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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 12 Dec 2013 01:56:57 -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/2013/Dec/12/t1386831533yi4s5gpho69bxt3.htm/, Retrieved Tue, 07 Dec 2021 11:14:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232207, Retrieved Tue, 07 Dec 2021 11:14:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact73
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-12-12 06:56:57] [2fe61b99b7ad1724c7814d9914ae1a60] [Current]
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Dataseries X:
9969
9692
8943
8802
8250
8515
13973
13905
12467
9490
8483
7610
7839
7107
6584
6053
5725
6480
11663
11628
9203
7781
7020
6908
6912
6668
6189
6007
5148
6685
11044
11034
8986
8146
7818
8176
8935
8929
8835
8455
7924
8973
13575
13844
11738
10467
10145
10833
10179
10107
9533
9165
8382
9018
13911
13761
11316
9855
9034
8932
9278
8876
8298
7733
7226
7688
12226
12081
10439
9008
8377
8346
9167
8945
8428
7973
7446
7785
10561
12791
11583
10112
9597
9332




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 4 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232207&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232207&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232207&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 time4 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.78681967507462
beta0.0321846698299134
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.78681967507462 \tabularnewline
beta & 0.0321846698299134 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232207&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]0.78681967507462[/C][/ROW]
[ROW][C]beta[/C][C]0.0321846698299134[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232207&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232207&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
alpha0.78681967507462
beta0.0321846698299134
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1378399028.54380341881-1189.54380341881
1471077327.41172842214-220.411728422145
1565846631.98023444035-47.9802344403452
1660536039.3395368830613.6604631169384
1757255623.50321744998101.496782550019
1864806320.39016596544159.609834034562
191166311657.16849142075.83150857926739
201162811566.223679198761.7763208012766
21920310160.4034072212-957.403407221185
2277816396.260970830981384.73902916902
2370206486.94543425269533.05456574731
2469086025.25662896334882.743371036662
2569126700.5183674956211.481632504396
2666686362.24418330192305.75581669808
2761896184.798710397054.20128960294915
2860075714.90550930815292.09449069185
2951485612.47193169638-464.471931696382
3066855937.70018862264747.299811377363
311104411780.2524923958-736.252492395801
321103411174.7059880402-140.70598804019
3389869444.53028606113-458.530286061134
3481466637.073651580631508.92634841937
3578186711.917561226761106.08243877324
3681766858.16501399321317.8349860068
3789357826.203536370941108.79646362906
3889298330.31283387182598.687166128177
3988358442.7451909291392.254809070895
4084558473.05935845234-18.0593584523449
4179248090.9574218867-166.957421886703
4289739041.78782832887-68.7878283288737
431357514038.4819230709-463.481923070878
441384413893.9427454783-49.9427454783036
451173812289.1531859576-551.153185957644
46104679947.62226173041519.37773826959
47101459252.31278019624892.687219803764
48108339364.715552673971468.28444732603
491017910499.2950826065-320.295082606506
50101079826.7594349372280.240565062799
5195339693.09789802272-160.097898022725
5291659235.82513347562-70.8251334756169
5383828813.61364664943-431.613646649434
5490189603.58286117847-585.582861178471
551391114122.8720724674-211.872072467369
561376114284.1951737247-523.195173724691
571131612207.9409467752-891.940946775214
5898559825.6055469496329.3944530503704
5990348811.05961494944222.940385050557
6089328488.94785170599443.052148294009
6192788379.35141670824898.648583291757
6288768768.58191575954107.41808424046
6382988375.34718155623-77.347181556228
6477337974.58947373133-241.589473731328
6572267309.15384350742-83.1538435074217
6676888317.34872451046-629.348724510464
671222612857.6354191528-631.63541915285
681208112587.4481485195-506.448148519539
691043910411.321208645827.6787913542285
7090088937.8190534944570.1809465055485
7183777986.50554097093390.494459029065
7283467837.27579712117508.72420287883
7391677872.262351301541294.73764869846
7489458410.28584760664534.714152393361
7584288330.5054953228497.4945046771572
7679738053.36879779096-80.3687977909576
7774467573.70816016925-127.708160169246
7877858454.42858698147-669.428586981468
791056112985.6969762654-2424.69697626542
801279111308.97920347341482.02079652655
811158310839.2373098809743.762690119138
82101129984.31165411436127.688345885635
8395979194.07389958776402.926100412242
8493329127.68795006766204.312049932343

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 7839 & 9028.54380341881 & -1189.54380341881 \tabularnewline
14 & 7107 & 7327.41172842214 & -220.411728422145 \tabularnewline
15 & 6584 & 6631.98023444035 & -47.9802344403452 \tabularnewline
16 & 6053 & 6039.33953688306 & 13.6604631169384 \tabularnewline
17 & 5725 & 5623.50321744998 & 101.496782550019 \tabularnewline
18 & 6480 & 6320.39016596544 & 159.609834034562 \tabularnewline
19 & 11663 & 11657.1684914207 & 5.83150857926739 \tabularnewline
20 & 11628 & 11566.2236791987 & 61.7763208012766 \tabularnewline
21 & 9203 & 10160.4034072212 & -957.403407221185 \tabularnewline
22 & 7781 & 6396.26097083098 & 1384.73902916902 \tabularnewline
23 & 7020 & 6486.94543425269 & 533.05456574731 \tabularnewline
24 & 6908 & 6025.25662896334 & 882.743371036662 \tabularnewline
25 & 6912 & 6700.5183674956 & 211.481632504396 \tabularnewline
26 & 6668 & 6362.24418330192 & 305.75581669808 \tabularnewline
27 & 6189 & 6184.79871039705 & 4.20128960294915 \tabularnewline
28 & 6007 & 5714.90550930815 & 292.09449069185 \tabularnewline
29 & 5148 & 5612.47193169638 & -464.471931696382 \tabularnewline
30 & 6685 & 5937.70018862264 & 747.299811377363 \tabularnewline
31 & 11044 & 11780.2524923958 & -736.252492395801 \tabularnewline
32 & 11034 & 11174.7059880402 & -140.70598804019 \tabularnewline
33 & 8986 & 9444.53028606113 & -458.530286061134 \tabularnewline
34 & 8146 & 6637.07365158063 & 1508.92634841937 \tabularnewline
35 & 7818 & 6711.91756122676 & 1106.08243877324 \tabularnewline
36 & 8176 & 6858.1650139932 & 1317.8349860068 \tabularnewline
37 & 8935 & 7826.20353637094 & 1108.79646362906 \tabularnewline
38 & 8929 & 8330.31283387182 & 598.687166128177 \tabularnewline
39 & 8835 & 8442.7451909291 & 392.254809070895 \tabularnewline
40 & 8455 & 8473.05935845234 & -18.0593584523449 \tabularnewline
41 & 7924 & 8090.9574218867 & -166.957421886703 \tabularnewline
42 & 8973 & 9041.78782832887 & -68.7878283288737 \tabularnewline
43 & 13575 & 14038.4819230709 & -463.481923070878 \tabularnewline
44 & 13844 & 13893.9427454783 & -49.9427454783036 \tabularnewline
45 & 11738 & 12289.1531859576 & -551.153185957644 \tabularnewline
46 & 10467 & 9947.62226173041 & 519.37773826959 \tabularnewline
47 & 10145 & 9252.31278019624 & 892.687219803764 \tabularnewline
48 & 10833 & 9364.71555267397 & 1468.28444732603 \tabularnewline
49 & 10179 & 10499.2950826065 & -320.295082606506 \tabularnewline
50 & 10107 & 9826.7594349372 & 280.240565062799 \tabularnewline
51 & 9533 & 9693.09789802272 & -160.097898022725 \tabularnewline
52 & 9165 & 9235.82513347562 & -70.8251334756169 \tabularnewline
53 & 8382 & 8813.61364664943 & -431.613646649434 \tabularnewline
54 & 9018 & 9603.58286117847 & -585.582861178471 \tabularnewline
55 & 13911 & 14122.8720724674 & -211.872072467369 \tabularnewline
56 & 13761 & 14284.1951737247 & -523.195173724691 \tabularnewline
57 & 11316 & 12207.9409467752 & -891.940946775214 \tabularnewline
58 & 9855 & 9825.60554694963 & 29.3944530503704 \tabularnewline
59 & 9034 & 8811.05961494944 & 222.940385050557 \tabularnewline
60 & 8932 & 8488.94785170599 & 443.052148294009 \tabularnewline
61 & 9278 & 8379.35141670824 & 898.648583291757 \tabularnewline
62 & 8876 & 8768.58191575954 & 107.41808424046 \tabularnewline
63 & 8298 & 8375.34718155623 & -77.347181556228 \tabularnewline
64 & 7733 & 7974.58947373133 & -241.589473731328 \tabularnewline
65 & 7226 & 7309.15384350742 & -83.1538435074217 \tabularnewline
66 & 7688 & 8317.34872451046 & -629.348724510464 \tabularnewline
67 & 12226 & 12857.6354191528 & -631.63541915285 \tabularnewline
68 & 12081 & 12587.4481485195 & -506.448148519539 \tabularnewline
69 & 10439 & 10411.3212086458 & 27.6787913542285 \tabularnewline
70 & 9008 & 8937.81905349445 & 70.1809465055485 \tabularnewline
71 & 8377 & 7986.50554097093 & 390.494459029065 \tabularnewline
72 & 8346 & 7837.27579712117 & 508.72420287883 \tabularnewline
73 & 9167 & 7872.26235130154 & 1294.73764869846 \tabularnewline
74 & 8945 & 8410.28584760664 & 534.714152393361 \tabularnewline
75 & 8428 & 8330.50549532284 & 97.4945046771572 \tabularnewline
76 & 7973 & 8053.36879779096 & -80.3687977909576 \tabularnewline
77 & 7446 & 7573.70816016925 & -127.708160169246 \tabularnewline
78 & 7785 & 8454.42858698147 & -669.428586981468 \tabularnewline
79 & 10561 & 12985.6969762654 & -2424.69697626542 \tabularnewline
80 & 12791 & 11308.9792034734 & 1482.02079652655 \tabularnewline
81 & 11583 & 10839.2373098809 & 743.762690119138 \tabularnewline
82 & 10112 & 9984.31165411436 & 127.688345885635 \tabularnewline
83 & 9597 & 9194.07389958776 & 402.926100412242 \tabularnewline
84 & 9332 & 9127.68795006766 & 204.312049932343 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232207&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]7839[/C][C]9028.54380341881[/C][C]-1189.54380341881[/C][/ROW]
[ROW][C]14[/C][C]7107[/C][C]7327.41172842214[/C][C]-220.411728422145[/C][/ROW]
[ROW][C]15[/C][C]6584[/C][C]6631.98023444035[/C][C]-47.9802344403452[/C][/ROW]
[ROW][C]16[/C][C]6053[/C][C]6039.33953688306[/C][C]13.6604631169384[/C][/ROW]
[ROW][C]17[/C][C]5725[/C][C]5623.50321744998[/C][C]101.496782550019[/C][/ROW]
[ROW][C]18[/C][C]6480[/C][C]6320.39016596544[/C][C]159.609834034562[/C][/ROW]
[ROW][C]19[/C][C]11663[/C][C]11657.1684914207[/C][C]5.83150857926739[/C][/ROW]
[ROW][C]20[/C][C]11628[/C][C]11566.2236791987[/C][C]61.7763208012766[/C][/ROW]
[ROW][C]21[/C][C]9203[/C][C]10160.4034072212[/C][C]-957.403407221185[/C][/ROW]
[ROW][C]22[/C][C]7781[/C][C]6396.26097083098[/C][C]1384.73902916902[/C][/ROW]
[ROW][C]23[/C][C]7020[/C][C]6486.94543425269[/C][C]533.05456574731[/C][/ROW]
[ROW][C]24[/C][C]6908[/C][C]6025.25662896334[/C][C]882.743371036662[/C][/ROW]
[ROW][C]25[/C][C]6912[/C][C]6700.5183674956[/C][C]211.481632504396[/C][/ROW]
[ROW][C]26[/C][C]6668[/C][C]6362.24418330192[/C][C]305.75581669808[/C][/ROW]
[ROW][C]27[/C][C]6189[/C][C]6184.79871039705[/C][C]4.20128960294915[/C][/ROW]
[ROW][C]28[/C][C]6007[/C][C]5714.90550930815[/C][C]292.09449069185[/C][/ROW]
[ROW][C]29[/C][C]5148[/C][C]5612.47193169638[/C][C]-464.471931696382[/C][/ROW]
[ROW][C]30[/C][C]6685[/C][C]5937.70018862264[/C][C]747.299811377363[/C][/ROW]
[ROW][C]31[/C][C]11044[/C][C]11780.2524923958[/C][C]-736.252492395801[/C][/ROW]
[ROW][C]32[/C][C]11034[/C][C]11174.7059880402[/C][C]-140.70598804019[/C][/ROW]
[ROW][C]33[/C][C]8986[/C][C]9444.53028606113[/C][C]-458.530286061134[/C][/ROW]
[ROW][C]34[/C][C]8146[/C][C]6637.07365158063[/C][C]1508.92634841937[/C][/ROW]
[ROW][C]35[/C][C]7818[/C][C]6711.91756122676[/C][C]1106.08243877324[/C][/ROW]
[ROW][C]36[/C][C]8176[/C][C]6858.1650139932[/C][C]1317.8349860068[/C][/ROW]
[ROW][C]37[/C][C]8935[/C][C]7826.20353637094[/C][C]1108.79646362906[/C][/ROW]
[ROW][C]38[/C][C]8929[/C][C]8330.31283387182[/C][C]598.687166128177[/C][/ROW]
[ROW][C]39[/C][C]8835[/C][C]8442.7451909291[/C][C]392.254809070895[/C][/ROW]
[ROW][C]40[/C][C]8455[/C][C]8473.05935845234[/C][C]-18.0593584523449[/C][/ROW]
[ROW][C]41[/C][C]7924[/C][C]8090.9574218867[/C][C]-166.957421886703[/C][/ROW]
[ROW][C]42[/C][C]8973[/C][C]9041.78782832887[/C][C]-68.7878283288737[/C][/ROW]
[ROW][C]43[/C][C]13575[/C][C]14038.4819230709[/C][C]-463.481923070878[/C][/ROW]
[ROW][C]44[/C][C]13844[/C][C]13893.9427454783[/C][C]-49.9427454783036[/C][/ROW]
[ROW][C]45[/C][C]11738[/C][C]12289.1531859576[/C][C]-551.153185957644[/C][/ROW]
[ROW][C]46[/C][C]10467[/C][C]9947.62226173041[/C][C]519.37773826959[/C][/ROW]
[ROW][C]47[/C][C]10145[/C][C]9252.31278019624[/C][C]892.687219803764[/C][/ROW]
[ROW][C]48[/C][C]10833[/C][C]9364.71555267397[/C][C]1468.28444732603[/C][/ROW]
[ROW][C]49[/C][C]10179[/C][C]10499.2950826065[/C][C]-320.295082606506[/C][/ROW]
[ROW][C]50[/C][C]10107[/C][C]9826.7594349372[/C][C]280.240565062799[/C][/ROW]
[ROW][C]51[/C][C]9533[/C][C]9693.09789802272[/C][C]-160.097898022725[/C][/ROW]
[ROW][C]52[/C][C]9165[/C][C]9235.82513347562[/C][C]-70.8251334756169[/C][/ROW]
[ROW][C]53[/C][C]8382[/C][C]8813.61364664943[/C][C]-431.613646649434[/C][/ROW]
[ROW][C]54[/C][C]9018[/C][C]9603.58286117847[/C][C]-585.582861178471[/C][/ROW]
[ROW][C]55[/C][C]13911[/C][C]14122.8720724674[/C][C]-211.872072467369[/C][/ROW]
[ROW][C]56[/C][C]13761[/C][C]14284.1951737247[/C][C]-523.195173724691[/C][/ROW]
[ROW][C]57[/C][C]11316[/C][C]12207.9409467752[/C][C]-891.940946775214[/C][/ROW]
[ROW][C]58[/C][C]9855[/C][C]9825.60554694963[/C][C]29.3944530503704[/C][/ROW]
[ROW][C]59[/C][C]9034[/C][C]8811.05961494944[/C][C]222.940385050557[/C][/ROW]
[ROW][C]60[/C][C]8932[/C][C]8488.94785170599[/C][C]443.052148294009[/C][/ROW]
[ROW][C]61[/C][C]9278[/C][C]8379.35141670824[/C][C]898.648583291757[/C][/ROW]
[ROW][C]62[/C][C]8876[/C][C]8768.58191575954[/C][C]107.41808424046[/C][/ROW]
[ROW][C]63[/C][C]8298[/C][C]8375.34718155623[/C][C]-77.347181556228[/C][/ROW]
[ROW][C]64[/C][C]7733[/C][C]7974.58947373133[/C][C]-241.589473731328[/C][/ROW]
[ROW][C]65[/C][C]7226[/C][C]7309.15384350742[/C][C]-83.1538435074217[/C][/ROW]
[ROW][C]66[/C][C]7688[/C][C]8317.34872451046[/C][C]-629.348724510464[/C][/ROW]
[ROW][C]67[/C][C]12226[/C][C]12857.6354191528[/C][C]-631.63541915285[/C][/ROW]
[ROW][C]68[/C][C]12081[/C][C]12587.4481485195[/C][C]-506.448148519539[/C][/ROW]
[ROW][C]69[/C][C]10439[/C][C]10411.3212086458[/C][C]27.6787913542285[/C][/ROW]
[ROW][C]70[/C][C]9008[/C][C]8937.81905349445[/C][C]70.1809465055485[/C][/ROW]
[ROW][C]71[/C][C]8377[/C][C]7986.50554097093[/C][C]390.494459029065[/C][/ROW]
[ROW][C]72[/C][C]8346[/C][C]7837.27579712117[/C][C]508.72420287883[/C][/ROW]
[ROW][C]73[/C][C]9167[/C][C]7872.26235130154[/C][C]1294.73764869846[/C][/ROW]
[ROW][C]74[/C][C]8945[/C][C]8410.28584760664[/C][C]534.714152393361[/C][/ROW]
[ROW][C]75[/C][C]8428[/C][C]8330.50549532284[/C][C]97.4945046771572[/C][/ROW]
[ROW][C]76[/C][C]7973[/C][C]8053.36879779096[/C][C]-80.3687977909576[/C][/ROW]
[ROW][C]77[/C][C]7446[/C][C]7573.70816016925[/C][C]-127.708160169246[/C][/ROW]
[ROW][C]78[/C][C]7785[/C][C]8454.42858698147[/C][C]-669.428586981468[/C][/ROW]
[ROW][C]79[/C][C]10561[/C][C]12985.6969762654[/C][C]-2424.69697626542[/C][/ROW]
[ROW][C]80[/C][C]12791[/C][C]11308.9792034734[/C][C]1482.02079652655[/C][/ROW]
[ROW][C]81[/C][C]11583[/C][C]10839.2373098809[/C][C]743.762690119138[/C][/ROW]
[ROW][C]82[/C][C]10112[/C][C]9984.31165411436[/C][C]127.688345885635[/C][/ROW]
[ROW][C]83[/C][C]9597[/C][C]9194.07389958776[/C][C]402.926100412242[/C][/ROW]
[ROW][C]84[/C][C]9332[/C][C]9127.68795006766[/C][C]204.312049932343[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232207&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232207&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
1378399028.54380341881-1189.54380341881
1471077327.41172842214-220.411728422145
1565846631.98023444035-47.9802344403452
1660536039.3395368830613.6604631169384
1757255623.50321744998101.496782550019
1864806320.39016596544159.609834034562
191166311657.16849142075.83150857926739
201162811566.223679198761.7763208012766
21920310160.4034072212-957.403407221185
2277816396.260970830981384.73902916902
2370206486.94543425269533.05456574731
2469086025.25662896334882.743371036662
2569126700.5183674956211.481632504396
2666686362.24418330192305.75581669808
2761896184.798710397054.20128960294915
2860075714.90550930815292.09449069185
2951485612.47193169638-464.471931696382
3066855937.70018862264747.299811377363
311104411780.2524923958-736.252492395801
321103411174.7059880402-140.70598804019
3389869444.53028606113-458.530286061134
3481466637.073651580631508.92634841937
3578186711.917561226761106.08243877324
3681766858.16501399321317.8349860068
3789357826.203536370941108.79646362906
3889298330.31283387182598.687166128177
3988358442.7451909291392.254809070895
4084558473.05935845234-18.0593584523449
4179248090.9574218867-166.957421886703
4289739041.78782832887-68.7878283288737
431357514038.4819230709-463.481923070878
441384413893.9427454783-49.9427454783036
451173812289.1531859576-551.153185957644
46104679947.62226173041519.37773826959
47101459252.31278019624892.687219803764
48108339364.715552673971468.28444732603
491017910499.2950826065-320.295082606506
50101079826.7594349372280.240565062799
5195339693.09789802272-160.097898022725
5291659235.82513347562-70.8251334756169
5383828813.61364664943-431.613646649434
5490189603.58286117847-585.582861178471
551391114122.8720724674-211.872072467369
561376114284.1951737247-523.195173724691
571131612207.9409467752-891.940946775214
5898559825.6055469496329.3944530503704
5990348811.05961494944222.940385050557
6089328488.94785170599443.052148294009
6192788379.35141670824898.648583291757
6288768768.58191575954107.41808424046
6382988375.34718155623-77.347181556228
6477337974.58947373133-241.589473731328
6572267309.15384350742-83.1538435074217
6676888317.34872451046-629.348724510464
671222612857.6354191528-631.63541915285
681208112587.4481485195-506.448148519539
691043910411.321208645827.6787913542285
7090088937.8190534944570.1809465055485
7183777986.50554097093390.494459029065
7283467837.27579712117508.72420287883
7391677872.262351301541294.73764869846
7489458410.28584760664534.714152393361
7584288330.5054953228497.4945046771572
7679738053.36879779096-80.3687977909576
7774467573.70816016925-127.708160169246
7877858454.42858698147-669.428586981468
791056112985.6969762654-2424.69697626542
801279111308.97920347341482.02079652655
811158310839.2373098809743.762690119138
82101129984.31165411436127.688345885635
8395979194.07389958776402.926100412242
8493329127.68795006766204.312049932343







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
859130.86892310837795.7811976793210465.9566485373
868495.507266242586775.5864498548310215.4280826303
877895.617779870025844.214270944079947.02128879598
887495.205734196965142.519700040149847.89176835377
897062.076452027714427.49121206149696.66169199403
907924.417481675635021.2698957294110827.5650676218
9112621.790510939459.6555915940815783.9254302659
9213760.683021742410346.620994054717174.74504943
9312004.92153569738344.2223041860115665.6207672085
9410452.06476712336548.7224342622914355.4070999843
959635.411998120555492.4428748941413778.381121347
969214.829160002664834.4935171036413595.1648029017

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 9130.8689231083 & 7795.78119767932 & 10465.9566485373 \tabularnewline
86 & 8495.50726624258 & 6775.58644985483 & 10215.4280826303 \tabularnewline
87 & 7895.61777987002 & 5844.21427094407 & 9947.02128879598 \tabularnewline
88 & 7495.20573419696 & 5142.51970004014 & 9847.89176835377 \tabularnewline
89 & 7062.07645202771 & 4427.4912120614 & 9696.66169199403 \tabularnewline
90 & 7924.41748167563 & 5021.26989572941 & 10827.5650676218 \tabularnewline
91 & 12621.79051093 & 9459.65559159408 & 15783.9254302659 \tabularnewline
92 & 13760.6830217424 & 10346.6209940547 & 17174.74504943 \tabularnewline
93 & 12004.9215356973 & 8344.22230418601 & 15665.6207672085 \tabularnewline
94 & 10452.0647671233 & 6548.72243426229 & 14355.4070999843 \tabularnewline
95 & 9635.41199812055 & 5492.44287489414 & 13778.381121347 \tabularnewline
96 & 9214.82916000266 & 4834.49351710364 & 13595.1648029017 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232207&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]85[/C][C]9130.8689231083[/C][C]7795.78119767932[/C][C]10465.9566485373[/C][/ROW]
[ROW][C]86[/C][C]8495.50726624258[/C][C]6775.58644985483[/C][C]10215.4280826303[/C][/ROW]
[ROW][C]87[/C][C]7895.61777987002[/C][C]5844.21427094407[/C][C]9947.02128879598[/C][/ROW]
[ROW][C]88[/C][C]7495.20573419696[/C][C]5142.51970004014[/C][C]9847.89176835377[/C][/ROW]
[ROW][C]89[/C][C]7062.07645202771[/C][C]4427.4912120614[/C][C]9696.66169199403[/C][/ROW]
[ROW][C]90[/C][C]7924.41748167563[/C][C]5021.26989572941[/C][C]10827.5650676218[/C][/ROW]
[ROW][C]91[/C][C]12621.79051093[/C][C]9459.65559159408[/C][C]15783.9254302659[/C][/ROW]
[ROW][C]92[/C][C]13760.6830217424[/C][C]10346.6209940547[/C][C]17174.74504943[/C][/ROW]
[ROW][C]93[/C][C]12004.9215356973[/C][C]8344.22230418601[/C][C]15665.6207672085[/C][/ROW]
[ROW][C]94[/C][C]10452.0647671233[/C][C]6548.72243426229[/C][C]14355.4070999843[/C][/ROW]
[ROW][C]95[/C][C]9635.41199812055[/C][C]5492.44287489414[/C][C]13778.381121347[/C][/ROW]
[ROW][C]96[/C][C]9214.82916000266[/C][C]4834.49351710364[/C][C]13595.1648029017[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232207&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232207&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
859130.86892310837795.7811976793210465.9566485373
868495.507266242586775.5864498548310215.4280826303
877895.617779870025844.214270944079947.02128879598
887495.205734196965142.519700040149847.89176835377
897062.076452027714427.49121206149696.66169199403
907924.417481675635021.2698957294110827.5650676218
9112621.790510939459.6555915940815783.9254302659
9213760.683021742410346.620994054717174.74504943
9312004.92153569738344.2223041860115665.6207672085
9410452.06476712336548.7224342622914355.4070999843
959635.411998120555492.4428748941413778.381121347
969214.829160002664834.4935171036413595.1648029017



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')