Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 21 Dec 2012 04:34:44 -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/2012/Dec/21/t1356082579glkmtpliq2gknxe.htm/, Retrieved Fri, 26 Apr 2024 16:57:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=203377, Retrieved Fri, 26 Apr 2024 16:57:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact98
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2012-12-21 09:34:44] [76c30f62b7052b57088120e90a652e05] [Current]
- R PD    [Exponential Smoothing] [] [2012-12-29 18:25:14] [6685c0b0549825358ff43299d2b5fc1b]
Feedback Forum

Post a new message
Dataseries X:
2.1
2.1
2.11
2.12
2.13
2.13
2.13
2.13
2.14
2.15
2.16
2.17
2.16
2.2
2.19
2.2
2.2
2.2
2.21
2.22
2.25
2.33
2.33
2.35
2.37
2.38
2.38
2.41
2.41
2.41
2.41
2.42
2.42
2.43
2.44
2.44
2.43
2.44
2.44
2.44
2.44
2.44
2.43
2.42
2.43
2.43
2.43
2.43
2.43
2.44
2.43
2.43
2.44
2.43
2.43
2.44
2.46
2.48
2.49
2.5
2.53
2.55
2.57
2.56
2.56
2.57
2.56
2.57
2.58
2.58
2.58
2.59




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203377&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203377&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203377&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.965791163757207
beta0.181749560390545
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.965791163757207 \tabularnewline
beta & 0.181749560390545 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203377&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]0.965791163757207[/C][/ROW]
[ROW][C]beta[/C][C]0.181749560390545[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203377&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203377&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
alpha0.965791163757207
beta0.181749560390545
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
32.112.10.00999999999999979
42.122.111413232831990.00858676716800888
52.132.122968831322670.00703116867733078
62.132.13425624247678-0.00425624247678202
72.132.13389526441375-0.00389526441374954
82.132.13319917175597-0.00319917175597162
92.142.132613801837450.00738619816255248
102.152.143548203669430.00645179633057325
112.162.15471266595280.00528733404720505
122.172.165680597803860.0043194021961388
132.162.17647190344826-0.0164719034482586
142.22.164291801694810.0357081983051941
152.192.20877471686875-0.0187747168687538
162.22.197342948148070.00265705185192555
172.22.20707619022455-0.0070761902245513
182.22.20616705444117-0.00616705444116672
192.212.205053437827260.0049465621727407
202.222.215541534478580.00445846552141926
212.252.226340835599430.0236591644005695
222.332.259836945307180.0701630546928165
232.332.35056197103627-0.0205619710362748
242.352.35005628222866-5.62822286629405e-05
252.372.369344927139310.000655072860686445
262.382.38943557883718-0.00943557883717716
272.382.39812452113724-0.0181245211372407
282.412.395240324132420.0147596758675839
292.412.42670619120942-0.0167061912094155
302.412.4248501287527-0.0148501287526992
312.412.42217996044211-0.012179960442114
322.422.419950642820514.93571794866199e-05
332.422.42954095586696-0.00954095586695969
342.432.428194285110650.00180571488934733
352.442.438123089670490.00187691032951465
362.442.44845011220547-0.00845011220547276
372.432.4473201215233-0.0173201215232992
382.442.434583316579550.0054166834204521
392.442.44475631886368-0.00475631886368078
402.442.44426943870203-0.00426943870203278
412.442.44350335947412-0.00350335947411784
422.442.4428622006816-0.00286220068160192
432.432.44233785923355-0.0123378592335532
442.422.43049631990461-0.0104963199046084
452.432.418590881708070.0114091182919274
462.432.429844188874730.000155811125273519
472.432.43025650127383-0.000256501273832477
482.432.43022558178894-0.000225581788939166
492.432.43018492721982-0.00018492721982355
502.442.430151075807490.00984892419251171
512.432.44153663196537-0.0115366319653729
522.432.43024315749384-0.000243157493835966
532.442.429814138924780.0101858610752239
542.432.44124532011925-0.0112453201192491
552.432.43000454101289-4.54101288527298e-06
562.442.429619209947580.0103807900524213
572.462.441086101937220.0189138980627783
582.482.464114190856520.0158858091434788
592.492.48700624800250.00299375199750473
602.52.497972769907440.00202723009255923
612.532.508361677491750.0216383225082448
622.552.541489025453810.00851097454619465
632.572.563432046151150.00656795384884878
642.562.58465140148749-0.0246514014874881
652.562.57139226655148-0.0113922665514816
662.572.568938978282710.00106102171729416
672.562.57869920917445-0.0186992091744451
682.572.566092871858860.00390712814113758
692.582.576005361851130.00399463814887113
702.582.58670355553628-0.00670355553627955
712.582.58589283898107-0.00589283898106885
722.592.584830722795320.00516927720468452

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 2.11 & 2.1 & 0.00999999999999979 \tabularnewline
4 & 2.12 & 2.11141323283199 & 0.00858676716800888 \tabularnewline
5 & 2.13 & 2.12296883132267 & 0.00703116867733078 \tabularnewline
6 & 2.13 & 2.13425624247678 & -0.00425624247678202 \tabularnewline
7 & 2.13 & 2.13389526441375 & -0.00389526441374954 \tabularnewline
8 & 2.13 & 2.13319917175597 & -0.00319917175597162 \tabularnewline
9 & 2.14 & 2.13261380183745 & 0.00738619816255248 \tabularnewline
10 & 2.15 & 2.14354820366943 & 0.00645179633057325 \tabularnewline
11 & 2.16 & 2.1547126659528 & 0.00528733404720505 \tabularnewline
12 & 2.17 & 2.16568059780386 & 0.0043194021961388 \tabularnewline
13 & 2.16 & 2.17647190344826 & -0.0164719034482586 \tabularnewline
14 & 2.2 & 2.16429180169481 & 0.0357081983051941 \tabularnewline
15 & 2.19 & 2.20877471686875 & -0.0187747168687538 \tabularnewline
16 & 2.2 & 2.19734294814807 & 0.00265705185192555 \tabularnewline
17 & 2.2 & 2.20707619022455 & -0.0070761902245513 \tabularnewline
18 & 2.2 & 2.20616705444117 & -0.00616705444116672 \tabularnewline
19 & 2.21 & 2.20505343782726 & 0.0049465621727407 \tabularnewline
20 & 2.22 & 2.21554153447858 & 0.00445846552141926 \tabularnewline
21 & 2.25 & 2.22634083559943 & 0.0236591644005695 \tabularnewline
22 & 2.33 & 2.25983694530718 & 0.0701630546928165 \tabularnewline
23 & 2.33 & 2.35056197103627 & -0.0205619710362748 \tabularnewline
24 & 2.35 & 2.35005628222866 & -5.62822286629405e-05 \tabularnewline
25 & 2.37 & 2.36934492713931 & 0.000655072860686445 \tabularnewline
26 & 2.38 & 2.38943557883718 & -0.00943557883717716 \tabularnewline
27 & 2.38 & 2.39812452113724 & -0.0181245211372407 \tabularnewline
28 & 2.41 & 2.39524032413242 & 0.0147596758675839 \tabularnewline
29 & 2.41 & 2.42670619120942 & -0.0167061912094155 \tabularnewline
30 & 2.41 & 2.4248501287527 & -0.0148501287526992 \tabularnewline
31 & 2.41 & 2.42217996044211 & -0.012179960442114 \tabularnewline
32 & 2.42 & 2.41995064282051 & 4.93571794866199e-05 \tabularnewline
33 & 2.42 & 2.42954095586696 & -0.00954095586695969 \tabularnewline
34 & 2.43 & 2.42819428511065 & 0.00180571488934733 \tabularnewline
35 & 2.44 & 2.43812308967049 & 0.00187691032951465 \tabularnewline
36 & 2.44 & 2.44845011220547 & -0.00845011220547276 \tabularnewline
37 & 2.43 & 2.4473201215233 & -0.0173201215232992 \tabularnewline
38 & 2.44 & 2.43458331657955 & 0.0054166834204521 \tabularnewline
39 & 2.44 & 2.44475631886368 & -0.00475631886368078 \tabularnewline
40 & 2.44 & 2.44426943870203 & -0.00426943870203278 \tabularnewline
41 & 2.44 & 2.44350335947412 & -0.00350335947411784 \tabularnewline
42 & 2.44 & 2.4428622006816 & -0.00286220068160192 \tabularnewline
43 & 2.43 & 2.44233785923355 & -0.0123378592335532 \tabularnewline
44 & 2.42 & 2.43049631990461 & -0.0104963199046084 \tabularnewline
45 & 2.43 & 2.41859088170807 & 0.0114091182919274 \tabularnewline
46 & 2.43 & 2.42984418887473 & 0.000155811125273519 \tabularnewline
47 & 2.43 & 2.43025650127383 & -0.000256501273832477 \tabularnewline
48 & 2.43 & 2.43022558178894 & -0.000225581788939166 \tabularnewline
49 & 2.43 & 2.43018492721982 & -0.00018492721982355 \tabularnewline
50 & 2.44 & 2.43015107580749 & 0.00984892419251171 \tabularnewline
51 & 2.43 & 2.44153663196537 & -0.0115366319653729 \tabularnewline
52 & 2.43 & 2.43024315749384 & -0.000243157493835966 \tabularnewline
53 & 2.44 & 2.42981413892478 & 0.0101858610752239 \tabularnewline
54 & 2.43 & 2.44124532011925 & -0.0112453201192491 \tabularnewline
55 & 2.43 & 2.43000454101289 & -4.54101288527298e-06 \tabularnewline
56 & 2.44 & 2.42961920994758 & 0.0103807900524213 \tabularnewline
57 & 2.46 & 2.44108610193722 & 0.0189138980627783 \tabularnewline
58 & 2.48 & 2.46411419085652 & 0.0158858091434788 \tabularnewline
59 & 2.49 & 2.4870062480025 & 0.00299375199750473 \tabularnewline
60 & 2.5 & 2.49797276990744 & 0.00202723009255923 \tabularnewline
61 & 2.53 & 2.50836167749175 & 0.0216383225082448 \tabularnewline
62 & 2.55 & 2.54148902545381 & 0.00851097454619465 \tabularnewline
63 & 2.57 & 2.56343204615115 & 0.00656795384884878 \tabularnewline
64 & 2.56 & 2.58465140148749 & -0.0246514014874881 \tabularnewline
65 & 2.56 & 2.57139226655148 & -0.0113922665514816 \tabularnewline
66 & 2.57 & 2.56893897828271 & 0.00106102171729416 \tabularnewline
67 & 2.56 & 2.57869920917445 & -0.0186992091744451 \tabularnewline
68 & 2.57 & 2.56609287185886 & 0.00390712814113758 \tabularnewline
69 & 2.58 & 2.57600536185113 & 0.00399463814887113 \tabularnewline
70 & 2.58 & 2.58670355553628 & -0.00670355553627955 \tabularnewline
71 & 2.58 & 2.58589283898107 & -0.00589283898106885 \tabularnewline
72 & 2.59 & 2.58483072279532 & 0.00516927720468452 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203377&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]2.11[/C][C]2.1[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]4[/C][C]2.12[/C][C]2.11141323283199[/C][C]0.00858676716800888[/C][/ROW]
[ROW][C]5[/C][C]2.13[/C][C]2.12296883132267[/C][C]0.00703116867733078[/C][/ROW]
[ROW][C]6[/C][C]2.13[/C][C]2.13425624247678[/C][C]-0.00425624247678202[/C][/ROW]
[ROW][C]7[/C][C]2.13[/C][C]2.13389526441375[/C][C]-0.00389526441374954[/C][/ROW]
[ROW][C]8[/C][C]2.13[/C][C]2.13319917175597[/C][C]-0.00319917175597162[/C][/ROW]
[ROW][C]9[/C][C]2.14[/C][C]2.13261380183745[/C][C]0.00738619816255248[/C][/ROW]
[ROW][C]10[/C][C]2.15[/C][C]2.14354820366943[/C][C]0.00645179633057325[/C][/ROW]
[ROW][C]11[/C][C]2.16[/C][C]2.1547126659528[/C][C]0.00528733404720505[/C][/ROW]
[ROW][C]12[/C][C]2.17[/C][C]2.16568059780386[/C][C]0.0043194021961388[/C][/ROW]
[ROW][C]13[/C][C]2.16[/C][C]2.17647190344826[/C][C]-0.0164719034482586[/C][/ROW]
[ROW][C]14[/C][C]2.2[/C][C]2.16429180169481[/C][C]0.0357081983051941[/C][/ROW]
[ROW][C]15[/C][C]2.19[/C][C]2.20877471686875[/C][C]-0.0187747168687538[/C][/ROW]
[ROW][C]16[/C][C]2.2[/C][C]2.19734294814807[/C][C]0.00265705185192555[/C][/ROW]
[ROW][C]17[/C][C]2.2[/C][C]2.20707619022455[/C][C]-0.0070761902245513[/C][/ROW]
[ROW][C]18[/C][C]2.2[/C][C]2.20616705444117[/C][C]-0.00616705444116672[/C][/ROW]
[ROW][C]19[/C][C]2.21[/C][C]2.20505343782726[/C][C]0.0049465621727407[/C][/ROW]
[ROW][C]20[/C][C]2.22[/C][C]2.21554153447858[/C][C]0.00445846552141926[/C][/ROW]
[ROW][C]21[/C][C]2.25[/C][C]2.22634083559943[/C][C]0.0236591644005695[/C][/ROW]
[ROW][C]22[/C][C]2.33[/C][C]2.25983694530718[/C][C]0.0701630546928165[/C][/ROW]
[ROW][C]23[/C][C]2.33[/C][C]2.35056197103627[/C][C]-0.0205619710362748[/C][/ROW]
[ROW][C]24[/C][C]2.35[/C][C]2.35005628222866[/C][C]-5.62822286629405e-05[/C][/ROW]
[ROW][C]25[/C][C]2.37[/C][C]2.36934492713931[/C][C]0.000655072860686445[/C][/ROW]
[ROW][C]26[/C][C]2.38[/C][C]2.38943557883718[/C][C]-0.00943557883717716[/C][/ROW]
[ROW][C]27[/C][C]2.38[/C][C]2.39812452113724[/C][C]-0.0181245211372407[/C][/ROW]
[ROW][C]28[/C][C]2.41[/C][C]2.39524032413242[/C][C]0.0147596758675839[/C][/ROW]
[ROW][C]29[/C][C]2.41[/C][C]2.42670619120942[/C][C]-0.0167061912094155[/C][/ROW]
[ROW][C]30[/C][C]2.41[/C][C]2.4248501287527[/C][C]-0.0148501287526992[/C][/ROW]
[ROW][C]31[/C][C]2.41[/C][C]2.42217996044211[/C][C]-0.012179960442114[/C][/ROW]
[ROW][C]32[/C][C]2.42[/C][C]2.41995064282051[/C][C]4.93571794866199e-05[/C][/ROW]
[ROW][C]33[/C][C]2.42[/C][C]2.42954095586696[/C][C]-0.00954095586695969[/C][/ROW]
[ROW][C]34[/C][C]2.43[/C][C]2.42819428511065[/C][C]0.00180571488934733[/C][/ROW]
[ROW][C]35[/C][C]2.44[/C][C]2.43812308967049[/C][C]0.00187691032951465[/C][/ROW]
[ROW][C]36[/C][C]2.44[/C][C]2.44845011220547[/C][C]-0.00845011220547276[/C][/ROW]
[ROW][C]37[/C][C]2.43[/C][C]2.4473201215233[/C][C]-0.0173201215232992[/C][/ROW]
[ROW][C]38[/C][C]2.44[/C][C]2.43458331657955[/C][C]0.0054166834204521[/C][/ROW]
[ROW][C]39[/C][C]2.44[/C][C]2.44475631886368[/C][C]-0.00475631886368078[/C][/ROW]
[ROW][C]40[/C][C]2.44[/C][C]2.44426943870203[/C][C]-0.00426943870203278[/C][/ROW]
[ROW][C]41[/C][C]2.44[/C][C]2.44350335947412[/C][C]-0.00350335947411784[/C][/ROW]
[ROW][C]42[/C][C]2.44[/C][C]2.4428622006816[/C][C]-0.00286220068160192[/C][/ROW]
[ROW][C]43[/C][C]2.43[/C][C]2.44233785923355[/C][C]-0.0123378592335532[/C][/ROW]
[ROW][C]44[/C][C]2.42[/C][C]2.43049631990461[/C][C]-0.0104963199046084[/C][/ROW]
[ROW][C]45[/C][C]2.43[/C][C]2.41859088170807[/C][C]0.0114091182919274[/C][/ROW]
[ROW][C]46[/C][C]2.43[/C][C]2.42984418887473[/C][C]0.000155811125273519[/C][/ROW]
[ROW][C]47[/C][C]2.43[/C][C]2.43025650127383[/C][C]-0.000256501273832477[/C][/ROW]
[ROW][C]48[/C][C]2.43[/C][C]2.43022558178894[/C][C]-0.000225581788939166[/C][/ROW]
[ROW][C]49[/C][C]2.43[/C][C]2.43018492721982[/C][C]-0.00018492721982355[/C][/ROW]
[ROW][C]50[/C][C]2.44[/C][C]2.43015107580749[/C][C]0.00984892419251171[/C][/ROW]
[ROW][C]51[/C][C]2.43[/C][C]2.44153663196537[/C][C]-0.0115366319653729[/C][/ROW]
[ROW][C]52[/C][C]2.43[/C][C]2.43024315749384[/C][C]-0.000243157493835966[/C][/ROW]
[ROW][C]53[/C][C]2.44[/C][C]2.42981413892478[/C][C]0.0101858610752239[/C][/ROW]
[ROW][C]54[/C][C]2.43[/C][C]2.44124532011925[/C][C]-0.0112453201192491[/C][/ROW]
[ROW][C]55[/C][C]2.43[/C][C]2.43000454101289[/C][C]-4.54101288527298e-06[/C][/ROW]
[ROW][C]56[/C][C]2.44[/C][C]2.42961920994758[/C][C]0.0103807900524213[/C][/ROW]
[ROW][C]57[/C][C]2.46[/C][C]2.44108610193722[/C][C]0.0189138980627783[/C][/ROW]
[ROW][C]58[/C][C]2.48[/C][C]2.46411419085652[/C][C]0.0158858091434788[/C][/ROW]
[ROW][C]59[/C][C]2.49[/C][C]2.4870062480025[/C][C]0.00299375199750473[/C][/ROW]
[ROW][C]60[/C][C]2.5[/C][C]2.49797276990744[/C][C]0.00202723009255923[/C][/ROW]
[ROW][C]61[/C][C]2.53[/C][C]2.50836167749175[/C][C]0.0216383225082448[/C][/ROW]
[ROW][C]62[/C][C]2.55[/C][C]2.54148902545381[/C][C]0.00851097454619465[/C][/ROW]
[ROW][C]63[/C][C]2.57[/C][C]2.56343204615115[/C][C]0.00656795384884878[/C][/ROW]
[ROW][C]64[/C][C]2.56[/C][C]2.58465140148749[/C][C]-0.0246514014874881[/C][/ROW]
[ROW][C]65[/C][C]2.56[/C][C]2.57139226655148[/C][C]-0.0113922665514816[/C][/ROW]
[ROW][C]66[/C][C]2.57[/C][C]2.56893897828271[/C][C]0.00106102171729416[/C][/ROW]
[ROW][C]67[/C][C]2.56[/C][C]2.57869920917445[/C][C]-0.0186992091744451[/C][/ROW]
[ROW][C]68[/C][C]2.57[/C][C]2.56609287185886[/C][C]0.00390712814113758[/C][/ROW]
[ROW][C]69[/C][C]2.58[/C][C]2.57600536185113[/C][C]0.00399463814887113[/C][/ROW]
[ROW][C]70[/C][C]2.58[/C][C]2.58670355553628[/C][C]-0.00670355553627955[/C][/ROW]
[ROW][C]71[/C][C]2.58[/C][C]2.58589283898107[/C][C]-0.00589283898106885[/C][/ROW]
[ROW][C]72[/C][C]2.59[/C][C]2.58483072279532[/C][C]0.00516927720468452[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203377&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203377&T=2

As an alternative you can also use a QR Code:  

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

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
32.112.10.00999999999999979
42.122.111413232831990.00858676716800888
52.132.122968831322670.00703116867733078
62.132.13425624247678-0.00425624247678202
72.132.13389526441375-0.00389526441374954
82.132.13319917175597-0.00319917175597162
92.142.132613801837450.00738619816255248
102.152.143548203669430.00645179633057325
112.162.15471266595280.00528733404720505
122.172.165680597803860.0043194021961388
132.162.17647190344826-0.0164719034482586
142.22.164291801694810.0357081983051941
152.192.20877471686875-0.0187747168687538
162.22.197342948148070.00265705185192555
172.22.20707619022455-0.0070761902245513
182.22.20616705444117-0.00616705444116672
192.212.205053437827260.0049465621727407
202.222.215541534478580.00445846552141926
212.252.226340835599430.0236591644005695
222.332.259836945307180.0701630546928165
232.332.35056197103627-0.0205619710362748
242.352.35005628222866-5.62822286629405e-05
252.372.369344927139310.000655072860686445
262.382.38943557883718-0.00943557883717716
272.382.39812452113724-0.0181245211372407
282.412.395240324132420.0147596758675839
292.412.42670619120942-0.0167061912094155
302.412.4248501287527-0.0148501287526992
312.412.42217996044211-0.012179960442114
322.422.419950642820514.93571794866199e-05
332.422.42954095586696-0.00954095586695969
342.432.428194285110650.00180571488934733
352.442.438123089670490.00187691032951465
362.442.44845011220547-0.00845011220547276
372.432.4473201215233-0.0173201215232992
382.442.434583316579550.0054166834204521
392.442.44475631886368-0.00475631886368078
402.442.44426943870203-0.00426943870203278
412.442.44350335947412-0.00350335947411784
422.442.4428622006816-0.00286220068160192
432.432.44233785923355-0.0123378592335532
442.422.43049631990461-0.0104963199046084
452.432.418590881708070.0114091182919274
462.432.429844188874730.000155811125273519
472.432.43025650127383-0.000256501273832477
482.432.43022558178894-0.000225581788939166
492.432.43018492721982-0.00018492721982355
502.442.430151075807490.00984892419251171
512.432.44153663196537-0.0115366319653729
522.432.43024315749384-0.000243157493835966
532.442.429814138924780.0101858610752239
542.432.44124532011925-0.0112453201192491
552.432.43000454101289-4.54101288527298e-06
562.442.429619209947580.0103807900524213
572.462.441086101937220.0189138980627783
582.482.464114190856520.0158858091434788
592.492.48700624800250.00299375199750473
602.52.497972769907440.00202723009255923
612.532.508361677491750.0216383225082448
622.552.541489025453810.00851097454619465
632.572.563432046151150.00656795384884878
642.562.58465140148749-0.0246514014874881
652.562.57139226655148-0.0113922665514816
662.572.568938978282710.00106102171729416
672.562.57869920917445-0.0186992091744451
682.572.566092871858860.00390712814113758
692.582.576005361851130.00399463814887113
702.582.58670355553628-0.00670355553627955
712.582.58589283898107-0.00589283898106885
722.592.584830722795320.00516927720468452







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
732.595359674857942.567867053685262.62285229603062
742.600896184673272.559177829765542.642614539581
752.606432694488592.551195598642442.66166979033475
762.611969204303922.543161003419852.68077740518799
772.617505714119252.534817783824722.70019364441379
782.623042223934582.526058255640742.72002619222842
792.628578733749912.516833779484352.74032368801546
802.634115243565232.507123096816732.76110739031374
812.639651753380562.496918859035912.78238464772521
822.645188263195892.486221179790362.80415534660142
832.650724773011222.475034288928552.82641525709389
842.656261282826552.463364693104862.84915787254823

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 2.59535967485794 & 2.56786705368526 & 2.62285229603062 \tabularnewline
74 & 2.60089618467327 & 2.55917782976554 & 2.642614539581 \tabularnewline
75 & 2.60643269448859 & 2.55119559864244 & 2.66166979033475 \tabularnewline
76 & 2.61196920430392 & 2.54316100341985 & 2.68077740518799 \tabularnewline
77 & 2.61750571411925 & 2.53481778382472 & 2.70019364441379 \tabularnewline
78 & 2.62304222393458 & 2.52605825564074 & 2.72002619222842 \tabularnewline
79 & 2.62857873374991 & 2.51683377948435 & 2.74032368801546 \tabularnewline
80 & 2.63411524356523 & 2.50712309681673 & 2.76110739031374 \tabularnewline
81 & 2.63965175338056 & 2.49691885903591 & 2.78238464772521 \tabularnewline
82 & 2.64518826319589 & 2.48622117979036 & 2.80415534660142 \tabularnewline
83 & 2.65072477301122 & 2.47503428892855 & 2.82641525709389 \tabularnewline
84 & 2.65626128282655 & 2.46336469310486 & 2.84915787254823 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203377&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]73[/C][C]2.59535967485794[/C][C]2.56786705368526[/C][C]2.62285229603062[/C][/ROW]
[ROW][C]74[/C][C]2.60089618467327[/C][C]2.55917782976554[/C][C]2.642614539581[/C][/ROW]
[ROW][C]75[/C][C]2.60643269448859[/C][C]2.55119559864244[/C][C]2.66166979033475[/C][/ROW]
[ROW][C]76[/C][C]2.61196920430392[/C][C]2.54316100341985[/C][C]2.68077740518799[/C][/ROW]
[ROW][C]77[/C][C]2.61750571411925[/C][C]2.53481778382472[/C][C]2.70019364441379[/C][/ROW]
[ROW][C]78[/C][C]2.62304222393458[/C][C]2.52605825564074[/C][C]2.72002619222842[/C][/ROW]
[ROW][C]79[/C][C]2.62857873374991[/C][C]2.51683377948435[/C][C]2.74032368801546[/C][/ROW]
[ROW][C]80[/C][C]2.63411524356523[/C][C]2.50712309681673[/C][C]2.76110739031374[/C][/ROW]
[ROW][C]81[/C][C]2.63965175338056[/C][C]2.49691885903591[/C][C]2.78238464772521[/C][/ROW]
[ROW][C]82[/C][C]2.64518826319589[/C][C]2.48622117979036[/C][C]2.80415534660142[/C][/ROW]
[ROW][C]83[/C][C]2.65072477301122[/C][C]2.47503428892855[/C][C]2.82641525709389[/C][/ROW]
[ROW][C]84[/C][C]2.65626128282655[/C][C]2.46336469310486[/C][C]2.84915787254823[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203377&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203377&T=3

As an alternative you can also use a QR Code:  

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

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
732.595359674857942.567867053685262.62285229603062
742.600896184673272.559177829765542.642614539581
752.606432694488592.551195598642442.66166979033475
762.611969204303922.543161003419852.68077740518799
772.617505714119252.534817783824722.70019364441379
782.623042223934582.526058255640742.72002619222842
792.628578733749912.516833779484352.74032368801546
802.634115243565232.507123096816732.76110739031374
812.639651753380562.496918859035912.78238464772521
822.645188263195892.486221179790362.80415534660142
832.650724773011222.475034288928552.82641525709389
842.656261282826552.463364693104862.84915787254823



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