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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 05 Jun 2010 14:15:29 +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/2010/Jun/05/t1275747391eydbtrbylcywrg7.htm/, Retrieved Fri, 03 May 2024 07:15:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=77558, Retrieved Fri, 03 May 2024 07:15:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact230

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Classical Decomposition] [Nieuwe personenwa...] [2009-01-13 17:37:29] [74be16979710d4c4e7c6647856088456]
-       [Classical Decomposition] [roger dirkx oefen...] [2009-01-14 16:39:03] [74be16979710d4c4e7c6647856088456]
- RMP     [Exponential Smoothing] [roger dirkx oef 10] [2009-01-24 20:53:30] [74be16979710d4c4e7c6647856088456]
-           [Exponential Smoothing] [Dennis Collin oef 10] [2009-01-25 12:25:31] [2097edf1f094fab6879a8cb46df74ec2]
-             [Exponential Smoothing] [Dennis Collin oef 2] [2009-01-25 12:34:26] [2097edf1f094fab6879a8cb46df74ec2]
-               [Exponential Smoothing] [Dennis Collin oef 10] [2009-01-25 12:39:06] [2097edf1f094fab6879a8cb46df74ec2]
- RM D            [Exponential Smoothing] [exponential smoot...] [2010-01-19 11:49:31] [74be16979710d4c4e7c6647856088456]
-   PD                [Exponential Smoothing] [] [2010-06-05 14:15:29] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1664.81
2397.53
2840.71
3547.29
3752.96
3714.74
4349.61
3566.34
5021.82
6423.48
7600.60
19756.21
2499.81
5198.24
7225.14
4806.03
5900.88
4951.34
6179.12
4752.15
5496.43
5835.10
12600.08
28541.72
4717.02
5702.63
9957.58
5304.78
6492.43
6630.80
7349.62
8176.62
8573.17
9690.50
15151.84
34061.01
5921.10
5814.58
12421.25
6369.77
7609.12
7224.75
8121.22
7979.25
8093.06
8476.70
17914.66
30114.41
4826.64
6470.23
9638.77
8821.17
8722.37
10209.48
11276.55
12552.22
11637.39
13606.89
21822.11
45060.69
7615.03
9849.69
14558.40
11587.33
9332.56
13082.09
16732.78
19888.61
23933.38
25391.35
36024.80
80721.71
10243.24
11266.88
21826.84
17357.33
15997.79
18601.53
26155.15
28586.52
30505.41
30821.33
46634.38
104660.67

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77558&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77558&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77558&T=0

As an alternative you can also use a QR Code:  
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'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0218820013470966
beta1
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0218820013470966 \tabularnewline
beta & 1 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77558&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]0.0218820013470966[/C][/ROW]
[ROW][C]beta[/C][C]1[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77558&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77558&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0218820013470966
beta1
gamma1






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
132499.811442.110657051281057.69934294872
145198.244216.98507326975981.254926730251
157225.146396.58272096476828.557279035236
164806.034218.88411335655587.145886643452
175900.885374.17461841729526.705381582714
184951.344104.69918213418846.64081786582
196179.125827.90910234919351.210897650813
204752.155169.9615550515-417.811555051501
215496.436576.9007877307-1080.47078773070
225835.17956.12559695512-2121.02559695512
2312600.089134.816616139243465.26338386076
2428541.7221490.98621636057050.73378363948
254717.025715.70909868618-998.689098686176
265702.638590.06100855337-2887.43100855337
279957.5810670.2402046897-712.660204689728
285304.788323.55537984434-3018.77537984434
296492.439362.785924832-2870.355924832
306630.88279.53885680331-1648.73885680331
317349.629356.58031188177-2006.96031188177
328176.627736.25940935995440.360590640047
338573.178374.01962039411199.150379605891
349690.58651.66176311011038.83823688991
3515151.8415320.8929183157-169.052918315658
3634061.0130982.36961529793078.64038470207
375921.17037.79247075986-1116.69247075986
385814.587850.47035009641-2035.89035009641
3912421.2511883.4194163748537.830583625248
406369.777142.76230407558-772.992304075576
417609.128259.76627715667-650.64627715667
427224.758352.00768933597-1127.25768933597
438121.229033.51954392351-912.299543923514
447979.259798.31620205185-1819.06620205185
458093.0610068.6583729870-1975.59837298696
468476.710990.3934007887-2513.69340078874
4717914.6616193.05840627141721.60159372864
4830114.4134906.5354178772-4792.12541787723
494826.646347.97321754052-1521.33321754052
506470.235905.6320364054564.597963594599
519638.7712222.7109280304-2583.94092803038
528821.175773.116307158543048.05369284146
538722.376818.525957893461903.84404210654
5410209.486281.504583680253927.97541631975
5511276.557175.530158124634101.01984187537
5612552.227164.445621710285387.77437828972
5711637.397598.423182257734038.96681774227
5813606.898416.101453677285190.78854632272
5921822.1118389.21664328323432.89335671677
6045060.6931265.635439887713795.0545601123
617615.037216.43227988702398.597720112984
629849.699801.8154157156347.8745842843691
6314558.413962.0634179994596.336582000629
6411587.3314094.5243893338-2507.19438933385
659332.5614781.3515428740-5448.79154287396
6613082.0916784.5382363052-3702.4482363052
6716732.7818235.1429173245-1502.3629173245
6819888.6119791.719874673196.890125326856
6923933.3819106.53116176164826.84883823835
7025391.3521401.20968259523990.14031740477
7136024.829935.49302519326089.30697480676
7280721.7153370.453156374327351.2568436257
7310243.2417176.2054264752-6932.96542647522
7411266.8819759.3155481584-8492.43554815835
7521826.8424583.4708185425-2756.63081854247
7617357.3321847.8988074668-4490.56880746677
7715997.7919811.6525941686-3813.86259416864
7818601.5323792.0760980126-5190.54609801263
7926155.1527562.8301822428-1407.68018224283
8028586.5230888.5779340407-2302.05793404075
8130505.4134927.7001630747-4422.29016307467
8230821.3336149.5466525105-5328.21665251051
8346634.3846277.2113898907357.168610109307
84104660.6790002.059060156814658.6109398432

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 2499.81 & 1442.11065705128 & 1057.69934294872 \tabularnewline
14 & 5198.24 & 4216.98507326975 & 981.254926730251 \tabularnewline
15 & 7225.14 & 6396.58272096476 & 828.557279035236 \tabularnewline
16 & 4806.03 & 4218.88411335655 & 587.145886643452 \tabularnewline
17 & 5900.88 & 5374.17461841729 & 526.705381582714 \tabularnewline
18 & 4951.34 & 4104.69918213418 & 846.64081786582 \tabularnewline
19 & 6179.12 & 5827.90910234919 & 351.210897650813 \tabularnewline
20 & 4752.15 & 5169.9615550515 & -417.811555051501 \tabularnewline
21 & 5496.43 & 6576.9007877307 & -1080.47078773070 \tabularnewline
22 & 5835.1 & 7956.12559695512 & -2121.02559695512 \tabularnewline
23 & 12600.08 & 9134.81661613924 & 3465.26338386076 \tabularnewline
24 & 28541.72 & 21490.9862163605 & 7050.73378363948 \tabularnewline
25 & 4717.02 & 5715.70909868618 & -998.689098686176 \tabularnewline
26 & 5702.63 & 8590.06100855337 & -2887.43100855337 \tabularnewline
27 & 9957.58 & 10670.2402046897 & -712.660204689728 \tabularnewline
28 & 5304.78 & 8323.55537984434 & -3018.77537984434 \tabularnewline
29 & 6492.43 & 9362.785924832 & -2870.355924832 \tabularnewline
30 & 6630.8 & 8279.53885680331 & -1648.73885680331 \tabularnewline
31 & 7349.62 & 9356.58031188177 & -2006.96031188177 \tabularnewline
32 & 8176.62 & 7736.25940935995 & 440.360590640047 \tabularnewline
33 & 8573.17 & 8374.01962039411 & 199.150379605891 \tabularnewline
34 & 9690.5 & 8651.6617631101 & 1038.83823688991 \tabularnewline
35 & 15151.84 & 15320.8929183157 & -169.052918315658 \tabularnewline
36 & 34061.01 & 30982.3696152979 & 3078.64038470207 \tabularnewline
37 & 5921.1 & 7037.79247075986 & -1116.69247075986 \tabularnewline
38 & 5814.58 & 7850.47035009641 & -2035.89035009641 \tabularnewline
39 & 12421.25 & 11883.4194163748 & 537.830583625248 \tabularnewline
40 & 6369.77 & 7142.76230407558 & -772.992304075576 \tabularnewline
41 & 7609.12 & 8259.76627715667 & -650.64627715667 \tabularnewline
42 & 7224.75 & 8352.00768933597 & -1127.25768933597 \tabularnewline
43 & 8121.22 & 9033.51954392351 & -912.299543923514 \tabularnewline
44 & 7979.25 & 9798.31620205185 & -1819.06620205185 \tabularnewline
45 & 8093.06 & 10068.6583729870 & -1975.59837298696 \tabularnewline
46 & 8476.7 & 10990.3934007887 & -2513.69340078874 \tabularnewline
47 & 17914.66 & 16193.0584062714 & 1721.60159372864 \tabularnewline
48 & 30114.41 & 34906.5354178772 & -4792.12541787723 \tabularnewline
49 & 4826.64 & 6347.97321754052 & -1521.33321754052 \tabularnewline
50 & 6470.23 & 5905.6320364054 & 564.597963594599 \tabularnewline
51 & 9638.77 & 12222.7109280304 & -2583.94092803038 \tabularnewline
52 & 8821.17 & 5773.11630715854 & 3048.05369284146 \tabularnewline
53 & 8722.37 & 6818.52595789346 & 1903.84404210654 \tabularnewline
54 & 10209.48 & 6281.50458368025 & 3927.97541631975 \tabularnewline
55 & 11276.55 & 7175.53015812463 & 4101.01984187537 \tabularnewline
56 & 12552.22 & 7164.44562171028 & 5387.77437828972 \tabularnewline
57 & 11637.39 & 7598.42318225773 & 4038.96681774227 \tabularnewline
58 & 13606.89 & 8416.10145367728 & 5190.78854632272 \tabularnewline
59 & 21822.11 & 18389.2166432832 & 3432.89335671677 \tabularnewline
60 & 45060.69 & 31265.6354398877 & 13795.0545601123 \tabularnewline
61 & 7615.03 & 7216.43227988702 & 398.597720112984 \tabularnewline
62 & 9849.69 & 9801.81541571563 & 47.8745842843691 \tabularnewline
63 & 14558.4 & 13962.0634179994 & 596.336582000629 \tabularnewline
64 & 11587.33 & 14094.5243893338 & -2507.19438933385 \tabularnewline
65 & 9332.56 & 14781.3515428740 & -5448.79154287396 \tabularnewline
66 & 13082.09 & 16784.5382363052 & -3702.4482363052 \tabularnewline
67 & 16732.78 & 18235.1429173245 & -1502.3629173245 \tabularnewline
68 & 19888.61 & 19791.7198746731 & 96.890125326856 \tabularnewline
69 & 23933.38 & 19106.5311617616 & 4826.84883823835 \tabularnewline
70 & 25391.35 & 21401.2096825952 & 3990.14031740477 \tabularnewline
71 & 36024.8 & 29935.4930251932 & 6089.30697480676 \tabularnewline
72 & 80721.71 & 53370.4531563743 & 27351.2568436257 \tabularnewline
73 & 10243.24 & 17176.2054264752 & -6932.96542647522 \tabularnewline
74 & 11266.88 & 19759.3155481584 & -8492.43554815835 \tabularnewline
75 & 21826.84 & 24583.4708185425 & -2756.63081854247 \tabularnewline
76 & 17357.33 & 21847.8988074668 & -4490.56880746677 \tabularnewline
77 & 15997.79 & 19811.6525941686 & -3813.86259416864 \tabularnewline
78 & 18601.53 & 23792.0760980126 & -5190.54609801263 \tabularnewline
79 & 26155.15 & 27562.8301822428 & -1407.68018224283 \tabularnewline
80 & 28586.52 & 30888.5779340407 & -2302.05793404075 \tabularnewline
81 & 30505.41 & 34927.7001630747 & -4422.29016307467 \tabularnewline
82 & 30821.33 & 36149.5466525105 & -5328.21665251051 \tabularnewline
83 & 46634.38 & 46277.2113898907 & 357.168610109307 \tabularnewline
84 & 104660.67 & 90002.0590601568 & 14658.6109398432 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77558&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]2499.81[/C][C]1442.11065705128[/C][C]1057.69934294872[/C][/ROW]
[ROW][C]14[/C][C]5198.24[/C][C]4216.98507326975[/C][C]981.254926730251[/C][/ROW]
[ROW][C]15[/C][C]7225.14[/C][C]6396.58272096476[/C][C]828.557279035236[/C][/ROW]
[ROW][C]16[/C][C]4806.03[/C][C]4218.88411335655[/C][C]587.145886643452[/C][/ROW]
[ROW][C]17[/C][C]5900.88[/C][C]5374.17461841729[/C][C]526.705381582714[/C][/ROW]
[ROW][C]18[/C][C]4951.34[/C][C]4104.69918213418[/C][C]846.64081786582[/C][/ROW]
[ROW][C]19[/C][C]6179.12[/C][C]5827.90910234919[/C][C]351.210897650813[/C][/ROW]
[ROW][C]20[/C][C]4752.15[/C][C]5169.9615550515[/C][C]-417.811555051501[/C][/ROW]
[ROW][C]21[/C][C]5496.43[/C][C]6576.9007877307[/C][C]-1080.47078773070[/C][/ROW]
[ROW][C]22[/C][C]5835.1[/C][C]7956.12559695512[/C][C]-2121.02559695512[/C][/ROW]
[ROW][C]23[/C][C]12600.08[/C][C]9134.81661613924[/C][C]3465.26338386076[/C][/ROW]
[ROW][C]24[/C][C]28541.72[/C][C]21490.9862163605[/C][C]7050.73378363948[/C][/ROW]
[ROW][C]25[/C][C]4717.02[/C][C]5715.70909868618[/C][C]-998.689098686176[/C][/ROW]
[ROW][C]26[/C][C]5702.63[/C][C]8590.06100855337[/C][C]-2887.43100855337[/C][/ROW]
[ROW][C]27[/C][C]9957.58[/C][C]10670.2402046897[/C][C]-712.660204689728[/C][/ROW]
[ROW][C]28[/C][C]5304.78[/C][C]8323.55537984434[/C][C]-3018.77537984434[/C][/ROW]
[ROW][C]29[/C][C]6492.43[/C][C]9362.785924832[/C][C]-2870.355924832[/C][/ROW]
[ROW][C]30[/C][C]6630.8[/C][C]8279.53885680331[/C][C]-1648.73885680331[/C][/ROW]
[ROW][C]31[/C][C]7349.62[/C][C]9356.58031188177[/C][C]-2006.96031188177[/C][/ROW]
[ROW][C]32[/C][C]8176.62[/C][C]7736.25940935995[/C][C]440.360590640047[/C][/ROW]
[ROW][C]33[/C][C]8573.17[/C][C]8374.01962039411[/C][C]199.150379605891[/C][/ROW]
[ROW][C]34[/C][C]9690.5[/C][C]8651.6617631101[/C][C]1038.83823688991[/C][/ROW]
[ROW][C]35[/C][C]15151.84[/C][C]15320.8929183157[/C][C]-169.052918315658[/C][/ROW]
[ROW][C]36[/C][C]34061.01[/C][C]30982.3696152979[/C][C]3078.64038470207[/C][/ROW]
[ROW][C]37[/C][C]5921.1[/C][C]7037.79247075986[/C][C]-1116.69247075986[/C][/ROW]
[ROW][C]38[/C][C]5814.58[/C][C]7850.47035009641[/C][C]-2035.89035009641[/C][/ROW]
[ROW][C]39[/C][C]12421.25[/C][C]11883.4194163748[/C][C]537.830583625248[/C][/ROW]
[ROW][C]40[/C][C]6369.77[/C][C]7142.76230407558[/C][C]-772.992304075576[/C][/ROW]
[ROW][C]41[/C][C]7609.12[/C][C]8259.76627715667[/C][C]-650.64627715667[/C][/ROW]
[ROW][C]42[/C][C]7224.75[/C][C]8352.00768933597[/C][C]-1127.25768933597[/C][/ROW]
[ROW][C]43[/C][C]8121.22[/C][C]9033.51954392351[/C][C]-912.299543923514[/C][/ROW]
[ROW][C]44[/C][C]7979.25[/C][C]9798.31620205185[/C][C]-1819.06620205185[/C][/ROW]
[ROW][C]45[/C][C]8093.06[/C][C]10068.6583729870[/C][C]-1975.59837298696[/C][/ROW]
[ROW][C]46[/C][C]8476.7[/C][C]10990.3934007887[/C][C]-2513.69340078874[/C][/ROW]
[ROW][C]47[/C][C]17914.66[/C][C]16193.0584062714[/C][C]1721.60159372864[/C][/ROW]
[ROW][C]48[/C][C]30114.41[/C][C]34906.5354178772[/C][C]-4792.12541787723[/C][/ROW]
[ROW][C]49[/C][C]4826.64[/C][C]6347.97321754052[/C][C]-1521.33321754052[/C][/ROW]
[ROW][C]50[/C][C]6470.23[/C][C]5905.6320364054[/C][C]564.597963594599[/C][/ROW]
[ROW][C]51[/C][C]9638.77[/C][C]12222.7109280304[/C][C]-2583.94092803038[/C][/ROW]
[ROW][C]52[/C][C]8821.17[/C][C]5773.11630715854[/C][C]3048.05369284146[/C][/ROW]
[ROW][C]53[/C][C]8722.37[/C][C]6818.52595789346[/C][C]1903.84404210654[/C][/ROW]
[ROW][C]54[/C][C]10209.48[/C][C]6281.50458368025[/C][C]3927.97541631975[/C][/ROW]
[ROW][C]55[/C][C]11276.55[/C][C]7175.53015812463[/C][C]4101.01984187537[/C][/ROW]
[ROW][C]56[/C][C]12552.22[/C][C]7164.44562171028[/C][C]5387.77437828972[/C][/ROW]
[ROW][C]57[/C][C]11637.39[/C][C]7598.42318225773[/C][C]4038.96681774227[/C][/ROW]
[ROW][C]58[/C][C]13606.89[/C][C]8416.10145367728[/C][C]5190.78854632272[/C][/ROW]
[ROW][C]59[/C][C]21822.11[/C][C]18389.2166432832[/C][C]3432.89335671677[/C][/ROW]
[ROW][C]60[/C][C]45060.69[/C][C]31265.6354398877[/C][C]13795.0545601123[/C][/ROW]
[ROW][C]61[/C][C]7615.03[/C][C]7216.43227988702[/C][C]398.597720112984[/C][/ROW]
[ROW][C]62[/C][C]9849.69[/C][C]9801.81541571563[/C][C]47.8745842843691[/C][/ROW]
[ROW][C]63[/C][C]14558.4[/C][C]13962.0634179994[/C][C]596.336582000629[/C][/ROW]
[ROW][C]64[/C][C]11587.33[/C][C]14094.5243893338[/C][C]-2507.19438933385[/C][/ROW]
[ROW][C]65[/C][C]9332.56[/C][C]14781.3515428740[/C][C]-5448.79154287396[/C][/ROW]
[ROW][C]66[/C][C]13082.09[/C][C]16784.5382363052[/C][C]-3702.4482363052[/C][/ROW]
[ROW][C]67[/C][C]16732.78[/C][C]18235.1429173245[/C][C]-1502.3629173245[/C][/ROW]
[ROW][C]68[/C][C]19888.61[/C][C]19791.7198746731[/C][C]96.890125326856[/C][/ROW]
[ROW][C]69[/C][C]23933.38[/C][C]19106.5311617616[/C][C]4826.84883823835[/C][/ROW]
[ROW][C]70[/C][C]25391.35[/C][C]21401.2096825952[/C][C]3990.14031740477[/C][/ROW]
[ROW][C]71[/C][C]36024.8[/C][C]29935.4930251932[/C][C]6089.30697480676[/C][/ROW]
[ROW][C]72[/C][C]80721.71[/C][C]53370.4531563743[/C][C]27351.2568436257[/C][/ROW]
[ROW][C]73[/C][C]10243.24[/C][C]17176.2054264752[/C][C]-6932.96542647522[/C][/ROW]
[ROW][C]74[/C][C]11266.88[/C][C]19759.3155481584[/C][C]-8492.43554815835[/C][/ROW]
[ROW][C]75[/C][C]21826.84[/C][C]24583.4708185425[/C][C]-2756.63081854247[/C][/ROW]
[ROW][C]76[/C][C]17357.33[/C][C]21847.8988074668[/C][C]-4490.56880746677[/C][/ROW]
[ROW][C]77[/C][C]15997.79[/C][C]19811.6525941686[/C][C]-3813.86259416864[/C][/ROW]
[ROW][C]78[/C][C]18601.53[/C][C]23792.0760980126[/C][C]-5190.54609801263[/C][/ROW]
[ROW][C]79[/C][C]26155.15[/C][C]27562.8301822428[/C][C]-1407.68018224283[/C][/ROW]
[ROW][C]80[/C][C]28586.52[/C][C]30888.5779340407[/C][C]-2302.05793404075[/C][/ROW]
[ROW][C]81[/C][C]30505.41[/C][C]34927.7001630747[/C][C]-4422.29016307467[/C][/ROW]
[ROW][C]82[/C][C]30821.33[/C][C]36149.5466525105[/C][C]-5328.21665251051[/C][/ROW]
[ROW][C]83[/C][C]46634.38[/C][C]46277.2113898907[/C][C]357.168610109307[/C][/ROW]
[ROW][C]84[/C][C]104660.67[/C][C]90002.0590601568[/C][C]14658.6109398432[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77558&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77558&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
132499.811442.110657051281057.69934294872
145198.244216.98507326975981.254926730251
157225.146396.58272096476828.557279035236
164806.034218.88411335655587.145886643452
175900.885374.17461841729526.705381582714
184951.344104.69918213418846.64081786582
196179.125827.90910234919351.210897650813
204752.155169.9615550515-417.811555051501
215496.436576.9007877307-1080.47078773070
225835.17956.12559695512-2121.02559695512
2312600.089134.816616139243465.26338386076
2428541.7221490.98621636057050.73378363948
254717.025715.70909868618-998.689098686176
265702.638590.06100855337-2887.43100855337
279957.5810670.2402046897-712.660204689728
285304.788323.55537984434-3018.77537984434
296492.439362.785924832-2870.355924832
306630.88279.53885680331-1648.73885680331
317349.629356.58031188177-2006.96031188177
328176.627736.25940935995440.360590640047
338573.178374.01962039411199.150379605891
349690.58651.66176311011038.83823688991
3515151.8415320.8929183157-169.052918315658
3634061.0130982.36961529793078.64038470207
375921.17037.79247075986-1116.69247075986
385814.587850.47035009641-2035.89035009641
3912421.2511883.4194163748537.830583625248
406369.777142.76230407558-772.992304075576
417609.128259.76627715667-650.64627715667
427224.758352.00768933597-1127.25768933597
438121.229033.51954392351-912.299543923514
447979.259798.31620205185-1819.06620205185
458093.0610068.6583729870-1975.59837298696
468476.710990.3934007887-2513.69340078874
4717914.6616193.05840627141721.60159372864
4830114.4134906.5354178772-4792.12541787723
494826.646347.97321754052-1521.33321754052
506470.235905.6320364054564.597963594599
519638.7712222.7109280304-2583.94092803038
528821.175773.116307158543048.05369284146
538722.376818.525957893461903.84404210654
5410209.486281.504583680253927.97541631975
5511276.557175.530158124634101.01984187537
5612552.227164.445621710285387.77437828972
5711637.397598.423182257734038.96681774227
5813606.898416.101453677285190.78854632272
5921822.1118389.21664328323432.89335671677
6045060.6931265.635439887713795.0545601123
617615.037216.43227988702398.597720112984
629849.699801.8154157156347.8745842843691
6314558.413962.0634179994596.336582000629
6411587.3314094.5243893338-2507.19438933385
659332.5614781.3515428740-5448.79154287396
6613082.0916784.5382363052-3702.4482363052
6716732.7818235.1429173245-1502.3629173245
6819888.6119791.719874673196.890125326856
6923933.3819106.53116176164826.84883823835
7025391.3521401.20968259523990.14031740477
7136024.829935.49302519326089.30697480676
7280721.7153370.453156374327351.2568436257
7310243.2417176.2054264752-6932.96542647522
7411266.8819759.3155481584-8492.43554815835
7521826.8424583.4708185425-2756.63081854247
7617357.3321847.8988074668-4490.56880746677
7715997.7919811.6525941686-3813.86259416864
7818601.5323792.0760980126-5190.54609801263
7926155.1527562.8301822428-1407.68018224283
8028586.5230888.5779340407-2302.05793404075
8130505.4134927.7001630747-4422.29016307467
8230821.3336149.5466525105-5328.21665251051
8346634.3846277.2113898907357.168610109307
84104660.6790002.059060156814658.6109398432






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8519336.93781388139416.5729263925529257.3027013701
8620038.998309378610109.137788858529968.8588298986
8730337.699404160620386.506838285740288.8919700354
8825705.193131636815716.189412177535694.1968510962
8924266.111805536314218.313008896234313.9106021764
9026903.890016144716772.025688079337035.75434421
9134522.351086397224277.172569207444767.5296035869
9237068.935791463426677.615849026747460.2557339002
9339199.809055835328626.424456694649773.193654976
9439844.304364175129050.383701000650638.2250273495
9555978.114108507344923.225616134867033.0026008798
96114004.404108507102646.753999570125362.054217444

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 19336.9378138813 & 9416.57292639255 & 29257.3027013701 \tabularnewline
86 & 20038.9983093786 & 10109.1377888585 & 29968.8588298986 \tabularnewline
87 & 30337.6994041606 & 20386.5068382857 & 40288.8919700354 \tabularnewline
88 & 25705.1931316368 & 15716.1894121775 & 35694.1968510962 \tabularnewline
89 & 24266.1118055363 & 14218.3130088962 & 34313.9106021764 \tabularnewline
90 & 26903.8900161447 & 16772.0256880793 & 37035.75434421 \tabularnewline
91 & 34522.3510863972 & 24277.1725692074 & 44767.5296035869 \tabularnewline
92 & 37068.9357914634 & 26677.6158490267 & 47460.2557339002 \tabularnewline
93 & 39199.8090558353 & 28626.4244566946 & 49773.193654976 \tabularnewline
94 & 39844.3043641751 & 29050.3837010006 & 50638.2250273495 \tabularnewline
95 & 55978.1141085073 & 44923.2256161348 & 67033.0026008798 \tabularnewline
96 & 114004.404108507 & 102646.753999570 & 125362.054217444 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77558&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]85[/C][C]19336.9378138813[/C][C]9416.57292639255[/C][C]29257.3027013701[/C][/ROW]
[ROW][C]86[/C][C]20038.9983093786[/C][C]10109.1377888585[/C][C]29968.8588298986[/C][/ROW]
[ROW][C]87[/C][C]30337.6994041606[/C][C]20386.5068382857[/C][C]40288.8919700354[/C][/ROW]
[ROW][C]88[/C][C]25705.1931316368[/C][C]15716.1894121775[/C][C]35694.1968510962[/C][/ROW]
[ROW][C]89[/C][C]24266.1118055363[/C][C]14218.3130088962[/C][C]34313.9106021764[/C][/ROW]
[ROW][C]90[/C][C]26903.8900161447[/C][C]16772.0256880793[/C][C]37035.75434421[/C][/ROW]
[ROW][C]91[/C][C]34522.3510863972[/C][C]24277.1725692074[/C][C]44767.5296035869[/C][/ROW]
[ROW][C]92[/C][C]37068.9357914634[/C][C]26677.6158490267[/C][C]47460.2557339002[/C][/ROW]
[ROW][C]93[/C][C]39199.8090558353[/C][C]28626.4244566946[/C][C]49773.193654976[/C][/ROW]
[ROW][C]94[/C][C]39844.3043641751[/C][C]29050.3837010006[/C][C]50638.2250273495[/C][/ROW]
[ROW][C]95[/C][C]55978.1141085073[/C][C]44923.2256161348[/C][C]67033.0026008798[/C][/ROW]
[ROW][C]96[/C][C]114004.404108507[/C][C]102646.753999570[/C][C]125362.054217444[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77558&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77558&T=3

As an alternative you can also use a QR Code:  
QR Code


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

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8519336.93781388139416.5729263925529257.3027013701
8620038.998309378610109.137788858529968.8588298986
8730337.699404160620386.506838285740288.8919700354
8825705.193131636815716.189412177535694.1968510962
8924266.111805536314218.313008896234313.9106021764
9026903.890016144716772.025688079337035.75434421
9134522.351086397224277.172569207444767.5296035869
9237068.935791463426677.615849026747460.2557339002
9339199.809055835328626.424456694649773.193654976
9439844.304364175129050.383701000650638.2250273495
9555978.114108507344923.225616134867033.0026008798
96114004.404108507102646.753999570125362.054217444


Figures (Output of Computation)

Input Parameters & R Code

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')