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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 25 Jan 2010 05:28:40 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Jan/25/t1264422596stwjogj24pjy80p.htm/, Retrieved Sun, 05 May 2024 23:13:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72434, Retrieved Sun, 05 May 2024 23:13:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact140
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2010-01-25 12:28:40] [6021303ec4295e707c1f24599760c44a] [Current]
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Dataseries X:
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'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72434&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72434&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72434&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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.867291126035387
beta0.0984720422261518
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.867291126035387 \tabularnewline
beta & 0.0984720422261518 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72434&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]0.867291126035387[/C][/ROW]
[ROW][C]beta[/C][C]0.0984720422261518[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72434&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72434&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
alpha0.867291126035387
beta0.0984720422261518
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13433800449533.520299145-15733.5202991454
14427700427800.552459051-100.552459050843
15413300411492.3313252551807.66867474484
16379500377201.8087866892298.19121331070
17379300375924.6533174063375.34668259404
18353700350203.3064276823496.69357231836
19378200370648.3339860237551.66601397679
20380600383909.311769447-3309.31176944723
21394000393434.698342544565.301657455857
22374000364489.6150732159510.38492678542
23375000355773.08071155919226.9192884405
24437600453254.831482233-15654.8314822327
25443900437896.4874797316003.51252026879
26488800440060.06790974548739.9320902545
27463900473504.751780232-9604.75178023247
28440000435547.5176944484452.48230555246
29453800442631.77553015911168.2244698409
30451600430700.83624552720899.1637544726
31453400475278.851952642-21878.8519526420
32461400467562.022050441-6162.02205044066
33509100480872.20874531428227.7912546864
34540600485212.86928512155387.1307148786
35555100529599.57421189325500.4257881066
36677400640454.22017304336945.7798269569
37694600690643.5294097043956.4705902962
38750100713581.76061740936518.2393825913
39733900744518.570950148-10618.5709501477
40709300723295.745452703-13995.7454527025
41720500729443.871771988-8943.87177198753
42693200713816.233987742-20616.2339877423
43687200725620.67539042-38420.6753904207
44686800713139.67895271-26339.6789527095
45720900719287.1924484751612.80755152507
46653100707649.571175018-54549.5711750181
47624700646834.264969296-22134.2649692957
48690000707937.822473186-17937.8224731860
49717800691504.97722949326295.0227705069
50736500725402.15313400911097.8468659912
51699900713129.289164922-13229.2891649222
52675600674063.7438800591536.25611994136
53635600680549.273728686-44949.2737286858
54632500615266.64944994617233.3505500542
55594900643888.60064159-48988.60064159
56604000609296.557880548-5296.55788054818
57620800624652.457793821-3852.45779382077
58578400587603.190453828-9203.19045382761
59571200561072.53179172610127.4682082739
60627400644122.923259774-16722.9232597742
61657700628127.21148327429572.788516726
62674100656643.66957786417456.3304221365
63672800640993.37976377131806.6202362288
64615300641129.186146105-25829.1861461053
65609100613557.340366392-4457.3403663924
66607600590948.83872493416651.1612750659
67566900609531.54260713-42631.5426071298
68572700586048.08024902-13348.0802490197
69589200593721.818103614-4521.8181036145
70534800554433.971746831-19633.9717468312
71543100519583.35022339223516.6497766075
72591100609987.474784758-18887.4747847581
73624800597378.15720607527421.8427939246
74665300621357.29718608543942.702813915
75642600631780.99369504110819.0063049587
76608700605471.4009004183228.59909958241
77594500607824.752111993-13324.7521119929
78563800581457.000756397-17657.0007563973
79596100560617.23978697635482.7602130243
80597600613639.103227117-16039.1032271167
81633100624791.748940348308.25105966022
82591000600363.014026969-9363.0140269685
83584200586761.176725511-2561.17672551086
84655800653308.0846686842491.91533131606
85670700671599.718225432-899.718225431745
86699700677002.6502367822697.3497632197
87712900666584.56134838446315.4386516155
88652000675064.858945096-23064.8589450957
89635100655183.250118581-20083.250118581
90603100624567.682693935-21467.6826939352
91610100609338.318846377761.681153623387
92602000624307.423410209-22307.4234102087
93597600631617.314816872-34017.3148168721
94585400562882.68311816322517.316881837
95567100575303.568170968-8203.56817096833
96620600634616.117938667-14016.1179386668
97646200633719.1776685612480.8223314396
98644800650580.021622272-5780.02162227186
99645200612887.55936778332312.4406322171
100644800593109.35698274351690.6430172565
101593000637936.188224223-44936.1882242232
102569100582937.593734109-13837.5937341086
103518800575282.843846143-56482.8438461425
104538700530660.9693287128039.03067128791
105554600558445.93531038-3845.93531037972
106507900521667.945711604-13767.9457116041
107488400493729.731561694-5329.73156169429
108563300550196.51543272113103.4845672792
109592400574085.82350360218314.1764963983
110598100591829.9777214336270.02227856684
111546300568920.210469729-22620.2104697287
112516100498656.19355854217443.8064414584
113518500492618.1218820725881.8781179304
114477400500874.920924275-23474.9209242754
115483400476087.7875362167312.2124637842
116469400497691.160947983-28291.1609479826
117501300491621.0289886559678.9710113448
118457400465642.407236377-8242.40723637666
119446700444474.2476039512225.75239604869
120501900511443.333164543-9543.3331645428
121550400515951.88118652934448.1188134711
122593700547037.51525840546662.4847415945
123548900559722.477973085-10822.4779730854
124534200510411.64900569723788.3509943034
125550500516942.06920922733557.9307907734
126541800531907.83814699892.16185309994
127569300549596.7680585419703.2319414604
128587400587731.483551768-331.483551767771
129627700623846.9758683813853.02413161891
130607000602837.1481361024162.85186389775
131629500607276.54715130522223.4528486948
132704600705194.85077707-594.850777070038
133767700739233.88178406228466.1182159383
134812200782172.93578243630027.0642175641
135824600786801.25217606337798.7478239366
136856300802404.65965368353895.3403463167
137812200857066.684285315-44866.684285315
138764100814900.622545487-50800.6225454874
139801700790095.65257334111604.3474266587
140806000826698.21368536-20698.2136853596
141867200852116.46505430815083.5349456918
142801600848258.328383487-46658.3283834871
143817500814047.8941390943452.10586090630
144920900894084.76030860826815.2396913918
145959700959520.874007458179.125992542249
146997700979486.10778971218213.8922102879
147949100975243.530750466-26143.5307504656
148910900932408.800769329-21508.8007693288
149920400897009.34865690723390.6513430928
150914200907526.689524716673.31047528947
151926300940030.451989342-13730.4519893415
152906400947390.245536353-40990.2455363529
153926100955241.64974575-29141.6497457498
154902500896340.4016043886159.59839561197
155895300910606.136208164-15306.1362081638
156979900971890.1634663958009.83653360454
15710097001010291.13671698-591.136716982699
15810438001024725.3860300119074.6139699878
1599798001008159.87472786-28359.8747278603
160921600956645.907643506-35045.9076435063
161923500906936.18505605116563.8149439488
162914500900202.87962446814297.1203755324
163891700928150.795546316-36450.7955463161
164916000901787.26477120514212.7352287947
165931700953402.134081721-21702.1340817214
166902400900587.2605585221812.73944147793
167893700902812.430476704-9112.43047670356
168941500967669.528021328-26169.5280213284
169980100967473.65200237712626.3479976233
1701006900989297.98904179717602.0109582026
171949200958351.419446583-9151.41944658256
172883200917441.051625647-34241.0516256473
173849900870178.75190878-20278.7519087794
174839200822945.21497899616254.7850210045
175803900837777.299826093-33877.2998260928
176797900812510.028344965-14610.0283449651
177830800824040.1606519456759.83934805507
178753300791140.712777618-37840.7127776179
179764100746248.34415533317851.6558446669
180807600823253.780860587-15653.7808605866
181853700829251.01675686224448.9832431383
182886200854923.37525176831276.6247482317
183815700826388.16515369-10688.1651536893
184743000774786.036391814-31786.0363918135
185753600725686.20042860427913.7995713955
186724800723394.1232554861405.87674451387
187709600715722.917063477-6122.91706347733
188721900716482.0545513885417.94544861186

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 433800 & 449533.520299145 & -15733.5202991454 \tabularnewline
14 & 427700 & 427800.552459051 & -100.552459050843 \tabularnewline
15 & 413300 & 411492.331325255 & 1807.66867474484 \tabularnewline
16 & 379500 & 377201.808786689 & 2298.19121331070 \tabularnewline
17 & 379300 & 375924.653317406 & 3375.34668259404 \tabularnewline
18 & 353700 & 350203.306427682 & 3496.69357231836 \tabularnewline
19 & 378200 & 370648.333986023 & 7551.66601397679 \tabularnewline
20 & 380600 & 383909.311769447 & -3309.31176944723 \tabularnewline
21 & 394000 & 393434.698342544 & 565.301657455857 \tabularnewline
22 & 374000 & 364489.615073215 & 9510.38492678542 \tabularnewline
23 & 375000 & 355773.080711559 & 19226.9192884405 \tabularnewline
24 & 437600 & 453254.831482233 & -15654.8314822327 \tabularnewline
25 & 443900 & 437896.487479731 & 6003.51252026879 \tabularnewline
26 & 488800 & 440060.067909745 & 48739.9320902545 \tabularnewline
27 & 463900 & 473504.751780232 & -9604.75178023247 \tabularnewline
28 & 440000 & 435547.517694448 & 4452.48230555246 \tabularnewline
29 & 453800 & 442631.775530159 & 11168.2244698409 \tabularnewline
30 & 451600 & 430700.836245527 & 20899.1637544726 \tabularnewline
31 & 453400 & 475278.851952642 & -21878.8519526420 \tabularnewline
32 & 461400 & 467562.022050441 & -6162.02205044066 \tabularnewline
33 & 509100 & 480872.208745314 & 28227.7912546864 \tabularnewline
34 & 540600 & 485212.869285121 & 55387.1307148786 \tabularnewline
35 & 555100 & 529599.574211893 & 25500.4257881066 \tabularnewline
36 & 677400 & 640454.220173043 & 36945.7798269569 \tabularnewline
37 & 694600 & 690643.529409704 & 3956.4705902962 \tabularnewline
38 & 750100 & 713581.760617409 & 36518.2393825913 \tabularnewline
39 & 733900 & 744518.570950148 & -10618.5709501477 \tabularnewline
40 & 709300 & 723295.745452703 & -13995.7454527025 \tabularnewline
41 & 720500 & 729443.871771988 & -8943.87177198753 \tabularnewline
42 & 693200 & 713816.233987742 & -20616.2339877423 \tabularnewline
43 & 687200 & 725620.67539042 & -38420.6753904207 \tabularnewline
44 & 686800 & 713139.67895271 & -26339.6789527095 \tabularnewline
45 & 720900 & 719287.192448475 & 1612.80755152507 \tabularnewline
46 & 653100 & 707649.571175018 & -54549.5711750181 \tabularnewline
47 & 624700 & 646834.264969296 & -22134.2649692957 \tabularnewline
48 & 690000 & 707937.822473186 & -17937.8224731860 \tabularnewline
49 & 717800 & 691504.977229493 & 26295.0227705069 \tabularnewline
50 & 736500 & 725402.153134009 & 11097.8468659912 \tabularnewline
51 & 699900 & 713129.289164922 & -13229.2891649222 \tabularnewline
52 & 675600 & 674063.743880059 & 1536.25611994136 \tabularnewline
53 & 635600 & 680549.273728686 & -44949.2737286858 \tabularnewline
54 & 632500 & 615266.649449946 & 17233.3505500542 \tabularnewline
55 & 594900 & 643888.60064159 & -48988.60064159 \tabularnewline
56 & 604000 & 609296.557880548 & -5296.55788054818 \tabularnewline
57 & 620800 & 624652.457793821 & -3852.45779382077 \tabularnewline
58 & 578400 & 587603.190453828 & -9203.19045382761 \tabularnewline
59 & 571200 & 561072.531791726 & 10127.4682082739 \tabularnewline
60 & 627400 & 644122.923259774 & -16722.9232597742 \tabularnewline
61 & 657700 & 628127.211483274 & 29572.788516726 \tabularnewline
62 & 674100 & 656643.669577864 & 17456.3304221365 \tabularnewline
63 & 672800 & 640993.379763771 & 31806.6202362288 \tabularnewline
64 & 615300 & 641129.186146105 & -25829.1861461053 \tabularnewline
65 & 609100 & 613557.340366392 & -4457.3403663924 \tabularnewline
66 & 607600 & 590948.838724934 & 16651.1612750659 \tabularnewline
67 & 566900 & 609531.54260713 & -42631.5426071298 \tabularnewline
68 & 572700 & 586048.08024902 & -13348.0802490197 \tabularnewline
69 & 589200 & 593721.818103614 & -4521.8181036145 \tabularnewline
70 & 534800 & 554433.971746831 & -19633.9717468312 \tabularnewline
71 & 543100 & 519583.350223392 & 23516.6497766075 \tabularnewline
72 & 591100 & 609987.474784758 & -18887.4747847581 \tabularnewline
73 & 624800 & 597378.157206075 & 27421.8427939246 \tabularnewline
74 & 665300 & 621357.297186085 & 43942.702813915 \tabularnewline
75 & 642600 & 631780.993695041 & 10819.0063049587 \tabularnewline
76 & 608700 & 605471.400900418 & 3228.59909958241 \tabularnewline
77 & 594500 & 607824.752111993 & -13324.7521119929 \tabularnewline
78 & 563800 & 581457.000756397 & -17657.0007563973 \tabularnewline
79 & 596100 & 560617.239786976 & 35482.7602130243 \tabularnewline
80 & 597600 & 613639.103227117 & -16039.1032271167 \tabularnewline
81 & 633100 & 624791.74894034 & 8308.25105966022 \tabularnewline
82 & 591000 & 600363.014026969 & -9363.0140269685 \tabularnewline
83 & 584200 & 586761.176725511 & -2561.17672551086 \tabularnewline
84 & 655800 & 653308.084668684 & 2491.91533131606 \tabularnewline
85 & 670700 & 671599.718225432 & -899.718225431745 \tabularnewline
86 & 699700 & 677002.65023678 & 22697.3497632197 \tabularnewline
87 & 712900 & 666584.561348384 & 46315.4386516155 \tabularnewline
88 & 652000 & 675064.858945096 & -23064.8589450957 \tabularnewline
89 & 635100 & 655183.250118581 & -20083.250118581 \tabularnewline
90 & 603100 & 624567.682693935 & -21467.6826939352 \tabularnewline
91 & 610100 & 609338.318846377 & 761.681153623387 \tabularnewline
92 & 602000 & 624307.423410209 & -22307.4234102087 \tabularnewline
93 & 597600 & 631617.314816872 & -34017.3148168721 \tabularnewline
94 & 585400 & 562882.683118163 & 22517.316881837 \tabularnewline
95 & 567100 & 575303.568170968 & -8203.56817096833 \tabularnewline
96 & 620600 & 634616.117938667 & -14016.1179386668 \tabularnewline
97 & 646200 & 633719.17766856 & 12480.8223314396 \tabularnewline
98 & 644800 & 650580.021622272 & -5780.02162227186 \tabularnewline
99 & 645200 & 612887.559367783 & 32312.4406322171 \tabularnewline
100 & 644800 & 593109.356982743 & 51690.6430172565 \tabularnewline
101 & 593000 & 637936.188224223 & -44936.1882242232 \tabularnewline
102 & 569100 & 582937.593734109 & -13837.5937341086 \tabularnewline
103 & 518800 & 575282.843846143 & -56482.8438461425 \tabularnewline
104 & 538700 & 530660.969328712 & 8039.03067128791 \tabularnewline
105 & 554600 & 558445.93531038 & -3845.93531037972 \tabularnewline
106 & 507900 & 521667.945711604 & -13767.9457116041 \tabularnewline
107 & 488400 & 493729.731561694 & -5329.73156169429 \tabularnewline
108 & 563300 & 550196.515432721 & 13103.4845672792 \tabularnewline
109 & 592400 & 574085.823503602 & 18314.1764963983 \tabularnewline
110 & 598100 & 591829.977721433 & 6270.02227856684 \tabularnewline
111 & 546300 & 568920.210469729 & -22620.2104697287 \tabularnewline
112 & 516100 & 498656.193558542 & 17443.8064414584 \tabularnewline
113 & 518500 & 492618.12188207 & 25881.8781179304 \tabularnewline
114 & 477400 & 500874.920924275 & -23474.9209242754 \tabularnewline
115 & 483400 & 476087.787536216 & 7312.2124637842 \tabularnewline
116 & 469400 & 497691.160947983 & -28291.1609479826 \tabularnewline
117 & 501300 & 491621.028988655 & 9678.9710113448 \tabularnewline
118 & 457400 & 465642.407236377 & -8242.40723637666 \tabularnewline
119 & 446700 & 444474.247603951 & 2225.75239604869 \tabularnewline
120 & 501900 & 511443.333164543 & -9543.3331645428 \tabularnewline
121 & 550400 & 515951.881186529 & 34448.1188134711 \tabularnewline
122 & 593700 & 547037.515258405 & 46662.4847415945 \tabularnewline
123 & 548900 & 559722.477973085 & -10822.4779730854 \tabularnewline
124 & 534200 & 510411.649005697 & 23788.3509943034 \tabularnewline
125 & 550500 & 516942.069209227 & 33557.9307907734 \tabularnewline
126 & 541800 & 531907.8381469 & 9892.16185309994 \tabularnewline
127 & 569300 & 549596.76805854 & 19703.2319414604 \tabularnewline
128 & 587400 & 587731.483551768 & -331.483551767771 \tabularnewline
129 & 627700 & 623846.975868381 & 3853.02413161891 \tabularnewline
130 & 607000 & 602837.148136102 & 4162.85186389775 \tabularnewline
131 & 629500 & 607276.547151305 & 22223.4528486948 \tabularnewline
132 & 704600 & 705194.85077707 & -594.850777070038 \tabularnewline
133 & 767700 & 739233.881784062 & 28466.1182159383 \tabularnewline
134 & 812200 & 782172.935782436 & 30027.0642175641 \tabularnewline
135 & 824600 & 786801.252176063 & 37798.7478239366 \tabularnewline
136 & 856300 & 802404.659653683 & 53895.3403463167 \tabularnewline
137 & 812200 & 857066.684285315 & -44866.684285315 \tabularnewline
138 & 764100 & 814900.622545487 & -50800.6225454874 \tabularnewline
139 & 801700 & 790095.652573341 & 11604.3474266587 \tabularnewline
140 & 806000 & 826698.21368536 & -20698.2136853596 \tabularnewline
141 & 867200 & 852116.465054308 & 15083.5349456918 \tabularnewline
142 & 801600 & 848258.328383487 & -46658.3283834871 \tabularnewline
143 & 817500 & 814047.894139094 & 3452.10586090630 \tabularnewline
144 & 920900 & 894084.760308608 & 26815.2396913918 \tabularnewline
145 & 959700 & 959520.874007458 & 179.125992542249 \tabularnewline
146 & 997700 & 979486.107789712 & 18213.8922102879 \tabularnewline
147 & 949100 & 975243.530750466 & -26143.5307504656 \tabularnewline
148 & 910900 & 932408.800769329 & -21508.8007693288 \tabularnewline
149 & 920400 & 897009.348656907 & 23390.6513430928 \tabularnewline
150 & 914200 & 907526.68952471 & 6673.31047528947 \tabularnewline
151 & 926300 & 940030.451989342 & -13730.4519893415 \tabularnewline
152 & 906400 & 947390.245536353 & -40990.2455363529 \tabularnewline
153 & 926100 & 955241.64974575 & -29141.6497457498 \tabularnewline
154 & 902500 & 896340.401604388 & 6159.59839561197 \tabularnewline
155 & 895300 & 910606.136208164 & -15306.1362081638 \tabularnewline
156 & 979900 & 971890.163466395 & 8009.83653360454 \tabularnewline
157 & 1009700 & 1010291.13671698 & -591.136716982699 \tabularnewline
158 & 1043800 & 1024725.38603001 & 19074.6139699878 \tabularnewline
159 & 979800 & 1008159.87472786 & -28359.8747278603 \tabularnewline
160 & 921600 & 956645.907643506 & -35045.9076435063 \tabularnewline
161 & 923500 & 906936.185056051 & 16563.8149439488 \tabularnewline
162 & 914500 & 900202.879624468 & 14297.1203755324 \tabularnewline
163 & 891700 & 928150.795546316 & -36450.7955463161 \tabularnewline
164 & 916000 & 901787.264771205 & 14212.7352287947 \tabularnewline
165 & 931700 & 953402.134081721 & -21702.1340817214 \tabularnewline
166 & 902400 & 900587.260558522 & 1812.73944147793 \tabularnewline
167 & 893700 & 902812.430476704 & -9112.43047670356 \tabularnewline
168 & 941500 & 967669.528021328 & -26169.5280213284 \tabularnewline
169 & 980100 & 967473.652002377 & 12626.3479976233 \tabularnewline
170 & 1006900 & 989297.989041797 & 17602.0109582026 \tabularnewline
171 & 949200 & 958351.419446583 & -9151.41944658256 \tabularnewline
172 & 883200 & 917441.051625647 & -34241.0516256473 \tabularnewline
173 & 849900 & 870178.75190878 & -20278.7519087794 \tabularnewline
174 & 839200 & 822945.214978996 & 16254.7850210045 \tabularnewline
175 & 803900 & 837777.299826093 & -33877.2998260928 \tabularnewline
176 & 797900 & 812510.028344965 & -14610.0283449651 \tabularnewline
177 & 830800 & 824040.160651945 & 6759.83934805507 \tabularnewline
178 & 753300 & 791140.712777618 & -37840.7127776179 \tabularnewline
179 & 764100 & 746248.344155333 & 17851.6558446669 \tabularnewline
180 & 807600 & 823253.780860587 & -15653.7808605866 \tabularnewline
181 & 853700 & 829251.016756862 & 24448.9832431383 \tabularnewline
182 & 886200 & 854923.375251768 & 31276.6247482317 \tabularnewline
183 & 815700 & 826388.16515369 & -10688.1651536893 \tabularnewline
184 & 743000 & 774786.036391814 & -31786.0363918135 \tabularnewline
185 & 753600 & 725686.200428604 & 27913.7995713955 \tabularnewline
186 & 724800 & 723394.123255486 & 1405.87674451387 \tabularnewline
187 & 709600 & 715722.917063477 & -6122.91706347733 \tabularnewline
188 & 721900 & 716482.054551388 & 5417.94544861186 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72434&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]433800[/C][C]449533.520299145[/C][C]-15733.5202991454[/C][/ROW]
[ROW][C]14[/C][C]427700[/C][C]427800.552459051[/C][C]-100.552459050843[/C][/ROW]
[ROW][C]15[/C][C]413300[/C][C]411492.331325255[/C][C]1807.66867474484[/C][/ROW]
[ROW][C]16[/C][C]379500[/C][C]377201.808786689[/C][C]2298.19121331070[/C][/ROW]
[ROW][C]17[/C][C]379300[/C][C]375924.653317406[/C][C]3375.34668259404[/C][/ROW]
[ROW][C]18[/C][C]353700[/C][C]350203.306427682[/C][C]3496.69357231836[/C][/ROW]
[ROW][C]19[/C][C]378200[/C][C]370648.333986023[/C][C]7551.66601397679[/C][/ROW]
[ROW][C]20[/C][C]380600[/C][C]383909.311769447[/C][C]-3309.31176944723[/C][/ROW]
[ROW][C]21[/C][C]394000[/C][C]393434.698342544[/C][C]565.301657455857[/C][/ROW]
[ROW][C]22[/C][C]374000[/C][C]364489.615073215[/C][C]9510.38492678542[/C][/ROW]
[ROW][C]23[/C][C]375000[/C][C]355773.080711559[/C][C]19226.9192884405[/C][/ROW]
[ROW][C]24[/C][C]437600[/C][C]453254.831482233[/C][C]-15654.8314822327[/C][/ROW]
[ROW][C]25[/C][C]443900[/C][C]437896.487479731[/C][C]6003.51252026879[/C][/ROW]
[ROW][C]26[/C][C]488800[/C][C]440060.067909745[/C][C]48739.9320902545[/C][/ROW]
[ROW][C]27[/C][C]463900[/C][C]473504.751780232[/C][C]-9604.75178023247[/C][/ROW]
[ROW][C]28[/C][C]440000[/C][C]435547.517694448[/C][C]4452.48230555246[/C][/ROW]
[ROW][C]29[/C][C]453800[/C][C]442631.775530159[/C][C]11168.2244698409[/C][/ROW]
[ROW][C]30[/C][C]451600[/C][C]430700.836245527[/C][C]20899.1637544726[/C][/ROW]
[ROW][C]31[/C][C]453400[/C][C]475278.851952642[/C][C]-21878.8519526420[/C][/ROW]
[ROW][C]32[/C][C]461400[/C][C]467562.022050441[/C][C]-6162.02205044066[/C][/ROW]
[ROW][C]33[/C][C]509100[/C][C]480872.208745314[/C][C]28227.7912546864[/C][/ROW]
[ROW][C]34[/C][C]540600[/C][C]485212.869285121[/C][C]55387.1307148786[/C][/ROW]
[ROW][C]35[/C][C]555100[/C][C]529599.574211893[/C][C]25500.4257881066[/C][/ROW]
[ROW][C]36[/C][C]677400[/C][C]640454.220173043[/C][C]36945.7798269569[/C][/ROW]
[ROW][C]37[/C][C]694600[/C][C]690643.529409704[/C][C]3956.4705902962[/C][/ROW]
[ROW][C]38[/C][C]750100[/C][C]713581.760617409[/C][C]36518.2393825913[/C][/ROW]
[ROW][C]39[/C][C]733900[/C][C]744518.570950148[/C][C]-10618.5709501477[/C][/ROW]
[ROW][C]40[/C][C]709300[/C][C]723295.745452703[/C][C]-13995.7454527025[/C][/ROW]
[ROW][C]41[/C][C]720500[/C][C]729443.871771988[/C][C]-8943.87177198753[/C][/ROW]
[ROW][C]42[/C][C]693200[/C][C]713816.233987742[/C][C]-20616.2339877423[/C][/ROW]
[ROW][C]43[/C][C]687200[/C][C]725620.67539042[/C][C]-38420.6753904207[/C][/ROW]
[ROW][C]44[/C][C]686800[/C][C]713139.67895271[/C][C]-26339.6789527095[/C][/ROW]
[ROW][C]45[/C][C]720900[/C][C]719287.192448475[/C][C]1612.80755152507[/C][/ROW]
[ROW][C]46[/C][C]653100[/C][C]707649.571175018[/C][C]-54549.5711750181[/C][/ROW]
[ROW][C]47[/C][C]624700[/C][C]646834.264969296[/C][C]-22134.2649692957[/C][/ROW]
[ROW][C]48[/C][C]690000[/C][C]707937.822473186[/C][C]-17937.8224731860[/C][/ROW]
[ROW][C]49[/C][C]717800[/C][C]691504.977229493[/C][C]26295.0227705069[/C][/ROW]
[ROW][C]50[/C][C]736500[/C][C]725402.153134009[/C][C]11097.8468659912[/C][/ROW]
[ROW][C]51[/C][C]699900[/C][C]713129.289164922[/C][C]-13229.2891649222[/C][/ROW]
[ROW][C]52[/C][C]675600[/C][C]674063.743880059[/C][C]1536.25611994136[/C][/ROW]
[ROW][C]53[/C][C]635600[/C][C]680549.273728686[/C][C]-44949.2737286858[/C][/ROW]
[ROW][C]54[/C][C]632500[/C][C]615266.649449946[/C][C]17233.3505500542[/C][/ROW]
[ROW][C]55[/C][C]594900[/C][C]643888.60064159[/C][C]-48988.60064159[/C][/ROW]
[ROW][C]56[/C][C]604000[/C][C]609296.557880548[/C][C]-5296.55788054818[/C][/ROW]
[ROW][C]57[/C][C]620800[/C][C]624652.457793821[/C][C]-3852.45779382077[/C][/ROW]
[ROW][C]58[/C][C]578400[/C][C]587603.190453828[/C][C]-9203.19045382761[/C][/ROW]
[ROW][C]59[/C][C]571200[/C][C]561072.531791726[/C][C]10127.4682082739[/C][/ROW]
[ROW][C]60[/C][C]627400[/C][C]644122.923259774[/C][C]-16722.9232597742[/C][/ROW]
[ROW][C]61[/C][C]657700[/C][C]628127.211483274[/C][C]29572.788516726[/C][/ROW]
[ROW][C]62[/C][C]674100[/C][C]656643.669577864[/C][C]17456.3304221365[/C][/ROW]
[ROW][C]63[/C][C]672800[/C][C]640993.379763771[/C][C]31806.6202362288[/C][/ROW]
[ROW][C]64[/C][C]615300[/C][C]641129.186146105[/C][C]-25829.1861461053[/C][/ROW]
[ROW][C]65[/C][C]609100[/C][C]613557.340366392[/C][C]-4457.3403663924[/C][/ROW]
[ROW][C]66[/C][C]607600[/C][C]590948.838724934[/C][C]16651.1612750659[/C][/ROW]
[ROW][C]67[/C][C]566900[/C][C]609531.54260713[/C][C]-42631.5426071298[/C][/ROW]
[ROW][C]68[/C][C]572700[/C][C]586048.08024902[/C][C]-13348.0802490197[/C][/ROW]
[ROW][C]69[/C][C]589200[/C][C]593721.818103614[/C][C]-4521.8181036145[/C][/ROW]
[ROW][C]70[/C][C]534800[/C][C]554433.971746831[/C][C]-19633.9717468312[/C][/ROW]
[ROW][C]71[/C][C]543100[/C][C]519583.350223392[/C][C]23516.6497766075[/C][/ROW]
[ROW][C]72[/C][C]591100[/C][C]609987.474784758[/C][C]-18887.4747847581[/C][/ROW]
[ROW][C]73[/C][C]624800[/C][C]597378.157206075[/C][C]27421.8427939246[/C][/ROW]
[ROW][C]74[/C][C]665300[/C][C]621357.297186085[/C][C]43942.702813915[/C][/ROW]
[ROW][C]75[/C][C]642600[/C][C]631780.993695041[/C][C]10819.0063049587[/C][/ROW]
[ROW][C]76[/C][C]608700[/C][C]605471.400900418[/C][C]3228.59909958241[/C][/ROW]
[ROW][C]77[/C][C]594500[/C][C]607824.752111993[/C][C]-13324.7521119929[/C][/ROW]
[ROW][C]78[/C][C]563800[/C][C]581457.000756397[/C][C]-17657.0007563973[/C][/ROW]
[ROW][C]79[/C][C]596100[/C][C]560617.239786976[/C][C]35482.7602130243[/C][/ROW]
[ROW][C]80[/C][C]597600[/C][C]613639.103227117[/C][C]-16039.1032271167[/C][/ROW]
[ROW][C]81[/C][C]633100[/C][C]624791.74894034[/C][C]8308.25105966022[/C][/ROW]
[ROW][C]82[/C][C]591000[/C][C]600363.014026969[/C][C]-9363.0140269685[/C][/ROW]
[ROW][C]83[/C][C]584200[/C][C]586761.176725511[/C][C]-2561.17672551086[/C][/ROW]
[ROW][C]84[/C][C]655800[/C][C]653308.084668684[/C][C]2491.91533131606[/C][/ROW]
[ROW][C]85[/C][C]670700[/C][C]671599.718225432[/C][C]-899.718225431745[/C][/ROW]
[ROW][C]86[/C][C]699700[/C][C]677002.65023678[/C][C]22697.3497632197[/C][/ROW]
[ROW][C]87[/C][C]712900[/C][C]666584.561348384[/C][C]46315.4386516155[/C][/ROW]
[ROW][C]88[/C][C]652000[/C][C]675064.858945096[/C][C]-23064.8589450957[/C][/ROW]
[ROW][C]89[/C][C]635100[/C][C]655183.250118581[/C][C]-20083.250118581[/C][/ROW]
[ROW][C]90[/C][C]603100[/C][C]624567.682693935[/C][C]-21467.6826939352[/C][/ROW]
[ROW][C]91[/C][C]610100[/C][C]609338.318846377[/C][C]761.681153623387[/C][/ROW]
[ROW][C]92[/C][C]602000[/C][C]624307.423410209[/C][C]-22307.4234102087[/C][/ROW]
[ROW][C]93[/C][C]597600[/C][C]631617.314816872[/C][C]-34017.3148168721[/C][/ROW]
[ROW][C]94[/C][C]585400[/C][C]562882.683118163[/C][C]22517.316881837[/C][/ROW]
[ROW][C]95[/C][C]567100[/C][C]575303.568170968[/C][C]-8203.56817096833[/C][/ROW]
[ROW][C]96[/C][C]620600[/C][C]634616.117938667[/C][C]-14016.1179386668[/C][/ROW]
[ROW][C]97[/C][C]646200[/C][C]633719.17766856[/C][C]12480.8223314396[/C][/ROW]
[ROW][C]98[/C][C]644800[/C][C]650580.021622272[/C][C]-5780.02162227186[/C][/ROW]
[ROW][C]99[/C][C]645200[/C][C]612887.559367783[/C][C]32312.4406322171[/C][/ROW]
[ROW][C]100[/C][C]644800[/C][C]593109.356982743[/C][C]51690.6430172565[/C][/ROW]
[ROW][C]101[/C][C]593000[/C][C]637936.188224223[/C][C]-44936.1882242232[/C][/ROW]
[ROW][C]102[/C][C]569100[/C][C]582937.593734109[/C][C]-13837.5937341086[/C][/ROW]
[ROW][C]103[/C][C]518800[/C][C]575282.843846143[/C][C]-56482.8438461425[/C][/ROW]
[ROW][C]104[/C][C]538700[/C][C]530660.969328712[/C][C]8039.03067128791[/C][/ROW]
[ROW][C]105[/C][C]554600[/C][C]558445.93531038[/C][C]-3845.93531037972[/C][/ROW]
[ROW][C]106[/C][C]507900[/C][C]521667.945711604[/C][C]-13767.9457116041[/C][/ROW]
[ROW][C]107[/C][C]488400[/C][C]493729.731561694[/C][C]-5329.73156169429[/C][/ROW]
[ROW][C]108[/C][C]563300[/C][C]550196.515432721[/C][C]13103.4845672792[/C][/ROW]
[ROW][C]109[/C][C]592400[/C][C]574085.823503602[/C][C]18314.1764963983[/C][/ROW]
[ROW][C]110[/C][C]598100[/C][C]591829.977721433[/C][C]6270.02227856684[/C][/ROW]
[ROW][C]111[/C][C]546300[/C][C]568920.210469729[/C][C]-22620.2104697287[/C][/ROW]
[ROW][C]112[/C][C]516100[/C][C]498656.193558542[/C][C]17443.8064414584[/C][/ROW]
[ROW][C]113[/C][C]518500[/C][C]492618.12188207[/C][C]25881.8781179304[/C][/ROW]
[ROW][C]114[/C][C]477400[/C][C]500874.920924275[/C][C]-23474.9209242754[/C][/ROW]
[ROW][C]115[/C][C]483400[/C][C]476087.787536216[/C][C]7312.2124637842[/C][/ROW]
[ROW][C]116[/C][C]469400[/C][C]497691.160947983[/C][C]-28291.1609479826[/C][/ROW]
[ROW][C]117[/C][C]501300[/C][C]491621.028988655[/C][C]9678.9710113448[/C][/ROW]
[ROW][C]118[/C][C]457400[/C][C]465642.407236377[/C][C]-8242.40723637666[/C][/ROW]
[ROW][C]119[/C][C]446700[/C][C]444474.247603951[/C][C]2225.75239604869[/C][/ROW]
[ROW][C]120[/C][C]501900[/C][C]511443.333164543[/C][C]-9543.3331645428[/C][/ROW]
[ROW][C]121[/C][C]550400[/C][C]515951.881186529[/C][C]34448.1188134711[/C][/ROW]
[ROW][C]122[/C][C]593700[/C][C]547037.515258405[/C][C]46662.4847415945[/C][/ROW]
[ROW][C]123[/C][C]548900[/C][C]559722.477973085[/C][C]-10822.4779730854[/C][/ROW]
[ROW][C]124[/C][C]534200[/C][C]510411.649005697[/C][C]23788.3509943034[/C][/ROW]
[ROW][C]125[/C][C]550500[/C][C]516942.069209227[/C][C]33557.9307907734[/C][/ROW]
[ROW][C]126[/C][C]541800[/C][C]531907.8381469[/C][C]9892.16185309994[/C][/ROW]
[ROW][C]127[/C][C]569300[/C][C]549596.76805854[/C][C]19703.2319414604[/C][/ROW]
[ROW][C]128[/C][C]587400[/C][C]587731.483551768[/C][C]-331.483551767771[/C][/ROW]
[ROW][C]129[/C][C]627700[/C][C]623846.975868381[/C][C]3853.02413161891[/C][/ROW]
[ROW][C]130[/C][C]607000[/C][C]602837.148136102[/C][C]4162.85186389775[/C][/ROW]
[ROW][C]131[/C][C]629500[/C][C]607276.547151305[/C][C]22223.4528486948[/C][/ROW]
[ROW][C]132[/C][C]704600[/C][C]705194.85077707[/C][C]-594.850777070038[/C][/ROW]
[ROW][C]133[/C][C]767700[/C][C]739233.881784062[/C][C]28466.1182159383[/C][/ROW]
[ROW][C]134[/C][C]812200[/C][C]782172.935782436[/C][C]30027.0642175641[/C][/ROW]
[ROW][C]135[/C][C]824600[/C][C]786801.252176063[/C][C]37798.7478239366[/C][/ROW]
[ROW][C]136[/C][C]856300[/C][C]802404.659653683[/C][C]53895.3403463167[/C][/ROW]
[ROW][C]137[/C][C]812200[/C][C]857066.684285315[/C][C]-44866.684285315[/C][/ROW]
[ROW][C]138[/C][C]764100[/C][C]814900.622545487[/C][C]-50800.6225454874[/C][/ROW]
[ROW][C]139[/C][C]801700[/C][C]790095.652573341[/C][C]11604.3474266587[/C][/ROW]
[ROW][C]140[/C][C]806000[/C][C]826698.21368536[/C][C]-20698.2136853596[/C][/ROW]
[ROW][C]141[/C][C]867200[/C][C]852116.465054308[/C][C]15083.5349456918[/C][/ROW]
[ROW][C]142[/C][C]801600[/C][C]848258.328383487[/C][C]-46658.3283834871[/C][/ROW]
[ROW][C]143[/C][C]817500[/C][C]814047.894139094[/C][C]3452.10586090630[/C][/ROW]
[ROW][C]144[/C][C]920900[/C][C]894084.760308608[/C][C]26815.2396913918[/C][/ROW]
[ROW][C]145[/C][C]959700[/C][C]959520.874007458[/C][C]179.125992542249[/C][/ROW]
[ROW][C]146[/C][C]997700[/C][C]979486.107789712[/C][C]18213.8922102879[/C][/ROW]
[ROW][C]147[/C][C]949100[/C][C]975243.530750466[/C][C]-26143.5307504656[/C][/ROW]
[ROW][C]148[/C][C]910900[/C][C]932408.800769329[/C][C]-21508.8007693288[/C][/ROW]
[ROW][C]149[/C][C]920400[/C][C]897009.348656907[/C][C]23390.6513430928[/C][/ROW]
[ROW][C]150[/C][C]914200[/C][C]907526.68952471[/C][C]6673.31047528947[/C][/ROW]
[ROW][C]151[/C][C]926300[/C][C]940030.451989342[/C][C]-13730.4519893415[/C][/ROW]
[ROW][C]152[/C][C]906400[/C][C]947390.245536353[/C][C]-40990.2455363529[/C][/ROW]
[ROW][C]153[/C][C]926100[/C][C]955241.64974575[/C][C]-29141.6497457498[/C][/ROW]
[ROW][C]154[/C][C]902500[/C][C]896340.401604388[/C][C]6159.59839561197[/C][/ROW]
[ROW][C]155[/C][C]895300[/C][C]910606.136208164[/C][C]-15306.1362081638[/C][/ROW]
[ROW][C]156[/C][C]979900[/C][C]971890.163466395[/C][C]8009.83653360454[/C][/ROW]
[ROW][C]157[/C][C]1009700[/C][C]1010291.13671698[/C][C]-591.136716982699[/C][/ROW]
[ROW][C]158[/C][C]1043800[/C][C]1024725.38603001[/C][C]19074.6139699878[/C][/ROW]
[ROW][C]159[/C][C]979800[/C][C]1008159.87472786[/C][C]-28359.8747278603[/C][/ROW]
[ROW][C]160[/C][C]921600[/C][C]956645.907643506[/C][C]-35045.9076435063[/C][/ROW]
[ROW][C]161[/C][C]923500[/C][C]906936.185056051[/C][C]16563.8149439488[/C][/ROW]
[ROW][C]162[/C][C]914500[/C][C]900202.879624468[/C][C]14297.1203755324[/C][/ROW]
[ROW][C]163[/C][C]891700[/C][C]928150.795546316[/C][C]-36450.7955463161[/C][/ROW]
[ROW][C]164[/C][C]916000[/C][C]901787.264771205[/C][C]14212.7352287947[/C][/ROW]
[ROW][C]165[/C][C]931700[/C][C]953402.134081721[/C][C]-21702.1340817214[/C][/ROW]
[ROW][C]166[/C][C]902400[/C][C]900587.260558522[/C][C]1812.73944147793[/C][/ROW]
[ROW][C]167[/C][C]893700[/C][C]902812.430476704[/C][C]-9112.43047670356[/C][/ROW]
[ROW][C]168[/C][C]941500[/C][C]967669.528021328[/C][C]-26169.5280213284[/C][/ROW]
[ROW][C]169[/C][C]980100[/C][C]967473.652002377[/C][C]12626.3479976233[/C][/ROW]
[ROW][C]170[/C][C]1006900[/C][C]989297.989041797[/C][C]17602.0109582026[/C][/ROW]
[ROW][C]171[/C][C]949200[/C][C]958351.419446583[/C][C]-9151.41944658256[/C][/ROW]
[ROW][C]172[/C][C]883200[/C][C]917441.051625647[/C][C]-34241.0516256473[/C][/ROW]
[ROW][C]173[/C][C]849900[/C][C]870178.75190878[/C][C]-20278.7519087794[/C][/ROW]
[ROW][C]174[/C][C]839200[/C][C]822945.214978996[/C][C]16254.7850210045[/C][/ROW]
[ROW][C]175[/C][C]803900[/C][C]837777.299826093[/C][C]-33877.2998260928[/C][/ROW]
[ROW][C]176[/C][C]797900[/C][C]812510.028344965[/C][C]-14610.0283449651[/C][/ROW]
[ROW][C]177[/C][C]830800[/C][C]824040.160651945[/C][C]6759.83934805507[/C][/ROW]
[ROW][C]178[/C][C]753300[/C][C]791140.712777618[/C][C]-37840.7127776179[/C][/ROW]
[ROW][C]179[/C][C]764100[/C][C]746248.344155333[/C][C]17851.6558446669[/C][/ROW]
[ROW][C]180[/C][C]807600[/C][C]823253.780860587[/C][C]-15653.7808605866[/C][/ROW]
[ROW][C]181[/C][C]853700[/C][C]829251.016756862[/C][C]24448.9832431383[/C][/ROW]
[ROW][C]182[/C][C]886200[/C][C]854923.375251768[/C][C]31276.6247482317[/C][/ROW]
[ROW][C]183[/C][C]815700[/C][C]826388.16515369[/C][C]-10688.1651536893[/C][/ROW]
[ROW][C]184[/C][C]743000[/C][C]774786.036391814[/C][C]-31786.0363918135[/C][/ROW]
[ROW][C]185[/C][C]753600[/C][C]725686.200428604[/C][C]27913.7995713955[/C][/ROW]
[ROW][C]186[/C][C]724800[/C][C]723394.123255486[/C][C]1405.87674451387[/C][/ROW]
[ROW][C]187[/C][C]709600[/C][C]715722.917063477[/C][C]-6122.91706347733[/C][/ROW]
[ROW][C]188[/C][C]721900[/C][C]716482.054551388[/C][C]5417.94544861186[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72434&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72434&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
13433800449533.520299145-15733.5202991454
14427700427800.552459051-100.552459050843
15413300411492.3313252551807.66867474484
16379500377201.8087866892298.19121331070
17379300375924.6533174063375.34668259404
18353700350203.3064276823496.69357231836
19378200370648.3339860237551.66601397679
20380600383909.311769447-3309.31176944723
21394000393434.698342544565.301657455857
22374000364489.6150732159510.38492678542
23375000355773.08071155919226.9192884405
24437600453254.831482233-15654.8314822327
25443900437896.4874797316003.51252026879
26488800440060.06790974548739.9320902545
27463900473504.751780232-9604.75178023247
28440000435547.5176944484452.48230555246
29453800442631.77553015911168.2244698409
30451600430700.83624552720899.1637544726
31453400475278.851952642-21878.8519526420
32461400467562.022050441-6162.02205044066
33509100480872.20874531428227.7912546864
34540600485212.86928512155387.1307148786
35555100529599.57421189325500.4257881066
36677400640454.22017304336945.7798269569
37694600690643.5294097043956.4705902962
38750100713581.76061740936518.2393825913
39733900744518.570950148-10618.5709501477
40709300723295.745452703-13995.7454527025
41720500729443.871771988-8943.87177198753
42693200713816.233987742-20616.2339877423
43687200725620.67539042-38420.6753904207
44686800713139.67895271-26339.6789527095
45720900719287.1924484751612.80755152507
46653100707649.571175018-54549.5711750181
47624700646834.264969296-22134.2649692957
48690000707937.822473186-17937.8224731860
49717800691504.97722949326295.0227705069
50736500725402.15313400911097.8468659912
51699900713129.289164922-13229.2891649222
52675600674063.7438800591536.25611994136
53635600680549.273728686-44949.2737286858
54632500615266.64944994617233.3505500542
55594900643888.60064159-48988.60064159
56604000609296.557880548-5296.55788054818
57620800624652.457793821-3852.45779382077
58578400587603.190453828-9203.19045382761
59571200561072.53179172610127.4682082739
60627400644122.923259774-16722.9232597742
61657700628127.21148327429572.788516726
62674100656643.66957786417456.3304221365
63672800640993.37976377131806.6202362288
64615300641129.186146105-25829.1861461053
65609100613557.340366392-4457.3403663924
66607600590948.83872493416651.1612750659
67566900609531.54260713-42631.5426071298
68572700586048.08024902-13348.0802490197
69589200593721.818103614-4521.8181036145
70534800554433.971746831-19633.9717468312
71543100519583.35022339223516.6497766075
72591100609987.474784758-18887.4747847581
73624800597378.15720607527421.8427939246
74665300621357.29718608543942.702813915
75642600631780.99369504110819.0063049587
76608700605471.4009004183228.59909958241
77594500607824.752111993-13324.7521119929
78563800581457.000756397-17657.0007563973
79596100560617.23978697635482.7602130243
80597600613639.103227117-16039.1032271167
81633100624791.748940348308.25105966022
82591000600363.014026969-9363.0140269685
83584200586761.176725511-2561.17672551086
84655800653308.0846686842491.91533131606
85670700671599.718225432-899.718225431745
86699700677002.6502367822697.3497632197
87712900666584.56134838446315.4386516155
88652000675064.858945096-23064.8589450957
89635100655183.250118581-20083.250118581
90603100624567.682693935-21467.6826939352
91610100609338.318846377761.681153623387
92602000624307.423410209-22307.4234102087
93597600631617.314816872-34017.3148168721
94585400562882.68311816322517.316881837
95567100575303.568170968-8203.56817096833
96620600634616.117938667-14016.1179386668
97646200633719.1776685612480.8223314396
98644800650580.021622272-5780.02162227186
99645200612887.55936778332312.4406322171
100644800593109.35698274351690.6430172565
101593000637936.188224223-44936.1882242232
102569100582937.593734109-13837.5937341086
103518800575282.843846143-56482.8438461425
104538700530660.9693287128039.03067128791
105554600558445.93531038-3845.93531037972
106507900521667.945711604-13767.9457116041
107488400493729.731561694-5329.73156169429
108563300550196.51543272113103.4845672792
109592400574085.82350360218314.1764963983
110598100591829.9777214336270.02227856684
111546300568920.210469729-22620.2104697287
112516100498656.19355854217443.8064414584
113518500492618.1218820725881.8781179304
114477400500874.920924275-23474.9209242754
115483400476087.7875362167312.2124637842
116469400497691.160947983-28291.1609479826
117501300491621.0289886559678.9710113448
118457400465642.407236377-8242.40723637666
119446700444474.2476039512225.75239604869
120501900511443.333164543-9543.3331645428
121550400515951.88118652934448.1188134711
122593700547037.51525840546662.4847415945
123548900559722.477973085-10822.4779730854
124534200510411.64900569723788.3509943034
125550500516942.06920922733557.9307907734
126541800531907.83814699892.16185309994
127569300549596.7680585419703.2319414604
128587400587731.483551768-331.483551767771
129627700623846.9758683813853.02413161891
130607000602837.1481361024162.85186389775
131629500607276.54715130522223.4528486948
132704600705194.85077707-594.850777070038
133767700739233.88178406228466.1182159383
134812200782172.93578243630027.0642175641
135824600786801.25217606337798.7478239366
136856300802404.65965368353895.3403463167
137812200857066.684285315-44866.684285315
138764100814900.622545487-50800.6225454874
139801700790095.65257334111604.3474266587
140806000826698.21368536-20698.2136853596
141867200852116.46505430815083.5349456918
142801600848258.328383487-46658.3283834871
143817500814047.8941390943452.10586090630
144920900894084.76030860826815.2396913918
145959700959520.874007458179.125992542249
146997700979486.10778971218213.8922102879
147949100975243.530750466-26143.5307504656
148910900932408.800769329-21508.8007693288
149920400897009.34865690723390.6513430928
150914200907526.689524716673.31047528947
151926300940030.451989342-13730.4519893415
152906400947390.245536353-40990.2455363529
153926100955241.64974575-29141.6497457498
154902500896340.4016043886159.59839561197
155895300910606.136208164-15306.1362081638
156979900971890.1634663958009.83653360454
15710097001010291.13671698-591.136716982699
15810438001024725.3860300119074.6139699878
1599798001008159.87472786-28359.8747278603
160921600956645.907643506-35045.9076435063
161923500906936.18505605116563.8149439488
162914500900202.87962446814297.1203755324
163891700928150.795546316-36450.7955463161
164916000901787.26477120514212.7352287947
165931700953402.134081721-21702.1340817214
166902400900587.2605585221812.73944147793
167893700902812.430476704-9112.43047670356
168941500967669.528021328-26169.5280213284
169980100967473.65200237712626.3479976233
1701006900989297.98904179717602.0109582026
171949200958351.419446583-9151.41944658256
172883200917441.051625647-34241.0516256473
173849900870178.75190878-20278.7519087794
174839200822945.21497899616254.7850210045
175803900837777.299826093-33877.2998260928
176797900812510.028344965-14610.0283449651
177830800824040.1606519456759.83934805507
178753300791140.712777618-37840.7127776179
179764100746248.34415533317851.6558446669
180807600823253.780860587-15653.7808605866
181853700829251.01675686224448.9832431383
182886200854923.37525176831276.6247482317
183815700826388.16515369-10688.1651536893
184743000774786.036391814-31786.0363918135
185753600725686.20042860427913.7995713955
186724800723394.1232554861405.87674451387
187709600715722.917063477-6122.91706347733
188721900716482.0545513885417.94544861186







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
189749327.050707691703244.451869429795409.649545954
190705177.457094367641529.599135961768825.315052773
191704258.111911153624636.804009918783879.419812388
192763573.133119028668598.963427645858547.30281041
193792044.277269829681936.834388177902151.72015148
194798905.82931752673681.233789091924130.42484595
195736491.924632955596050.754046174876933.095219736
196691088.827742808535261.36984541846916.285640206
197679923.245271661508495.124802909851351.365740414
198649963.800898342462691.50609987837236.095696815
199640013.945187637436634.716123001843393.174252274
200648077.723003801428316.092639857867839.353367745

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
189 & 749327.050707691 & 703244.451869429 & 795409.649545954 \tabularnewline
190 & 705177.457094367 & 641529.599135961 & 768825.315052773 \tabularnewline
191 & 704258.111911153 & 624636.804009918 & 783879.419812388 \tabularnewline
192 & 763573.133119028 & 668598.963427645 & 858547.30281041 \tabularnewline
193 & 792044.277269829 & 681936.834388177 & 902151.72015148 \tabularnewline
194 & 798905.82931752 & 673681.233789091 & 924130.42484595 \tabularnewline
195 & 736491.924632955 & 596050.754046174 & 876933.095219736 \tabularnewline
196 & 691088.827742808 & 535261.36984541 & 846916.285640206 \tabularnewline
197 & 679923.245271661 & 508495.124802909 & 851351.365740414 \tabularnewline
198 & 649963.800898342 & 462691.50609987 & 837236.095696815 \tabularnewline
199 & 640013.945187637 & 436634.716123001 & 843393.174252274 \tabularnewline
200 & 648077.723003801 & 428316.092639857 & 867839.353367745 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72434&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]189[/C][C]749327.050707691[/C][C]703244.451869429[/C][C]795409.649545954[/C][/ROW]
[ROW][C]190[/C][C]705177.457094367[/C][C]641529.599135961[/C][C]768825.315052773[/C][/ROW]
[ROW][C]191[/C][C]704258.111911153[/C][C]624636.804009918[/C][C]783879.419812388[/C][/ROW]
[ROW][C]192[/C][C]763573.133119028[/C][C]668598.963427645[/C][C]858547.30281041[/C][/ROW]
[ROW][C]193[/C][C]792044.277269829[/C][C]681936.834388177[/C][C]902151.72015148[/C][/ROW]
[ROW][C]194[/C][C]798905.82931752[/C][C]673681.233789091[/C][C]924130.42484595[/C][/ROW]
[ROW][C]195[/C][C]736491.924632955[/C][C]596050.754046174[/C][C]876933.095219736[/C][/ROW]
[ROW][C]196[/C][C]691088.827742808[/C][C]535261.36984541[/C][C]846916.285640206[/C][/ROW]
[ROW][C]197[/C][C]679923.245271661[/C][C]508495.124802909[/C][C]851351.365740414[/C][/ROW]
[ROW][C]198[/C][C]649963.800898342[/C][C]462691.50609987[/C][C]837236.095696815[/C][/ROW]
[ROW][C]199[/C][C]640013.945187637[/C][C]436634.716123001[/C][C]843393.174252274[/C][/ROW]
[ROW][C]200[/C][C]648077.723003801[/C][C]428316.092639857[/C][C]867839.353367745[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72434&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72434&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
189749327.050707691703244.451869429795409.649545954
190705177.457094367641529.599135961768825.315052773
191704258.111911153624636.804009918783879.419812388
192763573.133119028668598.963427645858547.30281041
193792044.277269829681936.834388177902151.72015148
194798905.82931752673681.233789091924130.42484595
195736491.924632955596050.754046174876933.095219736
196691088.827742808535261.36984541846916.285640206
197679923.245271661508495.124802909851351.365740414
198649963.800898342462691.50609987837236.095696815
199640013.945187637436634.716123001843393.174252274
200648077.723003801428316.092639857867839.353367745



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')