Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 07 Aug 2013 06:29:45 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Aug/07/t1375871410eukadnk03ngvsgq.htm/, Retrieved Tue, 30 Apr 2024 06:35:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=210969, Retrieved Tue, 30 Apr 2024 06:35:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsVan Camp Stef
Estimated Impact176
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-08-07 10:29:45] [941d89646656d1688f5e273fb31a8e6b] [Current]
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Dataseries X:
69731
68504
67277
64823
89654
88427
69731
57316
58542
58542
59770
62357
54862
47354
41207
41207
64823
67277
48581
27431
38620
38620
47354
52396
51168
38620
44900
42434
63584
58542
38620
23738
37392
41207
44900
49808
39846
31246
34939
36166
68504
68504
49808
47354
54862
51168
61130
73546
76012
58542
53622
48581
82280
84746
78466
84746
83507
73546
84746
97162
102203
87200
77238
84746
117084
127046
124592
129499
128273
115858
137008
142049
149423
127046
118312
128273
152010
173160
168119
168119
170585
161971
184361
184361
180546
159384
163199
165665
181895
203045
188041
195550
189269
185587
214246
207965
199230
186815
199230
205511
213006
222967
213006
219154
211657
210431
241542
244129
234168
216700
231581
237850
245357
256546
245357
254092
250277
236622
265279
265279




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'George Udny Yule' @ yule.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 4 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210969&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210969&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210969&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.653577978944095
beta0.05293490449785
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.653577978944095 \tabularnewline
beta & 0.05293490449785 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210969&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]0.653577978944095[/C][/ROW]
[ROW][C]beta[/C][C]0.05293490449785[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210969&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210969&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
alpha0.653577978944095
beta0.05293490449785
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
135486266223.4086538462-11361.4086538462
144735451171.0560418587-3817.05604185868
154120742227.3004723998-1020.30047239979
164120740808.0183305032398.981669496781
176482363633.40134634781189.59865365215
186727765439.62919533191837.37080466813
194858147423.16933682221157.83066317775
202743135011.6762419167-7580.67624191675
213862030734.32647606137885.67352393868
223862035715.01367185332904.98632814671
234735438717.31246380228636.68753619782
245239647020.77918505195375.22081494809
255116839207.372917328611960.6270826714
263862043012.1763957195-4392.17639571954
274490035642.35228451219257.64771548786
284243442768.7281518581-334.728151858129
296358466699.6243127483-3115.62431274835
305854267078.6701904872-8536.67019048719
313862042849.8607238173-4229.86072381731
322373824506.7843336121-768.784333612093
333739230891.99725697666500.00274302339
344120734046.25664463797160.74335536209
354490042767.48465478852132.51534521153
364980846416.97097547183391.02902452818
373984640246.2703463938-400.27034639378
383124630537.8411295304708.158870469633
393493931637.08913199193301.91086800813
403616631748.87080433344417.12919566657
416850458187.467536163210316.5324638368
426850466297.57405016552206.42594983452
434980851783.9375542573-1975.93755425733
444735437392.69623806499961.30376193513
455486254959.8836095425-97.8836095425067
465116855453.4944608551-4285.49446085506
476113055978.50768008565151.4923199144
487354663168.23863156610377.761368434
497601261623.374318632214388.6256813678
505854263849.130405581-5307.13040558103
515362263591.8433552013-9969.84335520134
524858156633.0636107281-8052.06361072814
538228077751.58465118954528.41534881049
548474679854.76473202934891.23526797065
557846666325.463192535512140.5368074645
568474666462.616352667818283.3836473322
578350787438.9820167178-3931.98201671781
587354685298.1554857592-11752.1554857592
598474685276.1043086369-530.104308636874
609716291430.19759936095731.80240063915
6110220388944.785979227613258.2140207724
628720084276.07475998452923.92524001552
637723888735.3170272572-11497.3170272572
648474682341.88816927712404.11183072295
65117084115913.5562970241170.44370297578
66127046117092.6189534789953.38104652229
67124592110703.1677016313888.8322983703
68129499115491.49723540314007.5027645969
69128273127209.9279381291063.07206187138
70115858127030.071279482-11172.071279482
71137008132700.1780600244307.82193997613
72142049145778.335993488-3729.33599348844
73149423140982.1597563268440.84024367351
74127046130683.739178794-3637.73917879358
75118312126730.416968066-8418.41696806607
76128273128143.402228384129.597771616056
77152010160700.788445042-8690.78844504175
78173160159035.86011112214124.1398888784
79168119157438.43836229110680.561637709
80168119160762.8124742037356.18752579682
81170585164011.5275921186573.47240788239
82161971163746.94140743-1775.94140742978
83184361181798.1236223962562.87637760362
84184361191768.600999923-7407.6009999227
85180546189474.177477723-8928.17747772258
86159384163728.314748987-4344.31474898689
87163199157721.4640286435477.53597135699
88165665171722.923959308-6057.9239593083
89181895197511.801266097-15616.8012660971
90203045199315.2522371543729.74776284551
91188041189463.212837803-1422.21283780277
92195550183038.98240246712511.0175975331
93189269188877.112029163391.887970836833
94185587180957.5735945484629.42640545161
95214246204197.44828001510048.551719985
96207965215364.610957502-7399.61095750169
97199230212307.130469339-13077.1304693391
98186815185052.4948238771762.5051761228
99199230186265.65109427212964.3489057279
100205511201249.4302627464261.56973725415
101213006230913.760752713-17907.760752713
102222967238284.966085897-15317.9660858969
103213006213903.016750002-897.016750002367
104219154212371.0000026416782.99999735926
105211657209791.0965988641865.90340113637
106210431203877.9219750656553.07802493509
107241542229893.91324229211648.0867577078
108244129235758.9641731228370.03582687801
109234168241283.838785575-7115.83878557524
110216700223514.871025577-6814.87102557652
111231581223154.5785422648426.42145773623
112237850232152.6049420285697.39505797153
113245357255120.061373952-9763.06137395234
114256546269038.054053632-12492.0540536324
115245357251922.990618735-6565.99061873514
116254092249574.4519354914517.54806450897
117250277243960.1980803756316.80191962537
118236622242883.450933178-6261.4509331783
119265279262149.5038128043129.49618719576
120265279260877.0164072544401.98359274649

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 54862 & 66223.4086538462 & -11361.4086538462 \tabularnewline
14 & 47354 & 51171.0560418587 & -3817.05604185868 \tabularnewline
15 & 41207 & 42227.3004723998 & -1020.30047239979 \tabularnewline
16 & 41207 & 40808.0183305032 & 398.981669496781 \tabularnewline
17 & 64823 & 63633.4013463478 & 1189.59865365215 \tabularnewline
18 & 67277 & 65439.6291953319 & 1837.37080466813 \tabularnewline
19 & 48581 & 47423.1693368222 & 1157.83066317775 \tabularnewline
20 & 27431 & 35011.6762419167 & -7580.67624191675 \tabularnewline
21 & 38620 & 30734.3264760613 & 7885.67352393868 \tabularnewline
22 & 38620 & 35715.0136718533 & 2904.98632814671 \tabularnewline
23 & 47354 & 38717.3124638022 & 8636.68753619782 \tabularnewline
24 & 52396 & 47020.7791850519 & 5375.22081494809 \tabularnewline
25 & 51168 & 39207.3729173286 & 11960.6270826714 \tabularnewline
26 & 38620 & 43012.1763957195 & -4392.17639571954 \tabularnewline
27 & 44900 & 35642.3522845121 & 9257.64771548786 \tabularnewline
28 & 42434 & 42768.7281518581 & -334.728151858129 \tabularnewline
29 & 63584 & 66699.6243127483 & -3115.62431274835 \tabularnewline
30 & 58542 & 67078.6701904872 & -8536.67019048719 \tabularnewline
31 & 38620 & 42849.8607238173 & -4229.86072381731 \tabularnewline
32 & 23738 & 24506.7843336121 & -768.784333612093 \tabularnewline
33 & 37392 & 30891.9972569766 & 6500.00274302339 \tabularnewline
34 & 41207 & 34046.2566446379 & 7160.74335536209 \tabularnewline
35 & 44900 & 42767.4846547885 & 2132.51534521153 \tabularnewline
36 & 49808 & 46416.9709754718 & 3391.02902452818 \tabularnewline
37 & 39846 & 40246.2703463938 & -400.27034639378 \tabularnewline
38 & 31246 & 30537.8411295304 & 708.158870469633 \tabularnewline
39 & 34939 & 31637.0891319919 & 3301.91086800813 \tabularnewline
40 & 36166 & 31748.8708043334 & 4417.12919566657 \tabularnewline
41 & 68504 & 58187.4675361632 & 10316.5324638368 \tabularnewline
42 & 68504 & 66297.5740501655 & 2206.42594983452 \tabularnewline
43 & 49808 & 51783.9375542573 & -1975.93755425733 \tabularnewline
44 & 47354 & 37392.6962380649 & 9961.30376193513 \tabularnewline
45 & 54862 & 54959.8836095425 & -97.8836095425067 \tabularnewline
46 & 51168 & 55453.4944608551 & -4285.49446085506 \tabularnewline
47 & 61130 & 55978.5076800856 & 5151.4923199144 \tabularnewline
48 & 73546 & 63168.238631566 & 10377.761368434 \tabularnewline
49 & 76012 & 61623.3743186322 & 14388.6256813678 \tabularnewline
50 & 58542 & 63849.130405581 & -5307.13040558103 \tabularnewline
51 & 53622 & 63591.8433552013 & -9969.84335520134 \tabularnewline
52 & 48581 & 56633.0636107281 & -8052.06361072814 \tabularnewline
53 & 82280 & 77751.5846511895 & 4528.41534881049 \tabularnewline
54 & 84746 & 79854.7647320293 & 4891.23526797065 \tabularnewline
55 & 78466 & 66325.4631925355 & 12140.5368074645 \tabularnewline
56 & 84746 & 66462.6163526678 & 18283.3836473322 \tabularnewline
57 & 83507 & 87438.9820167178 & -3931.98201671781 \tabularnewline
58 & 73546 & 85298.1554857592 & -11752.1554857592 \tabularnewline
59 & 84746 & 85276.1043086369 & -530.104308636874 \tabularnewline
60 & 97162 & 91430.1975993609 & 5731.80240063915 \tabularnewline
61 & 102203 & 88944.7859792276 & 13258.2140207724 \tabularnewline
62 & 87200 & 84276.0747599845 & 2923.92524001552 \tabularnewline
63 & 77238 & 88735.3170272572 & -11497.3170272572 \tabularnewline
64 & 84746 & 82341.8881692771 & 2404.11183072295 \tabularnewline
65 & 117084 & 115913.556297024 & 1170.44370297578 \tabularnewline
66 & 127046 & 117092.618953478 & 9953.38104652229 \tabularnewline
67 & 124592 & 110703.16770163 & 13888.8322983703 \tabularnewline
68 & 129499 & 115491.497235403 & 14007.5027645969 \tabularnewline
69 & 128273 & 127209.927938129 & 1063.07206187138 \tabularnewline
70 & 115858 & 127030.071279482 & -11172.071279482 \tabularnewline
71 & 137008 & 132700.178060024 & 4307.82193997613 \tabularnewline
72 & 142049 & 145778.335993488 & -3729.33599348844 \tabularnewline
73 & 149423 & 140982.159756326 & 8440.84024367351 \tabularnewline
74 & 127046 & 130683.739178794 & -3637.73917879358 \tabularnewline
75 & 118312 & 126730.416968066 & -8418.41696806607 \tabularnewline
76 & 128273 & 128143.402228384 & 129.597771616056 \tabularnewline
77 & 152010 & 160700.788445042 & -8690.78844504175 \tabularnewline
78 & 173160 & 159035.860111122 & 14124.1398888784 \tabularnewline
79 & 168119 & 157438.438362291 & 10680.561637709 \tabularnewline
80 & 168119 & 160762.812474203 & 7356.18752579682 \tabularnewline
81 & 170585 & 164011.527592118 & 6573.47240788239 \tabularnewline
82 & 161971 & 163746.94140743 & -1775.94140742978 \tabularnewline
83 & 184361 & 181798.123622396 & 2562.87637760362 \tabularnewline
84 & 184361 & 191768.600999923 & -7407.6009999227 \tabularnewline
85 & 180546 & 189474.177477723 & -8928.17747772258 \tabularnewline
86 & 159384 & 163728.314748987 & -4344.31474898689 \tabularnewline
87 & 163199 & 157721.464028643 & 5477.53597135699 \tabularnewline
88 & 165665 & 171722.923959308 & -6057.9239593083 \tabularnewline
89 & 181895 & 197511.801266097 & -15616.8012660971 \tabularnewline
90 & 203045 & 199315.252237154 & 3729.74776284551 \tabularnewline
91 & 188041 & 189463.212837803 & -1422.21283780277 \tabularnewline
92 & 195550 & 183038.982402467 & 12511.0175975331 \tabularnewline
93 & 189269 & 188877.112029163 & 391.887970836833 \tabularnewline
94 & 185587 & 180957.573594548 & 4629.42640545161 \tabularnewline
95 & 214246 & 204197.448280015 & 10048.551719985 \tabularnewline
96 & 207965 & 215364.610957502 & -7399.61095750169 \tabularnewline
97 & 199230 & 212307.130469339 & -13077.1304693391 \tabularnewline
98 & 186815 & 185052.494823877 & 1762.5051761228 \tabularnewline
99 & 199230 & 186265.651094272 & 12964.3489057279 \tabularnewline
100 & 205511 & 201249.430262746 & 4261.56973725415 \tabularnewline
101 & 213006 & 230913.760752713 & -17907.760752713 \tabularnewline
102 & 222967 & 238284.966085897 & -15317.9660858969 \tabularnewline
103 & 213006 & 213903.016750002 & -897.016750002367 \tabularnewline
104 & 219154 & 212371.000002641 & 6782.99999735926 \tabularnewline
105 & 211657 & 209791.096598864 & 1865.90340113637 \tabularnewline
106 & 210431 & 203877.921975065 & 6553.07802493509 \tabularnewline
107 & 241542 & 229893.913242292 & 11648.0867577078 \tabularnewline
108 & 244129 & 235758.964173122 & 8370.03582687801 \tabularnewline
109 & 234168 & 241283.838785575 & -7115.83878557524 \tabularnewline
110 & 216700 & 223514.871025577 & -6814.87102557652 \tabularnewline
111 & 231581 & 223154.578542264 & 8426.42145773623 \tabularnewline
112 & 237850 & 232152.604942028 & 5697.39505797153 \tabularnewline
113 & 245357 & 255120.061373952 & -9763.06137395234 \tabularnewline
114 & 256546 & 269038.054053632 & -12492.0540536324 \tabularnewline
115 & 245357 & 251922.990618735 & -6565.99061873514 \tabularnewline
116 & 254092 & 249574.451935491 & 4517.54806450897 \tabularnewline
117 & 250277 & 243960.198080375 & 6316.80191962537 \tabularnewline
118 & 236622 & 242883.450933178 & -6261.4509331783 \tabularnewline
119 & 265279 & 262149.503812804 & 3129.49618719576 \tabularnewline
120 & 265279 & 260877.016407254 & 4401.98359274649 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210969&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]54862[/C][C]66223.4086538462[/C][C]-11361.4086538462[/C][/ROW]
[ROW][C]14[/C][C]47354[/C][C]51171.0560418587[/C][C]-3817.05604185868[/C][/ROW]
[ROW][C]15[/C][C]41207[/C][C]42227.3004723998[/C][C]-1020.30047239979[/C][/ROW]
[ROW][C]16[/C][C]41207[/C][C]40808.0183305032[/C][C]398.981669496781[/C][/ROW]
[ROW][C]17[/C][C]64823[/C][C]63633.4013463478[/C][C]1189.59865365215[/C][/ROW]
[ROW][C]18[/C][C]67277[/C][C]65439.6291953319[/C][C]1837.37080466813[/C][/ROW]
[ROW][C]19[/C][C]48581[/C][C]47423.1693368222[/C][C]1157.83066317775[/C][/ROW]
[ROW][C]20[/C][C]27431[/C][C]35011.6762419167[/C][C]-7580.67624191675[/C][/ROW]
[ROW][C]21[/C][C]38620[/C][C]30734.3264760613[/C][C]7885.67352393868[/C][/ROW]
[ROW][C]22[/C][C]38620[/C][C]35715.0136718533[/C][C]2904.98632814671[/C][/ROW]
[ROW][C]23[/C][C]47354[/C][C]38717.3124638022[/C][C]8636.68753619782[/C][/ROW]
[ROW][C]24[/C][C]52396[/C][C]47020.7791850519[/C][C]5375.22081494809[/C][/ROW]
[ROW][C]25[/C][C]51168[/C][C]39207.3729173286[/C][C]11960.6270826714[/C][/ROW]
[ROW][C]26[/C][C]38620[/C][C]43012.1763957195[/C][C]-4392.17639571954[/C][/ROW]
[ROW][C]27[/C][C]44900[/C][C]35642.3522845121[/C][C]9257.64771548786[/C][/ROW]
[ROW][C]28[/C][C]42434[/C][C]42768.7281518581[/C][C]-334.728151858129[/C][/ROW]
[ROW][C]29[/C][C]63584[/C][C]66699.6243127483[/C][C]-3115.62431274835[/C][/ROW]
[ROW][C]30[/C][C]58542[/C][C]67078.6701904872[/C][C]-8536.67019048719[/C][/ROW]
[ROW][C]31[/C][C]38620[/C][C]42849.8607238173[/C][C]-4229.86072381731[/C][/ROW]
[ROW][C]32[/C][C]23738[/C][C]24506.7843336121[/C][C]-768.784333612093[/C][/ROW]
[ROW][C]33[/C][C]37392[/C][C]30891.9972569766[/C][C]6500.00274302339[/C][/ROW]
[ROW][C]34[/C][C]41207[/C][C]34046.2566446379[/C][C]7160.74335536209[/C][/ROW]
[ROW][C]35[/C][C]44900[/C][C]42767.4846547885[/C][C]2132.51534521153[/C][/ROW]
[ROW][C]36[/C][C]49808[/C][C]46416.9709754718[/C][C]3391.02902452818[/C][/ROW]
[ROW][C]37[/C][C]39846[/C][C]40246.2703463938[/C][C]-400.27034639378[/C][/ROW]
[ROW][C]38[/C][C]31246[/C][C]30537.8411295304[/C][C]708.158870469633[/C][/ROW]
[ROW][C]39[/C][C]34939[/C][C]31637.0891319919[/C][C]3301.91086800813[/C][/ROW]
[ROW][C]40[/C][C]36166[/C][C]31748.8708043334[/C][C]4417.12919566657[/C][/ROW]
[ROW][C]41[/C][C]68504[/C][C]58187.4675361632[/C][C]10316.5324638368[/C][/ROW]
[ROW][C]42[/C][C]68504[/C][C]66297.5740501655[/C][C]2206.42594983452[/C][/ROW]
[ROW][C]43[/C][C]49808[/C][C]51783.9375542573[/C][C]-1975.93755425733[/C][/ROW]
[ROW][C]44[/C][C]47354[/C][C]37392.6962380649[/C][C]9961.30376193513[/C][/ROW]
[ROW][C]45[/C][C]54862[/C][C]54959.8836095425[/C][C]-97.8836095425067[/C][/ROW]
[ROW][C]46[/C][C]51168[/C][C]55453.4944608551[/C][C]-4285.49446085506[/C][/ROW]
[ROW][C]47[/C][C]61130[/C][C]55978.5076800856[/C][C]5151.4923199144[/C][/ROW]
[ROW][C]48[/C][C]73546[/C][C]63168.238631566[/C][C]10377.761368434[/C][/ROW]
[ROW][C]49[/C][C]76012[/C][C]61623.3743186322[/C][C]14388.6256813678[/C][/ROW]
[ROW][C]50[/C][C]58542[/C][C]63849.130405581[/C][C]-5307.13040558103[/C][/ROW]
[ROW][C]51[/C][C]53622[/C][C]63591.8433552013[/C][C]-9969.84335520134[/C][/ROW]
[ROW][C]52[/C][C]48581[/C][C]56633.0636107281[/C][C]-8052.06361072814[/C][/ROW]
[ROW][C]53[/C][C]82280[/C][C]77751.5846511895[/C][C]4528.41534881049[/C][/ROW]
[ROW][C]54[/C][C]84746[/C][C]79854.7647320293[/C][C]4891.23526797065[/C][/ROW]
[ROW][C]55[/C][C]78466[/C][C]66325.4631925355[/C][C]12140.5368074645[/C][/ROW]
[ROW][C]56[/C][C]84746[/C][C]66462.6163526678[/C][C]18283.3836473322[/C][/ROW]
[ROW][C]57[/C][C]83507[/C][C]87438.9820167178[/C][C]-3931.98201671781[/C][/ROW]
[ROW][C]58[/C][C]73546[/C][C]85298.1554857592[/C][C]-11752.1554857592[/C][/ROW]
[ROW][C]59[/C][C]84746[/C][C]85276.1043086369[/C][C]-530.104308636874[/C][/ROW]
[ROW][C]60[/C][C]97162[/C][C]91430.1975993609[/C][C]5731.80240063915[/C][/ROW]
[ROW][C]61[/C][C]102203[/C][C]88944.7859792276[/C][C]13258.2140207724[/C][/ROW]
[ROW][C]62[/C][C]87200[/C][C]84276.0747599845[/C][C]2923.92524001552[/C][/ROW]
[ROW][C]63[/C][C]77238[/C][C]88735.3170272572[/C][C]-11497.3170272572[/C][/ROW]
[ROW][C]64[/C][C]84746[/C][C]82341.8881692771[/C][C]2404.11183072295[/C][/ROW]
[ROW][C]65[/C][C]117084[/C][C]115913.556297024[/C][C]1170.44370297578[/C][/ROW]
[ROW][C]66[/C][C]127046[/C][C]117092.618953478[/C][C]9953.38104652229[/C][/ROW]
[ROW][C]67[/C][C]124592[/C][C]110703.16770163[/C][C]13888.8322983703[/C][/ROW]
[ROW][C]68[/C][C]129499[/C][C]115491.497235403[/C][C]14007.5027645969[/C][/ROW]
[ROW][C]69[/C][C]128273[/C][C]127209.927938129[/C][C]1063.07206187138[/C][/ROW]
[ROW][C]70[/C][C]115858[/C][C]127030.071279482[/C][C]-11172.071279482[/C][/ROW]
[ROW][C]71[/C][C]137008[/C][C]132700.178060024[/C][C]4307.82193997613[/C][/ROW]
[ROW][C]72[/C][C]142049[/C][C]145778.335993488[/C][C]-3729.33599348844[/C][/ROW]
[ROW][C]73[/C][C]149423[/C][C]140982.159756326[/C][C]8440.84024367351[/C][/ROW]
[ROW][C]74[/C][C]127046[/C][C]130683.739178794[/C][C]-3637.73917879358[/C][/ROW]
[ROW][C]75[/C][C]118312[/C][C]126730.416968066[/C][C]-8418.41696806607[/C][/ROW]
[ROW][C]76[/C][C]128273[/C][C]128143.402228384[/C][C]129.597771616056[/C][/ROW]
[ROW][C]77[/C][C]152010[/C][C]160700.788445042[/C][C]-8690.78844504175[/C][/ROW]
[ROW][C]78[/C][C]173160[/C][C]159035.860111122[/C][C]14124.1398888784[/C][/ROW]
[ROW][C]79[/C][C]168119[/C][C]157438.438362291[/C][C]10680.561637709[/C][/ROW]
[ROW][C]80[/C][C]168119[/C][C]160762.812474203[/C][C]7356.18752579682[/C][/ROW]
[ROW][C]81[/C][C]170585[/C][C]164011.527592118[/C][C]6573.47240788239[/C][/ROW]
[ROW][C]82[/C][C]161971[/C][C]163746.94140743[/C][C]-1775.94140742978[/C][/ROW]
[ROW][C]83[/C][C]184361[/C][C]181798.123622396[/C][C]2562.87637760362[/C][/ROW]
[ROW][C]84[/C][C]184361[/C][C]191768.600999923[/C][C]-7407.6009999227[/C][/ROW]
[ROW][C]85[/C][C]180546[/C][C]189474.177477723[/C][C]-8928.17747772258[/C][/ROW]
[ROW][C]86[/C][C]159384[/C][C]163728.314748987[/C][C]-4344.31474898689[/C][/ROW]
[ROW][C]87[/C][C]163199[/C][C]157721.464028643[/C][C]5477.53597135699[/C][/ROW]
[ROW][C]88[/C][C]165665[/C][C]171722.923959308[/C][C]-6057.9239593083[/C][/ROW]
[ROW][C]89[/C][C]181895[/C][C]197511.801266097[/C][C]-15616.8012660971[/C][/ROW]
[ROW][C]90[/C][C]203045[/C][C]199315.252237154[/C][C]3729.74776284551[/C][/ROW]
[ROW][C]91[/C][C]188041[/C][C]189463.212837803[/C][C]-1422.21283780277[/C][/ROW]
[ROW][C]92[/C][C]195550[/C][C]183038.982402467[/C][C]12511.0175975331[/C][/ROW]
[ROW][C]93[/C][C]189269[/C][C]188877.112029163[/C][C]391.887970836833[/C][/ROW]
[ROW][C]94[/C][C]185587[/C][C]180957.573594548[/C][C]4629.42640545161[/C][/ROW]
[ROW][C]95[/C][C]214246[/C][C]204197.448280015[/C][C]10048.551719985[/C][/ROW]
[ROW][C]96[/C][C]207965[/C][C]215364.610957502[/C][C]-7399.61095750169[/C][/ROW]
[ROW][C]97[/C][C]199230[/C][C]212307.130469339[/C][C]-13077.1304693391[/C][/ROW]
[ROW][C]98[/C][C]186815[/C][C]185052.494823877[/C][C]1762.5051761228[/C][/ROW]
[ROW][C]99[/C][C]199230[/C][C]186265.651094272[/C][C]12964.3489057279[/C][/ROW]
[ROW][C]100[/C][C]205511[/C][C]201249.430262746[/C][C]4261.56973725415[/C][/ROW]
[ROW][C]101[/C][C]213006[/C][C]230913.760752713[/C][C]-17907.760752713[/C][/ROW]
[ROW][C]102[/C][C]222967[/C][C]238284.966085897[/C][C]-15317.9660858969[/C][/ROW]
[ROW][C]103[/C][C]213006[/C][C]213903.016750002[/C][C]-897.016750002367[/C][/ROW]
[ROW][C]104[/C][C]219154[/C][C]212371.000002641[/C][C]6782.99999735926[/C][/ROW]
[ROW][C]105[/C][C]211657[/C][C]209791.096598864[/C][C]1865.90340113637[/C][/ROW]
[ROW][C]106[/C][C]210431[/C][C]203877.921975065[/C][C]6553.07802493509[/C][/ROW]
[ROW][C]107[/C][C]241542[/C][C]229893.913242292[/C][C]11648.0867577078[/C][/ROW]
[ROW][C]108[/C][C]244129[/C][C]235758.964173122[/C][C]8370.03582687801[/C][/ROW]
[ROW][C]109[/C][C]234168[/C][C]241283.838785575[/C][C]-7115.83878557524[/C][/ROW]
[ROW][C]110[/C][C]216700[/C][C]223514.871025577[/C][C]-6814.87102557652[/C][/ROW]
[ROW][C]111[/C][C]231581[/C][C]223154.578542264[/C][C]8426.42145773623[/C][/ROW]
[ROW][C]112[/C][C]237850[/C][C]232152.604942028[/C][C]5697.39505797153[/C][/ROW]
[ROW][C]113[/C][C]245357[/C][C]255120.061373952[/C][C]-9763.06137395234[/C][/ROW]
[ROW][C]114[/C][C]256546[/C][C]269038.054053632[/C][C]-12492.0540536324[/C][/ROW]
[ROW][C]115[/C][C]245357[/C][C]251922.990618735[/C][C]-6565.99061873514[/C][/ROW]
[ROW][C]116[/C][C]254092[/C][C]249574.451935491[/C][C]4517.54806450897[/C][/ROW]
[ROW][C]117[/C][C]250277[/C][C]243960.198080375[/C][C]6316.80191962537[/C][/ROW]
[ROW][C]118[/C][C]236622[/C][C]242883.450933178[/C][C]-6261.4509331783[/C][/ROW]
[ROW][C]119[/C][C]265279[/C][C]262149.503812804[/C][C]3129.49618719576[/C][/ROW]
[ROW][C]120[/C][C]265279[/C][C]260877.016407254[/C][C]4401.98359274649[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210969&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210969&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
135486266223.4086538462-11361.4086538462
144735451171.0560418587-3817.05604185868
154120742227.3004723998-1020.30047239979
164120740808.0183305032398.981669496781
176482363633.40134634781189.59865365215
186727765439.62919533191837.37080466813
194858147423.16933682221157.83066317775
202743135011.6762419167-7580.67624191675
213862030734.32647606137885.67352393868
223862035715.01367185332904.98632814671
234735438717.31246380228636.68753619782
245239647020.77918505195375.22081494809
255116839207.372917328611960.6270826714
263862043012.1763957195-4392.17639571954
274490035642.35228451219257.64771548786
284243442768.7281518581-334.728151858129
296358466699.6243127483-3115.62431274835
305854267078.6701904872-8536.67019048719
313862042849.8607238173-4229.86072381731
322373824506.7843336121-768.784333612093
333739230891.99725697666500.00274302339
344120734046.25664463797160.74335536209
354490042767.48465478852132.51534521153
364980846416.97097547183391.02902452818
373984640246.2703463938-400.27034639378
383124630537.8411295304708.158870469633
393493931637.08913199193301.91086800813
403616631748.87080433344417.12919566657
416850458187.467536163210316.5324638368
426850466297.57405016552206.42594983452
434980851783.9375542573-1975.93755425733
444735437392.69623806499961.30376193513
455486254959.8836095425-97.8836095425067
465116855453.4944608551-4285.49446085506
476113055978.50768008565151.4923199144
487354663168.23863156610377.761368434
497601261623.374318632214388.6256813678
505854263849.130405581-5307.13040558103
515362263591.8433552013-9969.84335520134
524858156633.0636107281-8052.06361072814
538228077751.58465118954528.41534881049
548474679854.76473202934891.23526797065
557846666325.463192535512140.5368074645
568474666462.616352667818283.3836473322
578350787438.9820167178-3931.98201671781
587354685298.1554857592-11752.1554857592
598474685276.1043086369-530.104308636874
609716291430.19759936095731.80240063915
6110220388944.785979227613258.2140207724
628720084276.07475998452923.92524001552
637723888735.3170272572-11497.3170272572
648474682341.88816927712404.11183072295
65117084115913.5562970241170.44370297578
66127046117092.6189534789953.38104652229
67124592110703.1677016313888.8322983703
68129499115491.49723540314007.5027645969
69128273127209.9279381291063.07206187138
70115858127030.071279482-11172.071279482
71137008132700.1780600244307.82193997613
72142049145778.335993488-3729.33599348844
73149423140982.1597563268440.84024367351
74127046130683.739178794-3637.73917879358
75118312126730.416968066-8418.41696806607
76128273128143.402228384129.597771616056
77152010160700.788445042-8690.78844504175
78173160159035.86011112214124.1398888784
79168119157438.43836229110680.561637709
80168119160762.8124742037356.18752579682
81170585164011.5275921186573.47240788239
82161971163746.94140743-1775.94140742978
83184361181798.1236223962562.87637760362
84184361191768.600999923-7407.6009999227
85180546189474.177477723-8928.17747772258
86159384163728.314748987-4344.31474898689
87163199157721.4640286435477.53597135699
88165665171722.923959308-6057.9239593083
89181895197511.801266097-15616.8012660971
90203045199315.2522371543729.74776284551
91188041189463.212837803-1422.21283780277
92195550183038.98240246712511.0175975331
93189269188877.112029163391.887970836833
94185587180957.5735945484629.42640545161
95214246204197.44828001510048.551719985
96207965215364.610957502-7399.61095750169
97199230212307.130469339-13077.1304693391
98186815185052.4948238771762.5051761228
99199230186265.65109427212964.3489057279
100205511201249.4302627464261.56973725415
101213006230913.760752713-17907.760752713
102222967238284.966085897-15317.9660858969
103213006213903.016750002-897.016750002367
104219154212371.0000026416782.99999735926
105211657209791.0965988641865.90340113637
106210431203877.9219750656553.07802493509
107241542229893.91324229211648.0867577078
108244129235758.9641731228370.03582687801
109234168241283.838785575-7115.83878557524
110216700223514.871025577-6814.87102557652
111231581223154.5785422648426.42145773623
112237850232152.6049420285697.39505797153
113245357255120.061373952-9763.06137395234
114256546269038.054053632-12492.0540536324
115245357251922.990618735-6565.99061873514
116254092249574.4519354914517.54806450897
117250277243960.1980803756316.80191962537
118236622242883.450933178-6261.4509331783
119265279262149.5038128043129.49618719576
120265279260877.0164072544401.98359274649







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121257872.142327918242617.706242496273126.57841334
122244532.71010831226015.150887455263050.269329166
123253816.679442844232265.316496036275368.042389652
124255980.750692388231527.967299707280433.534085069
125269290.322532656242015.990806388296564.654258924
126288403.277385564258355.482615829318451.072155298
127281697.276367708248903.403873876314491.14886154
128287898.482692278252371.724632597323425.240751959
129280217.442311146241960.88176193318474.002860362
130270698.728056954229708.036517537311689.419596371
131297570.925531757253836.217336023341305.633727491
132294846.181805145248353.330649525341339.032960765

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 257872.142327918 & 242617.706242496 & 273126.57841334 \tabularnewline
122 & 244532.71010831 & 226015.150887455 & 263050.269329166 \tabularnewline
123 & 253816.679442844 & 232265.316496036 & 275368.042389652 \tabularnewline
124 & 255980.750692388 & 231527.967299707 & 280433.534085069 \tabularnewline
125 & 269290.322532656 & 242015.990806388 & 296564.654258924 \tabularnewline
126 & 288403.277385564 & 258355.482615829 & 318451.072155298 \tabularnewline
127 & 281697.276367708 & 248903.403873876 & 314491.14886154 \tabularnewline
128 & 287898.482692278 & 252371.724632597 & 323425.240751959 \tabularnewline
129 & 280217.442311146 & 241960.88176193 & 318474.002860362 \tabularnewline
130 & 270698.728056954 & 229708.036517537 & 311689.419596371 \tabularnewline
131 & 297570.925531757 & 253836.217336023 & 341305.633727491 \tabularnewline
132 & 294846.181805145 & 248353.330649525 & 341339.032960765 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210969&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]257872.142327918[/C][C]242617.706242496[/C][C]273126.57841334[/C][/ROW]
[ROW][C]122[/C][C]244532.71010831[/C][C]226015.150887455[/C][C]263050.269329166[/C][/ROW]
[ROW][C]123[/C][C]253816.679442844[/C][C]232265.316496036[/C][C]275368.042389652[/C][/ROW]
[ROW][C]124[/C][C]255980.750692388[/C][C]231527.967299707[/C][C]280433.534085069[/C][/ROW]
[ROW][C]125[/C][C]269290.322532656[/C][C]242015.990806388[/C][C]296564.654258924[/C][/ROW]
[ROW][C]126[/C][C]288403.277385564[/C][C]258355.482615829[/C][C]318451.072155298[/C][/ROW]
[ROW][C]127[/C][C]281697.276367708[/C][C]248903.403873876[/C][C]314491.14886154[/C][/ROW]
[ROW][C]128[/C][C]287898.482692278[/C][C]252371.724632597[/C][C]323425.240751959[/C][/ROW]
[ROW][C]129[/C][C]280217.442311146[/C][C]241960.88176193[/C][C]318474.002860362[/C][/ROW]
[ROW][C]130[/C][C]270698.728056954[/C][C]229708.036517537[/C][C]311689.419596371[/C][/ROW]
[ROW][C]131[/C][C]297570.925531757[/C][C]253836.217336023[/C][C]341305.633727491[/C][/ROW]
[ROW][C]132[/C][C]294846.181805145[/C][C]248353.330649525[/C][C]341339.032960765[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210969&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210969&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
121257872.142327918242617.706242496273126.57841334
122244532.71010831226015.150887455263050.269329166
123253816.679442844232265.316496036275368.042389652
124255980.750692388231527.967299707280433.534085069
125269290.322532656242015.990806388296564.654258924
126288403.277385564258355.482615829318451.072155298
127281697.276367708248903.403873876314491.14886154
128287898.482692278252371.724632597323425.240751959
129280217.442311146241960.88176193318474.002860362
130270698.728056954229708.036517537311689.419596371
131297570.925531757253836.217336023341305.633727491
132294846.181805145248353.330649525341339.032960765



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')