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Author's title

extraponential smoothing - werkloosheid in australie - Magali van de Wildeb...

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 02 Jun 2009 05:41:08 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jun/02/t1243943074uuj09g1du3akh6g.htm/, Retrieved Thu, 09 May 2024 21:09:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41199, Retrieved Thu, 09 May 2024 21:09:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact119
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [extraponential sm...] [2009-06-02 11:41:08] [946afef1f31655e4e01d6b8ef4c25a2b] [Current]
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Dataseries X:
428800
424800
403400
398400
393500
380500
398300
387300
370400
372800
444600
449900
458100
424800
420600
400100
393000
387100
377500
400400
391400
363600
431000
441700
448500
415600
408000
416600
409300
387600
394500
407600
378500
359600
435700
433800
427700
413300
379500
379300
353700
378200
380600
394000
374000
375000
437600
443900
488800
463900
440000
453800
451600
453400
461400
509100
540600
555100
677400
694600
750100
733900
709300
720500
693200
687200
686800
720900
653100
624700
690000
717800
736500
699900
675600
635600
632500
594900
604000
620800
578400
571200
627400
657700
674100
672800
615300
609100
607600
566900
572700
589200
534800
543100
591100
624800
665300
642600
608700
594500
563800
596100
597600
633100
591000
584200
655800
670700
699700
712900
652000
635100
603100
610100
602000
597600
585400
567100
620600
646200
644800
645200
644800
593000
569100
518800
538700
554600
507900
488400
563300
592400
598100
546300
516100
518500
477400
483400
469400
501300
457400
446700
501900
550400
593700
548900
534200
550500
541800
569300
587400
627700
607000
629500
704600
767700
812200
824600
856300
812200
764100
801700
806000
867200
801600
817500
920900
959700
997700
949100
910900
920400
914200
926300
906400
926100
902500
895300
979900
1009700
1043800
979800
921600
923500
914500
891700
916000
931700
902400
893700
941500
980100
1006900
949200
883200
849900
839200
803900
797900
830800
753300
764100
807600
853700
886200
815700
743000
753600
724800
709600
721900




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41199&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41199&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41199&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.72210178265567
beta0.166056440303876
gamma0.526285174526362

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.72210178265567 \tabularnewline
beta & 0.166056440303876 \tabularnewline
gamma & 0.526285174526362 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41199&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]0.72210178265567[/C][/ROW]
[ROW][C]beta[/C][C]0.166056440303876[/C][/ROW]
[ROW][C]gamma[/C][C]0.526285174526362[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41199&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41199&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
alpha0.72210178265567
beta0.166056440303876
gamma0.526285174526362







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13458100456110.2029914531989.79700854671
14424800425004.865593658-204.865593658236
15420600419648.526389863951.473610136658
16400100399870.439322215229.560677785252
17393000394440.250846746-1440.25084674591
18387100388789.921848848-1689.92184884817
19377500401119.167035188-23619.1670351877
20400400369189.43242406931210.5675759307
21391400375198.96186801616201.0381319843
22363600391541.910847728-27941.9108477278
23431000442796.152883703-11796.1528837035
24441700437590.636279074109.3637209296
25448500448400.12247222599.877527774719
26415600413943.5017339761656.49826602405
27408000408657.979521394-657.979521393776
28416600385976.73599748330623.2640025173
29409300404258.7920813315041.20791866921
30387600406038.523504067-18438.5235040669
31394500403844.323886398-9344.32388639846
32407600392731.2064470414868.7935529604
33378500385275.251196561-6775.25119656051
34359600376345.970560008-16745.9705600080
35435700437163.75937287-1463.75937287020
36433800442102.0383933-8302.03839330014
37427700442231.09486336-14531.0948633598
38413300394550.95774593718749.0422540632
39379500400432.925349469-20932.9253494691
40379300364418.37788525214881.6221147476
41353700362436.593457869-8736.59345786914
42378200344025.95852612434174.0414738762
43380600380654.807107233-54.8071072332677
44394000380406.18810249113593.8118975091
45374000369326.4253446174673.57465538307
46375000369041.3131696055958.68683039455
47437600453046.968847030-15446.9688470304
48443900449768.815091445-5868.81509144505
49488800453916.64217551534883.3578244845
50463900455884.1411801628015.8588198385
51440000456023.038716392-16023.0387163921
52453800437191.69831987816608.3016801223
53451600441609.30480959990.69519050024
54453400453849.904905493-449.904905493138
55461400467171.285456483-5771.28545648284
56509100470806.12903795838293.8709620417
57540600485234.6612335355365.3387664703
58555100536797.50256474318302.4974352574
59677400643121.51916659734278.4808334028
60694600699649.133031355-5049.13303135522
61750100732945.38955960617154.6104403938
62733900738651.98810968-4751.98810967989
63709300744994.965640613-35694.9656406129
64720500733311.635511074-12811.6355110742
65693200728570.158091934-35370.1580919340
66687200714142.379235556-26942.3792355565
67686800711992.272405551-25192.2724055512
68720900710156.16281727710743.8371827226
69653100705992.300529198-52892.3005291984
70624700659785.162104691-35085.1621046915
71690000709316.33848042-19316.3384804192
72717800694386.62919098323413.3708090172
73736500727891.4202163168608.57978368353
74699900699606.571721198293.42827880173
75675600681055.900500962-5455.90050096181
76635600674169.553348291-38569.5533482911
77632500624054.8750915118445.12490848894
78594900624278.564665846-29378.5646658456
79604000602112.9019960551887.09800394485
80620800609821.37972191310978.6202780871
81578400581282.922391457-2882.92239145702
82571200564551.5012804886648.49871951155
83627400642288.642367468-14888.6423674682
84657700633100.24726810524599.7527318948
85674100661733.41814321612366.5818567839
86672800631833.67558004140966.3244199587
87615300643576.755006667-28276.7550066673
88609100614396.633292866-5296.63329286571
89607600598202.4051773939397.59482260747
90566900596714.17436561-29814.1743656107
91572700581886.596951374-9186.59695137397
92589200584680.4863628944519.51363710559
93534800550428.162993806-15628.1629938064
94543100525336.6777282217763.3222717802
95591100608732.031598043-17632.0315980432
96624800603791.06146265721008.9385373431
97665300628064.68594100337235.3140589965
98642600623310.05233556319289.9476644371
99608700609678.851893173-978.851893173298
100594500607250.132641147-12750.1326411475
101563800590607.668115761-26807.6681157607
102596100555684.18849262740415.8115073731
103597600601451.424859782-3851.4248597821
104633100617606.9157481115493.0842518904
105591000597152.286469738-6152.28646973835
106584200593743.557929223-9543.55792922259
107655800658926.085284109-3126.08528410888
108670700678532.895361163-7832.89536116295
109699700689316.15877201710383.8412279827
110712900664290.91252842748609.0874715734
111652000674125.83608096-22125.8360809603
112635100657428.628884928-22328.6288849284
113603100633388.374795499-30288.3747954987
114610100606940.6101557973159.38984420313
115602000616020.721919631-14020.7219196314
116597600623132.806191955-25532.8061919553
117585400560438.84690755824961.1530924417
118567100573283.258627779-6183.25862777897
119620600636515.831738768-15915.8317387683
120646200639350.1290610886849.87093891227
121644800658312.089330393-13512.089330393
122645200613668.76026902131531.2397309791
123644800590825.3227159953974.6772840095
124593000628174.787039401-35174.7870394011
125569100591277.792871466-22177.7928714656
126518800574134.72669012-55334.7266901197
127538700530005.6414447028694.35855529818
128554600546102.5620805148497.43791948631
129507900513713.307731813-5813.30773181305
130488400494436.761768649-6036.76176864904
131563300551025.58312157712274.4168784230
132592400575599.848173616800.1518264000
133598100598016.2168856783.7831143303774
134546300570655.82709393-24355.8270939301
135516100504914.85777009111185.1422299088
136518500487372.78701211731127.2129878835
137477400497248.998142214-19848.9981422142
138483400474213.0333526359186.9666473646
139469400491051.242243692-21651.2422436916
140501300486579.59263075414720.4073692461
141457400458709.992601083-1309.99260108336
142446700445311.6451438831388.35485611670
143501900513489.60504465-11589.6050446497
144550400522181.36705760628218.6329423937
145593700552455.24065663841244.7593433616
146548900558235.510075241-9335.51007524051
147534200517332.44671968816867.5532803118
148550500516285.34249763934214.6575023613
149541800530780.84263637811019.1573636224
150569300547828.13527559521471.8647244048
151587400584046.8559838073353.14401619346
152627700620968.4418001536731.55819984747
153607000602045.6687020954954.3312979046
154629500611376.69158264118123.3084173588
155704600709558.846477612-4958.84647761239
156767700749473.81559026918226.1844097311
157812200793852.07455729818347.9254427025
158824600792370.22680679732229.7731932029
159856300806967.18206141949332.817938581
160812200857446.63846711-45246.6384671098
161764100827188.647590749-63088.6475907486
162801700799383.1487927312316.85120726866
163806000823955.038318916-17955.0383189163
164867200848263.96496347118936.0350365289
165801600841637.486542566-40037.4865425657
166817500818754.242367754-1254.24236775434
167920900895592.82013200925307.1798679914
168959700960407.863986725-707.863986724522
169997700988515.2691239669184.7308760339
170949100978731.829726943-29631.8297269433
171910900940026.88748547-29126.8874854703
172920400899476.87071081720923.1292891834
173914200901784.1373582312415.8626417693
174926300934513.506813203-8213.50681320345
175906400943701.005234177-37301.005234177
176926100952300.30122322-26200.3012232207
177902500891908.085273110591.9147268991
178895300904779.957068015-9479.95706801547
179979900972100.4372345327799.56276546803
18010097001010906.06963403-1206.06963402720
18110438001030478.4754291813321.5245708239
1829798001008879.12468186-29079.1246818635
183921600961587.384701492-39987.3847014921
184923500910152.94910505413347.0508949463
185914500894474.81664208320025.1833579167
186891700919323.719219721-27623.7192197209
187916000897555.393166218444.6068337996
188931700942031.130206948-10331.1302069485
189902400894380.8518895778019.14811042347
190893700898052.621826747-4352.62182674708
191941500967810.854062996-26310.8540629956
192980100972786.1185389227313.8814610776
1931006900993775.06719242613124.9328075737
194949200958948.488004216-9748.48800421564
195883200919453.974778265-36253.9747782646
196849900874397.38526633-24497.3852663293
197839200823712.09144462715487.9085553734
198803900829115.399688619-25215.3996886188
199797900806912.178655593-9012.17865559319
200830800815148.81952631415651.1804736863
201753300779855.79613657-26555.7961365693
202764100743517.23615605620582.7638439441
203807600817825.591507595-10225.5915075951
204853700831018.28299756222681.7170024378
205886200857481.50059417528718.4994058247
206815700825966.799760484-10266.7997604843
207743000777556.395096687-34556.395096687
208753600730983.54017106522616.4598289349
209724800721355.1046867663444.89531323384
210709600711852.917331436-2252.91733143583
211721900711097.94586592710802.0541340732

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 458100 & 456110.202991453 & 1989.79700854671 \tabularnewline
14 & 424800 & 425004.865593658 & -204.865593658236 \tabularnewline
15 & 420600 & 419648.526389863 & 951.473610136658 \tabularnewline
16 & 400100 & 399870.439322215 & 229.560677785252 \tabularnewline
17 & 393000 & 394440.250846746 & -1440.25084674591 \tabularnewline
18 & 387100 & 388789.921848848 & -1689.92184884817 \tabularnewline
19 & 377500 & 401119.167035188 & -23619.1670351877 \tabularnewline
20 & 400400 & 369189.432424069 & 31210.5675759307 \tabularnewline
21 & 391400 & 375198.961868016 & 16201.0381319843 \tabularnewline
22 & 363600 & 391541.910847728 & -27941.9108477278 \tabularnewline
23 & 431000 & 442796.152883703 & -11796.1528837035 \tabularnewline
24 & 441700 & 437590.63627907 & 4109.3637209296 \tabularnewline
25 & 448500 & 448400.122472225 & 99.877527774719 \tabularnewline
26 & 415600 & 413943.501733976 & 1656.49826602405 \tabularnewline
27 & 408000 & 408657.979521394 & -657.979521393776 \tabularnewline
28 & 416600 & 385976.735997483 & 30623.2640025173 \tabularnewline
29 & 409300 & 404258.792081331 & 5041.20791866921 \tabularnewline
30 & 387600 & 406038.523504067 & -18438.5235040669 \tabularnewline
31 & 394500 & 403844.323886398 & -9344.32388639846 \tabularnewline
32 & 407600 & 392731.20644704 & 14868.7935529604 \tabularnewline
33 & 378500 & 385275.251196561 & -6775.25119656051 \tabularnewline
34 & 359600 & 376345.970560008 & -16745.9705600080 \tabularnewline
35 & 435700 & 437163.75937287 & -1463.75937287020 \tabularnewline
36 & 433800 & 442102.0383933 & -8302.03839330014 \tabularnewline
37 & 427700 & 442231.09486336 & -14531.0948633598 \tabularnewline
38 & 413300 & 394550.957745937 & 18749.0422540632 \tabularnewline
39 & 379500 & 400432.925349469 & -20932.9253494691 \tabularnewline
40 & 379300 & 364418.377885252 & 14881.6221147476 \tabularnewline
41 & 353700 & 362436.593457869 & -8736.59345786914 \tabularnewline
42 & 378200 & 344025.958526124 & 34174.0414738762 \tabularnewline
43 & 380600 & 380654.807107233 & -54.8071072332677 \tabularnewline
44 & 394000 & 380406.188102491 & 13593.8118975091 \tabularnewline
45 & 374000 & 369326.425344617 & 4673.57465538307 \tabularnewline
46 & 375000 & 369041.313169605 & 5958.68683039455 \tabularnewline
47 & 437600 & 453046.968847030 & -15446.9688470304 \tabularnewline
48 & 443900 & 449768.815091445 & -5868.81509144505 \tabularnewline
49 & 488800 & 453916.642175515 & 34883.3578244845 \tabularnewline
50 & 463900 & 455884.141180162 & 8015.8588198385 \tabularnewline
51 & 440000 & 456023.038716392 & -16023.0387163921 \tabularnewline
52 & 453800 & 437191.698319878 & 16608.3016801223 \tabularnewline
53 & 451600 & 441609.3048095 & 9990.69519050024 \tabularnewline
54 & 453400 & 453849.904905493 & -449.904905493138 \tabularnewline
55 & 461400 & 467171.285456483 & -5771.28545648284 \tabularnewline
56 & 509100 & 470806.129037958 & 38293.8709620417 \tabularnewline
57 & 540600 & 485234.66123353 & 55365.3387664703 \tabularnewline
58 & 555100 & 536797.502564743 & 18302.4974352574 \tabularnewline
59 & 677400 & 643121.519166597 & 34278.4808334028 \tabularnewline
60 & 694600 & 699649.133031355 & -5049.13303135522 \tabularnewline
61 & 750100 & 732945.389559606 & 17154.6104403938 \tabularnewline
62 & 733900 & 738651.98810968 & -4751.98810967989 \tabularnewline
63 & 709300 & 744994.965640613 & -35694.9656406129 \tabularnewline
64 & 720500 & 733311.635511074 & -12811.6355110742 \tabularnewline
65 & 693200 & 728570.158091934 & -35370.1580919340 \tabularnewline
66 & 687200 & 714142.379235556 & -26942.3792355565 \tabularnewline
67 & 686800 & 711992.272405551 & -25192.2724055512 \tabularnewline
68 & 720900 & 710156.162817277 & 10743.8371827226 \tabularnewline
69 & 653100 & 705992.300529198 & -52892.3005291984 \tabularnewline
70 & 624700 & 659785.162104691 & -35085.1621046915 \tabularnewline
71 & 690000 & 709316.33848042 & -19316.3384804192 \tabularnewline
72 & 717800 & 694386.629190983 & 23413.3708090172 \tabularnewline
73 & 736500 & 727891.420216316 & 8608.57978368353 \tabularnewline
74 & 699900 & 699606.571721198 & 293.42827880173 \tabularnewline
75 & 675600 & 681055.900500962 & -5455.90050096181 \tabularnewline
76 & 635600 & 674169.553348291 & -38569.5533482911 \tabularnewline
77 & 632500 & 624054.875091511 & 8445.12490848894 \tabularnewline
78 & 594900 & 624278.564665846 & -29378.5646658456 \tabularnewline
79 & 604000 & 602112.901996055 & 1887.09800394485 \tabularnewline
80 & 620800 & 609821.379721913 & 10978.6202780871 \tabularnewline
81 & 578400 & 581282.922391457 & -2882.92239145702 \tabularnewline
82 & 571200 & 564551.501280488 & 6648.49871951155 \tabularnewline
83 & 627400 & 642288.642367468 & -14888.6423674682 \tabularnewline
84 & 657700 & 633100.247268105 & 24599.7527318948 \tabularnewline
85 & 674100 & 661733.418143216 & 12366.5818567839 \tabularnewline
86 & 672800 & 631833.675580041 & 40966.3244199587 \tabularnewline
87 & 615300 & 643576.755006667 & -28276.7550066673 \tabularnewline
88 & 609100 & 614396.633292866 & -5296.63329286571 \tabularnewline
89 & 607600 & 598202.405177393 & 9397.59482260747 \tabularnewline
90 & 566900 & 596714.17436561 & -29814.1743656107 \tabularnewline
91 & 572700 & 581886.596951374 & -9186.59695137397 \tabularnewline
92 & 589200 & 584680.486362894 & 4519.51363710559 \tabularnewline
93 & 534800 & 550428.162993806 & -15628.1629938064 \tabularnewline
94 & 543100 & 525336.67772822 & 17763.3222717802 \tabularnewline
95 & 591100 & 608732.031598043 & -17632.0315980432 \tabularnewline
96 & 624800 & 603791.061462657 & 21008.9385373431 \tabularnewline
97 & 665300 & 628064.685941003 & 37235.3140589965 \tabularnewline
98 & 642600 & 623310.052335563 & 19289.9476644371 \tabularnewline
99 & 608700 & 609678.851893173 & -978.851893173298 \tabularnewline
100 & 594500 & 607250.132641147 & -12750.1326411475 \tabularnewline
101 & 563800 & 590607.668115761 & -26807.6681157607 \tabularnewline
102 & 596100 & 555684.188492627 & 40415.8115073731 \tabularnewline
103 & 597600 & 601451.424859782 & -3851.4248597821 \tabularnewline
104 & 633100 & 617606.91574811 & 15493.0842518904 \tabularnewline
105 & 591000 & 597152.286469738 & -6152.28646973835 \tabularnewline
106 & 584200 & 593743.557929223 & -9543.55792922259 \tabularnewline
107 & 655800 & 658926.085284109 & -3126.08528410888 \tabularnewline
108 & 670700 & 678532.895361163 & -7832.89536116295 \tabularnewline
109 & 699700 & 689316.158772017 & 10383.8412279827 \tabularnewline
110 & 712900 & 664290.912528427 & 48609.0874715734 \tabularnewline
111 & 652000 & 674125.83608096 & -22125.8360809603 \tabularnewline
112 & 635100 & 657428.628884928 & -22328.6288849284 \tabularnewline
113 & 603100 & 633388.374795499 & -30288.3747954987 \tabularnewline
114 & 610100 & 606940.610155797 & 3159.38984420313 \tabularnewline
115 & 602000 & 616020.721919631 & -14020.7219196314 \tabularnewline
116 & 597600 & 623132.806191955 & -25532.8061919553 \tabularnewline
117 & 585400 & 560438.846907558 & 24961.1530924417 \tabularnewline
118 & 567100 & 573283.258627779 & -6183.25862777897 \tabularnewline
119 & 620600 & 636515.831738768 & -15915.8317387683 \tabularnewline
120 & 646200 & 639350.129061088 & 6849.87093891227 \tabularnewline
121 & 644800 & 658312.089330393 & -13512.089330393 \tabularnewline
122 & 645200 & 613668.760269021 & 31531.2397309791 \tabularnewline
123 & 644800 & 590825.32271599 & 53974.6772840095 \tabularnewline
124 & 593000 & 628174.787039401 & -35174.7870394011 \tabularnewline
125 & 569100 & 591277.792871466 & -22177.7928714656 \tabularnewline
126 & 518800 & 574134.72669012 & -55334.7266901197 \tabularnewline
127 & 538700 & 530005.641444702 & 8694.35855529818 \tabularnewline
128 & 554600 & 546102.562080514 & 8497.43791948631 \tabularnewline
129 & 507900 & 513713.307731813 & -5813.30773181305 \tabularnewline
130 & 488400 & 494436.761768649 & -6036.76176864904 \tabularnewline
131 & 563300 & 551025.583121577 & 12274.4168784230 \tabularnewline
132 & 592400 & 575599.8481736 & 16800.1518264000 \tabularnewline
133 & 598100 & 598016.21688567 & 83.7831143303774 \tabularnewline
134 & 546300 & 570655.82709393 & -24355.8270939301 \tabularnewline
135 & 516100 & 504914.857770091 & 11185.1422299088 \tabularnewline
136 & 518500 & 487372.787012117 & 31127.2129878835 \tabularnewline
137 & 477400 & 497248.998142214 & -19848.9981422142 \tabularnewline
138 & 483400 & 474213.033352635 & 9186.9666473646 \tabularnewline
139 & 469400 & 491051.242243692 & -21651.2422436916 \tabularnewline
140 & 501300 & 486579.592630754 & 14720.4073692461 \tabularnewline
141 & 457400 & 458709.992601083 & -1309.99260108336 \tabularnewline
142 & 446700 & 445311.645143883 & 1388.35485611670 \tabularnewline
143 & 501900 & 513489.60504465 & -11589.6050446497 \tabularnewline
144 & 550400 & 522181.367057606 & 28218.6329423937 \tabularnewline
145 & 593700 & 552455.240656638 & 41244.7593433616 \tabularnewline
146 & 548900 & 558235.510075241 & -9335.51007524051 \tabularnewline
147 & 534200 & 517332.446719688 & 16867.5532803118 \tabularnewline
148 & 550500 & 516285.342497639 & 34214.6575023613 \tabularnewline
149 & 541800 & 530780.842636378 & 11019.1573636224 \tabularnewline
150 & 569300 & 547828.135275595 & 21471.8647244048 \tabularnewline
151 & 587400 & 584046.855983807 & 3353.14401619346 \tabularnewline
152 & 627700 & 620968.441800153 & 6731.55819984747 \tabularnewline
153 & 607000 & 602045.668702095 & 4954.3312979046 \tabularnewline
154 & 629500 & 611376.691582641 & 18123.3084173588 \tabularnewline
155 & 704600 & 709558.846477612 & -4958.84647761239 \tabularnewline
156 & 767700 & 749473.815590269 & 18226.1844097311 \tabularnewline
157 & 812200 & 793852.074557298 & 18347.9254427025 \tabularnewline
158 & 824600 & 792370.226806797 & 32229.7731932029 \tabularnewline
159 & 856300 & 806967.182061419 & 49332.817938581 \tabularnewline
160 & 812200 & 857446.63846711 & -45246.6384671098 \tabularnewline
161 & 764100 & 827188.647590749 & -63088.6475907486 \tabularnewline
162 & 801700 & 799383.148792731 & 2316.85120726866 \tabularnewline
163 & 806000 & 823955.038318916 & -17955.0383189163 \tabularnewline
164 & 867200 & 848263.964963471 & 18936.0350365289 \tabularnewline
165 & 801600 & 841637.486542566 & -40037.4865425657 \tabularnewline
166 & 817500 & 818754.242367754 & -1254.24236775434 \tabularnewline
167 & 920900 & 895592.820132009 & 25307.1798679914 \tabularnewline
168 & 959700 & 960407.863986725 & -707.863986724522 \tabularnewline
169 & 997700 & 988515.269123966 & 9184.7308760339 \tabularnewline
170 & 949100 & 978731.829726943 & -29631.8297269433 \tabularnewline
171 & 910900 & 940026.88748547 & -29126.8874854703 \tabularnewline
172 & 920400 & 899476.870710817 & 20923.1292891834 \tabularnewline
173 & 914200 & 901784.13735823 & 12415.8626417693 \tabularnewline
174 & 926300 & 934513.506813203 & -8213.50681320345 \tabularnewline
175 & 906400 & 943701.005234177 & -37301.005234177 \tabularnewline
176 & 926100 & 952300.30122322 & -26200.3012232207 \tabularnewline
177 & 902500 & 891908.0852731 & 10591.9147268991 \tabularnewline
178 & 895300 & 904779.957068015 & -9479.95706801547 \tabularnewline
179 & 979900 & 972100.437234532 & 7799.56276546803 \tabularnewline
180 & 1009700 & 1010906.06963403 & -1206.06963402720 \tabularnewline
181 & 1043800 & 1030478.47542918 & 13321.5245708239 \tabularnewline
182 & 979800 & 1008879.12468186 & -29079.1246818635 \tabularnewline
183 & 921600 & 961587.384701492 & -39987.3847014921 \tabularnewline
184 & 923500 & 910152.949105054 & 13347.0508949463 \tabularnewline
185 & 914500 & 894474.816642083 & 20025.1833579167 \tabularnewline
186 & 891700 & 919323.719219721 & -27623.7192197209 \tabularnewline
187 & 916000 & 897555.3931662 & 18444.6068337996 \tabularnewline
188 & 931700 & 942031.130206948 & -10331.1302069485 \tabularnewline
189 & 902400 & 894380.851889577 & 8019.14811042347 \tabularnewline
190 & 893700 & 898052.621826747 & -4352.62182674708 \tabularnewline
191 & 941500 & 967810.854062996 & -26310.8540629956 \tabularnewline
192 & 980100 & 972786.118538922 & 7313.8814610776 \tabularnewline
193 & 1006900 & 993775.067192426 & 13124.9328075737 \tabularnewline
194 & 949200 & 958948.488004216 & -9748.48800421564 \tabularnewline
195 & 883200 & 919453.974778265 & -36253.9747782646 \tabularnewline
196 & 849900 & 874397.38526633 & -24497.3852663293 \tabularnewline
197 & 839200 & 823712.091444627 & 15487.9085553734 \tabularnewline
198 & 803900 & 829115.399688619 & -25215.3996886188 \tabularnewline
199 & 797900 & 806912.178655593 & -9012.17865559319 \tabularnewline
200 & 830800 & 815148.819526314 & 15651.1804736863 \tabularnewline
201 & 753300 & 779855.79613657 & -26555.7961365693 \tabularnewline
202 & 764100 & 743517.236156056 & 20582.7638439441 \tabularnewline
203 & 807600 & 817825.591507595 & -10225.5915075951 \tabularnewline
204 & 853700 & 831018.282997562 & 22681.7170024378 \tabularnewline
205 & 886200 & 857481.500594175 & 28718.4994058247 \tabularnewline
206 & 815700 & 825966.799760484 & -10266.7997604843 \tabularnewline
207 & 743000 & 777556.395096687 & -34556.395096687 \tabularnewline
208 & 753600 & 730983.540171065 & 22616.4598289349 \tabularnewline
209 & 724800 & 721355.104686766 & 3444.89531323384 \tabularnewline
210 & 709600 & 711852.917331436 & -2252.91733143583 \tabularnewline
211 & 721900 & 711097.945865927 & 10802.0541340732 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41199&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]458100[/C][C]456110.202991453[/C][C]1989.79700854671[/C][/ROW]
[ROW][C]14[/C][C]424800[/C][C]425004.865593658[/C][C]-204.865593658236[/C][/ROW]
[ROW][C]15[/C][C]420600[/C][C]419648.526389863[/C][C]951.473610136658[/C][/ROW]
[ROW][C]16[/C][C]400100[/C][C]399870.439322215[/C][C]229.560677785252[/C][/ROW]
[ROW][C]17[/C][C]393000[/C][C]394440.250846746[/C][C]-1440.25084674591[/C][/ROW]
[ROW][C]18[/C][C]387100[/C][C]388789.921848848[/C][C]-1689.92184884817[/C][/ROW]
[ROW][C]19[/C][C]377500[/C][C]401119.167035188[/C][C]-23619.1670351877[/C][/ROW]
[ROW][C]20[/C][C]400400[/C][C]369189.432424069[/C][C]31210.5675759307[/C][/ROW]
[ROW][C]21[/C][C]391400[/C][C]375198.961868016[/C][C]16201.0381319843[/C][/ROW]
[ROW][C]22[/C][C]363600[/C][C]391541.910847728[/C][C]-27941.9108477278[/C][/ROW]
[ROW][C]23[/C][C]431000[/C][C]442796.152883703[/C][C]-11796.1528837035[/C][/ROW]
[ROW][C]24[/C][C]441700[/C][C]437590.63627907[/C][C]4109.3637209296[/C][/ROW]
[ROW][C]25[/C][C]448500[/C][C]448400.122472225[/C][C]99.877527774719[/C][/ROW]
[ROW][C]26[/C][C]415600[/C][C]413943.501733976[/C][C]1656.49826602405[/C][/ROW]
[ROW][C]27[/C][C]408000[/C][C]408657.979521394[/C][C]-657.979521393776[/C][/ROW]
[ROW][C]28[/C][C]416600[/C][C]385976.735997483[/C][C]30623.2640025173[/C][/ROW]
[ROW][C]29[/C][C]409300[/C][C]404258.792081331[/C][C]5041.20791866921[/C][/ROW]
[ROW][C]30[/C][C]387600[/C][C]406038.523504067[/C][C]-18438.5235040669[/C][/ROW]
[ROW][C]31[/C][C]394500[/C][C]403844.323886398[/C][C]-9344.32388639846[/C][/ROW]
[ROW][C]32[/C][C]407600[/C][C]392731.20644704[/C][C]14868.7935529604[/C][/ROW]
[ROW][C]33[/C][C]378500[/C][C]385275.251196561[/C][C]-6775.25119656051[/C][/ROW]
[ROW][C]34[/C][C]359600[/C][C]376345.970560008[/C][C]-16745.9705600080[/C][/ROW]
[ROW][C]35[/C][C]435700[/C][C]437163.75937287[/C][C]-1463.75937287020[/C][/ROW]
[ROW][C]36[/C][C]433800[/C][C]442102.0383933[/C][C]-8302.03839330014[/C][/ROW]
[ROW][C]37[/C][C]427700[/C][C]442231.09486336[/C][C]-14531.0948633598[/C][/ROW]
[ROW][C]38[/C][C]413300[/C][C]394550.957745937[/C][C]18749.0422540632[/C][/ROW]
[ROW][C]39[/C][C]379500[/C][C]400432.925349469[/C][C]-20932.9253494691[/C][/ROW]
[ROW][C]40[/C][C]379300[/C][C]364418.377885252[/C][C]14881.6221147476[/C][/ROW]
[ROW][C]41[/C][C]353700[/C][C]362436.593457869[/C][C]-8736.59345786914[/C][/ROW]
[ROW][C]42[/C][C]378200[/C][C]344025.958526124[/C][C]34174.0414738762[/C][/ROW]
[ROW][C]43[/C][C]380600[/C][C]380654.807107233[/C][C]-54.8071072332677[/C][/ROW]
[ROW][C]44[/C][C]394000[/C][C]380406.188102491[/C][C]13593.8118975091[/C][/ROW]
[ROW][C]45[/C][C]374000[/C][C]369326.425344617[/C][C]4673.57465538307[/C][/ROW]
[ROW][C]46[/C][C]375000[/C][C]369041.313169605[/C][C]5958.68683039455[/C][/ROW]
[ROW][C]47[/C][C]437600[/C][C]453046.968847030[/C][C]-15446.9688470304[/C][/ROW]
[ROW][C]48[/C][C]443900[/C][C]449768.815091445[/C][C]-5868.81509144505[/C][/ROW]
[ROW][C]49[/C][C]488800[/C][C]453916.642175515[/C][C]34883.3578244845[/C][/ROW]
[ROW][C]50[/C][C]463900[/C][C]455884.141180162[/C][C]8015.8588198385[/C][/ROW]
[ROW][C]51[/C][C]440000[/C][C]456023.038716392[/C][C]-16023.0387163921[/C][/ROW]
[ROW][C]52[/C][C]453800[/C][C]437191.698319878[/C][C]16608.3016801223[/C][/ROW]
[ROW][C]53[/C][C]451600[/C][C]441609.3048095[/C][C]9990.69519050024[/C][/ROW]
[ROW][C]54[/C][C]453400[/C][C]453849.904905493[/C][C]-449.904905493138[/C][/ROW]
[ROW][C]55[/C][C]461400[/C][C]467171.285456483[/C][C]-5771.28545648284[/C][/ROW]
[ROW][C]56[/C][C]509100[/C][C]470806.129037958[/C][C]38293.8709620417[/C][/ROW]
[ROW][C]57[/C][C]540600[/C][C]485234.66123353[/C][C]55365.3387664703[/C][/ROW]
[ROW][C]58[/C][C]555100[/C][C]536797.502564743[/C][C]18302.4974352574[/C][/ROW]
[ROW][C]59[/C][C]677400[/C][C]643121.519166597[/C][C]34278.4808334028[/C][/ROW]
[ROW][C]60[/C][C]694600[/C][C]699649.133031355[/C][C]-5049.13303135522[/C][/ROW]
[ROW][C]61[/C][C]750100[/C][C]732945.389559606[/C][C]17154.6104403938[/C][/ROW]
[ROW][C]62[/C][C]733900[/C][C]738651.98810968[/C][C]-4751.98810967989[/C][/ROW]
[ROW][C]63[/C][C]709300[/C][C]744994.965640613[/C][C]-35694.9656406129[/C][/ROW]
[ROW][C]64[/C][C]720500[/C][C]733311.635511074[/C][C]-12811.6355110742[/C][/ROW]
[ROW][C]65[/C][C]693200[/C][C]728570.158091934[/C][C]-35370.1580919340[/C][/ROW]
[ROW][C]66[/C][C]687200[/C][C]714142.379235556[/C][C]-26942.3792355565[/C][/ROW]
[ROW][C]67[/C][C]686800[/C][C]711992.272405551[/C][C]-25192.2724055512[/C][/ROW]
[ROW][C]68[/C][C]720900[/C][C]710156.162817277[/C][C]10743.8371827226[/C][/ROW]
[ROW][C]69[/C][C]653100[/C][C]705992.300529198[/C][C]-52892.3005291984[/C][/ROW]
[ROW][C]70[/C][C]624700[/C][C]659785.162104691[/C][C]-35085.1621046915[/C][/ROW]
[ROW][C]71[/C][C]690000[/C][C]709316.33848042[/C][C]-19316.3384804192[/C][/ROW]
[ROW][C]72[/C][C]717800[/C][C]694386.629190983[/C][C]23413.3708090172[/C][/ROW]
[ROW][C]73[/C][C]736500[/C][C]727891.420216316[/C][C]8608.57978368353[/C][/ROW]
[ROW][C]74[/C][C]699900[/C][C]699606.571721198[/C][C]293.42827880173[/C][/ROW]
[ROW][C]75[/C][C]675600[/C][C]681055.900500962[/C][C]-5455.90050096181[/C][/ROW]
[ROW][C]76[/C][C]635600[/C][C]674169.553348291[/C][C]-38569.5533482911[/C][/ROW]
[ROW][C]77[/C][C]632500[/C][C]624054.875091511[/C][C]8445.12490848894[/C][/ROW]
[ROW][C]78[/C][C]594900[/C][C]624278.564665846[/C][C]-29378.5646658456[/C][/ROW]
[ROW][C]79[/C][C]604000[/C][C]602112.901996055[/C][C]1887.09800394485[/C][/ROW]
[ROW][C]80[/C][C]620800[/C][C]609821.379721913[/C][C]10978.6202780871[/C][/ROW]
[ROW][C]81[/C][C]578400[/C][C]581282.922391457[/C][C]-2882.92239145702[/C][/ROW]
[ROW][C]82[/C][C]571200[/C][C]564551.501280488[/C][C]6648.49871951155[/C][/ROW]
[ROW][C]83[/C][C]627400[/C][C]642288.642367468[/C][C]-14888.6423674682[/C][/ROW]
[ROW][C]84[/C][C]657700[/C][C]633100.247268105[/C][C]24599.7527318948[/C][/ROW]
[ROW][C]85[/C][C]674100[/C][C]661733.418143216[/C][C]12366.5818567839[/C][/ROW]
[ROW][C]86[/C][C]672800[/C][C]631833.675580041[/C][C]40966.3244199587[/C][/ROW]
[ROW][C]87[/C][C]615300[/C][C]643576.755006667[/C][C]-28276.7550066673[/C][/ROW]
[ROW][C]88[/C][C]609100[/C][C]614396.633292866[/C][C]-5296.63329286571[/C][/ROW]
[ROW][C]89[/C][C]607600[/C][C]598202.405177393[/C][C]9397.59482260747[/C][/ROW]
[ROW][C]90[/C][C]566900[/C][C]596714.17436561[/C][C]-29814.1743656107[/C][/ROW]
[ROW][C]91[/C][C]572700[/C][C]581886.596951374[/C][C]-9186.59695137397[/C][/ROW]
[ROW][C]92[/C][C]589200[/C][C]584680.486362894[/C][C]4519.51363710559[/C][/ROW]
[ROW][C]93[/C][C]534800[/C][C]550428.162993806[/C][C]-15628.1629938064[/C][/ROW]
[ROW][C]94[/C][C]543100[/C][C]525336.67772822[/C][C]17763.3222717802[/C][/ROW]
[ROW][C]95[/C][C]591100[/C][C]608732.031598043[/C][C]-17632.0315980432[/C][/ROW]
[ROW][C]96[/C][C]624800[/C][C]603791.061462657[/C][C]21008.9385373431[/C][/ROW]
[ROW][C]97[/C][C]665300[/C][C]628064.685941003[/C][C]37235.3140589965[/C][/ROW]
[ROW][C]98[/C][C]642600[/C][C]623310.052335563[/C][C]19289.9476644371[/C][/ROW]
[ROW][C]99[/C][C]608700[/C][C]609678.851893173[/C][C]-978.851893173298[/C][/ROW]
[ROW][C]100[/C][C]594500[/C][C]607250.132641147[/C][C]-12750.1326411475[/C][/ROW]
[ROW][C]101[/C][C]563800[/C][C]590607.668115761[/C][C]-26807.6681157607[/C][/ROW]
[ROW][C]102[/C][C]596100[/C][C]555684.188492627[/C][C]40415.8115073731[/C][/ROW]
[ROW][C]103[/C][C]597600[/C][C]601451.424859782[/C][C]-3851.4248597821[/C][/ROW]
[ROW][C]104[/C][C]633100[/C][C]617606.91574811[/C][C]15493.0842518904[/C][/ROW]
[ROW][C]105[/C][C]591000[/C][C]597152.286469738[/C][C]-6152.28646973835[/C][/ROW]
[ROW][C]106[/C][C]584200[/C][C]593743.557929223[/C][C]-9543.55792922259[/C][/ROW]
[ROW][C]107[/C][C]655800[/C][C]658926.085284109[/C][C]-3126.08528410888[/C][/ROW]
[ROW][C]108[/C][C]670700[/C][C]678532.895361163[/C][C]-7832.89536116295[/C][/ROW]
[ROW][C]109[/C][C]699700[/C][C]689316.158772017[/C][C]10383.8412279827[/C][/ROW]
[ROW][C]110[/C][C]712900[/C][C]664290.912528427[/C][C]48609.0874715734[/C][/ROW]
[ROW][C]111[/C][C]652000[/C][C]674125.83608096[/C][C]-22125.8360809603[/C][/ROW]
[ROW][C]112[/C][C]635100[/C][C]657428.628884928[/C][C]-22328.6288849284[/C][/ROW]
[ROW][C]113[/C][C]603100[/C][C]633388.374795499[/C][C]-30288.3747954987[/C][/ROW]
[ROW][C]114[/C][C]610100[/C][C]606940.610155797[/C][C]3159.38984420313[/C][/ROW]
[ROW][C]115[/C][C]602000[/C][C]616020.721919631[/C][C]-14020.7219196314[/C][/ROW]
[ROW][C]116[/C][C]597600[/C][C]623132.806191955[/C][C]-25532.8061919553[/C][/ROW]
[ROW][C]117[/C][C]585400[/C][C]560438.846907558[/C][C]24961.1530924417[/C][/ROW]
[ROW][C]118[/C][C]567100[/C][C]573283.258627779[/C][C]-6183.25862777897[/C][/ROW]
[ROW][C]119[/C][C]620600[/C][C]636515.831738768[/C][C]-15915.8317387683[/C][/ROW]
[ROW][C]120[/C][C]646200[/C][C]639350.129061088[/C][C]6849.87093891227[/C][/ROW]
[ROW][C]121[/C][C]644800[/C][C]658312.089330393[/C][C]-13512.089330393[/C][/ROW]
[ROW][C]122[/C][C]645200[/C][C]613668.760269021[/C][C]31531.2397309791[/C][/ROW]
[ROW][C]123[/C][C]644800[/C][C]590825.32271599[/C][C]53974.6772840095[/C][/ROW]
[ROW][C]124[/C][C]593000[/C][C]628174.787039401[/C][C]-35174.7870394011[/C][/ROW]
[ROW][C]125[/C][C]569100[/C][C]591277.792871466[/C][C]-22177.7928714656[/C][/ROW]
[ROW][C]126[/C][C]518800[/C][C]574134.72669012[/C][C]-55334.7266901197[/C][/ROW]
[ROW][C]127[/C][C]538700[/C][C]530005.641444702[/C][C]8694.35855529818[/C][/ROW]
[ROW][C]128[/C][C]554600[/C][C]546102.562080514[/C][C]8497.43791948631[/C][/ROW]
[ROW][C]129[/C][C]507900[/C][C]513713.307731813[/C][C]-5813.30773181305[/C][/ROW]
[ROW][C]130[/C][C]488400[/C][C]494436.761768649[/C][C]-6036.76176864904[/C][/ROW]
[ROW][C]131[/C][C]563300[/C][C]551025.583121577[/C][C]12274.4168784230[/C][/ROW]
[ROW][C]132[/C][C]592400[/C][C]575599.8481736[/C][C]16800.1518264000[/C][/ROW]
[ROW][C]133[/C][C]598100[/C][C]598016.21688567[/C][C]83.7831143303774[/C][/ROW]
[ROW][C]134[/C][C]546300[/C][C]570655.82709393[/C][C]-24355.8270939301[/C][/ROW]
[ROW][C]135[/C][C]516100[/C][C]504914.857770091[/C][C]11185.1422299088[/C][/ROW]
[ROW][C]136[/C][C]518500[/C][C]487372.787012117[/C][C]31127.2129878835[/C][/ROW]
[ROW][C]137[/C][C]477400[/C][C]497248.998142214[/C][C]-19848.9981422142[/C][/ROW]
[ROW][C]138[/C][C]483400[/C][C]474213.033352635[/C][C]9186.9666473646[/C][/ROW]
[ROW][C]139[/C][C]469400[/C][C]491051.242243692[/C][C]-21651.2422436916[/C][/ROW]
[ROW][C]140[/C][C]501300[/C][C]486579.592630754[/C][C]14720.4073692461[/C][/ROW]
[ROW][C]141[/C][C]457400[/C][C]458709.992601083[/C][C]-1309.99260108336[/C][/ROW]
[ROW][C]142[/C][C]446700[/C][C]445311.645143883[/C][C]1388.35485611670[/C][/ROW]
[ROW][C]143[/C][C]501900[/C][C]513489.60504465[/C][C]-11589.6050446497[/C][/ROW]
[ROW][C]144[/C][C]550400[/C][C]522181.367057606[/C][C]28218.6329423937[/C][/ROW]
[ROW][C]145[/C][C]593700[/C][C]552455.240656638[/C][C]41244.7593433616[/C][/ROW]
[ROW][C]146[/C][C]548900[/C][C]558235.510075241[/C][C]-9335.51007524051[/C][/ROW]
[ROW][C]147[/C][C]534200[/C][C]517332.446719688[/C][C]16867.5532803118[/C][/ROW]
[ROW][C]148[/C][C]550500[/C][C]516285.342497639[/C][C]34214.6575023613[/C][/ROW]
[ROW][C]149[/C][C]541800[/C][C]530780.842636378[/C][C]11019.1573636224[/C][/ROW]
[ROW][C]150[/C][C]569300[/C][C]547828.135275595[/C][C]21471.8647244048[/C][/ROW]
[ROW][C]151[/C][C]587400[/C][C]584046.855983807[/C][C]3353.14401619346[/C][/ROW]
[ROW][C]152[/C][C]627700[/C][C]620968.441800153[/C][C]6731.55819984747[/C][/ROW]
[ROW][C]153[/C][C]607000[/C][C]602045.668702095[/C][C]4954.3312979046[/C][/ROW]
[ROW][C]154[/C][C]629500[/C][C]611376.691582641[/C][C]18123.3084173588[/C][/ROW]
[ROW][C]155[/C][C]704600[/C][C]709558.846477612[/C][C]-4958.84647761239[/C][/ROW]
[ROW][C]156[/C][C]767700[/C][C]749473.815590269[/C][C]18226.1844097311[/C][/ROW]
[ROW][C]157[/C][C]812200[/C][C]793852.074557298[/C][C]18347.9254427025[/C][/ROW]
[ROW][C]158[/C][C]824600[/C][C]792370.226806797[/C][C]32229.7731932029[/C][/ROW]
[ROW][C]159[/C][C]856300[/C][C]806967.182061419[/C][C]49332.817938581[/C][/ROW]
[ROW][C]160[/C][C]812200[/C][C]857446.63846711[/C][C]-45246.6384671098[/C][/ROW]
[ROW][C]161[/C][C]764100[/C][C]827188.647590749[/C][C]-63088.6475907486[/C][/ROW]
[ROW][C]162[/C][C]801700[/C][C]799383.148792731[/C][C]2316.85120726866[/C][/ROW]
[ROW][C]163[/C][C]806000[/C][C]823955.038318916[/C][C]-17955.0383189163[/C][/ROW]
[ROW][C]164[/C][C]867200[/C][C]848263.964963471[/C][C]18936.0350365289[/C][/ROW]
[ROW][C]165[/C][C]801600[/C][C]841637.486542566[/C][C]-40037.4865425657[/C][/ROW]
[ROW][C]166[/C][C]817500[/C][C]818754.242367754[/C][C]-1254.24236775434[/C][/ROW]
[ROW][C]167[/C][C]920900[/C][C]895592.820132009[/C][C]25307.1798679914[/C][/ROW]
[ROW][C]168[/C][C]959700[/C][C]960407.863986725[/C][C]-707.863986724522[/C][/ROW]
[ROW][C]169[/C][C]997700[/C][C]988515.269123966[/C][C]9184.7308760339[/C][/ROW]
[ROW][C]170[/C][C]949100[/C][C]978731.829726943[/C][C]-29631.8297269433[/C][/ROW]
[ROW][C]171[/C][C]910900[/C][C]940026.88748547[/C][C]-29126.8874854703[/C][/ROW]
[ROW][C]172[/C][C]920400[/C][C]899476.870710817[/C][C]20923.1292891834[/C][/ROW]
[ROW][C]173[/C][C]914200[/C][C]901784.13735823[/C][C]12415.8626417693[/C][/ROW]
[ROW][C]174[/C][C]926300[/C][C]934513.506813203[/C][C]-8213.50681320345[/C][/ROW]
[ROW][C]175[/C][C]906400[/C][C]943701.005234177[/C][C]-37301.005234177[/C][/ROW]
[ROW][C]176[/C][C]926100[/C][C]952300.30122322[/C][C]-26200.3012232207[/C][/ROW]
[ROW][C]177[/C][C]902500[/C][C]891908.0852731[/C][C]10591.9147268991[/C][/ROW]
[ROW][C]178[/C][C]895300[/C][C]904779.957068015[/C][C]-9479.95706801547[/C][/ROW]
[ROW][C]179[/C][C]979900[/C][C]972100.437234532[/C][C]7799.56276546803[/C][/ROW]
[ROW][C]180[/C][C]1009700[/C][C]1010906.06963403[/C][C]-1206.06963402720[/C][/ROW]
[ROW][C]181[/C][C]1043800[/C][C]1030478.47542918[/C][C]13321.5245708239[/C][/ROW]
[ROW][C]182[/C][C]979800[/C][C]1008879.12468186[/C][C]-29079.1246818635[/C][/ROW]
[ROW][C]183[/C][C]921600[/C][C]961587.384701492[/C][C]-39987.3847014921[/C][/ROW]
[ROW][C]184[/C][C]923500[/C][C]910152.949105054[/C][C]13347.0508949463[/C][/ROW]
[ROW][C]185[/C][C]914500[/C][C]894474.816642083[/C][C]20025.1833579167[/C][/ROW]
[ROW][C]186[/C][C]891700[/C][C]919323.719219721[/C][C]-27623.7192197209[/C][/ROW]
[ROW][C]187[/C][C]916000[/C][C]897555.3931662[/C][C]18444.6068337996[/C][/ROW]
[ROW][C]188[/C][C]931700[/C][C]942031.130206948[/C][C]-10331.1302069485[/C][/ROW]
[ROW][C]189[/C][C]902400[/C][C]894380.851889577[/C][C]8019.14811042347[/C][/ROW]
[ROW][C]190[/C][C]893700[/C][C]898052.621826747[/C][C]-4352.62182674708[/C][/ROW]
[ROW][C]191[/C][C]941500[/C][C]967810.854062996[/C][C]-26310.8540629956[/C][/ROW]
[ROW][C]192[/C][C]980100[/C][C]972786.118538922[/C][C]7313.8814610776[/C][/ROW]
[ROW][C]193[/C][C]1006900[/C][C]993775.067192426[/C][C]13124.9328075737[/C][/ROW]
[ROW][C]194[/C][C]949200[/C][C]958948.488004216[/C][C]-9748.48800421564[/C][/ROW]
[ROW][C]195[/C][C]883200[/C][C]919453.974778265[/C][C]-36253.9747782646[/C][/ROW]
[ROW][C]196[/C][C]849900[/C][C]874397.38526633[/C][C]-24497.3852663293[/C][/ROW]
[ROW][C]197[/C][C]839200[/C][C]823712.091444627[/C][C]15487.9085553734[/C][/ROW]
[ROW][C]198[/C][C]803900[/C][C]829115.399688619[/C][C]-25215.3996886188[/C][/ROW]
[ROW][C]199[/C][C]797900[/C][C]806912.178655593[/C][C]-9012.17865559319[/C][/ROW]
[ROW][C]200[/C][C]830800[/C][C]815148.819526314[/C][C]15651.1804736863[/C][/ROW]
[ROW][C]201[/C][C]753300[/C][C]779855.79613657[/C][C]-26555.7961365693[/C][/ROW]
[ROW][C]202[/C][C]764100[/C][C]743517.236156056[/C][C]20582.7638439441[/C][/ROW]
[ROW][C]203[/C][C]807600[/C][C]817825.591507595[/C][C]-10225.5915075951[/C][/ROW]
[ROW][C]204[/C][C]853700[/C][C]831018.282997562[/C][C]22681.7170024378[/C][/ROW]
[ROW][C]205[/C][C]886200[/C][C]857481.500594175[/C][C]28718.4994058247[/C][/ROW]
[ROW][C]206[/C][C]815700[/C][C]825966.799760484[/C][C]-10266.7997604843[/C][/ROW]
[ROW][C]207[/C][C]743000[/C][C]777556.395096687[/C][C]-34556.395096687[/C][/ROW]
[ROW][C]208[/C][C]753600[/C][C]730983.540171065[/C][C]22616.4598289349[/C][/ROW]
[ROW][C]209[/C][C]724800[/C][C]721355.104686766[/C][C]3444.89531323384[/C][/ROW]
[ROW][C]210[/C][C]709600[/C][C]711852.917331436[/C][C]-2252.91733143583[/C][/ROW]
[ROW][C]211[/C][C]721900[/C][C]711097.945865927[/C][C]10802.0541340732[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41199&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41199&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
13458100456110.2029914531989.79700854671
14424800425004.865593658-204.865593658236
15420600419648.526389863951.473610136658
16400100399870.439322215229.560677785252
17393000394440.250846746-1440.25084674591
18387100388789.921848848-1689.92184884817
19377500401119.167035188-23619.1670351877
20400400369189.43242406931210.5675759307
21391400375198.96186801616201.0381319843
22363600391541.910847728-27941.9108477278
23431000442796.152883703-11796.1528837035
24441700437590.636279074109.3637209296
25448500448400.12247222599.877527774719
26415600413943.5017339761656.49826602405
27408000408657.979521394-657.979521393776
28416600385976.73599748330623.2640025173
29409300404258.7920813315041.20791866921
30387600406038.523504067-18438.5235040669
31394500403844.323886398-9344.32388639846
32407600392731.2064470414868.7935529604
33378500385275.251196561-6775.25119656051
34359600376345.970560008-16745.9705600080
35435700437163.75937287-1463.75937287020
36433800442102.0383933-8302.03839330014
37427700442231.09486336-14531.0948633598
38413300394550.95774593718749.0422540632
39379500400432.925349469-20932.9253494691
40379300364418.37788525214881.6221147476
41353700362436.593457869-8736.59345786914
42378200344025.95852612434174.0414738762
43380600380654.807107233-54.8071072332677
44394000380406.18810249113593.8118975091
45374000369326.4253446174673.57465538307
46375000369041.3131696055958.68683039455
47437600453046.968847030-15446.9688470304
48443900449768.815091445-5868.81509144505
49488800453916.64217551534883.3578244845
50463900455884.1411801628015.8588198385
51440000456023.038716392-16023.0387163921
52453800437191.69831987816608.3016801223
53451600441609.30480959990.69519050024
54453400453849.904905493-449.904905493138
55461400467171.285456483-5771.28545648284
56509100470806.12903795838293.8709620417
57540600485234.6612335355365.3387664703
58555100536797.50256474318302.4974352574
59677400643121.51916659734278.4808334028
60694600699649.133031355-5049.13303135522
61750100732945.38955960617154.6104403938
62733900738651.98810968-4751.98810967989
63709300744994.965640613-35694.9656406129
64720500733311.635511074-12811.6355110742
65693200728570.158091934-35370.1580919340
66687200714142.379235556-26942.3792355565
67686800711992.272405551-25192.2724055512
68720900710156.16281727710743.8371827226
69653100705992.300529198-52892.3005291984
70624700659785.162104691-35085.1621046915
71690000709316.33848042-19316.3384804192
72717800694386.62919098323413.3708090172
73736500727891.4202163168608.57978368353
74699900699606.571721198293.42827880173
75675600681055.900500962-5455.90050096181
76635600674169.553348291-38569.5533482911
77632500624054.8750915118445.12490848894
78594900624278.564665846-29378.5646658456
79604000602112.9019960551887.09800394485
80620800609821.37972191310978.6202780871
81578400581282.922391457-2882.92239145702
82571200564551.5012804886648.49871951155
83627400642288.642367468-14888.6423674682
84657700633100.24726810524599.7527318948
85674100661733.41814321612366.5818567839
86672800631833.67558004140966.3244199587
87615300643576.755006667-28276.7550066673
88609100614396.633292866-5296.63329286571
89607600598202.4051773939397.59482260747
90566900596714.17436561-29814.1743656107
91572700581886.596951374-9186.59695137397
92589200584680.4863628944519.51363710559
93534800550428.162993806-15628.1629938064
94543100525336.6777282217763.3222717802
95591100608732.031598043-17632.0315980432
96624800603791.06146265721008.9385373431
97665300628064.68594100337235.3140589965
98642600623310.05233556319289.9476644371
99608700609678.851893173-978.851893173298
100594500607250.132641147-12750.1326411475
101563800590607.668115761-26807.6681157607
102596100555684.18849262740415.8115073731
103597600601451.424859782-3851.4248597821
104633100617606.9157481115493.0842518904
105591000597152.286469738-6152.28646973835
106584200593743.557929223-9543.55792922259
107655800658926.085284109-3126.08528410888
108670700678532.895361163-7832.89536116295
109699700689316.15877201710383.8412279827
110712900664290.91252842748609.0874715734
111652000674125.83608096-22125.8360809603
112635100657428.628884928-22328.6288849284
113603100633388.374795499-30288.3747954987
114610100606940.6101557973159.38984420313
115602000616020.721919631-14020.7219196314
116597600623132.806191955-25532.8061919553
117585400560438.84690755824961.1530924417
118567100573283.258627779-6183.25862777897
119620600636515.831738768-15915.8317387683
120646200639350.1290610886849.87093891227
121644800658312.089330393-13512.089330393
122645200613668.76026902131531.2397309791
123644800590825.3227159953974.6772840095
124593000628174.787039401-35174.7870394011
125569100591277.792871466-22177.7928714656
126518800574134.72669012-55334.7266901197
127538700530005.6414447028694.35855529818
128554600546102.5620805148497.43791948631
129507900513713.307731813-5813.30773181305
130488400494436.761768649-6036.76176864904
131563300551025.58312157712274.4168784230
132592400575599.848173616800.1518264000
133598100598016.2168856783.7831143303774
134546300570655.82709393-24355.8270939301
135516100504914.85777009111185.1422299088
136518500487372.78701211731127.2129878835
137477400497248.998142214-19848.9981422142
138483400474213.0333526359186.9666473646
139469400491051.242243692-21651.2422436916
140501300486579.59263075414720.4073692461
141457400458709.992601083-1309.99260108336
142446700445311.6451438831388.35485611670
143501900513489.60504465-11589.6050446497
144550400522181.36705760628218.6329423937
145593700552455.24065663841244.7593433616
146548900558235.510075241-9335.51007524051
147534200517332.44671968816867.5532803118
148550500516285.34249763934214.6575023613
149541800530780.84263637811019.1573636224
150569300547828.13527559521471.8647244048
151587400584046.8559838073353.14401619346
152627700620968.4418001536731.55819984747
153607000602045.6687020954954.3312979046
154629500611376.69158264118123.3084173588
155704600709558.846477612-4958.84647761239
156767700749473.81559026918226.1844097311
157812200793852.07455729818347.9254427025
158824600792370.22680679732229.7731932029
159856300806967.18206141949332.817938581
160812200857446.63846711-45246.6384671098
161764100827188.647590749-63088.6475907486
162801700799383.1487927312316.85120726866
163806000823955.038318916-17955.0383189163
164867200848263.96496347118936.0350365289
165801600841637.486542566-40037.4865425657
166817500818754.242367754-1254.24236775434
167920900895592.82013200925307.1798679914
168959700960407.863986725-707.863986724522
169997700988515.2691239669184.7308760339
170949100978731.829726943-29631.8297269433
171910900940026.88748547-29126.8874854703
172920400899476.87071081720923.1292891834
173914200901784.1373582312415.8626417693
174926300934513.506813203-8213.50681320345
175906400943701.005234177-37301.005234177
176926100952300.30122322-26200.3012232207
177902500891908.085273110591.9147268991
178895300904779.957068015-9479.95706801547
179979900972100.4372345327799.56276546803
18010097001010906.06963403-1206.06963402720
18110438001030478.4754291813321.5245708239
1829798001008879.12468186-29079.1246818635
183921600961587.384701492-39987.3847014921
184923500910152.94910505413347.0508949463
185914500894474.81664208320025.1833579167
186891700919323.719219721-27623.7192197209
187916000897555.393166218444.6068337996
188931700942031.130206948-10331.1302069485
189902400894380.8518895778019.14811042347
190893700898052.621826747-4352.62182674708
191941500967810.854062996-26310.8540629956
192980100972786.1185389227313.8814610776
1931006900993775.06719242613124.9328075737
194949200958948.488004216-9748.48800421564
195883200919453.974778265-36253.9747782646
196849900874397.38526633-24497.3852663293
197839200823712.09144462715487.9085553734
198803900829115.399688619-25215.3996886188
199797900806912.178655593-9012.17865559319
200830800815148.81952631415651.1804736863
201753300779855.79613657-26555.7961365693
202764100743517.23615605620582.7638439441
203807600817825.591507595-10225.5915075951
204853700831018.28299756222681.7170024378
205886200857481.50059417528718.4994058247
206815700825966.799760484-10266.7997604843
207743000777556.395096687-34556.395096687
208753600730983.54017106522616.4598289349
209724800721355.1046867663444.89531323384
210709600711852.917331436-2252.91733143583
211721900711097.94586592710802.0541340732







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
212742122.7240281699575.884474405784669.563581794
213692351.437380277636730.768240965747972.10651959
214688263.759814781619208.319910993757319.199718569
215746916.061654926663926.456031525829905.667278328
216777244.267408808679768.231018893874720.303798722
217790430.902167649677898.155299443902963.649035854
218731252.175360743603090.34315282859414.007568667
219686709.48836395542351.799711872831067.177016029
220677601.742217359516490.797576544838712.686858174
221650276.208513364471865.743247826828686.673778902
222638478.253877957442233.836317312834722.671438603
223642554.726615533427953.876998094857155.576232973

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
212 & 742122.7240281 & 699575.884474405 & 784669.563581794 \tabularnewline
213 & 692351.437380277 & 636730.768240965 & 747972.10651959 \tabularnewline
214 & 688263.759814781 & 619208.319910993 & 757319.199718569 \tabularnewline
215 & 746916.061654926 & 663926.456031525 & 829905.667278328 \tabularnewline
216 & 777244.267408808 & 679768.231018893 & 874720.303798722 \tabularnewline
217 & 790430.902167649 & 677898.155299443 & 902963.649035854 \tabularnewline
218 & 731252.175360743 & 603090.34315282 & 859414.007568667 \tabularnewline
219 & 686709.48836395 & 542351.799711872 & 831067.177016029 \tabularnewline
220 & 677601.742217359 & 516490.797576544 & 838712.686858174 \tabularnewline
221 & 650276.208513364 & 471865.743247826 & 828686.673778902 \tabularnewline
222 & 638478.253877957 & 442233.836317312 & 834722.671438603 \tabularnewline
223 & 642554.726615533 & 427953.876998094 & 857155.576232973 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41199&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]212[/C][C]742122.7240281[/C][C]699575.884474405[/C][C]784669.563581794[/C][/ROW]
[ROW][C]213[/C][C]692351.437380277[/C][C]636730.768240965[/C][C]747972.10651959[/C][/ROW]
[ROW][C]214[/C][C]688263.759814781[/C][C]619208.319910993[/C][C]757319.199718569[/C][/ROW]
[ROW][C]215[/C][C]746916.061654926[/C][C]663926.456031525[/C][C]829905.667278328[/C][/ROW]
[ROW][C]216[/C][C]777244.267408808[/C][C]679768.231018893[/C][C]874720.303798722[/C][/ROW]
[ROW][C]217[/C][C]790430.902167649[/C][C]677898.155299443[/C][C]902963.649035854[/C][/ROW]
[ROW][C]218[/C][C]731252.175360743[/C][C]603090.34315282[/C][C]859414.007568667[/C][/ROW]
[ROW][C]219[/C][C]686709.48836395[/C][C]542351.799711872[/C][C]831067.177016029[/C][/ROW]
[ROW][C]220[/C][C]677601.742217359[/C][C]516490.797576544[/C][C]838712.686858174[/C][/ROW]
[ROW][C]221[/C][C]650276.208513364[/C][C]471865.743247826[/C][C]828686.673778902[/C][/ROW]
[ROW][C]222[/C][C]638478.253877957[/C][C]442233.836317312[/C][C]834722.671438603[/C][/ROW]
[ROW][C]223[/C][C]642554.726615533[/C][C]427953.876998094[/C][C]857155.576232973[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41199&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41199&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
212742122.7240281699575.884474405784669.563581794
213692351.437380277636730.768240965747972.10651959
214688263.759814781619208.319910993757319.199718569
215746916.061654926663926.456031525829905.667278328
216777244.267408808679768.231018893874720.303798722
217790430.902167649677898.155299443902963.649035854
218731252.175360743603090.34315282859414.007568667
219686709.48836395542351.799711872831067.177016029
220677601.742217359516490.797576544838712.686858174
221650276.208513364471865.743247826828686.673778902
222638478.253877957442233.836317312834722.671438603
223642554.726615533427953.876998094857155.576232973



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')