Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 20 Jul 2011 09:42:35 -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/Jul/20/t13111694909xfaq60h8r1zkfm.htm/, Retrieved Fri, 17 May 2024 07:49:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=123097, Retrieved Fri, 17 May 2024 07:49:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsLynn Pelgrims
Estimated Impact195
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks B - Sta...] [2011-07-20 13:42:35] [cedc01334dbefab590f7f4b747b64ab1] [Current]
- R P     [Exponential Smoothing] [Tijdreeks B - Sta...] [2011-08-18 10:15:26] [74be16979710d4c4e7c6647856088456]
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Dataseries X:
1070
1240
1200
1280
1180
1190
1190
1230
1170
1190
1190
1400
1130
1260
1260
1260
1130
1220
1180
1280
1140
1160
1170
1410
1100
1280
1330
1260
1070
1260
1270
1410
1160
1130
1160
1300
1080
1380
1260
1250
990
1180
1240
1500
1150
1110
1080
1270
1050
1490
1280
1230
960
1100
1270
1530
1290
1120
1100
1310
1020
1510
1260
1160
970
1020
1210
1530
1350
1070
1140
1250
930
1510
1230
1180
960
960
1240
1640
1350
1100
1120
1290
890
1560
1250
1170
900
860
1310
1610
1440
1130
1220
1400
930
1490
1250
1160
910
880
1300
1550
1460
1120
1270
1410




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123097&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123097&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123097&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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.281853316417035
beta0.276533445657515
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.281853316417035 \tabularnewline
beta & 0.276533445657515 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123097&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]0.281853316417035[/C][/ROW]
[ROW][C]beta[/C][C]0.276533445657515[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123097&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123097&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
alpha0.281853316417035
beta0.276533445657515
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
312001410-210
412801504.44301111307-224.443011113075
511801577.32170392888-397.321703928876
611901570.50596773405-380.505967734054
711901538.77245635467-348.772456354669
812301488.79916337924-258.799163379241
911701444.01385099091-274.013850990907
1011901373.58307682895-183.583076828949
1111901314.33170819016-124.33170819016
1214001262.08988862215137.910111377853
1311301294.51076740414-164.51076740414
1412601228.8710419052531.1289580947484
1512601220.7992710275639.2007289724377
1612601218.0579336139341.9420663860731
1711301219.35829427548-89.3582942754792
1812201176.6864603928943.3135396071095
1911801174.784561104785.21543889522422
2012801162.55108683572117.448913164283
2111401191.10517727811-51.1051772781129
2211601168.16850531336-8.16850531335649
2311701156.6970081686913.3029918313121
2414101152.3141837461257.685816253902
2511001236.89598293384-136.895982933844
2612801199.5936646872980.4063353127137
2713301229.80574553795100.19425446205
2812601273.40444445751-13.404444457514
2910701283.94020589525-213.940205895246
3012601221.2793984614238.72060153858
3112701232.8498335748137.1501664251946
3214101246.87318973915163.126810260854
3311601309.11788919605-149.117889196047
3411301271.73285762807-141.732857628073
3511601225.38239791132-65.3823979113204
3613001195.45554219856104.544457801441
3710801221.57152472618-141.571524726179
3813801167.28455215496212.715447845039
3912601229.433977285230.5660227148007
4012501242.626355789947.373644210061
419901249.85660110681-259.856601106813
4211801161.5134064346118.4865935653863
4312401153.0630439323686.9369560676435
4415001170.68167193142329.318328068577
4511501282.28397937285-132.283979372851
4611101253.47168503699-143.471685036987
4710801210.32364751083-130.323647510832
4812701160.72375933534109.276240664658
4910501187.1730886636-137.173088663604
5014901133.46833031808356.531669681916
5112801246.7046400498233.295359950177
5212301271.43082647278-41.4308264727813
539601271.86599338972-311.865993389721
5411001171.77069330821-71.7706933082125
5512701133.75310785226136.246892147737
5615301164.98530611671365.014693883289
5712901289.146395355440.853604644556526
5811201310.73400542338-190.734005423378
5911001263.4558473907-163.455847390702
6013101211.126074460198.8739255399014
6110201240.44123655301-220.441236553012
6215101162.57475929935347.425240700647
6312601271.84230445588-11.8423044558799
6411601278.92608918933-118.926089189331
659701246.55863242558-276.558632425579
6610201148.20642394281-128.206423942811
6712101081.67512914972128.324870850283
6815301097.44991080112432.550089198884
6913501232.68534146571117.314658534289
7010701288.2143442643-218.2143442643
7111401232.16535108807-92.165351088071
7212501204.4601449709845.5398550290247
739301219.11706928984-289.117069289841
7415101116.91550495699393.084495043008
7512301237.63245412001-7.63245412000765
7611801244.81111447958-64.8111144795812
779601230.82228040965-270.822280409647
789601137.66012136674-177.660121366735
7912401056.9088639514183.091136048599
8016401092.10701013699547.892989863006
8113501272.8295721650377.1704278349707
8211001326.89222633151-226.892226331513
8311201277.56940889548-157.569408895484
8412901235.5042032686454.4957967313605
858901257.45778338112-367.457783381123
8615601131.84200123817428.157998761829
8712501263.84460043347-13.8446004334687
8811701270.18822715062-100.188227150619
899001244.38675867431-344.386758674315
908601122.91497667703-262.914976677025
9113101003.91420202319306.085797976806
9216101069.14508184425540.854918155753
9314401242.70165982849197.298340171506
9411301334.80347826697-204.80347826697
9512201297.60879981681-77.6087998168105
9614001290.21538842858109.784611571423
979301344.19624930166-414.196249301655
9814901218.20813709515271.791862904854
9912501306.75201504494-56.7520150449423
10011601298.27135329764-138.271353297645
1019101256.03706803987-346.037068039874
1028801128.27255130141-248.272551301407
10313001008.71246122364291.287538776362
10415501063.93266705894486.067332941056
10514601211.93720012263248.062799877372
10611201312.19384441201-192.193844412008
10712701273.38274603638-3.38274603638115
10814101287.52502436666122.474975633344

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1200 & 1410 & -210 \tabularnewline
4 & 1280 & 1504.44301111307 & -224.443011113075 \tabularnewline
5 & 1180 & 1577.32170392888 & -397.321703928876 \tabularnewline
6 & 1190 & 1570.50596773405 & -380.505967734054 \tabularnewline
7 & 1190 & 1538.77245635467 & -348.772456354669 \tabularnewline
8 & 1230 & 1488.79916337924 & -258.799163379241 \tabularnewline
9 & 1170 & 1444.01385099091 & -274.013850990907 \tabularnewline
10 & 1190 & 1373.58307682895 & -183.583076828949 \tabularnewline
11 & 1190 & 1314.33170819016 & -124.33170819016 \tabularnewline
12 & 1400 & 1262.08988862215 & 137.910111377853 \tabularnewline
13 & 1130 & 1294.51076740414 & -164.51076740414 \tabularnewline
14 & 1260 & 1228.87104190525 & 31.1289580947484 \tabularnewline
15 & 1260 & 1220.79927102756 & 39.2007289724377 \tabularnewline
16 & 1260 & 1218.05793361393 & 41.9420663860731 \tabularnewline
17 & 1130 & 1219.35829427548 & -89.3582942754792 \tabularnewline
18 & 1220 & 1176.68646039289 & 43.3135396071095 \tabularnewline
19 & 1180 & 1174.78456110478 & 5.21543889522422 \tabularnewline
20 & 1280 & 1162.55108683572 & 117.448913164283 \tabularnewline
21 & 1140 & 1191.10517727811 & -51.1051772781129 \tabularnewline
22 & 1160 & 1168.16850531336 & -8.16850531335649 \tabularnewline
23 & 1170 & 1156.69700816869 & 13.3029918313121 \tabularnewline
24 & 1410 & 1152.3141837461 & 257.685816253902 \tabularnewline
25 & 1100 & 1236.89598293384 & -136.895982933844 \tabularnewline
26 & 1280 & 1199.59366468729 & 80.4063353127137 \tabularnewline
27 & 1330 & 1229.80574553795 & 100.19425446205 \tabularnewline
28 & 1260 & 1273.40444445751 & -13.404444457514 \tabularnewline
29 & 1070 & 1283.94020589525 & -213.940205895246 \tabularnewline
30 & 1260 & 1221.27939846142 & 38.72060153858 \tabularnewline
31 & 1270 & 1232.84983357481 & 37.1501664251946 \tabularnewline
32 & 1410 & 1246.87318973915 & 163.126810260854 \tabularnewline
33 & 1160 & 1309.11788919605 & -149.117889196047 \tabularnewline
34 & 1130 & 1271.73285762807 & -141.732857628073 \tabularnewline
35 & 1160 & 1225.38239791132 & -65.3823979113204 \tabularnewline
36 & 1300 & 1195.45554219856 & 104.544457801441 \tabularnewline
37 & 1080 & 1221.57152472618 & -141.571524726179 \tabularnewline
38 & 1380 & 1167.28455215496 & 212.715447845039 \tabularnewline
39 & 1260 & 1229.4339772852 & 30.5660227148007 \tabularnewline
40 & 1250 & 1242.62635578994 & 7.373644210061 \tabularnewline
41 & 990 & 1249.85660110681 & -259.856601106813 \tabularnewline
42 & 1180 & 1161.51340643461 & 18.4865935653863 \tabularnewline
43 & 1240 & 1153.06304393236 & 86.9369560676435 \tabularnewline
44 & 1500 & 1170.68167193142 & 329.318328068577 \tabularnewline
45 & 1150 & 1282.28397937285 & -132.283979372851 \tabularnewline
46 & 1110 & 1253.47168503699 & -143.471685036987 \tabularnewline
47 & 1080 & 1210.32364751083 & -130.323647510832 \tabularnewline
48 & 1270 & 1160.72375933534 & 109.276240664658 \tabularnewline
49 & 1050 & 1187.1730886636 & -137.173088663604 \tabularnewline
50 & 1490 & 1133.46833031808 & 356.531669681916 \tabularnewline
51 & 1280 & 1246.70464004982 & 33.295359950177 \tabularnewline
52 & 1230 & 1271.43082647278 & -41.4308264727813 \tabularnewline
53 & 960 & 1271.86599338972 & -311.865993389721 \tabularnewline
54 & 1100 & 1171.77069330821 & -71.7706933082125 \tabularnewline
55 & 1270 & 1133.75310785226 & 136.246892147737 \tabularnewline
56 & 1530 & 1164.98530611671 & 365.014693883289 \tabularnewline
57 & 1290 & 1289.14639535544 & 0.853604644556526 \tabularnewline
58 & 1120 & 1310.73400542338 & -190.734005423378 \tabularnewline
59 & 1100 & 1263.4558473907 & -163.455847390702 \tabularnewline
60 & 1310 & 1211.1260744601 & 98.8739255399014 \tabularnewline
61 & 1020 & 1240.44123655301 & -220.441236553012 \tabularnewline
62 & 1510 & 1162.57475929935 & 347.425240700647 \tabularnewline
63 & 1260 & 1271.84230445588 & -11.8423044558799 \tabularnewline
64 & 1160 & 1278.92608918933 & -118.926089189331 \tabularnewline
65 & 970 & 1246.55863242558 & -276.558632425579 \tabularnewline
66 & 1020 & 1148.20642394281 & -128.206423942811 \tabularnewline
67 & 1210 & 1081.67512914972 & 128.324870850283 \tabularnewline
68 & 1530 & 1097.44991080112 & 432.550089198884 \tabularnewline
69 & 1350 & 1232.68534146571 & 117.314658534289 \tabularnewline
70 & 1070 & 1288.2143442643 & -218.2143442643 \tabularnewline
71 & 1140 & 1232.16535108807 & -92.165351088071 \tabularnewline
72 & 1250 & 1204.46014497098 & 45.5398550290247 \tabularnewline
73 & 930 & 1219.11706928984 & -289.117069289841 \tabularnewline
74 & 1510 & 1116.91550495699 & 393.084495043008 \tabularnewline
75 & 1230 & 1237.63245412001 & -7.63245412000765 \tabularnewline
76 & 1180 & 1244.81111447958 & -64.8111144795812 \tabularnewline
77 & 960 & 1230.82228040965 & -270.822280409647 \tabularnewline
78 & 960 & 1137.66012136674 & -177.660121366735 \tabularnewline
79 & 1240 & 1056.9088639514 & 183.091136048599 \tabularnewline
80 & 1640 & 1092.10701013699 & 547.892989863006 \tabularnewline
81 & 1350 & 1272.82957216503 & 77.1704278349707 \tabularnewline
82 & 1100 & 1326.89222633151 & -226.892226331513 \tabularnewline
83 & 1120 & 1277.56940889548 & -157.569408895484 \tabularnewline
84 & 1290 & 1235.50420326864 & 54.4957967313605 \tabularnewline
85 & 890 & 1257.45778338112 & -367.457783381123 \tabularnewline
86 & 1560 & 1131.84200123817 & 428.157998761829 \tabularnewline
87 & 1250 & 1263.84460043347 & -13.8446004334687 \tabularnewline
88 & 1170 & 1270.18822715062 & -100.188227150619 \tabularnewline
89 & 900 & 1244.38675867431 & -344.386758674315 \tabularnewline
90 & 860 & 1122.91497667703 & -262.914976677025 \tabularnewline
91 & 1310 & 1003.91420202319 & 306.085797976806 \tabularnewline
92 & 1610 & 1069.14508184425 & 540.854918155753 \tabularnewline
93 & 1440 & 1242.70165982849 & 197.298340171506 \tabularnewline
94 & 1130 & 1334.80347826697 & -204.80347826697 \tabularnewline
95 & 1220 & 1297.60879981681 & -77.6087998168105 \tabularnewline
96 & 1400 & 1290.21538842858 & 109.784611571423 \tabularnewline
97 & 930 & 1344.19624930166 & -414.196249301655 \tabularnewline
98 & 1490 & 1218.20813709515 & 271.791862904854 \tabularnewline
99 & 1250 & 1306.75201504494 & -56.7520150449423 \tabularnewline
100 & 1160 & 1298.27135329764 & -138.271353297645 \tabularnewline
101 & 910 & 1256.03706803987 & -346.037068039874 \tabularnewline
102 & 880 & 1128.27255130141 & -248.272551301407 \tabularnewline
103 & 1300 & 1008.71246122364 & 291.287538776362 \tabularnewline
104 & 1550 & 1063.93266705894 & 486.067332941056 \tabularnewline
105 & 1460 & 1211.93720012263 & 248.062799877372 \tabularnewline
106 & 1120 & 1312.19384441201 & -192.193844412008 \tabularnewline
107 & 1270 & 1273.38274603638 & -3.38274603638115 \tabularnewline
108 & 1410 & 1287.52502436666 & 122.474975633344 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123097&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]3[/C][C]1200[/C][C]1410[/C][C]-210[/C][/ROW]
[ROW][C]4[/C][C]1280[/C][C]1504.44301111307[/C][C]-224.443011113075[/C][/ROW]
[ROW][C]5[/C][C]1180[/C][C]1577.32170392888[/C][C]-397.321703928876[/C][/ROW]
[ROW][C]6[/C][C]1190[/C][C]1570.50596773405[/C][C]-380.505967734054[/C][/ROW]
[ROW][C]7[/C][C]1190[/C][C]1538.77245635467[/C][C]-348.772456354669[/C][/ROW]
[ROW][C]8[/C][C]1230[/C][C]1488.79916337924[/C][C]-258.799163379241[/C][/ROW]
[ROW][C]9[/C][C]1170[/C][C]1444.01385099091[/C][C]-274.013850990907[/C][/ROW]
[ROW][C]10[/C][C]1190[/C][C]1373.58307682895[/C][C]-183.583076828949[/C][/ROW]
[ROW][C]11[/C][C]1190[/C][C]1314.33170819016[/C][C]-124.33170819016[/C][/ROW]
[ROW][C]12[/C][C]1400[/C][C]1262.08988862215[/C][C]137.910111377853[/C][/ROW]
[ROW][C]13[/C][C]1130[/C][C]1294.51076740414[/C][C]-164.51076740414[/C][/ROW]
[ROW][C]14[/C][C]1260[/C][C]1228.87104190525[/C][C]31.1289580947484[/C][/ROW]
[ROW][C]15[/C][C]1260[/C][C]1220.79927102756[/C][C]39.2007289724377[/C][/ROW]
[ROW][C]16[/C][C]1260[/C][C]1218.05793361393[/C][C]41.9420663860731[/C][/ROW]
[ROW][C]17[/C][C]1130[/C][C]1219.35829427548[/C][C]-89.3582942754792[/C][/ROW]
[ROW][C]18[/C][C]1220[/C][C]1176.68646039289[/C][C]43.3135396071095[/C][/ROW]
[ROW][C]19[/C][C]1180[/C][C]1174.78456110478[/C][C]5.21543889522422[/C][/ROW]
[ROW][C]20[/C][C]1280[/C][C]1162.55108683572[/C][C]117.448913164283[/C][/ROW]
[ROW][C]21[/C][C]1140[/C][C]1191.10517727811[/C][C]-51.1051772781129[/C][/ROW]
[ROW][C]22[/C][C]1160[/C][C]1168.16850531336[/C][C]-8.16850531335649[/C][/ROW]
[ROW][C]23[/C][C]1170[/C][C]1156.69700816869[/C][C]13.3029918313121[/C][/ROW]
[ROW][C]24[/C][C]1410[/C][C]1152.3141837461[/C][C]257.685816253902[/C][/ROW]
[ROW][C]25[/C][C]1100[/C][C]1236.89598293384[/C][C]-136.895982933844[/C][/ROW]
[ROW][C]26[/C][C]1280[/C][C]1199.59366468729[/C][C]80.4063353127137[/C][/ROW]
[ROW][C]27[/C][C]1330[/C][C]1229.80574553795[/C][C]100.19425446205[/C][/ROW]
[ROW][C]28[/C][C]1260[/C][C]1273.40444445751[/C][C]-13.404444457514[/C][/ROW]
[ROW][C]29[/C][C]1070[/C][C]1283.94020589525[/C][C]-213.940205895246[/C][/ROW]
[ROW][C]30[/C][C]1260[/C][C]1221.27939846142[/C][C]38.72060153858[/C][/ROW]
[ROW][C]31[/C][C]1270[/C][C]1232.84983357481[/C][C]37.1501664251946[/C][/ROW]
[ROW][C]32[/C][C]1410[/C][C]1246.87318973915[/C][C]163.126810260854[/C][/ROW]
[ROW][C]33[/C][C]1160[/C][C]1309.11788919605[/C][C]-149.117889196047[/C][/ROW]
[ROW][C]34[/C][C]1130[/C][C]1271.73285762807[/C][C]-141.732857628073[/C][/ROW]
[ROW][C]35[/C][C]1160[/C][C]1225.38239791132[/C][C]-65.3823979113204[/C][/ROW]
[ROW][C]36[/C][C]1300[/C][C]1195.45554219856[/C][C]104.544457801441[/C][/ROW]
[ROW][C]37[/C][C]1080[/C][C]1221.57152472618[/C][C]-141.571524726179[/C][/ROW]
[ROW][C]38[/C][C]1380[/C][C]1167.28455215496[/C][C]212.715447845039[/C][/ROW]
[ROW][C]39[/C][C]1260[/C][C]1229.4339772852[/C][C]30.5660227148007[/C][/ROW]
[ROW][C]40[/C][C]1250[/C][C]1242.62635578994[/C][C]7.373644210061[/C][/ROW]
[ROW][C]41[/C][C]990[/C][C]1249.85660110681[/C][C]-259.856601106813[/C][/ROW]
[ROW][C]42[/C][C]1180[/C][C]1161.51340643461[/C][C]18.4865935653863[/C][/ROW]
[ROW][C]43[/C][C]1240[/C][C]1153.06304393236[/C][C]86.9369560676435[/C][/ROW]
[ROW][C]44[/C][C]1500[/C][C]1170.68167193142[/C][C]329.318328068577[/C][/ROW]
[ROW][C]45[/C][C]1150[/C][C]1282.28397937285[/C][C]-132.283979372851[/C][/ROW]
[ROW][C]46[/C][C]1110[/C][C]1253.47168503699[/C][C]-143.471685036987[/C][/ROW]
[ROW][C]47[/C][C]1080[/C][C]1210.32364751083[/C][C]-130.323647510832[/C][/ROW]
[ROW][C]48[/C][C]1270[/C][C]1160.72375933534[/C][C]109.276240664658[/C][/ROW]
[ROW][C]49[/C][C]1050[/C][C]1187.1730886636[/C][C]-137.173088663604[/C][/ROW]
[ROW][C]50[/C][C]1490[/C][C]1133.46833031808[/C][C]356.531669681916[/C][/ROW]
[ROW][C]51[/C][C]1280[/C][C]1246.70464004982[/C][C]33.295359950177[/C][/ROW]
[ROW][C]52[/C][C]1230[/C][C]1271.43082647278[/C][C]-41.4308264727813[/C][/ROW]
[ROW][C]53[/C][C]960[/C][C]1271.86599338972[/C][C]-311.865993389721[/C][/ROW]
[ROW][C]54[/C][C]1100[/C][C]1171.77069330821[/C][C]-71.7706933082125[/C][/ROW]
[ROW][C]55[/C][C]1270[/C][C]1133.75310785226[/C][C]136.246892147737[/C][/ROW]
[ROW][C]56[/C][C]1530[/C][C]1164.98530611671[/C][C]365.014693883289[/C][/ROW]
[ROW][C]57[/C][C]1290[/C][C]1289.14639535544[/C][C]0.853604644556526[/C][/ROW]
[ROW][C]58[/C][C]1120[/C][C]1310.73400542338[/C][C]-190.734005423378[/C][/ROW]
[ROW][C]59[/C][C]1100[/C][C]1263.4558473907[/C][C]-163.455847390702[/C][/ROW]
[ROW][C]60[/C][C]1310[/C][C]1211.1260744601[/C][C]98.8739255399014[/C][/ROW]
[ROW][C]61[/C][C]1020[/C][C]1240.44123655301[/C][C]-220.441236553012[/C][/ROW]
[ROW][C]62[/C][C]1510[/C][C]1162.57475929935[/C][C]347.425240700647[/C][/ROW]
[ROW][C]63[/C][C]1260[/C][C]1271.84230445588[/C][C]-11.8423044558799[/C][/ROW]
[ROW][C]64[/C][C]1160[/C][C]1278.92608918933[/C][C]-118.926089189331[/C][/ROW]
[ROW][C]65[/C][C]970[/C][C]1246.55863242558[/C][C]-276.558632425579[/C][/ROW]
[ROW][C]66[/C][C]1020[/C][C]1148.20642394281[/C][C]-128.206423942811[/C][/ROW]
[ROW][C]67[/C][C]1210[/C][C]1081.67512914972[/C][C]128.324870850283[/C][/ROW]
[ROW][C]68[/C][C]1530[/C][C]1097.44991080112[/C][C]432.550089198884[/C][/ROW]
[ROW][C]69[/C][C]1350[/C][C]1232.68534146571[/C][C]117.314658534289[/C][/ROW]
[ROW][C]70[/C][C]1070[/C][C]1288.2143442643[/C][C]-218.2143442643[/C][/ROW]
[ROW][C]71[/C][C]1140[/C][C]1232.16535108807[/C][C]-92.165351088071[/C][/ROW]
[ROW][C]72[/C][C]1250[/C][C]1204.46014497098[/C][C]45.5398550290247[/C][/ROW]
[ROW][C]73[/C][C]930[/C][C]1219.11706928984[/C][C]-289.117069289841[/C][/ROW]
[ROW][C]74[/C][C]1510[/C][C]1116.91550495699[/C][C]393.084495043008[/C][/ROW]
[ROW][C]75[/C][C]1230[/C][C]1237.63245412001[/C][C]-7.63245412000765[/C][/ROW]
[ROW][C]76[/C][C]1180[/C][C]1244.81111447958[/C][C]-64.8111144795812[/C][/ROW]
[ROW][C]77[/C][C]960[/C][C]1230.82228040965[/C][C]-270.822280409647[/C][/ROW]
[ROW][C]78[/C][C]960[/C][C]1137.66012136674[/C][C]-177.660121366735[/C][/ROW]
[ROW][C]79[/C][C]1240[/C][C]1056.9088639514[/C][C]183.091136048599[/C][/ROW]
[ROW][C]80[/C][C]1640[/C][C]1092.10701013699[/C][C]547.892989863006[/C][/ROW]
[ROW][C]81[/C][C]1350[/C][C]1272.82957216503[/C][C]77.1704278349707[/C][/ROW]
[ROW][C]82[/C][C]1100[/C][C]1326.89222633151[/C][C]-226.892226331513[/C][/ROW]
[ROW][C]83[/C][C]1120[/C][C]1277.56940889548[/C][C]-157.569408895484[/C][/ROW]
[ROW][C]84[/C][C]1290[/C][C]1235.50420326864[/C][C]54.4957967313605[/C][/ROW]
[ROW][C]85[/C][C]890[/C][C]1257.45778338112[/C][C]-367.457783381123[/C][/ROW]
[ROW][C]86[/C][C]1560[/C][C]1131.84200123817[/C][C]428.157998761829[/C][/ROW]
[ROW][C]87[/C][C]1250[/C][C]1263.84460043347[/C][C]-13.8446004334687[/C][/ROW]
[ROW][C]88[/C][C]1170[/C][C]1270.18822715062[/C][C]-100.188227150619[/C][/ROW]
[ROW][C]89[/C][C]900[/C][C]1244.38675867431[/C][C]-344.386758674315[/C][/ROW]
[ROW][C]90[/C][C]860[/C][C]1122.91497667703[/C][C]-262.914976677025[/C][/ROW]
[ROW][C]91[/C][C]1310[/C][C]1003.91420202319[/C][C]306.085797976806[/C][/ROW]
[ROW][C]92[/C][C]1610[/C][C]1069.14508184425[/C][C]540.854918155753[/C][/ROW]
[ROW][C]93[/C][C]1440[/C][C]1242.70165982849[/C][C]197.298340171506[/C][/ROW]
[ROW][C]94[/C][C]1130[/C][C]1334.80347826697[/C][C]-204.80347826697[/C][/ROW]
[ROW][C]95[/C][C]1220[/C][C]1297.60879981681[/C][C]-77.6087998168105[/C][/ROW]
[ROW][C]96[/C][C]1400[/C][C]1290.21538842858[/C][C]109.784611571423[/C][/ROW]
[ROW][C]97[/C][C]930[/C][C]1344.19624930166[/C][C]-414.196249301655[/C][/ROW]
[ROW][C]98[/C][C]1490[/C][C]1218.20813709515[/C][C]271.791862904854[/C][/ROW]
[ROW][C]99[/C][C]1250[/C][C]1306.75201504494[/C][C]-56.7520150449423[/C][/ROW]
[ROW][C]100[/C][C]1160[/C][C]1298.27135329764[/C][C]-138.271353297645[/C][/ROW]
[ROW][C]101[/C][C]910[/C][C]1256.03706803987[/C][C]-346.037068039874[/C][/ROW]
[ROW][C]102[/C][C]880[/C][C]1128.27255130141[/C][C]-248.272551301407[/C][/ROW]
[ROW][C]103[/C][C]1300[/C][C]1008.71246122364[/C][C]291.287538776362[/C][/ROW]
[ROW][C]104[/C][C]1550[/C][C]1063.93266705894[/C][C]486.067332941056[/C][/ROW]
[ROW][C]105[/C][C]1460[/C][C]1211.93720012263[/C][C]248.062799877372[/C][/ROW]
[ROW][C]106[/C][C]1120[/C][C]1312.19384441201[/C][C]-192.193844412008[/C][/ROW]
[ROW][C]107[/C][C]1270[/C][C]1273.38274603638[/C][C]-3.38274603638115[/C][/ROW]
[ROW][C]108[/C][C]1410[/C][C]1287.52502436666[/C][C]122.474975633344[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123097&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123097&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
312001410-210
412801504.44301111307-224.443011113075
511801577.32170392888-397.321703928876
611901570.50596773405-380.505967734054
711901538.77245635467-348.772456354669
812301488.79916337924-258.799163379241
911701444.01385099091-274.013850990907
1011901373.58307682895-183.583076828949
1111901314.33170819016-124.33170819016
1214001262.08988862215137.910111377853
1311301294.51076740414-164.51076740414
1412601228.8710419052531.1289580947484
1512601220.7992710275639.2007289724377
1612601218.0579336139341.9420663860731
1711301219.35829427548-89.3582942754792
1812201176.6864603928943.3135396071095
1911801174.784561104785.21543889522422
2012801162.55108683572117.448913164283
2111401191.10517727811-51.1051772781129
2211601168.16850531336-8.16850531335649
2311701156.6970081686913.3029918313121
2414101152.3141837461257.685816253902
2511001236.89598293384-136.895982933844
2612801199.5936646872980.4063353127137
2713301229.80574553795100.19425446205
2812601273.40444445751-13.404444457514
2910701283.94020589525-213.940205895246
3012601221.2793984614238.72060153858
3112701232.8498335748137.1501664251946
3214101246.87318973915163.126810260854
3311601309.11788919605-149.117889196047
3411301271.73285762807-141.732857628073
3511601225.38239791132-65.3823979113204
3613001195.45554219856104.544457801441
3710801221.57152472618-141.571524726179
3813801167.28455215496212.715447845039
3912601229.433977285230.5660227148007
4012501242.626355789947.373644210061
419901249.85660110681-259.856601106813
4211801161.5134064346118.4865935653863
4312401153.0630439323686.9369560676435
4415001170.68167193142329.318328068577
4511501282.28397937285-132.283979372851
4611101253.47168503699-143.471685036987
4710801210.32364751083-130.323647510832
4812701160.72375933534109.276240664658
4910501187.1730886636-137.173088663604
5014901133.46833031808356.531669681916
5112801246.7046400498233.295359950177
5212301271.43082647278-41.4308264727813
539601271.86599338972-311.865993389721
5411001171.77069330821-71.7706933082125
5512701133.75310785226136.246892147737
5615301164.98530611671365.014693883289
5712901289.146395355440.853604644556526
5811201310.73400542338-190.734005423378
5911001263.4558473907-163.455847390702
6013101211.126074460198.8739255399014
6110201240.44123655301-220.441236553012
6215101162.57475929935347.425240700647
6312601271.84230445588-11.8423044558799
6411601278.92608918933-118.926089189331
659701246.55863242558-276.558632425579
6610201148.20642394281-128.206423942811
6712101081.67512914972128.324870850283
6815301097.44991080112432.550089198884
6913501232.68534146571117.314658534289
7010701288.2143442643-218.2143442643
7111401232.16535108807-92.165351088071
7212501204.4601449709845.5398550290247
739301219.11706928984-289.117069289841
7415101116.91550495699393.084495043008
7512301237.63245412001-7.63245412000765
7611801244.81111447958-64.8111144795812
779601230.82228040965-270.822280409647
789601137.66012136674-177.660121366735
7912401056.9088639514183.091136048599
8016401092.10701013699547.892989863006
8113501272.8295721650377.1704278349707
8211001326.89222633151-226.892226331513
8311201277.56940889548-157.569408895484
8412901235.5042032686454.4957967313605
858901257.45778338112-367.457783381123
8615601131.84200123817428.157998761829
8712501263.84460043347-13.8446004334687
8811701270.18822715062-100.188227150619
899001244.38675867431-344.386758674315
908601122.91497667703-262.914976677025
9113101003.91420202319306.085797976806
9216101069.14508184425540.854918155753
9314401242.70165982849197.298340171506
9411301334.80347826697-204.80347826697
9512201297.60879981681-77.6087998168105
9614001290.21538842858109.784611571423
979301344.19624930166-414.196249301655
9814901218.20813709515271.791862904854
9912501306.75201504494-56.7520150449423
10011601298.27135329764-138.271353297645
1019101256.03706803987-346.037068039874
1028801128.27255130141-248.272551301407
10313001008.71246122364291.287538776362
10415501063.93266705894486.067332941056
10514601211.93720012263248.062799877372
10611201312.19384441201-192.193844412008
10712701273.38274603638-3.38274603638115
10814101287.52502436666122.474975633344







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1091346.68664742329919.6244026342451773.74889221233
1101371.32829241956917.4648753652141825.19170947391
1111395.96993741584905.1146357369311886.82523909475
1121420.61158241212882.6163612683751958.60680355586
1131445.25322740839850.5199147269842039.9865400898
1141469.89487240467809.6211318879722130.16861292137
1151494.53651740095760.7682466959862228.30478810591
1161519.17816239722704.7538130826692333.60251171177
1171543.8198073935642.2707133801512445.36890140685
1181568.46145238978573.9047475790182563.01815720053
1191593.10309738605500.1439257923532686.06226897975
1201617.74474238233421.3932791878092814.09620557685

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 1346.68664742329 & 919.624402634245 & 1773.74889221233 \tabularnewline
110 & 1371.32829241956 & 917.464875365214 & 1825.19170947391 \tabularnewline
111 & 1395.96993741584 & 905.114635736931 & 1886.82523909475 \tabularnewline
112 & 1420.61158241212 & 882.616361268375 & 1958.60680355586 \tabularnewline
113 & 1445.25322740839 & 850.519914726984 & 2039.9865400898 \tabularnewline
114 & 1469.89487240467 & 809.621131887972 & 2130.16861292137 \tabularnewline
115 & 1494.53651740095 & 760.768246695986 & 2228.30478810591 \tabularnewline
116 & 1519.17816239722 & 704.753813082669 & 2333.60251171177 \tabularnewline
117 & 1543.8198073935 & 642.270713380151 & 2445.36890140685 \tabularnewline
118 & 1568.46145238978 & 573.904747579018 & 2563.01815720053 \tabularnewline
119 & 1593.10309738605 & 500.143925792353 & 2686.06226897975 \tabularnewline
120 & 1617.74474238233 & 421.393279187809 & 2814.09620557685 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123097&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]1346.68664742329[/C][C]919.624402634245[/C][C]1773.74889221233[/C][/ROW]
[ROW][C]110[/C][C]1371.32829241956[/C][C]917.464875365214[/C][C]1825.19170947391[/C][/ROW]
[ROW][C]111[/C][C]1395.96993741584[/C][C]905.114635736931[/C][C]1886.82523909475[/C][/ROW]
[ROW][C]112[/C][C]1420.61158241212[/C][C]882.616361268375[/C][C]1958.60680355586[/C][/ROW]
[ROW][C]113[/C][C]1445.25322740839[/C][C]850.519914726984[/C][C]2039.9865400898[/C][/ROW]
[ROW][C]114[/C][C]1469.89487240467[/C][C]809.621131887972[/C][C]2130.16861292137[/C][/ROW]
[ROW][C]115[/C][C]1494.53651740095[/C][C]760.768246695986[/C][C]2228.30478810591[/C][/ROW]
[ROW][C]116[/C][C]1519.17816239722[/C][C]704.753813082669[/C][C]2333.60251171177[/C][/ROW]
[ROW][C]117[/C][C]1543.8198073935[/C][C]642.270713380151[/C][C]2445.36890140685[/C][/ROW]
[ROW][C]118[/C][C]1568.46145238978[/C][C]573.904747579018[/C][C]2563.01815720053[/C][/ROW]
[ROW][C]119[/C][C]1593.10309738605[/C][C]500.143925792353[/C][C]2686.06226897975[/C][/ROW]
[ROW][C]120[/C][C]1617.74474238233[/C][C]421.393279187809[/C][C]2814.09620557685[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123097&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123097&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
1091346.68664742329919.6244026342451773.74889221233
1101371.32829241956917.4648753652141825.19170947391
1111395.96993741584905.1146357369311886.82523909475
1121420.61158241212882.6163612683751958.60680355586
1131445.25322740839850.5199147269842039.9865400898
1141469.89487240467809.6211318879722130.16861292137
1151494.53651740095760.7682466959862228.30478810591
1161519.17816239722704.7538130826692333.60251171177
1171543.8198073935642.2707133801512445.36890140685
1181568.46145238978573.9047475790182563.01815720053
1191593.10309738605500.1439257923532686.06226897975
1201617.74474238233421.3932791878092814.09620557685



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