 & 12.84 & 12.8366447296073 & 0.0033552703926869 \tabularnewline
66 & 12.83 & 12.8396120931573 & -0.0096120931572834 \tabularnewline
67 & 12.88 & 12.8311112656425 & 0.0488887343575453 \tabularnewline
68 & 13.07 & 12.8743479146627 & 0.195652085337262 \tabularnewline
69 & 12.99 & 13.0473804272647 & -0.0573804272646541 \tabularnewline
70 & 13.2 & 12.9966338201602 & 0.203366179839787 \tabularnewline
71 & 13.23 & 13.1764885915278 & 0.0535114084721684 \tabularnewline
72 & 13.18 & 13.2238134817525 & -0.0438134817524674 \tabularnewline
73 & 13.18 & 13.1850653292838 & -0.00506532928376657 \tabularnewline
74 & 13.1 & 13.1805856088064 & -0.080585608806393 \tabularnewline
75 & 13.23 & 13.109316599088 & 0.120683400912002 \tabularnewline
76 & 13.33 & 13.2160476469741 & 0.113952353025894 \tabularnewline
77 & 13.38 & 13.3168258315101 & 0.0631741684898994 \tabularnewline
78 & 13.26 & 13.3726963584534 & -0.11269635845338 \tabularnewline
79 & 13.17 & 13.2730289614478 & -0.103028961447821 \tabularnewline
80 & 13.27 & 13.181911302061 & 0.0880886979390016 \tabularnewline
81 & 13.47 & 13.2598159597596 & 0.210184040240403 \tabularnewline
82 & 13.63 & 13.4457003704927 & 0.184299629507302 \tabularnewline
83 & 13.64 & 13.6086928983274 & 0.0313071016726028 \tabularnewline
84 & 13.69 & 13.6363805483484 & 0.0536194516516169 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232289&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]2[/C][C]10.98[/C][C]10.92[/C][C]0.0600000000000005[/C][/ROW]
[ROW][C]3[/C][C]11.15[/C][C]10.9730633278875[/C][C]0.176936672112548[/C][/ROW]
[ROW][C]4[/C][C]11.19[/C][C]11.1295441386812[/C][C]0.0604558613188342[/C][/ROW]
[ROW][C]5[/C][C]11.33[/C][C]11.1830106252125[/C][C]0.146989374787507[/C][/ROW]
[ROW][C]6[/C][C]11.38[/C][C]11.3130063817178[/C][C]0.0669936182821562[/C][/ROW]
[ROW][C]7[/C][C]11.4[/C][C]11.3722547872724[/C][C]0.0277452127276074[/C][/ROW]
[ROW][C]8[/C][C]11.45[/C][C]11.3967923426103[/C][C]0.0532076573897378[/C][/ROW]
[ROW][C]9[/C][C]11.56[/C][C]11.4438485987802[/C][C]0.116151401219824[/C][/ROW]
[ROW][C]10[/C][C]11.61[/C][C]11.5465715969054[/C][C]0.06342840309458[/C][/ROW]
[ROW][C]11[/C][C]11.82[/C][C]11.6026669660852[/C][C]0.217333033914828[/C][/ROW]
[ROW][C]12[/C][C]11.77[/C][C]11.7948738667418[/C][C]-0.0248738667417943[/C][/ROW]
[ROW][C]13[/C][C]11.85[/C][C]11.7728756976293[/C][C]0.0771243023706827[/C][/ROW]
[ROW][C]14[/C][C]11.82[/C][C]11.8410835667091[/C][C]-0.0210835667090929[/C][/ROW]
[ROW][C]15[/C][C]11.92[/C][C]11.8224374964871[/C][C]0.0975625035129326[/C][/ROW]
[ROW][C]16[/C][C]11.86[/C][C]11.9087206817109[/C][C]-0.0487206817108596[/C][/ROW]
[ROW][C]17[/C][C]11.87[/C][C]11.8656326565688[/C][C]0.00436734343120015[/C][/ROW]
[ROW][C]18[/C][C]11.94[/C][C]11.8694950861769[/C][C]0.0705049138230862[/C][/ROW]
[ROW][C]19[/C][C]11.86[/C][C]11.9318488421748[/C][C]-0.071848842174763[/C][/ROW]
[ROW][C]20[/C][C]11.92[/C][C]11.8683065309972[/C][C]0.0516934690027924[/C][/ROW]
[ROW][C]21[/C][C]11.83[/C][C]11.9140236559195[/C][C]-0.0840236559194576[/C][/ROW]
[ROW][C]22[/C][C]11.91[/C][C]11.8397140758468[/C][C]0.0702859241531542[/C][/ROW]
[ROW][C]23[/C][C]11.93[/C][C]11.9018741598337[/C][C]0.0281258401662967[/C][/ROW]
[ROW][C]24[/C][C]11.99[/C][C]11.9267483378146[/C][C]0.063251662185392[/C][/ROW]
[ROW][C]25[/C][C]11.96[/C][C]11.9826873993141[/C][C]-0.0226873993141048[/C][/ROW]
[ROW][C]26[/C][C]12.12[/C][C]11.9626229175021[/C][C]0.15737708249786[/C][/ROW]
[ROW][C]27[/C][C]11.85[/C][C]12.1018054463447[/C][C]-0.251805446344717[/C][/ROW]
[ROW][C]28[/C][C]12.01[/C][C]11.8791115302908[/C][C]0.130888469709216[/C][/ROW]
[ROW][C]29[/C][C]12.1[/C][C]11.9948678267052[/C][C]0.105132173294766[/C][/ROW]
[ROW][C]30[/C][C]12.21[/C][C]12.0878455430896[/C][C]0.122154456910424[/C][/ROW]
[ROW][C]31[/C][C]12.31[/C][C]12.1958775764221[/C][C]0.114122423577898[/C][/ROW]
[ROW][C]32[/C][C]12.31[/C][C]12.2968061694492[/C][C]0.0131938305508186[/C][/ROW]
[ROW][C]33[/C][C]12.39[/C][C]12.3084746453927[/C][C]0.0815253546073258[/C][/ROW]
[ROW][C]34[/C][C]12.35[/C][C]12.3805747557705[/C][C]-0.0305747557704983[/C][/ROW]
[ROW][C]35[/C][C]12.41[/C][C]12.3535347842617[/C][C]0.0564652157383136[/C][/ROW]
[ROW][C]36[/C][C]12.51[/C][C]12.4034719885443[/C][C]0.106528011455682[/C][/ROW]
[ROW][C]37[/C][C]12.27[/C][C]12.4976841685622[/C][C]-0.22768416856217[/C][/ROW]
[ROW][C]38[/C][C]12.51[/C][C]12.2963228403756[/C][C]0.213677159624437[/C][/ROW]
[ROW][C]39[/C][C]12.44[/C][C]12.4852965267624[/C][C]-0.0452965267624137[/C][/ROW]
[ROW][C]40[/C][C]12.47[/C][C]12.4452367858998[/C][C]0.024763214100199[/C][/ROW]
[ROW][C]41[/C][C]12.51[/C][C]12.4671370950556[/C][C]0.04286290494443[/C][/ROW]
[ROW][C]42[/C][C]12.58[/C][C]12.5050445680435[/C][C]0.0749554319565142[/C][/ROW]
[ROW][C]43[/C][C]12.5[/C][C]12.5713343124244[/C][C]-0.0713343124243888[/C][/ROW]
[ROW][C]44[/C][C]12.52[/C][C]12.5082470455944[/C][C]0.0117529544056332[/C][/ROW]
[ROW][C]45[/C][C]12.59[/C][C]12.5186412268156[/C][C]0.0713587731844267[/C][/ROW]
[ROW][C]46[/C][C]12.51[/C][C]12.5817501264678[/C][C]-0.0717501264677658[/C][/ROW]
[ROW][C]47[/C][C]12.67[/C][C]12.5182951183557[/C][C]0.151704881644321[/C][/ROW]
[ROW][C]48[/C][C]12.64[/C][C]12.6524612163027[/C][C]-0.0124612163026736[/C][/ROW]
[ROW][C]49[/C][C]12.54[/C][C]12.6414406561936[/C][C]-0.101440656193589[/C][/ROW]
[ROW][C]50[/C][C]12.6[/C][C]12.5517276761816[/C][C]0.0482723238183898[/C][/ROW]
[ROW][C]51[/C][C]12.67[/C][C]12.594419178626[/C][C]0.0755808213739826[/C][/ROW]
[ROW][C]52[/C][C]12.62[/C][C]12.6612620104022[/C][C]-0.0412620104021943[/C][/ROW]
[ROW][C]53[/C][C]12.72[/C][C]12.6247703506144[/C][C]0.0952296493855922[/C][/ROW]
[ROW][C]54[/C][C]12.85[/C][C]12.7089903857803[/C][C]0.141009614219678[/C][/ROW]
[ROW][C]55[/C][C]12.85[/C][C]12.833697709024[/C][C]0.0163022909759789[/C][/ROW]
[ROW][C]56[/C][C]12.82[/C][C]12.8481152725469[/C][C]-0.0281152725469376[/C][/ROW]
[ROW][C]57[/C][C]12.79[/C][C]12.8232504404502[/C][C]-0.0332504404502174[/C][/ROW]
[ROW][C]58[/C][C]12.94[/C][C]12.7938441233833[/C][C]0.146155876616652[/C][/ROW]
[ROW][C]59[/C][C]12.71[/C][C]12.9231027434431[/C][C]-0.213102743443137[/C][/ROW]
[ROW][C]60[/C][C]12.56[/C][C]12.7346370642925[/C][C]-0.17463706429249[/C][/ROW]
[ROW][C]61[/C][C]12.64[/C][C]12.5801900008949[/C][C]0.0598099991050844[/C][/ROW]
[ROW][C]62[/C][C]12.7[/C][C]12.6330852941193[/C][C]0.0669147058807269[/C][/ROW]
[ROW][C]63[/C][C]12.74[/C][C]12.69226391043[/C][C]0.0477360895700372[/C][/ROW]
[ROW][C]64[/C][C]12.85[/C][C]12.734481173312[/C][C]0.115518826688042[/C][/ROW]
[ROW][C]65[/C][C]12.84[/C][C]12.8366447296073[/C][C]0.0033552703926869[/C][/ROW]
[ROW][C]66[/C][C]12.83[/C][C]12.8396120931573[/C][C]-0.0096120931572834[/C][/ROW]
[ROW][C]67[/C][C]12.88[/C][C]12.8311112656425[/C][C]0.0488887343575453[/C][/ROW]
[ROW][C]68[/C][C]13.07[/C][C]12.8743479146627[/C][C]0.195652085337262[/C][/ROW]
[ROW][C]69[/C][C]12.99[/C][C]13.0473804272647[/C][C]-0.0573804272646541[/C][/ROW]
[ROW][C]70[/C][C]13.2[/C][C]12.9966338201602[/C][C]0.203366179839787[/C][/ROW]
[ROW][C]71[/C][C]13.23[/C][C]13.1764885915278[/C][C]0.0535114084721684[/C][/ROW]
[ROW][C]72[/C][C]13.18[/C][C]13.2238134817525[/C][C]-0.0438134817524674[/C][/ROW]
[ROW][C]73[/C][C]13.18[/C][C]13.1850653292838[/C][C]-0.00506532928376657[/C][/ROW]
[ROW][C]74[/C][C]13.1[/C][C]13.1805856088064[/C][C]-0.080585608806393[/C][/ROW]
[ROW][C]75[/C][C]13.23[/C][C]13.109316599088[/C][C]0.120683400912002[/C][/ROW]
[ROW][C]76[/C][C]13.33[/C][C]13.2160476469741[/C][C]0.113952353025894[/C][/ROW]
[ROW][C]77[/C][C]13.38[/C][C]13.3168258315101[/C][C]0.0631741684898994[/C][/ROW]
[ROW][C]78[/C][C]13.26[/C][C]13.3726963584534[/C][C]-0.11269635845338[/C][/ROW]
[ROW][C]79[/C][C]13.17[/C][C]13.2730289614478[/C][C]-0.103028961447821[/C][/ROW]
[ROW][C]80[/C][C]13.27[/C][C]13.181911302061[/C][C]0.0880886979390016[/C][/ROW]
[ROW][C]81[/C][C]13.47[/C][C]13.2598159597596[/C][C]0.210184040240403[/C][/ROW]
[ROW][C]82[/C][C]13.63[/C][C]13.4457003704927[/C][C]0.184299629507302[/C][/ROW]
[ROW][C]83[/C][C]13.64[/C][C]13.6086928983274[/C][C]0.0313071016726028[/C][/ROW]
[ROW][C]84[/C][C]13.69[/C][C]13.6363805483484[/C][C]0.0536194516516169[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232289&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232289&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
210.9810.920.0600000000000005
311.1510.97306332788750.176936672112548
411.1911.12954413868120.0604558613188342
511.3311.18301062521250.146989374787507
611.3811.31300638171780.0669936182821562
711.411.37225478727240.0277452127276074
811.4511.39679234261030.0532076573897378
911.5611.44384859878020.116151401219824
1011.6111.54657159690540.06342840309458
1111.8211.60266696608520.217333033914828
1211.7711.7948738667418-0.0248738667417943
1311.8511.77287569762930.0771243023706827
1411.8211.8410835667091-0.0210835667090929
1511.9211.82243749648710.0975625035129326
1611.8611.9087206817109-0.0487206817108596
1711.8711.86563265656880.00436734343120015
1811.9411.86949508617690.0705049138230862
1911.8611.9318488421748-0.071848842174763
2011.9211.86830653099720.0516934690027924
2111.8311.9140236559195-0.0840236559194576
2211.9111.83971407584680.0702859241531542
2311.9311.90187415983370.0281258401662967
2411.9911.92674833781460.063251662185392
2511.9611.9826873993141-0.0226873993141048
2612.1211.96262291750210.15737708249786
2711.8512.1018054463447-0.251805446344717
2812.0111.87911153029080.130888469709216
2912.111.99486782670520.105132173294766
3012.2112.08784554308960.122154456910424
3112.3112.19587757642210.114122423577898
3212.3112.29680616944920.0131938305508186
3312.3912.30847464539270.0815253546073258
3412.3512.3805747557705-0.0305747557704983
3512.4112.35353478426170.0564652157383136
3612.5112.40347198854430.106528011455682
3712.2712.4976841685622-0.22768416856217
3812.5112.29632284037560.213677159624437
3912.4412.4852965267624-0.0452965267624137
4012.4712.44523678589980.024763214100199
4112.5112.46713709505560.04286290494443
4212.5812.50504456804350.0749554319565142
4312.512.5713343124244-0.0713343124243888
4412.5212.50824704559440.0117529544056332
4512.5912.51864122681560.0713587731844267
4612.5112.5817501264678-0.0717501264677658
4712.6712.51829511835570.151704881644321
4812.6412.6524612163027-0.0124612163026736
4912.5412.6414406561936-0.101440656193589
5012.612.55172767618160.0482723238183898
5112.6712.5944191786260.0755808213739826
5212.6212.6612620104022-0.0412620104021943
5312.7212.62477035061440.0952296493855922
5412.8512.70899038578030.141009614219678
5512.8512.8336977090240.0163022909759789
5612.8212.8481152725469-0.0281152725469376
5712.7912.8232504404502-0.0332504404502174
5812.9412.79384412338330.146155876616652
5912.7112.9231027434431-0.213102743443137
6012.5612.7346370642925-0.17463706429249
6112.6412.58019000089490.0598099991050844
6212.712.63308529411930.0669147058807269
6312.7412.692263910430.0477360895700372
6412.8512.7344811733120.115518826688042
6512.8412.83664472960730.0033552703926869
6612.8312.8396120931573-0.0096120931572834
6712.8812.83111126564250.0488887343575453
6813.0712.87434791466270.195652085337262
6912.9913.0473804272647-0.0573804272646541
7013.212.99663382016020.203366179839787
7113.2313.17648859152780.0535114084721684
7213.1813.2238134817525-0.0438134817524674
7313.1813.1850653292838-0.00506532928376657
7413.113.1805856088064-0.080585608806393
7513.2313.1093165990880.120683400912002
7613.3313.21604764697410.113952353025894
7713.3813.31682583151010.0631741684898994
7813.2613.3726963584534-0.11269635845338
7913.1713.2730289614478-0.103028961447821
8013.2713.1819113020610.0880886979390016
8113.4713.25981595975960.210184040240403
8213.6313.44570037049270.184299629507302
8313.6413.60869289832740.0313071016726028
8413.6913.63638054834840.0536194516516169







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8513.683800990750613.491342285518113.8762596959832
8613.683800990750613.426874490674413.9407274908268
8713.683800990750613.375609330151313.99199265135
8813.683800990750613.331731433866514.0358705476348
8913.683800990750613.292746204171814.0748557773294
9013.683800990750613.257309819297114.1102921622042
9113.683800990750613.224599953568214.143002027933
9213.683800990750613.194069977059514.1735320044418
9313.683800990750613.165334657231714.2022673242696
9413.683800990750613.138110407897914.2294915736034
9513.683800990750613.112181287245114.2554206942562
9613.683800990750613.087378356490814.2802236250104

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 13.6838009907506 & 13.4913422855181 & 13.8762596959832 \tabularnewline
86 & 13.6838009907506 & 13.4268744906744 & 13.9407274908268 \tabularnewline
87 & 13.6838009907506 & 13.3756093301513 & 13.99199265135 \tabularnewline
88 & 13.6838009907506 & 13.3317314338665 & 14.0358705476348 \tabularnewline
89 & 13.6838009907506 & 13.2927462041718 & 14.0748557773294 \tabularnewline
90 & 13.6838009907506 & 13.2573098192971 & 14.1102921622042 \tabularnewline
91 & 13.6838009907506 & 13.2245999535682 & 14.143002027933 \tabularnewline
92 & 13.6838009907506 & 13.1940699770595 & 14.1735320044418 \tabularnewline
93 & 13.6838009907506 & 13.1653346572317 & 14.2022673242696 \tabularnewline
94 & 13.6838009907506 & 13.1381104078979 & 14.2294915736034 \tabularnewline
95 & 13.6838009907506 & 13.1121812872451 & 14.2554206942562 \tabularnewline
96 & 13.6838009907506 & 13.0873783564908 & 14.2802236250104 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232289&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]13.6838009907506[/C][C]13.4913422855181[/C][C]13.8762596959832[/C][/ROW]
[ROW][C]86[/C][C]13.6838009907506[/C][C]13.4268744906744[/C][C]13.9407274908268[/C][/ROW]
[ROW][C]87[/C][C]13.6838009907506[/C][C]13.3756093301513[/C][C]13.99199265135[/C][/ROW]
[ROW][C]88[/C][C]13.6838009907506[/C][C]13.3317314338665[/C][C]14.0358705476348[/C][/ROW]
[ROW][C]89[/C][C]13.6838009907506[/C][C]13.2927462041718[/C][C]14.0748557773294[/C][/ROW]
[ROW][C]90[/C][C]13.6838009907506[/C][C]13.2573098192971[/C][C]14.1102921622042[/C][/ROW]
[ROW][C]91[/C][C]13.6838009907506[/C][C]13.2245999535682[/C][C]14.143002027933[/C][/ROW]
[ROW][C]92[/C][C]13.6838009907506[/C][C]13.1940699770595[/C][C]14.1735320044418[/C][/ROW]
[ROW][C]93[/C][C]13.6838009907506[/C][C]13.1653346572317[/C][C]14.2022673242696[/C][/ROW]
[ROW][C]94[/C][C]13.6838009907506[/C][C]13.1381104078979[/C][C]14.2294915736034[/C][/ROW]
[ROW][C]95[/C][C]13.6838009907506[/C][C]13.1121812872451[/C][C]14.2554206942562[/C][/ROW]
[ROW][C]96[/C][C]13.6838009907506[/C][C]13.0873783564908[/C][C]14.2802236250104[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232289&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232289&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
8513.683800990750613.491342285518113.8762596959832
8613.683800990750613.426874490674413.9407274908268
8713.683800990750613.375609330151313.99199265135
8813.683800990750613.331731433866514.0358705476348
8913.683800990750613.292746204171814.0748557773294
9013.683800990750613.257309819297114.1102921622042
9113.683800990750613.224599953568214.143002027933
9213.683800990750613.194069977059514.1735320044418
9313.683800990750613.165334657231714.2022673242696
9413.683800990750613.138110407897914.2294915736034
9513.683800990750613.112181287245114.2554206942562
9613.683800990750613.087378356490814.2802236250104



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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')