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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 13 Dec 2016 12:16:55 +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/2016/Dec/13/t1481627917eln1s4r39xe6fxy.htm/, Retrieved Sun, 05 May 2024 06:20:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299063, Retrieved Sun, 05 May 2024 06:20:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact79
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2016-12-13 11:16:55] [94c1b173d9287822f5e2740a4a602bdd] [Current]
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Dataseries X:
13430
13020
11710
9265
7280
5040
3860
6160
13610
15455
14530
13815
12860
11500
10660
9340
8050
6540
5060
6350
14130
16380
16160
15850
15930
15320
13420
12255
8785
6380
4760
5730
10810
12845
12865
13515
13880
12960
12090
9510
8130
6625
4920
4650
10085
13960
14495
14340
13875
13135
13415
9280
7075
5660
4270
5085
11945
14335
14105
13755
12920
11650
10720
8600
7795
6550
4800
5900
14095
15170
14875
15230
13685
12780
11510
9915
8740
7870
6650
5285
13195
13390
13490
13445
13070
12480
11550
10725
9130
7885
6415
5540
9350
12645
11985
10055
10295
10280
9420
9575
8090
5855
4445
3555
12870
14750
13615
13705
13940
11900
9000
7340
6425
5535
4050
3485
8090
11380
11355
10530
9285




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=299063&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=299063&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299063&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
alpha0.87164642738043
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.87164642738043 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299063&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]0.87164642738043[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299063&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299063&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
alpha0.87164642738043
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131286012590.6398735141269.360126485943
141150011454.714084923245.2859150768145
151066010669.4979469604-9.4979469603677
1693409327.3593402367912.6406597632085
1780508002.5617742066847.4382257933175
1865406470.7006134460869.2993865539192
1950604022.040434004591037.95956599541
2063507953.82481725652-1603.82481725652
211413014692.3438853349-562.343885334914
221638016257.291346006122.708653994046
231616015394.8965247539765.103475246058
241585015192.1280625589657.871937441141
251593014613.02321694471316.97678305534
261532014034.92250281121285.0774971888
271342014044.8673260424-624.867326042411
281225511804.2374097111450.762590288949
29878510448.3745757979-1663.37457579787
3063807239.84635751154-859.846357511544
3147604099.5767895863660.423210413699
3257307120.1695513857-1390.1695513857
331081013605.2227700132-2795.22277001324
341284512876.5629957221-31.5629957221463
351286512163.6441961432701.355803856839
361351512086.52763982571428.47236017435
371388012431.73950329731448.26049670265
381296012203.1566839337756.843316066284
391209011729.265402178360.734597821975
40951010647.8821563749-1137.8821563749
4181308044.0789091241185.9210908758905
4266256579.1623806426145.8376193573913
4349204329.7052071886590.294792811401
4446507026.90226245115-2376.90226245115
451008511394.9287132926-1309.9287132926
461396012212.81567180421747.18432819577
471449513094.41966638421400.58033361576
481434013627.2254045472712.774595452795
491387513281.3590353593593.640964640666
501313512223.6787376754911.321262324576
511341511826.87958762561588.12041237444
52928011455.7663279336-2175.76632793364
5370758096.56768107652-1021.56768107652
5456605839.66490675914-179.664906759137
5542703774.65149726086495.348502739141
5650855641.18803996666-556.188039966657
571194512422.6251853069-477.625185306879
581433514763.9949912275-428.994991227542
591410513665.3530864567439.646913543291
601375513294.1785386168460.82146138319
611292012757.3163917682162.68360823178
621165011469.5259331414180.474066858606
631072010635.611938443784.3880615562866
6486008885.44946443485-285.449464434849
6577957400.34004170413394.65995829587
6665506363.74296450635186.257035493648
6748004415.3548508938384.645149106201
6859006186.71044196095-286.71044196095
691409514420.3088305327-325.308830532733
701517017393.7834998428-2223.78349984284
711487514787.611024944987.3889750551425
721523014066.59356846871163.4064315313
731368514004.0882439001-319.088243900147
741278012206.1884192615573.811580738466
751151011607.6296080364-97.6296080364009
7699159507.35233408036407.647665919636
7787408537.70306215488202.296937845116
7878707137.01915694423732.980843055766
7966505292.912185291431357.08781470857
8052858287.04599484649-3002.04599484649
811319513820.1498993845-625.149899384485
821339016083.4662765851-2693.46627658513
831349013405.654785598684.3452144013772
841344512878.5703145362566.429685463801
851307012266.0275713754803.972428624616
861248011635.2564273976844.743572602398
871155011225.8888250242324.111174975758
88107259556.466182913721168.53381708628
8991309131.03584696417-1.03584696416874
9078857544.62651576662340.373484233375
9164155415.5346740036999.465325996403
9255407303.10220720427-1763.10220720427
93935014982.6394442965-5632.63944429654
941264511984.2222901238660.777709876229
951198512588.9528390693-603.952839069349
961005511584.8945167401-1529.89451674011
97102959440.2146485861854.785351413897
98102809157.762409433211122.23759056679
9994209158.84010821014261.159891789865
10095757883.593091009131691.40690899087
10180907971.08496180761118.915038192395
10258556712.84642312367-857.84642312367
10344454185.0360975289259.963902471096
10435554831.59080245833-1276.59080245833
105128709352.206904239733517.79309576027
1061475016003.3925538433-1253.39255384327
1071361514737.9484445613-1122.94844456134
1081370513036.1288234648668.871176535227
1091394012904.04646002251035.95353997748
1101190012438.9934759148-538.993475914842
111900010694.4290212323-1694.42902123234
11273407893.90286557468-553.902865574679
11364256188.5727952998236.4272047002
11455355213.61031561955321.389684380453
11540503957.6730092369992.3269907630138
11634854197.72602202601-712.726022026007
11780909750.49062673218-1660.49062673218
1181138010236.02399692871143.97600307132
1191135511121.4721062981233.52789370193
1201053010922.0625661153-392.062566115297
121928510070.9941922621-785.994192262066

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 12860 & 12590.6398735141 & 269.360126485943 \tabularnewline
14 & 11500 & 11454.7140849232 & 45.2859150768145 \tabularnewline
15 & 10660 & 10669.4979469604 & -9.4979469603677 \tabularnewline
16 & 9340 & 9327.35934023679 & 12.6406597632085 \tabularnewline
17 & 8050 & 8002.56177420668 & 47.4382257933175 \tabularnewline
18 & 6540 & 6470.70061344608 & 69.2993865539192 \tabularnewline
19 & 5060 & 4022.04043400459 & 1037.95956599541 \tabularnewline
20 & 6350 & 7953.82481725652 & -1603.82481725652 \tabularnewline
21 & 14130 & 14692.3438853349 & -562.343885334914 \tabularnewline
22 & 16380 & 16257.291346006 & 122.708653994046 \tabularnewline
23 & 16160 & 15394.8965247539 & 765.103475246058 \tabularnewline
24 & 15850 & 15192.1280625589 & 657.871937441141 \tabularnewline
25 & 15930 & 14613.0232169447 & 1316.97678305534 \tabularnewline
26 & 15320 & 14034.9225028112 & 1285.0774971888 \tabularnewline
27 & 13420 & 14044.8673260424 & -624.867326042411 \tabularnewline
28 & 12255 & 11804.2374097111 & 450.762590288949 \tabularnewline
29 & 8785 & 10448.3745757979 & -1663.37457579787 \tabularnewline
30 & 6380 & 7239.84635751154 & -859.846357511544 \tabularnewline
31 & 4760 & 4099.5767895863 & 660.423210413699 \tabularnewline
32 & 5730 & 7120.1695513857 & -1390.1695513857 \tabularnewline
33 & 10810 & 13605.2227700132 & -2795.22277001324 \tabularnewline
34 & 12845 & 12876.5629957221 & -31.5629957221463 \tabularnewline
35 & 12865 & 12163.6441961432 & 701.355803856839 \tabularnewline
36 & 13515 & 12086.5276398257 & 1428.47236017435 \tabularnewline
37 & 13880 & 12431.7395032973 & 1448.26049670265 \tabularnewline
38 & 12960 & 12203.1566839337 & 756.843316066284 \tabularnewline
39 & 12090 & 11729.265402178 & 360.734597821975 \tabularnewline
40 & 9510 & 10647.8821563749 & -1137.8821563749 \tabularnewline
41 & 8130 & 8044.07890912411 & 85.9210908758905 \tabularnewline
42 & 6625 & 6579.16238064261 & 45.8376193573913 \tabularnewline
43 & 4920 & 4329.7052071886 & 590.294792811401 \tabularnewline
44 & 4650 & 7026.90226245115 & -2376.90226245115 \tabularnewline
45 & 10085 & 11394.9287132926 & -1309.9287132926 \tabularnewline
46 & 13960 & 12212.8156718042 & 1747.18432819577 \tabularnewline
47 & 14495 & 13094.4196663842 & 1400.58033361576 \tabularnewline
48 & 14340 & 13627.2254045472 & 712.774595452795 \tabularnewline
49 & 13875 & 13281.3590353593 & 593.640964640666 \tabularnewline
50 & 13135 & 12223.6787376754 & 911.321262324576 \tabularnewline
51 & 13415 & 11826.8795876256 & 1588.12041237444 \tabularnewline
52 & 9280 & 11455.7663279336 & -2175.76632793364 \tabularnewline
53 & 7075 & 8096.56768107652 & -1021.56768107652 \tabularnewline
54 & 5660 & 5839.66490675914 & -179.664906759137 \tabularnewline
55 & 4270 & 3774.65149726086 & 495.348502739141 \tabularnewline
56 & 5085 & 5641.18803996666 & -556.188039966657 \tabularnewline
57 & 11945 & 12422.6251853069 & -477.625185306879 \tabularnewline
58 & 14335 & 14763.9949912275 & -428.994991227542 \tabularnewline
59 & 14105 & 13665.3530864567 & 439.646913543291 \tabularnewline
60 & 13755 & 13294.1785386168 & 460.82146138319 \tabularnewline
61 & 12920 & 12757.3163917682 & 162.68360823178 \tabularnewline
62 & 11650 & 11469.5259331414 & 180.474066858606 \tabularnewline
63 & 10720 & 10635.6119384437 & 84.3880615562866 \tabularnewline
64 & 8600 & 8885.44946443485 & -285.449464434849 \tabularnewline
65 & 7795 & 7400.34004170413 & 394.65995829587 \tabularnewline
66 & 6550 & 6363.74296450635 & 186.257035493648 \tabularnewline
67 & 4800 & 4415.3548508938 & 384.645149106201 \tabularnewline
68 & 5900 & 6186.71044196095 & -286.71044196095 \tabularnewline
69 & 14095 & 14420.3088305327 & -325.308830532733 \tabularnewline
70 & 15170 & 17393.7834998428 & -2223.78349984284 \tabularnewline
71 & 14875 & 14787.6110249449 & 87.3889750551425 \tabularnewline
72 & 15230 & 14066.5935684687 & 1163.4064315313 \tabularnewline
73 & 13685 & 14004.0882439001 & -319.088243900147 \tabularnewline
74 & 12780 & 12206.1884192615 & 573.811580738466 \tabularnewline
75 & 11510 & 11607.6296080364 & -97.6296080364009 \tabularnewline
76 & 9915 & 9507.35233408036 & 407.647665919636 \tabularnewline
77 & 8740 & 8537.70306215488 & 202.296937845116 \tabularnewline
78 & 7870 & 7137.01915694423 & 732.980843055766 \tabularnewline
79 & 6650 & 5292.91218529143 & 1357.08781470857 \tabularnewline
80 & 5285 & 8287.04599484649 & -3002.04599484649 \tabularnewline
81 & 13195 & 13820.1498993845 & -625.149899384485 \tabularnewline
82 & 13390 & 16083.4662765851 & -2693.46627658513 \tabularnewline
83 & 13490 & 13405.6547855986 & 84.3452144013772 \tabularnewline
84 & 13445 & 12878.5703145362 & 566.429685463801 \tabularnewline
85 & 13070 & 12266.0275713754 & 803.972428624616 \tabularnewline
86 & 12480 & 11635.2564273976 & 844.743572602398 \tabularnewline
87 & 11550 & 11225.8888250242 & 324.111174975758 \tabularnewline
88 & 10725 & 9556.46618291372 & 1168.53381708628 \tabularnewline
89 & 9130 & 9131.03584696417 & -1.03584696416874 \tabularnewline
90 & 7885 & 7544.62651576662 & 340.373484233375 \tabularnewline
91 & 6415 & 5415.5346740036 & 999.465325996403 \tabularnewline
92 & 5540 & 7303.10220720427 & -1763.10220720427 \tabularnewline
93 & 9350 & 14982.6394442965 & -5632.63944429654 \tabularnewline
94 & 12645 & 11984.2222901238 & 660.777709876229 \tabularnewline
95 & 11985 & 12588.9528390693 & -603.952839069349 \tabularnewline
96 & 10055 & 11584.8945167401 & -1529.89451674011 \tabularnewline
97 & 10295 & 9440.2146485861 & 854.785351413897 \tabularnewline
98 & 10280 & 9157.76240943321 & 1122.23759056679 \tabularnewline
99 & 9420 & 9158.84010821014 & 261.159891789865 \tabularnewline
100 & 9575 & 7883.59309100913 & 1691.40690899087 \tabularnewline
101 & 8090 & 7971.08496180761 & 118.915038192395 \tabularnewline
102 & 5855 & 6712.84642312367 & -857.84642312367 \tabularnewline
103 & 4445 & 4185.0360975289 & 259.963902471096 \tabularnewline
104 & 3555 & 4831.59080245833 & -1276.59080245833 \tabularnewline
105 & 12870 & 9352.20690423973 & 3517.79309576027 \tabularnewline
106 & 14750 & 16003.3925538433 & -1253.39255384327 \tabularnewline
107 & 13615 & 14737.9484445613 & -1122.94844456134 \tabularnewline
108 & 13705 & 13036.1288234648 & 668.871176535227 \tabularnewline
109 & 13940 & 12904.0464600225 & 1035.95353997748 \tabularnewline
110 & 11900 & 12438.9934759148 & -538.993475914842 \tabularnewline
111 & 9000 & 10694.4290212323 & -1694.42902123234 \tabularnewline
112 & 7340 & 7893.90286557468 & -553.902865574679 \tabularnewline
113 & 6425 & 6188.5727952998 & 236.4272047002 \tabularnewline
114 & 5535 & 5213.61031561955 & 321.389684380453 \tabularnewline
115 & 4050 & 3957.67300923699 & 92.3269907630138 \tabularnewline
116 & 3485 & 4197.72602202601 & -712.726022026007 \tabularnewline
117 & 8090 & 9750.49062673218 & -1660.49062673218 \tabularnewline
118 & 11380 & 10236.0239969287 & 1143.97600307132 \tabularnewline
119 & 11355 & 11121.4721062981 & 233.52789370193 \tabularnewline
120 & 10530 & 10922.0625661153 & -392.062566115297 \tabularnewline
121 & 9285 & 10070.9941922621 & -785.994192262066 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299063&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]12860[/C][C]12590.6398735141[/C][C]269.360126485943[/C][/ROW]
[ROW][C]14[/C][C]11500[/C][C]11454.7140849232[/C][C]45.2859150768145[/C][/ROW]
[ROW][C]15[/C][C]10660[/C][C]10669.4979469604[/C][C]-9.4979469603677[/C][/ROW]
[ROW][C]16[/C][C]9340[/C][C]9327.35934023679[/C][C]12.6406597632085[/C][/ROW]
[ROW][C]17[/C][C]8050[/C][C]8002.56177420668[/C][C]47.4382257933175[/C][/ROW]
[ROW][C]18[/C][C]6540[/C][C]6470.70061344608[/C][C]69.2993865539192[/C][/ROW]
[ROW][C]19[/C][C]5060[/C][C]4022.04043400459[/C][C]1037.95956599541[/C][/ROW]
[ROW][C]20[/C][C]6350[/C][C]7953.82481725652[/C][C]-1603.82481725652[/C][/ROW]
[ROW][C]21[/C][C]14130[/C][C]14692.3438853349[/C][C]-562.343885334914[/C][/ROW]
[ROW][C]22[/C][C]16380[/C][C]16257.291346006[/C][C]122.708653994046[/C][/ROW]
[ROW][C]23[/C][C]16160[/C][C]15394.8965247539[/C][C]765.103475246058[/C][/ROW]
[ROW][C]24[/C][C]15850[/C][C]15192.1280625589[/C][C]657.871937441141[/C][/ROW]
[ROW][C]25[/C][C]15930[/C][C]14613.0232169447[/C][C]1316.97678305534[/C][/ROW]
[ROW][C]26[/C][C]15320[/C][C]14034.9225028112[/C][C]1285.0774971888[/C][/ROW]
[ROW][C]27[/C][C]13420[/C][C]14044.8673260424[/C][C]-624.867326042411[/C][/ROW]
[ROW][C]28[/C][C]12255[/C][C]11804.2374097111[/C][C]450.762590288949[/C][/ROW]
[ROW][C]29[/C][C]8785[/C][C]10448.3745757979[/C][C]-1663.37457579787[/C][/ROW]
[ROW][C]30[/C][C]6380[/C][C]7239.84635751154[/C][C]-859.846357511544[/C][/ROW]
[ROW][C]31[/C][C]4760[/C][C]4099.5767895863[/C][C]660.423210413699[/C][/ROW]
[ROW][C]32[/C][C]5730[/C][C]7120.1695513857[/C][C]-1390.1695513857[/C][/ROW]
[ROW][C]33[/C][C]10810[/C][C]13605.2227700132[/C][C]-2795.22277001324[/C][/ROW]
[ROW][C]34[/C][C]12845[/C][C]12876.5629957221[/C][C]-31.5629957221463[/C][/ROW]
[ROW][C]35[/C][C]12865[/C][C]12163.6441961432[/C][C]701.355803856839[/C][/ROW]
[ROW][C]36[/C][C]13515[/C][C]12086.5276398257[/C][C]1428.47236017435[/C][/ROW]
[ROW][C]37[/C][C]13880[/C][C]12431.7395032973[/C][C]1448.26049670265[/C][/ROW]
[ROW][C]38[/C][C]12960[/C][C]12203.1566839337[/C][C]756.843316066284[/C][/ROW]
[ROW][C]39[/C][C]12090[/C][C]11729.265402178[/C][C]360.734597821975[/C][/ROW]
[ROW][C]40[/C][C]9510[/C][C]10647.8821563749[/C][C]-1137.8821563749[/C][/ROW]
[ROW][C]41[/C][C]8130[/C][C]8044.07890912411[/C][C]85.9210908758905[/C][/ROW]
[ROW][C]42[/C][C]6625[/C][C]6579.16238064261[/C][C]45.8376193573913[/C][/ROW]
[ROW][C]43[/C][C]4920[/C][C]4329.7052071886[/C][C]590.294792811401[/C][/ROW]
[ROW][C]44[/C][C]4650[/C][C]7026.90226245115[/C][C]-2376.90226245115[/C][/ROW]
[ROW][C]45[/C][C]10085[/C][C]11394.9287132926[/C][C]-1309.9287132926[/C][/ROW]
[ROW][C]46[/C][C]13960[/C][C]12212.8156718042[/C][C]1747.18432819577[/C][/ROW]
[ROW][C]47[/C][C]14495[/C][C]13094.4196663842[/C][C]1400.58033361576[/C][/ROW]
[ROW][C]48[/C][C]14340[/C][C]13627.2254045472[/C][C]712.774595452795[/C][/ROW]
[ROW][C]49[/C][C]13875[/C][C]13281.3590353593[/C][C]593.640964640666[/C][/ROW]
[ROW][C]50[/C][C]13135[/C][C]12223.6787376754[/C][C]911.321262324576[/C][/ROW]
[ROW][C]51[/C][C]13415[/C][C]11826.8795876256[/C][C]1588.12041237444[/C][/ROW]
[ROW][C]52[/C][C]9280[/C][C]11455.7663279336[/C][C]-2175.76632793364[/C][/ROW]
[ROW][C]53[/C][C]7075[/C][C]8096.56768107652[/C][C]-1021.56768107652[/C][/ROW]
[ROW][C]54[/C][C]5660[/C][C]5839.66490675914[/C][C]-179.664906759137[/C][/ROW]
[ROW][C]55[/C][C]4270[/C][C]3774.65149726086[/C][C]495.348502739141[/C][/ROW]
[ROW][C]56[/C][C]5085[/C][C]5641.18803996666[/C][C]-556.188039966657[/C][/ROW]
[ROW][C]57[/C][C]11945[/C][C]12422.6251853069[/C][C]-477.625185306879[/C][/ROW]
[ROW][C]58[/C][C]14335[/C][C]14763.9949912275[/C][C]-428.994991227542[/C][/ROW]
[ROW][C]59[/C][C]14105[/C][C]13665.3530864567[/C][C]439.646913543291[/C][/ROW]
[ROW][C]60[/C][C]13755[/C][C]13294.1785386168[/C][C]460.82146138319[/C][/ROW]
[ROW][C]61[/C][C]12920[/C][C]12757.3163917682[/C][C]162.68360823178[/C][/ROW]
[ROW][C]62[/C][C]11650[/C][C]11469.5259331414[/C][C]180.474066858606[/C][/ROW]
[ROW][C]63[/C][C]10720[/C][C]10635.6119384437[/C][C]84.3880615562866[/C][/ROW]
[ROW][C]64[/C][C]8600[/C][C]8885.44946443485[/C][C]-285.449464434849[/C][/ROW]
[ROW][C]65[/C][C]7795[/C][C]7400.34004170413[/C][C]394.65995829587[/C][/ROW]
[ROW][C]66[/C][C]6550[/C][C]6363.74296450635[/C][C]186.257035493648[/C][/ROW]
[ROW][C]67[/C][C]4800[/C][C]4415.3548508938[/C][C]384.645149106201[/C][/ROW]
[ROW][C]68[/C][C]5900[/C][C]6186.71044196095[/C][C]-286.71044196095[/C][/ROW]
[ROW][C]69[/C][C]14095[/C][C]14420.3088305327[/C][C]-325.308830532733[/C][/ROW]
[ROW][C]70[/C][C]15170[/C][C]17393.7834998428[/C][C]-2223.78349984284[/C][/ROW]
[ROW][C]71[/C][C]14875[/C][C]14787.6110249449[/C][C]87.3889750551425[/C][/ROW]
[ROW][C]72[/C][C]15230[/C][C]14066.5935684687[/C][C]1163.4064315313[/C][/ROW]
[ROW][C]73[/C][C]13685[/C][C]14004.0882439001[/C][C]-319.088243900147[/C][/ROW]
[ROW][C]74[/C][C]12780[/C][C]12206.1884192615[/C][C]573.811580738466[/C][/ROW]
[ROW][C]75[/C][C]11510[/C][C]11607.6296080364[/C][C]-97.6296080364009[/C][/ROW]
[ROW][C]76[/C][C]9915[/C][C]9507.35233408036[/C][C]407.647665919636[/C][/ROW]
[ROW][C]77[/C][C]8740[/C][C]8537.70306215488[/C][C]202.296937845116[/C][/ROW]
[ROW][C]78[/C][C]7870[/C][C]7137.01915694423[/C][C]732.980843055766[/C][/ROW]
[ROW][C]79[/C][C]6650[/C][C]5292.91218529143[/C][C]1357.08781470857[/C][/ROW]
[ROW][C]80[/C][C]5285[/C][C]8287.04599484649[/C][C]-3002.04599484649[/C][/ROW]
[ROW][C]81[/C][C]13195[/C][C]13820.1498993845[/C][C]-625.149899384485[/C][/ROW]
[ROW][C]82[/C][C]13390[/C][C]16083.4662765851[/C][C]-2693.46627658513[/C][/ROW]
[ROW][C]83[/C][C]13490[/C][C]13405.6547855986[/C][C]84.3452144013772[/C][/ROW]
[ROW][C]84[/C][C]13445[/C][C]12878.5703145362[/C][C]566.429685463801[/C][/ROW]
[ROW][C]85[/C][C]13070[/C][C]12266.0275713754[/C][C]803.972428624616[/C][/ROW]
[ROW][C]86[/C][C]12480[/C][C]11635.2564273976[/C][C]844.743572602398[/C][/ROW]
[ROW][C]87[/C][C]11550[/C][C]11225.8888250242[/C][C]324.111174975758[/C][/ROW]
[ROW][C]88[/C][C]10725[/C][C]9556.46618291372[/C][C]1168.53381708628[/C][/ROW]
[ROW][C]89[/C][C]9130[/C][C]9131.03584696417[/C][C]-1.03584696416874[/C][/ROW]
[ROW][C]90[/C][C]7885[/C][C]7544.62651576662[/C][C]340.373484233375[/C][/ROW]
[ROW][C]91[/C][C]6415[/C][C]5415.5346740036[/C][C]999.465325996403[/C][/ROW]
[ROW][C]92[/C][C]5540[/C][C]7303.10220720427[/C][C]-1763.10220720427[/C][/ROW]
[ROW][C]93[/C][C]9350[/C][C]14982.6394442965[/C][C]-5632.63944429654[/C][/ROW]
[ROW][C]94[/C][C]12645[/C][C]11984.2222901238[/C][C]660.777709876229[/C][/ROW]
[ROW][C]95[/C][C]11985[/C][C]12588.9528390693[/C][C]-603.952839069349[/C][/ROW]
[ROW][C]96[/C][C]10055[/C][C]11584.8945167401[/C][C]-1529.89451674011[/C][/ROW]
[ROW][C]97[/C][C]10295[/C][C]9440.2146485861[/C][C]854.785351413897[/C][/ROW]
[ROW][C]98[/C][C]10280[/C][C]9157.76240943321[/C][C]1122.23759056679[/C][/ROW]
[ROW][C]99[/C][C]9420[/C][C]9158.84010821014[/C][C]261.159891789865[/C][/ROW]
[ROW][C]100[/C][C]9575[/C][C]7883.59309100913[/C][C]1691.40690899087[/C][/ROW]
[ROW][C]101[/C][C]8090[/C][C]7971.08496180761[/C][C]118.915038192395[/C][/ROW]
[ROW][C]102[/C][C]5855[/C][C]6712.84642312367[/C][C]-857.84642312367[/C][/ROW]
[ROW][C]103[/C][C]4445[/C][C]4185.0360975289[/C][C]259.963902471096[/C][/ROW]
[ROW][C]104[/C][C]3555[/C][C]4831.59080245833[/C][C]-1276.59080245833[/C][/ROW]
[ROW][C]105[/C][C]12870[/C][C]9352.20690423973[/C][C]3517.79309576027[/C][/ROW]
[ROW][C]106[/C][C]14750[/C][C]16003.3925538433[/C][C]-1253.39255384327[/C][/ROW]
[ROW][C]107[/C][C]13615[/C][C]14737.9484445613[/C][C]-1122.94844456134[/C][/ROW]
[ROW][C]108[/C][C]13705[/C][C]13036.1288234648[/C][C]668.871176535227[/C][/ROW]
[ROW][C]109[/C][C]13940[/C][C]12904.0464600225[/C][C]1035.95353997748[/C][/ROW]
[ROW][C]110[/C][C]11900[/C][C]12438.9934759148[/C][C]-538.993475914842[/C][/ROW]
[ROW][C]111[/C][C]9000[/C][C]10694.4290212323[/C][C]-1694.42902123234[/C][/ROW]
[ROW][C]112[/C][C]7340[/C][C]7893.90286557468[/C][C]-553.902865574679[/C][/ROW]
[ROW][C]113[/C][C]6425[/C][C]6188.5727952998[/C][C]236.4272047002[/C][/ROW]
[ROW][C]114[/C][C]5535[/C][C]5213.61031561955[/C][C]321.389684380453[/C][/ROW]
[ROW][C]115[/C][C]4050[/C][C]3957.67300923699[/C][C]92.3269907630138[/C][/ROW]
[ROW][C]116[/C][C]3485[/C][C]4197.72602202601[/C][C]-712.726022026007[/C][/ROW]
[ROW][C]117[/C][C]8090[/C][C]9750.49062673218[/C][C]-1660.49062673218[/C][/ROW]
[ROW][C]118[/C][C]11380[/C][C]10236.0239969287[/C][C]1143.97600307132[/C][/ROW]
[ROW][C]119[/C][C]11355[/C][C]11121.4721062981[/C][C]233.52789370193[/C][/ROW]
[ROW][C]120[/C][C]10530[/C][C]10922.0625661153[/C][C]-392.062566115297[/C][/ROW]
[ROW][C]121[/C][C]9285[/C][C]10070.9941922621[/C][C]-785.994192262066[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299063&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299063&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
131286012590.6398735141269.360126485943
141150011454.714084923245.2859150768145
151066010669.4979469604-9.4979469603677
1693409327.3593402367912.6406597632085
1780508002.5617742066847.4382257933175
1865406470.7006134460869.2993865539192
1950604022.040434004591037.95956599541
2063507953.82481725652-1603.82481725652
211413014692.3438853349-562.343885334914
221638016257.291346006122.708653994046
231616015394.8965247539765.103475246058
241585015192.1280625589657.871937441141
251593014613.02321694471316.97678305534
261532014034.92250281121285.0774971888
271342014044.8673260424-624.867326042411
281225511804.2374097111450.762590288949
29878510448.3745757979-1663.37457579787
3063807239.84635751154-859.846357511544
3147604099.5767895863660.423210413699
3257307120.1695513857-1390.1695513857
331081013605.2227700132-2795.22277001324
341284512876.5629957221-31.5629957221463
351286512163.6441961432701.355803856839
361351512086.52763982571428.47236017435
371388012431.73950329731448.26049670265
381296012203.1566839337756.843316066284
391209011729.265402178360.734597821975
40951010647.8821563749-1137.8821563749
4181308044.0789091241185.9210908758905
4266256579.1623806426145.8376193573913
4349204329.7052071886590.294792811401
4446507026.90226245115-2376.90226245115
451008511394.9287132926-1309.9287132926
461396012212.81567180421747.18432819577
471449513094.41966638421400.58033361576
481434013627.2254045472712.774595452795
491387513281.3590353593593.640964640666
501313512223.6787376754911.321262324576
511341511826.87958762561588.12041237444
52928011455.7663279336-2175.76632793364
5370758096.56768107652-1021.56768107652
5456605839.66490675914-179.664906759137
5542703774.65149726086495.348502739141
5650855641.18803996666-556.188039966657
571194512422.6251853069-477.625185306879
581433514763.9949912275-428.994991227542
591410513665.3530864567439.646913543291
601375513294.1785386168460.82146138319
611292012757.3163917682162.68360823178
621165011469.5259331414180.474066858606
631072010635.611938443784.3880615562866
6486008885.44946443485-285.449464434849
6577957400.34004170413394.65995829587
6665506363.74296450635186.257035493648
6748004415.3548508938384.645149106201
6859006186.71044196095-286.71044196095
691409514420.3088305327-325.308830532733
701517017393.7834998428-2223.78349984284
711487514787.611024944987.3889750551425
721523014066.59356846871163.4064315313
731368514004.0882439001-319.088243900147
741278012206.1884192615573.811580738466
751151011607.6296080364-97.6296080364009
7699159507.35233408036407.647665919636
7787408537.70306215488202.296937845116
7878707137.01915694423732.980843055766
7966505292.912185291431357.08781470857
8052858287.04599484649-3002.04599484649
811319513820.1498993845-625.149899384485
821339016083.4662765851-2693.46627658513
831349013405.654785598684.3452144013772
841344512878.5703145362566.429685463801
851307012266.0275713754803.972428624616
861248011635.2564273976844.743572602398
871155011225.8888250242324.111174975758
88107259556.466182913721168.53381708628
8991309131.03584696417-1.03584696416874
9078857544.62651576662340.373484233375
9164155415.5346740036999.465325996403
9255407303.10220720427-1763.10220720427
93935014982.6394442965-5632.63944429654
941264511984.2222901238660.777709876229
951198512588.9528390693-603.952839069349
961005511584.8945167401-1529.89451674011
97102959440.2146485861854.785351413897
98102809157.762409433211122.23759056679
9994209158.84010821014261.159891789865
10095757883.593091009131691.40690899087
10180907971.08496180761118.915038192395
10258556712.84642312367-857.84642312367
10344454185.0360975289259.963902471096
10435554831.59080245833-1276.59080245833
105128709352.206904239733517.79309576027
1061475016003.3925538433-1253.39255384327
1071361514737.9484445613-1122.94844456134
1081370513036.1288234648668.871176535227
1091394012904.04646002251035.95353997748
1101190012438.9934759148-538.993475914842
111900010694.4290212323-1694.42902123234
11273407893.90286557468-553.902865574679
11364256188.5727952998236.4272047002
11455355213.61031561955321.389684380453
11540503957.6730092369992.3269907630138
11634854197.72602202601-712.726022026007
11780909750.49062673218-1660.49062673218
1181138010236.02399692871143.97600307132
1191135511121.4721062981233.52789370193
1201053010922.0625661153-392.062566115297
121928510070.9941922621-785.994192262066







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1228343.389825204555993.3912521353610693.3883982737
1237334.445207756654380.4875995436610288.4028159696
1246378.41253483313054.030963072969702.79410659324
1255407.575093236741882.0773598988933.07282657548
1264425.11650695299837.7348855374418012.49812836854
1273177.11629084296-199.6623445516656553.89492623758
1283212.83002773507-750.2333161747787175.89337164491
1298762.25149850009-1784.436540687919308.9395376881
13011226.11868691-2332.8061419968724785.0435158168
13111000.9804108408-2369.9058359975224371.866657679
13210533.0922351092-2364.4089781351823430.5934483536
1339965.65406254627-2119.2882425103422050.5963676029

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
122 & 8343.38982520455 & 5993.39125213536 & 10693.3883982737 \tabularnewline
123 & 7334.44520775665 & 4380.48759954366 & 10288.4028159696 \tabularnewline
124 & 6378.4125348331 & 3054.03096307296 & 9702.79410659324 \tabularnewline
125 & 5407.57509323674 & 1882.077359898 & 8933.07282657548 \tabularnewline
126 & 4425.11650695299 & 837.734885537441 & 8012.49812836854 \tabularnewline
127 & 3177.11629084296 & -199.662344551665 & 6553.89492623758 \tabularnewline
128 & 3212.83002773507 & -750.233316174778 & 7175.89337164491 \tabularnewline
129 & 8762.25149850009 & -1784.4365406879 & 19308.9395376881 \tabularnewline
130 & 11226.11868691 & -2332.80614199687 & 24785.0435158168 \tabularnewline
131 & 11000.9804108408 & -2369.90583599752 & 24371.866657679 \tabularnewline
132 & 10533.0922351092 & -2364.40897813518 & 23430.5934483536 \tabularnewline
133 & 9965.65406254627 & -2119.28824251034 & 22050.5963676029 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299063&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]122[/C][C]8343.38982520455[/C][C]5993.39125213536[/C][C]10693.3883982737[/C][/ROW]
[ROW][C]123[/C][C]7334.44520775665[/C][C]4380.48759954366[/C][C]10288.4028159696[/C][/ROW]
[ROW][C]124[/C][C]6378.4125348331[/C][C]3054.03096307296[/C][C]9702.79410659324[/C][/ROW]
[ROW][C]125[/C][C]5407.57509323674[/C][C]1882.077359898[/C][C]8933.07282657548[/C][/ROW]
[ROW][C]126[/C][C]4425.11650695299[/C][C]837.734885537441[/C][C]8012.49812836854[/C][/ROW]
[ROW][C]127[/C][C]3177.11629084296[/C][C]-199.662344551665[/C][C]6553.89492623758[/C][/ROW]
[ROW][C]128[/C][C]3212.83002773507[/C][C]-750.233316174778[/C][C]7175.89337164491[/C][/ROW]
[ROW][C]129[/C][C]8762.25149850009[/C][C]-1784.4365406879[/C][C]19308.9395376881[/C][/ROW]
[ROW][C]130[/C][C]11226.11868691[/C][C]-2332.80614199687[/C][C]24785.0435158168[/C][/ROW]
[ROW][C]131[/C][C]11000.9804108408[/C][C]-2369.90583599752[/C][C]24371.866657679[/C][/ROW]
[ROW][C]132[/C][C]10533.0922351092[/C][C]-2364.40897813518[/C][C]23430.5934483536[/C][/ROW]
[ROW][C]133[/C][C]9965.65406254627[/C][C]-2119.28824251034[/C][C]22050.5963676029[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299063&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299063&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
1228343.389825204555993.3912521353610693.3883982737
1237334.445207756654380.4875995436610288.4028159696
1246378.41253483313054.030963072969702.79410659324
1255407.575093236741882.0773598988933.07282657548
1264425.11650695299837.7348855374418012.49812836854
1273177.11629084296-199.6623445516656553.89492623758
1283212.83002773507-750.2333161747787175.89337164491
1298762.25149850009-1784.436540687919308.9395376881
13011226.11868691-2332.8061419968724785.0435158168
13111000.9804108408-2369.9058359975224371.866657679
13210533.0922351092-2364.4089781351823430.5934483536
1339965.65406254627-2119.2882425103422050.5963676029



Parameters (Session):
par1 = 8 ; par2 = 0 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = 12 ;
R code (references can be found in the software module):
par4 <- '12'
par3 <- 'additive'
par2 <- 'Triple'
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')