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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, 18 Aug 2011 17:04:11 -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/18/t13137014705bo382dxpnanemn.htm/, Retrieved Wed, 15 May 2024 04:22:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=124163, Retrieved Wed, 15 May 2024 04:22:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsGregory Goris
Estimated Impact96
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks B - Sta...] [2011-08-18 21:04:11] [4069dbe0e58b4004934f5f5b0dc60f40] [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'AstonUniversity' @ aston.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 & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124163&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124163&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124163&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'AstonUniversity' @ aston.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.014029072016702
beta0.0667812856950594
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.014029072016702 \tabularnewline
beta & 0.0667812856950594 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124163&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]0.014029072016702[/C][/ROW]
[ROW][C]beta[/C][C]0.0667812856950594[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124163&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124163&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
alpha0.014029072016702
beta0.0667812856950594
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1312201218.544337606841.4556623931619
1412301228.931798970271.06820102973415
1514001399.314825385930.685174614066682
1613201321.35978688912-1.35978688912405
1713201324.6247855237-4.62478552370021
1813801385.3396463907-5.3396463907045
1913401353.1228091514-13.1228091513954
2012201222.8678202041-2.86782020409669
2113101320.67067910007-10.6706791000743
2212801320.02074065319-40.0207406531897
2313301370.5882201356-40.5882201356012
2413501327.3597121374622.6402878625363
2512401207.7246934529732.2753065470317
2612601218.1044834374541.8955165625509
2713401388.66285981981-48.6628598198133
2812701307.93324197023-37.9332419702257
2913301307.3656906840622.6343093159392
3014401367.6834132575872.3165867424227
3113501328.8800771602121.11992283979
3212201209.2467127119410.7532872880586
3313101299.5901421922510.4098578077469
3413501270.3602577250579.6397422749546
3513001322.22167295266-22.2216729526556
3614101341.7842369990268.2157630009758
3712601232.5230827032127.476917296787
3812101252.55094207566-42.5509420756568
3914101332.7877093966777.212290603334
4012401264.67204699612-24.6720469961176
4113601324.2897594884135.7102405115857
4214201434.06983376416-14.0698337641611
4313101343.78884781425-33.7888478142547
4413601213.32521377312146.674786226883
4512601305.52547710865-45.5254771086463
4614101344.0057134065965.9942865934147
4713301295.466705483534.5332945165001
4814001405.27074829849-5.27074829848857
4912401255.01905752704-15.0190575270383
5012801205.5732192994774.4267807005251
5114601405.8116501882954.1883498117134
5212501237.1739267248512.8260732751517
5313401357.14395266404-17.1439526640352
5414401417.3423771896922.6576228103086
5511701308.41022955218-138.41022955218
5614201354.5886944716565.4113055283549
5712501256.24684363484-6.24684363484016
5813901405.37197601175-15.3719760117488
5912601324.73422939225-64.7342293922522
6013901393.86938824355-3.86938824355252
6112901233.9964969722856.0035030277181
6213101273.7752642770536.2247357229508
6315401453.5246895238386.475310476173
6412501244.589607049485.41039295051678
6513201334.93076306276-14.9307630627616
6614301434.43024585661-4.43024585661169
6710801166.31129559499-86.3112955949864
6813701414.23301361702-44.2330136170235
6912901243.6476247112546.3523752887506
7013801384.51036101753-4.51036101753061
7112601255.362222964854.63777703515416
7214001385.5535407683214.4464592316751
7312501285.05966391864-35.0596639186435
7412901304.06342464168-14.0634246416832
7515501532.6096602406817.3903397593224
7612001242.66970424115-42.6697042411454
7713201312.127483845827.87251615418313
7815001422.1683753122777.8316246877348
7910601074.41651275152-14.4165127515173
8012201364.84753192481-144.847531924806
8112601282.08363231606-22.0836323160577
8212701371.69143699629-101.691436996293
8312801249.9630312094130.0369687905882
8413501389.96884198626-39.968841986255
8513201239.636080590780.3639194093025
8613501280.8050564029969.194943597013
8715301541.45407777888-11.4540777788825
8811501191.78723116592-41.7872311659164
8912701310.98660488068-40.9866048806837
9014601489.16997416018-29.1699741601806
9110001048.71302796576-48.7130279657608
9212901209.779605322480.2203946776024
9313301251.1435968809778.8564031190288
9411801263.69984517523-83.6998451752252
9513501272.1444088169177.8555911830906
9613001343.88236215636-43.8823621563602
9713501312.2206215089737.7793784910295
9813501341.821313086188.17868691381614
9915401522.0810004804717.9189995195266
10011801142.9304004481237.0695995518806
10112801264.1111128644515.8888871355482
10215201454.8821886581765.1178113418316
103960996.706407774312-36.7064077743119
10414201285.30456007173134.695439928275
10513701326.3774933214843.6225066785155
10612101178.420261231931.5797387680998
10713201348.13561050775-28.1356105077496
10812601298.62177838219-38.6217783821889

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1220 & 1218.54433760684 & 1.4556623931619 \tabularnewline
14 & 1230 & 1228.93179897027 & 1.06820102973415 \tabularnewline
15 & 1400 & 1399.31482538593 & 0.685174614066682 \tabularnewline
16 & 1320 & 1321.35978688912 & -1.35978688912405 \tabularnewline
17 & 1320 & 1324.6247855237 & -4.62478552370021 \tabularnewline
18 & 1380 & 1385.3396463907 & -5.3396463907045 \tabularnewline
19 & 1340 & 1353.1228091514 & -13.1228091513954 \tabularnewline
20 & 1220 & 1222.8678202041 & -2.86782020409669 \tabularnewline
21 & 1310 & 1320.67067910007 & -10.6706791000743 \tabularnewline
22 & 1280 & 1320.02074065319 & -40.0207406531897 \tabularnewline
23 & 1330 & 1370.5882201356 & -40.5882201356012 \tabularnewline
24 & 1350 & 1327.35971213746 & 22.6402878625363 \tabularnewline
25 & 1240 & 1207.72469345297 & 32.2753065470317 \tabularnewline
26 & 1260 & 1218.10448343745 & 41.8955165625509 \tabularnewline
27 & 1340 & 1388.66285981981 & -48.6628598198133 \tabularnewline
28 & 1270 & 1307.93324197023 & -37.9332419702257 \tabularnewline
29 & 1330 & 1307.36569068406 & 22.6343093159392 \tabularnewline
30 & 1440 & 1367.68341325758 & 72.3165867424227 \tabularnewline
31 & 1350 & 1328.88007716021 & 21.11992283979 \tabularnewline
32 & 1220 & 1209.24671271194 & 10.7532872880586 \tabularnewline
33 & 1310 & 1299.59014219225 & 10.4098578077469 \tabularnewline
34 & 1350 & 1270.36025772505 & 79.6397422749546 \tabularnewline
35 & 1300 & 1322.22167295266 & -22.2216729526556 \tabularnewline
36 & 1410 & 1341.78423699902 & 68.2157630009758 \tabularnewline
37 & 1260 & 1232.52308270321 & 27.476917296787 \tabularnewline
38 & 1210 & 1252.55094207566 & -42.5509420756568 \tabularnewline
39 & 1410 & 1332.78770939667 & 77.212290603334 \tabularnewline
40 & 1240 & 1264.67204699612 & -24.6720469961176 \tabularnewline
41 & 1360 & 1324.28975948841 & 35.7102405115857 \tabularnewline
42 & 1420 & 1434.06983376416 & -14.0698337641611 \tabularnewline
43 & 1310 & 1343.78884781425 & -33.7888478142547 \tabularnewline
44 & 1360 & 1213.32521377312 & 146.674786226883 \tabularnewline
45 & 1260 & 1305.52547710865 & -45.5254771086463 \tabularnewline
46 & 1410 & 1344.00571340659 & 65.9942865934147 \tabularnewline
47 & 1330 & 1295.4667054835 & 34.5332945165001 \tabularnewline
48 & 1400 & 1405.27074829849 & -5.27074829848857 \tabularnewline
49 & 1240 & 1255.01905752704 & -15.0190575270383 \tabularnewline
50 & 1280 & 1205.57321929947 & 74.4267807005251 \tabularnewline
51 & 1460 & 1405.81165018829 & 54.1883498117134 \tabularnewline
52 & 1250 & 1237.17392672485 & 12.8260732751517 \tabularnewline
53 & 1340 & 1357.14395266404 & -17.1439526640352 \tabularnewline
54 & 1440 & 1417.34237718969 & 22.6576228103086 \tabularnewline
55 & 1170 & 1308.41022955218 & -138.41022955218 \tabularnewline
56 & 1420 & 1354.58869447165 & 65.4113055283549 \tabularnewline
57 & 1250 & 1256.24684363484 & -6.24684363484016 \tabularnewline
58 & 1390 & 1405.37197601175 & -15.3719760117488 \tabularnewline
59 & 1260 & 1324.73422939225 & -64.7342293922522 \tabularnewline
60 & 1390 & 1393.86938824355 & -3.86938824355252 \tabularnewline
61 & 1290 & 1233.99649697228 & 56.0035030277181 \tabularnewline
62 & 1310 & 1273.77526427705 & 36.2247357229508 \tabularnewline
63 & 1540 & 1453.52468952383 & 86.475310476173 \tabularnewline
64 & 1250 & 1244.58960704948 & 5.41039295051678 \tabularnewline
65 & 1320 & 1334.93076306276 & -14.9307630627616 \tabularnewline
66 & 1430 & 1434.43024585661 & -4.43024585661169 \tabularnewline
67 & 1080 & 1166.31129559499 & -86.3112955949864 \tabularnewline
68 & 1370 & 1414.23301361702 & -44.2330136170235 \tabularnewline
69 & 1290 & 1243.64762471125 & 46.3523752887506 \tabularnewline
70 & 1380 & 1384.51036101753 & -4.51036101753061 \tabularnewline
71 & 1260 & 1255.36222296485 & 4.63777703515416 \tabularnewline
72 & 1400 & 1385.55354076832 & 14.4464592316751 \tabularnewline
73 & 1250 & 1285.05966391864 & -35.0596639186435 \tabularnewline
74 & 1290 & 1304.06342464168 & -14.0634246416832 \tabularnewline
75 & 1550 & 1532.60966024068 & 17.3903397593224 \tabularnewline
76 & 1200 & 1242.66970424115 & -42.6697042411454 \tabularnewline
77 & 1320 & 1312.12748384582 & 7.87251615418313 \tabularnewline
78 & 1500 & 1422.16837531227 & 77.8316246877348 \tabularnewline
79 & 1060 & 1074.41651275152 & -14.4165127515173 \tabularnewline
80 & 1220 & 1364.84753192481 & -144.847531924806 \tabularnewline
81 & 1260 & 1282.08363231606 & -22.0836323160577 \tabularnewline
82 & 1270 & 1371.69143699629 & -101.691436996293 \tabularnewline
83 & 1280 & 1249.96303120941 & 30.0369687905882 \tabularnewline
84 & 1350 & 1389.96884198626 & -39.968841986255 \tabularnewline
85 & 1320 & 1239.6360805907 & 80.3639194093025 \tabularnewline
86 & 1350 & 1280.80505640299 & 69.194943597013 \tabularnewline
87 & 1530 & 1541.45407777888 & -11.4540777788825 \tabularnewline
88 & 1150 & 1191.78723116592 & -41.7872311659164 \tabularnewline
89 & 1270 & 1310.98660488068 & -40.9866048806837 \tabularnewline
90 & 1460 & 1489.16997416018 & -29.1699741601806 \tabularnewline
91 & 1000 & 1048.71302796576 & -48.7130279657608 \tabularnewline
92 & 1290 & 1209.7796053224 & 80.2203946776024 \tabularnewline
93 & 1330 & 1251.14359688097 & 78.8564031190288 \tabularnewline
94 & 1180 & 1263.69984517523 & -83.6998451752252 \tabularnewline
95 & 1350 & 1272.14440881691 & 77.8555911830906 \tabularnewline
96 & 1300 & 1343.88236215636 & -43.8823621563602 \tabularnewline
97 & 1350 & 1312.22062150897 & 37.7793784910295 \tabularnewline
98 & 1350 & 1341.82131308618 & 8.17868691381614 \tabularnewline
99 & 1540 & 1522.08100048047 & 17.9189995195266 \tabularnewline
100 & 1180 & 1142.93040044812 & 37.0695995518806 \tabularnewline
101 & 1280 & 1264.11111286445 & 15.8888871355482 \tabularnewline
102 & 1520 & 1454.88218865817 & 65.1178113418316 \tabularnewline
103 & 960 & 996.706407774312 & -36.7064077743119 \tabularnewline
104 & 1420 & 1285.30456007173 & 134.695439928275 \tabularnewline
105 & 1370 & 1326.37749332148 & 43.6225066785155 \tabularnewline
106 & 1210 & 1178.4202612319 & 31.5797387680998 \tabularnewline
107 & 1320 & 1348.13561050775 & -28.1356105077496 \tabularnewline
108 & 1260 & 1298.62177838219 & -38.6217783821889 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124163&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]1220[/C][C]1218.54433760684[/C][C]1.4556623931619[/C][/ROW]
[ROW][C]14[/C][C]1230[/C][C]1228.93179897027[/C][C]1.06820102973415[/C][/ROW]
[ROW][C]15[/C][C]1400[/C][C]1399.31482538593[/C][C]0.685174614066682[/C][/ROW]
[ROW][C]16[/C][C]1320[/C][C]1321.35978688912[/C][C]-1.35978688912405[/C][/ROW]
[ROW][C]17[/C][C]1320[/C][C]1324.6247855237[/C][C]-4.62478552370021[/C][/ROW]
[ROW][C]18[/C][C]1380[/C][C]1385.3396463907[/C][C]-5.3396463907045[/C][/ROW]
[ROW][C]19[/C][C]1340[/C][C]1353.1228091514[/C][C]-13.1228091513954[/C][/ROW]
[ROW][C]20[/C][C]1220[/C][C]1222.8678202041[/C][C]-2.86782020409669[/C][/ROW]
[ROW][C]21[/C][C]1310[/C][C]1320.67067910007[/C][C]-10.6706791000743[/C][/ROW]
[ROW][C]22[/C][C]1280[/C][C]1320.02074065319[/C][C]-40.0207406531897[/C][/ROW]
[ROW][C]23[/C][C]1330[/C][C]1370.5882201356[/C][C]-40.5882201356012[/C][/ROW]
[ROW][C]24[/C][C]1350[/C][C]1327.35971213746[/C][C]22.6402878625363[/C][/ROW]
[ROW][C]25[/C][C]1240[/C][C]1207.72469345297[/C][C]32.2753065470317[/C][/ROW]
[ROW][C]26[/C][C]1260[/C][C]1218.10448343745[/C][C]41.8955165625509[/C][/ROW]
[ROW][C]27[/C][C]1340[/C][C]1388.66285981981[/C][C]-48.6628598198133[/C][/ROW]
[ROW][C]28[/C][C]1270[/C][C]1307.93324197023[/C][C]-37.9332419702257[/C][/ROW]
[ROW][C]29[/C][C]1330[/C][C]1307.36569068406[/C][C]22.6343093159392[/C][/ROW]
[ROW][C]30[/C][C]1440[/C][C]1367.68341325758[/C][C]72.3165867424227[/C][/ROW]
[ROW][C]31[/C][C]1350[/C][C]1328.88007716021[/C][C]21.11992283979[/C][/ROW]
[ROW][C]32[/C][C]1220[/C][C]1209.24671271194[/C][C]10.7532872880586[/C][/ROW]
[ROW][C]33[/C][C]1310[/C][C]1299.59014219225[/C][C]10.4098578077469[/C][/ROW]
[ROW][C]34[/C][C]1350[/C][C]1270.36025772505[/C][C]79.6397422749546[/C][/ROW]
[ROW][C]35[/C][C]1300[/C][C]1322.22167295266[/C][C]-22.2216729526556[/C][/ROW]
[ROW][C]36[/C][C]1410[/C][C]1341.78423699902[/C][C]68.2157630009758[/C][/ROW]
[ROW][C]37[/C][C]1260[/C][C]1232.52308270321[/C][C]27.476917296787[/C][/ROW]
[ROW][C]38[/C][C]1210[/C][C]1252.55094207566[/C][C]-42.5509420756568[/C][/ROW]
[ROW][C]39[/C][C]1410[/C][C]1332.78770939667[/C][C]77.212290603334[/C][/ROW]
[ROW][C]40[/C][C]1240[/C][C]1264.67204699612[/C][C]-24.6720469961176[/C][/ROW]
[ROW][C]41[/C][C]1360[/C][C]1324.28975948841[/C][C]35.7102405115857[/C][/ROW]
[ROW][C]42[/C][C]1420[/C][C]1434.06983376416[/C][C]-14.0698337641611[/C][/ROW]
[ROW][C]43[/C][C]1310[/C][C]1343.78884781425[/C][C]-33.7888478142547[/C][/ROW]
[ROW][C]44[/C][C]1360[/C][C]1213.32521377312[/C][C]146.674786226883[/C][/ROW]
[ROW][C]45[/C][C]1260[/C][C]1305.52547710865[/C][C]-45.5254771086463[/C][/ROW]
[ROW][C]46[/C][C]1410[/C][C]1344.00571340659[/C][C]65.9942865934147[/C][/ROW]
[ROW][C]47[/C][C]1330[/C][C]1295.4667054835[/C][C]34.5332945165001[/C][/ROW]
[ROW][C]48[/C][C]1400[/C][C]1405.27074829849[/C][C]-5.27074829848857[/C][/ROW]
[ROW][C]49[/C][C]1240[/C][C]1255.01905752704[/C][C]-15.0190575270383[/C][/ROW]
[ROW][C]50[/C][C]1280[/C][C]1205.57321929947[/C][C]74.4267807005251[/C][/ROW]
[ROW][C]51[/C][C]1460[/C][C]1405.81165018829[/C][C]54.1883498117134[/C][/ROW]
[ROW][C]52[/C][C]1250[/C][C]1237.17392672485[/C][C]12.8260732751517[/C][/ROW]
[ROW][C]53[/C][C]1340[/C][C]1357.14395266404[/C][C]-17.1439526640352[/C][/ROW]
[ROW][C]54[/C][C]1440[/C][C]1417.34237718969[/C][C]22.6576228103086[/C][/ROW]
[ROW][C]55[/C][C]1170[/C][C]1308.41022955218[/C][C]-138.41022955218[/C][/ROW]
[ROW][C]56[/C][C]1420[/C][C]1354.58869447165[/C][C]65.4113055283549[/C][/ROW]
[ROW][C]57[/C][C]1250[/C][C]1256.24684363484[/C][C]-6.24684363484016[/C][/ROW]
[ROW][C]58[/C][C]1390[/C][C]1405.37197601175[/C][C]-15.3719760117488[/C][/ROW]
[ROW][C]59[/C][C]1260[/C][C]1324.73422939225[/C][C]-64.7342293922522[/C][/ROW]
[ROW][C]60[/C][C]1390[/C][C]1393.86938824355[/C][C]-3.86938824355252[/C][/ROW]
[ROW][C]61[/C][C]1290[/C][C]1233.99649697228[/C][C]56.0035030277181[/C][/ROW]
[ROW][C]62[/C][C]1310[/C][C]1273.77526427705[/C][C]36.2247357229508[/C][/ROW]
[ROW][C]63[/C][C]1540[/C][C]1453.52468952383[/C][C]86.475310476173[/C][/ROW]
[ROW][C]64[/C][C]1250[/C][C]1244.58960704948[/C][C]5.41039295051678[/C][/ROW]
[ROW][C]65[/C][C]1320[/C][C]1334.93076306276[/C][C]-14.9307630627616[/C][/ROW]
[ROW][C]66[/C][C]1430[/C][C]1434.43024585661[/C][C]-4.43024585661169[/C][/ROW]
[ROW][C]67[/C][C]1080[/C][C]1166.31129559499[/C][C]-86.3112955949864[/C][/ROW]
[ROW][C]68[/C][C]1370[/C][C]1414.23301361702[/C][C]-44.2330136170235[/C][/ROW]
[ROW][C]69[/C][C]1290[/C][C]1243.64762471125[/C][C]46.3523752887506[/C][/ROW]
[ROW][C]70[/C][C]1380[/C][C]1384.51036101753[/C][C]-4.51036101753061[/C][/ROW]
[ROW][C]71[/C][C]1260[/C][C]1255.36222296485[/C][C]4.63777703515416[/C][/ROW]
[ROW][C]72[/C][C]1400[/C][C]1385.55354076832[/C][C]14.4464592316751[/C][/ROW]
[ROW][C]73[/C][C]1250[/C][C]1285.05966391864[/C][C]-35.0596639186435[/C][/ROW]
[ROW][C]74[/C][C]1290[/C][C]1304.06342464168[/C][C]-14.0634246416832[/C][/ROW]
[ROW][C]75[/C][C]1550[/C][C]1532.60966024068[/C][C]17.3903397593224[/C][/ROW]
[ROW][C]76[/C][C]1200[/C][C]1242.66970424115[/C][C]-42.6697042411454[/C][/ROW]
[ROW][C]77[/C][C]1320[/C][C]1312.12748384582[/C][C]7.87251615418313[/C][/ROW]
[ROW][C]78[/C][C]1500[/C][C]1422.16837531227[/C][C]77.8316246877348[/C][/ROW]
[ROW][C]79[/C][C]1060[/C][C]1074.41651275152[/C][C]-14.4165127515173[/C][/ROW]
[ROW][C]80[/C][C]1220[/C][C]1364.84753192481[/C][C]-144.847531924806[/C][/ROW]
[ROW][C]81[/C][C]1260[/C][C]1282.08363231606[/C][C]-22.0836323160577[/C][/ROW]
[ROW][C]82[/C][C]1270[/C][C]1371.69143699629[/C][C]-101.691436996293[/C][/ROW]
[ROW][C]83[/C][C]1280[/C][C]1249.96303120941[/C][C]30.0369687905882[/C][/ROW]
[ROW][C]84[/C][C]1350[/C][C]1389.96884198626[/C][C]-39.968841986255[/C][/ROW]
[ROW][C]85[/C][C]1320[/C][C]1239.6360805907[/C][C]80.3639194093025[/C][/ROW]
[ROW][C]86[/C][C]1350[/C][C]1280.80505640299[/C][C]69.194943597013[/C][/ROW]
[ROW][C]87[/C][C]1530[/C][C]1541.45407777888[/C][C]-11.4540777788825[/C][/ROW]
[ROW][C]88[/C][C]1150[/C][C]1191.78723116592[/C][C]-41.7872311659164[/C][/ROW]
[ROW][C]89[/C][C]1270[/C][C]1310.98660488068[/C][C]-40.9866048806837[/C][/ROW]
[ROW][C]90[/C][C]1460[/C][C]1489.16997416018[/C][C]-29.1699741601806[/C][/ROW]
[ROW][C]91[/C][C]1000[/C][C]1048.71302796576[/C][C]-48.7130279657608[/C][/ROW]
[ROW][C]92[/C][C]1290[/C][C]1209.7796053224[/C][C]80.2203946776024[/C][/ROW]
[ROW][C]93[/C][C]1330[/C][C]1251.14359688097[/C][C]78.8564031190288[/C][/ROW]
[ROW][C]94[/C][C]1180[/C][C]1263.69984517523[/C][C]-83.6998451752252[/C][/ROW]
[ROW][C]95[/C][C]1350[/C][C]1272.14440881691[/C][C]77.8555911830906[/C][/ROW]
[ROW][C]96[/C][C]1300[/C][C]1343.88236215636[/C][C]-43.8823621563602[/C][/ROW]
[ROW][C]97[/C][C]1350[/C][C]1312.22062150897[/C][C]37.7793784910295[/C][/ROW]
[ROW][C]98[/C][C]1350[/C][C]1341.82131308618[/C][C]8.17868691381614[/C][/ROW]
[ROW][C]99[/C][C]1540[/C][C]1522.08100048047[/C][C]17.9189995195266[/C][/ROW]
[ROW][C]100[/C][C]1180[/C][C]1142.93040044812[/C][C]37.0695995518806[/C][/ROW]
[ROW][C]101[/C][C]1280[/C][C]1264.11111286445[/C][C]15.8888871355482[/C][/ROW]
[ROW][C]102[/C][C]1520[/C][C]1454.88218865817[/C][C]65.1178113418316[/C][/ROW]
[ROW][C]103[/C][C]960[/C][C]996.706407774312[/C][C]-36.7064077743119[/C][/ROW]
[ROW][C]104[/C][C]1420[/C][C]1285.30456007173[/C][C]134.695439928275[/C][/ROW]
[ROW][C]105[/C][C]1370[/C][C]1326.37749332148[/C][C]43.6225066785155[/C][/ROW]
[ROW][C]106[/C][C]1210[/C][C]1178.4202612319[/C][C]31.5797387680998[/C][/ROW]
[ROW][C]107[/C][C]1320[/C][C]1348.13561050775[/C][C]-28.1356105077496[/C][/ROW]
[ROW][C]108[/C][C]1260[/C][C]1298.62177838219[/C][C]-38.6217783821889[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124163&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124163&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
1312201218.544337606841.4556623931619
1412301228.931798970271.06820102973415
1514001399.314825385930.685174614066682
1613201321.35978688912-1.35978688912405
1713201324.6247855237-4.62478552370021
1813801385.3396463907-5.3396463907045
1913401353.1228091514-13.1228091513954
2012201222.8678202041-2.86782020409669
2113101320.67067910007-10.6706791000743
2212801320.02074065319-40.0207406531897
2313301370.5882201356-40.5882201356012
2413501327.3597121374622.6402878625363
2512401207.7246934529732.2753065470317
2612601218.1044834374541.8955165625509
2713401388.66285981981-48.6628598198133
2812701307.93324197023-37.9332419702257
2913301307.3656906840622.6343093159392
3014401367.6834132575872.3165867424227
3113501328.8800771602121.11992283979
3212201209.2467127119410.7532872880586
3313101299.5901421922510.4098578077469
3413501270.3602577250579.6397422749546
3513001322.22167295266-22.2216729526556
3614101341.7842369990268.2157630009758
3712601232.5230827032127.476917296787
3812101252.55094207566-42.5509420756568
3914101332.7877093966777.212290603334
4012401264.67204699612-24.6720469961176
4113601324.2897594884135.7102405115857
4214201434.06983376416-14.0698337641611
4313101343.78884781425-33.7888478142547
4413601213.32521377312146.674786226883
4512601305.52547710865-45.5254771086463
4614101344.0057134065965.9942865934147
4713301295.466705483534.5332945165001
4814001405.27074829849-5.27074829848857
4912401255.01905752704-15.0190575270383
5012801205.5732192994774.4267807005251
5114601405.8116501882954.1883498117134
5212501237.1739267248512.8260732751517
5313401357.14395266404-17.1439526640352
5414401417.3423771896922.6576228103086
5511701308.41022955218-138.41022955218
5614201354.5886944716565.4113055283549
5712501256.24684363484-6.24684363484016
5813901405.37197601175-15.3719760117488
5912601324.73422939225-64.7342293922522
6013901393.86938824355-3.86938824355252
6112901233.9964969722856.0035030277181
6213101273.7752642770536.2247357229508
6315401453.5246895238386.475310476173
6412501244.589607049485.41039295051678
6513201334.93076306276-14.9307630627616
6614301434.43024585661-4.43024585661169
6710801166.31129559499-86.3112955949864
6813701414.23301361702-44.2330136170235
6912901243.6476247112546.3523752887506
7013801384.51036101753-4.51036101753061
7112601255.362222964854.63777703515416
7214001385.5535407683214.4464592316751
7312501285.05966391864-35.0596639186435
7412901304.06342464168-14.0634246416832
7515501532.6096602406817.3903397593224
7612001242.66970424115-42.6697042411454
7713201312.127483845827.87251615418313
7815001422.1683753122777.8316246877348
7910601074.41651275152-14.4165127515173
8012201364.84753192481-144.847531924806
8112601282.08363231606-22.0836323160577
8212701371.69143699629-101.691436996293
8312801249.9630312094130.0369687905882
8413501389.96884198626-39.968841986255
8513201239.636080590780.3639194093025
8613501280.8050564029969.194943597013
8715301541.45407777888-11.4540777788825
8811501191.78723116592-41.7872311659164
8912701310.98660488068-40.9866048806837
9014601489.16997416018-29.1699741601806
9110001048.71302796576-48.7130279657608
9212901209.779605322480.2203946776024
9313301251.1435968809778.8564031190288
9411801263.69984517523-83.6998451752252
9513501272.1444088169177.8555911830906
9613001343.88236215636-43.8823621563602
9713501312.2206215089737.7793784910295
9813501341.821313086188.17868691381614
9915401522.0810004804717.9189995195266
10011801142.9304004481237.0695995518806
10112801264.1111128644515.8888871355482
10215201454.8821886581765.1178113418316
103960996.706407774312-36.7064077743119
10414201285.30456007173134.695439928275
10513701326.3774933214843.6225066785155
10612101178.420261231931.5797387680998
10713201348.13561050775-28.1356105077496
10812601298.62177838219-38.6217783821889







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1091347.820125144711247.208029751611448.4322205378
1101347.940175127481247.316812831581448.56353742338
1111537.915915119411437.279832650971638.55199758785
1121177.606202021621076.955858383841278.2565456594
1131277.558904917031176.892671503931378.22513833013
1141516.806085717351416.122246445331617.48992498937
115957.420758280351856.7175097341981058.1240068265
1161415.665211457861314.940663051881516.38975986385
1171365.061139982831264.313314137791465.80896582787
1181204.585148335311103.811980671921305.35831599869
1191314.917321214471214.116660764031415.71798166491
1201255.422964973691154.592574406531356.25335554085

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 1347.82012514471 & 1247.20802975161 & 1448.4322205378 \tabularnewline
110 & 1347.94017512748 & 1247.31681283158 & 1448.56353742338 \tabularnewline
111 & 1537.91591511941 & 1437.27983265097 & 1638.55199758785 \tabularnewline
112 & 1177.60620202162 & 1076.95585838384 & 1278.2565456594 \tabularnewline
113 & 1277.55890491703 & 1176.89267150393 & 1378.22513833013 \tabularnewline
114 & 1516.80608571735 & 1416.12224644533 & 1617.48992498937 \tabularnewline
115 & 957.420758280351 & 856.717509734198 & 1058.1240068265 \tabularnewline
116 & 1415.66521145786 & 1314.94066305188 & 1516.38975986385 \tabularnewline
117 & 1365.06113998283 & 1264.31331413779 & 1465.80896582787 \tabularnewline
118 & 1204.58514833531 & 1103.81198067192 & 1305.35831599869 \tabularnewline
119 & 1314.91732121447 & 1214.11666076403 & 1415.71798166491 \tabularnewline
120 & 1255.42296497369 & 1154.59257440653 & 1356.25335554085 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124163&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]1347.82012514471[/C][C]1247.20802975161[/C][C]1448.4322205378[/C][/ROW]
[ROW][C]110[/C][C]1347.94017512748[/C][C]1247.31681283158[/C][C]1448.56353742338[/C][/ROW]
[ROW][C]111[/C][C]1537.91591511941[/C][C]1437.27983265097[/C][C]1638.55199758785[/C][/ROW]
[ROW][C]112[/C][C]1177.60620202162[/C][C]1076.95585838384[/C][C]1278.2565456594[/C][/ROW]
[ROW][C]113[/C][C]1277.55890491703[/C][C]1176.89267150393[/C][C]1378.22513833013[/C][/ROW]
[ROW][C]114[/C][C]1516.80608571735[/C][C]1416.12224644533[/C][C]1617.48992498937[/C][/ROW]
[ROW][C]115[/C][C]957.420758280351[/C][C]856.717509734198[/C][C]1058.1240068265[/C][/ROW]
[ROW][C]116[/C][C]1415.66521145786[/C][C]1314.94066305188[/C][C]1516.38975986385[/C][/ROW]
[ROW][C]117[/C][C]1365.06113998283[/C][C]1264.31331413779[/C][C]1465.80896582787[/C][/ROW]
[ROW][C]118[/C][C]1204.58514833531[/C][C]1103.81198067192[/C][C]1305.35831599869[/C][/ROW]
[ROW][C]119[/C][C]1314.91732121447[/C][C]1214.11666076403[/C][C]1415.71798166491[/C][/ROW]
[ROW][C]120[/C][C]1255.42296497369[/C][C]1154.59257440653[/C][C]1356.25335554085[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124163&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124163&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
1091347.820125144711247.208029751611448.4322205378
1101347.940175127481247.316812831581448.56353742338
1111537.915915119411437.279832650971638.55199758785
1121177.606202021621076.955858383841278.2565456594
1131277.558904917031176.892671503931378.22513833013
1141516.806085717351416.122246445331617.48992498937
115957.420758280351856.7175097341981058.1240068265
1161415.665211457861314.940663051881516.38975986385
1171365.061139982831264.313314137791465.80896582787
1181204.585148335311103.811980671921305.35831599869
1191314.917321214471214.116660764031415.71798166491
1201255.422964973691154.592574406531356.25335554085



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
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')