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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 computationThu, 16 Aug 2012 23:45:22 -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/16/t13451751764c0on6lcr8ooplr.htm/, Retrieved Sat, 04 May 2024 11:20:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=169439, Retrieved Sat, 04 May 2024 11:20:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsOcak Akif
Estimated Impact59
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks A - Sta...] [2012-08-17 03:45:22] [919141dca056cde38faaf6352f12d0de] [Current]
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Dataseries X:
1943
1932
1922
1901
2108
2098
1943
1839
1850
1850
1860
1881
1839
1819
1757
1664
1922
1839
1633
1674
1633
1736
1591
1684
1602
1581
1416
1354
1664
1602
1405
1529
1426
1509
1426
1571
1447
1426
1230
1168
1612
1509
1333
1498
1374
1333
1312
1416
1240
1240
1095
1044
1560
1426
1302
1405
1261
1199
1250
1405
1199
1281
1178
1137
1591
1498
1250
1374
1312
1354
1426
1622
1488
1540
1457
1395
1860
1746
1467
1426
1343
1374
1354
1529
1343
1405
1364
1323
1829
1726
1447
1343
1188
1199
1178
1323
1064
1054
1013
899
1467
1405
1095
1002
847
816
713
858
486
444
403
331
940
889
568
506
351
362
300
403




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=169439&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=169439&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169439&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
alpha0.670019604263073
beta0.0548037596931145
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.670019604263073 \tabularnewline
beta & 0.0548037596931145 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169439&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]0.670019604263073[/C][/ROW]
[ROW][C]beta[/C][C]0.0548037596931145[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169439&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169439&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
alpha0.670019604263073
beta0.0548037596931145
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1318391943.50747863248-104.507478632478
1418191852.10744587038-33.1074458703802
1517571761.45614285365-4.45614285364627
1616641656.713146792177.28685320783075
1719221913.272425258168.72757474184436
1818391833.575821725285.42417827472241
1916331737.32338475279-104.323384752786
2016741546.87388343011127.126116569893
2116331633.70977136584-0.70977136584429
2217361629.03371240698106.966287593021
2315911711.30548244631-120.305482446306
2416841648.7998093333635.2001906666367
2516021599.459769978512.54023002149165
2615811604.45955648684-23.4595564868443
2714161531.1963081942-115.196308194202
2813541353.533266409910.466733590085596
2916641603.1509864185560.8490135814527
3016021556.3532362057845.6467637942169
3114051451.37965634023-46.3796563402313
3215291378.79853773767150.201462262329
3314261442.43049078308-16.4304907830808
3415091465.6934397545343.3065602454731
3514261430.92036613489-4.92036613489358
3615711501.8793513805269.1206486194781
3714471470.57562736117-23.5756273611682
3814261454.62498419593-28.6249841959348
3912301352.56692263271-122.566922632712
4011681212.79876920505-44.7987692050458
4116121455.01736096008156.982639039919
4215091474.1492450385534.8507549614505
4313331337.7134530246-4.71345302460486
4414981365.58562878469132.414371215309
4513741369.329675561844.67032443816083
4613331434.23252473535-101.232524735351
4713121289.1839585152322.816041484768
4814161406.659901748029.34009825197836
4912401306.01990347649-66.0199034764896
5012401259.71185817746-19.7118581774625
5110951132.70133784216-37.7013378421595
5210441078.64755584275-34.647555842753
5315601397.81511677715162.184883222848
5414261383.8860515696542.113948430351
5513021243.2826026376158.7173973623906
5614051365.254614491839.7453855081994
5712611267.7032546657-6.70325466569966
5811991292.5697472253-93.5697472253048
5912501196.4003896425453.5996103574601
6014051333.9968930707871.0031069292218
6111991256.01099952552-57.0109995255159
6212811237.556650137843.4433498621963
6311781155.7810217783422.2189782216569
6411371153.93880416597-16.9388041659745
6515911561.6287699264329.3712300735747
6614981425.9203833754572.0796166245464
6712501318.80314394873-68.8031439487334
6813741352.3208104850721.6791895149258
6913121229.9215304185882.0784695814182
7013541291.453233862662.5467661373957
7114261360.0244932580765.9755067419273
7216221523.6868300736898.3131699263233
7314881434.7908105342653.2091894657412
7415401540.41509695491-0.41509695490663
7514571437.7203409629519.2796590370483
7613951436.35000884069-41.3500088406868
7718601857.431610316172.56838968382522
7817461731.3397541347414.6602458652585
7914671550.63547418708-83.6354741870816
8014261614.90156039382-188.901560393824
8113431374.43616393941-31.436163939411
8213741352.394083128921.6059168710988
8313541392.09058155161-38.0905815516098
8415291490.3011229886838.6988770113214
8513431337.993645606975.00635439303005
8614051383.2708522166721.7291477833339
8713641292.3699132826571.6300867173477
8813231298.4489342013824.5510657986172
8918291772.9777608199656.0222391800357
9017261683.4539134979642.5460865020439
9114471486.78479587116-39.7847958711639
9213431545.09289351788-202.092893517882
9311881346.66210080466-158.662100804662
9411991251.11987197474-52.1198719747383
9511781213.25366840366-35.2536684036556
9613231330.34187953403-7.34187953403148
9710641126.01558920911-62.0155892091077
9810541119.39122363783-65.3912236378285
991013970.87148485170942.1285151482914
100899924.852660150457-25.8526601504575
10114671357.34800782171109.651992178286
10214051282.63267822963122.367321770365
10310951098.53117726752-3.53117726751998
10410021115.15603929041-113.156039290414
105847981.496337220672-134.496337220672
106816929.040192191474-113.040192191474
107713845.422428534591-132.422428534591
108858892.548743459247-34.5487434592468
109486636.885778465417-150.885778465417
110444551.273183346434-107.273183346434
111403390.30366058748412.6963394125158
112331281.18405263676549.8159473632348
113940790.92305668614149.07694331386
114889730.097022034544158.902977965456
115568513.55066017378254.4493398262179
116506519.598140704846-13.5981407048464
117351436.006618787475-85.0066187874747
118362416.01122118012-54.0112211801202
119300359.937345749248-59.9373457492482
120403484.977185703922-81.9771857039218

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1839 & 1943.50747863248 & -104.507478632478 \tabularnewline
14 & 1819 & 1852.10744587038 & -33.1074458703802 \tabularnewline
15 & 1757 & 1761.45614285365 & -4.45614285364627 \tabularnewline
16 & 1664 & 1656.71314679217 & 7.28685320783075 \tabularnewline
17 & 1922 & 1913.27242525816 & 8.72757474184436 \tabularnewline
18 & 1839 & 1833.57582172528 & 5.42417827472241 \tabularnewline
19 & 1633 & 1737.32338475279 & -104.323384752786 \tabularnewline
20 & 1674 & 1546.87388343011 & 127.126116569893 \tabularnewline
21 & 1633 & 1633.70977136584 & -0.70977136584429 \tabularnewline
22 & 1736 & 1629.03371240698 & 106.966287593021 \tabularnewline
23 & 1591 & 1711.30548244631 & -120.305482446306 \tabularnewline
24 & 1684 & 1648.79980933336 & 35.2001906666367 \tabularnewline
25 & 1602 & 1599.45976997851 & 2.54023002149165 \tabularnewline
26 & 1581 & 1604.45955648684 & -23.4595564868443 \tabularnewline
27 & 1416 & 1531.1963081942 & -115.196308194202 \tabularnewline
28 & 1354 & 1353.53326640991 & 0.466733590085596 \tabularnewline
29 & 1664 & 1603.15098641855 & 60.8490135814527 \tabularnewline
30 & 1602 & 1556.35323620578 & 45.6467637942169 \tabularnewline
31 & 1405 & 1451.37965634023 & -46.3796563402313 \tabularnewline
32 & 1529 & 1378.79853773767 & 150.201462262329 \tabularnewline
33 & 1426 & 1442.43049078308 & -16.4304907830808 \tabularnewline
34 & 1509 & 1465.69343975453 & 43.3065602454731 \tabularnewline
35 & 1426 & 1430.92036613489 & -4.92036613489358 \tabularnewline
36 & 1571 & 1501.87935138052 & 69.1206486194781 \tabularnewline
37 & 1447 & 1470.57562736117 & -23.5756273611682 \tabularnewline
38 & 1426 & 1454.62498419593 & -28.6249841959348 \tabularnewline
39 & 1230 & 1352.56692263271 & -122.566922632712 \tabularnewline
40 & 1168 & 1212.79876920505 & -44.7987692050458 \tabularnewline
41 & 1612 & 1455.01736096008 & 156.982639039919 \tabularnewline
42 & 1509 & 1474.14924503855 & 34.8507549614505 \tabularnewline
43 & 1333 & 1337.7134530246 & -4.71345302460486 \tabularnewline
44 & 1498 & 1365.58562878469 & 132.414371215309 \tabularnewline
45 & 1374 & 1369.32967556184 & 4.67032443816083 \tabularnewline
46 & 1333 & 1434.23252473535 & -101.232524735351 \tabularnewline
47 & 1312 & 1289.18395851523 & 22.816041484768 \tabularnewline
48 & 1416 & 1406.65990174802 & 9.34009825197836 \tabularnewline
49 & 1240 & 1306.01990347649 & -66.0199034764896 \tabularnewline
50 & 1240 & 1259.71185817746 & -19.7118581774625 \tabularnewline
51 & 1095 & 1132.70133784216 & -37.7013378421595 \tabularnewline
52 & 1044 & 1078.64755584275 & -34.647555842753 \tabularnewline
53 & 1560 & 1397.81511677715 & 162.184883222848 \tabularnewline
54 & 1426 & 1383.88605156965 & 42.113948430351 \tabularnewline
55 & 1302 & 1243.28260263761 & 58.7173973623906 \tabularnewline
56 & 1405 & 1365.2546144918 & 39.7453855081994 \tabularnewline
57 & 1261 & 1267.7032546657 & -6.70325466569966 \tabularnewline
58 & 1199 & 1292.5697472253 & -93.5697472253048 \tabularnewline
59 & 1250 & 1196.40038964254 & 53.5996103574601 \tabularnewline
60 & 1405 & 1333.99689307078 & 71.0031069292218 \tabularnewline
61 & 1199 & 1256.01099952552 & -57.0109995255159 \tabularnewline
62 & 1281 & 1237.5566501378 & 43.4433498621963 \tabularnewline
63 & 1178 & 1155.78102177834 & 22.2189782216569 \tabularnewline
64 & 1137 & 1153.93880416597 & -16.9388041659745 \tabularnewline
65 & 1591 & 1561.62876992643 & 29.3712300735747 \tabularnewline
66 & 1498 & 1425.92038337545 & 72.0796166245464 \tabularnewline
67 & 1250 & 1318.80314394873 & -68.8031439487334 \tabularnewline
68 & 1374 & 1352.32081048507 & 21.6791895149258 \tabularnewline
69 & 1312 & 1229.92153041858 & 82.0784695814182 \tabularnewline
70 & 1354 & 1291.4532338626 & 62.5467661373957 \tabularnewline
71 & 1426 & 1360.02449325807 & 65.9755067419273 \tabularnewline
72 & 1622 & 1523.68683007368 & 98.3131699263233 \tabularnewline
73 & 1488 & 1434.79081053426 & 53.2091894657412 \tabularnewline
74 & 1540 & 1540.41509695491 & -0.41509695490663 \tabularnewline
75 & 1457 & 1437.72034096295 & 19.2796590370483 \tabularnewline
76 & 1395 & 1436.35000884069 & -41.3500088406868 \tabularnewline
77 & 1860 & 1857.43161031617 & 2.56838968382522 \tabularnewline
78 & 1746 & 1731.33975413474 & 14.6602458652585 \tabularnewline
79 & 1467 & 1550.63547418708 & -83.6354741870816 \tabularnewline
80 & 1426 & 1614.90156039382 & -188.901560393824 \tabularnewline
81 & 1343 & 1374.43616393941 & -31.436163939411 \tabularnewline
82 & 1374 & 1352.3940831289 & 21.6059168710988 \tabularnewline
83 & 1354 & 1392.09058155161 & -38.0905815516098 \tabularnewline
84 & 1529 & 1490.30112298868 & 38.6988770113214 \tabularnewline
85 & 1343 & 1337.99364560697 & 5.00635439303005 \tabularnewline
86 & 1405 & 1383.27085221667 & 21.7291477833339 \tabularnewline
87 & 1364 & 1292.36991328265 & 71.6300867173477 \tabularnewline
88 & 1323 & 1298.44893420138 & 24.5510657986172 \tabularnewline
89 & 1829 & 1772.97776081996 & 56.0222391800357 \tabularnewline
90 & 1726 & 1683.45391349796 & 42.5460865020439 \tabularnewline
91 & 1447 & 1486.78479587116 & -39.7847958711639 \tabularnewline
92 & 1343 & 1545.09289351788 & -202.092893517882 \tabularnewline
93 & 1188 & 1346.66210080466 & -158.662100804662 \tabularnewline
94 & 1199 & 1251.11987197474 & -52.1198719747383 \tabularnewline
95 & 1178 & 1213.25366840366 & -35.2536684036556 \tabularnewline
96 & 1323 & 1330.34187953403 & -7.34187953403148 \tabularnewline
97 & 1064 & 1126.01558920911 & -62.0155892091077 \tabularnewline
98 & 1054 & 1119.39122363783 & -65.3912236378285 \tabularnewline
99 & 1013 & 970.871484851709 & 42.1285151482914 \tabularnewline
100 & 899 & 924.852660150457 & -25.8526601504575 \tabularnewline
101 & 1467 & 1357.34800782171 & 109.651992178286 \tabularnewline
102 & 1405 & 1282.63267822963 & 122.367321770365 \tabularnewline
103 & 1095 & 1098.53117726752 & -3.53117726751998 \tabularnewline
104 & 1002 & 1115.15603929041 & -113.156039290414 \tabularnewline
105 & 847 & 981.496337220672 & -134.496337220672 \tabularnewline
106 & 816 & 929.040192191474 & -113.040192191474 \tabularnewline
107 & 713 & 845.422428534591 & -132.422428534591 \tabularnewline
108 & 858 & 892.548743459247 & -34.5487434592468 \tabularnewline
109 & 486 & 636.885778465417 & -150.885778465417 \tabularnewline
110 & 444 & 551.273183346434 & -107.273183346434 \tabularnewline
111 & 403 & 390.303660587484 & 12.6963394125158 \tabularnewline
112 & 331 & 281.184052636765 & 49.8159473632348 \tabularnewline
113 & 940 & 790.92305668614 & 149.07694331386 \tabularnewline
114 & 889 & 730.097022034544 & 158.902977965456 \tabularnewline
115 & 568 & 513.550660173782 & 54.4493398262179 \tabularnewline
116 & 506 & 519.598140704846 & -13.5981407048464 \tabularnewline
117 & 351 & 436.006618787475 & -85.0066187874747 \tabularnewline
118 & 362 & 416.01122118012 & -54.0112211801202 \tabularnewline
119 & 300 & 359.937345749248 & -59.9373457492482 \tabularnewline
120 & 403 & 484.977185703922 & -81.9771857039218 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169439&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]1839[/C][C]1943.50747863248[/C][C]-104.507478632478[/C][/ROW]
[ROW][C]14[/C][C]1819[/C][C]1852.10744587038[/C][C]-33.1074458703802[/C][/ROW]
[ROW][C]15[/C][C]1757[/C][C]1761.45614285365[/C][C]-4.45614285364627[/C][/ROW]
[ROW][C]16[/C][C]1664[/C][C]1656.71314679217[/C][C]7.28685320783075[/C][/ROW]
[ROW][C]17[/C][C]1922[/C][C]1913.27242525816[/C][C]8.72757474184436[/C][/ROW]
[ROW][C]18[/C][C]1839[/C][C]1833.57582172528[/C][C]5.42417827472241[/C][/ROW]
[ROW][C]19[/C][C]1633[/C][C]1737.32338475279[/C][C]-104.323384752786[/C][/ROW]
[ROW][C]20[/C][C]1674[/C][C]1546.87388343011[/C][C]127.126116569893[/C][/ROW]
[ROW][C]21[/C][C]1633[/C][C]1633.70977136584[/C][C]-0.70977136584429[/C][/ROW]
[ROW][C]22[/C][C]1736[/C][C]1629.03371240698[/C][C]106.966287593021[/C][/ROW]
[ROW][C]23[/C][C]1591[/C][C]1711.30548244631[/C][C]-120.305482446306[/C][/ROW]
[ROW][C]24[/C][C]1684[/C][C]1648.79980933336[/C][C]35.2001906666367[/C][/ROW]
[ROW][C]25[/C][C]1602[/C][C]1599.45976997851[/C][C]2.54023002149165[/C][/ROW]
[ROW][C]26[/C][C]1581[/C][C]1604.45955648684[/C][C]-23.4595564868443[/C][/ROW]
[ROW][C]27[/C][C]1416[/C][C]1531.1963081942[/C][C]-115.196308194202[/C][/ROW]
[ROW][C]28[/C][C]1354[/C][C]1353.53326640991[/C][C]0.466733590085596[/C][/ROW]
[ROW][C]29[/C][C]1664[/C][C]1603.15098641855[/C][C]60.8490135814527[/C][/ROW]
[ROW][C]30[/C][C]1602[/C][C]1556.35323620578[/C][C]45.6467637942169[/C][/ROW]
[ROW][C]31[/C][C]1405[/C][C]1451.37965634023[/C][C]-46.3796563402313[/C][/ROW]
[ROW][C]32[/C][C]1529[/C][C]1378.79853773767[/C][C]150.201462262329[/C][/ROW]
[ROW][C]33[/C][C]1426[/C][C]1442.43049078308[/C][C]-16.4304907830808[/C][/ROW]
[ROW][C]34[/C][C]1509[/C][C]1465.69343975453[/C][C]43.3065602454731[/C][/ROW]
[ROW][C]35[/C][C]1426[/C][C]1430.92036613489[/C][C]-4.92036613489358[/C][/ROW]
[ROW][C]36[/C][C]1571[/C][C]1501.87935138052[/C][C]69.1206486194781[/C][/ROW]
[ROW][C]37[/C][C]1447[/C][C]1470.57562736117[/C][C]-23.5756273611682[/C][/ROW]
[ROW][C]38[/C][C]1426[/C][C]1454.62498419593[/C][C]-28.6249841959348[/C][/ROW]
[ROW][C]39[/C][C]1230[/C][C]1352.56692263271[/C][C]-122.566922632712[/C][/ROW]
[ROW][C]40[/C][C]1168[/C][C]1212.79876920505[/C][C]-44.7987692050458[/C][/ROW]
[ROW][C]41[/C][C]1612[/C][C]1455.01736096008[/C][C]156.982639039919[/C][/ROW]
[ROW][C]42[/C][C]1509[/C][C]1474.14924503855[/C][C]34.8507549614505[/C][/ROW]
[ROW][C]43[/C][C]1333[/C][C]1337.7134530246[/C][C]-4.71345302460486[/C][/ROW]
[ROW][C]44[/C][C]1498[/C][C]1365.58562878469[/C][C]132.414371215309[/C][/ROW]
[ROW][C]45[/C][C]1374[/C][C]1369.32967556184[/C][C]4.67032443816083[/C][/ROW]
[ROW][C]46[/C][C]1333[/C][C]1434.23252473535[/C][C]-101.232524735351[/C][/ROW]
[ROW][C]47[/C][C]1312[/C][C]1289.18395851523[/C][C]22.816041484768[/C][/ROW]
[ROW][C]48[/C][C]1416[/C][C]1406.65990174802[/C][C]9.34009825197836[/C][/ROW]
[ROW][C]49[/C][C]1240[/C][C]1306.01990347649[/C][C]-66.0199034764896[/C][/ROW]
[ROW][C]50[/C][C]1240[/C][C]1259.71185817746[/C][C]-19.7118581774625[/C][/ROW]
[ROW][C]51[/C][C]1095[/C][C]1132.70133784216[/C][C]-37.7013378421595[/C][/ROW]
[ROW][C]52[/C][C]1044[/C][C]1078.64755584275[/C][C]-34.647555842753[/C][/ROW]
[ROW][C]53[/C][C]1560[/C][C]1397.81511677715[/C][C]162.184883222848[/C][/ROW]
[ROW][C]54[/C][C]1426[/C][C]1383.88605156965[/C][C]42.113948430351[/C][/ROW]
[ROW][C]55[/C][C]1302[/C][C]1243.28260263761[/C][C]58.7173973623906[/C][/ROW]
[ROW][C]56[/C][C]1405[/C][C]1365.2546144918[/C][C]39.7453855081994[/C][/ROW]
[ROW][C]57[/C][C]1261[/C][C]1267.7032546657[/C][C]-6.70325466569966[/C][/ROW]
[ROW][C]58[/C][C]1199[/C][C]1292.5697472253[/C][C]-93.5697472253048[/C][/ROW]
[ROW][C]59[/C][C]1250[/C][C]1196.40038964254[/C][C]53.5996103574601[/C][/ROW]
[ROW][C]60[/C][C]1405[/C][C]1333.99689307078[/C][C]71.0031069292218[/C][/ROW]
[ROW][C]61[/C][C]1199[/C][C]1256.01099952552[/C][C]-57.0109995255159[/C][/ROW]
[ROW][C]62[/C][C]1281[/C][C]1237.5566501378[/C][C]43.4433498621963[/C][/ROW]
[ROW][C]63[/C][C]1178[/C][C]1155.78102177834[/C][C]22.2189782216569[/C][/ROW]
[ROW][C]64[/C][C]1137[/C][C]1153.93880416597[/C][C]-16.9388041659745[/C][/ROW]
[ROW][C]65[/C][C]1591[/C][C]1561.62876992643[/C][C]29.3712300735747[/C][/ROW]
[ROW][C]66[/C][C]1498[/C][C]1425.92038337545[/C][C]72.0796166245464[/C][/ROW]
[ROW][C]67[/C][C]1250[/C][C]1318.80314394873[/C][C]-68.8031439487334[/C][/ROW]
[ROW][C]68[/C][C]1374[/C][C]1352.32081048507[/C][C]21.6791895149258[/C][/ROW]
[ROW][C]69[/C][C]1312[/C][C]1229.92153041858[/C][C]82.0784695814182[/C][/ROW]
[ROW][C]70[/C][C]1354[/C][C]1291.4532338626[/C][C]62.5467661373957[/C][/ROW]
[ROW][C]71[/C][C]1426[/C][C]1360.02449325807[/C][C]65.9755067419273[/C][/ROW]
[ROW][C]72[/C][C]1622[/C][C]1523.68683007368[/C][C]98.3131699263233[/C][/ROW]
[ROW][C]73[/C][C]1488[/C][C]1434.79081053426[/C][C]53.2091894657412[/C][/ROW]
[ROW][C]74[/C][C]1540[/C][C]1540.41509695491[/C][C]-0.41509695490663[/C][/ROW]
[ROW][C]75[/C][C]1457[/C][C]1437.72034096295[/C][C]19.2796590370483[/C][/ROW]
[ROW][C]76[/C][C]1395[/C][C]1436.35000884069[/C][C]-41.3500088406868[/C][/ROW]
[ROW][C]77[/C][C]1860[/C][C]1857.43161031617[/C][C]2.56838968382522[/C][/ROW]
[ROW][C]78[/C][C]1746[/C][C]1731.33975413474[/C][C]14.6602458652585[/C][/ROW]
[ROW][C]79[/C][C]1467[/C][C]1550.63547418708[/C][C]-83.6354741870816[/C][/ROW]
[ROW][C]80[/C][C]1426[/C][C]1614.90156039382[/C][C]-188.901560393824[/C][/ROW]
[ROW][C]81[/C][C]1343[/C][C]1374.43616393941[/C][C]-31.436163939411[/C][/ROW]
[ROW][C]82[/C][C]1374[/C][C]1352.3940831289[/C][C]21.6059168710988[/C][/ROW]
[ROW][C]83[/C][C]1354[/C][C]1392.09058155161[/C][C]-38.0905815516098[/C][/ROW]
[ROW][C]84[/C][C]1529[/C][C]1490.30112298868[/C][C]38.6988770113214[/C][/ROW]
[ROW][C]85[/C][C]1343[/C][C]1337.99364560697[/C][C]5.00635439303005[/C][/ROW]
[ROW][C]86[/C][C]1405[/C][C]1383.27085221667[/C][C]21.7291477833339[/C][/ROW]
[ROW][C]87[/C][C]1364[/C][C]1292.36991328265[/C][C]71.6300867173477[/C][/ROW]
[ROW][C]88[/C][C]1323[/C][C]1298.44893420138[/C][C]24.5510657986172[/C][/ROW]
[ROW][C]89[/C][C]1829[/C][C]1772.97776081996[/C][C]56.0222391800357[/C][/ROW]
[ROW][C]90[/C][C]1726[/C][C]1683.45391349796[/C][C]42.5460865020439[/C][/ROW]
[ROW][C]91[/C][C]1447[/C][C]1486.78479587116[/C][C]-39.7847958711639[/C][/ROW]
[ROW][C]92[/C][C]1343[/C][C]1545.09289351788[/C][C]-202.092893517882[/C][/ROW]
[ROW][C]93[/C][C]1188[/C][C]1346.66210080466[/C][C]-158.662100804662[/C][/ROW]
[ROW][C]94[/C][C]1199[/C][C]1251.11987197474[/C][C]-52.1198719747383[/C][/ROW]
[ROW][C]95[/C][C]1178[/C][C]1213.25366840366[/C][C]-35.2536684036556[/C][/ROW]
[ROW][C]96[/C][C]1323[/C][C]1330.34187953403[/C][C]-7.34187953403148[/C][/ROW]
[ROW][C]97[/C][C]1064[/C][C]1126.01558920911[/C][C]-62.0155892091077[/C][/ROW]
[ROW][C]98[/C][C]1054[/C][C]1119.39122363783[/C][C]-65.3912236378285[/C][/ROW]
[ROW][C]99[/C][C]1013[/C][C]970.871484851709[/C][C]42.1285151482914[/C][/ROW]
[ROW][C]100[/C][C]899[/C][C]924.852660150457[/C][C]-25.8526601504575[/C][/ROW]
[ROW][C]101[/C][C]1467[/C][C]1357.34800782171[/C][C]109.651992178286[/C][/ROW]
[ROW][C]102[/C][C]1405[/C][C]1282.63267822963[/C][C]122.367321770365[/C][/ROW]
[ROW][C]103[/C][C]1095[/C][C]1098.53117726752[/C][C]-3.53117726751998[/C][/ROW]
[ROW][C]104[/C][C]1002[/C][C]1115.15603929041[/C][C]-113.156039290414[/C][/ROW]
[ROW][C]105[/C][C]847[/C][C]981.496337220672[/C][C]-134.496337220672[/C][/ROW]
[ROW][C]106[/C][C]816[/C][C]929.040192191474[/C][C]-113.040192191474[/C][/ROW]
[ROW][C]107[/C][C]713[/C][C]845.422428534591[/C][C]-132.422428534591[/C][/ROW]
[ROW][C]108[/C][C]858[/C][C]892.548743459247[/C][C]-34.5487434592468[/C][/ROW]
[ROW][C]109[/C][C]486[/C][C]636.885778465417[/C][C]-150.885778465417[/C][/ROW]
[ROW][C]110[/C][C]444[/C][C]551.273183346434[/C][C]-107.273183346434[/C][/ROW]
[ROW][C]111[/C][C]403[/C][C]390.303660587484[/C][C]12.6963394125158[/C][/ROW]
[ROW][C]112[/C][C]331[/C][C]281.184052636765[/C][C]49.8159473632348[/C][/ROW]
[ROW][C]113[/C][C]940[/C][C]790.92305668614[/C][C]149.07694331386[/C][/ROW]
[ROW][C]114[/C][C]889[/C][C]730.097022034544[/C][C]158.902977965456[/C][/ROW]
[ROW][C]115[/C][C]568[/C][C]513.550660173782[/C][C]54.4493398262179[/C][/ROW]
[ROW][C]116[/C][C]506[/C][C]519.598140704846[/C][C]-13.5981407048464[/C][/ROW]
[ROW][C]117[/C][C]351[/C][C]436.006618787475[/C][C]-85.0066187874747[/C][/ROW]
[ROW][C]118[/C][C]362[/C][C]416.01122118012[/C][C]-54.0112211801202[/C][/ROW]
[ROW][C]119[/C][C]300[/C][C]359.937345749248[/C][C]-59.9373457492482[/C][/ROW]
[ROW][C]120[/C][C]403[/C][C]484.977185703922[/C][C]-81.9771857039218[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169439&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169439&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
1318391943.50747863248-104.507478632478
1418191852.10744587038-33.1074458703802
1517571761.45614285365-4.45614285364627
1616641656.713146792177.28685320783075
1719221913.272425258168.72757474184436
1818391833.575821725285.42417827472241
1916331737.32338475279-104.323384752786
2016741546.87388343011127.126116569893
2116331633.70977136584-0.70977136584429
2217361629.03371240698106.966287593021
2315911711.30548244631-120.305482446306
2416841648.7998093333635.2001906666367
2516021599.459769978512.54023002149165
2615811604.45955648684-23.4595564868443
2714161531.1963081942-115.196308194202
2813541353.533266409910.466733590085596
2916641603.1509864185560.8490135814527
3016021556.3532362057845.6467637942169
3114051451.37965634023-46.3796563402313
3215291378.79853773767150.201462262329
3314261442.43049078308-16.4304907830808
3415091465.6934397545343.3065602454731
3514261430.92036613489-4.92036613489358
3615711501.8793513805269.1206486194781
3714471470.57562736117-23.5756273611682
3814261454.62498419593-28.6249841959348
3912301352.56692263271-122.566922632712
4011681212.79876920505-44.7987692050458
4116121455.01736096008156.982639039919
4215091474.1492450385534.8507549614505
4313331337.7134530246-4.71345302460486
4414981365.58562878469132.414371215309
4513741369.329675561844.67032443816083
4613331434.23252473535-101.232524735351
4713121289.1839585152322.816041484768
4814161406.659901748029.34009825197836
4912401306.01990347649-66.0199034764896
5012401259.71185817746-19.7118581774625
5110951132.70133784216-37.7013378421595
5210441078.64755584275-34.647555842753
5315601397.81511677715162.184883222848
5414261383.8860515696542.113948430351
5513021243.2826026376158.7173973623906
5614051365.254614491839.7453855081994
5712611267.7032546657-6.70325466569966
5811991292.5697472253-93.5697472253048
5912501196.4003896425453.5996103574601
6014051333.9968930707871.0031069292218
6111991256.01099952552-57.0109995255159
6212811237.556650137843.4433498621963
6311781155.7810217783422.2189782216569
6411371153.93880416597-16.9388041659745
6515911561.6287699264329.3712300735747
6614981425.9203833754572.0796166245464
6712501318.80314394873-68.8031439487334
6813741352.3208104850721.6791895149258
6913121229.9215304185882.0784695814182
7013541291.453233862662.5467661373957
7114261360.0244932580765.9755067419273
7216221523.6868300736898.3131699263233
7314881434.7908105342653.2091894657412
7415401540.41509695491-0.41509695490663
7514571437.7203409629519.2796590370483
7613951436.35000884069-41.3500088406868
7718601857.431610316172.56838968382522
7817461731.3397541347414.6602458652585
7914671550.63547418708-83.6354741870816
8014261614.90156039382-188.901560393824
8113431374.43616393941-31.436163939411
8213741352.394083128921.6059168710988
8313541392.09058155161-38.0905815516098
8415291490.3011229886838.6988770113214
8513431337.993645606975.00635439303005
8614051383.2708522166721.7291477833339
8713641292.3699132826571.6300867173477
8813231298.4489342013824.5510657986172
8918291772.9777608199656.0222391800357
9017261683.4539134979642.5460865020439
9114471486.78479587116-39.7847958711639
9213431545.09289351788-202.092893517882
9311881346.66210080466-158.662100804662
9411991251.11987197474-52.1198719747383
9511781213.25366840366-35.2536684036556
9613231330.34187953403-7.34187953403148
9710641126.01558920911-62.0155892091077
9810541119.39122363783-65.3912236378285
991013970.87148485170942.1285151482914
100899924.852660150457-25.8526601504575
10114671357.34800782171109.651992178286
10214051282.63267822963122.367321770365
10310951098.53117726752-3.53117726751998
10410021115.15603929041-113.156039290414
105847981.496337220672-134.496337220672
106816929.040192191474-113.040192191474
107713845.422428534591-132.422428534591
108858892.548743459247-34.5487434592468
109486636.885778465417-150.885778465417
110444551.273183346434-107.273183346434
111403390.30366058748412.6963394125158
112331281.18405263676549.8159473632348
113940790.92305668614149.07694331386
114889730.097022034544158.902977965456
115568513.55066017378254.4493398262179
116506519.598140704846-13.5981407048464
117351436.006618787475-85.0066187874747
118362416.01122118012-54.0112211801202
119300359.937345749248-59.9373457492482
120403484.977185703922-81.9771857039218







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121154.4564418561643.95400075524336304.958882957085
122185.1811902421760.886032135124339369.476348349227
123140.463034138848-75.1398558666208356.065924144317
12439.4078085853153-206.095285787732284.910902958363
125551.016548475084276.449112779989825.583984170179
126390.56760777504287.4303281319577693.704887418126
12724.269799626856-307.162926549684355.702525803396
128-39.4342201631283-399.037729179344320.169288853087
129-147.793841529732-535.549418402173239.961735342708
130-107.799578458563-523.765736956952308.166580039827
131-134.851425668988-579.144277846294309.441426508317
13220.0647269293287-452.714661130127492.844114988785

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 154.456441856164 & 3.95400075524336 & 304.958882957085 \tabularnewline
122 & 185.181190242176 & 0.886032135124339 & 369.476348349227 \tabularnewline
123 & 140.463034138848 & -75.1398558666208 & 356.065924144317 \tabularnewline
124 & 39.4078085853153 & -206.095285787732 & 284.910902958363 \tabularnewline
125 & 551.016548475084 & 276.449112779989 & 825.583984170179 \tabularnewline
126 & 390.567607775042 & 87.4303281319577 & 693.704887418126 \tabularnewline
127 & 24.269799626856 & -307.162926549684 & 355.702525803396 \tabularnewline
128 & -39.4342201631283 & -399.037729179344 & 320.169288853087 \tabularnewline
129 & -147.793841529732 & -535.549418402173 & 239.961735342708 \tabularnewline
130 & -107.799578458563 & -523.765736956952 & 308.166580039827 \tabularnewline
131 & -134.851425668988 & -579.144277846294 & 309.441426508317 \tabularnewline
132 & 20.0647269293287 & -452.714661130127 & 492.844114988785 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169439&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]121[/C][C]154.456441856164[/C][C]3.95400075524336[/C][C]304.958882957085[/C][/ROW]
[ROW][C]122[/C][C]185.181190242176[/C][C]0.886032135124339[/C][C]369.476348349227[/C][/ROW]
[ROW][C]123[/C][C]140.463034138848[/C][C]-75.1398558666208[/C][C]356.065924144317[/C][/ROW]
[ROW][C]124[/C][C]39.4078085853153[/C][C]-206.095285787732[/C][C]284.910902958363[/C][/ROW]
[ROW][C]125[/C][C]551.016548475084[/C][C]276.449112779989[/C][C]825.583984170179[/C][/ROW]
[ROW][C]126[/C][C]390.567607775042[/C][C]87.4303281319577[/C][C]693.704887418126[/C][/ROW]
[ROW][C]127[/C][C]24.269799626856[/C][C]-307.162926549684[/C][C]355.702525803396[/C][/ROW]
[ROW][C]128[/C][C]-39.4342201631283[/C][C]-399.037729179344[/C][C]320.169288853087[/C][/ROW]
[ROW][C]129[/C][C]-147.793841529732[/C][C]-535.549418402173[/C][C]239.961735342708[/C][/ROW]
[ROW][C]130[/C][C]-107.799578458563[/C][C]-523.765736956952[/C][C]308.166580039827[/C][/ROW]
[ROW][C]131[/C][C]-134.851425668988[/C][C]-579.144277846294[/C][C]309.441426508317[/C][/ROW]
[ROW][C]132[/C][C]20.0647269293287[/C][C]-452.714661130127[/C][C]492.844114988785[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169439&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169439&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
121154.4564418561643.95400075524336304.958882957085
122185.1811902421760.886032135124339369.476348349227
123140.463034138848-75.1398558666208356.065924144317
12439.4078085853153-206.095285787732284.910902958363
125551.016548475084276.449112779989825.583984170179
126390.56760777504287.4303281319577693.704887418126
12724.269799626856-307.162926549684355.702525803396
128-39.4342201631283-399.037729179344320.169288853087
129-147.793841529732-535.549418402173239.961735342708
130-107.799578458563-523.765736956952308.166580039827
131-134.851425668988-579.144277846294309.441426508317
13220.0647269293287-452.714661130127492.844114988785



Parameters (Session):
par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; 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')