Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 29 Jul 2016 12:12:03 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Jul/29/t1469790751cs0zdymhpfbivrf.htm/, Retrieved Mon, 29 Apr 2024 09:34:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=295964, Retrieved Mon, 29 Apr 2024 09:34:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact167
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2016-07-29 11:12:03] [b1d105767b629000b6b6bd83f6a3d689] [Current]
Feedback Forum

Post a new message
Dataseries X:
1200
1400
1210
1260
1320
1320
1310
1260
1340
1180
1330
1390
1130
1340
1140
1290
1260
1280
1330
1270
1300
1150
1410
1250
1030
1320
1160
1300
1190
1310
1290
1320
1300
1230
1330
1220
1010
1290
1170
1240
1260
1260
1310
1360
1250
1170
1360
1140
1030
1260
1210
1190
1230
1350
1300
1340
1270
1220
1400
1120
1000
1260
1260
1150
1240
1360
1350
1280
1320
1210
1370
1060
1040
1260
1210
1200
1200
1290
1400
1280
1280
1220
1350
1000
980
1240
1190
1200
1150
1270
1410
1420
1260
1300
1410
1000
950
1280
1330
1190
1170
1270
1340
1470
1270
1280
1430
980




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=295964&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=295964&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295964&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
alpha0.0330442684200226
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0330442684200226 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295964&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]0.0330442684200226[/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=295964&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295964&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
alpha0.0330442684200226
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
214001200200
312101206.6088536843.39114631599546
412601206.7209116331253.2790883668781
513201208.48148013029111.518519869709
613201212.16652803467107.833471965331
713101215.7298062269594.2701937730455
812601218.84489581441.1551041860014
913401220.20483612357119.795163876425
1011801224.16337967413-44.163379674128
1113301222.70403310184107.295966898159
1213901226.24954983241163.750450167591
1311301231.66056366165-101.660563661647
1413401228.30126470828111.69873529172
1511401231.99226769944-91.992267699437
1612901228.9524505130161.0475494869897
1712601230.9697221246429.0302778753571
1812801231.9290064190648.0709935809361
1913301233.5174772341796.4825227658305
2012701236.7056716142833.2943283857153
2113001237.8058583383362.1941416616733
2211501239.86101824955-89.8610182495479
2314101236.89162664201173.108373357987
2412501242.611866197017.38813380299189
2510301242.85600167352-212.856001673517
2613201235.822330819484.1776691805951
2711601238.60392031478-78.6039203147802
2813001236.0065112730363.9934887269674
2911901238.12112929166-48.1211292916603
3013101236.5310017786773.4689982213279
3112901238.9587310764551.041268923552
3213201240.6453524672679.3546475327437
3313001243.267568740756.7324312592955
3412301245.14225042736-15.1422504273571
3513301244.6418858397585.3581141602479
3612201247.46248227589-27.4624822758904
3710101246.55500464009-236.555004640086
3812901238.7382175706651.2617824293409
3911701240.43212566894-70.4321256689429
4012401238.104747602951.89525239705426
4112601238.1673748318821.8326251681224
4212601238.8888179582521.1111820417532
4313101239.586421524370.4135784757016
4413601241.91318671186118.086813288136
4512501245.815279067024.1847209329776
4611701245.95356010879-75.9535601087946
4713601243.4437302811116.556269718897
4811401247.29524694373-107.295246943731
4910301243.74975400353-213.74975400353
5012601236.6865497575223.3134502424764
5112101237.45692566513-27.4569256651328
5211901236.54963164347-46.5496316434655
5312301235.01143312059-5.01143312058571
5413501234.84583397938115.15416602062
5513001238.6510191510561.348980848951
5613401240.6782513415299.3217486584833
5712701243.9602658641326.0397341358662
5812201244.82072982851-24.8207298285054
5914001244.00054696967155.999453030329
6011201249.15543476898-129.155434768982
6110001244.88758791457-244.887587914571
6212601236.7954567267923.20454327321
6312601237.5622338832722.4377661167262
6411501238.30367344958-88.3036734495806
6512401235.385743161644.61425683836137
6613601235.53821790316124.461782096836
6713501239.65096643881110.349033561193
6812801243.2973695236936.7026304763074
6913201244.5101810968775.4898189031273
7012101247.00468693569-37.0046869356865
7113701245.78189412778124.218105872215
7210601249.88659056085-189.886590560853
7310401243.611927093-203.611927092998
7412601236.8837199206223.1162800793816
7512101237.64758048443-27.6475804844338
7612001236.73398641374-36.7339864137418
7712001235.52013870655-35.5201387065488
7812901234.3464017088155.6535982911867
7914001236.18543414929163.814565850713
8012801241.5985666343738.4014333656323
8112801242.8675139062237.1324860937846
8212201244.0945297438-24.0945297438013
8313501243.29834363549106.701656364507
8410001246.82422180926-246.824221809263
859801238.66809597123-258.668095971234
8612401230.120597976269.87940202373534
8711901230.44705558857-40.4470555885662
8812001229.1105122269-29.110512226898
8911501228.14857664703-78.1485766470282
9012701225.5662141036644.433785896339
9114101227.03449605174182.965503948262
9214201233.08045727581186.919542724191
9312601239.2570768185320.7429231814654
9413001239.9425115399660.0574884600412
9514101241.92706730926168.072932690735
9610001247.48091441124-247.480914411238
979501239.3030886466-289.303088646601
9812801229.7432797306250.2567202693792
9913301231.4039762851198.5960237148877
10011901234.66200975789-44.6620097578941
10111701233.18618631928-63.1861863192767
10212701231.098245018138.901754981895
10313401232.38372505174107.616274948263
10414701235.93982612749234.06017387251
10512701243.6741733393726.3258266606292
10612801244.5440910219235.4559089780764
10714301245.71570559527184.284294404729
1089801251.80524528518-271.805245285175

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 1400 & 1200 & 200 \tabularnewline
3 & 1210 & 1206.608853684 & 3.39114631599546 \tabularnewline
4 & 1260 & 1206.72091163312 & 53.2790883668781 \tabularnewline
5 & 1320 & 1208.48148013029 & 111.518519869709 \tabularnewline
6 & 1320 & 1212.16652803467 & 107.833471965331 \tabularnewline
7 & 1310 & 1215.72980622695 & 94.2701937730455 \tabularnewline
8 & 1260 & 1218.844895814 & 41.1551041860014 \tabularnewline
9 & 1340 & 1220.20483612357 & 119.795163876425 \tabularnewline
10 & 1180 & 1224.16337967413 & -44.163379674128 \tabularnewline
11 & 1330 & 1222.70403310184 & 107.295966898159 \tabularnewline
12 & 1390 & 1226.24954983241 & 163.750450167591 \tabularnewline
13 & 1130 & 1231.66056366165 & -101.660563661647 \tabularnewline
14 & 1340 & 1228.30126470828 & 111.69873529172 \tabularnewline
15 & 1140 & 1231.99226769944 & -91.992267699437 \tabularnewline
16 & 1290 & 1228.95245051301 & 61.0475494869897 \tabularnewline
17 & 1260 & 1230.96972212464 & 29.0302778753571 \tabularnewline
18 & 1280 & 1231.92900641906 & 48.0709935809361 \tabularnewline
19 & 1330 & 1233.51747723417 & 96.4825227658305 \tabularnewline
20 & 1270 & 1236.70567161428 & 33.2943283857153 \tabularnewline
21 & 1300 & 1237.80585833833 & 62.1941416616733 \tabularnewline
22 & 1150 & 1239.86101824955 & -89.8610182495479 \tabularnewline
23 & 1410 & 1236.89162664201 & 173.108373357987 \tabularnewline
24 & 1250 & 1242.61186619701 & 7.38813380299189 \tabularnewline
25 & 1030 & 1242.85600167352 & -212.856001673517 \tabularnewline
26 & 1320 & 1235.8223308194 & 84.1776691805951 \tabularnewline
27 & 1160 & 1238.60392031478 & -78.6039203147802 \tabularnewline
28 & 1300 & 1236.00651127303 & 63.9934887269674 \tabularnewline
29 & 1190 & 1238.12112929166 & -48.1211292916603 \tabularnewline
30 & 1310 & 1236.53100177867 & 73.4689982213279 \tabularnewline
31 & 1290 & 1238.95873107645 & 51.041268923552 \tabularnewline
32 & 1320 & 1240.64535246726 & 79.3546475327437 \tabularnewline
33 & 1300 & 1243.2675687407 & 56.7324312592955 \tabularnewline
34 & 1230 & 1245.14225042736 & -15.1422504273571 \tabularnewline
35 & 1330 & 1244.64188583975 & 85.3581141602479 \tabularnewline
36 & 1220 & 1247.46248227589 & -27.4624822758904 \tabularnewline
37 & 1010 & 1246.55500464009 & -236.555004640086 \tabularnewline
38 & 1290 & 1238.73821757066 & 51.2617824293409 \tabularnewline
39 & 1170 & 1240.43212566894 & -70.4321256689429 \tabularnewline
40 & 1240 & 1238.10474760295 & 1.89525239705426 \tabularnewline
41 & 1260 & 1238.16737483188 & 21.8326251681224 \tabularnewline
42 & 1260 & 1238.88881795825 & 21.1111820417532 \tabularnewline
43 & 1310 & 1239.5864215243 & 70.4135784757016 \tabularnewline
44 & 1360 & 1241.91318671186 & 118.086813288136 \tabularnewline
45 & 1250 & 1245.81527906702 & 4.1847209329776 \tabularnewline
46 & 1170 & 1245.95356010879 & -75.9535601087946 \tabularnewline
47 & 1360 & 1243.4437302811 & 116.556269718897 \tabularnewline
48 & 1140 & 1247.29524694373 & -107.295246943731 \tabularnewline
49 & 1030 & 1243.74975400353 & -213.74975400353 \tabularnewline
50 & 1260 & 1236.68654975752 & 23.3134502424764 \tabularnewline
51 & 1210 & 1237.45692566513 & -27.4569256651328 \tabularnewline
52 & 1190 & 1236.54963164347 & -46.5496316434655 \tabularnewline
53 & 1230 & 1235.01143312059 & -5.01143312058571 \tabularnewline
54 & 1350 & 1234.84583397938 & 115.15416602062 \tabularnewline
55 & 1300 & 1238.65101915105 & 61.348980848951 \tabularnewline
56 & 1340 & 1240.67825134152 & 99.3217486584833 \tabularnewline
57 & 1270 & 1243.96026586413 & 26.0397341358662 \tabularnewline
58 & 1220 & 1244.82072982851 & -24.8207298285054 \tabularnewline
59 & 1400 & 1244.00054696967 & 155.999453030329 \tabularnewline
60 & 1120 & 1249.15543476898 & -129.155434768982 \tabularnewline
61 & 1000 & 1244.88758791457 & -244.887587914571 \tabularnewline
62 & 1260 & 1236.79545672679 & 23.20454327321 \tabularnewline
63 & 1260 & 1237.56223388327 & 22.4377661167262 \tabularnewline
64 & 1150 & 1238.30367344958 & -88.3036734495806 \tabularnewline
65 & 1240 & 1235.38574316164 & 4.61425683836137 \tabularnewline
66 & 1360 & 1235.53821790316 & 124.461782096836 \tabularnewline
67 & 1350 & 1239.65096643881 & 110.349033561193 \tabularnewline
68 & 1280 & 1243.29736952369 & 36.7026304763074 \tabularnewline
69 & 1320 & 1244.51018109687 & 75.4898189031273 \tabularnewline
70 & 1210 & 1247.00468693569 & -37.0046869356865 \tabularnewline
71 & 1370 & 1245.78189412778 & 124.218105872215 \tabularnewline
72 & 1060 & 1249.88659056085 & -189.886590560853 \tabularnewline
73 & 1040 & 1243.611927093 & -203.611927092998 \tabularnewline
74 & 1260 & 1236.88371992062 & 23.1162800793816 \tabularnewline
75 & 1210 & 1237.64758048443 & -27.6475804844338 \tabularnewline
76 & 1200 & 1236.73398641374 & -36.7339864137418 \tabularnewline
77 & 1200 & 1235.52013870655 & -35.5201387065488 \tabularnewline
78 & 1290 & 1234.34640170881 & 55.6535982911867 \tabularnewline
79 & 1400 & 1236.18543414929 & 163.814565850713 \tabularnewline
80 & 1280 & 1241.59856663437 & 38.4014333656323 \tabularnewline
81 & 1280 & 1242.86751390622 & 37.1324860937846 \tabularnewline
82 & 1220 & 1244.0945297438 & -24.0945297438013 \tabularnewline
83 & 1350 & 1243.29834363549 & 106.701656364507 \tabularnewline
84 & 1000 & 1246.82422180926 & -246.824221809263 \tabularnewline
85 & 980 & 1238.66809597123 & -258.668095971234 \tabularnewline
86 & 1240 & 1230.12059797626 & 9.87940202373534 \tabularnewline
87 & 1190 & 1230.44705558857 & -40.4470555885662 \tabularnewline
88 & 1200 & 1229.1105122269 & -29.110512226898 \tabularnewline
89 & 1150 & 1228.14857664703 & -78.1485766470282 \tabularnewline
90 & 1270 & 1225.56621410366 & 44.433785896339 \tabularnewline
91 & 1410 & 1227.03449605174 & 182.965503948262 \tabularnewline
92 & 1420 & 1233.08045727581 & 186.919542724191 \tabularnewline
93 & 1260 & 1239.25707681853 & 20.7429231814654 \tabularnewline
94 & 1300 & 1239.94251153996 & 60.0574884600412 \tabularnewline
95 & 1410 & 1241.92706730926 & 168.072932690735 \tabularnewline
96 & 1000 & 1247.48091441124 & -247.480914411238 \tabularnewline
97 & 950 & 1239.3030886466 & -289.303088646601 \tabularnewline
98 & 1280 & 1229.74327973062 & 50.2567202693792 \tabularnewline
99 & 1330 & 1231.40397628511 & 98.5960237148877 \tabularnewline
100 & 1190 & 1234.66200975789 & -44.6620097578941 \tabularnewline
101 & 1170 & 1233.18618631928 & -63.1861863192767 \tabularnewline
102 & 1270 & 1231.0982450181 & 38.901754981895 \tabularnewline
103 & 1340 & 1232.38372505174 & 107.616274948263 \tabularnewline
104 & 1470 & 1235.93982612749 & 234.06017387251 \tabularnewline
105 & 1270 & 1243.67417333937 & 26.3258266606292 \tabularnewline
106 & 1280 & 1244.54409102192 & 35.4559089780764 \tabularnewline
107 & 1430 & 1245.71570559527 & 184.284294404729 \tabularnewline
108 & 980 & 1251.80524528518 & -271.805245285175 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295964&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]1400[/C][C]1200[/C][C]200[/C][/ROW]
[ROW][C]3[/C][C]1210[/C][C]1206.608853684[/C][C]3.39114631599546[/C][/ROW]
[ROW][C]4[/C][C]1260[/C][C]1206.72091163312[/C][C]53.2790883668781[/C][/ROW]
[ROW][C]5[/C][C]1320[/C][C]1208.48148013029[/C][C]111.518519869709[/C][/ROW]
[ROW][C]6[/C][C]1320[/C][C]1212.16652803467[/C][C]107.833471965331[/C][/ROW]
[ROW][C]7[/C][C]1310[/C][C]1215.72980622695[/C][C]94.2701937730455[/C][/ROW]
[ROW][C]8[/C][C]1260[/C][C]1218.844895814[/C][C]41.1551041860014[/C][/ROW]
[ROW][C]9[/C][C]1340[/C][C]1220.20483612357[/C][C]119.795163876425[/C][/ROW]
[ROW][C]10[/C][C]1180[/C][C]1224.16337967413[/C][C]-44.163379674128[/C][/ROW]
[ROW][C]11[/C][C]1330[/C][C]1222.70403310184[/C][C]107.295966898159[/C][/ROW]
[ROW][C]12[/C][C]1390[/C][C]1226.24954983241[/C][C]163.750450167591[/C][/ROW]
[ROW][C]13[/C][C]1130[/C][C]1231.66056366165[/C][C]-101.660563661647[/C][/ROW]
[ROW][C]14[/C][C]1340[/C][C]1228.30126470828[/C][C]111.69873529172[/C][/ROW]
[ROW][C]15[/C][C]1140[/C][C]1231.99226769944[/C][C]-91.992267699437[/C][/ROW]
[ROW][C]16[/C][C]1290[/C][C]1228.95245051301[/C][C]61.0475494869897[/C][/ROW]
[ROW][C]17[/C][C]1260[/C][C]1230.96972212464[/C][C]29.0302778753571[/C][/ROW]
[ROW][C]18[/C][C]1280[/C][C]1231.92900641906[/C][C]48.0709935809361[/C][/ROW]
[ROW][C]19[/C][C]1330[/C][C]1233.51747723417[/C][C]96.4825227658305[/C][/ROW]
[ROW][C]20[/C][C]1270[/C][C]1236.70567161428[/C][C]33.2943283857153[/C][/ROW]
[ROW][C]21[/C][C]1300[/C][C]1237.80585833833[/C][C]62.1941416616733[/C][/ROW]
[ROW][C]22[/C][C]1150[/C][C]1239.86101824955[/C][C]-89.8610182495479[/C][/ROW]
[ROW][C]23[/C][C]1410[/C][C]1236.89162664201[/C][C]173.108373357987[/C][/ROW]
[ROW][C]24[/C][C]1250[/C][C]1242.61186619701[/C][C]7.38813380299189[/C][/ROW]
[ROW][C]25[/C][C]1030[/C][C]1242.85600167352[/C][C]-212.856001673517[/C][/ROW]
[ROW][C]26[/C][C]1320[/C][C]1235.8223308194[/C][C]84.1776691805951[/C][/ROW]
[ROW][C]27[/C][C]1160[/C][C]1238.60392031478[/C][C]-78.6039203147802[/C][/ROW]
[ROW][C]28[/C][C]1300[/C][C]1236.00651127303[/C][C]63.9934887269674[/C][/ROW]
[ROW][C]29[/C][C]1190[/C][C]1238.12112929166[/C][C]-48.1211292916603[/C][/ROW]
[ROW][C]30[/C][C]1310[/C][C]1236.53100177867[/C][C]73.4689982213279[/C][/ROW]
[ROW][C]31[/C][C]1290[/C][C]1238.95873107645[/C][C]51.041268923552[/C][/ROW]
[ROW][C]32[/C][C]1320[/C][C]1240.64535246726[/C][C]79.3546475327437[/C][/ROW]
[ROW][C]33[/C][C]1300[/C][C]1243.2675687407[/C][C]56.7324312592955[/C][/ROW]
[ROW][C]34[/C][C]1230[/C][C]1245.14225042736[/C][C]-15.1422504273571[/C][/ROW]
[ROW][C]35[/C][C]1330[/C][C]1244.64188583975[/C][C]85.3581141602479[/C][/ROW]
[ROW][C]36[/C][C]1220[/C][C]1247.46248227589[/C][C]-27.4624822758904[/C][/ROW]
[ROW][C]37[/C][C]1010[/C][C]1246.55500464009[/C][C]-236.555004640086[/C][/ROW]
[ROW][C]38[/C][C]1290[/C][C]1238.73821757066[/C][C]51.2617824293409[/C][/ROW]
[ROW][C]39[/C][C]1170[/C][C]1240.43212566894[/C][C]-70.4321256689429[/C][/ROW]
[ROW][C]40[/C][C]1240[/C][C]1238.10474760295[/C][C]1.89525239705426[/C][/ROW]
[ROW][C]41[/C][C]1260[/C][C]1238.16737483188[/C][C]21.8326251681224[/C][/ROW]
[ROW][C]42[/C][C]1260[/C][C]1238.88881795825[/C][C]21.1111820417532[/C][/ROW]
[ROW][C]43[/C][C]1310[/C][C]1239.5864215243[/C][C]70.4135784757016[/C][/ROW]
[ROW][C]44[/C][C]1360[/C][C]1241.91318671186[/C][C]118.086813288136[/C][/ROW]
[ROW][C]45[/C][C]1250[/C][C]1245.81527906702[/C][C]4.1847209329776[/C][/ROW]
[ROW][C]46[/C][C]1170[/C][C]1245.95356010879[/C][C]-75.9535601087946[/C][/ROW]
[ROW][C]47[/C][C]1360[/C][C]1243.4437302811[/C][C]116.556269718897[/C][/ROW]
[ROW][C]48[/C][C]1140[/C][C]1247.29524694373[/C][C]-107.295246943731[/C][/ROW]
[ROW][C]49[/C][C]1030[/C][C]1243.74975400353[/C][C]-213.74975400353[/C][/ROW]
[ROW][C]50[/C][C]1260[/C][C]1236.68654975752[/C][C]23.3134502424764[/C][/ROW]
[ROW][C]51[/C][C]1210[/C][C]1237.45692566513[/C][C]-27.4569256651328[/C][/ROW]
[ROW][C]52[/C][C]1190[/C][C]1236.54963164347[/C][C]-46.5496316434655[/C][/ROW]
[ROW][C]53[/C][C]1230[/C][C]1235.01143312059[/C][C]-5.01143312058571[/C][/ROW]
[ROW][C]54[/C][C]1350[/C][C]1234.84583397938[/C][C]115.15416602062[/C][/ROW]
[ROW][C]55[/C][C]1300[/C][C]1238.65101915105[/C][C]61.348980848951[/C][/ROW]
[ROW][C]56[/C][C]1340[/C][C]1240.67825134152[/C][C]99.3217486584833[/C][/ROW]
[ROW][C]57[/C][C]1270[/C][C]1243.96026586413[/C][C]26.0397341358662[/C][/ROW]
[ROW][C]58[/C][C]1220[/C][C]1244.82072982851[/C][C]-24.8207298285054[/C][/ROW]
[ROW][C]59[/C][C]1400[/C][C]1244.00054696967[/C][C]155.999453030329[/C][/ROW]
[ROW][C]60[/C][C]1120[/C][C]1249.15543476898[/C][C]-129.155434768982[/C][/ROW]
[ROW][C]61[/C][C]1000[/C][C]1244.88758791457[/C][C]-244.887587914571[/C][/ROW]
[ROW][C]62[/C][C]1260[/C][C]1236.79545672679[/C][C]23.20454327321[/C][/ROW]
[ROW][C]63[/C][C]1260[/C][C]1237.56223388327[/C][C]22.4377661167262[/C][/ROW]
[ROW][C]64[/C][C]1150[/C][C]1238.30367344958[/C][C]-88.3036734495806[/C][/ROW]
[ROW][C]65[/C][C]1240[/C][C]1235.38574316164[/C][C]4.61425683836137[/C][/ROW]
[ROW][C]66[/C][C]1360[/C][C]1235.53821790316[/C][C]124.461782096836[/C][/ROW]
[ROW][C]67[/C][C]1350[/C][C]1239.65096643881[/C][C]110.349033561193[/C][/ROW]
[ROW][C]68[/C][C]1280[/C][C]1243.29736952369[/C][C]36.7026304763074[/C][/ROW]
[ROW][C]69[/C][C]1320[/C][C]1244.51018109687[/C][C]75.4898189031273[/C][/ROW]
[ROW][C]70[/C][C]1210[/C][C]1247.00468693569[/C][C]-37.0046869356865[/C][/ROW]
[ROW][C]71[/C][C]1370[/C][C]1245.78189412778[/C][C]124.218105872215[/C][/ROW]
[ROW][C]72[/C][C]1060[/C][C]1249.88659056085[/C][C]-189.886590560853[/C][/ROW]
[ROW][C]73[/C][C]1040[/C][C]1243.611927093[/C][C]-203.611927092998[/C][/ROW]
[ROW][C]74[/C][C]1260[/C][C]1236.88371992062[/C][C]23.1162800793816[/C][/ROW]
[ROW][C]75[/C][C]1210[/C][C]1237.64758048443[/C][C]-27.6475804844338[/C][/ROW]
[ROW][C]76[/C][C]1200[/C][C]1236.73398641374[/C][C]-36.7339864137418[/C][/ROW]
[ROW][C]77[/C][C]1200[/C][C]1235.52013870655[/C][C]-35.5201387065488[/C][/ROW]
[ROW][C]78[/C][C]1290[/C][C]1234.34640170881[/C][C]55.6535982911867[/C][/ROW]
[ROW][C]79[/C][C]1400[/C][C]1236.18543414929[/C][C]163.814565850713[/C][/ROW]
[ROW][C]80[/C][C]1280[/C][C]1241.59856663437[/C][C]38.4014333656323[/C][/ROW]
[ROW][C]81[/C][C]1280[/C][C]1242.86751390622[/C][C]37.1324860937846[/C][/ROW]
[ROW][C]82[/C][C]1220[/C][C]1244.0945297438[/C][C]-24.0945297438013[/C][/ROW]
[ROW][C]83[/C][C]1350[/C][C]1243.29834363549[/C][C]106.701656364507[/C][/ROW]
[ROW][C]84[/C][C]1000[/C][C]1246.82422180926[/C][C]-246.824221809263[/C][/ROW]
[ROW][C]85[/C][C]980[/C][C]1238.66809597123[/C][C]-258.668095971234[/C][/ROW]
[ROW][C]86[/C][C]1240[/C][C]1230.12059797626[/C][C]9.87940202373534[/C][/ROW]
[ROW][C]87[/C][C]1190[/C][C]1230.44705558857[/C][C]-40.4470555885662[/C][/ROW]
[ROW][C]88[/C][C]1200[/C][C]1229.1105122269[/C][C]-29.110512226898[/C][/ROW]
[ROW][C]89[/C][C]1150[/C][C]1228.14857664703[/C][C]-78.1485766470282[/C][/ROW]
[ROW][C]90[/C][C]1270[/C][C]1225.56621410366[/C][C]44.433785896339[/C][/ROW]
[ROW][C]91[/C][C]1410[/C][C]1227.03449605174[/C][C]182.965503948262[/C][/ROW]
[ROW][C]92[/C][C]1420[/C][C]1233.08045727581[/C][C]186.919542724191[/C][/ROW]
[ROW][C]93[/C][C]1260[/C][C]1239.25707681853[/C][C]20.7429231814654[/C][/ROW]
[ROW][C]94[/C][C]1300[/C][C]1239.94251153996[/C][C]60.0574884600412[/C][/ROW]
[ROW][C]95[/C][C]1410[/C][C]1241.92706730926[/C][C]168.072932690735[/C][/ROW]
[ROW][C]96[/C][C]1000[/C][C]1247.48091441124[/C][C]-247.480914411238[/C][/ROW]
[ROW][C]97[/C][C]950[/C][C]1239.3030886466[/C][C]-289.303088646601[/C][/ROW]
[ROW][C]98[/C][C]1280[/C][C]1229.74327973062[/C][C]50.2567202693792[/C][/ROW]
[ROW][C]99[/C][C]1330[/C][C]1231.40397628511[/C][C]98.5960237148877[/C][/ROW]
[ROW][C]100[/C][C]1190[/C][C]1234.66200975789[/C][C]-44.6620097578941[/C][/ROW]
[ROW][C]101[/C][C]1170[/C][C]1233.18618631928[/C][C]-63.1861863192767[/C][/ROW]
[ROW][C]102[/C][C]1270[/C][C]1231.0982450181[/C][C]38.901754981895[/C][/ROW]
[ROW][C]103[/C][C]1340[/C][C]1232.38372505174[/C][C]107.616274948263[/C][/ROW]
[ROW][C]104[/C][C]1470[/C][C]1235.93982612749[/C][C]234.06017387251[/C][/ROW]
[ROW][C]105[/C][C]1270[/C][C]1243.67417333937[/C][C]26.3258266606292[/C][/ROW]
[ROW][C]106[/C][C]1280[/C][C]1244.54409102192[/C][C]35.4559089780764[/C][/ROW]
[ROW][C]107[/C][C]1430[/C][C]1245.71570559527[/C][C]184.284294404729[/C][/ROW]
[ROW][C]108[/C][C]980[/C][C]1251.80524528518[/C][C]-271.805245285175[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295964&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295964&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
214001200200
312101206.6088536843.39114631599546
412601206.7209116331253.2790883668781
513201208.48148013029111.518519869709
613201212.16652803467107.833471965331
713101215.7298062269594.2701937730455
812601218.84489581441.1551041860014
913401220.20483612357119.795163876425
1011801224.16337967413-44.163379674128
1113301222.70403310184107.295966898159
1213901226.24954983241163.750450167591
1311301231.66056366165-101.660563661647
1413401228.30126470828111.69873529172
1511401231.99226769944-91.992267699437
1612901228.9524505130161.0475494869897
1712601230.9697221246429.0302778753571
1812801231.9290064190648.0709935809361
1913301233.5174772341796.4825227658305
2012701236.7056716142833.2943283857153
2113001237.8058583383362.1941416616733
2211501239.86101824955-89.8610182495479
2314101236.89162664201173.108373357987
2412501242.611866197017.38813380299189
2510301242.85600167352-212.856001673517
2613201235.822330819484.1776691805951
2711601238.60392031478-78.6039203147802
2813001236.0065112730363.9934887269674
2911901238.12112929166-48.1211292916603
3013101236.5310017786773.4689982213279
3112901238.9587310764551.041268923552
3213201240.6453524672679.3546475327437
3313001243.267568740756.7324312592955
3412301245.14225042736-15.1422504273571
3513301244.6418858397585.3581141602479
3612201247.46248227589-27.4624822758904
3710101246.55500464009-236.555004640086
3812901238.7382175706651.2617824293409
3911701240.43212566894-70.4321256689429
4012401238.104747602951.89525239705426
4112601238.1673748318821.8326251681224
4212601238.8888179582521.1111820417532
4313101239.586421524370.4135784757016
4413601241.91318671186118.086813288136
4512501245.815279067024.1847209329776
4611701245.95356010879-75.9535601087946
4713601243.4437302811116.556269718897
4811401247.29524694373-107.295246943731
4910301243.74975400353-213.74975400353
5012601236.6865497575223.3134502424764
5112101237.45692566513-27.4569256651328
5211901236.54963164347-46.5496316434655
5312301235.01143312059-5.01143312058571
5413501234.84583397938115.15416602062
5513001238.6510191510561.348980848951
5613401240.6782513415299.3217486584833
5712701243.9602658641326.0397341358662
5812201244.82072982851-24.8207298285054
5914001244.00054696967155.999453030329
6011201249.15543476898-129.155434768982
6110001244.88758791457-244.887587914571
6212601236.7954567267923.20454327321
6312601237.5622338832722.4377661167262
6411501238.30367344958-88.3036734495806
6512401235.385743161644.61425683836137
6613601235.53821790316124.461782096836
6713501239.65096643881110.349033561193
6812801243.2973695236936.7026304763074
6913201244.5101810968775.4898189031273
7012101247.00468693569-37.0046869356865
7113701245.78189412778124.218105872215
7210601249.88659056085-189.886590560853
7310401243.611927093-203.611927092998
7412601236.8837199206223.1162800793816
7512101237.64758048443-27.6475804844338
7612001236.73398641374-36.7339864137418
7712001235.52013870655-35.5201387065488
7812901234.3464017088155.6535982911867
7914001236.18543414929163.814565850713
8012801241.5985666343738.4014333656323
8112801242.8675139062237.1324860937846
8212201244.0945297438-24.0945297438013
8313501243.29834363549106.701656364507
8410001246.82422180926-246.824221809263
859801238.66809597123-258.668095971234
8612401230.120597976269.87940202373534
8711901230.44705558857-40.4470555885662
8812001229.1105122269-29.110512226898
8911501228.14857664703-78.1485766470282
9012701225.5662141036644.433785896339
9114101227.03449605174182.965503948262
9214201233.08045727581186.919542724191
9312601239.2570768185320.7429231814654
9413001239.9425115399660.0574884600412
9514101241.92706730926168.072932690735
9610001247.48091441124-247.480914411238
979501239.3030886466-289.303088646601
9812801229.7432797306250.2567202693792
9913301231.4039762851198.5960237148877
10011901234.66200975789-44.6620097578941
10111701233.18618631928-63.1861863192767
10212701231.098245018138.901754981895
10313401232.38372505174107.616274948263
10414701235.93982612749234.06017387251
10512701243.6741733393726.3258266606292
10612801244.5440910219235.4559089780764
10714301245.71570559527184.284294404729
1089801251.80524528518-271.805245285175







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1091242.8236398021021.068268688341464.57901091567
1101242.8236398021020.947231750161464.70004785384
1111242.8236398021020.826260803481464.82101880052
1121242.8236398021020.705355740471464.94192386354
1131242.8236398021020.58451645361465.06276315041
1141242.8236398021020.463742835631465.18353676837
1151242.8236398021020.343034779631465.30424482438
1161242.8236398021020.222392178931465.42488742508
1171242.8236398021020.101814927171465.54546467684
1181242.8236398021019.981302918271465.66597668574
1191242.8236398021019.860856046441465.78642355757
1201242.8236398021019.740474206171465.90680539783

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 1242.823639802 & 1021.06826868834 & 1464.57901091567 \tabularnewline
110 & 1242.823639802 & 1020.94723175016 & 1464.70004785384 \tabularnewline
111 & 1242.823639802 & 1020.82626080348 & 1464.82101880052 \tabularnewline
112 & 1242.823639802 & 1020.70535574047 & 1464.94192386354 \tabularnewline
113 & 1242.823639802 & 1020.5845164536 & 1465.06276315041 \tabularnewline
114 & 1242.823639802 & 1020.46374283563 & 1465.18353676837 \tabularnewline
115 & 1242.823639802 & 1020.34303477963 & 1465.30424482438 \tabularnewline
116 & 1242.823639802 & 1020.22239217893 & 1465.42488742508 \tabularnewline
117 & 1242.823639802 & 1020.10181492717 & 1465.54546467684 \tabularnewline
118 & 1242.823639802 & 1019.98130291827 & 1465.66597668574 \tabularnewline
119 & 1242.823639802 & 1019.86085604644 & 1465.78642355757 \tabularnewline
120 & 1242.823639802 & 1019.74047420617 & 1465.90680539783 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295964&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]1242.823639802[/C][C]1021.06826868834[/C][C]1464.57901091567[/C][/ROW]
[ROW][C]110[/C][C]1242.823639802[/C][C]1020.94723175016[/C][C]1464.70004785384[/C][/ROW]
[ROW][C]111[/C][C]1242.823639802[/C][C]1020.82626080348[/C][C]1464.82101880052[/C][/ROW]
[ROW][C]112[/C][C]1242.823639802[/C][C]1020.70535574047[/C][C]1464.94192386354[/C][/ROW]
[ROW][C]113[/C][C]1242.823639802[/C][C]1020.5845164536[/C][C]1465.06276315041[/C][/ROW]
[ROW][C]114[/C][C]1242.823639802[/C][C]1020.46374283563[/C][C]1465.18353676837[/C][/ROW]
[ROW][C]115[/C][C]1242.823639802[/C][C]1020.34303477963[/C][C]1465.30424482438[/C][/ROW]
[ROW][C]116[/C][C]1242.823639802[/C][C]1020.22239217893[/C][C]1465.42488742508[/C][/ROW]
[ROW][C]117[/C][C]1242.823639802[/C][C]1020.10181492717[/C][C]1465.54546467684[/C][/ROW]
[ROW][C]118[/C][C]1242.823639802[/C][C]1019.98130291827[/C][C]1465.66597668574[/C][/ROW]
[ROW][C]119[/C][C]1242.823639802[/C][C]1019.86085604644[/C][C]1465.78642355757[/C][/ROW]
[ROW][C]120[/C][C]1242.823639802[/C][C]1019.74047420617[/C][C]1465.90680539783[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295964&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295964&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
1091242.8236398021021.068268688341464.57901091567
1101242.8236398021020.947231750161464.70004785384
1111242.8236398021020.826260803481464.82101880052
1121242.8236398021020.705355740471464.94192386354
1131242.8236398021020.58451645361465.06276315041
1141242.8236398021020.463742835631465.18353676837
1151242.8236398021020.343034779631465.30424482438
1161242.8236398021020.222392178931465.42488742508
1171242.8236398021020.101814927171465.54546467684
1181242.8236398021019.981302918271465.66597668574
1191242.8236398021019.860856046441465.78642355757
1201242.8236398021019.740474206171465.90680539783



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