Free Statistics

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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 27 Nov 2013 11:55:28 -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/2013/Nov/27/t1385571392ronsuf2j15649nf.htm/, Retrieved Mon, 29 Apr 2024 14:28:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=229061, Retrieved Mon, 29 Apr 2024 14:28:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact64
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-11-27 16:55:28] [be82f1b59bd963d0cf04f5c957f6be33] [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 time5 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 5 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=229061&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=229061&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=229061&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 time5 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.599546669114855
beta0.000254057295303989
gamma0.204732865939058

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.599546669114855 \tabularnewline
beta & 0.000254057295303989 \tabularnewline
gamma & 0.204732865939058 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=229061&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]0.599546669114855[/C][/ROW]
[ROW][C]beta[/C][C]0.000254057295303989[/C][/ROW]
[ROW][C]gamma[/C][C]0.204732865939058[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=229061&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=229061&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
alpha0.599546669114855
beta0.000254057295303989
gamma0.204732865939058







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
135047.79006410256412.20993589743588
145957.7368639210121.263136078988
156361.74120546187451.25879453812552
163231.07646911829090.923530881709127
173937.25253390438411.74746609561593
184743.92285247618833.07714752381174
195357.5575124945828-4.55751249458279
206045.655809999110514.3441900008895
215757.9220785043515-0.922078504351525
225254.2020327938641-2.20203279386408
237048.422592673928521.5774073260715
249082.19498999151667.80501000848344
257488.3508982697787-14.3508982697787
266288.2956449523528-26.2956449523528
275575.7772215610942-20.7772215610942
288431.870388129587352.1296118704127
299468.819248875384225.1807511246158
307089.6563095245326-19.6563095245326
3110889.040182319510218.9598176804898
3213992.796389270773346.2036107292267
33120122.925598789992-2.92559878999204
3497117.912456798863-20.9124567988632
35126102.87502042544823.1249795745517
36149136.45654802025412.5434519797456
37158143.64805346691214.3519465330883
38124159.83771907421-35.83771907421
39140142.064882144732-2.06488214473163
40109115.371228310759-6.37122831075924
41114115.044688453582-1.0446884535823
4277116.486381579621-39.4863815796208
43120107.14817721022512.8518227897754
44133109.47603057770923.5239694222912
45110121.976442768578-11.976442768578
4692110.057460400272-18.0574604002716
4797100.337846662451-3.33784666245091
4878117.177775097578-39.1777750975779
499993.49202099415775.5079790058423
50107100.2468791087276.75312089127283
51112110.7670358137761.23296418622445
529085.68693617651484.31306382348524
539892.19385830684165.80614169315844
5412594.583337051822830.4166629481772
55155131.44898786304423.5510121369565
56190141.07082026676748.9291797332332
57236165.90052560668870.0994743933123
58189202.712048904629-13.7120489046292
59174196.825896653929-22.8258966539286
60178199.061873217312-21.0618732173125
61136189.922225967323-53.9222259673228
62161161.160108293495-0.160108293495
63171167.0939546116713.90604538832943
64149143.8804924668815.11950753311859
65184151.00492513533632.9950748646638
66155171.728895239889-16.7288952398893
67276179.77425541736396.2257445826367
68224235.068263431824-11.0682634318237
69213225.672858153722-12.6728581537218
70279205.98501902021573.0149809797847
71268251.35965319140916.6403468085908
72287277.4192132558689.5807867441315
73238283.978954219321-45.9789542193208
74213264.40991830875-51.4099183087499
75257239.96565383211917.0343461678812
76293224.73988182694968.2601181730512
77212272.032254193065-60.032254193065
78246232.91795365284113.0820463471587
79353268.11422166775184.8857783322491
80339307.82822408533731.1717759146632
81308323.648008876894-15.6480088768942
82247309.223043865918-62.2230438659178
83257268.895059198539-11.8950591985392
84322277.26399724431844.7360027556817
85298300.347637489439-2.34763748943891
86273306.500820501525-33.5008205015253
87312298.41656356413113.5834364358686
88249285.332277483523-36.3322774835232
89286259.39319628436726.6068037156325
90279278.225339033720.774660966279669
91309311.935716973363-2.93571697336267
92401294.585527624356106.414472375644
93309351.682403620074-42.6824036200738
94328317.23058864458510.7694113554147
95353324.80232379371928.1976762062812
96354361.868934949182-7.86893494918195
97327349.562505184488-22.5625051844882
98324341.047971460294-17.0479714602938
99285346.696882778886-61.6968827788856
100243284.383347293607-41.3833472936065
101241260.572468374607-19.5724683746066
102287249.589508882637.4104911173997
103355304.95555770556650.0444422944335
104460328.337676149729131.662323850271
105364388.354862634803-24.3548626348034
106487369.283249174597117.716750825403
107452442.4297557005169.5702442994837
108391465.39453635014-74.3945363501397
109500412.01124421345487.9887557865464
110451470.25931097455-19.25931097455
111375470.951346323492-95.9513463234917
112372389.790377417659-17.7903774176593
113302381.94065590069-79.9406559006899
114316339.454643045351-23.4546430453505
115398359.37442893758838.6255710624122
116394382.60960100401711.3903989959832
117431357.71629693200473.2837030679958
118431408.83566978658422.1643302134156

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 50 & 47.7900641025641 & 2.20993589743588 \tabularnewline
14 & 59 & 57.736863921012 & 1.263136078988 \tabularnewline
15 & 63 & 61.7412054618745 & 1.25879453812552 \tabularnewline
16 & 32 & 31.0764691182909 & 0.923530881709127 \tabularnewline
17 & 39 & 37.2525339043841 & 1.74746609561593 \tabularnewline
18 & 47 & 43.9228524761883 & 3.07714752381174 \tabularnewline
19 & 53 & 57.5575124945828 & -4.55751249458279 \tabularnewline
20 & 60 & 45.6558099991105 & 14.3441900008895 \tabularnewline
21 & 57 & 57.9220785043515 & -0.922078504351525 \tabularnewline
22 & 52 & 54.2020327938641 & -2.20203279386408 \tabularnewline
23 & 70 & 48.4225926739285 & 21.5774073260715 \tabularnewline
24 & 90 & 82.1949899915166 & 7.80501000848344 \tabularnewline
25 & 74 & 88.3508982697787 & -14.3508982697787 \tabularnewline
26 & 62 & 88.2956449523528 & -26.2956449523528 \tabularnewline
27 & 55 & 75.7772215610942 & -20.7772215610942 \tabularnewline
28 & 84 & 31.8703881295873 & 52.1296118704127 \tabularnewline
29 & 94 & 68.8192488753842 & 25.1807511246158 \tabularnewline
30 & 70 & 89.6563095245326 & -19.6563095245326 \tabularnewline
31 & 108 & 89.0401823195102 & 18.9598176804898 \tabularnewline
32 & 139 & 92.7963892707733 & 46.2036107292267 \tabularnewline
33 & 120 & 122.925598789992 & -2.92559878999204 \tabularnewline
34 & 97 & 117.912456798863 & -20.9124567988632 \tabularnewline
35 & 126 & 102.875020425448 & 23.1249795745517 \tabularnewline
36 & 149 & 136.456548020254 & 12.5434519797456 \tabularnewline
37 & 158 & 143.648053466912 & 14.3519465330883 \tabularnewline
38 & 124 & 159.83771907421 & -35.83771907421 \tabularnewline
39 & 140 & 142.064882144732 & -2.06488214473163 \tabularnewline
40 & 109 & 115.371228310759 & -6.37122831075924 \tabularnewline
41 & 114 & 115.044688453582 & -1.0446884535823 \tabularnewline
42 & 77 & 116.486381579621 & -39.4863815796208 \tabularnewline
43 & 120 & 107.148177210225 & 12.8518227897754 \tabularnewline
44 & 133 & 109.476030577709 & 23.5239694222912 \tabularnewline
45 & 110 & 121.976442768578 & -11.976442768578 \tabularnewline
46 & 92 & 110.057460400272 & -18.0574604002716 \tabularnewline
47 & 97 & 100.337846662451 & -3.33784666245091 \tabularnewline
48 & 78 & 117.177775097578 & -39.1777750975779 \tabularnewline
49 & 99 & 93.4920209941577 & 5.5079790058423 \tabularnewline
50 & 107 & 100.246879108727 & 6.75312089127283 \tabularnewline
51 & 112 & 110.767035813776 & 1.23296418622445 \tabularnewline
52 & 90 & 85.6869361765148 & 4.31306382348524 \tabularnewline
53 & 98 & 92.1938583068416 & 5.80614169315844 \tabularnewline
54 & 125 & 94.5833370518228 & 30.4166629481772 \tabularnewline
55 & 155 & 131.448987863044 & 23.5510121369565 \tabularnewline
56 & 190 & 141.070820266767 & 48.9291797332332 \tabularnewline
57 & 236 & 165.900525606688 & 70.0994743933123 \tabularnewline
58 & 189 & 202.712048904629 & -13.7120489046292 \tabularnewline
59 & 174 & 196.825896653929 & -22.8258966539286 \tabularnewline
60 & 178 & 199.061873217312 & -21.0618732173125 \tabularnewline
61 & 136 & 189.922225967323 & -53.9222259673228 \tabularnewline
62 & 161 & 161.160108293495 & -0.160108293495 \tabularnewline
63 & 171 & 167.093954611671 & 3.90604538832943 \tabularnewline
64 & 149 & 143.880492466881 & 5.11950753311859 \tabularnewline
65 & 184 & 151.004925135336 & 32.9950748646638 \tabularnewline
66 & 155 & 171.728895239889 & -16.7288952398893 \tabularnewline
67 & 276 & 179.774255417363 & 96.2257445826367 \tabularnewline
68 & 224 & 235.068263431824 & -11.0682634318237 \tabularnewline
69 & 213 & 225.672858153722 & -12.6728581537218 \tabularnewline
70 & 279 & 205.985019020215 & 73.0149809797847 \tabularnewline
71 & 268 & 251.359653191409 & 16.6403468085908 \tabularnewline
72 & 287 & 277.419213255868 & 9.5807867441315 \tabularnewline
73 & 238 & 283.978954219321 & -45.9789542193208 \tabularnewline
74 & 213 & 264.40991830875 & -51.4099183087499 \tabularnewline
75 & 257 & 239.965653832119 & 17.0343461678812 \tabularnewline
76 & 293 & 224.739881826949 & 68.2601181730512 \tabularnewline
77 & 212 & 272.032254193065 & -60.032254193065 \tabularnewline
78 & 246 & 232.917953652841 & 13.0820463471587 \tabularnewline
79 & 353 & 268.114221667751 & 84.8857783322491 \tabularnewline
80 & 339 & 307.828224085337 & 31.1717759146632 \tabularnewline
81 & 308 & 323.648008876894 & -15.6480088768942 \tabularnewline
82 & 247 & 309.223043865918 & -62.2230438659178 \tabularnewline
83 & 257 & 268.895059198539 & -11.8950591985392 \tabularnewline
84 & 322 & 277.263997244318 & 44.7360027556817 \tabularnewline
85 & 298 & 300.347637489439 & -2.34763748943891 \tabularnewline
86 & 273 & 306.500820501525 & -33.5008205015253 \tabularnewline
87 & 312 & 298.416563564131 & 13.5834364358686 \tabularnewline
88 & 249 & 285.332277483523 & -36.3322774835232 \tabularnewline
89 & 286 & 259.393196284367 & 26.6068037156325 \tabularnewline
90 & 279 & 278.22533903372 & 0.774660966279669 \tabularnewline
91 & 309 & 311.935716973363 & -2.93571697336267 \tabularnewline
92 & 401 & 294.585527624356 & 106.414472375644 \tabularnewline
93 & 309 & 351.682403620074 & -42.6824036200738 \tabularnewline
94 & 328 & 317.230588644585 & 10.7694113554147 \tabularnewline
95 & 353 & 324.802323793719 & 28.1976762062812 \tabularnewline
96 & 354 & 361.868934949182 & -7.86893494918195 \tabularnewline
97 & 327 & 349.562505184488 & -22.5625051844882 \tabularnewline
98 & 324 & 341.047971460294 & -17.0479714602938 \tabularnewline
99 & 285 & 346.696882778886 & -61.6968827788856 \tabularnewline
100 & 243 & 284.383347293607 & -41.3833472936065 \tabularnewline
101 & 241 & 260.572468374607 & -19.5724683746066 \tabularnewline
102 & 287 & 249.5895088826 & 37.4104911173997 \tabularnewline
103 & 355 & 304.955557705566 & 50.0444422944335 \tabularnewline
104 & 460 & 328.337676149729 & 131.662323850271 \tabularnewline
105 & 364 & 388.354862634803 & -24.3548626348034 \tabularnewline
106 & 487 & 369.283249174597 & 117.716750825403 \tabularnewline
107 & 452 & 442.429755700516 & 9.5702442994837 \tabularnewline
108 & 391 & 465.39453635014 & -74.3945363501397 \tabularnewline
109 & 500 & 412.011244213454 & 87.9887557865464 \tabularnewline
110 & 451 & 470.25931097455 & -19.25931097455 \tabularnewline
111 & 375 & 470.951346323492 & -95.9513463234917 \tabularnewline
112 & 372 & 389.790377417659 & -17.7903774176593 \tabularnewline
113 & 302 & 381.94065590069 & -79.9406559006899 \tabularnewline
114 & 316 & 339.454643045351 & -23.4546430453505 \tabularnewline
115 & 398 & 359.374428937588 & 38.6255710624122 \tabularnewline
116 & 394 & 382.609601004017 & 11.3903989959832 \tabularnewline
117 & 431 & 357.716296932004 & 73.2837030679958 \tabularnewline
118 & 431 & 408.835669786584 & 22.1643302134156 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=229061&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]2.20993589743588[/C][/ROW]
[ROW][C]14[/C][C]59[/C][C]57.736863921012[/C][C]1.263136078988[/C][/ROW]
[ROW][C]15[/C][C]63[/C][C]61.7412054618745[/C][C]1.25879453812552[/C][/ROW]
[ROW][C]16[/C][C]32[/C][C]31.0764691182909[/C][C]0.923530881709127[/C][/ROW]
[ROW][C]17[/C][C]39[/C][C]37.2525339043841[/C][C]1.74746609561593[/C][/ROW]
[ROW][C]18[/C][C]47[/C][C]43.9228524761883[/C][C]3.07714752381174[/C][/ROW]
[ROW][C]19[/C][C]53[/C][C]57.5575124945828[/C][C]-4.55751249458279[/C][/ROW]
[ROW][C]20[/C][C]60[/C][C]45.6558099991105[/C][C]14.3441900008895[/C][/ROW]
[ROW][C]21[/C][C]57[/C][C]57.9220785043515[/C][C]-0.922078504351525[/C][/ROW]
[ROW][C]22[/C][C]52[/C][C]54.2020327938641[/C][C]-2.20203279386408[/C][/ROW]
[ROW][C]23[/C][C]70[/C][C]48.4225926739285[/C][C]21.5774073260715[/C][/ROW]
[ROW][C]24[/C][C]90[/C][C]82.1949899915166[/C][C]7.80501000848344[/C][/ROW]
[ROW][C]25[/C][C]74[/C][C]88.3508982697787[/C][C]-14.3508982697787[/C][/ROW]
[ROW][C]26[/C][C]62[/C][C]88.2956449523528[/C][C]-26.2956449523528[/C][/ROW]
[ROW][C]27[/C][C]55[/C][C]75.7772215610942[/C][C]-20.7772215610942[/C][/ROW]
[ROW][C]28[/C][C]84[/C][C]31.8703881295873[/C][C]52.1296118704127[/C][/ROW]
[ROW][C]29[/C][C]94[/C][C]68.8192488753842[/C][C]25.1807511246158[/C][/ROW]
[ROW][C]30[/C][C]70[/C][C]89.6563095245326[/C][C]-19.6563095245326[/C][/ROW]
[ROW][C]31[/C][C]108[/C][C]89.0401823195102[/C][C]18.9598176804898[/C][/ROW]
[ROW][C]32[/C][C]139[/C][C]92.7963892707733[/C][C]46.2036107292267[/C][/ROW]
[ROW][C]33[/C][C]120[/C][C]122.925598789992[/C][C]-2.92559878999204[/C][/ROW]
[ROW][C]34[/C][C]97[/C][C]117.912456798863[/C][C]-20.9124567988632[/C][/ROW]
[ROW][C]35[/C][C]126[/C][C]102.875020425448[/C][C]23.1249795745517[/C][/ROW]
[ROW][C]36[/C][C]149[/C][C]136.456548020254[/C][C]12.5434519797456[/C][/ROW]
[ROW][C]37[/C][C]158[/C][C]143.648053466912[/C][C]14.3519465330883[/C][/ROW]
[ROW][C]38[/C][C]124[/C][C]159.83771907421[/C][C]-35.83771907421[/C][/ROW]
[ROW][C]39[/C][C]140[/C][C]142.064882144732[/C][C]-2.06488214473163[/C][/ROW]
[ROW][C]40[/C][C]109[/C][C]115.371228310759[/C][C]-6.37122831075924[/C][/ROW]
[ROW][C]41[/C][C]114[/C][C]115.044688453582[/C][C]-1.0446884535823[/C][/ROW]
[ROW][C]42[/C][C]77[/C][C]116.486381579621[/C][C]-39.4863815796208[/C][/ROW]
[ROW][C]43[/C][C]120[/C][C]107.148177210225[/C][C]12.8518227897754[/C][/ROW]
[ROW][C]44[/C][C]133[/C][C]109.476030577709[/C][C]23.5239694222912[/C][/ROW]
[ROW][C]45[/C][C]110[/C][C]121.976442768578[/C][C]-11.976442768578[/C][/ROW]
[ROW][C]46[/C][C]92[/C][C]110.057460400272[/C][C]-18.0574604002716[/C][/ROW]
[ROW][C]47[/C][C]97[/C][C]100.337846662451[/C][C]-3.33784666245091[/C][/ROW]
[ROW][C]48[/C][C]78[/C][C]117.177775097578[/C][C]-39.1777750975779[/C][/ROW]
[ROW][C]49[/C][C]99[/C][C]93.4920209941577[/C][C]5.5079790058423[/C][/ROW]
[ROW][C]50[/C][C]107[/C][C]100.246879108727[/C][C]6.75312089127283[/C][/ROW]
[ROW][C]51[/C][C]112[/C][C]110.767035813776[/C][C]1.23296418622445[/C][/ROW]
[ROW][C]52[/C][C]90[/C][C]85.6869361765148[/C][C]4.31306382348524[/C][/ROW]
[ROW][C]53[/C][C]98[/C][C]92.1938583068416[/C][C]5.80614169315844[/C][/ROW]
[ROW][C]54[/C][C]125[/C][C]94.5833370518228[/C][C]30.4166629481772[/C][/ROW]
[ROW][C]55[/C][C]155[/C][C]131.448987863044[/C][C]23.5510121369565[/C][/ROW]
[ROW][C]56[/C][C]190[/C][C]141.070820266767[/C][C]48.9291797332332[/C][/ROW]
[ROW][C]57[/C][C]236[/C][C]165.900525606688[/C][C]70.0994743933123[/C][/ROW]
[ROW][C]58[/C][C]189[/C][C]202.712048904629[/C][C]-13.7120489046292[/C][/ROW]
[ROW][C]59[/C][C]174[/C][C]196.825896653929[/C][C]-22.8258966539286[/C][/ROW]
[ROW][C]60[/C][C]178[/C][C]199.061873217312[/C][C]-21.0618732173125[/C][/ROW]
[ROW][C]61[/C][C]136[/C][C]189.922225967323[/C][C]-53.9222259673228[/C][/ROW]
[ROW][C]62[/C][C]161[/C][C]161.160108293495[/C][C]-0.160108293495[/C][/ROW]
[ROW][C]63[/C][C]171[/C][C]167.093954611671[/C][C]3.90604538832943[/C][/ROW]
[ROW][C]64[/C][C]149[/C][C]143.880492466881[/C][C]5.11950753311859[/C][/ROW]
[ROW][C]65[/C][C]184[/C][C]151.004925135336[/C][C]32.9950748646638[/C][/ROW]
[ROW][C]66[/C][C]155[/C][C]171.728895239889[/C][C]-16.7288952398893[/C][/ROW]
[ROW][C]67[/C][C]276[/C][C]179.774255417363[/C][C]96.2257445826367[/C][/ROW]
[ROW][C]68[/C][C]224[/C][C]235.068263431824[/C][C]-11.0682634318237[/C][/ROW]
[ROW][C]69[/C][C]213[/C][C]225.672858153722[/C][C]-12.6728581537218[/C][/ROW]
[ROW][C]70[/C][C]279[/C][C]205.985019020215[/C][C]73.0149809797847[/C][/ROW]
[ROW][C]71[/C][C]268[/C][C]251.359653191409[/C][C]16.6403468085908[/C][/ROW]
[ROW][C]72[/C][C]287[/C][C]277.419213255868[/C][C]9.5807867441315[/C][/ROW]
[ROW][C]73[/C][C]238[/C][C]283.978954219321[/C][C]-45.9789542193208[/C][/ROW]
[ROW][C]74[/C][C]213[/C][C]264.40991830875[/C][C]-51.4099183087499[/C][/ROW]
[ROW][C]75[/C][C]257[/C][C]239.965653832119[/C][C]17.0343461678812[/C][/ROW]
[ROW][C]76[/C][C]293[/C][C]224.739881826949[/C][C]68.2601181730512[/C][/ROW]
[ROW][C]77[/C][C]212[/C][C]272.032254193065[/C][C]-60.032254193065[/C][/ROW]
[ROW][C]78[/C][C]246[/C][C]232.917953652841[/C][C]13.0820463471587[/C][/ROW]
[ROW][C]79[/C][C]353[/C][C]268.114221667751[/C][C]84.8857783322491[/C][/ROW]
[ROW][C]80[/C][C]339[/C][C]307.828224085337[/C][C]31.1717759146632[/C][/ROW]
[ROW][C]81[/C][C]308[/C][C]323.648008876894[/C][C]-15.6480088768942[/C][/ROW]
[ROW][C]82[/C][C]247[/C][C]309.223043865918[/C][C]-62.2230438659178[/C][/ROW]
[ROW][C]83[/C][C]257[/C][C]268.895059198539[/C][C]-11.8950591985392[/C][/ROW]
[ROW][C]84[/C][C]322[/C][C]277.263997244318[/C][C]44.7360027556817[/C][/ROW]
[ROW][C]85[/C][C]298[/C][C]300.347637489439[/C][C]-2.34763748943891[/C][/ROW]
[ROW][C]86[/C][C]273[/C][C]306.500820501525[/C][C]-33.5008205015253[/C][/ROW]
[ROW][C]87[/C][C]312[/C][C]298.416563564131[/C][C]13.5834364358686[/C][/ROW]
[ROW][C]88[/C][C]249[/C][C]285.332277483523[/C][C]-36.3322774835232[/C][/ROW]
[ROW][C]89[/C][C]286[/C][C]259.393196284367[/C][C]26.6068037156325[/C][/ROW]
[ROW][C]90[/C][C]279[/C][C]278.22533903372[/C][C]0.774660966279669[/C][/ROW]
[ROW][C]91[/C][C]309[/C][C]311.935716973363[/C][C]-2.93571697336267[/C][/ROW]
[ROW][C]92[/C][C]401[/C][C]294.585527624356[/C][C]106.414472375644[/C][/ROW]
[ROW][C]93[/C][C]309[/C][C]351.682403620074[/C][C]-42.6824036200738[/C][/ROW]
[ROW][C]94[/C][C]328[/C][C]317.230588644585[/C][C]10.7694113554147[/C][/ROW]
[ROW][C]95[/C][C]353[/C][C]324.802323793719[/C][C]28.1976762062812[/C][/ROW]
[ROW][C]96[/C][C]354[/C][C]361.868934949182[/C][C]-7.86893494918195[/C][/ROW]
[ROW][C]97[/C][C]327[/C][C]349.562505184488[/C][C]-22.5625051844882[/C][/ROW]
[ROW][C]98[/C][C]324[/C][C]341.047971460294[/C][C]-17.0479714602938[/C][/ROW]
[ROW][C]99[/C][C]285[/C][C]346.696882778886[/C][C]-61.6968827788856[/C][/ROW]
[ROW][C]100[/C][C]243[/C][C]284.383347293607[/C][C]-41.3833472936065[/C][/ROW]
[ROW][C]101[/C][C]241[/C][C]260.572468374607[/C][C]-19.5724683746066[/C][/ROW]
[ROW][C]102[/C][C]287[/C][C]249.5895088826[/C][C]37.4104911173997[/C][/ROW]
[ROW][C]103[/C][C]355[/C][C]304.955557705566[/C][C]50.0444422944335[/C][/ROW]
[ROW][C]104[/C][C]460[/C][C]328.337676149729[/C][C]131.662323850271[/C][/ROW]
[ROW][C]105[/C][C]364[/C][C]388.354862634803[/C][C]-24.3548626348034[/C][/ROW]
[ROW][C]106[/C][C]487[/C][C]369.283249174597[/C][C]117.716750825403[/C][/ROW]
[ROW][C]107[/C][C]452[/C][C]442.429755700516[/C][C]9.5702442994837[/C][/ROW]
[ROW][C]108[/C][C]391[/C][C]465.39453635014[/C][C]-74.3945363501397[/C][/ROW]
[ROW][C]109[/C][C]500[/C][C]412.011244213454[/C][C]87.9887557865464[/C][/ROW]
[ROW][C]110[/C][C]451[/C][C]470.25931097455[/C][C]-19.25931097455[/C][/ROW]
[ROW][C]111[/C][C]375[/C][C]470.951346323492[/C][C]-95.9513463234917[/C][/ROW]
[ROW][C]112[/C][C]372[/C][C]389.790377417659[/C][C]-17.7903774176593[/C][/ROW]
[ROW][C]113[/C][C]302[/C][C]381.94065590069[/C][C]-79.9406559006899[/C][/ROW]
[ROW][C]114[/C][C]316[/C][C]339.454643045351[/C][C]-23.4546430453505[/C][/ROW]
[ROW][C]115[/C][C]398[/C][C]359.374428937588[/C][C]38.6255710624122[/C][/ROW]
[ROW][C]116[/C][C]394[/C][C]382.609601004017[/C][C]11.3903989959832[/C][/ROW]
[ROW][C]117[/C][C]431[/C][C]357.716296932004[/C][C]73.2837030679958[/C][/ROW]
[ROW][C]118[/C][C]431[/C][C]408.835669786584[/C][C]22.1643302134156[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=229061&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=229061&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
135047.79006410256412.20993589743588
145957.7368639210121.263136078988
156361.74120546187451.25879453812552
163231.07646911829090.923530881709127
173937.25253390438411.74746609561593
184743.92285247618833.07714752381174
195357.5575124945828-4.55751249458279
206045.655809999110514.3441900008895
215757.9220785043515-0.922078504351525
225254.2020327938641-2.20203279386408
237048.422592673928521.5774073260715
249082.19498999151667.80501000848344
257488.3508982697787-14.3508982697787
266288.2956449523528-26.2956449523528
275575.7772215610942-20.7772215610942
288431.870388129587352.1296118704127
299468.819248875384225.1807511246158
307089.6563095245326-19.6563095245326
3110889.040182319510218.9598176804898
3213992.796389270773346.2036107292267
33120122.925598789992-2.92559878999204
3497117.912456798863-20.9124567988632
35126102.87502042544823.1249795745517
36149136.45654802025412.5434519797456
37158143.64805346691214.3519465330883
38124159.83771907421-35.83771907421
39140142.064882144732-2.06488214473163
40109115.371228310759-6.37122831075924
41114115.044688453582-1.0446884535823
4277116.486381579621-39.4863815796208
43120107.14817721022512.8518227897754
44133109.47603057770923.5239694222912
45110121.976442768578-11.976442768578
4692110.057460400272-18.0574604002716
4797100.337846662451-3.33784666245091
4878117.177775097578-39.1777750975779
499993.49202099415775.5079790058423
50107100.2468791087276.75312089127283
51112110.7670358137761.23296418622445
529085.68693617651484.31306382348524
539892.19385830684165.80614169315844
5412594.583337051822830.4166629481772
55155131.44898786304423.5510121369565
56190141.07082026676748.9291797332332
57236165.90052560668870.0994743933123
58189202.712048904629-13.7120489046292
59174196.825896653929-22.8258966539286
60178199.061873217312-21.0618732173125
61136189.922225967323-53.9222259673228
62161161.160108293495-0.160108293495
63171167.0939546116713.90604538832943
64149143.8804924668815.11950753311859
65184151.00492513533632.9950748646638
66155171.728895239889-16.7288952398893
67276179.77425541736396.2257445826367
68224235.068263431824-11.0682634318237
69213225.672858153722-12.6728581537218
70279205.98501902021573.0149809797847
71268251.35965319140916.6403468085908
72287277.4192132558689.5807867441315
73238283.978954219321-45.9789542193208
74213264.40991830875-51.4099183087499
75257239.96565383211917.0343461678812
76293224.73988182694968.2601181730512
77212272.032254193065-60.032254193065
78246232.91795365284113.0820463471587
79353268.11422166775184.8857783322491
80339307.82822408533731.1717759146632
81308323.648008876894-15.6480088768942
82247309.223043865918-62.2230438659178
83257268.895059198539-11.8950591985392
84322277.26399724431844.7360027556817
85298300.347637489439-2.34763748943891
86273306.500820501525-33.5008205015253
87312298.41656356413113.5834364358686
88249285.332277483523-36.3322774835232
89286259.39319628436726.6068037156325
90279278.225339033720.774660966279669
91309311.935716973363-2.93571697336267
92401294.585527624356106.414472375644
93309351.682403620074-42.6824036200738
94328317.23058864458510.7694113554147
95353324.80232379371928.1976762062812
96354361.868934949182-7.86893494918195
97327349.562505184488-22.5625051844882
98324341.047971460294-17.0479714602938
99285346.696882778886-61.6968827788856
100243284.383347293607-41.3833472936065
101241260.572468374607-19.5724683746066
102287249.589508882637.4104911173997
103355304.95555770556650.0444422944335
104460328.337676149729131.662323850271
105364388.354862634803-24.3548626348034
106487369.283249174597117.716750825403
107452442.4297557005169.5702442994837
108391465.39453635014-74.3945363501397
109500412.01124421345487.9887557865464
110451470.25931097455-19.25931097455
111375470.951346323492-95.9513463234917
112372389.790377417659-17.7903774176593
113302381.94065590069-79.9406559006899
114316339.454643045351-23.4546430453505
115398359.37442893758838.6255710624122
116394382.60960100401711.3903989959832
117431357.71629693200473.2837030679958
118431408.83566978658422.1643302134156







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
119415.817223507703337.30404946931494.330397546096
120426.148482996577334.599331842624517.69763415053
121430.680888752416327.727977345786533.633800159046
122427.368903813322314.150162193847540.587645432797
123433.309207731908310.676455893599555.941959570217
124416.087348889191284.709164392085547.465533386298
125413.814746638846274.233980217054553.395513060638
126423.906532007991276.575336774627571.237727241355
127463.000333807825308.302887643434617.697779972216
128460.861045270137299.129023321444622.59306721883
129434.227585823507265.751110918511602.704060728502
130437.222263895119262.257904226568612.18662356367

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
119 & 415.817223507703 & 337.30404946931 & 494.330397546096 \tabularnewline
120 & 426.148482996577 & 334.599331842624 & 517.69763415053 \tabularnewline
121 & 430.680888752416 & 327.727977345786 & 533.633800159046 \tabularnewline
122 & 427.368903813322 & 314.150162193847 & 540.587645432797 \tabularnewline
123 & 433.309207731908 & 310.676455893599 & 555.941959570217 \tabularnewline
124 & 416.087348889191 & 284.709164392085 & 547.465533386298 \tabularnewline
125 & 413.814746638846 & 274.233980217054 & 553.395513060638 \tabularnewline
126 & 423.906532007991 & 276.575336774627 & 571.237727241355 \tabularnewline
127 & 463.000333807825 & 308.302887643434 & 617.697779972216 \tabularnewline
128 & 460.861045270137 & 299.129023321444 & 622.59306721883 \tabularnewline
129 & 434.227585823507 & 265.751110918511 & 602.704060728502 \tabularnewline
130 & 437.222263895119 & 262.257904226568 & 612.18662356367 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=229061&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]415.817223507703[/C][C]337.30404946931[/C][C]494.330397546096[/C][/ROW]
[ROW][C]120[/C][C]426.148482996577[/C][C]334.599331842624[/C][C]517.69763415053[/C][/ROW]
[ROW][C]121[/C][C]430.680888752416[/C][C]327.727977345786[/C][C]533.633800159046[/C][/ROW]
[ROW][C]122[/C][C]427.368903813322[/C][C]314.150162193847[/C][C]540.587645432797[/C][/ROW]
[ROW][C]123[/C][C]433.309207731908[/C][C]310.676455893599[/C][C]555.941959570217[/C][/ROW]
[ROW][C]124[/C][C]416.087348889191[/C][C]284.709164392085[/C][C]547.465533386298[/C][/ROW]
[ROW][C]125[/C][C]413.814746638846[/C][C]274.233980217054[/C][C]553.395513060638[/C][/ROW]
[ROW][C]126[/C][C]423.906532007991[/C][C]276.575336774627[/C][C]571.237727241355[/C][/ROW]
[ROW][C]127[/C][C]463.000333807825[/C][C]308.302887643434[/C][C]617.697779972216[/C][/ROW]
[ROW][C]128[/C][C]460.861045270137[/C][C]299.129023321444[/C][C]622.59306721883[/C][/ROW]
[ROW][C]129[/C][C]434.227585823507[/C][C]265.751110918511[/C][C]602.704060728502[/C][/ROW]
[ROW][C]130[/C][C]437.222263895119[/C][C]262.257904226568[/C][C]612.18662356367[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=229061&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=229061&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
119415.817223507703337.30404946931494.330397546096
120426.148482996577334.599331842624517.69763415053
121430.680888752416327.727977345786533.633800159046
122427.368903813322314.150162193847540.587645432797
123433.309207731908310.676455893599555.941959570217
124416.087348889191284.709164392085547.465533386298
125413.814746638846274.233980217054553.395513060638
126423.906532007991276.575336774627571.237727241355
127463.000333807825308.302887643434617.697779972216
128460.861045270137299.129023321444622.59306721883
129434.227585823507265.751110918511602.704060728502
130437.222263895119262.257904226568612.18662356367



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):
par3 <- 'additive'
par2 <- 'Double'
par1 <- '12'
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')