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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 07:04:23 -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/t13851219061mshso0q055g2qp.htm/, Retrieved Mon, 29 Apr 2024 17:27:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=227514, Retrieved Mon, 29 Apr 2024 17:27:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact70
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [WS8O3] [2013-11-22 12:04:23] [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'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=227514&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=227514&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=227514&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.790057878929683
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.790057878929683 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=227514&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]0.790057878929683[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=227514&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=227514&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
alpha0.790057878929683
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2339105338881224
3342435339057.972964883377.02703511977
4354980341726.01978133513253.9802186649
5339890352197.431280269-12307.4312802695
6339890342473.848227907-2583.84822790691
7340471340432.45857749138.5414225094137
8343833340462.9085320093370.09146799071
9346109343125.4758490092983.52415099094
10345455345482.632611476-27.632611476467
11350419345460.8012490644958.1987509359
12344660349378.06523754-4718.06523754034
13341499345650.520623317-4151.52062331734
14342376342370.5790453265.42095467360923
15344148342374.8619132781773.13808672241
16359079343775.74362912315303.2563708771
17344090355866.201898215-11776.2018982152
18342681346562.320804664-3881.32080466358
19348552343495.8527222855056.14727771457
20349867347490.5017160732376.49828392733
21353247349368.0729095523878.92709044769
22356048352432.6498191543615.35018084571
23363887355288.9857146218598.01428537868
24358905362081.914643935-3176.9146439347
25359647359571.96819880775.0318011930212
26361488359631.247664511856.75233549019
27363229361098.1894763852130.8105236151
28393301362781.65311907330519.3468809267
29366190386893.703582137-20703.7035821375
30363811370536.579444045-6725.57944404508
31366190365222.98241391967.017586090253
32372656365986.9822768646669.01772313606
33371781371255.892273749525.107726250717
34374306371670.7577701612635.2422298395
35377689373752.7516567333936.2483432666
36373240376862.615673755-3622.61567375506
37373456374000.539618371-544.539618370705
38372610373570.321802488-960.321802487539
39372209372811.611996124-602.611996124324
40390212372335.51364064917876.4863593513
41373113386458.972536433-13345.9725364332
42370518375914.881782045-5396.88178204501
43370469371651.032808488-1182.03280848829
44372493370717.1584749891775.84152501129
45369536372120.176063554-2584.17606355436
46368835370078.527404002-1243.52740400174
47366859369096.068780805-2237.06878080522
48356044367328.654964822-11284.6549648225
49346106358413.124398861-12307.1243988615
50333829348689.783800573-14860.7838005732
51317388336948.90447186-19560.9044718597
52285871321494.657774876-35623.6577748761
53339729293349.90627354146379.0937264594
54308216329992.074689748-21776.0746897481
55309137312787.715308951-3650.71530895133
56311245309903.4389153851341.56108461489
57319568310963.3498203518604.65017964947
58329201317761.52149021611439.4785097837
59339880326799.37161771813080.6283822823
60342305337133.8251324915171.17486750893
61346975341219.352579895755.64742011036
62355294345766.6471724899527.35282751085
63360766353293.8073392077472.19266079291
64392946359197.27202374733748.7279762529
65352108385860.72046524-33752.7204652403
66358071359194.117726366-1123.11772636604
67365429358306.7897176857122.21028231503
68378731363933.74806662214797.2519333781
69384120375624.4335430958495.56645690522
70391390382336.4227583439053.57724165655
71403547389489.27279061314057.7272093873
72404124400595.6909322333528.30906776671
73406439403383.2593105213055.74068947858
74412232405797.471318216434.52868178999
75419221410881.1214004578339.87859954278
76450521417470.10819734333050.8918026569
77430027443582.225671685-13555.2256716847
78433442432872.8128291569.187170899706
79439938433322.5036380556615.49636194471
80450200438549.1286618411650.8713381597
81459279447753.99135894911525.0086410506
82465090456859.4152405448230.58475945587
83478567463362.05357795115204.9464220492
84475726475374.841297394351.15870260552
85480634475652.2769971434981.7230028573
86486952479588.1265061957363.87349380465
87491912485406.0127794176505.98722058284
88517281490546.11924325426734.8807567455
89502379511668.222427367-9289.22242736683
90504942504329.199059495612.800940504647
91516387504813.34727075711573.6527292434
92523270513957.2027974919312.79720250866
93528995521314.8516022087680.14839779236
94540850527382.61335523313467.3866447674
95550679538022.62828252312656.3717174765
96544432548021.894476579-3589.89447657857
97550296545185.6700608315110.32993916853
98554659549223.1264932025435.87350679818
99558856553517.7811861135338.2188138871
100582661557735.28301947524925.7169805249
101564317577428.04210791-13111.0421079102
102568569567069.5599895771499.44001042307
103574693568254.2043837946438.7956162059
104586558573341.22559119613216.7744088045
105588751583783.2423469084967.75765309227
106598250587708.05842134610541.9415786535
107607706596036.80242477811669.1975752219
108603869605256.143909869-1387.14390986937
109607696604160.2199346683535.78006533231
110613285606953.6908334466331.30916655401
111617160611955.7915244225204.20847557834
112647083616067.41743414531015.582565855
113621246640571.522809893-19325.5228098929
114623252625303.241249502-2051.24124950171
115632722623682.6419387479039.35806125263
116641716630824.25799550710891.7420044935
117644953639429.3645814265523.63541857398
118652723643793.3562642058929.64373579458
119660093650848.2916537059244.70834629494
120657090658152.146321102-1062.14632110239
121657281657312.989251539-31.9892515392276
122661949657287.715891324661.28410868044
123665608660970.4001273124637.59987268772
124697124664634.37244605232489.6275539475
125671310690303.05867854-18993.0586785396
126674708675297.443024586-589.443024585606
127681915674831.7489188327083.25108116842
128690556680427.92724394610128.0727560541
129692885688429.6909232394455.30907676055
130699740691949.6429624017790.35703759897
131707885698104.4759196319780.52408036857
132704785705831.656029388-1046.65602938808
133705363705004.737186841358.262813159265
134749101705287.78554510543813.2144548952
135752891739902.76082643112988.2391735694
136784662750164.22151893234497.7784810677
137761914777419.463213471-15505.4632134706
138763768765169.249835214-1401.24983521376
139768877764062.1813625544814.8186374458
140781031767866.16676268613164.8332373142
141783454778267.1469866215186.8530133788
142785988782365.0610766913622.93892330874
143795068785227.3925179329840.60748206766
144790001793002.041992594-3001.04199259426
145789721790631.045121346-910.045121346368
146794064789912.0568030454151.9431969549
147798690793192.3322386685497.66776133224
148829281797535.80796924631745.1920307539
149806249822616.347051279-16367.347051279
150807048809685.19555624-2637.19555623957
151819928807601.65842875412326.3415712458
152821105817340.1817054953764.81829450454
153828422820314.6060618078107.39393819263
154835360826719.9165202638640.08347973682
155844092833546.08254803910545.9174519605
156837469841877.967721503-4408.967721503
157836969838394.628035183-1425.62803518295
158838721837268.2993735641452.70062643639
159840537838416.0169492062120.98305079422
160863719840091.71631956223627.2836804379
161845413858758.637948999-13345.6379489987
162844366848214.811538049-3848.81153804925
163848357845174.0276578983182.97234210197
164858754847688.76003519111065.239964809
165862431856430.9400516366000.05994836404
166871565861171.33468789110393.6653121086
167880366869382.93185868110983.0681413191
168874476878060.191378552-3584.19137855165
169882077875228.4727403356848.52725966496
170889199880639.2056608988559.79433910199
171892665887401.9386205235263.0613794768
172913625891560.06173066922064.9382693307
173893597908992.640058451-15395.6400584511
174892114896829.193329106-4715.19332910632
175894801893103.9176887691697.08231123083
176898843894444.7109399494398.28906005074
177908135897919.61386565310215.3861343474
178918920905990.36016740312929.6398325972
179923125916205.5239888696919.47601113073
180921770921672.31052952897.6894704719307
181917843921749.490865363-3906.49086536292
182916761918663.136978216-1902.13697821612
183915087917160.338671773-2073.33867177297
184938173915522.28111844922650.7188815508
185907953933417.66003424-25464.6600342398
186905374913299.104739923-7925.1047399228
187921867907037.81329880414829.1867011961
188927104918753.7290902038350.27090979682
189930989925350.9264136855638.07358631457
190936820929805.3308725397014.66912746138
191944281935347.3254847748933.67451522569
192945322942405.4454233222916.55457667832
193944555944709.692345955-154.692345954827

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 339105 & 338881 & 224 \tabularnewline
3 & 342435 & 339057.97296488 & 3377.02703511977 \tabularnewline
4 & 354980 & 341726.019781335 & 13253.9802186649 \tabularnewline
5 & 339890 & 352197.431280269 & -12307.4312802695 \tabularnewline
6 & 339890 & 342473.848227907 & -2583.84822790691 \tabularnewline
7 & 340471 & 340432.458577491 & 38.5414225094137 \tabularnewline
8 & 343833 & 340462.908532009 & 3370.09146799071 \tabularnewline
9 & 346109 & 343125.475849009 & 2983.52415099094 \tabularnewline
10 & 345455 & 345482.632611476 & -27.632611476467 \tabularnewline
11 & 350419 & 345460.801249064 & 4958.1987509359 \tabularnewline
12 & 344660 & 349378.06523754 & -4718.06523754034 \tabularnewline
13 & 341499 & 345650.520623317 & -4151.52062331734 \tabularnewline
14 & 342376 & 342370.579045326 & 5.42095467360923 \tabularnewline
15 & 344148 & 342374.861913278 & 1773.13808672241 \tabularnewline
16 & 359079 & 343775.743629123 & 15303.2563708771 \tabularnewline
17 & 344090 & 355866.201898215 & -11776.2018982152 \tabularnewline
18 & 342681 & 346562.320804664 & -3881.32080466358 \tabularnewline
19 & 348552 & 343495.852722285 & 5056.14727771457 \tabularnewline
20 & 349867 & 347490.501716073 & 2376.49828392733 \tabularnewline
21 & 353247 & 349368.072909552 & 3878.92709044769 \tabularnewline
22 & 356048 & 352432.649819154 & 3615.35018084571 \tabularnewline
23 & 363887 & 355288.985714621 & 8598.01428537868 \tabularnewline
24 & 358905 & 362081.914643935 & -3176.9146439347 \tabularnewline
25 & 359647 & 359571.968198807 & 75.0318011930212 \tabularnewline
26 & 361488 & 359631.24766451 & 1856.75233549019 \tabularnewline
27 & 363229 & 361098.189476385 & 2130.8105236151 \tabularnewline
28 & 393301 & 362781.653119073 & 30519.3468809267 \tabularnewline
29 & 366190 & 386893.703582137 & -20703.7035821375 \tabularnewline
30 & 363811 & 370536.579444045 & -6725.57944404508 \tabularnewline
31 & 366190 & 365222.98241391 & 967.017586090253 \tabularnewline
32 & 372656 & 365986.982276864 & 6669.01772313606 \tabularnewline
33 & 371781 & 371255.892273749 & 525.107726250717 \tabularnewline
34 & 374306 & 371670.757770161 & 2635.2422298395 \tabularnewline
35 & 377689 & 373752.751656733 & 3936.2483432666 \tabularnewline
36 & 373240 & 376862.615673755 & -3622.61567375506 \tabularnewline
37 & 373456 & 374000.539618371 & -544.539618370705 \tabularnewline
38 & 372610 & 373570.321802488 & -960.321802487539 \tabularnewline
39 & 372209 & 372811.611996124 & -602.611996124324 \tabularnewline
40 & 390212 & 372335.513640649 & 17876.4863593513 \tabularnewline
41 & 373113 & 386458.972536433 & -13345.9725364332 \tabularnewline
42 & 370518 & 375914.881782045 & -5396.88178204501 \tabularnewline
43 & 370469 & 371651.032808488 & -1182.03280848829 \tabularnewline
44 & 372493 & 370717.158474989 & 1775.84152501129 \tabularnewline
45 & 369536 & 372120.176063554 & -2584.17606355436 \tabularnewline
46 & 368835 & 370078.527404002 & -1243.52740400174 \tabularnewline
47 & 366859 & 369096.068780805 & -2237.06878080522 \tabularnewline
48 & 356044 & 367328.654964822 & -11284.6549648225 \tabularnewline
49 & 346106 & 358413.124398861 & -12307.1243988615 \tabularnewline
50 & 333829 & 348689.783800573 & -14860.7838005732 \tabularnewline
51 & 317388 & 336948.90447186 & -19560.9044718597 \tabularnewline
52 & 285871 & 321494.657774876 & -35623.6577748761 \tabularnewline
53 & 339729 & 293349.906273541 & 46379.0937264594 \tabularnewline
54 & 308216 & 329992.074689748 & -21776.0746897481 \tabularnewline
55 & 309137 & 312787.715308951 & -3650.71530895133 \tabularnewline
56 & 311245 & 309903.438915385 & 1341.56108461489 \tabularnewline
57 & 319568 & 310963.349820351 & 8604.65017964947 \tabularnewline
58 & 329201 & 317761.521490216 & 11439.4785097837 \tabularnewline
59 & 339880 & 326799.371617718 & 13080.6283822823 \tabularnewline
60 & 342305 & 337133.825132491 & 5171.17486750893 \tabularnewline
61 & 346975 & 341219.35257989 & 5755.64742011036 \tabularnewline
62 & 355294 & 345766.647172489 & 9527.35282751085 \tabularnewline
63 & 360766 & 353293.807339207 & 7472.19266079291 \tabularnewline
64 & 392946 & 359197.272023747 & 33748.7279762529 \tabularnewline
65 & 352108 & 385860.72046524 & -33752.7204652403 \tabularnewline
66 & 358071 & 359194.117726366 & -1123.11772636604 \tabularnewline
67 & 365429 & 358306.789717685 & 7122.21028231503 \tabularnewline
68 & 378731 & 363933.748066622 & 14797.2519333781 \tabularnewline
69 & 384120 & 375624.433543095 & 8495.56645690522 \tabularnewline
70 & 391390 & 382336.422758343 & 9053.57724165655 \tabularnewline
71 & 403547 & 389489.272790613 & 14057.7272093873 \tabularnewline
72 & 404124 & 400595.690932233 & 3528.30906776671 \tabularnewline
73 & 406439 & 403383.259310521 & 3055.74068947858 \tabularnewline
74 & 412232 & 405797.47131821 & 6434.52868178999 \tabularnewline
75 & 419221 & 410881.121400457 & 8339.87859954278 \tabularnewline
76 & 450521 & 417470.108197343 & 33050.8918026569 \tabularnewline
77 & 430027 & 443582.225671685 & -13555.2256716847 \tabularnewline
78 & 433442 & 432872.8128291 & 569.187170899706 \tabularnewline
79 & 439938 & 433322.503638055 & 6615.49636194471 \tabularnewline
80 & 450200 & 438549.12866184 & 11650.8713381597 \tabularnewline
81 & 459279 & 447753.991358949 & 11525.0086410506 \tabularnewline
82 & 465090 & 456859.415240544 & 8230.58475945587 \tabularnewline
83 & 478567 & 463362.053577951 & 15204.9464220492 \tabularnewline
84 & 475726 & 475374.841297394 & 351.15870260552 \tabularnewline
85 & 480634 & 475652.276997143 & 4981.7230028573 \tabularnewline
86 & 486952 & 479588.126506195 & 7363.87349380465 \tabularnewline
87 & 491912 & 485406.012779417 & 6505.98722058284 \tabularnewline
88 & 517281 & 490546.119243254 & 26734.8807567455 \tabularnewline
89 & 502379 & 511668.222427367 & -9289.22242736683 \tabularnewline
90 & 504942 & 504329.199059495 & 612.800940504647 \tabularnewline
91 & 516387 & 504813.347270757 & 11573.6527292434 \tabularnewline
92 & 523270 & 513957.202797491 & 9312.79720250866 \tabularnewline
93 & 528995 & 521314.851602208 & 7680.14839779236 \tabularnewline
94 & 540850 & 527382.613355233 & 13467.3866447674 \tabularnewline
95 & 550679 & 538022.628282523 & 12656.3717174765 \tabularnewline
96 & 544432 & 548021.894476579 & -3589.89447657857 \tabularnewline
97 & 550296 & 545185.670060831 & 5110.32993916853 \tabularnewline
98 & 554659 & 549223.126493202 & 5435.87350679818 \tabularnewline
99 & 558856 & 553517.781186113 & 5338.2188138871 \tabularnewline
100 & 582661 & 557735.283019475 & 24925.7169805249 \tabularnewline
101 & 564317 & 577428.04210791 & -13111.0421079102 \tabularnewline
102 & 568569 & 567069.559989577 & 1499.44001042307 \tabularnewline
103 & 574693 & 568254.204383794 & 6438.7956162059 \tabularnewline
104 & 586558 & 573341.225591196 & 13216.7744088045 \tabularnewline
105 & 588751 & 583783.242346908 & 4967.75765309227 \tabularnewline
106 & 598250 & 587708.058421346 & 10541.9415786535 \tabularnewline
107 & 607706 & 596036.802424778 & 11669.1975752219 \tabularnewline
108 & 603869 & 605256.143909869 & -1387.14390986937 \tabularnewline
109 & 607696 & 604160.219934668 & 3535.78006533231 \tabularnewline
110 & 613285 & 606953.690833446 & 6331.30916655401 \tabularnewline
111 & 617160 & 611955.791524422 & 5204.20847557834 \tabularnewline
112 & 647083 & 616067.417434145 & 31015.582565855 \tabularnewline
113 & 621246 & 640571.522809893 & -19325.5228098929 \tabularnewline
114 & 623252 & 625303.241249502 & -2051.24124950171 \tabularnewline
115 & 632722 & 623682.641938747 & 9039.35806125263 \tabularnewline
116 & 641716 & 630824.257995507 & 10891.7420044935 \tabularnewline
117 & 644953 & 639429.364581426 & 5523.63541857398 \tabularnewline
118 & 652723 & 643793.356264205 & 8929.64373579458 \tabularnewline
119 & 660093 & 650848.291653705 & 9244.70834629494 \tabularnewline
120 & 657090 & 658152.146321102 & -1062.14632110239 \tabularnewline
121 & 657281 & 657312.989251539 & -31.9892515392276 \tabularnewline
122 & 661949 & 657287.71589132 & 4661.28410868044 \tabularnewline
123 & 665608 & 660970.400127312 & 4637.59987268772 \tabularnewline
124 & 697124 & 664634.372446052 & 32489.6275539475 \tabularnewline
125 & 671310 & 690303.05867854 & -18993.0586785396 \tabularnewline
126 & 674708 & 675297.443024586 & -589.443024585606 \tabularnewline
127 & 681915 & 674831.748918832 & 7083.25108116842 \tabularnewline
128 & 690556 & 680427.927243946 & 10128.0727560541 \tabularnewline
129 & 692885 & 688429.690923239 & 4455.30907676055 \tabularnewline
130 & 699740 & 691949.642962401 & 7790.35703759897 \tabularnewline
131 & 707885 & 698104.475919631 & 9780.52408036857 \tabularnewline
132 & 704785 & 705831.656029388 & -1046.65602938808 \tabularnewline
133 & 705363 & 705004.737186841 & 358.262813159265 \tabularnewline
134 & 749101 & 705287.785545105 & 43813.2144548952 \tabularnewline
135 & 752891 & 739902.760826431 & 12988.2391735694 \tabularnewline
136 & 784662 & 750164.221518932 & 34497.7784810677 \tabularnewline
137 & 761914 & 777419.463213471 & -15505.4632134706 \tabularnewline
138 & 763768 & 765169.249835214 & -1401.24983521376 \tabularnewline
139 & 768877 & 764062.181362554 & 4814.8186374458 \tabularnewline
140 & 781031 & 767866.166762686 & 13164.8332373142 \tabularnewline
141 & 783454 & 778267.146986621 & 5186.8530133788 \tabularnewline
142 & 785988 & 782365.061076691 & 3622.93892330874 \tabularnewline
143 & 795068 & 785227.392517932 & 9840.60748206766 \tabularnewline
144 & 790001 & 793002.041992594 & -3001.04199259426 \tabularnewline
145 & 789721 & 790631.045121346 & -910.045121346368 \tabularnewline
146 & 794064 & 789912.056803045 & 4151.9431969549 \tabularnewline
147 & 798690 & 793192.332238668 & 5497.66776133224 \tabularnewline
148 & 829281 & 797535.807969246 & 31745.1920307539 \tabularnewline
149 & 806249 & 822616.347051279 & -16367.347051279 \tabularnewline
150 & 807048 & 809685.19555624 & -2637.19555623957 \tabularnewline
151 & 819928 & 807601.658428754 & 12326.3415712458 \tabularnewline
152 & 821105 & 817340.181705495 & 3764.81829450454 \tabularnewline
153 & 828422 & 820314.606061807 & 8107.39393819263 \tabularnewline
154 & 835360 & 826719.916520263 & 8640.08347973682 \tabularnewline
155 & 844092 & 833546.082548039 & 10545.9174519605 \tabularnewline
156 & 837469 & 841877.967721503 & -4408.967721503 \tabularnewline
157 & 836969 & 838394.628035183 & -1425.62803518295 \tabularnewline
158 & 838721 & 837268.299373564 & 1452.70062643639 \tabularnewline
159 & 840537 & 838416.016949206 & 2120.98305079422 \tabularnewline
160 & 863719 & 840091.716319562 & 23627.2836804379 \tabularnewline
161 & 845413 & 858758.637948999 & -13345.6379489987 \tabularnewline
162 & 844366 & 848214.811538049 & -3848.81153804925 \tabularnewline
163 & 848357 & 845174.027657898 & 3182.97234210197 \tabularnewline
164 & 858754 & 847688.760035191 & 11065.239964809 \tabularnewline
165 & 862431 & 856430.940051636 & 6000.05994836404 \tabularnewline
166 & 871565 & 861171.334687891 & 10393.6653121086 \tabularnewline
167 & 880366 & 869382.931858681 & 10983.0681413191 \tabularnewline
168 & 874476 & 878060.191378552 & -3584.19137855165 \tabularnewline
169 & 882077 & 875228.472740335 & 6848.52725966496 \tabularnewline
170 & 889199 & 880639.205660898 & 8559.79433910199 \tabularnewline
171 & 892665 & 887401.938620523 & 5263.0613794768 \tabularnewline
172 & 913625 & 891560.061730669 & 22064.9382693307 \tabularnewline
173 & 893597 & 908992.640058451 & -15395.6400584511 \tabularnewline
174 & 892114 & 896829.193329106 & -4715.19332910632 \tabularnewline
175 & 894801 & 893103.917688769 & 1697.08231123083 \tabularnewline
176 & 898843 & 894444.710939949 & 4398.28906005074 \tabularnewline
177 & 908135 & 897919.613865653 & 10215.3861343474 \tabularnewline
178 & 918920 & 905990.360167403 & 12929.6398325972 \tabularnewline
179 & 923125 & 916205.523988869 & 6919.47601113073 \tabularnewline
180 & 921770 & 921672.310529528 & 97.6894704719307 \tabularnewline
181 & 917843 & 921749.490865363 & -3906.49086536292 \tabularnewline
182 & 916761 & 918663.136978216 & -1902.13697821612 \tabularnewline
183 & 915087 & 917160.338671773 & -2073.33867177297 \tabularnewline
184 & 938173 & 915522.281118449 & 22650.7188815508 \tabularnewline
185 & 907953 & 933417.66003424 & -25464.6600342398 \tabularnewline
186 & 905374 & 913299.104739923 & -7925.1047399228 \tabularnewline
187 & 921867 & 907037.813298804 & 14829.1867011961 \tabularnewline
188 & 927104 & 918753.729090203 & 8350.27090979682 \tabularnewline
189 & 930989 & 925350.926413685 & 5638.07358631457 \tabularnewline
190 & 936820 & 929805.330872539 & 7014.66912746138 \tabularnewline
191 & 944281 & 935347.325484774 & 8933.67451522569 \tabularnewline
192 & 945322 & 942405.445423322 & 2916.55457667832 \tabularnewline
193 & 944555 & 944709.692345955 & -154.692345954827 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=227514&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]2[/C][C]339105[/C][C]338881[/C][C]224[/C][/ROW]
[ROW][C]3[/C][C]342435[/C][C]339057.97296488[/C][C]3377.02703511977[/C][/ROW]
[ROW][C]4[/C][C]354980[/C][C]341726.019781335[/C][C]13253.9802186649[/C][/ROW]
[ROW][C]5[/C][C]339890[/C][C]352197.431280269[/C][C]-12307.4312802695[/C][/ROW]
[ROW][C]6[/C][C]339890[/C][C]342473.848227907[/C][C]-2583.84822790691[/C][/ROW]
[ROW][C]7[/C][C]340471[/C][C]340432.458577491[/C][C]38.5414225094137[/C][/ROW]
[ROW][C]8[/C][C]343833[/C][C]340462.908532009[/C][C]3370.09146799071[/C][/ROW]
[ROW][C]9[/C][C]346109[/C][C]343125.475849009[/C][C]2983.52415099094[/C][/ROW]
[ROW][C]10[/C][C]345455[/C][C]345482.632611476[/C][C]-27.632611476467[/C][/ROW]
[ROW][C]11[/C][C]350419[/C][C]345460.801249064[/C][C]4958.1987509359[/C][/ROW]
[ROW][C]12[/C][C]344660[/C][C]349378.06523754[/C][C]-4718.06523754034[/C][/ROW]
[ROW][C]13[/C][C]341499[/C][C]345650.520623317[/C][C]-4151.52062331734[/C][/ROW]
[ROW][C]14[/C][C]342376[/C][C]342370.579045326[/C][C]5.42095467360923[/C][/ROW]
[ROW][C]15[/C][C]344148[/C][C]342374.861913278[/C][C]1773.13808672241[/C][/ROW]
[ROW][C]16[/C][C]359079[/C][C]343775.743629123[/C][C]15303.2563708771[/C][/ROW]
[ROW][C]17[/C][C]344090[/C][C]355866.201898215[/C][C]-11776.2018982152[/C][/ROW]
[ROW][C]18[/C][C]342681[/C][C]346562.320804664[/C][C]-3881.32080466358[/C][/ROW]
[ROW][C]19[/C][C]348552[/C][C]343495.852722285[/C][C]5056.14727771457[/C][/ROW]
[ROW][C]20[/C][C]349867[/C][C]347490.501716073[/C][C]2376.49828392733[/C][/ROW]
[ROW][C]21[/C][C]353247[/C][C]349368.072909552[/C][C]3878.92709044769[/C][/ROW]
[ROW][C]22[/C][C]356048[/C][C]352432.649819154[/C][C]3615.35018084571[/C][/ROW]
[ROW][C]23[/C][C]363887[/C][C]355288.985714621[/C][C]8598.01428537868[/C][/ROW]
[ROW][C]24[/C][C]358905[/C][C]362081.914643935[/C][C]-3176.9146439347[/C][/ROW]
[ROW][C]25[/C][C]359647[/C][C]359571.968198807[/C][C]75.0318011930212[/C][/ROW]
[ROW][C]26[/C][C]361488[/C][C]359631.24766451[/C][C]1856.75233549019[/C][/ROW]
[ROW][C]27[/C][C]363229[/C][C]361098.189476385[/C][C]2130.8105236151[/C][/ROW]
[ROW][C]28[/C][C]393301[/C][C]362781.653119073[/C][C]30519.3468809267[/C][/ROW]
[ROW][C]29[/C][C]366190[/C][C]386893.703582137[/C][C]-20703.7035821375[/C][/ROW]
[ROW][C]30[/C][C]363811[/C][C]370536.579444045[/C][C]-6725.57944404508[/C][/ROW]
[ROW][C]31[/C][C]366190[/C][C]365222.98241391[/C][C]967.017586090253[/C][/ROW]
[ROW][C]32[/C][C]372656[/C][C]365986.982276864[/C][C]6669.01772313606[/C][/ROW]
[ROW][C]33[/C][C]371781[/C][C]371255.892273749[/C][C]525.107726250717[/C][/ROW]
[ROW][C]34[/C][C]374306[/C][C]371670.757770161[/C][C]2635.2422298395[/C][/ROW]
[ROW][C]35[/C][C]377689[/C][C]373752.751656733[/C][C]3936.2483432666[/C][/ROW]
[ROW][C]36[/C][C]373240[/C][C]376862.615673755[/C][C]-3622.61567375506[/C][/ROW]
[ROW][C]37[/C][C]373456[/C][C]374000.539618371[/C][C]-544.539618370705[/C][/ROW]
[ROW][C]38[/C][C]372610[/C][C]373570.321802488[/C][C]-960.321802487539[/C][/ROW]
[ROW][C]39[/C][C]372209[/C][C]372811.611996124[/C][C]-602.611996124324[/C][/ROW]
[ROW][C]40[/C][C]390212[/C][C]372335.513640649[/C][C]17876.4863593513[/C][/ROW]
[ROW][C]41[/C][C]373113[/C][C]386458.972536433[/C][C]-13345.9725364332[/C][/ROW]
[ROW][C]42[/C][C]370518[/C][C]375914.881782045[/C][C]-5396.88178204501[/C][/ROW]
[ROW][C]43[/C][C]370469[/C][C]371651.032808488[/C][C]-1182.03280848829[/C][/ROW]
[ROW][C]44[/C][C]372493[/C][C]370717.158474989[/C][C]1775.84152501129[/C][/ROW]
[ROW][C]45[/C][C]369536[/C][C]372120.176063554[/C][C]-2584.17606355436[/C][/ROW]
[ROW][C]46[/C][C]368835[/C][C]370078.527404002[/C][C]-1243.52740400174[/C][/ROW]
[ROW][C]47[/C][C]366859[/C][C]369096.068780805[/C][C]-2237.06878080522[/C][/ROW]
[ROW][C]48[/C][C]356044[/C][C]367328.654964822[/C][C]-11284.6549648225[/C][/ROW]
[ROW][C]49[/C][C]346106[/C][C]358413.124398861[/C][C]-12307.1243988615[/C][/ROW]
[ROW][C]50[/C][C]333829[/C][C]348689.783800573[/C][C]-14860.7838005732[/C][/ROW]
[ROW][C]51[/C][C]317388[/C][C]336948.90447186[/C][C]-19560.9044718597[/C][/ROW]
[ROW][C]52[/C][C]285871[/C][C]321494.657774876[/C][C]-35623.6577748761[/C][/ROW]
[ROW][C]53[/C][C]339729[/C][C]293349.906273541[/C][C]46379.0937264594[/C][/ROW]
[ROW][C]54[/C][C]308216[/C][C]329992.074689748[/C][C]-21776.0746897481[/C][/ROW]
[ROW][C]55[/C][C]309137[/C][C]312787.715308951[/C][C]-3650.71530895133[/C][/ROW]
[ROW][C]56[/C][C]311245[/C][C]309903.438915385[/C][C]1341.56108461489[/C][/ROW]
[ROW][C]57[/C][C]319568[/C][C]310963.349820351[/C][C]8604.65017964947[/C][/ROW]
[ROW][C]58[/C][C]329201[/C][C]317761.521490216[/C][C]11439.4785097837[/C][/ROW]
[ROW][C]59[/C][C]339880[/C][C]326799.371617718[/C][C]13080.6283822823[/C][/ROW]
[ROW][C]60[/C][C]342305[/C][C]337133.825132491[/C][C]5171.17486750893[/C][/ROW]
[ROW][C]61[/C][C]346975[/C][C]341219.35257989[/C][C]5755.64742011036[/C][/ROW]
[ROW][C]62[/C][C]355294[/C][C]345766.647172489[/C][C]9527.35282751085[/C][/ROW]
[ROW][C]63[/C][C]360766[/C][C]353293.807339207[/C][C]7472.19266079291[/C][/ROW]
[ROW][C]64[/C][C]392946[/C][C]359197.272023747[/C][C]33748.7279762529[/C][/ROW]
[ROW][C]65[/C][C]352108[/C][C]385860.72046524[/C][C]-33752.7204652403[/C][/ROW]
[ROW][C]66[/C][C]358071[/C][C]359194.117726366[/C][C]-1123.11772636604[/C][/ROW]
[ROW][C]67[/C][C]365429[/C][C]358306.789717685[/C][C]7122.21028231503[/C][/ROW]
[ROW][C]68[/C][C]378731[/C][C]363933.748066622[/C][C]14797.2519333781[/C][/ROW]
[ROW][C]69[/C][C]384120[/C][C]375624.433543095[/C][C]8495.56645690522[/C][/ROW]
[ROW][C]70[/C][C]391390[/C][C]382336.422758343[/C][C]9053.57724165655[/C][/ROW]
[ROW][C]71[/C][C]403547[/C][C]389489.272790613[/C][C]14057.7272093873[/C][/ROW]
[ROW][C]72[/C][C]404124[/C][C]400595.690932233[/C][C]3528.30906776671[/C][/ROW]
[ROW][C]73[/C][C]406439[/C][C]403383.259310521[/C][C]3055.74068947858[/C][/ROW]
[ROW][C]74[/C][C]412232[/C][C]405797.47131821[/C][C]6434.52868178999[/C][/ROW]
[ROW][C]75[/C][C]419221[/C][C]410881.121400457[/C][C]8339.87859954278[/C][/ROW]
[ROW][C]76[/C][C]450521[/C][C]417470.108197343[/C][C]33050.8918026569[/C][/ROW]
[ROW][C]77[/C][C]430027[/C][C]443582.225671685[/C][C]-13555.2256716847[/C][/ROW]
[ROW][C]78[/C][C]433442[/C][C]432872.8128291[/C][C]569.187170899706[/C][/ROW]
[ROW][C]79[/C][C]439938[/C][C]433322.503638055[/C][C]6615.49636194471[/C][/ROW]
[ROW][C]80[/C][C]450200[/C][C]438549.12866184[/C][C]11650.8713381597[/C][/ROW]
[ROW][C]81[/C][C]459279[/C][C]447753.991358949[/C][C]11525.0086410506[/C][/ROW]
[ROW][C]82[/C][C]465090[/C][C]456859.415240544[/C][C]8230.58475945587[/C][/ROW]
[ROW][C]83[/C][C]478567[/C][C]463362.053577951[/C][C]15204.9464220492[/C][/ROW]
[ROW][C]84[/C][C]475726[/C][C]475374.841297394[/C][C]351.15870260552[/C][/ROW]
[ROW][C]85[/C][C]480634[/C][C]475652.276997143[/C][C]4981.7230028573[/C][/ROW]
[ROW][C]86[/C][C]486952[/C][C]479588.126506195[/C][C]7363.87349380465[/C][/ROW]
[ROW][C]87[/C][C]491912[/C][C]485406.012779417[/C][C]6505.98722058284[/C][/ROW]
[ROW][C]88[/C][C]517281[/C][C]490546.119243254[/C][C]26734.8807567455[/C][/ROW]
[ROW][C]89[/C][C]502379[/C][C]511668.222427367[/C][C]-9289.22242736683[/C][/ROW]
[ROW][C]90[/C][C]504942[/C][C]504329.199059495[/C][C]612.800940504647[/C][/ROW]
[ROW][C]91[/C][C]516387[/C][C]504813.347270757[/C][C]11573.6527292434[/C][/ROW]
[ROW][C]92[/C][C]523270[/C][C]513957.202797491[/C][C]9312.79720250866[/C][/ROW]
[ROW][C]93[/C][C]528995[/C][C]521314.851602208[/C][C]7680.14839779236[/C][/ROW]
[ROW][C]94[/C][C]540850[/C][C]527382.613355233[/C][C]13467.3866447674[/C][/ROW]
[ROW][C]95[/C][C]550679[/C][C]538022.628282523[/C][C]12656.3717174765[/C][/ROW]
[ROW][C]96[/C][C]544432[/C][C]548021.894476579[/C][C]-3589.89447657857[/C][/ROW]
[ROW][C]97[/C][C]550296[/C][C]545185.670060831[/C][C]5110.32993916853[/C][/ROW]
[ROW][C]98[/C][C]554659[/C][C]549223.126493202[/C][C]5435.87350679818[/C][/ROW]
[ROW][C]99[/C][C]558856[/C][C]553517.781186113[/C][C]5338.2188138871[/C][/ROW]
[ROW][C]100[/C][C]582661[/C][C]557735.283019475[/C][C]24925.7169805249[/C][/ROW]
[ROW][C]101[/C][C]564317[/C][C]577428.04210791[/C][C]-13111.0421079102[/C][/ROW]
[ROW][C]102[/C][C]568569[/C][C]567069.559989577[/C][C]1499.44001042307[/C][/ROW]
[ROW][C]103[/C][C]574693[/C][C]568254.204383794[/C][C]6438.7956162059[/C][/ROW]
[ROW][C]104[/C][C]586558[/C][C]573341.225591196[/C][C]13216.7744088045[/C][/ROW]
[ROW][C]105[/C][C]588751[/C][C]583783.242346908[/C][C]4967.75765309227[/C][/ROW]
[ROW][C]106[/C][C]598250[/C][C]587708.058421346[/C][C]10541.9415786535[/C][/ROW]
[ROW][C]107[/C][C]607706[/C][C]596036.802424778[/C][C]11669.1975752219[/C][/ROW]
[ROW][C]108[/C][C]603869[/C][C]605256.143909869[/C][C]-1387.14390986937[/C][/ROW]
[ROW][C]109[/C][C]607696[/C][C]604160.219934668[/C][C]3535.78006533231[/C][/ROW]
[ROW][C]110[/C][C]613285[/C][C]606953.690833446[/C][C]6331.30916655401[/C][/ROW]
[ROW][C]111[/C][C]617160[/C][C]611955.791524422[/C][C]5204.20847557834[/C][/ROW]
[ROW][C]112[/C][C]647083[/C][C]616067.417434145[/C][C]31015.582565855[/C][/ROW]
[ROW][C]113[/C][C]621246[/C][C]640571.522809893[/C][C]-19325.5228098929[/C][/ROW]
[ROW][C]114[/C][C]623252[/C][C]625303.241249502[/C][C]-2051.24124950171[/C][/ROW]
[ROW][C]115[/C][C]632722[/C][C]623682.641938747[/C][C]9039.35806125263[/C][/ROW]
[ROW][C]116[/C][C]641716[/C][C]630824.257995507[/C][C]10891.7420044935[/C][/ROW]
[ROW][C]117[/C][C]644953[/C][C]639429.364581426[/C][C]5523.63541857398[/C][/ROW]
[ROW][C]118[/C][C]652723[/C][C]643793.356264205[/C][C]8929.64373579458[/C][/ROW]
[ROW][C]119[/C][C]660093[/C][C]650848.291653705[/C][C]9244.70834629494[/C][/ROW]
[ROW][C]120[/C][C]657090[/C][C]658152.146321102[/C][C]-1062.14632110239[/C][/ROW]
[ROW][C]121[/C][C]657281[/C][C]657312.989251539[/C][C]-31.9892515392276[/C][/ROW]
[ROW][C]122[/C][C]661949[/C][C]657287.71589132[/C][C]4661.28410868044[/C][/ROW]
[ROW][C]123[/C][C]665608[/C][C]660970.400127312[/C][C]4637.59987268772[/C][/ROW]
[ROW][C]124[/C][C]697124[/C][C]664634.372446052[/C][C]32489.6275539475[/C][/ROW]
[ROW][C]125[/C][C]671310[/C][C]690303.05867854[/C][C]-18993.0586785396[/C][/ROW]
[ROW][C]126[/C][C]674708[/C][C]675297.443024586[/C][C]-589.443024585606[/C][/ROW]
[ROW][C]127[/C][C]681915[/C][C]674831.748918832[/C][C]7083.25108116842[/C][/ROW]
[ROW][C]128[/C][C]690556[/C][C]680427.927243946[/C][C]10128.0727560541[/C][/ROW]
[ROW][C]129[/C][C]692885[/C][C]688429.690923239[/C][C]4455.30907676055[/C][/ROW]
[ROW][C]130[/C][C]699740[/C][C]691949.642962401[/C][C]7790.35703759897[/C][/ROW]
[ROW][C]131[/C][C]707885[/C][C]698104.475919631[/C][C]9780.52408036857[/C][/ROW]
[ROW][C]132[/C][C]704785[/C][C]705831.656029388[/C][C]-1046.65602938808[/C][/ROW]
[ROW][C]133[/C][C]705363[/C][C]705004.737186841[/C][C]358.262813159265[/C][/ROW]
[ROW][C]134[/C][C]749101[/C][C]705287.785545105[/C][C]43813.2144548952[/C][/ROW]
[ROW][C]135[/C][C]752891[/C][C]739902.760826431[/C][C]12988.2391735694[/C][/ROW]
[ROW][C]136[/C][C]784662[/C][C]750164.221518932[/C][C]34497.7784810677[/C][/ROW]
[ROW][C]137[/C][C]761914[/C][C]777419.463213471[/C][C]-15505.4632134706[/C][/ROW]
[ROW][C]138[/C][C]763768[/C][C]765169.249835214[/C][C]-1401.24983521376[/C][/ROW]
[ROW][C]139[/C][C]768877[/C][C]764062.181362554[/C][C]4814.8186374458[/C][/ROW]
[ROW][C]140[/C][C]781031[/C][C]767866.166762686[/C][C]13164.8332373142[/C][/ROW]
[ROW][C]141[/C][C]783454[/C][C]778267.146986621[/C][C]5186.8530133788[/C][/ROW]
[ROW][C]142[/C][C]785988[/C][C]782365.061076691[/C][C]3622.93892330874[/C][/ROW]
[ROW][C]143[/C][C]795068[/C][C]785227.392517932[/C][C]9840.60748206766[/C][/ROW]
[ROW][C]144[/C][C]790001[/C][C]793002.041992594[/C][C]-3001.04199259426[/C][/ROW]
[ROW][C]145[/C][C]789721[/C][C]790631.045121346[/C][C]-910.045121346368[/C][/ROW]
[ROW][C]146[/C][C]794064[/C][C]789912.056803045[/C][C]4151.9431969549[/C][/ROW]
[ROW][C]147[/C][C]798690[/C][C]793192.332238668[/C][C]5497.66776133224[/C][/ROW]
[ROW][C]148[/C][C]829281[/C][C]797535.807969246[/C][C]31745.1920307539[/C][/ROW]
[ROW][C]149[/C][C]806249[/C][C]822616.347051279[/C][C]-16367.347051279[/C][/ROW]
[ROW][C]150[/C][C]807048[/C][C]809685.19555624[/C][C]-2637.19555623957[/C][/ROW]
[ROW][C]151[/C][C]819928[/C][C]807601.658428754[/C][C]12326.3415712458[/C][/ROW]
[ROW][C]152[/C][C]821105[/C][C]817340.181705495[/C][C]3764.81829450454[/C][/ROW]
[ROW][C]153[/C][C]828422[/C][C]820314.606061807[/C][C]8107.39393819263[/C][/ROW]
[ROW][C]154[/C][C]835360[/C][C]826719.916520263[/C][C]8640.08347973682[/C][/ROW]
[ROW][C]155[/C][C]844092[/C][C]833546.082548039[/C][C]10545.9174519605[/C][/ROW]
[ROW][C]156[/C][C]837469[/C][C]841877.967721503[/C][C]-4408.967721503[/C][/ROW]
[ROW][C]157[/C][C]836969[/C][C]838394.628035183[/C][C]-1425.62803518295[/C][/ROW]
[ROW][C]158[/C][C]838721[/C][C]837268.299373564[/C][C]1452.70062643639[/C][/ROW]
[ROW][C]159[/C][C]840537[/C][C]838416.016949206[/C][C]2120.98305079422[/C][/ROW]
[ROW][C]160[/C][C]863719[/C][C]840091.716319562[/C][C]23627.2836804379[/C][/ROW]
[ROW][C]161[/C][C]845413[/C][C]858758.637948999[/C][C]-13345.6379489987[/C][/ROW]
[ROW][C]162[/C][C]844366[/C][C]848214.811538049[/C][C]-3848.81153804925[/C][/ROW]
[ROW][C]163[/C][C]848357[/C][C]845174.027657898[/C][C]3182.97234210197[/C][/ROW]
[ROW][C]164[/C][C]858754[/C][C]847688.760035191[/C][C]11065.239964809[/C][/ROW]
[ROW][C]165[/C][C]862431[/C][C]856430.940051636[/C][C]6000.05994836404[/C][/ROW]
[ROW][C]166[/C][C]871565[/C][C]861171.334687891[/C][C]10393.6653121086[/C][/ROW]
[ROW][C]167[/C][C]880366[/C][C]869382.931858681[/C][C]10983.0681413191[/C][/ROW]
[ROW][C]168[/C][C]874476[/C][C]878060.191378552[/C][C]-3584.19137855165[/C][/ROW]
[ROW][C]169[/C][C]882077[/C][C]875228.472740335[/C][C]6848.52725966496[/C][/ROW]
[ROW][C]170[/C][C]889199[/C][C]880639.205660898[/C][C]8559.79433910199[/C][/ROW]
[ROW][C]171[/C][C]892665[/C][C]887401.938620523[/C][C]5263.0613794768[/C][/ROW]
[ROW][C]172[/C][C]913625[/C][C]891560.061730669[/C][C]22064.9382693307[/C][/ROW]
[ROW][C]173[/C][C]893597[/C][C]908992.640058451[/C][C]-15395.6400584511[/C][/ROW]
[ROW][C]174[/C][C]892114[/C][C]896829.193329106[/C][C]-4715.19332910632[/C][/ROW]
[ROW][C]175[/C][C]894801[/C][C]893103.917688769[/C][C]1697.08231123083[/C][/ROW]
[ROW][C]176[/C][C]898843[/C][C]894444.710939949[/C][C]4398.28906005074[/C][/ROW]
[ROW][C]177[/C][C]908135[/C][C]897919.613865653[/C][C]10215.3861343474[/C][/ROW]
[ROW][C]178[/C][C]918920[/C][C]905990.360167403[/C][C]12929.6398325972[/C][/ROW]
[ROW][C]179[/C][C]923125[/C][C]916205.523988869[/C][C]6919.47601113073[/C][/ROW]
[ROW][C]180[/C][C]921770[/C][C]921672.310529528[/C][C]97.6894704719307[/C][/ROW]
[ROW][C]181[/C][C]917843[/C][C]921749.490865363[/C][C]-3906.49086536292[/C][/ROW]
[ROW][C]182[/C][C]916761[/C][C]918663.136978216[/C][C]-1902.13697821612[/C][/ROW]
[ROW][C]183[/C][C]915087[/C][C]917160.338671773[/C][C]-2073.33867177297[/C][/ROW]
[ROW][C]184[/C][C]938173[/C][C]915522.281118449[/C][C]22650.7188815508[/C][/ROW]
[ROW][C]185[/C][C]907953[/C][C]933417.66003424[/C][C]-25464.6600342398[/C][/ROW]
[ROW][C]186[/C][C]905374[/C][C]913299.104739923[/C][C]-7925.1047399228[/C][/ROW]
[ROW][C]187[/C][C]921867[/C][C]907037.813298804[/C][C]14829.1867011961[/C][/ROW]
[ROW][C]188[/C][C]927104[/C][C]918753.729090203[/C][C]8350.27090979682[/C][/ROW]
[ROW][C]189[/C][C]930989[/C][C]925350.926413685[/C][C]5638.07358631457[/C][/ROW]
[ROW][C]190[/C][C]936820[/C][C]929805.330872539[/C][C]7014.66912746138[/C][/ROW]
[ROW][C]191[/C][C]944281[/C][C]935347.325484774[/C][C]8933.67451522569[/C][/ROW]
[ROW][C]192[/C][C]945322[/C][C]942405.445423322[/C][C]2916.55457667832[/C][/ROW]
[ROW][C]193[/C][C]944555[/C][C]944709.692345955[/C][C]-154.692345954827[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=227514&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=227514&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
2339105338881224
3342435339057.972964883377.02703511977
4354980341726.01978133513253.9802186649
5339890352197.431280269-12307.4312802695
6339890342473.848227907-2583.84822790691
7340471340432.45857749138.5414225094137
8343833340462.9085320093370.09146799071
9346109343125.4758490092983.52415099094
10345455345482.632611476-27.632611476467
11350419345460.8012490644958.1987509359
12344660349378.06523754-4718.06523754034
13341499345650.520623317-4151.52062331734
14342376342370.5790453265.42095467360923
15344148342374.8619132781773.13808672241
16359079343775.74362912315303.2563708771
17344090355866.201898215-11776.2018982152
18342681346562.320804664-3881.32080466358
19348552343495.8527222855056.14727771457
20349867347490.5017160732376.49828392733
21353247349368.0729095523878.92709044769
22356048352432.6498191543615.35018084571
23363887355288.9857146218598.01428537868
24358905362081.914643935-3176.9146439347
25359647359571.96819880775.0318011930212
26361488359631.247664511856.75233549019
27363229361098.1894763852130.8105236151
28393301362781.65311907330519.3468809267
29366190386893.703582137-20703.7035821375
30363811370536.579444045-6725.57944404508
31366190365222.98241391967.017586090253
32372656365986.9822768646669.01772313606
33371781371255.892273749525.107726250717
34374306371670.7577701612635.2422298395
35377689373752.7516567333936.2483432666
36373240376862.615673755-3622.61567375506
37373456374000.539618371-544.539618370705
38372610373570.321802488-960.321802487539
39372209372811.611996124-602.611996124324
40390212372335.51364064917876.4863593513
41373113386458.972536433-13345.9725364332
42370518375914.881782045-5396.88178204501
43370469371651.032808488-1182.03280848829
44372493370717.1584749891775.84152501129
45369536372120.176063554-2584.17606355436
46368835370078.527404002-1243.52740400174
47366859369096.068780805-2237.06878080522
48356044367328.654964822-11284.6549648225
49346106358413.124398861-12307.1243988615
50333829348689.783800573-14860.7838005732
51317388336948.90447186-19560.9044718597
52285871321494.657774876-35623.6577748761
53339729293349.90627354146379.0937264594
54308216329992.074689748-21776.0746897481
55309137312787.715308951-3650.71530895133
56311245309903.4389153851341.56108461489
57319568310963.3498203518604.65017964947
58329201317761.52149021611439.4785097837
59339880326799.37161771813080.6283822823
60342305337133.8251324915171.17486750893
61346975341219.352579895755.64742011036
62355294345766.6471724899527.35282751085
63360766353293.8073392077472.19266079291
64392946359197.27202374733748.7279762529
65352108385860.72046524-33752.7204652403
66358071359194.117726366-1123.11772636604
67365429358306.7897176857122.21028231503
68378731363933.74806662214797.2519333781
69384120375624.4335430958495.56645690522
70391390382336.4227583439053.57724165655
71403547389489.27279061314057.7272093873
72404124400595.6909322333528.30906776671
73406439403383.2593105213055.74068947858
74412232405797.471318216434.52868178999
75419221410881.1214004578339.87859954278
76450521417470.10819734333050.8918026569
77430027443582.225671685-13555.2256716847
78433442432872.8128291569.187170899706
79439938433322.5036380556615.49636194471
80450200438549.1286618411650.8713381597
81459279447753.99135894911525.0086410506
82465090456859.4152405448230.58475945587
83478567463362.05357795115204.9464220492
84475726475374.841297394351.15870260552
85480634475652.2769971434981.7230028573
86486952479588.1265061957363.87349380465
87491912485406.0127794176505.98722058284
88517281490546.11924325426734.8807567455
89502379511668.222427367-9289.22242736683
90504942504329.199059495612.800940504647
91516387504813.34727075711573.6527292434
92523270513957.2027974919312.79720250866
93528995521314.8516022087680.14839779236
94540850527382.61335523313467.3866447674
95550679538022.62828252312656.3717174765
96544432548021.894476579-3589.89447657857
97550296545185.6700608315110.32993916853
98554659549223.1264932025435.87350679818
99558856553517.7811861135338.2188138871
100582661557735.28301947524925.7169805249
101564317577428.04210791-13111.0421079102
102568569567069.5599895771499.44001042307
103574693568254.2043837946438.7956162059
104586558573341.22559119613216.7744088045
105588751583783.2423469084967.75765309227
106598250587708.05842134610541.9415786535
107607706596036.80242477811669.1975752219
108603869605256.143909869-1387.14390986937
109607696604160.2199346683535.78006533231
110613285606953.6908334466331.30916655401
111617160611955.7915244225204.20847557834
112647083616067.41743414531015.582565855
113621246640571.522809893-19325.5228098929
114623252625303.241249502-2051.24124950171
115632722623682.6419387479039.35806125263
116641716630824.25799550710891.7420044935
117644953639429.3645814265523.63541857398
118652723643793.3562642058929.64373579458
119660093650848.2916537059244.70834629494
120657090658152.146321102-1062.14632110239
121657281657312.989251539-31.9892515392276
122661949657287.715891324661.28410868044
123665608660970.4001273124637.59987268772
124697124664634.37244605232489.6275539475
125671310690303.05867854-18993.0586785396
126674708675297.443024586-589.443024585606
127681915674831.7489188327083.25108116842
128690556680427.92724394610128.0727560541
129692885688429.6909232394455.30907676055
130699740691949.6429624017790.35703759897
131707885698104.4759196319780.52408036857
132704785705831.656029388-1046.65602938808
133705363705004.737186841358.262813159265
134749101705287.78554510543813.2144548952
135752891739902.76082643112988.2391735694
136784662750164.22151893234497.7784810677
137761914777419.463213471-15505.4632134706
138763768765169.249835214-1401.24983521376
139768877764062.1813625544814.8186374458
140781031767866.16676268613164.8332373142
141783454778267.1469866215186.8530133788
142785988782365.0610766913622.93892330874
143795068785227.3925179329840.60748206766
144790001793002.041992594-3001.04199259426
145789721790631.045121346-910.045121346368
146794064789912.0568030454151.9431969549
147798690793192.3322386685497.66776133224
148829281797535.80796924631745.1920307539
149806249822616.347051279-16367.347051279
150807048809685.19555624-2637.19555623957
151819928807601.65842875412326.3415712458
152821105817340.1817054953764.81829450454
153828422820314.6060618078107.39393819263
154835360826719.9165202638640.08347973682
155844092833546.08254803910545.9174519605
156837469841877.967721503-4408.967721503
157836969838394.628035183-1425.62803518295
158838721837268.2993735641452.70062643639
159840537838416.0169492062120.98305079422
160863719840091.71631956223627.2836804379
161845413858758.637948999-13345.6379489987
162844366848214.811538049-3848.81153804925
163848357845174.0276578983182.97234210197
164858754847688.76003519111065.239964809
165862431856430.9400516366000.05994836404
166871565861171.33468789110393.6653121086
167880366869382.93185868110983.0681413191
168874476878060.191378552-3584.19137855165
169882077875228.4727403356848.52725966496
170889199880639.2056608988559.79433910199
171892665887401.9386205235263.0613794768
172913625891560.06173066922064.9382693307
173893597908992.640058451-15395.6400584511
174892114896829.193329106-4715.19332910632
175894801893103.9176887691697.08231123083
176898843894444.7109399494398.28906005074
177908135897919.61386565310215.3861343474
178918920905990.36016740312929.6398325972
179923125916205.5239888696919.47601113073
180921770921672.31052952897.6894704719307
181917843921749.490865363-3906.49086536292
182916761918663.136978216-1902.13697821612
183915087917160.338671773-2073.33867177297
184938173915522.28111844922650.7188815508
185907953933417.66003424-25464.6600342398
186905374913299.104739923-7925.1047399228
187921867907037.81329880414829.1867011961
188927104918753.7290902038350.27090979682
189930989925350.9264136855638.07358631457
190936820929805.3308725397014.66912746138
191944281935347.3254847748933.67451522569
192945322942405.4454233222916.55457667832
193944555944709.692345955-154.692345954827







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
194944587.476439223921494.481713743967680.471164703
195944587.476439223915156.893347219974018.059531227
196944587.476439223909960.434450632979214.518427814
197944587.476439223905447.920327484983727.032550962
198944587.476439223901404.40489066987770.547987786
199944587.476439223897708.371455098991466.581423348
200944587.476439223894283.169467982994891.783410464
201944587.476439223891076.766150523998098.186727923
202944587.476439223888051.9218620771001123.03101637
203944587.476439223885180.8964409621003994.05643748
204944587.476439223882442.3675179721006732.58536047
205944587.476439223879819.5261970051009355.42668144

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
194 & 944587.476439223 & 921494.481713743 & 967680.471164703 \tabularnewline
195 & 944587.476439223 & 915156.893347219 & 974018.059531227 \tabularnewline
196 & 944587.476439223 & 909960.434450632 & 979214.518427814 \tabularnewline
197 & 944587.476439223 & 905447.920327484 & 983727.032550962 \tabularnewline
198 & 944587.476439223 & 901404.40489066 & 987770.547987786 \tabularnewline
199 & 944587.476439223 & 897708.371455098 & 991466.581423348 \tabularnewline
200 & 944587.476439223 & 894283.169467982 & 994891.783410464 \tabularnewline
201 & 944587.476439223 & 891076.766150523 & 998098.186727923 \tabularnewline
202 & 944587.476439223 & 888051.921862077 & 1001123.03101637 \tabularnewline
203 & 944587.476439223 & 885180.896440962 & 1003994.05643748 \tabularnewline
204 & 944587.476439223 & 882442.367517972 & 1006732.58536047 \tabularnewline
205 & 944587.476439223 & 879819.526197005 & 1009355.42668144 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=227514&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]944587.476439223[/C][C]921494.481713743[/C][C]967680.471164703[/C][/ROW]
[ROW][C]195[/C][C]944587.476439223[/C][C]915156.893347219[/C][C]974018.059531227[/C][/ROW]
[ROW][C]196[/C][C]944587.476439223[/C][C]909960.434450632[/C][C]979214.518427814[/C][/ROW]
[ROW][C]197[/C][C]944587.476439223[/C][C]905447.920327484[/C][C]983727.032550962[/C][/ROW]
[ROW][C]198[/C][C]944587.476439223[/C][C]901404.40489066[/C][C]987770.547987786[/C][/ROW]
[ROW][C]199[/C][C]944587.476439223[/C][C]897708.371455098[/C][C]991466.581423348[/C][/ROW]
[ROW][C]200[/C][C]944587.476439223[/C][C]894283.169467982[/C][C]994891.783410464[/C][/ROW]
[ROW][C]201[/C][C]944587.476439223[/C][C]891076.766150523[/C][C]998098.186727923[/C][/ROW]
[ROW][C]202[/C][C]944587.476439223[/C][C]888051.921862077[/C][C]1001123.03101637[/C][/ROW]
[ROW][C]203[/C][C]944587.476439223[/C][C]885180.896440962[/C][C]1003994.05643748[/C][/ROW]
[ROW][C]204[/C][C]944587.476439223[/C][C]882442.367517972[/C][C]1006732.58536047[/C][/ROW]
[ROW][C]205[/C][C]944587.476439223[/C][C]879819.526197005[/C][C]1009355.42668144[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=227514&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=227514&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
194944587.476439223921494.481713743967680.471164703
195944587.476439223915156.893347219974018.059531227
196944587.476439223909960.434450632979214.518427814
197944587.476439223905447.920327484983727.032550962
198944587.476439223901404.40489066987770.547987786
199944587.476439223897708.371455098991466.581423348
200944587.476439223894283.169467982994891.783410464
201944587.476439223891076.766150523998098.186727923
202944587.476439223888051.9218620771001123.03101637
203944587.476439223885180.8964409621003994.05643748
204944587.476439223882442.3675179721006732.58536047
205944587.476439223879819.5261970051009355.42668144



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