Free Statistics

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 computationMon, 19 Dec 2016 23:20:22 +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/19/t148218610031c60fswj0257x7.htm/, Retrieved Fri, 01 Nov 2024 03:45:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301538, Retrieved Fri, 01 Nov 2024 03:45:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact128
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential smoot...] [2016-12-19 22:20:22] [86c9a777e8dbb7ef3face68c75fc8376] [Current]
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Dataseries X:
150
114
258
282
882
1302
2736
2484
1800
3468
5526
5766
6162
6132
6240
5904
5922
8460
7896
7290
6552
8442
9570
9312
6588
6084
11298
9798
14400
13734
13482
14814
13548
15516
15480
10488
14262
14946
14166
11544
10194
11850
12702
18222
19560
19494
15282
11034
8772
7110
6312
7080
7080
8226
7614
7326
7422
8886
7698
8634
5460
9744
12330
12870
9264
9822
21126
13050
13938
10764
8886
10830
7308
18336
17484
20082
16308
18600
19794
24114
24708
22482
21288
15870
10734
11142
13080
13098
18282
15678
6096
7854
9342
9162
7092
4692
4764
3852
9456
5490
6528
9306
9018
5964
5856
20574
7704
4464
9258
6240
9354
11916
13026
10062
7638
8844
13476
19074
16896
21162
16014
13746
14550
13146
11022
10386




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301538&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]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=301538&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301538&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 time1 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.531366682764013
beta0.00647027308766291
gamma0.756848064561584

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.531366682764013 \tabularnewline
beta & 0.00647027308766291 \tabularnewline
gamma & 0.756848064561584 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301538&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]0.531366682764013[/C][/ROW]
[ROW][C]beta[/C][C]0.00647027308766291[/C][/ROW]
[ROW][C]gamma[/C][C]0.756848064561584[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301538&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301538&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
alpha0.531366682764013
beta0.00647027308766291
gamma0.756848064561584







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1361622784.846741249483377.15325875052
1461324708.308045166691423.69195483331
1562405661.99147152276578.008528477239
1659045709.19011478476194.809885215238
1759225904.6474220056217.3525779943757
1884608613.63083951069-153.630839510693
1978969093.22265109392-1197.22265109392
2072906710.07537006318579.924629936823
2165524565.403875644261986.59612435574
2284429877.78056034395-1435.78056034395
23957013604.3034156186-4034.3034156186
24931211226.3426698937-1914.34266989375
25658813079.9523603617-6491.9523603617
2660848199.16957493052-2115.16957493052
27112986820.903963691654477.09603630835
2897988387.418436170871410.58156382913
29144008953.541117898745446.45888210126
301373416604.5501979034-2870.55019790337
311348214965.8071699541-1483.80716995411
321481411876.96616085372937.03383914629
33135489323.915616650884224.08438334912
341551616739.674448488-1223.67444848803
351548021826.254759089-6346.25475908902
361048818867.3883799074-8379.38837990741
371426214789.0172511015-527.017251101479
381494614074.8731716052871.126828394841
391416617716.6974505097-3550.69745050966
401154412773.3850031002-1229.38500310021
411019412962.4245238286-2768.42452382864
421185012942.3690566355-1092.36905663547
431270212680.017449583121.982550416893
441822211889.95475422056332.04524577951
451956011058.04655848358501.9534415165
461949419328.3314473456165.668552654381
471528223646.75401935-8364.75401935003
481103417659.0181407771-6625.01814077711
49877217907.2530800474-9135.25308004737
50711013097.6534311628-5987.65343116278
51631210986.1946325731-4674.19463257313
5270807289.96402505589-209.96402505589
5370807375.27559633403-295.275596334028
5482268689.80237423193-463.802374231933
5576149019.88134610947-1405.88134610947
5673268981.90965999932-1655.90965999932
5774226232.407923363381189.59207663662
5888867307.982493907421578.01750609258
5976988499.17942922783-801.179429227828
6086347422.586461831491211.41353816851
6154609272.09157323134-3812.09157323134
6297447647.374850753752096.62514924625
63123309882.023045003022447.97695499698
641287011576.62375591821293.37624408179
65926412317.4010575784-3053.40105757836
66982212619.6520145416-2797.65201454163
672112611262.6591302699863.34086973101
681305017300.2907729653-4250.29077296535
691393812952.7574061179985.242593882112
701076414190.3765131358-3426.37651313578
71888611525.3181265521-2639.31812655213
721083010068.0296318288761.970368171163
7373089231.75205948589-1923.75205948589
741833611424.54860742026911.45139257976
751748416717.831638997766.168361002965
762008216923.23947059713158.7605294029
771630816055.9194632209252.08053677912
781860019152.7471034467-552.747103446727
791979425054.7113504386-5260.7113504386
802411417267.1759946546846.82400534597
812470820366.332667534341.66733247
822248220820.75089235971661.24910764028
832128820141.09561807091146.90438192907
841587023031.735299876-7161.73529987597
851073414999.6396337202-4265.63963372021
861114222238.0005268065-11096.0005268065
871308015803.3288333861-2723.32883338613
881309814822.3842207243-1724.38422072435
891828211421.31752299776860.68247700227
901567817532.596512835-1854.59651283502
91609620351.7881064041-14255.7881064041
92785412142.0634447232-4288.0634447232
9393429303.1445171905438.8554828094566
9491628337.12280033589824.877199664114
9570928174.28535204796-1082.28535204796
9646927268.8656771997-2576.8656771997
9747644743.1161298348520.8838701651493
9838527242.97874537189-3390.97874537189
9994566564.75326379762891.2467362024
10054908638.93673684955-3148.93673684955
10165287032.02318401505-504.023184015051
10293066611.299126094992694.70087390501
10390186285.421294950152732.57870504985
104596410273.5998486554-4309.59984865544
10558568905.1615995295-3049.1615995295
106205746744.543061199313829.4569388007
107770411962.533331046-4258.533331046
10844648202.19551363265-3738.19551363265
10992585882.940041097893375.05995890211
11062409001.91703661252-2761.91703661252
111935412954.0158044267-3600.01580442666
112119168723.281357680453192.71864231955
1131302612029.9195226316996.080477368365
1141006213901.5163010753-3839.51630107532
11576389257.48499187884-1619.48499187884
11688448001.42098616077842.579013839227
117134769859.053746716283616.94625328372
1181907417038.55649705092035.44350294909
119168969625.864389657677270.13561034233
1202116210560.690136327710601.3098636723
1211601422227.895489581-6213.89548958101
1221374616574.4305372223-2828.43053722234
1231455026092.1337026841-11542.1337026841
1241314619572.9434028973-6426.94340289729
1251102217207.8198036373-6185.81980363729
1261038613233.3110501571-2847.3110501571

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 6162 & 2784.84674124948 & 3377.15325875052 \tabularnewline
14 & 6132 & 4708.30804516669 & 1423.69195483331 \tabularnewline
15 & 6240 & 5661.99147152276 & 578.008528477239 \tabularnewline
16 & 5904 & 5709.19011478476 & 194.809885215238 \tabularnewline
17 & 5922 & 5904.64742200562 & 17.3525779943757 \tabularnewline
18 & 8460 & 8613.63083951069 & -153.630839510693 \tabularnewline
19 & 7896 & 9093.22265109392 & -1197.22265109392 \tabularnewline
20 & 7290 & 6710.07537006318 & 579.924629936823 \tabularnewline
21 & 6552 & 4565.40387564426 & 1986.59612435574 \tabularnewline
22 & 8442 & 9877.78056034395 & -1435.78056034395 \tabularnewline
23 & 9570 & 13604.3034156186 & -4034.3034156186 \tabularnewline
24 & 9312 & 11226.3426698937 & -1914.34266989375 \tabularnewline
25 & 6588 & 13079.9523603617 & -6491.9523603617 \tabularnewline
26 & 6084 & 8199.16957493052 & -2115.16957493052 \tabularnewline
27 & 11298 & 6820.90396369165 & 4477.09603630835 \tabularnewline
28 & 9798 & 8387.41843617087 & 1410.58156382913 \tabularnewline
29 & 14400 & 8953.54111789874 & 5446.45888210126 \tabularnewline
30 & 13734 & 16604.5501979034 & -2870.55019790337 \tabularnewline
31 & 13482 & 14965.8071699541 & -1483.80716995411 \tabularnewline
32 & 14814 & 11876.9661608537 & 2937.03383914629 \tabularnewline
33 & 13548 & 9323.91561665088 & 4224.08438334912 \tabularnewline
34 & 15516 & 16739.674448488 & -1223.67444848803 \tabularnewline
35 & 15480 & 21826.254759089 & -6346.25475908902 \tabularnewline
36 & 10488 & 18867.3883799074 & -8379.38837990741 \tabularnewline
37 & 14262 & 14789.0172511015 & -527.017251101479 \tabularnewline
38 & 14946 & 14074.8731716052 & 871.126828394841 \tabularnewline
39 & 14166 & 17716.6974505097 & -3550.69745050966 \tabularnewline
40 & 11544 & 12773.3850031002 & -1229.38500310021 \tabularnewline
41 & 10194 & 12962.4245238286 & -2768.42452382864 \tabularnewline
42 & 11850 & 12942.3690566355 & -1092.36905663547 \tabularnewline
43 & 12702 & 12680.0174495831 & 21.982550416893 \tabularnewline
44 & 18222 & 11889.9547542205 & 6332.04524577951 \tabularnewline
45 & 19560 & 11058.0465584835 & 8501.9534415165 \tabularnewline
46 & 19494 & 19328.3314473456 & 165.668552654381 \tabularnewline
47 & 15282 & 23646.75401935 & -8364.75401935003 \tabularnewline
48 & 11034 & 17659.0181407771 & -6625.01814077711 \tabularnewline
49 & 8772 & 17907.2530800474 & -9135.25308004737 \tabularnewline
50 & 7110 & 13097.6534311628 & -5987.65343116278 \tabularnewline
51 & 6312 & 10986.1946325731 & -4674.19463257313 \tabularnewline
52 & 7080 & 7289.96402505589 & -209.96402505589 \tabularnewline
53 & 7080 & 7375.27559633403 & -295.275596334028 \tabularnewline
54 & 8226 & 8689.80237423193 & -463.802374231933 \tabularnewline
55 & 7614 & 9019.88134610947 & -1405.88134610947 \tabularnewline
56 & 7326 & 8981.90965999932 & -1655.90965999932 \tabularnewline
57 & 7422 & 6232.40792336338 & 1189.59207663662 \tabularnewline
58 & 8886 & 7307.98249390742 & 1578.01750609258 \tabularnewline
59 & 7698 & 8499.17942922783 & -801.179429227828 \tabularnewline
60 & 8634 & 7422.58646183149 & 1211.41353816851 \tabularnewline
61 & 5460 & 9272.09157323134 & -3812.09157323134 \tabularnewline
62 & 9744 & 7647.37485075375 & 2096.62514924625 \tabularnewline
63 & 12330 & 9882.02304500302 & 2447.97695499698 \tabularnewline
64 & 12870 & 11576.6237559182 & 1293.37624408179 \tabularnewline
65 & 9264 & 12317.4010575784 & -3053.40105757836 \tabularnewline
66 & 9822 & 12619.6520145416 & -2797.65201454163 \tabularnewline
67 & 21126 & 11262.659130269 & 9863.34086973101 \tabularnewline
68 & 13050 & 17300.2907729653 & -4250.29077296535 \tabularnewline
69 & 13938 & 12952.7574061179 & 985.242593882112 \tabularnewline
70 & 10764 & 14190.3765131358 & -3426.37651313578 \tabularnewline
71 & 8886 & 11525.3181265521 & -2639.31812655213 \tabularnewline
72 & 10830 & 10068.0296318288 & 761.970368171163 \tabularnewline
73 & 7308 & 9231.75205948589 & -1923.75205948589 \tabularnewline
74 & 18336 & 11424.5486074202 & 6911.45139257976 \tabularnewline
75 & 17484 & 16717.831638997 & 766.168361002965 \tabularnewline
76 & 20082 & 16923.2394705971 & 3158.7605294029 \tabularnewline
77 & 16308 & 16055.9194632209 & 252.08053677912 \tabularnewline
78 & 18600 & 19152.7471034467 & -552.747103446727 \tabularnewline
79 & 19794 & 25054.7113504386 & -5260.7113504386 \tabularnewline
80 & 24114 & 17267.175994654 & 6846.82400534597 \tabularnewline
81 & 24708 & 20366.33266753 & 4341.66733247 \tabularnewline
82 & 22482 & 20820.7508923597 & 1661.24910764028 \tabularnewline
83 & 21288 & 20141.0956180709 & 1146.90438192907 \tabularnewline
84 & 15870 & 23031.735299876 & -7161.73529987597 \tabularnewline
85 & 10734 & 14999.6396337202 & -4265.63963372021 \tabularnewline
86 & 11142 & 22238.0005268065 & -11096.0005268065 \tabularnewline
87 & 13080 & 15803.3288333861 & -2723.32883338613 \tabularnewline
88 & 13098 & 14822.3842207243 & -1724.38422072435 \tabularnewline
89 & 18282 & 11421.3175229977 & 6860.68247700227 \tabularnewline
90 & 15678 & 17532.596512835 & -1854.59651283502 \tabularnewline
91 & 6096 & 20351.7881064041 & -14255.7881064041 \tabularnewline
92 & 7854 & 12142.0634447232 & -4288.0634447232 \tabularnewline
93 & 9342 & 9303.14451719054 & 38.8554828094566 \tabularnewline
94 & 9162 & 8337.12280033589 & 824.877199664114 \tabularnewline
95 & 7092 & 8174.28535204796 & -1082.28535204796 \tabularnewline
96 & 4692 & 7268.8656771997 & -2576.8656771997 \tabularnewline
97 & 4764 & 4743.11612983485 & 20.8838701651493 \tabularnewline
98 & 3852 & 7242.97874537189 & -3390.97874537189 \tabularnewline
99 & 9456 & 6564.7532637976 & 2891.2467362024 \tabularnewline
100 & 5490 & 8638.93673684955 & -3148.93673684955 \tabularnewline
101 & 6528 & 7032.02318401505 & -504.023184015051 \tabularnewline
102 & 9306 & 6611.29912609499 & 2694.70087390501 \tabularnewline
103 & 9018 & 6285.42129495015 & 2732.57870504985 \tabularnewline
104 & 5964 & 10273.5998486554 & -4309.59984865544 \tabularnewline
105 & 5856 & 8905.1615995295 & -3049.1615995295 \tabularnewline
106 & 20574 & 6744.5430611993 & 13829.4569388007 \tabularnewline
107 & 7704 & 11962.533331046 & -4258.533331046 \tabularnewline
108 & 4464 & 8202.19551363265 & -3738.19551363265 \tabularnewline
109 & 9258 & 5882.94004109789 & 3375.05995890211 \tabularnewline
110 & 6240 & 9001.91703661252 & -2761.91703661252 \tabularnewline
111 & 9354 & 12954.0158044267 & -3600.01580442666 \tabularnewline
112 & 11916 & 8723.28135768045 & 3192.71864231955 \tabularnewline
113 & 13026 & 12029.9195226316 & 996.080477368365 \tabularnewline
114 & 10062 & 13901.5163010753 & -3839.51630107532 \tabularnewline
115 & 7638 & 9257.48499187884 & -1619.48499187884 \tabularnewline
116 & 8844 & 8001.42098616077 & 842.579013839227 \tabularnewline
117 & 13476 & 9859.05374671628 & 3616.94625328372 \tabularnewline
118 & 19074 & 17038.5564970509 & 2035.44350294909 \tabularnewline
119 & 16896 & 9625.86438965767 & 7270.13561034233 \tabularnewline
120 & 21162 & 10560.6901363277 & 10601.3098636723 \tabularnewline
121 & 16014 & 22227.895489581 & -6213.89548958101 \tabularnewline
122 & 13746 & 16574.4305372223 & -2828.43053722234 \tabularnewline
123 & 14550 & 26092.1337026841 & -11542.1337026841 \tabularnewline
124 & 13146 & 19572.9434028973 & -6426.94340289729 \tabularnewline
125 & 11022 & 17207.8198036373 & -6185.81980363729 \tabularnewline
126 & 10386 & 13233.3110501571 & -2847.3110501571 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301538&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]6162[/C][C]2784.84674124948[/C][C]3377.15325875052[/C][/ROW]
[ROW][C]14[/C][C]6132[/C][C]4708.30804516669[/C][C]1423.69195483331[/C][/ROW]
[ROW][C]15[/C][C]6240[/C][C]5661.99147152276[/C][C]578.008528477239[/C][/ROW]
[ROW][C]16[/C][C]5904[/C][C]5709.19011478476[/C][C]194.809885215238[/C][/ROW]
[ROW][C]17[/C][C]5922[/C][C]5904.64742200562[/C][C]17.3525779943757[/C][/ROW]
[ROW][C]18[/C][C]8460[/C][C]8613.63083951069[/C][C]-153.630839510693[/C][/ROW]
[ROW][C]19[/C][C]7896[/C][C]9093.22265109392[/C][C]-1197.22265109392[/C][/ROW]
[ROW][C]20[/C][C]7290[/C][C]6710.07537006318[/C][C]579.924629936823[/C][/ROW]
[ROW][C]21[/C][C]6552[/C][C]4565.40387564426[/C][C]1986.59612435574[/C][/ROW]
[ROW][C]22[/C][C]8442[/C][C]9877.78056034395[/C][C]-1435.78056034395[/C][/ROW]
[ROW][C]23[/C][C]9570[/C][C]13604.3034156186[/C][C]-4034.3034156186[/C][/ROW]
[ROW][C]24[/C][C]9312[/C][C]11226.3426698937[/C][C]-1914.34266989375[/C][/ROW]
[ROW][C]25[/C][C]6588[/C][C]13079.9523603617[/C][C]-6491.9523603617[/C][/ROW]
[ROW][C]26[/C][C]6084[/C][C]8199.16957493052[/C][C]-2115.16957493052[/C][/ROW]
[ROW][C]27[/C][C]11298[/C][C]6820.90396369165[/C][C]4477.09603630835[/C][/ROW]
[ROW][C]28[/C][C]9798[/C][C]8387.41843617087[/C][C]1410.58156382913[/C][/ROW]
[ROW][C]29[/C][C]14400[/C][C]8953.54111789874[/C][C]5446.45888210126[/C][/ROW]
[ROW][C]30[/C][C]13734[/C][C]16604.5501979034[/C][C]-2870.55019790337[/C][/ROW]
[ROW][C]31[/C][C]13482[/C][C]14965.8071699541[/C][C]-1483.80716995411[/C][/ROW]
[ROW][C]32[/C][C]14814[/C][C]11876.9661608537[/C][C]2937.03383914629[/C][/ROW]
[ROW][C]33[/C][C]13548[/C][C]9323.91561665088[/C][C]4224.08438334912[/C][/ROW]
[ROW][C]34[/C][C]15516[/C][C]16739.674448488[/C][C]-1223.67444848803[/C][/ROW]
[ROW][C]35[/C][C]15480[/C][C]21826.254759089[/C][C]-6346.25475908902[/C][/ROW]
[ROW][C]36[/C][C]10488[/C][C]18867.3883799074[/C][C]-8379.38837990741[/C][/ROW]
[ROW][C]37[/C][C]14262[/C][C]14789.0172511015[/C][C]-527.017251101479[/C][/ROW]
[ROW][C]38[/C][C]14946[/C][C]14074.8731716052[/C][C]871.126828394841[/C][/ROW]
[ROW][C]39[/C][C]14166[/C][C]17716.6974505097[/C][C]-3550.69745050966[/C][/ROW]
[ROW][C]40[/C][C]11544[/C][C]12773.3850031002[/C][C]-1229.38500310021[/C][/ROW]
[ROW][C]41[/C][C]10194[/C][C]12962.4245238286[/C][C]-2768.42452382864[/C][/ROW]
[ROW][C]42[/C][C]11850[/C][C]12942.3690566355[/C][C]-1092.36905663547[/C][/ROW]
[ROW][C]43[/C][C]12702[/C][C]12680.0174495831[/C][C]21.982550416893[/C][/ROW]
[ROW][C]44[/C][C]18222[/C][C]11889.9547542205[/C][C]6332.04524577951[/C][/ROW]
[ROW][C]45[/C][C]19560[/C][C]11058.0465584835[/C][C]8501.9534415165[/C][/ROW]
[ROW][C]46[/C][C]19494[/C][C]19328.3314473456[/C][C]165.668552654381[/C][/ROW]
[ROW][C]47[/C][C]15282[/C][C]23646.75401935[/C][C]-8364.75401935003[/C][/ROW]
[ROW][C]48[/C][C]11034[/C][C]17659.0181407771[/C][C]-6625.01814077711[/C][/ROW]
[ROW][C]49[/C][C]8772[/C][C]17907.2530800474[/C][C]-9135.25308004737[/C][/ROW]
[ROW][C]50[/C][C]7110[/C][C]13097.6534311628[/C][C]-5987.65343116278[/C][/ROW]
[ROW][C]51[/C][C]6312[/C][C]10986.1946325731[/C][C]-4674.19463257313[/C][/ROW]
[ROW][C]52[/C][C]7080[/C][C]7289.96402505589[/C][C]-209.96402505589[/C][/ROW]
[ROW][C]53[/C][C]7080[/C][C]7375.27559633403[/C][C]-295.275596334028[/C][/ROW]
[ROW][C]54[/C][C]8226[/C][C]8689.80237423193[/C][C]-463.802374231933[/C][/ROW]
[ROW][C]55[/C][C]7614[/C][C]9019.88134610947[/C][C]-1405.88134610947[/C][/ROW]
[ROW][C]56[/C][C]7326[/C][C]8981.90965999932[/C][C]-1655.90965999932[/C][/ROW]
[ROW][C]57[/C][C]7422[/C][C]6232.40792336338[/C][C]1189.59207663662[/C][/ROW]
[ROW][C]58[/C][C]8886[/C][C]7307.98249390742[/C][C]1578.01750609258[/C][/ROW]
[ROW][C]59[/C][C]7698[/C][C]8499.17942922783[/C][C]-801.179429227828[/C][/ROW]
[ROW][C]60[/C][C]8634[/C][C]7422.58646183149[/C][C]1211.41353816851[/C][/ROW]
[ROW][C]61[/C][C]5460[/C][C]9272.09157323134[/C][C]-3812.09157323134[/C][/ROW]
[ROW][C]62[/C][C]9744[/C][C]7647.37485075375[/C][C]2096.62514924625[/C][/ROW]
[ROW][C]63[/C][C]12330[/C][C]9882.02304500302[/C][C]2447.97695499698[/C][/ROW]
[ROW][C]64[/C][C]12870[/C][C]11576.6237559182[/C][C]1293.37624408179[/C][/ROW]
[ROW][C]65[/C][C]9264[/C][C]12317.4010575784[/C][C]-3053.40105757836[/C][/ROW]
[ROW][C]66[/C][C]9822[/C][C]12619.6520145416[/C][C]-2797.65201454163[/C][/ROW]
[ROW][C]67[/C][C]21126[/C][C]11262.659130269[/C][C]9863.34086973101[/C][/ROW]
[ROW][C]68[/C][C]13050[/C][C]17300.2907729653[/C][C]-4250.29077296535[/C][/ROW]
[ROW][C]69[/C][C]13938[/C][C]12952.7574061179[/C][C]985.242593882112[/C][/ROW]
[ROW][C]70[/C][C]10764[/C][C]14190.3765131358[/C][C]-3426.37651313578[/C][/ROW]
[ROW][C]71[/C][C]8886[/C][C]11525.3181265521[/C][C]-2639.31812655213[/C][/ROW]
[ROW][C]72[/C][C]10830[/C][C]10068.0296318288[/C][C]761.970368171163[/C][/ROW]
[ROW][C]73[/C][C]7308[/C][C]9231.75205948589[/C][C]-1923.75205948589[/C][/ROW]
[ROW][C]74[/C][C]18336[/C][C]11424.5486074202[/C][C]6911.45139257976[/C][/ROW]
[ROW][C]75[/C][C]17484[/C][C]16717.831638997[/C][C]766.168361002965[/C][/ROW]
[ROW][C]76[/C][C]20082[/C][C]16923.2394705971[/C][C]3158.7605294029[/C][/ROW]
[ROW][C]77[/C][C]16308[/C][C]16055.9194632209[/C][C]252.08053677912[/C][/ROW]
[ROW][C]78[/C][C]18600[/C][C]19152.7471034467[/C][C]-552.747103446727[/C][/ROW]
[ROW][C]79[/C][C]19794[/C][C]25054.7113504386[/C][C]-5260.7113504386[/C][/ROW]
[ROW][C]80[/C][C]24114[/C][C]17267.175994654[/C][C]6846.82400534597[/C][/ROW]
[ROW][C]81[/C][C]24708[/C][C]20366.33266753[/C][C]4341.66733247[/C][/ROW]
[ROW][C]82[/C][C]22482[/C][C]20820.7508923597[/C][C]1661.24910764028[/C][/ROW]
[ROW][C]83[/C][C]21288[/C][C]20141.0956180709[/C][C]1146.90438192907[/C][/ROW]
[ROW][C]84[/C][C]15870[/C][C]23031.735299876[/C][C]-7161.73529987597[/C][/ROW]
[ROW][C]85[/C][C]10734[/C][C]14999.6396337202[/C][C]-4265.63963372021[/C][/ROW]
[ROW][C]86[/C][C]11142[/C][C]22238.0005268065[/C][C]-11096.0005268065[/C][/ROW]
[ROW][C]87[/C][C]13080[/C][C]15803.3288333861[/C][C]-2723.32883338613[/C][/ROW]
[ROW][C]88[/C][C]13098[/C][C]14822.3842207243[/C][C]-1724.38422072435[/C][/ROW]
[ROW][C]89[/C][C]18282[/C][C]11421.3175229977[/C][C]6860.68247700227[/C][/ROW]
[ROW][C]90[/C][C]15678[/C][C]17532.596512835[/C][C]-1854.59651283502[/C][/ROW]
[ROW][C]91[/C][C]6096[/C][C]20351.7881064041[/C][C]-14255.7881064041[/C][/ROW]
[ROW][C]92[/C][C]7854[/C][C]12142.0634447232[/C][C]-4288.0634447232[/C][/ROW]
[ROW][C]93[/C][C]9342[/C][C]9303.14451719054[/C][C]38.8554828094566[/C][/ROW]
[ROW][C]94[/C][C]9162[/C][C]8337.12280033589[/C][C]824.877199664114[/C][/ROW]
[ROW][C]95[/C][C]7092[/C][C]8174.28535204796[/C][C]-1082.28535204796[/C][/ROW]
[ROW][C]96[/C][C]4692[/C][C]7268.8656771997[/C][C]-2576.8656771997[/C][/ROW]
[ROW][C]97[/C][C]4764[/C][C]4743.11612983485[/C][C]20.8838701651493[/C][/ROW]
[ROW][C]98[/C][C]3852[/C][C]7242.97874537189[/C][C]-3390.97874537189[/C][/ROW]
[ROW][C]99[/C][C]9456[/C][C]6564.7532637976[/C][C]2891.2467362024[/C][/ROW]
[ROW][C]100[/C][C]5490[/C][C]8638.93673684955[/C][C]-3148.93673684955[/C][/ROW]
[ROW][C]101[/C][C]6528[/C][C]7032.02318401505[/C][C]-504.023184015051[/C][/ROW]
[ROW][C]102[/C][C]9306[/C][C]6611.29912609499[/C][C]2694.70087390501[/C][/ROW]
[ROW][C]103[/C][C]9018[/C][C]6285.42129495015[/C][C]2732.57870504985[/C][/ROW]
[ROW][C]104[/C][C]5964[/C][C]10273.5998486554[/C][C]-4309.59984865544[/C][/ROW]
[ROW][C]105[/C][C]5856[/C][C]8905.1615995295[/C][C]-3049.1615995295[/C][/ROW]
[ROW][C]106[/C][C]20574[/C][C]6744.5430611993[/C][C]13829.4569388007[/C][/ROW]
[ROW][C]107[/C][C]7704[/C][C]11962.533331046[/C][C]-4258.533331046[/C][/ROW]
[ROW][C]108[/C][C]4464[/C][C]8202.19551363265[/C][C]-3738.19551363265[/C][/ROW]
[ROW][C]109[/C][C]9258[/C][C]5882.94004109789[/C][C]3375.05995890211[/C][/ROW]
[ROW][C]110[/C][C]6240[/C][C]9001.91703661252[/C][C]-2761.91703661252[/C][/ROW]
[ROW][C]111[/C][C]9354[/C][C]12954.0158044267[/C][C]-3600.01580442666[/C][/ROW]
[ROW][C]112[/C][C]11916[/C][C]8723.28135768045[/C][C]3192.71864231955[/C][/ROW]
[ROW][C]113[/C][C]13026[/C][C]12029.9195226316[/C][C]996.080477368365[/C][/ROW]
[ROW][C]114[/C][C]10062[/C][C]13901.5163010753[/C][C]-3839.51630107532[/C][/ROW]
[ROW][C]115[/C][C]7638[/C][C]9257.48499187884[/C][C]-1619.48499187884[/C][/ROW]
[ROW][C]116[/C][C]8844[/C][C]8001.42098616077[/C][C]842.579013839227[/C][/ROW]
[ROW][C]117[/C][C]13476[/C][C]9859.05374671628[/C][C]3616.94625328372[/C][/ROW]
[ROW][C]118[/C][C]19074[/C][C]17038.5564970509[/C][C]2035.44350294909[/C][/ROW]
[ROW][C]119[/C][C]16896[/C][C]9625.86438965767[/C][C]7270.13561034233[/C][/ROW]
[ROW][C]120[/C][C]21162[/C][C]10560.6901363277[/C][C]10601.3098636723[/C][/ROW]
[ROW][C]121[/C][C]16014[/C][C]22227.895489581[/C][C]-6213.89548958101[/C][/ROW]
[ROW][C]122[/C][C]13746[/C][C]16574.4305372223[/C][C]-2828.43053722234[/C][/ROW]
[ROW][C]123[/C][C]14550[/C][C]26092.1337026841[/C][C]-11542.1337026841[/C][/ROW]
[ROW][C]124[/C][C]13146[/C][C]19572.9434028973[/C][C]-6426.94340289729[/C][/ROW]
[ROW][C]125[/C][C]11022[/C][C]17207.8198036373[/C][C]-6185.81980363729[/C][/ROW]
[ROW][C]126[/C][C]10386[/C][C]13233.3110501571[/C][C]-2847.3110501571[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301538&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301538&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
1361622784.846741249483377.15325875052
1461324708.308045166691423.69195483331
1562405661.99147152276578.008528477239
1659045709.19011478476194.809885215238
1759225904.6474220056217.3525779943757
1884608613.63083951069-153.630839510693
1978969093.22265109392-1197.22265109392
2072906710.07537006318579.924629936823
2165524565.403875644261986.59612435574
2284429877.78056034395-1435.78056034395
23957013604.3034156186-4034.3034156186
24931211226.3426698937-1914.34266989375
25658813079.9523603617-6491.9523603617
2660848199.16957493052-2115.16957493052
27112986820.903963691654477.09603630835
2897988387.418436170871410.58156382913
29144008953.541117898745446.45888210126
301373416604.5501979034-2870.55019790337
311348214965.8071699541-1483.80716995411
321481411876.96616085372937.03383914629
33135489323.915616650884224.08438334912
341551616739.674448488-1223.67444848803
351548021826.254759089-6346.25475908902
361048818867.3883799074-8379.38837990741
371426214789.0172511015-527.017251101479
381494614074.8731716052871.126828394841
391416617716.6974505097-3550.69745050966
401154412773.3850031002-1229.38500310021
411019412962.4245238286-2768.42452382864
421185012942.3690566355-1092.36905663547
431270212680.017449583121.982550416893
441822211889.95475422056332.04524577951
451956011058.04655848358501.9534415165
461949419328.3314473456165.668552654381
471528223646.75401935-8364.75401935003
481103417659.0181407771-6625.01814077711
49877217907.2530800474-9135.25308004737
50711013097.6534311628-5987.65343116278
51631210986.1946325731-4674.19463257313
5270807289.96402505589-209.96402505589
5370807375.27559633403-295.275596334028
5482268689.80237423193-463.802374231933
5576149019.88134610947-1405.88134610947
5673268981.90965999932-1655.90965999932
5774226232.407923363381189.59207663662
5888867307.982493907421578.01750609258
5976988499.17942922783-801.179429227828
6086347422.586461831491211.41353816851
6154609272.09157323134-3812.09157323134
6297447647.374850753752096.62514924625
63123309882.023045003022447.97695499698
641287011576.62375591821293.37624408179
65926412317.4010575784-3053.40105757836
66982212619.6520145416-2797.65201454163
672112611262.6591302699863.34086973101
681305017300.2907729653-4250.29077296535
691393812952.7574061179985.242593882112
701076414190.3765131358-3426.37651313578
71888611525.3181265521-2639.31812655213
721083010068.0296318288761.970368171163
7373089231.75205948589-1923.75205948589
741833611424.54860742026911.45139257976
751748416717.831638997766.168361002965
762008216923.23947059713158.7605294029
771630816055.9194632209252.08053677912
781860019152.7471034467-552.747103446727
791979425054.7113504386-5260.7113504386
802411417267.1759946546846.82400534597
812470820366.332667534341.66733247
822248220820.75089235971661.24910764028
832128820141.09561807091146.90438192907
841587023031.735299876-7161.73529987597
851073414999.6396337202-4265.63963372021
861114222238.0005268065-11096.0005268065
871308015803.3288333861-2723.32883338613
881309814822.3842207243-1724.38422072435
891828211421.31752299776860.68247700227
901567817532.596512835-1854.59651283502
91609620351.7881064041-14255.7881064041
92785412142.0634447232-4288.0634447232
9393429303.1445171905438.8554828094566
9491628337.12280033589824.877199664114
9570928174.28535204796-1082.28535204796
9646927268.8656771997-2576.8656771997
9747644743.1161298348520.8838701651493
9838527242.97874537189-3390.97874537189
9994566564.75326379762891.2467362024
10054908638.93673684955-3148.93673684955
10165287032.02318401505-504.023184015051
10293066611.299126094992694.70087390501
10390186285.421294950152732.57870504985
104596410273.5998486554-4309.59984865544
10558568905.1615995295-3049.1615995295
106205746744.543061199313829.4569388007
107770411962.533331046-4258.533331046
10844648202.19551363265-3738.19551363265
10992585882.940041097893375.05995890211
11062409001.91703661252-2761.91703661252
111935412954.0158044267-3600.01580442666
112119168723.281357680453192.71864231955
1131302612029.9195226316996.080477368365
1141006213901.5163010753-3839.51630107532
11576389257.48499187884-1619.48499187884
11688448001.42098616077842.579013839227
117134769859.053746716283616.94625328372
1181907417038.55649705092035.44350294909
119168969625.864389657677270.13561034233
1202116210560.690136327710601.3098636723
1211601422227.895489581-6213.89548958101
1221374616574.4305372223-2828.43053722234
1231455026092.1337026841-11542.1337026841
1241314619572.9434028973-6426.94340289729
1251102217207.8198036373-6185.81980363729
1261038613233.3110501571-2847.3110501571







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1279595.615506760851831.5796550647717359.6513584569
12810115.3298734439959.69692977998219270.9628171079
12912595.74743205541244.3222297418323947.1726343689
13017062.71482056612151.8853946925431973.5442464397
13110378.7404874079-883.15290646412521640.6338812798
1328427.69473056978-2401.1410365216919256.5304976612
1338337.52412916359-3312.8731374000519987.9213957272
1347746.08782517619-4190.7386548244519682.9143051768
13511460.0106665904-5373.0589665613828293.0802997423
13612163.6382367858-6026.9366633238630354.2131368955
13712705.3664893749-6618.5634938570432029.2964726068
13813075.959994297-5588.2055824011131740.125570995

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
127 & 9595.61550676085 & 1831.57965506477 & 17359.6513584569 \tabularnewline
128 & 10115.3298734439 & 959.696929779982 & 19270.9628171079 \tabularnewline
129 & 12595.7474320554 & 1244.32222974183 & 23947.1726343689 \tabularnewline
130 & 17062.7148205661 & 2151.88539469254 & 31973.5442464397 \tabularnewline
131 & 10378.7404874079 & -883.152906464125 & 21640.6338812798 \tabularnewline
132 & 8427.69473056978 & -2401.14103652169 & 19256.5304976612 \tabularnewline
133 & 8337.52412916359 & -3312.87313740005 & 19987.9213957272 \tabularnewline
134 & 7746.08782517619 & -4190.73865482445 & 19682.9143051768 \tabularnewline
135 & 11460.0106665904 & -5373.05896656138 & 28293.0802997423 \tabularnewline
136 & 12163.6382367858 & -6026.93666332386 & 30354.2131368955 \tabularnewline
137 & 12705.3664893749 & -6618.56349385704 & 32029.2964726068 \tabularnewline
138 & 13075.959994297 & -5588.20558240111 & 31740.125570995 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301538&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]127[/C][C]9595.61550676085[/C][C]1831.57965506477[/C][C]17359.6513584569[/C][/ROW]
[ROW][C]128[/C][C]10115.3298734439[/C][C]959.696929779982[/C][C]19270.9628171079[/C][/ROW]
[ROW][C]129[/C][C]12595.7474320554[/C][C]1244.32222974183[/C][C]23947.1726343689[/C][/ROW]
[ROW][C]130[/C][C]17062.7148205661[/C][C]2151.88539469254[/C][C]31973.5442464397[/C][/ROW]
[ROW][C]131[/C][C]10378.7404874079[/C][C]-883.152906464125[/C][C]21640.6338812798[/C][/ROW]
[ROW][C]132[/C][C]8427.69473056978[/C][C]-2401.14103652169[/C][C]19256.5304976612[/C][/ROW]
[ROW][C]133[/C][C]8337.52412916359[/C][C]-3312.87313740005[/C][C]19987.9213957272[/C][/ROW]
[ROW][C]134[/C][C]7746.08782517619[/C][C]-4190.73865482445[/C][C]19682.9143051768[/C][/ROW]
[ROW][C]135[/C][C]11460.0106665904[/C][C]-5373.05896656138[/C][C]28293.0802997423[/C][/ROW]
[ROW][C]136[/C][C]12163.6382367858[/C][C]-6026.93666332386[/C][C]30354.2131368955[/C][/ROW]
[ROW][C]137[/C][C]12705.3664893749[/C][C]-6618.56349385704[/C][C]32029.2964726068[/C][/ROW]
[ROW][C]138[/C][C]13075.959994297[/C][C]-5588.20558240111[/C][C]31740.125570995[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301538&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301538&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
1279595.615506760851831.5796550647717359.6513584569
12810115.3298734439959.69692977998219270.9628171079
12912595.74743205541244.3222297418323947.1726343689
13017062.71482056612151.8853946925431973.5442464397
13110378.7404874079-883.15290646412521640.6338812798
1328427.69473056978-2401.1410365216919256.5304976612
1338337.52412916359-3312.8731374000519987.9213957272
1347746.08782517619-4190.7386548244519682.9143051768
13511460.0106665904-5373.0589665613828293.0802997423
13612163.6382367858-6026.9366633238630354.2131368955
13712705.3664893749-6618.5634938570432029.2964726068
13813075.959994297-5588.2055824011131740.125570995



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