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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 15 Aug 2012 18:14:00 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Aug/15/t1345068913kpt4vsbyeluu4p2.htm/, Retrieved Tue, 07 May 2024 07:08:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=169372, Retrieved Tue, 07 May 2024 07:08:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsSam De Maeyer
Estimated Impact132
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks 2 Expon...] [2012-08-15 22:14:00] [df2e1cb801e9c7e9e5c4a0dfd693d83a] [Current]
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Dataseries X:
1230
1360
1360
1250
1420
1390
1280
1330
1400
1370
1290
1500
1260
1360
1320
1300
1440
1360
1330
1420
1510
1280
1310
1460
1280
1370
1390
1390
1460
1410
1230
1260
1590
1250
1400
1450
1220
1290
1400
1400
1460
1450
1270
1260
1550
1230
1380
1490
1180
1190
1400
1380
1510
1400
1290
1200
1600
1220
1380
1450
1260
1130
1390
1380
1570
1320
1210
1190
1580
1150
1330
1420
1260
1040
1450
1360
1500
1240
1260
1220
1680
1210
1350
1480
1270
1040
1450
1310
1510
1160
1290
1230
1680
1190
1310
1480
1320
1050
1380
1320
1480
1150
1250
1260
1680
1150
1310
1470




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169372&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169372&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169372&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

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







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.018194061774641
beta0.206794860190384
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.018194061774641 \tabularnewline
beta & 0.206794860190384 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169372&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]0.018194061774641[/C][/ROW]
[ROW][C]beta[/C][C]0.206794860190384[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169372&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169372&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
alpha0.018194061774641
beta0.206794860190384
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1312601259.381693414450.61830658554868
1413601355.360957383054.63904261694915
1513201309.3634274105110.6365725894934
1613001290.74395351719.25604648289664
1714401435.041929148984.95807085102024
1813601358.188146105771.81185389422853
1913301294.0079243754535.9920756245526
2014201346.0713276055973.9286723944138
2115101422.5711345169887.4288654830164
2212801395.96755488944-115.967554889442
2313101311.81156352198-1.81156352198013
2414601528.31873140404-68.318731404036
2512801284.47603135997-4.47603135997338
2613701386.38472563129-16.3847256312861
2713901345.1798860056944.8201139943149
2813901325.6113437761564.3886562238529
2914601470.00346473703-10.0034647370287
3014101388.4815939557321.5184060442739
3112301357.96258901141-127.962589011409
3212601445.70476325601-185.704763256014
3315901530.7469501800759.2530498199299
3412501299.27277030251-49.2727703025066
3514001327.8470421275772.1529578724278
3614501481.76263600476-31.7626360047632
3712201298.07157499738-78.0715749973756
3812901387.20367227088-97.203672270876
3914001403.57627099938-3.5762709993769
4014001400.85657007494-0.856570074935007
4114601469.81754003931-9.81754003931314
4214501417.2240380727232.7759619272806
4312701237.5142291611832.485770838822
4412601270.37970065924-10.3797006592417
4515501601.32778977433-51.3277897743305
4612301258.38946525589-28.3894652558872
4713801406.78073094817-26.7807309481736
4814901456.0192393569433.9807606430606
4911801226.23554821402-46.2355482140231
5011901296.73596465017-106.735964650167
5114001404.52932065687-4.52932065686514
5213801403.72114201785-23.7211420178503
5315101462.7465266638147.2534733361906
5414001452.32782255066-52.3278225506592
5512901269.7543847160220.2456152839795
5612001259.42430656984-59.4243065698365
5716001547.550767697852.4492323021952
5812201228.57998875956-8.57998875956173
5913801377.962032601852.03796739815061
6014501486.5169576505-36.5169576504961
6112601176.7642286858283.2357713141782
6211301189.76420762641-59.7642076264117
6313901398.36265858738-8.36265858738102
6413801378.485182831791.51481716821127
6515701507.3975935580162.6024064419867
6613201399.52659484626-79.5265948462622
6712101287.7246858408-77.7246858408023
6811901197.1286775289-7.12867752889656
6915801594.6399167372-14.6399167371997
7011501215.38099461656-65.3809946165645
7113301372.6036821872-42.6036821871955
7214201441.05239440475-21.0523944047509
7312601249.456450860110.5435491399037
7410401120.73676846629-80.7367684662852
7514501375.5990723041174.4009276958923
7613601365.9883172608-5.98831726079993
7715001551.55761869257-51.5576186925737
7812401303.67396854482-63.6739685448169
7912601194.0537137454165.9462862545934
8012201174.9247090386545.0752909613493
8116801560.66428562383119.335714376174
8212101138.5004663623471.4995336376639
8313501319.3900973902730.6099026097259
8414801410.4011075390769.5988924609292
8512701253.3916392371116.6083607628864
8610401036.981133876433.01886612356975
8714501446.011751271333.98824872866726
8813101357.64365477891-47.6436547789092
8915101498.5119141376211.4880858623833
9011601241.19945428098-81.1994542809773
9112901259.5488732675230.4511267324801
9212301220.167979913259.8320200867463
9316801679.217353730140.782646269861061
9411901208.4936357125-18.493635712495
9513101347.45549968138-37.4554996813788
9614801474.943384426195.0566155738079
9713201265.0482197386554.9517802613457
9810501036.5099498558313.4900501441664
9913801445.18140770113-65.181407701134
10013201304.9724973231615.0275026768397
10114801504.07139036359-24.0713903635929
10211501156.19880104342-6.19880104342178
10312501285.05412040708-35.0541204070771
10412601224.2323077474735.7676922525268
10516801672.769059996957.23094000305309
10611501185.15705683253-35.157056832526
10713101304.39477009165.60522990839786
10814701473.60947529082-3.60947529082

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1260 & 1259.38169341445 & 0.61830658554868 \tabularnewline
14 & 1360 & 1355.36095738305 & 4.63904261694915 \tabularnewline
15 & 1320 & 1309.36342741051 & 10.6365725894934 \tabularnewline
16 & 1300 & 1290.7439535171 & 9.25604648289664 \tabularnewline
17 & 1440 & 1435.04192914898 & 4.95807085102024 \tabularnewline
18 & 1360 & 1358.18814610577 & 1.81185389422853 \tabularnewline
19 & 1330 & 1294.00792437545 & 35.9920756245526 \tabularnewline
20 & 1420 & 1346.07132760559 & 73.9286723944138 \tabularnewline
21 & 1510 & 1422.57113451698 & 87.4288654830164 \tabularnewline
22 & 1280 & 1395.96755488944 & -115.967554889442 \tabularnewline
23 & 1310 & 1311.81156352198 & -1.81156352198013 \tabularnewline
24 & 1460 & 1528.31873140404 & -68.318731404036 \tabularnewline
25 & 1280 & 1284.47603135997 & -4.47603135997338 \tabularnewline
26 & 1370 & 1386.38472563129 & -16.3847256312861 \tabularnewline
27 & 1390 & 1345.17988600569 & 44.8201139943149 \tabularnewline
28 & 1390 & 1325.61134377615 & 64.3886562238529 \tabularnewline
29 & 1460 & 1470.00346473703 & -10.0034647370287 \tabularnewline
30 & 1410 & 1388.48159395573 & 21.5184060442739 \tabularnewline
31 & 1230 & 1357.96258901141 & -127.962589011409 \tabularnewline
32 & 1260 & 1445.70476325601 & -185.704763256014 \tabularnewline
33 & 1590 & 1530.74695018007 & 59.2530498199299 \tabularnewline
34 & 1250 & 1299.27277030251 & -49.2727703025066 \tabularnewline
35 & 1400 & 1327.84704212757 & 72.1529578724278 \tabularnewline
36 & 1450 & 1481.76263600476 & -31.7626360047632 \tabularnewline
37 & 1220 & 1298.07157499738 & -78.0715749973756 \tabularnewline
38 & 1290 & 1387.20367227088 & -97.203672270876 \tabularnewline
39 & 1400 & 1403.57627099938 & -3.5762709993769 \tabularnewline
40 & 1400 & 1400.85657007494 & -0.856570074935007 \tabularnewline
41 & 1460 & 1469.81754003931 & -9.81754003931314 \tabularnewline
42 & 1450 & 1417.22403807272 & 32.7759619272806 \tabularnewline
43 & 1270 & 1237.51422916118 & 32.485770838822 \tabularnewline
44 & 1260 & 1270.37970065924 & -10.3797006592417 \tabularnewline
45 & 1550 & 1601.32778977433 & -51.3277897743305 \tabularnewline
46 & 1230 & 1258.38946525589 & -28.3894652558872 \tabularnewline
47 & 1380 & 1406.78073094817 & -26.7807309481736 \tabularnewline
48 & 1490 & 1456.01923935694 & 33.9807606430606 \tabularnewline
49 & 1180 & 1226.23554821402 & -46.2355482140231 \tabularnewline
50 & 1190 & 1296.73596465017 & -106.735964650167 \tabularnewline
51 & 1400 & 1404.52932065687 & -4.52932065686514 \tabularnewline
52 & 1380 & 1403.72114201785 & -23.7211420178503 \tabularnewline
53 & 1510 & 1462.74652666381 & 47.2534733361906 \tabularnewline
54 & 1400 & 1452.32782255066 & -52.3278225506592 \tabularnewline
55 & 1290 & 1269.75438471602 & 20.2456152839795 \tabularnewline
56 & 1200 & 1259.42430656984 & -59.4243065698365 \tabularnewline
57 & 1600 & 1547.5507676978 & 52.4492323021952 \tabularnewline
58 & 1220 & 1228.57998875956 & -8.57998875956173 \tabularnewline
59 & 1380 & 1377.96203260185 & 2.03796739815061 \tabularnewline
60 & 1450 & 1486.5169576505 & -36.5169576504961 \tabularnewline
61 & 1260 & 1176.76422868582 & 83.2357713141782 \tabularnewline
62 & 1130 & 1189.76420762641 & -59.7642076264117 \tabularnewline
63 & 1390 & 1398.36265858738 & -8.36265858738102 \tabularnewline
64 & 1380 & 1378.48518283179 & 1.51481716821127 \tabularnewline
65 & 1570 & 1507.39759355801 & 62.6024064419867 \tabularnewline
66 & 1320 & 1399.52659484626 & -79.5265948462622 \tabularnewline
67 & 1210 & 1287.7246858408 & -77.7246858408023 \tabularnewline
68 & 1190 & 1197.1286775289 & -7.12867752889656 \tabularnewline
69 & 1580 & 1594.6399167372 & -14.6399167371997 \tabularnewline
70 & 1150 & 1215.38099461656 & -65.3809946165645 \tabularnewline
71 & 1330 & 1372.6036821872 & -42.6036821871955 \tabularnewline
72 & 1420 & 1441.05239440475 & -21.0523944047509 \tabularnewline
73 & 1260 & 1249.4564508601 & 10.5435491399037 \tabularnewline
74 & 1040 & 1120.73676846629 & -80.7367684662852 \tabularnewline
75 & 1450 & 1375.59907230411 & 74.4009276958923 \tabularnewline
76 & 1360 & 1365.9883172608 & -5.98831726079993 \tabularnewline
77 & 1500 & 1551.55761869257 & -51.5576186925737 \tabularnewline
78 & 1240 & 1303.67396854482 & -63.6739685448169 \tabularnewline
79 & 1260 & 1194.05371374541 & 65.9462862545934 \tabularnewline
80 & 1220 & 1174.92470903865 & 45.0752909613493 \tabularnewline
81 & 1680 & 1560.66428562383 & 119.335714376174 \tabularnewline
82 & 1210 & 1138.50046636234 & 71.4995336376639 \tabularnewline
83 & 1350 & 1319.39009739027 & 30.6099026097259 \tabularnewline
84 & 1480 & 1410.40110753907 & 69.5988924609292 \tabularnewline
85 & 1270 & 1253.39163923711 & 16.6083607628864 \tabularnewline
86 & 1040 & 1036.98113387643 & 3.01886612356975 \tabularnewline
87 & 1450 & 1446.01175127133 & 3.98824872866726 \tabularnewline
88 & 1310 & 1357.64365477891 & -47.6436547789092 \tabularnewline
89 & 1510 & 1498.51191413762 & 11.4880858623833 \tabularnewline
90 & 1160 & 1241.19945428098 & -81.1994542809773 \tabularnewline
91 & 1290 & 1259.54887326752 & 30.4511267324801 \tabularnewline
92 & 1230 & 1220.16797991325 & 9.8320200867463 \tabularnewline
93 & 1680 & 1679.21735373014 & 0.782646269861061 \tabularnewline
94 & 1190 & 1208.4936357125 & -18.493635712495 \tabularnewline
95 & 1310 & 1347.45549968138 & -37.4554996813788 \tabularnewline
96 & 1480 & 1474.94338442619 & 5.0566155738079 \tabularnewline
97 & 1320 & 1265.04821973865 & 54.9517802613457 \tabularnewline
98 & 1050 & 1036.50994985583 & 13.4900501441664 \tabularnewline
99 & 1380 & 1445.18140770113 & -65.181407701134 \tabularnewline
100 & 1320 & 1304.97249732316 & 15.0275026768397 \tabularnewline
101 & 1480 & 1504.07139036359 & -24.0713903635929 \tabularnewline
102 & 1150 & 1156.19880104342 & -6.19880104342178 \tabularnewline
103 & 1250 & 1285.05412040708 & -35.0541204070771 \tabularnewline
104 & 1260 & 1224.23230774747 & 35.7676922525268 \tabularnewline
105 & 1680 & 1672.76905999695 & 7.23094000305309 \tabularnewline
106 & 1150 & 1185.15705683253 & -35.157056832526 \tabularnewline
107 & 1310 & 1304.3947700916 & 5.60522990839786 \tabularnewline
108 & 1470 & 1473.60947529082 & -3.60947529082 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169372&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]1260[/C][C]1259.38169341445[/C][C]0.61830658554868[/C][/ROW]
[ROW][C]14[/C][C]1360[/C][C]1355.36095738305[/C][C]4.63904261694915[/C][/ROW]
[ROW][C]15[/C][C]1320[/C][C]1309.36342741051[/C][C]10.6365725894934[/C][/ROW]
[ROW][C]16[/C][C]1300[/C][C]1290.7439535171[/C][C]9.25604648289664[/C][/ROW]
[ROW][C]17[/C][C]1440[/C][C]1435.04192914898[/C][C]4.95807085102024[/C][/ROW]
[ROW][C]18[/C][C]1360[/C][C]1358.18814610577[/C][C]1.81185389422853[/C][/ROW]
[ROW][C]19[/C][C]1330[/C][C]1294.00792437545[/C][C]35.9920756245526[/C][/ROW]
[ROW][C]20[/C][C]1420[/C][C]1346.07132760559[/C][C]73.9286723944138[/C][/ROW]
[ROW][C]21[/C][C]1510[/C][C]1422.57113451698[/C][C]87.4288654830164[/C][/ROW]
[ROW][C]22[/C][C]1280[/C][C]1395.96755488944[/C][C]-115.967554889442[/C][/ROW]
[ROW][C]23[/C][C]1310[/C][C]1311.81156352198[/C][C]-1.81156352198013[/C][/ROW]
[ROW][C]24[/C][C]1460[/C][C]1528.31873140404[/C][C]-68.318731404036[/C][/ROW]
[ROW][C]25[/C][C]1280[/C][C]1284.47603135997[/C][C]-4.47603135997338[/C][/ROW]
[ROW][C]26[/C][C]1370[/C][C]1386.38472563129[/C][C]-16.3847256312861[/C][/ROW]
[ROW][C]27[/C][C]1390[/C][C]1345.17988600569[/C][C]44.8201139943149[/C][/ROW]
[ROW][C]28[/C][C]1390[/C][C]1325.61134377615[/C][C]64.3886562238529[/C][/ROW]
[ROW][C]29[/C][C]1460[/C][C]1470.00346473703[/C][C]-10.0034647370287[/C][/ROW]
[ROW][C]30[/C][C]1410[/C][C]1388.48159395573[/C][C]21.5184060442739[/C][/ROW]
[ROW][C]31[/C][C]1230[/C][C]1357.96258901141[/C][C]-127.962589011409[/C][/ROW]
[ROW][C]32[/C][C]1260[/C][C]1445.70476325601[/C][C]-185.704763256014[/C][/ROW]
[ROW][C]33[/C][C]1590[/C][C]1530.74695018007[/C][C]59.2530498199299[/C][/ROW]
[ROW][C]34[/C][C]1250[/C][C]1299.27277030251[/C][C]-49.2727703025066[/C][/ROW]
[ROW][C]35[/C][C]1400[/C][C]1327.84704212757[/C][C]72.1529578724278[/C][/ROW]
[ROW][C]36[/C][C]1450[/C][C]1481.76263600476[/C][C]-31.7626360047632[/C][/ROW]
[ROW][C]37[/C][C]1220[/C][C]1298.07157499738[/C][C]-78.0715749973756[/C][/ROW]
[ROW][C]38[/C][C]1290[/C][C]1387.20367227088[/C][C]-97.203672270876[/C][/ROW]
[ROW][C]39[/C][C]1400[/C][C]1403.57627099938[/C][C]-3.5762709993769[/C][/ROW]
[ROW][C]40[/C][C]1400[/C][C]1400.85657007494[/C][C]-0.856570074935007[/C][/ROW]
[ROW][C]41[/C][C]1460[/C][C]1469.81754003931[/C][C]-9.81754003931314[/C][/ROW]
[ROW][C]42[/C][C]1450[/C][C]1417.22403807272[/C][C]32.7759619272806[/C][/ROW]
[ROW][C]43[/C][C]1270[/C][C]1237.51422916118[/C][C]32.485770838822[/C][/ROW]
[ROW][C]44[/C][C]1260[/C][C]1270.37970065924[/C][C]-10.3797006592417[/C][/ROW]
[ROW][C]45[/C][C]1550[/C][C]1601.32778977433[/C][C]-51.3277897743305[/C][/ROW]
[ROW][C]46[/C][C]1230[/C][C]1258.38946525589[/C][C]-28.3894652558872[/C][/ROW]
[ROW][C]47[/C][C]1380[/C][C]1406.78073094817[/C][C]-26.7807309481736[/C][/ROW]
[ROW][C]48[/C][C]1490[/C][C]1456.01923935694[/C][C]33.9807606430606[/C][/ROW]
[ROW][C]49[/C][C]1180[/C][C]1226.23554821402[/C][C]-46.2355482140231[/C][/ROW]
[ROW][C]50[/C][C]1190[/C][C]1296.73596465017[/C][C]-106.735964650167[/C][/ROW]
[ROW][C]51[/C][C]1400[/C][C]1404.52932065687[/C][C]-4.52932065686514[/C][/ROW]
[ROW][C]52[/C][C]1380[/C][C]1403.72114201785[/C][C]-23.7211420178503[/C][/ROW]
[ROW][C]53[/C][C]1510[/C][C]1462.74652666381[/C][C]47.2534733361906[/C][/ROW]
[ROW][C]54[/C][C]1400[/C][C]1452.32782255066[/C][C]-52.3278225506592[/C][/ROW]
[ROW][C]55[/C][C]1290[/C][C]1269.75438471602[/C][C]20.2456152839795[/C][/ROW]
[ROW][C]56[/C][C]1200[/C][C]1259.42430656984[/C][C]-59.4243065698365[/C][/ROW]
[ROW][C]57[/C][C]1600[/C][C]1547.5507676978[/C][C]52.4492323021952[/C][/ROW]
[ROW][C]58[/C][C]1220[/C][C]1228.57998875956[/C][C]-8.57998875956173[/C][/ROW]
[ROW][C]59[/C][C]1380[/C][C]1377.96203260185[/C][C]2.03796739815061[/C][/ROW]
[ROW][C]60[/C][C]1450[/C][C]1486.5169576505[/C][C]-36.5169576504961[/C][/ROW]
[ROW][C]61[/C][C]1260[/C][C]1176.76422868582[/C][C]83.2357713141782[/C][/ROW]
[ROW][C]62[/C][C]1130[/C][C]1189.76420762641[/C][C]-59.7642076264117[/C][/ROW]
[ROW][C]63[/C][C]1390[/C][C]1398.36265858738[/C][C]-8.36265858738102[/C][/ROW]
[ROW][C]64[/C][C]1380[/C][C]1378.48518283179[/C][C]1.51481716821127[/C][/ROW]
[ROW][C]65[/C][C]1570[/C][C]1507.39759355801[/C][C]62.6024064419867[/C][/ROW]
[ROW][C]66[/C][C]1320[/C][C]1399.52659484626[/C][C]-79.5265948462622[/C][/ROW]
[ROW][C]67[/C][C]1210[/C][C]1287.7246858408[/C][C]-77.7246858408023[/C][/ROW]
[ROW][C]68[/C][C]1190[/C][C]1197.1286775289[/C][C]-7.12867752889656[/C][/ROW]
[ROW][C]69[/C][C]1580[/C][C]1594.6399167372[/C][C]-14.6399167371997[/C][/ROW]
[ROW][C]70[/C][C]1150[/C][C]1215.38099461656[/C][C]-65.3809946165645[/C][/ROW]
[ROW][C]71[/C][C]1330[/C][C]1372.6036821872[/C][C]-42.6036821871955[/C][/ROW]
[ROW][C]72[/C][C]1420[/C][C]1441.05239440475[/C][C]-21.0523944047509[/C][/ROW]
[ROW][C]73[/C][C]1260[/C][C]1249.4564508601[/C][C]10.5435491399037[/C][/ROW]
[ROW][C]74[/C][C]1040[/C][C]1120.73676846629[/C][C]-80.7367684662852[/C][/ROW]
[ROW][C]75[/C][C]1450[/C][C]1375.59907230411[/C][C]74.4009276958923[/C][/ROW]
[ROW][C]76[/C][C]1360[/C][C]1365.9883172608[/C][C]-5.98831726079993[/C][/ROW]
[ROW][C]77[/C][C]1500[/C][C]1551.55761869257[/C][C]-51.5576186925737[/C][/ROW]
[ROW][C]78[/C][C]1240[/C][C]1303.67396854482[/C][C]-63.6739685448169[/C][/ROW]
[ROW][C]79[/C][C]1260[/C][C]1194.05371374541[/C][C]65.9462862545934[/C][/ROW]
[ROW][C]80[/C][C]1220[/C][C]1174.92470903865[/C][C]45.0752909613493[/C][/ROW]
[ROW][C]81[/C][C]1680[/C][C]1560.66428562383[/C][C]119.335714376174[/C][/ROW]
[ROW][C]82[/C][C]1210[/C][C]1138.50046636234[/C][C]71.4995336376639[/C][/ROW]
[ROW][C]83[/C][C]1350[/C][C]1319.39009739027[/C][C]30.6099026097259[/C][/ROW]
[ROW][C]84[/C][C]1480[/C][C]1410.40110753907[/C][C]69.5988924609292[/C][/ROW]
[ROW][C]85[/C][C]1270[/C][C]1253.39163923711[/C][C]16.6083607628864[/C][/ROW]
[ROW][C]86[/C][C]1040[/C][C]1036.98113387643[/C][C]3.01886612356975[/C][/ROW]
[ROW][C]87[/C][C]1450[/C][C]1446.01175127133[/C][C]3.98824872866726[/C][/ROW]
[ROW][C]88[/C][C]1310[/C][C]1357.64365477891[/C][C]-47.6436547789092[/C][/ROW]
[ROW][C]89[/C][C]1510[/C][C]1498.51191413762[/C][C]11.4880858623833[/C][/ROW]
[ROW][C]90[/C][C]1160[/C][C]1241.19945428098[/C][C]-81.1994542809773[/C][/ROW]
[ROW][C]91[/C][C]1290[/C][C]1259.54887326752[/C][C]30.4511267324801[/C][/ROW]
[ROW][C]92[/C][C]1230[/C][C]1220.16797991325[/C][C]9.8320200867463[/C][/ROW]
[ROW][C]93[/C][C]1680[/C][C]1679.21735373014[/C][C]0.782646269861061[/C][/ROW]
[ROW][C]94[/C][C]1190[/C][C]1208.4936357125[/C][C]-18.493635712495[/C][/ROW]
[ROW][C]95[/C][C]1310[/C][C]1347.45549968138[/C][C]-37.4554996813788[/C][/ROW]
[ROW][C]96[/C][C]1480[/C][C]1474.94338442619[/C][C]5.0566155738079[/C][/ROW]
[ROW][C]97[/C][C]1320[/C][C]1265.04821973865[/C][C]54.9517802613457[/C][/ROW]
[ROW][C]98[/C][C]1050[/C][C]1036.50994985583[/C][C]13.4900501441664[/C][/ROW]
[ROW][C]99[/C][C]1380[/C][C]1445.18140770113[/C][C]-65.181407701134[/C][/ROW]
[ROW][C]100[/C][C]1320[/C][C]1304.97249732316[/C][C]15.0275026768397[/C][/ROW]
[ROW][C]101[/C][C]1480[/C][C]1504.07139036359[/C][C]-24.0713903635929[/C][/ROW]
[ROW][C]102[/C][C]1150[/C][C]1156.19880104342[/C][C]-6.19880104342178[/C][/ROW]
[ROW][C]103[/C][C]1250[/C][C]1285.05412040708[/C][C]-35.0541204070771[/C][/ROW]
[ROW][C]104[/C][C]1260[/C][C]1224.23230774747[/C][C]35.7676922525268[/C][/ROW]
[ROW][C]105[/C][C]1680[/C][C]1672.76905999695[/C][C]7.23094000305309[/C][/ROW]
[ROW][C]106[/C][C]1150[/C][C]1185.15705683253[/C][C]-35.157056832526[/C][/ROW]
[ROW][C]107[/C][C]1310[/C][C]1304.3947700916[/C][C]5.60522990839786[/C][/ROW]
[ROW][C]108[/C][C]1470[/C][C]1473.60947529082[/C][C]-3.60947529082[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169372&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169372&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
1312601259.381693414450.61830658554868
1413601355.360957383054.63904261694915
1513201309.3634274105110.6365725894934
1613001290.74395351719.25604648289664
1714401435.041929148984.95807085102024
1813601358.188146105771.81185389422853
1913301294.0079243754535.9920756245526
2014201346.0713276055973.9286723944138
2115101422.5711345169887.4288654830164
2212801395.96755488944-115.967554889442
2313101311.81156352198-1.81156352198013
2414601528.31873140404-68.318731404036
2512801284.47603135997-4.47603135997338
2613701386.38472563129-16.3847256312861
2713901345.1798860056944.8201139943149
2813901325.6113437761564.3886562238529
2914601470.00346473703-10.0034647370287
3014101388.4815939557321.5184060442739
3112301357.96258901141-127.962589011409
3212601445.70476325601-185.704763256014
3315901530.7469501800759.2530498199299
3412501299.27277030251-49.2727703025066
3514001327.8470421275772.1529578724278
3614501481.76263600476-31.7626360047632
3712201298.07157499738-78.0715749973756
3812901387.20367227088-97.203672270876
3914001403.57627099938-3.5762709993769
4014001400.85657007494-0.856570074935007
4114601469.81754003931-9.81754003931314
4214501417.2240380727232.7759619272806
4312701237.5142291611832.485770838822
4412601270.37970065924-10.3797006592417
4515501601.32778977433-51.3277897743305
4612301258.38946525589-28.3894652558872
4713801406.78073094817-26.7807309481736
4814901456.0192393569433.9807606430606
4911801226.23554821402-46.2355482140231
5011901296.73596465017-106.735964650167
5114001404.52932065687-4.52932065686514
5213801403.72114201785-23.7211420178503
5315101462.7465266638147.2534733361906
5414001452.32782255066-52.3278225506592
5512901269.7543847160220.2456152839795
5612001259.42430656984-59.4243065698365
5716001547.550767697852.4492323021952
5812201228.57998875956-8.57998875956173
5913801377.962032601852.03796739815061
6014501486.5169576505-36.5169576504961
6112601176.7642286858283.2357713141782
6211301189.76420762641-59.7642076264117
6313901398.36265858738-8.36265858738102
6413801378.485182831791.51481716821127
6515701507.3975935580162.6024064419867
6613201399.52659484626-79.5265948462622
6712101287.7246858408-77.7246858408023
6811901197.1286775289-7.12867752889656
6915801594.6399167372-14.6399167371997
7011501215.38099461656-65.3809946165645
7113301372.6036821872-42.6036821871955
7214201441.05239440475-21.0523944047509
7312601249.456450860110.5435491399037
7410401120.73676846629-80.7367684662852
7514501375.5990723041174.4009276958923
7613601365.9883172608-5.98831726079993
7715001551.55761869257-51.5576186925737
7812401303.67396854482-63.6739685448169
7912601194.0537137454165.9462862545934
8012201174.9247090386545.0752909613493
8116801560.66428562383119.335714376174
8212101138.5004663623471.4995336376639
8313501319.3900973902730.6099026097259
8414801410.4011075390769.5988924609292
8512701253.3916392371116.6083607628864
8610401036.981133876433.01886612356975
8714501446.011751271333.98824872866726
8813101357.64365477891-47.6436547789092
8915101498.5119141376211.4880858623833
9011601241.19945428098-81.1994542809773
9112901259.5488732675230.4511267324801
9212301220.167979913259.8320200867463
9316801679.217353730140.782646269861061
9411901208.4936357125-18.493635712495
9513101347.45549968138-37.4554996813788
9614801474.943384426195.0566155738079
9713201265.0482197386554.9517802613457
9810501036.5099498558313.4900501441664
9913801445.18140770113-65.181407701134
10013201304.9724973231615.0275026768397
10114801504.07139036359-24.0713903635929
10211501156.19880104342-6.19880104342178
10312501285.05412040708-35.0541204070771
10412601224.2323077474735.7676922525268
10516801672.769059996957.23094000305309
10611501185.15705683253-35.157056832526
10713101304.39477009165.60522990839786
10814701473.60947529082-3.60947529082







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1091313.102402263781211.084162172681415.12064235488
1101044.01435716921941.9805596616351146.04815467678
1111372.861631955481270.763917023261474.9593468877
1121312.738936532771210.600397390431414.8774756751
1131472.046322992541369.799063589611574.29358239548
1141143.812838133731041.602261450511246.02341481696
1151243.788331512651141.45495440311346.1217086222
1161253.096798230461150.656196955491355.53739950544
1171670.512671626651567.532300116121773.49304313717
1181144.000611622531041.422621385431246.57860185963
1191303.070106987811200.152174955721405.9880390199
1201462.271991497061277.872020214791646.67196277933

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 1313.10240226378 & 1211.08416217268 & 1415.12064235488 \tabularnewline
110 & 1044.01435716921 & 941.980559661635 & 1146.04815467678 \tabularnewline
111 & 1372.86163195548 & 1270.76391702326 & 1474.9593468877 \tabularnewline
112 & 1312.73893653277 & 1210.60039739043 & 1414.8774756751 \tabularnewline
113 & 1472.04632299254 & 1369.79906358961 & 1574.29358239548 \tabularnewline
114 & 1143.81283813373 & 1041.60226145051 & 1246.02341481696 \tabularnewline
115 & 1243.78833151265 & 1141.4549544031 & 1346.1217086222 \tabularnewline
116 & 1253.09679823046 & 1150.65619695549 & 1355.53739950544 \tabularnewline
117 & 1670.51267162665 & 1567.53230011612 & 1773.49304313717 \tabularnewline
118 & 1144.00061162253 & 1041.42262138543 & 1246.57860185963 \tabularnewline
119 & 1303.07010698781 & 1200.15217495572 & 1405.9880390199 \tabularnewline
120 & 1462.27199149706 & 1277.87202021479 & 1646.67196277933 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169372&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]1313.10240226378[/C][C]1211.08416217268[/C][C]1415.12064235488[/C][/ROW]
[ROW][C]110[/C][C]1044.01435716921[/C][C]941.980559661635[/C][C]1146.04815467678[/C][/ROW]
[ROW][C]111[/C][C]1372.86163195548[/C][C]1270.76391702326[/C][C]1474.9593468877[/C][/ROW]
[ROW][C]112[/C][C]1312.73893653277[/C][C]1210.60039739043[/C][C]1414.8774756751[/C][/ROW]
[ROW][C]113[/C][C]1472.04632299254[/C][C]1369.79906358961[/C][C]1574.29358239548[/C][/ROW]
[ROW][C]114[/C][C]1143.81283813373[/C][C]1041.60226145051[/C][C]1246.02341481696[/C][/ROW]
[ROW][C]115[/C][C]1243.78833151265[/C][C]1141.4549544031[/C][C]1346.1217086222[/C][/ROW]
[ROW][C]116[/C][C]1253.09679823046[/C][C]1150.65619695549[/C][C]1355.53739950544[/C][/ROW]
[ROW][C]117[/C][C]1670.51267162665[/C][C]1567.53230011612[/C][C]1773.49304313717[/C][/ROW]
[ROW][C]118[/C][C]1144.00061162253[/C][C]1041.42262138543[/C][C]1246.57860185963[/C][/ROW]
[ROW][C]119[/C][C]1303.07010698781[/C][C]1200.15217495572[/C][C]1405.9880390199[/C][/ROW]
[ROW][C]120[/C][C]1462.27199149706[/C][C]1277.87202021479[/C][C]1646.67196277933[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169372&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169372&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
1091313.102402263781211.084162172681415.12064235488
1101044.01435716921941.9805596616351146.04815467678
1111372.861631955481270.763917023261474.9593468877
1121312.738936532771210.600397390431414.8774756751
1131472.046322992541369.799063589611574.29358239548
1141143.812838133731041.602261450511246.02341481696
1151243.788331512651141.45495440311346.1217086222
1161253.096798230461150.656196955491355.53739950544
1171670.512671626651567.532300116121773.49304313717
1181144.000611622531041.422621385431246.57860185963
1191303.070106987811200.152174955721405.9880390199
1201462.271991497061277.872020214791646.67196277933



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