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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 09:24:54 -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/t13135875257akah9c8zyx1ina.htm/, Retrieved Wed, 15 May 2024 09:12:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=123942, Retrieved Wed, 15 May 2024 09:12:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsAnouk Rosa
Estimated Impact139
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2011-08-17 13:24:54] [14c807ad44ed334b6797e1f02ccdc29d] [Current]
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Dataseries X:
1220
1250
1350
1380
1310
1350
1360
1230
1330
1330
1380
1340
1220
1230
1400
1320
1320
1380
1340
1220
1310
1280
1330
1350
1240
1260
1340
1270
1330
1440
1350
1220
1310
1350
1300
1410
1260
1210
1410
1240
1360
1420
1310
1360
1260
1410
1330
1400
1240
1280
1460
1250
1340
1440
1170
1420
1250
1390
1260
1390
1290
1310
1540
1250
1320
1430
1080
1370
1290
1380
1260
1400
1250
1290
1550
1200
1320
1500
1060
1220
1260
1270
1280
1350
1320
1350
1530
1150
1270
1460
1000
1290
1330
1180
1350
1300
1350
1350
1540
1180
1280
1520
960
1420
1370
1210
1320
1260




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=123942&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=123942&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123942&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
alpha0.0689701132988946
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0689701132988946 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123942&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]0.0689701132988946[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123942&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123942&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
alpha0.0689701132988946
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
21250122030
313501222.06910339897127.930896601033
413801230.89251183197149.107488168031
513101241.1764721846368.8235278153679
613501245.92323869569104.076761304312
713601253.10142471463106.898575285372
812301260.47423156355-30.4742315635506
913301258.3724203599271.6275796400842
1013301263.3125826430266.687417356982
1113801267.91202137374112.08797862626
1213401275.6427419590464.3572580409632
1312201280.08146933773-60.0814693377283
1412301275.93764359034-45.9376435903412
1514001272.76931910723127.230680892769
1613201281.544433583538.4555664164991
1713201284.1967183562235.8032816437799
1813801286.6660747476693.3339252523363
1913401293.1033261469546.8966738530521
2012201296.33779505593-76.3377950559343
2113101291.0727686819418.9272313180613
2212801292.37818197038-12.3781819703797
2313301291.5244573574538.4755426425518
2413501294.1781198927455.8218801072585
2512401298.0281612883-58.0281612882964
2612601294.02595242972-34.025952429716
2713401291.6791786355448.3208213644643
2812701295.01187115974-25.0118711597383
2913301293.2867995720336.7132004279661
3014401295.81891316512144.181086834884
3113501305.7630990596844.2369009403244
3212201308.81412312952-88.8141231295217
3313101302.688602994747.31139700526342
3413501303.1928708745646.8071291254371
3513001306.42116387354-6.42116387354031
3614101305.97829547367104.021704526328
3712601313.1526842204-53.1526842203966
3812101309.48673756758-99.4867375675756
3914101302.6251260058107.374873994198
4012401310.03078323064-70.0307832306369
4113601305.2007521768154.7992478231904
4214201308.98026250787111.019737492131
4313101316.63730638111-6.63730638111497
4413601316.1795306080143.8204693919899
4512601319.20183334679-59.2018333467863
4614101315.1186761933694.8813238066439
4713301321.662651846258.33734815375055
4814001322.2376796930377.7623203069741
4912401327.60095573498-87.6009557349828
5012801321.55910789285-41.5591078928496
5114601318.69277151288141.307228487121
5212501328.43874707159-78.4387470715883
5313401323.0288177990416.9711822009624
5414401324.19932215825115.800677841746
5511701332.18610802909-162.186108029088
5614201321.0001137828298.9998862171849
5712501327.82814715179-77.8281471517921
5813901322.4603310248967.5396689751101
5912601327.11854964627-67.1185496462731
6013901322.4893756727167.5106243272878
6112901327.14559108144-37.1455910814443
6213101324.583655456-14.5836554560026
6315401323.57781908689216.42218091311
6412501338.50448142486-88.5044814248611
6513201332.40031731353-12.4003173135284
6614301331.5450660234798.4549339765279
6710801338.33551397467-258.335513974668
6813701320.5180843067149.4819156932926
6912901323.93085763832-33.93085763832
7013801321.5906425426858.4093574573235
7112601325.61914254422-65.6191425442237
7214001321.0933828483778.9066171516276
7312501326.53558117335-76.5355811733525
7412901321.25691346843-31.2569134684297
7515501319.10112060514230.898879394862
7612001335.02624247759-135.02624247759
7713201325.71346723559-5.71346723558645
7815001325.31940875302174.680591246982
7910601337.36714892244-277.367148922441
8012201318.23710523587-98.2371052358685
8112601311.4616809576-51.4616809575953
8212701307.9123629914-37.9123629913984
8312801305.29754302045-25.2975430204528
8413501303.5527686121546.4472313878514
8513201306.7562394233913.2437605766113
8613501307.6696630908642.3303369091391
8715301310.58919122346219.410808776535
8811501325.72197956378-175.721979563785
8912701313.60241472416-43.6024147241642
9014601310.59515124053149.404848759467
9110001320.89962058688-320.899620586878
9212901298.76713739743-8.76713739742854
9313301298.1624669378231.8375330621791
9411801300.35830520028-120.358305200277
9513501292.0571792541557.9428207458493
9613001296.053502165853.94649783415048
9713501296.325692568653.6743074313952
9813501300.0276156333949.9723843666122
9915401303.47421664497236.525783355031
10011801319.78742672108-139.787426721075
10112801310.14627206236-30.1462720623617
10215201308.06708026268211.932919737319
1039601322.68411774873-362.68411774873
10414201297.66975305589122.33024694411
10513701306.1068840475163.8931159524925
10612101310.51359949377-100.51359949377
10713201303.5811651486116.4188348513949
10812601304.71357404854-44.7135740485417

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 1250 & 1220 & 30 \tabularnewline
3 & 1350 & 1222.06910339897 & 127.930896601033 \tabularnewline
4 & 1380 & 1230.89251183197 & 149.107488168031 \tabularnewline
5 & 1310 & 1241.17647218463 & 68.8235278153679 \tabularnewline
6 & 1350 & 1245.92323869569 & 104.076761304312 \tabularnewline
7 & 1360 & 1253.10142471463 & 106.898575285372 \tabularnewline
8 & 1230 & 1260.47423156355 & -30.4742315635506 \tabularnewline
9 & 1330 & 1258.37242035992 & 71.6275796400842 \tabularnewline
10 & 1330 & 1263.31258264302 & 66.687417356982 \tabularnewline
11 & 1380 & 1267.91202137374 & 112.08797862626 \tabularnewline
12 & 1340 & 1275.64274195904 & 64.3572580409632 \tabularnewline
13 & 1220 & 1280.08146933773 & -60.0814693377283 \tabularnewline
14 & 1230 & 1275.93764359034 & -45.9376435903412 \tabularnewline
15 & 1400 & 1272.76931910723 & 127.230680892769 \tabularnewline
16 & 1320 & 1281.5444335835 & 38.4555664164991 \tabularnewline
17 & 1320 & 1284.19671835622 & 35.8032816437799 \tabularnewline
18 & 1380 & 1286.66607474766 & 93.3339252523363 \tabularnewline
19 & 1340 & 1293.10332614695 & 46.8966738530521 \tabularnewline
20 & 1220 & 1296.33779505593 & -76.3377950559343 \tabularnewline
21 & 1310 & 1291.07276868194 & 18.9272313180613 \tabularnewline
22 & 1280 & 1292.37818197038 & -12.3781819703797 \tabularnewline
23 & 1330 & 1291.52445735745 & 38.4755426425518 \tabularnewline
24 & 1350 & 1294.17811989274 & 55.8218801072585 \tabularnewline
25 & 1240 & 1298.0281612883 & -58.0281612882964 \tabularnewline
26 & 1260 & 1294.02595242972 & -34.025952429716 \tabularnewline
27 & 1340 & 1291.67917863554 & 48.3208213644643 \tabularnewline
28 & 1270 & 1295.01187115974 & -25.0118711597383 \tabularnewline
29 & 1330 & 1293.28679957203 & 36.7132004279661 \tabularnewline
30 & 1440 & 1295.81891316512 & 144.181086834884 \tabularnewline
31 & 1350 & 1305.76309905968 & 44.2369009403244 \tabularnewline
32 & 1220 & 1308.81412312952 & -88.8141231295217 \tabularnewline
33 & 1310 & 1302.68860299474 & 7.31139700526342 \tabularnewline
34 & 1350 & 1303.19287087456 & 46.8071291254371 \tabularnewline
35 & 1300 & 1306.42116387354 & -6.42116387354031 \tabularnewline
36 & 1410 & 1305.97829547367 & 104.021704526328 \tabularnewline
37 & 1260 & 1313.1526842204 & -53.1526842203966 \tabularnewline
38 & 1210 & 1309.48673756758 & -99.4867375675756 \tabularnewline
39 & 1410 & 1302.6251260058 & 107.374873994198 \tabularnewline
40 & 1240 & 1310.03078323064 & -70.0307832306369 \tabularnewline
41 & 1360 & 1305.20075217681 & 54.7992478231904 \tabularnewline
42 & 1420 & 1308.98026250787 & 111.019737492131 \tabularnewline
43 & 1310 & 1316.63730638111 & -6.63730638111497 \tabularnewline
44 & 1360 & 1316.17953060801 & 43.8204693919899 \tabularnewline
45 & 1260 & 1319.20183334679 & -59.2018333467863 \tabularnewline
46 & 1410 & 1315.11867619336 & 94.8813238066439 \tabularnewline
47 & 1330 & 1321.66265184625 & 8.33734815375055 \tabularnewline
48 & 1400 & 1322.23767969303 & 77.7623203069741 \tabularnewline
49 & 1240 & 1327.60095573498 & -87.6009557349828 \tabularnewline
50 & 1280 & 1321.55910789285 & -41.5591078928496 \tabularnewline
51 & 1460 & 1318.69277151288 & 141.307228487121 \tabularnewline
52 & 1250 & 1328.43874707159 & -78.4387470715883 \tabularnewline
53 & 1340 & 1323.02881779904 & 16.9711822009624 \tabularnewline
54 & 1440 & 1324.19932215825 & 115.800677841746 \tabularnewline
55 & 1170 & 1332.18610802909 & -162.186108029088 \tabularnewline
56 & 1420 & 1321.00011378282 & 98.9998862171849 \tabularnewline
57 & 1250 & 1327.82814715179 & -77.8281471517921 \tabularnewline
58 & 1390 & 1322.46033102489 & 67.5396689751101 \tabularnewline
59 & 1260 & 1327.11854964627 & -67.1185496462731 \tabularnewline
60 & 1390 & 1322.48937567271 & 67.5106243272878 \tabularnewline
61 & 1290 & 1327.14559108144 & -37.1455910814443 \tabularnewline
62 & 1310 & 1324.583655456 & -14.5836554560026 \tabularnewline
63 & 1540 & 1323.57781908689 & 216.42218091311 \tabularnewline
64 & 1250 & 1338.50448142486 & -88.5044814248611 \tabularnewline
65 & 1320 & 1332.40031731353 & -12.4003173135284 \tabularnewline
66 & 1430 & 1331.54506602347 & 98.4549339765279 \tabularnewline
67 & 1080 & 1338.33551397467 & -258.335513974668 \tabularnewline
68 & 1370 & 1320.51808430671 & 49.4819156932926 \tabularnewline
69 & 1290 & 1323.93085763832 & -33.93085763832 \tabularnewline
70 & 1380 & 1321.59064254268 & 58.4093574573235 \tabularnewline
71 & 1260 & 1325.61914254422 & -65.6191425442237 \tabularnewline
72 & 1400 & 1321.09338284837 & 78.9066171516276 \tabularnewline
73 & 1250 & 1326.53558117335 & -76.5355811733525 \tabularnewline
74 & 1290 & 1321.25691346843 & -31.2569134684297 \tabularnewline
75 & 1550 & 1319.10112060514 & 230.898879394862 \tabularnewline
76 & 1200 & 1335.02624247759 & -135.02624247759 \tabularnewline
77 & 1320 & 1325.71346723559 & -5.71346723558645 \tabularnewline
78 & 1500 & 1325.31940875302 & 174.680591246982 \tabularnewline
79 & 1060 & 1337.36714892244 & -277.367148922441 \tabularnewline
80 & 1220 & 1318.23710523587 & -98.2371052358685 \tabularnewline
81 & 1260 & 1311.4616809576 & -51.4616809575953 \tabularnewline
82 & 1270 & 1307.9123629914 & -37.9123629913984 \tabularnewline
83 & 1280 & 1305.29754302045 & -25.2975430204528 \tabularnewline
84 & 1350 & 1303.55276861215 & 46.4472313878514 \tabularnewline
85 & 1320 & 1306.75623942339 & 13.2437605766113 \tabularnewline
86 & 1350 & 1307.66966309086 & 42.3303369091391 \tabularnewline
87 & 1530 & 1310.58919122346 & 219.410808776535 \tabularnewline
88 & 1150 & 1325.72197956378 & -175.721979563785 \tabularnewline
89 & 1270 & 1313.60241472416 & -43.6024147241642 \tabularnewline
90 & 1460 & 1310.59515124053 & 149.404848759467 \tabularnewline
91 & 1000 & 1320.89962058688 & -320.899620586878 \tabularnewline
92 & 1290 & 1298.76713739743 & -8.76713739742854 \tabularnewline
93 & 1330 & 1298.16246693782 & 31.8375330621791 \tabularnewline
94 & 1180 & 1300.35830520028 & -120.358305200277 \tabularnewline
95 & 1350 & 1292.05717925415 & 57.9428207458493 \tabularnewline
96 & 1300 & 1296.05350216585 & 3.94649783415048 \tabularnewline
97 & 1350 & 1296.3256925686 & 53.6743074313952 \tabularnewline
98 & 1350 & 1300.02761563339 & 49.9723843666122 \tabularnewline
99 & 1540 & 1303.47421664497 & 236.525783355031 \tabularnewline
100 & 1180 & 1319.78742672108 & -139.787426721075 \tabularnewline
101 & 1280 & 1310.14627206236 & -30.1462720623617 \tabularnewline
102 & 1520 & 1308.06708026268 & 211.932919737319 \tabularnewline
103 & 960 & 1322.68411774873 & -362.68411774873 \tabularnewline
104 & 1420 & 1297.66975305589 & 122.33024694411 \tabularnewline
105 & 1370 & 1306.10688404751 & 63.8931159524925 \tabularnewline
106 & 1210 & 1310.51359949377 & -100.51359949377 \tabularnewline
107 & 1320 & 1303.58116514861 & 16.4188348513949 \tabularnewline
108 & 1260 & 1304.71357404854 & -44.7135740485417 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123942&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]2[/C][C]1250[/C][C]1220[/C][C]30[/C][/ROW]
[ROW][C]3[/C][C]1350[/C][C]1222.06910339897[/C][C]127.930896601033[/C][/ROW]
[ROW][C]4[/C][C]1380[/C][C]1230.89251183197[/C][C]149.107488168031[/C][/ROW]
[ROW][C]5[/C][C]1310[/C][C]1241.17647218463[/C][C]68.8235278153679[/C][/ROW]
[ROW][C]6[/C][C]1350[/C][C]1245.92323869569[/C][C]104.076761304312[/C][/ROW]
[ROW][C]7[/C][C]1360[/C][C]1253.10142471463[/C][C]106.898575285372[/C][/ROW]
[ROW][C]8[/C][C]1230[/C][C]1260.47423156355[/C][C]-30.4742315635506[/C][/ROW]
[ROW][C]9[/C][C]1330[/C][C]1258.37242035992[/C][C]71.6275796400842[/C][/ROW]
[ROW][C]10[/C][C]1330[/C][C]1263.31258264302[/C][C]66.687417356982[/C][/ROW]
[ROW][C]11[/C][C]1380[/C][C]1267.91202137374[/C][C]112.08797862626[/C][/ROW]
[ROW][C]12[/C][C]1340[/C][C]1275.64274195904[/C][C]64.3572580409632[/C][/ROW]
[ROW][C]13[/C][C]1220[/C][C]1280.08146933773[/C][C]-60.0814693377283[/C][/ROW]
[ROW][C]14[/C][C]1230[/C][C]1275.93764359034[/C][C]-45.9376435903412[/C][/ROW]
[ROW][C]15[/C][C]1400[/C][C]1272.76931910723[/C][C]127.230680892769[/C][/ROW]
[ROW][C]16[/C][C]1320[/C][C]1281.5444335835[/C][C]38.4555664164991[/C][/ROW]
[ROW][C]17[/C][C]1320[/C][C]1284.19671835622[/C][C]35.8032816437799[/C][/ROW]
[ROW][C]18[/C][C]1380[/C][C]1286.66607474766[/C][C]93.3339252523363[/C][/ROW]
[ROW][C]19[/C][C]1340[/C][C]1293.10332614695[/C][C]46.8966738530521[/C][/ROW]
[ROW][C]20[/C][C]1220[/C][C]1296.33779505593[/C][C]-76.3377950559343[/C][/ROW]
[ROW][C]21[/C][C]1310[/C][C]1291.07276868194[/C][C]18.9272313180613[/C][/ROW]
[ROW][C]22[/C][C]1280[/C][C]1292.37818197038[/C][C]-12.3781819703797[/C][/ROW]
[ROW][C]23[/C][C]1330[/C][C]1291.52445735745[/C][C]38.4755426425518[/C][/ROW]
[ROW][C]24[/C][C]1350[/C][C]1294.17811989274[/C][C]55.8218801072585[/C][/ROW]
[ROW][C]25[/C][C]1240[/C][C]1298.0281612883[/C][C]-58.0281612882964[/C][/ROW]
[ROW][C]26[/C][C]1260[/C][C]1294.02595242972[/C][C]-34.025952429716[/C][/ROW]
[ROW][C]27[/C][C]1340[/C][C]1291.67917863554[/C][C]48.3208213644643[/C][/ROW]
[ROW][C]28[/C][C]1270[/C][C]1295.01187115974[/C][C]-25.0118711597383[/C][/ROW]
[ROW][C]29[/C][C]1330[/C][C]1293.28679957203[/C][C]36.7132004279661[/C][/ROW]
[ROW][C]30[/C][C]1440[/C][C]1295.81891316512[/C][C]144.181086834884[/C][/ROW]
[ROW][C]31[/C][C]1350[/C][C]1305.76309905968[/C][C]44.2369009403244[/C][/ROW]
[ROW][C]32[/C][C]1220[/C][C]1308.81412312952[/C][C]-88.8141231295217[/C][/ROW]
[ROW][C]33[/C][C]1310[/C][C]1302.68860299474[/C][C]7.31139700526342[/C][/ROW]
[ROW][C]34[/C][C]1350[/C][C]1303.19287087456[/C][C]46.8071291254371[/C][/ROW]
[ROW][C]35[/C][C]1300[/C][C]1306.42116387354[/C][C]-6.42116387354031[/C][/ROW]
[ROW][C]36[/C][C]1410[/C][C]1305.97829547367[/C][C]104.021704526328[/C][/ROW]
[ROW][C]37[/C][C]1260[/C][C]1313.1526842204[/C][C]-53.1526842203966[/C][/ROW]
[ROW][C]38[/C][C]1210[/C][C]1309.48673756758[/C][C]-99.4867375675756[/C][/ROW]
[ROW][C]39[/C][C]1410[/C][C]1302.6251260058[/C][C]107.374873994198[/C][/ROW]
[ROW][C]40[/C][C]1240[/C][C]1310.03078323064[/C][C]-70.0307832306369[/C][/ROW]
[ROW][C]41[/C][C]1360[/C][C]1305.20075217681[/C][C]54.7992478231904[/C][/ROW]
[ROW][C]42[/C][C]1420[/C][C]1308.98026250787[/C][C]111.019737492131[/C][/ROW]
[ROW][C]43[/C][C]1310[/C][C]1316.63730638111[/C][C]-6.63730638111497[/C][/ROW]
[ROW][C]44[/C][C]1360[/C][C]1316.17953060801[/C][C]43.8204693919899[/C][/ROW]
[ROW][C]45[/C][C]1260[/C][C]1319.20183334679[/C][C]-59.2018333467863[/C][/ROW]
[ROW][C]46[/C][C]1410[/C][C]1315.11867619336[/C][C]94.8813238066439[/C][/ROW]
[ROW][C]47[/C][C]1330[/C][C]1321.66265184625[/C][C]8.33734815375055[/C][/ROW]
[ROW][C]48[/C][C]1400[/C][C]1322.23767969303[/C][C]77.7623203069741[/C][/ROW]
[ROW][C]49[/C][C]1240[/C][C]1327.60095573498[/C][C]-87.6009557349828[/C][/ROW]
[ROW][C]50[/C][C]1280[/C][C]1321.55910789285[/C][C]-41.5591078928496[/C][/ROW]
[ROW][C]51[/C][C]1460[/C][C]1318.69277151288[/C][C]141.307228487121[/C][/ROW]
[ROW][C]52[/C][C]1250[/C][C]1328.43874707159[/C][C]-78.4387470715883[/C][/ROW]
[ROW][C]53[/C][C]1340[/C][C]1323.02881779904[/C][C]16.9711822009624[/C][/ROW]
[ROW][C]54[/C][C]1440[/C][C]1324.19932215825[/C][C]115.800677841746[/C][/ROW]
[ROW][C]55[/C][C]1170[/C][C]1332.18610802909[/C][C]-162.186108029088[/C][/ROW]
[ROW][C]56[/C][C]1420[/C][C]1321.00011378282[/C][C]98.9998862171849[/C][/ROW]
[ROW][C]57[/C][C]1250[/C][C]1327.82814715179[/C][C]-77.8281471517921[/C][/ROW]
[ROW][C]58[/C][C]1390[/C][C]1322.46033102489[/C][C]67.5396689751101[/C][/ROW]
[ROW][C]59[/C][C]1260[/C][C]1327.11854964627[/C][C]-67.1185496462731[/C][/ROW]
[ROW][C]60[/C][C]1390[/C][C]1322.48937567271[/C][C]67.5106243272878[/C][/ROW]
[ROW][C]61[/C][C]1290[/C][C]1327.14559108144[/C][C]-37.1455910814443[/C][/ROW]
[ROW][C]62[/C][C]1310[/C][C]1324.583655456[/C][C]-14.5836554560026[/C][/ROW]
[ROW][C]63[/C][C]1540[/C][C]1323.57781908689[/C][C]216.42218091311[/C][/ROW]
[ROW][C]64[/C][C]1250[/C][C]1338.50448142486[/C][C]-88.5044814248611[/C][/ROW]
[ROW][C]65[/C][C]1320[/C][C]1332.40031731353[/C][C]-12.4003173135284[/C][/ROW]
[ROW][C]66[/C][C]1430[/C][C]1331.54506602347[/C][C]98.4549339765279[/C][/ROW]
[ROW][C]67[/C][C]1080[/C][C]1338.33551397467[/C][C]-258.335513974668[/C][/ROW]
[ROW][C]68[/C][C]1370[/C][C]1320.51808430671[/C][C]49.4819156932926[/C][/ROW]
[ROW][C]69[/C][C]1290[/C][C]1323.93085763832[/C][C]-33.93085763832[/C][/ROW]
[ROW][C]70[/C][C]1380[/C][C]1321.59064254268[/C][C]58.4093574573235[/C][/ROW]
[ROW][C]71[/C][C]1260[/C][C]1325.61914254422[/C][C]-65.6191425442237[/C][/ROW]
[ROW][C]72[/C][C]1400[/C][C]1321.09338284837[/C][C]78.9066171516276[/C][/ROW]
[ROW][C]73[/C][C]1250[/C][C]1326.53558117335[/C][C]-76.5355811733525[/C][/ROW]
[ROW][C]74[/C][C]1290[/C][C]1321.25691346843[/C][C]-31.2569134684297[/C][/ROW]
[ROW][C]75[/C][C]1550[/C][C]1319.10112060514[/C][C]230.898879394862[/C][/ROW]
[ROW][C]76[/C][C]1200[/C][C]1335.02624247759[/C][C]-135.02624247759[/C][/ROW]
[ROW][C]77[/C][C]1320[/C][C]1325.71346723559[/C][C]-5.71346723558645[/C][/ROW]
[ROW][C]78[/C][C]1500[/C][C]1325.31940875302[/C][C]174.680591246982[/C][/ROW]
[ROW][C]79[/C][C]1060[/C][C]1337.36714892244[/C][C]-277.367148922441[/C][/ROW]
[ROW][C]80[/C][C]1220[/C][C]1318.23710523587[/C][C]-98.2371052358685[/C][/ROW]
[ROW][C]81[/C][C]1260[/C][C]1311.4616809576[/C][C]-51.4616809575953[/C][/ROW]
[ROW][C]82[/C][C]1270[/C][C]1307.9123629914[/C][C]-37.9123629913984[/C][/ROW]
[ROW][C]83[/C][C]1280[/C][C]1305.29754302045[/C][C]-25.2975430204528[/C][/ROW]
[ROW][C]84[/C][C]1350[/C][C]1303.55276861215[/C][C]46.4472313878514[/C][/ROW]
[ROW][C]85[/C][C]1320[/C][C]1306.75623942339[/C][C]13.2437605766113[/C][/ROW]
[ROW][C]86[/C][C]1350[/C][C]1307.66966309086[/C][C]42.3303369091391[/C][/ROW]
[ROW][C]87[/C][C]1530[/C][C]1310.58919122346[/C][C]219.410808776535[/C][/ROW]
[ROW][C]88[/C][C]1150[/C][C]1325.72197956378[/C][C]-175.721979563785[/C][/ROW]
[ROW][C]89[/C][C]1270[/C][C]1313.60241472416[/C][C]-43.6024147241642[/C][/ROW]
[ROW][C]90[/C][C]1460[/C][C]1310.59515124053[/C][C]149.404848759467[/C][/ROW]
[ROW][C]91[/C][C]1000[/C][C]1320.89962058688[/C][C]-320.899620586878[/C][/ROW]
[ROW][C]92[/C][C]1290[/C][C]1298.76713739743[/C][C]-8.76713739742854[/C][/ROW]
[ROW][C]93[/C][C]1330[/C][C]1298.16246693782[/C][C]31.8375330621791[/C][/ROW]
[ROW][C]94[/C][C]1180[/C][C]1300.35830520028[/C][C]-120.358305200277[/C][/ROW]
[ROW][C]95[/C][C]1350[/C][C]1292.05717925415[/C][C]57.9428207458493[/C][/ROW]
[ROW][C]96[/C][C]1300[/C][C]1296.05350216585[/C][C]3.94649783415048[/C][/ROW]
[ROW][C]97[/C][C]1350[/C][C]1296.3256925686[/C][C]53.6743074313952[/C][/ROW]
[ROW][C]98[/C][C]1350[/C][C]1300.02761563339[/C][C]49.9723843666122[/C][/ROW]
[ROW][C]99[/C][C]1540[/C][C]1303.47421664497[/C][C]236.525783355031[/C][/ROW]
[ROW][C]100[/C][C]1180[/C][C]1319.78742672108[/C][C]-139.787426721075[/C][/ROW]
[ROW][C]101[/C][C]1280[/C][C]1310.14627206236[/C][C]-30.1462720623617[/C][/ROW]
[ROW][C]102[/C][C]1520[/C][C]1308.06708026268[/C][C]211.932919737319[/C][/ROW]
[ROW][C]103[/C][C]960[/C][C]1322.68411774873[/C][C]-362.68411774873[/C][/ROW]
[ROW][C]104[/C][C]1420[/C][C]1297.66975305589[/C][C]122.33024694411[/C][/ROW]
[ROW][C]105[/C][C]1370[/C][C]1306.10688404751[/C][C]63.8931159524925[/C][/ROW]
[ROW][C]106[/C][C]1210[/C][C]1310.51359949377[/C][C]-100.51359949377[/C][/ROW]
[ROW][C]107[/C][C]1320[/C][C]1303.58116514861[/C][C]16.4188348513949[/C][/ROW]
[ROW][C]108[/C][C]1260[/C][C]1304.71357404854[/C][C]-44.7135740485417[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123942&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123942&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
21250122030
313501222.06910339897127.930896601033
413801230.89251183197149.107488168031
513101241.1764721846368.8235278153679
613501245.92323869569104.076761304312
713601253.10142471463106.898575285372
812301260.47423156355-30.4742315635506
913301258.3724203599271.6275796400842
1013301263.3125826430266.687417356982
1113801267.91202137374112.08797862626
1213401275.6427419590464.3572580409632
1312201280.08146933773-60.0814693377283
1412301275.93764359034-45.9376435903412
1514001272.76931910723127.230680892769
1613201281.544433583538.4555664164991
1713201284.1967183562235.8032816437799
1813801286.6660747476693.3339252523363
1913401293.1033261469546.8966738530521
2012201296.33779505593-76.3377950559343
2113101291.0727686819418.9272313180613
2212801292.37818197038-12.3781819703797
2313301291.5244573574538.4755426425518
2413501294.1781198927455.8218801072585
2512401298.0281612883-58.0281612882964
2612601294.02595242972-34.025952429716
2713401291.6791786355448.3208213644643
2812701295.01187115974-25.0118711597383
2913301293.2867995720336.7132004279661
3014401295.81891316512144.181086834884
3113501305.7630990596844.2369009403244
3212201308.81412312952-88.8141231295217
3313101302.688602994747.31139700526342
3413501303.1928708745646.8071291254371
3513001306.42116387354-6.42116387354031
3614101305.97829547367104.021704526328
3712601313.1526842204-53.1526842203966
3812101309.48673756758-99.4867375675756
3914101302.6251260058107.374873994198
4012401310.03078323064-70.0307832306369
4113601305.2007521768154.7992478231904
4214201308.98026250787111.019737492131
4313101316.63730638111-6.63730638111497
4413601316.1795306080143.8204693919899
4512601319.20183334679-59.2018333467863
4614101315.1186761933694.8813238066439
4713301321.662651846258.33734815375055
4814001322.2376796930377.7623203069741
4912401327.60095573498-87.6009557349828
5012801321.55910789285-41.5591078928496
5114601318.69277151288141.307228487121
5212501328.43874707159-78.4387470715883
5313401323.0288177990416.9711822009624
5414401324.19932215825115.800677841746
5511701332.18610802909-162.186108029088
5614201321.0001137828298.9998862171849
5712501327.82814715179-77.8281471517921
5813901322.4603310248967.5396689751101
5912601327.11854964627-67.1185496462731
6013901322.4893756727167.5106243272878
6112901327.14559108144-37.1455910814443
6213101324.583655456-14.5836554560026
6315401323.57781908689216.42218091311
6412501338.50448142486-88.5044814248611
6513201332.40031731353-12.4003173135284
6614301331.5450660234798.4549339765279
6710801338.33551397467-258.335513974668
6813701320.5180843067149.4819156932926
6912901323.93085763832-33.93085763832
7013801321.5906425426858.4093574573235
7112601325.61914254422-65.6191425442237
7214001321.0933828483778.9066171516276
7312501326.53558117335-76.5355811733525
7412901321.25691346843-31.2569134684297
7515501319.10112060514230.898879394862
7612001335.02624247759-135.02624247759
7713201325.71346723559-5.71346723558645
7815001325.31940875302174.680591246982
7910601337.36714892244-277.367148922441
8012201318.23710523587-98.2371052358685
8112601311.4616809576-51.4616809575953
8212701307.9123629914-37.9123629913984
8312801305.29754302045-25.2975430204528
8413501303.5527686121546.4472313878514
8513201306.7562394233913.2437605766113
8613501307.6696630908642.3303369091391
8715301310.58919122346219.410808776535
8811501325.72197956378-175.721979563785
8912701313.60241472416-43.6024147241642
9014601310.59515124053149.404848759467
9110001320.89962058688-320.899620586878
9212901298.76713739743-8.76713739742854
9313301298.1624669378231.8375330621791
9411801300.35830520028-120.358305200277
9513501292.0571792541557.9428207458493
9613001296.053502165853.94649783415048
9713501296.325692568653.6743074313952
9813501300.0276156333949.9723843666122
9915401303.47421664497236.525783355031
10011801319.78742672108-139.787426721075
10112801310.14627206236-30.1462720623617
10215201308.06708026268211.932919737319
1039601322.68411774873-362.68411774873
10414201297.66975305589122.33024694411
10513701306.1068840475163.8931159524925
10612101310.51359949377-100.51359949377
10713201303.5811651486116.4188348513949
10812601304.71357404854-44.7135740485417







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1091301.629673780421091.416919158471511.84242840236
1101301.629673780421090.917534272731512.3418132881
1111301.629673780421090.419330127311512.84001743352
1121301.629673780421089.92229838641513.33704917443
1131301.629673780421089.426430811841513.832916749
1141301.629673780421088.931719261471514.32762829936
1151301.629673780421088.438155687641514.82119187319
1161301.629673780421087.945732135611515.31361542522
1171301.629673780421087.454440742091515.80490681874
1181301.629673780421086.964273733791516.29507382704
1191301.629673780421086.475223425941516.78412413489
1201301.629673780421085.987282220921517.27206533991

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 1301.62967378042 & 1091.41691915847 & 1511.84242840236 \tabularnewline
110 & 1301.62967378042 & 1090.91753427273 & 1512.3418132881 \tabularnewline
111 & 1301.62967378042 & 1090.41933012731 & 1512.84001743352 \tabularnewline
112 & 1301.62967378042 & 1089.9222983864 & 1513.33704917443 \tabularnewline
113 & 1301.62967378042 & 1089.42643081184 & 1513.832916749 \tabularnewline
114 & 1301.62967378042 & 1088.93171926147 & 1514.32762829936 \tabularnewline
115 & 1301.62967378042 & 1088.43815568764 & 1514.82119187319 \tabularnewline
116 & 1301.62967378042 & 1087.94573213561 & 1515.31361542522 \tabularnewline
117 & 1301.62967378042 & 1087.45444074209 & 1515.80490681874 \tabularnewline
118 & 1301.62967378042 & 1086.96427373379 & 1516.29507382704 \tabularnewline
119 & 1301.62967378042 & 1086.47522342594 & 1516.78412413489 \tabularnewline
120 & 1301.62967378042 & 1085.98728222092 & 1517.27206533991 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123942&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]1301.62967378042[/C][C]1091.41691915847[/C][C]1511.84242840236[/C][/ROW]
[ROW][C]110[/C][C]1301.62967378042[/C][C]1090.91753427273[/C][C]1512.3418132881[/C][/ROW]
[ROW][C]111[/C][C]1301.62967378042[/C][C]1090.41933012731[/C][C]1512.84001743352[/C][/ROW]
[ROW][C]112[/C][C]1301.62967378042[/C][C]1089.9222983864[/C][C]1513.33704917443[/C][/ROW]
[ROW][C]113[/C][C]1301.62967378042[/C][C]1089.42643081184[/C][C]1513.832916749[/C][/ROW]
[ROW][C]114[/C][C]1301.62967378042[/C][C]1088.93171926147[/C][C]1514.32762829936[/C][/ROW]
[ROW][C]115[/C][C]1301.62967378042[/C][C]1088.43815568764[/C][C]1514.82119187319[/C][/ROW]
[ROW][C]116[/C][C]1301.62967378042[/C][C]1087.94573213561[/C][C]1515.31361542522[/C][/ROW]
[ROW][C]117[/C][C]1301.62967378042[/C][C]1087.45444074209[/C][C]1515.80490681874[/C][/ROW]
[ROW][C]118[/C][C]1301.62967378042[/C][C]1086.96427373379[/C][C]1516.29507382704[/C][/ROW]
[ROW][C]119[/C][C]1301.62967378042[/C][C]1086.47522342594[/C][C]1516.78412413489[/C][/ROW]
[ROW][C]120[/C][C]1301.62967378042[/C][C]1085.98728222092[/C][C]1517.27206533991[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123942&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123942&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
1091301.629673780421091.416919158471511.84242840236
1101301.629673780421090.917534272731512.3418132881
1111301.629673780421090.419330127311512.84001743352
1121301.629673780421089.92229838641513.33704917443
1131301.629673780421089.426430811841513.832916749
1141301.629673780421088.931719261471514.32762829936
1151301.629673780421088.438155687641514.82119187319
1161301.629673780421087.945732135611515.31361542522
1171301.629673780421087.454440742091515.80490681874
1181301.629673780421086.964273733791516.29507382704
1191301.629673780421086.475223425941516.78412413489
1201301.629673780421085.987282220921517.27206533991



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