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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 05 Aug 2012 07:05:38 -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/05/t1344164762b2d1lgzh1wqxim5.htm/, Retrieved Sat, 04 May 2024 10:54:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=169026, Retrieved Sat, 04 May 2024 10:54:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsBlij Arnaud
Estimated Impact139
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks B - Sta...] [2012-08-05 11:05:38] [50083fea611f0183deb36cab794727ad] [Current]
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Dataseries X:
1160
1220
1100
1030
1110
1160
1170
1090
1160
1210
1250
1200
1180
1210
950
1070
1120
1220
1170
1120
1180
1250
1240
1230
1120
1330
990
1110
1090
1210
1220
1220
1100
1200
1320
1180
1110
1300
1060
1130
1160
1260
1210
1190
1130
1170
1370
1170
1040
1340
1050
1130
1150
1220
1210
1150
1130
1150
1440
1160
1130
1350
1050
1150
1120
1170
1100
1120
1210
1170
1370
1170
1110
1320
1060
1150
1160
1230
1140
1100
1270
1160
1380
1150
1180
1370
1080
1160
1230
1210
1130
1110
1250
1210
1370
1080
1220
1360
1120
1150
1180
1250
1040
1180
1250
1120
1430
1150




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169026&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169026&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169026&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0
beta0
gamma0.808068340483991

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.808068340483991 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169026&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[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.808068340483991[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169026&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169026&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
beta0
gamma0.808068340483991







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1311801177.94322295742.05677704259938
1412101207.38359972292.61640027710132
15950946.8651809436653.13481905633546
1610701064.873277803895.12672219610704
1711201114.170157142055.82984285794873
1812201213.581379864936.41862013506534
1911701169.232977156040.76702284395833
2011201089.6131821041430.3868178958644
2111801167.0840253639712.9159746360315
2212501223.0699217803126.9300782196899
2312401262.03983885714-22.0398388571373
2412301209.2827468225620.7172531774384
2511201189.00614812419-69.0061481241944
2613301219.13057146909110.869428530908
27990956.95455840652533.0454415934752
2811101077.5186429752832.4813570247156
2910901127.77440848547-37.7744084854667
3012101228.44893525817-18.4489352581718
3112201179.1389669310740.8610330689262
3212201123.0061218575296.9938781424785
3311001186.85571849515-86.8557184951489
3412001254.69305004281-54.6930500428118
3513201254.0806621521165.9193378478897
3611801235.72368335276-55.7236833527556
3711101142.20449204607-32.2044920460696
3813001319.06126801614-19.0612680161412
391060991.42461292108568.5753870789146
4011301112.4755369677917.5244630322125
4111601105.9027379741254.0972620258758
4212601223.1043229660936.8956770339075
4312101221.70369073598-11.7036907359811
4411901210.83896847887-20.8389684788651
4511301125.453052411784.54694758822438
4611701220.01173774724-50.0117377472418
4713701317.6169141985952.3830858014121
4811701200.04166150887-30.0416615088684
4910401124.93694822211-84.9369482221055
5013401313.8783337805226.1216662194845
5110501055.03941613131-5.03941613130974
5211301135.4571067608-5.45710676080171
5311501158.61167833242-8.61167833241893
5412201262.7150555642-42.7150555642017
5512101221.71862678787-11.7186267878685
5611501203.32332795204-53.3233279520377
5711301137.93865970182-7.93865970182469
5811501188.79808077982-38.7980807798174
5914401370.5448438606269.4551561393816
6011601184.9233970663-24.9233970662958
6111301064.5237602907465.4762397092602
6213501345.370485437634.62951456236601
6310501059.13677284636-9.13677284636015
6411501139.833741464510.1662585354982
6511201160.59348584528-40.5934858452836
6611701237.72708529264-67.7270852926424
6711001221.64807424831-121.648074248307
6811201169.22424073549-49.2242407354879
6912101140.285370129369.7146298706973
7011701166.403218494173.59678150582954
7113701437.70220002702-67.7022000270213
7211701173.78539346934-3.78539346933758
7311101126.06334344716-16.0633434471608
7413201359.52438389773-39.5243838977283
7510601059.866236206140.13376379385636
7611501156.898448186-6.89844818599977
7711601136.4791146287223.5208853712825
7812301192.1063581092437.8936418907574
7911401131.990732792568.00926720743837
8011001138.13166644898-38.1316664489837
8112701205.8141042918164.1858957081911
8211601178.28862038569-18.2886203856863
8313801393.60721295378-13.6072129537843
8411501179.70488287319-29.7048828731927
8511801121.6138882846458.3861117153556
8613701337.7542907541732.2457092458262
8710801068.0877540864111.9122459135929
8811601160.1310642535-0.131064253496334
8912301164.3188341095165.6811658904903
9012101232.06833057662-22.0683305766199
9111301147.15479730607-17.1547973060735
9211101115.76754626956-5.76754626955926
9312501267.27073547116-17.2707354711602
9412101172.3765050782737.6234949217317
9513701393.14093562867-23.140935628669
9610801164.49697016729-84.4969701672921
9712201177.6835244470642.3164755529367
9813601374.17739570478-14.177395704781
9911201085.9002109697134.099789030287
10011501168.83138502678-18.8313850267837
10111801226.62960002026-46.629600020259
10212501223.4417269948726.5582730051306
10310401141.87954325937-101.879543259369
10411801119.5205559558460.479444044156
10512501262.79923067139-12.7992306713888
10611201211.87512409925-91.8751240992542
10714301384.8294293976345.1705706023652
10811501104.4975799285945.5024200714122

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1180 & 1177.9432229574 & 2.05677704259938 \tabularnewline
14 & 1210 & 1207.3835997229 & 2.61640027710132 \tabularnewline
15 & 950 & 946.865180943665 & 3.13481905633546 \tabularnewline
16 & 1070 & 1064.87327780389 & 5.12672219610704 \tabularnewline
17 & 1120 & 1114.17015714205 & 5.82984285794873 \tabularnewline
18 & 1220 & 1213.58137986493 & 6.41862013506534 \tabularnewline
19 & 1170 & 1169.23297715604 & 0.76702284395833 \tabularnewline
20 & 1120 & 1089.61318210414 & 30.3868178958644 \tabularnewline
21 & 1180 & 1167.08402536397 & 12.9159746360315 \tabularnewline
22 & 1250 & 1223.06992178031 & 26.9300782196899 \tabularnewline
23 & 1240 & 1262.03983885714 & -22.0398388571373 \tabularnewline
24 & 1230 & 1209.28274682256 & 20.7172531774384 \tabularnewline
25 & 1120 & 1189.00614812419 & -69.0061481241944 \tabularnewline
26 & 1330 & 1219.13057146909 & 110.869428530908 \tabularnewline
27 & 990 & 956.954558406525 & 33.0454415934752 \tabularnewline
28 & 1110 & 1077.51864297528 & 32.4813570247156 \tabularnewline
29 & 1090 & 1127.77440848547 & -37.7744084854667 \tabularnewline
30 & 1210 & 1228.44893525817 & -18.4489352581718 \tabularnewline
31 & 1220 & 1179.13896693107 & 40.8610330689262 \tabularnewline
32 & 1220 & 1123.00612185752 & 96.9938781424785 \tabularnewline
33 & 1100 & 1186.85571849515 & -86.8557184951489 \tabularnewline
34 & 1200 & 1254.69305004281 & -54.6930500428118 \tabularnewline
35 & 1320 & 1254.08066215211 & 65.9193378478897 \tabularnewline
36 & 1180 & 1235.72368335276 & -55.7236833527556 \tabularnewline
37 & 1110 & 1142.20449204607 & -32.2044920460696 \tabularnewline
38 & 1300 & 1319.06126801614 & -19.0612680161412 \tabularnewline
39 & 1060 & 991.424612921085 & 68.5753870789146 \tabularnewline
40 & 1130 & 1112.47553696779 & 17.5244630322125 \tabularnewline
41 & 1160 & 1105.90273797412 & 54.0972620258758 \tabularnewline
42 & 1260 & 1223.10432296609 & 36.8956770339075 \tabularnewline
43 & 1210 & 1221.70369073598 & -11.7036907359811 \tabularnewline
44 & 1190 & 1210.83896847887 & -20.8389684788651 \tabularnewline
45 & 1130 & 1125.45305241178 & 4.54694758822438 \tabularnewline
46 & 1170 & 1220.01173774724 & -50.0117377472418 \tabularnewline
47 & 1370 & 1317.61691419859 & 52.3830858014121 \tabularnewline
48 & 1170 & 1200.04166150887 & -30.0416615088684 \tabularnewline
49 & 1040 & 1124.93694822211 & -84.9369482221055 \tabularnewline
50 & 1340 & 1313.87833378052 & 26.1216662194845 \tabularnewline
51 & 1050 & 1055.03941613131 & -5.03941613130974 \tabularnewline
52 & 1130 & 1135.4571067608 & -5.45710676080171 \tabularnewline
53 & 1150 & 1158.61167833242 & -8.61167833241893 \tabularnewline
54 & 1220 & 1262.7150555642 & -42.7150555642017 \tabularnewline
55 & 1210 & 1221.71862678787 & -11.7186267878685 \tabularnewline
56 & 1150 & 1203.32332795204 & -53.3233279520377 \tabularnewline
57 & 1130 & 1137.93865970182 & -7.93865970182469 \tabularnewline
58 & 1150 & 1188.79808077982 & -38.7980807798174 \tabularnewline
59 & 1440 & 1370.54484386062 & 69.4551561393816 \tabularnewline
60 & 1160 & 1184.9233970663 & -24.9233970662958 \tabularnewline
61 & 1130 & 1064.52376029074 & 65.4762397092602 \tabularnewline
62 & 1350 & 1345.37048543763 & 4.62951456236601 \tabularnewline
63 & 1050 & 1059.13677284636 & -9.13677284636015 \tabularnewline
64 & 1150 & 1139.8337414645 & 10.1662585354982 \tabularnewline
65 & 1120 & 1160.59348584528 & -40.5934858452836 \tabularnewline
66 & 1170 & 1237.72708529264 & -67.7270852926424 \tabularnewline
67 & 1100 & 1221.64807424831 & -121.648074248307 \tabularnewline
68 & 1120 & 1169.22424073549 & -49.2242407354879 \tabularnewline
69 & 1210 & 1140.2853701293 & 69.7146298706973 \tabularnewline
70 & 1170 & 1166.40321849417 & 3.59678150582954 \tabularnewline
71 & 1370 & 1437.70220002702 & -67.7022000270213 \tabularnewline
72 & 1170 & 1173.78539346934 & -3.78539346933758 \tabularnewline
73 & 1110 & 1126.06334344716 & -16.0633434471608 \tabularnewline
74 & 1320 & 1359.52438389773 & -39.5243838977283 \tabularnewline
75 & 1060 & 1059.86623620614 & 0.13376379385636 \tabularnewline
76 & 1150 & 1156.898448186 & -6.89844818599977 \tabularnewline
77 & 1160 & 1136.47911462872 & 23.5208853712825 \tabularnewline
78 & 1230 & 1192.10635810924 & 37.8936418907574 \tabularnewline
79 & 1140 & 1131.99073279256 & 8.00926720743837 \tabularnewline
80 & 1100 & 1138.13166644898 & -38.1316664489837 \tabularnewline
81 & 1270 & 1205.81410429181 & 64.1858957081911 \tabularnewline
82 & 1160 & 1178.28862038569 & -18.2886203856863 \tabularnewline
83 & 1380 & 1393.60721295378 & -13.6072129537843 \tabularnewline
84 & 1150 & 1179.70488287319 & -29.7048828731927 \tabularnewline
85 & 1180 & 1121.61388828464 & 58.3861117153556 \tabularnewline
86 & 1370 & 1337.75429075417 & 32.2457092458262 \tabularnewline
87 & 1080 & 1068.08775408641 & 11.9122459135929 \tabularnewline
88 & 1160 & 1160.1310642535 & -0.131064253496334 \tabularnewline
89 & 1230 & 1164.31883410951 & 65.6811658904903 \tabularnewline
90 & 1210 & 1232.06833057662 & -22.0683305766199 \tabularnewline
91 & 1130 & 1147.15479730607 & -17.1547973060735 \tabularnewline
92 & 1110 & 1115.76754626956 & -5.76754626955926 \tabularnewline
93 & 1250 & 1267.27073547116 & -17.2707354711602 \tabularnewline
94 & 1210 & 1172.37650507827 & 37.6234949217317 \tabularnewline
95 & 1370 & 1393.14093562867 & -23.140935628669 \tabularnewline
96 & 1080 & 1164.49697016729 & -84.4969701672921 \tabularnewline
97 & 1220 & 1177.68352444706 & 42.3164755529367 \tabularnewline
98 & 1360 & 1374.17739570478 & -14.177395704781 \tabularnewline
99 & 1120 & 1085.90021096971 & 34.099789030287 \tabularnewline
100 & 1150 & 1168.83138502678 & -18.8313850267837 \tabularnewline
101 & 1180 & 1226.62960002026 & -46.629600020259 \tabularnewline
102 & 1250 & 1223.44172699487 & 26.5582730051306 \tabularnewline
103 & 1040 & 1141.87954325937 & -101.879543259369 \tabularnewline
104 & 1180 & 1119.52055595584 & 60.479444044156 \tabularnewline
105 & 1250 & 1262.79923067139 & -12.7992306713888 \tabularnewline
106 & 1120 & 1211.87512409925 & -91.8751240992542 \tabularnewline
107 & 1430 & 1384.82942939763 & 45.1705706023652 \tabularnewline
108 & 1150 & 1104.49757992859 & 45.5024200714122 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169026&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]1180[/C][C]1177.9432229574[/C][C]2.05677704259938[/C][/ROW]
[ROW][C]14[/C][C]1210[/C][C]1207.3835997229[/C][C]2.61640027710132[/C][/ROW]
[ROW][C]15[/C][C]950[/C][C]946.865180943665[/C][C]3.13481905633546[/C][/ROW]
[ROW][C]16[/C][C]1070[/C][C]1064.87327780389[/C][C]5.12672219610704[/C][/ROW]
[ROW][C]17[/C][C]1120[/C][C]1114.17015714205[/C][C]5.82984285794873[/C][/ROW]
[ROW][C]18[/C][C]1220[/C][C]1213.58137986493[/C][C]6.41862013506534[/C][/ROW]
[ROW][C]19[/C][C]1170[/C][C]1169.23297715604[/C][C]0.76702284395833[/C][/ROW]
[ROW][C]20[/C][C]1120[/C][C]1089.61318210414[/C][C]30.3868178958644[/C][/ROW]
[ROW][C]21[/C][C]1180[/C][C]1167.08402536397[/C][C]12.9159746360315[/C][/ROW]
[ROW][C]22[/C][C]1250[/C][C]1223.06992178031[/C][C]26.9300782196899[/C][/ROW]
[ROW][C]23[/C][C]1240[/C][C]1262.03983885714[/C][C]-22.0398388571373[/C][/ROW]
[ROW][C]24[/C][C]1230[/C][C]1209.28274682256[/C][C]20.7172531774384[/C][/ROW]
[ROW][C]25[/C][C]1120[/C][C]1189.00614812419[/C][C]-69.0061481241944[/C][/ROW]
[ROW][C]26[/C][C]1330[/C][C]1219.13057146909[/C][C]110.869428530908[/C][/ROW]
[ROW][C]27[/C][C]990[/C][C]956.954558406525[/C][C]33.0454415934752[/C][/ROW]
[ROW][C]28[/C][C]1110[/C][C]1077.51864297528[/C][C]32.4813570247156[/C][/ROW]
[ROW][C]29[/C][C]1090[/C][C]1127.77440848547[/C][C]-37.7744084854667[/C][/ROW]
[ROW][C]30[/C][C]1210[/C][C]1228.44893525817[/C][C]-18.4489352581718[/C][/ROW]
[ROW][C]31[/C][C]1220[/C][C]1179.13896693107[/C][C]40.8610330689262[/C][/ROW]
[ROW][C]32[/C][C]1220[/C][C]1123.00612185752[/C][C]96.9938781424785[/C][/ROW]
[ROW][C]33[/C][C]1100[/C][C]1186.85571849515[/C][C]-86.8557184951489[/C][/ROW]
[ROW][C]34[/C][C]1200[/C][C]1254.69305004281[/C][C]-54.6930500428118[/C][/ROW]
[ROW][C]35[/C][C]1320[/C][C]1254.08066215211[/C][C]65.9193378478897[/C][/ROW]
[ROW][C]36[/C][C]1180[/C][C]1235.72368335276[/C][C]-55.7236833527556[/C][/ROW]
[ROW][C]37[/C][C]1110[/C][C]1142.20449204607[/C][C]-32.2044920460696[/C][/ROW]
[ROW][C]38[/C][C]1300[/C][C]1319.06126801614[/C][C]-19.0612680161412[/C][/ROW]
[ROW][C]39[/C][C]1060[/C][C]991.424612921085[/C][C]68.5753870789146[/C][/ROW]
[ROW][C]40[/C][C]1130[/C][C]1112.47553696779[/C][C]17.5244630322125[/C][/ROW]
[ROW][C]41[/C][C]1160[/C][C]1105.90273797412[/C][C]54.0972620258758[/C][/ROW]
[ROW][C]42[/C][C]1260[/C][C]1223.10432296609[/C][C]36.8956770339075[/C][/ROW]
[ROW][C]43[/C][C]1210[/C][C]1221.70369073598[/C][C]-11.7036907359811[/C][/ROW]
[ROW][C]44[/C][C]1190[/C][C]1210.83896847887[/C][C]-20.8389684788651[/C][/ROW]
[ROW][C]45[/C][C]1130[/C][C]1125.45305241178[/C][C]4.54694758822438[/C][/ROW]
[ROW][C]46[/C][C]1170[/C][C]1220.01173774724[/C][C]-50.0117377472418[/C][/ROW]
[ROW][C]47[/C][C]1370[/C][C]1317.61691419859[/C][C]52.3830858014121[/C][/ROW]
[ROW][C]48[/C][C]1170[/C][C]1200.04166150887[/C][C]-30.0416615088684[/C][/ROW]
[ROW][C]49[/C][C]1040[/C][C]1124.93694822211[/C][C]-84.9369482221055[/C][/ROW]
[ROW][C]50[/C][C]1340[/C][C]1313.87833378052[/C][C]26.1216662194845[/C][/ROW]
[ROW][C]51[/C][C]1050[/C][C]1055.03941613131[/C][C]-5.03941613130974[/C][/ROW]
[ROW][C]52[/C][C]1130[/C][C]1135.4571067608[/C][C]-5.45710676080171[/C][/ROW]
[ROW][C]53[/C][C]1150[/C][C]1158.61167833242[/C][C]-8.61167833241893[/C][/ROW]
[ROW][C]54[/C][C]1220[/C][C]1262.7150555642[/C][C]-42.7150555642017[/C][/ROW]
[ROW][C]55[/C][C]1210[/C][C]1221.71862678787[/C][C]-11.7186267878685[/C][/ROW]
[ROW][C]56[/C][C]1150[/C][C]1203.32332795204[/C][C]-53.3233279520377[/C][/ROW]
[ROW][C]57[/C][C]1130[/C][C]1137.93865970182[/C][C]-7.93865970182469[/C][/ROW]
[ROW][C]58[/C][C]1150[/C][C]1188.79808077982[/C][C]-38.7980807798174[/C][/ROW]
[ROW][C]59[/C][C]1440[/C][C]1370.54484386062[/C][C]69.4551561393816[/C][/ROW]
[ROW][C]60[/C][C]1160[/C][C]1184.9233970663[/C][C]-24.9233970662958[/C][/ROW]
[ROW][C]61[/C][C]1130[/C][C]1064.52376029074[/C][C]65.4762397092602[/C][/ROW]
[ROW][C]62[/C][C]1350[/C][C]1345.37048543763[/C][C]4.62951456236601[/C][/ROW]
[ROW][C]63[/C][C]1050[/C][C]1059.13677284636[/C][C]-9.13677284636015[/C][/ROW]
[ROW][C]64[/C][C]1150[/C][C]1139.8337414645[/C][C]10.1662585354982[/C][/ROW]
[ROW][C]65[/C][C]1120[/C][C]1160.59348584528[/C][C]-40.5934858452836[/C][/ROW]
[ROW][C]66[/C][C]1170[/C][C]1237.72708529264[/C][C]-67.7270852926424[/C][/ROW]
[ROW][C]67[/C][C]1100[/C][C]1221.64807424831[/C][C]-121.648074248307[/C][/ROW]
[ROW][C]68[/C][C]1120[/C][C]1169.22424073549[/C][C]-49.2242407354879[/C][/ROW]
[ROW][C]69[/C][C]1210[/C][C]1140.2853701293[/C][C]69.7146298706973[/C][/ROW]
[ROW][C]70[/C][C]1170[/C][C]1166.40321849417[/C][C]3.59678150582954[/C][/ROW]
[ROW][C]71[/C][C]1370[/C][C]1437.70220002702[/C][C]-67.7022000270213[/C][/ROW]
[ROW][C]72[/C][C]1170[/C][C]1173.78539346934[/C][C]-3.78539346933758[/C][/ROW]
[ROW][C]73[/C][C]1110[/C][C]1126.06334344716[/C][C]-16.0633434471608[/C][/ROW]
[ROW][C]74[/C][C]1320[/C][C]1359.52438389773[/C][C]-39.5243838977283[/C][/ROW]
[ROW][C]75[/C][C]1060[/C][C]1059.86623620614[/C][C]0.13376379385636[/C][/ROW]
[ROW][C]76[/C][C]1150[/C][C]1156.898448186[/C][C]-6.89844818599977[/C][/ROW]
[ROW][C]77[/C][C]1160[/C][C]1136.47911462872[/C][C]23.5208853712825[/C][/ROW]
[ROW][C]78[/C][C]1230[/C][C]1192.10635810924[/C][C]37.8936418907574[/C][/ROW]
[ROW][C]79[/C][C]1140[/C][C]1131.99073279256[/C][C]8.00926720743837[/C][/ROW]
[ROW][C]80[/C][C]1100[/C][C]1138.13166644898[/C][C]-38.1316664489837[/C][/ROW]
[ROW][C]81[/C][C]1270[/C][C]1205.81410429181[/C][C]64.1858957081911[/C][/ROW]
[ROW][C]82[/C][C]1160[/C][C]1178.28862038569[/C][C]-18.2886203856863[/C][/ROW]
[ROW][C]83[/C][C]1380[/C][C]1393.60721295378[/C][C]-13.6072129537843[/C][/ROW]
[ROW][C]84[/C][C]1150[/C][C]1179.70488287319[/C][C]-29.7048828731927[/C][/ROW]
[ROW][C]85[/C][C]1180[/C][C]1121.61388828464[/C][C]58.3861117153556[/C][/ROW]
[ROW][C]86[/C][C]1370[/C][C]1337.75429075417[/C][C]32.2457092458262[/C][/ROW]
[ROW][C]87[/C][C]1080[/C][C]1068.08775408641[/C][C]11.9122459135929[/C][/ROW]
[ROW][C]88[/C][C]1160[/C][C]1160.1310642535[/C][C]-0.131064253496334[/C][/ROW]
[ROW][C]89[/C][C]1230[/C][C]1164.31883410951[/C][C]65.6811658904903[/C][/ROW]
[ROW][C]90[/C][C]1210[/C][C]1232.06833057662[/C][C]-22.0683305766199[/C][/ROW]
[ROW][C]91[/C][C]1130[/C][C]1147.15479730607[/C][C]-17.1547973060735[/C][/ROW]
[ROW][C]92[/C][C]1110[/C][C]1115.76754626956[/C][C]-5.76754626955926[/C][/ROW]
[ROW][C]93[/C][C]1250[/C][C]1267.27073547116[/C][C]-17.2707354711602[/C][/ROW]
[ROW][C]94[/C][C]1210[/C][C]1172.37650507827[/C][C]37.6234949217317[/C][/ROW]
[ROW][C]95[/C][C]1370[/C][C]1393.14093562867[/C][C]-23.140935628669[/C][/ROW]
[ROW][C]96[/C][C]1080[/C][C]1164.49697016729[/C][C]-84.4969701672921[/C][/ROW]
[ROW][C]97[/C][C]1220[/C][C]1177.68352444706[/C][C]42.3164755529367[/C][/ROW]
[ROW][C]98[/C][C]1360[/C][C]1374.17739570478[/C][C]-14.177395704781[/C][/ROW]
[ROW][C]99[/C][C]1120[/C][C]1085.90021096971[/C][C]34.099789030287[/C][/ROW]
[ROW][C]100[/C][C]1150[/C][C]1168.83138502678[/C][C]-18.8313850267837[/C][/ROW]
[ROW][C]101[/C][C]1180[/C][C]1226.62960002026[/C][C]-46.629600020259[/C][/ROW]
[ROW][C]102[/C][C]1250[/C][C]1223.44172699487[/C][C]26.5582730051306[/C][/ROW]
[ROW][C]103[/C][C]1040[/C][C]1141.87954325937[/C][C]-101.879543259369[/C][/ROW]
[ROW][C]104[/C][C]1180[/C][C]1119.52055595584[/C][C]60.479444044156[/C][/ROW]
[ROW][C]105[/C][C]1250[/C][C]1262.79923067139[/C][C]-12.7992306713888[/C][/ROW]
[ROW][C]106[/C][C]1120[/C][C]1211.87512409925[/C][C]-91.8751240992542[/C][/ROW]
[ROW][C]107[/C][C]1430[/C][C]1384.82942939763[/C][C]45.1705706023652[/C][/ROW]
[ROW][C]108[/C][C]1150[/C][C]1104.49757992859[/C][C]45.5024200714122[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169026&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169026&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
1311801177.94322295742.05677704259938
1412101207.38359972292.61640027710132
15950946.8651809436653.13481905633546
1610701064.873277803895.12672219610704
1711201114.170157142055.82984285794873
1812201213.581379864936.41862013506534
1911701169.232977156040.76702284395833
2011201089.6131821041430.3868178958644
2111801167.0840253639712.9159746360315
2212501223.0699217803126.9300782196899
2312401262.03983885714-22.0398388571373
2412301209.2827468225620.7172531774384
2511201189.00614812419-69.0061481241944
2613301219.13057146909110.869428530908
27990956.95455840652533.0454415934752
2811101077.5186429752832.4813570247156
2910901127.77440848547-37.7744084854667
3012101228.44893525817-18.4489352581718
3112201179.1389669310740.8610330689262
3212201123.0061218575296.9938781424785
3311001186.85571849515-86.8557184951489
3412001254.69305004281-54.6930500428118
3513201254.0806621521165.9193378478897
3611801235.72368335276-55.7236833527556
3711101142.20449204607-32.2044920460696
3813001319.06126801614-19.0612680161412
391060991.42461292108568.5753870789146
4011301112.4755369677917.5244630322125
4111601105.9027379741254.0972620258758
4212601223.1043229660936.8956770339075
4312101221.70369073598-11.7036907359811
4411901210.83896847887-20.8389684788651
4511301125.453052411784.54694758822438
4611701220.01173774724-50.0117377472418
4713701317.6169141985952.3830858014121
4811701200.04166150887-30.0416615088684
4910401124.93694822211-84.9369482221055
5013401313.8783337805226.1216662194845
5110501055.03941613131-5.03941613130974
5211301135.4571067608-5.45710676080171
5311501158.61167833242-8.61167833241893
5412201262.7150555642-42.7150555642017
5512101221.71862678787-11.7186267878685
5611501203.32332795204-53.3233279520377
5711301137.93865970182-7.93865970182469
5811501188.79808077982-38.7980807798174
5914401370.5448438606269.4551561393816
6011601184.9233970663-24.9233970662958
6111301064.5237602907465.4762397092602
6213501345.370485437634.62951456236601
6310501059.13677284636-9.13677284636015
6411501139.833741464510.1662585354982
6511201160.59348584528-40.5934858452836
6611701237.72708529264-67.7270852926424
6711001221.64807424831-121.648074248307
6811201169.22424073549-49.2242407354879
6912101140.285370129369.7146298706973
7011701166.403218494173.59678150582954
7113701437.70220002702-67.7022000270213
7211701173.78539346934-3.78539346933758
7311101126.06334344716-16.0633434471608
7413201359.52438389773-39.5243838977283
7510601059.866236206140.13376379385636
7611501156.898448186-6.89844818599977
7711601136.4791146287223.5208853712825
7812301192.1063581092437.8936418907574
7911401131.990732792568.00926720743837
8011001138.13166644898-38.1316664489837
8112701205.8141042918164.1858957081911
8211601178.28862038569-18.2886203856863
8313801393.60721295378-13.6072129537843
8411501179.70488287319-29.7048828731927
8511801121.6138882846458.3861117153556
8613701337.7542907541732.2457092458262
8710801068.0877540864111.9122459135929
8811601160.1310642535-0.131064253496334
8912301164.3188341095165.6811658904903
9012101232.06833057662-22.0683305766199
9111301147.15479730607-17.1547973060735
9211101115.76754626956-5.76754626955926
9312501267.27073547116-17.2707354711602
9412101172.3765050782737.6234949217317
9513701393.14093562867-23.140935628669
9610801164.49697016729-84.4969701672921
9712201177.6835244470642.3164755529367
9813601374.17739570478-14.177395704781
9911201085.9002109697134.099789030287
10011501168.83138502678-18.8313850267837
10111801226.62960002026-46.629600020259
10212501223.4417269948726.5582730051306
10310401141.87954325937-101.879543259369
10411801119.5205559558460.479444044156
10512501262.79923067139-12.7992306713888
10611201211.87512409925-91.8751240992542
10714301384.8294293976345.1705706023652
10811501104.4975799285945.5024200714122







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1091221.025912137081150.134380484391291.91744378976
1101373.001036467961302.109504815271443.89256812064
1111121.849454481711050.957922829031192.7409861344
1121162.305920094631091.414388441941233.19745174732
1131197.901881250021127.010349597331268.7934129027
1141254.270230572561183.378698919871325.16176222525
1151067.52181123563996.6302795829381138.41334288831
1161177.17294744381106.281415791111248.06447909649
1171261.863327396071190.971795743381332.75485904876
1181146.172757496921075.281225844231217.06428914961
1191431.992091064831361.100559412141502.88362271752
1201149.82222285441063.095200301251236.54924540756

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 1221.02591213708 & 1150.13438048439 & 1291.91744378976 \tabularnewline
110 & 1373.00103646796 & 1302.10950481527 & 1443.89256812064 \tabularnewline
111 & 1121.84945448171 & 1050.95792282903 & 1192.7409861344 \tabularnewline
112 & 1162.30592009463 & 1091.41438844194 & 1233.19745174732 \tabularnewline
113 & 1197.90188125002 & 1127.01034959733 & 1268.7934129027 \tabularnewline
114 & 1254.27023057256 & 1183.37869891987 & 1325.16176222525 \tabularnewline
115 & 1067.52181123563 & 996.630279582938 & 1138.41334288831 \tabularnewline
116 & 1177.1729474438 & 1106.28141579111 & 1248.06447909649 \tabularnewline
117 & 1261.86332739607 & 1190.97179574338 & 1332.75485904876 \tabularnewline
118 & 1146.17275749692 & 1075.28122584423 & 1217.06428914961 \tabularnewline
119 & 1431.99209106483 & 1361.10055941214 & 1502.88362271752 \tabularnewline
120 & 1149.8222228544 & 1063.09520030125 & 1236.54924540756 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169026&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]1221.02591213708[/C][C]1150.13438048439[/C][C]1291.91744378976[/C][/ROW]
[ROW][C]110[/C][C]1373.00103646796[/C][C]1302.10950481527[/C][C]1443.89256812064[/C][/ROW]
[ROW][C]111[/C][C]1121.84945448171[/C][C]1050.95792282903[/C][C]1192.7409861344[/C][/ROW]
[ROW][C]112[/C][C]1162.30592009463[/C][C]1091.41438844194[/C][C]1233.19745174732[/C][/ROW]
[ROW][C]113[/C][C]1197.90188125002[/C][C]1127.01034959733[/C][C]1268.7934129027[/C][/ROW]
[ROW][C]114[/C][C]1254.27023057256[/C][C]1183.37869891987[/C][C]1325.16176222525[/C][/ROW]
[ROW][C]115[/C][C]1067.52181123563[/C][C]996.630279582938[/C][C]1138.41334288831[/C][/ROW]
[ROW][C]116[/C][C]1177.1729474438[/C][C]1106.28141579111[/C][C]1248.06447909649[/C][/ROW]
[ROW][C]117[/C][C]1261.86332739607[/C][C]1190.97179574338[/C][C]1332.75485904876[/C][/ROW]
[ROW][C]118[/C][C]1146.17275749692[/C][C]1075.28122584423[/C][C]1217.06428914961[/C][/ROW]
[ROW][C]119[/C][C]1431.99209106483[/C][C]1361.10055941214[/C][C]1502.88362271752[/C][/ROW]
[ROW][C]120[/C][C]1149.8222228544[/C][C]1063.09520030125[/C][C]1236.54924540756[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169026&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169026&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
1091221.025912137081150.134380484391291.91744378976
1101373.001036467961302.109504815271443.89256812064
1111121.849454481711050.957922829031192.7409861344
1121162.305920094631091.414388441941233.19745174732
1131197.901881250021127.010349597331268.7934129027
1141254.270230572561183.378698919871325.16176222525
1151067.52181123563996.6302795829381138.41334288831
1161177.17294744381106.281415791111248.06447909649
1171261.863327396071190.971795743381332.75485904876
1181146.172757496921075.281225844231217.06428914961
1191431.992091064831361.100559412141502.88362271752
1201149.82222285441063.095200301251236.54924540756



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')