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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, 30 Nov 2017 10:19:40 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Nov/30/t15120337499310887c78yh6gm.htm/, Retrieved Sat, 18 May 2024 17:54:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=308370, Retrieved Sat, 18 May 2024 17:54:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact114
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [triple exponetial...] [2017-11-30 09:19:40] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
1028
869
2698
2367
1928
1846
1404
1316
1008
865
586
343
1143
1807
2380
2334
2116
1788
1571
1306
952
806
473
278
993
1038
2259
2283
1746
1515
1230
882
1028
704
390
238
594
692
2125
1849
1468
1531
1203
878
818
605
316
136
528
654
1892
1597
1515
1241
1026
758
733
481
280
117
651
611
1898
1385
1047
1007
842
827
711
443
313
202
473
566
1609
1296
1153
1155
859
798
557
402
223
153
548
647
1757
1326
1308
1175
992
808
758
551
310
146
649
602
1801
1481
1400
1319
1153
950
829
636
310
191
679
842
1975
1677
1418
1540
1173
941
989
614
352
405




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308370&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=308370&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308370&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0946984806706098
beta0.150918560035112
gamma0.920146284251121

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0946984806706098 \tabularnewline
beta & 0.150918560035112 \tabularnewline
gamma & 0.920146284251121 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308370&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]0.0946984806706098[/C][/ROW]
[ROW][C]beta[/C][C]0.150918560035112[/C][/ROW]
[ROW][C]gamma[/C][C]0.920146284251121[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308370&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308370&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
alpha0.0946984806706098
beta0.150918560035112
gamma0.920146284251121







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1311431107.2980769230835.7019230769229
1418071771.9721634603135.0278365396935
1523802355.374691068324.6253089317047
1623342321.1857207476512.8142792523522
1721162116.43640244359-0.436402443590396
1817881800.67602775681-12.6760277568146
1915711476.0754164234894.9245835765169
2013061359.22939204501-53.229392045012
219521025.63433632883-73.6343363288277
22806894.51293258377-88.5129325837701
23473603.634209603044-130.634209603044
24278343.941339796728-65.9413397967282
259931163.04742162048-170.04742162048
2610381801.56296545736-763.562965457356
2722592283.14861129109-24.1486112910898
2822832216.2789175304466.7210824695585
2917461988.14376301443-242.143763014433
3015151618.39113665853-103.391136658526
3112301352.62862712071-122.62862712071
328821066.45402631264-184.454026312644
331028676.246347199106351.753652800894
34704551.905734383312152.094265616688
35390231.054621256604158.945378743396
3623839.1428079395653198.857192060435
37594786.856468623813-192.856468623813
38692918.734716856008-226.734716856008
3921252064.6957948930160.3042051069924
4018492080.32516970365-231.325169703648
4114681561.22459786034-93.2245978603391
4215311317.83157056742213.168429432581
4312031067.22082396312135.779176036876
44878758.908057792131119.091942207869
45818853.342367001082-35.3423670010818
46605529.72421359195675.275786408044
47316209.90577699056106.09422300944
4813648.080861588595387.9191384114047
49528459.24691700564668.7530829943544
50654591.67652844431862.3234715556819
5118922012.24662077539-120.246620775388
5215971773.39698192268-176.396981922681
5315151380.87119106321134.12880893679
5412411423.81990053132-182.819900531316
5510261075.16759369821-49.1675936982081
56758736.72074681912621.2792531808743
57733693.12985733699939.8701426630007
58481469.73795428090611.2620457190945
59280169.572436279002110.427563720998
60117-6.87734942151371123.877349421514
61651392.347080495141258.652919504859
62611540.73669007479770.2633099252033
6318981813.4221675388884.5778324611217
6413851553.5687679754-168.568767975398
6510471426.94068952068-379.940689520684
6610071156.32480761504-149.324807615043
67842921.795223652259-79.7952236522593
68827638.310283128498188.689716871502
69711627.63127426443883.368725735562
70443386.72143661403356.2785633859669
71313176.261772463807136.738227536193
7220216.7204028057851185.279597194215
73473538.119485455509-65.1194854555091
74566498.38124529825167.618754701749
7516091782.16593161148-173.16593161148
7612961282.7728774607213.2271225392753
771153995.625782962609157.374217037391
781155974.017355113229180.982644886771
79859839.42613858342519.5738614165748
80798801.161979493408-3.16197949340847
81557693.999673177426-136.999673177426
82402415.923647087576-13.9236470875757
83223271.105053960592-48.1050539605918
84153137.11843152615415.8815684738464
85548434.093572581901113.906427418099
86647524.642359620098122.357640379902
8717571616.57832625399140.421673746009
8813261310.1741077707415.8258922292553
8913081151.41152005328156.588479946715
9011751157.4459676604317.554032339571
91992878.63875556422113.36124443578
92808837.372875693721-29.3728756937205
93758622.921658681506135.078341318494
94551483.70435558413367.2956444158669
95310329.834233483194-19.8342334831937
96146263.960915369348-117.960915369348
97649640.1388182744748.86118172552642
98602736.500413061091-134.500413061091
9918011824.20936585827-23.2093658582687
10014811401.2309868106979.769013189305
10114001369.4051552226130.5948447773881
10213191249.515285554969.4847144451023
10311531058.0005102871594.9994897128497
104950898.40078411396951.5992158860313
105829832.06812389434-3.06812389433969
106636624.79169432795411.208305672046
107310393.715341732359-83.7153417323586
108191239.824315821044-48.8243158210436
109679728.953713276374-49.9537132763739
110842700.243751203549141.756248796451
11119751910.688261736164.3117382638975
11216771586.8987660479590.1012339520471
11314181520.35524588064-102.35524588064
11415401423.63718918207116.362810817932
11511731261.85206830103-88.8520683010315
1169411050.09777348957-109.097773489569
117989922.1210278792666.8789721207396
118614733.47266190087-119.47266190087
119352409.192801824092-57.192801824092
120405285.501154315405119.498845684595

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1143 & 1107.29807692308 & 35.7019230769229 \tabularnewline
14 & 1807 & 1771.97216346031 & 35.0278365396935 \tabularnewline
15 & 2380 & 2355.3746910683 & 24.6253089317047 \tabularnewline
16 & 2334 & 2321.18572074765 & 12.8142792523522 \tabularnewline
17 & 2116 & 2116.43640244359 & -0.436402443590396 \tabularnewline
18 & 1788 & 1800.67602775681 & -12.6760277568146 \tabularnewline
19 & 1571 & 1476.07541642348 & 94.9245835765169 \tabularnewline
20 & 1306 & 1359.22939204501 & -53.229392045012 \tabularnewline
21 & 952 & 1025.63433632883 & -73.6343363288277 \tabularnewline
22 & 806 & 894.51293258377 & -88.5129325837701 \tabularnewline
23 & 473 & 603.634209603044 & -130.634209603044 \tabularnewline
24 & 278 & 343.941339796728 & -65.9413397967282 \tabularnewline
25 & 993 & 1163.04742162048 & -170.04742162048 \tabularnewline
26 & 1038 & 1801.56296545736 & -763.562965457356 \tabularnewline
27 & 2259 & 2283.14861129109 & -24.1486112910898 \tabularnewline
28 & 2283 & 2216.27891753044 & 66.7210824695585 \tabularnewline
29 & 1746 & 1988.14376301443 & -242.143763014433 \tabularnewline
30 & 1515 & 1618.39113665853 & -103.391136658526 \tabularnewline
31 & 1230 & 1352.62862712071 & -122.62862712071 \tabularnewline
32 & 882 & 1066.45402631264 & -184.454026312644 \tabularnewline
33 & 1028 & 676.246347199106 & 351.753652800894 \tabularnewline
34 & 704 & 551.905734383312 & 152.094265616688 \tabularnewline
35 & 390 & 231.054621256604 & 158.945378743396 \tabularnewline
36 & 238 & 39.1428079395653 & 198.857192060435 \tabularnewline
37 & 594 & 786.856468623813 & -192.856468623813 \tabularnewline
38 & 692 & 918.734716856008 & -226.734716856008 \tabularnewline
39 & 2125 & 2064.69579489301 & 60.3042051069924 \tabularnewline
40 & 1849 & 2080.32516970365 & -231.325169703648 \tabularnewline
41 & 1468 & 1561.22459786034 & -93.2245978603391 \tabularnewline
42 & 1531 & 1317.83157056742 & 213.168429432581 \tabularnewline
43 & 1203 & 1067.22082396312 & 135.779176036876 \tabularnewline
44 & 878 & 758.908057792131 & 119.091942207869 \tabularnewline
45 & 818 & 853.342367001082 & -35.3423670010818 \tabularnewline
46 & 605 & 529.724213591956 & 75.275786408044 \tabularnewline
47 & 316 & 209.90577699056 & 106.09422300944 \tabularnewline
48 & 136 & 48.0808615885953 & 87.9191384114047 \tabularnewline
49 & 528 & 459.246917005646 & 68.7530829943544 \tabularnewline
50 & 654 & 591.676528444318 & 62.3234715556819 \tabularnewline
51 & 1892 & 2012.24662077539 & -120.246620775388 \tabularnewline
52 & 1597 & 1773.39698192268 & -176.396981922681 \tabularnewline
53 & 1515 & 1380.87119106321 & 134.12880893679 \tabularnewline
54 & 1241 & 1423.81990053132 & -182.819900531316 \tabularnewline
55 & 1026 & 1075.16759369821 & -49.1675936982081 \tabularnewline
56 & 758 & 736.720746819126 & 21.2792531808743 \tabularnewline
57 & 733 & 693.129857336999 & 39.8701426630007 \tabularnewline
58 & 481 & 469.737954280906 & 11.2620457190945 \tabularnewline
59 & 280 & 169.572436279002 & 110.427563720998 \tabularnewline
60 & 117 & -6.87734942151371 & 123.877349421514 \tabularnewline
61 & 651 & 392.347080495141 & 258.652919504859 \tabularnewline
62 & 611 & 540.736690074797 & 70.2633099252033 \tabularnewline
63 & 1898 & 1813.42216753888 & 84.5778324611217 \tabularnewline
64 & 1385 & 1553.5687679754 & -168.568767975398 \tabularnewline
65 & 1047 & 1426.94068952068 & -379.940689520684 \tabularnewline
66 & 1007 & 1156.32480761504 & -149.324807615043 \tabularnewline
67 & 842 & 921.795223652259 & -79.7952236522593 \tabularnewline
68 & 827 & 638.310283128498 & 188.689716871502 \tabularnewline
69 & 711 & 627.631274264438 & 83.368725735562 \tabularnewline
70 & 443 & 386.721436614033 & 56.2785633859669 \tabularnewline
71 & 313 & 176.261772463807 & 136.738227536193 \tabularnewline
72 & 202 & 16.7204028057851 & 185.279597194215 \tabularnewline
73 & 473 & 538.119485455509 & -65.1194854555091 \tabularnewline
74 & 566 & 498.381245298251 & 67.618754701749 \tabularnewline
75 & 1609 & 1782.16593161148 & -173.16593161148 \tabularnewline
76 & 1296 & 1282.77287746072 & 13.2271225392753 \tabularnewline
77 & 1153 & 995.625782962609 & 157.374217037391 \tabularnewline
78 & 1155 & 974.017355113229 & 180.982644886771 \tabularnewline
79 & 859 & 839.426138583425 & 19.5738614165748 \tabularnewline
80 & 798 & 801.161979493408 & -3.16197949340847 \tabularnewline
81 & 557 & 693.999673177426 & -136.999673177426 \tabularnewline
82 & 402 & 415.923647087576 & -13.9236470875757 \tabularnewline
83 & 223 & 271.105053960592 & -48.1050539605918 \tabularnewline
84 & 153 & 137.118431526154 & 15.8815684738464 \tabularnewline
85 & 548 & 434.093572581901 & 113.906427418099 \tabularnewline
86 & 647 & 524.642359620098 & 122.357640379902 \tabularnewline
87 & 1757 & 1616.57832625399 & 140.421673746009 \tabularnewline
88 & 1326 & 1310.17410777074 & 15.8258922292553 \tabularnewline
89 & 1308 & 1151.41152005328 & 156.588479946715 \tabularnewline
90 & 1175 & 1157.44596766043 & 17.554032339571 \tabularnewline
91 & 992 & 878.63875556422 & 113.36124443578 \tabularnewline
92 & 808 & 837.372875693721 & -29.3728756937205 \tabularnewline
93 & 758 & 622.921658681506 & 135.078341318494 \tabularnewline
94 & 551 & 483.704355584133 & 67.2956444158669 \tabularnewline
95 & 310 & 329.834233483194 & -19.8342334831937 \tabularnewline
96 & 146 & 263.960915369348 & -117.960915369348 \tabularnewline
97 & 649 & 640.138818274474 & 8.86118172552642 \tabularnewline
98 & 602 & 736.500413061091 & -134.500413061091 \tabularnewline
99 & 1801 & 1824.20936585827 & -23.2093658582687 \tabularnewline
100 & 1481 & 1401.23098681069 & 79.769013189305 \tabularnewline
101 & 1400 & 1369.40515522261 & 30.5948447773881 \tabularnewline
102 & 1319 & 1249.5152855549 & 69.4847144451023 \tabularnewline
103 & 1153 & 1058.00051028715 & 94.9994897128497 \tabularnewline
104 & 950 & 898.400784113969 & 51.5992158860313 \tabularnewline
105 & 829 & 832.06812389434 & -3.06812389433969 \tabularnewline
106 & 636 & 624.791694327954 & 11.208305672046 \tabularnewline
107 & 310 & 393.715341732359 & -83.7153417323586 \tabularnewline
108 & 191 & 239.824315821044 & -48.8243158210436 \tabularnewline
109 & 679 & 728.953713276374 & -49.9537132763739 \tabularnewline
110 & 842 & 700.243751203549 & 141.756248796451 \tabularnewline
111 & 1975 & 1910.6882617361 & 64.3117382638975 \tabularnewline
112 & 1677 & 1586.89876604795 & 90.1012339520471 \tabularnewline
113 & 1418 & 1520.35524588064 & -102.35524588064 \tabularnewline
114 & 1540 & 1423.63718918207 & 116.362810817932 \tabularnewline
115 & 1173 & 1261.85206830103 & -88.8520683010315 \tabularnewline
116 & 941 & 1050.09777348957 & -109.097773489569 \tabularnewline
117 & 989 & 922.12102787926 & 66.8789721207396 \tabularnewline
118 & 614 & 733.47266190087 & -119.47266190087 \tabularnewline
119 & 352 & 409.192801824092 & -57.192801824092 \tabularnewline
120 & 405 & 285.501154315405 & 119.498845684595 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308370&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]1143[/C][C]1107.29807692308[/C][C]35.7019230769229[/C][/ROW]
[ROW][C]14[/C][C]1807[/C][C]1771.97216346031[/C][C]35.0278365396935[/C][/ROW]
[ROW][C]15[/C][C]2380[/C][C]2355.3746910683[/C][C]24.6253089317047[/C][/ROW]
[ROW][C]16[/C][C]2334[/C][C]2321.18572074765[/C][C]12.8142792523522[/C][/ROW]
[ROW][C]17[/C][C]2116[/C][C]2116.43640244359[/C][C]-0.436402443590396[/C][/ROW]
[ROW][C]18[/C][C]1788[/C][C]1800.67602775681[/C][C]-12.6760277568146[/C][/ROW]
[ROW][C]19[/C][C]1571[/C][C]1476.07541642348[/C][C]94.9245835765169[/C][/ROW]
[ROW][C]20[/C][C]1306[/C][C]1359.22939204501[/C][C]-53.229392045012[/C][/ROW]
[ROW][C]21[/C][C]952[/C][C]1025.63433632883[/C][C]-73.6343363288277[/C][/ROW]
[ROW][C]22[/C][C]806[/C][C]894.51293258377[/C][C]-88.5129325837701[/C][/ROW]
[ROW][C]23[/C][C]473[/C][C]603.634209603044[/C][C]-130.634209603044[/C][/ROW]
[ROW][C]24[/C][C]278[/C][C]343.941339796728[/C][C]-65.9413397967282[/C][/ROW]
[ROW][C]25[/C][C]993[/C][C]1163.04742162048[/C][C]-170.04742162048[/C][/ROW]
[ROW][C]26[/C][C]1038[/C][C]1801.56296545736[/C][C]-763.562965457356[/C][/ROW]
[ROW][C]27[/C][C]2259[/C][C]2283.14861129109[/C][C]-24.1486112910898[/C][/ROW]
[ROW][C]28[/C][C]2283[/C][C]2216.27891753044[/C][C]66.7210824695585[/C][/ROW]
[ROW][C]29[/C][C]1746[/C][C]1988.14376301443[/C][C]-242.143763014433[/C][/ROW]
[ROW][C]30[/C][C]1515[/C][C]1618.39113665853[/C][C]-103.391136658526[/C][/ROW]
[ROW][C]31[/C][C]1230[/C][C]1352.62862712071[/C][C]-122.62862712071[/C][/ROW]
[ROW][C]32[/C][C]882[/C][C]1066.45402631264[/C][C]-184.454026312644[/C][/ROW]
[ROW][C]33[/C][C]1028[/C][C]676.246347199106[/C][C]351.753652800894[/C][/ROW]
[ROW][C]34[/C][C]704[/C][C]551.905734383312[/C][C]152.094265616688[/C][/ROW]
[ROW][C]35[/C][C]390[/C][C]231.054621256604[/C][C]158.945378743396[/C][/ROW]
[ROW][C]36[/C][C]238[/C][C]39.1428079395653[/C][C]198.857192060435[/C][/ROW]
[ROW][C]37[/C][C]594[/C][C]786.856468623813[/C][C]-192.856468623813[/C][/ROW]
[ROW][C]38[/C][C]692[/C][C]918.734716856008[/C][C]-226.734716856008[/C][/ROW]
[ROW][C]39[/C][C]2125[/C][C]2064.69579489301[/C][C]60.3042051069924[/C][/ROW]
[ROW][C]40[/C][C]1849[/C][C]2080.32516970365[/C][C]-231.325169703648[/C][/ROW]
[ROW][C]41[/C][C]1468[/C][C]1561.22459786034[/C][C]-93.2245978603391[/C][/ROW]
[ROW][C]42[/C][C]1531[/C][C]1317.83157056742[/C][C]213.168429432581[/C][/ROW]
[ROW][C]43[/C][C]1203[/C][C]1067.22082396312[/C][C]135.779176036876[/C][/ROW]
[ROW][C]44[/C][C]878[/C][C]758.908057792131[/C][C]119.091942207869[/C][/ROW]
[ROW][C]45[/C][C]818[/C][C]853.342367001082[/C][C]-35.3423670010818[/C][/ROW]
[ROW][C]46[/C][C]605[/C][C]529.724213591956[/C][C]75.275786408044[/C][/ROW]
[ROW][C]47[/C][C]316[/C][C]209.90577699056[/C][C]106.09422300944[/C][/ROW]
[ROW][C]48[/C][C]136[/C][C]48.0808615885953[/C][C]87.9191384114047[/C][/ROW]
[ROW][C]49[/C][C]528[/C][C]459.246917005646[/C][C]68.7530829943544[/C][/ROW]
[ROW][C]50[/C][C]654[/C][C]591.676528444318[/C][C]62.3234715556819[/C][/ROW]
[ROW][C]51[/C][C]1892[/C][C]2012.24662077539[/C][C]-120.246620775388[/C][/ROW]
[ROW][C]52[/C][C]1597[/C][C]1773.39698192268[/C][C]-176.396981922681[/C][/ROW]
[ROW][C]53[/C][C]1515[/C][C]1380.87119106321[/C][C]134.12880893679[/C][/ROW]
[ROW][C]54[/C][C]1241[/C][C]1423.81990053132[/C][C]-182.819900531316[/C][/ROW]
[ROW][C]55[/C][C]1026[/C][C]1075.16759369821[/C][C]-49.1675936982081[/C][/ROW]
[ROW][C]56[/C][C]758[/C][C]736.720746819126[/C][C]21.2792531808743[/C][/ROW]
[ROW][C]57[/C][C]733[/C][C]693.129857336999[/C][C]39.8701426630007[/C][/ROW]
[ROW][C]58[/C][C]481[/C][C]469.737954280906[/C][C]11.2620457190945[/C][/ROW]
[ROW][C]59[/C][C]280[/C][C]169.572436279002[/C][C]110.427563720998[/C][/ROW]
[ROW][C]60[/C][C]117[/C][C]-6.87734942151371[/C][C]123.877349421514[/C][/ROW]
[ROW][C]61[/C][C]651[/C][C]392.347080495141[/C][C]258.652919504859[/C][/ROW]
[ROW][C]62[/C][C]611[/C][C]540.736690074797[/C][C]70.2633099252033[/C][/ROW]
[ROW][C]63[/C][C]1898[/C][C]1813.42216753888[/C][C]84.5778324611217[/C][/ROW]
[ROW][C]64[/C][C]1385[/C][C]1553.5687679754[/C][C]-168.568767975398[/C][/ROW]
[ROW][C]65[/C][C]1047[/C][C]1426.94068952068[/C][C]-379.940689520684[/C][/ROW]
[ROW][C]66[/C][C]1007[/C][C]1156.32480761504[/C][C]-149.324807615043[/C][/ROW]
[ROW][C]67[/C][C]842[/C][C]921.795223652259[/C][C]-79.7952236522593[/C][/ROW]
[ROW][C]68[/C][C]827[/C][C]638.310283128498[/C][C]188.689716871502[/C][/ROW]
[ROW][C]69[/C][C]711[/C][C]627.631274264438[/C][C]83.368725735562[/C][/ROW]
[ROW][C]70[/C][C]443[/C][C]386.721436614033[/C][C]56.2785633859669[/C][/ROW]
[ROW][C]71[/C][C]313[/C][C]176.261772463807[/C][C]136.738227536193[/C][/ROW]
[ROW][C]72[/C][C]202[/C][C]16.7204028057851[/C][C]185.279597194215[/C][/ROW]
[ROW][C]73[/C][C]473[/C][C]538.119485455509[/C][C]-65.1194854555091[/C][/ROW]
[ROW][C]74[/C][C]566[/C][C]498.381245298251[/C][C]67.618754701749[/C][/ROW]
[ROW][C]75[/C][C]1609[/C][C]1782.16593161148[/C][C]-173.16593161148[/C][/ROW]
[ROW][C]76[/C][C]1296[/C][C]1282.77287746072[/C][C]13.2271225392753[/C][/ROW]
[ROW][C]77[/C][C]1153[/C][C]995.625782962609[/C][C]157.374217037391[/C][/ROW]
[ROW][C]78[/C][C]1155[/C][C]974.017355113229[/C][C]180.982644886771[/C][/ROW]
[ROW][C]79[/C][C]859[/C][C]839.426138583425[/C][C]19.5738614165748[/C][/ROW]
[ROW][C]80[/C][C]798[/C][C]801.161979493408[/C][C]-3.16197949340847[/C][/ROW]
[ROW][C]81[/C][C]557[/C][C]693.999673177426[/C][C]-136.999673177426[/C][/ROW]
[ROW][C]82[/C][C]402[/C][C]415.923647087576[/C][C]-13.9236470875757[/C][/ROW]
[ROW][C]83[/C][C]223[/C][C]271.105053960592[/C][C]-48.1050539605918[/C][/ROW]
[ROW][C]84[/C][C]153[/C][C]137.118431526154[/C][C]15.8815684738464[/C][/ROW]
[ROW][C]85[/C][C]548[/C][C]434.093572581901[/C][C]113.906427418099[/C][/ROW]
[ROW][C]86[/C][C]647[/C][C]524.642359620098[/C][C]122.357640379902[/C][/ROW]
[ROW][C]87[/C][C]1757[/C][C]1616.57832625399[/C][C]140.421673746009[/C][/ROW]
[ROW][C]88[/C][C]1326[/C][C]1310.17410777074[/C][C]15.8258922292553[/C][/ROW]
[ROW][C]89[/C][C]1308[/C][C]1151.41152005328[/C][C]156.588479946715[/C][/ROW]
[ROW][C]90[/C][C]1175[/C][C]1157.44596766043[/C][C]17.554032339571[/C][/ROW]
[ROW][C]91[/C][C]992[/C][C]878.63875556422[/C][C]113.36124443578[/C][/ROW]
[ROW][C]92[/C][C]808[/C][C]837.372875693721[/C][C]-29.3728756937205[/C][/ROW]
[ROW][C]93[/C][C]758[/C][C]622.921658681506[/C][C]135.078341318494[/C][/ROW]
[ROW][C]94[/C][C]551[/C][C]483.704355584133[/C][C]67.2956444158669[/C][/ROW]
[ROW][C]95[/C][C]310[/C][C]329.834233483194[/C][C]-19.8342334831937[/C][/ROW]
[ROW][C]96[/C][C]146[/C][C]263.960915369348[/C][C]-117.960915369348[/C][/ROW]
[ROW][C]97[/C][C]649[/C][C]640.138818274474[/C][C]8.86118172552642[/C][/ROW]
[ROW][C]98[/C][C]602[/C][C]736.500413061091[/C][C]-134.500413061091[/C][/ROW]
[ROW][C]99[/C][C]1801[/C][C]1824.20936585827[/C][C]-23.2093658582687[/C][/ROW]
[ROW][C]100[/C][C]1481[/C][C]1401.23098681069[/C][C]79.769013189305[/C][/ROW]
[ROW][C]101[/C][C]1400[/C][C]1369.40515522261[/C][C]30.5948447773881[/C][/ROW]
[ROW][C]102[/C][C]1319[/C][C]1249.5152855549[/C][C]69.4847144451023[/C][/ROW]
[ROW][C]103[/C][C]1153[/C][C]1058.00051028715[/C][C]94.9994897128497[/C][/ROW]
[ROW][C]104[/C][C]950[/C][C]898.400784113969[/C][C]51.5992158860313[/C][/ROW]
[ROW][C]105[/C][C]829[/C][C]832.06812389434[/C][C]-3.06812389433969[/C][/ROW]
[ROW][C]106[/C][C]636[/C][C]624.791694327954[/C][C]11.208305672046[/C][/ROW]
[ROW][C]107[/C][C]310[/C][C]393.715341732359[/C][C]-83.7153417323586[/C][/ROW]
[ROW][C]108[/C][C]191[/C][C]239.824315821044[/C][C]-48.8243158210436[/C][/ROW]
[ROW][C]109[/C][C]679[/C][C]728.953713276374[/C][C]-49.9537132763739[/C][/ROW]
[ROW][C]110[/C][C]842[/C][C]700.243751203549[/C][C]141.756248796451[/C][/ROW]
[ROW][C]111[/C][C]1975[/C][C]1910.6882617361[/C][C]64.3117382638975[/C][/ROW]
[ROW][C]112[/C][C]1677[/C][C]1586.89876604795[/C][C]90.1012339520471[/C][/ROW]
[ROW][C]113[/C][C]1418[/C][C]1520.35524588064[/C][C]-102.35524588064[/C][/ROW]
[ROW][C]114[/C][C]1540[/C][C]1423.63718918207[/C][C]116.362810817932[/C][/ROW]
[ROW][C]115[/C][C]1173[/C][C]1261.85206830103[/C][C]-88.8520683010315[/C][/ROW]
[ROW][C]116[/C][C]941[/C][C]1050.09777348957[/C][C]-109.097773489569[/C][/ROW]
[ROW][C]117[/C][C]989[/C][C]922.12102787926[/C][C]66.8789721207396[/C][/ROW]
[ROW][C]118[/C][C]614[/C][C]733.47266190087[/C][C]-119.47266190087[/C][/ROW]
[ROW][C]119[/C][C]352[/C][C]409.192801824092[/C][C]-57.192801824092[/C][/ROW]
[ROW][C]120[/C][C]405[/C][C]285.501154315405[/C][C]119.498845684595[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308370&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308370&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
1311431107.2980769230835.7019230769229
1418071771.9721634603135.0278365396935
1523802355.374691068324.6253089317047
1623342321.1857207476512.8142792523522
1721162116.43640244359-0.436402443590396
1817881800.67602775681-12.6760277568146
1915711476.0754164234894.9245835765169
2013061359.22939204501-53.229392045012
219521025.63433632883-73.6343363288277
22806894.51293258377-88.5129325837701
23473603.634209603044-130.634209603044
24278343.941339796728-65.9413397967282
259931163.04742162048-170.04742162048
2610381801.56296545736-763.562965457356
2722592283.14861129109-24.1486112910898
2822832216.2789175304466.7210824695585
2917461988.14376301443-242.143763014433
3015151618.39113665853-103.391136658526
3112301352.62862712071-122.62862712071
328821066.45402631264-184.454026312644
331028676.246347199106351.753652800894
34704551.905734383312152.094265616688
35390231.054621256604158.945378743396
3623839.1428079395653198.857192060435
37594786.856468623813-192.856468623813
38692918.734716856008-226.734716856008
3921252064.6957948930160.3042051069924
4018492080.32516970365-231.325169703648
4114681561.22459786034-93.2245978603391
4215311317.83157056742213.168429432581
4312031067.22082396312135.779176036876
44878758.908057792131119.091942207869
45818853.342367001082-35.3423670010818
46605529.72421359195675.275786408044
47316209.90577699056106.09422300944
4813648.080861588595387.9191384114047
49528459.24691700564668.7530829943544
50654591.67652844431862.3234715556819
5118922012.24662077539-120.246620775388
5215971773.39698192268-176.396981922681
5315151380.87119106321134.12880893679
5412411423.81990053132-182.819900531316
5510261075.16759369821-49.1675936982081
56758736.72074681912621.2792531808743
57733693.12985733699939.8701426630007
58481469.73795428090611.2620457190945
59280169.572436279002110.427563720998
60117-6.87734942151371123.877349421514
61651392.347080495141258.652919504859
62611540.73669007479770.2633099252033
6318981813.4221675388884.5778324611217
6413851553.5687679754-168.568767975398
6510471426.94068952068-379.940689520684
6610071156.32480761504-149.324807615043
67842921.795223652259-79.7952236522593
68827638.310283128498188.689716871502
69711627.63127426443883.368725735562
70443386.72143661403356.2785633859669
71313176.261772463807136.738227536193
7220216.7204028057851185.279597194215
73473538.119485455509-65.1194854555091
74566498.38124529825167.618754701749
7516091782.16593161148-173.16593161148
7612961282.7728774607213.2271225392753
771153995.625782962609157.374217037391
781155974.017355113229180.982644886771
79859839.42613858342519.5738614165748
80798801.161979493408-3.16197949340847
81557693.999673177426-136.999673177426
82402415.923647087576-13.9236470875757
83223271.105053960592-48.1050539605918
84153137.11843152615415.8815684738464
85548434.093572581901113.906427418099
86647524.642359620098122.357640379902
8717571616.57832625399140.421673746009
8813261310.1741077707415.8258922292553
8913081151.41152005328156.588479946715
9011751157.4459676604317.554032339571
91992878.63875556422113.36124443578
92808837.372875693721-29.3728756937205
93758622.921658681506135.078341318494
94551483.70435558413367.2956444158669
95310329.834233483194-19.8342334831937
96146263.960915369348-117.960915369348
97649640.1388182744748.86118172552642
98602736.500413061091-134.500413061091
9918011824.20936585827-23.2093658582687
10014811401.2309868106979.769013189305
10114001369.4051552226130.5948447773881
10213191249.515285554969.4847144451023
10311531058.0005102871594.9994897128497
104950898.40078411396951.5992158860313
105829832.06812389434-3.06812389433969
106636624.79169432795411.208305672046
107310393.715341732359-83.7153417323586
108191239.824315821044-48.8243158210436
109679728.953713276374-49.9537132763739
110842700.243751203549141.756248796451
11119751910.688261736164.3117382638975
11216771586.8987660479590.1012339520471
11314181520.35524588064-102.35524588064
11415401423.63718918207116.362810817932
11511731261.85206830103-88.8520683010315
1169411050.09777348957-109.097773489569
117989922.1210278792666.8789721207396
118614733.47266190087-119.47266190087
119352409.192801824092-57.192801824092
120405285.501154315405119.498845684595







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121790.658500829979510.8720613565191070.44494030344
122928.118089241213646.6747819928981209.56139648953
1232060.343240832391776.794167840812343.89231382397
1241750.744077747981464.594370849022036.89378464694
1251512.859916285041223.572779804051802.14705276604
1261607.001821386941314.003130662911900.00051211097
1271260.56106303851963.2444148285521557.87771124847
1281038.93566028297736.6677407308351341.2035798351
1291068.01947347718760.1455891100781375.89335784428
130716.988016144078402.8376254008681031.13840688729
131456.792234154266135.684321726953777.900146581579
132487.410385809381158.65853839281816.162233225953

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 790.658500829979 & 510.872061356519 & 1070.44494030344 \tabularnewline
122 & 928.118089241213 & 646.674781992898 & 1209.56139648953 \tabularnewline
123 & 2060.34324083239 & 1776.79416784081 & 2343.89231382397 \tabularnewline
124 & 1750.74407774798 & 1464.59437084902 & 2036.89378464694 \tabularnewline
125 & 1512.85991628504 & 1223.57277980405 & 1802.14705276604 \tabularnewline
126 & 1607.00182138694 & 1314.00313066291 & 1900.00051211097 \tabularnewline
127 & 1260.56106303851 & 963.244414828552 & 1557.87771124847 \tabularnewline
128 & 1038.93566028297 & 736.667740730835 & 1341.2035798351 \tabularnewline
129 & 1068.01947347718 & 760.145589110078 & 1375.89335784428 \tabularnewline
130 & 716.988016144078 & 402.837625400868 & 1031.13840688729 \tabularnewline
131 & 456.792234154266 & 135.684321726953 & 777.900146581579 \tabularnewline
132 & 487.410385809381 & 158.65853839281 & 816.162233225953 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308370&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]121[/C][C]790.658500829979[/C][C]510.872061356519[/C][C]1070.44494030344[/C][/ROW]
[ROW][C]122[/C][C]928.118089241213[/C][C]646.674781992898[/C][C]1209.56139648953[/C][/ROW]
[ROW][C]123[/C][C]2060.34324083239[/C][C]1776.79416784081[/C][C]2343.89231382397[/C][/ROW]
[ROW][C]124[/C][C]1750.74407774798[/C][C]1464.59437084902[/C][C]2036.89378464694[/C][/ROW]
[ROW][C]125[/C][C]1512.85991628504[/C][C]1223.57277980405[/C][C]1802.14705276604[/C][/ROW]
[ROW][C]126[/C][C]1607.00182138694[/C][C]1314.00313066291[/C][C]1900.00051211097[/C][/ROW]
[ROW][C]127[/C][C]1260.56106303851[/C][C]963.244414828552[/C][C]1557.87771124847[/C][/ROW]
[ROW][C]128[/C][C]1038.93566028297[/C][C]736.667740730835[/C][C]1341.2035798351[/C][/ROW]
[ROW][C]129[/C][C]1068.01947347718[/C][C]760.145589110078[/C][C]1375.89335784428[/C][/ROW]
[ROW][C]130[/C][C]716.988016144078[/C][C]402.837625400868[/C][C]1031.13840688729[/C][/ROW]
[ROW][C]131[/C][C]456.792234154266[/C][C]135.684321726953[/C][C]777.900146581579[/C][/ROW]
[ROW][C]132[/C][C]487.410385809381[/C][C]158.65853839281[/C][C]816.162233225953[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308370&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308370&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
121790.658500829979510.8720613565191070.44494030344
122928.118089241213646.6747819928981209.56139648953
1232060.343240832391776.794167840812343.89231382397
1241750.744077747981464.594370849022036.89378464694
1251512.859916285041223.572779804051802.14705276604
1261607.001821386941314.003130662911900.00051211097
1271260.56106303851963.2444148285521557.87771124847
1281038.93566028297736.6677407308351341.2035798351
1291068.01947347718760.1455891100781375.89335784428
130716.988016144078402.8376254008681031.13840688729
131456.792234154266135.684321726953777.900146581579
132487.410385809381158.65853839281816.162233225953



Parameters (Session):
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par4 <- '12'
par3 <- 'additive'
par2 <- 'Single'
par1 <- '12'
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')