Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 08 Aug 2012 15:41:57 -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/2012/Aug/08/t134445501353g2bwiqquzt6ue.htm/, Retrieved Fri, 03 May 2024 21:52:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=169141, Retrieved Fri, 03 May 2024 21:52:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsmatthew lauwers
Estimated Impact74
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [tijdreeks 2 - 27] [2012-08-08 19:41:57] [21ec67e1bcc74ce82382f49324ef9e61] [Current]
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Dataseries X:
990
1050
1000
1040
1030
980
990
940
1050
990
980
1110
1000
1000
1080
1010
960
990
900
920
1080
950
950
1060
1070
970
1070
980
970
1050
950
960
1170
990
870
1090
1070
990
1080
890
920
1100
930
950
1240
950
830
1220
1040
1080
1160
900
790
1100
1000
990
1250
970
840
1220
1100
1030
1210
830
810
1100
1020
950
1280
950
720
1150
1030
1030
1200
870
880
1090
950
1060
1280
920
630
1110
1020
1130
1160
930
930
1110
930
1070
1250
840
680
1110
990
1210
1130
920
1030
1120
880
1050
1260
790
640
1110




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169141&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169141&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169141&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.00832585196403887
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.00832585196403887 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169141&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]0.00832585196403887[/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=169141&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169141&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
alpha0.00832585196403887
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2105099060
31000990.4995511178429.50044888215768
41040990.57865044882749.421349551173
51030990.99012528905339.0098747109469
6980991.314915731032-11.3149157310322
7990991.22070941767-1.22070941767004
8940991.210545971767-51.2105459717674
91050990.78417454700959.2158254529911
10990991.277196743659-1.27719674365881
11980991.266562992642-11.2665629926421
121110991.172759257022118.827240742978
131000992.1620972727437.83790272725685
141000992.2273544905597.77264550944119
151080992.29206838643987.7079316135606
161010993.02231164112616.977688358874
17960993.163665361094-33.1636653610935
18990992.887549592712-2.88754959271216
19900992.863508282264-92.8635082822644
20920992.090340459445-72.090340459445
211080991.49012695674388.5098730432575
22950992.227047057057-42.2270470570566
23950991.875470914381-41.875470914381
241060991.52682194262368.4731780573766
251070992.09691948663677.9030805133635
26970992.745529002533-22.7455290025333
271070992.55615309521477.4438469047856
28980993.200939100069-13.2009391000694
29970993.091030035336-23.091030035336
301050992.89877753756557.1012224624354
31950993.374193862752-43.3741938627525
32960993.013066745592-33.0130667455917
331170992.738204838989177.261795161011
34990994.214060304379-4.21406030437936
35870994.178974662118-124.178974662118
361090993.14507890203596.8549210979654
371070993.95147863708576.048521362915
38990994.584647368037-4.5846473680366
391080994.54647627274385.453523727257
40890995.257949661102-105.257949661102
41920994.381587554185-74.3815875541851
421100993.762297467359106.237702532641
43930994.646816851645-64.6468168516451
44950994.108577024592-44.108577024592
451240993.741335541941246.258664458059
46950995.791648727081-45.7916487270807
47830995.41039423859-165.41039423859
481220994.033211782846225.966788217154
491040995.91457781033144.0854221896687
501080996.28162650925583.7183734907454
511160996.978653293609163.021346706391
52900998.335944893264-98.3359448932644
53790997.517214373339-207.517214373339
541100995.789456766477104.210543233523
551000996.6570983225313.3429016774686
56990996.684930827028-6.68493082702832
571250996.629273082573253.370726917427
58970998.738800246908-28.7388002469081
59840998.499525250428-158.499525250428
601220997.179881666823222.820118333177
611100999.035048986674100.964951013326
621030999.87566822236830.1243317776323
6312101000.12647894926209.873521050736
648301001.8738548167-171.873854816704
658101000.44285854501-190.442858545011
661100998.857259497157101.142740502843
671020999.69935898182120.300641018179
68950999.868379113713-49.8683791137134
691280999.453182371526280.546817628474
709501001.78897364408-51.7889736440829
717201001.35778631615-281.357786316153
721150999.015243038355150.984756961645
7310301000.2723197736429.7276802263561
7410301000.5198280384429.4801719615572
7512001000.76527558607199.234724413931
768701002.42407440764-132.424074407636
778801001.32153116764-121.321531167643
7810901000.3114260590989.6885739409096
799501001.05815984859-51.0581598485882
8010601000.6330571681359.3669428318674
8112801001.12733754571278.872662454292
829201003.44919005012-83.4491900501201
836301002.75440444724-372.754404447244
841110999.650906456873110.349093543127
8510201000.5696566740819.4303433259214
8611301000.73143083622129.268569163779
8711601001.80770180668158.192298193319
889301003.12478746329-73.1247874632901
899301002.51596130797-72.515961307969
9011101001.91220414909108.087795850911
919301002.81212713646-72.8121271364628
9210701002.2059041447467.7940958552622
9312501002.77034775086247.229652249135
948401004.82874523661-164.828745236612
956801003.45640550435-323.456405504353
9611101000.7633553553109.236644644696
979901001.67284348766-11.6728434876642
9812101001.57565712079208.424342879214
9911301003.3109673453126.689032654699
1009201004.36576147665-84.3657614766511
10110301003.6633446357626.3366553642369
10211201003.88261972955116.117380270446
1038801004.84939584814-124.849395848137
10410501003.8099182605146.1900817394938
10512601004.19449004328255.805509956724
1067901006.32428885076-216.324288850761
1076401004.52320484556-364.523204845564
10811101001.48823860456108.511761395437

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 1050 & 990 & 60 \tabularnewline
3 & 1000 & 990.499551117842 & 9.50044888215768 \tabularnewline
4 & 1040 & 990.578650448827 & 49.421349551173 \tabularnewline
5 & 1030 & 990.990125289053 & 39.0098747109469 \tabularnewline
6 & 980 & 991.314915731032 & -11.3149157310322 \tabularnewline
7 & 990 & 991.22070941767 & -1.22070941767004 \tabularnewline
8 & 940 & 991.210545971767 & -51.2105459717674 \tabularnewline
9 & 1050 & 990.784174547009 & 59.2158254529911 \tabularnewline
10 & 990 & 991.277196743659 & -1.27719674365881 \tabularnewline
11 & 980 & 991.266562992642 & -11.2665629926421 \tabularnewline
12 & 1110 & 991.172759257022 & 118.827240742978 \tabularnewline
13 & 1000 & 992.162097272743 & 7.83790272725685 \tabularnewline
14 & 1000 & 992.227354490559 & 7.77264550944119 \tabularnewline
15 & 1080 & 992.292068386439 & 87.7079316135606 \tabularnewline
16 & 1010 & 993.022311641126 & 16.977688358874 \tabularnewline
17 & 960 & 993.163665361094 & -33.1636653610935 \tabularnewline
18 & 990 & 992.887549592712 & -2.88754959271216 \tabularnewline
19 & 900 & 992.863508282264 & -92.8635082822644 \tabularnewline
20 & 920 & 992.090340459445 & -72.090340459445 \tabularnewline
21 & 1080 & 991.490126956743 & 88.5098730432575 \tabularnewline
22 & 950 & 992.227047057057 & -42.2270470570566 \tabularnewline
23 & 950 & 991.875470914381 & -41.875470914381 \tabularnewline
24 & 1060 & 991.526821942623 & 68.4731780573766 \tabularnewline
25 & 1070 & 992.096919486636 & 77.9030805133635 \tabularnewline
26 & 970 & 992.745529002533 & -22.7455290025333 \tabularnewline
27 & 1070 & 992.556153095214 & 77.4438469047856 \tabularnewline
28 & 980 & 993.200939100069 & -13.2009391000694 \tabularnewline
29 & 970 & 993.091030035336 & -23.091030035336 \tabularnewline
30 & 1050 & 992.898777537565 & 57.1012224624354 \tabularnewline
31 & 950 & 993.374193862752 & -43.3741938627525 \tabularnewline
32 & 960 & 993.013066745592 & -33.0130667455917 \tabularnewline
33 & 1170 & 992.738204838989 & 177.261795161011 \tabularnewline
34 & 990 & 994.214060304379 & -4.21406030437936 \tabularnewline
35 & 870 & 994.178974662118 & -124.178974662118 \tabularnewline
36 & 1090 & 993.145078902035 & 96.8549210979654 \tabularnewline
37 & 1070 & 993.951478637085 & 76.048521362915 \tabularnewline
38 & 990 & 994.584647368037 & -4.5846473680366 \tabularnewline
39 & 1080 & 994.546476272743 & 85.453523727257 \tabularnewline
40 & 890 & 995.257949661102 & -105.257949661102 \tabularnewline
41 & 920 & 994.381587554185 & -74.3815875541851 \tabularnewline
42 & 1100 & 993.762297467359 & 106.237702532641 \tabularnewline
43 & 930 & 994.646816851645 & -64.6468168516451 \tabularnewline
44 & 950 & 994.108577024592 & -44.108577024592 \tabularnewline
45 & 1240 & 993.741335541941 & 246.258664458059 \tabularnewline
46 & 950 & 995.791648727081 & -45.7916487270807 \tabularnewline
47 & 830 & 995.41039423859 & -165.41039423859 \tabularnewline
48 & 1220 & 994.033211782846 & 225.966788217154 \tabularnewline
49 & 1040 & 995.914577810331 & 44.0854221896687 \tabularnewline
50 & 1080 & 996.281626509255 & 83.7183734907454 \tabularnewline
51 & 1160 & 996.978653293609 & 163.021346706391 \tabularnewline
52 & 900 & 998.335944893264 & -98.3359448932644 \tabularnewline
53 & 790 & 997.517214373339 & -207.517214373339 \tabularnewline
54 & 1100 & 995.789456766477 & 104.210543233523 \tabularnewline
55 & 1000 & 996.657098322531 & 3.3429016774686 \tabularnewline
56 & 990 & 996.684930827028 & -6.68493082702832 \tabularnewline
57 & 1250 & 996.629273082573 & 253.370726917427 \tabularnewline
58 & 970 & 998.738800246908 & -28.7388002469081 \tabularnewline
59 & 840 & 998.499525250428 & -158.499525250428 \tabularnewline
60 & 1220 & 997.179881666823 & 222.820118333177 \tabularnewline
61 & 1100 & 999.035048986674 & 100.964951013326 \tabularnewline
62 & 1030 & 999.875668222368 & 30.1243317776323 \tabularnewline
63 & 1210 & 1000.12647894926 & 209.873521050736 \tabularnewline
64 & 830 & 1001.8738548167 & -171.873854816704 \tabularnewline
65 & 810 & 1000.44285854501 & -190.442858545011 \tabularnewline
66 & 1100 & 998.857259497157 & 101.142740502843 \tabularnewline
67 & 1020 & 999.699358981821 & 20.300641018179 \tabularnewline
68 & 950 & 999.868379113713 & -49.8683791137134 \tabularnewline
69 & 1280 & 999.453182371526 & 280.546817628474 \tabularnewline
70 & 950 & 1001.78897364408 & -51.7889736440829 \tabularnewline
71 & 720 & 1001.35778631615 & -281.357786316153 \tabularnewline
72 & 1150 & 999.015243038355 & 150.984756961645 \tabularnewline
73 & 1030 & 1000.27231977364 & 29.7276802263561 \tabularnewline
74 & 1030 & 1000.51982803844 & 29.4801719615572 \tabularnewline
75 & 1200 & 1000.76527558607 & 199.234724413931 \tabularnewline
76 & 870 & 1002.42407440764 & -132.424074407636 \tabularnewline
77 & 880 & 1001.32153116764 & -121.321531167643 \tabularnewline
78 & 1090 & 1000.31142605909 & 89.6885739409096 \tabularnewline
79 & 950 & 1001.05815984859 & -51.0581598485882 \tabularnewline
80 & 1060 & 1000.63305716813 & 59.3669428318674 \tabularnewline
81 & 1280 & 1001.12733754571 & 278.872662454292 \tabularnewline
82 & 920 & 1003.44919005012 & -83.4491900501201 \tabularnewline
83 & 630 & 1002.75440444724 & -372.754404447244 \tabularnewline
84 & 1110 & 999.650906456873 & 110.349093543127 \tabularnewline
85 & 1020 & 1000.56965667408 & 19.4303433259214 \tabularnewline
86 & 1130 & 1000.73143083622 & 129.268569163779 \tabularnewline
87 & 1160 & 1001.80770180668 & 158.192298193319 \tabularnewline
88 & 930 & 1003.12478746329 & -73.1247874632901 \tabularnewline
89 & 930 & 1002.51596130797 & -72.515961307969 \tabularnewline
90 & 1110 & 1001.91220414909 & 108.087795850911 \tabularnewline
91 & 930 & 1002.81212713646 & -72.8121271364628 \tabularnewline
92 & 1070 & 1002.20590414474 & 67.7940958552622 \tabularnewline
93 & 1250 & 1002.77034775086 & 247.229652249135 \tabularnewline
94 & 840 & 1004.82874523661 & -164.828745236612 \tabularnewline
95 & 680 & 1003.45640550435 & -323.456405504353 \tabularnewline
96 & 1110 & 1000.7633553553 & 109.236644644696 \tabularnewline
97 & 990 & 1001.67284348766 & -11.6728434876642 \tabularnewline
98 & 1210 & 1001.57565712079 & 208.424342879214 \tabularnewline
99 & 1130 & 1003.3109673453 & 126.689032654699 \tabularnewline
100 & 920 & 1004.36576147665 & -84.3657614766511 \tabularnewline
101 & 1030 & 1003.66334463576 & 26.3366553642369 \tabularnewline
102 & 1120 & 1003.88261972955 & 116.117380270446 \tabularnewline
103 & 880 & 1004.84939584814 & -124.849395848137 \tabularnewline
104 & 1050 & 1003.80991826051 & 46.1900817394938 \tabularnewline
105 & 1260 & 1004.19449004328 & 255.805509956724 \tabularnewline
106 & 790 & 1006.32428885076 & -216.324288850761 \tabularnewline
107 & 640 & 1004.52320484556 & -364.523204845564 \tabularnewline
108 & 1110 & 1001.48823860456 & 108.511761395437 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169141&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]1050[/C][C]990[/C][C]60[/C][/ROW]
[ROW][C]3[/C][C]1000[/C][C]990.499551117842[/C][C]9.50044888215768[/C][/ROW]
[ROW][C]4[/C][C]1040[/C][C]990.578650448827[/C][C]49.421349551173[/C][/ROW]
[ROW][C]5[/C][C]1030[/C][C]990.990125289053[/C][C]39.0098747109469[/C][/ROW]
[ROW][C]6[/C][C]980[/C][C]991.314915731032[/C][C]-11.3149157310322[/C][/ROW]
[ROW][C]7[/C][C]990[/C][C]991.22070941767[/C][C]-1.22070941767004[/C][/ROW]
[ROW][C]8[/C][C]940[/C][C]991.210545971767[/C][C]-51.2105459717674[/C][/ROW]
[ROW][C]9[/C][C]1050[/C][C]990.784174547009[/C][C]59.2158254529911[/C][/ROW]
[ROW][C]10[/C][C]990[/C][C]991.277196743659[/C][C]-1.27719674365881[/C][/ROW]
[ROW][C]11[/C][C]980[/C][C]991.266562992642[/C][C]-11.2665629926421[/C][/ROW]
[ROW][C]12[/C][C]1110[/C][C]991.172759257022[/C][C]118.827240742978[/C][/ROW]
[ROW][C]13[/C][C]1000[/C][C]992.162097272743[/C][C]7.83790272725685[/C][/ROW]
[ROW][C]14[/C][C]1000[/C][C]992.227354490559[/C][C]7.77264550944119[/C][/ROW]
[ROW][C]15[/C][C]1080[/C][C]992.292068386439[/C][C]87.7079316135606[/C][/ROW]
[ROW][C]16[/C][C]1010[/C][C]993.022311641126[/C][C]16.977688358874[/C][/ROW]
[ROW][C]17[/C][C]960[/C][C]993.163665361094[/C][C]-33.1636653610935[/C][/ROW]
[ROW][C]18[/C][C]990[/C][C]992.887549592712[/C][C]-2.88754959271216[/C][/ROW]
[ROW][C]19[/C][C]900[/C][C]992.863508282264[/C][C]-92.8635082822644[/C][/ROW]
[ROW][C]20[/C][C]920[/C][C]992.090340459445[/C][C]-72.090340459445[/C][/ROW]
[ROW][C]21[/C][C]1080[/C][C]991.490126956743[/C][C]88.5098730432575[/C][/ROW]
[ROW][C]22[/C][C]950[/C][C]992.227047057057[/C][C]-42.2270470570566[/C][/ROW]
[ROW][C]23[/C][C]950[/C][C]991.875470914381[/C][C]-41.875470914381[/C][/ROW]
[ROW][C]24[/C][C]1060[/C][C]991.526821942623[/C][C]68.4731780573766[/C][/ROW]
[ROW][C]25[/C][C]1070[/C][C]992.096919486636[/C][C]77.9030805133635[/C][/ROW]
[ROW][C]26[/C][C]970[/C][C]992.745529002533[/C][C]-22.7455290025333[/C][/ROW]
[ROW][C]27[/C][C]1070[/C][C]992.556153095214[/C][C]77.4438469047856[/C][/ROW]
[ROW][C]28[/C][C]980[/C][C]993.200939100069[/C][C]-13.2009391000694[/C][/ROW]
[ROW][C]29[/C][C]970[/C][C]993.091030035336[/C][C]-23.091030035336[/C][/ROW]
[ROW][C]30[/C][C]1050[/C][C]992.898777537565[/C][C]57.1012224624354[/C][/ROW]
[ROW][C]31[/C][C]950[/C][C]993.374193862752[/C][C]-43.3741938627525[/C][/ROW]
[ROW][C]32[/C][C]960[/C][C]993.013066745592[/C][C]-33.0130667455917[/C][/ROW]
[ROW][C]33[/C][C]1170[/C][C]992.738204838989[/C][C]177.261795161011[/C][/ROW]
[ROW][C]34[/C][C]990[/C][C]994.214060304379[/C][C]-4.21406030437936[/C][/ROW]
[ROW][C]35[/C][C]870[/C][C]994.178974662118[/C][C]-124.178974662118[/C][/ROW]
[ROW][C]36[/C][C]1090[/C][C]993.145078902035[/C][C]96.8549210979654[/C][/ROW]
[ROW][C]37[/C][C]1070[/C][C]993.951478637085[/C][C]76.048521362915[/C][/ROW]
[ROW][C]38[/C][C]990[/C][C]994.584647368037[/C][C]-4.5846473680366[/C][/ROW]
[ROW][C]39[/C][C]1080[/C][C]994.546476272743[/C][C]85.453523727257[/C][/ROW]
[ROW][C]40[/C][C]890[/C][C]995.257949661102[/C][C]-105.257949661102[/C][/ROW]
[ROW][C]41[/C][C]920[/C][C]994.381587554185[/C][C]-74.3815875541851[/C][/ROW]
[ROW][C]42[/C][C]1100[/C][C]993.762297467359[/C][C]106.237702532641[/C][/ROW]
[ROW][C]43[/C][C]930[/C][C]994.646816851645[/C][C]-64.6468168516451[/C][/ROW]
[ROW][C]44[/C][C]950[/C][C]994.108577024592[/C][C]-44.108577024592[/C][/ROW]
[ROW][C]45[/C][C]1240[/C][C]993.741335541941[/C][C]246.258664458059[/C][/ROW]
[ROW][C]46[/C][C]950[/C][C]995.791648727081[/C][C]-45.7916487270807[/C][/ROW]
[ROW][C]47[/C][C]830[/C][C]995.41039423859[/C][C]-165.41039423859[/C][/ROW]
[ROW][C]48[/C][C]1220[/C][C]994.033211782846[/C][C]225.966788217154[/C][/ROW]
[ROW][C]49[/C][C]1040[/C][C]995.914577810331[/C][C]44.0854221896687[/C][/ROW]
[ROW][C]50[/C][C]1080[/C][C]996.281626509255[/C][C]83.7183734907454[/C][/ROW]
[ROW][C]51[/C][C]1160[/C][C]996.978653293609[/C][C]163.021346706391[/C][/ROW]
[ROW][C]52[/C][C]900[/C][C]998.335944893264[/C][C]-98.3359448932644[/C][/ROW]
[ROW][C]53[/C][C]790[/C][C]997.517214373339[/C][C]-207.517214373339[/C][/ROW]
[ROW][C]54[/C][C]1100[/C][C]995.789456766477[/C][C]104.210543233523[/C][/ROW]
[ROW][C]55[/C][C]1000[/C][C]996.657098322531[/C][C]3.3429016774686[/C][/ROW]
[ROW][C]56[/C][C]990[/C][C]996.684930827028[/C][C]-6.68493082702832[/C][/ROW]
[ROW][C]57[/C][C]1250[/C][C]996.629273082573[/C][C]253.370726917427[/C][/ROW]
[ROW][C]58[/C][C]970[/C][C]998.738800246908[/C][C]-28.7388002469081[/C][/ROW]
[ROW][C]59[/C][C]840[/C][C]998.499525250428[/C][C]-158.499525250428[/C][/ROW]
[ROW][C]60[/C][C]1220[/C][C]997.179881666823[/C][C]222.820118333177[/C][/ROW]
[ROW][C]61[/C][C]1100[/C][C]999.035048986674[/C][C]100.964951013326[/C][/ROW]
[ROW][C]62[/C][C]1030[/C][C]999.875668222368[/C][C]30.1243317776323[/C][/ROW]
[ROW][C]63[/C][C]1210[/C][C]1000.12647894926[/C][C]209.873521050736[/C][/ROW]
[ROW][C]64[/C][C]830[/C][C]1001.8738548167[/C][C]-171.873854816704[/C][/ROW]
[ROW][C]65[/C][C]810[/C][C]1000.44285854501[/C][C]-190.442858545011[/C][/ROW]
[ROW][C]66[/C][C]1100[/C][C]998.857259497157[/C][C]101.142740502843[/C][/ROW]
[ROW][C]67[/C][C]1020[/C][C]999.699358981821[/C][C]20.300641018179[/C][/ROW]
[ROW][C]68[/C][C]950[/C][C]999.868379113713[/C][C]-49.8683791137134[/C][/ROW]
[ROW][C]69[/C][C]1280[/C][C]999.453182371526[/C][C]280.546817628474[/C][/ROW]
[ROW][C]70[/C][C]950[/C][C]1001.78897364408[/C][C]-51.7889736440829[/C][/ROW]
[ROW][C]71[/C][C]720[/C][C]1001.35778631615[/C][C]-281.357786316153[/C][/ROW]
[ROW][C]72[/C][C]1150[/C][C]999.015243038355[/C][C]150.984756961645[/C][/ROW]
[ROW][C]73[/C][C]1030[/C][C]1000.27231977364[/C][C]29.7276802263561[/C][/ROW]
[ROW][C]74[/C][C]1030[/C][C]1000.51982803844[/C][C]29.4801719615572[/C][/ROW]
[ROW][C]75[/C][C]1200[/C][C]1000.76527558607[/C][C]199.234724413931[/C][/ROW]
[ROW][C]76[/C][C]870[/C][C]1002.42407440764[/C][C]-132.424074407636[/C][/ROW]
[ROW][C]77[/C][C]880[/C][C]1001.32153116764[/C][C]-121.321531167643[/C][/ROW]
[ROW][C]78[/C][C]1090[/C][C]1000.31142605909[/C][C]89.6885739409096[/C][/ROW]
[ROW][C]79[/C][C]950[/C][C]1001.05815984859[/C][C]-51.0581598485882[/C][/ROW]
[ROW][C]80[/C][C]1060[/C][C]1000.63305716813[/C][C]59.3669428318674[/C][/ROW]
[ROW][C]81[/C][C]1280[/C][C]1001.12733754571[/C][C]278.872662454292[/C][/ROW]
[ROW][C]82[/C][C]920[/C][C]1003.44919005012[/C][C]-83.4491900501201[/C][/ROW]
[ROW][C]83[/C][C]630[/C][C]1002.75440444724[/C][C]-372.754404447244[/C][/ROW]
[ROW][C]84[/C][C]1110[/C][C]999.650906456873[/C][C]110.349093543127[/C][/ROW]
[ROW][C]85[/C][C]1020[/C][C]1000.56965667408[/C][C]19.4303433259214[/C][/ROW]
[ROW][C]86[/C][C]1130[/C][C]1000.73143083622[/C][C]129.268569163779[/C][/ROW]
[ROW][C]87[/C][C]1160[/C][C]1001.80770180668[/C][C]158.192298193319[/C][/ROW]
[ROW][C]88[/C][C]930[/C][C]1003.12478746329[/C][C]-73.1247874632901[/C][/ROW]
[ROW][C]89[/C][C]930[/C][C]1002.51596130797[/C][C]-72.515961307969[/C][/ROW]
[ROW][C]90[/C][C]1110[/C][C]1001.91220414909[/C][C]108.087795850911[/C][/ROW]
[ROW][C]91[/C][C]930[/C][C]1002.81212713646[/C][C]-72.8121271364628[/C][/ROW]
[ROW][C]92[/C][C]1070[/C][C]1002.20590414474[/C][C]67.7940958552622[/C][/ROW]
[ROW][C]93[/C][C]1250[/C][C]1002.77034775086[/C][C]247.229652249135[/C][/ROW]
[ROW][C]94[/C][C]840[/C][C]1004.82874523661[/C][C]-164.828745236612[/C][/ROW]
[ROW][C]95[/C][C]680[/C][C]1003.45640550435[/C][C]-323.456405504353[/C][/ROW]
[ROW][C]96[/C][C]1110[/C][C]1000.7633553553[/C][C]109.236644644696[/C][/ROW]
[ROW][C]97[/C][C]990[/C][C]1001.67284348766[/C][C]-11.6728434876642[/C][/ROW]
[ROW][C]98[/C][C]1210[/C][C]1001.57565712079[/C][C]208.424342879214[/C][/ROW]
[ROW][C]99[/C][C]1130[/C][C]1003.3109673453[/C][C]126.689032654699[/C][/ROW]
[ROW][C]100[/C][C]920[/C][C]1004.36576147665[/C][C]-84.3657614766511[/C][/ROW]
[ROW][C]101[/C][C]1030[/C][C]1003.66334463576[/C][C]26.3366553642369[/C][/ROW]
[ROW][C]102[/C][C]1120[/C][C]1003.88261972955[/C][C]116.117380270446[/C][/ROW]
[ROW][C]103[/C][C]880[/C][C]1004.84939584814[/C][C]-124.849395848137[/C][/ROW]
[ROW][C]104[/C][C]1050[/C][C]1003.80991826051[/C][C]46.1900817394938[/C][/ROW]
[ROW][C]105[/C][C]1260[/C][C]1004.19449004328[/C][C]255.805509956724[/C][/ROW]
[ROW][C]106[/C][C]790[/C][C]1006.32428885076[/C][C]-216.324288850761[/C][/ROW]
[ROW][C]107[/C][C]640[/C][C]1004.52320484556[/C][C]-364.523204845564[/C][/ROW]
[ROW][C]108[/C][C]1110[/C][C]1001.48823860456[/C][C]108.511761395437[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169141&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169141&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
2105099060
31000990.4995511178429.50044888215768
41040990.57865044882749.421349551173
51030990.99012528905339.0098747109469
6980991.314915731032-11.3149157310322
7990991.22070941767-1.22070941767004
8940991.210545971767-51.2105459717674
91050990.78417454700959.2158254529911
10990991.277196743659-1.27719674365881
11980991.266562992642-11.2665629926421
121110991.172759257022118.827240742978
131000992.1620972727437.83790272725685
141000992.2273544905597.77264550944119
151080992.29206838643987.7079316135606
161010993.02231164112616.977688358874
17960993.163665361094-33.1636653610935
18990992.887549592712-2.88754959271216
19900992.863508282264-92.8635082822644
20920992.090340459445-72.090340459445
211080991.49012695674388.5098730432575
22950992.227047057057-42.2270470570566
23950991.875470914381-41.875470914381
241060991.52682194262368.4731780573766
251070992.09691948663677.9030805133635
26970992.745529002533-22.7455290025333
271070992.55615309521477.4438469047856
28980993.200939100069-13.2009391000694
29970993.091030035336-23.091030035336
301050992.89877753756557.1012224624354
31950993.374193862752-43.3741938627525
32960993.013066745592-33.0130667455917
331170992.738204838989177.261795161011
34990994.214060304379-4.21406030437936
35870994.178974662118-124.178974662118
361090993.14507890203596.8549210979654
371070993.95147863708576.048521362915
38990994.584647368037-4.5846473680366
391080994.54647627274385.453523727257
40890995.257949661102-105.257949661102
41920994.381587554185-74.3815875541851
421100993.762297467359106.237702532641
43930994.646816851645-64.6468168516451
44950994.108577024592-44.108577024592
451240993.741335541941246.258664458059
46950995.791648727081-45.7916487270807
47830995.41039423859-165.41039423859
481220994.033211782846225.966788217154
491040995.91457781033144.0854221896687
501080996.28162650925583.7183734907454
511160996.978653293609163.021346706391
52900998.335944893264-98.3359448932644
53790997.517214373339-207.517214373339
541100995.789456766477104.210543233523
551000996.6570983225313.3429016774686
56990996.684930827028-6.68493082702832
571250996.629273082573253.370726917427
58970998.738800246908-28.7388002469081
59840998.499525250428-158.499525250428
601220997.179881666823222.820118333177
611100999.035048986674100.964951013326
621030999.87566822236830.1243317776323
6312101000.12647894926209.873521050736
648301001.8738548167-171.873854816704
658101000.44285854501-190.442858545011
661100998.857259497157101.142740502843
671020999.69935898182120.300641018179
68950999.868379113713-49.8683791137134
691280999.453182371526280.546817628474
709501001.78897364408-51.7889736440829
717201001.35778631615-281.357786316153
721150999.015243038355150.984756961645
7310301000.2723197736429.7276802263561
7410301000.5198280384429.4801719615572
7512001000.76527558607199.234724413931
768701002.42407440764-132.424074407636
778801001.32153116764-121.321531167643
7810901000.3114260590989.6885739409096
799501001.05815984859-51.0581598485882
8010601000.6330571681359.3669428318674
8112801001.12733754571278.872662454292
829201003.44919005012-83.4491900501201
836301002.75440444724-372.754404447244
841110999.650906456873110.349093543127
8510201000.5696566740819.4303433259214
8611301000.73143083622129.268569163779
8711601001.80770180668158.192298193319
889301003.12478746329-73.1247874632901
899301002.51596130797-72.515961307969
9011101001.91220414909108.087795850911
919301002.81212713646-72.8121271364628
9210701002.2059041447467.7940958552622
9312501002.77034775086247.229652249135
948401004.82874523661-164.828745236612
956801003.45640550435-323.456405504353
9611101000.7633553553109.236644644696
979901001.67284348766-11.6728434876642
9812101001.57565712079208.424342879214
9911301003.3109673453126.689032654699
1009201004.36576147665-84.3657614766511
10110301003.6633446357626.3366553642369
10211201003.88261972955116.117380270446
1038801004.84939584814-124.849395848137
10410501003.8099182605146.1900817394938
10512601004.19449004328255.805509956724
1067901006.32428885076-216.324288850761
1076401004.52320484556-364.523204845564
10811101001.48823860456108.511761395437







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1091002.3916914663745.1885343207251259.59484861187
1101002.3916914663745.1796198380981259.6037630945
1111002.3916914663745.170705664421259.61267726818
1121002.3916914663745.1617917996571259.62159113294
1131002.3916914663745.1528782437791259.63050468882
1141002.3916914663745.1439649967531259.63941793584
1151002.3916914663745.1350520585471259.64833087405
1161002.3916914663745.1261394291291259.65724350347
1171002.3916914663745.1172271084671259.66615582413
1181002.3916914663745.1083150965281259.67506783607
1191002.3916914663745.099403393281259.68397953932
1201002.3916914663745.0904919986921259.6928909339

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 1002.3916914663 & 745.188534320725 & 1259.59484861187 \tabularnewline
110 & 1002.3916914663 & 745.179619838098 & 1259.6037630945 \tabularnewline
111 & 1002.3916914663 & 745.17070566442 & 1259.61267726818 \tabularnewline
112 & 1002.3916914663 & 745.161791799657 & 1259.62159113294 \tabularnewline
113 & 1002.3916914663 & 745.152878243779 & 1259.63050468882 \tabularnewline
114 & 1002.3916914663 & 745.143964996753 & 1259.63941793584 \tabularnewline
115 & 1002.3916914663 & 745.135052058547 & 1259.64833087405 \tabularnewline
116 & 1002.3916914663 & 745.126139429129 & 1259.65724350347 \tabularnewline
117 & 1002.3916914663 & 745.117227108467 & 1259.66615582413 \tabularnewline
118 & 1002.3916914663 & 745.108315096528 & 1259.67506783607 \tabularnewline
119 & 1002.3916914663 & 745.09940339328 & 1259.68397953932 \tabularnewline
120 & 1002.3916914663 & 745.090491998692 & 1259.6928909339 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169141&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]1002.3916914663[/C][C]745.188534320725[/C][C]1259.59484861187[/C][/ROW]
[ROW][C]110[/C][C]1002.3916914663[/C][C]745.179619838098[/C][C]1259.6037630945[/C][/ROW]
[ROW][C]111[/C][C]1002.3916914663[/C][C]745.17070566442[/C][C]1259.61267726818[/C][/ROW]
[ROW][C]112[/C][C]1002.3916914663[/C][C]745.161791799657[/C][C]1259.62159113294[/C][/ROW]
[ROW][C]113[/C][C]1002.3916914663[/C][C]745.152878243779[/C][C]1259.63050468882[/C][/ROW]
[ROW][C]114[/C][C]1002.3916914663[/C][C]745.143964996753[/C][C]1259.63941793584[/C][/ROW]
[ROW][C]115[/C][C]1002.3916914663[/C][C]745.135052058547[/C][C]1259.64833087405[/C][/ROW]
[ROW][C]116[/C][C]1002.3916914663[/C][C]745.126139429129[/C][C]1259.65724350347[/C][/ROW]
[ROW][C]117[/C][C]1002.3916914663[/C][C]745.117227108467[/C][C]1259.66615582413[/C][/ROW]
[ROW][C]118[/C][C]1002.3916914663[/C][C]745.108315096528[/C][C]1259.67506783607[/C][/ROW]
[ROW][C]119[/C][C]1002.3916914663[/C][C]745.09940339328[/C][C]1259.68397953932[/C][/ROW]
[ROW][C]120[/C][C]1002.3916914663[/C][C]745.090491998692[/C][C]1259.6928909339[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169141&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169141&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
1091002.3916914663745.1885343207251259.59484861187
1101002.3916914663745.1796198380981259.6037630945
1111002.3916914663745.170705664421259.61267726818
1121002.3916914663745.1617917996571259.62159113294
1131002.3916914663745.1528782437791259.63050468882
1141002.3916914663745.1439649967531259.63941793584
1151002.3916914663745.1350520585471259.64833087405
1161002.3916914663745.1261394291291259.65724350347
1171002.3916914663745.1172271084671259.66615582413
1181002.3916914663745.1083150965281259.67506783607
1191002.3916914663745.099403393281259.68397953932
1201002.3916914663745.0904919986921259.6928909339



Parameters (Session):
par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
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')