Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 04 Aug 2013 10:16:33 -0400
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/Aug/04/t1375625855lug1nvr271ykwp6.htm/, Retrieved Sat, 04 May 2024 06:38:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=210923, Retrieved Sat, 04 May 2024 06:38:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsOngenae Olivier
Estimated Impact166
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [TIJDREEKS A - STA...] [2013-08-04 14:16:33] [084e0343a0486ff05530df6c705c8bb4] [Current]
Feedback Forum

Post a new message
Dataseries X:
545688
544740
543702
541794
561369
560421
545688
535914
536862
536862
537807
539808
544740
538848
544740
539808
555474
562407
532968
525075
531915
530967
525075
526035
537807
535914
537807
537807
550635
552528
517194
517194
530967
524127
512355
517194
528981
523089
522141
509409
528021
531915
493635
492687
512355
501528
482901
490794
499527
501528
495636
483861
508368
508368
465234
462303
474075
452514
430848
437796
452514
440730
432849
416130
438741
439689
396570
395517
403410
378903
352395
363129
377850
362184
361236
345462
371010
375957
327798
317064
323904
297396
269943
278784
295410
275838
278784
267012
291516
294450
235572
231663
242397
213999
188451
197292
218850
193386
191397
171732
193386
200226
139344
139344
148173
124626
98118
111891
136398
109893
120732
105999
129558
137439
74559
69720
79506
55947
37332
45120
562407




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=210923&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=210923&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210923&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
alpha0.0725298686175101
beta0.626267158445527
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0725298686175101 \tabularnewline
beta & 0.626267158445527 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210923&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]0.0725298686175101[/C][/ROW]
[ROW][C]beta[/C][C]0.626267158445527[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210923&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210923&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
alpha0.0725298686175101
beta0.626267158445527
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13544740545833.489583333-1093.48958333326
14538848540319.208132105-1471.20813210495
15544740546170.829007244-1430.82900724432
16539808540930.385922095-1122.38592209481
17555474556583.706953782-1109.70695378154
18562407563782.791287494-1375.79128749366
19532968540706.833888987-7738.83388898743
20525075529484.71921659-4409.7192165904
21531915528943.0117885192971.98821148125
22530967527960.945472983006.05452702031
23525075528351.769222229-3276.76922222879
24526035529028.559657171-2993.55965717137
25537807531791.1106331486015.88936685165
26535914525854.60721084510059.3927891547
27537807532516.2052151265290.79478487419
28537807528290.8829159849516.11708401644
29550635545452.336601135182.66339886957
30552528553871.603330303-1343.60333030275
31517194525908.493510924-8714.49351092381
32517194518670.996285439-1476.99628543889
33530967526289.2528057464677.74719425384
34524127526640.922054351-2513.92205435119
35512355521731.938549578-9376.93854957761
36517194522879.55176037-5685.55176037038
37528981534331.168057519-5350.16805751901
38523089531332.553642922-8243.55364292162
39522141531424.572035287-9283.57203528727
40509409528579.68340598-19170.6834059804
41528021536856.946032216-8835.94603221584
42531915534785.366727117-2870.36672711687
43493635496384.729513783-2749.72951378295
44492687493072.845299537-385.845299536886
45512355503308.5739935869046.4260064144
46501528494335.4737360817192.52626391948
47482901481234.5807857821666.41921421775
48490794484577.7674832466216.23251675355
49499527495715.2418424133811.75815758726
50501528489625.33972764511902.6602723546
51495636490056.8050576475579.19494235347
52483861479637.8537417724223.14625822782
53508368500777.5909219437590.40907805669
54508368507757.008104387610.991895612795
55465234472205.593287181-6971.59328718082
56462303473072.992317756-10769.9923177559
57474075493125.092681173-19050.0926811735
58452514480939.871290085-28425.8712900848
59430848459057.53659303-28209.5365930301
60437796462023.837489054-24227.8374890537
61452514464910.463440627-12396.4634406268
62440730460600.158069357-19870.1580693572
63432849446870.207616522-14021.207616522
64416130426889.524254476-10759.5242544763
65438741442502.624266002-3761.62426600244
66439689434106.8529967325582.14700326789
67396570384030.55328701112539.4467129895
68395517375823.61442163419693.3855783657
69403410384822.84468420518587.1553157947
70378903362798.46372994116104.5362700589
71352395342496.0360452919898.96395470866
72363129351799.73217093211329.2678290681
73377850369734.1530951128115.84690488834
74362184362407.303316892-223.303316892358
75361236358846.8130122752389.18698772485
76345462347146.647400813-1684.64740081347
77371010374385.659159032-3375.65915903164
78375957379178.851275937-3221.85127593711
79327798339011.682352833-11213.6823528326
80317064338733.052569278-21669.0525692775
81323904344843.521774537-20939.5217745368
82297396316991.544578738-19595.5445787382
83269943286064.527777146-16121.5277771455
84278784291345.81046543-12561.8104654304
85295410300020.141745544-4610.14174554439
86275838278910.990449795-3072.99044979538
87278784272312.4034054436471.59659455688
88267012252060.99427501114951.0057249888
89291516274624.88695039216891.1130496076
90294450277637.91879797616812.0812020241
91235572229028.867745976543.13225402977
92231663218664.90692077612998.0930792236
93242397227864.89913064414532.1008693563
94213999205341.9044003988657.09559960171
95188451182479.1481135175971.85188648332
96197292196460.994859294831.005140705762
97218850217886.586042483963.413957516517
98193386203265.459475399-9879.45947539856
99191397209374.462327313-17977.4623273131
100171732198452.556235851-26720.5562358509
101193386221138.948489824-27752.948489824
102200226220158.323095599-19932.3230955989
103139344157008.688329753-17664.6883297532
104139344147424.753711742-8080.75371174209
105148173152110.213196108-3937.21319610818
106124626117551.3834571767074.61654282376
1079811886764.119591724711353.8804082753
10811189191293.563394966620597.4366050334
109136398110098.68961401326299.3103859872
11010989384232.638491397825660.3615086022
11112073283996.919517711936735.0804822881
11210599970007.795828904735991.2041710953
113129558100207.15914240429350.8408575961
114137439117137.49853526220301.5014647379
1157455967352.56329857837206.43670142167
1166972077934.4461870894-8214.44618708944
1177950695920.2512932232-16414.2512932232
1185594779569.8936143283-23622.8936143283
1193733258030.9443113993-20698.9443113993
1204512074858.6968984693-29738.6968984693
12156240799064.8193085362463342.180691464

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 544740 & 545833.489583333 & -1093.48958333326 \tabularnewline
14 & 538848 & 540319.208132105 & -1471.20813210495 \tabularnewline
15 & 544740 & 546170.829007244 & -1430.82900724432 \tabularnewline
16 & 539808 & 540930.385922095 & -1122.38592209481 \tabularnewline
17 & 555474 & 556583.706953782 & -1109.70695378154 \tabularnewline
18 & 562407 & 563782.791287494 & -1375.79128749366 \tabularnewline
19 & 532968 & 540706.833888987 & -7738.83388898743 \tabularnewline
20 & 525075 & 529484.71921659 & -4409.7192165904 \tabularnewline
21 & 531915 & 528943.011788519 & 2971.98821148125 \tabularnewline
22 & 530967 & 527960.94547298 & 3006.05452702031 \tabularnewline
23 & 525075 & 528351.769222229 & -3276.76922222879 \tabularnewline
24 & 526035 & 529028.559657171 & -2993.55965717137 \tabularnewline
25 & 537807 & 531791.110633148 & 6015.88936685165 \tabularnewline
26 & 535914 & 525854.607210845 & 10059.3927891547 \tabularnewline
27 & 537807 & 532516.205215126 & 5290.79478487419 \tabularnewline
28 & 537807 & 528290.882915984 & 9516.11708401644 \tabularnewline
29 & 550635 & 545452.33660113 & 5182.66339886957 \tabularnewline
30 & 552528 & 553871.603330303 & -1343.60333030275 \tabularnewline
31 & 517194 & 525908.493510924 & -8714.49351092381 \tabularnewline
32 & 517194 & 518670.996285439 & -1476.99628543889 \tabularnewline
33 & 530967 & 526289.252805746 & 4677.74719425384 \tabularnewline
34 & 524127 & 526640.922054351 & -2513.92205435119 \tabularnewline
35 & 512355 & 521731.938549578 & -9376.93854957761 \tabularnewline
36 & 517194 & 522879.55176037 & -5685.55176037038 \tabularnewline
37 & 528981 & 534331.168057519 & -5350.16805751901 \tabularnewline
38 & 523089 & 531332.553642922 & -8243.55364292162 \tabularnewline
39 & 522141 & 531424.572035287 & -9283.57203528727 \tabularnewline
40 & 509409 & 528579.68340598 & -19170.6834059804 \tabularnewline
41 & 528021 & 536856.946032216 & -8835.94603221584 \tabularnewline
42 & 531915 & 534785.366727117 & -2870.36672711687 \tabularnewline
43 & 493635 & 496384.729513783 & -2749.72951378295 \tabularnewline
44 & 492687 & 493072.845299537 & -385.845299536886 \tabularnewline
45 & 512355 & 503308.573993586 & 9046.4260064144 \tabularnewline
46 & 501528 & 494335.473736081 & 7192.52626391948 \tabularnewline
47 & 482901 & 481234.580785782 & 1666.41921421775 \tabularnewline
48 & 490794 & 484577.767483246 & 6216.23251675355 \tabularnewline
49 & 499527 & 495715.241842413 & 3811.75815758726 \tabularnewline
50 & 501528 & 489625.339727645 & 11902.6602723546 \tabularnewline
51 & 495636 & 490056.805057647 & 5579.19494235347 \tabularnewline
52 & 483861 & 479637.853741772 & 4223.14625822782 \tabularnewline
53 & 508368 & 500777.590921943 & 7590.40907805669 \tabularnewline
54 & 508368 & 507757.008104387 & 610.991895612795 \tabularnewline
55 & 465234 & 472205.593287181 & -6971.59328718082 \tabularnewline
56 & 462303 & 473072.992317756 & -10769.9923177559 \tabularnewline
57 & 474075 & 493125.092681173 & -19050.0926811735 \tabularnewline
58 & 452514 & 480939.871290085 & -28425.8712900848 \tabularnewline
59 & 430848 & 459057.53659303 & -28209.5365930301 \tabularnewline
60 & 437796 & 462023.837489054 & -24227.8374890537 \tabularnewline
61 & 452514 & 464910.463440627 & -12396.4634406268 \tabularnewline
62 & 440730 & 460600.158069357 & -19870.1580693572 \tabularnewline
63 & 432849 & 446870.207616522 & -14021.207616522 \tabularnewline
64 & 416130 & 426889.524254476 & -10759.5242544763 \tabularnewline
65 & 438741 & 442502.624266002 & -3761.62426600244 \tabularnewline
66 & 439689 & 434106.852996732 & 5582.14700326789 \tabularnewline
67 & 396570 & 384030.553287011 & 12539.4467129895 \tabularnewline
68 & 395517 & 375823.614421634 & 19693.3855783657 \tabularnewline
69 & 403410 & 384822.844684205 & 18587.1553157947 \tabularnewline
70 & 378903 & 362798.463729941 & 16104.5362700589 \tabularnewline
71 & 352395 & 342496.036045291 & 9898.96395470866 \tabularnewline
72 & 363129 & 351799.732170932 & 11329.2678290681 \tabularnewline
73 & 377850 & 369734.153095112 & 8115.84690488834 \tabularnewline
74 & 362184 & 362407.303316892 & -223.303316892358 \tabularnewline
75 & 361236 & 358846.813012275 & 2389.18698772485 \tabularnewline
76 & 345462 & 347146.647400813 & -1684.64740081347 \tabularnewline
77 & 371010 & 374385.659159032 & -3375.65915903164 \tabularnewline
78 & 375957 & 379178.851275937 & -3221.85127593711 \tabularnewline
79 & 327798 & 339011.682352833 & -11213.6823528326 \tabularnewline
80 & 317064 & 338733.052569278 & -21669.0525692775 \tabularnewline
81 & 323904 & 344843.521774537 & -20939.5217745368 \tabularnewline
82 & 297396 & 316991.544578738 & -19595.5445787382 \tabularnewline
83 & 269943 & 286064.527777146 & -16121.5277771455 \tabularnewline
84 & 278784 & 291345.81046543 & -12561.8104654304 \tabularnewline
85 & 295410 & 300020.141745544 & -4610.14174554439 \tabularnewline
86 & 275838 & 278910.990449795 & -3072.99044979538 \tabularnewline
87 & 278784 & 272312.403405443 & 6471.59659455688 \tabularnewline
88 & 267012 & 252060.994275011 & 14951.0057249888 \tabularnewline
89 & 291516 & 274624.886950392 & 16891.1130496076 \tabularnewline
90 & 294450 & 277637.918797976 & 16812.0812020241 \tabularnewline
91 & 235572 & 229028.86774597 & 6543.13225402977 \tabularnewline
92 & 231663 & 218664.906920776 & 12998.0930792236 \tabularnewline
93 & 242397 & 227864.899130644 & 14532.1008693563 \tabularnewline
94 & 213999 & 205341.904400398 & 8657.09559960171 \tabularnewline
95 & 188451 & 182479.148113517 & 5971.85188648332 \tabularnewline
96 & 197292 & 196460.994859294 & 831.005140705762 \tabularnewline
97 & 218850 & 217886.586042483 & 963.413957516517 \tabularnewline
98 & 193386 & 203265.459475399 & -9879.45947539856 \tabularnewline
99 & 191397 & 209374.462327313 & -17977.4623273131 \tabularnewline
100 & 171732 & 198452.556235851 & -26720.5562358509 \tabularnewline
101 & 193386 & 221138.948489824 & -27752.948489824 \tabularnewline
102 & 200226 & 220158.323095599 & -19932.3230955989 \tabularnewline
103 & 139344 & 157008.688329753 & -17664.6883297532 \tabularnewline
104 & 139344 & 147424.753711742 & -8080.75371174209 \tabularnewline
105 & 148173 & 152110.213196108 & -3937.21319610818 \tabularnewline
106 & 124626 & 117551.383457176 & 7074.61654282376 \tabularnewline
107 & 98118 & 86764.1195917247 & 11353.8804082753 \tabularnewline
108 & 111891 & 91293.5633949666 & 20597.4366050334 \tabularnewline
109 & 136398 & 110098.689614013 & 26299.3103859872 \tabularnewline
110 & 109893 & 84232.6384913978 & 25660.3615086022 \tabularnewline
111 & 120732 & 83996.9195177119 & 36735.0804822881 \tabularnewline
112 & 105999 & 70007.7958289047 & 35991.2041710953 \tabularnewline
113 & 129558 & 100207.159142404 & 29350.8408575961 \tabularnewline
114 & 137439 & 117137.498535262 & 20301.5014647379 \tabularnewline
115 & 74559 & 67352.5632985783 & 7206.43670142167 \tabularnewline
116 & 69720 & 77934.4461870894 & -8214.44618708944 \tabularnewline
117 & 79506 & 95920.2512932232 & -16414.2512932232 \tabularnewline
118 & 55947 & 79569.8936143283 & -23622.8936143283 \tabularnewline
119 & 37332 & 58030.9443113993 & -20698.9443113993 \tabularnewline
120 & 45120 & 74858.6968984693 & -29738.6968984693 \tabularnewline
121 & 562407 & 99064.8193085362 & 463342.180691464 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210923&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]544740[/C][C]545833.489583333[/C][C]-1093.48958333326[/C][/ROW]
[ROW][C]14[/C][C]538848[/C][C]540319.208132105[/C][C]-1471.20813210495[/C][/ROW]
[ROW][C]15[/C][C]544740[/C][C]546170.829007244[/C][C]-1430.82900724432[/C][/ROW]
[ROW][C]16[/C][C]539808[/C][C]540930.385922095[/C][C]-1122.38592209481[/C][/ROW]
[ROW][C]17[/C][C]555474[/C][C]556583.706953782[/C][C]-1109.70695378154[/C][/ROW]
[ROW][C]18[/C][C]562407[/C][C]563782.791287494[/C][C]-1375.79128749366[/C][/ROW]
[ROW][C]19[/C][C]532968[/C][C]540706.833888987[/C][C]-7738.83388898743[/C][/ROW]
[ROW][C]20[/C][C]525075[/C][C]529484.71921659[/C][C]-4409.7192165904[/C][/ROW]
[ROW][C]21[/C][C]531915[/C][C]528943.011788519[/C][C]2971.98821148125[/C][/ROW]
[ROW][C]22[/C][C]530967[/C][C]527960.94547298[/C][C]3006.05452702031[/C][/ROW]
[ROW][C]23[/C][C]525075[/C][C]528351.769222229[/C][C]-3276.76922222879[/C][/ROW]
[ROW][C]24[/C][C]526035[/C][C]529028.559657171[/C][C]-2993.55965717137[/C][/ROW]
[ROW][C]25[/C][C]537807[/C][C]531791.110633148[/C][C]6015.88936685165[/C][/ROW]
[ROW][C]26[/C][C]535914[/C][C]525854.607210845[/C][C]10059.3927891547[/C][/ROW]
[ROW][C]27[/C][C]537807[/C][C]532516.205215126[/C][C]5290.79478487419[/C][/ROW]
[ROW][C]28[/C][C]537807[/C][C]528290.882915984[/C][C]9516.11708401644[/C][/ROW]
[ROW][C]29[/C][C]550635[/C][C]545452.33660113[/C][C]5182.66339886957[/C][/ROW]
[ROW][C]30[/C][C]552528[/C][C]553871.603330303[/C][C]-1343.60333030275[/C][/ROW]
[ROW][C]31[/C][C]517194[/C][C]525908.493510924[/C][C]-8714.49351092381[/C][/ROW]
[ROW][C]32[/C][C]517194[/C][C]518670.996285439[/C][C]-1476.99628543889[/C][/ROW]
[ROW][C]33[/C][C]530967[/C][C]526289.252805746[/C][C]4677.74719425384[/C][/ROW]
[ROW][C]34[/C][C]524127[/C][C]526640.922054351[/C][C]-2513.92205435119[/C][/ROW]
[ROW][C]35[/C][C]512355[/C][C]521731.938549578[/C][C]-9376.93854957761[/C][/ROW]
[ROW][C]36[/C][C]517194[/C][C]522879.55176037[/C][C]-5685.55176037038[/C][/ROW]
[ROW][C]37[/C][C]528981[/C][C]534331.168057519[/C][C]-5350.16805751901[/C][/ROW]
[ROW][C]38[/C][C]523089[/C][C]531332.553642922[/C][C]-8243.55364292162[/C][/ROW]
[ROW][C]39[/C][C]522141[/C][C]531424.572035287[/C][C]-9283.57203528727[/C][/ROW]
[ROW][C]40[/C][C]509409[/C][C]528579.68340598[/C][C]-19170.6834059804[/C][/ROW]
[ROW][C]41[/C][C]528021[/C][C]536856.946032216[/C][C]-8835.94603221584[/C][/ROW]
[ROW][C]42[/C][C]531915[/C][C]534785.366727117[/C][C]-2870.36672711687[/C][/ROW]
[ROW][C]43[/C][C]493635[/C][C]496384.729513783[/C][C]-2749.72951378295[/C][/ROW]
[ROW][C]44[/C][C]492687[/C][C]493072.845299537[/C][C]-385.845299536886[/C][/ROW]
[ROW][C]45[/C][C]512355[/C][C]503308.573993586[/C][C]9046.4260064144[/C][/ROW]
[ROW][C]46[/C][C]501528[/C][C]494335.473736081[/C][C]7192.52626391948[/C][/ROW]
[ROW][C]47[/C][C]482901[/C][C]481234.580785782[/C][C]1666.41921421775[/C][/ROW]
[ROW][C]48[/C][C]490794[/C][C]484577.767483246[/C][C]6216.23251675355[/C][/ROW]
[ROW][C]49[/C][C]499527[/C][C]495715.241842413[/C][C]3811.75815758726[/C][/ROW]
[ROW][C]50[/C][C]501528[/C][C]489625.339727645[/C][C]11902.6602723546[/C][/ROW]
[ROW][C]51[/C][C]495636[/C][C]490056.805057647[/C][C]5579.19494235347[/C][/ROW]
[ROW][C]52[/C][C]483861[/C][C]479637.853741772[/C][C]4223.14625822782[/C][/ROW]
[ROW][C]53[/C][C]508368[/C][C]500777.590921943[/C][C]7590.40907805669[/C][/ROW]
[ROW][C]54[/C][C]508368[/C][C]507757.008104387[/C][C]610.991895612795[/C][/ROW]
[ROW][C]55[/C][C]465234[/C][C]472205.593287181[/C][C]-6971.59328718082[/C][/ROW]
[ROW][C]56[/C][C]462303[/C][C]473072.992317756[/C][C]-10769.9923177559[/C][/ROW]
[ROW][C]57[/C][C]474075[/C][C]493125.092681173[/C][C]-19050.0926811735[/C][/ROW]
[ROW][C]58[/C][C]452514[/C][C]480939.871290085[/C][C]-28425.8712900848[/C][/ROW]
[ROW][C]59[/C][C]430848[/C][C]459057.53659303[/C][C]-28209.5365930301[/C][/ROW]
[ROW][C]60[/C][C]437796[/C][C]462023.837489054[/C][C]-24227.8374890537[/C][/ROW]
[ROW][C]61[/C][C]452514[/C][C]464910.463440627[/C][C]-12396.4634406268[/C][/ROW]
[ROW][C]62[/C][C]440730[/C][C]460600.158069357[/C][C]-19870.1580693572[/C][/ROW]
[ROW][C]63[/C][C]432849[/C][C]446870.207616522[/C][C]-14021.207616522[/C][/ROW]
[ROW][C]64[/C][C]416130[/C][C]426889.524254476[/C][C]-10759.5242544763[/C][/ROW]
[ROW][C]65[/C][C]438741[/C][C]442502.624266002[/C][C]-3761.62426600244[/C][/ROW]
[ROW][C]66[/C][C]439689[/C][C]434106.852996732[/C][C]5582.14700326789[/C][/ROW]
[ROW][C]67[/C][C]396570[/C][C]384030.553287011[/C][C]12539.4467129895[/C][/ROW]
[ROW][C]68[/C][C]395517[/C][C]375823.614421634[/C][C]19693.3855783657[/C][/ROW]
[ROW][C]69[/C][C]403410[/C][C]384822.844684205[/C][C]18587.1553157947[/C][/ROW]
[ROW][C]70[/C][C]378903[/C][C]362798.463729941[/C][C]16104.5362700589[/C][/ROW]
[ROW][C]71[/C][C]352395[/C][C]342496.036045291[/C][C]9898.96395470866[/C][/ROW]
[ROW][C]72[/C][C]363129[/C][C]351799.732170932[/C][C]11329.2678290681[/C][/ROW]
[ROW][C]73[/C][C]377850[/C][C]369734.153095112[/C][C]8115.84690488834[/C][/ROW]
[ROW][C]74[/C][C]362184[/C][C]362407.303316892[/C][C]-223.303316892358[/C][/ROW]
[ROW][C]75[/C][C]361236[/C][C]358846.813012275[/C][C]2389.18698772485[/C][/ROW]
[ROW][C]76[/C][C]345462[/C][C]347146.647400813[/C][C]-1684.64740081347[/C][/ROW]
[ROW][C]77[/C][C]371010[/C][C]374385.659159032[/C][C]-3375.65915903164[/C][/ROW]
[ROW][C]78[/C][C]375957[/C][C]379178.851275937[/C][C]-3221.85127593711[/C][/ROW]
[ROW][C]79[/C][C]327798[/C][C]339011.682352833[/C][C]-11213.6823528326[/C][/ROW]
[ROW][C]80[/C][C]317064[/C][C]338733.052569278[/C][C]-21669.0525692775[/C][/ROW]
[ROW][C]81[/C][C]323904[/C][C]344843.521774537[/C][C]-20939.5217745368[/C][/ROW]
[ROW][C]82[/C][C]297396[/C][C]316991.544578738[/C][C]-19595.5445787382[/C][/ROW]
[ROW][C]83[/C][C]269943[/C][C]286064.527777146[/C][C]-16121.5277771455[/C][/ROW]
[ROW][C]84[/C][C]278784[/C][C]291345.81046543[/C][C]-12561.8104654304[/C][/ROW]
[ROW][C]85[/C][C]295410[/C][C]300020.141745544[/C][C]-4610.14174554439[/C][/ROW]
[ROW][C]86[/C][C]275838[/C][C]278910.990449795[/C][C]-3072.99044979538[/C][/ROW]
[ROW][C]87[/C][C]278784[/C][C]272312.403405443[/C][C]6471.59659455688[/C][/ROW]
[ROW][C]88[/C][C]267012[/C][C]252060.994275011[/C][C]14951.0057249888[/C][/ROW]
[ROW][C]89[/C][C]291516[/C][C]274624.886950392[/C][C]16891.1130496076[/C][/ROW]
[ROW][C]90[/C][C]294450[/C][C]277637.918797976[/C][C]16812.0812020241[/C][/ROW]
[ROW][C]91[/C][C]235572[/C][C]229028.86774597[/C][C]6543.13225402977[/C][/ROW]
[ROW][C]92[/C][C]231663[/C][C]218664.906920776[/C][C]12998.0930792236[/C][/ROW]
[ROW][C]93[/C][C]242397[/C][C]227864.899130644[/C][C]14532.1008693563[/C][/ROW]
[ROW][C]94[/C][C]213999[/C][C]205341.904400398[/C][C]8657.09559960171[/C][/ROW]
[ROW][C]95[/C][C]188451[/C][C]182479.148113517[/C][C]5971.85188648332[/C][/ROW]
[ROW][C]96[/C][C]197292[/C][C]196460.994859294[/C][C]831.005140705762[/C][/ROW]
[ROW][C]97[/C][C]218850[/C][C]217886.586042483[/C][C]963.413957516517[/C][/ROW]
[ROW][C]98[/C][C]193386[/C][C]203265.459475399[/C][C]-9879.45947539856[/C][/ROW]
[ROW][C]99[/C][C]191397[/C][C]209374.462327313[/C][C]-17977.4623273131[/C][/ROW]
[ROW][C]100[/C][C]171732[/C][C]198452.556235851[/C][C]-26720.5562358509[/C][/ROW]
[ROW][C]101[/C][C]193386[/C][C]221138.948489824[/C][C]-27752.948489824[/C][/ROW]
[ROW][C]102[/C][C]200226[/C][C]220158.323095599[/C][C]-19932.3230955989[/C][/ROW]
[ROW][C]103[/C][C]139344[/C][C]157008.688329753[/C][C]-17664.6883297532[/C][/ROW]
[ROW][C]104[/C][C]139344[/C][C]147424.753711742[/C][C]-8080.75371174209[/C][/ROW]
[ROW][C]105[/C][C]148173[/C][C]152110.213196108[/C][C]-3937.21319610818[/C][/ROW]
[ROW][C]106[/C][C]124626[/C][C]117551.383457176[/C][C]7074.61654282376[/C][/ROW]
[ROW][C]107[/C][C]98118[/C][C]86764.1195917247[/C][C]11353.8804082753[/C][/ROW]
[ROW][C]108[/C][C]111891[/C][C]91293.5633949666[/C][C]20597.4366050334[/C][/ROW]
[ROW][C]109[/C][C]136398[/C][C]110098.689614013[/C][C]26299.3103859872[/C][/ROW]
[ROW][C]110[/C][C]109893[/C][C]84232.6384913978[/C][C]25660.3615086022[/C][/ROW]
[ROW][C]111[/C][C]120732[/C][C]83996.9195177119[/C][C]36735.0804822881[/C][/ROW]
[ROW][C]112[/C][C]105999[/C][C]70007.7958289047[/C][C]35991.2041710953[/C][/ROW]
[ROW][C]113[/C][C]129558[/C][C]100207.159142404[/C][C]29350.8408575961[/C][/ROW]
[ROW][C]114[/C][C]137439[/C][C]117137.498535262[/C][C]20301.5014647379[/C][/ROW]
[ROW][C]115[/C][C]74559[/C][C]67352.5632985783[/C][C]7206.43670142167[/C][/ROW]
[ROW][C]116[/C][C]69720[/C][C]77934.4461870894[/C][C]-8214.44618708944[/C][/ROW]
[ROW][C]117[/C][C]79506[/C][C]95920.2512932232[/C][C]-16414.2512932232[/C][/ROW]
[ROW][C]118[/C][C]55947[/C][C]79569.8936143283[/C][C]-23622.8936143283[/C][/ROW]
[ROW][C]119[/C][C]37332[/C][C]58030.9443113993[/C][C]-20698.9443113993[/C][/ROW]
[ROW][C]120[/C][C]45120[/C][C]74858.6968984693[/C][C]-29738.6968984693[/C][/ROW]
[ROW][C]121[/C][C]562407[/C][C]99064.8193085362[/C][C]463342.180691464[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210923&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210923&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
13544740545833.489583333-1093.48958333326
14538848540319.208132105-1471.20813210495
15544740546170.829007244-1430.82900724432
16539808540930.385922095-1122.38592209481
17555474556583.706953782-1109.70695378154
18562407563782.791287494-1375.79128749366
19532968540706.833888987-7738.83388898743
20525075529484.71921659-4409.7192165904
21531915528943.0117885192971.98821148125
22530967527960.945472983006.05452702031
23525075528351.769222229-3276.76922222879
24526035529028.559657171-2993.55965717137
25537807531791.1106331486015.88936685165
26535914525854.60721084510059.3927891547
27537807532516.2052151265290.79478487419
28537807528290.8829159849516.11708401644
29550635545452.336601135182.66339886957
30552528553871.603330303-1343.60333030275
31517194525908.493510924-8714.49351092381
32517194518670.996285439-1476.99628543889
33530967526289.2528057464677.74719425384
34524127526640.922054351-2513.92205435119
35512355521731.938549578-9376.93854957761
36517194522879.55176037-5685.55176037038
37528981534331.168057519-5350.16805751901
38523089531332.553642922-8243.55364292162
39522141531424.572035287-9283.57203528727
40509409528579.68340598-19170.6834059804
41528021536856.946032216-8835.94603221584
42531915534785.366727117-2870.36672711687
43493635496384.729513783-2749.72951378295
44492687493072.845299537-385.845299536886
45512355503308.5739935869046.4260064144
46501528494335.4737360817192.52626391948
47482901481234.5807857821666.41921421775
48490794484577.7674832466216.23251675355
49499527495715.2418424133811.75815758726
50501528489625.33972764511902.6602723546
51495636490056.8050576475579.19494235347
52483861479637.8537417724223.14625822782
53508368500777.5909219437590.40907805669
54508368507757.008104387610.991895612795
55465234472205.593287181-6971.59328718082
56462303473072.992317756-10769.9923177559
57474075493125.092681173-19050.0926811735
58452514480939.871290085-28425.8712900848
59430848459057.53659303-28209.5365930301
60437796462023.837489054-24227.8374890537
61452514464910.463440627-12396.4634406268
62440730460600.158069357-19870.1580693572
63432849446870.207616522-14021.207616522
64416130426889.524254476-10759.5242544763
65438741442502.624266002-3761.62426600244
66439689434106.8529967325582.14700326789
67396570384030.55328701112539.4467129895
68395517375823.61442163419693.3855783657
69403410384822.84468420518587.1553157947
70378903362798.46372994116104.5362700589
71352395342496.0360452919898.96395470866
72363129351799.73217093211329.2678290681
73377850369734.1530951128115.84690488834
74362184362407.303316892-223.303316892358
75361236358846.8130122752389.18698772485
76345462347146.647400813-1684.64740081347
77371010374385.659159032-3375.65915903164
78375957379178.851275937-3221.85127593711
79327798339011.682352833-11213.6823528326
80317064338733.052569278-21669.0525692775
81323904344843.521774537-20939.5217745368
82297396316991.544578738-19595.5445787382
83269943286064.527777146-16121.5277771455
84278784291345.81046543-12561.8104654304
85295410300020.141745544-4610.14174554439
86275838278910.990449795-3072.99044979538
87278784272312.4034054436471.59659455688
88267012252060.99427501114951.0057249888
89291516274624.88695039216891.1130496076
90294450277637.91879797616812.0812020241
91235572229028.867745976543.13225402977
92231663218664.90692077612998.0930792236
93242397227864.89913064414532.1008693563
94213999205341.9044003988657.09559960171
95188451182479.1481135175971.85188648332
96197292196460.994859294831.005140705762
97218850217886.586042483963.413957516517
98193386203265.459475399-9879.45947539856
99191397209374.462327313-17977.4623273131
100171732198452.556235851-26720.5562358509
101193386221138.948489824-27752.948489824
102200226220158.323095599-19932.3230955989
103139344157008.688329753-17664.6883297532
104139344147424.753711742-8080.75371174209
105148173152110.213196108-3937.21319610818
106124626117551.3834571767074.61654282376
1079811886764.119591724711353.8804082753
10811189191293.563394966620597.4366050334
109136398110098.68961401326299.3103859872
11010989384232.638491397825660.3615086022
11112073283996.919517711936735.0804822881
11210599970007.795828904735991.2041710953
113129558100207.15914240429350.8408575961
114137439117137.49853526220301.5014647379
1157455967352.56329857837206.43670142167
1166972077934.4461870894-8214.44618708944
1177950695920.2512932232-16414.2512932232
1185594779569.8936143283-23622.8936143283
1193733258030.9443113993-20698.9443113993
1204512074858.6968984693-29738.6968984693
12156240799064.8193085362463342.180691464







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
122127920.20682052936614.2809214646219226.132719593
123158544.62641169566605.7295585656250483.523264825
124161982.37894833368841.1766337602255123.581262905
125202558.925007289107486.624457655297631.225556923
126226780.613026072128915.712118894324645.513933249
127180268.92775368378651.6317488553281886.223758511
128192589.378578486199.754222935298979.002933865
129220502.685593106108297.638538717332707.732647495
130216339.42025126297284.2318943968335394.608608127
131217981.10571241491073.0688252913344889.142599537
132247621.652935155111905.367156861383337.938713448
133752348.93193983606924.309345036897773.554534625

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
122 & 127920.206820529 & 36614.2809214646 & 219226.132719593 \tabularnewline
123 & 158544.626411695 & 66605.7295585656 & 250483.523264825 \tabularnewline
124 & 161982.378948333 & 68841.1766337602 & 255123.581262905 \tabularnewline
125 & 202558.925007289 & 107486.624457655 & 297631.225556923 \tabularnewline
126 & 226780.613026072 & 128915.712118894 & 324645.513933249 \tabularnewline
127 & 180268.927753683 & 78651.6317488553 & 281886.223758511 \tabularnewline
128 & 192589.3785784 & 86199.754222935 & 298979.002933865 \tabularnewline
129 & 220502.685593106 & 108297.638538717 & 332707.732647495 \tabularnewline
130 & 216339.420251262 & 97284.2318943968 & 335394.608608127 \tabularnewline
131 & 217981.105712414 & 91073.0688252913 & 344889.142599537 \tabularnewline
132 & 247621.652935155 & 111905.367156861 & 383337.938713448 \tabularnewline
133 & 752348.93193983 & 606924.309345036 & 897773.554534625 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210923&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]122[/C][C]127920.206820529[/C][C]36614.2809214646[/C][C]219226.132719593[/C][/ROW]
[ROW][C]123[/C][C]158544.626411695[/C][C]66605.7295585656[/C][C]250483.523264825[/C][/ROW]
[ROW][C]124[/C][C]161982.378948333[/C][C]68841.1766337602[/C][C]255123.581262905[/C][/ROW]
[ROW][C]125[/C][C]202558.925007289[/C][C]107486.624457655[/C][C]297631.225556923[/C][/ROW]
[ROW][C]126[/C][C]226780.613026072[/C][C]128915.712118894[/C][C]324645.513933249[/C][/ROW]
[ROW][C]127[/C][C]180268.927753683[/C][C]78651.6317488553[/C][C]281886.223758511[/C][/ROW]
[ROW][C]128[/C][C]192589.3785784[/C][C]86199.754222935[/C][C]298979.002933865[/C][/ROW]
[ROW][C]129[/C][C]220502.685593106[/C][C]108297.638538717[/C][C]332707.732647495[/C][/ROW]
[ROW][C]130[/C][C]216339.420251262[/C][C]97284.2318943968[/C][C]335394.608608127[/C][/ROW]
[ROW][C]131[/C][C]217981.105712414[/C][C]91073.0688252913[/C][C]344889.142599537[/C][/ROW]
[ROW][C]132[/C][C]247621.652935155[/C][C]111905.367156861[/C][C]383337.938713448[/C][/ROW]
[ROW][C]133[/C][C]752348.93193983[/C][C]606924.309345036[/C][C]897773.554534625[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210923&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210923&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
122127920.20682052936614.2809214646219226.132719593
123158544.62641169566605.7295585656250483.523264825
124161982.37894833368841.1766337602255123.581262905
125202558.925007289107486.624457655297631.225556923
126226780.613026072128915.712118894324645.513933249
127180268.92775368378651.6317488553281886.223758511
128192589.378578486199.754222935298979.002933865
129220502.685593106108297.638538717332707.732647495
130216339.42025126297284.2318943968335394.608608127
131217981.10571241491073.0688252913344889.142599537
132247621.652935155111905.367156861383337.938713448
133752348.93193983606924.309345036897773.554534625



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