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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 20 Dec 2012 12:48:18 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/20/t1356025736u98j3kp96bk8h2k.htm/, Retrieved Thu, 28 Mar 2024 21:01:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=202960, Retrieved Thu, 28 Mar 2024 21:01:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact55
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2012-12-20 17:48:18] [e5cf4d544f75f57c12196ef0ffd71d75] [Current]
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Dataseries X:
41
39
50
40
43
38
44
35
39
35
29
49
50
59
63
32
39
47
53
60
57
52
70
90
74
62
55
84
94
70
108
139
120
97
126
149
158
124
140
109
114
77
120
133
110
92
97
78
99
107
112
90
98
125
155
190
236
189
174
178
136
161
171
149
184
155
276
224
213
279
268
287
238
213
257
293
212
246
353
339
308
247
257
322
298
273
312
249
286
279
309
401
309
328
353
354
327
324
285
243
241
287
355
460
364
487
452
391
500
451
375
372
302
316
398
394
431
431




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 3 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=202960&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=202960&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=202960&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 time3 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.599546669115242
beta0.000254057295288893
gamma0.204732865941466

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.599546669115242 \tabularnewline
beta & 0.000254057295288893 \tabularnewline
gamma & 0.204732865941466 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=202960&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]0.599546669115242[/C][/ROW]
[ROW][C]beta[/C][C]0.000254057295288893[/C][/ROW]
[ROW][C]gamma[/C][C]0.204732865941466[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=202960&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=202960&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
alpha0.599546669115242
beta0.000254057295288893
gamma0.204732865941466







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
135047.79006410256412.2099358974359
145957.73686392101281.26313607898717
156361.74120546187531.25879453812473
163231.07646911829160.923530881708373
173937.25253390438471.74746609561532
184743.92285247618913.07714752381089
195357.5575124945842-4.55751249458423
206045.655809999109314.3441900008907
215757.9220785043564-0.922078504356406
225254.2020327938655-2.20203279386551
237048.422592673928121.5774073260719
249082.19498999152447.80501000847562
257488.3508982697864-14.3508982697864
266288.2956449523492-26.2956449523492
275575.7772215610825-20.7772215610825
288431.870388129574552.1296118704255
299468.819248875399625.1807511246004
307089.6563095245492-19.6563095245492
3110889.040182319502118.9598176804979
3213992.796389270793746.2036107292063
33120122.925598790003-2.92559879000314
3497117.912456798865-20.9124567988647
35126102.87502042546123.1249795745388
36149136.45654802025512.5434519797453
37158143.64805346689814.3519465331021
38124159.837719074198-35.8377190741984
39140142.064882144718-2.06488214471773
40109115.371228310816-6.37122831081633
41114115.044688453576-1.04468845357644
4277116.486381579579-39.4863815795786
43120107.14817721022112.8518227897786
44133109.47603057775123.5239694222494
45110121.976442768546-11.9764427685463
4692110.057460400238-18.0574604002376
4797100.337846662489-3.33784666248906
4878117.17777509757-39.1777750975702
499993.49202099412455.50797900587554
50107100.2468791086616.75312089133931
51112110.7670358137871.23296418621307
529085.68693617657434.31306382342572
539892.19385830685135.80614169314875
5412594.583337051758930.4166629482411
55155131.44898786310223.5510121368983
56190141.07082026684348.9291797331572
57236165.90052560665470.0994743933463
58189202.71204890462-13.7120489046197
59174196.825896653984-22.8258966539841
60178199.061873217275-21.0618732172751
61136189.922225967325-53.9222259673251
62161161.160108293423-0.160108293422866
63171167.0939546116653.90604538833495
64149143.8804924669335.11950753306672
65184151.00492513534832.9950748646522
66155171.728895239864-16.7288952398636
67276179.77425541740296.2257445825981
68224235.06826343194-11.0682634319398
69213225.672858153708-12.6728581537078
70279205.98501902010673.0149809798943
71268251.35965319144416.640346808556
72287277.4192132558469.58078674415367
73238283.978954219307-45.9789542193074
74213264.409918308727-51.4099183087268
75257239.9656538321117.0343461678896
76293224.73988182768.260118173
77212272.032254193127-60.0322541931271
78246232.91795365275813.0820463472418
79353268.11422166787284.8857783321283
80339307.82822408537931.1717759146207
81308323.648008876875-15.648008876875
82247309.223043865887-62.2230438658873
83257268.895059198492-11.8950591984917
84322277.26399724425144.7360027557493
85298300.347637489371-2.34763748937092
86273306.500820501493-33.5008205014928
87312298.41656356418513.5834364358151
88249285.332277483638-36.3322774836376
89286259.393196284326.6068037156996
90279278.2253390336950.774660966304907
91309311.935716973548-2.93571697354838
92401294.585527624349106.414472375651
93309351.682403620028-42.6824036200276
94328317.23058864449310.7694113555067
95353324.8023237937228.1976762062799
96354361.8689349492-7.8689349492002
97327349.562505184392-22.5625051843921
98324341.047971460211-17.0479714602114
99285346.69688277896-61.6968827789595
100243284.383347293651-41.383347293651
101241260.57246837458-19.5724683745803
102287249.58950888254837.4104911174522
103355304.95555770573550.0444422942648
104460328.337676149848131.662323850152
105364388.354862634688-24.3548626346883
106487369.283249174535117.716750825465
107452442.4297557005779.57024429942271
108391465.39453635014-74.39453635014
109500412.0112442133287.9887557866799
110451470.259310974497-19.2593109744974
111375470.951346323523-95.9513463235227
112372389.790377417692-17.7903774176923
113302381.940655900692-79.9406559006916
114316339.454643045337-23.4546430453374
115398359.37442893774138.6255710622588
116394382.60960100420211.3903989957981
117431357.7162969317573.2837030682496
118431408.83566978662622.1643302133742

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 50 & 47.7900641025641 & 2.2099358974359 \tabularnewline
14 & 59 & 57.7368639210128 & 1.26313607898717 \tabularnewline
15 & 63 & 61.7412054618753 & 1.25879453812473 \tabularnewline
16 & 32 & 31.0764691182916 & 0.923530881708373 \tabularnewline
17 & 39 & 37.2525339043847 & 1.74746609561532 \tabularnewline
18 & 47 & 43.9228524761891 & 3.07714752381089 \tabularnewline
19 & 53 & 57.5575124945842 & -4.55751249458423 \tabularnewline
20 & 60 & 45.6558099991093 & 14.3441900008907 \tabularnewline
21 & 57 & 57.9220785043564 & -0.922078504356406 \tabularnewline
22 & 52 & 54.2020327938655 & -2.20203279386551 \tabularnewline
23 & 70 & 48.4225926739281 & 21.5774073260719 \tabularnewline
24 & 90 & 82.1949899915244 & 7.80501000847562 \tabularnewline
25 & 74 & 88.3508982697864 & -14.3508982697864 \tabularnewline
26 & 62 & 88.2956449523492 & -26.2956449523492 \tabularnewline
27 & 55 & 75.7772215610825 & -20.7772215610825 \tabularnewline
28 & 84 & 31.8703881295745 & 52.1296118704255 \tabularnewline
29 & 94 & 68.8192488753996 & 25.1807511246004 \tabularnewline
30 & 70 & 89.6563095245492 & -19.6563095245492 \tabularnewline
31 & 108 & 89.0401823195021 & 18.9598176804979 \tabularnewline
32 & 139 & 92.7963892707937 & 46.2036107292063 \tabularnewline
33 & 120 & 122.925598790003 & -2.92559879000314 \tabularnewline
34 & 97 & 117.912456798865 & -20.9124567988647 \tabularnewline
35 & 126 & 102.875020425461 & 23.1249795745388 \tabularnewline
36 & 149 & 136.456548020255 & 12.5434519797453 \tabularnewline
37 & 158 & 143.648053466898 & 14.3519465331021 \tabularnewline
38 & 124 & 159.837719074198 & -35.8377190741984 \tabularnewline
39 & 140 & 142.064882144718 & -2.06488214471773 \tabularnewline
40 & 109 & 115.371228310816 & -6.37122831081633 \tabularnewline
41 & 114 & 115.044688453576 & -1.04468845357644 \tabularnewline
42 & 77 & 116.486381579579 & -39.4863815795786 \tabularnewline
43 & 120 & 107.148177210221 & 12.8518227897786 \tabularnewline
44 & 133 & 109.476030577751 & 23.5239694222494 \tabularnewline
45 & 110 & 121.976442768546 & -11.9764427685463 \tabularnewline
46 & 92 & 110.057460400238 & -18.0574604002376 \tabularnewline
47 & 97 & 100.337846662489 & -3.33784666248906 \tabularnewline
48 & 78 & 117.17777509757 & -39.1777750975702 \tabularnewline
49 & 99 & 93.4920209941245 & 5.50797900587554 \tabularnewline
50 & 107 & 100.246879108661 & 6.75312089133931 \tabularnewline
51 & 112 & 110.767035813787 & 1.23296418621307 \tabularnewline
52 & 90 & 85.6869361765743 & 4.31306382342572 \tabularnewline
53 & 98 & 92.1938583068513 & 5.80614169314875 \tabularnewline
54 & 125 & 94.5833370517589 & 30.4166629482411 \tabularnewline
55 & 155 & 131.448987863102 & 23.5510121368983 \tabularnewline
56 & 190 & 141.070820266843 & 48.9291797331572 \tabularnewline
57 & 236 & 165.900525606654 & 70.0994743933463 \tabularnewline
58 & 189 & 202.71204890462 & -13.7120489046197 \tabularnewline
59 & 174 & 196.825896653984 & -22.8258966539841 \tabularnewline
60 & 178 & 199.061873217275 & -21.0618732172751 \tabularnewline
61 & 136 & 189.922225967325 & -53.9222259673251 \tabularnewline
62 & 161 & 161.160108293423 & -0.160108293422866 \tabularnewline
63 & 171 & 167.093954611665 & 3.90604538833495 \tabularnewline
64 & 149 & 143.880492466933 & 5.11950753306672 \tabularnewline
65 & 184 & 151.004925135348 & 32.9950748646522 \tabularnewline
66 & 155 & 171.728895239864 & -16.7288952398636 \tabularnewline
67 & 276 & 179.774255417402 & 96.2257445825981 \tabularnewline
68 & 224 & 235.06826343194 & -11.0682634319398 \tabularnewline
69 & 213 & 225.672858153708 & -12.6728581537078 \tabularnewline
70 & 279 & 205.985019020106 & 73.0149809798943 \tabularnewline
71 & 268 & 251.359653191444 & 16.640346808556 \tabularnewline
72 & 287 & 277.419213255846 & 9.58078674415367 \tabularnewline
73 & 238 & 283.978954219307 & -45.9789542193074 \tabularnewline
74 & 213 & 264.409918308727 & -51.4099183087268 \tabularnewline
75 & 257 & 239.96565383211 & 17.0343461678896 \tabularnewline
76 & 293 & 224.739881827 & 68.260118173 \tabularnewline
77 & 212 & 272.032254193127 & -60.0322541931271 \tabularnewline
78 & 246 & 232.917953652758 & 13.0820463472418 \tabularnewline
79 & 353 & 268.114221667872 & 84.8857783321283 \tabularnewline
80 & 339 & 307.828224085379 & 31.1717759146207 \tabularnewline
81 & 308 & 323.648008876875 & -15.648008876875 \tabularnewline
82 & 247 & 309.223043865887 & -62.2230438658873 \tabularnewline
83 & 257 & 268.895059198492 & -11.8950591984917 \tabularnewline
84 & 322 & 277.263997244251 & 44.7360027557493 \tabularnewline
85 & 298 & 300.347637489371 & -2.34763748937092 \tabularnewline
86 & 273 & 306.500820501493 & -33.5008205014928 \tabularnewline
87 & 312 & 298.416563564185 & 13.5834364358151 \tabularnewline
88 & 249 & 285.332277483638 & -36.3322774836376 \tabularnewline
89 & 286 & 259.3931962843 & 26.6068037156996 \tabularnewline
90 & 279 & 278.225339033695 & 0.774660966304907 \tabularnewline
91 & 309 & 311.935716973548 & -2.93571697354838 \tabularnewline
92 & 401 & 294.585527624349 & 106.414472375651 \tabularnewline
93 & 309 & 351.682403620028 & -42.6824036200276 \tabularnewline
94 & 328 & 317.230588644493 & 10.7694113555067 \tabularnewline
95 & 353 & 324.80232379372 & 28.1976762062799 \tabularnewline
96 & 354 & 361.8689349492 & -7.8689349492002 \tabularnewline
97 & 327 & 349.562505184392 & -22.5625051843921 \tabularnewline
98 & 324 & 341.047971460211 & -17.0479714602114 \tabularnewline
99 & 285 & 346.69688277896 & -61.6968827789595 \tabularnewline
100 & 243 & 284.383347293651 & -41.383347293651 \tabularnewline
101 & 241 & 260.57246837458 & -19.5724683745803 \tabularnewline
102 & 287 & 249.589508882548 & 37.4104911174522 \tabularnewline
103 & 355 & 304.955557705735 & 50.0444422942648 \tabularnewline
104 & 460 & 328.337676149848 & 131.662323850152 \tabularnewline
105 & 364 & 388.354862634688 & -24.3548626346883 \tabularnewline
106 & 487 & 369.283249174535 & 117.716750825465 \tabularnewline
107 & 452 & 442.429755700577 & 9.57024429942271 \tabularnewline
108 & 391 & 465.39453635014 & -74.39453635014 \tabularnewline
109 & 500 & 412.01124421332 & 87.9887557866799 \tabularnewline
110 & 451 & 470.259310974497 & -19.2593109744974 \tabularnewline
111 & 375 & 470.951346323523 & -95.9513463235227 \tabularnewline
112 & 372 & 389.790377417692 & -17.7903774176923 \tabularnewline
113 & 302 & 381.940655900692 & -79.9406559006916 \tabularnewline
114 & 316 & 339.454643045337 & -23.4546430453374 \tabularnewline
115 & 398 & 359.374428937741 & 38.6255710622588 \tabularnewline
116 & 394 & 382.609601004202 & 11.3903989957981 \tabularnewline
117 & 431 & 357.71629693175 & 73.2837030682496 \tabularnewline
118 & 431 & 408.835669786626 & 22.1643302133742 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=202960&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]50[/C][C]47.7900641025641[/C][C]2.2099358974359[/C][/ROW]
[ROW][C]14[/C][C]59[/C][C]57.7368639210128[/C][C]1.26313607898717[/C][/ROW]
[ROW][C]15[/C][C]63[/C][C]61.7412054618753[/C][C]1.25879453812473[/C][/ROW]
[ROW][C]16[/C][C]32[/C][C]31.0764691182916[/C][C]0.923530881708373[/C][/ROW]
[ROW][C]17[/C][C]39[/C][C]37.2525339043847[/C][C]1.74746609561532[/C][/ROW]
[ROW][C]18[/C][C]47[/C][C]43.9228524761891[/C][C]3.07714752381089[/C][/ROW]
[ROW][C]19[/C][C]53[/C][C]57.5575124945842[/C][C]-4.55751249458423[/C][/ROW]
[ROW][C]20[/C][C]60[/C][C]45.6558099991093[/C][C]14.3441900008907[/C][/ROW]
[ROW][C]21[/C][C]57[/C][C]57.9220785043564[/C][C]-0.922078504356406[/C][/ROW]
[ROW][C]22[/C][C]52[/C][C]54.2020327938655[/C][C]-2.20203279386551[/C][/ROW]
[ROW][C]23[/C][C]70[/C][C]48.4225926739281[/C][C]21.5774073260719[/C][/ROW]
[ROW][C]24[/C][C]90[/C][C]82.1949899915244[/C][C]7.80501000847562[/C][/ROW]
[ROW][C]25[/C][C]74[/C][C]88.3508982697864[/C][C]-14.3508982697864[/C][/ROW]
[ROW][C]26[/C][C]62[/C][C]88.2956449523492[/C][C]-26.2956449523492[/C][/ROW]
[ROW][C]27[/C][C]55[/C][C]75.7772215610825[/C][C]-20.7772215610825[/C][/ROW]
[ROW][C]28[/C][C]84[/C][C]31.8703881295745[/C][C]52.1296118704255[/C][/ROW]
[ROW][C]29[/C][C]94[/C][C]68.8192488753996[/C][C]25.1807511246004[/C][/ROW]
[ROW][C]30[/C][C]70[/C][C]89.6563095245492[/C][C]-19.6563095245492[/C][/ROW]
[ROW][C]31[/C][C]108[/C][C]89.0401823195021[/C][C]18.9598176804979[/C][/ROW]
[ROW][C]32[/C][C]139[/C][C]92.7963892707937[/C][C]46.2036107292063[/C][/ROW]
[ROW][C]33[/C][C]120[/C][C]122.925598790003[/C][C]-2.92559879000314[/C][/ROW]
[ROW][C]34[/C][C]97[/C][C]117.912456798865[/C][C]-20.9124567988647[/C][/ROW]
[ROW][C]35[/C][C]126[/C][C]102.875020425461[/C][C]23.1249795745388[/C][/ROW]
[ROW][C]36[/C][C]149[/C][C]136.456548020255[/C][C]12.5434519797453[/C][/ROW]
[ROW][C]37[/C][C]158[/C][C]143.648053466898[/C][C]14.3519465331021[/C][/ROW]
[ROW][C]38[/C][C]124[/C][C]159.837719074198[/C][C]-35.8377190741984[/C][/ROW]
[ROW][C]39[/C][C]140[/C][C]142.064882144718[/C][C]-2.06488214471773[/C][/ROW]
[ROW][C]40[/C][C]109[/C][C]115.371228310816[/C][C]-6.37122831081633[/C][/ROW]
[ROW][C]41[/C][C]114[/C][C]115.044688453576[/C][C]-1.04468845357644[/C][/ROW]
[ROW][C]42[/C][C]77[/C][C]116.486381579579[/C][C]-39.4863815795786[/C][/ROW]
[ROW][C]43[/C][C]120[/C][C]107.148177210221[/C][C]12.8518227897786[/C][/ROW]
[ROW][C]44[/C][C]133[/C][C]109.476030577751[/C][C]23.5239694222494[/C][/ROW]
[ROW][C]45[/C][C]110[/C][C]121.976442768546[/C][C]-11.9764427685463[/C][/ROW]
[ROW][C]46[/C][C]92[/C][C]110.057460400238[/C][C]-18.0574604002376[/C][/ROW]
[ROW][C]47[/C][C]97[/C][C]100.337846662489[/C][C]-3.33784666248906[/C][/ROW]
[ROW][C]48[/C][C]78[/C][C]117.17777509757[/C][C]-39.1777750975702[/C][/ROW]
[ROW][C]49[/C][C]99[/C][C]93.4920209941245[/C][C]5.50797900587554[/C][/ROW]
[ROW][C]50[/C][C]107[/C][C]100.246879108661[/C][C]6.75312089133931[/C][/ROW]
[ROW][C]51[/C][C]112[/C][C]110.767035813787[/C][C]1.23296418621307[/C][/ROW]
[ROW][C]52[/C][C]90[/C][C]85.6869361765743[/C][C]4.31306382342572[/C][/ROW]
[ROW][C]53[/C][C]98[/C][C]92.1938583068513[/C][C]5.80614169314875[/C][/ROW]
[ROW][C]54[/C][C]125[/C][C]94.5833370517589[/C][C]30.4166629482411[/C][/ROW]
[ROW][C]55[/C][C]155[/C][C]131.448987863102[/C][C]23.5510121368983[/C][/ROW]
[ROW][C]56[/C][C]190[/C][C]141.070820266843[/C][C]48.9291797331572[/C][/ROW]
[ROW][C]57[/C][C]236[/C][C]165.900525606654[/C][C]70.0994743933463[/C][/ROW]
[ROW][C]58[/C][C]189[/C][C]202.71204890462[/C][C]-13.7120489046197[/C][/ROW]
[ROW][C]59[/C][C]174[/C][C]196.825896653984[/C][C]-22.8258966539841[/C][/ROW]
[ROW][C]60[/C][C]178[/C][C]199.061873217275[/C][C]-21.0618732172751[/C][/ROW]
[ROW][C]61[/C][C]136[/C][C]189.922225967325[/C][C]-53.9222259673251[/C][/ROW]
[ROW][C]62[/C][C]161[/C][C]161.160108293423[/C][C]-0.160108293422866[/C][/ROW]
[ROW][C]63[/C][C]171[/C][C]167.093954611665[/C][C]3.90604538833495[/C][/ROW]
[ROW][C]64[/C][C]149[/C][C]143.880492466933[/C][C]5.11950753306672[/C][/ROW]
[ROW][C]65[/C][C]184[/C][C]151.004925135348[/C][C]32.9950748646522[/C][/ROW]
[ROW][C]66[/C][C]155[/C][C]171.728895239864[/C][C]-16.7288952398636[/C][/ROW]
[ROW][C]67[/C][C]276[/C][C]179.774255417402[/C][C]96.2257445825981[/C][/ROW]
[ROW][C]68[/C][C]224[/C][C]235.06826343194[/C][C]-11.0682634319398[/C][/ROW]
[ROW][C]69[/C][C]213[/C][C]225.672858153708[/C][C]-12.6728581537078[/C][/ROW]
[ROW][C]70[/C][C]279[/C][C]205.985019020106[/C][C]73.0149809798943[/C][/ROW]
[ROW][C]71[/C][C]268[/C][C]251.359653191444[/C][C]16.640346808556[/C][/ROW]
[ROW][C]72[/C][C]287[/C][C]277.419213255846[/C][C]9.58078674415367[/C][/ROW]
[ROW][C]73[/C][C]238[/C][C]283.978954219307[/C][C]-45.9789542193074[/C][/ROW]
[ROW][C]74[/C][C]213[/C][C]264.409918308727[/C][C]-51.4099183087268[/C][/ROW]
[ROW][C]75[/C][C]257[/C][C]239.96565383211[/C][C]17.0343461678896[/C][/ROW]
[ROW][C]76[/C][C]293[/C][C]224.739881827[/C][C]68.260118173[/C][/ROW]
[ROW][C]77[/C][C]212[/C][C]272.032254193127[/C][C]-60.0322541931271[/C][/ROW]
[ROW][C]78[/C][C]246[/C][C]232.917953652758[/C][C]13.0820463472418[/C][/ROW]
[ROW][C]79[/C][C]353[/C][C]268.114221667872[/C][C]84.8857783321283[/C][/ROW]
[ROW][C]80[/C][C]339[/C][C]307.828224085379[/C][C]31.1717759146207[/C][/ROW]
[ROW][C]81[/C][C]308[/C][C]323.648008876875[/C][C]-15.648008876875[/C][/ROW]
[ROW][C]82[/C][C]247[/C][C]309.223043865887[/C][C]-62.2230438658873[/C][/ROW]
[ROW][C]83[/C][C]257[/C][C]268.895059198492[/C][C]-11.8950591984917[/C][/ROW]
[ROW][C]84[/C][C]322[/C][C]277.263997244251[/C][C]44.7360027557493[/C][/ROW]
[ROW][C]85[/C][C]298[/C][C]300.347637489371[/C][C]-2.34763748937092[/C][/ROW]
[ROW][C]86[/C][C]273[/C][C]306.500820501493[/C][C]-33.5008205014928[/C][/ROW]
[ROW][C]87[/C][C]312[/C][C]298.416563564185[/C][C]13.5834364358151[/C][/ROW]
[ROW][C]88[/C][C]249[/C][C]285.332277483638[/C][C]-36.3322774836376[/C][/ROW]
[ROW][C]89[/C][C]286[/C][C]259.3931962843[/C][C]26.6068037156996[/C][/ROW]
[ROW][C]90[/C][C]279[/C][C]278.225339033695[/C][C]0.774660966304907[/C][/ROW]
[ROW][C]91[/C][C]309[/C][C]311.935716973548[/C][C]-2.93571697354838[/C][/ROW]
[ROW][C]92[/C][C]401[/C][C]294.585527624349[/C][C]106.414472375651[/C][/ROW]
[ROW][C]93[/C][C]309[/C][C]351.682403620028[/C][C]-42.6824036200276[/C][/ROW]
[ROW][C]94[/C][C]328[/C][C]317.230588644493[/C][C]10.7694113555067[/C][/ROW]
[ROW][C]95[/C][C]353[/C][C]324.80232379372[/C][C]28.1976762062799[/C][/ROW]
[ROW][C]96[/C][C]354[/C][C]361.8689349492[/C][C]-7.8689349492002[/C][/ROW]
[ROW][C]97[/C][C]327[/C][C]349.562505184392[/C][C]-22.5625051843921[/C][/ROW]
[ROW][C]98[/C][C]324[/C][C]341.047971460211[/C][C]-17.0479714602114[/C][/ROW]
[ROW][C]99[/C][C]285[/C][C]346.69688277896[/C][C]-61.6968827789595[/C][/ROW]
[ROW][C]100[/C][C]243[/C][C]284.383347293651[/C][C]-41.383347293651[/C][/ROW]
[ROW][C]101[/C][C]241[/C][C]260.57246837458[/C][C]-19.5724683745803[/C][/ROW]
[ROW][C]102[/C][C]287[/C][C]249.589508882548[/C][C]37.4104911174522[/C][/ROW]
[ROW][C]103[/C][C]355[/C][C]304.955557705735[/C][C]50.0444422942648[/C][/ROW]
[ROW][C]104[/C][C]460[/C][C]328.337676149848[/C][C]131.662323850152[/C][/ROW]
[ROW][C]105[/C][C]364[/C][C]388.354862634688[/C][C]-24.3548626346883[/C][/ROW]
[ROW][C]106[/C][C]487[/C][C]369.283249174535[/C][C]117.716750825465[/C][/ROW]
[ROW][C]107[/C][C]452[/C][C]442.429755700577[/C][C]9.57024429942271[/C][/ROW]
[ROW][C]108[/C][C]391[/C][C]465.39453635014[/C][C]-74.39453635014[/C][/ROW]
[ROW][C]109[/C][C]500[/C][C]412.01124421332[/C][C]87.9887557866799[/C][/ROW]
[ROW][C]110[/C][C]451[/C][C]470.259310974497[/C][C]-19.2593109744974[/C][/ROW]
[ROW][C]111[/C][C]375[/C][C]470.951346323523[/C][C]-95.9513463235227[/C][/ROW]
[ROW][C]112[/C][C]372[/C][C]389.790377417692[/C][C]-17.7903774176923[/C][/ROW]
[ROW][C]113[/C][C]302[/C][C]381.940655900692[/C][C]-79.9406559006916[/C][/ROW]
[ROW][C]114[/C][C]316[/C][C]339.454643045337[/C][C]-23.4546430453374[/C][/ROW]
[ROW][C]115[/C][C]398[/C][C]359.374428937741[/C][C]38.6255710622588[/C][/ROW]
[ROW][C]116[/C][C]394[/C][C]382.609601004202[/C][C]11.3903989957981[/C][/ROW]
[ROW][C]117[/C][C]431[/C][C]357.71629693175[/C][C]73.2837030682496[/C][/ROW]
[ROW][C]118[/C][C]431[/C][C]408.835669786626[/C][C]22.1643302133742[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=202960&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=202960&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
135047.79006410256412.2099358974359
145957.73686392101281.26313607898717
156361.74120546187531.25879453812473
163231.07646911829160.923530881708373
173937.25253390438471.74746609561532
184743.92285247618913.07714752381089
195357.5575124945842-4.55751249458423
206045.655809999109314.3441900008907
215757.9220785043564-0.922078504356406
225254.2020327938655-2.20203279386551
237048.422592673928121.5774073260719
249082.19498999152447.80501000847562
257488.3508982697864-14.3508982697864
266288.2956449523492-26.2956449523492
275575.7772215610825-20.7772215610825
288431.870388129574552.1296118704255
299468.819248875399625.1807511246004
307089.6563095245492-19.6563095245492
3110889.040182319502118.9598176804979
3213992.796389270793746.2036107292063
33120122.925598790003-2.92559879000314
3497117.912456798865-20.9124567988647
35126102.87502042546123.1249795745388
36149136.45654802025512.5434519797453
37158143.64805346689814.3519465331021
38124159.837719074198-35.8377190741984
39140142.064882144718-2.06488214471773
40109115.371228310816-6.37122831081633
41114115.044688453576-1.04468845357644
4277116.486381579579-39.4863815795786
43120107.14817721022112.8518227897786
44133109.47603057775123.5239694222494
45110121.976442768546-11.9764427685463
4692110.057460400238-18.0574604002376
4797100.337846662489-3.33784666248906
4878117.17777509757-39.1777750975702
499993.49202099412455.50797900587554
50107100.2468791086616.75312089133931
51112110.7670358137871.23296418621307
529085.68693617657434.31306382342572
539892.19385830685135.80614169314875
5412594.583337051758930.4166629482411
55155131.44898786310223.5510121368983
56190141.07082026684348.9291797331572
57236165.90052560665470.0994743933463
58189202.71204890462-13.7120489046197
59174196.825896653984-22.8258966539841
60178199.061873217275-21.0618732172751
61136189.922225967325-53.9222259673251
62161161.160108293423-0.160108293422866
63171167.0939546116653.90604538833495
64149143.8804924669335.11950753306672
65184151.00492513534832.9950748646522
66155171.728895239864-16.7288952398636
67276179.77425541740296.2257445825981
68224235.06826343194-11.0682634319398
69213225.672858153708-12.6728581537078
70279205.98501902010673.0149809798943
71268251.35965319144416.640346808556
72287277.4192132558469.58078674415367
73238283.978954219307-45.9789542193074
74213264.409918308727-51.4099183087268
75257239.9656538321117.0343461678896
76293224.73988182768.260118173
77212272.032254193127-60.0322541931271
78246232.91795365275813.0820463472418
79353268.11422166787284.8857783321283
80339307.82822408537931.1717759146207
81308323.648008876875-15.648008876875
82247309.223043865887-62.2230438658873
83257268.895059198492-11.8950591984917
84322277.26399724425144.7360027557493
85298300.347637489371-2.34763748937092
86273306.500820501493-33.5008205014928
87312298.41656356418513.5834364358151
88249285.332277483638-36.3322774836376
89286259.393196284326.6068037156996
90279278.2253390336950.774660966304907
91309311.935716973548-2.93571697354838
92401294.585527624349106.414472375651
93309351.682403620028-42.6824036200276
94328317.23058864449310.7694113555067
95353324.8023237937228.1976762062799
96354361.8689349492-7.8689349492002
97327349.562505184392-22.5625051843921
98324341.047971460211-17.0479714602114
99285346.69688277896-61.6968827789595
100243284.383347293651-41.383347293651
101241260.57246837458-19.5724683745803
102287249.58950888254837.4104911174522
103355304.95555770573550.0444422942648
104460328.337676149848131.662323850152
105364388.354862634688-24.3548626346883
106487369.283249174535117.716750825465
107452442.4297557005779.57024429942271
108391465.39453635014-74.39453635014
109500412.0112442133287.9887557866799
110451470.259310974497-19.2593109744974
111375470.951346323523-95.9513463235227
112372389.790377417692-17.7903774176923
113302381.940655900692-79.9406559006916
114316339.454643045337-23.4546430453374
115398359.37442893774138.6255710622588
116394382.60960100420211.3903989957981
117431357.7162969317573.2837030682496
118431408.83566978662622.1643302133742







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
119415.817223507663337.30404946927494.330397546057
120426.148482996441334.599331842472517.697634150409
121430.680888752329327.727977345672533.633800158986
122427.368903813102314.15016219359540.587645432614
123433.309207731673310.67645589332555.941959570026
124416.087348889083284.709164391925547.465533386241
125413.81474663868274.233980216831553.395513060529
126423.906532007893276.575336774466571.237727241319
127463.000333807934308.302887643476617.697779972392
128460.861045270327299.129023321563622.593067219091
129434.227585823454265.751110918384602.704060728524
130437.222263895112262.257904226483612.186623563741

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
119 & 415.817223507663 & 337.30404946927 & 494.330397546057 \tabularnewline
120 & 426.148482996441 & 334.599331842472 & 517.697634150409 \tabularnewline
121 & 430.680888752329 & 327.727977345672 & 533.633800158986 \tabularnewline
122 & 427.368903813102 & 314.15016219359 & 540.587645432614 \tabularnewline
123 & 433.309207731673 & 310.67645589332 & 555.941959570026 \tabularnewline
124 & 416.087348889083 & 284.709164391925 & 547.465533386241 \tabularnewline
125 & 413.81474663868 & 274.233980216831 & 553.395513060529 \tabularnewline
126 & 423.906532007893 & 276.575336774466 & 571.237727241319 \tabularnewline
127 & 463.000333807934 & 308.302887643476 & 617.697779972392 \tabularnewline
128 & 460.861045270327 & 299.129023321563 & 622.593067219091 \tabularnewline
129 & 434.227585823454 & 265.751110918384 & 602.704060728524 \tabularnewline
130 & 437.222263895112 & 262.257904226483 & 612.186623563741 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=202960&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]119[/C][C]415.817223507663[/C][C]337.30404946927[/C][C]494.330397546057[/C][/ROW]
[ROW][C]120[/C][C]426.148482996441[/C][C]334.599331842472[/C][C]517.697634150409[/C][/ROW]
[ROW][C]121[/C][C]430.680888752329[/C][C]327.727977345672[/C][C]533.633800158986[/C][/ROW]
[ROW][C]122[/C][C]427.368903813102[/C][C]314.15016219359[/C][C]540.587645432614[/C][/ROW]
[ROW][C]123[/C][C]433.309207731673[/C][C]310.67645589332[/C][C]555.941959570026[/C][/ROW]
[ROW][C]124[/C][C]416.087348889083[/C][C]284.709164391925[/C][C]547.465533386241[/C][/ROW]
[ROW][C]125[/C][C]413.81474663868[/C][C]274.233980216831[/C][C]553.395513060529[/C][/ROW]
[ROW][C]126[/C][C]423.906532007893[/C][C]276.575336774466[/C][C]571.237727241319[/C][/ROW]
[ROW][C]127[/C][C]463.000333807934[/C][C]308.302887643476[/C][C]617.697779972392[/C][/ROW]
[ROW][C]128[/C][C]460.861045270327[/C][C]299.129023321563[/C][C]622.593067219091[/C][/ROW]
[ROW][C]129[/C][C]434.227585823454[/C][C]265.751110918384[/C][C]602.704060728524[/C][/ROW]
[ROW][C]130[/C][C]437.222263895112[/C][C]262.257904226483[/C][C]612.186623563741[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=202960&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=202960&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
119415.817223507663337.30404946927494.330397546057
120426.148482996441334.599331842472517.697634150409
121430.680888752329327.727977345672533.633800158986
122427.368903813102314.15016219359540.587645432614
123433.309207731673310.67645589332555.941959570026
124416.087348889083284.709164391925547.465533386241
125413.81474663868274.233980216831553.395513060529
126423.906532007893276.575336774466571.237727241319
127463.000333807934308.302887643476617.697779972392
128460.861045270327299.129023321563622.593067219091
129434.227585823454265.751110918384602.704060728524
130437.222263895112262.257904226483612.186623563741



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')