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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 10 May 2011 19:33:00 +0000
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/May/10/t1305055746xhts7t0dq5c7ecf.htm/, Retrieved Mon, 13 May 2024 10:51:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=121449, Retrieved Mon, 13 May 2024 10:51:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W101
Estimated Impact75
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Alexander De Raey...] [2011-05-10 19:33:00] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
2435
1379
1511
2021
1614
1680
1630
870
1877
2428
1711
127
3192
1934
2075
1700
1198
1582
1705
911
1817
1168
920
84
2254
1485
1886
1358
1167
1781
1218
779
1418
1641
1196
132
2926
1777
2094
1648
1646
1537
1917
977
1475
2124
1209
135
2917
1981
1398
1171
903
1390
1280
781
1828
1631
1063
186
2275
1342
1070
950
1121
1305
1586
548
1225
1419
880
124
2044
1143
897
1264
1326
1529
1373
587
1137
1426
1016
176
2614




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' @ www.yougetit.org

\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' @ www.yougetit.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121449&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' @ www.yougetit.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121449&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121449&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' @ www.yougetit.org







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.122697358324306
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.122697358324306 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121449&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]0.122697358324306[/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=121449&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121449&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
alpha0.122697358324306
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
213792435-1056
315112305.43158960953-794.431589609533
420212207.95693219506-186.956932195064
516142185.01781049431-571.017810494313
616802114.95543359053-434.955433590532
716302061.58755090017-431.587550900171
88702008.63289851906-1138.63289851906
918771868.925649769638.07435023037397
1024281869.91635121308558.083648786922
1117111938.39174064322-227.391740643224
121271910.49137476153-1783.49137476153
1331921691.661694484111500.33830551589
1419341875.7492411636758.2507588363251
1520751882.89645539328192.103544606721
1617001906.46705284126-206.467052841259
1711981881.13409087663-683.134090876632
1815821797.31534254479-215.315342544793
1917051770.89671880785-65.8967188078536
209111762.81136548789-851.81136548789
2118171658.29636115191158.703638848094
2211681677.76887839502-509.768878395022
239201615.22158366001-695.221583660008
24841529.91973189488-1445.91973189488
2522541352.50920044239901.490799557607
2614851463.1197401017821.8802598982215
2718861465.80439019074420.19560980926
2813581517.36128149381-159.361281493807
2911671497.80807323534-330.808073235341
3017811457.21879653701323.781203462989
3112181496.94589487698-278.945894876984
327791462.71997046017-683.719970460169
3314181378.8293362511339.1706637488664
3416411383.63547321693257.364526783071
3511961415.2134207796-219.213420779597
361321388.31651314071-1256.31651314071
3729261234.169795759141691.83020424086
3817771441.75289255276335.247107447236
3920941482.8868270224611.113172977596
4016481557.8687989839490.1312010160595
4116461568.9276592512177.072340748792
4215371578.38423186096-41.3842318609559
4319171573.30649593534343.693504064664
449771615.47678095729-638.476780957295
4514751537.13736658243-62.1373665824278
4621241529.51327584953594.486724150465
4712091602.45522646167-393.455226461668
481351554.17930955593-1419.17930955593
4929171380.04975728491536.9502427151
5019811568.62949194195412.370508058052
5113981619.22626393152-221.226263931523
5211711592.08238575517-421.082385755169
539031540.41668938611-637.416689386113
5413901462.20734544661-72.2073454466124
5512801453.3476949087-173.347694908703
567811432.0783906718-651.078390671797
5718281352.19279207433475.807207925673
5816311410.57307955847220.426920441529
5910631437.61888040021-374.618880400209
601861391.65413339669-1205.65413339669
6122751243.723556176141031.27644382386
6213421370.25845153541-28.2584515354115
6310701366.79121418168-296.791214181681
649501330.37571622773-380.375716227725
6511211283.70462067587-162.704620675868
6613051263.7411935317841.2588064682195
6715861268.80354009304317.196459906955
685481307.72270779345-759.72270779345
6912251214.506738488210.493261511795
7014191215.79423395591203.205766044091
718801240.72704464579-360.727044645786
721241196.46678919161-1072.46678919161
7320441064.87794726725979.122052732748
7411431185.01363661463-42.0136366146328
758971179.85867438842-282.85867438842
7612641145.15266226185118.847337738154
7713261159.73491664619166.265083353806
7815291180.13520315528348.864796844723
7913731222.93999214047150.06000785953
805871241.35195869496-654.351958694959
8111371161.06470194875-24.0647019487521
8214261158.11202659078267.887973409221
8310161190.98117325494-174.981173254942
841761169.51144554007-993.511445540073
8526141047.610215707341566.38978429266

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 1379 & 2435 & -1056 \tabularnewline
3 & 1511 & 2305.43158960953 & -794.431589609533 \tabularnewline
4 & 2021 & 2207.95693219506 & -186.956932195064 \tabularnewline
5 & 1614 & 2185.01781049431 & -571.017810494313 \tabularnewline
6 & 1680 & 2114.95543359053 & -434.955433590532 \tabularnewline
7 & 1630 & 2061.58755090017 & -431.587550900171 \tabularnewline
8 & 870 & 2008.63289851906 & -1138.63289851906 \tabularnewline
9 & 1877 & 1868.92564976963 & 8.07435023037397 \tabularnewline
10 & 2428 & 1869.91635121308 & 558.083648786922 \tabularnewline
11 & 1711 & 1938.39174064322 & -227.391740643224 \tabularnewline
12 & 127 & 1910.49137476153 & -1783.49137476153 \tabularnewline
13 & 3192 & 1691.66169448411 & 1500.33830551589 \tabularnewline
14 & 1934 & 1875.74924116367 & 58.2507588363251 \tabularnewline
15 & 2075 & 1882.89645539328 & 192.103544606721 \tabularnewline
16 & 1700 & 1906.46705284126 & -206.467052841259 \tabularnewline
17 & 1198 & 1881.13409087663 & -683.134090876632 \tabularnewline
18 & 1582 & 1797.31534254479 & -215.315342544793 \tabularnewline
19 & 1705 & 1770.89671880785 & -65.8967188078536 \tabularnewline
20 & 911 & 1762.81136548789 & -851.81136548789 \tabularnewline
21 & 1817 & 1658.29636115191 & 158.703638848094 \tabularnewline
22 & 1168 & 1677.76887839502 & -509.768878395022 \tabularnewline
23 & 920 & 1615.22158366001 & -695.221583660008 \tabularnewline
24 & 84 & 1529.91973189488 & -1445.91973189488 \tabularnewline
25 & 2254 & 1352.50920044239 & 901.490799557607 \tabularnewline
26 & 1485 & 1463.11974010178 & 21.8802598982215 \tabularnewline
27 & 1886 & 1465.80439019074 & 420.19560980926 \tabularnewline
28 & 1358 & 1517.36128149381 & -159.361281493807 \tabularnewline
29 & 1167 & 1497.80807323534 & -330.808073235341 \tabularnewline
30 & 1781 & 1457.21879653701 & 323.781203462989 \tabularnewline
31 & 1218 & 1496.94589487698 & -278.945894876984 \tabularnewline
32 & 779 & 1462.71997046017 & -683.719970460169 \tabularnewline
33 & 1418 & 1378.82933625113 & 39.1706637488664 \tabularnewline
34 & 1641 & 1383.63547321693 & 257.364526783071 \tabularnewline
35 & 1196 & 1415.2134207796 & -219.213420779597 \tabularnewline
36 & 132 & 1388.31651314071 & -1256.31651314071 \tabularnewline
37 & 2926 & 1234.16979575914 & 1691.83020424086 \tabularnewline
38 & 1777 & 1441.75289255276 & 335.247107447236 \tabularnewline
39 & 2094 & 1482.8868270224 & 611.113172977596 \tabularnewline
40 & 1648 & 1557.86879898394 & 90.1312010160595 \tabularnewline
41 & 1646 & 1568.92765925121 & 77.072340748792 \tabularnewline
42 & 1537 & 1578.38423186096 & -41.3842318609559 \tabularnewline
43 & 1917 & 1573.30649593534 & 343.693504064664 \tabularnewline
44 & 977 & 1615.47678095729 & -638.476780957295 \tabularnewline
45 & 1475 & 1537.13736658243 & -62.1373665824278 \tabularnewline
46 & 2124 & 1529.51327584953 & 594.486724150465 \tabularnewline
47 & 1209 & 1602.45522646167 & -393.455226461668 \tabularnewline
48 & 135 & 1554.17930955593 & -1419.17930955593 \tabularnewline
49 & 2917 & 1380.0497572849 & 1536.9502427151 \tabularnewline
50 & 1981 & 1568.62949194195 & 412.370508058052 \tabularnewline
51 & 1398 & 1619.22626393152 & -221.226263931523 \tabularnewline
52 & 1171 & 1592.08238575517 & -421.082385755169 \tabularnewline
53 & 903 & 1540.41668938611 & -637.416689386113 \tabularnewline
54 & 1390 & 1462.20734544661 & -72.2073454466124 \tabularnewline
55 & 1280 & 1453.3476949087 & -173.347694908703 \tabularnewline
56 & 781 & 1432.0783906718 & -651.078390671797 \tabularnewline
57 & 1828 & 1352.19279207433 & 475.807207925673 \tabularnewline
58 & 1631 & 1410.57307955847 & 220.426920441529 \tabularnewline
59 & 1063 & 1437.61888040021 & -374.618880400209 \tabularnewline
60 & 186 & 1391.65413339669 & -1205.65413339669 \tabularnewline
61 & 2275 & 1243.72355617614 & 1031.27644382386 \tabularnewline
62 & 1342 & 1370.25845153541 & -28.2584515354115 \tabularnewline
63 & 1070 & 1366.79121418168 & -296.791214181681 \tabularnewline
64 & 950 & 1330.37571622773 & -380.375716227725 \tabularnewline
65 & 1121 & 1283.70462067587 & -162.704620675868 \tabularnewline
66 & 1305 & 1263.74119353178 & 41.2588064682195 \tabularnewline
67 & 1586 & 1268.80354009304 & 317.196459906955 \tabularnewline
68 & 548 & 1307.72270779345 & -759.72270779345 \tabularnewline
69 & 1225 & 1214.5067384882 & 10.493261511795 \tabularnewline
70 & 1419 & 1215.79423395591 & 203.205766044091 \tabularnewline
71 & 880 & 1240.72704464579 & -360.727044645786 \tabularnewline
72 & 124 & 1196.46678919161 & -1072.46678919161 \tabularnewline
73 & 2044 & 1064.87794726725 & 979.122052732748 \tabularnewline
74 & 1143 & 1185.01363661463 & -42.0136366146328 \tabularnewline
75 & 897 & 1179.85867438842 & -282.85867438842 \tabularnewline
76 & 1264 & 1145.15266226185 & 118.847337738154 \tabularnewline
77 & 1326 & 1159.73491664619 & 166.265083353806 \tabularnewline
78 & 1529 & 1180.13520315528 & 348.864796844723 \tabularnewline
79 & 1373 & 1222.93999214047 & 150.06000785953 \tabularnewline
80 & 587 & 1241.35195869496 & -654.351958694959 \tabularnewline
81 & 1137 & 1161.06470194875 & -24.0647019487521 \tabularnewline
82 & 1426 & 1158.11202659078 & 267.887973409221 \tabularnewline
83 & 1016 & 1190.98117325494 & -174.981173254942 \tabularnewline
84 & 176 & 1169.51144554007 & -993.511445540073 \tabularnewline
85 & 2614 & 1047.61021570734 & 1566.38978429266 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121449&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]1379[/C][C]2435[/C][C]-1056[/C][/ROW]
[ROW][C]3[/C][C]1511[/C][C]2305.43158960953[/C][C]-794.431589609533[/C][/ROW]
[ROW][C]4[/C][C]2021[/C][C]2207.95693219506[/C][C]-186.956932195064[/C][/ROW]
[ROW][C]5[/C][C]1614[/C][C]2185.01781049431[/C][C]-571.017810494313[/C][/ROW]
[ROW][C]6[/C][C]1680[/C][C]2114.95543359053[/C][C]-434.955433590532[/C][/ROW]
[ROW][C]7[/C][C]1630[/C][C]2061.58755090017[/C][C]-431.587550900171[/C][/ROW]
[ROW][C]8[/C][C]870[/C][C]2008.63289851906[/C][C]-1138.63289851906[/C][/ROW]
[ROW][C]9[/C][C]1877[/C][C]1868.92564976963[/C][C]8.07435023037397[/C][/ROW]
[ROW][C]10[/C][C]2428[/C][C]1869.91635121308[/C][C]558.083648786922[/C][/ROW]
[ROW][C]11[/C][C]1711[/C][C]1938.39174064322[/C][C]-227.391740643224[/C][/ROW]
[ROW][C]12[/C][C]127[/C][C]1910.49137476153[/C][C]-1783.49137476153[/C][/ROW]
[ROW][C]13[/C][C]3192[/C][C]1691.66169448411[/C][C]1500.33830551589[/C][/ROW]
[ROW][C]14[/C][C]1934[/C][C]1875.74924116367[/C][C]58.2507588363251[/C][/ROW]
[ROW][C]15[/C][C]2075[/C][C]1882.89645539328[/C][C]192.103544606721[/C][/ROW]
[ROW][C]16[/C][C]1700[/C][C]1906.46705284126[/C][C]-206.467052841259[/C][/ROW]
[ROW][C]17[/C][C]1198[/C][C]1881.13409087663[/C][C]-683.134090876632[/C][/ROW]
[ROW][C]18[/C][C]1582[/C][C]1797.31534254479[/C][C]-215.315342544793[/C][/ROW]
[ROW][C]19[/C][C]1705[/C][C]1770.89671880785[/C][C]-65.8967188078536[/C][/ROW]
[ROW][C]20[/C][C]911[/C][C]1762.81136548789[/C][C]-851.81136548789[/C][/ROW]
[ROW][C]21[/C][C]1817[/C][C]1658.29636115191[/C][C]158.703638848094[/C][/ROW]
[ROW][C]22[/C][C]1168[/C][C]1677.76887839502[/C][C]-509.768878395022[/C][/ROW]
[ROW][C]23[/C][C]920[/C][C]1615.22158366001[/C][C]-695.221583660008[/C][/ROW]
[ROW][C]24[/C][C]84[/C][C]1529.91973189488[/C][C]-1445.91973189488[/C][/ROW]
[ROW][C]25[/C][C]2254[/C][C]1352.50920044239[/C][C]901.490799557607[/C][/ROW]
[ROW][C]26[/C][C]1485[/C][C]1463.11974010178[/C][C]21.8802598982215[/C][/ROW]
[ROW][C]27[/C][C]1886[/C][C]1465.80439019074[/C][C]420.19560980926[/C][/ROW]
[ROW][C]28[/C][C]1358[/C][C]1517.36128149381[/C][C]-159.361281493807[/C][/ROW]
[ROW][C]29[/C][C]1167[/C][C]1497.80807323534[/C][C]-330.808073235341[/C][/ROW]
[ROW][C]30[/C][C]1781[/C][C]1457.21879653701[/C][C]323.781203462989[/C][/ROW]
[ROW][C]31[/C][C]1218[/C][C]1496.94589487698[/C][C]-278.945894876984[/C][/ROW]
[ROW][C]32[/C][C]779[/C][C]1462.71997046017[/C][C]-683.719970460169[/C][/ROW]
[ROW][C]33[/C][C]1418[/C][C]1378.82933625113[/C][C]39.1706637488664[/C][/ROW]
[ROW][C]34[/C][C]1641[/C][C]1383.63547321693[/C][C]257.364526783071[/C][/ROW]
[ROW][C]35[/C][C]1196[/C][C]1415.2134207796[/C][C]-219.213420779597[/C][/ROW]
[ROW][C]36[/C][C]132[/C][C]1388.31651314071[/C][C]-1256.31651314071[/C][/ROW]
[ROW][C]37[/C][C]2926[/C][C]1234.16979575914[/C][C]1691.83020424086[/C][/ROW]
[ROW][C]38[/C][C]1777[/C][C]1441.75289255276[/C][C]335.247107447236[/C][/ROW]
[ROW][C]39[/C][C]2094[/C][C]1482.8868270224[/C][C]611.113172977596[/C][/ROW]
[ROW][C]40[/C][C]1648[/C][C]1557.86879898394[/C][C]90.1312010160595[/C][/ROW]
[ROW][C]41[/C][C]1646[/C][C]1568.92765925121[/C][C]77.072340748792[/C][/ROW]
[ROW][C]42[/C][C]1537[/C][C]1578.38423186096[/C][C]-41.3842318609559[/C][/ROW]
[ROW][C]43[/C][C]1917[/C][C]1573.30649593534[/C][C]343.693504064664[/C][/ROW]
[ROW][C]44[/C][C]977[/C][C]1615.47678095729[/C][C]-638.476780957295[/C][/ROW]
[ROW][C]45[/C][C]1475[/C][C]1537.13736658243[/C][C]-62.1373665824278[/C][/ROW]
[ROW][C]46[/C][C]2124[/C][C]1529.51327584953[/C][C]594.486724150465[/C][/ROW]
[ROW][C]47[/C][C]1209[/C][C]1602.45522646167[/C][C]-393.455226461668[/C][/ROW]
[ROW][C]48[/C][C]135[/C][C]1554.17930955593[/C][C]-1419.17930955593[/C][/ROW]
[ROW][C]49[/C][C]2917[/C][C]1380.0497572849[/C][C]1536.9502427151[/C][/ROW]
[ROW][C]50[/C][C]1981[/C][C]1568.62949194195[/C][C]412.370508058052[/C][/ROW]
[ROW][C]51[/C][C]1398[/C][C]1619.22626393152[/C][C]-221.226263931523[/C][/ROW]
[ROW][C]52[/C][C]1171[/C][C]1592.08238575517[/C][C]-421.082385755169[/C][/ROW]
[ROW][C]53[/C][C]903[/C][C]1540.41668938611[/C][C]-637.416689386113[/C][/ROW]
[ROW][C]54[/C][C]1390[/C][C]1462.20734544661[/C][C]-72.2073454466124[/C][/ROW]
[ROW][C]55[/C][C]1280[/C][C]1453.3476949087[/C][C]-173.347694908703[/C][/ROW]
[ROW][C]56[/C][C]781[/C][C]1432.0783906718[/C][C]-651.078390671797[/C][/ROW]
[ROW][C]57[/C][C]1828[/C][C]1352.19279207433[/C][C]475.807207925673[/C][/ROW]
[ROW][C]58[/C][C]1631[/C][C]1410.57307955847[/C][C]220.426920441529[/C][/ROW]
[ROW][C]59[/C][C]1063[/C][C]1437.61888040021[/C][C]-374.618880400209[/C][/ROW]
[ROW][C]60[/C][C]186[/C][C]1391.65413339669[/C][C]-1205.65413339669[/C][/ROW]
[ROW][C]61[/C][C]2275[/C][C]1243.72355617614[/C][C]1031.27644382386[/C][/ROW]
[ROW][C]62[/C][C]1342[/C][C]1370.25845153541[/C][C]-28.2584515354115[/C][/ROW]
[ROW][C]63[/C][C]1070[/C][C]1366.79121418168[/C][C]-296.791214181681[/C][/ROW]
[ROW][C]64[/C][C]950[/C][C]1330.37571622773[/C][C]-380.375716227725[/C][/ROW]
[ROW][C]65[/C][C]1121[/C][C]1283.70462067587[/C][C]-162.704620675868[/C][/ROW]
[ROW][C]66[/C][C]1305[/C][C]1263.74119353178[/C][C]41.2588064682195[/C][/ROW]
[ROW][C]67[/C][C]1586[/C][C]1268.80354009304[/C][C]317.196459906955[/C][/ROW]
[ROW][C]68[/C][C]548[/C][C]1307.72270779345[/C][C]-759.72270779345[/C][/ROW]
[ROW][C]69[/C][C]1225[/C][C]1214.5067384882[/C][C]10.493261511795[/C][/ROW]
[ROW][C]70[/C][C]1419[/C][C]1215.79423395591[/C][C]203.205766044091[/C][/ROW]
[ROW][C]71[/C][C]880[/C][C]1240.72704464579[/C][C]-360.727044645786[/C][/ROW]
[ROW][C]72[/C][C]124[/C][C]1196.46678919161[/C][C]-1072.46678919161[/C][/ROW]
[ROW][C]73[/C][C]2044[/C][C]1064.87794726725[/C][C]979.122052732748[/C][/ROW]
[ROW][C]74[/C][C]1143[/C][C]1185.01363661463[/C][C]-42.0136366146328[/C][/ROW]
[ROW][C]75[/C][C]897[/C][C]1179.85867438842[/C][C]-282.85867438842[/C][/ROW]
[ROW][C]76[/C][C]1264[/C][C]1145.15266226185[/C][C]118.847337738154[/C][/ROW]
[ROW][C]77[/C][C]1326[/C][C]1159.73491664619[/C][C]166.265083353806[/C][/ROW]
[ROW][C]78[/C][C]1529[/C][C]1180.13520315528[/C][C]348.864796844723[/C][/ROW]
[ROW][C]79[/C][C]1373[/C][C]1222.93999214047[/C][C]150.06000785953[/C][/ROW]
[ROW][C]80[/C][C]587[/C][C]1241.35195869496[/C][C]-654.351958694959[/C][/ROW]
[ROW][C]81[/C][C]1137[/C][C]1161.06470194875[/C][C]-24.0647019487521[/C][/ROW]
[ROW][C]82[/C][C]1426[/C][C]1158.11202659078[/C][C]267.887973409221[/C][/ROW]
[ROW][C]83[/C][C]1016[/C][C]1190.98117325494[/C][C]-174.981173254942[/C][/ROW]
[ROW][C]84[/C][C]176[/C][C]1169.51144554007[/C][C]-993.511445540073[/C][/ROW]
[ROW][C]85[/C][C]2614[/C][C]1047.61021570734[/C][C]1566.38978429266[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121449&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121449&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
213792435-1056
315112305.43158960953-794.431589609533
420212207.95693219506-186.956932195064
516142185.01781049431-571.017810494313
616802114.95543359053-434.955433590532
716302061.58755090017-431.587550900171
88702008.63289851906-1138.63289851906
918771868.925649769638.07435023037397
1024281869.91635121308558.083648786922
1117111938.39174064322-227.391740643224
121271910.49137476153-1783.49137476153
1331921691.661694484111500.33830551589
1419341875.7492411636758.2507588363251
1520751882.89645539328192.103544606721
1617001906.46705284126-206.467052841259
1711981881.13409087663-683.134090876632
1815821797.31534254479-215.315342544793
1917051770.89671880785-65.8967188078536
209111762.81136548789-851.81136548789
2118171658.29636115191158.703638848094
2211681677.76887839502-509.768878395022
239201615.22158366001-695.221583660008
24841529.91973189488-1445.91973189488
2522541352.50920044239901.490799557607
2614851463.1197401017821.8802598982215
2718861465.80439019074420.19560980926
2813581517.36128149381-159.361281493807
2911671497.80807323534-330.808073235341
3017811457.21879653701323.781203462989
3112181496.94589487698-278.945894876984
327791462.71997046017-683.719970460169
3314181378.8293362511339.1706637488664
3416411383.63547321693257.364526783071
3511961415.2134207796-219.213420779597
361321388.31651314071-1256.31651314071
3729261234.169795759141691.83020424086
3817771441.75289255276335.247107447236
3920941482.8868270224611.113172977596
4016481557.8687989839490.1312010160595
4116461568.9276592512177.072340748792
4215371578.38423186096-41.3842318609559
4319171573.30649593534343.693504064664
449771615.47678095729-638.476780957295
4514751537.13736658243-62.1373665824278
4621241529.51327584953594.486724150465
4712091602.45522646167-393.455226461668
481351554.17930955593-1419.17930955593
4929171380.04975728491536.9502427151
5019811568.62949194195412.370508058052
5113981619.22626393152-221.226263931523
5211711592.08238575517-421.082385755169
539031540.41668938611-637.416689386113
5413901462.20734544661-72.2073454466124
5512801453.3476949087-173.347694908703
567811432.0783906718-651.078390671797
5718281352.19279207433475.807207925673
5816311410.57307955847220.426920441529
5910631437.61888040021-374.618880400209
601861391.65413339669-1205.65413339669
6122751243.723556176141031.27644382386
6213421370.25845153541-28.2584515354115
6310701366.79121418168-296.791214181681
649501330.37571622773-380.375716227725
6511211283.70462067587-162.704620675868
6613051263.7411935317841.2588064682195
6715861268.80354009304317.196459906955
685481307.72270779345-759.72270779345
6912251214.506738488210.493261511795
7014191215.79423395591203.205766044091
718801240.72704464579-360.727044645786
721241196.46678919161-1072.46678919161
7320441064.87794726725979.122052732748
7411431185.01363661463-42.0136366146328
758971179.85867438842-282.85867438842
7612641145.15266226185118.847337738154
7713261159.73491664619166.265083353806
7815291180.13520315528348.864796844723
7913731222.93999214047150.06000785953
805871241.35195869496-654.351958694959
8111371161.06470194875-24.0647019487521
8214261158.11202659078267.887973409221
8310161190.98117325494-174.981173254942
841761169.51144554007-993.511445540073
8526141047.610215707341566.38978429266







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
861239.80210434623-60.4729311545122540.07713984698
871239.80210434623-70.22395611358912549.82816480605
881239.80210434623-79.90293475201162559.50714344448
891239.80210434623-89.51144081860752569.11564951107
901239.80210434623-99.05099158928972578.65520028175
911239.80210434623-108.5230506640682588.12725935653
921239.80210434623-117.929030588432597.5332392809
931239.80210434623-127.270295312392606.87450400485
941239.80210434623-136.5481624993132616.15237119178
951239.80210434623-145.7639056955922625.36811438806
961239.80210434623-154.9187563712942634.52296506376
971239.80210434623-164.013905841022643.61811453348

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
86 & 1239.80210434623 & -60.472931154512 & 2540.07713984698 \tabularnewline
87 & 1239.80210434623 & -70.2239561135891 & 2549.82816480605 \tabularnewline
88 & 1239.80210434623 & -79.9029347520116 & 2559.50714344448 \tabularnewline
89 & 1239.80210434623 & -89.5114408186075 & 2569.11564951107 \tabularnewline
90 & 1239.80210434623 & -99.0509915892897 & 2578.65520028175 \tabularnewline
91 & 1239.80210434623 & -108.523050664068 & 2588.12725935653 \tabularnewline
92 & 1239.80210434623 & -117.92903058843 & 2597.5332392809 \tabularnewline
93 & 1239.80210434623 & -127.27029531239 & 2606.87450400485 \tabularnewline
94 & 1239.80210434623 & -136.548162499313 & 2616.15237119178 \tabularnewline
95 & 1239.80210434623 & -145.763905695592 & 2625.36811438806 \tabularnewline
96 & 1239.80210434623 & -154.918756371294 & 2634.52296506376 \tabularnewline
97 & 1239.80210434623 & -164.01390584102 & 2643.61811453348 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121449&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]86[/C][C]1239.80210434623[/C][C]-60.472931154512[/C][C]2540.07713984698[/C][/ROW]
[ROW][C]87[/C][C]1239.80210434623[/C][C]-70.2239561135891[/C][C]2549.82816480605[/C][/ROW]
[ROW][C]88[/C][C]1239.80210434623[/C][C]-79.9029347520116[/C][C]2559.50714344448[/C][/ROW]
[ROW][C]89[/C][C]1239.80210434623[/C][C]-89.5114408186075[/C][C]2569.11564951107[/C][/ROW]
[ROW][C]90[/C][C]1239.80210434623[/C][C]-99.0509915892897[/C][C]2578.65520028175[/C][/ROW]
[ROW][C]91[/C][C]1239.80210434623[/C][C]-108.523050664068[/C][C]2588.12725935653[/C][/ROW]
[ROW][C]92[/C][C]1239.80210434623[/C][C]-117.92903058843[/C][C]2597.5332392809[/C][/ROW]
[ROW][C]93[/C][C]1239.80210434623[/C][C]-127.27029531239[/C][C]2606.87450400485[/C][/ROW]
[ROW][C]94[/C][C]1239.80210434623[/C][C]-136.548162499313[/C][C]2616.15237119178[/C][/ROW]
[ROW][C]95[/C][C]1239.80210434623[/C][C]-145.763905695592[/C][C]2625.36811438806[/C][/ROW]
[ROW][C]96[/C][C]1239.80210434623[/C][C]-154.918756371294[/C][C]2634.52296506376[/C][/ROW]
[ROW][C]97[/C][C]1239.80210434623[/C][C]-164.01390584102[/C][C]2643.61811453348[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121449&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121449&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
861239.80210434623-60.4729311545122540.07713984698
871239.80210434623-70.22395611358912549.82816480605
881239.80210434623-79.90293475201162559.50714344448
891239.80210434623-89.51144081860752569.11564951107
901239.80210434623-99.05099158928972578.65520028175
911239.80210434623-108.5230506640682588.12725935653
921239.80210434623-117.929030588432597.5332392809
931239.80210434623-127.270295312392606.87450400485
941239.80210434623-136.5481624993132616.15237119178
951239.80210434623-145.7639056955922625.36811438806
961239.80210434623-154.9187563712942634.52296506376
971239.80210434623-164.013905841022643.61811453348



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')