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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 29 May 2012 02:57:22 -0400
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/May/29/t13382747185gwj7o4ve05sxmb.htm/, Retrieved Mon, 29 Apr 2024 23:47:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167925, Retrieved Mon, 29 Apr 2024 23:47:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact132
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential smoot...] [2012-05-29 06:57:22] [f04aaaaa8bc197d3d2d83dbea45e225d] [Current]
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Dataseries X:
530.3
527.76
521.41
1601.93
1577.49
1551.43
1551.43
1516.88
1485.95
1438.22
1385.06
1329.49
1329.49
1276.16
1242.34
1181.59
1160.21
1135.18
1135.18
1084.96
1077.35
1061.13
1029.98
1013.08
1013.08
996.04
975.02
951.89
944.4
932.47
932.47
920.44
900.18
886.9
869.74
859.03
859.03
844.99
834.82
825.62
816.92
813.21
813.21
811.03
804.16
788.62
778.76
765.91
765.91
753.85
742.22
732.11
729.94
731.22
731.22
729.11
726.94
720.52
709.36
703.21




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167925&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167925&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167925&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.989110454997596
beta0
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.989110454997596 \tabularnewline
beta & 0 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167925&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]0.989110454997596[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167925&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167925&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
alpha0.989110454997596
beta0
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3521.41525.22-3.81000000000006
41601.93518.9114891664591083.01851083354
51577.491587.59642118784-10.1064211878411
61551.431575.06005432834-23.6300543283382
71551.431549.147320540022.28267945998232
81516.881548.86514265929-31.9851426592945
91485.951514.6883036504-28.7383036503968
101438.221483.72294705089-45.5029470508939
111385.061436.17550638965-51.1155063896529
121329.491383.07662460715-53.5866246071507
131329.491327.533533960191.95646603981345
141276.161326.92869497501-50.7686949750137
151242.341274.17284798864-31.8328479886441
161181.591240.14664523073-58.5566452307271
171160.211179.68765522343-19.4776552234298
181135.181157.8821028031-22.702102803097
191135.181132.887215570122.29278442987652
201084.961132.61503262077-47.65503262077
211077.351082.93894162232-5.58894162231513
221061.131074.87086103131-13.7408610313119
231029.981058.73963172457-28.7596317245723
241013.081027.75317930392-14.6731793039172
251013.081010.699784246362.38021575364155
26996.041010.51408053344-14.4740805334354
27975.02993.657616151337-18.6376161513373
28951.89972.682955159818-20.7929551598176
29944.4949.576425820946-5.17642582094584
30932.47941.916368921929-9.44636892192875
31932.47930.0328666594852.43713334051529
32920.44929.903460726812-9.4634607268116
33900.18918.003052781463-17.8230527814633
34886.9897.834084935344-10.934084935344
35869.74884.479067209964-14.7390672099635
36859.03867.360501735676-8.33050173567642
37859.03856.5807153735432.44928462645669
38844.99856.463328404836-11.4733284048365
39834.82842.574939325992-7.75493932599181
40825.62832.364447760781-6.74444776078144
41816.92823.153443967407-6.23344396740742
42813.21814.447879368603-1.23787936860299
43813.21810.6834799430922.526520056908
44811.03810.6424873461410.387512653859062
45804.16808.485780163517-4.32578016351681
46788.62801.667105777761-13.0471057777611
47778.76786.222077045518-7.46207704551807
48765.91776.301258623799-10.3912586237986
49765.91763.4831560784162.42684392158446
50753.85763.343572773902-9.49357277390209
51742.22751.413380687955-9.19338068795503
52732.11739.780111732726-7.67011173272579
53729.94729.6535240268870.286475973113056
54731.22727.3968804069993.82311959300125
55731.22728.6383679671422.58163203285756
56729.11728.6518872017990.458112798201455
57726.94726.5650113600680.374988639932212
58720.52724.39591654433-3.87591654433015
59709.36718.022206967635-8.66220696763503
60703.21706.914327492594-3.70432749259419

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 521.41 & 525.22 & -3.81000000000006 \tabularnewline
4 & 1601.93 & 518.911489166459 & 1083.01851083354 \tabularnewline
5 & 1577.49 & 1587.59642118784 & -10.1064211878411 \tabularnewline
6 & 1551.43 & 1575.06005432834 & -23.6300543283382 \tabularnewline
7 & 1551.43 & 1549.14732054002 & 2.28267945998232 \tabularnewline
8 & 1516.88 & 1548.86514265929 & -31.9851426592945 \tabularnewline
9 & 1485.95 & 1514.6883036504 & -28.7383036503968 \tabularnewline
10 & 1438.22 & 1483.72294705089 & -45.5029470508939 \tabularnewline
11 & 1385.06 & 1436.17550638965 & -51.1155063896529 \tabularnewline
12 & 1329.49 & 1383.07662460715 & -53.5866246071507 \tabularnewline
13 & 1329.49 & 1327.53353396019 & 1.95646603981345 \tabularnewline
14 & 1276.16 & 1326.92869497501 & -50.7686949750137 \tabularnewline
15 & 1242.34 & 1274.17284798864 & -31.8328479886441 \tabularnewline
16 & 1181.59 & 1240.14664523073 & -58.5566452307271 \tabularnewline
17 & 1160.21 & 1179.68765522343 & -19.4776552234298 \tabularnewline
18 & 1135.18 & 1157.8821028031 & -22.702102803097 \tabularnewline
19 & 1135.18 & 1132.88721557012 & 2.29278442987652 \tabularnewline
20 & 1084.96 & 1132.61503262077 & -47.65503262077 \tabularnewline
21 & 1077.35 & 1082.93894162232 & -5.58894162231513 \tabularnewline
22 & 1061.13 & 1074.87086103131 & -13.7408610313119 \tabularnewline
23 & 1029.98 & 1058.73963172457 & -28.7596317245723 \tabularnewline
24 & 1013.08 & 1027.75317930392 & -14.6731793039172 \tabularnewline
25 & 1013.08 & 1010.69978424636 & 2.38021575364155 \tabularnewline
26 & 996.04 & 1010.51408053344 & -14.4740805334354 \tabularnewline
27 & 975.02 & 993.657616151337 & -18.6376161513373 \tabularnewline
28 & 951.89 & 972.682955159818 & -20.7929551598176 \tabularnewline
29 & 944.4 & 949.576425820946 & -5.17642582094584 \tabularnewline
30 & 932.47 & 941.916368921929 & -9.44636892192875 \tabularnewline
31 & 932.47 & 930.032866659485 & 2.43713334051529 \tabularnewline
32 & 920.44 & 929.903460726812 & -9.4634607268116 \tabularnewline
33 & 900.18 & 918.003052781463 & -17.8230527814633 \tabularnewline
34 & 886.9 & 897.834084935344 & -10.934084935344 \tabularnewline
35 & 869.74 & 884.479067209964 & -14.7390672099635 \tabularnewline
36 & 859.03 & 867.360501735676 & -8.33050173567642 \tabularnewline
37 & 859.03 & 856.580715373543 & 2.44928462645669 \tabularnewline
38 & 844.99 & 856.463328404836 & -11.4733284048365 \tabularnewline
39 & 834.82 & 842.574939325992 & -7.75493932599181 \tabularnewline
40 & 825.62 & 832.364447760781 & -6.74444776078144 \tabularnewline
41 & 816.92 & 823.153443967407 & -6.23344396740742 \tabularnewline
42 & 813.21 & 814.447879368603 & -1.23787936860299 \tabularnewline
43 & 813.21 & 810.683479943092 & 2.526520056908 \tabularnewline
44 & 811.03 & 810.642487346141 & 0.387512653859062 \tabularnewline
45 & 804.16 & 808.485780163517 & -4.32578016351681 \tabularnewline
46 & 788.62 & 801.667105777761 & -13.0471057777611 \tabularnewline
47 & 778.76 & 786.222077045518 & -7.46207704551807 \tabularnewline
48 & 765.91 & 776.301258623799 & -10.3912586237986 \tabularnewline
49 & 765.91 & 763.483156078416 & 2.42684392158446 \tabularnewline
50 & 753.85 & 763.343572773902 & -9.49357277390209 \tabularnewline
51 & 742.22 & 751.413380687955 & -9.19338068795503 \tabularnewline
52 & 732.11 & 739.780111732726 & -7.67011173272579 \tabularnewline
53 & 729.94 & 729.653524026887 & 0.286475973113056 \tabularnewline
54 & 731.22 & 727.396880406999 & 3.82311959300125 \tabularnewline
55 & 731.22 & 728.638367967142 & 2.58163203285756 \tabularnewline
56 & 729.11 & 728.651887201799 & 0.458112798201455 \tabularnewline
57 & 726.94 & 726.565011360068 & 0.374988639932212 \tabularnewline
58 & 720.52 & 724.39591654433 & -3.87591654433015 \tabularnewline
59 & 709.36 & 718.022206967635 & -8.66220696763503 \tabularnewline
60 & 703.21 & 706.914327492594 & -3.70432749259419 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167925&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]521.41[/C][C]525.22[/C][C]-3.81000000000006[/C][/ROW]
[ROW][C]4[/C][C]1601.93[/C][C]518.911489166459[/C][C]1083.01851083354[/C][/ROW]
[ROW][C]5[/C][C]1577.49[/C][C]1587.59642118784[/C][C]-10.1064211878411[/C][/ROW]
[ROW][C]6[/C][C]1551.43[/C][C]1575.06005432834[/C][C]-23.6300543283382[/C][/ROW]
[ROW][C]7[/C][C]1551.43[/C][C]1549.14732054002[/C][C]2.28267945998232[/C][/ROW]
[ROW][C]8[/C][C]1516.88[/C][C]1548.86514265929[/C][C]-31.9851426592945[/C][/ROW]
[ROW][C]9[/C][C]1485.95[/C][C]1514.6883036504[/C][C]-28.7383036503968[/C][/ROW]
[ROW][C]10[/C][C]1438.22[/C][C]1483.72294705089[/C][C]-45.5029470508939[/C][/ROW]
[ROW][C]11[/C][C]1385.06[/C][C]1436.17550638965[/C][C]-51.1155063896529[/C][/ROW]
[ROW][C]12[/C][C]1329.49[/C][C]1383.07662460715[/C][C]-53.5866246071507[/C][/ROW]
[ROW][C]13[/C][C]1329.49[/C][C]1327.53353396019[/C][C]1.95646603981345[/C][/ROW]
[ROW][C]14[/C][C]1276.16[/C][C]1326.92869497501[/C][C]-50.7686949750137[/C][/ROW]
[ROW][C]15[/C][C]1242.34[/C][C]1274.17284798864[/C][C]-31.8328479886441[/C][/ROW]
[ROW][C]16[/C][C]1181.59[/C][C]1240.14664523073[/C][C]-58.5566452307271[/C][/ROW]
[ROW][C]17[/C][C]1160.21[/C][C]1179.68765522343[/C][C]-19.4776552234298[/C][/ROW]
[ROW][C]18[/C][C]1135.18[/C][C]1157.8821028031[/C][C]-22.702102803097[/C][/ROW]
[ROW][C]19[/C][C]1135.18[/C][C]1132.88721557012[/C][C]2.29278442987652[/C][/ROW]
[ROW][C]20[/C][C]1084.96[/C][C]1132.61503262077[/C][C]-47.65503262077[/C][/ROW]
[ROW][C]21[/C][C]1077.35[/C][C]1082.93894162232[/C][C]-5.58894162231513[/C][/ROW]
[ROW][C]22[/C][C]1061.13[/C][C]1074.87086103131[/C][C]-13.7408610313119[/C][/ROW]
[ROW][C]23[/C][C]1029.98[/C][C]1058.73963172457[/C][C]-28.7596317245723[/C][/ROW]
[ROW][C]24[/C][C]1013.08[/C][C]1027.75317930392[/C][C]-14.6731793039172[/C][/ROW]
[ROW][C]25[/C][C]1013.08[/C][C]1010.69978424636[/C][C]2.38021575364155[/C][/ROW]
[ROW][C]26[/C][C]996.04[/C][C]1010.51408053344[/C][C]-14.4740805334354[/C][/ROW]
[ROW][C]27[/C][C]975.02[/C][C]993.657616151337[/C][C]-18.6376161513373[/C][/ROW]
[ROW][C]28[/C][C]951.89[/C][C]972.682955159818[/C][C]-20.7929551598176[/C][/ROW]
[ROW][C]29[/C][C]944.4[/C][C]949.576425820946[/C][C]-5.17642582094584[/C][/ROW]
[ROW][C]30[/C][C]932.47[/C][C]941.916368921929[/C][C]-9.44636892192875[/C][/ROW]
[ROW][C]31[/C][C]932.47[/C][C]930.032866659485[/C][C]2.43713334051529[/C][/ROW]
[ROW][C]32[/C][C]920.44[/C][C]929.903460726812[/C][C]-9.4634607268116[/C][/ROW]
[ROW][C]33[/C][C]900.18[/C][C]918.003052781463[/C][C]-17.8230527814633[/C][/ROW]
[ROW][C]34[/C][C]886.9[/C][C]897.834084935344[/C][C]-10.934084935344[/C][/ROW]
[ROW][C]35[/C][C]869.74[/C][C]884.479067209964[/C][C]-14.7390672099635[/C][/ROW]
[ROW][C]36[/C][C]859.03[/C][C]867.360501735676[/C][C]-8.33050173567642[/C][/ROW]
[ROW][C]37[/C][C]859.03[/C][C]856.580715373543[/C][C]2.44928462645669[/C][/ROW]
[ROW][C]38[/C][C]844.99[/C][C]856.463328404836[/C][C]-11.4733284048365[/C][/ROW]
[ROW][C]39[/C][C]834.82[/C][C]842.574939325992[/C][C]-7.75493932599181[/C][/ROW]
[ROW][C]40[/C][C]825.62[/C][C]832.364447760781[/C][C]-6.74444776078144[/C][/ROW]
[ROW][C]41[/C][C]816.92[/C][C]823.153443967407[/C][C]-6.23344396740742[/C][/ROW]
[ROW][C]42[/C][C]813.21[/C][C]814.447879368603[/C][C]-1.23787936860299[/C][/ROW]
[ROW][C]43[/C][C]813.21[/C][C]810.683479943092[/C][C]2.526520056908[/C][/ROW]
[ROW][C]44[/C][C]811.03[/C][C]810.642487346141[/C][C]0.387512653859062[/C][/ROW]
[ROW][C]45[/C][C]804.16[/C][C]808.485780163517[/C][C]-4.32578016351681[/C][/ROW]
[ROW][C]46[/C][C]788.62[/C][C]801.667105777761[/C][C]-13.0471057777611[/C][/ROW]
[ROW][C]47[/C][C]778.76[/C][C]786.222077045518[/C][C]-7.46207704551807[/C][/ROW]
[ROW][C]48[/C][C]765.91[/C][C]776.301258623799[/C][C]-10.3912586237986[/C][/ROW]
[ROW][C]49[/C][C]765.91[/C][C]763.483156078416[/C][C]2.42684392158446[/C][/ROW]
[ROW][C]50[/C][C]753.85[/C][C]763.343572773902[/C][C]-9.49357277390209[/C][/ROW]
[ROW][C]51[/C][C]742.22[/C][C]751.413380687955[/C][C]-9.19338068795503[/C][/ROW]
[ROW][C]52[/C][C]732.11[/C][C]739.780111732726[/C][C]-7.67011173272579[/C][/ROW]
[ROW][C]53[/C][C]729.94[/C][C]729.653524026887[/C][C]0.286475973113056[/C][/ROW]
[ROW][C]54[/C][C]731.22[/C][C]727.396880406999[/C][C]3.82311959300125[/C][/ROW]
[ROW][C]55[/C][C]731.22[/C][C]728.638367967142[/C][C]2.58163203285756[/C][/ROW]
[ROW][C]56[/C][C]729.11[/C][C]728.651887201799[/C][C]0.458112798201455[/C][/ROW]
[ROW][C]57[/C][C]726.94[/C][C]726.565011360068[/C][C]0.374988639932212[/C][/ROW]
[ROW][C]58[/C][C]720.52[/C][C]724.39591654433[/C][C]-3.87591654433015[/C][/ROW]
[ROW][C]59[/C][C]709.36[/C][C]718.022206967635[/C][C]-8.66220696763503[/C][/ROW]
[ROW][C]60[/C][C]703.21[/C][C]706.914327492594[/C][C]-3.70432749259419[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167925&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167925&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
3521.41525.22-3.81000000000006
41601.93518.9114891664591083.01851083354
51577.491587.59642118784-10.1064211878411
61551.431575.06005432834-23.6300543283382
71551.431549.147320540022.28267945998232
81516.881548.86514265929-31.9851426592945
91485.951514.6883036504-28.7383036503968
101438.221483.72294705089-45.5029470508939
111385.061436.17550638965-51.1155063896529
121329.491383.07662460715-53.5866246071507
131329.491327.533533960191.95646603981345
141276.161326.92869497501-50.7686949750137
151242.341274.17284798864-31.8328479886441
161181.591240.14664523073-58.5566452307271
171160.211179.68765522343-19.4776552234298
181135.181157.8821028031-22.702102803097
191135.181132.887215570122.29278442987652
201084.961132.61503262077-47.65503262077
211077.351082.93894162232-5.58894162231513
221061.131074.87086103131-13.7408610313119
231029.981058.73963172457-28.7596317245723
241013.081027.75317930392-14.6731793039172
251013.081010.699784246362.38021575364155
26996.041010.51408053344-14.4740805334354
27975.02993.657616151337-18.6376161513373
28951.89972.682955159818-20.7929551598176
29944.4949.576425820946-5.17642582094584
30932.47941.916368921929-9.44636892192875
31932.47930.0328666594852.43713334051529
32920.44929.903460726812-9.4634607268116
33900.18918.003052781463-17.8230527814633
34886.9897.834084935344-10.934084935344
35869.74884.479067209964-14.7390672099635
36859.03867.360501735676-8.33050173567642
37859.03856.5807153735432.44928462645669
38844.99856.463328404836-11.4733284048365
39834.82842.574939325992-7.75493932599181
40825.62832.364447760781-6.74444776078144
41816.92823.153443967407-6.23344396740742
42813.21814.447879368603-1.23787936860299
43813.21810.6834799430922.526520056908
44811.03810.6424873461410.387512653859062
45804.16808.485780163517-4.32578016351681
46788.62801.667105777761-13.0471057777611
47778.76786.222077045518-7.46207704551807
48765.91776.301258623799-10.3912586237986
49765.91763.4831560784162.42684392158446
50753.85763.343572773902-9.49357277390209
51742.22751.413380687955-9.19338068795503
52732.11739.780111732726-7.67011173272579
53729.94729.6535240268870.286475973113056
54731.22727.3968804069993.82311959300125
55731.22728.6383679671422.58163203285756
56729.11728.6518872017990.458112798201455
57726.94726.5650113600680.374988639932212
58720.52724.39591654433-3.87591654433015
59709.36718.022206967635-8.66220696763503
60703.21706.914327492594-3.70432749259419







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61700.710338440934416.85409497733984.566581904538
62698.170338440934298.9167195449971097.42395733687
63695.630338440934207.5396322707231183.72104461115
64693.090338440934130.0080862805871256.17259060128
65690.55033844093461.35187376845751319.74880311341
66688.010338440934-0.9887857924968561377.00946267437
67685.470338440934-58.53831637611051429.47899325798
68682.930338440935-112.291620317061478.15229719893
69680.390338440935-162.9405864866031523.72126336847
70677.850338440935-210.9894301267011566.69010700857
71675.310338440935-256.8190621444141607.43973902628
72672.770338440935-300.7255807512491646.26625763312

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 700.710338440934 & 416.85409497733 & 984.566581904538 \tabularnewline
62 & 698.170338440934 & 298.916719544997 & 1097.42395733687 \tabularnewline
63 & 695.630338440934 & 207.539632270723 & 1183.72104461115 \tabularnewline
64 & 693.090338440934 & 130.008086280587 & 1256.17259060128 \tabularnewline
65 & 690.550338440934 & 61.3518737684575 & 1319.74880311341 \tabularnewline
66 & 688.010338440934 & -0.988785792496856 & 1377.00946267437 \tabularnewline
67 & 685.470338440934 & -58.5383163761105 & 1429.47899325798 \tabularnewline
68 & 682.930338440935 & -112.29162031706 & 1478.15229719893 \tabularnewline
69 & 680.390338440935 & -162.940586486603 & 1523.72126336847 \tabularnewline
70 & 677.850338440935 & -210.989430126701 & 1566.69010700857 \tabularnewline
71 & 675.310338440935 & -256.819062144414 & 1607.43973902628 \tabularnewline
72 & 672.770338440935 & -300.725580751249 & 1646.26625763312 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167925&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]61[/C][C]700.710338440934[/C][C]416.85409497733[/C][C]984.566581904538[/C][/ROW]
[ROW][C]62[/C][C]698.170338440934[/C][C]298.916719544997[/C][C]1097.42395733687[/C][/ROW]
[ROW][C]63[/C][C]695.630338440934[/C][C]207.539632270723[/C][C]1183.72104461115[/C][/ROW]
[ROW][C]64[/C][C]693.090338440934[/C][C]130.008086280587[/C][C]1256.17259060128[/C][/ROW]
[ROW][C]65[/C][C]690.550338440934[/C][C]61.3518737684575[/C][C]1319.74880311341[/C][/ROW]
[ROW][C]66[/C][C]688.010338440934[/C][C]-0.988785792496856[/C][C]1377.00946267437[/C][/ROW]
[ROW][C]67[/C][C]685.470338440934[/C][C]-58.5383163761105[/C][C]1429.47899325798[/C][/ROW]
[ROW][C]68[/C][C]682.930338440935[/C][C]-112.29162031706[/C][C]1478.15229719893[/C][/ROW]
[ROW][C]69[/C][C]680.390338440935[/C][C]-162.940586486603[/C][C]1523.72126336847[/C][/ROW]
[ROW][C]70[/C][C]677.850338440935[/C][C]-210.989430126701[/C][C]1566.69010700857[/C][/ROW]
[ROW][C]71[/C][C]675.310338440935[/C][C]-256.819062144414[/C][C]1607.43973902628[/C][/ROW]
[ROW][C]72[/C][C]672.770338440935[/C][C]-300.725580751249[/C][C]1646.26625763312[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167925&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167925&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
61700.710338440934416.85409497733984.566581904538
62698.170338440934298.9167195449971097.42395733687
63695.630338440934207.5396322707231183.72104461115
64693.090338440934130.0080862805871256.17259060128
65690.55033844093461.35187376845751319.74880311341
66688.010338440934-0.9887857924968561377.00946267437
67685.470338440934-58.53831637611051429.47899325798
68682.930338440935-112.291620317061478.15229719893
69680.390338440935-162.9405864866031523.72126336847
70677.850338440935-210.9894301267011566.69010700857
71675.310338440935-256.8190621444141607.43973902628
72672.770338440935-300.7255807512491646.26625763312



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')