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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 computationFri, 22 Nov 2013 07:06:15 -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/2013/Nov/22/t1385122009eh4psf919zhihcg.htm/, Retrieved Mon, 29 Apr 2024 16:56:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=227518, Retrieved Mon, 29 Apr 2024 16:56:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact77
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [WS8O5] [2013-11-22 12:06:15] [f1e366d257cd544a6a94e0c7cf247a26] [Current]
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Dataseries X:
338881
339105
342435
354980
339890
339890
340471
343833
346109
345455
350419
344660
341499
342376
344148
359079
344090
342681
348552
349867
353247
356048
363887
358905
359647
361488
363229
393301
366190
363811
366190
372656
371781
374306
377689
373240
373456
372610
372209
390212
373113
370518
370469
372493
369536
368835
366859
356044
346106
333829
317388
285871
339729
308216
309137
311245
319568
329201
339880
342305
346975
355294
360766
392946
352108
358071
365429
378731
384120
391390
403547
404124
406439
412232
419221
450521
430027
433442
439938
450200
459279
465090
478567
475726
480634
486952
491912
517281
502379
504942
516387
523270
528995
540850
550679
544432
550296
554659
558856
582661
564317
568569
574693
586558
588751
598250
607706
603869
607696
613285
617160
647083
621246
623252
632722
641716
644953
652723
660093
657090
657281
661949
665608
697124
671310
674708
681915
690556
692885
699740
707885
704785
705363
749101
752891
784662
761914
763768
768877
781031
783454
785988
795068
790001
789721
794064
798690
829281
806249
807048
819928
821105
828422
835360
844092
837469
836969
838721
840537
863719
845413
844366
848357
858754
862431
871565
880366
874476
882077
889199
892665
913625
893597
892114
894801
898843
908135
918920
923125
921770
917843
916761
915087
938173
907953
905374
921867
927104
930989
936820
944281
945322
944555




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=227518&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=227518&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=227518&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 time4 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.65589684882898
beta0.112531861924501
gamma0.072253821026611

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.65589684882898 \tabularnewline
beta & 0.112531861924501 \tabularnewline
gamma & 0.072253821026611 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=227518&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]0.65589684882898[/C][/ROW]
[ROW][C]beta[/C][C]0.112531861924501[/C][/ROW]
[ROW][C]gamma[/C][C]0.072253821026611[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=227518&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=227518&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
alpha0.65589684882898
beta0.112531861924501
gamma0.072253821026611







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13341499339703.2080662391795.79193376075
14342376341798.310539646577.689460354159
15344148344071.39395686776.6060431333608
16359079358990.5142443388.4857556701172
17344090343740.207468933349.792531066865
18342681342114.942257065566.057742934965
19348552346845.3050383321706.69496166823
20349867351958.111459917-2091.11145991721
21353247353377.313490699-130.313490699336
22356048353108.4783839832939.5216160171
23363887360584.4774642723302.52253572771
24358905357873.8245594781031.17544052185
25359647356230.4526072073416.54739279283
26361488360231.7527955151256.24720448465
27363229363860.960361327-631.960361327277
28393301379186.84933661514114.1506633854
29366190375048.873003205-8858.87300320476
30363811368615.8091555-4804.8091554998
31366190370682.135886955-4492.13588695519
32372656372007.532610555648.467389444937
33371781375847.380919605-4066.38091960503
34374306373357.712109237948.287890762615
35377689379674.216839834-1985.21683983417
36373240373186.12042675153.8795732487342
37373456370636.1566856912819.84331430908
38372610373823.433744069-1213.43374406855
39372209375234.618122251-3025.61812225124
40390212388629.2482862171582.75171378325
41373113374047.964860824-934.964860823704
42370518371844.991640422-1326.99164042162
43370469375388.906097189-4919.90609718877
44372493375718.690148479-3225.69014847907
45369536375771.46856449-6235.46856449038
46368835370694.883726094-1859.88372609403
47366859373600.416511086-6741.41651108564
48356044362196.223578098-6152.22357809788
49346106353339.18003702-7233.18003702001
50333829346785.139962947-12956.1399629474
51317388336535.251199926-19147.251199926
52285871334366.390291785-48495.3902917847
53339729278076.24207394861652.7579260525
54308216312733.995888962-4517.99588896212
55309137309679.468902973-542.468902972993
56311245308829.4766455792415.52335442108
57319568308830.80531704810737.1946829517
58329201312571.39376901116629.606230989
59339880326423.52033354513456.4796664549
60342305328713.26926785613591.7307321441
61346975334668.19133882812306.8086611716
62355294344119.15618499611174.8438150038
63360766354654.9428780456111.0571219555
64392946375299.71613791617646.2838620837
65352108376988.606913971-24880.6069139714
66358071358715.580350755-644.580350755132
67365429364057.7200847011371.27991529915
68378731370435.0090399628295.99096003803
69384120380832.7663427633287.23365723668
70391390385616.1228112375773.87718876288
71403547397250.5368236246296.46317637572
72404124399300.3590872344823.64091276628
73406439403278.1483075813160.85169241874
74412232409832.8847470642399.11525293556
75419221416969.7883800442251.2116199559
76450521437567.79572984612953.2042701536
77430027436972.878233954-6945.87823395379
78433442434241.212086957-799.212086957181
79439938442696.089655126-2758.08965512627
80450200449396.360188695803.639811304805
81459279457061.6258550272217.37414497347
82465090463432.3735463981657.62645360228
83478567474303.4109130514263.58908694884
84475726476756.680335793-1030.68033579347
85480634478194.615145322439.3848546801
86486952485545.2719156631406.72808433749
87491912493242.414274638-1330.41427463794
88517281512707.7880005474573.21199945308
89502379506453.654768234-4074.65476823441
90504942506301.902200747-1359.90220074716
91516387514842.8016560821544.19834391813
92523270525273.512504304-2003.51250430429
93528995531745.55995287-2750.55995287001
94540850535090.093533195759.90646680992
95550679549265.5363522531413.4636477473
96544432550056.363021164-5624.36302116385
97550296548567.1105129561728.88948704419
98554659555373.15900024-714.159000240499
99558856561401.702186925-2545.7021869251
100582661579917.5902631292743.40973687102
101564317571814.066554444-7497.06655444368
102568569568798.236308888-229.23630888795
103574693577549.568753215-2856.56875321479
104586558584077.4357259642480.56427403644
105588751592874.779181854-4123.7791818541
106598250594831.6378492763418.3621507244
107607706606491.7983050321214.20169496757
108603869606090.83622714-2221.83622713969
109607696606381.1370161711314.86298382853
110613285612189.3513618971095.64863810281
111617160618827.450550294-1667.4505502939
112647083637583.7523075639499.24769243714
113621246633688.267711472-12442.2677114719
114623252627276.105047016-4024.10504701559
115632722632859.486770801-137.486770800664
116641716640890.594947757825.40505224315
117644953647903.064299593-2950.0642995931
118652723650368.8503021552354.14969784545
119660093660749.219801264-656.219801264117
120657090658370.994423232-1280.99442323239
121657281658770.735063052-1489.73506305215
122661949661931.37925769417.6207423063461
123665608666911.543721495-1303.54372149473
124697124685328.86421707211795.1357829281
125671310681707.874840823-10397.874840823
126674708676310.973284872-1602.97328487237
127681915683222.753259534-1307.75325953425
128690556690067.604417799488.395582200959
129692885696297.664200619-3412.66420061875
130699740698090.2681503921649.73184960778
131707885707380.13182702504.868172980146
132704785705279.991590942-494.991590942489
133705363705780.158280078-417.158280078089
134749101709351.02451688339749.975483117
135752891742960.5297576439930.47024235735
136784662772502.91098096812159.0890190317
137761914772026.757799511-10112.757799511
138763768770514.473569851-6746.47356985114
139768877777159.294144461-8282.29414446128
140781031782058.743451181-1027.74345118145
141783454789669.996432002-6215.99643200159
142785988792015.471963935-6027.47196393483
143795068797940.471564465-2872.47156446485
144790001795050.060688397-5049.06068839703
145789721793678.80546752-3957.80546752014
146794064796778.348320089-2714.34832008893
147798690799512.290061521-822.290061520995
148829281818981.77376981310299.2262301872
149806249813519.121991979-7270.12199197884
150807048810951.941009298-3903.94100929808
151819928816629.7225399253298.27746007498
152821105827366.691843575-6261.69184357463
153828422829091.197572242-669.197572242469
154835360833164.0708760812195.92912391876
155844092843252.761442391839.238557608682
156837469841708.238276302-4239.23827630177
157836969839920.551835144-2951.55183514382
158838721842810.557116756-4089.5571167561
159840537843687.590413169-3150.59041316877
160863719860732.6555937962986.34440620418
161845413848323.121072274-2910.12107227405
162844366847307.588137444-2941.58813744353
163848357852474.91616175-4117.91616174974
164858754856241.8313260822512.16867391835
165862431862639.613033885-208.613033885485
166871565865899.2963122255665.70368777472
167880366877299.6506568773066.34934312268
168874476876323.57958002-1847.57958002028
169882077875547.0787605946529.92123940564
170889199884737.9679942954461.03200570529
171892665891988.073606808676.926393191912
172913625912720.105039177904.89496082277
173893597899669.050477922-6072.05047792208
174892114897215.754418195-5101.75441819476
175894801901414.467835347-6613.46783534717
176898843904002.684291913-5159.68429191282
177908135905027.9051167623107.09488323785
178918920910580.1620647238339.83793527668
179923125923838.98097709-713.980977089959
180921770920151.341256881618.65874311957
181917843922002.575661705-4159.57566170522
182916761923487.787610592-6726.78761059185
183915087921836.957550534-6749.95755053428
184938173935686.41737642486.58262360038
185907953921599.094085135-13646.0940851346
186905374911742.869615759-6368.86961575935
187921867912520.1145907089346.88540929195
188927104924238.0577301222865.94226987835
189930989929950.3987640421038.60123595758
190936820933340.9656945483479.03430545155
191944281941892.6513200812388.34867991915
192945322939232.9519768896089.0480231113
193944555943137.7302518711417.26974812883

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 341499 & 339703.208066239 & 1795.79193376075 \tabularnewline
14 & 342376 & 341798.310539646 & 577.689460354159 \tabularnewline
15 & 344148 & 344071.393956867 & 76.6060431333608 \tabularnewline
16 & 359079 & 358990.51424433 & 88.4857556701172 \tabularnewline
17 & 344090 & 343740.207468933 & 349.792531066865 \tabularnewline
18 & 342681 & 342114.942257065 & 566.057742934965 \tabularnewline
19 & 348552 & 346845.305038332 & 1706.69496166823 \tabularnewline
20 & 349867 & 351958.111459917 & -2091.11145991721 \tabularnewline
21 & 353247 & 353377.313490699 & -130.313490699336 \tabularnewline
22 & 356048 & 353108.478383983 & 2939.5216160171 \tabularnewline
23 & 363887 & 360584.477464272 & 3302.52253572771 \tabularnewline
24 & 358905 & 357873.824559478 & 1031.17544052185 \tabularnewline
25 & 359647 & 356230.452607207 & 3416.54739279283 \tabularnewline
26 & 361488 & 360231.752795515 & 1256.24720448465 \tabularnewline
27 & 363229 & 363860.960361327 & -631.960361327277 \tabularnewline
28 & 393301 & 379186.849336615 & 14114.1506633854 \tabularnewline
29 & 366190 & 375048.873003205 & -8858.87300320476 \tabularnewline
30 & 363811 & 368615.8091555 & -4804.8091554998 \tabularnewline
31 & 366190 & 370682.135886955 & -4492.13588695519 \tabularnewline
32 & 372656 & 372007.532610555 & 648.467389444937 \tabularnewline
33 & 371781 & 375847.380919605 & -4066.38091960503 \tabularnewline
34 & 374306 & 373357.712109237 & 948.287890762615 \tabularnewline
35 & 377689 & 379674.216839834 & -1985.21683983417 \tabularnewline
36 & 373240 & 373186.120426751 & 53.8795732487342 \tabularnewline
37 & 373456 & 370636.156685691 & 2819.84331430908 \tabularnewline
38 & 372610 & 373823.433744069 & -1213.43374406855 \tabularnewline
39 & 372209 & 375234.618122251 & -3025.61812225124 \tabularnewline
40 & 390212 & 388629.248286217 & 1582.75171378325 \tabularnewline
41 & 373113 & 374047.964860824 & -934.964860823704 \tabularnewline
42 & 370518 & 371844.991640422 & -1326.99164042162 \tabularnewline
43 & 370469 & 375388.906097189 & -4919.90609718877 \tabularnewline
44 & 372493 & 375718.690148479 & -3225.69014847907 \tabularnewline
45 & 369536 & 375771.46856449 & -6235.46856449038 \tabularnewline
46 & 368835 & 370694.883726094 & -1859.88372609403 \tabularnewline
47 & 366859 & 373600.416511086 & -6741.41651108564 \tabularnewline
48 & 356044 & 362196.223578098 & -6152.22357809788 \tabularnewline
49 & 346106 & 353339.18003702 & -7233.18003702001 \tabularnewline
50 & 333829 & 346785.139962947 & -12956.1399629474 \tabularnewline
51 & 317388 & 336535.251199926 & -19147.251199926 \tabularnewline
52 & 285871 & 334366.390291785 & -48495.3902917847 \tabularnewline
53 & 339729 & 278076.242073948 & 61652.7579260525 \tabularnewline
54 & 308216 & 312733.995888962 & -4517.99588896212 \tabularnewline
55 & 309137 & 309679.468902973 & -542.468902972993 \tabularnewline
56 & 311245 & 308829.476645579 & 2415.52335442108 \tabularnewline
57 & 319568 & 308830.805317048 & 10737.1946829517 \tabularnewline
58 & 329201 & 312571.393769011 & 16629.606230989 \tabularnewline
59 & 339880 & 326423.520333545 & 13456.4796664549 \tabularnewline
60 & 342305 & 328713.269267856 & 13591.7307321441 \tabularnewline
61 & 346975 & 334668.191338828 & 12306.8086611716 \tabularnewline
62 & 355294 & 344119.156184996 & 11174.8438150038 \tabularnewline
63 & 360766 & 354654.942878045 & 6111.0571219555 \tabularnewline
64 & 392946 & 375299.716137916 & 17646.2838620837 \tabularnewline
65 & 352108 & 376988.606913971 & -24880.6069139714 \tabularnewline
66 & 358071 & 358715.580350755 & -644.580350755132 \tabularnewline
67 & 365429 & 364057.720084701 & 1371.27991529915 \tabularnewline
68 & 378731 & 370435.009039962 & 8295.99096003803 \tabularnewline
69 & 384120 & 380832.766342763 & 3287.23365723668 \tabularnewline
70 & 391390 & 385616.122811237 & 5773.87718876288 \tabularnewline
71 & 403547 & 397250.536823624 & 6296.46317637572 \tabularnewline
72 & 404124 & 399300.359087234 & 4823.64091276628 \tabularnewline
73 & 406439 & 403278.148307581 & 3160.85169241874 \tabularnewline
74 & 412232 & 409832.884747064 & 2399.11525293556 \tabularnewline
75 & 419221 & 416969.788380044 & 2251.2116199559 \tabularnewline
76 & 450521 & 437567.795729846 & 12953.2042701536 \tabularnewline
77 & 430027 & 436972.878233954 & -6945.87823395379 \tabularnewline
78 & 433442 & 434241.212086957 & -799.212086957181 \tabularnewline
79 & 439938 & 442696.089655126 & -2758.08965512627 \tabularnewline
80 & 450200 & 449396.360188695 & 803.639811304805 \tabularnewline
81 & 459279 & 457061.625855027 & 2217.37414497347 \tabularnewline
82 & 465090 & 463432.373546398 & 1657.62645360228 \tabularnewline
83 & 478567 & 474303.410913051 & 4263.58908694884 \tabularnewline
84 & 475726 & 476756.680335793 & -1030.68033579347 \tabularnewline
85 & 480634 & 478194.61514532 & 2439.3848546801 \tabularnewline
86 & 486952 & 485545.271915663 & 1406.72808433749 \tabularnewline
87 & 491912 & 493242.414274638 & -1330.41427463794 \tabularnewline
88 & 517281 & 512707.788000547 & 4573.21199945308 \tabularnewline
89 & 502379 & 506453.654768234 & -4074.65476823441 \tabularnewline
90 & 504942 & 506301.902200747 & -1359.90220074716 \tabularnewline
91 & 516387 & 514842.801656082 & 1544.19834391813 \tabularnewline
92 & 523270 & 525273.512504304 & -2003.51250430429 \tabularnewline
93 & 528995 & 531745.55995287 & -2750.55995287001 \tabularnewline
94 & 540850 & 535090.09353319 & 5759.90646680992 \tabularnewline
95 & 550679 & 549265.536352253 & 1413.4636477473 \tabularnewline
96 & 544432 & 550056.363021164 & -5624.36302116385 \tabularnewline
97 & 550296 & 548567.110512956 & 1728.88948704419 \tabularnewline
98 & 554659 & 555373.15900024 & -714.159000240499 \tabularnewline
99 & 558856 & 561401.702186925 & -2545.7021869251 \tabularnewline
100 & 582661 & 579917.590263129 & 2743.40973687102 \tabularnewline
101 & 564317 & 571814.066554444 & -7497.06655444368 \tabularnewline
102 & 568569 & 568798.236308888 & -229.23630888795 \tabularnewline
103 & 574693 & 577549.568753215 & -2856.56875321479 \tabularnewline
104 & 586558 & 584077.435725964 & 2480.56427403644 \tabularnewline
105 & 588751 & 592874.779181854 & -4123.7791818541 \tabularnewline
106 & 598250 & 594831.637849276 & 3418.3621507244 \tabularnewline
107 & 607706 & 606491.798305032 & 1214.20169496757 \tabularnewline
108 & 603869 & 606090.83622714 & -2221.83622713969 \tabularnewline
109 & 607696 & 606381.137016171 & 1314.86298382853 \tabularnewline
110 & 613285 & 612189.351361897 & 1095.64863810281 \tabularnewline
111 & 617160 & 618827.450550294 & -1667.4505502939 \tabularnewline
112 & 647083 & 637583.752307563 & 9499.24769243714 \tabularnewline
113 & 621246 & 633688.267711472 & -12442.2677114719 \tabularnewline
114 & 623252 & 627276.105047016 & -4024.10504701559 \tabularnewline
115 & 632722 & 632859.486770801 & -137.486770800664 \tabularnewline
116 & 641716 & 640890.594947757 & 825.40505224315 \tabularnewline
117 & 644953 & 647903.064299593 & -2950.0642995931 \tabularnewline
118 & 652723 & 650368.850302155 & 2354.14969784545 \tabularnewline
119 & 660093 & 660749.219801264 & -656.219801264117 \tabularnewline
120 & 657090 & 658370.994423232 & -1280.99442323239 \tabularnewline
121 & 657281 & 658770.735063052 & -1489.73506305215 \tabularnewline
122 & 661949 & 661931.379257694 & 17.6207423063461 \tabularnewline
123 & 665608 & 666911.543721495 & -1303.54372149473 \tabularnewline
124 & 697124 & 685328.864217072 & 11795.1357829281 \tabularnewline
125 & 671310 & 681707.874840823 & -10397.874840823 \tabularnewline
126 & 674708 & 676310.973284872 & -1602.97328487237 \tabularnewline
127 & 681915 & 683222.753259534 & -1307.75325953425 \tabularnewline
128 & 690556 & 690067.604417799 & 488.395582200959 \tabularnewline
129 & 692885 & 696297.664200619 & -3412.66420061875 \tabularnewline
130 & 699740 & 698090.268150392 & 1649.73184960778 \tabularnewline
131 & 707885 & 707380.13182702 & 504.868172980146 \tabularnewline
132 & 704785 & 705279.991590942 & -494.991590942489 \tabularnewline
133 & 705363 & 705780.158280078 & -417.158280078089 \tabularnewline
134 & 749101 & 709351.024516883 & 39749.975483117 \tabularnewline
135 & 752891 & 742960.529757643 & 9930.47024235735 \tabularnewline
136 & 784662 & 772502.910980968 & 12159.0890190317 \tabularnewline
137 & 761914 & 772026.757799511 & -10112.757799511 \tabularnewline
138 & 763768 & 770514.473569851 & -6746.47356985114 \tabularnewline
139 & 768877 & 777159.294144461 & -8282.29414446128 \tabularnewline
140 & 781031 & 782058.743451181 & -1027.74345118145 \tabularnewline
141 & 783454 & 789669.996432002 & -6215.99643200159 \tabularnewline
142 & 785988 & 792015.471963935 & -6027.47196393483 \tabularnewline
143 & 795068 & 797940.471564465 & -2872.47156446485 \tabularnewline
144 & 790001 & 795050.060688397 & -5049.06068839703 \tabularnewline
145 & 789721 & 793678.80546752 & -3957.80546752014 \tabularnewline
146 & 794064 & 796778.348320089 & -2714.34832008893 \tabularnewline
147 & 798690 & 799512.290061521 & -822.290061520995 \tabularnewline
148 & 829281 & 818981.773769813 & 10299.2262301872 \tabularnewline
149 & 806249 & 813519.121991979 & -7270.12199197884 \tabularnewline
150 & 807048 & 810951.941009298 & -3903.94100929808 \tabularnewline
151 & 819928 & 816629.722539925 & 3298.27746007498 \tabularnewline
152 & 821105 & 827366.691843575 & -6261.69184357463 \tabularnewline
153 & 828422 & 829091.197572242 & -669.197572242469 \tabularnewline
154 & 835360 & 833164.070876081 & 2195.92912391876 \tabularnewline
155 & 844092 & 843252.761442391 & 839.238557608682 \tabularnewline
156 & 837469 & 841708.238276302 & -4239.23827630177 \tabularnewline
157 & 836969 & 839920.551835144 & -2951.55183514382 \tabularnewline
158 & 838721 & 842810.557116756 & -4089.5571167561 \tabularnewline
159 & 840537 & 843687.590413169 & -3150.59041316877 \tabularnewline
160 & 863719 & 860732.655593796 & 2986.34440620418 \tabularnewline
161 & 845413 & 848323.121072274 & -2910.12107227405 \tabularnewline
162 & 844366 & 847307.588137444 & -2941.58813744353 \tabularnewline
163 & 848357 & 852474.91616175 & -4117.91616174974 \tabularnewline
164 & 858754 & 856241.831326082 & 2512.16867391835 \tabularnewline
165 & 862431 & 862639.613033885 & -208.613033885485 \tabularnewline
166 & 871565 & 865899.296312225 & 5665.70368777472 \tabularnewline
167 & 880366 & 877299.650656877 & 3066.34934312268 \tabularnewline
168 & 874476 & 876323.57958002 & -1847.57958002028 \tabularnewline
169 & 882077 & 875547.078760594 & 6529.92123940564 \tabularnewline
170 & 889199 & 884737.967994295 & 4461.03200570529 \tabularnewline
171 & 892665 & 891988.073606808 & 676.926393191912 \tabularnewline
172 & 913625 & 912720.105039177 & 904.89496082277 \tabularnewline
173 & 893597 & 899669.050477922 & -6072.05047792208 \tabularnewline
174 & 892114 & 897215.754418195 & -5101.75441819476 \tabularnewline
175 & 894801 & 901414.467835347 & -6613.46783534717 \tabularnewline
176 & 898843 & 904002.684291913 & -5159.68429191282 \tabularnewline
177 & 908135 & 905027.905116762 & 3107.09488323785 \tabularnewline
178 & 918920 & 910580.162064723 & 8339.83793527668 \tabularnewline
179 & 923125 & 923838.98097709 & -713.980977089959 \tabularnewline
180 & 921770 & 920151.34125688 & 1618.65874311957 \tabularnewline
181 & 917843 & 922002.575661705 & -4159.57566170522 \tabularnewline
182 & 916761 & 923487.787610592 & -6726.78761059185 \tabularnewline
183 & 915087 & 921836.957550534 & -6749.95755053428 \tabularnewline
184 & 938173 & 935686.4173764 & 2486.58262360038 \tabularnewline
185 & 907953 & 921599.094085135 & -13646.0940851346 \tabularnewline
186 & 905374 & 911742.869615759 & -6368.86961575935 \tabularnewline
187 & 921867 & 912520.114590708 & 9346.88540929195 \tabularnewline
188 & 927104 & 924238.057730122 & 2865.94226987835 \tabularnewline
189 & 930989 & 929950.398764042 & 1038.60123595758 \tabularnewline
190 & 936820 & 933340.965694548 & 3479.03430545155 \tabularnewline
191 & 944281 & 941892.651320081 & 2388.34867991915 \tabularnewline
192 & 945322 & 939232.951976889 & 6089.0480231113 \tabularnewline
193 & 944555 & 943137.730251871 & 1417.26974812883 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=227518&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]341499[/C][C]339703.208066239[/C][C]1795.79193376075[/C][/ROW]
[ROW][C]14[/C][C]342376[/C][C]341798.310539646[/C][C]577.689460354159[/C][/ROW]
[ROW][C]15[/C][C]344148[/C][C]344071.393956867[/C][C]76.6060431333608[/C][/ROW]
[ROW][C]16[/C][C]359079[/C][C]358990.51424433[/C][C]88.4857556701172[/C][/ROW]
[ROW][C]17[/C][C]344090[/C][C]343740.207468933[/C][C]349.792531066865[/C][/ROW]
[ROW][C]18[/C][C]342681[/C][C]342114.942257065[/C][C]566.057742934965[/C][/ROW]
[ROW][C]19[/C][C]348552[/C][C]346845.305038332[/C][C]1706.69496166823[/C][/ROW]
[ROW][C]20[/C][C]349867[/C][C]351958.111459917[/C][C]-2091.11145991721[/C][/ROW]
[ROW][C]21[/C][C]353247[/C][C]353377.313490699[/C][C]-130.313490699336[/C][/ROW]
[ROW][C]22[/C][C]356048[/C][C]353108.478383983[/C][C]2939.5216160171[/C][/ROW]
[ROW][C]23[/C][C]363887[/C][C]360584.477464272[/C][C]3302.52253572771[/C][/ROW]
[ROW][C]24[/C][C]358905[/C][C]357873.824559478[/C][C]1031.17544052185[/C][/ROW]
[ROW][C]25[/C][C]359647[/C][C]356230.452607207[/C][C]3416.54739279283[/C][/ROW]
[ROW][C]26[/C][C]361488[/C][C]360231.752795515[/C][C]1256.24720448465[/C][/ROW]
[ROW][C]27[/C][C]363229[/C][C]363860.960361327[/C][C]-631.960361327277[/C][/ROW]
[ROW][C]28[/C][C]393301[/C][C]379186.849336615[/C][C]14114.1506633854[/C][/ROW]
[ROW][C]29[/C][C]366190[/C][C]375048.873003205[/C][C]-8858.87300320476[/C][/ROW]
[ROW][C]30[/C][C]363811[/C][C]368615.8091555[/C][C]-4804.8091554998[/C][/ROW]
[ROW][C]31[/C][C]366190[/C][C]370682.135886955[/C][C]-4492.13588695519[/C][/ROW]
[ROW][C]32[/C][C]372656[/C][C]372007.532610555[/C][C]648.467389444937[/C][/ROW]
[ROW][C]33[/C][C]371781[/C][C]375847.380919605[/C][C]-4066.38091960503[/C][/ROW]
[ROW][C]34[/C][C]374306[/C][C]373357.712109237[/C][C]948.287890762615[/C][/ROW]
[ROW][C]35[/C][C]377689[/C][C]379674.216839834[/C][C]-1985.21683983417[/C][/ROW]
[ROW][C]36[/C][C]373240[/C][C]373186.120426751[/C][C]53.8795732487342[/C][/ROW]
[ROW][C]37[/C][C]373456[/C][C]370636.156685691[/C][C]2819.84331430908[/C][/ROW]
[ROW][C]38[/C][C]372610[/C][C]373823.433744069[/C][C]-1213.43374406855[/C][/ROW]
[ROW][C]39[/C][C]372209[/C][C]375234.618122251[/C][C]-3025.61812225124[/C][/ROW]
[ROW][C]40[/C][C]390212[/C][C]388629.248286217[/C][C]1582.75171378325[/C][/ROW]
[ROW][C]41[/C][C]373113[/C][C]374047.964860824[/C][C]-934.964860823704[/C][/ROW]
[ROW][C]42[/C][C]370518[/C][C]371844.991640422[/C][C]-1326.99164042162[/C][/ROW]
[ROW][C]43[/C][C]370469[/C][C]375388.906097189[/C][C]-4919.90609718877[/C][/ROW]
[ROW][C]44[/C][C]372493[/C][C]375718.690148479[/C][C]-3225.69014847907[/C][/ROW]
[ROW][C]45[/C][C]369536[/C][C]375771.46856449[/C][C]-6235.46856449038[/C][/ROW]
[ROW][C]46[/C][C]368835[/C][C]370694.883726094[/C][C]-1859.88372609403[/C][/ROW]
[ROW][C]47[/C][C]366859[/C][C]373600.416511086[/C][C]-6741.41651108564[/C][/ROW]
[ROW][C]48[/C][C]356044[/C][C]362196.223578098[/C][C]-6152.22357809788[/C][/ROW]
[ROW][C]49[/C][C]346106[/C][C]353339.18003702[/C][C]-7233.18003702001[/C][/ROW]
[ROW][C]50[/C][C]333829[/C][C]346785.139962947[/C][C]-12956.1399629474[/C][/ROW]
[ROW][C]51[/C][C]317388[/C][C]336535.251199926[/C][C]-19147.251199926[/C][/ROW]
[ROW][C]52[/C][C]285871[/C][C]334366.390291785[/C][C]-48495.3902917847[/C][/ROW]
[ROW][C]53[/C][C]339729[/C][C]278076.242073948[/C][C]61652.7579260525[/C][/ROW]
[ROW][C]54[/C][C]308216[/C][C]312733.995888962[/C][C]-4517.99588896212[/C][/ROW]
[ROW][C]55[/C][C]309137[/C][C]309679.468902973[/C][C]-542.468902972993[/C][/ROW]
[ROW][C]56[/C][C]311245[/C][C]308829.476645579[/C][C]2415.52335442108[/C][/ROW]
[ROW][C]57[/C][C]319568[/C][C]308830.805317048[/C][C]10737.1946829517[/C][/ROW]
[ROW][C]58[/C][C]329201[/C][C]312571.393769011[/C][C]16629.606230989[/C][/ROW]
[ROW][C]59[/C][C]339880[/C][C]326423.520333545[/C][C]13456.4796664549[/C][/ROW]
[ROW][C]60[/C][C]342305[/C][C]328713.269267856[/C][C]13591.7307321441[/C][/ROW]
[ROW][C]61[/C][C]346975[/C][C]334668.191338828[/C][C]12306.8086611716[/C][/ROW]
[ROW][C]62[/C][C]355294[/C][C]344119.156184996[/C][C]11174.8438150038[/C][/ROW]
[ROW][C]63[/C][C]360766[/C][C]354654.942878045[/C][C]6111.0571219555[/C][/ROW]
[ROW][C]64[/C][C]392946[/C][C]375299.716137916[/C][C]17646.2838620837[/C][/ROW]
[ROW][C]65[/C][C]352108[/C][C]376988.606913971[/C][C]-24880.6069139714[/C][/ROW]
[ROW][C]66[/C][C]358071[/C][C]358715.580350755[/C][C]-644.580350755132[/C][/ROW]
[ROW][C]67[/C][C]365429[/C][C]364057.720084701[/C][C]1371.27991529915[/C][/ROW]
[ROW][C]68[/C][C]378731[/C][C]370435.009039962[/C][C]8295.99096003803[/C][/ROW]
[ROW][C]69[/C][C]384120[/C][C]380832.766342763[/C][C]3287.23365723668[/C][/ROW]
[ROW][C]70[/C][C]391390[/C][C]385616.122811237[/C][C]5773.87718876288[/C][/ROW]
[ROW][C]71[/C][C]403547[/C][C]397250.536823624[/C][C]6296.46317637572[/C][/ROW]
[ROW][C]72[/C][C]404124[/C][C]399300.359087234[/C][C]4823.64091276628[/C][/ROW]
[ROW][C]73[/C][C]406439[/C][C]403278.148307581[/C][C]3160.85169241874[/C][/ROW]
[ROW][C]74[/C][C]412232[/C][C]409832.884747064[/C][C]2399.11525293556[/C][/ROW]
[ROW][C]75[/C][C]419221[/C][C]416969.788380044[/C][C]2251.2116199559[/C][/ROW]
[ROW][C]76[/C][C]450521[/C][C]437567.795729846[/C][C]12953.2042701536[/C][/ROW]
[ROW][C]77[/C][C]430027[/C][C]436972.878233954[/C][C]-6945.87823395379[/C][/ROW]
[ROW][C]78[/C][C]433442[/C][C]434241.212086957[/C][C]-799.212086957181[/C][/ROW]
[ROW][C]79[/C][C]439938[/C][C]442696.089655126[/C][C]-2758.08965512627[/C][/ROW]
[ROW][C]80[/C][C]450200[/C][C]449396.360188695[/C][C]803.639811304805[/C][/ROW]
[ROW][C]81[/C][C]459279[/C][C]457061.625855027[/C][C]2217.37414497347[/C][/ROW]
[ROW][C]82[/C][C]465090[/C][C]463432.373546398[/C][C]1657.62645360228[/C][/ROW]
[ROW][C]83[/C][C]478567[/C][C]474303.410913051[/C][C]4263.58908694884[/C][/ROW]
[ROW][C]84[/C][C]475726[/C][C]476756.680335793[/C][C]-1030.68033579347[/C][/ROW]
[ROW][C]85[/C][C]480634[/C][C]478194.61514532[/C][C]2439.3848546801[/C][/ROW]
[ROW][C]86[/C][C]486952[/C][C]485545.271915663[/C][C]1406.72808433749[/C][/ROW]
[ROW][C]87[/C][C]491912[/C][C]493242.414274638[/C][C]-1330.41427463794[/C][/ROW]
[ROW][C]88[/C][C]517281[/C][C]512707.788000547[/C][C]4573.21199945308[/C][/ROW]
[ROW][C]89[/C][C]502379[/C][C]506453.654768234[/C][C]-4074.65476823441[/C][/ROW]
[ROW][C]90[/C][C]504942[/C][C]506301.902200747[/C][C]-1359.90220074716[/C][/ROW]
[ROW][C]91[/C][C]516387[/C][C]514842.801656082[/C][C]1544.19834391813[/C][/ROW]
[ROW][C]92[/C][C]523270[/C][C]525273.512504304[/C][C]-2003.51250430429[/C][/ROW]
[ROW][C]93[/C][C]528995[/C][C]531745.55995287[/C][C]-2750.55995287001[/C][/ROW]
[ROW][C]94[/C][C]540850[/C][C]535090.09353319[/C][C]5759.90646680992[/C][/ROW]
[ROW][C]95[/C][C]550679[/C][C]549265.536352253[/C][C]1413.4636477473[/C][/ROW]
[ROW][C]96[/C][C]544432[/C][C]550056.363021164[/C][C]-5624.36302116385[/C][/ROW]
[ROW][C]97[/C][C]550296[/C][C]548567.110512956[/C][C]1728.88948704419[/C][/ROW]
[ROW][C]98[/C][C]554659[/C][C]555373.15900024[/C][C]-714.159000240499[/C][/ROW]
[ROW][C]99[/C][C]558856[/C][C]561401.702186925[/C][C]-2545.7021869251[/C][/ROW]
[ROW][C]100[/C][C]582661[/C][C]579917.590263129[/C][C]2743.40973687102[/C][/ROW]
[ROW][C]101[/C][C]564317[/C][C]571814.066554444[/C][C]-7497.06655444368[/C][/ROW]
[ROW][C]102[/C][C]568569[/C][C]568798.236308888[/C][C]-229.23630888795[/C][/ROW]
[ROW][C]103[/C][C]574693[/C][C]577549.568753215[/C][C]-2856.56875321479[/C][/ROW]
[ROW][C]104[/C][C]586558[/C][C]584077.435725964[/C][C]2480.56427403644[/C][/ROW]
[ROW][C]105[/C][C]588751[/C][C]592874.779181854[/C][C]-4123.7791818541[/C][/ROW]
[ROW][C]106[/C][C]598250[/C][C]594831.637849276[/C][C]3418.3621507244[/C][/ROW]
[ROW][C]107[/C][C]607706[/C][C]606491.798305032[/C][C]1214.20169496757[/C][/ROW]
[ROW][C]108[/C][C]603869[/C][C]606090.83622714[/C][C]-2221.83622713969[/C][/ROW]
[ROW][C]109[/C][C]607696[/C][C]606381.137016171[/C][C]1314.86298382853[/C][/ROW]
[ROW][C]110[/C][C]613285[/C][C]612189.351361897[/C][C]1095.64863810281[/C][/ROW]
[ROW][C]111[/C][C]617160[/C][C]618827.450550294[/C][C]-1667.4505502939[/C][/ROW]
[ROW][C]112[/C][C]647083[/C][C]637583.752307563[/C][C]9499.24769243714[/C][/ROW]
[ROW][C]113[/C][C]621246[/C][C]633688.267711472[/C][C]-12442.2677114719[/C][/ROW]
[ROW][C]114[/C][C]623252[/C][C]627276.105047016[/C][C]-4024.10504701559[/C][/ROW]
[ROW][C]115[/C][C]632722[/C][C]632859.486770801[/C][C]-137.486770800664[/C][/ROW]
[ROW][C]116[/C][C]641716[/C][C]640890.594947757[/C][C]825.40505224315[/C][/ROW]
[ROW][C]117[/C][C]644953[/C][C]647903.064299593[/C][C]-2950.0642995931[/C][/ROW]
[ROW][C]118[/C][C]652723[/C][C]650368.850302155[/C][C]2354.14969784545[/C][/ROW]
[ROW][C]119[/C][C]660093[/C][C]660749.219801264[/C][C]-656.219801264117[/C][/ROW]
[ROW][C]120[/C][C]657090[/C][C]658370.994423232[/C][C]-1280.99442323239[/C][/ROW]
[ROW][C]121[/C][C]657281[/C][C]658770.735063052[/C][C]-1489.73506305215[/C][/ROW]
[ROW][C]122[/C][C]661949[/C][C]661931.379257694[/C][C]17.6207423063461[/C][/ROW]
[ROW][C]123[/C][C]665608[/C][C]666911.543721495[/C][C]-1303.54372149473[/C][/ROW]
[ROW][C]124[/C][C]697124[/C][C]685328.864217072[/C][C]11795.1357829281[/C][/ROW]
[ROW][C]125[/C][C]671310[/C][C]681707.874840823[/C][C]-10397.874840823[/C][/ROW]
[ROW][C]126[/C][C]674708[/C][C]676310.973284872[/C][C]-1602.97328487237[/C][/ROW]
[ROW][C]127[/C][C]681915[/C][C]683222.753259534[/C][C]-1307.75325953425[/C][/ROW]
[ROW][C]128[/C][C]690556[/C][C]690067.604417799[/C][C]488.395582200959[/C][/ROW]
[ROW][C]129[/C][C]692885[/C][C]696297.664200619[/C][C]-3412.66420061875[/C][/ROW]
[ROW][C]130[/C][C]699740[/C][C]698090.268150392[/C][C]1649.73184960778[/C][/ROW]
[ROW][C]131[/C][C]707885[/C][C]707380.13182702[/C][C]504.868172980146[/C][/ROW]
[ROW][C]132[/C][C]704785[/C][C]705279.991590942[/C][C]-494.991590942489[/C][/ROW]
[ROW][C]133[/C][C]705363[/C][C]705780.158280078[/C][C]-417.158280078089[/C][/ROW]
[ROW][C]134[/C][C]749101[/C][C]709351.024516883[/C][C]39749.975483117[/C][/ROW]
[ROW][C]135[/C][C]752891[/C][C]742960.529757643[/C][C]9930.47024235735[/C][/ROW]
[ROW][C]136[/C][C]784662[/C][C]772502.910980968[/C][C]12159.0890190317[/C][/ROW]
[ROW][C]137[/C][C]761914[/C][C]772026.757799511[/C][C]-10112.757799511[/C][/ROW]
[ROW][C]138[/C][C]763768[/C][C]770514.473569851[/C][C]-6746.47356985114[/C][/ROW]
[ROW][C]139[/C][C]768877[/C][C]777159.294144461[/C][C]-8282.29414446128[/C][/ROW]
[ROW][C]140[/C][C]781031[/C][C]782058.743451181[/C][C]-1027.74345118145[/C][/ROW]
[ROW][C]141[/C][C]783454[/C][C]789669.996432002[/C][C]-6215.99643200159[/C][/ROW]
[ROW][C]142[/C][C]785988[/C][C]792015.471963935[/C][C]-6027.47196393483[/C][/ROW]
[ROW][C]143[/C][C]795068[/C][C]797940.471564465[/C][C]-2872.47156446485[/C][/ROW]
[ROW][C]144[/C][C]790001[/C][C]795050.060688397[/C][C]-5049.06068839703[/C][/ROW]
[ROW][C]145[/C][C]789721[/C][C]793678.80546752[/C][C]-3957.80546752014[/C][/ROW]
[ROW][C]146[/C][C]794064[/C][C]796778.348320089[/C][C]-2714.34832008893[/C][/ROW]
[ROW][C]147[/C][C]798690[/C][C]799512.290061521[/C][C]-822.290061520995[/C][/ROW]
[ROW][C]148[/C][C]829281[/C][C]818981.773769813[/C][C]10299.2262301872[/C][/ROW]
[ROW][C]149[/C][C]806249[/C][C]813519.121991979[/C][C]-7270.12199197884[/C][/ROW]
[ROW][C]150[/C][C]807048[/C][C]810951.941009298[/C][C]-3903.94100929808[/C][/ROW]
[ROW][C]151[/C][C]819928[/C][C]816629.722539925[/C][C]3298.27746007498[/C][/ROW]
[ROW][C]152[/C][C]821105[/C][C]827366.691843575[/C][C]-6261.69184357463[/C][/ROW]
[ROW][C]153[/C][C]828422[/C][C]829091.197572242[/C][C]-669.197572242469[/C][/ROW]
[ROW][C]154[/C][C]835360[/C][C]833164.070876081[/C][C]2195.92912391876[/C][/ROW]
[ROW][C]155[/C][C]844092[/C][C]843252.761442391[/C][C]839.238557608682[/C][/ROW]
[ROW][C]156[/C][C]837469[/C][C]841708.238276302[/C][C]-4239.23827630177[/C][/ROW]
[ROW][C]157[/C][C]836969[/C][C]839920.551835144[/C][C]-2951.55183514382[/C][/ROW]
[ROW][C]158[/C][C]838721[/C][C]842810.557116756[/C][C]-4089.5571167561[/C][/ROW]
[ROW][C]159[/C][C]840537[/C][C]843687.590413169[/C][C]-3150.59041316877[/C][/ROW]
[ROW][C]160[/C][C]863719[/C][C]860732.655593796[/C][C]2986.34440620418[/C][/ROW]
[ROW][C]161[/C][C]845413[/C][C]848323.121072274[/C][C]-2910.12107227405[/C][/ROW]
[ROW][C]162[/C][C]844366[/C][C]847307.588137444[/C][C]-2941.58813744353[/C][/ROW]
[ROW][C]163[/C][C]848357[/C][C]852474.91616175[/C][C]-4117.91616174974[/C][/ROW]
[ROW][C]164[/C][C]858754[/C][C]856241.831326082[/C][C]2512.16867391835[/C][/ROW]
[ROW][C]165[/C][C]862431[/C][C]862639.613033885[/C][C]-208.613033885485[/C][/ROW]
[ROW][C]166[/C][C]871565[/C][C]865899.296312225[/C][C]5665.70368777472[/C][/ROW]
[ROW][C]167[/C][C]880366[/C][C]877299.650656877[/C][C]3066.34934312268[/C][/ROW]
[ROW][C]168[/C][C]874476[/C][C]876323.57958002[/C][C]-1847.57958002028[/C][/ROW]
[ROW][C]169[/C][C]882077[/C][C]875547.078760594[/C][C]6529.92123940564[/C][/ROW]
[ROW][C]170[/C][C]889199[/C][C]884737.967994295[/C][C]4461.03200570529[/C][/ROW]
[ROW][C]171[/C][C]892665[/C][C]891988.073606808[/C][C]676.926393191912[/C][/ROW]
[ROW][C]172[/C][C]913625[/C][C]912720.105039177[/C][C]904.89496082277[/C][/ROW]
[ROW][C]173[/C][C]893597[/C][C]899669.050477922[/C][C]-6072.05047792208[/C][/ROW]
[ROW][C]174[/C][C]892114[/C][C]897215.754418195[/C][C]-5101.75441819476[/C][/ROW]
[ROW][C]175[/C][C]894801[/C][C]901414.467835347[/C][C]-6613.46783534717[/C][/ROW]
[ROW][C]176[/C][C]898843[/C][C]904002.684291913[/C][C]-5159.68429191282[/C][/ROW]
[ROW][C]177[/C][C]908135[/C][C]905027.905116762[/C][C]3107.09488323785[/C][/ROW]
[ROW][C]178[/C][C]918920[/C][C]910580.162064723[/C][C]8339.83793527668[/C][/ROW]
[ROW][C]179[/C][C]923125[/C][C]923838.98097709[/C][C]-713.980977089959[/C][/ROW]
[ROW][C]180[/C][C]921770[/C][C]920151.34125688[/C][C]1618.65874311957[/C][/ROW]
[ROW][C]181[/C][C]917843[/C][C]922002.575661705[/C][C]-4159.57566170522[/C][/ROW]
[ROW][C]182[/C][C]916761[/C][C]923487.787610592[/C][C]-6726.78761059185[/C][/ROW]
[ROW][C]183[/C][C]915087[/C][C]921836.957550534[/C][C]-6749.95755053428[/C][/ROW]
[ROW][C]184[/C][C]938173[/C][C]935686.4173764[/C][C]2486.58262360038[/C][/ROW]
[ROW][C]185[/C][C]907953[/C][C]921599.094085135[/C][C]-13646.0940851346[/C][/ROW]
[ROW][C]186[/C][C]905374[/C][C]911742.869615759[/C][C]-6368.86961575935[/C][/ROW]
[ROW][C]187[/C][C]921867[/C][C]912520.114590708[/C][C]9346.88540929195[/C][/ROW]
[ROW][C]188[/C][C]927104[/C][C]924238.057730122[/C][C]2865.94226987835[/C][/ROW]
[ROW][C]189[/C][C]930989[/C][C]929950.398764042[/C][C]1038.60123595758[/C][/ROW]
[ROW][C]190[/C][C]936820[/C][C]933340.965694548[/C][C]3479.03430545155[/C][/ROW]
[ROW][C]191[/C][C]944281[/C][C]941892.651320081[/C][C]2388.34867991915[/C][/ROW]
[ROW][C]192[/C][C]945322[/C][C]939232.951976889[/C][C]6089.0480231113[/C][/ROW]
[ROW][C]193[/C][C]944555[/C][C]943137.730251871[/C][C]1417.26974812883[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=227518&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=227518&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
13341499339703.2080662391795.79193376075
14342376341798.310539646577.689460354159
15344148344071.39395686776.6060431333608
16359079358990.5142443388.4857556701172
17344090343740.207468933349.792531066865
18342681342114.942257065566.057742934965
19348552346845.3050383321706.69496166823
20349867351958.111459917-2091.11145991721
21353247353377.313490699-130.313490699336
22356048353108.4783839832939.5216160171
23363887360584.4774642723302.52253572771
24358905357873.8245594781031.17544052185
25359647356230.4526072073416.54739279283
26361488360231.7527955151256.24720448465
27363229363860.960361327-631.960361327277
28393301379186.84933661514114.1506633854
29366190375048.873003205-8858.87300320476
30363811368615.8091555-4804.8091554998
31366190370682.135886955-4492.13588695519
32372656372007.532610555648.467389444937
33371781375847.380919605-4066.38091960503
34374306373357.712109237948.287890762615
35377689379674.216839834-1985.21683983417
36373240373186.12042675153.8795732487342
37373456370636.1566856912819.84331430908
38372610373823.433744069-1213.43374406855
39372209375234.618122251-3025.61812225124
40390212388629.2482862171582.75171378325
41373113374047.964860824-934.964860823704
42370518371844.991640422-1326.99164042162
43370469375388.906097189-4919.90609718877
44372493375718.690148479-3225.69014847907
45369536375771.46856449-6235.46856449038
46368835370694.883726094-1859.88372609403
47366859373600.416511086-6741.41651108564
48356044362196.223578098-6152.22357809788
49346106353339.18003702-7233.18003702001
50333829346785.139962947-12956.1399629474
51317388336535.251199926-19147.251199926
52285871334366.390291785-48495.3902917847
53339729278076.24207394861652.7579260525
54308216312733.995888962-4517.99588896212
55309137309679.468902973-542.468902972993
56311245308829.4766455792415.52335442108
57319568308830.80531704810737.1946829517
58329201312571.39376901116629.606230989
59339880326423.52033354513456.4796664549
60342305328713.26926785613591.7307321441
61346975334668.19133882812306.8086611716
62355294344119.15618499611174.8438150038
63360766354654.9428780456111.0571219555
64392946375299.71613791617646.2838620837
65352108376988.606913971-24880.6069139714
66358071358715.580350755-644.580350755132
67365429364057.7200847011371.27991529915
68378731370435.0090399628295.99096003803
69384120380832.7663427633287.23365723668
70391390385616.1228112375773.87718876288
71403547397250.5368236246296.46317637572
72404124399300.3590872344823.64091276628
73406439403278.1483075813160.85169241874
74412232409832.8847470642399.11525293556
75419221416969.7883800442251.2116199559
76450521437567.79572984612953.2042701536
77430027436972.878233954-6945.87823395379
78433442434241.212086957-799.212086957181
79439938442696.089655126-2758.08965512627
80450200449396.360188695803.639811304805
81459279457061.6258550272217.37414497347
82465090463432.3735463981657.62645360228
83478567474303.4109130514263.58908694884
84475726476756.680335793-1030.68033579347
85480634478194.615145322439.3848546801
86486952485545.2719156631406.72808433749
87491912493242.414274638-1330.41427463794
88517281512707.7880005474573.21199945308
89502379506453.654768234-4074.65476823441
90504942506301.902200747-1359.90220074716
91516387514842.8016560821544.19834391813
92523270525273.512504304-2003.51250430429
93528995531745.55995287-2750.55995287001
94540850535090.093533195759.90646680992
95550679549265.5363522531413.4636477473
96544432550056.363021164-5624.36302116385
97550296548567.1105129561728.88948704419
98554659555373.15900024-714.159000240499
99558856561401.702186925-2545.7021869251
100582661579917.5902631292743.40973687102
101564317571814.066554444-7497.06655444368
102568569568798.236308888-229.23630888795
103574693577549.568753215-2856.56875321479
104586558584077.4357259642480.56427403644
105588751592874.779181854-4123.7791818541
106598250594831.6378492763418.3621507244
107607706606491.7983050321214.20169496757
108603869606090.83622714-2221.83622713969
109607696606381.1370161711314.86298382853
110613285612189.3513618971095.64863810281
111617160618827.450550294-1667.4505502939
112647083637583.7523075639499.24769243714
113621246633688.267711472-12442.2677114719
114623252627276.105047016-4024.10504701559
115632722632859.486770801-137.486770800664
116641716640890.594947757825.40505224315
117644953647903.064299593-2950.0642995931
118652723650368.8503021552354.14969784545
119660093660749.219801264-656.219801264117
120657090658370.994423232-1280.99442323239
121657281658770.735063052-1489.73506305215
122661949661931.37925769417.6207423063461
123665608666911.543721495-1303.54372149473
124697124685328.86421707211795.1357829281
125671310681707.874840823-10397.874840823
126674708676310.973284872-1602.97328487237
127681915683222.753259534-1307.75325953425
128690556690067.604417799488.395582200959
129692885696297.664200619-3412.66420061875
130699740698090.2681503921649.73184960778
131707885707380.13182702504.868172980146
132704785705279.991590942-494.991590942489
133705363705780.158280078-417.158280078089
134749101709351.02451688339749.975483117
135752891742960.5297576439930.47024235735
136784662772502.91098096812159.0890190317
137761914772026.757799511-10112.757799511
138763768770514.473569851-6746.47356985114
139768877777159.294144461-8282.29414446128
140781031782058.743451181-1027.74345118145
141783454789669.996432002-6215.99643200159
142785988792015.471963935-6027.47196393483
143795068797940.471564465-2872.47156446485
144790001795050.060688397-5049.06068839703
145789721793678.80546752-3957.80546752014
146794064796778.348320089-2714.34832008893
147798690799512.290061521-822.290061520995
148829281818981.77376981310299.2262301872
149806249813519.121991979-7270.12199197884
150807048810951.941009298-3903.94100929808
151819928816629.7225399253298.27746007498
152821105827366.691843575-6261.69184357463
153828422829091.197572242-669.197572242469
154835360833164.0708760812195.92912391876
155844092843252.761442391839.238557608682
156837469841708.238276302-4239.23827630177
157836969839920.551835144-2951.55183514382
158838721842810.557116756-4089.5571167561
159840537843687.590413169-3150.59041316877
160863719860732.6555937962986.34440620418
161845413848323.121072274-2910.12107227405
162844366847307.588137444-2941.58813744353
163848357852474.91616175-4117.91616174974
164858754856241.8313260822512.16867391835
165862431862639.613033885-208.613033885485
166871565865899.2963122255665.70368777472
167880366877299.6506568773066.34934312268
168874476876323.57958002-1847.57958002028
169882077875547.0787605946529.92123940564
170889199884737.9679942954461.03200570529
171892665891988.073606808676.926393191912
172913625912720.105039177904.89496082277
173893597899669.050477922-6072.05047792208
174892114897215.754418195-5101.75441819476
175894801901414.467835347-6613.46783534717
176898843904002.684291913-5159.68429191282
177908135905027.9051167623107.09488323785
178918920910580.1620647238339.83793527668
179923125923838.98097709-713.980977089959
180921770920151.341256881618.65874311957
181917843922002.575661705-4159.57566170522
182916761923487.787610592-6726.78761059185
183915087921836.957550534-6749.95755053428
184938173935686.41737642486.58262360038
185907953921599.094085135-13646.0940851346
186905374911742.869615759-6368.86961575935
187921867912520.1145907089346.88540929195
188927104924238.0577301222865.94226987835
189930989929950.3987640421038.60123595758
190936820933340.9656945483479.03430545155
191944281941892.6513200812388.34867991915
192945322939232.9519768896089.0480231113
193944555943137.7302518711417.26974812883







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
194947893.665084983930657.705574655965129.62459531
195950827.552741871929490.638813348972164.466670393
196970005.358993787944567.814788976995442.903198599
197954373.882686277924781.15670282983966.608669734
198955144.120512488921313.910976802988974.330048175
199962454.606176137924289.6163711351000619.59598114
200969156.117450941926550.7610594161011761.47384247
201974007.025055496926851.2219143981021162.82819659
202977764.156034205925945.5934328571029582.71863555
203984737.154900157928142.6831986991041331.62660162
204981156.990823707919673.5051179621042640.47652945
205981056.436029894914571.4403879561047541.43167183

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
194 & 947893.665084983 & 930657.705574655 & 965129.62459531 \tabularnewline
195 & 950827.552741871 & 929490.638813348 & 972164.466670393 \tabularnewline
196 & 970005.358993787 & 944567.814788976 & 995442.903198599 \tabularnewline
197 & 954373.882686277 & 924781.15670282 & 983966.608669734 \tabularnewline
198 & 955144.120512488 & 921313.910976802 & 988974.330048175 \tabularnewline
199 & 962454.606176137 & 924289.616371135 & 1000619.59598114 \tabularnewline
200 & 969156.117450941 & 926550.761059416 & 1011761.47384247 \tabularnewline
201 & 974007.025055496 & 926851.221914398 & 1021162.82819659 \tabularnewline
202 & 977764.156034205 & 925945.593432857 & 1029582.71863555 \tabularnewline
203 & 984737.154900157 & 928142.683198699 & 1041331.62660162 \tabularnewline
204 & 981156.990823707 & 919673.505117962 & 1042640.47652945 \tabularnewline
205 & 981056.436029894 & 914571.440387956 & 1047541.43167183 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=227518&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]194[/C][C]947893.665084983[/C][C]930657.705574655[/C][C]965129.62459531[/C][/ROW]
[ROW][C]195[/C][C]950827.552741871[/C][C]929490.638813348[/C][C]972164.466670393[/C][/ROW]
[ROW][C]196[/C][C]970005.358993787[/C][C]944567.814788976[/C][C]995442.903198599[/C][/ROW]
[ROW][C]197[/C][C]954373.882686277[/C][C]924781.15670282[/C][C]983966.608669734[/C][/ROW]
[ROW][C]198[/C][C]955144.120512488[/C][C]921313.910976802[/C][C]988974.330048175[/C][/ROW]
[ROW][C]199[/C][C]962454.606176137[/C][C]924289.616371135[/C][C]1000619.59598114[/C][/ROW]
[ROW][C]200[/C][C]969156.117450941[/C][C]926550.761059416[/C][C]1011761.47384247[/C][/ROW]
[ROW][C]201[/C][C]974007.025055496[/C][C]926851.221914398[/C][C]1021162.82819659[/C][/ROW]
[ROW][C]202[/C][C]977764.156034205[/C][C]925945.593432857[/C][C]1029582.71863555[/C][/ROW]
[ROW][C]203[/C][C]984737.154900157[/C][C]928142.683198699[/C][C]1041331.62660162[/C][/ROW]
[ROW][C]204[/C][C]981156.990823707[/C][C]919673.505117962[/C][C]1042640.47652945[/C][/ROW]
[ROW][C]205[/C][C]981056.436029894[/C][C]914571.440387956[/C][C]1047541.43167183[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=227518&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=227518&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
194947893.665084983930657.705574655965129.62459531
195950827.552741871929490.638813348972164.466670393
196970005.358993787944567.814788976995442.903198599
197954373.882686277924781.15670282983966.608669734
198955144.120512488921313.910976802988974.330048175
199962454.606176137924289.6163711351000619.59598114
200969156.117450941926550.7610594161011761.47384247
201974007.025055496926851.2219143981021162.82819659
202977764.156034205925945.5934328571029582.71863555
203984737.154900157928142.6831986991041331.62660162
204981156.990823707919673.5051179621042640.47652945
205981056.436029894914571.4403879561047541.43167183



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):
par3 <- 'additive'
par2 <- 'Double'
par1 <- '12'
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')