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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 29 Nov 2011 07:38:02 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/29/t13225705487s78puoxyr4micp.htm/, Retrieved Tue, 16 Apr 2024 06:43:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=148283, Retrieved Tue, 16 Apr 2024 06:43:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact112
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RMPD  [Multiple Regression] [Seatbelt] [2009-11-12 13:54:52] [b98453cac15ba1066b407e146608df68]
- R PD    [Multiple Regression] [Aantal reizigers ...] [2010-11-26 01:03:33] [97ad38b1c3b35a5feca8b85f7bc7b3ff]
-    D      [Multiple Regression] [Aantal reizigers ...] [2010-11-26 01:44:20] [97ad38b1c3b35a5feca8b85f7bc7b3ff]
-    D        [Multiple Regression] [Aantal reizigers ...] [2010-11-26 01:59:36] [97ad38b1c3b35a5feca8b85f7bc7b3ff]
- RMPD            [Exponential Smoothing] [] [2011-11-29 12:38:02] [ce4468323d272130d499477f5e05a6d2] [Current]
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Dataseries X:
276986
260633
291551
275383
275302
231693
238829
274215
277808
299060
286629
232313
294053
267510
309739
280733
287298
235672
256449
288997
290789
321898
291834
241380
295469
258200
306102
281480
283101
237414
274834
299340
300383
340862
318794
265740
322656
281563
323461
312579
310784
262785
273754
320036
310336
342206
320052
265582
326988
300713
346414
317325
326208
270657
278158
324584
321801
343542
354040
278179
330246
307344
375874
335309
339271
280264
293689
341161
345097
368712
369403
288384
340981
319072
374214
344529
337271
281016
282224
320984
325426
366276
380296
300727
359326
327610
383563
352405
329351
294486
333454
334339
358000
396057
386976
307155
363909
344700
397561
376791
337085
299252
323136
329091
346991
461999
436533
360372
415467
382110
432197
424254
386728
354508
375765
367986
402378
426516
433313
338461
416834
381099
445673
412408
393997
348241
380134
373688
393588
434192
430731
344468
411891
370497
437305
411270
385495
341273
384217
373223
415771
448634
454341
350297
419104
398027
456059
430052
399757
362731
384896
385349
432289
468891
442702
370178
439400
393900
468700
438800
430100
366300
391000
380900
431400
465400
471500
387500
446400
421500
504800
492071
421253
396682
428000
421900
465600
525793
499855
435287
479499
473027
554410
489574
462157
420331




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148283&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148283&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148283&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.323374787803211
beta0
gamma0.517269003255542

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.323374787803211 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.517269003255542 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148283&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]0.323374787803211[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.517269003255542[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148283&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148283&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
alpha0.323374787803211
beta0
gamma0.517269003255542







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13294053289368.4887820514684.51121794869
14267510264009.9875821383500.01241786184
15309739307233.741000762505.25899923954
16280733278565.1495770532167.85042294738
17287298285682.4487265831615.55127341673
18235672235003.939922497668.060077502683
19256449250470.2863539875978.71364601282
20288997287811.714256291185.28574370965
21290789291763.360094503-974.360094502917
22321898312739.2559180539158.74408194656
23291834303566.942154451-11732.9421544512
24241380245810.908787302-4430.90878730244
25295469307877.40161707-12408.4016170703
26258200276576.912034613-18376.9120346126
27306102312378.058690588-6276.05869058782
28281480280751.718448778728.281551222317
29283101287210.194136875-4109.19413687527
30237414234348.8276884013065.17231159876
31274834252449.05391978422384.9460802159
32299340293418.1571746285921.84282537235
33300383298145.6160516562237.38394834369
34340862323706.66751004617155.3324899536
35318794309808.216114438985.78388557018
36265740261307.7879752964432.21202470432
37322656323448.290071862-792.290071861702
38281563293815.195868126-12252.1958681258
39323461335832.186696851-12371.1866968511
40312579304686.335545717892.66445428965
41310784311768.488851451-984.48885145149
42262785262428.581832533356.418167467229
43273754286414.732939415-12660.7329394148
44320036310288.9063271769747.09367282398
45310336314963.804413946-4627.80441394594
46342206343526.06799409-1320.06799409015
47320052320793.81834952-741.818349520443
48265582267553.99127694-1971.99127694039
49326988325794.9741281221193.02587187773
50300713292792.9455428867920.05445711449
51346414341291.4870773285122.51292267221
52317325322894.949487424-5569.94948742416
53326208322516.6536297223691.34637027793
54270657275158.107601341-4501.10760134074
55278158293017.490265081-14859.4902650805
56324584324023.318641607560.681358393398
57321801320696.3878091971104.61219080252
58343542352270.069040168-8728.06904016819
59354040327344.64441416426695.355585836
60278179282546.750500347-4367.75050034694
61330246341120.752516443-10874.752516443
62307344306570.750155014773.249844986363
63375874351779.06342326624094.9365767336
64335309335775.396877069-466.396877069084
65339271340288.889334993-1017.88933499297
66280264288540.158856336-8276.15885633643
67293689301553.379684209-7864.37968420901
68341161340218.268109205942.731890794763
69345097337205.257081687891.74291831977
70368712367532.313889431179.6861105701
71369403358208.90865537211194.0913446283
72288384297526.295028499-9142.29502849898
73340981352278.896915486-11297.8969154863
74319072321668.829107707-2596.82910770731
75374214373949.870010017264.129989982874
76344529341643.5222978222885.477702178
77337271347047.905643385-9776.90564338537
78281016289926.355759009-8910.3557590092
79282224302878.614875532-20654.6148755319
80320984340489.928533266-19505.9285332662
81325426333296.471023785-7870.47102378466
82366276356177.22382424510098.7761757547
83380296353243.04173061327052.9582693872
84300727290571.10654329510155.8934567049
85359326350809.8013060928516.19869390846
86327610329652.462258387-2042.46225838654
87383563383114.099236913448.900763087149
88352405351784.966222441620.033777559234
89329351352024.962781723-22673.9627817226
90294486291036.1198576823449.88014231779
91333454303874.90925260429579.090747396
92334339358132.573866583-23793.5738665825
93358000353624.9780774944375.02192250645
94396057386754.8016490759302.19835092541
95386976389496.943463722-2520.94346372166
96307155311347.627876803-4192.62787680258
97363909366372.483941759-2463.4839417591
98344700337969.0900642156730.90993578511
99397561395139.7846183522421.21538164804
100376791364508.34450943212282.655490568
101337085360366.904174313-23281.9041743126
102299252308324.741490536-9072.74149053579
103323136326259.18260488-3123.18260488007
104329091351261.470721356-22170.4707213559
105346991357137.676604364-10146.6766043635
106461999387296.04719200674702.9528079935
107436533407049.07699064329483.9230093567
108360372338664.243362221707.7566378
109415467402669.82639413512797.1736058653
110382110382419.356976987-309.356976986921
111432197435805.02547376-3608.02547375963
112424254406675.35779280117578.6422071985
113386728391799.007990554-5071.00799055427
114354508350618.9578471093889.0421528907
115375765374827.24223998937.757760020264
116367986394476.237641834-26490.237641834
117402378403163.834678152-785.834678151819
118426516466046.402418025-39530.402418025
119433313433032.70917433280.290825669654
120338461352482.520346889-14021.5203468885
121416834401815.47646656715018.5235334332
122381099377696.0859617633402.91403823713
123445673431127.68441081914545.3155891806
124412408415283.624949741-2875.624949741
125393997385865.565583878131.4344161296
126348241352090.845354091-3849.8453540905
127380134372763.6272227697370.37277723069
128373688384893.045202115-11205.0452021151
129393588407519.958426963-13931.9584269634
130434192452590.90906297-18398.9090629697
131430731440344.241118614-9613.24111861404
132344468351589.138930657-7121.1389306566
133411891413317.439898153-1426.43989815313
134370497379814.731463399-9317.73146339913
135437305433032.6037637374272.39623626281
136411270407769.2599215963500.74007840402
137385495384265.5967422891229.40325771074
138341273344065.518691083-2792.5186910826
139384217369007.25882520915209.7411747908
140373223377170.385703148-3947.38570314797
141415771401189.83090121714581.169098783
142448634453917.787666042-5283.78766604175
143454341448987.1789323795353.821067621
144350297365944.276213171-15647.2762131706
145419104426908.568341928-7804.56834192818
146398027388581.4036354799445.59636452119
147456059452623.3704003243435.62959967559
148430052426819.3597921423232.64020785841
149399757402434.038235086-2677.03823508619
150362731359563.0538769463167.94612305408
151384896392732.999486022-7836.99948602234
152385349386738.449785457-1389.44978545682
153432289418070.01017842414218.9898215762
154468891463728.1670753435162.83292465738
155442702465898.865852142-23196.865852142
156370178366273.0645324583904.93546754192
157439400436304.9751449063095.02485509438
158393900407539.974269302-13639.9742693018
159468700462013.1776942976686.82230570307
160438800437189.4751088031610.52489119745
161430100410211.23115738919888.7688426111
162366300376683.188320934-10383.1883209339
163391000401619.338015124-10619.3380151245
164380900396981.674841687-16081.6748416867
165431400429025.0509997972374.94900020334
166465400467683.513708117-2283.51370811701
167471500457520.43516571613979.5648342842
168387500379402.1101378258097.88986217481
169446400450506.45000154-4106.45000153978
170421500413555.4700652297944.52993477054
171504800482122.8808411322677.1191588701
172492071460693.34697679631377.6530232039
173421253449738.376869783-28485.3768697828
174396682389972.2531965916709.74680340855
175428000420353.175416217646.82458378997
176421900419710.5258342722189.47416572791
177465600464122.0984977371477.90150226286
178525793500860.02952885824932.9704711417
179499855505190.108534259-5335.10853425926
180435287418767.33504404416519.6649559558
181479499488323.57926237-8824.57926236972
182473027454064.68510406518962.3148959349
183554410531351.3354542623058.6645457398
184489574513090.346666579-23516.3466665791
185462157463432.145273439-1275.14527343883
186420331424783.320935812-4452.32093581202

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 294053 & 289368.488782051 & 4684.51121794869 \tabularnewline
14 & 267510 & 264009.987582138 & 3500.01241786184 \tabularnewline
15 & 309739 & 307233.74100076 & 2505.25899923954 \tabularnewline
16 & 280733 & 278565.149577053 & 2167.85042294738 \tabularnewline
17 & 287298 & 285682.448726583 & 1615.55127341673 \tabularnewline
18 & 235672 & 235003.939922497 & 668.060077502683 \tabularnewline
19 & 256449 & 250470.286353987 & 5978.71364601282 \tabularnewline
20 & 288997 & 287811.71425629 & 1185.28574370965 \tabularnewline
21 & 290789 & 291763.360094503 & -974.360094502917 \tabularnewline
22 & 321898 & 312739.255918053 & 9158.74408194656 \tabularnewline
23 & 291834 & 303566.942154451 & -11732.9421544512 \tabularnewline
24 & 241380 & 245810.908787302 & -4430.90878730244 \tabularnewline
25 & 295469 & 307877.40161707 & -12408.4016170703 \tabularnewline
26 & 258200 & 276576.912034613 & -18376.9120346126 \tabularnewline
27 & 306102 & 312378.058690588 & -6276.05869058782 \tabularnewline
28 & 281480 & 280751.718448778 & 728.281551222317 \tabularnewline
29 & 283101 & 287210.194136875 & -4109.19413687527 \tabularnewline
30 & 237414 & 234348.827688401 & 3065.17231159876 \tabularnewline
31 & 274834 & 252449.053919784 & 22384.9460802159 \tabularnewline
32 & 299340 & 293418.157174628 & 5921.84282537235 \tabularnewline
33 & 300383 & 298145.616051656 & 2237.38394834369 \tabularnewline
34 & 340862 & 323706.667510046 & 17155.3324899536 \tabularnewline
35 & 318794 & 309808.21611443 & 8985.78388557018 \tabularnewline
36 & 265740 & 261307.787975296 & 4432.21202470432 \tabularnewline
37 & 322656 & 323448.290071862 & -792.290071861702 \tabularnewline
38 & 281563 & 293815.195868126 & -12252.1958681258 \tabularnewline
39 & 323461 & 335832.186696851 & -12371.1866968511 \tabularnewline
40 & 312579 & 304686.33554571 & 7892.66445428965 \tabularnewline
41 & 310784 & 311768.488851451 & -984.48885145149 \tabularnewline
42 & 262785 & 262428.581832533 & 356.418167467229 \tabularnewline
43 & 273754 & 286414.732939415 & -12660.7329394148 \tabularnewline
44 & 320036 & 310288.906327176 & 9747.09367282398 \tabularnewline
45 & 310336 & 314963.804413946 & -4627.80441394594 \tabularnewline
46 & 342206 & 343526.06799409 & -1320.06799409015 \tabularnewline
47 & 320052 & 320793.81834952 & -741.818349520443 \tabularnewline
48 & 265582 & 267553.99127694 & -1971.99127694039 \tabularnewline
49 & 326988 & 325794.974128122 & 1193.02587187773 \tabularnewline
50 & 300713 & 292792.945542886 & 7920.05445711449 \tabularnewline
51 & 346414 & 341291.487077328 & 5122.51292267221 \tabularnewline
52 & 317325 & 322894.949487424 & -5569.94948742416 \tabularnewline
53 & 326208 & 322516.653629722 & 3691.34637027793 \tabularnewline
54 & 270657 & 275158.107601341 & -4501.10760134074 \tabularnewline
55 & 278158 & 293017.490265081 & -14859.4902650805 \tabularnewline
56 & 324584 & 324023.318641607 & 560.681358393398 \tabularnewline
57 & 321801 & 320696.387809197 & 1104.61219080252 \tabularnewline
58 & 343542 & 352270.069040168 & -8728.06904016819 \tabularnewline
59 & 354040 & 327344.644414164 & 26695.355585836 \tabularnewline
60 & 278179 & 282546.750500347 & -4367.75050034694 \tabularnewline
61 & 330246 & 341120.752516443 & -10874.752516443 \tabularnewline
62 & 307344 & 306570.750155014 & 773.249844986363 \tabularnewline
63 & 375874 & 351779.063423266 & 24094.9365767336 \tabularnewline
64 & 335309 & 335775.396877069 & -466.396877069084 \tabularnewline
65 & 339271 & 340288.889334993 & -1017.88933499297 \tabularnewline
66 & 280264 & 288540.158856336 & -8276.15885633643 \tabularnewline
67 & 293689 & 301553.379684209 & -7864.37968420901 \tabularnewline
68 & 341161 & 340218.268109205 & 942.731890794763 \tabularnewline
69 & 345097 & 337205.25708168 & 7891.74291831977 \tabularnewline
70 & 368712 & 367532.31388943 & 1179.6861105701 \tabularnewline
71 & 369403 & 358208.908655372 & 11194.0913446283 \tabularnewline
72 & 288384 & 297526.295028499 & -9142.29502849898 \tabularnewline
73 & 340981 & 352278.896915486 & -11297.8969154863 \tabularnewline
74 & 319072 & 321668.829107707 & -2596.82910770731 \tabularnewline
75 & 374214 & 373949.870010017 & 264.129989982874 \tabularnewline
76 & 344529 & 341643.522297822 & 2885.477702178 \tabularnewline
77 & 337271 & 347047.905643385 & -9776.90564338537 \tabularnewline
78 & 281016 & 289926.355759009 & -8910.3557590092 \tabularnewline
79 & 282224 & 302878.614875532 & -20654.6148755319 \tabularnewline
80 & 320984 & 340489.928533266 & -19505.9285332662 \tabularnewline
81 & 325426 & 333296.471023785 & -7870.47102378466 \tabularnewline
82 & 366276 & 356177.223824245 & 10098.7761757547 \tabularnewline
83 & 380296 & 353243.041730613 & 27052.9582693872 \tabularnewline
84 & 300727 & 290571.106543295 & 10155.8934567049 \tabularnewline
85 & 359326 & 350809.801306092 & 8516.19869390846 \tabularnewline
86 & 327610 & 329652.462258387 & -2042.46225838654 \tabularnewline
87 & 383563 & 383114.099236913 & 448.900763087149 \tabularnewline
88 & 352405 & 351784.966222441 & 620.033777559234 \tabularnewline
89 & 329351 & 352024.962781723 & -22673.9627817226 \tabularnewline
90 & 294486 & 291036.119857682 & 3449.88014231779 \tabularnewline
91 & 333454 & 303874.909252604 & 29579.090747396 \tabularnewline
92 & 334339 & 358132.573866583 & -23793.5738665825 \tabularnewline
93 & 358000 & 353624.978077494 & 4375.02192250645 \tabularnewline
94 & 396057 & 386754.801649075 & 9302.19835092541 \tabularnewline
95 & 386976 & 389496.943463722 & -2520.94346372166 \tabularnewline
96 & 307155 & 311347.627876803 & -4192.62787680258 \tabularnewline
97 & 363909 & 366372.483941759 & -2463.4839417591 \tabularnewline
98 & 344700 & 337969.090064215 & 6730.90993578511 \tabularnewline
99 & 397561 & 395139.784618352 & 2421.21538164804 \tabularnewline
100 & 376791 & 364508.344509432 & 12282.655490568 \tabularnewline
101 & 337085 & 360366.904174313 & -23281.9041743126 \tabularnewline
102 & 299252 & 308324.741490536 & -9072.74149053579 \tabularnewline
103 & 323136 & 326259.18260488 & -3123.18260488007 \tabularnewline
104 & 329091 & 351261.470721356 & -22170.4707213559 \tabularnewline
105 & 346991 & 357137.676604364 & -10146.6766043635 \tabularnewline
106 & 461999 & 387296.047192006 & 74702.9528079935 \tabularnewline
107 & 436533 & 407049.076990643 & 29483.9230093567 \tabularnewline
108 & 360372 & 338664.2433622 & 21707.7566378 \tabularnewline
109 & 415467 & 402669.826394135 & 12797.1736058653 \tabularnewline
110 & 382110 & 382419.356976987 & -309.356976986921 \tabularnewline
111 & 432197 & 435805.02547376 & -3608.02547375963 \tabularnewline
112 & 424254 & 406675.357792801 & 17578.6422071985 \tabularnewline
113 & 386728 & 391799.007990554 & -5071.00799055427 \tabularnewline
114 & 354508 & 350618.957847109 & 3889.0421528907 \tabularnewline
115 & 375765 & 374827.24223998 & 937.757760020264 \tabularnewline
116 & 367986 & 394476.237641834 & -26490.237641834 \tabularnewline
117 & 402378 & 403163.834678152 & -785.834678151819 \tabularnewline
118 & 426516 & 466046.402418025 & -39530.402418025 \tabularnewline
119 & 433313 & 433032.70917433 & 280.290825669654 \tabularnewline
120 & 338461 & 352482.520346889 & -14021.5203468885 \tabularnewline
121 & 416834 & 401815.476466567 & 15018.5235334332 \tabularnewline
122 & 381099 & 377696.085961763 & 3402.91403823713 \tabularnewline
123 & 445673 & 431127.684410819 & 14545.3155891806 \tabularnewline
124 & 412408 & 415283.624949741 & -2875.624949741 \tabularnewline
125 & 393997 & 385865.56558387 & 8131.4344161296 \tabularnewline
126 & 348241 & 352090.845354091 & -3849.8453540905 \tabularnewline
127 & 380134 & 372763.627222769 & 7370.37277723069 \tabularnewline
128 & 373688 & 384893.045202115 & -11205.0452021151 \tabularnewline
129 & 393588 & 407519.958426963 & -13931.9584269634 \tabularnewline
130 & 434192 & 452590.90906297 & -18398.9090629697 \tabularnewline
131 & 430731 & 440344.241118614 & -9613.24111861404 \tabularnewline
132 & 344468 & 351589.138930657 & -7121.1389306566 \tabularnewline
133 & 411891 & 413317.439898153 & -1426.43989815313 \tabularnewline
134 & 370497 & 379814.731463399 & -9317.73146339913 \tabularnewline
135 & 437305 & 433032.603763737 & 4272.39623626281 \tabularnewline
136 & 411270 & 407769.259921596 & 3500.74007840402 \tabularnewline
137 & 385495 & 384265.596742289 & 1229.40325771074 \tabularnewline
138 & 341273 & 344065.518691083 & -2792.5186910826 \tabularnewline
139 & 384217 & 369007.258825209 & 15209.7411747908 \tabularnewline
140 & 373223 & 377170.385703148 & -3947.38570314797 \tabularnewline
141 & 415771 & 401189.830901217 & 14581.169098783 \tabularnewline
142 & 448634 & 453917.787666042 & -5283.78766604175 \tabularnewline
143 & 454341 & 448987.178932379 & 5353.821067621 \tabularnewline
144 & 350297 & 365944.276213171 & -15647.2762131706 \tabularnewline
145 & 419104 & 426908.568341928 & -7804.56834192818 \tabularnewline
146 & 398027 & 388581.403635479 & 9445.59636452119 \tabularnewline
147 & 456059 & 452623.370400324 & 3435.62959967559 \tabularnewline
148 & 430052 & 426819.359792142 & 3232.64020785841 \tabularnewline
149 & 399757 & 402434.038235086 & -2677.03823508619 \tabularnewline
150 & 362731 & 359563.053876946 & 3167.94612305408 \tabularnewline
151 & 384896 & 392732.999486022 & -7836.99948602234 \tabularnewline
152 & 385349 & 386738.449785457 & -1389.44978545682 \tabularnewline
153 & 432289 & 418070.010178424 & 14218.9898215762 \tabularnewline
154 & 468891 & 463728.167075343 & 5162.83292465738 \tabularnewline
155 & 442702 & 465898.865852142 & -23196.865852142 \tabularnewline
156 & 370178 & 366273.064532458 & 3904.93546754192 \tabularnewline
157 & 439400 & 436304.975144906 & 3095.02485509438 \tabularnewline
158 & 393900 & 407539.974269302 & -13639.9742693018 \tabularnewline
159 & 468700 & 462013.177694297 & 6686.82230570307 \tabularnewline
160 & 438800 & 437189.475108803 & 1610.52489119745 \tabularnewline
161 & 430100 & 410211.231157389 & 19888.7688426111 \tabularnewline
162 & 366300 & 376683.188320934 & -10383.1883209339 \tabularnewline
163 & 391000 & 401619.338015124 & -10619.3380151245 \tabularnewline
164 & 380900 & 396981.674841687 & -16081.6748416867 \tabularnewline
165 & 431400 & 429025.050999797 & 2374.94900020334 \tabularnewline
166 & 465400 & 467683.513708117 & -2283.51370811701 \tabularnewline
167 & 471500 & 457520.435165716 & 13979.5648342842 \tabularnewline
168 & 387500 & 379402.110137825 & 8097.88986217481 \tabularnewline
169 & 446400 & 450506.45000154 & -4106.45000153978 \tabularnewline
170 & 421500 & 413555.470065229 & 7944.52993477054 \tabularnewline
171 & 504800 & 482122.88084113 & 22677.1191588701 \tabularnewline
172 & 492071 & 460693.346976796 & 31377.6530232039 \tabularnewline
173 & 421253 & 449738.376869783 & -28485.3768697828 \tabularnewline
174 & 396682 & 389972.253196591 & 6709.74680340855 \tabularnewline
175 & 428000 & 420353.17541621 & 7646.82458378997 \tabularnewline
176 & 421900 & 419710.525834272 & 2189.47416572791 \tabularnewline
177 & 465600 & 464122.098497737 & 1477.90150226286 \tabularnewline
178 & 525793 & 500860.029528858 & 24932.9704711417 \tabularnewline
179 & 499855 & 505190.108534259 & -5335.10853425926 \tabularnewline
180 & 435287 & 418767.335044044 & 16519.6649559558 \tabularnewline
181 & 479499 & 488323.57926237 & -8824.57926236972 \tabularnewline
182 & 473027 & 454064.685104065 & 18962.3148959349 \tabularnewline
183 & 554410 & 531351.33545426 & 23058.6645457398 \tabularnewline
184 & 489574 & 513090.346666579 & -23516.3466665791 \tabularnewline
185 & 462157 & 463432.145273439 & -1275.14527343883 \tabularnewline
186 & 420331 & 424783.320935812 & -4452.32093581202 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148283&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]294053[/C][C]289368.488782051[/C][C]4684.51121794869[/C][/ROW]
[ROW][C]14[/C][C]267510[/C][C]264009.987582138[/C][C]3500.01241786184[/C][/ROW]
[ROW][C]15[/C][C]309739[/C][C]307233.74100076[/C][C]2505.25899923954[/C][/ROW]
[ROW][C]16[/C][C]280733[/C][C]278565.149577053[/C][C]2167.85042294738[/C][/ROW]
[ROW][C]17[/C][C]287298[/C][C]285682.448726583[/C][C]1615.55127341673[/C][/ROW]
[ROW][C]18[/C][C]235672[/C][C]235003.939922497[/C][C]668.060077502683[/C][/ROW]
[ROW][C]19[/C][C]256449[/C][C]250470.286353987[/C][C]5978.71364601282[/C][/ROW]
[ROW][C]20[/C][C]288997[/C][C]287811.71425629[/C][C]1185.28574370965[/C][/ROW]
[ROW][C]21[/C][C]290789[/C][C]291763.360094503[/C][C]-974.360094502917[/C][/ROW]
[ROW][C]22[/C][C]321898[/C][C]312739.255918053[/C][C]9158.74408194656[/C][/ROW]
[ROW][C]23[/C][C]291834[/C][C]303566.942154451[/C][C]-11732.9421544512[/C][/ROW]
[ROW][C]24[/C][C]241380[/C][C]245810.908787302[/C][C]-4430.90878730244[/C][/ROW]
[ROW][C]25[/C][C]295469[/C][C]307877.40161707[/C][C]-12408.4016170703[/C][/ROW]
[ROW][C]26[/C][C]258200[/C][C]276576.912034613[/C][C]-18376.9120346126[/C][/ROW]
[ROW][C]27[/C][C]306102[/C][C]312378.058690588[/C][C]-6276.05869058782[/C][/ROW]
[ROW][C]28[/C][C]281480[/C][C]280751.718448778[/C][C]728.281551222317[/C][/ROW]
[ROW][C]29[/C][C]283101[/C][C]287210.194136875[/C][C]-4109.19413687527[/C][/ROW]
[ROW][C]30[/C][C]237414[/C][C]234348.827688401[/C][C]3065.17231159876[/C][/ROW]
[ROW][C]31[/C][C]274834[/C][C]252449.053919784[/C][C]22384.9460802159[/C][/ROW]
[ROW][C]32[/C][C]299340[/C][C]293418.157174628[/C][C]5921.84282537235[/C][/ROW]
[ROW][C]33[/C][C]300383[/C][C]298145.616051656[/C][C]2237.38394834369[/C][/ROW]
[ROW][C]34[/C][C]340862[/C][C]323706.667510046[/C][C]17155.3324899536[/C][/ROW]
[ROW][C]35[/C][C]318794[/C][C]309808.21611443[/C][C]8985.78388557018[/C][/ROW]
[ROW][C]36[/C][C]265740[/C][C]261307.787975296[/C][C]4432.21202470432[/C][/ROW]
[ROW][C]37[/C][C]322656[/C][C]323448.290071862[/C][C]-792.290071861702[/C][/ROW]
[ROW][C]38[/C][C]281563[/C][C]293815.195868126[/C][C]-12252.1958681258[/C][/ROW]
[ROW][C]39[/C][C]323461[/C][C]335832.186696851[/C][C]-12371.1866968511[/C][/ROW]
[ROW][C]40[/C][C]312579[/C][C]304686.33554571[/C][C]7892.66445428965[/C][/ROW]
[ROW][C]41[/C][C]310784[/C][C]311768.488851451[/C][C]-984.48885145149[/C][/ROW]
[ROW][C]42[/C][C]262785[/C][C]262428.581832533[/C][C]356.418167467229[/C][/ROW]
[ROW][C]43[/C][C]273754[/C][C]286414.732939415[/C][C]-12660.7329394148[/C][/ROW]
[ROW][C]44[/C][C]320036[/C][C]310288.906327176[/C][C]9747.09367282398[/C][/ROW]
[ROW][C]45[/C][C]310336[/C][C]314963.804413946[/C][C]-4627.80441394594[/C][/ROW]
[ROW][C]46[/C][C]342206[/C][C]343526.06799409[/C][C]-1320.06799409015[/C][/ROW]
[ROW][C]47[/C][C]320052[/C][C]320793.81834952[/C][C]-741.818349520443[/C][/ROW]
[ROW][C]48[/C][C]265582[/C][C]267553.99127694[/C][C]-1971.99127694039[/C][/ROW]
[ROW][C]49[/C][C]326988[/C][C]325794.974128122[/C][C]1193.02587187773[/C][/ROW]
[ROW][C]50[/C][C]300713[/C][C]292792.945542886[/C][C]7920.05445711449[/C][/ROW]
[ROW][C]51[/C][C]346414[/C][C]341291.487077328[/C][C]5122.51292267221[/C][/ROW]
[ROW][C]52[/C][C]317325[/C][C]322894.949487424[/C][C]-5569.94948742416[/C][/ROW]
[ROW][C]53[/C][C]326208[/C][C]322516.653629722[/C][C]3691.34637027793[/C][/ROW]
[ROW][C]54[/C][C]270657[/C][C]275158.107601341[/C][C]-4501.10760134074[/C][/ROW]
[ROW][C]55[/C][C]278158[/C][C]293017.490265081[/C][C]-14859.4902650805[/C][/ROW]
[ROW][C]56[/C][C]324584[/C][C]324023.318641607[/C][C]560.681358393398[/C][/ROW]
[ROW][C]57[/C][C]321801[/C][C]320696.387809197[/C][C]1104.61219080252[/C][/ROW]
[ROW][C]58[/C][C]343542[/C][C]352270.069040168[/C][C]-8728.06904016819[/C][/ROW]
[ROW][C]59[/C][C]354040[/C][C]327344.644414164[/C][C]26695.355585836[/C][/ROW]
[ROW][C]60[/C][C]278179[/C][C]282546.750500347[/C][C]-4367.75050034694[/C][/ROW]
[ROW][C]61[/C][C]330246[/C][C]341120.752516443[/C][C]-10874.752516443[/C][/ROW]
[ROW][C]62[/C][C]307344[/C][C]306570.750155014[/C][C]773.249844986363[/C][/ROW]
[ROW][C]63[/C][C]375874[/C][C]351779.063423266[/C][C]24094.9365767336[/C][/ROW]
[ROW][C]64[/C][C]335309[/C][C]335775.396877069[/C][C]-466.396877069084[/C][/ROW]
[ROW][C]65[/C][C]339271[/C][C]340288.889334993[/C][C]-1017.88933499297[/C][/ROW]
[ROW][C]66[/C][C]280264[/C][C]288540.158856336[/C][C]-8276.15885633643[/C][/ROW]
[ROW][C]67[/C][C]293689[/C][C]301553.379684209[/C][C]-7864.37968420901[/C][/ROW]
[ROW][C]68[/C][C]341161[/C][C]340218.268109205[/C][C]942.731890794763[/C][/ROW]
[ROW][C]69[/C][C]345097[/C][C]337205.25708168[/C][C]7891.74291831977[/C][/ROW]
[ROW][C]70[/C][C]368712[/C][C]367532.31388943[/C][C]1179.6861105701[/C][/ROW]
[ROW][C]71[/C][C]369403[/C][C]358208.908655372[/C][C]11194.0913446283[/C][/ROW]
[ROW][C]72[/C][C]288384[/C][C]297526.295028499[/C][C]-9142.29502849898[/C][/ROW]
[ROW][C]73[/C][C]340981[/C][C]352278.896915486[/C][C]-11297.8969154863[/C][/ROW]
[ROW][C]74[/C][C]319072[/C][C]321668.829107707[/C][C]-2596.82910770731[/C][/ROW]
[ROW][C]75[/C][C]374214[/C][C]373949.870010017[/C][C]264.129989982874[/C][/ROW]
[ROW][C]76[/C][C]344529[/C][C]341643.522297822[/C][C]2885.477702178[/C][/ROW]
[ROW][C]77[/C][C]337271[/C][C]347047.905643385[/C][C]-9776.90564338537[/C][/ROW]
[ROW][C]78[/C][C]281016[/C][C]289926.355759009[/C][C]-8910.3557590092[/C][/ROW]
[ROW][C]79[/C][C]282224[/C][C]302878.614875532[/C][C]-20654.6148755319[/C][/ROW]
[ROW][C]80[/C][C]320984[/C][C]340489.928533266[/C][C]-19505.9285332662[/C][/ROW]
[ROW][C]81[/C][C]325426[/C][C]333296.471023785[/C][C]-7870.47102378466[/C][/ROW]
[ROW][C]82[/C][C]366276[/C][C]356177.223824245[/C][C]10098.7761757547[/C][/ROW]
[ROW][C]83[/C][C]380296[/C][C]353243.041730613[/C][C]27052.9582693872[/C][/ROW]
[ROW][C]84[/C][C]300727[/C][C]290571.106543295[/C][C]10155.8934567049[/C][/ROW]
[ROW][C]85[/C][C]359326[/C][C]350809.801306092[/C][C]8516.19869390846[/C][/ROW]
[ROW][C]86[/C][C]327610[/C][C]329652.462258387[/C][C]-2042.46225838654[/C][/ROW]
[ROW][C]87[/C][C]383563[/C][C]383114.099236913[/C][C]448.900763087149[/C][/ROW]
[ROW][C]88[/C][C]352405[/C][C]351784.966222441[/C][C]620.033777559234[/C][/ROW]
[ROW][C]89[/C][C]329351[/C][C]352024.962781723[/C][C]-22673.9627817226[/C][/ROW]
[ROW][C]90[/C][C]294486[/C][C]291036.119857682[/C][C]3449.88014231779[/C][/ROW]
[ROW][C]91[/C][C]333454[/C][C]303874.909252604[/C][C]29579.090747396[/C][/ROW]
[ROW][C]92[/C][C]334339[/C][C]358132.573866583[/C][C]-23793.5738665825[/C][/ROW]
[ROW][C]93[/C][C]358000[/C][C]353624.978077494[/C][C]4375.02192250645[/C][/ROW]
[ROW][C]94[/C][C]396057[/C][C]386754.801649075[/C][C]9302.19835092541[/C][/ROW]
[ROW][C]95[/C][C]386976[/C][C]389496.943463722[/C][C]-2520.94346372166[/C][/ROW]
[ROW][C]96[/C][C]307155[/C][C]311347.627876803[/C][C]-4192.62787680258[/C][/ROW]
[ROW][C]97[/C][C]363909[/C][C]366372.483941759[/C][C]-2463.4839417591[/C][/ROW]
[ROW][C]98[/C][C]344700[/C][C]337969.090064215[/C][C]6730.90993578511[/C][/ROW]
[ROW][C]99[/C][C]397561[/C][C]395139.784618352[/C][C]2421.21538164804[/C][/ROW]
[ROW][C]100[/C][C]376791[/C][C]364508.344509432[/C][C]12282.655490568[/C][/ROW]
[ROW][C]101[/C][C]337085[/C][C]360366.904174313[/C][C]-23281.9041743126[/C][/ROW]
[ROW][C]102[/C][C]299252[/C][C]308324.741490536[/C][C]-9072.74149053579[/C][/ROW]
[ROW][C]103[/C][C]323136[/C][C]326259.18260488[/C][C]-3123.18260488007[/C][/ROW]
[ROW][C]104[/C][C]329091[/C][C]351261.470721356[/C][C]-22170.4707213559[/C][/ROW]
[ROW][C]105[/C][C]346991[/C][C]357137.676604364[/C][C]-10146.6766043635[/C][/ROW]
[ROW][C]106[/C][C]461999[/C][C]387296.047192006[/C][C]74702.9528079935[/C][/ROW]
[ROW][C]107[/C][C]436533[/C][C]407049.076990643[/C][C]29483.9230093567[/C][/ROW]
[ROW][C]108[/C][C]360372[/C][C]338664.2433622[/C][C]21707.7566378[/C][/ROW]
[ROW][C]109[/C][C]415467[/C][C]402669.826394135[/C][C]12797.1736058653[/C][/ROW]
[ROW][C]110[/C][C]382110[/C][C]382419.356976987[/C][C]-309.356976986921[/C][/ROW]
[ROW][C]111[/C][C]432197[/C][C]435805.02547376[/C][C]-3608.02547375963[/C][/ROW]
[ROW][C]112[/C][C]424254[/C][C]406675.357792801[/C][C]17578.6422071985[/C][/ROW]
[ROW][C]113[/C][C]386728[/C][C]391799.007990554[/C][C]-5071.00799055427[/C][/ROW]
[ROW][C]114[/C][C]354508[/C][C]350618.957847109[/C][C]3889.0421528907[/C][/ROW]
[ROW][C]115[/C][C]375765[/C][C]374827.24223998[/C][C]937.757760020264[/C][/ROW]
[ROW][C]116[/C][C]367986[/C][C]394476.237641834[/C][C]-26490.237641834[/C][/ROW]
[ROW][C]117[/C][C]402378[/C][C]403163.834678152[/C][C]-785.834678151819[/C][/ROW]
[ROW][C]118[/C][C]426516[/C][C]466046.402418025[/C][C]-39530.402418025[/C][/ROW]
[ROW][C]119[/C][C]433313[/C][C]433032.70917433[/C][C]280.290825669654[/C][/ROW]
[ROW][C]120[/C][C]338461[/C][C]352482.520346889[/C][C]-14021.5203468885[/C][/ROW]
[ROW][C]121[/C][C]416834[/C][C]401815.476466567[/C][C]15018.5235334332[/C][/ROW]
[ROW][C]122[/C][C]381099[/C][C]377696.085961763[/C][C]3402.91403823713[/C][/ROW]
[ROW][C]123[/C][C]445673[/C][C]431127.684410819[/C][C]14545.3155891806[/C][/ROW]
[ROW][C]124[/C][C]412408[/C][C]415283.624949741[/C][C]-2875.624949741[/C][/ROW]
[ROW][C]125[/C][C]393997[/C][C]385865.56558387[/C][C]8131.4344161296[/C][/ROW]
[ROW][C]126[/C][C]348241[/C][C]352090.845354091[/C][C]-3849.8453540905[/C][/ROW]
[ROW][C]127[/C][C]380134[/C][C]372763.627222769[/C][C]7370.37277723069[/C][/ROW]
[ROW][C]128[/C][C]373688[/C][C]384893.045202115[/C][C]-11205.0452021151[/C][/ROW]
[ROW][C]129[/C][C]393588[/C][C]407519.958426963[/C][C]-13931.9584269634[/C][/ROW]
[ROW][C]130[/C][C]434192[/C][C]452590.90906297[/C][C]-18398.9090629697[/C][/ROW]
[ROW][C]131[/C][C]430731[/C][C]440344.241118614[/C][C]-9613.24111861404[/C][/ROW]
[ROW][C]132[/C][C]344468[/C][C]351589.138930657[/C][C]-7121.1389306566[/C][/ROW]
[ROW][C]133[/C][C]411891[/C][C]413317.439898153[/C][C]-1426.43989815313[/C][/ROW]
[ROW][C]134[/C][C]370497[/C][C]379814.731463399[/C][C]-9317.73146339913[/C][/ROW]
[ROW][C]135[/C][C]437305[/C][C]433032.603763737[/C][C]4272.39623626281[/C][/ROW]
[ROW][C]136[/C][C]411270[/C][C]407769.259921596[/C][C]3500.74007840402[/C][/ROW]
[ROW][C]137[/C][C]385495[/C][C]384265.596742289[/C][C]1229.40325771074[/C][/ROW]
[ROW][C]138[/C][C]341273[/C][C]344065.518691083[/C][C]-2792.5186910826[/C][/ROW]
[ROW][C]139[/C][C]384217[/C][C]369007.258825209[/C][C]15209.7411747908[/C][/ROW]
[ROW][C]140[/C][C]373223[/C][C]377170.385703148[/C][C]-3947.38570314797[/C][/ROW]
[ROW][C]141[/C][C]415771[/C][C]401189.830901217[/C][C]14581.169098783[/C][/ROW]
[ROW][C]142[/C][C]448634[/C][C]453917.787666042[/C][C]-5283.78766604175[/C][/ROW]
[ROW][C]143[/C][C]454341[/C][C]448987.178932379[/C][C]5353.821067621[/C][/ROW]
[ROW][C]144[/C][C]350297[/C][C]365944.276213171[/C][C]-15647.2762131706[/C][/ROW]
[ROW][C]145[/C][C]419104[/C][C]426908.568341928[/C][C]-7804.56834192818[/C][/ROW]
[ROW][C]146[/C][C]398027[/C][C]388581.403635479[/C][C]9445.59636452119[/C][/ROW]
[ROW][C]147[/C][C]456059[/C][C]452623.370400324[/C][C]3435.62959967559[/C][/ROW]
[ROW][C]148[/C][C]430052[/C][C]426819.359792142[/C][C]3232.64020785841[/C][/ROW]
[ROW][C]149[/C][C]399757[/C][C]402434.038235086[/C][C]-2677.03823508619[/C][/ROW]
[ROW][C]150[/C][C]362731[/C][C]359563.053876946[/C][C]3167.94612305408[/C][/ROW]
[ROW][C]151[/C][C]384896[/C][C]392732.999486022[/C][C]-7836.99948602234[/C][/ROW]
[ROW][C]152[/C][C]385349[/C][C]386738.449785457[/C][C]-1389.44978545682[/C][/ROW]
[ROW][C]153[/C][C]432289[/C][C]418070.010178424[/C][C]14218.9898215762[/C][/ROW]
[ROW][C]154[/C][C]468891[/C][C]463728.167075343[/C][C]5162.83292465738[/C][/ROW]
[ROW][C]155[/C][C]442702[/C][C]465898.865852142[/C][C]-23196.865852142[/C][/ROW]
[ROW][C]156[/C][C]370178[/C][C]366273.064532458[/C][C]3904.93546754192[/C][/ROW]
[ROW][C]157[/C][C]439400[/C][C]436304.975144906[/C][C]3095.02485509438[/C][/ROW]
[ROW][C]158[/C][C]393900[/C][C]407539.974269302[/C][C]-13639.9742693018[/C][/ROW]
[ROW][C]159[/C][C]468700[/C][C]462013.177694297[/C][C]6686.82230570307[/C][/ROW]
[ROW][C]160[/C][C]438800[/C][C]437189.475108803[/C][C]1610.52489119745[/C][/ROW]
[ROW][C]161[/C][C]430100[/C][C]410211.231157389[/C][C]19888.7688426111[/C][/ROW]
[ROW][C]162[/C][C]366300[/C][C]376683.188320934[/C][C]-10383.1883209339[/C][/ROW]
[ROW][C]163[/C][C]391000[/C][C]401619.338015124[/C][C]-10619.3380151245[/C][/ROW]
[ROW][C]164[/C][C]380900[/C][C]396981.674841687[/C][C]-16081.6748416867[/C][/ROW]
[ROW][C]165[/C][C]431400[/C][C]429025.050999797[/C][C]2374.94900020334[/C][/ROW]
[ROW][C]166[/C][C]465400[/C][C]467683.513708117[/C][C]-2283.51370811701[/C][/ROW]
[ROW][C]167[/C][C]471500[/C][C]457520.435165716[/C][C]13979.5648342842[/C][/ROW]
[ROW][C]168[/C][C]387500[/C][C]379402.110137825[/C][C]8097.88986217481[/C][/ROW]
[ROW][C]169[/C][C]446400[/C][C]450506.45000154[/C][C]-4106.45000153978[/C][/ROW]
[ROW][C]170[/C][C]421500[/C][C]413555.470065229[/C][C]7944.52993477054[/C][/ROW]
[ROW][C]171[/C][C]504800[/C][C]482122.88084113[/C][C]22677.1191588701[/C][/ROW]
[ROW][C]172[/C][C]492071[/C][C]460693.346976796[/C][C]31377.6530232039[/C][/ROW]
[ROW][C]173[/C][C]421253[/C][C]449738.376869783[/C][C]-28485.3768697828[/C][/ROW]
[ROW][C]174[/C][C]396682[/C][C]389972.253196591[/C][C]6709.74680340855[/C][/ROW]
[ROW][C]175[/C][C]428000[/C][C]420353.17541621[/C][C]7646.82458378997[/C][/ROW]
[ROW][C]176[/C][C]421900[/C][C]419710.525834272[/C][C]2189.47416572791[/C][/ROW]
[ROW][C]177[/C][C]465600[/C][C]464122.098497737[/C][C]1477.90150226286[/C][/ROW]
[ROW][C]178[/C][C]525793[/C][C]500860.029528858[/C][C]24932.9704711417[/C][/ROW]
[ROW][C]179[/C][C]499855[/C][C]505190.108534259[/C][C]-5335.10853425926[/C][/ROW]
[ROW][C]180[/C][C]435287[/C][C]418767.335044044[/C][C]16519.6649559558[/C][/ROW]
[ROW][C]181[/C][C]479499[/C][C]488323.57926237[/C][C]-8824.57926236972[/C][/ROW]
[ROW][C]182[/C][C]473027[/C][C]454064.685104065[/C][C]18962.3148959349[/C][/ROW]
[ROW][C]183[/C][C]554410[/C][C]531351.33545426[/C][C]23058.6645457398[/C][/ROW]
[ROW][C]184[/C][C]489574[/C][C]513090.346666579[/C][C]-23516.3466665791[/C][/ROW]
[ROW][C]185[/C][C]462157[/C][C]463432.145273439[/C][C]-1275.14527343883[/C][/ROW]
[ROW][C]186[/C][C]420331[/C][C]424783.320935812[/C][C]-4452.32093581202[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148283&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148283&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
13294053289368.4887820514684.51121794869
14267510264009.9875821383500.01241786184
15309739307233.741000762505.25899923954
16280733278565.1495770532167.85042294738
17287298285682.4487265831615.55127341673
18235672235003.939922497668.060077502683
19256449250470.2863539875978.71364601282
20288997287811.714256291185.28574370965
21290789291763.360094503-974.360094502917
22321898312739.2559180539158.74408194656
23291834303566.942154451-11732.9421544512
24241380245810.908787302-4430.90878730244
25295469307877.40161707-12408.4016170703
26258200276576.912034613-18376.9120346126
27306102312378.058690588-6276.05869058782
28281480280751.718448778728.281551222317
29283101287210.194136875-4109.19413687527
30237414234348.8276884013065.17231159876
31274834252449.05391978422384.9460802159
32299340293418.1571746285921.84282537235
33300383298145.6160516562237.38394834369
34340862323706.66751004617155.3324899536
35318794309808.216114438985.78388557018
36265740261307.7879752964432.21202470432
37322656323448.290071862-792.290071861702
38281563293815.195868126-12252.1958681258
39323461335832.186696851-12371.1866968511
40312579304686.335545717892.66445428965
41310784311768.488851451-984.48885145149
42262785262428.581832533356.418167467229
43273754286414.732939415-12660.7329394148
44320036310288.9063271769747.09367282398
45310336314963.804413946-4627.80441394594
46342206343526.06799409-1320.06799409015
47320052320793.81834952-741.818349520443
48265582267553.99127694-1971.99127694039
49326988325794.9741281221193.02587187773
50300713292792.9455428867920.05445711449
51346414341291.4870773285122.51292267221
52317325322894.949487424-5569.94948742416
53326208322516.6536297223691.34637027793
54270657275158.107601341-4501.10760134074
55278158293017.490265081-14859.4902650805
56324584324023.318641607560.681358393398
57321801320696.3878091971104.61219080252
58343542352270.069040168-8728.06904016819
59354040327344.64441416426695.355585836
60278179282546.750500347-4367.75050034694
61330246341120.752516443-10874.752516443
62307344306570.750155014773.249844986363
63375874351779.06342326624094.9365767336
64335309335775.396877069-466.396877069084
65339271340288.889334993-1017.88933499297
66280264288540.158856336-8276.15885633643
67293689301553.379684209-7864.37968420901
68341161340218.268109205942.731890794763
69345097337205.257081687891.74291831977
70368712367532.313889431179.6861105701
71369403358208.90865537211194.0913446283
72288384297526.295028499-9142.29502849898
73340981352278.896915486-11297.8969154863
74319072321668.829107707-2596.82910770731
75374214373949.870010017264.129989982874
76344529341643.5222978222885.477702178
77337271347047.905643385-9776.90564338537
78281016289926.355759009-8910.3557590092
79282224302878.614875532-20654.6148755319
80320984340489.928533266-19505.9285332662
81325426333296.471023785-7870.47102378466
82366276356177.22382424510098.7761757547
83380296353243.04173061327052.9582693872
84300727290571.10654329510155.8934567049
85359326350809.8013060928516.19869390846
86327610329652.462258387-2042.46225838654
87383563383114.099236913448.900763087149
88352405351784.966222441620.033777559234
89329351352024.962781723-22673.9627817226
90294486291036.1198576823449.88014231779
91333454303874.90925260429579.090747396
92334339358132.573866583-23793.5738665825
93358000353624.9780774944375.02192250645
94396057386754.8016490759302.19835092541
95386976389496.943463722-2520.94346372166
96307155311347.627876803-4192.62787680258
97363909366372.483941759-2463.4839417591
98344700337969.0900642156730.90993578511
99397561395139.7846183522421.21538164804
100376791364508.34450943212282.655490568
101337085360366.904174313-23281.9041743126
102299252308324.741490536-9072.74149053579
103323136326259.18260488-3123.18260488007
104329091351261.470721356-22170.4707213559
105346991357137.676604364-10146.6766043635
106461999387296.04719200674702.9528079935
107436533407049.07699064329483.9230093567
108360372338664.243362221707.7566378
109415467402669.82639413512797.1736058653
110382110382419.356976987-309.356976986921
111432197435805.02547376-3608.02547375963
112424254406675.35779280117578.6422071985
113386728391799.007990554-5071.00799055427
114354508350618.9578471093889.0421528907
115375765374827.24223998937.757760020264
116367986394476.237641834-26490.237641834
117402378403163.834678152-785.834678151819
118426516466046.402418025-39530.402418025
119433313433032.70917433280.290825669654
120338461352482.520346889-14021.5203468885
121416834401815.47646656715018.5235334332
122381099377696.0859617633402.91403823713
123445673431127.68441081914545.3155891806
124412408415283.624949741-2875.624949741
125393997385865.565583878131.4344161296
126348241352090.845354091-3849.8453540905
127380134372763.6272227697370.37277723069
128373688384893.045202115-11205.0452021151
129393588407519.958426963-13931.9584269634
130434192452590.90906297-18398.9090629697
131430731440344.241118614-9613.24111861404
132344468351589.138930657-7121.1389306566
133411891413317.439898153-1426.43989815313
134370497379814.731463399-9317.73146339913
135437305433032.6037637374272.39623626281
136411270407769.2599215963500.74007840402
137385495384265.5967422891229.40325771074
138341273344065.518691083-2792.5186910826
139384217369007.25882520915209.7411747908
140373223377170.385703148-3947.38570314797
141415771401189.83090121714581.169098783
142448634453917.787666042-5283.78766604175
143454341448987.1789323795353.821067621
144350297365944.276213171-15647.2762131706
145419104426908.568341928-7804.56834192818
146398027388581.4036354799445.59636452119
147456059452623.3704003243435.62959967559
148430052426819.3597921423232.64020785841
149399757402434.038235086-2677.03823508619
150362731359563.0538769463167.94612305408
151384896392732.999486022-7836.99948602234
152385349386738.449785457-1389.44978545682
153432289418070.01017842414218.9898215762
154468891463728.1670753435162.83292465738
155442702465898.865852142-23196.865852142
156370178366273.0645324583904.93546754192
157439400436304.9751449063095.02485509438
158393900407539.974269302-13639.9742693018
159468700462013.1776942976686.82230570307
160438800437189.4751088031610.52489119745
161430100410211.23115738919888.7688426111
162366300376683.188320934-10383.1883209339
163391000401619.338015124-10619.3380151245
164380900396981.674841687-16081.6748416867
165431400429025.0509997972374.94900020334
166465400467683.513708117-2283.51370811701
167471500457520.43516571613979.5648342842
168387500379402.1101378258097.88986217481
169446400450506.45000154-4106.45000153978
170421500413555.4700652297944.52993477054
171504800482122.8808411322677.1191588701
172492071460693.34697679631377.6530232039
173421253449738.376869783-28485.3768697828
174396682389972.2531965916709.74680340855
175428000420353.175416217646.82458378997
176421900419710.5258342722189.47416572791
177465600464122.0984977371477.90150226286
178525793500860.02952885824932.9704711417
179499855505190.108534259-5335.10853425926
180435287418767.33504404416519.6649559558
181479499488323.57926237-8824.57926236972
182473027454064.68510406518962.3148959349
183554410531351.3354542623058.6645457398
184489574513090.346666579-23516.3466665791
185462157463432.145273439-1275.14527343883
186420331424783.320935812-4452.32093581202







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
187451882.686514132426060.554742559477704.818285706
188446857.189021398419718.4939558473995.884086996
189490311.692466379461917.413984642518705.970948117
190534780.91702915505184.273112424564377.560945876
191520454.557611995489702.523341585551206.591882404
192443406.134313026411540.574653679475271.693972373
193498749.919624945465808.453764446531691.385485444
194477070.00842924443086.682316669511053.334541811
195549658.43533245514664.253897412584652.616767487
196507639.729989589471663.084579777543616.375399401
197473370.48151373436437.49767031510303.465357149
198434022.004266611396156.827966833471887.180566389

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
187 & 451882.686514132 & 426060.554742559 & 477704.818285706 \tabularnewline
188 & 446857.189021398 & 419718.4939558 & 473995.884086996 \tabularnewline
189 & 490311.692466379 & 461917.413984642 & 518705.970948117 \tabularnewline
190 & 534780.91702915 & 505184.273112424 & 564377.560945876 \tabularnewline
191 & 520454.557611995 & 489702.523341585 & 551206.591882404 \tabularnewline
192 & 443406.134313026 & 411540.574653679 & 475271.693972373 \tabularnewline
193 & 498749.919624945 & 465808.453764446 & 531691.385485444 \tabularnewline
194 & 477070.00842924 & 443086.682316669 & 511053.334541811 \tabularnewline
195 & 549658.43533245 & 514664.253897412 & 584652.616767487 \tabularnewline
196 & 507639.729989589 & 471663.084579777 & 543616.375399401 \tabularnewline
197 & 473370.48151373 & 436437.49767031 & 510303.465357149 \tabularnewline
198 & 434022.004266611 & 396156.827966833 & 471887.180566389 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148283&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]187[/C][C]451882.686514132[/C][C]426060.554742559[/C][C]477704.818285706[/C][/ROW]
[ROW][C]188[/C][C]446857.189021398[/C][C]419718.4939558[/C][C]473995.884086996[/C][/ROW]
[ROW][C]189[/C][C]490311.692466379[/C][C]461917.413984642[/C][C]518705.970948117[/C][/ROW]
[ROW][C]190[/C][C]534780.91702915[/C][C]505184.273112424[/C][C]564377.560945876[/C][/ROW]
[ROW][C]191[/C][C]520454.557611995[/C][C]489702.523341585[/C][C]551206.591882404[/C][/ROW]
[ROW][C]192[/C][C]443406.134313026[/C][C]411540.574653679[/C][C]475271.693972373[/C][/ROW]
[ROW][C]193[/C][C]498749.919624945[/C][C]465808.453764446[/C][C]531691.385485444[/C][/ROW]
[ROW][C]194[/C][C]477070.00842924[/C][C]443086.682316669[/C][C]511053.334541811[/C][/ROW]
[ROW][C]195[/C][C]549658.43533245[/C][C]514664.253897412[/C][C]584652.616767487[/C][/ROW]
[ROW][C]196[/C][C]507639.729989589[/C][C]471663.084579777[/C][C]543616.375399401[/C][/ROW]
[ROW][C]197[/C][C]473370.48151373[/C][C]436437.49767031[/C][C]510303.465357149[/C][/ROW]
[ROW][C]198[/C][C]434022.004266611[/C][C]396156.827966833[/C][C]471887.180566389[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148283&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148283&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
187451882.686514132426060.554742559477704.818285706
188446857.189021398419718.4939558473995.884086996
189490311.692466379461917.413984642518705.970948117
190534780.91702915505184.273112424564377.560945876
191520454.557611995489702.523341585551206.591882404
192443406.134313026411540.574653679475271.693972373
193498749.919624945465808.453764446531691.385485444
194477070.00842924443086.682316669511053.334541811
195549658.43533245514664.253897412584652.616767487
196507639.729989589471663.084579777543616.375399401
197473370.48151373436437.49767031510303.465357149
198434022.004266611396156.827966833471887.180566389



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')