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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 22 May 2014 05:38:10 -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/2014/May/22/t1400751561x0ik0jaicnnxypd.htm/, Retrieved Wed, 15 May 2024 22:36:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235081, Retrieved Wed, 15 May 2024 22:36:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact103
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-05-22 09:38:10] [62c8c0f0c987c854521aa0b45bb2685a] [Current]
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Dataseries X:
1516
1289
1428
1335
1402
1475
1582
1317
1450
1497
1556
981
1807
1573
1756
1708
1737
1679
1872
1598
1747
1882
1369
865
1432
1172
1268
1120
1235
1272
1360
1069
1434
1552
1584
1070
1676
1690
1643
1446
1566
1352
1805
1613
1824
1866
1774
1505
1972
1856
2037
1888
2167
2191
2036
2103
2131
2039
1983
1629
2032
2216
2141
2073
2145
2429
2157
1994
2116
2287
2162
1699




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235081&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235081&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235081&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 time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.463738070808993
beta0.310216256161838
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.463738070808993 \tabularnewline
beta & 0.310216256161838 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235081&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]0.463738070808993[/C][/ROW]
[ROW][C]beta[/C][C]0.310216256161838[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235081&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235081&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
alpha0.463738070808993
beta0.310216256161838
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
314281062366
413351057.38056018488277.619439815124
514021051.71376936158350.286230638419
614751130.13719366334344.862806336663
715821255.65721850421326.342781495794
813171419.5361777296-102.536177729602
914501369.7768747610380.2231252389709
1014971416.3108440202180.6891559797903
1115561474.6687978802281.3312021197812
129811545.02472555496-564.02472555496
1318071234.96445762321572.03554237679
1415731534.0310981897938.9689018102097
1517561591.50047392864164.499526071356
1617081730.84793101419-22.8479310141879
1717371780.02835725773-43.0283572577284
1816791813.66033132661-134.660331326605
1918721785.4269580395786.5730419604261
2015981872.24224135543-274.242241355427
2117471752.28150248997-5.28150248997281
2218821756.28830565699125.711694343009
2313691839.12641093244-470.126410932437
248651578.01974595343-713.01974595343
2514321101.69982388216330.300176117844
2611721156.7237518662115.2762481337884
2712681067.8567183554200.143281644604
2811201093.5119963210326.4880036789737
2912351042.44725075367192.552749246327
3012721096.09351285556175.906487144441
3113601167.32601632723192.673983672768
3210691274.05214989574-205.052149895739
3314341166.83891826237267.161081737629
3415521317.04248928938234.95751071062
3515841486.1128116637797.8871883362349
3610701605.70036883228-535.700368832278
3716761354.40388796044321.596112039561
3816901546.93294667521143.067053324788
3916431677.25277995616-34.2527799561631
4014461720.41508214359-274.415082143586
4115661612.72787813737-46.727878137372
4213521603.90566892411-251.905668924115
4318051463.69578700327341.304212996727
4416131647.67962417818-34.6796241781833
4518241652.31646293402171.683537065978
4618661777.3499930667188.6500069332876
4717741876.63082328655-102.630823286548
4815051872.44307366176-367.443073661758
4919721692.59177639146279.408223608542
5018561852.905464092013.09453590799035
5120371885.52715243421151.47284756579
5218882008.74825850723-120.748258507228
5321671988.35933964996178.640660350038
5421912132.507542952558.4924570475023
5520362229.3531217798-193.353121779796
5621032181.59271394664-78.5927139466426
5721312175.74480008243-44.7448000824274
5820392179.15650635448-140.156506354481
5919832118.15938482264-135.159384822639
6016292040.0357129319-411.035712931899
6120321774.84646199582257.153538004176
6222161856.51587872011359.484121279887
6321412037.35494061495103.645059385052
6420732114.46197324514-41.461973245142
6521452118.3126688379826.6873311620202
6624292157.60600651012271.393993489876
6721572349.4216321215-192.4216321215
6819942298.46669376036-304.466693760363
6921162151.75189372984-35.7518937298382
7022872124.50714183111162.492858168892
7121622212.57210313558-50.5721031355793
7216992194.555473684-495.555473683997

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1428 & 1062 & 366 \tabularnewline
4 & 1335 & 1057.38056018488 & 277.619439815124 \tabularnewline
5 & 1402 & 1051.71376936158 & 350.286230638419 \tabularnewline
6 & 1475 & 1130.13719366334 & 344.862806336663 \tabularnewline
7 & 1582 & 1255.65721850421 & 326.342781495794 \tabularnewline
8 & 1317 & 1419.5361777296 & -102.536177729602 \tabularnewline
9 & 1450 & 1369.77687476103 & 80.2231252389709 \tabularnewline
10 & 1497 & 1416.31084402021 & 80.6891559797903 \tabularnewline
11 & 1556 & 1474.66879788022 & 81.3312021197812 \tabularnewline
12 & 981 & 1545.02472555496 & -564.02472555496 \tabularnewline
13 & 1807 & 1234.96445762321 & 572.03554237679 \tabularnewline
14 & 1573 & 1534.03109818979 & 38.9689018102097 \tabularnewline
15 & 1756 & 1591.50047392864 & 164.499526071356 \tabularnewline
16 & 1708 & 1730.84793101419 & -22.8479310141879 \tabularnewline
17 & 1737 & 1780.02835725773 & -43.0283572577284 \tabularnewline
18 & 1679 & 1813.66033132661 & -134.660331326605 \tabularnewline
19 & 1872 & 1785.42695803957 & 86.5730419604261 \tabularnewline
20 & 1598 & 1872.24224135543 & -274.242241355427 \tabularnewline
21 & 1747 & 1752.28150248997 & -5.28150248997281 \tabularnewline
22 & 1882 & 1756.28830565699 & 125.711694343009 \tabularnewline
23 & 1369 & 1839.12641093244 & -470.126410932437 \tabularnewline
24 & 865 & 1578.01974595343 & -713.01974595343 \tabularnewline
25 & 1432 & 1101.69982388216 & 330.300176117844 \tabularnewline
26 & 1172 & 1156.72375186621 & 15.2762481337884 \tabularnewline
27 & 1268 & 1067.8567183554 & 200.143281644604 \tabularnewline
28 & 1120 & 1093.51199632103 & 26.4880036789737 \tabularnewline
29 & 1235 & 1042.44725075367 & 192.552749246327 \tabularnewline
30 & 1272 & 1096.09351285556 & 175.906487144441 \tabularnewline
31 & 1360 & 1167.32601632723 & 192.673983672768 \tabularnewline
32 & 1069 & 1274.05214989574 & -205.052149895739 \tabularnewline
33 & 1434 & 1166.83891826237 & 267.161081737629 \tabularnewline
34 & 1552 & 1317.04248928938 & 234.95751071062 \tabularnewline
35 & 1584 & 1486.11281166377 & 97.8871883362349 \tabularnewline
36 & 1070 & 1605.70036883228 & -535.700368832278 \tabularnewline
37 & 1676 & 1354.40388796044 & 321.596112039561 \tabularnewline
38 & 1690 & 1546.93294667521 & 143.067053324788 \tabularnewline
39 & 1643 & 1677.25277995616 & -34.2527799561631 \tabularnewline
40 & 1446 & 1720.41508214359 & -274.415082143586 \tabularnewline
41 & 1566 & 1612.72787813737 & -46.727878137372 \tabularnewline
42 & 1352 & 1603.90566892411 & -251.905668924115 \tabularnewline
43 & 1805 & 1463.69578700327 & 341.304212996727 \tabularnewline
44 & 1613 & 1647.67962417818 & -34.6796241781833 \tabularnewline
45 & 1824 & 1652.31646293402 & 171.683537065978 \tabularnewline
46 & 1866 & 1777.34999306671 & 88.6500069332876 \tabularnewline
47 & 1774 & 1876.63082328655 & -102.630823286548 \tabularnewline
48 & 1505 & 1872.44307366176 & -367.443073661758 \tabularnewline
49 & 1972 & 1692.59177639146 & 279.408223608542 \tabularnewline
50 & 1856 & 1852.90546409201 & 3.09453590799035 \tabularnewline
51 & 2037 & 1885.52715243421 & 151.47284756579 \tabularnewline
52 & 1888 & 2008.74825850723 & -120.748258507228 \tabularnewline
53 & 2167 & 1988.35933964996 & 178.640660350038 \tabularnewline
54 & 2191 & 2132.5075429525 & 58.4924570475023 \tabularnewline
55 & 2036 & 2229.3531217798 & -193.353121779796 \tabularnewline
56 & 2103 & 2181.59271394664 & -78.5927139466426 \tabularnewline
57 & 2131 & 2175.74480008243 & -44.7448000824274 \tabularnewline
58 & 2039 & 2179.15650635448 & -140.156506354481 \tabularnewline
59 & 1983 & 2118.15938482264 & -135.159384822639 \tabularnewline
60 & 1629 & 2040.0357129319 & -411.035712931899 \tabularnewline
61 & 2032 & 1774.84646199582 & 257.153538004176 \tabularnewline
62 & 2216 & 1856.51587872011 & 359.484121279887 \tabularnewline
63 & 2141 & 2037.35494061495 & 103.645059385052 \tabularnewline
64 & 2073 & 2114.46197324514 & -41.461973245142 \tabularnewline
65 & 2145 & 2118.31266883798 & 26.6873311620202 \tabularnewline
66 & 2429 & 2157.60600651012 & 271.393993489876 \tabularnewline
67 & 2157 & 2349.4216321215 & -192.4216321215 \tabularnewline
68 & 1994 & 2298.46669376036 & -304.466693760363 \tabularnewline
69 & 2116 & 2151.75189372984 & -35.7518937298382 \tabularnewline
70 & 2287 & 2124.50714183111 & 162.492858168892 \tabularnewline
71 & 2162 & 2212.57210313558 & -50.5721031355793 \tabularnewline
72 & 1699 & 2194.555473684 & -495.555473683997 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235081&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]1428[/C][C]1062[/C][C]366[/C][/ROW]
[ROW][C]4[/C][C]1335[/C][C]1057.38056018488[/C][C]277.619439815124[/C][/ROW]
[ROW][C]5[/C][C]1402[/C][C]1051.71376936158[/C][C]350.286230638419[/C][/ROW]
[ROW][C]6[/C][C]1475[/C][C]1130.13719366334[/C][C]344.862806336663[/C][/ROW]
[ROW][C]7[/C][C]1582[/C][C]1255.65721850421[/C][C]326.342781495794[/C][/ROW]
[ROW][C]8[/C][C]1317[/C][C]1419.5361777296[/C][C]-102.536177729602[/C][/ROW]
[ROW][C]9[/C][C]1450[/C][C]1369.77687476103[/C][C]80.2231252389709[/C][/ROW]
[ROW][C]10[/C][C]1497[/C][C]1416.31084402021[/C][C]80.6891559797903[/C][/ROW]
[ROW][C]11[/C][C]1556[/C][C]1474.66879788022[/C][C]81.3312021197812[/C][/ROW]
[ROW][C]12[/C][C]981[/C][C]1545.02472555496[/C][C]-564.02472555496[/C][/ROW]
[ROW][C]13[/C][C]1807[/C][C]1234.96445762321[/C][C]572.03554237679[/C][/ROW]
[ROW][C]14[/C][C]1573[/C][C]1534.03109818979[/C][C]38.9689018102097[/C][/ROW]
[ROW][C]15[/C][C]1756[/C][C]1591.50047392864[/C][C]164.499526071356[/C][/ROW]
[ROW][C]16[/C][C]1708[/C][C]1730.84793101419[/C][C]-22.8479310141879[/C][/ROW]
[ROW][C]17[/C][C]1737[/C][C]1780.02835725773[/C][C]-43.0283572577284[/C][/ROW]
[ROW][C]18[/C][C]1679[/C][C]1813.66033132661[/C][C]-134.660331326605[/C][/ROW]
[ROW][C]19[/C][C]1872[/C][C]1785.42695803957[/C][C]86.5730419604261[/C][/ROW]
[ROW][C]20[/C][C]1598[/C][C]1872.24224135543[/C][C]-274.242241355427[/C][/ROW]
[ROW][C]21[/C][C]1747[/C][C]1752.28150248997[/C][C]-5.28150248997281[/C][/ROW]
[ROW][C]22[/C][C]1882[/C][C]1756.28830565699[/C][C]125.711694343009[/C][/ROW]
[ROW][C]23[/C][C]1369[/C][C]1839.12641093244[/C][C]-470.126410932437[/C][/ROW]
[ROW][C]24[/C][C]865[/C][C]1578.01974595343[/C][C]-713.01974595343[/C][/ROW]
[ROW][C]25[/C][C]1432[/C][C]1101.69982388216[/C][C]330.300176117844[/C][/ROW]
[ROW][C]26[/C][C]1172[/C][C]1156.72375186621[/C][C]15.2762481337884[/C][/ROW]
[ROW][C]27[/C][C]1268[/C][C]1067.8567183554[/C][C]200.143281644604[/C][/ROW]
[ROW][C]28[/C][C]1120[/C][C]1093.51199632103[/C][C]26.4880036789737[/C][/ROW]
[ROW][C]29[/C][C]1235[/C][C]1042.44725075367[/C][C]192.552749246327[/C][/ROW]
[ROW][C]30[/C][C]1272[/C][C]1096.09351285556[/C][C]175.906487144441[/C][/ROW]
[ROW][C]31[/C][C]1360[/C][C]1167.32601632723[/C][C]192.673983672768[/C][/ROW]
[ROW][C]32[/C][C]1069[/C][C]1274.05214989574[/C][C]-205.052149895739[/C][/ROW]
[ROW][C]33[/C][C]1434[/C][C]1166.83891826237[/C][C]267.161081737629[/C][/ROW]
[ROW][C]34[/C][C]1552[/C][C]1317.04248928938[/C][C]234.95751071062[/C][/ROW]
[ROW][C]35[/C][C]1584[/C][C]1486.11281166377[/C][C]97.8871883362349[/C][/ROW]
[ROW][C]36[/C][C]1070[/C][C]1605.70036883228[/C][C]-535.700368832278[/C][/ROW]
[ROW][C]37[/C][C]1676[/C][C]1354.40388796044[/C][C]321.596112039561[/C][/ROW]
[ROW][C]38[/C][C]1690[/C][C]1546.93294667521[/C][C]143.067053324788[/C][/ROW]
[ROW][C]39[/C][C]1643[/C][C]1677.25277995616[/C][C]-34.2527799561631[/C][/ROW]
[ROW][C]40[/C][C]1446[/C][C]1720.41508214359[/C][C]-274.415082143586[/C][/ROW]
[ROW][C]41[/C][C]1566[/C][C]1612.72787813737[/C][C]-46.727878137372[/C][/ROW]
[ROW][C]42[/C][C]1352[/C][C]1603.90566892411[/C][C]-251.905668924115[/C][/ROW]
[ROW][C]43[/C][C]1805[/C][C]1463.69578700327[/C][C]341.304212996727[/C][/ROW]
[ROW][C]44[/C][C]1613[/C][C]1647.67962417818[/C][C]-34.6796241781833[/C][/ROW]
[ROW][C]45[/C][C]1824[/C][C]1652.31646293402[/C][C]171.683537065978[/C][/ROW]
[ROW][C]46[/C][C]1866[/C][C]1777.34999306671[/C][C]88.6500069332876[/C][/ROW]
[ROW][C]47[/C][C]1774[/C][C]1876.63082328655[/C][C]-102.630823286548[/C][/ROW]
[ROW][C]48[/C][C]1505[/C][C]1872.44307366176[/C][C]-367.443073661758[/C][/ROW]
[ROW][C]49[/C][C]1972[/C][C]1692.59177639146[/C][C]279.408223608542[/C][/ROW]
[ROW][C]50[/C][C]1856[/C][C]1852.90546409201[/C][C]3.09453590799035[/C][/ROW]
[ROW][C]51[/C][C]2037[/C][C]1885.52715243421[/C][C]151.47284756579[/C][/ROW]
[ROW][C]52[/C][C]1888[/C][C]2008.74825850723[/C][C]-120.748258507228[/C][/ROW]
[ROW][C]53[/C][C]2167[/C][C]1988.35933964996[/C][C]178.640660350038[/C][/ROW]
[ROW][C]54[/C][C]2191[/C][C]2132.5075429525[/C][C]58.4924570475023[/C][/ROW]
[ROW][C]55[/C][C]2036[/C][C]2229.3531217798[/C][C]-193.353121779796[/C][/ROW]
[ROW][C]56[/C][C]2103[/C][C]2181.59271394664[/C][C]-78.5927139466426[/C][/ROW]
[ROW][C]57[/C][C]2131[/C][C]2175.74480008243[/C][C]-44.7448000824274[/C][/ROW]
[ROW][C]58[/C][C]2039[/C][C]2179.15650635448[/C][C]-140.156506354481[/C][/ROW]
[ROW][C]59[/C][C]1983[/C][C]2118.15938482264[/C][C]-135.159384822639[/C][/ROW]
[ROW][C]60[/C][C]1629[/C][C]2040.0357129319[/C][C]-411.035712931899[/C][/ROW]
[ROW][C]61[/C][C]2032[/C][C]1774.84646199582[/C][C]257.153538004176[/C][/ROW]
[ROW][C]62[/C][C]2216[/C][C]1856.51587872011[/C][C]359.484121279887[/C][/ROW]
[ROW][C]63[/C][C]2141[/C][C]2037.35494061495[/C][C]103.645059385052[/C][/ROW]
[ROW][C]64[/C][C]2073[/C][C]2114.46197324514[/C][C]-41.461973245142[/C][/ROW]
[ROW][C]65[/C][C]2145[/C][C]2118.31266883798[/C][C]26.6873311620202[/C][/ROW]
[ROW][C]66[/C][C]2429[/C][C]2157.60600651012[/C][C]271.393993489876[/C][/ROW]
[ROW][C]67[/C][C]2157[/C][C]2349.4216321215[/C][C]-192.4216321215[/C][/ROW]
[ROW][C]68[/C][C]1994[/C][C]2298.46669376036[/C][C]-304.466693760363[/C][/ROW]
[ROW][C]69[/C][C]2116[/C][C]2151.75189372984[/C][C]-35.7518937298382[/C][/ROW]
[ROW][C]70[/C][C]2287[/C][C]2124.50714183111[/C][C]162.492858168892[/C][/ROW]
[ROW][C]71[/C][C]2162[/C][C]2212.57210313558[/C][C]-50.5721031355793[/C][/ROW]
[ROW][C]72[/C][C]1699[/C][C]2194.555473684[/C][C]-495.555473683997[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235081&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235081&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
314281062366
413351057.38056018488277.619439815124
514021051.71376936158350.286230638419
614751130.13719366334344.862806336663
715821255.65721850421326.342781495794
813171419.5361777296-102.536177729602
914501369.7768747610380.2231252389709
1014971416.3108440202180.6891559797903
1115561474.6687978802281.3312021197812
129811545.02472555496-564.02472555496
1318071234.96445762321572.03554237679
1415731534.0310981897938.9689018102097
1517561591.50047392864164.499526071356
1617081730.84793101419-22.8479310141879
1717371780.02835725773-43.0283572577284
1816791813.66033132661-134.660331326605
1918721785.4269580395786.5730419604261
2015981872.24224135543-274.242241355427
2117471752.28150248997-5.28150248997281
2218821756.28830565699125.711694343009
2313691839.12641093244-470.126410932437
248651578.01974595343-713.01974595343
2514321101.69982388216330.300176117844
2611721156.7237518662115.2762481337884
2712681067.8567183554200.143281644604
2811201093.5119963210326.4880036789737
2912351042.44725075367192.552749246327
3012721096.09351285556175.906487144441
3113601167.32601632723192.673983672768
3210691274.05214989574-205.052149895739
3314341166.83891826237267.161081737629
3415521317.04248928938234.95751071062
3515841486.1128116637797.8871883362349
3610701605.70036883228-535.700368832278
3716761354.40388796044321.596112039561
3816901546.93294667521143.067053324788
3916431677.25277995616-34.2527799561631
4014461720.41508214359-274.415082143586
4115661612.72787813737-46.727878137372
4213521603.90566892411-251.905668924115
4318051463.69578700327341.304212996727
4416131647.67962417818-34.6796241781833
4518241652.31646293402171.683537065978
4618661777.3499930667188.6500069332876
4717741876.63082328655-102.630823286548
4815051872.44307366176-367.443073661758
4919721692.59177639146279.408223608542
5018561852.905464092013.09453590799035
5120371885.52715243421151.47284756579
5218882008.74825850723-120.748258507228
5321671988.35933964996178.640660350038
5421912132.507542952558.4924570475023
5520362229.3531217798-193.353121779796
5621032181.59271394664-78.5927139466426
5721312175.74480008243-44.7448000824274
5820392179.15650635448-140.156506354481
5919832118.15938482264-135.159384822639
6016292040.0357129319-411.035712931899
6120321774.84646199582257.153538004176
6222161856.51587872011359.484121279887
6321412037.35494061495103.645059385052
6420732114.46197324514-41.461973245142
6521452118.3126688379826.6873311620202
6624292157.60600651012271.393993489876
6721572349.4216321215-192.4216321215
6819942298.46669376036-304.466693760363
6921162151.75189372984-35.7518937298382
7022872124.50714183111162.492858168892
7121622212.57210313558-50.5721031355793
7216992194.555473684-495.555473683997







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
731898.892955852321399.935131488522397.85078021612
741833.038377365691249.199235225562416.87751950583
751767.183798879071073.31646461672461.05113314144
761701.32922039245876.0930490468812526.56539173801
771635.47464190582660.8663340528792610.08294975876
781569.6200634192430.1919830683862709.04814377001
791503.76548493257185.9550451560972821.57592470905
801437.91090644595-70.44912863542162946.27094152732
811372.05632795932-337.9664490969493082.0791050156
821306.2017494727-615.7796994659993228.1831984114
831240.34717098608-903.2383762896393383.93271826179
841174.49259249945-1199.811821501553548.79700650045

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 1898.89295585232 & 1399.93513148852 & 2397.85078021612 \tabularnewline
74 & 1833.03837736569 & 1249.19923522556 & 2416.87751950583 \tabularnewline
75 & 1767.18379887907 & 1073.3164646167 & 2461.05113314144 \tabularnewline
76 & 1701.32922039245 & 876.093049046881 & 2526.56539173801 \tabularnewline
77 & 1635.47464190582 & 660.866334052879 & 2610.08294975876 \tabularnewline
78 & 1569.6200634192 & 430.191983068386 & 2709.04814377001 \tabularnewline
79 & 1503.76548493257 & 185.955045156097 & 2821.57592470905 \tabularnewline
80 & 1437.91090644595 & -70.4491286354216 & 2946.27094152732 \tabularnewline
81 & 1372.05632795932 & -337.966449096949 & 3082.0791050156 \tabularnewline
82 & 1306.2017494727 & -615.779699465999 & 3228.1831984114 \tabularnewline
83 & 1240.34717098608 & -903.238376289639 & 3383.93271826179 \tabularnewline
84 & 1174.49259249945 & -1199.81182150155 & 3548.79700650045 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235081&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]1898.89295585232[/C][C]1399.93513148852[/C][C]2397.85078021612[/C][/ROW]
[ROW][C]74[/C][C]1833.03837736569[/C][C]1249.19923522556[/C][C]2416.87751950583[/C][/ROW]
[ROW][C]75[/C][C]1767.18379887907[/C][C]1073.3164646167[/C][C]2461.05113314144[/C][/ROW]
[ROW][C]76[/C][C]1701.32922039245[/C][C]876.093049046881[/C][C]2526.56539173801[/C][/ROW]
[ROW][C]77[/C][C]1635.47464190582[/C][C]660.866334052879[/C][C]2610.08294975876[/C][/ROW]
[ROW][C]78[/C][C]1569.6200634192[/C][C]430.191983068386[/C][C]2709.04814377001[/C][/ROW]
[ROW][C]79[/C][C]1503.76548493257[/C][C]185.955045156097[/C][C]2821.57592470905[/C][/ROW]
[ROW][C]80[/C][C]1437.91090644595[/C][C]-70.4491286354216[/C][C]2946.27094152732[/C][/ROW]
[ROW][C]81[/C][C]1372.05632795932[/C][C]-337.966449096949[/C][C]3082.0791050156[/C][/ROW]
[ROW][C]82[/C][C]1306.2017494727[/C][C]-615.779699465999[/C][C]3228.1831984114[/C][/ROW]
[ROW][C]83[/C][C]1240.34717098608[/C][C]-903.238376289639[/C][C]3383.93271826179[/C][/ROW]
[ROW][C]84[/C][C]1174.49259249945[/C][C]-1199.81182150155[/C][C]3548.79700650045[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235081&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235081&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
731898.892955852321399.935131488522397.85078021612
741833.038377365691249.199235225562416.87751950583
751767.183798879071073.31646461672461.05113314144
761701.32922039245876.0930490468812526.56539173801
771635.47464190582660.8663340528792610.08294975876
781569.6200634192430.1919830683862709.04814377001
791503.76548493257185.9550451560972821.57592470905
801437.91090644595-70.44912863542162946.27094152732
811372.05632795932-337.9664490969493082.0791050156
821306.2017494727-615.7796994659993228.1831984114
831240.34717098608-903.2383762896393383.93271826179
841174.49259249945-1199.811821501553548.79700650045



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')