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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 19 Dec 2012 12:17:27 -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/19/t1355937472njfxkhcsc2c8h7z.htm/, Retrieved Fri, 03 May 2024 23:13:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=202206, Retrieved Fri, 03 May 2024 23:13:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact69
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-12-19 17:17:27] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
104,42
104,42
104,42
104,42
104,42
104,42
104,42
104,44
104,44
104,44
105,19
105,19
105,19
106,38
106,38
106,38
106,38
106,38
106,38
106,72
106,73
106,72
108,6
108,6
109,65
109,65
109,65
109,65
109,65
109,65
109,65
109,65
112,27
112,27
112,27
112,27
112,27
114,98
114,98
114,98
114,98
114,98
114,98
116,04
116,59
116,59
116,59
116,59
118,75
118,75
118,75
118,75
118,75
118,75
118,75
119,31
119,31
119,31
119,31
119,31
121,19
121,19
121,19
121,19
121,19
122,91
122,91
122,91
122,91
122,91
122,91
122,91




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=202206&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=202206&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=202206&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
alpha0.790051014944359
beta0.0588166529110655
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.790051014944359 \tabularnewline
beta & 0.0588166529110655 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=202206&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]0.790051014944359[/C][/ROW]
[ROW][C]beta[/C][C]0.0588166529110655[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=202206&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=202206&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
alpha0.790051014944359
beta0.0588166529110655
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3104.42104.420
4104.42104.420
5104.42104.420
6104.42104.420
7104.42104.420
8104.44104.420.019999999999996
9104.44104.4367303834250.00326961657455627
10104.44104.440394843499-0.000394843499336162
11105.19104.4411458455230.748854154476831
12105.19105.0686396507610.121360349238756
13105.19105.20602072998-0.0160207299801129
14106.38105.2341192943431.14588070565723
15106.38106.233426230960.146573769040245
16106.38106.450040720875-0.0700407208748999
17106.38106.492264050014-0.112264050013991
18106.38106.495912091686-0.11591209168634
19106.38106.491291773136-0.111291773136102
20106.72106.4851502184340.234849781566268
21106.73106.763391186702-0.033391186701806
22106.72106.828156478856-0.108156478856401
23108.6106.8288275438941.77117245610575
24108.6108.3965674599870.203432540012543
25109.65108.7351659992740.91483400072606
26109.65109.67831863399-0.0283186339899686
27109.65109.87501665769-0.22501665768992
28109.65109.905857098902-0.255857098902226
29109.65109.900442810564-0.250442810563996
30109.65109.88766847055-0.237668470550076
31109.65109.873942495186-0.223942495185625
32109.65109.860654545714-0.210654545714192
33112.27109.8480760258482.42192397415225
34112.27112.0279111793680.24208882063202
35112.27112.496814778601-0.226814778600541
36112.27112.584720948759-0.314720948758847
37112.27112.588552257717-0.318552257717087
38114.98112.5745541010342.40544589896594
39114.98114.8244300888170.155569911183235
40114.98115.304018315906-0.32401831590559
41114.98115.389650843671-0.409650843670889
42114.98115.388593586519-0.408593586519359
43114.98115.3693850258-0.389385025800451
44116.04115.3472582037220.692741796277545
45116.59116.212257209810.377742790189942
46116.59116.845943942458-0.255943942458032
47116.59116.967092585691-0.377092585691344
48116.59116.975004823157-0.385004823157004
49118.75116.9587755250731.79122447492706
50118.75118.7451132916110.00488670838868188
51118.75119.120380168992-0.370380168991929
52118.75119.181956185429-0.431956185429485
53118.75119.174811800033-0.424811800032927
54118.75119.153571622436-0.403571622436161
55118.75119.130359039466-0.380359039466398
56119.31119.1078109979250.202189002075315
57119.31119.554900978013-0.244900978013092
58119.31119.63738696863-0.327386968630009
59119.31119.639491749803-0.329491749803267
60119.31119.624622772336-0.31462277233571
61121.19119.6068811054381.58311889456165
62121.19121.1620167848540.0279832151462358
63121.19121.489816270787-0.29981627078682
64121.19121.54470553082-0.354705530819629
65121.19121.539746963197-0.349746963197433
66122.91121.5224538203971.38754617960329
67122.91122.942187601108-0.0321876011077222
68122.91123.238763568937-0.328763568937106
69122.91123.285752355458-0.375752355458459
70122.91123.278157084304-0.368157084303547
71122.91123.259454883887-0.349454883886665
72122.91123.239289851717-0.329289851716808

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 104.42 & 104.42 & 0 \tabularnewline
4 & 104.42 & 104.42 & 0 \tabularnewline
5 & 104.42 & 104.42 & 0 \tabularnewline
6 & 104.42 & 104.42 & 0 \tabularnewline
7 & 104.42 & 104.42 & 0 \tabularnewline
8 & 104.44 & 104.42 & 0.019999999999996 \tabularnewline
9 & 104.44 & 104.436730383425 & 0.00326961657455627 \tabularnewline
10 & 104.44 & 104.440394843499 & -0.000394843499336162 \tabularnewline
11 & 105.19 & 104.441145845523 & 0.748854154476831 \tabularnewline
12 & 105.19 & 105.068639650761 & 0.121360349238756 \tabularnewline
13 & 105.19 & 105.20602072998 & -0.0160207299801129 \tabularnewline
14 & 106.38 & 105.234119294343 & 1.14588070565723 \tabularnewline
15 & 106.38 & 106.23342623096 & 0.146573769040245 \tabularnewline
16 & 106.38 & 106.450040720875 & -0.0700407208748999 \tabularnewline
17 & 106.38 & 106.492264050014 & -0.112264050013991 \tabularnewline
18 & 106.38 & 106.495912091686 & -0.11591209168634 \tabularnewline
19 & 106.38 & 106.491291773136 & -0.111291773136102 \tabularnewline
20 & 106.72 & 106.485150218434 & 0.234849781566268 \tabularnewline
21 & 106.73 & 106.763391186702 & -0.033391186701806 \tabularnewline
22 & 106.72 & 106.828156478856 & -0.108156478856401 \tabularnewline
23 & 108.6 & 106.828827543894 & 1.77117245610575 \tabularnewline
24 & 108.6 & 108.396567459987 & 0.203432540012543 \tabularnewline
25 & 109.65 & 108.735165999274 & 0.91483400072606 \tabularnewline
26 & 109.65 & 109.67831863399 & -0.0283186339899686 \tabularnewline
27 & 109.65 & 109.87501665769 & -0.22501665768992 \tabularnewline
28 & 109.65 & 109.905857098902 & -0.255857098902226 \tabularnewline
29 & 109.65 & 109.900442810564 & -0.250442810563996 \tabularnewline
30 & 109.65 & 109.88766847055 & -0.237668470550076 \tabularnewline
31 & 109.65 & 109.873942495186 & -0.223942495185625 \tabularnewline
32 & 109.65 & 109.860654545714 & -0.210654545714192 \tabularnewline
33 & 112.27 & 109.848076025848 & 2.42192397415225 \tabularnewline
34 & 112.27 & 112.027911179368 & 0.24208882063202 \tabularnewline
35 & 112.27 & 112.496814778601 & -0.226814778600541 \tabularnewline
36 & 112.27 & 112.584720948759 & -0.314720948758847 \tabularnewline
37 & 112.27 & 112.588552257717 & -0.318552257717087 \tabularnewline
38 & 114.98 & 112.574554101034 & 2.40544589896594 \tabularnewline
39 & 114.98 & 114.824430088817 & 0.155569911183235 \tabularnewline
40 & 114.98 & 115.304018315906 & -0.32401831590559 \tabularnewline
41 & 114.98 & 115.389650843671 & -0.409650843670889 \tabularnewline
42 & 114.98 & 115.388593586519 & -0.408593586519359 \tabularnewline
43 & 114.98 & 115.3693850258 & -0.389385025800451 \tabularnewline
44 & 116.04 & 115.347258203722 & 0.692741796277545 \tabularnewline
45 & 116.59 & 116.21225720981 & 0.377742790189942 \tabularnewline
46 & 116.59 & 116.845943942458 & -0.255943942458032 \tabularnewline
47 & 116.59 & 116.967092585691 & -0.377092585691344 \tabularnewline
48 & 116.59 & 116.975004823157 & -0.385004823157004 \tabularnewline
49 & 118.75 & 116.958775525073 & 1.79122447492706 \tabularnewline
50 & 118.75 & 118.745113291611 & 0.00488670838868188 \tabularnewline
51 & 118.75 & 119.120380168992 & -0.370380168991929 \tabularnewline
52 & 118.75 & 119.181956185429 & -0.431956185429485 \tabularnewline
53 & 118.75 & 119.174811800033 & -0.424811800032927 \tabularnewline
54 & 118.75 & 119.153571622436 & -0.403571622436161 \tabularnewline
55 & 118.75 & 119.130359039466 & -0.380359039466398 \tabularnewline
56 & 119.31 & 119.107810997925 & 0.202189002075315 \tabularnewline
57 & 119.31 & 119.554900978013 & -0.244900978013092 \tabularnewline
58 & 119.31 & 119.63738696863 & -0.327386968630009 \tabularnewline
59 & 119.31 & 119.639491749803 & -0.329491749803267 \tabularnewline
60 & 119.31 & 119.624622772336 & -0.31462277233571 \tabularnewline
61 & 121.19 & 119.606881105438 & 1.58311889456165 \tabularnewline
62 & 121.19 & 121.162016784854 & 0.0279832151462358 \tabularnewline
63 & 121.19 & 121.489816270787 & -0.29981627078682 \tabularnewline
64 & 121.19 & 121.54470553082 & -0.354705530819629 \tabularnewline
65 & 121.19 & 121.539746963197 & -0.349746963197433 \tabularnewline
66 & 122.91 & 121.522453820397 & 1.38754617960329 \tabularnewline
67 & 122.91 & 122.942187601108 & -0.0321876011077222 \tabularnewline
68 & 122.91 & 123.238763568937 & -0.328763568937106 \tabularnewline
69 & 122.91 & 123.285752355458 & -0.375752355458459 \tabularnewline
70 & 122.91 & 123.278157084304 & -0.368157084303547 \tabularnewline
71 & 122.91 & 123.259454883887 & -0.349454883886665 \tabularnewline
72 & 122.91 & 123.239289851717 & -0.329289851716808 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=202206&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]104.42[/C][C]104.42[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]104.42[/C][C]104.42[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]104.42[/C][C]104.42[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]104.42[/C][C]104.42[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]104.42[/C][C]104.42[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]104.44[/C][C]104.42[/C][C]0.019999999999996[/C][/ROW]
[ROW][C]9[/C][C]104.44[/C][C]104.436730383425[/C][C]0.00326961657455627[/C][/ROW]
[ROW][C]10[/C][C]104.44[/C][C]104.440394843499[/C][C]-0.000394843499336162[/C][/ROW]
[ROW][C]11[/C][C]105.19[/C][C]104.441145845523[/C][C]0.748854154476831[/C][/ROW]
[ROW][C]12[/C][C]105.19[/C][C]105.068639650761[/C][C]0.121360349238756[/C][/ROW]
[ROW][C]13[/C][C]105.19[/C][C]105.20602072998[/C][C]-0.0160207299801129[/C][/ROW]
[ROW][C]14[/C][C]106.38[/C][C]105.234119294343[/C][C]1.14588070565723[/C][/ROW]
[ROW][C]15[/C][C]106.38[/C][C]106.23342623096[/C][C]0.146573769040245[/C][/ROW]
[ROW][C]16[/C][C]106.38[/C][C]106.450040720875[/C][C]-0.0700407208748999[/C][/ROW]
[ROW][C]17[/C][C]106.38[/C][C]106.492264050014[/C][C]-0.112264050013991[/C][/ROW]
[ROW][C]18[/C][C]106.38[/C][C]106.495912091686[/C][C]-0.11591209168634[/C][/ROW]
[ROW][C]19[/C][C]106.38[/C][C]106.491291773136[/C][C]-0.111291773136102[/C][/ROW]
[ROW][C]20[/C][C]106.72[/C][C]106.485150218434[/C][C]0.234849781566268[/C][/ROW]
[ROW][C]21[/C][C]106.73[/C][C]106.763391186702[/C][C]-0.033391186701806[/C][/ROW]
[ROW][C]22[/C][C]106.72[/C][C]106.828156478856[/C][C]-0.108156478856401[/C][/ROW]
[ROW][C]23[/C][C]108.6[/C][C]106.828827543894[/C][C]1.77117245610575[/C][/ROW]
[ROW][C]24[/C][C]108.6[/C][C]108.396567459987[/C][C]0.203432540012543[/C][/ROW]
[ROW][C]25[/C][C]109.65[/C][C]108.735165999274[/C][C]0.91483400072606[/C][/ROW]
[ROW][C]26[/C][C]109.65[/C][C]109.67831863399[/C][C]-0.0283186339899686[/C][/ROW]
[ROW][C]27[/C][C]109.65[/C][C]109.87501665769[/C][C]-0.22501665768992[/C][/ROW]
[ROW][C]28[/C][C]109.65[/C][C]109.905857098902[/C][C]-0.255857098902226[/C][/ROW]
[ROW][C]29[/C][C]109.65[/C][C]109.900442810564[/C][C]-0.250442810563996[/C][/ROW]
[ROW][C]30[/C][C]109.65[/C][C]109.88766847055[/C][C]-0.237668470550076[/C][/ROW]
[ROW][C]31[/C][C]109.65[/C][C]109.873942495186[/C][C]-0.223942495185625[/C][/ROW]
[ROW][C]32[/C][C]109.65[/C][C]109.860654545714[/C][C]-0.210654545714192[/C][/ROW]
[ROW][C]33[/C][C]112.27[/C][C]109.848076025848[/C][C]2.42192397415225[/C][/ROW]
[ROW][C]34[/C][C]112.27[/C][C]112.027911179368[/C][C]0.24208882063202[/C][/ROW]
[ROW][C]35[/C][C]112.27[/C][C]112.496814778601[/C][C]-0.226814778600541[/C][/ROW]
[ROW][C]36[/C][C]112.27[/C][C]112.584720948759[/C][C]-0.314720948758847[/C][/ROW]
[ROW][C]37[/C][C]112.27[/C][C]112.588552257717[/C][C]-0.318552257717087[/C][/ROW]
[ROW][C]38[/C][C]114.98[/C][C]112.574554101034[/C][C]2.40544589896594[/C][/ROW]
[ROW][C]39[/C][C]114.98[/C][C]114.824430088817[/C][C]0.155569911183235[/C][/ROW]
[ROW][C]40[/C][C]114.98[/C][C]115.304018315906[/C][C]-0.32401831590559[/C][/ROW]
[ROW][C]41[/C][C]114.98[/C][C]115.389650843671[/C][C]-0.409650843670889[/C][/ROW]
[ROW][C]42[/C][C]114.98[/C][C]115.388593586519[/C][C]-0.408593586519359[/C][/ROW]
[ROW][C]43[/C][C]114.98[/C][C]115.3693850258[/C][C]-0.389385025800451[/C][/ROW]
[ROW][C]44[/C][C]116.04[/C][C]115.347258203722[/C][C]0.692741796277545[/C][/ROW]
[ROW][C]45[/C][C]116.59[/C][C]116.21225720981[/C][C]0.377742790189942[/C][/ROW]
[ROW][C]46[/C][C]116.59[/C][C]116.845943942458[/C][C]-0.255943942458032[/C][/ROW]
[ROW][C]47[/C][C]116.59[/C][C]116.967092585691[/C][C]-0.377092585691344[/C][/ROW]
[ROW][C]48[/C][C]116.59[/C][C]116.975004823157[/C][C]-0.385004823157004[/C][/ROW]
[ROW][C]49[/C][C]118.75[/C][C]116.958775525073[/C][C]1.79122447492706[/C][/ROW]
[ROW][C]50[/C][C]118.75[/C][C]118.745113291611[/C][C]0.00488670838868188[/C][/ROW]
[ROW][C]51[/C][C]118.75[/C][C]119.120380168992[/C][C]-0.370380168991929[/C][/ROW]
[ROW][C]52[/C][C]118.75[/C][C]119.181956185429[/C][C]-0.431956185429485[/C][/ROW]
[ROW][C]53[/C][C]118.75[/C][C]119.174811800033[/C][C]-0.424811800032927[/C][/ROW]
[ROW][C]54[/C][C]118.75[/C][C]119.153571622436[/C][C]-0.403571622436161[/C][/ROW]
[ROW][C]55[/C][C]118.75[/C][C]119.130359039466[/C][C]-0.380359039466398[/C][/ROW]
[ROW][C]56[/C][C]119.31[/C][C]119.107810997925[/C][C]0.202189002075315[/C][/ROW]
[ROW][C]57[/C][C]119.31[/C][C]119.554900978013[/C][C]-0.244900978013092[/C][/ROW]
[ROW][C]58[/C][C]119.31[/C][C]119.63738696863[/C][C]-0.327386968630009[/C][/ROW]
[ROW][C]59[/C][C]119.31[/C][C]119.639491749803[/C][C]-0.329491749803267[/C][/ROW]
[ROW][C]60[/C][C]119.31[/C][C]119.624622772336[/C][C]-0.31462277233571[/C][/ROW]
[ROW][C]61[/C][C]121.19[/C][C]119.606881105438[/C][C]1.58311889456165[/C][/ROW]
[ROW][C]62[/C][C]121.19[/C][C]121.162016784854[/C][C]0.0279832151462358[/C][/ROW]
[ROW][C]63[/C][C]121.19[/C][C]121.489816270787[/C][C]-0.29981627078682[/C][/ROW]
[ROW][C]64[/C][C]121.19[/C][C]121.54470553082[/C][C]-0.354705530819629[/C][/ROW]
[ROW][C]65[/C][C]121.19[/C][C]121.539746963197[/C][C]-0.349746963197433[/C][/ROW]
[ROW][C]66[/C][C]122.91[/C][C]121.522453820397[/C][C]1.38754617960329[/C][/ROW]
[ROW][C]67[/C][C]122.91[/C][C]122.942187601108[/C][C]-0.0321876011077222[/C][/ROW]
[ROW][C]68[/C][C]122.91[/C][C]123.238763568937[/C][C]-0.328763568937106[/C][/ROW]
[ROW][C]69[/C][C]122.91[/C][C]123.285752355458[/C][C]-0.375752355458459[/C][/ROW]
[ROW][C]70[/C][C]122.91[/C][C]123.278157084304[/C][C]-0.368157084303547[/C][/ROW]
[ROW][C]71[/C][C]122.91[/C][C]123.259454883887[/C][C]-0.349454883886665[/C][/ROW]
[ROW][C]72[/C][C]122.91[/C][C]123.239289851717[/C][C]-0.329289851716808[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=202206&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=202206&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
3104.42104.420
4104.42104.420
5104.42104.420
6104.42104.420
7104.42104.420
8104.44104.420.019999999999996
9104.44104.4367303834250.00326961657455627
10104.44104.440394843499-0.000394843499336162
11105.19104.4411458455230.748854154476831
12105.19105.0686396507610.121360349238756
13105.19105.20602072998-0.0160207299801129
14106.38105.2341192943431.14588070565723
15106.38106.233426230960.146573769040245
16106.38106.450040720875-0.0700407208748999
17106.38106.492264050014-0.112264050013991
18106.38106.495912091686-0.11591209168634
19106.38106.491291773136-0.111291773136102
20106.72106.4851502184340.234849781566268
21106.73106.763391186702-0.033391186701806
22106.72106.828156478856-0.108156478856401
23108.6106.8288275438941.77117245610575
24108.6108.3965674599870.203432540012543
25109.65108.7351659992740.91483400072606
26109.65109.67831863399-0.0283186339899686
27109.65109.87501665769-0.22501665768992
28109.65109.905857098902-0.255857098902226
29109.65109.900442810564-0.250442810563996
30109.65109.88766847055-0.237668470550076
31109.65109.873942495186-0.223942495185625
32109.65109.860654545714-0.210654545714192
33112.27109.8480760258482.42192397415225
34112.27112.0279111793680.24208882063202
35112.27112.496814778601-0.226814778600541
36112.27112.584720948759-0.314720948758847
37112.27112.588552257717-0.318552257717087
38114.98112.5745541010342.40544589896594
39114.98114.8244300888170.155569911183235
40114.98115.304018315906-0.32401831590559
41114.98115.389650843671-0.409650843670889
42114.98115.388593586519-0.408593586519359
43114.98115.3693850258-0.389385025800451
44116.04115.3472582037220.692741796277545
45116.59116.212257209810.377742790189942
46116.59116.845943942458-0.255943942458032
47116.59116.967092585691-0.377092585691344
48116.59116.975004823157-0.385004823157004
49118.75116.9587755250731.79122447492706
50118.75118.7451132916110.00488670838868188
51118.75119.120380168992-0.370380168991929
52118.75119.181956185429-0.431956185429485
53118.75119.174811800033-0.424811800032927
54118.75119.153571622436-0.403571622436161
55118.75119.130359039466-0.380359039466398
56119.31119.1078109979250.202189002075315
57119.31119.554900978013-0.244900978013092
58119.31119.63738696863-0.327386968630009
59119.31119.639491749803-0.329491749803267
60119.31119.624622772336-0.31462277233571
61121.19119.6068811054381.58311889456165
62121.19121.1620167848540.0279832151462358
63121.19121.489816270787-0.29981627078682
64121.19121.54470553082-0.354705530819629
65121.19121.539746963197-0.349746963197433
66122.91121.5224538203971.38754617960329
67122.91122.942187601108-0.0321876011077222
68122.91123.238763568937-0.328763568937106
69122.91123.285752355458-0.375752355458459
70122.91123.278157084304-0.368157084303547
71122.91123.259454883887-0.349454883886665
72122.91123.239289851717-0.329289851716808







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73123.219754731372121.94116233432124.498347128424
74123.460375392588121.79341042675125.127340358425
75123.700996053803121.687697756671125.714294350934
76123.941616715018121.603743315489126.279490114548
77124.182237376233121.53220375361126.832270998857
78124.422858037449121.467945425141127.377770649756
79124.663478698664121.407836968534127.919120428793
80124.904099359879121.349831250476128.458367469283
81125.144720021094121.292522634047128.996917408142
82125.38534068231121.234910363964129.535771000655
83125.625961343525121.176262122652130.075660564398
84125.86658200474121.116030594442130.617133415038

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 123.219754731372 & 121.94116233432 & 124.498347128424 \tabularnewline
74 & 123.460375392588 & 121.79341042675 & 125.127340358425 \tabularnewline
75 & 123.700996053803 & 121.687697756671 & 125.714294350934 \tabularnewline
76 & 123.941616715018 & 121.603743315489 & 126.279490114548 \tabularnewline
77 & 124.182237376233 & 121.53220375361 & 126.832270998857 \tabularnewline
78 & 124.422858037449 & 121.467945425141 & 127.377770649756 \tabularnewline
79 & 124.663478698664 & 121.407836968534 & 127.919120428793 \tabularnewline
80 & 124.904099359879 & 121.349831250476 & 128.458367469283 \tabularnewline
81 & 125.144720021094 & 121.292522634047 & 128.996917408142 \tabularnewline
82 & 125.38534068231 & 121.234910363964 & 129.535771000655 \tabularnewline
83 & 125.625961343525 & 121.176262122652 & 130.075660564398 \tabularnewline
84 & 125.86658200474 & 121.116030594442 & 130.617133415038 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=202206&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]123.219754731372[/C][C]121.94116233432[/C][C]124.498347128424[/C][/ROW]
[ROW][C]74[/C][C]123.460375392588[/C][C]121.79341042675[/C][C]125.127340358425[/C][/ROW]
[ROW][C]75[/C][C]123.700996053803[/C][C]121.687697756671[/C][C]125.714294350934[/C][/ROW]
[ROW][C]76[/C][C]123.941616715018[/C][C]121.603743315489[/C][C]126.279490114548[/C][/ROW]
[ROW][C]77[/C][C]124.182237376233[/C][C]121.53220375361[/C][C]126.832270998857[/C][/ROW]
[ROW][C]78[/C][C]124.422858037449[/C][C]121.467945425141[/C][C]127.377770649756[/C][/ROW]
[ROW][C]79[/C][C]124.663478698664[/C][C]121.407836968534[/C][C]127.919120428793[/C][/ROW]
[ROW][C]80[/C][C]124.904099359879[/C][C]121.349831250476[/C][C]128.458367469283[/C][/ROW]
[ROW][C]81[/C][C]125.144720021094[/C][C]121.292522634047[/C][C]128.996917408142[/C][/ROW]
[ROW][C]82[/C][C]125.38534068231[/C][C]121.234910363964[/C][C]129.535771000655[/C][/ROW]
[ROW][C]83[/C][C]125.625961343525[/C][C]121.176262122652[/C][C]130.075660564398[/C][/ROW]
[ROW][C]84[/C][C]125.86658200474[/C][C]121.116030594442[/C][C]130.617133415038[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=202206&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=202206&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
73123.219754731372121.94116233432124.498347128424
74123.460375392588121.79341042675125.127340358425
75123.700996053803121.687697756671125.714294350934
76123.941616715018121.603743315489126.279490114548
77124.182237376233121.53220375361126.832270998857
78124.422858037449121.467945425141127.377770649756
79124.663478698664121.407836968534127.919120428793
80124.904099359879121.349831250476128.458367469283
81125.144720021094121.292522634047128.996917408142
82125.38534068231121.234910363964129.535771000655
83125.625961343525121.176262122652130.075660564398
84125.86658200474121.116030594442130.617133415038



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')