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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 21 Aug 2013 06:10:37 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Aug/21/t13770798520vxunyly4rafzp1.htm/, Retrieved Sat, 27 Apr 2024 09:30:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=211325, Retrieved Sat, 27 Apr 2024 09:30:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact90
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-08-21 10:10:37] [bdb7c0ed7ba273e65f9ee772c5dda4f0] [Current]
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Dataseries X:
293544
282672
298980
239184
309852
304416
326160
337032
375084
326160
309852
385956
326160
244620
288108
217440
304416
250056
331596
298980
315288
353340
347904
413136
298980
250056
277236
201132
288108
222876
315288
298980
266364
380520
342468
391392
293544
271800
244620
201132
266364
239184
326160
315288
271800
364212
337032
434880
347904
212004
212004
212004
250056
250056
337032
309852
277236
347904
320724
462060
364212
212004
222876
184824
255492
293544
369648
364212
293544
342468
304416
434880
331596
266364
239184
179388
266364
320724
375084
353340
260928
375084
293544
451188
375084
271800
250056
168516
266364
255492
385956
385956
293544
380520
282672
440316
375084
277236
212004
146772
288108
277236
364212
418572
309852
347904
260928
451188




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ yule.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211325&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211325&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211325&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'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.00903806239705356
beta1
gamma0.930857409776002

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.00903806239705356 \tabularnewline
beta & 1 \tabularnewline
gamma & 0.930857409776002 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211325&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]0.00903806239705356[/C][/ROW]
[ROW][C]beta[/C][C]1[/C][/ROW]
[ROW][C]gamma[/C][C]0.930857409776002[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211325&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211325&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
alpha0.00903806239705356
beta1
gamma0.930857409776002







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13326160338557.461834503-12397.4618345029
14244620253730.357566054-9110.3575660541
15288108301203.255518599-13095.2555185987
16217440226983.04099333-9543.04099332969
17304416312921.851084317-8505.85108431731
18250056253098.385567753-3042.38556775317
19331596316956.43890993414639.5610900663
20298980325905.06346127-26925.06346127
21315288362277.818566687-46989.8185666869
22353340313465.78838491439874.2116150857
23347904297125.11023789650778.8897621041
24413136371606.51596772641529.4840322745
25298980304364.942468195-5384.94246819546
26250056228331.81936199521724.1806380051
27277236269773.1110705967462.8889294042
28201132204116.677673828-2984.67767382826
29288108286133.1637614321974.83623856807
30222876235436.759631797-12560.7596317975
31315288311427.3690785733860.63092142704
32298980284187.42286862314792.5771313772
33266364302358.957966326-35994.9579663256
34380520333209.04691310747310.9530868928
35342468328404.13194697614063.8680530238
36391392391899.322573395-507.322573394573
37293544286368.5959288277175.40407117252
38271800238062.44202051633737.5579794836
39244620265890.874258132-21270.8742581318
40201132193581.3902023377550.609797663
41266364277444.056420095-11080.0564200954
42239184215869.14776699223314.8522330075
43326160305062.01842187721097.9815781231
44315288289551.70562330525736.2943766952
45271800262693.8668332429106.1331667584
46364212370188.30614101-5976.30614100985
47337032336140.249986462891.750013538171
48434880386573.11245248148306.8875475189
49347904290976.80945858356927.1905414168
50212004269322.778556533-57318.7785565326
51212004246320.054817142-34316.0548171416
52212004200944.78469821711059.2153017834
53250056268441.323693771-18385.3236937714
54250056238895.62256488411160.3774351156
55337032326965.2516085110066.7483914896
56309852315933.046483671-6081.04648367141
57277236273205.938813064030.06118693994
58347904367494.689135199-19590.6891351989
59320724339378.529039575-18654.5290395747
60462060433624.53504715128435.4649528491
61364212344794.08082888719417.9191711127
62212004216407.372088731-4403.3720887308
63222876214890.3135269657985.68647303476
64184824211910.960639693-27086.9606396935
65255492251758.8900726683733.10992733249
66293544249636.52016669143907.4798333094
67369648337612.20510934632035.7948906537
68364212312276.13965979551935.8603402051
69293544280059.73776904713484.2622309533
70342468354753.277475003-12285.2774750029
71304416328369.697918337-23953.6979183374
72434880470304.427955428-35424.4279554284
73331596371333.141203704-39737.1412037038
74266364217259.10398428849104.8960157116
75239184228597.4957364510586.5042635504
76179388192843.826667727-13455.8266677274
77266364264417.7542754511946.24572454928
78320724301595.74270449419128.2572955063
79375084382292.933079347-7208.93307934742
80353340375145.933773744-21805.9337737436
81260928303920.592978065-42992.5929780652
82375084355423.94265813719660.0573418626
83293544316772.63226706-23228.6322670601
84451188451982.680003519-794.680003518763
85375084345606.33067535929477.6693246407
86271800271800.383894589-0.383894588798285
87250056246075.7103186773980.2896813229
88168516185968.958265323-17452.9582653227
89266364273916.14005761-7552.14005760965
90255492327761.857421514-72269.8574215141
91385956383007.1086428922948.89135710831
92385956360573.7709653225382.2290346799
93293544267860.68880436325683.3111956373
94380520379212.7243527071307.27564729343
95282672299283.766371395-16611.7663713953
96440316456851.276984049-16535.2769840487
97375084376748.924383557-1664.92438355664
98277236273861.6388532963374.36114670365
99212004251137.403443475-39133.4034434753
100146772169912.245499493-23140.2454994927
101288108265854.90396050722253.096039493
102277236259365.2351794417870.7648205603
103364212384203.657038996-19991.6570389961
104418572381878.1706185636693.8293814398
105309852289794.04342025320057.9565797469
106347904377689.723921234-29785.7239212344
107260928281220.804978116-20292.8049781162
108451188436459.40932504314728.5906749566

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 326160 & 338557.461834503 & -12397.4618345029 \tabularnewline
14 & 244620 & 253730.357566054 & -9110.3575660541 \tabularnewline
15 & 288108 & 301203.255518599 & -13095.2555185987 \tabularnewline
16 & 217440 & 226983.04099333 & -9543.04099332969 \tabularnewline
17 & 304416 & 312921.851084317 & -8505.85108431731 \tabularnewline
18 & 250056 & 253098.385567753 & -3042.38556775317 \tabularnewline
19 & 331596 & 316956.438909934 & 14639.5610900663 \tabularnewline
20 & 298980 & 325905.06346127 & -26925.06346127 \tabularnewline
21 & 315288 & 362277.818566687 & -46989.8185666869 \tabularnewline
22 & 353340 & 313465.788384914 & 39874.2116150857 \tabularnewline
23 & 347904 & 297125.110237896 & 50778.8897621041 \tabularnewline
24 & 413136 & 371606.515967726 & 41529.4840322745 \tabularnewline
25 & 298980 & 304364.942468195 & -5384.94246819546 \tabularnewline
26 & 250056 & 228331.819361995 & 21724.1806380051 \tabularnewline
27 & 277236 & 269773.111070596 & 7462.8889294042 \tabularnewline
28 & 201132 & 204116.677673828 & -2984.67767382826 \tabularnewline
29 & 288108 & 286133.163761432 & 1974.83623856807 \tabularnewline
30 & 222876 & 235436.759631797 & -12560.7596317975 \tabularnewline
31 & 315288 & 311427.369078573 & 3860.63092142704 \tabularnewline
32 & 298980 & 284187.422868623 & 14792.5771313772 \tabularnewline
33 & 266364 & 302358.957966326 & -35994.9579663256 \tabularnewline
34 & 380520 & 333209.046913107 & 47310.9530868928 \tabularnewline
35 & 342468 & 328404.131946976 & 14063.8680530238 \tabularnewline
36 & 391392 & 391899.322573395 & -507.322573394573 \tabularnewline
37 & 293544 & 286368.595928827 & 7175.40407117252 \tabularnewline
38 & 271800 & 238062.442020516 & 33737.5579794836 \tabularnewline
39 & 244620 & 265890.874258132 & -21270.8742581318 \tabularnewline
40 & 201132 & 193581.390202337 & 7550.609797663 \tabularnewline
41 & 266364 & 277444.056420095 & -11080.0564200954 \tabularnewline
42 & 239184 & 215869.147766992 & 23314.8522330075 \tabularnewline
43 & 326160 & 305062.018421877 & 21097.9815781231 \tabularnewline
44 & 315288 & 289551.705623305 & 25736.2943766952 \tabularnewline
45 & 271800 & 262693.866833242 & 9106.1331667584 \tabularnewline
46 & 364212 & 370188.30614101 & -5976.30614100985 \tabularnewline
47 & 337032 & 336140.249986462 & 891.750013538171 \tabularnewline
48 & 434880 & 386573.112452481 & 48306.8875475189 \tabularnewline
49 & 347904 & 290976.809458583 & 56927.1905414168 \tabularnewline
50 & 212004 & 269322.778556533 & -57318.7785565326 \tabularnewline
51 & 212004 & 246320.054817142 & -34316.0548171416 \tabularnewline
52 & 212004 & 200944.784698217 & 11059.2153017834 \tabularnewline
53 & 250056 & 268441.323693771 & -18385.3236937714 \tabularnewline
54 & 250056 & 238895.622564884 & 11160.3774351156 \tabularnewline
55 & 337032 & 326965.25160851 & 10066.7483914896 \tabularnewline
56 & 309852 & 315933.046483671 & -6081.04648367141 \tabularnewline
57 & 277236 & 273205.93881306 & 4030.06118693994 \tabularnewline
58 & 347904 & 367494.689135199 & -19590.6891351989 \tabularnewline
59 & 320724 & 339378.529039575 & -18654.5290395747 \tabularnewline
60 & 462060 & 433624.535047151 & 28435.4649528491 \tabularnewline
61 & 364212 & 344794.080828887 & 19417.9191711127 \tabularnewline
62 & 212004 & 216407.372088731 & -4403.3720887308 \tabularnewline
63 & 222876 & 214890.313526965 & 7985.68647303476 \tabularnewline
64 & 184824 & 211910.960639693 & -27086.9606396935 \tabularnewline
65 & 255492 & 251758.890072668 & 3733.10992733249 \tabularnewline
66 & 293544 & 249636.520166691 & 43907.4798333094 \tabularnewline
67 & 369648 & 337612.205109346 & 32035.7948906537 \tabularnewline
68 & 364212 & 312276.139659795 & 51935.8603402051 \tabularnewline
69 & 293544 & 280059.737769047 & 13484.2622309533 \tabularnewline
70 & 342468 & 354753.277475003 & -12285.2774750029 \tabularnewline
71 & 304416 & 328369.697918337 & -23953.6979183374 \tabularnewline
72 & 434880 & 470304.427955428 & -35424.4279554284 \tabularnewline
73 & 331596 & 371333.141203704 & -39737.1412037038 \tabularnewline
74 & 266364 & 217259.103984288 & 49104.8960157116 \tabularnewline
75 & 239184 & 228597.49573645 & 10586.5042635504 \tabularnewline
76 & 179388 & 192843.826667727 & -13455.8266677274 \tabularnewline
77 & 266364 & 264417.754275451 & 1946.24572454928 \tabularnewline
78 & 320724 & 301595.742704494 & 19128.2572955063 \tabularnewline
79 & 375084 & 382292.933079347 & -7208.93307934742 \tabularnewline
80 & 353340 & 375145.933773744 & -21805.9337737436 \tabularnewline
81 & 260928 & 303920.592978065 & -42992.5929780652 \tabularnewline
82 & 375084 & 355423.942658137 & 19660.0573418626 \tabularnewline
83 & 293544 & 316772.63226706 & -23228.6322670601 \tabularnewline
84 & 451188 & 451982.680003519 & -794.680003518763 \tabularnewline
85 & 375084 & 345606.330675359 & 29477.6693246407 \tabularnewline
86 & 271800 & 271800.383894589 & -0.383894588798285 \tabularnewline
87 & 250056 & 246075.710318677 & 3980.2896813229 \tabularnewline
88 & 168516 & 185968.958265323 & -17452.9582653227 \tabularnewline
89 & 266364 & 273916.14005761 & -7552.14005760965 \tabularnewline
90 & 255492 & 327761.857421514 & -72269.8574215141 \tabularnewline
91 & 385956 & 383007.108642892 & 2948.89135710831 \tabularnewline
92 & 385956 & 360573.77096532 & 25382.2290346799 \tabularnewline
93 & 293544 & 267860.688804363 & 25683.3111956373 \tabularnewline
94 & 380520 & 379212.724352707 & 1307.27564729343 \tabularnewline
95 & 282672 & 299283.766371395 & -16611.7663713953 \tabularnewline
96 & 440316 & 456851.276984049 & -16535.2769840487 \tabularnewline
97 & 375084 & 376748.924383557 & -1664.92438355664 \tabularnewline
98 & 277236 & 273861.638853296 & 3374.36114670365 \tabularnewline
99 & 212004 & 251137.403443475 & -39133.4034434753 \tabularnewline
100 & 146772 & 169912.245499493 & -23140.2454994927 \tabularnewline
101 & 288108 & 265854.903960507 & 22253.096039493 \tabularnewline
102 & 277236 & 259365.23517944 & 17870.7648205603 \tabularnewline
103 & 364212 & 384203.657038996 & -19991.6570389961 \tabularnewline
104 & 418572 & 381878.17061856 & 36693.8293814398 \tabularnewline
105 & 309852 & 289794.043420253 & 20057.9565797469 \tabularnewline
106 & 347904 & 377689.723921234 & -29785.7239212344 \tabularnewline
107 & 260928 & 281220.804978116 & -20292.8049781162 \tabularnewline
108 & 451188 & 436459.409325043 & 14728.5906749566 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211325&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]326160[/C][C]338557.461834503[/C][C]-12397.4618345029[/C][/ROW]
[ROW][C]14[/C][C]244620[/C][C]253730.357566054[/C][C]-9110.3575660541[/C][/ROW]
[ROW][C]15[/C][C]288108[/C][C]301203.255518599[/C][C]-13095.2555185987[/C][/ROW]
[ROW][C]16[/C][C]217440[/C][C]226983.04099333[/C][C]-9543.04099332969[/C][/ROW]
[ROW][C]17[/C][C]304416[/C][C]312921.851084317[/C][C]-8505.85108431731[/C][/ROW]
[ROW][C]18[/C][C]250056[/C][C]253098.385567753[/C][C]-3042.38556775317[/C][/ROW]
[ROW][C]19[/C][C]331596[/C][C]316956.438909934[/C][C]14639.5610900663[/C][/ROW]
[ROW][C]20[/C][C]298980[/C][C]325905.06346127[/C][C]-26925.06346127[/C][/ROW]
[ROW][C]21[/C][C]315288[/C][C]362277.818566687[/C][C]-46989.8185666869[/C][/ROW]
[ROW][C]22[/C][C]353340[/C][C]313465.788384914[/C][C]39874.2116150857[/C][/ROW]
[ROW][C]23[/C][C]347904[/C][C]297125.110237896[/C][C]50778.8897621041[/C][/ROW]
[ROW][C]24[/C][C]413136[/C][C]371606.515967726[/C][C]41529.4840322745[/C][/ROW]
[ROW][C]25[/C][C]298980[/C][C]304364.942468195[/C][C]-5384.94246819546[/C][/ROW]
[ROW][C]26[/C][C]250056[/C][C]228331.819361995[/C][C]21724.1806380051[/C][/ROW]
[ROW][C]27[/C][C]277236[/C][C]269773.111070596[/C][C]7462.8889294042[/C][/ROW]
[ROW][C]28[/C][C]201132[/C][C]204116.677673828[/C][C]-2984.67767382826[/C][/ROW]
[ROW][C]29[/C][C]288108[/C][C]286133.163761432[/C][C]1974.83623856807[/C][/ROW]
[ROW][C]30[/C][C]222876[/C][C]235436.759631797[/C][C]-12560.7596317975[/C][/ROW]
[ROW][C]31[/C][C]315288[/C][C]311427.369078573[/C][C]3860.63092142704[/C][/ROW]
[ROW][C]32[/C][C]298980[/C][C]284187.422868623[/C][C]14792.5771313772[/C][/ROW]
[ROW][C]33[/C][C]266364[/C][C]302358.957966326[/C][C]-35994.9579663256[/C][/ROW]
[ROW][C]34[/C][C]380520[/C][C]333209.046913107[/C][C]47310.9530868928[/C][/ROW]
[ROW][C]35[/C][C]342468[/C][C]328404.131946976[/C][C]14063.8680530238[/C][/ROW]
[ROW][C]36[/C][C]391392[/C][C]391899.322573395[/C][C]-507.322573394573[/C][/ROW]
[ROW][C]37[/C][C]293544[/C][C]286368.595928827[/C][C]7175.40407117252[/C][/ROW]
[ROW][C]38[/C][C]271800[/C][C]238062.442020516[/C][C]33737.5579794836[/C][/ROW]
[ROW][C]39[/C][C]244620[/C][C]265890.874258132[/C][C]-21270.8742581318[/C][/ROW]
[ROW][C]40[/C][C]201132[/C][C]193581.390202337[/C][C]7550.609797663[/C][/ROW]
[ROW][C]41[/C][C]266364[/C][C]277444.056420095[/C][C]-11080.0564200954[/C][/ROW]
[ROW][C]42[/C][C]239184[/C][C]215869.147766992[/C][C]23314.8522330075[/C][/ROW]
[ROW][C]43[/C][C]326160[/C][C]305062.018421877[/C][C]21097.9815781231[/C][/ROW]
[ROW][C]44[/C][C]315288[/C][C]289551.705623305[/C][C]25736.2943766952[/C][/ROW]
[ROW][C]45[/C][C]271800[/C][C]262693.866833242[/C][C]9106.1331667584[/C][/ROW]
[ROW][C]46[/C][C]364212[/C][C]370188.30614101[/C][C]-5976.30614100985[/C][/ROW]
[ROW][C]47[/C][C]337032[/C][C]336140.249986462[/C][C]891.750013538171[/C][/ROW]
[ROW][C]48[/C][C]434880[/C][C]386573.112452481[/C][C]48306.8875475189[/C][/ROW]
[ROW][C]49[/C][C]347904[/C][C]290976.809458583[/C][C]56927.1905414168[/C][/ROW]
[ROW][C]50[/C][C]212004[/C][C]269322.778556533[/C][C]-57318.7785565326[/C][/ROW]
[ROW][C]51[/C][C]212004[/C][C]246320.054817142[/C][C]-34316.0548171416[/C][/ROW]
[ROW][C]52[/C][C]212004[/C][C]200944.784698217[/C][C]11059.2153017834[/C][/ROW]
[ROW][C]53[/C][C]250056[/C][C]268441.323693771[/C][C]-18385.3236937714[/C][/ROW]
[ROW][C]54[/C][C]250056[/C][C]238895.622564884[/C][C]11160.3774351156[/C][/ROW]
[ROW][C]55[/C][C]337032[/C][C]326965.25160851[/C][C]10066.7483914896[/C][/ROW]
[ROW][C]56[/C][C]309852[/C][C]315933.046483671[/C][C]-6081.04648367141[/C][/ROW]
[ROW][C]57[/C][C]277236[/C][C]273205.93881306[/C][C]4030.06118693994[/C][/ROW]
[ROW][C]58[/C][C]347904[/C][C]367494.689135199[/C][C]-19590.6891351989[/C][/ROW]
[ROW][C]59[/C][C]320724[/C][C]339378.529039575[/C][C]-18654.5290395747[/C][/ROW]
[ROW][C]60[/C][C]462060[/C][C]433624.535047151[/C][C]28435.4649528491[/C][/ROW]
[ROW][C]61[/C][C]364212[/C][C]344794.080828887[/C][C]19417.9191711127[/C][/ROW]
[ROW][C]62[/C][C]212004[/C][C]216407.372088731[/C][C]-4403.3720887308[/C][/ROW]
[ROW][C]63[/C][C]222876[/C][C]214890.313526965[/C][C]7985.68647303476[/C][/ROW]
[ROW][C]64[/C][C]184824[/C][C]211910.960639693[/C][C]-27086.9606396935[/C][/ROW]
[ROW][C]65[/C][C]255492[/C][C]251758.890072668[/C][C]3733.10992733249[/C][/ROW]
[ROW][C]66[/C][C]293544[/C][C]249636.520166691[/C][C]43907.4798333094[/C][/ROW]
[ROW][C]67[/C][C]369648[/C][C]337612.205109346[/C][C]32035.7948906537[/C][/ROW]
[ROW][C]68[/C][C]364212[/C][C]312276.139659795[/C][C]51935.8603402051[/C][/ROW]
[ROW][C]69[/C][C]293544[/C][C]280059.737769047[/C][C]13484.2622309533[/C][/ROW]
[ROW][C]70[/C][C]342468[/C][C]354753.277475003[/C][C]-12285.2774750029[/C][/ROW]
[ROW][C]71[/C][C]304416[/C][C]328369.697918337[/C][C]-23953.6979183374[/C][/ROW]
[ROW][C]72[/C][C]434880[/C][C]470304.427955428[/C][C]-35424.4279554284[/C][/ROW]
[ROW][C]73[/C][C]331596[/C][C]371333.141203704[/C][C]-39737.1412037038[/C][/ROW]
[ROW][C]74[/C][C]266364[/C][C]217259.103984288[/C][C]49104.8960157116[/C][/ROW]
[ROW][C]75[/C][C]239184[/C][C]228597.49573645[/C][C]10586.5042635504[/C][/ROW]
[ROW][C]76[/C][C]179388[/C][C]192843.826667727[/C][C]-13455.8266677274[/C][/ROW]
[ROW][C]77[/C][C]266364[/C][C]264417.754275451[/C][C]1946.24572454928[/C][/ROW]
[ROW][C]78[/C][C]320724[/C][C]301595.742704494[/C][C]19128.2572955063[/C][/ROW]
[ROW][C]79[/C][C]375084[/C][C]382292.933079347[/C][C]-7208.93307934742[/C][/ROW]
[ROW][C]80[/C][C]353340[/C][C]375145.933773744[/C][C]-21805.9337737436[/C][/ROW]
[ROW][C]81[/C][C]260928[/C][C]303920.592978065[/C][C]-42992.5929780652[/C][/ROW]
[ROW][C]82[/C][C]375084[/C][C]355423.942658137[/C][C]19660.0573418626[/C][/ROW]
[ROW][C]83[/C][C]293544[/C][C]316772.63226706[/C][C]-23228.6322670601[/C][/ROW]
[ROW][C]84[/C][C]451188[/C][C]451982.680003519[/C][C]-794.680003518763[/C][/ROW]
[ROW][C]85[/C][C]375084[/C][C]345606.330675359[/C][C]29477.6693246407[/C][/ROW]
[ROW][C]86[/C][C]271800[/C][C]271800.383894589[/C][C]-0.383894588798285[/C][/ROW]
[ROW][C]87[/C][C]250056[/C][C]246075.710318677[/C][C]3980.2896813229[/C][/ROW]
[ROW][C]88[/C][C]168516[/C][C]185968.958265323[/C][C]-17452.9582653227[/C][/ROW]
[ROW][C]89[/C][C]266364[/C][C]273916.14005761[/C][C]-7552.14005760965[/C][/ROW]
[ROW][C]90[/C][C]255492[/C][C]327761.857421514[/C][C]-72269.8574215141[/C][/ROW]
[ROW][C]91[/C][C]385956[/C][C]383007.108642892[/C][C]2948.89135710831[/C][/ROW]
[ROW][C]92[/C][C]385956[/C][C]360573.77096532[/C][C]25382.2290346799[/C][/ROW]
[ROW][C]93[/C][C]293544[/C][C]267860.688804363[/C][C]25683.3111956373[/C][/ROW]
[ROW][C]94[/C][C]380520[/C][C]379212.724352707[/C][C]1307.27564729343[/C][/ROW]
[ROW][C]95[/C][C]282672[/C][C]299283.766371395[/C][C]-16611.7663713953[/C][/ROW]
[ROW][C]96[/C][C]440316[/C][C]456851.276984049[/C][C]-16535.2769840487[/C][/ROW]
[ROW][C]97[/C][C]375084[/C][C]376748.924383557[/C][C]-1664.92438355664[/C][/ROW]
[ROW][C]98[/C][C]277236[/C][C]273861.638853296[/C][C]3374.36114670365[/C][/ROW]
[ROW][C]99[/C][C]212004[/C][C]251137.403443475[/C][C]-39133.4034434753[/C][/ROW]
[ROW][C]100[/C][C]146772[/C][C]169912.245499493[/C][C]-23140.2454994927[/C][/ROW]
[ROW][C]101[/C][C]288108[/C][C]265854.903960507[/C][C]22253.096039493[/C][/ROW]
[ROW][C]102[/C][C]277236[/C][C]259365.23517944[/C][C]17870.7648205603[/C][/ROW]
[ROW][C]103[/C][C]364212[/C][C]384203.657038996[/C][C]-19991.6570389961[/C][/ROW]
[ROW][C]104[/C][C]418572[/C][C]381878.17061856[/C][C]36693.8293814398[/C][/ROW]
[ROW][C]105[/C][C]309852[/C][C]289794.043420253[/C][C]20057.9565797469[/C][/ROW]
[ROW][C]106[/C][C]347904[/C][C]377689.723921234[/C][C]-29785.7239212344[/C][/ROW]
[ROW][C]107[/C][C]260928[/C][C]281220.804978116[/C][C]-20292.8049781162[/C][/ROW]
[ROW][C]108[/C][C]451188[/C][C]436459.409325043[/C][C]14728.5906749566[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211325&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211325&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
13326160338557.461834503-12397.4618345029
14244620253730.357566054-9110.3575660541
15288108301203.255518599-13095.2555185987
16217440226983.04099333-9543.04099332969
17304416312921.851084317-8505.85108431731
18250056253098.385567753-3042.38556775317
19331596316956.43890993414639.5610900663
20298980325905.06346127-26925.06346127
21315288362277.818566687-46989.8185666869
22353340313465.78838491439874.2116150857
23347904297125.11023789650778.8897621041
24413136371606.51596772641529.4840322745
25298980304364.942468195-5384.94246819546
26250056228331.81936199521724.1806380051
27277236269773.1110705967462.8889294042
28201132204116.677673828-2984.67767382826
29288108286133.1637614321974.83623856807
30222876235436.759631797-12560.7596317975
31315288311427.3690785733860.63092142704
32298980284187.42286862314792.5771313772
33266364302358.957966326-35994.9579663256
34380520333209.04691310747310.9530868928
35342468328404.13194697614063.8680530238
36391392391899.322573395-507.322573394573
37293544286368.5959288277175.40407117252
38271800238062.44202051633737.5579794836
39244620265890.874258132-21270.8742581318
40201132193581.3902023377550.609797663
41266364277444.056420095-11080.0564200954
42239184215869.14776699223314.8522330075
43326160305062.01842187721097.9815781231
44315288289551.70562330525736.2943766952
45271800262693.8668332429106.1331667584
46364212370188.30614101-5976.30614100985
47337032336140.249986462891.750013538171
48434880386573.11245248148306.8875475189
49347904290976.80945858356927.1905414168
50212004269322.778556533-57318.7785565326
51212004246320.054817142-34316.0548171416
52212004200944.78469821711059.2153017834
53250056268441.323693771-18385.3236937714
54250056238895.62256488411160.3774351156
55337032326965.2516085110066.7483914896
56309852315933.046483671-6081.04648367141
57277236273205.938813064030.06118693994
58347904367494.689135199-19590.6891351989
59320724339378.529039575-18654.5290395747
60462060433624.53504715128435.4649528491
61364212344794.08082888719417.9191711127
62212004216407.372088731-4403.3720887308
63222876214890.3135269657985.68647303476
64184824211910.960639693-27086.9606396935
65255492251758.8900726683733.10992733249
66293544249636.52016669143907.4798333094
67369648337612.20510934632035.7948906537
68364212312276.13965979551935.8603402051
69293544280059.73776904713484.2622309533
70342468354753.277475003-12285.2774750029
71304416328369.697918337-23953.6979183374
72434880470304.427955428-35424.4279554284
73331596371333.141203704-39737.1412037038
74266364217259.10398428849104.8960157116
75239184228597.4957364510586.5042635504
76179388192843.826667727-13455.8266677274
77266364264417.7542754511946.24572454928
78320724301595.74270449419128.2572955063
79375084382292.933079347-7208.93307934742
80353340375145.933773744-21805.9337737436
81260928303920.592978065-42992.5929780652
82375084355423.94265813719660.0573418626
83293544316772.63226706-23228.6322670601
84451188451982.680003519-794.680003518763
85375084345606.33067535929477.6693246407
86271800271800.383894589-0.383894588798285
87250056246075.7103186773980.2896813229
88168516185968.958265323-17452.9582653227
89266364273916.14005761-7552.14005760965
90255492327761.857421514-72269.8574215141
91385956383007.1086428922948.89135710831
92385956360573.7709653225382.2290346799
93293544267860.68880436325683.3111956373
94380520379212.7243527071307.27564729343
95282672299283.766371395-16611.7663713953
96440316456851.276984049-16535.2769840487
97375084376748.924383557-1664.92438355664
98277236273861.6388532963374.36114670365
99212004251137.403443475-39133.4034434753
100146772169912.245499493-23140.2454994927
101288108265854.90396050722253.096039493
102277236259365.2351794417870.7648205603
103364212384203.657038996-19991.6570389961
104418572381878.1706185636693.8293814398
105309852289794.04342025320057.9565797469
106347904377689.723921234-29785.7239212344
107260928281220.804978116-20292.8049781162
108451188436459.40932504314728.5906749566







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109370623.506419812324021.93310029417225.079739334
110273267.106443028226660.752955272319873.459930783
111211807.705458884165194.375159184258421.035758584
112146562.62752242899945.618967415193179.63607744
113283277.699592274236537.743235892330017.655948656
114272814.190840954225979.363551886319649.018130022
115361498.650722347314234.762690334408762.538754361
116411227.085709149363353.648649377459100.522768922
117304569.013786841256982.063564487352155.964009195
118345385.978523302297083.991311083393687.965735521
119258976.317408518211118.591762821306834.043054215
120444437.179219777423310.755369726465563.603069829

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 370623.506419812 & 324021.93310029 & 417225.079739334 \tabularnewline
110 & 273267.106443028 & 226660.752955272 & 319873.459930783 \tabularnewline
111 & 211807.705458884 & 165194.375159184 & 258421.035758584 \tabularnewline
112 & 146562.627522428 & 99945.618967415 & 193179.63607744 \tabularnewline
113 & 283277.699592274 & 236537.743235892 & 330017.655948656 \tabularnewline
114 & 272814.190840954 & 225979.363551886 & 319649.018130022 \tabularnewline
115 & 361498.650722347 & 314234.762690334 & 408762.538754361 \tabularnewline
116 & 411227.085709149 & 363353.648649377 & 459100.522768922 \tabularnewline
117 & 304569.013786841 & 256982.063564487 & 352155.964009195 \tabularnewline
118 & 345385.978523302 & 297083.991311083 & 393687.965735521 \tabularnewline
119 & 258976.317408518 & 211118.591762821 & 306834.043054215 \tabularnewline
120 & 444437.179219777 & 423310.755369726 & 465563.603069829 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211325&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]109[/C][C]370623.506419812[/C][C]324021.93310029[/C][C]417225.079739334[/C][/ROW]
[ROW][C]110[/C][C]273267.106443028[/C][C]226660.752955272[/C][C]319873.459930783[/C][/ROW]
[ROW][C]111[/C][C]211807.705458884[/C][C]165194.375159184[/C][C]258421.035758584[/C][/ROW]
[ROW][C]112[/C][C]146562.627522428[/C][C]99945.618967415[/C][C]193179.63607744[/C][/ROW]
[ROW][C]113[/C][C]283277.699592274[/C][C]236537.743235892[/C][C]330017.655948656[/C][/ROW]
[ROW][C]114[/C][C]272814.190840954[/C][C]225979.363551886[/C][C]319649.018130022[/C][/ROW]
[ROW][C]115[/C][C]361498.650722347[/C][C]314234.762690334[/C][C]408762.538754361[/C][/ROW]
[ROW][C]116[/C][C]411227.085709149[/C][C]363353.648649377[/C][C]459100.522768922[/C][/ROW]
[ROW][C]117[/C][C]304569.013786841[/C][C]256982.063564487[/C][C]352155.964009195[/C][/ROW]
[ROW][C]118[/C][C]345385.978523302[/C][C]297083.991311083[/C][C]393687.965735521[/C][/ROW]
[ROW][C]119[/C][C]258976.317408518[/C][C]211118.591762821[/C][C]306834.043054215[/C][/ROW]
[ROW][C]120[/C][C]444437.179219777[/C][C]423310.755369726[/C][C]465563.603069829[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211325&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211325&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
109370623.506419812324021.93310029417225.079739334
110273267.106443028226660.752955272319873.459930783
111211807.705458884165194.375159184258421.035758584
112146562.62752242899945.618967415193179.63607744
113283277.699592274236537.743235892330017.655948656
114272814.190840954225979.363551886319649.018130022
115361498.650722347314234.762690334408762.538754361
116411227.085709149363353.648649377459100.522768922
117304569.013786841256982.063564487352155.964009195
118345385.978523302297083.991311083393687.965735521
119258976.317408518211118.591762821306834.043054215
120444437.179219777423310.755369726465563.603069829



Parameters (Session):
par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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')