Free Statistics

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 computationTue, 27 Nov 2012 16:03:36 -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/Nov/27/t1354050238qjzw379ucfpt0m2.htm/, Retrieved Sat, 04 May 2024 17:15:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=194039, Retrieved Sat, 04 May 2024 17:15:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact83
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Workshop 8 - Trip...] [2012-11-27 21:03:36] [729cfeb7382ca95684eaaf6b24800101] [Current]
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Dataseries X:
178421
139871
118159
109763
97415
119190
97903
96953
87888
84637
90549
95680
99371
79984
86752
85733
84906
78356
108895
101768
73285
65724
67457
67203
69273
80807
75129
74991
68157
73858
71349
85634
91624
116014
120033
108651
105378
138939
132974
135277
152741
158417
157460
193997
154089
147570
162924
153629
155907
197675
250708
266652
209842
165826
137152
150581
145973
126532
115437
119526
110856
97243
103876
116370
109616
98365
90440
88899
92358
88394
98219
113546
107168
77540
74944
75641
75910
87384
84615
80420
80784
79933
82118
91420
112426
114528
131025
116460
111258
155318
155078
134794
139985
198778
172436
169585
203702
282392
220658
194472
269246
215340
218319
195724
174614
172085
152347
189615
173804
145683
133550
121156
112040
120767
127019
136295
113425
107815
100298
97048
98750
98235
101254
139589
134921
80355
80396
82183
79709
90781




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=194039&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=194039&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=194039&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.769011136609184
beta0.0296873720366851
gamma0.390549194716412

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.769011136609184 \tabularnewline
beta & 0.0296873720366851 \tabularnewline
gamma & 0.390549194716412 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=194039&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]0.769011136609184[/C][/ROW]
[ROW][C]beta[/C][C]0.0296873720366851[/C][/ROW]
[ROW][C]gamma[/C][C]0.390549194716412[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=194039&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=194039&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
alpha0.769011136609184
beta0.0296873720366851
gamma0.390549194716412







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
597415114939.06875-17524.06875
6119190119870.95413994-680.954139939699
79790388839.33611185769063.66388814236
89695392815.4855882444137.51441175595
98788879971.19007080817916.80992919189
1084637106453.430060023-21816.4300600234
119054960031.536796928330517.4632030717
129568080535.339682555415144.6603174446
139937177221.73710313322149.262896867
1479984113016.642740384-33032.642740384
158675263484.525050700523267.4749492995
168573377654.66630045518078.33369954488
178490670006.038276069414899.9617239306
187835695549.7067545321-17193.7067545321
1910889563940.13869816644954.861301834
2010176894576.24851953547191.75148046463
217328587999.3620810333-14714.3620810333
226572488336.0795480143-22612.0795480143
236745758504.64439098788952.35560901221
246720357564.13029630889638.86970369119
256927350465.175950578218807.8240494218
268080776205.94025683384601.05974316619
277512971108.07846262164020.92153737835
287499167283.44368506277707.55631493729
296815760328.62540802357828.37459197655
307385876895.966071142-3037.96607114197
317134966248.39747617555100.60252382453
328563463988.403874702821645.5961252972
339162468482.970964618623141.0290353814
3411601496915.198391438619098.8016085614
35120033105600.19691884514432.8030811549
36108651113797.333851162-5146.33385116249
3710537898999.85647036356378.14352963648
38138939114970.22471983123968.7752801688
39132974127884.1828423845089.81715761573
40135277127821.7038226197455.29617738098
41152741124733.89400719528007.1059928052
42158417160397.079514203-1980.07951420313
43157460152533.5598877334926.44011226681
44193997153435.70688147140561.293118529
45154089179293.484067527-25204.4840675273
46147570171749.0047051-24179.0047051002
47162924147348.37910237515575.620897625
48153629159808.754568503-6179.75456850257
49155907142876.33520291713030.6647970829
50197675164787.6133681232887.3866318795
51250708189120.85527308861587.1447269115
52266652237315.24954605129336.7504539492
53209842252552.528967838-42710.5289678381
54165826235241.056844176-69415.056844176
55137152183007.624864595-45855.6248645947
56150581142731.000911427849.99908858034
57145973131517.67949103414455.3205089661
58126532153635.907885132-27103.9078851318
59115437134909.144639492-19472.1446394925
60119526119212.531302044313.468697956298
61110856102073.2594670258782.7405329747
6297243115224.386375359-17981.3863753588
63103876103554.028938205321.971061795033
64116370104668.72363881811701.2763611818
6510961697115.322454636612500.6775453634
6698365110860.490772412-12495.4907724119
6790440105334.648234931-14894.6482349315
688889995701.3629702353-6802.36297023534
699235873495.350453168918862.6495468311
708839489527.9995917096-1133.99959170959
719821992432.2389043655786.76109563497
7211354699814.770683956613731.2293160434
7310716896564.962434818310603.0375651817
7477540105103.701504071-27563.7015040711
757494488365.9284913644-13421.9284913644
767564181313.3052310869-5672.30523108687
777591062036.630362808613873.3696371914
788738468898.70471064618485.295289354
798461589151.7138653672-4536.7138653672
808042090136.7072410156-9716.70724101564
818078469926.447928116610857.5520718834
827993375229.86878232634703.13121767374
838211882837.2116333725-719.211633372543
849142086407.60447164625012.39552835377
8511242679833.507082822232592.4929171778
86114528102245.60286780312282.397132197
87131025116314.82561148714710.1743885127
88116460133742.405650994-17282.4056509945
89111258113477.194108475-2219.19410847528
90155318107457.50835821647860.4916417845
91155078150088.9612153244989.03878467574
92134794157916.079201261-23122.079201261
93139985135146.9951568284838.0048431718
94198778139861.31496172658916.685038274
95172436188169.100697508-15733.1006975077
96169585178093.141819743-8508.141819743
97203702169986.77669198733715.2233080129
98282392203347.92622650979044.0737734908
99220658262420.413244865-41762.4132448646
100194472234406.017811247-39934.0178112471
101269246206651.04274818462594.9572518165
102215340267678.74363625-52338.7436362501
103218319213187.149506795131.85049320967
104195724220839.527128261-25115.5271282606
105174614213507.455886746-38893.4558867462
106172085183581.929143221-11496.9291432214
107152347164076.077831701-11729.0778317013
108189615154041.95398526535573.0460147347
109173804191531.077191269-17727.0771912692
110145683180231.415115653-34548.4151156525
111133550142328.682245934-8778.68224593403
112121156138248.95688107-17092.9568810701
113112040128644.906460937-16604.9064609374
114120767114932.2373125185834.76268748246
115127019109572.84134570517446.1586542951
116136295124672.4411176111622.5588823898
117113425137612.725338574-24187.7253385741
118107815120337.762830413-12522.7628304132
119100298101734.257517769-1436.25751776878
12097048101182.16233271-4134.16233271026
1219875097809.546939741940.453060258966
12298235100519.163623299-2284.16362329907
12310125490631.547604200310622.4523957997
12413958999226.800195289340362.1998047107
125134921131663.4753518023257.52464819798
12680355137050.242381583-56695.2423815834
1278039686428.2358391541-6032.23583915412
1288218384462.5166132995-2279.51661329948
1297970979350.1954648205358.804535179457
1309078175623.411581542515157.5884184575

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
5 & 97415 & 114939.06875 & -17524.06875 \tabularnewline
6 & 119190 & 119870.95413994 & -680.954139939699 \tabularnewline
7 & 97903 & 88839.3361118576 & 9063.66388814236 \tabularnewline
8 & 96953 & 92815.485588244 & 4137.51441175595 \tabularnewline
9 & 87888 & 79971.1900708081 & 7916.80992919189 \tabularnewline
10 & 84637 & 106453.430060023 & -21816.4300600234 \tabularnewline
11 & 90549 & 60031.5367969283 & 30517.4632030717 \tabularnewline
12 & 95680 & 80535.3396825554 & 15144.6603174446 \tabularnewline
13 & 99371 & 77221.737103133 & 22149.262896867 \tabularnewline
14 & 79984 & 113016.642740384 & -33032.642740384 \tabularnewline
15 & 86752 & 63484.5250507005 & 23267.4749492995 \tabularnewline
16 & 85733 & 77654.6663004551 & 8078.33369954488 \tabularnewline
17 & 84906 & 70006.0382760694 & 14899.9617239306 \tabularnewline
18 & 78356 & 95549.7067545321 & -17193.7067545321 \tabularnewline
19 & 108895 & 63940.138698166 & 44954.861301834 \tabularnewline
20 & 101768 & 94576.2485195354 & 7191.75148046463 \tabularnewline
21 & 73285 & 87999.3620810333 & -14714.3620810333 \tabularnewline
22 & 65724 & 88336.0795480143 & -22612.0795480143 \tabularnewline
23 & 67457 & 58504.6443909878 & 8952.35560901221 \tabularnewline
24 & 67203 & 57564.1302963088 & 9638.86970369119 \tabularnewline
25 & 69273 & 50465.1759505782 & 18807.8240494218 \tabularnewline
26 & 80807 & 76205.9402568338 & 4601.05974316619 \tabularnewline
27 & 75129 & 71108.0784626216 & 4020.92153737835 \tabularnewline
28 & 74991 & 67283.4436850627 & 7707.55631493729 \tabularnewline
29 & 68157 & 60328.6254080235 & 7828.37459197655 \tabularnewline
30 & 73858 & 76895.966071142 & -3037.96607114197 \tabularnewline
31 & 71349 & 66248.3974761755 & 5100.60252382453 \tabularnewline
32 & 85634 & 63988.4038747028 & 21645.5961252972 \tabularnewline
33 & 91624 & 68482.9709646186 & 23141.0290353814 \tabularnewline
34 & 116014 & 96915.1983914386 & 19098.8016085614 \tabularnewline
35 & 120033 & 105600.196918845 & 14432.8030811549 \tabularnewline
36 & 108651 & 113797.333851162 & -5146.33385116249 \tabularnewline
37 & 105378 & 98999.8564703635 & 6378.14352963648 \tabularnewline
38 & 138939 & 114970.224719831 & 23968.7752801688 \tabularnewline
39 & 132974 & 127884.182842384 & 5089.81715761573 \tabularnewline
40 & 135277 & 127821.703822619 & 7455.29617738098 \tabularnewline
41 & 152741 & 124733.894007195 & 28007.1059928052 \tabularnewline
42 & 158417 & 160397.079514203 & -1980.07951420313 \tabularnewline
43 & 157460 & 152533.559887733 & 4926.44011226681 \tabularnewline
44 & 193997 & 153435.706881471 & 40561.293118529 \tabularnewline
45 & 154089 & 179293.484067527 & -25204.4840675273 \tabularnewline
46 & 147570 & 171749.0047051 & -24179.0047051002 \tabularnewline
47 & 162924 & 147348.379102375 & 15575.620897625 \tabularnewline
48 & 153629 & 159808.754568503 & -6179.75456850257 \tabularnewline
49 & 155907 & 142876.335202917 & 13030.6647970829 \tabularnewline
50 & 197675 & 164787.61336812 & 32887.3866318795 \tabularnewline
51 & 250708 & 189120.855273088 & 61587.1447269115 \tabularnewline
52 & 266652 & 237315.249546051 & 29336.7504539492 \tabularnewline
53 & 209842 & 252552.528967838 & -42710.5289678381 \tabularnewline
54 & 165826 & 235241.056844176 & -69415.056844176 \tabularnewline
55 & 137152 & 183007.624864595 & -45855.6248645947 \tabularnewline
56 & 150581 & 142731.00091142 & 7849.99908858034 \tabularnewline
57 & 145973 & 131517.679491034 & 14455.3205089661 \tabularnewline
58 & 126532 & 153635.907885132 & -27103.9078851318 \tabularnewline
59 & 115437 & 134909.144639492 & -19472.1446394925 \tabularnewline
60 & 119526 & 119212.531302044 & 313.468697956298 \tabularnewline
61 & 110856 & 102073.259467025 & 8782.7405329747 \tabularnewline
62 & 97243 & 115224.386375359 & -17981.3863753588 \tabularnewline
63 & 103876 & 103554.028938205 & 321.971061795033 \tabularnewline
64 & 116370 & 104668.723638818 & 11701.2763611818 \tabularnewline
65 & 109616 & 97115.3224546366 & 12500.6775453634 \tabularnewline
66 & 98365 & 110860.490772412 & -12495.4907724119 \tabularnewline
67 & 90440 & 105334.648234931 & -14894.6482349315 \tabularnewline
68 & 88899 & 95701.3629702353 & -6802.36297023534 \tabularnewline
69 & 92358 & 73495.3504531689 & 18862.6495468311 \tabularnewline
70 & 88394 & 89527.9995917096 & -1133.99959170959 \tabularnewline
71 & 98219 & 92432.238904365 & 5786.76109563497 \tabularnewline
72 & 113546 & 99814.7706839566 & 13731.2293160434 \tabularnewline
73 & 107168 & 96564.9624348183 & 10603.0375651817 \tabularnewline
74 & 77540 & 105103.701504071 & -27563.7015040711 \tabularnewline
75 & 74944 & 88365.9284913644 & -13421.9284913644 \tabularnewline
76 & 75641 & 81313.3052310869 & -5672.30523108687 \tabularnewline
77 & 75910 & 62036.6303628086 & 13873.3696371914 \tabularnewline
78 & 87384 & 68898.704710646 & 18485.295289354 \tabularnewline
79 & 84615 & 89151.7138653672 & -4536.7138653672 \tabularnewline
80 & 80420 & 90136.7072410156 & -9716.70724101564 \tabularnewline
81 & 80784 & 69926.4479281166 & 10857.5520718834 \tabularnewline
82 & 79933 & 75229.8687823263 & 4703.13121767374 \tabularnewline
83 & 82118 & 82837.2116333725 & -719.211633372543 \tabularnewline
84 & 91420 & 86407.6044716462 & 5012.39552835377 \tabularnewline
85 & 112426 & 79833.5070828222 & 32592.4929171778 \tabularnewline
86 & 114528 & 102245.602867803 & 12282.397132197 \tabularnewline
87 & 131025 & 116314.825611487 & 14710.1743885127 \tabularnewline
88 & 116460 & 133742.405650994 & -17282.4056509945 \tabularnewline
89 & 111258 & 113477.194108475 & -2219.19410847528 \tabularnewline
90 & 155318 & 107457.508358216 & 47860.4916417845 \tabularnewline
91 & 155078 & 150088.961215324 & 4989.03878467574 \tabularnewline
92 & 134794 & 157916.079201261 & -23122.079201261 \tabularnewline
93 & 139985 & 135146.995156828 & 4838.0048431718 \tabularnewline
94 & 198778 & 139861.314961726 & 58916.685038274 \tabularnewline
95 & 172436 & 188169.100697508 & -15733.1006975077 \tabularnewline
96 & 169585 & 178093.141819743 & -8508.141819743 \tabularnewline
97 & 203702 & 169986.776691987 & 33715.2233080129 \tabularnewline
98 & 282392 & 203347.926226509 & 79044.0737734908 \tabularnewline
99 & 220658 & 262420.413244865 & -41762.4132448646 \tabularnewline
100 & 194472 & 234406.017811247 & -39934.0178112471 \tabularnewline
101 & 269246 & 206651.042748184 & 62594.9572518165 \tabularnewline
102 & 215340 & 267678.74363625 & -52338.7436362501 \tabularnewline
103 & 218319 & 213187.14950679 & 5131.85049320967 \tabularnewline
104 & 195724 & 220839.527128261 & -25115.5271282606 \tabularnewline
105 & 174614 & 213507.455886746 & -38893.4558867462 \tabularnewline
106 & 172085 & 183581.929143221 & -11496.9291432214 \tabularnewline
107 & 152347 & 164076.077831701 & -11729.0778317013 \tabularnewline
108 & 189615 & 154041.953985265 & 35573.0460147347 \tabularnewline
109 & 173804 & 191531.077191269 & -17727.0771912692 \tabularnewline
110 & 145683 & 180231.415115653 & -34548.4151156525 \tabularnewline
111 & 133550 & 142328.682245934 & -8778.68224593403 \tabularnewline
112 & 121156 & 138248.95688107 & -17092.9568810701 \tabularnewline
113 & 112040 & 128644.906460937 & -16604.9064609374 \tabularnewline
114 & 120767 & 114932.237312518 & 5834.76268748246 \tabularnewline
115 & 127019 & 109572.841345705 & 17446.1586542951 \tabularnewline
116 & 136295 & 124672.44111761 & 11622.5588823898 \tabularnewline
117 & 113425 & 137612.725338574 & -24187.7253385741 \tabularnewline
118 & 107815 & 120337.762830413 & -12522.7628304132 \tabularnewline
119 & 100298 & 101734.257517769 & -1436.25751776878 \tabularnewline
120 & 97048 & 101182.16233271 & -4134.16233271026 \tabularnewline
121 & 98750 & 97809.546939741 & 940.453060258966 \tabularnewline
122 & 98235 & 100519.163623299 & -2284.16362329907 \tabularnewline
123 & 101254 & 90631.5476042003 & 10622.4523957997 \tabularnewline
124 & 139589 & 99226.8001952893 & 40362.1998047107 \tabularnewline
125 & 134921 & 131663.475351802 & 3257.52464819798 \tabularnewline
126 & 80355 & 137050.242381583 & -56695.2423815834 \tabularnewline
127 & 80396 & 86428.2358391541 & -6032.23583915412 \tabularnewline
128 & 82183 & 84462.5166132995 & -2279.51661329948 \tabularnewline
129 & 79709 & 79350.1954648205 & 358.804535179457 \tabularnewline
130 & 90781 & 75623.4115815425 & 15157.5884184575 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=194039&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]5[/C][C]97415[/C][C]114939.06875[/C][C]-17524.06875[/C][/ROW]
[ROW][C]6[/C][C]119190[/C][C]119870.95413994[/C][C]-680.954139939699[/C][/ROW]
[ROW][C]7[/C][C]97903[/C][C]88839.3361118576[/C][C]9063.66388814236[/C][/ROW]
[ROW][C]8[/C][C]96953[/C][C]92815.485588244[/C][C]4137.51441175595[/C][/ROW]
[ROW][C]9[/C][C]87888[/C][C]79971.1900708081[/C][C]7916.80992919189[/C][/ROW]
[ROW][C]10[/C][C]84637[/C][C]106453.430060023[/C][C]-21816.4300600234[/C][/ROW]
[ROW][C]11[/C][C]90549[/C][C]60031.5367969283[/C][C]30517.4632030717[/C][/ROW]
[ROW][C]12[/C][C]95680[/C][C]80535.3396825554[/C][C]15144.6603174446[/C][/ROW]
[ROW][C]13[/C][C]99371[/C][C]77221.737103133[/C][C]22149.262896867[/C][/ROW]
[ROW][C]14[/C][C]79984[/C][C]113016.642740384[/C][C]-33032.642740384[/C][/ROW]
[ROW][C]15[/C][C]86752[/C][C]63484.5250507005[/C][C]23267.4749492995[/C][/ROW]
[ROW][C]16[/C][C]85733[/C][C]77654.6663004551[/C][C]8078.33369954488[/C][/ROW]
[ROW][C]17[/C][C]84906[/C][C]70006.0382760694[/C][C]14899.9617239306[/C][/ROW]
[ROW][C]18[/C][C]78356[/C][C]95549.7067545321[/C][C]-17193.7067545321[/C][/ROW]
[ROW][C]19[/C][C]108895[/C][C]63940.138698166[/C][C]44954.861301834[/C][/ROW]
[ROW][C]20[/C][C]101768[/C][C]94576.2485195354[/C][C]7191.75148046463[/C][/ROW]
[ROW][C]21[/C][C]73285[/C][C]87999.3620810333[/C][C]-14714.3620810333[/C][/ROW]
[ROW][C]22[/C][C]65724[/C][C]88336.0795480143[/C][C]-22612.0795480143[/C][/ROW]
[ROW][C]23[/C][C]67457[/C][C]58504.6443909878[/C][C]8952.35560901221[/C][/ROW]
[ROW][C]24[/C][C]67203[/C][C]57564.1302963088[/C][C]9638.86970369119[/C][/ROW]
[ROW][C]25[/C][C]69273[/C][C]50465.1759505782[/C][C]18807.8240494218[/C][/ROW]
[ROW][C]26[/C][C]80807[/C][C]76205.9402568338[/C][C]4601.05974316619[/C][/ROW]
[ROW][C]27[/C][C]75129[/C][C]71108.0784626216[/C][C]4020.92153737835[/C][/ROW]
[ROW][C]28[/C][C]74991[/C][C]67283.4436850627[/C][C]7707.55631493729[/C][/ROW]
[ROW][C]29[/C][C]68157[/C][C]60328.6254080235[/C][C]7828.37459197655[/C][/ROW]
[ROW][C]30[/C][C]73858[/C][C]76895.966071142[/C][C]-3037.96607114197[/C][/ROW]
[ROW][C]31[/C][C]71349[/C][C]66248.3974761755[/C][C]5100.60252382453[/C][/ROW]
[ROW][C]32[/C][C]85634[/C][C]63988.4038747028[/C][C]21645.5961252972[/C][/ROW]
[ROW][C]33[/C][C]91624[/C][C]68482.9709646186[/C][C]23141.0290353814[/C][/ROW]
[ROW][C]34[/C][C]116014[/C][C]96915.1983914386[/C][C]19098.8016085614[/C][/ROW]
[ROW][C]35[/C][C]120033[/C][C]105600.196918845[/C][C]14432.8030811549[/C][/ROW]
[ROW][C]36[/C][C]108651[/C][C]113797.333851162[/C][C]-5146.33385116249[/C][/ROW]
[ROW][C]37[/C][C]105378[/C][C]98999.8564703635[/C][C]6378.14352963648[/C][/ROW]
[ROW][C]38[/C][C]138939[/C][C]114970.224719831[/C][C]23968.7752801688[/C][/ROW]
[ROW][C]39[/C][C]132974[/C][C]127884.182842384[/C][C]5089.81715761573[/C][/ROW]
[ROW][C]40[/C][C]135277[/C][C]127821.703822619[/C][C]7455.29617738098[/C][/ROW]
[ROW][C]41[/C][C]152741[/C][C]124733.894007195[/C][C]28007.1059928052[/C][/ROW]
[ROW][C]42[/C][C]158417[/C][C]160397.079514203[/C][C]-1980.07951420313[/C][/ROW]
[ROW][C]43[/C][C]157460[/C][C]152533.559887733[/C][C]4926.44011226681[/C][/ROW]
[ROW][C]44[/C][C]193997[/C][C]153435.706881471[/C][C]40561.293118529[/C][/ROW]
[ROW][C]45[/C][C]154089[/C][C]179293.484067527[/C][C]-25204.4840675273[/C][/ROW]
[ROW][C]46[/C][C]147570[/C][C]171749.0047051[/C][C]-24179.0047051002[/C][/ROW]
[ROW][C]47[/C][C]162924[/C][C]147348.379102375[/C][C]15575.620897625[/C][/ROW]
[ROW][C]48[/C][C]153629[/C][C]159808.754568503[/C][C]-6179.75456850257[/C][/ROW]
[ROW][C]49[/C][C]155907[/C][C]142876.335202917[/C][C]13030.6647970829[/C][/ROW]
[ROW][C]50[/C][C]197675[/C][C]164787.61336812[/C][C]32887.3866318795[/C][/ROW]
[ROW][C]51[/C][C]250708[/C][C]189120.855273088[/C][C]61587.1447269115[/C][/ROW]
[ROW][C]52[/C][C]266652[/C][C]237315.249546051[/C][C]29336.7504539492[/C][/ROW]
[ROW][C]53[/C][C]209842[/C][C]252552.528967838[/C][C]-42710.5289678381[/C][/ROW]
[ROW][C]54[/C][C]165826[/C][C]235241.056844176[/C][C]-69415.056844176[/C][/ROW]
[ROW][C]55[/C][C]137152[/C][C]183007.624864595[/C][C]-45855.6248645947[/C][/ROW]
[ROW][C]56[/C][C]150581[/C][C]142731.00091142[/C][C]7849.99908858034[/C][/ROW]
[ROW][C]57[/C][C]145973[/C][C]131517.679491034[/C][C]14455.3205089661[/C][/ROW]
[ROW][C]58[/C][C]126532[/C][C]153635.907885132[/C][C]-27103.9078851318[/C][/ROW]
[ROW][C]59[/C][C]115437[/C][C]134909.144639492[/C][C]-19472.1446394925[/C][/ROW]
[ROW][C]60[/C][C]119526[/C][C]119212.531302044[/C][C]313.468697956298[/C][/ROW]
[ROW][C]61[/C][C]110856[/C][C]102073.259467025[/C][C]8782.7405329747[/C][/ROW]
[ROW][C]62[/C][C]97243[/C][C]115224.386375359[/C][C]-17981.3863753588[/C][/ROW]
[ROW][C]63[/C][C]103876[/C][C]103554.028938205[/C][C]321.971061795033[/C][/ROW]
[ROW][C]64[/C][C]116370[/C][C]104668.723638818[/C][C]11701.2763611818[/C][/ROW]
[ROW][C]65[/C][C]109616[/C][C]97115.3224546366[/C][C]12500.6775453634[/C][/ROW]
[ROW][C]66[/C][C]98365[/C][C]110860.490772412[/C][C]-12495.4907724119[/C][/ROW]
[ROW][C]67[/C][C]90440[/C][C]105334.648234931[/C][C]-14894.6482349315[/C][/ROW]
[ROW][C]68[/C][C]88899[/C][C]95701.3629702353[/C][C]-6802.36297023534[/C][/ROW]
[ROW][C]69[/C][C]92358[/C][C]73495.3504531689[/C][C]18862.6495468311[/C][/ROW]
[ROW][C]70[/C][C]88394[/C][C]89527.9995917096[/C][C]-1133.99959170959[/C][/ROW]
[ROW][C]71[/C][C]98219[/C][C]92432.238904365[/C][C]5786.76109563497[/C][/ROW]
[ROW][C]72[/C][C]113546[/C][C]99814.7706839566[/C][C]13731.2293160434[/C][/ROW]
[ROW][C]73[/C][C]107168[/C][C]96564.9624348183[/C][C]10603.0375651817[/C][/ROW]
[ROW][C]74[/C][C]77540[/C][C]105103.701504071[/C][C]-27563.7015040711[/C][/ROW]
[ROW][C]75[/C][C]74944[/C][C]88365.9284913644[/C][C]-13421.9284913644[/C][/ROW]
[ROW][C]76[/C][C]75641[/C][C]81313.3052310869[/C][C]-5672.30523108687[/C][/ROW]
[ROW][C]77[/C][C]75910[/C][C]62036.6303628086[/C][C]13873.3696371914[/C][/ROW]
[ROW][C]78[/C][C]87384[/C][C]68898.704710646[/C][C]18485.295289354[/C][/ROW]
[ROW][C]79[/C][C]84615[/C][C]89151.7138653672[/C][C]-4536.7138653672[/C][/ROW]
[ROW][C]80[/C][C]80420[/C][C]90136.7072410156[/C][C]-9716.70724101564[/C][/ROW]
[ROW][C]81[/C][C]80784[/C][C]69926.4479281166[/C][C]10857.5520718834[/C][/ROW]
[ROW][C]82[/C][C]79933[/C][C]75229.8687823263[/C][C]4703.13121767374[/C][/ROW]
[ROW][C]83[/C][C]82118[/C][C]82837.2116333725[/C][C]-719.211633372543[/C][/ROW]
[ROW][C]84[/C][C]91420[/C][C]86407.6044716462[/C][C]5012.39552835377[/C][/ROW]
[ROW][C]85[/C][C]112426[/C][C]79833.5070828222[/C][C]32592.4929171778[/C][/ROW]
[ROW][C]86[/C][C]114528[/C][C]102245.602867803[/C][C]12282.397132197[/C][/ROW]
[ROW][C]87[/C][C]131025[/C][C]116314.825611487[/C][C]14710.1743885127[/C][/ROW]
[ROW][C]88[/C][C]116460[/C][C]133742.405650994[/C][C]-17282.4056509945[/C][/ROW]
[ROW][C]89[/C][C]111258[/C][C]113477.194108475[/C][C]-2219.19410847528[/C][/ROW]
[ROW][C]90[/C][C]155318[/C][C]107457.508358216[/C][C]47860.4916417845[/C][/ROW]
[ROW][C]91[/C][C]155078[/C][C]150088.961215324[/C][C]4989.03878467574[/C][/ROW]
[ROW][C]92[/C][C]134794[/C][C]157916.079201261[/C][C]-23122.079201261[/C][/ROW]
[ROW][C]93[/C][C]139985[/C][C]135146.995156828[/C][C]4838.0048431718[/C][/ROW]
[ROW][C]94[/C][C]198778[/C][C]139861.314961726[/C][C]58916.685038274[/C][/ROW]
[ROW][C]95[/C][C]172436[/C][C]188169.100697508[/C][C]-15733.1006975077[/C][/ROW]
[ROW][C]96[/C][C]169585[/C][C]178093.141819743[/C][C]-8508.141819743[/C][/ROW]
[ROW][C]97[/C][C]203702[/C][C]169986.776691987[/C][C]33715.2233080129[/C][/ROW]
[ROW][C]98[/C][C]282392[/C][C]203347.926226509[/C][C]79044.0737734908[/C][/ROW]
[ROW][C]99[/C][C]220658[/C][C]262420.413244865[/C][C]-41762.4132448646[/C][/ROW]
[ROW][C]100[/C][C]194472[/C][C]234406.017811247[/C][C]-39934.0178112471[/C][/ROW]
[ROW][C]101[/C][C]269246[/C][C]206651.042748184[/C][C]62594.9572518165[/C][/ROW]
[ROW][C]102[/C][C]215340[/C][C]267678.74363625[/C][C]-52338.7436362501[/C][/ROW]
[ROW][C]103[/C][C]218319[/C][C]213187.14950679[/C][C]5131.85049320967[/C][/ROW]
[ROW][C]104[/C][C]195724[/C][C]220839.527128261[/C][C]-25115.5271282606[/C][/ROW]
[ROW][C]105[/C][C]174614[/C][C]213507.455886746[/C][C]-38893.4558867462[/C][/ROW]
[ROW][C]106[/C][C]172085[/C][C]183581.929143221[/C][C]-11496.9291432214[/C][/ROW]
[ROW][C]107[/C][C]152347[/C][C]164076.077831701[/C][C]-11729.0778317013[/C][/ROW]
[ROW][C]108[/C][C]189615[/C][C]154041.953985265[/C][C]35573.0460147347[/C][/ROW]
[ROW][C]109[/C][C]173804[/C][C]191531.077191269[/C][C]-17727.0771912692[/C][/ROW]
[ROW][C]110[/C][C]145683[/C][C]180231.415115653[/C][C]-34548.4151156525[/C][/ROW]
[ROW][C]111[/C][C]133550[/C][C]142328.682245934[/C][C]-8778.68224593403[/C][/ROW]
[ROW][C]112[/C][C]121156[/C][C]138248.95688107[/C][C]-17092.9568810701[/C][/ROW]
[ROW][C]113[/C][C]112040[/C][C]128644.906460937[/C][C]-16604.9064609374[/C][/ROW]
[ROW][C]114[/C][C]120767[/C][C]114932.237312518[/C][C]5834.76268748246[/C][/ROW]
[ROW][C]115[/C][C]127019[/C][C]109572.841345705[/C][C]17446.1586542951[/C][/ROW]
[ROW][C]116[/C][C]136295[/C][C]124672.44111761[/C][C]11622.5588823898[/C][/ROW]
[ROW][C]117[/C][C]113425[/C][C]137612.725338574[/C][C]-24187.7253385741[/C][/ROW]
[ROW][C]118[/C][C]107815[/C][C]120337.762830413[/C][C]-12522.7628304132[/C][/ROW]
[ROW][C]119[/C][C]100298[/C][C]101734.257517769[/C][C]-1436.25751776878[/C][/ROW]
[ROW][C]120[/C][C]97048[/C][C]101182.16233271[/C][C]-4134.16233271026[/C][/ROW]
[ROW][C]121[/C][C]98750[/C][C]97809.546939741[/C][C]940.453060258966[/C][/ROW]
[ROW][C]122[/C][C]98235[/C][C]100519.163623299[/C][C]-2284.16362329907[/C][/ROW]
[ROW][C]123[/C][C]101254[/C][C]90631.5476042003[/C][C]10622.4523957997[/C][/ROW]
[ROW][C]124[/C][C]139589[/C][C]99226.8001952893[/C][C]40362.1998047107[/C][/ROW]
[ROW][C]125[/C][C]134921[/C][C]131663.475351802[/C][C]3257.52464819798[/C][/ROW]
[ROW][C]126[/C][C]80355[/C][C]137050.242381583[/C][C]-56695.2423815834[/C][/ROW]
[ROW][C]127[/C][C]80396[/C][C]86428.2358391541[/C][C]-6032.23583915412[/C][/ROW]
[ROW][C]128[/C][C]82183[/C][C]84462.5166132995[/C][C]-2279.51661329948[/C][/ROW]
[ROW][C]129[/C][C]79709[/C][C]79350.1954648205[/C][C]358.804535179457[/C][/ROW]
[ROW][C]130[/C][C]90781[/C][C]75623.4115815425[/C][C]15157.5884184575[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=194039&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=194039&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
597415114939.06875-17524.06875
6119190119870.95413994-680.954139939699
79790388839.33611185769063.66388814236
89695392815.4855882444137.51441175595
98788879971.19007080817916.80992919189
1084637106453.430060023-21816.4300600234
119054960031.536796928330517.4632030717
129568080535.339682555415144.6603174446
139937177221.73710313322149.262896867
1479984113016.642740384-33032.642740384
158675263484.525050700523267.4749492995
168573377654.66630045518078.33369954488
178490670006.038276069414899.9617239306
187835695549.7067545321-17193.7067545321
1910889563940.13869816644954.861301834
2010176894576.24851953547191.75148046463
217328587999.3620810333-14714.3620810333
226572488336.0795480143-22612.0795480143
236745758504.64439098788952.35560901221
246720357564.13029630889638.86970369119
256927350465.175950578218807.8240494218
268080776205.94025683384601.05974316619
277512971108.07846262164020.92153737835
287499167283.44368506277707.55631493729
296815760328.62540802357828.37459197655
307385876895.966071142-3037.96607114197
317134966248.39747617555100.60252382453
328563463988.403874702821645.5961252972
339162468482.970964618623141.0290353814
3411601496915.198391438619098.8016085614
35120033105600.19691884514432.8030811549
36108651113797.333851162-5146.33385116249
3710537898999.85647036356378.14352963648
38138939114970.22471983123968.7752801688
39132974127884.1828423845089.81715761573
40135277127821.7038226197455.29617738098
41152741124733.89400719528007.1059928052
42158417160397.079514203-1980.07951420313
43157460152533.5598877334926.44011226681
44193997153435.70688147140561.293118529
45154089179293.484067527-25204.4840675273
46147570171749.0047051-24179.0047051002
47162924147348.37910237515575.620897625
48153629159808.754568503-6179.75456850257
49155907142876.33520291713030.6647970829
50197675164787.6133681232887.3866318795
51250708189120.85527308861587.1447269115
52266652237315.24954605129336.7504539492
53209842252552.528967838-42710.5289678381
54165826235241.056844176-69415.056844176
55137152183007.624864595-45855.6248645947
56150581142731.000911427849.99908858034
57145973131517.67949103414455.3205089661
58126532153635.907885132-27103.9078851318
59115437134909.144639492-19472.1446394925
60119526119212.531302044313.468697956298
61110856102073.2594670258782.7405329747
6297243115224.386375359-17981.3863753588
63103876103554.028938205321.971061795033
64116370104668.72363881811701.2763611818
6510961697115.322454636612500.6775453634
6698365110860.490772412-12495.4907724119
6790440105334.648234931-14894.6482349315
688889995701.3629702353-6802.36297023534
699235873495.350453168918862.6495468311
708839489527.9995917096-1133.99959170959
719821992432.2389043655786.76109563497
7211354699814.770683956613731.2293160434
7310716896564.962434818310603.0375651817
7477540105103.701504071-27563.7015040711
757494488365.9284913644-13421.9284913644
767564181313.3052310869-5672.30523108687
777591062036.630362808613873.3696371914
788738468898.70471064618485.295289354
798461589151.7138653672-4536.7138653672
808042090136.7072410156-9716.70724101564
818078469926.447928116610857.5520718834
827993375229.86878232634703.13121767374
838211882837.2116333725-719.211633372543
849142086407.60447164625012.39552835377
8511242679833.507082822232592.4929171778
86114528102245.60286780312282.397132197
87131025116314.82561148714710.1743885127
88116460133742.405650994-17282.4056509945
89111258113477.194108475-2219.19410847528
90155318107457.50835821647860.4916417845
91155078150088.9612153244989.03878467574
92134794157916.079201261-23122.079201261
93139985135146.9951568284838.0048431718
94198778139861.31496172658916.685038274
95172436188169.100697508-15733.1006975077
96169585178093.141819743-8508.141819743
97203702169986.77669198733715.2233080129
98282392203347.92622650979044.0737734908
99220658262420.413244865-41762.4132448646
100194472234406.017811247-39934.0178112471
101269246206651.04274818462594.9572518165
102215340267678.74363625-52338.7436362501
103218319213187.149506795131.85049320967
104195724220839.527128261-25115.5271282606
105174614213507.455886746-38893.4558867462
106172085183581.929143221-11496.9291432214
107152347164076.077831701-11729.0778317013
108189615154041.95398526535573.0460147347
109173804191531.077191269-17727.0771912692
110145683180231.415115653-34548.4151156525
111133550142328.682245934-8778.68224593403
112121156138248.95688107-17092.9568810701
113112040128644.906460937-16604.9064609374
114120767114932.2373125185834.76268748246
115127019109572.84134570517446.1586542951
116136295124672.4411176111622.5588823898
117113425137612.725338574-24187.7253385741
118107815120337.762830413-12522.7628304132
119100298101734.257517769-1436.25751776878
12097048101182.16233271-4134.16233271026
1219875097809.546939741940.453060258966
12298235100519.163623299-2284.16362329907
12310125490631.547604200310622.4523957997
12413958999226.800195289340362.1998047107
125134921131663.4753518023257.52464819798
12680355137050.242381583-56695.2423815834
1278039686428.2358391541-6032.23583915412
1288218384462.5166132995-2279.51661329948
1297970979350.1954648205358.804535179457
1309078175623.411581542515157.5884184575







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
13184991.950702108638006.3693029821131977.532101235
13288305.827077214328373.6550105293148237.999143899
13385538.727180902214425.7577982269156651.696563578
13483217.10064776091942.7896454694164491.411650052

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
131 & 84991.9507021086 & 38006.3693029821 & 131977.532101235 \tabularnewline
132 & 88305.8270772143 & 28373.6550105293 & 148237.999143899 \tabularnewline
133 & 85538.7271809022 & 14425.7577982269 & 156651.696563578 \tabularnewline
134 & 83217.1006477609 & 1942.7896454694 & 164491.411650052 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=194039&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]131[/C][C]84991.9507021086[/C][C]38006.3693029821[/C][C]131977.532101235[/C][/ROW]
[ROW][C]132[/C][C]88305.8270772143[/C][C]28373.6550105293[/C][C]148237.999143899[/C][/ROW]
[ROW][C]133[/C][C]85538.7271809022[/C][C]14425.7577982269[/C][C]156651.696563578[/C][/ROW]
[ROW][C]134[/C][C]83217.1006477609[/C][C]1942.7896454694[/C][C]164491.411650052[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=194039&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=194039&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
13184991.950702108638006.3693029821131977.532101235
13288305.827077214328373.6550105293148237.999143899
13385538.727180902214425.7577982269156651.696563578
13483217.10064776091942.7896454694164491.411650052



Parameters (Session):
par1 = 4 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 4 ; 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')