Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 19 Aug 2011 04:48:02 -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/2011/Aug/19/t1313743917sz3ie4qry72fvp5.htm/, Retrieved Tue, 14 May 2024 07:27:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=124199, Retrieved Tue, 14 May 2024 07:27:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact180
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Voorspelling tijd...] [2011-08-19 08:48:02] [be417f314f65e9d8a38b0902dfa3287c] [Current]
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Dataseries X:
760
730
730
680
730
710
800
830
820
770
800
840
800
710
800
780
760
730
770
880
850
810
770
810
890
790
840
830
740
760
630
890
900
820
810
820
890
810
810
840
830
790
610
870
870
820
800
840
860
860
730
850
860
900
610
960
820
860
810
820
820
880
840
910
860
880
620
970
810
880
870
800
740
1010
850
980
880
870
660
940
860
880
1000
840
800
1060
790
930
920
840
690
940
1010
890
1000
820
800
1000
780
1010
950
830
670
1000
960
920
1040
860




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124199&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124199&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124199&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'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0774296439411905
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0774296439411905 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124199&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]0.0774296439411905[/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=124199&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124199&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
alpha0.0774296439411905
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2730760-30
3730757.677110681764-27.6771106817642
4680755.534081856354-75.5340818563543
5730749.685504792792-19.685504792792
6710748.161263165883-38.1612631658835
7800745.20645014660354.793549853397
8830749.44909520202580.5509047979746
9820755.68612307967364.3138769203266
10770760.6659236700929.33407632990816
11800761.38865787683738.6113421231635
12840764.37832034952575.6216796504755
13800770.23368007909629.7663199209044
14710772.538475632011-62.5384756320108
15800767.696143731232.3038562688006
16780770.197419820029.80258017997994
17760770.956430113061-10.9564301130608
18730770.10807763054-40.10807763054
19770767.0025234604422.99747653955831
20880767.234617001622112.765382998378
21850775.96600045607874.0339995439218
22810781.69842668030628.3015733196937
23770783.889807425426-13.8898074254257
24810782.81432458206327.1856754179367
25890784.919301749975105.080698250025
26790793.055662800566-3.0556628005661
27840792.81906391791447.1809360820861
28830796.47226699956233.527733000438
29740799.068307427941-59.0683074279411
30760794.494669415587-34.4946694155868
31630791.823759444869-161.823759444869
32890779.293803369828110.706196630172
33900787.865744756985112.134255243015
34820796.54826021406323.4517397859373
35810798.3641200754911.6358799245107
36820799.26508211498720.7349178850134
37890800.87057942397389.129420576027
38810807.771838723862.22816127614055
39810807.9443644581152.05563554188541
40840808.10353158619631.8964684138043
41830810.57326377845819.426736221542
42790812.077469047031-22.0774690470314
43610810.368018479597-200.368018479597
44870794.8535941515275.14640584848
45870800.67215359982869.327846400172
46820806.04018406180313.9598159381972
47800807.121087639382-7.12108763938204
48840806.5697043589933.4302956410094
49860809.15820024732350.8417997526773
50860813.09486269950246.9051373004982
51730816.726710779692-86.726710779692
52850810.0114924438339.98850755617
53860813.10778834564446.8922116543562
54900816.73863559765683.2613644023444
55610823.185533397387-213.185533397387
56960806.678653453014153.321346546986
57820818.5502707247311.44972927526862
58860818.66252274632741.3374772536735
59810821.863268891506-11.8632688915055
60820820.944700205258-0.944700205257618
61820820.871552404733-0.871552404733393
62880820.80406841235959.1959315876412
63840825.38758831795714.6124116820431
64910826.5190221516283.4809778483805
65860832.98292454228227.017075457718
66880835.07484707530544.9251529246945
67620838.553385670268-218.553385670268
68970821.630874835678148.369125164322
69810833.119043369017-23.1190433690169
70880831.32894407269348.671055927307
71870835.09752660338634.9024733966138
72800837.800012691153-37.8000126911529
73740834.873171167504-94.8731711675044
741010827.527175304433182.472824695567
75850841.6559811495548.34401885044599
76980842.302055558183137.697944441817
77880852.96395836774627.0360416322536
78870855.05734944491114.942650555089
79660856.21435355693-196.214353556929
80940841.02154602486598.9784539751347
81860848.6854124740111.3145875259905
82880849.56149695748830.4385030425117
831000851.918339410173148.081660589827
84840863.384249663863-23.3842496638634
85800861.573615538559-61.5736155385586
861060856.805992411236203.194007588764
87790872.539232069818-82.5392320698177
88930866.14824871947263.8517512805277
89920871.09226708614548.9077329138549
90840874.879175431636-34.8791754316356
91690872.178493297002-182.178493297002
92940858.07247742727281.9275225727276
931010864.416096329062145.583903670938
94890875.68860615387214.3113938461282
951000876.79673228368123.20326771632
96820886.336317435345-66.3363174353454
97800881.199919995957-81.1999199959569
981000874.912639102617125.087360897383
99780884.598108918444-104.598108918444
1001010876.499114587967133.500885412033
101950886.83604061125563.1639593887453
102830891.726803496641-61.7268034966411
103670886.947319080268-216.947319080268
1041000870.149165409887129.850834590113
105960880.20346929766679.7965307023338
106920886.3820862576933.6179137423098
1071040888.985109348803151.014890651197
108860900.678138561743-40.6781385617429

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 730 & 760 & -30 \tabularnewline
3 & 730 & 757.677110681764 & -27.6771106817642 \tabularnewline
4 & 680 & 755.534081856354 & -75.5340818563543 \tabularnewline
5 & 730 & 749.685504792792 & -19.685504792792 \tabularnewline
6 & 710 & 748.161263165883 & -38.1612631658835 \tabularnewline
7 & 800 & 745.206450146603 & 54.793549853397 \tabularnewline
8 & 830 & 749.449095202025 & 80.5509047979746 \tabularnewline
9 & 820 & 755.686123079673 & 64.3138769203266 \tabularnewline
10 & 770 & 760.665923670092 & 9.33407632990816 \tabularnewline
11 & 800 & 761.388657876837 & 38.6113421231635 \tabularnewline
12 & 840 & 764.378320349525 & 75.6216796504755 \tabularnewline
13 & 800 & 770.233680079096 & 29.7663199209044 \tabularnewline
14 & 710 & 772.538475632011 & -62.5384756320108 \tabularnewline
15 & 800 & 767.6961437312 & 32.3038562688006 \tabularnewline
16 & 780 & 770.19741982002 & 9.80258017997994 \tabularnewline
17 & 760 & 770.956430113061 & -10.9564301130608 \tabularnewline
18 & 730 & 770.10807763054 & -40.10807763054 \tabularnewline
19 & 770 & 767.002523460442 & 2.99747653955831 \tabularnewline
20 & 880 & 767.234617001622 & 112.765382998378 \tabularnewline
21 & 850 & 775.966000456078 & 74.0339995439218 \tabularnewline
22 & 810 & 781.698426680306 & 28.3015733196937 \tabularnewline
23 & 770 & 783.889807425426 & -13.8898074254257 \tabularnewline
24 & 810 & 782.814324582063 & 27.1856754179367 \tabularnewline
25 & 890 & 784.919301749975 & 105.080698250025 \tabularnewline
26 & 790 & 793.055662800566 & -3.0556628005661 \tabularnewline
27 & 840 & 792.819063917914 & 47.1809360820861 \tabularnewline
28 & 830 & 796.472266999562 & 33.527733000438 \tabularnewline
29 & 740 & 799.068307427941 & -59.0683074279411 \tabularnewline
30 & 760 & 794.494669415587 & -34.4946694155868 \tabularnewline
31 & 630 & 791.823759444869 & -161.823759444869 \tabularnewline
32 & 890 & 779.293803369828 & 110.706196630172 \tabularnewline
33 & 900 & 787.865744756985 & 112.134255243015 \tabularnewline
34 & 820 & 796.548260214063 & 23.4517397859373 \tabularnewline
35 & 810 & 798.36412007549 & 11.6358799245107 \tabularnewline
36 & 820 & 799.265082114987 & 20.7349178850134 \tabularnewline
37 & 890 & 800.870579423973 & 89.129420576027 \tabularnewline
38 & 810 & 807.77183872386 & 2.22816127614055 \tabularnewline
39 & 810 & 807.944364458115 & 2.05563554188541 \tabularnewline
40 & 840 & 808.103531586196 & 31.8964684138043 \tabularnewline
41 & 830 & 810.573263778458 & 19.426736221542 \tabularnewline
42 & 790 & 812.077469047031 & -22.0774690470314 \tabularnewline
43 & 610 & 810.368018479597 & -200.368018479597 \tabularnewline
44 & 870 & 794.85359415152 & 75.14640584848 \tabularnewline
45 & 870 & 800.672153599828 & 69.327846400172 \tabularnewline
46 & 820 & 806.040184061803 & 13.9598159381972 \tabularnewline
47 & 800 & 807.121087639382 & -7.12108763938204 \tabularnewline
48 & 840 & 806.56970435899 & 33.4302956410094 \tabularnewline
49 & 860 & 809.158200247323 & 50.8417997526773 \tabularnewline
50 & 860 & 813.094862699502 & 46.9051373004982 \tabularnewline
51 & 730 & 816.726710779692 & -86.726710779692 \tabularnewline
52 & 850 & 810.01149244383 & 39.98850755617 \tabularnewline
53 & 860 & 813.107788345644 & 46.8922116543562 \tabularnewline
54 & 900 & 816.738635597656 & 83.2613644023444 \tabularnewline
55 & 610 & 823.185533397387 & -213.185533397387 \tabularnewline
56 & 960 & 806.678653453014 & 153.321346546986 \tabularnewline
57 & 820 & 818.550270724731 & 1.44972927526862 \tabularnewline
58 & 860 & 818.662522746327 & 41.3374772536735 \tabularnewline
59 & 810 & 821.863268891506 & -11.8632688915055 \tabularnewline
60 & 820 & 820.944700205258 & -0.944700205257618 \tabularnewline
61 & 820 & 820.871552404733 & -0.871552404733393 \tabularnewline
62 & 880 & 820.804068412359 & 59.1959315876412 \tabularnewline
63 & 840 & 825.387588317957 & 14.6124116820431 \tabularnewline
64 & 910 & 826.51902215162 & 83.4809778483805 \tabularnewline
65 & 860 & 832.982924542282 & 27.017075457718 \tabularnewline
66 & 880 & 835.074847075305 & 44.9251529246945 \tabularnewline
67 & 620 & 838.553385670268 & -218.553385670268 \tabularnewline
68 & 970 & 821.630874835678 & 148.369125164322 \tabularnewline
69 & 810 & 833.119043369017 & -23.1190433690169 \tabularnewline
70 & 880 & 831.328944072693 & 48.671055927307 \tabularnewline
71 & 870 & 835.097526603386 & 34.9024733966138 \tabularnewline
72 & 800 & 837.800012691153 & -37.8000126911529 \tabularnewline
73 & 740 & 834.873171167504 & -94.8731711675044 \tabularnewline
74 & 1010 & 827.527175304433 & 182.472824695567 \tabularnewline
75 & 850 & 841.655981149554 & 8.34401885044599 \tabularnewline
76 & 980 & 842.302055558183 & 137.697944441817 \tabularnewline
77 & 880 & 852.963958367746 & 27.0360416322536 \tabularnewline
78 & 870 & 855.057349444911 & 14.942650555089 \tabularnewline
79 & 660 & 856.21435355693 & -196.214353556929 \tabularnewline
80 & 940 & 841.021546024865 & 98.9784539751347 \tabularnewline
81 & 860 & 848.68541247401 & 11.3145875259905 \tabularnewline
82 & 880 & 849.561496957488 & 30.4385030425117 \tabularnewline
83 & 1000 & 851.918339410173 & 148.081660589827 \tabularnewline
84 & 840 & 863.384249663863 & -23.3842496638634 \tabularnewline
85 & 800 & 861.573615538559 & -61.5736155385586 \tabularnewline
86 & 1060 & 856.805992411236 & 203.194007588764 \tabularnewline
87 & 790 & 872.539232069818 & -82.5392320698177 \tabularnewline
88 & 930 & 866.148248719472 & 63.8517512805277 \tabularnewline
89 & 920 & 871.092267086145 & 48.9077329138549 \tabularnewline
90 & 840 & 874.879175431636 & -34.8791754316356 \tabularnewline
91 & 690 & 872.178493297002 & -182.178493297002 \tabularnewline
92 & 940 & 858.072477427272 & 81.9275225727276 \tabularnewline
93 & 1010 & 864.416096329062 & 145.583903670938 \tabularnewline
94 & 890 & 875.688606153872 & 14.3113938461282 \tabularnewline
95 & 1000 & 876.79673228368 & 123.20326771632 \tabularnewline
96 & 820 & 886.336317435345 & -66.3363174353454 \tabularnewline
97 & 800 & 881.199919995957 & -81.1999199959569 \tabularnewline
98 & 1000 & 874.912639102617 & 125.087360897383 \tabularnewline
99 & 780 & 884.598108918444 & -104.598108918444 \tabularnewline
100 & 1010 & 876.499114587967 & 133.500885412033 \tabularnewline
101 & 950 & 886.836040611255 & 63.1639593887453 \tabularnewline
102 & 830 & 891.726803496641 & -61.7268034966411 \tabularnewline
103 & 670 & 886.947319080268 & -216.947319080268 \tabularnewline
104 & 1000 & 870.149165409887 & 129.850834590113 \tabularnewline
105 & 960 & 880.203469297666 & 79.7965307023338 \tabularnewline
106 & 920 & 886.38208625769 & 33.6179137423098 \tabularnewline
107 & 1040 & 888.985109348803 & 151.014890651197 \tabularnewline
108 & 860 & 900.678138561743 & -40.6781385617429 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124199&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]730[/C][C]760[/C][C]-30[/C][/ROW]
[ROW][C]3[/C][C]730[/C][C]757.677110681764[/C][C]-27.6771106817642[/C][/ROW]
[ROW][C]4[/C][C]680[/C][C]755.534081856354[/C][C]-75.5340818563543[/C][/ROW]
[ROW][C]5[/C][C]730[/C][C]749.685504792792[/C][C]-19.685504792792[/C][/ROW]
[ROW][C]6[/C][C]710[/C][C]748.161263165883[/C][C]-38.1612631658835[/C][/ROW]
[ROW][C]7[/C][C]800[/C][C]745.206450146603[/C][C]54.793549853397[/C][/ROW]
[ROW][C]8[/C][C]830[/C][C]749.449095202025[/C][C]80.5509047979746[/C][/ROW]
[ROW][C]9[/C][C]820[/C][C]755.686123079673[/C][C]64.3138769203266[/C][/ROW]
[ROW][C]10[/C][C]770[/C][C]760.665923670092[/C][C]9.33407632990816[/C][/ROW]
[ROW][C]11[/C][C]800[/C][C]761.388657876837[/C][C]38.6113421231635[/C][/ROW]
[ROW][C]12[/C][C]840[/C][C]764.378320349525[/C][C]75.6216796504755[/C][/ROW]
[ROW][C]13[/C][C]800[/C][C]770.233680079096[/C][C]29.7663199209044[/C][/ROW]
[ROW][C]14[/C][C]710[/C][C]772.538475632011[/C][C]-62.5384756320108[/C][/ROW]
[ROW][C]15[/C][C]800[/C][C]767.6961437312[/C][C]32.3038562688006[/C][/ROW]
[ROW][C]16[/C][C]780[/C][C]770.19741982002[/C][C]9.80258017997994[/C][/ROW]
[ROW][C]17[/C][C]760[/C][C]770.956430113061[/C][C]-10.9564301130608[/C][/ROW]
[ROW][C]18[/C][C]730[/C][C]770.10807763054[/C][C]-40.10807763054[/C][/ROW]
[ROW][C]19[/C][C]770[/C][C]767.002523460442[/C][C]2.99747653955831[/C][/ROW]
[ROW][C]20[/C][C]880[/C][C]767.234617001622[/C][C]112.765382998378[/C][/ROW]
[ROW][C]21[/C][C]850[/C][C]775.966000456078[/C][C]74.0339995439218[/C][/ROW]
[ROW][C]22[/C][C]810[/C][C]781.698426680306[/C][C]28.3015733196937[/C][/ROW]
[ROW][C]23[/C][C]770[/C][C]783.889807425426[/C][C]-13.8898074254257[/C][/ROW]
[ROW][C]24[/C][C]810[/C][C]782.814324582063[/C][C]27.1856754179367[/C][/ROW]
[ROW][C]25[/C][C]890[/C][C]784.919301749975[/C][C]105.080698250025[/C][/ROW]
[ROW][C]26[/C][C]790[/C][C]793.055662800566[/C][C]-3.0556628005661[/C][/ROW]
[ROW][C]27[/C][C]840[/C][C]792.819063917914[/C][C]47.1809360820861[/C][/ROW]
[ROW][C]28[/C][C]830[/C][C]796.472266999562[/C][C]33.527733000438[/C][/ROW]
[ROW][C]29[/C][C]740[/C][C]799.068307427941[/C][C]-59.0683074279411[/C][/ROW]
[ROW][C]30[/C][C]760[/C][C]794.494669415587[/C][C]-34.4946694155868[/C][/ROW]
[ROW][C]31[/C][C]630[/C][C]791.823759444869[/C][C]-161.823759444869[/C][/ROW]
[ROW][C]32[/C][C]890[/C][C]779.293803369828[/C][C]110.706196630172[/C][/ROW]
[ROW][C]33[/C][C]900[/C][C]787.865744756985[/C][C]112.134255243015[/C][/ROW]
[ROW][C]34[/C][C]820[/C][C]796.548260214063[/C][C]23.4517397859373[/C][/ROW]
[ROW][C]35[/C][C]810[/C][C]798.36412007549[/C][C]11.6358799245107[/C][/ROW]
[ROW][C]36[/C][C]820[/C][C]799.265082114987[/C][C]20.7349178850134[/C][/ROW]
[ROW][C]37[/C][C]890[/C][C]800.870579423973[/C][C]89.129420576027[/C][/ROW]
[ROW][C]38[/C][C]810[/C][C]807.77183872386[/C][C]2.22816127614055[/C][/ROW]
[ROW][C]39[/C][C]810[/C][C]807.944364458115[/C][C]2.05563554188541[/C][/ROW]
[ROW][C]40[/C][C]840[/C][C]808.103531586196[/C][C]31.8964684138043[/C][/ROW]
[ROW][C]41[/C][C]830[/C][C]810.573263778458[/C][C]19.426736221542[/C][/ROW]
[ROW][C]42[/C][C]790[/C][C]812.077469047031[/C][C]-22.0774690470314[/C][/ROW]
[ROW][C]43[/C][C]610[/C][C]810.368018479597[/C][C]-200.368018479597[/C][/ROW]
[ROW][C]44[/C][C]870[/C][C]794.85359415152[/C][C]75.14640584848[/C][/ROW]
[ROW][C]45[/C][C]870[/C][C]800.672153599828[/C][C]69.327846400172[/C][/ROW]
[ROW][C]46[/C][C]820[/C][C]806.040184061803[/C][C]13.9598159381972[/C][/ROW]
[ROW][C]47[/C][C]800[/C][C]807.121087639382[/C][C]-7.12108763938204[/C][/ROW]
[ROW][C]48[/C][C]840[/C][C]806.56970435899[/C][C]33.4302956410094[/C][/ROW]
[ROW][C]49[/C][C]860[/C][C]809.158200247323[/C][C]50.8417997526773[/C][/ROW]
[ROW][C]50[/C][C]860[/C][C]813.094862699502[/C][C]46.9051373004982[/C][/ROW]
[ROW][C]51[/C][C]730[/C][C]816.726710779692[/C][C]-86.726710779692[/C][/ROW]
[ROW][C]52[/C][C]850[/C][C]810.01149244383[/C][C]39.98850755617[/C][/ROW]
[ROW][C]53[/C][C]860[/C][C]813.107788345644[/C][C]46.8922116543562[/C][/ROW]
[ROW][C]54[/C][C]900[/C][C]816.738635597656[/C][C]83.2613644023444[/C][/ROW]
[ROW][C]55[/C][C]610[/C][C]823.185533397387[/C][C]-213.185533397387[/C][/ROW]
[ROW][C]56[/C][C]960[/C][C]806.678653453014[/C][C]153.321346546986[/C][/ROW]
[ROW][C]57[/C][C]820[/C][C]818.550270724731[/C][C]1.44972927526862[/C][/ROW]
[ROW][C]58[/C][C]860[/C][C]818.662522746327[/C][C]41.3374772536735[/C][/ROW]
[ROW][C]59[/C][C]810[/C][C]821.863268891506[/C][C]-11.8632688915055[/C][/ROW]
[ROW][C]60[/C][C]820[/C][C]820.944700205258[/C][C]-0.944700205257618[/C][/ROW]
[ROW][C]61[/C][C]820[/C][C]820.871552404733[/C][C]-0.871552404733393[/C][/ROW]
[ROW][C]62[/C][C]880[/C][C]820.804068412359[/C][C]59.1959315876412[/C][/ROW]
[ROW][C]63[/C][C]840[/C][C]825.387588317957[/C][C]14.6124116820431[/C][/ROW]
[ROW][C]64[/C][C]910[/C][C]826.51902215162[/C][C]83.4809778483805[/C][/ROW]
[ROW][C]65[/C][C]860[/C][C]832.982924542282[/C][C]27.017075457718[/C][/ROW]
[ROW][C]66[/C][C]880[/C][C]835.074847075305[/C][C]44.9251529246945[/C][/ROW]
[ROW][C]67[/C][C]620[/C][C]838.553385670268[/C][C]-218.553385670268[/C][/ROW]
[ROW][C]68[/C][C]970[/C][C]821.630874835678[/C][C]148.369125164322[/C][/ROW]
[ROW][C]69[/C][C]810[/C][C]833.119043369017[/C][C]-23.1190433690169[/C][/ROW]
[ROW][C]70[/C][C]880[/C][C]831.328944072693[/C][C]48.671055927307[/C][/ROW]
[ROW][C]71[/C][C]870[/C][C]835.097526603386[/C][C]34.9024733966138[/C][/ROW]
[ROW][C]72[/C][C]800[/C][C]837.800012691153[/C][C]-37.8000126911529[/C][/ROW]
[ROW][C]73[/C][C]740[/C][C]834.873171167504[/C][C]-94.8731711675044[/C][/ROW]
[ROW][C]74[/C][C]1010[/C][C]827.527175304433[/C][C]182.472824695567[/C][/ROW]
[ROW][C]75[/C][C]850[/C][C]841.655981149554[/C][C]8.34401885044599[/C][/ROW]
[ROW][C]76[/C][C]980[/C][C]842.302055558183[/C][C]137.697944441817[/C][/ROW]
[ROW][C]77[/C][C]880[/C][C]852.963958367746[/C][C]27.0360416322536[/C][/ROW]
[ROW][C]78[/C][C]870[/C][C]855.057349444911[/C][C]14.942650555089[/C][/ROW]
[ROW][C]79[/C][C]660[/C][C]856.21435355693[/C][C]-196.214353556929[/C][/ROW]
[ROW][C]80[/C][C]940[/C][C]841.021546024865[/C][C]98.9784539751347[/C][/ROW]
[ROW][C]81[/C][C]860[/C][C]848.68541247401[/C][C]11.3145875259905[/C][/ROW]
[ROW][C]82[/C][C]880[/C][C]849.561496957488[/C][C]30.4385030425117[/C][/ROW]
[ROW][C]83[/C][C]1000[/C][C]851.918339410173[/C][C]148.081660589827[/C][/ROW]
[ROW][C]84[/C][C]840[/C][C]863.384249663863[/C][C]-23.3842496638634[/C][/ROW]
[ROW][C]85[/C][C]800[/C][C]861.573615538559[/C][C]-61.5736155385586[/C][/ROW]
[ROW][C]86[/C][C]1060[/C][C]856.805992411236[/C][C]203.194007588764[/C][/ROW]
[ROW][C]87[/C][C]790[/C][C]872.539232069818[/C][C]-82.5392320698177[/C][/ROW]
[ROW][C]88[/C][C]930[/C][C]866.148248719472[/C][C]63.8517512805277[/C][/ROW]
[ROW][C]89[/C][C]920[/C][C]871.092267086145[/C][C]48.9077329138549[/C][/ROW]
[ROW][C]90[/C][C]840[/C][C]874.879175431636[/C][C]-34.8791754316356[/C][/ROW]
[ROW][C]91[/C][C]690[/C][C]872.178493297002[/C][C]-182.178493297002[/C][/ROW]
[ROW][C]92[/C][C]940[/C][C]858.072477427272[/C][C]81.9275225727276[/C][/ROW]
[ROW][C]93[/C][C]1010[/C][C]864.416096329062[/C][C]145.583903670938[/C][/ROW]
[ROW][C]94[/C][C]890[/C][C]875.688606153872[/C][C]14.3113938461282[/C][/ROW]
[ROW][C]95[/C][C]1000[/C][C]876.79673228368[/C][C]123.20326771632[/C][/ROW]
[ROW][C]96[/C][C]820[/C][C]886.336317435345[/C][C]-66.3363174353454[/C][/ROW]
[ROW][C]97[/C][C]800[/C][C]881.199919995957[/C][C]-81.1999199959569[/C][/ROW]
[ROW][C]98[/C][C]1000[/C][C]874.912639102617[/C][C]125.087360897383[/C][/ROW]
[ROW][C]99[/C][C]780[/C][C]884.598108918444[/C][C]-104.598108918444[/C][/ROW]
[ROW][C]100[/C][C]1010[/C][C]876.499114587967[/C][C]133.500885412033[/C][/ROW]
[ROW][C]101[/C][C]950[/C][C]886.836040611255[/C][C]63.1639593887453[/C][/ROW]
[ROW][C]102[/C][C]830[/C][C]891.726803496641[/C][C]-61.7268034966411[/C][/ROW]
[ROW][C]103[/C][C]670[/C][C]886.947319080268[/C][C]-216.947319080268[/C][/ROW]
[ROW][C]104[/C][C]1000[/C][C]870.149165409887[/C][C]129.850834590113[/C][/ROW]
[ROW][C]105[/C][C]960[/C][C]880.203469297666[/C][C]79.7965307023338[/C][/ROW]
[ROW][C]106[/C][C]920[/C][C]886.38208625769[/C][C]33.6179137423098[/C][/ROW]
[ROW][C]107[/C][C]1040[/C][C]888.985109348803[/C][C]151.014890651197[/C][/ROW]
[ROW][C]108[/C][C]860[/C][C]900.678138561743[/C][C]-40.6781385617429[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124199&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124199&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
2730760-30
3730757.677110681764-27.6771106817642
4680755.534081856354-75.5340818563543
5730749.685504792792-19.685504792792
6710748.161263165883-38.1612631658835
7800745.20645014660354.793549853397
8830749.44909520202580.5509047979746
9820755.68612307967364.3138769203266
10770760.6659236700929.33407632990816
11800761.38865787683738.6113421231635
12840764.37832034952575.6216796504755
13800770.23368007909629.7663199209044
14710772.538475632011-62.5384756320108
15800767.696143731232.3038562688006
16780770.197419820029.80258017997994
17760770.956430113061-10.9564301130608
18730770.10807763054-40.10807763054
19770767.0025234604422.99747653955831
20880767.234617001622112.765382998378
21850775.96600045607874.0339995439218
22810781.69842668030628.3015733196937
23770783.889807425426-13.8898074254257
24810782.81432458206327.1856754179367
25890784.919301749975105.080698250025
26790793.055662800566-3.0556628005661
27840792.81906391791447.1809360820861
28830796.47226699956233.527733000438
29740799.068307427941-59.0683074279411
30760794.494669415587-34.4946694155868
31630791.823759444869-161.823759444869
32890779.293803369828110.706196630172
33900787.865744756985112.134255243015
34820796.54826021406323.4517397859373
35810798.3641200754911.6358799245107
36820799.26508211498720.7349178850134
37890800.87057942397389.129420576027
38810807.771838723862.22816127614055
39810807.9443644581152.05563554188541
40840808.10353158619631.8964684138043
41830810.57326377845819.426736221542
42790812.077469047031-22.0774690470314
43610810.368018479597-200.368018479597
44870794.8535941515275.14640584848
45870800.67215359982869.327846400172
46820806.04018406180313.9598159381972
47800807.121087639382-7.12108763938204
48840806.5697043589933.4302956410094
49860809.15820024732350.8417997526773
50860813.09486269950246.9051373004982
51730816.726710779692-86.726710779692
52850810.0114924438339.98850755617
53860813.10778834564446.8922116543562
54900816.73863559765683.2613644023444
55610823.185533397387-213.185533397387
56960806.678653453014153.321346546986
57820818.5502707247311.44972927526862
58860818.66252274632741.3374772536735
59810821.863268891506-11.8632688915055
60820820.944700205258-0.944700205257618
61820820.871552404733-0.871552404733393
62880820.80406841235959.1959315876412
63840825.38758831795714.6124116820431
64910826.5190221516283.4809778483805
65860832.98292454228227.017075457718
66880835.07484707530544.9251529246945
67620838.553385670268-218.553385670268
68970821.630874835678148.369125164322
69810833.119043369017-23.1190433690169
70880831.32894407269348.671055927307
71870835.09752660338634.9024733966138
72800837.800012691153-37.8000126911529
73740834.873171167504-94.8731711675044
741010827.527175304433182.472824695567
75850841.6559811495548.34401885044599
76980842.302055558183137.697944441817
77880852.96395836774627.0360416322536
78870855.05734944491114.942650555089
79660856.21435355693-196.214353556929
80940841.02154602486598.9784539751347
81860848.6854124740111.3145875259905
82880849.56149695748830.4385030425117
831000851.918339410173148.081660589827
84840863.384249663863-23.3842496638634
85800861.573615538559-61.5736155385586
861060856.805992411236203.194007588764
87790872.539232069818-82.5392320698177
88930866.14824871947263.8517512805277
89920871.09226708614548.9077329138549
90840874.879175431636-34.8791754316356
91690872.178493297002-182.178493297002
92940858.07247742727281.9275225727276
931010864.416096329062145.583903670938
94890875.68860615387214.3113938461282
951000876.79673228368123.20326771632
96820886.336317435345-66.3363174353454
97800881.199919995957-81.1999199959569
981000874.912639102617125.087360897383
99780884.598108918444-104.598108918444
1001010876.499114587967133.500885412033
101950886.83604061125563.1639593887453
102830891.726803496641-61.7268034966411
103670886.947319080268-216.947319080268
1041000870.149165409887129.850834590113
105960880.20346929766679.7965307023338
106920886.3820862576933.6179137423098
1071040888.985109348803151.014890651197
108860900.678138561743-40.6781385617429







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109897.528444776717730.1409605769871064.91592897645
110897.528444776717729.6399371507781065.41695240265
111897.528444776717729.1404044679861065.91648508545
112897.528444776717728.642349300611066.41454025282
113897.528444776717728.1457586151291066.9111309383
114897.528444776717727.6506195685251067.40626998491
115897.528444776717727.1569195044021067.89997004903
116897.528444776717726.6646459492151068.39224360422
117897.528444776717726.1737866085921068.88310294484
118897.528444776717725.684329363751069.37256018968
119897.528444776717725.1962622680081069.86062728543
120897.528444776717724.7095735433791070.34731601005

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 897.528444776717 & 730.140960576987 & 1064.91592897645 \tabularnewline
110 & 897.528444776717 & 729.639937150778 & 1065.41695240265 \tabularnewline
111 & 897.528444776717 & 729.140404467986 & 1065.91648508545 \tabularnewline
112 & 897.528444776717 & 728.64234930061 & 1066.41454025282 \tabularnewline
113 & 897.528444776717 & 728.145758615129 & 1066.9111309383 \tabularnewline
114 & 897.528444776717 & 727.650619568525 & 1067.40626998491 \tabularnewline
115 & 897.528444776717 & 727.156919504402 & 1067.89997004903 \tabularnewline
116 & 897.528444776717 & 726.664645949215 & 1068.39224360422 \tabularnewline
117 & 897.528444776717 & 726.173786608592 & 1068.88310294484 \tabularnewline
118 & 897.528444776717 & 725.68432936375 & 1069.37256018968 \tabularnewline
119 & 897.528444776717 & 725.196262268008 & 1069.86062728543 \tabularnewline
120 & 897.528444776717 & 724.709573543379 & 1070.34731601005 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124199&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]109[/C][C]897.528444776717[/C][C]730.140960576987[/C][C]1064.91592897645[/C][/ROW]
[ROW][C]110[/C][C]897.528444776717[/C][C]729.639937150778[/C][C]1065.41695240265[/C][/ROW]
[ROW][C]111[/C][C]897.528444776717[/C][C]729.140404467986[/C][C]1065.91648508545[/C][/ROW]
[ROW][C]112[/C][C]897.528444776717[/C][C]728.64234930061[/C][C]1066.41454025282[/C][/ROW]
[ROW][C]113[/C][C]897.528444776717[/C][C]728.145758615129[/C][C]1066.9111309383[/C][/ROW]
[ROW][C]114[/C][C]897.528444776717[/C][C]727.650619568525[/C][C]1067.40626998491[/C][/ROW]
[ROW][C]115[/C][C]897.528444776717[/C][C]727.156919504402[/C][C]1067.89997004903[/C][/ROW]
[ROW][C]116[/C][C]897.528444776717[/C][C]726.664645949215[/C][C]1068.39224360422[/C][/ROW]
[ROW][C]117[/C][C]897.528444776717[/C][C]726.173786608592[/C][C]1068.88310294484[/C][/ROW]
[ROW][C]118[/C][C]897.528444776717[/C][C]725.68432936375[/C][C]1069.37256018968[/C][/ROW]
[ROW][C]119[/C][C]897.528444776717[/C][C]725.196262268008[/C][C]1069.86062728543[/C][/ROW]
[ROW][C]120[/C][C]897.528444776717[/C][C]724.709573543379[/C][C]1070.34731601005[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124199&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124199&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
109897.528444776717730.1409605769871064.91592897645
110897.528444776717729.6399371507781065.41695240265
111897.528444776717729.1404044679861065.91648508545
112897.528444776717728.642349300611066.41454025282
113897.528444776717728.1457586151291066.9111309383
114897.528444776717727.6506195685251067.40626998491
115897.528444776717727.1569195044021067.89997004903
116897.528444776717726.6646459492151068.39224360422
117897.528444776717726.1737866085921068.88310294484
118897.528444776717725.684329363751069.37256018968
119897.528444776717725.1962622680081069.86062728543
120897.528444776717724.7095735433791070.34731601005



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