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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 18 Dec 2012 11:03:27 -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/18/t1355846624e14r4o2tk6we2l8.htm/, Retrieved Fri, 19 Apr 2024 17:06:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=201471, Retrieved Fri, 19 Apr 2024 17:06:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact166
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [HPC Retail Sales] [2008-03-10 17:43:04] [74be16979710d4c4e7c6647856088456]
- RMPD    [Exponential Smoothing] [] [2012-12-18 16:03:27] [7d61013405aa85534cb0146e7095f1e4] [Current]
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Dataseries X:
7116
6927
6731
6850
6766
6979
7149
7067
7170
7237
7240
7645
7678
7491
7816
7631
8395
8578
8950
9450
9501
10083
10544
11299
12049
12860
13389
13796
14505
14727
14646
14861
15012
15421
15227
15124
14953
15039
15128
15221
14876
14517
14609
14735
14574
14636
15104
14393
13919
13751
13628
13792
13892
14024
13908
13920
13897
13759
13323
13097
12758
12806
12673
12500
12720
12749
12794
12544
12088
12258




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time8 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 & 8 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201471&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]8 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=201471&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201471&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 time8 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.89023521238114
beta0.216268546344721
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.89023521238114 \tabularnewline
beta & 0.216268546344721 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201471&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]0.89023521238114[/C][/ROW]
[ROW][C]beta[/C][C]0.216268546344721[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201471&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201471&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
alpha0.89023521238114
beta0.216268546344721
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1376787043.34054487179634.659455128206
1474917521.41648576916-30.4164857691576
1578167891.47898962704-75.4789896270449
1676317677.60163866626-46.6016386662632
1783958388.918048023836.08195197617351
1885788533.6395356747744.3604643252347
1989509101.4786175606-151.478617560597
2094509063.31069344374386.689306556256
2195019741.89638284903-240.896382849029
22100839770.36177554566312.638224454337
231054410265.1286986327278.871301367342
241129911151.4428413138147.557158686237
251204911639.7622652918409.237734708211
261286012044.4975960946815.502403905448
271338913525.884926987-136.884926987013
281379613611.893407966184.106592034026
291450514930.1772814329-425.177281432911
301472715007.9480304085-280.948030408479
311464615514.8279800358-868.82798003578
321486115009.1492783349-148.149278334888
331501215151.7706071488-139.770607148801
341542115359.544658376361.4553416236686
351522715607.1574296862-380.15742968622
361512415745.6487160372-621.648716037189
371495315283.1035814942-330.103581494184
381503914637.0857862514401.91421374864
391512815128.9566635386-0.95666353857996
401522114880.5899983232340.410001676762
411487615810.6189932773-934.618993277341
421451714892.0915729519-375.091572951882
431460914673.9011517991-64.9011517990875
441473514541.0595410125193.940458987487
451457414633.0513529183-59.0513529182681
461463614594.223388129641.776611870413
471510414431.5065238606672.493476139392
481439315338.9268154182-945.926815418219
491391914415.5954081985-496.595408198526
501375113465.5519736682285.448026331813
511362813550.937762633777.0622373662591
521379213165.9355280557626.064471944284
531389214021.7471420257-129.74714202571
541402413847.5595085896176.44049141038
551390814226.9948521486-318.994852148637
561392013920.0256626222-0.0256626222071645
571389713797.892023476299.107976523841
581375913927.7004319547-168.70043195469
591332313623.0868844207-300.086884420691
601309713276.0324469236-179.032446923571
611275813021.3843686899-263.384368689873
621280612346.3407287894459.65927121055
631267312579.029233563693.9707664364087
641250012287.6832307206212.316769279352
651272012630.884325941689.1156740584138
661274912665.96608579883.033914201993
671279412870.7040805105-76.7040805105044
681254412823.9282954403-279.928295440257
691208812419.0932829429-331.093282942898
701225812009.2952774957248.704722504262

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 7678 & 7043.34054487179 & 634.659455128206 \tabularnewline
14 & 7491 & 7521.41648576916 & -30.4164857691576 \tabularnewline
15 & 7816 & 7891.47898962704 & -75.4789896270449 \tabularnewline
16 & 7631 & 7677.60163866626 & -46.6016386662632 \tabularnewline
17 & 8395 & 8388.91804802383 & 6.08195197617351 \tabularnewline
18 & 8578 & 8533.63953567477 & 44.3604643252347 \tabularnewline
19 & 8950 & 9101.4786175606 & -151.478617560597 \tabularnewline
20 & 9450 & 9063.31069344374 & 386.689306556256 \tabularnewline
21 & 9501 & 9741.89638284903 & -240.896382849029 \tabularnewline
22 & 10083 & 9770.36177554566 & 312.638224454337 \tabularnewline
23 & 10544 & 10265.1286986327 & 278.871301367342 \tabularnewline
24 & 11299 & 11151.4428413138 & 147.557158686237 \tabularnewline
25 & 12049 & 11639.7622652918 & 409.237734708211 \tabularnewline
26 & 12860 & 12044.4975960946 & 815.502403905448 \tabularnewline
27 & 13389 & 13525.884926987 & -136.884926987013 \tabularnewline
28 & 13796 & 13611.893407966 & 184.106592034026 \tabularnewline
29 & 14505 & 14930.1772814329 & -425.177281432911 \tabularnewline
30 & 14727 & 15007.9480304085 & -280.948030408479 \tabularnewline
31 & 14646 & 15514.8279800358 & -868.82798003578 \tabularnewline
32 & 14861 & 15009.1492783349 & -148.149278334888 \tabularnewline
33 & 15012 & 15151.7706071488 & -139.770607148801 \tabularnewline
34 & 15421 & 15359.5446583763 & 61.4553416236686 \tabularnewline
35 & 15227 & 15607.1574296862 & -380.15742968622 \tabularnewline
36 & 15124 & 15745.6487160372 & -621.648716037189 \tabularnewline
37 & 14953 & 15283.1035814942 & -330.103581494184 \tabularnewline
38 & 15039 & 14637.0857862514 & 401.91421374864 \tabularnewline
39 & 15128 & 15128.9566635386 & -0.95666353857996 \tabularnewline
40 & 15221 & 14880.5899983232 & 340.410001676762 \tabularnewline
41 & 14876 & 15810.6189932773 & -934.618993277341 \tabularnewline
42 & 14517 & 14892.0915729519 & -375.091572951882 \tabularnewline
43 & 14609 & 14673.9011517991 & -64.9011517990875 \tabularnewline
44 & 14735 & 14541.0595410125 & 193.940458987487 \tabularnewline
45 & 14574 & 14633.0513529183 & -59.0513529182681 \tabularnewline
46 & 14636 & 14594.2233881296 & 41.776611870413 \tabularnewline
47 & 15104 & 14431.5065238606 & 672.493476139392 \tabularnewline
48 & 14393 & 15338.9268154182 & -945.926815418219 \tabularnewline
49 & 13919 & 14415.5954081985 & -496.595408198526 \tabularnewline
50 & 13751 & 13465.5519736682 & 285.448026331813 \tabularnewline
51 & 13628 & 13550.9377626337 & 77.0622373662591 \tabularnewline
52 & 13792 & 13165.9355280557 & 626.064471944284 \tabularnewline
53 & 13892 & 14021.7471420257 & -129.74714202571 \tabularnewline
54 & 14024 & 13847.5595085896 & 176.44049141038 \tabularnewline
55 & 13908 & 14226.9948521486 & -318.994852148637 \tabularnewline
56 & 13920 & 13920.0256626222 & -0.0256626222071645 \tabularnewline
57 & 13897 & 13797.8920234762 & 99.107976523841 \tabularnewline
58 & 13759 & 13927.7004319547 & -168.70043195469 \tabularnewline
59 & 13323 & 13623.0868844207 & -300.086884420691 \tabularnewline
60 & 13097 & 13276.0324469236 & -179.032446923571 \tabularnewline
61 & 12758 & 13021.3843686899 & -263.384368689873 \tabularnewline
62 & 12806 & 12346.3407287894 & 459.65927121055 \tabularnewline
63 & 12673 & 12579.0292335636 & 93.9707664364087 \tabularnewline
64 & 12500 & 12287.6832307206 & 212.316769279352 \tabularnewline
65 & 12720 & 12630.8843259416 & 89.1156740584138 \tabularnewline
66 & 12749 & 12665.966085798 & 83.033914201993 \tabularnewline
67 & 12794 & 12870.7040805105 & -76.7040805105044 \tabularnewline
68 & 12544 & 12823.9282954403 & -279.928295440257 \tabularnewline
69 & 12088 & 12419.0932829429 & -331.093282942898 \tabularnewline
70 & 12258 & 12009.2952774957 & 248.704722504262 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201471&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]13[/C][C]7678[/C][C]7043.34054487179[/C][C]634.659455128206[/C][/ROW]
[ROW][C]14[/C][C]7491[/C][C]7521.41648576916[/C][C]-30.4164857691576[/C][/ROW]
[ROW][C]15[/C][C]7816[/C][C]7891.47898962704[/C][C]-75.4789896270449[/C][/ROW]
[ROW][C]16[/C][C]7631[/C][C]7677.60163866626[/C][C]-46.6016386662632[/C][/ROW]
[ROW][C]17[/C][C]8395[/C][C]8388.91804802383[/C][C]6.08195197617351[/C][/ROW]
[ROW][C]18[/C][C]8578[/C][C]8533.63953567477[/C][C]44.3604643252347[/C][/ROW]
[ROW][C]19[/C][C]8950[/C][C]9101.4786175606[/C][C]-151.478617560597[/C][/ROW]
[ROW][C]20[/C][C]9450[/C][C]9063.31069344374[/C][C]386.689306556256[/C][/ROW]
[ROW][C]21[/C][C]9501[/C][C]9741.89638284903[/C][C]-240.896382849029[/C][/ROW]
[ROW][C]22[/C][C]10083[/C][C]9770.36177554566[/C][C]312.638224454337[/C][/ROW]
[ROW][C]23[/C][C]10544[/C][C]10265.1286986327[/C][C]278.871301367342[/C][/ROW]
[ROW][C]24[/C][C]11299[/C][C]11151.4428413138[/C][C]147.557158686237[/C][/ROW]
[ROW][C]25[/C][C]12049[/C][C]11639.7622652918[/C][C]409.237734708211[/C][/ROW]
[ROW][C]26[/C][C]12860[/C][C]12044.4975960946[/C][C]815.502403905448[/C][/ROW]
[ROW][C]27[/C][C]13389[/C][C]13525.884926987[/C][C]-136.884926987013[/C][/ROW]
[ROW][C]28[/C][C]13796[/C][C]13611.893407966[/C][C]184.106592034026[/C][/ROW]
[ROW][C]29[/C][C]14505[/C][C]14930.1772814329[/C][C]-425.177281432911[/C][/ROW]
[ROW][C]30[/C][C]14727[/C][C]15007.9480304085[/C][C]-280.948030408479[/C][/ROW]
[ROW][C]31[/C][C]14646[/C][C]15514.8279800358[/C][C]-868.82798003578[/C][/ROW]
[ROW][C]32[/C][C]14861[/C][C]15009.1492783349[/C][C]-148.149278334888[/C][/ROW]
[ROW][C]33[/C][C]15012[/C][C]15151.7706071488[/C][C]-139.770607148801[/C][/ROW]
[ROW][C]34[/C][C]15421[/C][C]15359.5446583763[/C][C]61.4553416236686[/C][/ROW]
[ROW][C]35[/C][C]15227[/C][C]15607.1574296862[/C][C]-380.15742968622[/C][/ROW]
[ROW][C]36[/C][C]15124[/C][C]15745.6487160372[/C][C]-621.648716037189[/C][/ROW]
[ROW][C]37[/C][C]14953[/C][C]15283.1035814942[/C][C]-330.103581494184[/C][/ROW]
[ROW][C]38[/C][C]15039[/C][C]14637.0857862514[/C][C]401.91421374864[/C][/ROW]
[ROW][C]39[/C][C]15128[/C][C]15128.9566635386[/C][C]-0.95666353857996[/C][/ROW]
[ROW][C]40[/C][C]15221[/C][C]14880.5899983232[/C][C]340.410001676762[/C][/ROW]
[ROW][C]41[/C][C]14876[/C][C]15810.6189932773[/C][C]-934.618993277341[/C][/ROW]
[ROW][C]42[/C][C]14517[/C][C]14892.0915729519[/C][C]-375.091572951882[/C][/ROW]
[ROW][C]43[/C][C]14609[/C][C]14673.9011517991[/C][C]-64.9011517990875[/C][/ROW]
[ROW][C]44[/C][C]14735[/C][C]14541.0595410125[/C][C]193.940458987487[/C][/ROW]
[ROW][C]45[/C][C]14574[/C][C]14633.0513529183[/C][C]-59.0513529182681[/C][/ROW]
[ROW][C]46[/C][C]14636[/C][C]14594.2233881296[/C][C]41.776611870413[/C][/ROW]
[ROW][C]47[/C][C]15104[/C][C]14431.5065238606[/C][C]672.493476139392[/C][/ROW]
[ROW][C]48[/C][C]14393[/C][C]15338.9268154182[/C][C]-945.926815418219[/C][/ROW]
[ROW][C]49[/C][C]13919[/C][C]14415.5954081985[/C][C]-496.595408198526[/C][/ROW]
[ROW][C]50[/C][C]13751[/C][C]13465.5519736682[/C][C]285.448026331813[/C][/ROW]
[ROW][C]51[/C][C]13628[/C][C]13550.9377626337[/C][C]77.0622373662591[/C][/ROW]
[ROW][C]52[/C][C]13792[/C][C]13165.9355280557[/C][C]626.064471944284[/C][/ROW]
[ROW][C]53[/C][C]13892[/C][C]14021.7471420257[/C][C]-129.74714202571[/C][/ROW]
[ROW][C]54[/C][C]14024[/C][C]13847.5595085896[/C][C]176.44049141038[/C][/ROW]
[ROW][C]55[/C][C]13908[/C][C]14226.9948521486[/C][C]-318.994852148637[/C][/ROW]
[ROW][C]56[/C][C]13920[/C][C]13920.0256626222[/C][C]-0.0256626222071645[/C][/ROW]
[ROW][C]57[/C][C]13897[/C][C]13797.8920234762[/C][C]99.107976523841[/C][/ROW]
[ROW][C]58[/C][C]13759[/C][C]13927.7004319547[/C][C]-168.70043195469[/C][/ROW]
[ROW][C]59[/C][C]13323[/C][C]13623.0868844207[/C][C]-300.086884420691[/C][/ROW]
[ROW][C]60[/C][C]13097[/C][C]13276.0324469236[/C][C]-179.032446923571[/C][/ROW]
[ROW][C]61[/C][C]12758[/C][C]13021.3843686899[/C][C]-263.384368689873[/C][/ROW]
[ROW][C]62[/C][C]12806[/C][C]12346.3407287894[/C][C]459.65927121055[/C][/ROW]
[ROW][C]63[/C][C]12673[/C][C]12579.0292335636[/C][C]93.9707664364087[/C][/ROW]
[ROW][C]64[/C][C]12500[/C][C]12287.6832307206[/C][C]212.316769279352[/C][/ROW]
[ROW][C]65[/C][C]12720[/C][C]12630.8843259416[/C][C]89.1156740584138[/C][/ROW]
[ROW][C]66[/C][C]12749[/C][C]12665.966085798[/C][C]83.033914201993[/C][/ROW]
[ROW][C]67[/C][C]12794[/C][C]12870.7040805105[/C][C]-76.7040805105044[/C][/ROW]
[ROW][C]68[/C][C]12544[/C][C]12823.9282954403[/C][C]-279.928295440257[/C][/ROW]
[ROW][C]69[/C][C]12088[/C][C]12419.0932829429[/C][C]-331.093282942898[/C][/ROW]
[ROW][C]70[/C][C]12258[/C][C]12009.2952774957[/C][C]248.704722504262[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201471&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201471&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
1376787043.34054487179634.659455128206
1474917521.41648576916-30.4164857691576
1578167891.47898962704-75.4789896270449
1676317677.60163866626-46.6016386662632
1783958388.918048023836.08195197617351
1885788533.6395356747744.3604643252347
1989509101.4786175606-151.478617560597
2094509063.31069344374386.689306556256
2195019741.89638284903-240.896382849029
22100839770.36177554566312.638224454337
231054410265.1286986327278.871301367342
241129911151.4428413138147.557158686237
251204911639.7622652918409.237734708211
261286012044.4975960946815.502403905448
271338913525.884926987-136.884926987013
281379613611.893407966184.106592034026
291450514930.1772814329-425.177281432911
301472715007.9480304085-280.948030408479
311464615514.8279800358-868.82798003578
321486115009.1492783349-148.149278334888
331501215151.7706071488-139.770607148801
341542115359.544658376361.4553416236686
351522715607.1574296862-380.15742968622
361512415745.6487160372-621.648716037189
371495315283.1035814942-330.103581494184
381503914637.0857862514401.91421374864
391512815128.9566635386-0.95666353857996
401522114880.5899983232340.410001676762
411487615810.6189932773-934.618993277341
421451714892.0915729519-375.091572951882
431460914673.9011517991-64.9011517990875
441473514541.0595410125193.940458987487
451457414633.0513529183-59.0513529182681
461463614594.223388129641.776611870413
471510414431.5065238606672.493476139392
481439315338.9268154182-945.926815418219
491391914415.5954081985-496.595408198526
501375113465.5519736682285.448026331813
511362813550.937762633777.0622373662591
521379213165.9355280557626.064471944284
531389214021.7471420257-129.74714202571
541402413847.5595085896176.44049141038
551390814226.9948521486-318.994852148637
561392013920.0256626222-0.0256626222071645
571389713797.892023476299.107976523841
581375913927.7004319547-168.70043195469
591332313623.0868844207-300.086884420691
601309713276.0324469236-179.032446923571
611275813021.3843686899-263.384368689873
621280612346.3407287894459.65927121055
631267312579.029233563693.9707664364087
641250012287.6832307206212.316769279352
651272012630.884325941689.1156740584138
661274912665.96608579883.033914201993
671279412870.7040805105-76.7040805105044
681254412823.9282954403-279.928295440257
691208812419.0932829429-331.093282942898
701225812009.2952774957248.704722504262







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7112014.98168131311293.745438630812736.2179239952
7211959.271151229210896.24129167513022.3010107835
7311900.122766812310494.404377500413305.8411561241
7411635.0048337249875.2375832826313394.7720841654
7511425.93754218829297.3684984256713554.5065859508
7611053.42229173458540.1208136393913566.7237698296
7711142.70767333988228.4360408989514056.9793057807
7811029.249822117697.8455247665514360.6541194534
7911058.00984938257293.5610731800314822.458625585
8010987.45505584876774.379804768715200.5303069287
8110810.3436956416133.4212059134115487.2661853687
8210806.82108338925651.1987897804615962.4433769979

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
71 & 12014.981681313 & 11293.7454386308 & 12736.2179239952 \tabularnewline
72 & 11959.2711512292 & 10896.241291675 & 13022.3010107835 \tabularnewline
73 & 11900.1227668123 & 10494.4043775004 & 13305.8411561241 \tabularnewline
74 & 11635.004833724 & 9875.23758328263 & 13394.7720841654 \tabularnewline
75 & 11425.9375421882 & 9297.36849842567 & 13554.5065859508 \tabularnewline
76 & 11053.4222917345 & 8540.12081363939 & 13566.7237698296 \tabularnewline
77 & 11142.7076733398 & 8228.43604089895 & 14056.9793057807 \tabularnewline
78 & 11029.24982211 & 7697.84552476655 & 14360.6541194534 \tabularnewline
79 & 11058.0098493825 & 7293.56107318003 & 14822.458625585 \tabularnewline
80 & 10987.4550558487 & 6774.3798047687 & 15200.5303069287 \tabularnewline
81 & 10810.343695641 & 6133.42120591341 & 15487.2661853687 \tabularnewline
82 & 10806.8210833892 & 5651.19878978046 & 15962.4433769979 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201471&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]71[/C][C]12014.981681313[/C][C]11293.7454386308[/C][C]12736.2179239952[/C][/ROW]
[ROW][C]72[/C][C]11959.2711512292[/C][C]10896.241291675[/C][C]13022.3010107835[/C][/ROW]
[ROW][C]73[/C][C]11900.1227668123[/C][C]10494.4043775004[/C][C]13305.8411561241[/C][/ROW]
[ROW][C]74[/C][C]11635.004833724[/C][C]9875.23758328263[/C][C]13394.7720841654[/C][/ROW]
[ROW][C]75[/C][C]11425.9375421882[/C][C]9297.36849842567[/C][C]13554.5065859508[/C][/ROW]
[ROW][C]76[/C][C]11053.4222917345[/C][C]8540.12081363939[/C][C]13566.7237698296[/C][/ROW]
[ROW][C]77[/C][C]11142.7076733398[/C][C]8228.43604089895[/C][C]14056.9793057807[/C][/ROW]
[ROW][C]78[/C][C]11029.24982211[/C][C]7697.84552476655[/C][C]14360.6541194534[/C][/ROW]
[ROW][C]79[/C][C]11058.0098493825[/C][C]7293.56107318003[/C][C]14822.458625585[/C][/ROW]
[ROW][C]80[/C][C]10987.4550558487[/C][C]6774.3798047687[/C][C]15200.5303069287[/C][/ROW]
[ROW][C]81[/C][C]10810.343695641[/C][C]6133.42120591341[/C][C]15487.2661853687[/C][/ROW]
[ROW][C]82[/C][C]10806.8210833892[/C][C]5651.19878978046[/C][C]15962.4433769979[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201471&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201471&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
7112014.98168131311293.745438630812736.2179239952
7211959.271151229210896.24129167513022.3010107835
7311900.122766812310494.404377500413305.8411561241
7411635.0048337249875.2375832826313394.7720841654
7511425.93754218829297.3684984256713554.5065859508
7611053.42229173458540.1208136393913566.7237698296
7711142.70767333988228.4360408989514056.9793057807
7811029.249822117697.8455247665514360.6541194534
7911058.00984938257293.5610731800314822.458625585
8010987.45505584876774.379804768715200.5303069287
8110810.3436956416133.4212059134115487.2661853687
8210806.82108338925651.1987897804615962.4433769979



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