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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 20 May 2011 08:24:02 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/May/20/t13058798932afrdy4hgsk9lnn.htm/, Retrieved Sun, 12 May 2024 23:49:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=122431, Retrieved Sun, 12 May 2024 23:49:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact85
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2011-05-20 08:24:02] [31b126aa1b32aa85c8fd6bf40153b92b] [Current]
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Dataseries X:
19097,1
19304,6
19601,7
16006,9
17681,2
19790,4
17014,2
17424,5
18908,9
15692,1
15160
15794,3
16032,1
16065
16236,8
12521
14762,1
15446,9
13635
14212,6
15021,7
14134,3
13721,4
14384,5
15638,6
19711,6
20359,8
16141,4
20056,9
20605,5
19325,8
20547,7
19211,2
19009,5
18746,8
16471,5
18957,2
20515,2
18374,4
16192,9
18147,5
19301,4
18344,7
17183,6
19630
17167,2
17428,5
16016,5
18466,5
18406,6
18174,1
14851,9
16260,7
18329,6
18003,8
15903,8
19554,2
16554,2
16198,9
16571,8
17535,2
16198,1
17487,5
13768
14915,8
17160,9
15607,4
16181,5
17413,2
15116,3
14544,5
15050,6
15535,4
15919,3
15853,1
12336,4
14355,5
16040,8
13867,7
14656,6




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ www.wessa.org

\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' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122431&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' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122431&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122431&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' @ www.wessa.org







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.380888896422215
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.380888896422215 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122431&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]0.380888896422215[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122431&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122431&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
alpha0.380888896422215
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
219304.619097.1207.5
319601.719176.1344460076425.565553992394
416006.919338.2276402231-3331.32764022308
517681.218069.3619317177-388.161931717685
619790.417921.51536191261868.88463808738
717014.218633.3527692542-1619.15276925415
817424.518016.635457834-592.135457833963
918908.917791.09763676711117.80236323288
1015692.118216.856145317-2524.75614531704
111516017255.204563392-2095.20456339202
1215794.316457.1644094628-662.864409462847
1316032.116204.686716065-172.586716064978
141606516138.9503522459-73.9503522458544
1516236.816110.7834841889126.016515811103
161252116158.7817758272-3637.78177582716
1714762.114773.1910898075-11.0910898075053
1815446.914768.9666168506677.933383149395
191363515027.1839150062-1392.18391500616
2014212.614496.9165200027-284.3165200027
2115021.714388.6235144643633.076485535734
2214134.314629.7553183908-495.455318390828
2313721.414441.0418889424-719.641888942428
2414384.514166.9382840439217.561715956053
2515638.614249.80512593821388.79487406183
2619711.614778.78167287644932.81832712359
2720359.816657.63740174583702.16259825421
2816141.418067.7500281704-1926.35002817044
2920056.917334.02469181772722.87530818231
3020605.518371.13766304652234.36233695345
3119325.819222.1814677761103.618532223889
3220547.719261.64861616381286.05138383625
3319211.219751.4913084954-540.291308495402
3419009.519545.7003482561-536.200348256076
3518746.819341.4675893476-594.667589347613
3616471.519114.9653075029-2643.46530750294
3718957.218108.0987237977849.101276202269
3820515.218431.51197184112083.68802815889
3918374.419225.1656053747-850.765605374727
4016192.918901.1184328296-2708.21843282957
4118147.517869.5881026788277.911897321188
4219301.417975.44165855211325.95834144792
4318344.718480.484467928-135.78446792801
4417183.618428.7656717876-1245.16567178763
451963017954.49589319761675.50410680239
4617167.218592.6768033885-1425.47680338846
4717428.518049.7285168704-621.228516870364
4816016.517813.1094726536-1796.6094726536
4918466.517128.80087331291337.69912668713
5018406.617638.3156174217768.284382578306
5118174.117930.9466080404243.153391959633
5214851.918023.5610351652-3171.66103516519
5316260.716815.5105636558-554.810563655778
5418329.616604.18938034151725.41061965846
5518003.817261.3791271384742.420872861578
5615903.817544.1589940835-1640.35899408349
5719554.216919.36446709082634.83553290923
5816554.217922.9440654746-1368.74406547461
5916198.917401.6046488915-1202.70464889153
6016571.816943.5078024534-371.707802453366
6117535.216801.9284277854733.271572214628
6216198.117081.223427704-883.123427703986
6317487.516744.8515199212742.648480078791
641376817027.7180799281-3259.71807992805
6514915.815786.1276578167-870.327657816715
6617160.915454.62951670521706.27048329483
6715607.416104.5289980851-497.128998085142
6816181.515915.178082625266.321917374989
6917413.216016.6171438271396.58285617298
7015116.316548.5600466769-1432.26004667693
7114544.516003.0280981085-1458.52809810852
7215050.615447.4909404192-396.890940419175
7315535.415296.3195881229239.080411877059
7415919.315387.382662359531.91733764104
7515853.115589.9840700809263.115929919104
7612336.415690.2020062589-3353.80200625889
7714355.514412.7760612763-57.2760612763268
7816040.814390.96024550541649.83975449462
7913867.715019.3658888683-1151.66588886833
8014656.614580.709139410275.8908605898378

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 19304.6 & 19097.1 & 207.5 \tabularnewline
3 & 19601.7 & 19176.1344460076 & 425.565553992394 \tabularnewline
4 & 16006.9 & 19338.2276402231 & -3331.32764022308 \tabularnewline
5 & 17681.2 & 18069.3619317177 & -388.161931717685 \tabularnewline
6 & 19790.4 & 17921.5153619126 & 1868.88463808738 \tabularnewline
7 & 17014.2 & 18633.3527692542 & -1619.15276925415 \tabularnewline
8 & 17424.5 & 18016.635457834 & -592.135457833963 \tabularnewline
9 & 18908.9 & 17791.0976367671 & 1117.80236323288 \tabularnewline
10 & 15692.1 & 18216.856145317 & -2524.75614531704 \tabularnewline
11 & 15160 & 17255.204563392 & -2095.20456339202 \tabularnewline
12 & 15794.3 & 16457.1644094628 & -662.864409462847 \tabularnewline
13 & 16032.1 & 16204.686716065 & -172.586716064978 \tabularnewline
14 & 16065 & 16138.9503522459 & -73.9503522458544 \tabularnewline
15 & 16236.8 & 16110.7834841889 & 126.016515811103 \tabularnewline
16 & 12521 & 16158.7817758272 & -3637.78177582716 \tabularnewline
17 & 14762.1 & 14773.1910898075 & -11.0910898075053 \tabularnewline
18 & 15446.9 & 14768.9666168506 & 677.933383149395 \tabularnewline
19 & 13635 & 15027.1839150062 & -1392.18391500616 \tabularnewline
20 & 14212.6 & 14496.9165200027 & -284.3165200027 \tabularnewline
21 & 15021.7 & 14388.6235144643 & 633.076485535734 \tabularnewline
22 & 14134.3 & 14629.7553183908 & -495.455318390828 \tabularnewline
23 & 13721.4 & 14441.0418889424 & -719.641888942428 \tabularnewline
24 & 14384.5 & 14166.9382840439 & 217.561715956053 \tabularnewline
25 & 15638.6 & 14249.8051259382 & 1388.79487406183 \tabularnewline
26 & 19711.6 & 14778.7816728764 & 4932.81832712359 \tabularnewline
27 & 20359.8 & 16657.6374017458 & 3702.16259825421 \tabularnewline
28 & 16141.4 & 18067.7500281704 & -1926.35002817044 \tabularnewline
29 & 20056.9 & 17334.0246918177 & 2722.87530818231 \tabularnewline
30 & 20605.5 & 18371.1376630465 & 2234.36233695345 \tabularnewline
31 & 19325.8 & 19222.1814677761 & 103.618532223889 \tabularnewline
32 & 20547.7 & 19261.6486161638 & 1286.05138383625 \tabularnewline
33 & 19211.2 & 19751.4913084954 & -540.291308495402 \tabularnewline
34 & 19009.5 & 19545.7003482561 & -536.200348256076 \tabularnewline
35 & 18746.8 & 19341.4675893476 & -594.667589347613 \tabularnewline
36 & 16471.5 & 19114.9653075029 & -2643.46530750294 \tabularnewline
37 & 18957.2 & 18108.0987237977 & 849.101276202269 \tabularnewline
38 & 20515.2 & 18431.5119718411 & 2083.68802815889 \tabularnewline
39 & 18374.4 & 19225.1656053747 & -850.765605374727 \tabularnewline
40 & 16192.9 & 18901.1184328296 & -2708.21843282957 \tabularnewline
41 & 18147.5 & 17869.5881026788 & 277.911897321188 \tabularnewline
42 & 19301.4 & 17975.4416585521 & 1325.95834144792 \tabularnewline
43 & 18344.7 & 18480.484467928 & -135.78446792801 \tabularnewline
44 & 17183.6 & 18428.7656717876 & -1245.16567178763 \tabularnewline
45 & 19630 & 17954.4958931976 & 1675.50410680239 \tabularnewline
46 & 17167.2 & 18592.6768033885 & -1425.47680338846 \tabularnewline
47 & 17428.5 & 18049.7285168704 & -621.228516870364 \tabularnewline
48 & 16016.5 & 17813.1094726536 & -1796.6094726536 \tabularnewline
49 & 18466.5 & 17128.8008733129 & 1337.69912668713 \tabularnewline
50 & 18406.6 & 17638.3156174217 & 768.284382578306 \tabularnewline
51 & 18174.1 & 17930.9466080404 & 243.153391959633 \tabularnewline
52 & 14851.9 & 18023.5610351652 & -3171.66103516519 \tabularnewline
53 & 16260.7 & 16815.5105636558 & -554.810563655778 \tabularnewline
54 & 18329.6 & 16604.1893803415 & 1725.41061965846 \tabularnewline
55 & 18003.8 & 17261.3791271384 & 742.420872861578 \tabularnewline
56 & 15903.8 & 17544.1589940835 & -1640.35899408349 \tabularnewline
57 & 19554.2 & 16919.3644670908 & 2634.83553290923 \tabularnewline
58 & 16554.2 & 17922.9440654746 & -1368.74406547461 \tabularnewline
59 & 16198.9 & 17401.6046488915 & -1202.70464889153 \tabularnewline
60 & 16571.8 & 16943.5078024534 & -371.707802453366 \tabularnewline
61 & 17535.2 & 16801.9284277854 & 733.271572214628 \tabularnewline
62 & 16198.1 & 17081.223427704 & -883.123427703986 \tabularnewline
63 & 17487.5 & 16744.8515199212 & 742.648480078791 \tabularnewline
64 & 13768 & 17027.7180799281 & -3259.71807992805 \tabularnewline
65 & 14915.8 & 15786.1276578167 & -870.327657816715 \tabularnewline
66 & 17160.9 & 15454.6295167052 & 1706.27048329483 \tabularnewline
67 & 15607.4 & 16104.5289980851 & -497.128998085142 \tabularnewline
68 & 16181.5 & 15915.178082625 & 266.321917374989 \tabularnewline
69 & 17413.2 & 16016.617143827 & 1396.58285617298 \tabularnewline
70 & 15116.3 & 16548.5600466769 & -1432.26004667693 \tabularnewline
71 & 14544.5 & 16003.0280981085 & -1458.52809810852 \tabularnewline
72 & 15050.6 & 15447.4909404192 & -396.890940419175 \tabularnewline
73 & 15535.4 & 15296.3195881229 & 239.080411877059 \tabularnewline
74 & 15919.3 & 15387.382662359 & 531.91733764104 \tabularnewline
75 & 15853.1 & 15589.9840700809 & 263.115929919104 \tabularnewline
76 & 12336.4 & 15690.2020062589 & -3353.80200625889 \tabularnewline
77 & 14355.5 & 14412.7760612763 & -57.2760612763268 \tabularnewline
78 & 16040.8 & 14390.9602455054 & 1649.83975449462 \tabularnewline
79 & 13867.7 & 15019.3658888683 & -1151.66588886833 \tabularnewline
80 & 14656.6 & 14580.7091394102 & 75.8908605898378 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122431&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]2[/C][C]19304.6[/C][C]19097.1[/C][C]207.5[/C][/ROW]
[ROW][C]3[/C][C]19601.7[/C][C]19176.1344460076[/C][C]425.565553992394[/C][/ROW]
[ROW][C]4[/C][C]16006.9[/C][C]19338.2276402231[/C][C]-3331.32764022308[/C][/ROW]
[ROW][C]5[/C][C]17681.2[/C][C]18069.3619317177[/C][C]-388.161931717685[/C][/ROW]
[ROW][C]6[/C][C]19790.4[/C][C]17921.5153619126[/C][C]1868.88463808738[/C][/ROW]
[ROW][C]7[/C][C]17014.2[/C][C]18633.3527692542[/C][C]-1619.15276925415[/C][/ROW]
[ROW][C]8[/C][C]17424.5[/C][C]18016.635457834[/C][C]-592.135457833963[/C][/ROW]
[ROW][C]9[/C][C]18908.9[/C][C]17791.0976367671[/C][C]1117.80236323288[/C][/ROW]
[ROW][C]10[/C][C]15692.1[/C][C]18216.856145317[/C][C]-2524.75614531704[/C][/ROW]
[ROW][C]11[/C][C]15160[/C][C]17255.204563392[/C][C]-2095.20456339202[/C][/ROW]
[ROW][C]12[/C][C]15794.3[/C][C]16457.1644094628[/C][C]-662.864409462847[/C][/ROW]
[ROW][C]13[/C][C]16032.1[/C][C]16204.686716065[/C][C]-172.586716064978[/C][/ROW]
[ROW][C]14[/C][C]16065[/C][C]16138.9503522459[/C][C]-73.9503522458544[/C][/ROW]
[ROW][C]15[/C][C]16236.8[/C][C]16110.7834841889[/C][C]126.016515811103[/C][/ROW]
[ROW][C]16[/C][C]12521[/C][C]16158.7817758272[/C][C]-3637.78177582716[/C][/ROW]
[ROW][C]17[/C][C]14762.1[/C][C]14773.1910898075[/C][C]-11.0910898075053[/C][/ROW]
[ROW][C]18[/C][C]15446.9[/C][C]14768.9666168506[/C][C]677.933383149395[/C][/ROW]
[ROW][C]19[/C][C]13635[/C][C]15027.1839150062[/C][C]-1392.18391500616[/C][/ROW]
[ROW][C]20[/C][C]14212.6[/C][C]14496.9165200027[/C][C]-284.3165200027[/C][/ROW]
[ROW][C]21[/C][C]15021.7[/C][C]14388.6235144643[/C][C]633.076485535734[/C][/ROW]
[ROW][C]22[/C][C]14134.3[/C][C]14629.7553183908[/C][C]-495.455318390828[/C][/ROW]
[ROW][C]23[/C][C]13721.4[/C][C]14441.0418889424[/C][C]-719.641888942428[/C][/ROW]
[ROW][C]24[/C][C]14384.5[/C][C]14166.9382840439[/C][C]217.561715956053[/C][/ROW]
[ROW][C]25[/C][C]15638.6[/C][C]14249.8051259382[/C][C]1388.79487406183[/C][/ROW]
[ROW][C]26[/C][C]19711.6[/C][C]14778.7816728764[/C][C]4932.81832712359[/C][/ROW]
[ROW][C]27[/C][C]20359.8[/C][C]16657.6374017458[/C][C]3702.16259825421[/C][/ROW]
[ROW][C]28[/C][C]16141.4[/C][C]18067.7500281704[/C][C]-1926.35002817044[/C][/ROW]
[ROW][C]29[/C][C]20056.9[/C][C]17334.0246918177[/C][C]2722.87530818231[/C][/ROW]
[ROW][C]30[/C][C]20605.5[/C][C]18371.1376630465[/C][C]2234.36233695345[/C][/ROW]
[ROW][C]31[/C][C]19325.8[/C][C]19222.1814677761[/C][C]103.618532223889[/C][/ROW]
[ROW][C]32[/C][C]20547.7[/C][C]19261.6486161638[/C][C]1286.05138383625[/C][/ROW]
[ROW][C]33[/C][C]19211.2[/C][C]19751.4913084954[/C][C]-540.291308495402[/C][/ROW]
[ROW][C]34[/C][C]19009.5[/C][C]19545.7003482561[/C][C]-536.200348256076[/C][/ROW]
[ROW][C]35[/C][C]18746.8[/C][C]19341.4675893476[/C][C]-594.667589347613[/C][/ROW]
[ROW][C]36[/C][C]16471.5[/C][C]19114.9653075029[/C][C]-2643.46530750294[/C][/ROW]
[ROW][C]37[/C][C]18957.2[/C][C]18108.0987237977[/C][C]849.101276202269[/C][/ROW]
[ROW][C]38[/C][C]20515.2[/C][C]18431.5119718411[/C][C]2083.68802815889[/C][/ROW]
[ROW][C]39[/C][C]18374.4[/C][C]19225.1656053747[/C][C]-850.765605374727[/C][/ROW]
[ROW][C]40[/C][C]16192.9[/C][C]18901.1184328296[/C][C]-2708.21843282957[/C][/ROW]
[ROW][C]41[/C][C]18147.5[/C][C]17869.5881026788[/C][C]277.911897321188[/C][/ROW]
[ROW][C]42[/C][C]19301.4[/C][C]17975.4416585521[/C][C]1325.95834144792[/C][/ROW]
[ROW][C]43[/C][C]18344.7[/C][C]18480.484467928[/C][C]-135.78446792801[/C][/ROW]
[ROW][C]44[/C][C]17183.6[/C][C]18428.7656717876[/C][C]-1245.16567178763[/C][/ROW]
[ROW][C]45[/C][C]19630[/C][C]17954.4958931976[/C][C]1675.50410680239[/C][/ROW]
[ROW][C]46[/C][C]17167.2[/C][C]18592.6768033885[/C][C]-1425.47680338846[/C][/ROW]
[ROW][C]47[/C][C]17428.5[/C][C]18049.7285168704[/C][C]-621.228516870364[/C][/ROW]
[ROW][C]48[/C][C]16016.5[/C][C]17813.1094726536[/C][C]-1796.6094726536[/C][/ROW]
[ROW][C]49[/C][C]18466.5[/C][C]17128.8008733129[/C][C]1337.69912668713[/C][/ROW]
[ROW][C]50[/C][C]18406.6[/C][C]17638.3156174217[/C][C]768.284382578306[/C][/ROW]
[ROW][C]51[/C][C]18174.1[/C][C]17930.9466080404[/C][C]243.153391959633[/C][/ROW]
[ROW][C]52[/C][C]14851.9[/C][C]18023.5610351652[/C][C]-3171.66103516519[/C][/ROW]
[ROW][C]53[/C][C]16260.7[/C][C]16815.5105636558[/C][C]-554.810563655778[/C][/ROW]
[ROW][C]54[/C][C]18329.6[/C][C]16604.1893803415[/C][C]1725.41061965846[/C][/ROW]
[ROW][C]55[/C][C]18003.8[/C][C]17261.3791271384[/C][C]742.420872861578[/C][/ROW]
[ROW][C]56[/C][C]15903.8[/C][C]17544.1589940835[/C][C]-1640.35899408349[/C][/ROW]
[ROW][C]57[/C][C]19554.2[/C][C]16919.3644670908[/C][C]2634.83553290923[/C][/ROW]
[ROW][C]58[/C][C]16554.2[/C][C]17922.9440654746[/C][C]-1368.74406547461[/C][/ROW]
[ROW][C]59[/C][C]16198.9[/C][C]17401.6046488915[/C][C]-1202.70464889153[/C][/ROW]
[ROW][C]60[/C][C]16571.8[/C][C]16943.5078024534[/C][C]-371.707802453366[/C][/ROW]
[ROW][C]61[/C][C]17535.2[/C][C]16801.9284277854[/C][C]733.271572214628[/C][/ROW]
[ROW][C]62[/C][C]16198.1[/C][C]17081.223427704[/C][C]-883.123427703986[/C][/ROW]
[ROW][C]63[/C][C]17487.5[/C][C]16744.8515199212[/C][C]742.648480078791[/C][/ROW]
[ROW][C]64[/C][C]13768[/C][C]17027.7180799281[/C][C]-3259.71807992805[/C][/ROW]
[ROW][C]65[/C][C]14915.8[/C][C]15786.1276578167[/C][C]-870.327657816715[/C][/ROW]
[ROW][C]66[/C][C]17160.9[/C][C]15454.6295167052[/C][C]1706.27048329483[/C][/ROW]
[ROW][C]67[/C][C]15607.4[/C][C]16104.5289980851[/C][C]-497.128998085142[/C][/ROW]
[ROW][C]68[/C][C]16181.5[/C][C]15915.178082625[/C][C]266.321917374989[/C][/ROW]
[ROW][C]69[/C][C]17413.2[/C][C]16016.617143827[/C][C]1396.58285617298[/C][/ROW]
[ROW][C]70[/C][C]15116.3[/C][C]16548.5600466769[/C][C]-1432.26004667693[/C][/ROW]
[ROW][C]71[/C][C]14544.5[/C][C]16003.0280981085[/C][C]-1458.52809810852[/C][/ROW]
[ROW][C]72[/C][C]15050.6[/C][C]15447.4909404192[/C][C]-396.890940419175[/C][/ROW]
[ROW][C]73[/C][C]15535.4[/C][C]15296.3195881229[/C][C]239.080411877059[/C][/ROW]
[ROW][C]74[/C][C]15919.3[/C][C]15387.382662359[/C][C]531.91733764104[/C][/ROW]
[ROW][C]75[/C][C]15853.1[/C][C]15589.9840700809[/C][C]263.115929919104[/C][/ROW]
[ROW][C]76[/C][C]12336.4[/C][C]15690.2020062589[/C][C]-3353.80200625889[/C][/ROW]
[ROW][C]77[/C][C]14355.5[/C][C]14412.7760612763[/C][C]-57.2760612763268[/C][/ROW]
[ROW][C]78[/C][C]16040.8[/C][C]14390.9602455054[/C][C]1649.83975449462[/C][/ROW]
[ROW][C]79[/C][C]13867.7[/C][C]15019.3658888683[/C][C]-1151.66588886833[/C][/ROW]
[ROW][C]80[/C][C]14656.6[/C][C]14580.7091394102[/C][C]75.8908605898378[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122431&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122431&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
219304.619097.1207.5
319601.719176.1344460076425.565553992394
416006.919338.2276402231-3331.32764022308
517681.218069.3619317177-388.161931717685
619790.417921.51536191261868.88463808738
717014.218633.3527692542-1619.15276925415
817424.518016.635457834-592.135457833963
918908.917791.09763676711117.80236323288
1015692.118216.856145317-2524.75614531704
111516017255.204563392-2095.20456339202
1215794.316457.1644094628-662.864409462847
1316032.116204.686716065-172.586716064978
141606516138.9503522459-73.9503522458544
1516236.816110.7834841889126.016515811103
161252116158.7817758272-3637.78177582716
1714762.114773.1910898075-11.0910898075053
1815446.914768.9666168506677.933383149395
191363515027.1839150062-1392.18391500616
2014212.614496.9165200027-284.3165200027
2115021.714388.6235144643633.076485535734
2214134.314629.7553183908-495.455318390828
2313721.414441.0418889424-719.641888942428
2414384.514166.9382840439217.561715956053
2515638.614249.80512593821388.79487406183
2619711.614778.78167287644932.81832712359
2720359.816657.63740174583702.16259825421
2816141.418067.7500281704-1926.35002817044
2920056.917334.02469181772722.87530818231
3020605.518371.13766304652234.36233695345
3119325.819222.1814677761103.618532223889
3220547.719261.64861616381286.05138383625
3319211.219751.4913084954-540.291308495402
3419009.519545.7003482561-536.200348256076
3518746.819341.4675893476-594.667589347613
3616471.519114.9653075029-2643.46530750294
3718957.218108.0987237977849.101276202269
3820515.218431.51197184112083.68802815889
3918374.419225.1656053747-850.765605374727
4016192.918901.1184328296-2708.21843282957
4118147.517869.5881026788277.911897321188
4219301.417975.44165855211325.95834144792
4318344.718480.484467928-135.78446792801
4417183.618428.7656717876-1245.16567178763
451963017954.49589319761675.50410680239
4617167.218592.6768033885-1425.47680338846
4717428.518049.7285168704-621.228516870364
4816016.517813.1094726536-1796.6094726536
4918466.517128.80087331291337.69912668713
5018406.617638.3156174217768.284382578306
5118174.117930.9466080404243.153391959633
5214851.918023.5610351652-3171.66103516519
5316260.716815.5105636558-554.810563655778
5418329.616604.18938034151725.41061965846
5518003.817261.3791271384742.420872861578
5615903.817544.1589940835-1640.35899408349
5719554.216919.36446709082634.83553290923
5816554.217922.9440654746-1368.74406547461
5916198.917401.6046488915-1202.70464889153
6016571.816943.5078024534-371.707802453366
6117535.216801.9284277854733.271572214628
6216198.117081.223427704-883.123427703986
6317487.516744.8515199212742.648480078791
641376817027.7180799281-3259.71807992805
6514915.815786.1276578167-870.327657816715
6617160.915454.62951670521706.27048329483
6715607.416104.5289980851-497.128998085142
6816181.515915.178082625266.321917374989
6917413.216016.6171438271396.58285617298
7015116.316548.5600466769-1432.26004667693
7114544.516003.0280981085-1458.52809810852
7215050.615447.4909404192-396.890940419175
7315535.415296.3195881229239.080411877059
7415919.315387.382662359531.91733764104
7515853.115589.9840700809263.115929919104
7612336.415690.2020062589-3353.80200625889
7714355.514412.7760612763-57.2760612763268
7816040.814390.96024550541649.83975449462
7913867.715019.3658888683-1151.66588886833
8014656.614580.709139410275.8908605898378







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8114609.615125548811438.644435937917780.5858151596
8214609.615125548811216.415186896718002.8150642008
8314609.615125548811007.8715848518211.3586662476
8414609.615125548810810.759081650418408.4711694471
8514609.615125548810623.381570981318595.8486801163
8614609.615125548810444.425014538618774.8052365589
8714609.615125548810272.846816063718946.3834350339
8814609.615125548810107.803259260819111.4269918368
8914609.61512554889948.6001299980419270.6301210995
9014609.61512554889794.6580646762719424.5721864212
9114609.61512554889645.4875881719219573.7426629256
9214609.61512554889500.6707221871219718.5595289104

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
81 & 14609.6151255488 & 11438.6444359379 & 17780.5858151596 \tabularnewline
82 & 14609.6151255488 & 11216.4151868967 & 18002.8150642008 \tabularnewline
83 & 14609.6151255488 & 11007.87158485 & 18211.3586662476 \tabularnewline
84 & 14609.6151255488 & 10810.7590816504 & 18408.4711694471 \tabularnewline
85 & 14609.6151255488 & 10623.3815709813 & 18595.8486801163 \tabularnewline
86 & 14609.6151255488 & 10444.4250145386 & 18774.8052365589 \tabularnewline
87 & 14609.6151255488 & 10272.8468160637 & 18946.3834350339 \tabularnewline
88 & 14609.6151255488 & 10107.8032592608 & 19111.4269918368 \tabularnewline
89 & 14609.6151255488 & 9948.60012999804 & 19270.6301210995 \tabularnewline
90 & 14609.6151255488 & 9794.65806467627 & 19424.5721864212 \tabularnewline
91 & 14609.6151255488 & 9645.48758817192 & 19573.7426629256 \tabularnewline
92 & 14609.6151255488 & 9500.67072218712 & 19718.5595289104 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122431&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]81[/C][C]14609.6151255488[/C][C]11438.6444359379[/C][C]17780.5858151596[/C][/ROW]
[ROW][C]82[/C][C]14609.6151255488[/C][C]11216.4151868967[/C][C]18002.8150642008[/C][/ROW]
[ROW][C]83[/C][C]14609.6151255488[/C][C]11007.87158485[/C][C]18211.3586662476[/C][/ROW]
[ROW][C]84[/C][C]14609.6151255488[/C][C]10810.7590816504[/C][C]18408.4711694471[/C][/ROW]
[ROW][C]85[/C][C]14609.6151255488[/C][C]10623.3815709813[/C][C]18595.8486801163[/C][/ROW]
[ROW][C]86[/C][C]14609.6151255488[/C][C]10444.4250145386[/C][C]18774.8052365589[/C][/ROW]
[ROW][C]87[/C][C]14609.6151255488[/C][C]10272.8468160637[/C][C]18946.3834350339[/C][/ROW]
[ROW][C]88[/C][C]14609.6151255488[/C][C]10107.8032592608[/C][C]19111.4269918368[/C][/ROW]
[ROW][C]89[/C][C]14609.6151255488[/C][C]9948.60012999804[/C][C]19270.6301210995[/C][/ROW]
[ROW][C]90[/C][C]14609.6151255488[/C][C]9794.65806467627[/C][C]19424.5721864212[/C][/ROW]
[ROW][C]91[/C][C]14609.6151255488[/C][C]9645.48758817192[/C][C]19573.7426629256[/C][/ROW]
[ROW][C]92[/C][C]14609.6151255488[/C][C]9500.67072218712[/C][C]19718.5595289104[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122431&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122431&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
8114609.615125548811438.644435937917780.5858151596
8214609.615125548811216.415186896718002.8150642008
8314609.615125548811007.8715848518211.3586662476
8414609.615125548810810.759081650418408.4711694471
8514609.615125548810623.381570981318595.8486801163
8614609.615125548810444.425014538618774.8052365589
8714609.615125548810272.846816063718946.3834350339
8814609.615125548810107.803259260819111.4269918368
8914609.61512554889948.6001299980419270.6301210995
9014609.61512554889794.6580646762719424.5721864212
9114609.61512554889645.4875881719219573.7426629256
9214609.61512554889500.6707221871219718.5595289104



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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')