Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 02 Jun 2010 09:13:49 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Jun/02/t1275470219l9rfujrunn35wec.htm/, Retrieved Fri, 26 Apr 2024 21:46:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=77015, Retrieved Fri, 26 Apr 2024 21:46:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact155
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Katleen van den A...] [2010-06-02 09:13:49] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
285708
905858
225733
405481
845758
805651
395747
695853
175625
405534
965639
575634
576023
566089
336141
26271
586226
376484
176583
287042
997142
207694
418003
838258
848182
658215
208304
398599
438399
578393
988390
958304
318251
78307
408520
748640
258520
518618
388588
238842
328957
499266
109011
168896
798921
878732
897576
518317
228370
758167
658491
518170
398212
498286
78136
647990
357927
698061
407932
637934
397784
217980
47737
467672
67651
167524
687406
367345
157553
887453
227566
817279
697059
997185
847075
547122
996977
346998
967154
547097
586853
46728
236883
36784
277085
446998
586725
496845
86765
146966
197113
657096
337200
17273
457284
507696
547628
157435
67793
267631
518397
918560
918895
429509
289569
9010172
1810617
7111400
1611919
9712714
2913310
1013816
6714518
2414721
9114534
8214993
6215159
515612
9415340
3715267




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77015&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77015&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77015&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.173659852690062
beta0.000673607157187447
gamma0.0799120898660841

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.173659852690062 \tabularnewline
beta & 0.000673607157187447 \tabularnewline
gamma & 0.0799120898660841 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77015&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]0.173659852690062[/C][/ROW]
[ROW][C]beta[/C][C]0.000673607157187447[/C][/ROW]
[ROW][C]gamma[/C][C]0.0799120898660841[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77015&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77015&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
alpha0.173659852690062
beta0.000673607157187447
gamma0.0799120898660841







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13576023739236.348343582-163213.348343582
14566089722597.22335502-156508.223355020
15336141387184.554260695-51043.5542606952
162627127219.7972199181-948.79721991812
17586226627443.268855386-41217.2688553861
18376484397321.350841869-20837.3508418691
19176583309024.876298841-132441.876298841
20287042487831.212121884-200789.212121884
21997142111930.940482397885211.059517603
22207694615987.623242758-408293.623242758
234180031339190.23642928-921187.236429283
24838258728062.325250325110195.674749675
25848182762595.51126038885586.4887396124
26658215792626.93376749-134411.933767490
27208304432249.652555293-223945.652555293
2839859928533.8767881063370065.123211894
294383992192383.68639341-1753984.68639341
305783931235199.51962694-656806.519626942
31988390873787.559488568114602.440511432
329583041563666.53137693-605362.53137693
33318251465543.10628409-147292.10628409
3478307798431.473768609-720124.473768609
354085201658292.15935405-1249772.15935405
36748640952307.363652946-203667.363652946
37258520937394.005680403-678874.005680403
38518618820844.364617842-302226.364617842
39388588420527.621090478-31939.6210904782
4023884239614.7499949613199227.250005039
413289571296548.27519747-967591.275197469
42499266752144.103420064-252878.103420064
43109011575868.96336755-466857.963367551
44168896827763.85529732-658867.85529732
45798921226363.709418321572557.290581679
46878732559760.11243461318971.88756539
478975761536469.43460782-638893.434607823
48518317985389.101518985-467072.101518985
49228370887028.133628562-658658.133628562
50758167797520.147968473-39353.1479684729
51658491442654.497684608215836.502315392
5251817054427.5431997364463742.456800264
533982121898231.69665058-1500019.69665058
544982861135850.29550629-637564.295506293
5578136804813.882360483-726677.882360483
566479901143970.69913980-495980.699139798
57357927402378.270111733-44451.2701117332
58698061629247.63993729268813.3600627081
594079321503017.21771447-1095085.21771447
60637934902609.559980435-264675.559980435
61397784820829.792641808-423045.792641808
62217980815303.86657468-597323.86657468
6347737410651.930193338-362914.930193338
6446767246558.0856360961421113.914363904
65676511285103.20654577-1217452.20654577
66167524756911.43381467-589387.43381467
67687406495339.173641111192066.826358889
68367345927128.056999731-559783.056999731
69157553322300.243151604-164747.243151604
70887453472840.802374417414612.197625583
712275661195209.45119596-967643.451195957
72817279729633.96798509687645.0320149038
73697059699827.566442166-2768.56644216599
74997185748295.097241629248889.902758371
75847075451961.163959089395113.836040911
7654712293313.8912772429453808.108722757
779969771389751.15843093-392774.158430927
78346998950519.584159758-603521.584159758
79967154699936.111890899267217.888109101
805470971226515.11523930-679418.115239301
81586853436094.680233765150758.319766235
8246728818005.68409107-771277.68409107
832368831343887.29824682-1107004.29824682
8436784882171.265927443-845387.265927443
85277085685219.690924196-408134.690924196
86446998669347.168823079-222349.168823079
87586725368482.338266265218242.661733735
8849684580959.0361636194415885.963836381
89867651029634.82821167-942869.828211673
90146966602295.422765024-455329.422765024
91197113462310.402054415-265197.402054415
92657096635365.15890527521730.8410947252
93337200265518.25098588771681.7490141131
9417273442027.094132448-424754.094132448
95457284724639.179859548-267355.179859548
96507696507573.661244126122.338755873789
97547628486041.8429851761586.1570148298
98157435550592.895460722-393157.895460722
9967793296661.622649114-228868.622649114
10026763157419.8798939864210211.120106014
101518397491087.36803446227309.6319655378
102918560346967.885466356571592.114533644
103918895400023.419307796518871.580692204
104429509785818.286904767-356309.286904767
105289569305955.351629511-16386.3516295106
1069010172438500.6799902978571671.3200097
10718106174079254.52753124-2268637.52753124
10871114002894967.209065534216432.79093447
10916119193585486.10766381-1973567.10766381
11097127143453102.027657836259611.97234217
11129133102860115.6435629453194.3564370624
1121013816810355.40686907203460.593130930
11367145183949731.223256452764786.77674355
11424147213424420.25408295-1009699.25408295
11591145342921745.612647096192788.38735291
11682149935877982.544774472337010.45522553
11762151592779197.896474473435961.10352553
1185156126448467.49319585-5932855.49319585
11994153408524589.71609453890750.283905465
12037152677673911.81918202-3958644.81918202

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 576023 & 739236.348343582 & -163213.348343582 \tabularnewline
14 & 566089 & 722597.22335502 & -156508.223355020 \tabularnewline
15 & 336141 & 387184.554260695 & -51043.5542606952 \tabularnewline
16 & 26271 & 27219.7972199181 & -948.79721991812 \tabularnewline
17 & 586226 & 627443.268855386 & -41217.2688553861 \tabularnewline
18 & 376484 & 397321.350841869 & -20837.3508418691 \tabularnewline
19 & 176583 & 309024.876298841 & -132441.876298841 \tabularnewline
20 & 287042 & 487831.212121884 & -200789.212121884 \tabularnewline
21 & 997142 & 111930.940482397 & 885211.059517603 \tabularnewline
22 & 207694 & 615987.623242758 & -408293.623242758 \tabularnewline
23 & 418003 & 1339190.23642928 & -921187.236429283 \tabularnewline
24 & 838258 & 728062.325250325 & 110195.674749675 \tabularnewline
25 & 848182 & 762595.511260388 & 85586.4887396124 \tabularnewline
26 & 658215 & 792626.93376749 & -134411.933767490 \tabularnewline
27 & 208304 & 432249.652555293 & -223945.652555293 \tabularnewline
28 & 398599 & 28533.8767881063 & 370065.123211894 \tabularnewline
29 & 438399 & 2192383.68639341 & -1753984.68639341 \tabularnewline
30 & 578393 & 1235199.51962694 & -656806.519626942 \tabularnewline
31 & 988390 & 873787.559488568 & 114602.440511432 \tabularnewline
32 & 958304 & 1563666.53137693 & -605362.53137693 \tabularnewline
33 & 318251 & 465543.10628409 & -147292.10628409 \tabularnewline
34 & 78307 & 798431.473768609 & -720124.473768609 \tabularnewline
35 & 408520 & 1658292.15935405 & -1249772.15935405 \tabularnewline
36 & 748640 & 952307.363652946 & -203667.363652946 \tabularnewline
37 & 258520 & 937394.005680403 & -678874.005680403 \tabularnewline
38 & 518618 & 820844.364617842 & -302226.364617842 \tabularnewline
39 & 388588 & 420527.621090478 & -31939.6210904782 \tabularnewline
40 & 238842 & 39614.7499949613 & 199227.250005039 \tabularnewline
41 & 328957 & 1296548.27519747 & -967591.275197469 \tabularnewline
42 & 499266 & 752144.103420064 & -252878.103420064 \tabularnewline
43 & 109011 & 575868.96336755 & -466857.963367551 \tabularnewline
44 & 168896 & 827763.85529732 & -658867.85529732 \tabularnewline
45 & 798921 & 226363.709418321 & 572557.290581679 \tabularnewline
46 & 878732 & 559760.11243461 & 318971.88756539 \tabularnewline
47 & 897576 & 1536469.43460782 & -638893.434607823 \tabularnewline
48 & 518317 & 985389.101518985 & -467072.101518985 \tabularnewline
49 & 228370 & 887028.133628562 & -658658.133628562 \tabularnewline
50 & 758167 & 797520.147968473 & -39353.1479684729 \tabularnewline
51 & 658491 & 442654.497684608 & 215836.502315392 \tabularnewline
52 & 518170 & 54427.5431997364 & 463742.456800264 \tabularnewline
53 & 398212 & 1898231.69665058 & -1500019.69665058 \tabularnewline
54 & 498286 & 1135850.29550629 & -637564.295506293 \tabularnewline
55 & 78136 & 804813.882360483 & -726677.882360483 \tabularnewline
56 & 647990 & 1143970.69913980 & -495980.699139798 \tabularnewline
57 & 357927 & 402378.270111733 & -44451.2701117332 \tabularnewline
58 & 698061 & 629247.639937292 & 68813.3600627081 \tabularnewline
59 & 407932 & 1503017.21771447 & -1095085.21771447 \tabularnewline
60 & 637934 & 902609.559980435 & -264675.559980435 \tabularnewline
61 & 397784 & 820829.792641808 & -423045.792641808 \tabularnewline
62 & 217980 & 815303.86657468 & -597323.86657468 \tabularnewline
63 & 47737 & 410651.930193338 & -362914.930193338 \tabularnewline
64 & 467672 & 46558.0856360961 & 421113.914363904 \tabularnewline
65 & 67651 & 1285103.20654577 & -1217452.20654577 \tabularnewline
66 & 167524 & 756911.43381467 & -589387.43381467 \tabularnewline
67 & 687406 & 495339.173641111 & 192066.826358889 \tabularnewline
68 & 367345 & 927128.056999731 & -559783.056999731 \tabularnewline
69 & 157553 & 322300.243151604 & -164747.243151604 \tabularnewline
70 & 887453 & 472840.802374417 & 414612.197625583 \tabularnewline
71 & 227566 & 1195209.45119596 & -967643.451195957 \tabularnewline
72 & 817279 & 729633.967985096 & 87645.0320149038 \tabularnewline
73 & 697059 & 699827.566442166 & -2768.56644216599 \tabularnewline
74 & 997185 & 748295.097241629 & 248889.902758371 \tabularnewline
75 & 847075 & 451961.163959089 & 395113.836040911 \tabularnewline
76 & 547122 & 93313.8912772429 & 453808.108722757 \tabularnewline
77 & 996977 & 1389751.15843093 & -392774.158430927 \tabularnewline
78 & 346998 & 950519.584159758 & -603521.584159758 \tabularnewline
79 & 967154 & 699936.111890899 & 267217.888109101 \tabularnewline
80 & 547097 & 1226515.11523930 & -679418.115239301 \tabularnewline
81 & 586853 & 436094.680233765 & 150758.319766235 \tabularnewline
82 & 46728 & 818005.68409107 & -771277.68409107 \tabularnewline
83 & 236883 & 1343887.29824682 & -1107004.29824682 \tabularnewline
84 & 36784 & 882171.265927443 & -845387.265927443 \tabularnewline
85 & 277085 & 685219.690924196 & -408134.690924196 \tabularnewline
86 & 446998 & 669347.168823079 & -222349.168823079 \tabularnewline
87 & 586725 & 368482.338266265 & 218242.661733735 \tabularnewline
88 & 496845 & 80959.0361636194 & 415885.963836381 \tabularnewline
89 & 86765 & 1029634.82821167 & -942869.828211673 \tabularnewline
90 & 146966 & 602295.422765024 & -455329.422765024 \tabularnewline
91 & 197113 & 462310.402054415 & -265197.402054415 \tabularnewline
92 & 657096 & 635365.158905275 & 21730.8410947252 \tabularnewline
93 & 337200 & 265518.250985887 & 71681.7490141131 \tabularnewline
94 & 17273 & 442027.094132448 & -424754.094132448 \tabularnewline
95 & 457284 & 724639.179859548 & -267355.179859548 \tabularnewline
96 & 507696 & 507573.661244126 & 122.338755873789 \tabularnewline
97 & 547628 & 486041.84298517 & 61586.1570148298 \tabularnewline
98 & 157435 & 550592.895460722 & -393157.895460722 \tabularnewline
99 & 67793 & 296661.622649114 & -228868.622649114 \tabularnewline
100 & 267631 & 57419.8798939864 & 210211.120106014 \tabularnewline
101 & 518397 & 491087.368034462 & 27309.6319655378 \tabularnewline
102 & 918560 & 346967.885466356 & 571592.114533644 \tabularnewline
103 & 918895 & 400023.419307796 & 518871.580692204 \tabularnewline
104 & 429509 & 785818.286904767 & -356309.286904767 \tabularnewline
105 & 289569 & 305955.351629511 & -16386.3516295106 \tabularnewline
106 & 9010172 & 438500.679990297 & 8571671.3200097 \tabularnewline
107 & 1810617 & 4079254.52753124 & -2268637.52753124 \tabularnewline
108 & 7111400 & 2894967.20906553 & 4216432.79093447 \tabularnewline
109 & 1611919 & 3585486.10766381 & -1973567.10766381 \tabularnewline
110 & 9712714 & 3453102.02765783 & 6259611.97234217 \tabularnewline
111 & 2913310 & 2860115.64356294 & 53194.3564370624 \tabularnewline
112 & 1013816 & 810355.40686907 & 203460.593130930 \tabularnewline
113 & 6714518 & 3949731.22325645 & 2764786.77674355 \tabularnewline
114 & 2414721 & 3424420.25408295 & -1009699.25408295 \tabularnewline
115 & 9114534 & 2921745.61264709 & 6192788.38735291 \tabularnewline
116 & 8214993 & 5877982.54477447 & 2337010.45522553 \tabularnewline
117 & 6215159 & 2779197.89647447 & 3435961.10352553 \tabularnewline
118 & 515612 & 6448467.49319585 & -5932855.49319585 \tabularnewline
119 & 9415340 & 8524589.71609453 & 890750.283905465 \tabularnewline
120 & 3715267 & 7673911.81918202 & -3958644.81918202 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77015&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]576023[/C][C]739236.348343582[/C][C]-163213.348343582[/C][/ROW]
[ROW][C]14[/C][C]566089[/C][C]722597.22335502[/C][C]-156508.223355020[/C][/ROW]
[ROW][C]15[/C][C]336141[/C][C]387184.554260695[/C][C]-51043.5542606952[/C][/ROW]
[ROW][C]16[/C][C]26271[/C][C]27219.7972199181[/C][C]-948.79721991812[/C][/ROW]
[ROW][C]17[/C][C]586226[/C][C]627443.268855386[/C][C]-41217.2688553861[/C][/ROW]
[ROW][C]18[/C][C]376484[/C][C]397321.350841869[/C][C]-20837.3508418691[/C][/ROW]
[ROW][C]19[/C][C]176583[/C][C]309024.876298841[/C][C]-132441.876298841[/C][/ROW]
[ROW][C]20[/C][C]287042[/C][C]487831.212121884[/C][C]-200789.212121884[/C][/ROW]
[ROW][C]21[/C][C]997142[/C][C]111930.940482397[/C][C]885211.059517603[/C][/ROW]
[ROW][C]22[/C][C]207694[/C][C]615987.623242758[/C][C]-408293.623242758[/C][/ROW]
[ROW][C]23[/C][C]418003[/C][C]1339190.23642928[/C][C]-921187.236429283[/C][/ROW]
[ROW][C]24[/C][C]838258[/C][C]728062.325250325[/C][C]110195.674749675[/C][/ROW]
[ROW][C]25[/C][C]848182[/C][C]762595.511260388[/C][C]85586.4887396124[/C][/ROW]
[ROW][C]26[/C][C]658215[/C][C]792626.93376749[/C][C]-134411.933767490[/C][/ROW]
[ROW][C]27[/C][C]208304[/C][C]432249.652555293[/C][C]-223945.652555293[/C][/ROW]
[ROW][C]28[/C][C]398599[/C][C]28533.8767881063[/C][C]370065.123211894[/C][/ROW]
[ROW][C]29[/C][C]438399[/C][C]2192383.68639341[/C][C]-1753984.68639341[/C][/ROW]
[ROW][C]30[/C][C]578393[/C][C]1235199.51962694[/C][C]-656806.519626942[/C][/ROW]
[ROW][C]31[/C][C]988390[/C][C]873787.559488568[/C][C]114602.440511432[/C][/ROW]
[ROW][C]32[/C][C]958304[/C][C]1563666.53137693[/C][C]-605362.53137693[/C][/ROW]
[ROW][C]33[/C][C]318251[/C][C]465543.10628409[/C][C]-147292.10628409[/C][/ROW]
[ROW][C]34[/C][C]78307[/C][C]798431.473768609[/C][C]-720124.473768609[/C][/ROW]
[ROW][C]35[/C][C]408520[/C][C]1658292.15935405[/C][C]-1249772.15935405[/C][/ROW]
[ROW][C]36[/C][C]748640[/C][C]952307.363652946[/C][C]-203667.363652946[/C][/ROW]
[ROW][C]37[/C][C]258520[/C][C]937394.005680403[/C][C]-678874.005680403[/C][/ROW]
[ROW][C]38[/C][C]518618[/C][C]820844.364617842[/C][C]-302226.364617842[/C][/ROW]
[ROW][C]39[/C][C]388588[/C][C]420527.621090478[/C][C]-31939.6210904782[/C][/ROW]
[ROW][C]40[/C][C]238842[/C][C]39614.7499949613[/C][C]199227.250005039[/C][/ROW]
[ROW][C]41[/C][C]328957[/C][C]1296548.27519747[/C][C]-967591.275197469[/C][/ROW]
[ROW][C]42[/C][C]499266[/C][C]752144.103420064[/C][C]-252878.103420064[/C][/ROW]
[ROW][C]43[/C][C]109011[/C][C]575868.96336755[/C][C]-466857.963367551[/C][/ROW]
[ROW][C]44[/C][C]168896[/C][C]827763.85529732[/C][C]-658867.85529732[/C][/ROW]
[ROW][C]45[/C][C]798921[/C][C]226363.709418321[/C][C]572557.290581679[/C][/ROW]
[ROW][C]46[/C][C]878732[/C][C]559760.11243461[/C][C]318971.88756539[/C][/ROW]
[ROW][C]47[/C][C]897576[/C][C]1536469.43460782[/C][C]-638893.434607823[/C][/ROW]
[ROW][C]48[/C][C]518317[/C][C]985389.101518985[/C][C]-467072.101518985[/C][/ROW]
[ROW][C]49[/C][C]228370[/C][C]887028.133628562[/C][C]-658658.133628562[/C][/ROW]
[ROW][C]50[/C][C]758167[/C][C]797520.147968473[/C][C]-39353.1479684729[/C][/ROW]
[ROW][C]51[/C][C]658491[/C][C]442654.497684608[/C][C]215836.502315392[/C][/ROW]
[ROW][C]52[/C][C]518170[/C][C]54427.5431997364[/C][C]463742.456800264[/C][/ROW]
[ROW][C]53[/C][C]398212[/C][C]1898231.69665058[/C][C]-1500019.69665058[/C][/ROW]
[ROW][C]54[/C][C]498286[/C][C]1135850.29550629[/C][C]-637564.295506293[/C][/ROW]
[ROW][C]55[/C][C]78136[/C][C]804813.882360483[/C][C]-726677.882360483[/C][/ROW]
[ROW][C]56[/C][C]647990[/C][C]1143970.69913980[/C][C]-495980.699139798[/C][/ROW]
[ROW][C]57[/C][C]357927[/C][C]402378.270111733[/C][C]-44451.2701117332[/C][/ROW]
[ROW][C]58[/C][C]698061[/C][C]629247.639937292[/C][C]68813.3600627081[/C][/ROW]
[ROW][C]59[/C][C]407932[/C][C]1503017.21771447[/C][C]-1095085.21771447[/C][/ROW]
[ROW][C]60[/C][C]637934[/C][C]902609.559980435[/C][C]-264675.559980435[/C][/ROW]
[ROW][C]61[/C][C]397784[/C][C]820829.792641808[/C][C]-423045.792641808[/C][/ROW]
[ROW][C]62[/C][C]217980[/C][C]815303.86657468[/C][C]-597323.86657468[/C][/ROW]
[ROW][C]63[/C][C]47737[/C][C]410651.930193338[/C][C]-362914.930193338[/C][/ROW]
[ROW][C]64[/C][C]467672[/C][C]46558.0856360961[/C][C]421113.914363904[/C][/ROW]
[ROW][C]65[/C][C]67651[/C][C]1285103.20654577[/C][C]-1217452.20654577[/C][/ROW]
[ROW][C]66[/C][C]167524[/C][C]756911.43381467[/C][C]-589387.43381467[/C][/ROW]
[ROW][C]67[/C][C]687406[/C][C]495339.173641111[/C][C]192066.826358889[/C][/ROW]
[ROW][C]68[/C][C]367345[/C][C]927128.056999731[/C][C]-559783.056999731[/C][/ROW]
[ROW][C]69[/C][C]157553[/C][C]322300.243151604[/C][C]-164747.243151604[/C][/ROW]
[ROW][C]70[/C][C]887453[/C][C]472840.802374417[/C][C]414612.197625583[/C][/ROW]
[ROW][C]71[/C][C]227566[/C][C]1195209.45119596[/C][C]-967643.451195957[/C][/ROW]
[ROW][C]72[/C][C]817279[/C][C]729633.967985096[/C][C]87645.0320149038[/C][/ROW]
[ROW][C]73[/C][C]697059[/C][C]699827.566442166[/C][C]-2768.56644216599[/C][/ROW]
[ROW][C]74[/C][C]997185[/C][C]748295.097241629[/C][C]248889.902758371[/C][/ROW]
[ROW][C]75[/C][C]847075[/C][C]451961.163959089[/C][C]395113.836040911[/C][/ROW]
[ROW][C]76[/C][C]547122[/C][C]93313.8912772429[/C][C]453808.108722757[/C][/ROW]
[ROW][C]77[/C][C]996977[/C][C]1389751.15843093[/C][C]-392774.158430927[/C][/ROW]
[ROW][C]78[/C][C]346998[/C][C]950519.584159758[/C][C]-603521.584159758[/C][/ROW]
[ROW][C]79[/C][C]967154[/C][C]699936.111890899[/C][C]267217.888109101[/C][/ROW]
[ROW][C]80[/C][C]547097[/C][C]1226515.11523930[/C][C]-679418.115239301[/C][/ROW]
[ROW][C]81[/C][C]586853[/C][C]436094.680233765[/C][C]150758.319766235[/C][/ROW]
[ROW][C]82[/C][C]46728[/C][C]818005.68409107[/C][C]-771277.68409107[/C][/ROW]
[ROW][C]83[/C][C]236883[/C][C]1343887.29824682[/C][C]-1107004.29824682[/C][/ROW]
[ROW][C]84[/C][C]36784[/C][C]882171.265927443[/C][C]-845387.265927443[/C][/ROW]
[ROW][C]85[/C][C]277085[/C][C]685219.690924196[/C][C]-408134.690924196[/C][/ROW]
[ROW][C]86[/C][C]446998[/C][C]669347.168823079[/C][C]-222349.168823079[/C][/ROW]
[ROW][C]87[/C][C]586725[/C][C]368482.338266265[/C][C]218242.661733735[/C][/ROW]
[ROW][C]88[/C][C]496845[/C][C]80959.0361636194[/C][C]415885.963836381[/C][/ROW]
[ROW][C]89[/C][C]86765[/C][C]1029634.82821167[/C][C]-942869.828211673[/C][/ROW]
[ROW][C]90[/C][C]146966[/C][C]602295.422765024[/C][C]-455329.422765024[/C][/ROW]
[ROW][C]91[/C][C]197113[/C][C]462310.402054415[/C][C]-265197.402054415[/C][/ROW]
[ROW][C]92[/C][C]657096[/C][C]635365.158905275[/C][C]21730.8410947252[/C][/ROW]
[ROW][C]93[/C][C]337200[/C][C]265518.250985887[/C][C]71681.7490141131[/C][/ROW]
[ROW][C]94[/C][C]17273[/C][C]442027.094132448[/C][C]-424754.094132448[/C][/ROW]
[ROW][C]95[/C][C]457284[/C][C]724639.179859548[/C][C]-267355.179859548[/C][/ROW]
[ROW][C]96[/C][C]507696[/C][C]507573.661244126[/C][C]122.338755873789[/C][/ROW]
[ROW][C]97[/C][C]547628[/C][C]486041.84298517[/C][C]61586.1570148298[/C][/ROW]
[ROW][C]98[/C][C]157435[/C][C]550592.895460722[/C][C]-393157.895460722[/C][/ROW]
[ROW][C]99[/C][C]67793[/C][C]296661.622649114[/C][C]-228868.622649114[/C][/ROW]
[ROW][C]100[/C][C]267631[/C][C]57419.8798939864[/C][C]210211.120106014[/C][/ROW]
[ROW][C]101[/C][C]518397[/C][C]491087.368034462[/C][C]27309.6319655378[/C][/ROW]
[ROW][C]102[/C][C]918560[/C][C]346967.885466356[/C][C]571592.114533644[/C][/ROW]
[ROW][C]103[/C][C]918895[/C][C]400023.419307796[/C][C]518871.580692204[/C][/ROW]
[ROW][C]104[/C][C]429509[/C][C]785818.286904767[/C][C]-356309.286904767[/C][/ROW]
[ROW][C]105[/C][C]289569[/C][C]305955.351629511[/C][C]-16386.3516295106[/C][/ROW]
[ROW][C]106[/C][C]9010172[/C][C]438500.679990297[/C][C]8571671.3200097[/C][/ROW]
[ROW][C]107[/C][C]1810617[/C][C]4079254.52753124[/C][C]-2268637.52753124[/C][/ROW]
[ROW][C]108[/C][C]7111400[/C][C]2894967.20906553[/C][C]4216432.79093447[/C][/ROW]
[ROW][C]109[/C][C]1611919[/C][C]3585486.10766381[/C][C]-1973567.10766381[/C][/ROW]
[ROW][C]110[/C][C]9712714[/C][C]3453102.02765783[/C][C]6259611.97234217[/C][/ROW]
[ROW][C]111[/C][C]2913310[/C][C]2860115.64356294[/C][C]53194.3564370624[/C][/ROW]
[ROW][C]112[/C][C]1013816[/C][C]810355.40686907[/C][C]203460.593130930[/C][/ROW]
[ROW][C]113[/C][C]6714518[/C][C]3949731.22325645[/C][C]2764786.77674355[/C][/ROW]
[ROW][C]114[/C][C]2414721[/C][C]3424420.25408295[/C][C]-1009699.25408295[/C][/ROW]
[ROW][C]115[/C][C]9114534[/C][C]2921745.61264709[/C][C]6192788.38735291[/C][/ROW]
[ROW][C]116[/C][C]8214993[/C][C]5877982.54477447[/C][C]2337010.45522553[/C][/ROW]
[ROW][C]117[/C][C]6215159[/C][C]2779197.89647447[/C][C]3435961.10352553[/C][/ROW]
[ROW][C]118[/C][C]515612[/C][C]6448467.49319585[/C][C]-5932855.49319585[/C][/ROW]
[ROW][C]119[/C][C]9415340[/C][C]8524589.71609453[/C][C]890750.283905465[/C][/ROW]
[ROW][C]120[/C][C]3715267[/C][C]7673911.81918202[/C][C]-3958644.81918202[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77015&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77015&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
13576023739236.348343582-163213.348343582
14566089722597.22335502-156508.223355020
15336141387184.554260695-51043.5542606952
162627127219.7972199181-948.79721991812
17586226627443.268855386-41217.2688553861
18376484397321.350841869-20837.3508418691
19176583309024.876298841-132441.876298841
20287042487831.212121884-200789.212121884
21997142111930.940482397885211.059517603
22207694615987.623242758-408293.623242758
234180031339190.23642928-921187.236429283
24838258728062.325250325110195.674749675
25848182762595.51126038885586.4887396124
26658215792626.93376749-134411.933767490
27208304432249.652555293-223945.652555293
2839859928533.8767881063370065.123211894
294383992192383.68639341-1753984.68639341
305783931235199.51962694-656806.519626942
31988390873787.559488568114602.440511432
329583041563666.53137693-605362.53137693
33318251465543.10628409-147292.10628409
3478307798431.473768609-720124.473768609
354085201658292.15935405-1249772.15935405
36748640952307.363652946-203667.363652946
37258520937394.005680403-678874.005680403
38518618820844.364617842-302226.364617842
39388588420527.621090478-31939.6210904782
4023884239614.7499949613199227.250005039
413289571296548.27519747-967591.275197469
42499266752144.103420064-252878.103420064
43109011575868.96336755-466857.963367551
44168896827763.85529732-658867.85529732
45798921226363.709418321572557.290581679
46878732559760.11243461318971.88756539
478975761536469.43460782-638893.434607823
48518317985389.101518985-467072.101518985
49228370887028.133628562-658658.133628562
50758167797520.147968473-39353.1479684729
51658491442654.497684608215836.502315392
5251817054427.5431997364463742.456800264
533982121898231.69665058-1500019.69665058
544982861135850.29550629-637564.295506293
5578136804813.882360483-726677.882360483
566479901143970.69913980-495980.699139798
57357927402378.270111733-44451.2701117332
58698061629247.63993729268813.3600627081
594079321503017.21771447-1095085.21771447
60637934902609.559980435-264675.559980435
61397784820829.792641808-423045.792641808
62217980815303.86657468-597323.86657468
6347737410651.930193338-362914.930193338
6446767246558.0856360961421113.914363904
65676511285103.20654577-1217452.20654577
66167524756911.43381467-589387.43381467
67687406495339.173641111192066.826358889
68367345927128.056999731-559783.056999731
69157553322300.243151604-164747.243151604
70887453472840.802374417414612.197625583
712275661195209.45119596-967643.451195957
72817279729633.96798509687645.0320149038
73697059699827.566442166-2768.56644216599
74997185748295.097241629248889.902758371
75847075451961.163959089395113.836040911
7654712293313.8912772429453808.108722757
779969771389751.15843093-392774.158430927
78346998950519.584159758-603521.584159758
79967154699936.111890899267217.888109101
805470971226515.11523930-679418.115239301
81586853436094.680233765150758.319766235
8246728818005.68409107-771277.68409107
832368831343887.29824682-1107004.29824682
8436784882171.265927443-845387.265927443
85277085685219.690924196-408134.690924196
86446998669347.168823079-222349.168823079
87586725368482.338266265218242.661733735
8849684580959.0361636194415885.963836381
89867651029634.82821167-942869.828211673
90146966602295.422765024-455329.422765024
91197113462310.402054415-265197.402054415
92657096635365.15890527521730.8410947252
93337200265518.25098588771681.7490141131
9417273442027.094132448-424754.094132448
95457284724639.179859548-267355.179859548
96507696507573.661244126122.338755873789
97547628486041.8429851761586.1570148298
98157435550592.895460722-393157.895460722
9967793296661.622649114-228868.622649114
10026763157419.8798939864210211.120106014
101518397491087.36803446227309.6319655378
102918560346967.885466356571592.114533644
103918895400023.419307796518871.580692204
104429509785818.286904767-356309.286904767
105289569305955.351629511-16386.3516295106
1069010172438500.6799902978571671.3200097
10718106174079254.52753124-2268637.52753124
10871114002894967.209065534216432.79093447
10916119193585486.10766381-1973567.10766381
11097127143453102.027657836259611.97234217
11129133102860115.6435629453194.3564370624
1121013816810355.40686907203460.593130930
11367145183949731.223256452764786.77674355
11424147213424420.25408295-1009699.25408295
11591145342921745.612647096192788.38735291
11682149935877982.544774472337010.45522553
11762151592779197.896474473435961.10352553
1185156126448467.49319585-5932855.49319585
11994153408524589.71609453890750.283905465
12037152677673911.81918202-3958644.81918202







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1216166347.075289425401927.39740076930766.75317815
1227479700.457461276461110.622974758498290.29194779
1234328727.018417423412254.212285295245199.82454954
1241241755.33515733447523.100835252035987.56947942
1255949794.521313282995648.537091428903940.50553514
1264329376.403570582076173.482294496582579.32484667
1274384821.064950082033626.901874256736015.2280259
1285993230.635819332762968.995306999223492.27633166
1292760643.422066541102778.639073674418508.2050594
1304581658.655887381857889.688933167305427.6228416
1317821611.383709553186432.9389047412456789.8285144
1326610628.313287642710255.7679836310511000.8585916

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 6166347.07528942 & 5401927.3974007 & 6930766.75317815 \tabularnewline
122 & 7479700.45746127 & 6461110.62297475 & 8498290.29194779 \tabularnewline
123 & 4328727.01841742 & 3412254.21228529 & 5245199.82454954 \tabularnewline
124 & 1241755.33515733 & 447523.10083525 & 2035987.56947942 \tabularnewline
125 & 5949794.52131328 & 2995648.53709142 & 8903940.50553514 \tabularnewline
126 & 4329376.40357058 & 2076173.48229449 & 6582579.32484667 \tabularnewline
127 & 4384821.06495008 & 2033626.90187425 & 6736015.2280259 \tabularnewline
128 & 5993230.63581933 & 2762968.99530699 & 9223492.27633166 \tabularnewline
129 & 2760643.42206654 & 1102778.63907367 & 4418508.2050594 \tabularnewline
130 & 4581658.65588738 & 1857889.68893316 & 7305427.6228416 \tabularnewline
131 & 7821611.38370955 & 3186432.93890474 & 12456789.8285144 \tabularnewline
132 & 6610628.31328764 & 2710255.76798363 & 10511000.8585916 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77015&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]121[/C][C]6166347.07528942[/C][C]5401927.3974007[/C][C]6930766.75317815[/C][/ROW]
[ROW][C]122[/C][C]7479700.45746127[/C][C]6461110.62297475[/C][C]8498290.29194779[/C][/ROW]
[ROW][C]123[/C][C]4328727.01841742[/C][C]3412254.21228529[/C][C]5245199.82454954[/C][/ROW]
[ROW][C]124[/C][C]1241755.33515733[/C][C]447523.10083525[/C][C]2035987.56947942[/C][/ROW]
[ROW][C]125[/C][C]5949794.52131328[/C][C]2995648.53709142[/C][C]8903940.50553514[/C][/ROW]
[ROW][C]126[/C][C]4329376.40357058[/C][C]2076173.48229449[/C][C]6582579.32484667[/C][/ROW]
[ROW][C]127[/C][C]4384821.06495008[/C][C]2033626.90187425[/C][C]6736015.2280259[/C][/ROW]
[ROW][C]128[/C][C]5993230.63581933[/C][C]2762968.99530699[/C][C]9223492.27633166[/C][/ROW]
[ROW][C]129[/C][C]2760643.42206654[/C][C]1102778.63907367[/C][C]4418508.2050594[/C][/ROW]
[ROW][C]130[/C][C]4581658.65588738[/C][C]1857889.68893316[/C][C]7305427.6228416[/C][/ROW]
[ROW][C]131[/C][C]7821611.38370955[/C][C]3186432.93890474[/C][C]12456789.8285144[/C][/ROW]
[ROW][C]132[/C][C]6610628.31328764[/C][C]2710255.76798363[/C][C]10511000.8585916[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77015&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77015&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
1216166347.075289425401927.39740076930766.75317815
1227479700.457461276461110.622974758498290.29194779
1234328727.018417423412254.212285295245199.82454954
1241241755.33515733447523.100835252035987.56947942
1255949794.521313282995648.537091428903940.50553514
1264329376.403570582076173.482294496582579.32484667
1274384821.064950082033626.901874256736015.2280259
1285993230.635819332762968.995306999223492.27633166
1292760643.422066541102778.639073674418508.2050594
1304581658.655887381857889.688933167305427.6228416
1317821611.383709553186432.9389047412456789.8285144
1326610628.313287642710255.7679836310511000.8585916



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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')