Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 17 Aug 2010 12:55:02 +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/Aug/17/t1282049834m4d7gdei9n8rj7k.htm/, Retrieved Sat, 27 Apr 2024 10:43:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79106, Retrieved Sat, 27 Apr 2024 10:43:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKalhöfer Pim
Estimated Impact157
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks A Stap 32] [2010-08-17 12:55:02] [06ce09a0492afa6d4f67026fd1b7902e] [Current]
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Dataseries X:
349
348
347
345
365
364
349
339
340
340
341
343
341
343
341
335
355
357
337
325
336
338
337
328
326
327
319
310
320
322
303
292
303
315
311
307
308
312
309
310
309
304
287
275
290
298
294
286
294
292
287
281
280
271
264
259
271
279
279
273
286
286
280
277
269
255
252
245
257
267
261
258
271
262
258
253
236
228
235
226
231
235
227
222
233
221
218
220
204
196
208
190
191
194
179
162
179
176
168
170
153
142
155
136
136
144
135
114
135
132
123
123
103
97
113
108
111
121
111
97




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79106&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79106&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79106&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.702888259538534
beta0.015960640491968
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.702888259538534 \tabularnewline
beta & 0.015960640491968 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79106&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]0.702888259538534[/C][/ROW]
[ROW][C]beta[/C][C]0.015960640491968[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79106&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79106&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
alpha0.702888259538534
beta0.015960640491968
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
33473470
4345346-1
5365344.28589319364520.7141068063551
6364358.0667593048125.93324069518786
7349361.524890499142-12.5248904991415
8339351.868506913518-12.8685069135184
9340341.826233437177-1.82623343717711
10340339.5249566606570.475043339343074
11341338.8465496082442.15345039175622
12343339.3720337517353.62796624826456
13341340.9746382884750.0253617115248517
14343340.0452989141282.95470108587165
15341341.208105246675-0.208105246674506
16335340.145477502427-5.1454775024273
17355335.55470398638619.4452960136142
18357348.4666444314318.53335556856916
19337353.804441897818-16.8044418978180
20325341.14407758436-16.1440775843603
21336328.7667625036617.23323749633943
22338332.9022341462055.09776585379456
23337335.5938973675191.40610263248146
24328335.706508280612-7.70650828061179
25326329.327516145211-3.32751614521112
26327325.9891362747371.01086372526260
27319325.711493102665-6.71149310266492
28310319.930602780694-9.93060278069396
29320311.7756311276588.22436887234193
30322316.4738413690275.52615863097333
31303319.337506779288-16.3375067792877
32292306.650175377529-14.6501753775289
33303294.9844957296748.01550427032595
34315299.34017851067315.6598214893275
35311309.2446425576121.75535744238823
36307309.395514630429-2.39551463042892
37308306.6019132633851.39808673661457
38312306.4904742601145.50952573988565
39309309.330726334501-0.330726334501094
40310308.0622235241891.93777647581129
41309308.4099637420890.590036257911038
42304307.817012533302-3.81701253330203
43287304.083577136154-17.0835771361538
44275290.833576325356-15.8335763253561
45290278.28455669160311.7154433083973
46298285.23084976944312.7691502305572
47294293.0610323815320.938967618467814
48286292.586452379574-6.58645237957404
49294286.7484525885217.25154741147924
50292290.7183722102231.28162778977662
51287290.506483420803-3.50648342080348
52281286.889749827684-5.88974982768434
53280281.531771823637-1.53177182363663
54271279.219781140045-8.21978114004548
55264272.114653228725-8.1146532287251
56259264.992383874875-5.99238387487532
57271259.29460689438211.7053931056179
58279266.1677070739712.8322929260299
59279273.9768515859565.02314841404433
60273276.353392529076-3.35339252907619
61286272.80454099665213.1954590033482
62286281.0357167898094.96428321019067
63280283.536987799363-3.53698779936263
64277280.023135361929-3.02313536192901
65269276.836548584312-7.83654858431225
66255270.178755477202-15.1787554772017
67252258.189927767039-6.1899277670388
68245252.449799526919-7.44979952691864
69257245.74054629348811.2594537065116
70267252.30812221110514.6918777888955
71261261.453130236783-0.453130236782897
72258259.94780646782-1.94780646781976
73271257.37004076620113.6299592337992
74262265.894612021863-3.89461202186340
75258262.057676001175-4.05767600117491
76253258.060602995689-5.06060299568924
77236253.301811768958-17.3018117689582
78228239.744717427596-11.7447174275957
79235229.9618807936175.03811920638339
80226232.032023367599-6.03202336759867
81231226.2534221583634.74657784163674
82235228.1042228990826.89577710091805
83227231.543031164801-4.54303116480131
84222226.890669189623-4.890669189623
85233221.93909032696011.0609096730396
86221228.323776300967-7.32377630096673
87218221.703920221235-3.70392022123511
88220217.5868658787592.41313412124055
89204217.796489074683-13.7964890746828
90196206.45778187606-10.4577818760602
91208197.34849165381310.6515083461873
92190203.196168141023-13.1961681410228
93191192.133550978011-1.13355097801104
94194189.5368890034734.46311099652746
95179190.924124643105-11.9241246431048
96162180.659193394793-18.6591933947934
97179165.45093235907713.5490676409227
98176173.0334807151682.96651928483172
99168173.210960111243-5.21096011124308
100170167.5821258472322.41787415276835
101153167.342634655738-14.3426346557384
102142155.161475080496-13.161475080496
103155143.66288607896811.3371139210320
104136149.511253605161-13.5112536051612
105136137.742418697375-1.74241869737526
106144134.2262122689899.77378773101117
107135138.914259828772-3.91425982877249
108114133.937227155638-19.9372271556380
109135117.47417214924317.5258278507569
110132127.5400729935324.45992700646849
111123128.472139433995-5.4721394339953
112123122.3616835280740.638316471926402
113103120.553356322076-17.5533563220762
11497105.761392738122-8.76139273812159
11511397.050907041008515.9490929589915
116108105.8880572739322.11194272606754
117111105.0229299910105.9770700089905
118121106.94160933659714.0583906634034
119111114.698268805559-3.69826880555915
12097109.932491603429-12.9324916034289

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 347 & 347 & 0 \tabularnewline
4 & 345 & 346 & -1 \tabularnewline
5 & 365 & 344.285893193645 & 20.7141068063551 \tabularnewline
6 & 364 & 358.066759304812 & 5.93324069518786 \tabularnewline
7 & 349 & 361.524890499142 & -12.5248904991415 \tabularnewline
8 & 339 & 351.868506913518 & -12.8685069135184 \tabularnewline
9 & 340 & 341.826233437177 & -1.82623343717711 \tabularnewline
10 & 340 & 339.524956660657 & 0.475043339343074 \tabularnewline
11 & 341 & 338.846549608244 & 2.15345039175622 \tabularnewline
12 & 343 & 339.372033751735 & 3.62796624826456 \tabularnewline
13 & 341 & 340.974638288475 & 0.0253617115248517 \tabularnewline
14 & 343 & 340.045298914128 & 2.95470108587165 \tabularnewline
15 & 341 & 341.208105246675 & -0.208105246674506 \tabularnewline
16 & 335 & 340.145477502427 & -5.1454775024273 \tabularnewline
17 & 355 & 335.554703986386 & 19.4452960136142 \tabularnewline
18 & 357 & 348.466644431431 & 8.53335556856916 \tabularnewline
19 & 337 & 353.804441897818 & -16.8044418978180 \tabularnewline
20 & 325 & 341.14407758436 & -16.1440775843603 \tabularnewline
21 & 336 & 328.766762503661 & 7.23323749633943 \tabularnewline
22 & 338 & 332.902234146205 & 5.09776585379456 \tabularnewline
23 & 337 & 335.593897367519 & 1.40610263248146 \tabularnewline
24 & 328 & 335.706508280612 & -7.70650828061179 \tabularnewline
25 & 326 & 329.327516145211 & -3.32751614521112 \tabularnewline
26 & 327 & 325.989136274737 & 1.01086372526260 \tabularnewline
27 & 319 & 325.711493102665 & -6.71149310266492 \tabularnewline
28 & 310 & 319.930602780694 & -9.93060278069396 \tabularnewline
29 & 320 & 311.775631127658 & 8.22436887234193 \tabularnewline
30 & 322 & 316.473841369027 & 5.52615863097333 \tabularnewline
31 & 303 & 319.337506779288 & -16.3375067792877 \tabularnewline
32 & 292 & 306.650175377529 & -14.6501753775289 \tabularnewline
33 & 303 & 294.984495729674 & 8.01550427032595 \tabularnewline
34 & 315 & 299.340178510673 & 15.6598214893275 \tabularnewline
35 & 311 & 309.244642557612 & 1.75535744238823 \tabularnewline
36 & 307 & 309.395514630429 & -2.39551463042892 \tabularnewline
37 & 308 & 306.601913263385 & 1.39808673661457 \tabularnewline
38 & 312 & 306.490474260114 & 5.50952573988565 \tabularnewline
39 & 309 & 309.330726334501 & -0.330726334501094 \tabularnewline
40 & 310 & 308.062223524189 & 1.93777647581129 \tabularnewline
41 & 309 & 308.409963742089 & 0.590036257911038 \tabularnewline
42 & 304 & 307.817012533302 & -3.81701253330203 \tabularnewline
43 & 287 & 304.083577136154 & -17.0835771361538 \tabularnewline
44 & 275 & 290.833576325356 & -15.8335763253561 \tabularnewline
45 & 290 & 278.284556691603 & 11.7154433083973 \tabularnewline
46 & 298 & 285.230849769443 & 12.7691502305572 \tabularnewline
47 & 294 & 293.061032381532 & 0.938967618467814 \tabularnewline
48 & 286 & 292.586452379574 & -6.58645237957404 \tabularnewline
49 & 294 & 286.748452588521 & 7.25154741147924 \tabularnewline
50 & 292 & 290.718372210223 & 1.28162778977662 \tabularnewline
51 & 287 & 290.506483420803 & -3.50648342080348 \tabularnewline
52 & 281 & 286.889749827684 & -5.88974982768434 \tabularnewline
53 & 280 & 281.531771823637 & -1.53177182363663 \tabularnewline
54 & 271 & 279.219781140045 & -8.21978114004548 \tabularnewline
55 & 264 & 272.114653228725 & -8.1146532287251 \tabularnewline
56 & 259 & 264.992383874875 & -5.99238387487532 \tabularnewline
57 & 271 & 259.294606894382 & 11.7053931056179 \tabularnewline
58 & 279 & 266.16770707397 & 12.8322929260299 \tabularnewline
59 & 279 & 273.976851585956 & 5.02314841404433 \tabularnewline
60 & 273 & 276.353392529076 & -3.35339252907619 \tabularnewline
61 & 286 & 272.804540996652 & 13.1954590033482 \tabularnewline
62 & 286 & 281.035716789809 & 4.96428321019067 \tabularnewline
63 & 280 & 283.536987799363 & -3.53698779936263 \tabularnewline
64 & 277 & 280.023135361929 & -3.02313536192901 \tabularnewline
65 & 269 & 276.836548584312 & -7.83654858431225 \tabularnewline
66 & 255 & 270.178755477202 & -15.1787554772017 \tabularnewline
67 & 252 & 258.189927767039 & -6.1899277670388 \tabularnewline
68 & 245 & 252.449799526919 & -7.44979952691864 \tabularnewline
69 & 257 & 245.740546293488 & 11.2594537065116 \tabularnewline
70 & 267 & 252.308122211105 & 14.6918777888955 \tabularnewline
71 & 261 & 261.453130236783 & -0.453130236782897 \tabularnewline
72 & 258 & 259.94780646782 & -1.94780646781976 \tabularnewline
73 & 271 & 257.370040766201 & 13.6299592337992 \tabularnewline
74 & 262 & 265.894612021863 & -3.89461202186340 \tabularnewline
75 & 258 & 262.057676001175 & -4.05767600117491 \tabularnewline
76 & 253 & 258.060602995689 & -5.06060299568924 \tabularnewline
77 & 236 & 253.301811768958 & -17.3018117689582 \tabularnewline
78 & 228 & 239.744717427596 & -11.7447174275957 \tabularnewline
79 & 235 & 229.961880793617 & 5.03811920638339 \tabularnewline
80 & 226 & 232.032023367599 & -6.03202336759867 \tabularnewline
81 & 231 & 226.253422158363 & 4.74657784163674 \tabularnewline
82 & 235 & 228.104222899082 & 6.89577710091805 \tabularnewline
83 & 227 & 231.543031164801 & -4.54303116480131 \tabularnewline
84 & 222 & 226.890669189623 & -4.890669189623 \tabularnewline
85 & 233 & 221.939090326960 & 11.0609096730396 \tabularnewline
86 & 221 & 228.323776300967 & -7.32377630096673 \tabularnewline
87 & 218 & 221.703920221235 & -3.70392022123511 \tabularnewline
88 & 220 & 217.586865878759 & 2.41313412124055 \tabularnewline
89 & 204 & 217.796489074683 & -13.7964890746828 \tabularnewline
90 & 196 & 206.45778187606 & -10.4577818760602 \tabularnewline
91 & 208 & 197.348491653813 & 10.6515083461873 \tabularnewline
92 & 190 & 203.196168141023 & -13.1961681410228 \tabularnewline
93 & 191 & 192.133550978011 & -1.13355097801104 \tabularnewline
94 & 194 & 189.536889003473 & 4.46311099652746 \tabularnewline
95 & 179 & 190.924124643105 & -11.9241246431048 \tabularnewline
96 & 162 & 180.659193394793 & -18.6591933947934 \tabularnewline
97 & 179 & 165.450932359077 & 13.5490676409227 \tabularnewline
98 & 176 & 173.033480715168 & 2.96651928483172 \tabularnewline
99 & 168 & 173.210960111243 & -5.21096011124308 \tabularnewline
100 & 170 & 167.582125847232 & 2.41787415276835 \tabularnewline
101 & 153 & 167.342634655738 & -14.3426346557384 \tabularnewline
102 & 142 & 155.161475080496 & -13.161475080496 \tabularnewline
103 & 155 & 143.662886078968 & 11.3371139210320 \tabularnewline
104 & 136 & 149.511253605161 & -13.5112536051612 \tabularnewline
105 & 136 & 137.742418697375 & -1.74241869737526 \tabularnewline
106 & 144 & 134.226212268989 & 9.77378773101117 \tabularnewline
107 & 135 & 138.914259828772 & -3.91425982877249 \tabularnewline
108 & 114 & 133.937227155638 & -19.9372271556380 \tabularnewline
109 & 135 & 117.474172149243 & 17.5258278507569 \tabularnewline
110 & 132 & 127.540072993532 & 4.45992700646849 \tabularnewline
111 & 123 & 128.472139433995 & -5.4721394339953 \tabularnewline
112 & 123 & 122.361683528074 & 0.638316471926402 \tabularnewline
113 & 103 & 120.553356322076 & -17.5533563220762 \tabularnewline
114 & 97 & 105.761392738122 & -8.76139273812159 \tabularnewline
115 & 113 & 97.0509070410085 & 15.9490929589915 \tabularnewline
116 & 108 & 105.888057273932 & 2.11194272606754 \tabularnewline
117 & 111 & 105.022929991010 & 5.9770700089905 \tabularnewline
118 & 121 & 106.941609336597 & 14.0583906634034 \tabularnewline
119 & 111 & 114.698268805559 & -3.69826880555915 \tabularnewline
120 & 97 & 109.932491603429 & -12.9324916034289 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79106&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]3[/C][C]347[/C][C]347[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]345[/C][C]346[/C][C]-1[/C][/ROW]
[ROW][C]5[/C][C]365[/C][C]344.285893193645[/C][C]20.7141068063551[/C][/ROW]
[ROW][C]6[/C][C]364[/C][C]358.066759304812[/C][C]5.93324069518786[/C][/ROW]
[ROW][C]7[/C][C]349[/C][C]361.524890499142[/C][C]-12.5248904991415[/C][/ROW]
[ROW][C]8[/C][C]339[/C][C]351.868506913518[/C][C]-12.8685069135184[/C][/ROW]
[ROW][C]9[/C][C]340[/C][C]341.826233437177[/C][C]-1.82623343717711[/C][/ROW]
[ROW][C]10[/C][C]340[/C][C]339.524956660657[/C][C]0.475043339343074[/C][/ROW]
[ROW][C]11[/C][C]341[/C][C]338.846549608244[/C][C]2.15345039175622[/C][/ROW]
[ROW][C]12[/C][C]343[/C][C]339.372033751735[/C][C]3.62796624826456[/C][/ROW]
[ROW][C]13[/C][C]341[/C][C]340.974638288475[/C][C]0.0253617115248517[/C][/ROW]
[ROW][C]14[/C][C]343[/C][C]340.045298914128[/C][C]2.95470108587165[/C][/ROW]
[ROW][C]15[/C][C]341[/C][C]341.208105246675[/C][C]-0.208105246674506[/C][/ROW]
[ROW][C]16[/C][C]335[/C][C]340.145477502427[/C][C]-5.1454775024273[/C][/ROW]
[ROW][C]17[/C][C]355[/C][C]335.554703986386[/C][C]19.4452960136142[/C][/ROW]
[ROW][C]18[/C][C]357[/C][C]348.466644431431[/C][C]8.53335556856916[/C][/ROW]
[ROW][C]19[/C][C]337[/C][C]353.804441897818[/C][C]-16.8044418978180[/C][/ROW]
[ROW][C]20[/C][C]325[/C][C]341.14407758436[/C][C]-16.1440775843603[/C][/ROW]
[ROW][C]21[/C][C]336[/C][C]328.766762503661[/C][C]7.23323749633943[/C][/ROW]
[ROW][C]22[/C][C]338[/C][C]332.902234146205[/C][C]5.09776585379456[/C][/ROW]
[ROW][C]23[/C][C]337[/C][C]335.593897367519[/C][C]1.40610263248146[/C][/ROW]
[ROW][C]24[/C][C]328[/C][C]335.706508280612[/C][C]-7.70650828061179[/C][/ROW]
[ROW][C]25[/C][C]326[/C][C]329.327516145211[/C][C]-3.32751614521112[/C][/ROW]
[ROW][C]26[/C][C]327[/C][C]325.989136274737[/C][C]1.01086372526260[/C][/ROW]
[ROW][C]27[/C][C]319[/C][C]325.711493102665[/C][C]-6.71149310266492[/C][/ROW]
[ROW][C]28[/C][C]310[/C][C]319.930602780694[/C][C]-9.93060278069396[/C][/ROW]
[ROW][C]29[/C][C]320[/C][C]311.775631127658[/C][C]8.22436887234193[/C][/ROW]
[ROW][C]30[/C][C]322[/C][C]316.473841369027[/C][C]5.52615863097333[/C][/ROW]
[ROW][C]31[/C][C]303[/C][C]319.337506779288[/C][C]-16.3375067792877[/C][/ROW]
[ROW][C]32[/C][C]292[/C][C]306.650175377529[/C][C]-14.6501753775289[/C][/ROW]
[ROW][C]33[/C][C]303[/C][C]294.984495729674[/C][C]8.01550427032595[/C][/ROW]
[ROW][C]34[/C][C]315[/C][C]299.340178510673[/C][C]15.6598214893275[/C][/ROW]
[ROW][C]35[/C][C]311[/C][C]309.244642557612[/C][C]1.75535744238823[/C][/ROW]
[ROW][C]36[/C][C]307[/C][C]309.395514630429[/C][C]-2.39551463042892[/C][/ROW]
[ROW][C]37[/C][C]308[/C][C]306.601913263385[/C][C]1.39808673661457[/C][/ROW]
[ROW][C]38[/C][C]312[/C][C]306.490474260114[/C][C]5.50952573988565[/C][/ROW]
[ROW][C]39[/C][C]309[/C][C]309.330726334501[/C][C]-0.330726334501094[/C][/ROW]
[ROW][C]40[/C][C]310[/C][C]308.062223524189[/C][C]1.93777647581129[/C][/ROW]
[ROW][C]41[/C][C]309[/C][C]308.409963742089[/C][C]0.590036257911038[/C][/ROW]
[ROW][C]42[/C][C]304[/C][C]307.817012533302[/C][C]-3.81701253330203[/C][/ROW]
[ROW][C]43[/C][C]287[/C][C]304.083577136154[/C][C]-17.0835771361538[/C][/ROW]
[ROW][C]44[/C][C]275[/C][C]290.833576325356[/C][C]-15.8335763253561[/C][/ROW]
[ROW][C]45[/C][C]290[/C][C]278.284556691603[/C][C]11.7154433083973[/C][/ROW]
[ROW][C]46[/C][C]298[/C][C]285.230849769443[/C][C]12.7691502305572[/C][/ROW]
[ROW][C]47[/C][C]294[/C][C]293.061032381532[/C][C]0.938967618467814[/C][/ROW]
[ROW][C]48[/C][C]286[/C][C]292.586452379574[/C][C]-6.58645237957404[/C][/ROW]
[ROW][C]49[/C][C]294[/C][C]286.748452588521[/C][C]7.25154741147924[/C][/ROW]
[ROW][C]50[/C][C]292[/C][C]290.718372210223[/C][C]1.28162778977662[/C][/ROW]
[ROW][C]51[/C][C]287[/C][C]290.506483420803[/C][C]-3.50648342080348[/C][/ROW]
[ROW][C]52[/C][C]281[/C][C]286.889749827684[/C][C]-5.88974982768434[/C][/ROW]
[ROW][C]53[/C][C]280[/C][C]281.531771823637[/C][C]-1.53177182363663[/C][/ROW]
[ROW][C]54[/C][C]271[/C][C]279.219781140045[/C][C]-8.21978114004548[/C][/ROW]
[ROW][C]55[/C][C]264[/C][C]272.114653228725[/C][C]-8.1146532287251[/C][/ROW]
[ROW][C]56[/C][C]259[/C][C]264.992383874875[/C][C]-5.99238387487532[/C][/ROW]
[ROW][C]57[/C][C]271[/C][C]259.294606894382[/C][C]11.7053931056179[/C][/ROW]
[ROW][C]58[/C][C]279[/C][C]266.16770707397[/C][C]12.8322929260299[/C][/ROW]
[ROW][C]59[/C][C]279[/C][C]273.976851585956[/C][C]5.02314841404433[/C][/ROW]
[ROW][C]60[/C][C]273[/C][C]276.353392529076[/C][C]-3.35339252907619[/C][/ROW]
[ROW][C]61[/C][C]286[/C][C]272.804540996652[/C][C]13.1954590033482[/C][/ROW]
[ROW][C]62[/C][C]286[/C][C]281.035716789809[/C][C]4.96428321019067[/C][/ROW]
[ROW][C]63[/C][C]280[/C][C]283.536987799363[/C][C]-3.53698779936263[/C][/ROW]
[ROW][C]64[/C][C]277[/C][C]280.023135361929[/C][C]-3.02313536192901[/C][/ROW]
[ROW][C]65[/C][C]269[/C][C]276.836548584312[/C][C]-7.83654858431225[/C][/ROW]
[ROW][C]66[/C][C]255[/C][C]270.178755477202[/C][C]-15.1787554772017[/C][/ROW]
[ROW][C]67[/C][C]252[/C][C]258.189927767039[/C][C]-6.1899277670388[/C][/ROW]
[ROW][C]68[/C][C]245[/C][C]252.449799526919[/C][C]-7.44979952691864[/C][/ROW]
[ROW][C]69[/C][C]257[/C][C]245.740546293488[/C][C]11.2594537065116[/C][/ROW]
[ROW][C]70[/C][C]267[/C][C]252.308122211105[/C][C]14.6918777888955[/C][/ROW]
[ROW][C]71[/C][C]261[/C][C]261.453130236783[/C][C]-0.453130236782897[/C][/ROW]
[ROW][C]72[/C][C]258[/C][C]259.94780646782[/C][C]-1.94780646781976[/C][/ROW]
[ROW][C]73[/C][C]271[/C][C]257.370040766201[/C][C]13.6299592337992[/C][/ROW]
[ROW][C]74[/C][C]262[/C][C]265.894612021863[/C][C]-3.89461202186340[/C][/ROW]
[ROW][C]75[/C][C]258[/C][C]262.057676001175[/C][C]-4.05767600117491[/C][/ROW]
[ROW][C]76[/C][C]253[/C][C]258.060602995689[/C][C]-5.06060299568924[/C][/ROW]
[ROW][C]77[/C][C]236[/C][C]253.301811768958[/C][C]-17.3018117689582[/C][/ROW]
[ROW][C]78[/C][C]228[/C][C]239.744717427596[/C][C]-11.7447174275957[/C][/ROW]
[ROW][C]79[/C][C]235[/C][C]229.961880793617[/C][C]5.03811920638339[/C][/ROW]
[ROW][C]80[/C][C]226[/C][C]232.032023367599[/C][C]-6.03202336759867[/C][/ROW]
[ROW][C]81[/C][C]231[/C][C]226.253422158363[/C][C]4.74657784163674[/C][/ROW]
[ROW][C]82[/C][C]235[/C][C]228.104222899082[/C][C]6.89577710091805[/C][/ROW]
[ROW][C]83[/C][C]227[/C][C]231.543031164801[/C][C]-4.54303116480131[/C][/ROW]
[ROW][C]84[/C][C]222[/C][C]226.890669189623[/C][C]-4.890669189623[/C][/ROW]
[ROW][C]85[/C][C]233[/C][C]221.939090326960[/C][C]11.0609096730396[/C][/ROW]
[ROW][C]86[/C][C]221[/C][C]228.323776300967[/C][C]-7.32377630096673[/C][/ROW]
[ROW][C]87[/C][C]218[/C][C]221.703920221235[/C][C]-3.70392022123511[/C][/ROW]
[ROW][C]88[/C][C]220[/C][C]217.586865878759[/C][C]2.41313412124055[/C][/ROW]
[ROW][C]89[/C][C]204[/C][C]217.796489074683[/C][C]-13.7964890746828[/C][/ROW]
[ROW][C]90[/C][C]196[/C][C]206.45778187606[/C][C]-10.4577818760602[/C][/ROW]
[ROW][C]91[/C][C]208[/C][C]197.348491653813[/C][C]10.6515083461873[/C][/ROW]
[ROW][C]92[/C][C]190[/C][C]203.196168141023[/C][C]-13.1961681410228[/C][/ROW]
[ROW][C]93[/C][C]191[/C][C]192.133550978011[/C][C]-1.13355097801104[/C][/ROW]
[ROW][C]94[/C][C]194[/C][C]189.536889003473[/C][C]4.46311099652746[/C][/ROW]
[ROW][C]95[/C][C]179[/C][C]190.924124643105[/C][C]-11.9241246431048[/C][/ROW]
[ROW][C]96[/C][C]162[/C][C]180.659193394793[/C][C]-18.6591933947934[/C][/ROW]
[ROW][C]97[/C][C]179[/C][C]165.450932359077[/C][C]13.5490676409227[/C][/ROW]
[ROW][C]98[/C][C]176[/C][C]173.033480715168[/C][C]2.96651928483172[/C][/ROW]
[ROW][C]99[/C][C]168[/C][C]173.210960111243[/C][C]-5.21096011124308[/C][/ROW]
[ROW][C]100[/C][C]170[/C][C]167.582125847232[/C][C]2.41787415276835[/C][/ROW]
[ROW][C]101[/C][C]153[/C][C]167.342634655738[/C][C]-14.3426346557384[/C][/ROW]
[ROW][C]102[/C][C]142[/C][C]155.161475080496[/C][C]-13.161475080496[/C][/ROW]
[ROW][C]103[/C][C]155[/C][C]143.662886078968[/C][C]11.3371139210320[/C][/ROW]
[ROW][C]104[/C][C]136[/C][C]149.511253605161[/C][C]-13.5112536051612[/C][/ROW]
[ROW][C]105[/C][C]136[/C][C]137.742418697375[/C][C]-1.74241869737526[/C][/ROW]
[ROW][C]106[/C][C]144[/C][C]134.226212268989[/C][C]9.77378773101117[/C][/ROW]
[ROW][C]107[/C][C]135[/C][C]138.914259828772[/C][C]-3.91425982877249[/C][/ROW]
[ROW][C]108[/C][C]114[/C][C]133.937227155638[/C][C]-19.9372271556380[/C][/ROW]
[ROW][C]109[/C][C]135[/C][C]117.474172149243[/C][C]17.5258278507569[/C][/ROW]
[ROW][C]110[/C][C]132[/C][C]127.540072993532[/C][C]4.45992700646849[/C][/ROW]
[ROW][C]111[/C][C]123[/C][C]128.472139433995[/C][C]-5.4721394339953[/C][/ROW]
[ROW][C]112[/C][C]123[/C][C]122.361683528074[/C][C]0.638316471926402[/C][/ROW]
[ROW][C]113[/C][C]103[/C][C]120.553356322076[/C][C]-17.5533563220762[/C][/ROW]
[ROW][C]114[/C][C]97[/C][C]105.761392738122[/C][C]-8.76139273812159[/C][/ROW]
[ROW][C]115[/C][C]113[/C][C]97.0509070410085[/C][C]15.9490929589915[/C][/ROW]
[ROW][C]116[/C][C]108[/C][C]105.888057273932[/C][C]2.11194272606754[/C][/ROW]
[ROW][C]117[/C][C]111[/C][C]105.022929991010[/C][C]5.9770700089905[/C][/ROW]
[ROW][C]118[/C][C]121[/C][C]106.941609336597[/C][C]14.0583906634034[/C][/ROW]
[ROW][C]119[/C][C]111[/C][C]114.698268805559[/C][C]-3.69826880555915[/C][/ROW]
[ROW][C]120[/C][C]97[/C][C]109.932491603429[/C][C]-12.9324916034289[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79106&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79106&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
33473470
4345346-1
5365344.28589319364520.7141068063551
6364358.0667593048125.93324069518786
7349361.524890499142-12.5248904991415
8339351.868506913518-12.8685069135184
9340341.826233437177-1.82623343717711
10340339.5249566606570.475043339343074
11341338.8465496082442.15345039175622
12343339.3720337517353.62796624826456
13341340.9746382884750.0253617115248517
14343340.0452989141282.95470108587165
15341341.208105246675-0.208105246674506
16335340.145477502427-5.1454775024273
17355335.55470398638619.4452960136142
18357348.4666444314318.53335556856916
19337353.804441897818-16.8044418978180
20325341.14407758436-16.1440775843603
21336328.7667625036617.23323749633943
22338332.9022341462055.09776585379456
23337335.5938973675191.40610263248146
24328335.706508280612-7.70650828061179
25326329.327516145211-3.32751614521112
26327325.9891362747371.01086372526260
27319325.711493102665-6.71149310266492
28310319.930602780694-9.93060278069396
29320311.7756311276588.22436887234193
30322316.4738413690275.52615863097333
31303319.337506779288-16.3375067792877
32292306.650175377529-14.6501753775289
33303294.9844957296748.01550427032595
34315299.34017851067315.6598214893275
35311309.2446425576121.75535744238823
36307309.395514630429-2.39551463042892
37308306.6019132633851.39808673661457
38312306.4904742601145.50952573988565
39309309.330726334501-0.330726334501094
40310308.0622235241891.93777647581129
41309308.4099637420890.590036257911038
42304307.817012533302-3.81701253330203
43287304.083577136154-17.0835771361538
44275290.833576325356-15.8335763253561
45290278.28455669160311.7154433083973
46298285.23084976944312.7691502305572
47294293.0610323815320.938967618467814
48286292.586452379574-6.58645237957404
49294286.7484525885217.25154741147924
50292290.7183722102231.28162778977662
51287290.506483420803-3.50648342080348
52281286.889749827684-5.88974982768434
53280281.531771823637-1.53177182363663
54271279.219781140045-8.21978114004548
55264272.114653228725-8.1146532287251
56259264.992383874875-5.99238387487532
57271259.29460689438211.7053931056179
58279266.1677070739712.8322929260299
59279273.9768515859565.02314841404433
60273276.353392529076-3.35339252907619
61286272.80454099665213.1954590033482
62286281.0357167898094.96428321019067
63280283.536987799363-3.53698779936263
64277280.023135361929-3.02313536192901
65269276.836548584312-7.83654858431225
66255270.178755477202-15.1787554772017
67252258.189927767039-6.1899277670388
68245252.449799526919-7.44979952691864
69257245.74054629348811.2594537065116
70267252.30812221110514.6918777888955
71261261.453130236783-0.453130236782897
72258259.94780646782-1.94780646781976
73271257.37004076620113.6299592337992
74262265.894612021863-3.89461202186340
75258262.057676001175-4.05767600117491
76253258.060602995689-5.06060299568924
77236253.301811768958-17.3018117689582
78228239.744717427596-11.7447174275957
79235229.9618807936175.03811920638339
80226232.032023367599-6.03202336759867
81231226.2534221583634.74657784163674
82235228.1042228990826.89577710091805
83227231.543031164801-4.54303116480131
84222226.890669189623-4.890669189623
85233221.93909032696011.0609096730396
86221228.323776300967-7.32377630096673
87218221.703920221235-3.70392022123511
88220217.5868658787592.41313412124055
89204217.796489074683-13.7964890746828
90196206.45778187606-10.4577818760602
91208197.34849165381310.6515083461873
92190203.196168141023-13.1961681410228
93191192.133550978011-1.13355097801104
94194189.5368890034734.46311099652746
95179190.924124643105-11.9241246431048
96162180.659193394793-18.6591933947934
97179165.45093235907713.5490676409227
98176173.0334807151682.96651928483172
99168173.210960111243-5.21096011124308
100170167.5821258472322.41787415276835
101153167.342634655738-14.3426346557384
102142155.161475080496-13.161475080496
103155143.66288607896811.3371139210320
104136149.511253605161-13.5112536051612
105136137.742418697375-1.74241869737526
106144134.2262122689899.77378773101117
107135138.914259828772-3.91425982877249
108114133.937227155638-19.9372271556380
109135117.47417214924317.5258278507569
110132127.5400729935324.45992700646849
111123128.472139433995-5.4721394339953
112123122.3616835280740.638316471926402
113103120.553356322076-17.5533563220762
11497105.761392738122-8.76139273812159
11511397.050907041008515.9490929589915
116108105.8880572739322.11194272606754
117111105.0229299910105.9770700089905
118121106.94160933659714.0583906634034
119111114.698268805559-3.69826880555915
12097109.932491603429-12.9324916034289







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12198.531003848205780.0423829634544117.019624732957
12296.219612607613373.5008021037576118.938423111469
12393.908221367020967.5267966374233120.289646096618
12491.596830126428561.9080981776696121.285562075187
12589.28543888583656.5355672076013122.035310564071
12686.974047645243751.3444885158435122.603606774644
12784.662656404651346.2928634222252123.032449387077
12882.351265164058941.3516709396948123.350859388423
12980.039873923466536.4999076252998123.579840221633
13077.728482682874131.7218215139909123.735143851757
13175.417091442281727.0052603583769123.828922526186
13273.105700201689322.3406309261031123.870769477275

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 98.5310038482057 & 80.0423829634544 & 117.019624732957 \tabularnewline
122 & 96.2196126076133 & 73.5008021037576 & 118.938423111469 \tabularnewline
123 & 93.9082213670209 & 67.5267966374233 & 120.289646096618 \tabularnewline
124 & 91.5968301264285 & 61.9080981776696 & 121.285562075187 \tabularnewline
125 & 89.285438885836 & 56.5355672076013 & 122.035310564071 \tabularnewline
126 & 86.9740476452437 & 51.3444885158435 & 122.603606774644 \tabularnewline
127 & 84.6626564046513 & 46.2928634222252 & 123.032449387077 \tabularnewline
128 & 82.3512651640589 & 41.3516709396948 & 123.350859388423 \tabularnewline
129 & 80.0398739234665 & 36.4999076252998 & 123.579840221633 \tabularnewline
130 & 77.7284826828741 & 31.7218215139909 & 123.735143851757 \tabularnewline
131 & 75.4170914422817 & 27.0052603583769 & 123.828922526186 \tabularnewline
132 & 73.1057002016893 & 22.3406309261031 & 123.870769477275 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79106&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]98.5310038482057[/C][C]80.0423829634544[/C][C]117.019624732957[/C][/ROW]
[ROW][C]122[/C][C]96.2196126076133[/C][C]73.5008021037576[/C][C]118.938423111469[/C][/ROW]
[ROW][C]123[/C][C]93.9082213670209[/C][C]67.5267966374233[/C][C]120.289646096618[/C][/ROW]
[ROW][C]124[/C][C]91.5968301264285[/C][C]61.9080981776696[/C][C]121.285562075187[/C][/ROW]
[ROW][C]125[/C][C]89.285438885836[/C][C]56.5355672076013[/C][C]122.035310564071[/C][/ROW]
[ROW][C]126[/C][C]86.9740476452437[/C][C]51.3444885158435[/C][C]122.603606774644[/C][/ROW]
[ROW][C]127[/C][C]84.6626564046513[/C][C]46.2928634222252[/C][C]123.032449387077[/C][/ROW]
[ROW][C]128[/C][C]82.3512651640589[/C][C]41.3516709396948[/C][C]123.350859388423[/C][/ROW]
[ROW][C]129[/C][C]80.0398739234665[/C][C]36.4999076252998[/C][C]123.579840221633[/C][/ROW]
[ROW][C]130[/C][C]77.7284826828741[/C][C]31.7218215139909[/C][C]123.735143851757[/C][/ROW]
[ROW][C]131[/C][C]75.4170914422817[/C][C]27.0052603583769[/C][C]123.828922526186[/C][/ROW]
[ROW][C]132[/C][C]73.1057002016893[/C][C]22.3406309261031[/C][C]123.870769477275[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79106&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79106&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
12198.531003848205780.0423829634544117.019624732957
12296.219612607613373.5008021037576118.938423111469
12393.908221367020967.5267966374233120.289646096618
12491.596830126428561.9080981776696121.285562075187
12589.28543888583656.5355672076013122.035310564071
12686.974047645243751.3444885158435122.603606774644
12784.662656404651346.2928634222252123.032449387077
12882.351265164058941.3516709396948123.350859388423
12980.039873923466536.4999076252998123.579840221633
13077.728482682874131.7218215139909123.735143851757
13175.417091442281727.0052603583769123.828922526186
13273.105700201689322.3406309261031123.870769477275



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')