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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 30 Dec 2012 08:09:59 -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/30/t1356873008msf7ignq5g1r5gk.htm/, Retrieved Tue, 23 Apr 2024 18:06:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=204947, Retrieved Tue, 23 Apr 2024 18:06:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact140
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Standard Deviation-Mean Plot] [] [2012-12-02 15:27:52] [d23b207f0d1ee449b1f7a501640a17a4]
- RMPD  [Classical Decomposition] [] [2012-12-30 12:24:29] [d23b207f0d1ee449b1f7a501640a17a4]
- RMPD      [Exponential Smoothing] [] [2012-12-30 13:09:59] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
0.36
0.37
0.38
0.38
0.38
0.38
0.38
0.38
0.38
0.38
0.38
0.38
0.37
0.37
0.37
0.38
0.38
0.39
0.39
0.38
0.38
0.38
0.38
0.39
0.39
0.4
0.4
0.4
0.41
0.41
0.41
0.41
0.41
0.42
0.42
0.42
0.42
0.42
0.42
0.42
0.42
0.42
0.42
0.42
0.42
0.42
0.42
0.42
0.42
0.43
0.44
0.43
0.43
0.43
0.44
0.44
0.44
0.44
0.44
0.44
0.44
0.44
0.44
0.44
0.45
0.45
0.45
0.45
0.45
0.45
0.45
0.45




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204947&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204947&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204947&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.22012398475082
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.22012398475082 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204947&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]0.22012398475082[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204947&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204947&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
beta0.22012398475082
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
30.380.380
40.380.39-0.01
50.380.387798760152492-0.00779876015249181
60.380.386082065991609-0.00608206599160938
70.380.384743257390019-0.00474325739001891
80.380.383699152672629-0.00369915267262916
90.380.382884880446128-0.00288488044612839
100.380.382249849066797-0.00224984906679687
110.380.381754603325126-0.00175460332512561
120.380.381368373049542-0.00136837304954196
130.370.381067161321251-0.0110671613212511
140.370.3686310136713370.00136898632866284
150.370.3689323603970720.00106763960292816
160.380.3691673734807460.0108326265192538
170.380.381551894395482-0.00155189439548176
180.390.3812102852172360.00878971478276419
190.390.393145112260041-0.00314511226004105
200.380.392452797616872-0.0124527976168722
210.380.3797116381841510.000288361815849236
220.380.3797751135361050.000224886463894514
230.380.3798246164406540.000175383559345543
240.390.3798632225685970.0101367774314026
250.390.39209457040933-0.00209457040932992
260.40.3916335052244870.00836649477551293
270.40.40347517139287-0.0034751713928699
280.40.402710202818179-0.0027102028181793
290.410.4021136221743590.00788637782564117
300.410.413849603086589-0.00384960308658944
310.410.41300221311546-0.00300221311546028
320.410.412341354001414-0.002341354001414
330.410.41182596582891-0.00182596582891048
340.420.4114240269546320.00857597304536817
350.420.423311804314494-0.0033118043144939
360.420.422582796752073-0.00258279675207257
370.420.422014261239205-0.0020142612392049
380.420.421570874028902-0.00157087402890199
390.420.421225086978119-0.00122508697811852
400.420.420955415950829-0.000955415950828709
410.420.420745105984638-0.000745105984637784
420.420.420581090286238-0.000581090286237651
430.420.420453178376931-0.00045317837693104
440.420.420353422946798-0.000353422946798077
450.420.420275626079446-0.000275626079446478
460.420.420214954168537-0.000214954168537507
470.420.42016763760042-0.000167637600420212
480.420.420130736543822-0.000130736543821675
490.420.420101958294843-0.000101958294843052
500.430.4200795148287040.00992048517129618
510.440.4322632515552710.00773674844472905
520.430.443966295451939-0.0139662954519394
530.430.430891978844851-0.00089197884485126
540.430.430695632907209-0.000695632907209143
550.440.430542507419750.00945749258024953
560.440.442624328372266-0.00262432837226634
570.440.442046650753668-0.00204665075366844
580.440.441596133834378-0.00159613383437768
590.440.441244786494559-0.00124478649455884
600.440.440970779131213-0.000970779131212574
610.440.440757087360537-0.00075708736053709
620.440.440590434273931-0.000590434273931184
630.440.44046046552882-0.000460465528820009
640.440.440359106021776-0.000359106021775746
650.450.4402800581733140.00971994182668556
660.450.452419650499751-0.00241965049975063
670.450.451887027390041-0.00188702739004121
680.450.451471647401611-0.00147164740161143
690.450.451147702511421-0.00114770251142049
700.450.450895065661298-0.0008950656612981
710.450.45069804024132-0.000698040241319531
720.450.450544384841884-0.000544384841883849

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 0.38 & 0.38 & 0 \tabularnewline
4 & 0.38 & 0.39 & -0.01 \tabularnewline
5 & 0.38 & 0.387798760152492 & -0.00779876015249181 \tabularnewline
6 & 0.38 & 0.386082065991609 & -0.00608206599160938 \tabularnewline
7 & 0.38 & 0.384743257390019 & -0.00474325739001891 \tabularnewline
8 & 0.38 & 0.383699152672629 & -0.00369915267262916 \tabularnewline
9 & 0.38 & 0.382884880446128 & -0.00288488044612839 \tabularnewline
10 & 0.38 & 0.382249849066797 & -0.00224984906679687 \tabularnewline
11 & 0.38 & 0.381754603325126 & -0.00175460332512561 \tabularnewline
12 & 0.38 & 0.381368373049542 & -0.00136837304954196 \tabularnewline
13 & 0.37 & 0.381067161321251 & -0.0110671613212511 \tabularnewline
14 & 0.37 & 0.368631013671337 & 0.00136898632866284 \tabularnewline
15 & 0.37 & 0.368932360397072 & 0.00106763960292816 \tabularnewline
16 & 0.38 & 0.369167373480746 & 0.0108326265192538 \tabularnewline
17 & 0.38 & 0.381551894395482 & -0.00155189439548176 \tabularnewline
18 & 0.39 & 0.381210285217236 & 0.00878971478276419 \tabularnewline
19 & 0.39 & 0.393145112260041 & -0.00314511226004105 \tabularnewline
20 & 0.38 & 0.392452797616872 & -0.0124527976168722 \tabularnewline
21 & 0.38 & 0.379711638184151 & 0.000288361815849236 \tabularnewline
22 & 0.38 & 0.379775113536105 & 0.000224886463894514 \tabularnewline
23 & 0.38 & 0.379824616440654 & 0.000175383559345543 \tabularnewline
24 & 0.39 & 0.379863222568597 & 0.0101367774314026 \tabularnewline
25 & 0.39 & 0.39209457040933 & -0.00209457040932992 \tabularnewline
26 & 0.4 & 0.391633505224487 & 0.00836649477551293 \tabularnewline
27 & 0.4 & 0.40347517139287 & -0.0034751713928699 \tabularnewline
28 & 0.4 & 0.402710202818179 & -0.0027102028181793 \tabularnewline
29 & 0.41 & 0.402113622174359 & 0.00788637782564117 \tabularnewline
30 & 0.41 & 0.413849603086589 & -0.00384960308658944 \tabularnewline
31 & 0.41 & 0.41300221311546 & -0.00300221311546028 \tabularnewline
32 & 0.41 & 0.412341354001414 & -0.002341354001414 \tabularnewline
33 & 0.41 & 0.41182596582891 & -0.00182596582891048 \tabularnewline
34 & 0.42 & 0.411424026954632 & 0.00857597304536817 \tabularnewline
35 & 0.42 & 0.423311804314494 & -0.0033118043144939 \tabularnewline
36 & 0.42 & 0.422582796752073 & -0.00258279675207257 \tabularnewline
37 & 0.42 & 0.422014261239205 & -0.0020142612392049 \tabularnewline
38 & 0.42 & 0.421570874028902 & -0.00157087402890199 \tabularnewline
39 & 0.42 & 0.421225086978119 & -0.00122508697811852 \tabularnewline
40 & 0.42 & 0.420955415950829 & -0.000955415950828709 \tabularnewline
41 & 0.42 & 0.420745105984638 & -0.000745105984637784 \tabularnewline
42 & 0.42 & 0.420581090286238 & -0.000581090286237651 \tabularnewline
43 & 0.42 & 0.420453178376931 & -0.00045317837693104 \tabularnewline
44 & 0.42 & 0.420353422946798 & -0.000353422946798077 \tabularnewline
45 & 0.42 & 0.420275626079446 & -0.000275626079446478 \tabularnewline
46 & 0.42 & 0.420214954168537 & -0.000214954168537507 \tabularnewline
47 & 0.42 & 0.42016763760042 & -0.000167637600420212 \tabularnewline
48 & 0.42 & 0.420130736543822 & -0.000130736543821675 \tabularnewline
49 & 0.42 & 0.420101958294843 & -0.000101958294843052 \tabularnewline
50 & 0.43 & 0.420079514828704 & 0.00992048517129618 \tabularnewline
51 & 0.44 & 0.432263251555271 & 0.00773674844472905 \tabularnewline
52 & 0.43 & 0.443966295451939 & -0.0139662954519394 \tabularnewline
53 & 0.43 & 0.430891978844851 & -0.00089197884485126 \tabularnewline
54 & 0.43 & 0.430695632907209 & -0.000695632907209143 \tabularnewline
55 & 0.44 & 0.43054250741975 & 0.00945749258024953 \tabularnewline
56 & 0.44 & 0.442624328372266 & -0.00262432837226634 \tabularnewline
57 & 0.44 & 0.442046650753668 & -0.00204665075366844 \tabularnewline
58 & 0.44 & 0.441596133834378 & -0.00159613383437768 \tabularnewline
59 & 0.44 & 0.441244786494559 & -0.00124478649455884 \tabularnewline
60 & 0.44 & 0.440970779131213 & -0.000970779131212574 \tabularnewline
61 & 0.44 & 0.440757087360537 & -0.00075708736053709 \tabularnewline
62 & 0.44 & 0.440590434273931 & -0.000590434273931184 \tabularnewline
63 & 0.44 & 0.44046046552882 & -0.000460465528820009 \tabularnewline
64 & 0.44 & 0.440359106021776 & -0.000359106021775746 \tabularnewline
65 & 0.45 & 0.440280058173314 & 0.00971994182668556 \tabularnewline
66 & 0.45 & 0.452419650499751 & -0.00241965049975063 \tabularnewline
67 & 0.45 & 0.451887027390041 & -0.00188702739004121 \tabularnewline
68 & 0.45 & 0.451471647401611 & -0.00147164740161143 \tabularnewline
69 & 0.45 & 0.451147702511421 & -0.00114770251142049 \tabularnewline
70 & 0.45 & 0.450895065661298 & -0.0008950656612981 \tabularnewline
71 & 0.45 & 0.45069804024132 & -0.000698040241319531 \tabularnewline
72 & 0.45 & 0.450544384841884 & -0.000544384841883849 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204947&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]0.38[/C][C]0.38[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.38[/C][C]0.39[/C][C]-0.01[/C][/ROW]
[ROW][C]5[/C][C]0.38[/C][C]0.387798760152492[/C][C]-0.00779876015249181[/C][/ROW]
[ROW][C]6[/C][C]0.38[/C][C]0.386082065991609[/C][C]-0.00608206599160938[/C][/ROW]
[ROW][C]7[/C][C]0.38[/C][C]0.384743257390019[/C][C]-0.00474325739001891[/C][/ROW]
[ROW][C]8[/C][C]0.38[/C][C]0.383699152672629[/C][C]-0.00369915267262916[/C][/ROW]
[ROW][C]9[/C][C]0.38[/C][C]0.382884880446128[/C][C]-0.00288488044612839[/C][/ROW]
[ROW][C]10[/C][C]0.38[/C][C]0.382249849066797[/C][C]-0.00224984906679687[/C][/ROW]
[ROW][C]11[/C][C]0.38[/C][C]0.381754603325126[/C][C]-0.00175460332512561[/C][/ROW]
[ROW][C]12[/C][C]0.38[/C][C]0.381368373049542[/C][C]-0.00136837304954196[/C][/ROW]
[ROW][C]13[/C][C]0.37[/C][C]0.381067161321251[/C][C]-0.0110671613212511[/C][/ROW]
[ROW][C]14[/C][C]0.37[/C][C]0.368631013671337[/C][C]0.00136898632866284[/C][/ROW]
[ROW][C]15[/C][C]0.37[/C][C]0.368932360397072[/C][C]0.00106763960292816[/C][/ROW]
[ROW][C]16[/C][C]0.38[/C][C]0.369167373480746[/C][C]0.0108326265192538[/C][/ROW]
[ROW][C]17[/C][C]0.38[/C][C]0.381551894395482[/C][C]-0.00155189439548176[/C][/ROW]
[ROW][C]18[/C][C]0.39[/C][C]0.381210285217236[/C][C]0.00878971478276419[/C][/ROW]
[ROW][C]19[/C][C]0.39[/C][C]0.393145112260041[/C][C]-0.00314511226004105[/C][/ROW]
[ROW][C]20[/C][C]0.38[/C][C]0.392452797616872[/C][C]-0.0124527976168722[/C][/ROW]
[ROW][C]21[/C][C]0.38[/C][C]0.379711638184151[/C][C]0.000288361815849236[/C][/ROW]
[ROW][C]22[/C][C]0.38[/C][C]0.379775113536105[/C][C]0.000224886463894514[/C][/ROW]
[ROW][C]23[/C][C]0.38[/C][C]0.379824616440654[/C][C]0.000175383559345543[/C][/ROW]
[ROW][C]24[/C][C]0.39[/C][C]0.379863222568597[/C][C]0.0101367774314026[/C][/ROW]
[ROW][C]25[/C][C]0.39[/C][C]0.39209457040933[/C][C]-0.00209457040932992[/C][/ROW]
[ROW][C]26[/C][C]0.4[/C][C]0.391633505224487[/C][C]0.00836649477551293[/C][/ROW]
[ROW][C]27[/C][C]0.4[/C][C]0.40347517139287[/C][C]-0.0034751713928699[/C][/ROW]
[ROW][C]28[/C][C]0.4[/C][C]0.402710202818179[/C][C]-0.0027102028181793[/C][/ROW]
[ROW][C]29[/C][C]0.41[/C][C]0.402113622174359[/C][C]0.00788637782564117[/C][/ROW]
[ROW][C]30[/C][C]0.41[/C][C]0.413849603086589[/C][C]-0.00384960308658944[/C][/ROW]
[ROW][C]31[/C][C]0.41[/C][C]0.41300221311546[/C][C]-0.00300221311546028[/C][/ROW]
[ROW][C]32[/C][C]0.41[/C][C]0.412341354001414[/C][C]-0.002341354001414[/C][/ROW]
[ROW][C]33[/C][C]0.41[/C][C]0.41182596582891[/C][C]-0.00182596582891048[/C][/ROW]
[ROW][C]34[/C][C]0.42[/C][C]0.411424026954632[/C][C]0.00857597304536817[/C][/ROW]
[ROW][C]35[/C][C]0.42[/C][C]0.423311804314494[/C][C]-0.0033118043144939[/C][/ROW]
[ROW][C]36[/C][C]0.42[/C][C]0.422582796752073[/C][C]-0.00258279675207257[/C][/ROW]
[ROW][C]37[/C][C]0.42[/C][C]0.422014261239205[/C][C]-0.0020142612392049[/C][/ROW]
[ROW][C]38[/C][C]0.42[/C][C]0.421570874028902[/C][C]-0.00157087402890199[/C][/ROW]
[ROW][C]39[/C][C]0.42[/C][C]0.421225086978119[/C][C]-0.00122508697811852[/C][/ROW]
[ROW][C]40[/C][C]0.42[/C][C]0.420955415950829[/C][C]-0.000955415950828709[/C][/ROW]
[ROW][C]41[/C][C]0.42[/C][C]0.420745105984638[/C][C]-0.000745105984637784[/C][/ROW]
[ROW][C]42[/C][C]0.42[/C][C]0.420581090286238[/C][C]-0.000581090286237651[/C][/ROW]
[ROW][C]43[/C][C]0.42[/C][C]0.420453178376931[/C][C]-0.00045317837693104[/C][/ROW]
[ROW][C]44[/C][C]0.42[/C][C]0.420353422946798[/C][C]-0.000353422946798077[/C][/ROW]
[ROW][C]45[/C][C]0.42[/C][C]0.420275626079446[/C][C]-0.000275626079446478[/C][/ROW]
[ROW][C]46[/C][C]0.42[/C][C]0.420214954168537[/C][C]-0.000214954168537507[/C][/ROW]
[ROW][C]47[/C][C]0.42[/C][C]0.42016763760042[/C][C]-0.000167637600420212[/C][/ROW]
[ROW][C]48[/C][C]0.42[/C][C]0.420130736543822[/C][C]-0.000130736543821675[/C][/ROW]
[ROW][C]49[/C][C]0.42[/C][C]0.420101958294843[/C][C]-0.000101958294843052[/C][/ROW]
[ROW][C]50[/C][C]0.43[/C][C]0.420079514828704[/C][C]0.00992048517129618[/C][/ROW]
[ROW][C]51[/C][C]0.44[/C][C]0.432263251555271[/C][C]0.00773674844472905[/C][/ROW]
[ROW][C]52[/C][C]0.43[/C][C]0.443966295451939[/C][C]-0.0139662954519394[/C][/ROW]
[ROW][C]53[/C][C]0.43[/C][C]0.430891978844851[/C][C]-0.00089197884485126[/C][/ROW]
[ROW][C]54[/C][C]0.43[/C][C]0.430695632907209[/C][C]-0.000695632907209143[/C][/ROW]
[ROW][C]55[/C][C]0.44[/C][C]0.43054250741975[/C][C]0.00945749258024953[/C][/ROW]
[ROW][C]56[/C][C]0.44[/C][C]0.442624328372266[/C][C]-0.00262432837226634[/C][/ROW]
[ROW][C]57[/C][C]0.44[/C][C]0.442046650753668[/C][C]-0.00204665075366844[/C][/ROW]
[ROW][C]58[/C][C]0.44[/C][C]0.441596133834378[/C][C]-0.00159613383437768[/C][/ROW]
[ROW][C]59[/C][C]0.44[/C][C]0.441244786494559[/C][C]-0.00124478649455884[/C][/ROW]
[ROW][C]60[/C][C]0.44[/C][C]0.440970779131213[/C][C]-0.000970779131212574[/C][/ROW]
[ROW][C]61[/C][C]0.44[/C][C]0.440757087360537[/C][C]-0.00075708736053709[/C][/ROW]
[ROW][C]62[/C][C]0.44[/C][C]0.440590434273931[/C][C]-0.000590434273931184[/C][/ROW]
[ROW][C]63[/C][C]0.44[/C][C]0.44046046552882[/C][C]-0.000460465528820009[/C][/ROW]
[ROW][C]64[/C][C]0.44[/C][C]0.440359106021776[/C][C]-0.000359106021775746[/C][/ROW]
[ROW][C]65[/C][C]0.45[/C][C]0.440280058173314[/C][C]0.00971994182668556[/C][/ROW]
[ROW][C]66[/C][C]0.45[/C][C]0.452419650499751[/C][C]-0.00241965049975063[/C][/ROW]
[ROW][C]67[/C][C]0.45[/C][C]0.451887027390041[/C][C]-0.00188702739004121[/C][/ROW]
[ROW][C]68[/C][C]0.45[/C][C]0.451471647401611[/C][C]-0.00147164740161143[/C][/ROW]
[ROW][C]69[/C][C]0.45[/C][C]0.451147702511421[/C][C]-0.00114770251142049[/C][/ROW]
[ROW][C]70[/C][C]0.45[/C][C]0.450895065661298[/C][C]-0.0008950656612981[/C][/ROW]
[ROW][C]71[/C][C]0.45[/C][C]0.45069804024132[/C][C]-0.000698040241319531[/C][/ROW]
[ROW][C]72[/C][C]0.45[/C][C]0.450544384841884[/C][C]-0.000544384841883849[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204947&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204947&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
30.380.380
40.380.39-0.01
50.380.387798760152492-0.00779876015249181
60.380.386082065991609-0.00608206599160938
70.380.384743257390019-0.00474325739001891
80.380.383699152672629-0.00369915267262916
90.380.382884880446128-0.00288488044612839
100.380.382249849066797-0.00224984906679687
110.380.381754603325126-0.00175460332512561
120.380.381368373049542-0.00136837304954196
130.370.381067161321251-0.0110671613212511
140.370.3686310136713370.00136898632866284
150.370.3689323603970720.00106763960292816
160.380.3691673734807460.0108326265192538
170.380.381551894395482-0.00155189439548176
180.390.3812102852172360.00878971478276419
190.390.393145112260041-0.00314511226004105
200.380.392452797616872-0.0124527976168722
210.380.3797116381841510.000288361815849236
220.380.3797751135361050.000224886463894514
230.380.3798246164406540.000175383559345543
240.390.3798632225685970.0101367774314026
250.390.39209457040933-0.00209457040932992
260.40.3916335052244870.00836649477551293
270.40.40347517139287-0.0034751713928699
280.40.402710202818179-0.0027102028181793
290.410.4021136221743590.00788637782564117
300.410.413849603086589-0.00384960308658944
310.410.41300221311546-0.00300221311546028
320.410.412341354001414-0.002341354001414
330.410.41182596582891-0.00182596582891048
340.420.4114240269546320.00857597304536817
350.420.423311804314494-0.0033118043144939
360.420.422582796752073-0.00258279675207257
370.420.422014261239205-0.0020142612392049
380.420.421570874028902-0.00157087402890199
390.420.421225086978119-0.00122508697811852
400.420.420955415950829-0.000955415950828709
410.420.420745105984638-0.000745105984637784
420.420.420581090286238-0.000581090286237651
430.420.420453178376931-0.00045317837693104
440.420.420353422946798-0.000353422946798077
450.420.420275626079446-0.000275626079446478
460.420.420214954168537-0.000214954168537507
470.420.42016763760042-0.000167637600420212
480.420.420130736543822-0.000130736543821675
490.420.420101958294843-0.000101958294843052
500.430.4200795148287040.00992048517129618
510.440.4322632515552710.00773674844472905
520.430.443966295451939-0.0139662954519394
530.430.430891978844851-0.00089197884485126
540.430.430695632907209-0.000695632907209143
550.440.430542507419750.00945749258024953
560.440.442624328372266-0.00262432837226634
570.440.442046650753668-0.00204665075366844
580.440.441596133834378-0.00159613383437768
590.440.441244786494559-0.00124478649455884
600.440.440970779131213-0.000970779131212574
610.440.440757087360537-0.00075708736053709
620.440.440590434273931-0.000590434273931184
630.440.44046046552882-0.000460465528820009
640.440.440359106021776-0.000359106021775746
650.450.4402800581733140.00971994182668556
660.450.452419650499751-0.00241965049975063
670.450.451887027390041-0.00188702739004121
680.450.451471647401611-0.00147164740161143
690.450.451147702511421-0.00114770251142049
700.450.450895065661298-0.0008950656612981
710.450.45069804024132-0.000698040241319531
720.450.450544384841884-0.000544384841883849







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
730.450424552681250.440764173778980.46008493158352
740.4508491053625010.435609256636040.466088954088962
750.4512736580437510.4306379111531810.471909404934322
760.4516982107250020.4255618386386530.47783458281135
770.4521227634062520.4202931463611130.483952380451391
780.4525473160875030.4147991820983110.490295450076694
790.4529718687687530.4090680524786510.496875685058855
800.4533964214500040.4030969307918550.503695912108152
810.4538209741312540.3968872715440330.510754676718475
820.4542455268125040.3904426105937330.518048443031276
830.4546700794937550.3837674738478450.525572685139665
840.4550946321750050.3768668082113320.533322456138678

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 0.45042455268125 & 0.44076417377898 & 0.46008493158352 \tabularnewline
74 & 0.450849105362501 & 0.43560925663604 & 0.466088954088962 \tabularnewline
75 & 0.451273658043751 & 0.430637911153181 & 0.471909404934322 \tabularnewline
76 & 0.451698210725002 & 0.425561838638653 & 0.47783458281135 \tabularnewline
77 & 0.452122763406252 & 0.420293146361113 & 0.483952380451391 \tabularnewline
78 & 0.452547316087503 & 0.414799182098311 & 0.490295450076694 \tabularnewline
79 & 0.452971868768753 & 0.409068052478651 & 0.496875685058855 \tabularnewline
80 & 0.453396421450004 & 0.403096930791855 & 0.503695912108152 \tabularnewline
81 & 0.453820974131254 & 0.396887271544033 & 0.510754676718475 \tabularnewline
82 & 0.454245526812504 & 0.390442610593733 & 0.518048443031276 \tabularnewline
83 & 0.454670079493755 & 0.383767473847845 & 0.525572685139665 \tabularnewline
84 & 0.455094632175005 & 0.376866808211332 & 0.533322456138678 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204947&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]0.45042455268125[/C][C]0.44076417377898[/C][C]0.46008493158352[/C][/ROW]
[ROW][C]74[/C][C]0.450849105362501[/C][C]0.43560925663604[/C][C]0.466088954088962[/C][/ROW]
[ROW][C]75[/C][C]0.451273658043751[/C][C]0.430637911153181[/C][C]0.471909404934322[/C][/ROW]
[ROW][C]76[/C][C]0.451698210725002[/C][C]0.425561838638653[/C][C]0.47783458281135[/C][/ROW]
[ROW][C]77[/C][C]0.452122763406252[/C][C]0.420293146361113[/C][C]0.483952380451391[/C][/ROW]
[ROW][C]78[/C][C]0.452547316087503[/C][C]0.414799182098311[/C][C]0.490295450076694[/C][/ROW]
[ROW][C]79[/C][C]0.452971868768753[/C][C]0.409068052478651[/C][C]0.496875685058855[/C][/ROW]
[ROW][C]80[/C][C]0.453396421450004[/C][C]0.403096930791855[/C][C]0.503695912108152[/C][/ROW]
[ROW][C]81[/C][C]0.453820974131254[/C][C]0.396887271544033[/C][C]0.510754676718475[/C][/ROW]
[ROW][C]82[/C][C]0.454245526812504[/C][C]0.390442610593733[/C][C]0.518048443031276[/C][/ROW]
[ROW][C]83[/C][C]0.454670079493755[/C][C]0.383767473847845[/C][C]0.525572685139665[/C][/ROW]
[ROW][C]84[/C][C]0.455094632175005[/C][C]0.376866808211332[/C][C]0.533322456138678[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204947&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204947&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
730.450424552681250.440764173778980.46008493158352
740.4508491053625010.435609256636040.466088954088962
750.4512736580437510.4306379111531810.471909404934322
760.4516982107250020.4255618386386530.47783458281135
770.4521227634062520.4202931463611130.483952380451391
780.4525473160875030.4147991820983110.490295450076694
790.4529718687687530.4090680524786510.496875685058855
800.4533964214500040.4030969307918550.503695912108152
810.4538209741312540.3968872715440330.510754676718475
820.4542455268125040.3904426105937330.518048443031276
830.4546700794937550.3837674738478450.525572685139665
840.4550946321750050.3768668082113320.533322456138678



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