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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 19 May 2011 14:54:11 +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/19/t1305816815x7vm4i8wshqqo16.htm/, Retrieved Sun, 12 May 2024 01:35:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=122072, Retrieved Sun, 12 May 2024 01:35:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords KDGP2W102
Estimated Impact107
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Standard Deviation Plot] [iko opgave 8 oplo...] [2011-05-18 10:29:49] [90e98241b01889302f4a0c1c0db1534e]
- RMPD    [Exponential Smoothing] [iko opgave 10 opl...] [2011-05-19 14:54:11] [93d78dde8d64c5a73537ad1fcc88d508] [Current]
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Dataseries X:
5939520,00
89948768,00
80953652,00
85942882,00
8944937,00
82975432,00
24940816,00
21973899,00
37950221,00
45949881,00
85950373,00
48960313,00
81954506,00
24960419,00
65973338,00
22950513,00
54963528,00
90995659,00
91967517,00
28999053,00
96990529,00
38979852,00
81496957,00
74982424,00
70976192,00
90990000,00
12998850,00
92986156,00
67994976,00
91022206,00
87992489,00
421022698,00
11018942,00
79100042,00
65996442,00
51000620,00
12996871,00
44994249,00
99996135,00
91977037,00
63974211,00
15998036,00
65974265,00
33984410,00
45939098,00
67935827,00
66921032,00
89911836,00
71890975,00
72880342,00
28871286,00
41844334,00
82847667,00
24871401,00
3867451,00
99896846,00
41890361,00
45884264,00
69884586,00
95896400,00
39904491,00
81900399,00
27909863,00
88900470,00
89917101,00
2945005,00
4934411,00
61957264,00
31946515,00
3938309,00
52933321,00
21947613,00




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=122072&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=122072&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122072&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
beta0
gamma0.286265298869626

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.286265298869626 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122072&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[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.286265298869626[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122072&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122072&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
beta0
gamma0.286265298869626







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
138195450682670206.492058-715700.492057994
142496041924260878.9253186699540.074681383
156597333862298285.86150933675052.13849071
162295051321293438.82478721657074.17521282
175496352852326926.82754682636601.17245318
189099565986895100.88072754100558.1192725
199196751727317458.618904864650058.3810952
202899905324279160.99970024719892.00029981
219699052945374218.187519651616310.8124804
223897985259576165.711869-20596313.711869
2381496957114931601.835332-33434644.8353319
247498242463545904.386176811436519.6138232
2570976192101479198.219442-30503006.219442
269099000029994766.172077760995233.8279223
271299885077416359.0218578-64417509.0218578
289298615626513226.044835566472929.9551645
296799497664447135.88879943547840.11120062
3091022206106595034.952606-15572828.9526062
318799248955298053.65011332694435.349887
3242102269830839239.9434361390183458.056564
331101894272171123.251915-61152181.2519149
347910004264232338.834542714867703.1654573
3565996442125737853.013862-59741411.0138623
365100062079538202.4456177-28537582.4456177
3712996871110125036.648192-97128165.6481924
384499424956210505.7607682-11216256.7607682
399999613569691380.086481230304754.9135188
409197703753693397.465422238283639.5345778
416397421177007309.225137-13033098.2251369
4215998036119888372.911339-103890336.911339
436597426575734271.9633996-9760006.96339965
4433984410166610301.805772-132625891.805772
454593909863770534.8285065-17831436.8285065
466793582779739828.9412088-11804001.9412088
4766921032126241809.09482-59320777.0948201
488991183682781001.24820317130834.75179686
497189097595310850.7855739-23419875.7855739
507288034261254507.724493311625834.2755067
512887128690415968.6659298-61544682.6659298
524184433474467698.2197461-32623364.2197461
538284766784261613.9031556-1413946.90315555
5424871401103495984.002679-78624583.0026795
55386745183608611.813972-79741160.813972
5699896846147233099.632839-47336253.6328389
574189036167042348.4970693-25151987.4970693
584588426487135343.8397751-41251079.8397751
5969884586124497918.506727-54613332.5067266
609589640096515843.4937258-619443.493725821
6139904491100683039.185061-60778548.1850609
628190039973285908.02719678614490.97280332
632790986382499353.0998738-54589490.0998738
648890047073712889.79060215187580.209398
658991710194789309.1321042-4872208.13210419
66294500591433527.4400052-88488522.4400052
67493441168537080.0952366-63602669.0952366
6861957264150560507.456261-88603243.4562607
693194651567318949.9976144-35372434.9976144
70393830984640988.4722276-80702679.4722276
7152933321122188136.380414-69254815.380414
7221947613108010565.90497-86062952.9049697

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 81954506 & 82670206.492058 & -715700.492057994 \tabularnewline
14 & 24960419 & 24260878.9253186 & 699540.074681383 \tabularnewline
15 & 65973338 & 62298285.8615093 & 3675052.13849071 \tabularnewline
16 & 22950513 & 21293438.8247872 & 1657074.17521282 \tabularnewline
17 & 54963528 & 52326926.8275468 & 2636601.17245318 \tabularnewline
18 & 90995659 & 86895100.8807275 & 4100558.1192725 \tabularnewline
19 & 91967517 & 27317458.6189048 & 64650058.3810952 \tabularnewline
20 & 28999053 & 24279160.9997002 & 4719892.00029981 \tabularnewline
21 & 96990529 & 45374218.1875196 & 51616310.8124804 \tabularnewline
22 & 38979852 & 59576165.711869 & -20596313.711869 \tabularnewline
23 & 81496957 & 114931601.835332 & -33434644.8353319 \tabularnewline
24 & 74982424 & 63545904.3861768 & 11436519.6138232 \tabularnewline
25 & 70976192 & 101479198.219442 & -30503006.219442 \tabularnewline
26 & 90990000 & 29994766.1720777 & 60995233.8279223 \tabularnewline
27 & 12998850 & 77416359.0218578 & -64417509.0218578 \tabularnewline
28 & 92986156 & 26513226.0448355 & 66472929.9551645 \tabularnewline
29 & 67994976 & 64447135.8887994 & 3547840.11120062 \tabularnewline
30 & 91022206 & 106595034.952606 & -15572828.9526062 \tabularnewline
31 & 87992489 & 55298053.650113 & 32694435.349887 \tabularnewline
32 & 421022698 & 30839239.9434361 & 390183458.056564 \tabularnewline
33 & 11018942 & 72171123.251915 & -61152181.2519149 \tabularnewline
34 & 79100042 & 64232338.8345427 & 14867703.1654573 \tabularnewline
35 & 65996442 & 125737853.013862 & -59741411.0138623 \tabularnewline
36 & 51000620 & 79538202.4456177 & -28537582.4456177 \tabularnewline
37 & 12996871 & 110125036.648192 & -97128165.6481924 \tabularnewline
38 & 44994249 & 56210505.7607682 & -11216256.7607682 \tabularnewline
39 & 99996135 & 69691380.0864812 & 30304754.9135188 \tabularnewline
40 & 91977037 & 53693397.4654222 & 38283639.5345778 \tabularnewline
41 & 63974211 & 77007309.225137 & -13033098.2251369 \tabularnewline
42 & 15998036 & 119888372.911339 & -103890336.911339 \tabularnewline
43 & 65974265 & 75734271.9633996 & -9760006.96339965 \tabularnewline
44 & 33984410 & 166610301.805772 & -132625891.805772 \tabularnewline
45 & 45939098 & 63770534.8285065 & -17831436.8285065 \tabularnewline
46 & 67935827 & 79739828.9412088 & -11804001.9412088 \tabularnewline
47 & 66921032 & 126241809.09482 & -59320777.0948201 \tabularnewline
48 & 89911836 & 82781001.2482031 & 7130834.75179686 \tabularnewline
49 & 71890975 & 95310850.7855739 & -23419875.7855739 \tabularnewline
50 & 72880342 & 61254507.7244933 & 11625834.2755067 \tabularnewline
51 & 28871286 & 90415968.6659298 & -61544682.6659298 \tabularnewline
52 & 41844334 & 74467698.2197461 & -32623364.2197461 \tabularnewline
53 & 82847667 & 84261613.9031556 & -1413946.90315555 \tabularnewline
54 & 24871401 & 103495984.002679 & -78624583.0026795 \tabularnewline
55 & 3867451 & 83608611.813972 & -79741160.813972 \tabularnewline
56 & 99896846 & 147233099.632839 & -47336253.6328389 \tabularnewline
57 & 41890361 & 67042348.4970693 & -25151987.4970693 \tabularnewline
58 & 45884264 & 87135343.8397751 & -41251079.8397751 \tabularnewline
59 & 69884586 & 124497918.506727 & -54613332.5067266 \tabularnewline
60 & 95896400 & 96515843.4937258 & -619443.493725821 \tabularnewline
61 & 39904491 & 100683039.185061 & -60778548.1850609 \tabularnewline
62 & 81900399 & 73285908.0271967 & 8614490.97280332 \tabularnewline
63 & 27909863 & 82499353.0998738 & -54589490.0998738 \tabularnewline
64 & 88900470 & 73712889.790602 & 15187580.209398 \tabularnewline
65 & 89917101 & 94789309.1321042 & -4872208.13210419 \tabularnewline
66 & 2945005 & 91433527.4400052 & -88488522.4400052 \tabularnewline
67 & 4934411 & 68537080.0952366 & -63602669.0952366 \tabularnewline
68 & 61957264 & 150560507.456261 & -88603243.4562607 \tabularnewline
69 & 31946515 & 67318949.9976144 & -35372434.9976144 \tabularnewline
70 & 3938309 & 84640988.4722276 & -80702679.4722276 \tabularnewline
71 & 52933321 & 122188136.380414 & -69254815.380414 \tabularnewline
72 & 21947613 & 108010565.90497 & -86062952.9049697 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122072&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]81954506[/C][C]82670206.492058[/C][C]-715700.492057994[/C][/ROW]
[ROW][C]14[/C][C]24960419[/C][C]24260878.9253186[/C][C]699540.074681383[/C][/ROW]
[ROW][C]15[/C][C]65973338[/C][C]62298285.8615093[/C][C]3675052.13849071[/C][/ROW]
[ROW][C]16[/C][C]22950513[/C][C]21293438.8247872[/C][C]1657074.17521282[/C][/ROW]
[ROW][C]17[/C][C]54963528[/C][C]52326926.8275468[/C][C]2636601.17245318[/C][/ROW]
[ROW][C]18[/C][C]90995659[/C][C]86895100.8807275[/C][C]4100558.1192725[/C][/ROW]
[ROW][C]19[/C][C]91967517[/C][C]27317458.6189048[/C][C]64650058.3810952[/C][/ROW]
[ROW][C]20[/C][C]28999053[/C][C]24279160.9997002[/C][C]4719892.00029981[/C][/ROW]
[ROW][C]21[/C][C]96990529[/C][C]45374218.1875196[/C][C]51616310.8124804[/C][/ROW]
[ROW][C]22[/C][C]38979852[/C][C]59576165.711869[/C][C]-20596313.711869[/C][/ROW]
[ROW][C]23[/C][C]81496957[/C][C]114931601.835332[/C][C]-33434644.8353319[/C][/ROW]
[ROW][C]24[/C][C]74982424[/C][C]63545904.3861768[/C][C]11436519.6138232[/C][/ROW]
[ROW][C]25[/C][C]70976192[/C][C]101479198.219442[/C][C]-30503006.219442[/C][/ROW]
[ROW][C]26[/C][C]90990000[/C][C]29994766.1720777[/C][C]60995233.8279223[/C][/ROW]
[ROW][C]27[/C][C]12998850[/C][C]77416359.0218578[/C][C]-64417509.0218578[/C][/ROW]
[ROW][C]28[/C][C]92986156[/C][C]26513226.0448355[/C][C]66472929.9551645[/C][/ROW]
[ROW][C]29[/C][C]67994976[/C][C]64447135.8887994[/C][C]3547840.11120062[/C][/ROW]
[ROW][C]30[/C][C]91022206[/C][C]106595034.952606[/C][C]-15572828.9526062[/C][/ROW]
[ROW][C]31[/C][C]87992489[/C][C]55298053.650113[/C][C]32694435.349887[/C][/ROW]
[ROW][C]32[/C][C]421022698[/C][C]30839239.9434361[/C][C]390183458.056564[/C][/ROW]
[ROW][C]33[/C][C]11018942[/C][C]72171123.251915[/C][C]-61152181.2519149[/C][/ROW]
[ROW][C]34[/C][C]79100042[/C][C]64232338.8345427[/C][C]14867703.1654573[/C][/ROW]
[ROW][C]35[/C][C]65996442[/C][C]125737853.013862[/C][C]-59741411.0138623[/C][/ROW]
[ROW][C]36[/C][C]51000620[/C][C]79538202.4456177[/C][C]-28537582.4456177[/C][/ROW]
[ROW][C]37[/C][C]12996871[/C][C]110125036.648192[/C][C]-97128165.6481924[/C][/ROW]
[ROW][C]38[/C][C]44994249[/C][C]56210505.7607682[/C][C]-11216256.7607682[/C][/ROW]
[ROW][C]39[/C][C]99996135[/C][C]69691380.0864812[/C][C]30304754.9135188[/C][/ROW]
[ROW][C]40[/C][C]91977037[/C][C]53693397.4654222[/C][C]38283639.5345778[/C][/ROW]
[ROW][C]41[/C][C]63974211[/C][C]77007309.225137[/C][C]-13033098.2251369[/C][/ROW]
[ROW][C]42[/C][C]15998036[/C][C]119888372.911339[/C][C]-103890336.911339[/C][/ROW]
[ROW][C]43[/C][C]65974265[/C][C]75734271.9633996[/C][C]-9760006.96339965[/C][/ROW]
[ROW][C]44[/C][C]33984410[/C][C]166610301.805772[/C][C]-132625891.805772[/C][/ROW]
[ROW][C]45[/C][C]45939098[/C][C]63770534.8285065[/C][C]-17831436.8285065[/C][/ROW]
[ROW][C]46[/C][C]67935827[/C][C]79739828.9412088[/C][C]-11804001.9412088[/C][/ROW]
[ROW][C]47[/C][C]66921032[/C][C]126241809.09482[/C][C]-59320777.0948201[/C][/ROW]
[ROW][C]48[/C][C]89911836[/C][C]82781001.2482031[/C][C]7130834.75179686[/C][/ROW]
[ROW][C]49[/C][C]71890975[/C][C]95310850.7855739[/C][C]-23419875.7855739[/C][/ROW]
[ROW][C]50[/C][C]72880342[/C][C]61254507.7244933[/C][C]11625834.2755067[/C][/ROW]
[ROW][C]51[/C][C]28871286[/C][C]90415968.6659298[/C][C]-61544682.6659298[/C][/ROW]
[ROW][C]52[/C][C]41844334[/C][C]74467698.2197461[/C][C]-32623364.2197461[/C][/ROW]
[ROW][C]53[/C][C]82847667[/C][C]84261613.9031556[/C][C]-1413946.90315555[/C][/ROW]
[ROW][C]54[/C][C]24871401[/C][C]103495984.002679[/C][C]-78624583.0026795[/C][/ROW]
[ROW][C]55[/C][C]3867451[/C][C]83608611.813972[/C][C]-79741160.813972[/C][/ROW]
[ROW][C]56[/C][C]99896846[/C][C]147233099.632839[/C][C]-47336253.6328389[/C][/ROW]
[ROW][C]57[/C][C]41890361[/C][C]67042348.4970693[/C][C]-25151987.4970693[/C][/ROW]
[ROW][C]58[/C][C]45884264[/C][C]87135343.8397751[/C][C]-41251079.8397751[/C][/ROW]
[ROW][C]59[/C][C]69884586[/C][C]124497918.506727[/C][C]-54613332.5067266[/C][/ROW]
[ROW][C]60[/C][C]95896400[/C][C]96515843.4937258[/C][C]-619443.493725821[/C][/ROW]
[ROW][C]61[/C][C]39904491[/C][C]100683039.185061[/C][C]-60778548.1850609[/C][/ROW]
[ROW][C]62[/C][C]81900399[/C][C]73285908.0271967[/C][C]8614490.97280332[/C][/ROW]
[ROW][C]63[/C][C]27909863[/C][C]82499353.0998738[/C][C]-54589490.0998738[/C][/ROW]
[ROW][C]64[/C][C]88900470[/C][C]73712889.790602[/C][C]15187580.209398[/C][/ROW]
[ROW][C]65[/C][C]89917101[/C][C]94789309.1321042[/C][C]-4872208.13210419[/C][/ROW]
[ROW][C]66[/C][C]2945005[/C][C]91433527.4400052[/C][C]-88488522.4400052[/C][/ROW]
[ROW][C]67[/C][C]4934411[/C][C]68537080.0952366[/C][C]-63602669.0952366[/C][/ROW]
[ROW][C]68[/C][C]61957264[/C][C]150560507.456261[/C][C]-88603243.4562607[/C][/ROW]
[ROW][C]69[/C][C]31946515[/C][C]67318949.9976144[/C][C]-35372434.9976144[/C][/ROW]
[ROW][C]70[/C][C]3938309[/C][C]84640988.4722276[/C][C]-80702679.4722276[/C][/ROW]
[ROW][C]71[/C][C]52933321[/C][C]122188136.380414[/C][C]-69254815.380414[/C][/ROW]
[ROW][C]72[/C][C]21947613[/C][C]108010565.90497[/C][C]-86062952.9049697[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122072&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122072&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
138195450682670206.492058-715700.492057994
142496041924260878.9253186699540.074681383
156597333862298285.86150933675052.13849071
162295051321293438.82478721657074.17521282
175496352852326926.82754682636601.17245318
189099565986895100.88072754100558.1192725
199196751727317458.618904864650058.3810952
202899905324279160.99970024719892.00029981
219699052945374218.187519651616310.8124804
223897985259576165.711869-20596313.711869
2381496957114931601.835332-33434644.8353319
247498242463545904.386176811436519.6138232
2570976192101479198.219442-30503006.219442
269099000029994766.172077760995233.8279223
271299885077416359.0218578-64417509.0218578
289298615626513226.044835566472929.9551645
296799497664447135.88879943547840.11120062
3091022206106595034.952606-15572828.9526062
318799248955298053.65011332694435.349887
3242102269830839239.9434361390183458.056564
331101894272171123.251915-61152181.2519149
347910004264232338.834542714867703.1654573
3565996442125737853.013862-59741411.0138623
365100062079538202.4456177-28537582.4456177
3712996871110125036.648192-97128165.6481924
384499424956210505.7607682-11216256.7607682
399999613569691380.086481230304754.9135188
409197703753693397.465422238283639.5345778
416397421177007309.225137-13033098.2251369
4215998036119888372.911339-103890336.911339
436597426575734271.9633996-9760006.96339965
4433984410166610301.805772-132625891.805772
454593909863770534.8285065-17831436.8285065
466793582779739828.9412088-11804001.9412088
4766921032126241809.09482-59320777.0948201
488991183682781001.24820317130834.75179686
497189097595310850.7855739-23419875.7855739
507288034261254507.724493311625834.2755067
512887128690415968.6659298-61544682.6659298
524184433474467698.2197461-32623364.2197461
538284766784261613.9031556-1413946.90315555
5424871401103495984.002679-78624583.0026795
55386745183608611.813972-79741160.813972
5699896846147233099.632839-47336253.6328389
574189036167042348.4970693-25151987.4970693
584588426487135343.8397751-41251079.8397751
5969884586124497918.506727-54613332.5067266
609589640096515843.4937258-619443.493725821
6139904491100683039.185061-60778548.1850609
628190039973285908.02719678614490.97280332
632790986382499353.0998738-54589490.0998738
648890047073712889.79060215187580.209398
658991710194789309.1321042-4872208.13210419
66294500591433527.4400052-88488522.4400052
67493441168537080.0952366-63602669.0952366
6861957264150560507.456261-88603243.4562607
693194651567318949.9976144-35372434.9976144
70393830984640988.4722276-80702679.4722276
7152933321122188136.380414-69254815.380414
7221947613108010565.90497-86062952.9049697







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7393273828.090191354404802.8448809132142853.335502
7484748127.339867545879102.0945571123617152.585178
7574736105.519629335867080.2743189113605130.76494
7687150998.158421248281972.9131108126020023.403732
77104166162.33232865297137.0870173143035187.577638
7873653624.033055834784598.7877453112522649.278366
7956025123.648077617156098.402767194894148.893388
80139231249.065672100362223.820362178100274.310983
8163545164.365853624676139.1205432102414189.611164
8268310686.336822129441661.0915117107179711.582132
83113525142.77406574656117.5287547152394168.019376
8492383422.827128692383391.139232492383454.5150247

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 93273828.0901913 & 54404802.8448809 & 132142853.335502 \tabularnewline
74 & 84748127.3398675 & 45879102.0945571 & 123617152.585178 \tabularnewline
75 & 74736105.5196293 & 35867080.2743189 & 113605130.76494 \tabularnewline
76 & 87150998.1584212 & 48281972.9131108 & 126020023.403732 \tabularnewline
77 & 104166162.332328 & 65297137.0870173 & 143035187.577638 \tabularnewline
78 & 73653624.0330558 & 34784598.7877453 & 112522649.278366 \tabularnewline
79 & 56025123.6480776 & 17156098.4027671 & 94894148.893388 \tabularnewline
80 & 139231249.065672 & 100362223.820362 & 178100274.310983 \tabularnewline
81 & 63545164.3658536 & 24676139.1205432 & 102414189.611164 \tabularnewline
82 & 68310686.3368221 & 29441661.0915117 & 107179711.582132 \tabularnewline
83 & 113525142.774065 & 74656117.5287547 & 152394168.019376 \tabularnewline
84 & 92383422.8271286 & 92383391.1392324 & 92383454.5150247 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122072&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]93273828.0901913[/C][C]54404802.8448809[/C][C]132142853.335502[/C][/ROW]
[ROW][C]74[/C][C]84748127.3398675[/C][C]45879102.0945571[/C][C]123617152.585178[/C][/ROW]
[ROW][C]75[/C][C]74736105.5196293[/C][C]35867080.2743189[/C][C]113605130.76494[/C][/ROW]
[ROW][C]76[/C][C]87150998.1584212[/C][C]48281972.9131108[/C][C]126020023.403732[/C][/ROW]
[ROW][C]77[/C][C]104166162.332328[/C][C]65297137.0870173[/C][C]143035187.577638[/C][/ROW]
[ROW][C]78[/C][C]73653624.0330558[/C][C]34784598.7877453[/C][C]112522649.278366[/C][/ROW]
[ROW][C]79[/C][C]56025123.6480776[/C][C]17156098.4027671[/C][C]94894148.893388[/C][/ROW]
[ROW][C]80[/C][C]139231249.065672[/C][C]100362223.820362[/C][C]178100274.310983[/C][/ROW]
[ROW][C]81[/C][C]63545164.3658536[/C][C]24676139.1205432[/C][C]102414189.611164[/C][/ROW]
[ROW][C]82[/C][C]68310686.3368221[/C][C]29441661.0915117[/C][C]107179711.582132[/C][/ROW]
[ROW][C]83[/C][C]113525142.774065[/C][C]74656117.5287547[/C][C]152394168.019376[/C][/ROW]
[ROW][C]84[/C][C]92383422.8271286[/C][C]92383391.1392324[/C][C]92383454.5150247[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122072&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122072&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
7393273828.090191354404802.8448809132142853.335502
7484748127.339867545879102.0945571123617152.585178
7574736105.519629335867080.2743189113605130.76494
7687150998.158421248281972.9131108126020023.403732
77104166162.33232865297137.0870173143035187.577638
7873653624.033055834784598.7877453112522649.278366
7956025123.648077617156098.402767194894148.893388
80139231249.065672100362223.820362178100274.310983
8163545164.365853624676139.1205432102414189.611164
8268310686.336822129441661.0915117107179711.582132
83113525142.77406574656117.5287547152394168.019376
8492383422.827128692383391.139232492383454.5150247



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')