Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 17 Aug 2017 08:48:55 +0200
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Aug/17/t1502952742qdi15we4ip5i3bl.htm/, Retrieved Fri, 10 May 2024 05:36:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=307539, Retrieved Fri, 10 May 2024 05:36:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact150
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2017-08-17 06:48:55] [eec775fda337aa2da775a098928b5865] [Current]
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Dataseries X:
3469648
3456726
3443622
3416504
3684772
3670576
3469648
3336060
3348982
3348982
3363360
3389204
3429426
3429426
3403582
3336060
3684772
3737916
3657654
3469648
3550092
3429426
3483844
3509870
3536988
3469648
3483844
3389204
3684772
3778138
3697876
3550092
3710798
3536988
3697876
3684772
3724994
3577210
3737916
3724994
3966144
3911726
3697876
3590132
3737916
3536988
3684772
3710798
3765216
3644732
3710798
3751020
3898804
3778138
3617432
3443622
3604510
3162250
3376282
3496766
3617432
3443622
3443622
3443622
3536988
3403582
3228498
3081988
3188276
2773316
3027570
3175354
3202472
3054688
3067610
3027570
3162250
3067610
2881060
2746198
2974244
2479022
2800616
2947126
2947126
2773316
2612610
2599688
2746198
2612610
2358538
2183454
2371460
1929382
2331238
2545088
2612610
2464826
2278094
2411682
2464826
2424604
2022566
1836016
1969422
1567566
1982526
2130310
2250794
2049866
1861860
1969422
2022566
1916278
1514422
1339338
1500044
1057966
1540266
1836016




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307539&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=307539&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307539&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center







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=307539&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=307539&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307539&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=307539&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=307539&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307539&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=307539&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=307539&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307539&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):
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')