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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 17 Aug 2011 16:03:28 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Aug/17/t1313611734qd48f5yaymozb02.htm/, Retrieved Wed, 15 May 2024 10:29:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=123980, Retrieved Wed, 15 May 2024 10:29:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsSimons Thomas
Estimated Impact142
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Harrell-Davis Quantiles] [Tijdsreeks B - St...] [2011-08-03 08:26:33] [7df349cccf6cf4c74b65932dd692edc2]
- RMP     [Exponential Smoothing] [Tijdsreeks B - St...] [2011-08-17 20:03:28] [93a9440e82e53db41c1ce1bc7dd7ea5d] [Current]
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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'George Udny Yule' @ yule.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123980&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123980&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123980&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'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.550917319349102
beta0.231717491065142
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.550917319349102 \tabularnewline
beta & 0.231717491065142 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123980&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]0.550917319349102[/C][/ROW]
[ROW][C]beta[/C][C]0.231717491065142[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123980&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123980&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
alpha0.550917319349102
beta0.231717491065142
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
312101600-390
412601535.35594563453-275.355945634526
513201498.72012313223-178.720123132228
613201492.50774216213-172.507742162125
713101467.69601773865-157.696017738647
812601430.91330006167-170.913300061669
913401365.03064289467-25.0306428946722
1011801376.32192689255-196.321926892552
1113301268.1839725148161.8160274851864
1213901310.1499476723479.850052327657
1311301372.24461187822-242.244611878221
1413401225.96748331703114.032516682967
1511401290.52666476491-150.526664764914
1612901190.1198017685799.8801982314305
1712601240.4168408273619.583159172638
1812801248.9767812325731.0232187674305
1913301267.7995851950362.2004148049741
2012701311.73877591143-41.7387759114272
2113001293.087811914276.91218808573012
2211501302.12189701808-152.121897018083
2314101204.12189803027205.878101969728
2412501329.63211653206-79.6321165320599
2510301287.68419945388-257.68419945388
2613201114.74906816657205.250931833429
2711601223.05467339047-63.0546733904748
2813001175.49669208879124.503307911215
2911901247.16139213544-57.1613921354422
3013101211.4468005429598.553199457054
3112901274.099097760615.9009022394036
3213201293.2466772808726.7533227191293
3313001321.78829690812-21.7882969081249
3412301320.80606505444-90.8060650544419
3513301270.2087032830259.7912967169796
3612201310.21082462883-90.2108246288287
3710101256.05811999659-246.058119996589
3812901084.63535569784205.364644302156
3911701188.12548176259-18.1254817625868
4012401166.1771788044973.8228211955127
4112601204.3088015321755.6911984678313
4212601239.5607805641320.4392194358695
4313101258.0010469006951.998953099313
4413601300.4661567713359.5338432286658
4512501354.68229059666-104.682290596657
4611701305.06546626973-135.06546626973
4713601221.46794784014138.532052159862
4811401306.28465182746-166.284651827464
4910301201.945124794-171.945124793997
5012601072.53711558944187.462884410556
5112101165.06418636444.9358136360024
5211901184.807004578675.19299542132967
5312301183.3177390653146.6822609346923
5413501210.64495423171139.355045768289
5513001306.81688362078-6.81688362078285
5613401321.5899413739818.4100586260224
5712701352.61113467502-82.6111346750195
5812201317.43209855663-97.4320985566271
5914001261.65002989829138.349970101709
6011201353.42575335702-233.425753357018
6110001210.5853186637-210.585318663702
6212601053.44534729994206.554652700063
6312601152.48319503121107.516804968788
6411501210.68466919625-60.6846691962476
6512401168.4742044241271.5257955758775
6613601208.23155578481151.768444215188
6713501311.570303484738.4296965152987
6812801357.37459877127-77.374598771271
6913201329.5028791222-9.5028791222046
7012101337.80975458047-127.80975458047
7113701264.62349062922105.376509370781
7210601333.35564604468-273.355646044684
7310401158.54188700303-118.541887003031
7412601053.88498619999206.115013800015
7512101154.3992561117255.6007438882752
7612001179.0904420363120.9095579636905
7712001187.3389079905612.6610920094377
7812901192.6594304818497.3405695181573
7914001257.05756623538142.942433764622
8012801364.8261866541-84.8261866541009
8112801336.28445758428-56.2844575842796
8212201316.28174630509-96.2817463050928
8313501261.952779817888.0472201822001
8410001320.41369317543-320.413693175433
859801112.94330689579-132.943306895786
861240991.782435754237248.217564245763
8711901112.2964440185677.7035559814417
8812001148.7907486951551.209251304854
8911501177.22611062279-27.2261106227941
9012701158.97446473719111.025535262813
9114101231.06125162975178.938748370251
9214201363.4054196708656.594580329139
9312601435.57277108963-175.572771089627
9413001357.42198295367-57.4219829536735
9514101337.0321819387472.9678180612618
9610001397.79124638264-397.791246382644
979501148.42008063021-198.42008063021
981280983.556195314663296.443804685337
9913301129.16457498508200.835425014916
10011901247.73872622564-57.7387262256366
10111701216.48913630138-46.489136301376
10212701185.5024683064784.4975316935256
10313401237.46534084427102.534659155727
10414701312.4544646323157.545535367696
10512701437.86185149093-167.86185149093
10612801362.56790265794-82.5679026579428
10714301323.72348194149106.276518058509
1089801402.48368375201-422.483683752013

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1210 & 1600 & -390 \tabularnewline
4 & 1260 & 1535.35594563453 & -275.355945634526 \tabularnewline
5 & 1320 & 1498.72012313223 & -178.720123132228 \tabularnewline
6 & 1320 & 1492.50774216213 & -172.507742162125 \tabularnewline
7 & 1310 & 1467.69601773865 & -157.696017738647 \tabularnewline
8 & 1260 & 1430.91330006167 & -170.913300061669 \tabularnewline
9 & 1340 & 1365.03064289467 & -25.0306428946722 \tabularnewline
10 & 1180 & 1376.32192689255 & -196.321926892552 \tabularnewline
11 & 1330 & 1268.18397251481 & 61.8160274851864 \tabularnewline
12 & 1390 & 1310.14994767234 & 79.850052327657 \tabularnewline
13 & 1130 & 1372.24461187822 & -242.244611878221 \tabularnewline
14 & 1340 & 1225.96748331703 & 114.032516682967 \tabularnewline
15 & 1140 & 1290.52666476491 & -150.526664764914 \tabularnewline
16 & 1290 & 1190.11980176857 & 99.8801982314305 \tabularnewline
17 & 1260 & 1240.41684082736 & 19.583159172638 \tabularnewline
18 & 1280 & 1248.97678123257 & 31.0232187674305 \tabularnewline
19 & 1330 & 1267.79958519503 & 62.2004148049741 \tabularnewline
20 & 1270 & 1311.73877591143 & -41.7387759114272 \tabularnewline
21 & 1300 & 1293.08781191427 & 6.91218808573012 \tabularnewline
22 & 1150 & 1302.12189701808 & -152.121897018083 \tabularnewline
23 & 1410 & 1204.12189803027 & 205.878101969728 \tabularnewline
24 & 1250 & 1329.63211653206 & -79.6321165320599 \tabularnewline
25 & 1030 & 1287.68419945388 & -257.68419945388 \tabularnewline
26 & 1320 & 1114.74906816657 & 205.250931833429 \tabularnewline
27 & 1160 & 1223.05467339047 & -63.0546733904748 \tabularnewline
28 & 1300 & 1175.49669208879 & 124.503307911215 \tabularnewline
29 & 1190 & 1247.16139213544 & -57.1613921354422 \tabularnewline
30 & 1310 & 1211.44680054295 & 98.553199457054 \tabularnewline
31 & 1290 & 1274.0990977606 & 15.9009022394036 \tabularnewline
32 & 1320 & 1293.24667728087 & 26.7533227191293 \tabularnewline
33 & 1300 & 1321.78829690812 & -21.7882969081249 \tabularnewline
34 & 1230 & 1320.80606505444 & -90.8060650544419 \tabularnewline
35 & 1330 & 1270.20870328302 & 59.7912967169796 \tabularnewline
36 & 1220 & 1310.21082462883 & -90.2108246288287 \tabularnewline
37 & 1010 & 1256.05811999659 & -246.058119996589 \tabularnewline
38 & 1290 & 1084.63535569784 & 205.364644302156 \tabularnewline
39 & 1170 & 1188.12548176259 & -18.1254817625868 \tabularnewline
40 & 1240 & 1166.17717880449 & 73.8228211955127 \tabularnewline
41 & 1260 & 1204.30880153217 & 55.6911984678313 \tabularnewline
42 & 1260 & 1239.56078056413 & 20.4392194358695 \tabularnewline
43 & 1310 & 1258.00104690069 & 51.998953099313 \tabularnewline
44 & 1360 & 1300.46615677133 & 59.5338432286658 \tabularnewline
45 & 1250 & 1354.68229059666 & -104.682290596657 \tabularnewline
46 & 1170 & 1305.06546626973 & -135.06546626973 \tabularnewline
47 & 1360 & 1221.46794784014 & 138.532052159862 \tabularnewline
48 & 1140 & 1306.28465182746 & -166.284651827464 \tabularnewline
49 & 1030 & 1201.945124794 & -171.945124793997 \tabularnewline
50 & 1260 & 1072.53711558944 & 187.462884410556 \tabularnewline
51 & 1210 & 1165.064186364 & 44.9358136360024 \tabularnewline
52 & 1190 & 1184.80700457867 & 5.19299542132967 \tabularnewline
53 & 1230 & 1183.31773906531 & 46.6822609346923 \tabularnewline
54 & 1350 & 1210.64495423171 & 139.355045768289 \tabularnewline
55 & 1300 & 1306.81688362078 & -6.81688362078285 \tabularnewline
56 & 1340 & 1321.58994137398 & 18.4100586260224 \tabularnewline
57 & 1270 & 1352.61113467502 & -82.6111346750195 \tabularnewline
58 & 1220 & 1317.43209855663 & -97.4320985566271 \tabularnewline
59 & 1400 & 1261.65002989829 & 138.349970101709 \tabularnewline
60 & 1120 & 1353.42575335702 & -233.425753357018 \tabularnewline
61 & 1000 & 1210.5853186637 & -210.585318663702 \tabularnewline
62 & 1260 & 1053.44534729994 & 206.554652700063 \tabularnewline
63 & 1260 & 1152.48319503121 & 107.516804968788 \tabularnewline
64 & 1150 & 1210.68466919625 & -60.6846691962476 \tabularnewline
65 & 1240 & 1168.47420442412 & 71.5257955758775 \tabularnewline
66 & 1360 & 1208.23155578481 & 151.768444215188 \tabularnewline
67 & 1350 & 1311.5703034847 & 38.4296965152987 \tabularnewline
68 & 1280 & 1357.37459877127 & -77.374598771271 \tabularnewline
69 & 1320 & 1329.5028791222 & -9.5028791222046 \tabularnewline
70 & 1210 & 1337.80975458047 & -127.80975458047 \tabularnewline
71 & 1370 & 1264.62349062922 & 105.376509370781 \tabularnewline
72 & 1060 & 1333.35564604468 & -273.355646044684 \tabularnewline
73 & 1040 & 1158.54188700303 & -118.541887003031 \tabularnewline
74 & 1260 & 1053.88498619999 & 206.115013800015 \tabularnewline
75 & 1210 & 1154.39925611172 & 55.6007438882752 \tabularnewline
76 & 1200 & 1179.09044203631 & 20.9095579636905 \tabularnewline
77 & 1200 & 1187.33890799056 & 12.6610920094377 \tabularnewline
78 & 1290 & 1192.65943048184 & 97.3405695181573 \tabularnewline
79 & 1400 & 1257.05756623538 & 142.942433764622 \tabularnewline
80 & 1280 & 1364.8261866541 & -84.8261866541009 \tabularnewline
81 & 1280 & 1336.28445758428 & -56.2844575842796 \tabularnewline
82 & 1220 & 1316.28174630509 & -96.2817463050928 \tabularnewline
83 & 1350 & 1261.9527798178 & 88.0472201822001 \tabularnewline
84 & 1000 & 1320.41369317543 & -320.413693175433 \tabularnewline
85 & 980 & 1112.94330689579 & -132.943306895786 \tabularnewline
86 & 1240 & 991.782435754237 & 248.217564245763 \tabularnewline
87 & 1190 & 1112.29644401856 & 77.7035559814417 \tabularnewline
88 & 1200 & 1148.79074869515 & 51.209251304854 \tabularnewline
89 & 1150 & 1177.22611062279 & -27.2261106227941 \tabularnewline
90 & 1270 & 1158.97446473719 & 111.025535262813 \tabularnewline
91 & 1410 & 1231.06125162975 & 178.938748370251 \tabularnewline
92 & 1420 & 1363.40541967086 & 56.594580329139 \tabularnewline
93 & 1260 & 1435.57277108963 & -175.572771089627 \tabularnewline
94 & 1300 & 1357.42198295367 & -57.4219829536735 \tabularnewline
95 & 1410 & 1337.03218193874 & 72.9678180612618 \tabularnewline
96 & 1000 & 1397.79124638264 & -397.791246382644 \tabularnewline
97 & 950 & 1148.42008063021 & -198.42008063021 \tabularnewline
98 & 1280 & 983.556195314663 & 296.443804685337 \tabularnewline
99 & 1330 & 1129.16457498508 & 200.835425014916 \tabularnewline
100 & 1190 & 1247.73872622564 & -57.7387262256366 \tabularnewline
101 & 1170 & 1216.48913630138 & -46.489136301376 \tabularnewline
102 & 1270 & 1185.50246830647 & 84.4975316935256 \tabularnewline
103 & 1340 & 1237.46534084427 & 102.534659155727 \tabularnewline
104 & 1470 & 1312.4544646323 & 157.545535367696 \tabularnewline
105 & 1270 & 1437.86185149093 & -167.86185149093 \tabularnewline
106 & 1280 & 1362.56790265794 & -82.5679026579428 \tabularnewline
107 & 1430 & 1323.72348194149 & 106.276518058509 \tabularnewline
108 & 980 & 1402.48368375201 & -422.483683752013 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123980&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]1210[/C][C]1600[/C][C]-390[/C][/ROW]
[ROW][C]4[/C][C]1260[/C][C]1535.35594563453[/C][C]-275.355945634526[/C][/ROW]
[ROW][C]5[/C][C]1320[/C][C]1498.72012313223[/C][C]-178.720123132228[/C][/ROW]
[ROW][C]6[/C][C]1320[/C][C]1492.50774216213[/C][C]-172.507742162125[/C][/ROW]
[ROW][C]7[/C][C]1310[/C][C]1467.69601773865[/C][C]-157.696017738647[/C][/ROW]
[ROW][C]8[/C][C]1260[/C][C]1430.91330006167[/C][C]-170.913300061669[/C][/ROW]
[ROW][C]9[/C][C]1340[/C][C]1365.03064289467[/C][C]-25.0306428946722[/C][/ROW]
[ROW][C]10[/C][C]1180[/C][C]1376.32192689255[/C][C]-196.321926892552[/C][/ROW]
[ROW][C]11[/C][C]1330[/C][C]1268.18397251481[/C][C]61.8160274851864[/C][/ROW]
[ROW][C]12[/C][C]1390[/C][C]1310.14994767234[/C][C]79.850052327657[/C][/ROW]
[ROW][C]13[/C][C]1130[/C][C]1372.24461187822[/C][C]-242.244611878221[/C][/ROW]
[ROW][C]14[/C][C]1340[/C][C]1225.96748331703[/C][C]114.032516682967[/C][/ROW]
[ROW][C]15[/C][C]1140[/C][C]1290.52666476491[/C][C]-150.526664764914[/C][/ROW]
[ROW][C]16[/C][C]1290[/C][C]1190.11980176857[/C][C]99.8801982314305[/C][/ROW]
[ROW][C]17[/C][C]1260[/C][C]1240.41684082736[/C][C]19.583159172638[/C][/ROW]
[ROW][C]18[/C][C]1280[/C][C]1248.97678123257[/C][C]31.0232187674305[/C][/ROW]
[ROW][C]19[/C][C]1330[/C][C]1267.79958519503[/C][C]62.2004148049741[/C][/ROW]
[ROW][C]20[/C][C]1270[/C][C]1311.73877591143[/C][C]-41.7387759114272[/C][/ROW]
[ROW][C]21[/C][C]1300[/C][C]1293.08781191427[/C][C]6.91218808573012[/C][/ROW]
[ROW][C]22[/C][C]1150[/C][C]1302.12189701808[/C][C]-152.121897018083[/C][/ROW]
[ROW][C]23[/C][C]1410[/C][C]1204.12189803027[/C][C]205.878101969728[/C][/ROW]
[ROW][C]24[/C][C]1250[/C][C]1329.63211653206[/C][C]-79.6321165320599[/C][/ROW]
[ROW][C]25[/C][C]1030[/C][C]1287.68419945388[/C][C]-257.68419945388[/C][/ROW]
[ROW][C]26[/C][C]1320[/C][C]1114.74906816657[/C][C]205.250931833429[/C][/ROW]
[ROW][C]27[/C][C]1160[/C][C]1223.05467339047[/C][C]-63.0546733904748[/C][/ROW]
[ROW][C]28[/C][C]1300[/C][C]1175.49669208879[/C][C]124.503307911215[/C][/ROW]
[ROW][C]29[/C][C]1190[/C][C]1247.16139213544[/C][C]-57.1613921354422[/C][/ROW]
[ROW][C]30[/C][C]1310[/C][C]1211.44680054295[/C][C]98.553199457054[/C][/ROW]
[ROW][C]31[/C][C]1290[/C][C]1274.0990977606[/C][C]15.9009022394036[/C][/ROW]
[ROW][C]32[/C][C]1320[/C][C]1293.24667728087[/C][C]26.7533227191293[/C][/ROW]
[ROW][C]33[/C][C]1300[/C][C]1321.78829690812[/C][C]-21.7882969081249[/C][/ROW]
[ROW][C]34[/C][C]1230[/C][C]1320.80606505444[/C][C]-90.8060650544419[/C][/ROW]
[ROW][C]35[/C][C]1330[/C][C]1270.20870328302[/C][C]59.7912967169796[/C][/ROW]
[ROW][C]36[/C][C]1220[/C][C]1310.21082462883[/C][C]-90.2108246288287[/C][/ROW]
[ROW][C]37[/C][C]1010[/C][C]1256.05811999659[/C][C]-246.058119996589[/C][/ROW]
[ROW][C]38[/C][C]1290[/C][C]1084.63535569784[/C][C]205.364644302156[/C][/ROW]
[ROW][C]39[/C][C]1170[/C][C]1188.12548176259[/C][C]-18.1254817625868[/C][/ROW]
[ROW][C]40[/C][C]1240[/C][C]1166.17717880449[/C][C]73.8228211955127[/C][/ROW]
[ROW][C]41[/C][C]1260[/C][C]1204.30880153217[/C][C]55.6911984678313[/C][/ROW]
[ROW][C]42[/C][C]1260[/C][C]1239.56078056413[/C][C]20.4392194358695[/C][/ROW]
[ROW][C]43[/C][C]1310[/C][C]1258.00104690069[/C][C]51.998953099313[/C][/ROW]
[ROW][C]44[/C][C]1360[/C][C]1300.46615677133[/C][C]59.5338432286658[/C][/ROW]
[ROW][C]45[/C][C]1250[/C][C]1354.68229059666[/C][C]-104.682290596657[/C][/ROW]
[ROW][C]46[/C][C]1170[/C][C]1305.06546626973[/C][C]-135.06546626973[/C][/ROW]
[ROW][C]47[/C][C]1360[/C][C]1221.46794784014[/C][C]138.532052159862[/C][/ROW]
[ROW][C]48[/C][C]1140[/C][C]1306.28465182746[/C][C]-166.284651827464[/C][/ROW]
[ROW][C]49[/C][C]1030[/C][C]1201.945124794[/C][C]-171.945124793997[/C][/ROW]
[ROW][C]50[/C][C]1260[/C][C]1072.53711558944[/C][C]187.462884410556[/C][/ROW]
[ROW][C]51[/C][C]1210[/C][C]1165.064186364[/C][C]44.9358136360024[/C][/ROW]
[ROW][C]52[/C][C]1190[/C][C]1184.80700457867[/C][C]5.19299542132967[/C][/ROW]
[ROW][C]53[/C][C]1230[/C][C]1183.31773906531[/C][C]46.6822609346923[/C][/ROW]
[ROW][C]54[/C][C]1350[/C][C]1210.64495423171[/C][C]139.355045768289[/C][/ROW]
[ROW][C]55[/C][C]1300[/C][C]1306.81688362078[/C][C]-6.81688362078285[/C][/ROW]
[ROW][C]56[/C][C]1340[/C][C]1321.58994137398[/C][C]18.4100586260224[/C][/ROW]
[ROW][C]57[/C][C]1270[/C][C]1352.61113467502[/C][C]-82.6111346750195[/C][/ROW]
[ROW][C]58[/C][C]1220[/C][C]1317.43209855663[/C][C]-97.4320985566271[/C][/ROW]
[ROW][C]59[/C][C]1400[/C][C]1261.65002989829[/C][C]138.349970101709[/C][/ROW]
[ROW][C]60[/C][C]1120[/C][C]1353.42575335702[/C][C]-233.425753357018[/C][/ROW]
[ROW][C]61[/C][C]1000[/C][C]1210.5853186637[/C][C]-210.585318663702[/C][/ROW]
[ROW][C]62[/C][C]1260[/C][C]1053.44534729994[/C][C]206.554652700063[/C][/ROW]
[ROW][C]63[/C][C]1260[/C][C]1152.48319503121[/C][C]107.516804968788[/C][/ROW]
[ROW][C]64[/C][C]1150[/C][C]1210.68466919625[/C][C]-60.6846691962476[/C][/ROW]
[ROW][C]65[/C][C]1240[/C][C]1168.47420442412[/C][C]71.5257955758775[/C][/ROW]
[ROW][C]66[/C][C]1360[/C][C]1208.23155578481[/C][C]151.768444215188[/C][/ROW]
[ROW][C]67[/C][C]1350[/C][C]1311.5703034847[/C][C]38.4296965152987[/C][/ROW]
[ROW][C]68[/C][C]1280[/C][C]1357.37459877127[/C][C]-77.374598771271[/C][/ROW]
[ROW][C]69[/C][C]1320[/C][C]1329.5028791222[/C][C]-9.5028791222046[/C][/ROW]
[ROW][C]70[/C][C]1210[/C][C]1337.80975458047[/C][C]-127.80975458047[/C][/ROW]
[ROW][C]71[/C][C]1370[/C][C]1264.62349062922[/C][C]105.376509370781[/C][/ROW]
[ROW][C]72[/C][C]1060[/C][C]1333.35564604468[/C][C]-273.355646044684[/C][/ROW]
[ROW][C]73[/C][C]1040[/C][C]1158.54188700303[/C][C]-118.541887003031[/C][/ROW]
[ROW][C]74[/C][C]1260[/C][C]1053.88498619999[/C][C]206.115013800015[/C][/ROW]
[ROW][C]75[/C][C]1210[/C][C]1154.39925611172[/C][C]55.6007438882752[/C][/ROW]
[ROW][C]76[/C][C]1200[/C][C]1179.09044203631[/C][C]20.9095579636905[/C][/ROW]
[ROW][C]77[/C][C]1200[/C][C]1187.33890799056[/C][C]12.6610920094377[/C][/ROW]
[ROW][C]78[/C][C]1290[/C][C]1192.65943048184[/C][C]97.3405695181573[/C][/ROW]
[ROW][C]79[/C][C]1400[/C][C]1257.05756623538[/C][C]142.942433764622[/C][/ROW]
[ROW][C]80[/C][C]1280[/C][C]1364.8261866541[/C][C]-84.8261866541009[/C][/ROW]
[ROW][C]81[/C][C]1280[/C][C]1336.28445758428[/C][C]-56.2844575842796[/C][/ROW]
[ROW][C]82[/C][C]1220[/C][C]1316.28174630509[/C][C]-96.2817463050928[/C][/ROW]
[ROW][C]83[/C][C]1350[/C][C]1261.9527798178[/C][C]88.0472201822001[/C][/ROW]
[ROW][C]84[/C][C]1000[/C][C]1320.41369317543[/C][C]-320.413693175433[/C][/ROW]
[ROW][C]85[/C][C]980[/C][C]1112.94330689579[/C][C]-132.943306895786[/C][/ROW]
[ROW][C]86[/C][C]1240[/C][C]991.782435754237[/C][C]248.217564245763[/C][/ROW]
[ROW][C]87[/C][C]1190[/C][C]1112.29644401856[/C][C]77.7035559814417[/C][/ROW]
[ROW][C]88[/C][C]1200[/C][C]1148.79074869515[/C][C]51.209251304854[/C][/ROW]
[ROW][C]89[/C][C]1150[/C][C]1177.22611062279[/C][C]-27.2261106227941[/C][/ROW]
[ROW][C]90[/C][C]1270[/C][C]1158.97446473719[/C][C]111.025535262813[/C][/ROW]
[ROW][C]91[/C][C]1410[/C][C]1231.06125162975[/C][C]178.938748370251[/C][/ROW]
[ROW][C]92[/C][C]1420[/C][C]1363.40541967086[/C][C]56.594580329139[/C][/ROW]
[ROW][C]93[/C][C]1260[/C][C]1435.57277108963[/C][C]-175.572771089627[/C][/ROW]
[ROW][C]94[/C][C]1300[/C][C]1357.42198295367[/C][C]-57.4219829536735[/C][/ROW]
[ROW][C]95[/C][C]1410[/C][C]1337.03218193874[/C][C]72.9678180612618[/C][/ROW]
[ROW][C]96[/C][C]1000[/C][C]1397.79124638264[/C][C]-397.791246382644[/C][/ROW]
[ROW][C]97[/C][C]950[/C][C]1148.42008063021[/C][C]-198.42008063021[/C][/ROW]
[ROW][C]98[/C][C]1280[/C][C]983.556195314663[/C][C]296.443804685337[/C][/ROW]
[ROW][C]99[/C][C]1330[/C][C]1129.16457498508[/C][C]200.835425014916[/C][/ROW]
[ROW][C]100[/C][C]1190[/C][C]1247.73872622564[/C][C]-57.7387262256366[/C][/ROW]
[ROW][C]101[/C][C]1170[/C][C]1216.48913630138[/C][C]-46.489136301376[/C][/ROW]
[ROW][C]102[/C][C]1270[/C][C]1185.50246830647[/C][C]84.4975316935256[/C][/ROW]
[ROW][C]103[/C][C]1340[/C][C]1237.46534084427[/C][C]102.534659155727[/C][/ROW]
[ROW][C]104[/C][C]1470[/C][C]1312.4544646323[/C][C]157.545535367696[/C][/ROW]
[ROW][C]105[/C][C]1270[/C][C]1437.86185149093[/C][C]-167.86185149093[/C][/ROW]
[ROW][C]106[/C][C]1280[/C][C]1362.56790265794[/C][C]-82.5679026579428[/C][/ROW]
[ROW][C]107[/C][C]1430[/C][C]1323.72348194149[/C][C]106.276518058509[/C][/ROW]
[ROW][C]108[/C][C]980[/C][C]1402.48368375201[/C][C]-422.483683752013[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123980&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123980&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
312101600-390
412601535.35594563453-275.355945634526
513201498.72012313223-178.720123132228
613201492.50774216213-172.507742162125
713101467.69601773865-157.696017738647
812601430.91330006167-170.913300061669
913401365.03064289467-25.0306428946722
1011801376.32192689255-196.321926892552
1113301268.1839725148161.8160274851864
1213901310.1499476723479.850052327657
1311301372.24461187822-242.244611878221
1413401225.96748331703114.032516682967
1511401290.52666476491-150.526664764914
1612901190.1198017685799.8801982314305
1712601240.4168408273619.583159172638
1812801248.9767812325731.0232187674305
1913301267.7995851950362.2004148049741
2012701311.73877591143-41.7387759114272
2113001293.087811914276.91218808573012
2211501302.12189701808-152.121897018083
2314101204.12189803027205.878101969728
2412501329.63211653206-79.6321165320599
2510301287.68419945388-257.68419945388
2613201114.74906816657205.250931833429
2711601223.05467339047-63.0546733904748
2813001175.49669208879124.503307911215
2911901247.16139213544-57.1613921354422
3013101211.4468005429598.553199457054
3112901274.099097760615.9009022394036
3213201293.2466772808726.7533227191293
3313001321.78829690812-21.7882969081249
3412301320.80606505444-90.8060650544419
3513301270.2087032830259.7912967169796
3612201310.21082462883-90.2108246288287
3710101256.05811999659-246.058119996589
3812901084.63535569784205.364644302156
3911701188.12548176259-18.1254817625868
4012401166.1771788044973.8228211955127
4112601204.3088015321755.6911984678313
4212601239.5607805641320.4392194358695
4313101258.0010469006951.998953099313
4413601300.4661567713359.5338432286658
4512501354.68229059666-104.682290596657
4611701305.06546626973-135.06546626973
4713601221.46794784014138.532052159862
4811401306.28465182746-166.284651827464
4910301201.945124794-171.945124793997
5012601072.53711558944187.462884410556
5112101165.06418636444.9358136360024
5211901184.807004578675.19299542132967
5312301183.3177390653146.6822609346923
5413501210.64495423171139.355045768289
5513001306.81688362078-6.81688362078285
5613401321.5899413739818.4100586260224
5712701352.61113467502-82.6111346750195
5812201317.43209855663-97.4320985566271
5914001261.65002989829138.349970101709
6011201353.42575335702-233.425753357018
6110001210.5853186637-210.585318663702
6212601053.44534729994206.554652700063
6312601152.48319503121107.516804968788
6411501210.68466919625-60.6846691962476
6512401168.4742044241271.5257955758775
6613601208.23155578481151.768444215188
6713501311.570303484738.4296965152987
6812801357.37459877127-77.374598771271
6913201329.5028791222-9.5028791222046
7012101337.80975458047-127.80975458047
7113701264.62349062922105.376509370781
7210601333.35564604468-273.355646044684
7310401158.54188700303-118.541887003031
7412601053.88498619999206.115013800015
7512101154.3992561117255.6007438882752
7612001179.0904420363120.9095579636905
7712001187.3389079905612.6610920094377
7812901192.6594304818497.3405695181573
7914001257.05756623538142.942433764622
8012801364.8261866541-84.8261866541009
8112801336.28445758428-56.2844575842796
8212201316.28174630509-96.2817463050928
8313501261.952779817888.0472201822001
8410001320.41369317543-320.413693175433
859801112.94330689579-132.943306895786
861240991.782435754237248.217564245763
8711901112.2964440185677.7035559814417
8812001148.7907486951551.209251304854
8911501177.22611062279-27.2261106227941
9012701158.97446473719111.025535262813
9114101231.06125162975178.938748370251
9214201363.4054196708656.594580329139
9312601435.57277108963-175.572771089627
9413001357.42198295367-57.4219829536735
9514101337.0321819387472.9678180612618
9610001397.79124638264-397.791246382644
979501148.42008063021-198.42008063021
981280983.556195314663296.443804685337
9913301129.16457498508200.835425014916
10011901247.73872622564-57.7387262256366
10111701216.48913630138-46.489136301376
10212701185.5024683064784.4975316935256
10313401237.46534084427102.534659155727
10414701312.4544646323157.545535367696
10512701437.86185149093-167.86185149093
10612801362.56790265794-82.5679026579428
10714301323.72348194149106.276518058509
1089801402.48368375201-422.483683752013







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1091136.00765735118845.0102263002031427.00508840216
1101102.28520947174750.6158855927691453.95453335072
1111068.5627615923645.8172146290471491.30830855556
1121034.84031371287532.2799771925951537.40065023314
1131001.11786583343411.2106434148521591.025088252
114967.395417953989283.4768191882111651.31401671977
115933.67297007455149.7155844485211717.63035570058
116899.95052219511110.40903137697641789.49201301325
117866.228074315673-134.0664965841151866.52264521546
118832.505626436234-283.4086225709691948.41987544344
119798.783178556796-437.3681658140712034.93452292766
120765.060730677357-595.735274730932125.85673608564

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 1136.00765735118 & 845.010226300203 & 1427.00508840216 \tabularnewline
110 & 1102.28520947174 & 750.615885592769 & 1453.95453335072 \tabularnewline
111 & 1068.5627615923 & 645.817214629047 & 1491.30830855556 \tabularnewline
112 & 1034.84031371287 & 532.279977192595 & 1537.40065023314 \tabularnewline
113 & 1001.11786583343 & 411.210643414852 & 1591.025088252 \tabularnewline
114 & 967.395417953989 & 283.476819188211 & 1651.31401671977 \tabularnewline
115 & 933.67297007455 & 149.715584448521 & 1717.63035570058 \tabularnewline
116 & 899.950522195111 & 10.4090313769764 & 1789.49201301325 \tabularnewline
117 & 866.228074315673 & -134.066496584115 & 1866.52264521546 \tabularnewline
118 & 832.505626436234 & -283.408622570969 & 1948.41987544344 \tabularnewline
119 & 798.783178556796 & -437.368165814071 & 2034.93452292766 \tabularnewline
120 & 765.060730677357 & -595.73527473093 & 2125.85673608564 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123980&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]1136.00765735118[/C][C]845.010226300203[/C][C]1427.00508840216[/C][/ROW]
[ROW][C]110[/C][C]1102.28520947174[/C][C]750.615885592769[/C][C]1453.95453335072[/C][/ROW]
[ROW][C]111[/C][C]1068.5627615923[/C][C]645.817214629047[/C][C]1491.30830855556[/C][/ROW]
[ROW][C]112[/C][C]1034.84031371287[/C][C]532.279977192595[/C][C]1537.40065023314[/C][/ROW]
[ROW][C]113[/C][C]1001.11786583343[/C][C]411.210643414852[/C][C]1591.025088252[/C][/ROW]
[ROW][C]114[/C][C]967.395417953989[/C][C]283.476819188211[/C][C]1651.31401671977[/C][/ROW]
[ROW][C]115[/C][C]933.67297007455[/C][C]149.715584448521[/C][C]1717.63035570058[/C][/ROW]
[ROW][C]116[/C][C]899.950522195111[/C][C]10.4090313769764[/C][C]1789.49201301325[/C][/ROW]
[ROW][C]117[/C][C]866.228074315673[/C][C]-134.066496584115[/C][C]1866.52264521546[/C][/ROW]
[ROW][C]118[/C][C]832.505626436234[/C][C]-283.408622570969[/C][C]1948.41987544344[/C][/ROW]
[ROW][C]119[/C][C]798.783178556796[/C][C]-437.368165814071[/C][C]2034.93452292766[/C][/ROW]
[ROW][C]120[/C][C]765.060730677357[/C][C]-595.73527473093[/C][C]2125.85673608564[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123980&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123980&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
1091136.00765735118845.0102263002031427.00508840216
1101102.28520947174750.6158855927691453.95453335072
1111068.5627615923645.8172146290471491.30830855556
1121034.84031371287532.2799771925951537.40065023314
1131001.11786583343411.2106434148521591.025088252
114967.395417953989283.4768191882111651.31401671977
115933.67297007455149.7155844485211717.63035570058
116899.95052219511110.40903137697641789.49201301325
117866.228074315673-134.0664965841151866.52264521546
118832.505626436234-283.4086225709691948.41987544344
119798.783178556796-437.3681658140712034.93452292766
120765.060730677357-595.735274730932125.85673608564



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