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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 07:05:53 -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/t1385121983vrcg8wxtnbt7o87.htm/, Retrieved Mon, 29 Apr 2024 17:34:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=227517, Retrieved Mon, 29 Apr 2024 17:34:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact67
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [WS804] [2013-11-22 12:05:53] [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 time3 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=227517&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=227517&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=227517&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.560350289484692
beta0.0738144826327317
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.560350289484692 \tabularnewline
beta & 0.0738144826327317 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=227517&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]0.560350289484692[/C][/ROW]
[ROW][C]beta[/C][C]0.0738144826327317[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=227517&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=227517&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
alpha0.560350289484692
beta0.0738144826327317
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
33424353393293106
4354980341421.91826774513558.0817322549
5339890349932.452485157-10042.452485157
6339890344803.044936457-4913.04493645683
7340471342344.689191442-1873.68919144233
8343833341511.937848032321.06215197034
9346109343125.7203296792983.27967032051
10345455345233.970903853221.029096146638
11350419345803.5357672774615.46423272329
12344660349026.428309554-4366.42830955406
13341499347035.710703258-5536.7107032584
14342376344160.215775073-1784.21577507275
15344148343313.633792691834.366207308776
16359079343968.88600946815110.1139905316
17344090353248.541661067-9158.54166106705
18342681348550.433797578-5869.43379757792
19348552345452.6071521913099.39284780901
20349867347508.6620976812358.33790231869
21353247349247.0121837523999.98781624797
22356048352070.7086372273977.29136277275
23363887355046.1957193768840.80428062403
24358905361112.626725313-2207.62672531256
25359647360896.754435597-1249.75443559728
26361488361165.933859351322.066140649258
27363229362329.20468701899.795312989678
28393301363853.42352741829447.5764725825
29366190382592.409482539-16402.409482539
30363811374960.906619835-11149.9066198354
31366190369811.463190322-3621.46319032187
32372656368730.7943759813925.20562401932
33371781372041.257840757-260.257840756793
34374306372995.6308652721310.36913472775
35377689374884.3046147032804.69538529683
36373240377726.332228387-4486.33222838741
37373456376297.266883816-2841.26688381587
38372610375672.49399503-3062.4939950296
39372209374797.085655757-2588.08565575653
40390212374080.46385398916131.5361460106
41373113384520.619608962-11407.6196089617
42370518379057.359881949-8539.35988194891
43370469374848.125604111-4379.12560411106
44372493372788.950560721-295.950560721394
45369536373005.542737671-3469.54273767106
46368835371300.304508341-2465.30450834124
47366859370055.82161852-3196.82161852048
48356044368269.20607488-12225.2060748802
49346106360917.87412083-14811.8741208303
50333829351504.453734112-17675.453734112
51317388339755.334153169-22367.3341531694
52285871324451.961090514-38580.9610905139
53339729298467.493051641261.5069483995
54308216318929.432168327-10713.4321683269
55309137309824.070480335-687.070480335096
56311245306308.5648803524936.43511964829
57319568306148.3729363313419.6270636703
58329201311296.80222178217904.1977782181
59339880319698.71483784320181.2851621573
60342305330211.33167374612093.6683262535
61346975336692.2679811410282.7320188603
62355294342583.75962391312710.2403760868
63360766350361.22681671510404.7731832851
64392946357277.1866826835668.8133173204
65352108379825.19102037-27717.1910203704
66358071365708.39194584-7637.39194583986
67365429362527.4165440912901.58345590893
68378731365371.97425789813359.0257421021
69384120374628.9183620849491.08163791569
70391390382111.0286705429278.97132945794
71403547389858.07940949813688.920590502
72404124400642.4471712723481.5528287277
73406439405851.117325066587.882674934401
74412232409462.6345541382769.36544586159
75419221414411.092686794809.90731321037
76450521420701.91627168929819.0837283107
77430027442240.015049099-12213.0150490995
78433442439720.260787032-6278.26078703185
79439938440266.366580056-328.366580055503
80450200444132.9154268086067.08457319171
81459279451834.103728827444.89627117995
82465090460615.2847663934474.71523360664
83478567467917.20702227610649.792977724
84475726479119.832262293-3393.83226229344
85480634482312.732456595-1678.7324565954
86486952486397.253647528554.746352471644
87491912491756.250735844155.749264155864
88517281496898.11178609820382.888213902
89502379514217.332346075-11838.3323460751
90504942512991.725929302-8049.72592930193
91516387513556.1137189872830.88628101273
92523270520334.5467346122935.4532653878
93528995527292.9900104481702.00998955185
94540850533630.6714701377219.32852986327
95550679543358.5895973997320.41040260089
96544432553445.935552698-9013.93555269798
97550296554007.491921132-3711.49192113243
98554659557386.759508199-2727.75950819941
99558856561204.436339654-2348.43633965391
100582661565137.53107270717523.4689272934
101564317580930.658813145-16613.6588131447
102568569576907.863539268-8338.86353926838
103574693577176.940396413-2483.94039641297
104586558580624.0844715785933.91552842234
105588751589033.614967619-282.614967619185
106598250593948.0212897314301.97871026944
107607706601609.3443066246096.65569337609
108603869610528.484760373-6659.4847603729
109607696612024.268831183-4328.26883118262
110613285614647.324711452-1362.32471145201
111617160618875.999808443-1715.99980844255
112647083622835.51583549724247.4841645026
113621246642346.601255671-21100.6012556709
114623252635574.111516346-12322.1115163458
115632722633210.984277337-488.984277336509
116641716637458.3279608144257.67203918635
117644953644541.567574492411.432425508392
118652723649486.5833615063236.41663849447
119660093656148.4444273223944.55557267845
120657090663370.265926191-6280.26592619147
121657281664602.841588062-7321.84158806223
122661949664948.924258252-2999.92425825191
123665608667592.711788023-1984.71178802312
124697124670723.28233646826400.7176635325
125671310690851.622100395-19541.6221003949
126674708684427.878555198-9719.87855519785
127681915683105.718555557-1190.71855555731
128690556686513.6253695194042.37463048089
129692885693021.098030079-136.09803007869
130699740697181.53304352558.46695649973
131707885702957.6915522734927.30844772665
132704785710265.034244391-5480.03424439055
133705363711513.95445222-6150.95445221965
134749101712132.50875407436968.4912459255
135752891738442.14643958914448.8535604106
136784662752730.5316289231931.4683710804
137761914778136.053420169-16222.0534201692
138763768775887.759302429-12119.7593024288
139768877775436.889800298-6559.88980029814
140781031777830.1648396333200.83516036696
141783454785825.257773609-2371.25777360902
142785988790599.9469339-4611.94693389954
143795068793928.3060790211139.69392097858
144790001800526.738824207-10525.7388242069
145789721800153.077694804-10432.0776948037
146794064799400.408356032-5336.40835603164
147798690801282.374461578-2592.37446157809
148829281804594.73504805424686.264951946
149806249824213.761595818-17964.7615958183
150807048819190.215199619-12142.2151996188
151819928816927.1084611783000.89153882163
152821105823273.568743254-2168.56874325383
153828422826633.6241916191788.37580838124
154835360832284.9254056213075.07459437882
155844092838784.4197898455307.58021015534
156837469846754.431298115-9285.43129811541
157836969846163.180883019-9194.18088301935
158838721845242.773260816-6521.77326081577
159840537845550.096654822-5013.09665482189
160863719846495.45588477817223.5441152224
161845413860613.522865741-15200.5228657412
162844366855934.031006882-11568.0310068819
163848357852811.530499262-4454.5304992618
164858754853490.8339181115263.16608188918
165862431859833.1463296082597.85367039207
166871565864789.4024967916775.59750320867
167880366872366.9106684647999.08933153597
168874476880960.860906975-6484.86090697476
169882077881170.498835492906.501164508401
170889199885559.3833114413639.61668855941
171892665891630.3115668011034.68843319884
172913625896284.36426871417340.6357312859
173893597910792.702057305-17195.7020573046
174892114905237.344912244-13123.3449122435
175894801901421.1269169-6620.12691689993
176898843900975.167538667-2132.1675386671
177908135902955.8468544655179.15314553503
178918920909247.646792179672.35320783011
179923125918457.2802368984667.71976310224
180921770925055.631951567-3285.63195156725
181917843927061.420531141-9218.42053114146
182916761925361.477309559-8600.47730955889
183915087923652.066094895-8565.06609489501
184938173921608.22958592116564.7704140791
185907953934331.055721903-26378.0557219028
186905374921899.808538615-16525.8085386152
187921867914305.7309739047561.26902609575
188927104920521.6032531736582.39674682729
189930989926461.2250425084527.7749574919
190936820931436.8165944765383.18340552354
191944281937114.3955707487166.60442925233
192945322944087.7398877751234.26011222496
193944555947787.944775108-3232.94477510825

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 342435 & 339329 & 3106 \tabularnewline
4 & 354980 & 341421.918267745 & 13558.0817322549 \tabularnewline
5 & 339890 & 349932.452485157 & -10042.452485157 \tabularnewline
6 & 339890 & 344803.044936457 & -4913.04493645683 \tabularnewline
7 & 340471 & 342344.689191442 & -1873.68919144233 \tabularnewline
8 & 343833 & 341511.93784803 & 2321.06215197034 \tabularnewline
9 & 346109 & 343125.720329679 & 2983.27967032051 \tabularnewline
10 & 345455 & 345233.970903853 & 221.029096146638 \tabularnewline
11 & 350419 & 345803.535767277 & 4615.46423272329 \tabularnewline
12 & 344660 & 349026.428309554 & -4366.42830955406 \tabularnewline
13 & 341499 & 347035.710703258 & -5536.7107032584 \tabularnewline
14 & 342376 & 344160.215775073 & -1784.21577507275 \tabularnewline
15 & 344148 & 343313.633792691 & 834.366207308776 \tabularnewline
16 & 359079 & 343968.886009468 & 15110.1139905316 \tabularnewline
17 & 344090 & 353248.541661067 & -9158.54166106705 \tabularnewline
18 & 342681 & 348550.433797578 & -5869.43379757792 \tabularnewline
19 & 348552 & 345452.607152191 & 3099.39284780901 \tabularnewline
20 & 349867 & 347508.662097681 & 2358.33790231869 \tabularnewline
21 & 353247 & 349247.012183752 & 3999.98781624797 \tabularnewline
22 & 356048 & 352070.708637227 & 3977.29136277275 \tabularnewline
23 & 363887 & 355046.195719376 & 8840.80428062403 \tabularnewline
24 & 358905 & 361112.626725313 & -2207.62672531256 \tabularnewline
25 & 359647 & 360896.754435597 & -1249.75443559728 \tabularnewline
26 & 361488 & 361165.933859351 & 322.066140649258 \tabularnewline
27 & 363229 & 362329.20468701 & 899.795312989678 \tabularnewline
28 & 393301 & 363853.423527418 & 29447.5764725825 \tabularnewline
29 & 366190 & 382592.409482539 & -16402.409482539 \tabularnewline
30 & 363811 & 374960.906619835 & -11149.9066198354 \tabularnewline
31 & 366190 & 369811.463190322 & -3621.46319032187 \tabularnewline
32 & 372656 & 368730.794375981 & 3925.20562401932 \tabularnewline
33 & 371781 & 372041.257840757 & -260.257840756793 \tabularnewline
34 & 374306 & 372995.630865272 & 1310.36913472775 \tabularnewline
35 & 377689 & 374884.304614703 & 2804.69538529683 \tabularnewline
36 & 373240 & 377726.332228387 & -4486.33222838741 \tabularnewline
37 & 373456 & 376297.266883816 & -2841.26688381587 \tabularnewline
38 & 372610 & 375672.49399503 & -3062.4939950296 \tabularnewline
39 & 372209 & 374797.085655757 & -2588.08565575653 \tabularnewline
40 & 390212 & 374080.463853989 & 16131.5361460106 \tabularnewline
41 & 373113 & 384520.619608962 & -11407.6196089617 \tabularnewline
42 & 370518 & 379057.359881949 & -8539.35988194891 \tabularnewline
43 & 370469 & 374848.125604111 & -4379.12560411106 \tabularnewline
44 & 372493 & 372788.950560721 & -295.950560721394 \tabularnewline
45 & 369536 & 373005.542737671 & -3469.54273767106 \tabularnewline
46 & 368835 & 371300.304508341 & -2465.30450834124 \tabularnewline
47 & 366859 & 370055.82161852 & -3196.82161852048 \tabularnewline
48 & 356044 & 368269.20607488 & -12225.2060748802 \tabularnewline
49 & 346106 & 360917.87412083 & -14811.8741208303 \tabularnewline
50 & 333829 & 351504.453734112 & -17675.453734112 \tabularnewline
51 & 317388 & 339755.334153169 & -22367.3341531694 \tabularnewline
52 & 285871 & 324451.961090514 & -38580.9610905139 \tabularnewline
53 & 339729 & 298467.4930516 & 41261.5069483995 \tabularnewline
54 & 308216 & 318929.432168327 & -10713.4321683269 \tabularnewline
55 & 309137 & 309824.070480335 & -687.070480335096 \tabularnewline
56 & 311245 & 306308.564880352 & 4936.43511964829 \tabularnewline
57 & 319568 & 306148.37293633 & 13419.6270636703 \tabularnewline
58 & 329201 & 311296.802221782 & 17904.1977782181 \tabularnewline
59 & 339880 & 319698.714837843 & 20181.2851621573 \tabularnewline
60 & 342305 & 330211.331673746 & 12093.6683262535 \tabularnewline
61 & 346975 & 336692.26798114 & 10282.7320188603 \tabularnewline
62 & 355294 & 342583.759623913 & 12710.2403760868 \tabularnewline
63 & 360766 & 350361.226816715 & 10404.7731832851 \tabularnewline
64 & 392946 & 357277.18668268 & 35668.8133173204 \tabularnewline
65 & 352108 & 379825.19102037 & -27717.1910203704 \tabularnewline
66 & 358071 & 365708.39194584 & -7637.39194583986 \tabularnewline
67 & 365429 & 362527.416544091 & 2901.58345590893 \tabularnewline
68 & 378731 & 365371.974257898 & 13359.0257421021 \tabularnewline
69 & 384120 & 374628.918362084 & 9491.08163791569 \tabularnewline
70 & 391390 & 382111.028670542 & 9278.97132945794 \tabularnewline
71 & 403547 & 389858.079409498 & 13688.920590502 \tabularnewline
72 & 404124 & 400642.447171272 & 3481.5528287277 \tabularnewline
73 & 406439 & 405851.117325066 & 587.882674934401 \tabularnewline
74 & 412232 & 409462.634554138 & 2769.36544586159 \tabularnewline
75 & 419221 & 414411.09268679 & 4809.90731321037 \tabularnewline
76 & 450521 & 420701.916271689 & 29819.0837283107 \tabularnewline
77 & 430027 & 442240.015049099 & -12213.0150490995 \tabularnewline
78 & 433442 & 439720.260787032 & -6278.26078703185 \tabularnewline
79 & 439938 & 440266.366580056 & -328.366580055503 \tabularnewline
80 & 450200 & 444132.915426808 & 6067.08457319171 \tabularnewline
81 & 459279 & 451834.10372882 & 7444.89627117995 \tabularnewline
82 & 465090 & 460615.284766393 & 4474.71523360664 \tabularnewline
83 & 478567 & 467917.207022276 & 10649.792977724 \tabularnewline
84 & 475726 & 479119.832262293 & -3393.83226229344 \tabularnewline
85 & 480634 & 482312.732456595 & -1678.7324565954 \tabularnewline
86 & 486952 & 486397.253647528 & 554.746352471644 \tabularnewline
87 & 491912 & 491756.250735844 & 155.749264155864 \tabularnewline
88 & 517281 & 496898.111786098 & 20382.888213902 \tabularnewline
89 & 502379 & 514217.332346075 & -11838.3323460751 \tabularnewline
90 & 504942 & 512991.725929302 & -8049.72592930193 \tabularnewline
91 & 516387 & 513556.113718987 & 2830.88628101273 \tabularnewline
92 & 523270 & 520334.546734612 & 2935.4532653878 \tabularnewline
93 & 528995 & 527292.990010448 & 1702.00998955185 \tabularnewline
94 & 540850 & 533630.671470137 & 7219.32852986327 \tabularnewline
95 & 550679 & 543358.589597399 & 7320.41040260089 \tabularnewline
96 & 544432 & 553445.935552698 & -9013.93555269798 \tabularnewline
97 & 550296 & 554007.491921132 & -3711.49192113243 \tabularnewline
98 & 554659 & 557386.759508199 & -2727.75950819941 \tabularnewline
99 & 558856 & 561204.436339654 & -2348.43633965391 \tabularnewline
100 & 582661 & 565137.531072707 & 17523.4689272934 \tabularnewline
101 & 564317 & 580930.658813145 & -16613.6588131447 \tabularnewline
102 & 568569 & 576907.863539268 & -8338.86353926838 \tabularnewline
103 & 574693 & 577176.940396413 & -2483.94039641297 \tabularnewline
104 & 586558 & 580624.084471578 & 5933.91552842234 \tabularnewline
105 & 588751 & 589033.614967619 & -282.614967619185 \tabularnewline
106 & 598250 & 593948.021289731 & 4301.97871026944 \tabularnewline
107 & 607706 & 601609.344306624 & 6096.65569337609 \tabularnewline
108 & 603869 & 610528.484760373 & -6659.4847603729 \tabularnewline
109 & 607696 & 612024.268831183 & -4328.26883118262 \tabularnewline
110 & 613285 & 614647.324711452 & -1362.32471145201 \tabularnewline
111 & 617160 & 618875.999808443 & -1715.99980844255 \tabularnewline
112 & 647083 & 622835.515835497 & 24247.4841645026 \tabularnewline
113 & 621246 & 642346.601255671 & -21100.6012556709 \tabularnewline
114 & 623252 & 635574.111516346 & -12322.1115163458 \tabularnewline
115 & 632722 & 633210.984277337 & -488.984277336509 \tabularnewline
116 & 641716 & 637458.327960814 & 4257.67203918635 \tabularnewline
117 & 644953 & 644541.567574492 & 411.432425508392 \tabularnewline
118 & 652723 & 649486.583361506 & 3236.41663849447 \tabularnewline
119 & 660093 & 656148.444427322 & 3944.55557267845 \tabularnewline
120 & 657090 & 663370.265926191 & -6280.26592619147 \tabularnewline
121 & 657281 & 664602.841588062 & -7321.84158806223 \tabularnewline
122 & 661949 & 664948.924258252 & -2999.92425825191 \tabularnewline
123 & 665608 & 667592.711788023 & -1984.71178802312 \tabularnewline
124 & 697124 & 670723.282336468 & 26400.7176635325 \tabularnewline
125 & 671310 & 690851.622100395 & -19541.6221003949 \tabularnewline
126 & 674708 & 684427.878555198 & -9719.87855519785 \tabularnewline
127 & 681915 & 683105.718555557 & -1190.71855555731 \tabularnewline
128 & 690556 & 686513.625369519 & 4042.37463048089 \tabularnewline
129 & 692885 & 693021.098030079 & -136.09803007869 \tabularnewline
130 & 699740 & 697181.5330435 & 2558.46695649973 \tabularnewline
131 & 707885 & 702957.691552273 & 4927.30844772665 \tabularnewline
132 & 704785 & 710265.034244391 & -5480.03424439055 \tabularnewline
133 & 705363 & 711513.95445222 & -6150.95445221965 \tabularnewline
134 & 749101 & 712132.508754074 & 36968.4912459255 \tabularnewline
135 & 752891 & 738442.146439589 & 14448.8535604106 \tabularnewline
136 & 784662 & 752730.53162892 & 31931.4683710804 \tabularnewline
137 & 761914 & 778136.053420169 & -16222.0534201692 \tabularnewline
138 & 763768 & 775887.759302429 & -12119.7593024288 \tabularnewline
139 & 768877 & 775436.889800298 & -6559.88980029814 \tabularnewline
140 & 781031 & 777830.164839633 & 3200.83516036696 \tabularnewline
141 & 783454 & 785825.257773609 & -2371.25777360902 \tabularnewline
142 & 785988 & 790599.9469339 & -4611.94693389954 \tabularnewline
143 & 795068 & 793928.306079021 & 1139.69392097858 \tabularnewline
144 & 790001 & 800526.738824207 & -10525.7388242069 \tabularnewline
145 & 789721 & 800153.077694804 & -10432.0776948037 \tabularnewline
146 & 794064 & 799400.408356032 & -5336.40835603164 \tabularnewline
147 & 798690 & 801282.374461578 & -2592.37446157809 \tabularnewline
148 & 829281 & 804594.735048054 & 24686.264951946 \tabularnewline
149 & 806249 & 824213.761595818 & -17964.7615958183 \tabularnewline
150 & 807048 & 819190.215199619 & -12142.2151996188 \tabularnewline
151 & 819928 & 816927.108461178 & 3000.89153882163 \tabularnewline
152 & 821105 & 823273.568743254 & -2168.56874325383 \tabularnewline
153 & 828422 & 826633.624191619 & 1788.37580838124 \tabularnewline
154 & 835360 & 832284.925405621 & 3075.07459437882 \tabularnewline
155 & 844092 & 838784.419789845 & 5307.58021015534 \tabularnewline
156 & 837469 & 846754.431298115 & -9285.43129811541 \tabularnewline
157 & 836969 & 846163.180883019 & -9194.18088301935 \tabularnewline
158 & 838721 & 845242.773260816 & -6521.77326081577 \tabularnewline
159 & 840537 & 845550.096654822 & -5013.09665482189 \tabularnewline
160 & 863719 & 846495.455884778 & 17223.5441152224 \tabularnewline
161 & 845413 & 860613.522865741 & -15200.5228657412 \tabularnewline
162 & 844366 & 855934.031006882 & -11568.0310068819 \tabularnewline
163 & 848357 & 852811.530499262 & -4454.5304992618 \tabularnewline
164 & 858754 & 853490.833918111 & 5263.16608188918 \tabularnewline
165 & 862431 & 859833.146329608 & 2597.85367039207 \tabularnewline
166 & 871565 & 864789.402496791 & 6775.59750320867 \tabularnewline
167 & 880366 & 872366.910668464 & 7999.08933153597 \tabularnewline
168 & 874476 & 880960.860906975 & -6484.86090697476 \tabularnewline
169 & 882077 & 881170.498835492 & 906.501164508401 \tabularnewline
170 & 889199 & 885559.383311441 & 3639.61668855941 \tabularnewline
171 & 892665 & 891630.311566801 & 1034.68843319884 \tabularnewline
172 & 913625 & 896284.364268714 & 17340.6357312859 \tabularnewline
173 & 893597 & 910792.702057305 & -17195.7020573046 \tabularnewline
174 & 892114 & 905237.344912244 & -13123.3449122435 \tabularnewline
175 & 894801 & 901421.1269169 & -6620.12691689993 \tabularnewline
176 & 898843 & 900975.167538667 & -2132.1675386671 \tabularnewline
177 & 908135 & 902955.846854465 & 5179.15314553503 \tabularnewline
178 & 918920 & 909247.64679217 & 9672.35320783011 \tabularnewline
179 & 923125 & 918457.280236898 & 4667.71976310224 \tabularnewline
180 & 921770 & 925055.631951567 & -3285.63195156725 \tabularnewline
181 & 917843 & 927061.420531141 & -9218.42053114146 \tabularnewline
182 & 916761 & 925361.477309559 & -8600.47730955889 \tabularnewline
183 & 915087 & 923652.066094895 & -8565.06609489501 \tabularnewline
184 & 938173 & 921608.229585921 & 16564.7704140791 \tabularnewline
185 & 907953 & 934331.055721903 & -26378.0557219028 \tabularnewline
186 & 905374 & 921899.808538615 & -16525.8085386152 \tabularnewline
187 & 921867 & 914305.730973904 & 7561.26902609575 \tabularnewline
188 & 927104 & 920521.603253173 & 6582.39674682729 \tabularnewline
189 & 930989 & 926461.225042508 & 4527.7749574919 \tabularnewline
190 & 936820 & 931436.816594476 & 5383.18340552354 \tabularnewline
191 & 944281 & 937114.395570748 & 7166.60442925233 \tabularnewline
192 & 945322 & 944087.739887775 & 1234.26011222496 \tabularnewline
193 & 944555 & 947787.944775108 & -3232.94477510825 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=227517&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]3[/C][C]342435[/C][C]339329[/C][C]3106[/C][/ROW]
[ROW][C]4[/C][C]354980[/C][C]341421.918267745[/C][C]13558.0817322549[/C][/ROW]
[ROW][C]5[/C][C]339890[/C][C]349932.452485157[/C][C]-10042.452485157[/C][/ROW]
[ROW][C]6[/C][C]339890[/C][C]344803.044936457[/C][C]-4913.04493645683[/C][/ROW]
[ROW][C]7[/C][C]340471[/C][C]342344.689191442[/C][C]-1873.68919144233[/C][/ROW]
[ROW][C]8[/C][C]343833[/C][C]341511.93784803[/C][C]2321.06215197034[/C][/ROW]
[ROW][C]9[/C][C]346109[/C][C]343125.720329679[/C][C]2983.27967032051[/C][/ROW]
[ROW][C]10[/C][C]345455[/C][C]345233.970903853[/C][C]221.029096146638[/C][/ROW]
[ROW][C]11[/C][C]350419[/C][C]345803.535767277[/C][C]4615.46423272329[/C][/ROW]
[ROW][C]12[/C][C]344660[/C][C]349026.428309554[/C][C]-4366.42830955406[/C][/ROW]
[ROW][C]13[/C][C]341499[/C][C]347035.710703258[/C][C]-5536.7107032584[/C][/ROW]
[ROW][C]14[/C][C]342376[/C][C]344160.215775073[/C][C]-1784.21577507275[/C][/ROW]
[ROW][C]15[/C][C]344148[/C][C]343313.633792691[/C][C]834.366207308776[/C][/ROW]
[ROW][C]16[/C][C]359079[/C][C]343968.886009468[/C][C]15110.1139905316[/C][/ROW]
[ROW][C]17[/C][C]344090[/C][C]353248.541661067[/C][C]-9158.54166106705[/C][/ROW]
[ROW][C]18[/C][C]342681[/C][C]348550.433797578[/C][C]-5869.43379757792[/C][/ROW]
[ROW][C]19[/C][C]348552[/C][C]345452.607152191[/C][C]3099.39284780901[/C][/ROW]
[ROW][C]20[/C][C]349867[/C][C]347508.662097681[/C][C]2358.33790231869[/C][/ROW]
[ROW][C]21[/C][C]353247[/C][C]349247.012183752[/C][C]3999.98781624797[/C][/ROW]
[ROW][C]22[/C][C]356048[/C][C]352070.708637227[/C][C]3977.29136277275[/C][/ROW]
[ROW][C]23[/C][C]363887[/C][C]355046.195719376[/C][C]8840.80428062403[/C][/ROW]
[ROW][C]24[/C][C]358905[/C][C]361112.626725313[/C][C]-2207.62672531256[/C][/ROW]
[ROW][C]25[/C][C]359647[/C][C]360896.754435597[/C][C]-1249.75443559728[/C][/ROW]
[ROW][C]26[/C][C]361488[/C][C]361165.933859351[/C][C]322.066140649258[/C][/ROW]
[ROW][C]27[/C][C]363229[/C][C]362329.20468701[/C][C]899.795312989678[/C][/ROW]
[ROW][C]28[/C][C]393301[/C][C]363853.423527418[/C][C]29447.5764725825[/C][/ROW]
[ROW][C]29[/C][C]366190[/C][C]382592.409482539[/C][C]-16402.409482539[/C][/ROW]
[ROW][C]30[/C][C]363811[/C][C]374960.906619835[/C][C]-11149.9066198354[/C][/ROW]
[ROW][C]31[/C][C]366190[/C][C]369811.463190322[/C][C]-3621.46319032187[/C][/ROW]
[ROW][C]32[/C][C]372656[/C][C]368730.794375981[/C][C]3925.20562401932[/C][/ROW]
[ROW][C]33[/C][C]371781[/C][C]372041.257840757[/C][C]-260.257840756793[/C][/ROW]
[ROW][C]34[/C][C]374306[/C][C]372995.630865272[/C][C]1310.36913472775[/C][/ROW]
[ROW][C]35[/C][C]377689[/C][C]374884.304614703[/C][C]2804.69538529683[/C][/ROW]
[ROW][C]36[/C][C]373240[/C][C]377726.332228387[/C][C]-4486.33222838741[/C][/ROW]
[ROW][C]37[/C][C]373456[/C][C]376297.266883816[/C][C]-2841.26688381587[/C][/ROW]
[ROW][C]38[/C][C]372610[/C][C]375672.49399503[/C][C]-3062.4939950296[/C][/ROW]
[ROW][C]39[/C][C]372209[/C][C]374797.085655757[/C][C]-2588.08565575653[/C][/ROW]
[ROW][C]40[/C][C]390212[/C][C]374080.463853989[/C][C]16131.5361460106[/C][/ROW]
[ROW][C]41[/C][C]373113[/C][C]384520.619608962[/C][C]-11407.6196089617[/C][/ROW]
[ROW][C]42[/C][C]370518[/C][C]379057.359881949[/C][C]-8539.35988194891[/C][/ROW]
[ROW][C]43[/C][C]370469[/C][C]374848.125604111[/C][C]-4379.12560411106[/C][/ROW]
[ROW][C]44[/C][C]372493[/C][C]372788.950560721[/C][C]-295.950560721394[/C][/ROW]
[ROW][C]45[/C][C]369536[/C][C]373005.542737671[/C][C]-3469.54273767106[/C][/ROW]
[ROW][C]46[/C][C]368835[/C][C]371300.304508341[/C][C]-2465.30450834124[/C][/ROW]
[ROW][C]47[/C][C]366859[/C][C]370055.82161852[/C][C]-3196.82161852048[/C][/ROW]
[ROW][C]48[/C][C]356044[/C][C]368269.20607488[/C][C]-12225.2060748802[/C][/ROW]
[ROW][C]49[/C][C]346106[/C][C]360917.87412083[/C][C]-14811.8741208303[/C][/ROW]
[ROW][C]50[/C][C]333829[/C][C]351504.453734112[/C][C]-17675.453734112[/C][/ROW]
[ROW][C]51[/C][C]317388[/C][C]339755.334153169[/C][C]-22367.3341531694[/C][/ROW]
[ROW][C]52[/C][C]285871[/C][C]324451.961090514[/C][C]-38580.9610905139[/C][/ROW]
[ROW][C]53[/C][C]339729[/C][C]298467.4930516[/C][C]41261.5069483995[/C][/ROW]
[ROW][C]54[/C][C]308216[/C][C]318929.432168327[/C][C]-10713.4321683269[/C][/ROW]
[ROW][C]55[/C][C]309137[/C][C]309824.070480335[/C][C]-687.070480335096[/C][/ROW]
[ROW][C]56[/C][C]311245[/C][C]306308.564880352[/C][C]4936.43511964829[/C][/ROW]
[ROW][C]57[/C][C]319568[/C][C]306148.37293633[/C][C]13419.6270636703[/C][/ROW]
[ROW][C]58[/C][C]329201[/C][C]311296.802221782[/C][C]17904.1977782181[/C][/ROW]
[ROW][C]59[/C][C]339880[/C][C]319698.714837843[/C][C]20181.2851621573[/C][/ROW]
[ROW][C]60[/C][C]342305[/C][C]330211.331673746[/C][C]12093.6683262535[/C][/ROW]
[ROW][C]61[/C][C]346975[/C][C]336692.26798114[/C][C]10282.7320188603[/C][/ROW]
[ROW][C]62[/C][C]355294[/C][C]342583.759623913[/C][C]12710.2403760868[/C][/ROW]
[ROW][C]63[/C][C]360766[/C][C]350361.226816715[/C][C]10404.7731832851[/C][/ROW]
[ROW][C]64[/C][C]392946[/C][C]357277.18668268[/C][C]35668.8133173204[/C][/ROW]
[ROW][C]65[/C][C]352108[/C][C]379825.19102037[/C][C]-27717.1910203704[/C][/ROW]
[ROW][C]66[/C][C]358071[/C][C]365708.39194584[/C][C]-7637.39194583986[/C][/ROW]
[ROW][C]67[/C][C]365429[/C][C]362527.416544091[/C][C]2901.58345590893[/C][/ROW]
[ROW][C]68[/C][C]378731[/C][C]365371.974257898[/C][C]13359.0257421021[/C][/ROW]
[ROW][C]69[/C][C]384120[/C][C]374628.918362084[/C][C]9491.08163791569[/C][/ROW]
[ROW][C]70[/C][C]391390[/C][C]382111.028670542[/C][C]9278.97132945794[/C][/ROW]
[ROW][C]71[/C][C]403547[/C][C]389858.079409498[/C][C]13688.920590502[/C][/ROW]
[ROW][C]72[/C][C]404124[/C][C]400642.447171272[/C][C]3481.5528287277[/C][/ROW]
[ROW][C]73[/C][C]406439[/C][C]405851.117325066[/C][C]587.882674934401[/C][/ROW]
[ROW][C]74[/C][C]412232[/C][C]409462.634554138[/C][C]2769.36544586159[/C][/ROW]
[ROW][C]75[/C][C]419221[/C][C]414411.09268679[/C][C]4809.90731321037[/C][/ROW]
[ROW][C]76[/C][C]450521[/C][C]420701.916271689[/C][C]29819.0837283107[/C][/ROW]
[ROW][C]77[/C][C]430027[/C][C]442240.015049099[/C][C]-12213.0150490995[/C][/ROW]
[ROW][C]78[/C][C]433442[/C][C]439720.260787032[/C][C]-6278.26078703185[/C][/ROW]
[ROW][C]79[/C][C]439938[/C][C]440266.366580056[/C][C]-328.366580055503[/C][/ROW]
[ROW][C]80[/C][C]450200[/C][C]444132.915426808[/C][C]6067.08457319171[/C][/ROW]
[ROW][C]81[/C][C]459279[/C][C]451834.10372882[/C][C]7444.89627117995[/C][/ROW]
[ROW][C]82[/C][C]465090[/C][C]460615.284766393[/C][C]4474.71523360664[/C][/ROW]
[ROW][C]83[/C][C]478567[/C][C]467917.207022276[/C][C]10649.792977724[/C][/ROW]
[ROW][C]84[/C][C]475726[/C][C]479119.832262293[/C][C]-3393.83226229344[/C][/ROW]
[ROW][C]85[/C][C]480634[/C][C]482312.732456595[/C][C]-1678.7324565954[/C][/ROW]
[ROW][C]86[/C][C]486952[/C][C]486397.253647528[/C][C]554.746352471644[/C][/ROW]
[ROW][C]87[/C][C]491912[/C][C]491756.250735844[/C][C]155.749264155864[/C][/ROW]
[ROW][C]88[/C][C]517281[/C][C]496898.111786098[/C][C]20382.888213902[/C][/ROW]
[ROW][C]89[/C][C]502379[/C][C]514217.332346075[/C][C]-11838.3323460751[/C][/ROW]
[ROW][C]90[/C][C]504942[/C][C]512991.725929302[/C][C]-8049.72592930193[/C][/ROW]
[ROW][C]91[/C][C]516387[/C][C]513556.113718987[/C][C]2830.88628101273[/C][/ROW]
[ROW][C]92[/C][C]523270[/C][C]520334.546734612[/C][C]2935.4532653878[/C][/ROW]
[ROW][C]93[/C][C]528995[/C][C]527292.990010448[/C][C]1702.00998955185[/C][/ROW]
[ROW][C]94[/C][C]540850[/C][C]533630.671470137[/C][C]7219.32852986327[/C][/ROW]
[ROW][C]95[/C][C]550679[/C][C]543358.589597399[/C][C]7320.41040260089[/C][/ROW]
[ROW][C]96[/C][C]544432[/C][C]553445.935552698[/C][C]-9013.93555269798[/C][/ROW]
[ROW][C]97[/C][C]550296[/C][C]554007.491921132[/C][C]-3711.49192113243[/C][/ROW]
[ROW][C]98[/C][C]554659[/C][C]557386.759508199[/C][C]-2727.75950819941[/C][/ROW]
[ROW][C]99[/C][C]558856[/C][C]561204.436339654[/C][C]-2348.43633965391[/C][/ROW]
[ROW][C]100[/C][C]582661[/C][C]565137.531072707[/C][C]17523.4689272934[/C][/ROW]
[ROW][C]101[/C][C]564317[/C][C]580930.658813145[/C][C]-16613.6588131447[/C][/ROW]
[ROW][C]102[/C][C]568569[/C][C]576907.863539268[/C][C]-8338.86353926838[/C][/ROW]
[ROW][C]103[/C][C]574693[/C][C]577176.940396413[/C][C]-2483.94039641297[/C][/ROW]
[ROW][C]104[/C][C]586558[/C][C]580624.084471578[/C][C]5933.91552842234[/C][/ROW]
[ROW][C]105[/C][C]588751[/C][C]589033.614967619[/C][C]-282.614967619185[/C][/ROW]
[ROW][C]106[/C][C]598250[/C][C]593948.021289731[/C][C]4301.97871026944[/C][/ROW]
[ROW][C]107[/C][C]607706[/C][C]601609.344306624[/C][C]6096.65569337609[/C][/ROW]
[ROW][C]108[/C][C]603869[/C][C]610528.484760373[/C][C]-6659.4847603729[/C][/ROW]
[ROW][C]109[/C][C]607696[/C][C]612024.268831183[/C][C]-4328.26883118262[/C][/ROW]
[ROW][C]110[/C][C]613285[/C][C]614647.324711452[/C][C]-1362.32471145201[/C][/ROW]
[ROW][C]111[/C][C]617160[/C][C]618875.999808443[/C][C]-1715.99980844255[/C][/ROW]
[ROW][C]112[/C][C]647083[/C][C]622835.515835497[/C][C]24247.4841645026[/C][/ROW]
[ROW][C]113[/C][C]621246[/C][C]642346.601255671[/C][C]-21100.6012556709[/C][/ROW]
[ROW][C]114[/C][C]623252[/C][C]635574.111516346[/C][C]-12322.1115163458[/C][/ROW]
[ROW][C]115[/C][C]632722[/C][C]633210.984277337[/C][C]-488.984277336509[/C][/ROW]
[ROW][C]116[/C][C]641716[/C][C]637458.327960814[/C][C]4257.67203918635[/C][/ROW]
[ROW][C]117[/C][C]644953[/C][C]644541.567574492[/C][C]411.432425508392[/C][/ROW]
[ROW][C]118[/C][C]652723[/C][C]649486.583361506[/C][C]3236.41663849447[/C][/ROW]
[ROW][C]119[/C][C]660093[/C][C]656148.444427322[/C][C]3944.55557267845[/C][/ROW]
[ROW][C]120[/C][C]657090[/C][C]663370.265926191[/C][C]-6280.26592619147[/C][/ROW]
[ROW][C]121[/C][C]657281[/C][C]664602.841588062[/C][C]-7321.84158806223[/C][/ROW]
[ROW][C]122[/C][C]661949[/C][C]664948.924258252[/C][C]-2999.92425825191[/C][/ROW]
[ROW][C]123[/C][C]665608[/C][C]667592.711788023[/C][C]-1984.71178802312[/C][/ROW]
[ROW][C]124[/C][C]697124[/C][C]670723.282336468[/C][C]26400.7176635325[/C][/ROW]
[ROW][C]125[/C][C]671310[/C][C]690851.622100395[/C][C]-19541.6221003949[/C][/ROW]
[ROW][C]126[/C][C]674708[/C][C]684427.878555198[/C][C]-9719.87855519785[/C][/ROW]
[ROW][C]127[/C][C]681915[/C][C]683105.718555557[/C][C]-1190.71855555731[/C][/ROW]
[ROW][C]128[/C][C]690556[/C][C]686513.625369519[/C][C]4042.37463048089[/C][/ROW]
[ROW][C]129[/C][C]692885[/C][C]693021.098030079[/C][C]-136.09803007869[/C][/ROW]
[ROW][C]130[/C][C]699740[/C][C]697181.5330435[/C][C]2558.46695649973[/C][/ROW]
[ROW][C]131[/C][C]707885[/C][C]702957.691552273[/C][C]4927.30844772665[/C][/ROW]
[ROW][C]132[/C][C]704785[/C][C]710265.034244391[/C][C]-5480.03424439055[/C][/ROW]
[ROW][C]133[/C][C]705363[/C][C]711513.95445222[/C][C]-6150.95445221965[/C][/ROW]
[ROW][C]134[/C][C]749101[/C][C]712132.508754074[/C][C]36968.4912459255[/C][/ROW]
[ROW][C]135[/C][C]752891[/C][C]738442.146439589[/C][C]14448.8535604106[/C][/ROW]
[ROW][C]136[/C][C]784662[/C][C]752730.53162892[/C][C]31931.4683710804[/C][/ROW]
[ROW][C]137[/C][C]761914[/C][C]778136.053420169[/C][C]-16222.0534201692[/C][/ROW]
[ROW][C]138[/C][C]763768[/C][C]775887.759302429[/C][C]-12119.7593024288[/C][/ROW]
[ROW][C]139[/C][C]768877[/C][C]775436.889800298[/C][C]-6559.88980029814[/C][/ROW]
[ROW][C]140[/C][C]781031[/C][C]777830.164839633[/C][C]3200.83516036696[/C][/ROW]
[ROW][C]141[/C][C]783454[/C][C]785825.257773609[/C][C]-2371.25777360902[/C][/ROW]
[ROW][C]142[/C][C]785988[/C][C]790599.9469339[/C][C]-4611.94693389954[/C][/ROW]
[ROW][C]143[/C][C]795068[/C][C]793928.306079021[/C][C]1139.69392097858[/C][/ROW]
[ROW][C]144[/C][C]790001[/C][C]800526.738824207[/C][C]-10525.7388242069[/C][/ROW]
[ROW][C]145[/C][C]789721[/C][C]800153.077694804[/C][C]-10432.0776948037[/C][/ROW]
[ROW][C]146[/C][C]794064[/C][C]799400.408356032[/C][C]-5336.40835603164[/C][/ROW]
[ROW][C]147[/C][C]798690[/C][C]801282.374461578[/C][C]-2592.37446157809[/C][/ROW]
[ROW][C]148[/C][C]829281[/C][C]804594.735048054[/C][C]24686.264951946[/C][/ROW]
[ROW][C]149[/C][C]806249[/C][C]824213.761595818[/C][C]-17964.7615958183[/C][/ROW]
[ROW][C]150[/C][C]807048[/C][C]819190.215199619[/C][C]-12142.2151996188[/C][/ROW]
[ROW][C]151[/C][C]819928[/C][C]816927.108461178[/C][C]3000.89153882163[/C][/ROW]
[ROW][C]152[/C][C]821105[/C][C]823273.568743254[/C][C]-2168.56874325383[/C][/ROW]
[ROW][C]153[/C][C]828422[/C][C]826633.624191619[/C][C]1788.37580838124[/C][/ROW]
[ROW][C]154[/C][C]835360[/C][C]832284.925405621[/C][C]3075.07459437882[/C][/ROW]
[ROW][C]155[/C][C]844092[/C][C]838784.419789845[/C][C]5307.58021015534[/C][/ROW]
[ROW][C]156[/C][C]837469[/C][C]846754.431298115[/C][C]-9285.43129811541[/C][/ROW]
[ROW][C]157[/C][C]836969[/C][C]846163.180883019[/C][C]-9194.18088301935[/C][/ROW]
[ROW][C]158[/C][C]838721[/C][C]845242.773260816[/C][C]-6521.77326081577[/C][/ROW]
[ROW][C]159[/C][C]840537[/C][C]845550.096654822[/C][C]-5013.09665482189[/C][/ROW]
[ROW][C]160[/C][C]863719[/C][C]846495.455884778[/C][C]17223.5441152224[/C][/ROW]
[ROW][C]161[/C][C]845413[/C][C]860613.522865741[/C][C]-15200.5228657412[/C][/ROW]
[ROW][C]162[/C][C]844366[/C][C]855934.031006882[/C][C]-11568.0310068819[/C][/ROW]
[ROW][C]163[/C][C]848357[/C][C]852811.530499262[/C][C]-4454.5304992618[/C][/ROW]
[ROW][C]164[/C][C]858754[/C][C]853490.833918111[/C][C]5263.16608188918[/C][/ROW]
[ROW][C]165[/C][C]862431[/C][C]859833.146329608[/C][C]2597.85367039207[/C][/ROW]
[ROW][C]166[/C][C]871565[/C][C]864789.402496791[/C][C]6775.59750320867[/C][/ROW]
[ROW][C]167[/C][C]880366[/C][C]872366.910668464[/C][C]7999.08933153597[/C][/ROW]
[ROW][C]168[/C][C]874476[/C][C]880960.860906975[/C][C]-6484.86090697476[/C][/ROW]
[ROW][C]169[/C][C]882077[/C][C]881170.498835492[/C][C]906.501164508401[/C][/ROW]
[ROW][C]170[/C][C]889199[/C][C]885559.383311441[/C][C]3639.61668855941[/C][/ROW]
[ROW][C]171[/C][C]892665[/C][C]891630.311566801[/C][C]1034.68843319884[/C][/ROW]
[ROW][C]172[/C][C]913625[/C][C]896284.364268714[/C][C]17340.6357312859[/C][/ROW]
[ROW][C]173[/C][C]893597[/C][C]910792.702057305[/C][C]-17195.7020573046[/C][/ROW]
[ROW][C]174[/C][C]892114[/C][C]905237.344912244[/C][C]-13123.3449122435[/C][/ROW]
[ROW][C]175[/C][C]894801[/C][C]901421.1269169[/C][C]-6620.12691689993[/C][/ROW]
[ROW][C]176[/C][C]898843[/C][C]900975.167538667[/C][C]-2132.1675386671[/C][/ROW]
[ROW][C]177[/C][C]908135[/C][C]902955.846854465[/C][C]5179.15314553503[/C][/ROW]
[ROW][C]178[/C][C]918920[/C][C]909247.64679217[/C][C]9672.35320783011[/C][/ROW]
[ROW][C]179[/C][C]923125[/C][C]918457.280236898[/C][C]4667.71976310224[/C][/ROW]
[ROW][C]180[/C][C]921770[/C][C]925055.631951567[/C][C]-3285.63195156725[/C][/ROW]
[ROW][C]181[/C][C]917843[/C][C]927061.420531141[/C][C]-9218.42053114146[/C][/ROW]
[ROW][C]182[/C][C]916761[/C][C]925361.477309559[/C][C]-8600.47730955889[/C][/ROW]
[ROW][C]183[/C][C]915087[/C][C]923652.066094895[/C][C]-8565.06609489501[/C][/ROW]
[ROW][C]184[/C][C]938173[/C][C]921608.229585921[/C][C]16564.7704140791[/C][/ROW]
[ROW][C]185[/C][C]907953[/C][C]934331.055721903[/C][C]-26378.0557219028[/C][/ROW]
[ROW][C]186[/C][C]905374[/C][C]921899.808538615[/C][C]-16525.8085386152[/C][/ROW]
[ROW][C]187[/C][C]921867[/C][C]914305.730973904[/C][C]7561.26902609575[/C][/ROW]
[ROW][C]188[/C][C]927104[/C][C]920521.603253173[/C][C]6582.39674682729[/C][/ROW]
[ROW][C]189[/C][C]930989[/C][C]926461.225042508[/C][C]4527.7749574919[/C][/ROW]
[ROW][C]190[/C][C]936820[/C][C]931436.816594476[/C][C]5383.18340552354[/C][/ROW]
[ROW][C]191[/C][C]944281[/C][C]937114.395570748[/C][C]7166.60442925233[/C][/ROW]
[ROW][C]192[/C][C]945322[/C][C]944087.739887775[/C][C]1234.26011222496[/C][/ROW]
[ROW][C]193[/C][C]944555[/C][C]947787.944775108[/C][C]-3232.94477510825[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=227517&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=227517&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
33424353393293106
4354980341421.91826774513558.0817322549
5339890349932.452485157-10042.452485157
6339890344803.044936457-4913.04493645683
7340471342344.689191442-1873.68919144233
8343833341511.937848032321.06215197034
9346109343125.7203296792983.27967032051
10345455345233.970903853221.029096146638
11350419345803.5357672774615.46423272329
12344660349026.428309554-4366.42830955406
13341499347035.710703258-5536.7107032584
14342376344160.215775073-1784.21577507275
15344148343313.633792691834.366207308776
16359079343968.88600946815110.1139905316
17344090353248.541661067-9158.54166106705
18342681348550.433797578-5869.43379757792
19348552345452.6071521913099.39284780901
20349867347508.6620976812358.33790231869
21353247349247.0121837523999.98781624797
22356048352070.7086372273977.29136277275
23363887355046.1957193768840.80428062403
24358905361112.626725313-2207.62672531256
25359647360896.754435597-1249.75443559728
26361488361165.933859351322.066140649258
27363229362329.20468701899.795312989678
28393301363853.42352741829447.5764725825
29366190382592.409482539-16402.409482539
30363811374960.906619835-11149.9066198354
31366190369811.463190322-3621.46319032187
32372656368730.7943759813925.20562401932
33371781372041.257840757-260.257840756793
34374306372995.6308652721310.36913472775
35377689374884.3046147032804.69538529683
36373240377726.332228387-4486.33222838741
37373456376297.266883816-2841.26688381587
38372610375672.49399503-3062.4939950296
39372209374797.085655757-2588.08565575653
40390212374080.46385398916131.5361460106
41373113384520.619608962-11407.6196089617
42370518379057.359881949-8539.35988194891
43370469374848.125604111-4379.12560411106
44372493372788.950560721-295.950560721394
45369536373005.542737671-3469.54273767106
46368835371300.304508341-2465.30450834124
47366859370055.82161852-3196.82161852048
48356044368269.20607488-12225.2060748802
49346106360917.87412083-14811.8741208303
50333829351504.453734112-17675.453734112
51317388339755.334153169-22367.3341531694
52285871324451.961090514-38580.9610905139
53339729298467.493051641261.5069483995
54308216318929.432168327-10713.4321683269
55309137309824.070480335-687.070480335096
56311245306308.5648803524936.43511964829
57319568306148.3729363313419.6270636703
58329201311296.80222178217904.1977782181
59339880319698.71483784320181.2851621573
60342305330211.33167374612093.6683262535
61346975336692.2679811410282.7320188603
62355294342583.75962391312710.2403760868
63360766350361.22681671510404.7731832851
64392946357277.1866826835668.8133173204
65352108379825.19102037-27717.1910203704
66358071365708.39194584-7637.39194583986
67365429362527.4165440912901.58345590893
68378731365371.97425789813359.0257421021
69384120374628.9183620849491.08163791569
70391390382111.0286705429278.97132945794
71403547389858.07940949813688.920590502
72404124400642.4471712723481.5528287277
73406439405851.117325066587.882674934401
74412232409462.6345541382769.36544586159
75419221414411.092686794809.90731321037
76450521420701.91627168929819.0837283107
77430027442240.015049099-12213.0150490995
78433442439720.260787032-6278.26078703185
79439938440266.366580056-328.366580055503
80450200444132.9154268086067.08457319171
81459279451834.103728827444.89627117995
82465090460615.2847663934474.71523360664
83478567467917.20702227610649.792977724
84475726479119.832262293-3393.83226229344
85480634482312.732456595-1678.7324565954
86486952486397.253647528554.746352471644
87491912491756.250735844155.749264155864
88517281496898.11178609820382.888213902
89502379514217.332346075-11838.3323460751
90504942512991.725929302-8049.72592930193
91516387513556.1137189872830.88628101273
92523270520334.5467346122935.4532653878
93528995527292.9900104481702.00998955185
94540850533630.6714701377219.32852986327
95550679543358.5895973997320.41040260089
96544432553445.935552698-9013.93555269798
97550296554007.491921132-3711.49192113243
98554659557386.759508199-2727.75950819941
99558856561204.436339654-2348.43633965391
100582661565137.53107270717523.4689272934
101564317580930.658813145-16613.6588131447
102568569576907.863539268-8338.86353926838
103574693577176.940396413-2483.94039641297
104586558580624.0844715785933.91552842234
105588751589033.614967619-282.614967619185
106598250593948.0212897314301.97871026944
107607706601609.3443066246096.65569337609
108603869610528.484760373-6659.4847603729
109607696612024.268831183-4328.26883118262
110613285614647.324711452-1362.32471145201
111617160618875.999808443-1715.99980844255
112647083622835.51583549724247.4841645026
113621246642346.601255671-21100.6012556709
114623252635574.111516346-12322.1115163458
115632722633210.984277337-488.984277336509
116641716637458.3279608144257.67203918635
117644953644541.567574492411.432425508392
118652723649486.5833615063236.41663849447
119660093656148.4444273223944.55557267845
120657090663370.265926191-6280.26592619147
121657281664602.841588062-7321.84158806223
122661949664948.924258252-2999.92425825191
123665608667592.711788023-1984.71178802312
124697124670723.28233646826400.7176635325
125671310690851.622100395-19541.6221003949
126674708684427.878555198-9719.87855519785
127681915683105.718555557-1190.71855555731
128690556686513.6253695194042.37463048089
129692885693021.098030079-136.09803007869
130699740697181.53304352558.46695649973
131707885702957.6915522734927.30844772665
132704785710265.034244391-5480.03424439055
133705363711513.95445222-6150.95445221965
134749101712132.50875407436968.4912459255
135752891738442.14643958914448.8535604106
136784662752730.5316289231931.4683710804
137761914778136.053420169-16222.0534201692
138763768775887.759302429-12119.7593024288
139768877775436.889800298-6559.88980029814
140781031777830.1648396333200.83516036696
141783454785825.257773609-2371.25777360902
142785988790599.9469339-4611.94693389954
143795068793928.3060790211139.69392097858
144790001800526.738824207-10525.7388242069
145789721800153.077694804-10432.0776948037
146794064799400.408356032-5336.40835603164
147798690801282.374461578-2592.37446157809
148829281804594.73504805424686.264951946
149806249824213.761595818-17964.7615958183
150807048819190.215199619-12142.2151996188
151819928816927.1084611783000.89153882163
152821105823273.568743254-2168.56874325383
153828422826633.6241916191788.37580838124
154835360832284.9254056213075.07459437882
155844092838784.4197898455307.58021015534
156837469846754.431298115-9285.43129811541
157836969846163.180883019-9194.18088301935
158838721845242.773260816-6521.77326081577
159840537845550.096654822-5013.09665482189
160863719846495.45588477817223.5441152224
161845413860613.522865741-15200.5228657412
162844366855934.031006882-11568.0310068819
163848357852811.530499262-4454.5304992618
164858754853490.8339181115263.16608188918
165862431859833.1463296082597.85367039207
166871565864789.4024967916775.59750320867
167880366872366.9106684647999.08933153597
168874476880960.860906975-6484.86090697476
169882077881170.498835492906.501164508401
170889199885559.3833114413639.61668855941
171892665891630.3115668011034.68843319884
172913625896284.36426871417340.6357312859
173893597910792.702057305-17195.7020573046
174892114905237.344912244-13123.3449122435
175894801901421.1269169-6620.12691689993
176898843900975.167538667-2132.1675386671
177908135902955.8468544655179.15314553503
178918920909247.646792179672.35320783011
179923125918457.2802368984667.71976310224
180921770925055.631951567-3285.63195156725
181917843927061.420531141-9218.42053114146
182916761925361.477309559-8600.47730955889
183915087923652.066094895-8565.06609489501
184938173921608.22958592116564.7704140791
185907953934331.055721903-26378.0557219028
186905374921899.808538615-16525.8085386152
187921867914305.7309739047561.26902609575
188927104920521.6032531736582.39674682729
189930989926461.2250425084527.7749574919
190936820931436.8165944765383.18340552354
191944281937114.3955707487166.60442925233
192945322944087.7398877751234.26011222496
193944555947787.944775108-3232.94477510825







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
194948851.229156469926266.743487383971435.714825555
195951726.09507845925368.368548994978083.821607905
196954600.96100043924506.745332807984695.176668054
197957475.826922411923643.882995578991307.770849245
198960350.692844392922756.932486505997944.453202279
199963225.558766373921831.3778834191004619.73964933
200966100.424688353920857.6590829061011343.1902938
201968975.290610334919829.3351896661018121.246031
202971850.156532315918742.0147355911024958.29832904
203974725.022454295917592.698480131031857.34642846
204977599.888376276916379.3581812321038820.41857132
205980474.754298257915100.6571380781045848.85145844

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
194 & 948851.229156469 & 926266.743487383 & 971435.714825555 \tabularnewline
195 & 951726.09507845 & 925368.368548994 & 978083.821607905 \tabularnewline
196 & 954600.96100043 & 924506.745332807 & 984695.176668054 \tabularnewline
197 & 957475.826922411 & 923643.882995578 & 991307.770849245 \tabularnewline
198 & 960350.692844392 & 922756.932486505 & 997944.453202279 \tabularnewline
199 & 963225.558766373 & 921831.377883419 & 1004619.73964933 \tabularnewline
200 & 966100.424688353 & 920857.659082906 & 1011343.1902938 \tabularnewline
201 & 968975.290610334 & 919829.335189666 & 1018121.246031 \tabularnewline
202 & 971850.156532315 & 918742.014735591 & 1024958.29832904 \tabularnewline
203 & 974725.022454295 & 917592.69848013 & 1031857.34642846 \tabularnewline
204 & 977599.888376276 & 916379.358181232 & 1038820.41857132 \tabularnewline
205 & 980474.754298257 & 915100.657138078 & 1045848.85145844 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=227517&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]948851.229156469[/C][C]926266.743487383[/C][C]971435.714825555[/C][/ROW]
[ROW][C]195[/C][C]951726.09507845[/C][C]925368.368548994[/C][C]978083.821607905[/C][/ROW]
[ROW][C]196[/C][C]954600.96100043[/C][C]924506.745332807[/C][C]984695.176668054[/C][/ROW]
[ROW][C]197[/C][C]957475.826922411[/C][C]923643.882995578[/C][C]991307.770849245[/C][/ROW]
[ROW][C]198[/C][C]960350.692844392[/C][C]922756.932486505[/C][C]997944.453202279[/C][/ROW]
[ROW][C]199[/C][C]963225.558766373[/C][C]921831.377883419[/C][C]1004619.73964933[/C][/ROW]
[ROW][C]200[/C][C]966100.424688353[/C][C]920857.659082906[/C][C]1011343.1902938[/C][/ROW]
[ROW][C]201[/C][C]968975.290610334[/C][C]919829.335189666[/C][C]1018121.246031[/C][/ROW]
[ROW][C]202[/C][C]971850.156532315[/C][C]918742.014735591[/C][C]1024958.29832904[/C][/ROW]
[ROW][C]203[/C][C]974725.022454295[/C][C]917592.69848013[/C][C]1031857.34642846[/C][/ROW]
[ROW][C]204[/C][C]977599.888376276[/C][C]916379.358181232[/C][C]1038820.41857132[/C][/ROW]
[ROW][C]205[/C][C]980474.754298257[/C][C]915100.657138078[/C][C]1045848.85145844[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=227517&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=227517&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
194948851.229156469926266.743487383971435.714825555
195951726.09507845925368.368548994978083.821607905
196954600.96100043924506.745332807984695.176668054
197957475.826922411923643.882995578991307.770849245
198960350.692844392922756.932486505997944.453202279
199963225.558766373921831.3778834191004619.73964933
200966100.424688353920857.6590829061011343.1902938
201968975.290610334919829.3351896661018121.246031
202971850.156532315918742.0147355911024958.29832904
203974725.022454295917592.698480131031857.34642846
204977599.888376276916379.3581812321038820.41857132
205980474.754298257915100.6571380781045848.85145844



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')