Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 10 Aug 2015 07:56:42 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Aug/10/t1439189941cub1kntitlk8fzq.htm/, Retrieved Sun, 19 May 2024 09:25:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279962, Retrieved Sun, 19 May 2024 09:25:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact152
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Notched Boxplots] [] [2014-10-04 09:51:16] [3d50c3f1d1505d45371c80c331b9aa00]
-    D  [Notched Boxplots] [] [2015-08-03 11:42:45] [74be16979710d4c4e7c6647856088456]
- RMP     [Harrell-Davis Quantiles] [] [2015-08-07 13:17:48] [74be16979710d4c4e7c6647856088456]
- R         [Harrell-Davis Quantiles] [] [2015-08-07 13:20:06] [74be16979710d4c4e7c6647856088456]
- RMP         [Mean Plot] [] [2015-08-07 14:32:20] [74be16979710d4c4e7c6647856088456]
- RM            [Standard Deviation-Mean Plot] [] [2015-08-07 16:54:54] [74be16979710d4c4e7c6647856088456]
- RMP               [Exponential Smoothing] [] [2015-08-10 06:56:42] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
3469648.00
3456726.00
3443622.00
3416504.00
3684772.00
3670576.00
3469648.00
3336060.00
3348982.00
3348982.00
3363360.00
3389204.00
3429426.00
3429426.00
3403582.00
3336060.00
3684772.00
3737916.00
3657654.00
3469648.00
3550092.00
3429426.00
3483844.00
3509870.00
3536988.00
3469648.00
3483844.00
3389204.00
3684772.00
3778138.00
3697876.00
3550092.00
3710798.00
3536988.00
3697876.00
3684772.00
3724994.00
3577210.00
3737916.00
3724994.00
3966144.00
3911726.00
3697876.00
3590132.00
3737916.00
3536988.00
3684772.00
3710798.00
3765216.00
3644732.00
3710798.00
3751020.00
3898804.00
3778138.00
3617432.00
3443622.00
3604510.00
3162250.00
3376282.00
3496766.00
3617432.00
3443622.00
3443622.00
3443622.00
3536988.00
3403582.00
3228498.00
3081988.00
3188276.00
2773316.00
3027570.00
3175354.00
3202472.00
3054688.00
3067610.00
3027570.00
3162250.00
3067610.00
2881060.00
2746198.00
2974244.00
2479022.00
2800616.00
2947126.00
2947126.00
2773316.00
2612610.00
2599688.00
2746198.00
2612610.00
2358538.00
2183454.00
2371460.00
1929382.00
2331238.00
2545088.00
2612610.00
2464826.00
2278094.00
2411682.00
2464826.00
2424604.00
2022566.00
1836016.00
1969422.00
1567566.00
1982526.00
2130310.00
2250794.00
2049866.00
1861860.00
1969422.00
2022566.00
1916278.00
1514422.00
1339338.00
1500044.00
1057966.00
1540266.00
1836016.00




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279962&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279962&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279962&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.405343002238513
beta0.0645195510983276
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.405343002238513 \tabularnewline
beta & 0.0645195510983276 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279962&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]0.405343002238513[/C][/ROW]
[ROW][C]beta[/C][C]0.0645195510983276[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279962&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279962&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
alpha0.405343002238513
beta0.0645195510983276
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1334294263429276.86111111149.138888885733
1434294263421750.297211457675.70278854994
1534035823391085.3125092112496.6874907874
1633360603323237.6337795212822.3662204826
1736847723675450.72086569321.27913440438
1837379163729244.52533958671.47466049716
1936576543528588.46727911129065.532720892
2034696483460651.274107938996.72589207068
2135500923490782.7342788759309.265721133
2234294263532151.45217865-102725.452178652
2334838443517863.6653498-34019.6653497973
2435098703535843.92080909-25973.9208090883
2535369883563039.28144146-26051.2814414646
2634696483550926.68115508-81278.68115508
2734838443486303.5046056-2459.50460560061
2833892043411427.97557874-22223.9755787407
2936847723745277.6465453-60505.6465453035
3037781383766479.3517042911658.6482957122
3136978763634803.5820461863072.4179538153
3235500923463167.1866352986924.8133647125
3337107983551293.37493694159504.625063065
3435369883536029.28503387958.714966129977
3536978763606445.9152497491430.0847502612
3636847723685162.02654265-390.02654264681
3737249943728451.93988598-3457.93988597672
3835772103699017.20949169-121807.209491686
3937379163670137.7048813667778.295118642
4037249943619117.64535959105876.354640407
4139661443992615.72520886-26471.7252088585
4239117264081904.21888617-170178.218886175
4336978763913718.58172925-215842.581729248
4435901323642538.47500655-52406.4750065506
4537379163713032.4633982824883.5366017167
4635369883541084.20777849-4096.20777848642
4736847723655283.0798101129488.9201898878
4837107983644702.1687072366095.8312927713
4937652163705267.9446832759948.0553167257
5036447323624966.0393104119765.9606895861
5137107983763721.94465138-52923.9446513765
5237510203680786.0525178870233.9474821216
5338988043954557.57837427-55753.5783742652
5437781383939177.56875735-161039.568757351
5536174323740437.34862615-123005.348626153
5634436223599400.28154312-155778.281543122
5736045103666574.53390236-62064.5339023592
5831622503432495.82103773-270245.821037726
5933762823442170.29295343-65888.2929534311
6034967663395588.9463869101177.053613099
6136174323448527.79030865168904.209691355
6234436223373154.3749972170467.6250027874
6334436223475220.70111863-31598.7011186262
6434436223460707.6759025-17085.6759025021
6535369883608423.93518475-71435.9351847535
6634035823507926.50303484-104344.50303484
6732284983340115.62867601-111617.628676008
6830819883169834.74065367-87846.7406536685
6931882763307677.58684932-119401.586849318
7027733162912467.21482954-139151.214829538
7130275703086137.03340031-58567.0334003149
7231753543131395.7864531343958.2135468726
7332024723189445.2836383813026.7163616153
7430546882976304.9019471878383.0980528151
7530676103005045.1530768562564.8469231483
7630275703023953.450352153616.54964785324
7731622503134905.3810616427344.6189383641
7830676103044625.9395434222984.0604565782
7928810602917179.05317972-36119.0531797237
8027461982786688.25033696-40490.2503369572
8129742442921252.6423191652991.3576808376
8224790222584975.03829867-105953.038298669
8328006162821688.41851274-21072.4185127388
8429471262945760.252315921365.74768408062
8529471262969685.20417171-22559.2041717102
8627733162781587.92972943-8271.92972942907
8726126102764133.46958568-151523.469585682
8825996882653946.32490525-54258.3249052544
8927461982746773.34367291-575.343672913965
9026126102633077.72691127-20467.7269112733
9123585382442229.53035058-83691.5303505831
9221834542277969.70015133-94515.7001513252
9323714602432925.34962133-61465.3496213276
9419293821939443.39146146-10061.3914614622
9523312382251715.7137221679522.2862778385
9625450882418751.80711876126336.192881236
9726126102471219.69741288141390.302587117
9824648262354476.11644946110349.883550543
9922780942299422.79081396-21328.7908139606
10024116822302757.61287976108924.387120245
10124648262500829.27215667-36003.2721566744
10224246042367194.2266388757409.7733611278
10320225662178603.52684498-156037.526844985
10418360161984976.92686424-148960.926864242
10519694222142488.1674218-173066.167421803
10615675661636389.6368694-68823.6368693979
10719825261978630.187249973895.81275003171
10821303102141387.54319103-11077.5431910325
10922507942142051.75665373108742.243346268
11020498661987706.2688078662159.7311921408
11118618601827645.6195323634214.3804676409
11219694221925232.8991839244189.1008160757
11320225662003471.7817290619094.2182709416
11419162781941749.24471723-25471.2447172275
11515144221584498.2287781-70076.2287780975
11613393381424034.55142381-84696.5514238074
11715000441589052.19637033-89008.1963703306
11810579661177004.49608313-119038.496083133
11915402661538810.657379071455.34262092761
12018360161688287.67354377147728.326456229

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 3429426 & 3429276.86111111 & 149.138888885733 \tabularnewline
14 & 3429426 & 3421750.29721145 & 7675.70278854994 \tabularnewline
15 & 3403582 & 3391085.31250921 & 12496.6874907874 \tabularnewline
16 & 3336060 & 3323237.63377952 & 12822.3662204826 \tabularnewline
17 & 3684772 & 3675450.7208656 & 9321.27913440438 \tabularnewline
18 & 3737916 & 3729244.5253395 & 8671.47466049716 \tabularnewline
19 & 3657654 & 3528588.46727911 & 129065.532720892 \tabularnewline
20 & 3469648 & 3460651.27410793 & 8996.72589207068 \tabularnewline
21 & 3550092 & 3490782.73427887 & 59309.265721133 \tabularnewline
22 & 3429426 & 3532151.45217865 & -102725.452178652 \tabularnewline
23 & 3483844 & 3517863.6653498 & -34019.6653497973 \tabularnewline
24 & 3509870 & 3535843.92080909 & -25973.9208090883 \tabularnewline
25 & 3536988 & 3563039.28144146 & -26051.2814414646 \tabularnewline
26 & 3469648 & 3550926.68115508 & -81278.68115508 \tabularnewline
27 & 3483844 & 3486303.5046056 & -2459.50460560061 \tabularnewline
28 & 3389204 & 3411427.97557874 & -22223.9755787407 \tabularnewline
29 & 3684772 & 3745277.6465453 & -60505.6465453035 \tabularnewline
30 & 3778138 & 3766479.35170429 & 11658.6482957122 \tabularnewline
31 & 3697876 & 3634803.58204618 & 63072.4179538153 \tabularnewline
32 & 3550092 & 3463167.18663529 & 86924.8133647125 \tabularnewline
33 & 3710798 & 3551293.37493694 & 159504.625063065 \tabularnewline
34 & 3536988 & 3536029.28503387 & 958.714966129977 \tabularnewline
35 & 3697876 & 3606445.91524974 & 91430.0847502612 \tabularnewline
36 & 3684772 & 3685162.02654265 & -390.02654264681 \tabularnewline
37 & 3724994 & 3728451.93988598 & -3457.93988597672 \tabularnewline
38 & 3577210 & 3699017.20949169 & -121807.209491686 \tabularnewline
39 & 3737916 & 3670137.70488136 & 67778.295118642 \tabularnewline
40 & 3724994 & 3619117.64535959 & 105876.354640407 \tabularnewline
41 & 3966144 & 3992615.72520886 & -26471.7252088585 \tabularnewline
42 & 3911726 & 4081904.21888617 & -170178.218886175 \tabularnewline
43 & 3697876 & 3913718.58172925 & -215842.581729248 \tabularnewline
44 & 3590132 & 3642538.47500655 & -52406.4750065506 \tabularnewline
45 & 3737916 & 3713032.46339828 & 24883.5366017167 \tabularnewline
46 & 3536988 & 3541084.20777849 & -4096.20777848642 \tabularnewline
47 & 3684772 & 3655283.07981011 & 29488.9201898878 \tabularnewline
48 & 3710798 & 3644702.16870723 & 66095.8312927713 \tabularnewline
49 & 3765216 & 3705267.94468327 & 59948.0553167257 \tabularnewline
50 & 3644732 & 3624966.03931041 & 19765.9606895861 \tabularnewline
51 & 3710798 & 3763721.94465138 & -52923.9446513765 \tabularnewline
52 & 3751020 & 3680786.05251788 & 70233.9474821216 \tabularnewline
53 & 3898804 & 3954557.57837427 & -55753.5783742652 \tabularnewline
54 & 3778138 & 3939177.56875735 & -161039.568757351 \tabularnewline
55 & 3617432 & 3740437.34862615 & -123005.348626153 \tabularnewline
56 & 3443622 & 3599400.28154312 & -155778.281543122 \tabularnewline
57 & 3604510 & 3666574.53390236 & -62064.5339023592 \tabularnewline
58 & 3162250 & 3432495.82103773 & -270245.821037726 \tabularnewline
59 & 3376282 & 3442170.29295343 & -65888.2929534311 \tabularnewline
60 & 3496766 & 3395588.9463869 & 101177.053613099 \tabularnewline
61 & 3617432 & 3448527.79030865 & 168904.209691355 \tabularnewline
62 & 3443622 & 3373154.37499721 & 70467.6250027874 \tabularnewline
63 & 3443622 & 3475220.70111863 & -31598.7011186262 \tabularnewline
64 & 3443622 & 3460707.6759025 & -17085.6759025021 \tabularnewline
65 & 3536988 & 3608423.93518475 & -71435.9351847535 \tabularnewline
66 & 3403582 & 3507926.50303484 & -104344.50303484 \tabularnewline
67 & 3228498 & 3340115.62867601 & -111617.628676008 \tabularnewline
68 & 3081988 & 3169834.74065367 & -87846.7406536685 \tabularnewline
69 & 3188276 & 3307677.58684932 & -119401.586849318 \tabularnewline
70 & 2773316 & 2912467.21482954 & -139151.214829538 \tabularnewline
71 & 3027570 & 3086137.03340031 & -58567.0334003149 \tabularnewline
72 & 3175354 & 3131395.78645313 & 43958.2135468726 \tabularnewline
73 & 3202472 & 3189445.28363838 & 13026.7163616153 \tabularnewline
74 & 3054688 & 2976304.90194718 & 78383.0980528151 \tabularnewline
75 & 3067610 & 3005045.15307685 & 62564.8469231483 \tabularnewline
76 & 3027570 & 3023953.45035215 & 3616.54964785324 \tabularnewline
77 & 3162250 & 3134905.38106164 & 27344.6189383641 \tabularnewline
78 & 3067610 & 3044625.93954342 & 22984.0604565782 \tabularnewline
79 & 2881060 & 2917179.05317972 & -36119.0531797237 \tabularnewline
80 & 2746198 & 2786688.25033696 & -40490.2503369572 \tabularnewline
81 & 2974244 & 2921252.64231916 & 52991.3576808376 \tabularnewline
82 & 2479022 & 2584975.03829867 & -105953.038298669 \tabularnewline
83 & 2800616 & 2821688.41851274 & -21072.4185127388 \tabularnewline
84 & 2947126 & 2945760.25231592 & 1365.74768408062 \tabularnewline
85 & 2947126 & 2969685.20417171 & -22559.2041717102 \tabularnewline
86 & 2773316 & 2781587.92972943 & -8271.92972942907 \tabularnewline
87 & 2612610 & 2764133.46958568 & -151523.469585682 \tabularnewline
88 & 2599688 & 2653946.32490525 & -54258.3249052544 \tabularnewline
89 & 2746198 & 2746773.34367291 & -575.343672913965 \tabularnewline
90 & 2612610 & 2633077.72691127 & -20467.7269112733 \tabularnewline
91 & 2358538 & 2442229.53035058 & -83691.5303505831 \tabularnewline
92 & 2183454 & 2277969.70015133 & -94515.7001513252 \tabularnewline
93 & 2371460 & 2432925.34962133 & -61465.3496213276 \tabularnewline
94 & 1929382 & 1939443.39146146 & -10061.3914614622 \tabularnewline
95 & 2331238 & 2251715.71372216 & 79522.2862778385 \tabularnewline
96 & 2545088 & 2418751.80711876 & 126336.192881236 \tabularnewline
97 & 2612610 & 2471219.69741288 & 141390.302587117 \tabularnewline
98 & 2464826 & 2354476.11644946 & 110349.883550543 \tabularnewline
99 & 2278094 & 2299422.79081396 & -21328.7908139606 \tabularnewline
100 & 2411682 & 2302757.61287976 & 108924.387120245 \tabularnewline
101 & 2464826 & 2500829.27215667 & -36003.2721566744 \tabularnewline
102 & 2424604 & 2367194.22663887 & 57409.7733611278 \tabularnewline
103 & 2022566 & 2178603.52684498 & -156037.526844985 \tabularnewline
104 & 1836016 & 1984976.92686424 & -148960.926864242 \tabularnewline
105 & 1969422 & 2142488.1674218 & -173066.167421803 \tabularnewline
106 & 1567566 & 1636389.6368694 & -68823.6368693979 \tabularnewline
107 & 1982526 & 1978630.18724997 & 3895.81275003171 \tabularnewline
108 & 2130310 & 2141387.54319103 & -11077.5431910325 \tabularnewline
109 & 2250794 & 2142051.75665373 & 108742.243346268 \tabularnewline
110 & 2049866 & 1987706.26880786 & 62159.7311921408 \tabularnewline
111 & 1861860 & 1827645.61953236 & 34214.3804676409 \tabularnewline
112 & 1969422 & 1925232.89918392 & 44189.1008160757 \tabularnewline
113 & 2022566 & 2003471.78172906 & 19094.2182709416 \tabularnewline
114 & 1916278 & 1941749.24471723 & -25471.2447172275 \tabularnewline
115 & 1514422 & 1584498.2287781 & -70076.2287780975 \tabularnewline
116 & 1339338 & 1424034.55142381 & -84696.5514238074 \tabularnewline
117 & 1500044 & 1589052.19637033 & -89008.1963703306 \tabularnewline
118 & 1057966 & 1177004.49608313 & -119038.496083133 \tabularnewline
119 & 1540266 & 1538810.65737907 & 1455.34262092761 \tabularnewline
120 & 1836016 & 1688287.67354377 & 147728.326456229 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279962&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]3429426[/C][C]3429276.86111111[/C][C]149.138888885733[/C][/ROW]
[ROW][C]14[/C][C]3429426[/C][C]3421750.29721145[/C][C]7675.70278854994[/C][/ROW]
[ROW][C]15[/C][C]3403582[/C][C]3391085.31250921[/C][C]12496.6874907874[/C][/ROW]
[ROW][C]16[/C][C]3336060[/C][C]3323237.63377952[/C][C]12822.3662204826[/C][/ROW]
[ROW][C]17[/C][C]3684772[/C][C]3675450.7208656[/C][C]9321.27913440438[/C][/ROW]
[ROW][C]18[/C][C]3737916[/C][C]3729244.5253395[/C][C]8671.47466049716[/C][/ROW]
[ROW][C]19[/C][C]3657654[/C][C]3528588.46727911[/C][C]129065.532720892[/C][/ROW]
[ROW][C]20[/C][C]3469648[/C][C]3460651.27410793[/C][C]8996.72589207068[/C][/ROW]
[ROW][C]21[/C][C]3550092[/C][C]3490782.73427887[/C][C]59309.265721133[/C][/ROW]
[ROW][C]22[/C][C]3429426[/C][C]3532151.45217865[/C][C]-102725.452178652[/C][/ROW]
[ROW][C]23[/C][C]3483844[/C][C]3517863.6653498[/C][C]-34019.6653497973[/C][/ROW]
[ROW][C]24[/C][C]3509870[/C][C]3535843.92080909[/C][C]-25973.9208090883[/C][/ROW]
[ROW][C]25[/C][C]3536988[/C][C]3563039.28144146[/C][C]-26051.2814414646[/C][/ROW]
[ROW][C]26[/C][C]3469648[/C][C]3550926.68115508[/C][C]-81278.68115508[/C][/ROW]
[ROW][C]27[/C][C]3483844[/C][C]3486303.5046056[/C][C]-2459.50460560061[/C][/ROW]
[ROW][C]28[/C][C]3389204[/C][C]3411427.97557874[/C][C]-22223.9755787407[/C][/ROW]
[ROW][C]29[/C][C]3684772[/C][C]3745277.6465453[/C][C]-60505.6465453035[/C][/ROW]
[ROW][C]30[/C][C]3778138[/C][C]3766479.35170429[/C][C]11658.6482957122[/C][/ROW]
[ROW][C]31[/C][C]3697876[/C][C]3634803.58204618[/C][C]63072.4179538153[/C][/ROW]
[ROW][C]32[/C][C]3550092[/C][C]3463167.18663529[/C][C]86924.8133647125[/C][/ROW]
[ROW][C]33[/C][C]3710798[/C][C]3551293.37493694[/C][C]159504.625063065[/C][/ROW]
[ROW][C]34[/C][C]3536988[/C][C]3536029.28503387[/C][C]958.714966129977[/C][/ROW]
[ROW][C]35[/C][C]3697876[/C][C]3606445.91524974[/C][C]91430.0847502612[/C][/ROW]
[ROW][C]36[/C][C]3684772[/C][C]3685162.02654265[/C][C]-390.02654264681[/C][/ROW]
[ROW][C]37[/C][C]3724994[/C][C]3728451.93988598[/C][C]-3457.93988597672[/C][/ROW]
[ROW][C]38[/C][C]3577210[/C][C]3699017.20949169[/C][C]-121807.209491686[/C][/ROW]
[ROW][C]39[/C][C]3737916[/C][C]3670137.70488136[/C][C]67778.295118642[/C][/ROW]
[ROW][C]40[/C][C]3724994[/C][C]3619117.64535959[/C][C]105876.354640407[/C][/ROW]
[ROW][C]41[/C][C]3966144[/C][C]3992615.72520886[/C][C]-26471.7252088585[/C][/ROW]
[ROW][C]42[/C][C]3911726[/C][C]4081904.21888617[/C][C]-170178.218886175[/C][/ROW]
[ROW][C]43[/C][C]3697876[/C][C]3913718.58172925[/C][C]-215842.581729248[/C][/ROW]
[ROW][C]44[/C][C]3590132[/C][C]3642538.47500655[/C][C]-52406.4750065506[/C][/ROW]
[ROW][C]45[/C][C]3737916[/C][C]3713032.46339828[/C][C]24883.5366017167[/C][/ROW]
[ROW][C]46[/C][C]3536988[/C][C]3541084.20777849[/C][C]-4096.20777848642[/C][/ROW]
[ROW][C]47[/C][C]3684772[/C][C]3655283.07981011[/C][C]29488.9201898878[/C][/ROW]
[ROW][C]48[/C][C]3710798[/C][C]3644702.16870723[/C][C]66095.8312927713[/C][/ROW]
[ROW][C]49[/C][C]3765216[/C][C]3705267.94468327[/C][C]59948.0553167257[/C][/ROW]
[ROW][C]50[/C][C]3644732[/C][C]3624966.03931041[/C][C]19765.9606895861[/C][/ROW]
[ROW][C]51[/C][C]3710798[/C][C]3763721.94465138[/C][C]-52923.9446513765[/C][/ROW]
[ROW][C]52[/C][C]3751020[/C][C]3680786.05251788[/C][C]70233.9474821216[/C][/ROW]
[ROW][C]53[/C][C]3898804[/C][C]3954557.57837427[/C][C]-55753.5783742652[/C][/ROW]
[ROW][C]54[/C][C]3778138[/C][C]3939177.56875735[/C][C]-161039.568757351[/C][/ROW]
[ROW][C]55[/C][C]3617432[/C][C]3740437.34862615[/C][C]-123005.348626153[/C][/ROW]
[ROW][C]56[/C][C]3443622[/C][C]3599400.28154312[/C][C]-155778.281543122[/C][/ROW]
[ROW][C]57[/C][C]3604510[/C][C]3666574.53390236[/C][C]-62064.5339023592[/C][/ROW]
[ROW][C]58[/C][C]3162250[/C][C]3432495.82103773[/C][C]-270245.821037726[/C][/ROW]
[ROW][C]59[/C][C]3376282[/C][C]3442170.29295343[/C][C]-65888.2929534311[/C][/ROW]
[ROW][C]60[/C][C]3496766[/C][C]3395588.9463869[/C][C]101177.053613099[/C][/ROW]
[ROW][C]61[/C][C]3617432[/C][C]3448527.79030865[/C][C]168904.209691355[/C][/ROW]
[ROW][C]62[/C][C]3443622[/C][C]3373154.37499721[/C][C]70467.6250027874[/C][/ROW]
[ROW][C]63[/C][C]3443622[/C][C]3475220.70111863[/C][C]-31598.7011186262[/C][/ROW]
[ROW][C]64[/C][C]3443622[/C][C]3460707.6759025[/C][C]-17085.6759025021[/C][/ROW]
[ROW][C]65[/C][C]3536988[/C][C]3608423.93518475[/C][C]-71435.9351847535[/C][/ROW]
[ROW][C]66[/C][C]3403582[/C][C]3507926.50303484[/C][C]-104344.50303484[/C][/ROW]
[ROW][C]67[/C][C]3228498[/C][C]3340115.62867601[/C][C]-111617.628676008[/C][/ROW]
[ROW][C]68[/C][C]3081988[/C][C]3169834.74065367[/C][C]-87846.7406536685[/C][/ROW]
[ROW][C]69[/C][C]3188276[/C][C]3307677.58684932[/C][C]-119401.586849318[/C][/ROW]
[ROW][C]70[/C][C]2773316[/C][C]2912467.21482954[/C][C]-139151.214829538[/C][/ROW]
[ROW][C]71[/C][C]3027570[/C][C]3086137.03340031[/C][C]-58567.0334003149[/C][/ROW]
[ROW][C]72[/C][C]3175354[/C][C]3131395.78645313[/C][C]43958.2135468726[/C][/ROW]
[ROW][C]73[/C][C]3202472[/C][C]3189445.28363838[/C][C]13026.7163616153[/C][/ROW]
[ROW][C]74[/C][C]3054688[/C][C]2976304.90194718[/C][C]78383.0980528151[/C][/ROW]
[ROW][C]75[/C][C]3067610[/C][C]3005045.15307685[/C][C]62564.8469231483[/C][/ROW]
[ROW][C]76[/C][C]3027570[/C][C]3023953.45035215[/C][C]3616.54964785324[/C][/ROW]
[ROW][C]77[/C][C]3162250[/C][C]3134905.38106164[/C][C]27344.6189383641[/C][/ROW]
[ROW][C]78[/C][C]3067610[/C][C]3044625.93954342[/C][C]22984.0604565782[/C][/ROW]
[ROW][C]79[/C][C]2881060[/C][C]2917179.05317972[/C][C]-36119.0531797237[/C][/ROW]
[ROW][C]80[/C][C]2746198[/C][C]2786688.25033696[/C][C]-40490.2503369572[/C][/ROW]
[ROW][C]81[/C][C]2974244[/C][C]2921252.64231916[/C][C]52991.3576808376[/C][/ROW]
[ROW][C]82[/C][C]2479022[/C][C]2584975.03829867[/C][C]-105953.038298669[/C][/ROW]
[ROW][C]83[/C][C]2800616[/C][C]2821688.41851274[/C][C]-21072.4185127388[/C][/ROW]
[ROW][C]84[/C][C]2947126[/C][C]2945760.25231592[/C][C]1365.74768408062[/C][/ROW]
[ROW][C]85[/C][C]2947126[/C][C]2969685.20417171[/C][C]-22559.2041717102[/C][/ROW]
[ROW][C]86[/C][C]2773316[/C][C]2781587.92972943[/C][C]-8271.92972942907[/C][/ROW]
[ROW][C]87[/C][C]2612610[/C][C]2764133.46958568[/C][C]-151523.469585682[/C][/ROW]
[ROW][C]88[/C][C]2599688[/C][C]2653946.32490525[/C][C]-54258.3249052544[/C][/ROW]
[ROW][C]89[/C][C]2746198[/C][C]2746773.34367291[/C][C]-575.343672913965[/C][/ROW]
[ROW][C]90[/C][C]2612610[/C][C]2633077.72691127[/C][C]-20467.7269112733[/C][/ROW]
[ROW][C]91[/C][C]2358538[/C][C]2442229.53035058[/C][C]-83691.5303505831[/C][/ROW]
[ROW][C]92[/C][C]2183454[/C][C]2277969.70015133[/C][C]-94515.7001513252[/C][/ROW]
[ROW][C]93[/C][C]2371460[/C][C]2432925.34962133[/C][C]-61465.3496213276[/C][/ROW]
[ROW][C]94[/C][C]1929382[/C][C]1939443.39146146[/C][C]-10061.3914614622[/C][/ROW]
[ROW][C]95[/C][C]2331238[/C][C]2251715.71372216[/C][C]79522.2862778385[/C][/ROW]
[ROW][C]96[/C][C]2545088[/C][C]2418751.80711876[/C][C]126336.192881236[/C][/ROW]
[ROW][C]97[/C][C]2612610[/C][C]2471219.69741288[/C][C]141390.302587117[/C][/ROW]
[ROW][C]98[/C][C]2464826[/C][C]2354476.11644946[/C][C]110349.883550543[/C][/ROW]
[ROW][C]99[/C][C]2278094[/C][C]2299422.79081396[/C][C]-21328.7908139606[/C][/ROW]
[ROW][C]100[/C][C]2411682[/C][C]2302757.61287976[/C][C]108924.387120245[/C][/ROW]
[ROW][C]101[/C][C]2464826[/C][C]2500829.27215667[/C][C]-36003.2721566744[/C][/ROW]
[ROW][C]102[/C][C]2424604[/C][C]2367194.22663887[/C][C]57409.7733611278[/C][/ROW]
[ROW][C]103[/C][C]2022566[/C][C]2178603.52684498[/C][C]-156037.526844985[/C][/ROW]
[ROW][C]104[/C][C]1836016[/C][C]1984976.92686424[/C][C]-148960.926864242[/C][/ROW]
[ROW][C]105[/C][C]1969422[/C][C]2142488.1674218[/C][C]-173066.167421803[/C][/ROW]
[ROW][C]106[/C][C]1567566[/C][C]1636389.6368694[/C][C]-68823.6368693979[/C][/ROW]
[ROW][C]107[/C][C]1982526[/C][C]1978630.18724997[/C][C]3895.81275003171[/C][/ROW]
[ROW][C]108[/C][C]2130310[/C][C]2141387.54319103[/C][C]-11077.5431910325[/C][/ROW]
[ROW][C]109[/C][C]2250794[/C][C]2142051.75665373[/C][C]108742.243346268[/C][/ROW]
[ROW][C]110[/C][C]2049866[/C][C]1987706.26880786[/C][C]62159.7311921408[/C][/ROW]
[ROW][C]111[/C][C]1861860[/C][C]1827645.61953236[/C][C]34214.3804676409[/C][/ROW]
[ROW][C]112[/C][C]1969422[/C][C]1925232.89918392[/C][C]44189.1008160757[/C][/ROW]
[ROW][C]113[/C][C]2022566[/C][C]2003471.78172906[/C][C]19094.2182709416[/C][/ROW]
[ROW][C]114[/C][C]1916278[/C][C]1941749.24471723[/C][C]-25471.2447172275[/C][/ROW]
[ROW][C]115[/C][C]1514422[/C][C]1584498.2287781[/C][C]-70076.2287780975[/C][/ROW]
[ROW][C]116[/C][C]1339338[/C][C]1424034.55142381[/C][C]-84696.5514238074[/C][/ROW]
[ROW][C]117[/C][C]1500044[/C][C]1589052.19637033[/C][C]-89008.1963703306[/C][/ROW]
[ROW][C]118[/C][C]1057966[/C][C]1177004.49608313[/C][C]-119038.496083133[/C][/ROW]
[ROW][C]119[/C][C]1540266[/C][C]1538810.65737907[/C][C]1455.34262092761[/C][/ROW]
[ROW][C]120[/C][C]1836016[/C][C]1688287.67354377[/C][C]147728.326456229[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279962&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279962&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
1334294263429276.86111111149.138888885733
1434294263421750.297211457675.70278854994
1534035823391085.3125092112496.6874907874
1633360603323237.6337795212822.3662204826
1736847723675450.72086569321.27913440438
1837379163729244.52533958671.47466049716
1936576543528588.46727911129065.532720892
2034696483460651.274107938996.72589207068
2135500923490782.7342788759309.265721133
2234294263532151.45217865-102725.452178652
2334838443517863.6653498-34019.6653497973
2435098703535843.92080909-25973.9208090883
2535369883563039.28144146-26051.2814414646
2634696483550926.68115508-81278.68115508
2734838443486303.5046056-2459.50460560061
2833892043411427.97557874-22223.9755787407
2936847723745277.6465453-60505.6465453035
3037781383766479.3517042911658.6482957122
3136978763634803.5820461863072.4179538153
3235500923463167.1866352986924.8133647125
3337107983551293.37493694159504.625063065
3435369883536029.28503387958.714966129977
3536978763606445.9152497491430.0847502612
3636847723685162.02654265-390.02654264681
3737249943728451.93988598-3457.93988597672
3835772103699017.20949169-121807.209491686
3937379163670137.7048813667778.295118642
4037249943619117.64535959105876.354640407
4139661443992615.72520886-26471.7252088585
4239117264081904.21888617-170178.218886175
4336978763913718.58172925-215842.581729248
4435901323642538.47500655-52406.4750065506
4537379163713032.4633982824883.5366017167
4635369883541084.20777849-4096.20777848642
4736847723655283.0798101129488.9201898878
4837107983644702.1687072366095.8312927713
4937652163705267.9446832759948.0553167257
5036447323624966.0393104119765.9606895861
5137107983763721.94465138-52923.9446513765
5237510203680786.0525178870233.9474821216
5338988043954557.57837427-55753.5783742652
5437781383939177.56875735-161039.568757351
5536174323740437.34862615-123005.348626153
5634436223599400.28154312-155778.281543122
5736045103666574.53390236-62064.5339023592
5831622503432495.82103773-270245.821037726
5933762823442170.29295343-65888.2929534311
6034967663395588.9463869101177.053613099
6136174323448527.79030865168904.209691355
6234436223373154.3749972170467.6250027874
6334436223475220.70111863-31598.7011186262
6434436223460707.6759025-17085.6759025021
6535369883608423.93518475-71435.9351847535
6634035823507926.50303484-104344.50303484
6732284983340115.62867601-111617.628676008
6830819883169834.74065367-87846.7406536685
6931882763307677.58684932-119401.586849318
7027733162912467.21482954-139151.214829538
7130275703086137.03340031-58567.0334003149
7231753543131395.7864531343958.2135468726
7332024723189445.2836383813026.7163616153
7430546882976304.9019471878383.0980528151
7530676103005045.1530768562564.8469231483
7630275703023953.450352153616.54964785324
7731622503134905.3810616427344.6189383641
7830676103044625.9395434222984.0604565782
7928810602917179.05317972-36119.0531797237
8027461982786688.25033696-40490.2503369572
8129742442921252.6423191652991.3576808376
8224790222584975.03829867-105953.038298669
8328006162821688.41851274-21072.4185127388
8429471262945760.252315921365.74768408062
8529471262969685.20417171-22559.2041717102
8627733162781587.92972943-8271.92972942907
8726126102764133.46958568-151523.469585682
8825996882653946.32490525-54258.3249052544
8927461982746773.34367291-575.343672913965
9026126102633077.72691127-20467.7269112733
9123585382442229.53035058-83691.5303505831
9221834542277969.70015133-94515.7001513252
9323714602432925.34962133-61465.3496213276
9419293821939443.39146146-10061.3914614622
9523312382251715.7137221679522.2862778385
9625450882418751.80711876126336.192881236
9726126102471219.69741288141390.302587117
9824648262354476.11644946110349.883550543
9922780942299422.79081396-21328.7908139606
10024116822302757.61287976108924.387120245
10124648262500829.27215667-36003.2721566744
10224246042367194.2266388757409.7733611278
10320225662178603.52684498-156037.526844985
10418360161984976.92686424-148960.926864242
10519694222142488.1674218-173066.167421803
10615675661636389.6368694-68823.6368693979
10719825261978630.187249973895.81275003171
10821303102141387.54319103-11077.5431910325
10922507942142051.75665373108742.243346268
11020498661987706.2688078662159.7311921408
11118618601827645.6195323634214.3804676409
11219694221925232.8991839244189.1008160757
11320225662003471.7817290619094.2182709416
11419162781941749.24471723-25471.2447172275
11515144221584498.2287781-70076.2287780975
11613393381424034.55142381-84696.5514238074
11715000441589052.19637033-89008.1963703306
11810579661177004.49608313-119038.496083133
11915402661538810.657379071455.34262092761
12018360161688287.67354377147728.326456229







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1211825340.486335271659179.675837771991501.29683278
1221597138.664295671416169.141932321778108.18665902
1231391560.659229781195263.605983571587857.71247598
1241476612.677825231264492.717778851688732.63787161
1251516263.073848091287845.105478831744681.04221735
1261414046.405964461168873.053367871659219.75856105
1271035008.19419884772637.734090751297378.65430693
128890500.899883114610505.5569677411170496.24279849
1291085746.33134733787710.8616242241383781.80107043
130692708.125831754376228.6272028991009187.62446061
1311178319.7460322843002.6501201141513636.8419443
1321418052.574899931063513.784740891772591.36505896

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 1825340.48633527 & 1659179.67583777 & 1991501.29683278 \tabularnewline
122 & 1597138.66429567 & 1416169.14193232 & 1778108.18665902 \tabularnewline
123 & 1391560.65922978 & 1195263.60598357 & 1587857.71247598 \tabularnewline
124 & 1476612.67782523 & 1264492.71777885 & 1688732.63787161 \tabularnewline
125 & 1516263.07384809 & 1287845.10547883 & 1744681.04221735 \tabularnewline
126 & 1414046.40596446 & 1168873.05336787 & 1659219.75856105 \tabularnewline
127 & 1035008.19419884 & 772637.73409075 & 1297378.65430693 \tabularnewline
128 & 890500.899883114 & 610505.556967741 & 1170496.24279849 \tabularnewline
129 & 1085746.33134733 & 787710.861624224 & 1383781.80107043 \tabularnewline
130 & 692708.125831754 & 376228.627202899 & 1009187.62446061 \tabularnewline
131 & 1178319.7460322 & 843002.650120114 & 1513636.8419443 \tabularnewline
132 & 1418052.57489993 & 1063513.78474089 & 1772591.36505896 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279962&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]121[/C][C]1825340.48633527[/C][C]1659179.67583777[/C][C]1991501.29683278[/C][/ROW]
[ROW][C]122[/C][C]1597138.66429567[/C][C]1416169.14193232[/C][C]1778108.18665902[/C][/ROW]
[ROW][C]123[/C][C]1391560.65922978[/C][C]1195263.60598357[/C][C]1587857.71247598[/C][/ROW]
[ROW][C]124[/C][C]1476612.67782523[/C][C]1264492.71777885[/C][C]1688732.63787161[/C][/ROW]
[ROW][C]125[/C][C]1516263.07384809[/C][C]1287845.10547883[/C][C]1744681.04221735[/C][/ROW]
[ROW][C]126[/C][C]1414046.40596446[/C][C]1168873.05336787[/C][C]1659219.75856105[/C][/ROW]
[ROW][C]127[/C][C]1035008.19419884[/C][C]772637.73409075[/C][C]1297378.65430693[/C][/ROW]
[ROW][C]128[/C][C]890500.899883114[/C][C]610505.556967741[/C][C]1170496.24279849[/C][/ROW]
[ROW][C]129[/C][C]1085746.33134733[/C][C]787710.861624224[/C][C]1383781.80107043[/C][/ROW]
[ROW][C]130[/C][C]692708.125831754[/C][C]376228.627202899[/C][C]1009187.62446061[/C][/ROW]
[ROW][C]131[/C][C]1178319.7460322[/C][C]843002.650120114[/C][C]1513636.8419443[/C][/ROW]
[ROW][C]132[/C][C]1418052.57489993[/C][C]1063513.78474089[/C][C]1772591.36505896[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279962&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279962&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
1211825340.486335271659179.675837771991501.29683278
1221597138.664295671416169.141932321778108.18665902
1231391560.659229781195263.605983571587857.71247598
1241476612.677825231264492.717778851688732.63787161
1251516263.073848091287845.105478831744681.04221735
1261414046.405964461168873.053367871659219.75856105
1271035008.19419884772637.734090751297378.65430693
128890500.899883114610505.5569677411170496.24279849
1291085746.33134733787710.8616242241383781.80107043
130692708.125831754376228.6272028991009187.62446061
1311178319.7460322843002.6501201141513636.8419443
1321418052.574899931063513.784740891772591.36505896



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')