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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 computationTue, 26 Jul 2011 10:47:14 -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/Jul/26/t1311691800reiccr7b89xp5kb.htm/, Retrieved Thu, 16 May 2024 12:17:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=123156, Retrieved Thu, 16 May 2024 12:17:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsThomas Schroeven
Estimated Impact181
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks 2 - Sta...] [2011-07-26 14:47:14] [1757923712b2aedbf315e1364d6f70a4] [Current]
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Dataseries X:
1070
1240
1200
1280
1180
1190
1190
1230
1470
1190
1190
1400
1130
1260
1260
1260
1130
1220
1180
1280
1140
1160
1170
1410
1100
1280
1330
1260
1070
1260
1270
1410
1160
1130
1160
1300
1080
1380
1260
1250
990
1180
1240
1500
1650
1110
1080
1270
1050
1490
1280
1230
960
1100
1270
1530
1290
1120
1100
1310
1020
1510
1260
1160
970
1020
1210
1530
1350
1070
1140
1250
930
1510
1230
1180
960
960
1240
1640
1350
1100
1120
1290
890
1560
1250
1170
900
860
1310
1610
1440
1130
1220
1400
930
1490
1250
1160
910
880
1300
1550
1460
1120
1270
1410




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123156&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123156&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123156&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 time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.00841523313111035
beta0.293735620041965
gamma0.771518212954272

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.00841523313111035 \tabularnewline
beta & 0.293735620041965 \tabularnewline
gamma & 0.771518212954272 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123156&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]0.00841523313111035[/C][/ROW]
[ROW][C]beta[/C][C]0.293735620041965[/C][/ROW]
[ROW][C]gamma[/C][C]0.771518212954272[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123156&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123156&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
alpha0.00841523313111035
beta0.293735620041965
gamma0.771518212954272







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1311301127.897970085472.10202991452957
1412601253.770214042086.22978595792438
1512601263.02592648103-3.02592648103223
1612601275.52960362772-15.5296036277207
1711301144.97300584104-14.9730058410357
1812201232.71741420761-12.717414207608
1911801177.949368315992.05063168401375
2012801212.0606678349967.9393321650073
2111401446.89437222031-306.894372220306
2211601159.481832268390.518167731614312
2311701159.2408546757610.7591453242437
2414101367.0293189971442.9706810028626
2511001095.136508394044.86349160596069
2612801223.6514379792756.3485620207257
2713301225.83354772869104.166452271314
2812601229.5240972405330.4759027594707
2910701099.74463497445-29.7446349744525
3012601189.0179857600970.9820142399117
3112701146.38678110672123.613218893282
3214101232.3626490419177.637350958096
3311601182.06826667231-22.068266672313
3411301133.64134775786-3.64134775786397
3511601142.599943424817.4000565752003
3613001376.50332621598-76.5033262159834
3710801075.573192983824.42680701617905
3813801244.59182927427135.408170725733
3912601285.33656225903-25.3365622590316
4012501232.5574393253517.4425606746529
419901057.56111283305-67.5611128330502
4211801224.44430226314-44.444302263141
4312401221.6902629042518.3097370957478
4415001348.43381262273151.566187377265
4516501145.39964513245504.600354867554
4611101117.06322110346-7.06322110345718
4710801143.64316674712-63.6431667471152
4812701306.37865369252-36.3786536925174
4910501069.15159728752-19.1515972875159
5014901339.5694297946150.430570205402
5112801258.8973634635221.1026365364776
5212301240.78159364285-10.7815936428472
539601001.99342052803-41.9934205280346
5411001188.31558366892-88.3155836689189
5512701234.6312284692435.3687715307647
5615301464.935529381665.0644706184014
5712901532.5124091926-242.512409192603
5811201105.8650802107514.1349197892473
5911001088.8027111716511.197288828354
6013101272.6754569977837.3245430022178
6110201049.07936032282-29.0793603228187
6215101448.955415183861.044584816201
6312601268.17805109206-8.17805109205756
6411601224.93734421383-64.9373442138312
65970961.195445299778.80455470023003
6610201112.01286219413-92.0128621941317
6712101252.41538829512-42.4153882951246
6815301504.0871029422525.9128970577492
6913501335.2375285110314.7624714889705
7010701106.94021329988-36.9402132998841
7111401086.9176029300753.0823970699278
7212501290.95130769752-40.9513076975165
739301015.52278681284-85.5227868128354
7415101483.3584504974626.6415495025419
7512301248.73690011264-18.7369001126447
7611801161.3613390284718.6386609715291
77960954.3201070560985.67989294390168
789601027.5584968135-67.5584968135011
7912401205.7457855562634.2542144437386
8016401510.16073456469129.839265435308
8113501333.7374002721616.2625997278376
8211001065.9845718142134.015428185792
8311201115.689818675214.31018132478948
8412901247.5154723836442.4845276163626
85890939.037577356946-49.0375773569457
8615601493.4258806014966.5741193985136
8712501224.9604063490425.0395936509628
8811701167.190423571192.80957642880708
89900950.706992154648-50.7069921546477
90860967.90703873789-107.90703873789
9113101224.0098073819885.9901926180182
9216101602.478712566597.52128743340927
9314401338.328187419101.671812581002
9411301085.2777990921944.7222009078073
9512201112.7766655719107.223334428104
9614001275.35589711125124.644102888752
97930898.43890080486331.5610991951371
9814901543.03687876063-53.0368787606303
9912501242.579707216487.4202927835197
10011601168.40120401191-8.40120401190961
101910911.600453867689-1.60045386768854
102880886.294194839398-6.29419483939751
10313001292.679555424257.32044457574625
10415501611.35237614056-61.3523761405618
10514601419.3762590259640.6237409740429
10611201122.81974196135-2.81974196135047
10712701198.191511029371.8084889707
10814101374.1705190249535.8294809750541

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1130 & 1127.89797008547 & 2.10202991452957 \tabularnewline
14 & 1260 & 1253.77021404208 & 6.22978595792438 \tabularnewline
15 & 1260 & 1263.02592648103 & -3.02592648103223 \tabularnewline
16 & 1260 & 1275.52960362772 & -15.5296036277207 \tabularnewline
17 & 1130 & 1144.97300584104 & -14.9730058410357 \tabularnewline
18 & 1220 & 1232.71741420761 & -12.717414207608 \tabularnewline
19 & 1180 & 1177.94936831599 & 2.05063168401375 \tabularnewline
20 & 1280 & 1212.06066783499 & 67.9393321650073 \tabularnewline
21 & 1140 & 1446.89437222031 & -306.894372220306 \tabularnewline
22 & 1160 & 1159.48183226839 & 0.518167731614312 \tabularnewline
23 & 1170 & 1159.24085467576 & 10.7591453242437 \tabularnewline
24 & 1410 & 1367.02931899714 & 42.9706810028626 \tabularnewline
25 & 1100 & 1095.13650839404 & 4.86349160596069 \tabularnewline
26 & 1280 & 1223.65143797927 & 56.3485620207257 \tabularnewline
27 & 1330 & 1225.83354772869 & 104.166452271314 \tabularnewline
28 & 1260 & 1229.52409724053 & 30.4759027594707 \tabularnewline
29 & 1070 & 1099.74463497445 & -29.7446349744525 \tabularnewline
30 & 1260 & 1189.01798576009 & 70.9820142399117 \tabularnewline
31 & 1270 & 1146.38678110672 & 123.613218893282 \tabularnewline
32 & 1410 & 1232.3626490419 & 177.637350958096 \tabularnewline
33 & 1160 & 1182.06826667231 & -22.068266672313 \tabularnewline
34 & 1130 & 1133.64134775786 & -3.64134775786397 \tabularnewline
35 & 1160 & 1142.5999434248 & 17.4000565752003 \tabularnewline
36 & 1300 & 1376.50332621598 & -76.5033262159834 \tabularnewline
37 & 1080 & 1075.57319298382 & 4.42680701617905 \tabularnewline
38 & 1380 & 1244.59182927427 & 135.408170725733 \tabularnewline
39 & 1260 & 1285.33656225903 & -25.3365622590316 \tabularnewline
40 & 1250 & 1232.55743932535 & 17.4425606746529 \tabularnewline
41 & 990 & 1057.56111283305 & -67.5611128330502 \tabularnewline
42 & 1180 & 1224.44430226314 & -44.444302263141 \tabularnewline
43 & 1240 & 1221.69026290425 & 18.3097370957478 \tabularnewline
44 & 1500 & 1348.43381262273 & 151.566187377265 \tabularnewline
45 & 1650 & 1145.39964513245 & 504.600354867554 \tabularnewline
46 & 1110 & 1117.06322110346 & -7.06322110345718 \tabularnewline
47 & 1080 & 1143.64316674712 & -63.6431667471152 \tabularnewline
48 & 1270 & 1306.37865369252 & -36.3786536925174 \tabularnewline
49 & 1050 & 1069.15159728752 & -19.1515972875159 \tabularnewline
50 & 1490 & 1339.5694297946 & 150.430570205402 \tabularnewline
51 & 1280 & 1258.89736346352 & 21.1026365364776 \tabularnewline
52 & 1230 & 1240.78159364285 & -10.7815936428472 \tabularnewline
53 & 960 & 1001.99342052803 & -41.9934205280346 \tabularnewline
54 & 1100 & 1188.31558366892 & -88.3155836689189 \tabularnewline
55 & 1270 & 1234.63122846924 & 35.3687715307647 \tabularnewline
56 & 1530 & 1464.9355293816 & 65.0644706184014 \tabularnewline
57 & 1290 & 1532.5124091926 & -242.512409192603 \tabularnewline
58 & 1120 & 1105.86508021075 & 14.1349197892473 \tabularnewline
59 & 1100 & 1088.80271117165 & 11.197288828354 \tabularnewline
60 & 1310 & 1272.67545699778 & 37.3245430022178 \tabularnewline
61 & 1020 & 1049.07936032282 & -29.0793603228187 \tabularnewline
62 & 1510 & 1448.9554151838 & 61.044584816201 \tabularnewline
63 & 1260 & 1268.17805109206 & -8.17805109205756 \tabularnewline
64 & 1160 & 1224.93734421383 & -64.9373442138312 \tabularnewline
65 & 970 & 961.19544529977 & 8.80455470023003 \tabularnewline
66 & 1020 & 1112.01286219413 & -92.0128621941317 \tabularnewline
67 & 1210 & 1252.41538829512 & -42.4153882951246 \tabularnewline
68 & 1530 & 1504.08710294225 & 25.9128970577492 \tabularnewline
69 & 1350 & 1335.23752851103 & 14.7624714889705 \tabularnewline
70 & 1070 & 1106.94021329988 & -36.9402132998841 \tabularnewline
71 & 1140 & 1086.91760293007 & 53.0823970699278 \tabularnewline
72 & 1250 & 1290.95130769752 & -40.9513076975165 \tabularnewline
73 & 930 & 1015.52278681284 & -85.5227868128354 \tabularnewline
74 & 1510 & 1483.35845049746 & 26.6415495025419 \tabularnewline
75 & 1230 & 1248.73690011264 & -18.7369001126447 \tabularnewline
76 & 1180 & 1161.36133902847 & 18.6386609715291 \tabularnewline
77 & 960 & 954.320107056098 & 5.67989294390168 \tabularnewline
78 & 960 & 1027.5584968135 & -67.5584968135011 \tabularnewline
79 & 1240 & 1205.74578555626 & 34.2542144437386 \tabularnewline
80 & 1640 & 1510.16073456469 & 129.839265435308 \tabularnewline
81 & 1350 & 1333.73740027216 & 16.2625997278376 \tabularnewline
82 & 1100 & 1065.98457181421 & 34.015428185792 \tabularnewline
83 & 1120 & 1115.68981867521 & 4.31018132478948 \tabularnewline
84 & 1290 & 1247.51547238364 & 42.4845276163626 \tabularnewline
85 & 890 & 939.037577356946 & -49.0375773569457 \tabularnewline
86 & 1560 & 1493.42588060149 & 66.5741193985136 \tabularnewline
87 & 1250 & 1224.96040634904 & 25.0395936509628 \tabularnewline
88 & 1170 & 1167.19042357119 & 2.80957642880708 \tabularnewline
89 & 900 & 950.706992154648 & -50.7069921546477 \tabularnewline
90 & 860 & 967.90703873789 & -107.90703873789 \tabularnewline
91 & 1310 & 1224.00980738198 & 85.9901926180182 \tabularnewline
92 & 1610 & 1602.47871256659 & 7.52128743340927 \tabularnewline
93 & 1440 & 1338.328187419 & 101.671812581002 \tabularnewline
94 & 1130 & 1085.27779909219 & 44.7222009078073 \tabularnewline
95 & 1220 & 1112.7766655719 & 107.223334428104 \tabularnewline
96 & 1400 & 1275.35589711125 & 124.644102888752 \tabularnewline
97 & 930 & 898.438900804863 & 31.5610991951371 \tabularnewline
98 & 1490 & 1543.03687876063 & -53.0368787606303 \tabularnewline
99 & 1250 & 1242.57970721648 & 7.4202927835197 \tabularnewline
100 & 1160 & 1168.40120401191 & -8.40120401190961 \tabularnewline
101 & 910 & 911.600453867689 & -1.60045386768854 \tabularnewline
102 & 880 & 886.294194839398 & -6.29419483939751 \tabularnewline
103 & 1300 & 1292.67955542425 & 7.32044457574625 \tabularnewline
104 & 1550 & 1611.35237614056 & -61.3523761405618 \tabularnewline
105 & 1460 & 1419.37625902596 & 40.6237409740429 \tabularnewline
106 & 1120 & 1122.81974196135 & -2.81974196135047 \tabularnewline
107 & 1270 & 1198.1915110293 & 71.8084889707 \tabularnewline
108 & 1410 & 1374.17051902495 & 35.8294809750541 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123156&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]1130[/C][C]1127.89797008547[/C][C]2.10202991452957[/C][/ROW]
[ROW][C]14[/C][C]1260[/C][C]1253.77021404208[/C][C]6.22978595792438[/C][/ROW]
[ROW][C]15[/C][C]1260[/C][C]1263.02592648103[/C][C]-3.02592648103223[/C][/ROW]
[ROW][C]16[/C][C]1260[/C][C]1275.52960362772[/C][C]-15.5296036277207[/C][/ROW]
[ROW][C]17[/C][C]1130[/C][C]1144.97300584104[/C][C]-14.9730058410357[/C][/ROW]
[ROW][C]18[/C][C]1220[/C][C]1232.71741420761[/C][C]-12.717414207608[/C][/ROW]
[ROW][C]19[/C][C]1180[/C][C]1177.94936831599[/C][C]2.05063168401375[/C][/ROW]
[ROW][C]20[/C][C]1280[/C][C]1212.06066783499[/C][C]67.9393321650073[/C][/ROW]
[ROW][C]21[/C][C]1140[/C][C]1446.89437222031[/C][C]-306.894372220306[/C][/ROW]
[ROW][C]22[/C][C]1160[/C][C]1159.48183226839[/C][C]0.518167731614312[/C][/ROW]
[ROW][C]23[/C][C]1170[/C][C]1159.24085467576[/C][C]10.7591453242437[/C][/ROW]
[ROW][C]24[/C][C]1410[/C][C]1367.02931899714[/C][C]42.9706810028626[/C][/ROW]
[ROW][C]25[/C][C]1100[/C][C]1095.13650839404[/C][C]4.86349160596069[/C][/ROW]
[ROW][C]26[/C][C]1280[/C][C]1223.65143797927[/C][C]56.3485620207257[/C][/ROW]
[ROW][C]27[/C][C]1330[/C][C]1225.83354772869[/C][C]104.166452271314[/C][/ROW]
[ROW][C]28[/C][C]1260[/C][C]1229.52409724053[/C][C]30.4759027594707[/C][/ROW]
[ROW][C]29[/C][C]1070[/C][C]1099.74463497445[/C][C]-29.7446349744525[/C][/ROW]
[ROW][C]30[/C][C]1260[/C][C]1189.01798576009[/C][C]70.9820142399117[/C][/ROW]
[ROW][C]31[/C][C]1270[/C][C]1146.38678110672[/C][C]123.613218893282[/C][/ROW]
[ROW][C]32[/C][C]1410[/C][C]1232.3626490419[/C][C]177.637350958096[/C][/ROW]
[ROW][C]33[/C][C]1160[/C][C]1182.06826667231[/C][C]-22.068266672313[/C][/ROW]
[ROW][C]34[/C][C]1130[/C][C]1133.64134775786[/C][C]-3.64134775786397[/C][/ROW]
[ROW][C]35[/C][C]1160[/C][C]1142.5999434248[/C][C]17.4000565752003[/C][/ROW]
[ROW][C]36[/C][C]1300[/C][C]1376.50332621598[/C][C]-76.5033262159834[/C][/ROW]
[ROW][C]37[/C][C]1080[/C][C]1075.57319298382[/C][C]4.42680701617905[/C][/ROW]
[ROW][C]38[/C][C]1380[/C][C]1244.59182927427[/C][C]135.408170725733[/C][/ROW]
[ROW][C]39[/C][C]1260[/C][C]1285.33656225903[/C][C]-25.3365622590316[/C][/ROW]
[ROW][C]40[/C][C]1250[/C][C]1232.55743932535[/C][C]17.4425606746529[/C][/ROW]
[ROW][C]41[/C][C]990[/C][C]1057.56111283305[/C][C]-67.5611128330502[/C][/ROW]
[ROW][C]42[/C][C]1180[/C][C]1224.44430226314[/C][C]-44.444302263141[/C][/ROW]
[ROW][C]43[/C][C]1240[/C][C]1221.69026290425[/C][C]18.3097370957478[/C][/ROW]
[ROW][C]44[/C][C]1500[/C][C]1348.43381262273[/C][C]151.566187377265[/C][/ROW]
[ROW][C]45[/C][C]1650[/C][C]1145.39964513245[/C][C]504.600354867554[/C][/ROW]
[ROW][C]46[/C][C]1110[/C][C]1117.06322110346[/C][C]-7.06322110345718[/C][/ROW]
[ROW][C]47[/C][C]1080[/C][C]1143.64316674712[/C][C]-63.6431667471152[/C][/ROW]
[ROW][C]48[/C][C]1270[/C][C]1306.37865369252[/C][C]-36.3786536925174[/C][/ROW]
[ROW][C]49[/C][C]1050[/C][C]1069.15159728752[/C][C]-19.1515972875159[/C][/ROW]
[ROW][C]50[/C][C]1490[/C][C]1339.5694297946[/C][C]150.430570205402[/C][/ROW]
[ROW][C]51[/C][C]1280[/C][C]1258.89736346352[/C][C]21.1026365364776[/C][/ROW]
[ROW][C]52[/C][C]1230[/C][C]1240.78159364285[/C][C]-10.7815936428472[/C][/ROW]
[ROW][C]53[/C][C]960[/C][C]1001.99342052803[/C][C]-41.9934205280346[/C][/ROW]
[ROW][C]54[/C][C]1100[/C][C]1188.31558366892[/C][C]-88.3155836689189[/C][/ROW]
[ROW][C]55[/C][C]1270[/C][C]1234.63122846924[/C][C]35.3687715307647[/C][/ROW]
[ROW][C]56[/C][C]1530[/C][C]1464.9355293816[/C][C]65.0644706184014[/C][/ROW]
[ROW][C]57[/C][C]1290[/C][C]1532.5124091926[/C][C]-242.512409192603[/C][/ROW]
[ROW][C]58[/C][C]1120[/C][C]1105.86508021075[/C][C]14.1349197892473[/C][/ROW]
[ROW][C]59[/C][C]1100[/C][C]1088.80271117165[/C][C]11.197288828354[/C][/ROW]
[ROW][C]60[/C][C]1310[/C][C]1272.67545699778[/C][C]37.3245430022178[/C][/ROW]
[ROW][C]61[/C][C]1020[/C][C]1049.07936032282[/C][C]-29.0793603228187[/C][/ROW]
[ROW][C]62[/C][C]1510[/C][C]1448.9554151838[/C][C]61.044584816201[/C][/ROW]
[ROW][C]63[/C][C]1260[/C][C]1268.17805109206[/C][C]-8.17805109205756[/C][/ROW]
[ROW][C]64[/C][C]1160[/C][C]1224.93734421383[/C][C]-64.9373442138312[/C][/ROW]
[ROW][C]65[/C][C]970[/C][C]961.19544529977[/C][C]8.80455470023003[/C][/ROW]
[ROW][C]66[/C][C]1020[/C][C]1112.01286219413[/C][C]-92.0128621941317[/C][/ROW]
[ROW][C]67[/C][C]1210[/C][C]1252.41538829512[/C][C]-42.4153882951246[/C][/ROW]
[ROW][C]68[/C][C]1530[/C][C]1504.08710294225[/C][C]25.9128970577492[/C][/ROW]
[ROW][C]69[/C][C]1350[/C][C]1335.23752851103[/C][C]14.7624714889705[/C][/ROW]
[ROW][C]70[/C][C]1070[/C][C]1106.94021329988[/C][C]-36.9402132998841[/C][/ROW]
[ROW][C]71[/C][C]1140[/C][C]1086.91760293007[/C][C]53.0823970699278[/C][/ROW]
[ROW][C]72[/C][C]1250[/C][C]1290.95130769752[/C][C]-40.9513076975165[/C][/ROW]
[ROW][C]73[/C][C]930[/C][C]1015.52278681284[/C][C]-85.5227868128354[/C][/ROW]
[ROW][C]74[/C][C]1510[/C][C]1483.35845049746[/C][C]26.6415495025419[/C][/ROW]
[ROW][C]75[/C][C]1230[/C][C]1248.73690011264[/C][C]-18.7369001126447[/C][/ROW]
[ROW][C]76[/C][C]1180[/C][C]1161.36133902847[/C][C]18.6386609715291[/C][/ROW]
[ROW][C]77[/C][C]960[/C][C]954.320107056098[/C][C]5.67989294390168[/C][/ROW]
[ROW][C]78[/C][C]960[/C][C]1027.5584968135[/C][C]-67.5584968135011[/C][/ROW]
[ROW][C]79[/C][C]1240[/C][C]1205.74578555626[/C][C]34.2542144437386[/C][/ROW]
[ROW][C]80[/C][C]1640[/C][C]1510.16073456469[/C][C]129.839265435308[/C][/ROW]
[ROW][C]81[/C][C]1350[/C][C]1333.73740027216[/C][C]16.2625997278376[/C][/ROW]
[ROW][C]82[/C][C]1100[/C][C]1065.98457181421[/C][C]34.015428185792[/C][/ROW]
[ROW][C]83[/C][C]1120[/C][C]1115.68981867521[/C][C]4.31018132478948[/C][/ROW]
[ROW][C]84[/C][C]1290[/C][C]1247.51547238364[/C][C]42.4845276163626[/C][/ROW]
[ROW][C]85[/C][C]890[/C][C]939.037577356946[/C][C]-49.0375773569457[/C][/ROW]
[ROW][C]86[/C][C]1560[/C][C]1493.42588060149[/C][C]66.5741193985136[/C][/ROW]
[ROW][C]87[/C][C]1250[/C][C]1224.96040634904[/C][C]25.0395936509628[/C][/ROW]
[ROW][C]88[/C][C]1170[/C][C]1167.19042357119[/C][C]2.80957642880708[/C][/ROW]
[ROW][C]89[/C][C]900[/C][C]950.706992154648[/C][C]-50.7069921546477[/C][/ROW]
[ROW][C]90[/C][C]860[/C][C]967.90703873789[/C][C]-107.90703873789[/C][/ROW]
[ROW][C]91[/C][C]1310[/C][C]1224.00980738198[/C][C]85.9901926180182[/C][/ROW]
[ROW][C]92[/C][C]1610[/C][C]1602.47871256659[/C][C]7.52128743340927[/C][/ROW]
[ROW][C]93[/C][C]1440[/C][C]1338.328187419[/C][C]101.671812581002[/C][/ROW]
[ROW][C]94[/C][C]1130[/C][C]1085.27779909219[/C][C]44.7222009078073[/C][/ROW]
[ROW][C]95[/C][C]1220[/C][C]1112.7766655719[/C][C]107.223334428104[/C][/ROW]
[ROW][C]96[/C][C]1400[/C][C]1275.35589711125[/C][C]124.644102888752[/C][/ROW]
[ROW][C]97[/C][C]930[/C][C]898.438900804863[/C][C]31.5610991951371[/C][/ROW]
[ROW][C]98[/C][C]1490[/C][C]1543.03687876063[/C][C]-53.0368787606303[/C][/ROW]
[ROW][C]99[/C][C]1250[/C][C]1242.57970721648[/C][C]7.4202927835197[/C][/ROW]
[ROW][C]100[/C][C]1160[/C][C]1168.40120401191[/C][C]-8.40120401190961[/C][/ROW]
[ROW][C]101[/C][C]910[/C][C]911.600453867689[/C][C]-1.60045386768854[/C][/ROW]
[ROW][C]102[/C][C]880[/C][C]886.294194839398[/C][C]-6.29419483939751[/C][/ROW]
[ROW][C]103[/C][C]1300[/C][C]1292.67955542425[/C][C]7.32044457574625[/C][/ROW]
[ROW][C]104[/C][C]1550[/C][C]1611.35237614056[/C][C]-61.3523761405618[/C][/ROW]
[ROW][C]105[/C][C]1460[/C][C]1419.37625902596[/C][C]40.6237409740429[/C][/ROW]
[ROW][C]106[/C][C]1120[/C][C]1122.81974196135[/C][C]-2.81974196135047[/C][/ROW]
[ROW][C]107[/C][C]1270[/C][C]1198.1915110293[/C][C]71.8084889707[/C][/ROW]
[ROW][C]108[/C][C]1410[/C][C]1374.17051902495[/C][C]35.8294809750541[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123156&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123156&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
1311301127.897970085472.10202991452957
1412601253.770214042086.22978595792438
1512601263.02592648103-3.02592648103223
1612601275.52960362772-15.5296036277207
1711301144.97300584104-14.9730058410357
1812201232.71741420761-12.717414207608
1911801177.949368315992.05063168401375
2012801212.0606678349967.9393321650073
2111401446.89437222031-306.894372220306
2211601159.481832268390.518167731614312
2311701159.2408546757610.7591453242437
2414101367.0293189971442.9706810028626
2511001095.136508394044.86349160596069
2612801223.6514379792756.3485620207257
2713301225.83354772869104.166452271314
2812601229.5240972405330.4759027594707
2910701099.74463497445-29.7446349744525
3012601189.0179857600970.9820142399117
3112701146.38678110672123.613218893282
3214101232.3626490419177.637350958096
3311601182.06826667231-22.068266672313
3411301133.64134775786-3.64134775786397
3511601142.599943424817.4000565752003
3613001376.50332621598-76.5033262159834
3710801075.573192983824.42680701617905
3813801244.59182927427135.408170725733
3912601285.33656225903-25.3365622590316
4012501232.5574393253517.4425606746529
419901057.56111283305-67.5611128330502
4211801224.44430226314-44.444302263141
4312401221.6902629042518.3097370957478
4415001348.43381262273151.566187377265
4516501145.39964513245504.600354867554
4611101117.06322110346-7.06322110345718
4710801143.64316674712-63.6431667471152
4812701306.37865369252-36.3786536925174
4910501069.15159728752-19.1515972875159
5014901339.5694297946150.430570205402
5112801258.8973634635221.1026365364776
5212301240.78159364285-10.7815936428472
539601001.99342052803-41.9934205280346
5411001188.31558366892-88.3155836689189
5512701234.6312284692435.3687715307647
5615301464.935529381665.0644706184014
5712901532.5124091926-242.512409192603
5811201105.8650802107514.1349197892473
5911001088.8027111716511.197288828354
6013101272.6754569977837.3245430022178
6110201049.07936032282-29.0793603228187
6215101448.955415183861.044584816201
6312601268.17805109206-8.17805109205756
6411601224.93734421383-64.9373442138312
65970961.195445299778.80455470023003
6610201112.01286219413-92.0128621941317
6712101252.41538829512-42.4153882951246
6815301504.0871029422525.9128970577492
6913501335.2375285110314.7624714889705
7010701106.94021329988-36.9402132998841
7111401086.9176029300753.0823970699278
7212501290.95130769752-40.9513076975165
739301015.52278681284-85.5227868128354
7415101483.3584504974626.6415495025419
7512301248.73690011264-18.7369001126447
7611801161.3613390284718.6386609715291
77960954.3201070560985.67989294390168
789601027.5584968135-67.5584968135011
7912401205.7457855562634.2542144437386
8016401510.16073456469129.839265435308
8113501333.7374002721616.2625997278376
8211001065.9845718142134.015428185792
8311201115.689818675214.31018132478948
8412901247.5154723836442.4845276163626
85890939.037577356946-49.0375773569457
8615601493.4258806014966.5741193985136
8712501224.9604063490425.0395936509628
8811701167.190423571192.80957642880708
89900950.706992154648-50.7069921546477
90860967.90703873789-107.90703873789
9113101224.0098073819885.9901926180182
9216101602.478712566597.52128743340927
9314401338.328187419101.671812581002
9411301085.2777990921944.7222009078073
9512201112.7766655719107.223334428104
9614001275.35589711125124.644102888752
97930898.43890080486331.5610991951371
9814901543.03687876063-53.0368787606303
9912501242.579707216487.4202927835197
10011601168.40120401191-8.40120401190961
101910911.600453867689-1.60045386768854
102880886.294194839398-6.29419483939751
10313001292.679555424257.32044457574625
10415501611.35237614056-61.3523761405618
10514601419.3762590259640.6237409740429
10611201122.81974196135-2.81974196135047
10712701198.191511029371.8084889707
10814101374.1705190249535.8294809750541







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109925.446164398462755.4027915821691095.48953721475
1101505.131834171671335.078384147411675.18528419593
1111251.576283905671081.507662377211421.64490543414
1121165.41715670746995.3272320476021335.50708136732
113914.096291167352743.9778955320961084.21468680261
114885.423061736762715.267992583681055.57813088984
1151302.502890828261132.301912900781472.70386875574
1161568.785492227131398.528340065461739.04264438881
1171455.699532059241285.374913097591626.02415102089
1181125.8248708092955.420469117521296.22927250087
1191258.578949135091088.081429861781429.07646840841
1201406.517371150341235.912385720431577.12235658026

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 925.446164398462 & 755.402791582169 & 1095.48953721475 \tabularnewline
110 & 1505.13183417167 & 1335.07838414741 & 1675.18528419593 \tabularnewline
111 & 1251.57628390567 & 1081.50766237721 & 1421.64490543414 \tabularnewline
112 & 1165.41715670746 & 995.327232047602 & 1335.50708136732 \tabularnewline
113 & 914.096291167352 & 743.977895532096 & 1084.21468680261 \tabularnewline
114 & 885.423061736762 & 715.26799258368 & 1055.57813088984 \tabularnewline
115 & 1302.50289082826 & 1132.30191290078 & 1472.70386875574 \tabularnewline
116 & 1568.78549222713 & 1398.52834006546 & 1739.04264438881 \tabularnewline
117 & 1455.69953205924 & 1285.37491309759 & 1626.02415102089 \tabularnewline
118 & 1125.8248708092 & 955.42046911752 & 1296.22927250087 \tabularnewline
119 & 1258.57894913509 & 1088.08142986178 & 1429.07646840841 \tabularnewline
120 & 1406.51737115034 & 1235.91238572043 & 1577.12235658026 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123156&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]925.446164398462[/C][C]755.402791582169[/C][C]1095.48953721475[/C][/ROW]
[ROW][C]110[/C][C]1505.13183417167[/C][C]1335.07838414741[/C][C]1675.18528419593[/C][/ROW]
[ROW][C]111[/C][C]1251.57628390567[/C][C]1081.50766237721[/C][C]1421.64490543414[/C][/ROW]
[ROW][C]112[/C][C]1165.41715670746[/C][C]995.327232047602[/C][C]1335.50708136732[/C][/ROW]
[ROW][C]113[/C][C]914.096291167352[/C][C]743.977895532096[/C][C]1084.21468680261[/C][/ROW]
[ROW][C]114[/C][C]885.423061736762[/C][C]715.26799258368[/C][C]1055.57813088984[/C][/ROW]
[ROW][C]115[/C][C]1302.50289082826[/C][C]1132.30191290078[/C][C]1472.70386875574[/C][/ROW]
[ROW][C]116[/C][C]1568.78549222713[/C][C]1398.52834006546[/C][C]1739.04264438881[/C][/ROW]
[ROW][C]117[/C][C]1455.69953205924[/C][C]1285.37491309759[/C][C]1626.02415102089[/C][/ROW]
[ROW][C]118[/C][C]1125.8248708092[/C][C]955.42046911752[/C][C]1296.22927250087[/C][/ROW]
[ROW][C]119[/C][C]1258.57894913509[/C][C]1088.08142986178[/C][C]1429.07646840841[/C][/ROW]
[ROW][C]120[/C][C]1406.51737115034[/C][C]1235.91238572043[/C][C]1577.12235658026[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123156&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123156&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
109925.446164398462755.4027915821691095.48953721475
1101505.131834171671335.078384147411675.18528419593
1111251.576283905671081.507662377211421.64490543414
1121165.41715670746995.3272320476021335.50708136732
113914.096291167352743.9778955320961084.21468680261
114885.423061736762715.267992583681055.57813088984
1151302.502890828261132.301912900781472.70386875574
1161568.785492227131398.528340065461739.04264438881
1171455.699532059241285.374913097591626.02415102089
1181125.8248708092955.420469117521296.22927250087
1191258.578949135091088.081429861781429.07646840841
1201406.517371150341235.912385720431577.12235658026



Parameters (Session):
par1 = 12 ;
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')