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 computationWed, 07 Dec 2016 11:47:29 +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/07/t1481107674nl4fsol543ncppc.htm/, Retrieved Tue, 07 May 2024 16:34:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=297998, Retrieved Tue, 07 May 2024 16:34:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact69
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential smoot...] [2016-12-07 10:47:29] [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=297998&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=297998&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297998&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
alpha0.699599703516602
beta0.00737315233314396
gamma0.154598877118169

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.699599703516602 \tabularnewline
beta & 0.00737315233314396 \tabularnewline
gamma & 0.154598877118169 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297998&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]0.699599703516602[/C][/ROW]
[ROW][C]beta[/C][C]0.00737315233314396[/C][/ROW]
[ROW][C]gamma[/C][C]0.154598877118169[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297998&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297998&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
alpha0.699599703516602
beta0.00737315233314396
gamma0.154598877118169







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1361623177.607371794872984.39262820513
1461325284.10473051446847.89526948554
1562406055.28283068104184.717169318958
1659045912.45454688901-8.45454688900918
1759226017.93977699975-95.9397769997522
1884608641.22548421066-181.225484210659
1978968119.4105286488-223.410528648804
2072907676.43051998712-386.430519987121
2165526686.65846648402-134.658466484024
2284428240.83146423235201.168535767654
23957010460.2366118317-890.236611831744
24931210029.5029741341-717.50297413414
25658810005.512489772-3417.51248977203
2660847509.14568644808-1425.14568644808
27112986622.710070732544675.28992926746
2897989599.08156590497198.918434095025
29144009833.219206341154566.78079365885
301373415726.2708284923-1992.27082849234
311348213937.8369006245-455.836900624494
321481413325.82860805951488.17139194055
331354813670.0378932844-122.037893284405
341551615259.5193793512256.480620648807
351548017478.1024268929-1998.10242689295
361048816285.781683351-5797.78168335104
371426212561.48519560061700.51480439938
381494613743.86555856591202.1344414341
391416614997.9883884978-831.988388497821
401154413904.3724049083-2360.37240490826
411019412528.4721731589-2334.47217315886
421185013230.7892760367-1380.78927603668
431270211886.6487340501815.351265949923
441822212205.94987659926016.05012340083
451956015618.14093642923941.85906357076
461949420064.3249012866-570.324901286636
471528221591.5262356663-6309.52623566626
481103417175.9897738422-6141.98977384218
49877213526.8604836667-4754.86048366669
50711010104.3607556046-2994.36075560458
5163128240.94648505984-1928.94648505984
5270806216.05754138288863.942458617124
5370807020.8608374327859.139162567224
5482269378.15604810974-1152.15604810974
5576148233.25657712064-619.256577120645
5673267720.33209796971-394.332097969706
5774226448.32371584858973.676284151424
5888868489.93513777731396.064862222685
59769810313.1900120309-2615.19001203092
6086348395.55200375036238.447996249639
6154609213.06871836828-3753.06871836828
6297446516.823243702153227.17675629785
63123309031.207236444393298.79276355561
641287010796.04819764842073.95180235163
65926412418.9378865679-3154.93788656788
66982212463.7728177463-2641.77281774626
672112610286.164246035410839.8357539646
681305017844.2498008698-4794.24980086976
691393813578.6834231258359.316576874198
701076415181.5854801323-4417.58548013233
71888613490.4562988629-4604.45629886289
721083010296.4860471616533.513952838362
73730811119.4111188841-3811.41111888412
74183368690.574300570639645.42569942937
751748415715.64784874371768.35215125628
762008216362.17363662013719.82636337991
771630818911.4329234638-2603.43292346376
781860019386.5315243065-786.53152430648
791979419163.1245786483630.875421351673
802411418830.46153466425283.53846533582
812470821884.14441263252823.85558736745
822248225031.595192728-2549.59519272805
832128824690.4731538005-3402.47315380045
841587022634.0656458565-6764.06564585654
851073418170.2187646763-7436.21876467627
861114213832.1238685553-2690.12386855533
871308011799.49712675561280.50287324443
881309812130.9067615228967.093238477217
891828212382.04709025375899.95290974634
901567818855.70852038-3177.70852037995
91609616978.1440365078-10882.1440365078
9278548700.54838326357-846.548383263573
9393427213.267798939372128.73220106063
9491629483.1484263639-321.148426363899
95709210531.2223457971-3439.22234579705
9646928162.58222600823-3470.58222600823
9747645858.22283795226-1094.22283795226
9838526096.69934240443-2244.69934240443
9994564481.688069028064974.31193097194
10054907323.37835389298-1833.37835389298
10165285770.60183878165757.398161218352
10293068124.628838151211181.37116184879
10390188861.03053749803156.969462501975
10459648751.56782797102-2787.56782797102
10558566013.61878986015-157.618789860154
106205746527.4906466390114046.509353361
107770417513.7755077965-9809.77550779653
108446410685.3909443768-6221.39094437678
10992586551.288090147352706.71190985265
11062409399.4333860212-3159.4333860212
11193547478.983956821691875.01604317831
112119167819.508567251874096.49143274813
1131302610549.43514004962476.56485995035
1141006214148.5967854144-4086.59678541438
115763811147.4975170951-3509.49751709514
11688448312.8567995254531.143200474604
117134768012.564752499155463.43524750085
1181907413141.32971844955932.6702815505
1191689617324.1427719758-428.142771975788
1202116217255.07909290173906.92090709833
1211601420702.9028141856-4688.90281418557
1221374618148.0245875772-4402.02458757721
1231455015629.0359642913-1079.03596429131
1241314614027.8072837962-881.807283796237
1251102213195.7381773534-2173.73817735335
1261038613208.8108821894-2822.81088218936

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 6162 & 3177.60737179487 & 2984.39262820513 \tabularnewline
14 & 6132 & 5284.10473051446 & 847.89526948554 \tabularnewline
15 & 6240 & 6055.28283068104 & 184.717169318958 \tabularnewline
16 & 5904 & 5912.45454688901 & -8.45454688900918 \tabularnewline
17 & 5922 & 6017.93977699975 & -95.9397769997522 \tabularnewline
18 & 8460 & 8641.22548421066 & -181.225484210659 \tabularnewline
19 & 7896 & 8119.4105286488 & -223.410528648804 \tabularnewline
20 & 7290 & 7676.43051998712 & -386.430519987121 \tabularnewline
21 & 6552 & 6686.65846648402 & -134.658466484024 \tabularnewline
22 & 8442 & 8240.83146423235 & 201.168535767654 \tabularnewline
23 & 9570 & 10460.2366118317 & -890.236611831744 \tabularnewline
24 & 9312 & 10029.5029741341 & -717.50297413414 \tabularnewline
25 & 6588 & 10005.512489772 & -3417.51248977203 \tabularnewline
26 & 6084 & 7509.14568644808 & -1425.14568644808 \tabularnewline
27 & 11298 & 6622.71007073254 & 4675.28992926746 \tabularnewline
28 & 9798 & 9599.08156590497 & 198.918434095025 \tabularnewline
29 & 14400 & 9833.21920634115 & 4566.78079365885 \tabularnewline
30 & 13734 & 15726.2708284923 & -1992.27082849234 \tabularnewline
31 & 13482 & 13937.8369006245 & -455.836900624494 \tabularnewline
32 & 14814 & 13325.8286080595 & 1488.17139194055 \tabularnewline
33 & 13548 & 13670.0378932844 & -122.037893284405 \tabularnewline
34 & 15516 & 15259.5193793512 & 256.480620648807 \tabularnewline
35 & 15480 & 17478.1024268929 & -1998.10242689295 \tabularnewline
36 & 10488 & 16285.781683351 & -5797.78168335104 \tabularnewline
37 & 14262 & 12561.4851956006 & 1700.51480439938 \tabularnewline
38 & 14946 & 13743.8655585659 & 1202.1344414341 \tabularnewline
39 & 14166 & 14997.9883884978 & -831.988388497821 \tabularnewline
40 & 11544 & 13904.3724049083 & -2360.37240490826 \tabularnewline
41 & 10194 & 12528.4721731589 & -2334.47217315886 \tabularnewline
42 & 11850 & 13230.7892760367 & -1380.78927603668 \tabularnewline
43 & 12702 & 11886.6487340501 & 815.351265949923 \tabularnewline
44 & 18222 & 12205.9498765992 & 6016.05012340083 \tabularnewline
45 & 19560 & 15618.1409364292 & 3941.85906357076 \tabularnewline
46 & 19494 & 20064.3249012866 & -570.324901286636 \tabularnewline
47 & 15282 & 21591.5262356663 & -6309.52623566626 \tabularnewline
48 & 11034 & 17175.9897738422 & -6141.98977384218 \tabularnewline
49 & 8772 & 13526.8604836667 & -4754.86048366669 \tabularnewline
50 & 7110 & 10104.3607556046 & -2994.36075560458 \tabularnewline
51 & 6312 & 8240.94648505984 & -1928.94648505984 \tabularnewline
52 & 7080 & 6216.05754138288 & 863.942458617124 \tabularnewline
53 & 7080 & 7020.86083743278 & 59.139162567224 \tabularnewline
54 & 8226 & 9378.15604810974 & -1152.15604810974 \tabularnewline
55 & 7614 & 8233.25657712064 & -619.256577120645 \tabularnewline
56 & 7326 & 7720.33209796971 & -394.332097969706 \tabularnewline
57 & 7422 & 6448.32371584858 & 973.676284151424 \tabularnewline
58 & 8886 & 8489.93513777731 & 396.064862222685 \tabularnewline
59 & 7698 & 10313.1900120309 & -2615.19001203092 \tabularnewline
60 & 8634 & 8395.55200375036 & 238.447996249639 \tabularnewline
61 & 5460 & 9213.06871836828 & -3753.06871836828 \tabularnewline
62 & 9744 & 6516.82324370215 & 3227.17675629785 \tabularnewline
63 & 12330 & 9031.20723644439 & 3298.79276355561 \tabularnewline
64 & 12870 & 10796.0481976484 & 2073.95180235163 \tabularnewline
65 & 9264 & 12418.9378865679 & -3154.93788656788 \tabularnewline
66 & 9822 & 12463.7728177463 & -2641.77281774626 \tabularnewline
67 & 21126 & 10286.1642460354 & 10839.8357539646 \tabularnewline
68 & 13050 & 17844.2498008698 & -4794.24980086976 \tabularnewline
69 & 13938 & 13578.6834231258 & 359.316576874198 \tabularnewline
70 & 10764 & 15181.5854801323 & -4417.58548013233 \tabularnewline
71 & 8886 & 13490.4562988629 & -4604.45629886289 \tabularnewline
72 & 10830 & 10296.4860471616 & 533.513952838362 \tabularnewline
73 & 7308 & 11119.4111188841 & -3811.41111888412 \tabularnewline
74 & 18336 & 8690.57430057063 & 9645.42569942937 \tabularnewline
75 & 17484 & 15715.6478487437 & 1768.35215125628 \tabularnewline
76 & 20082 & 16362.1736366201 & 3719.82636337991 \tabularnewline
77 & 16308 & 18911.4329234638 & -2603.43292346376 \tabularnewline
78 & 18600 & 19386.5315243065 & -786.53152430648 \tabularnewline
79 & 19794 & 19163.1245786483 & 630.875421351673 \tabularnewline
80 & 24114 & 18830.4615346642 & 5283.53846533582 \tabularnewline
81 & 24708 & 21884.1444126325 & 2823.85558736745 \tabularnewline
82 & 22482 & 25031.595192728 & -2549.59519272805 \tabularnewline
83 & 21288 & 24690.4731538005 & -3402.47315380045 \tabularnewline
84 & 15870 & 22634.0656458565 & -6764.06564585654 \tabularnewline
85 & 10734 & 18170.2187646763 & -7436.21876467627 \tabularnewline
86 & 11142 & 13832.1238685553 & -2690.12386855533 \tabularnewline
87 & 13080 & 11799.4971267556 & 1280.50287324443 \tabularnewline
88 & 13098 & 12130.9067615228 & 967.093238477217 \tabularnewline
89 & 18282 & 12382.0470902537 & 5899.95290974634 \tabularnewline
90 & 15678 & 18855.70852038 & -3177.70852037995 \tabularnewline
91 & 6096 & 16978.1440365078 & -10882.1440365078 \tabularnewline
92 & 7854 & 8700.54838326357 & -846.548383263573 \tabularnewline
93 & 9342 & 7213.26779893937 & 2128.73220106063 \tabularnewline
94 & 9162 & 9483.1484263639 & -321.148426363899 \tabularnewline
95 & 7092 & 10531.2223457971 & -3439.22234579705 \tabularnewline
96 & 4692 & 8162.58222600823 & -3470.58222600823 \tabularnewline
97 & 4764 & 5858.22283795226 & -1094.22283795226 \tabularnewline
98 & 3852 & 6096.69934240443 & -2244.69934240443 \tabularnewline
99 & 9456 & 4481.68806902806 & 4974.31193097194 \tabularnewline
100 & 5490 & 7323.37835389298 & -1833.37835389298 \tabularnewline
101 & 6528 & 5770.60183878165 & 757.398161218352 \tabularnewline
102 & 9306 & 8124.62883815121 & 1181.37116184879 \tabularnewline
103 & 9018 & 8861.03053749803 & 156.969462501975 \tabularnewline
104 & 5964 & 8751.56782797102 & -2787.56782797102 \tabularnewline
105 & 5856 & 6013.61878986015 & -157.618789860154 \tabularnewline
106 & 20574 & 6527.49064663901 & 14046.509353361 \tabularnewline
107 & 7704 & 17513.7755077965 & -9809.77550779653 \tabularnewline
108 & 4464 & 10685.3909443768 & -6221.39094437678 \tabularnewline
109 & 9258 & 6551.28809014735 & 2706.71190985265 \tabularnewline
110 & 6240 & 9399.4333860212 & -3159.4333860212 \tabularnewline
111 & 9354 & 7478.98395682169 & 1875.01604317831 \tabularnewline
112 & 11916 & 7819.50856725187 & 4096.49143274813 \tabularnewline
113 & 13026 & 10549.4351400496 & 2476.56485995035 \tabularnewline
114 & 10062 & 14148.5967854144 & -4086.59678541438 \tabularnewline
115 & 7638 & 11147.4975170951 & -3509.49751709514 \tabularnewline
116 & 8844 & 8312.8567995254 & 531.143200474604 \tabularnewline
117 & 13476 & 8012.56475249915 & 5463.43524750085 \tabularnewline
118 & 19074 & 13141.3297184495 & 5932.6702815505 \tabularnewline
119 & 16896 & 17324.1427719758 & -428.142771975788 \tabularnewline
120 & 21162 & 17255.0790929017 & 3906.92090709833 \tabularnewline
121 & 16014 & 20702.9028141856 & -4688.90281418557 \tabularnewline
122 & 13746 & 18148.0245875772 & -4402.02458757721 \tabularnewline
123 & 14550 & 15629.0359642913 & -1079.03596429131 \tabularnewline
124 & 13146 & 14027.8072837962 & -881.807283796237 \tabularnewline
125 & 11022 & 13195.7381773534 & -2173.73817735335 \tabularnewline
126 & 10386 & 13208.8108821894 & -2822.81088218936 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297998&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]3177.60737179487[/C][C]2984.39262820513[/C][/ROW]
[ROW][C]14[/C][C]6132[/C][C]5284.10473051446[/C][C]847.89526948554[/C][/ROW]
[ROW][C]15[/C][C]6240[/C][C]6055.28283068104[/C][C]184.717169318958[/C][/ROW]
[ROW][C]16[/C][C]5904[/C][C]5912.45454688901[/C][C]-8.45454688900918[/C][/ROW]
[ROW][C]17[/C][C]5922[/C][C]6017.93977699975[/C][C]-95.9397769997522[/C][/ROW]
[ROW][C]18[/C][C]8460[/C][C]8641.22548421066[/C][C]-181.225484210659[/C][/ROW]
[ROW][C]19[/C][C]7896[/C][C]8119.4105286488[/C][C]-223.410528648804[/C][/ROW]
[ROW][C]20[/C][C]7290[/C][C]7676.43051998712[/C][C]-386.430519987121[/C][/ROW]
[ROW][C]21[/C][C]6552[/C][C]6686.65846648402[/C][C]-134.658466484024[/C][/ROW]
[ROW][C]22[/C][C]8442[/C][C]8240.83146423235[/C][C]201.168535767654[/C][/ROW]
[ROW][C]23[/C][C]9570[/C][C]10460.2366118317[/C][C]-890.236611831744[/C][/ROW]
[ROW][C]24[/C][C]9312[/C][C]10029.5029741341[/C][C]-717.50297413414[/C][/ROW]
[ROW][C]25[/C][C]6588[/C][C]10005.512489772[/C][C]-3417.51248977203[/C][/ROW]
[ROW][C]26[/C][C]6084[/C][C]7509.14568644808[/C][C]-1425.14568644808[/C][/ROW]
[ROW][C]27[/C][C]11298[/C][C]6622.71007073254[/C][C]4675.28992926746[/C][/ROW]
[ROW][C]28[/C][C]9798[/C][C]9599.08156590497[/C][C]198.918434095025[/C][/ROW]
[ROW][C]29[/C][C]14400[/C][C]9833.21920634115[/C][C]4566.78079365885[/C][/ROW]
[ROW][C]30[/C][C]13734[/C][C]15726.2708284923[/C][C]-1992.27082849234[/C][/ROW]
[ROW][C]31[/C][C]13482[/C][C]13937.8369006245[/C][C]-455.836900624494[/C][/ROW]
[ROW][C]32[/C][C]14814[/C][C]13325.8286080595[/C][C]1488.17139194055[/C][/ROW]
[ROW][C]33[/C][C]13548[/C][C]13670.0378932844[/C][C]-122.037893284405[/C][/ROW]
[ROW][C]34[/C][C]15516[/C][C]15259.5193793512[/C][C]256.480620648807[/C][/ROW]
[ROW][C]35[/C][C]15480[/C][C]17478.1024268929[/C][C]-1998.10242689295[/C][/ROW]
[ROW][C]36[/C][C]10488[/C][C]16285.781683351[/C][C]-5797.78168335104[/C][/ROW]
[ROW][C]37[/C][C]14262[/C][C]12561.4851956006[/C][C]1700.51480439938[/C][/ROW]
[ROW][C]38[/C][C]14946[/C][C]13743.8655585659[/C][C]1202.1344414341[/C][/ROW]
[ROW][C]39[/C][C]14166[/C][C]14997.9883884978[/C][C]-831.988388497821[/C][/ROW]
[ROW][C]40[/C][C]11544[/C][C]13904.3724049083[/C][C]-2360.37240490826[/C][/ROW]
[ROW][C]41[/C][C]10194[/C][C]12528.4721731589[/C][C]-2334.47217315886[/C][/ROW]
[ROW][C]42[/C][C]11850[/C][C]13230.7892760367[/C][C]-1380.78927603668[/C][/ROW]
[ROW][C]43[/C][C]12702[/C][C]11886.6487340501[/C][C]815.351265949923[/C][/ROW]
[ROW][C]44[/C][C]18222[/C][C]12205.9498765992[/C][C]6016.05012340083[/C][/ROW]
[ROW][C]45[/C][C]19560[/C][C]15618.1409364292[/C][C]3941.85906357076[/C][/ROW]
[ROW][C]46[/C][C]19494[/C][C]20064.3249012866[/C][C]-570.324901286636[/C][/ROW]
[ROW][C]47[/C][C]15282[/C][C]21591.5262356663[/C][C]-6309.52623566626[/C][/ROW]
[ROW][C]48[/C][C]11034[/C][C]17175.9897738422[/C][C]-6141.98977384218[/C][/ROW]
[ROW][C]49[/C][C]8772[/C][C]13526.8604836667[/C][C]-4754.86048366669[/C][/ROW]
[ROW][C]50[/C][C]7110[/C][C]10104.3607556046[/C][C]-2994.36075560458[/C][/ROW]
[ROW][C]51[/C][C]6312[/C][C]8240.94648505984[/C][C]-1928.94648505984[/C][/ROW]
[ROW][C]52[/C][C]7080[/C][C]6216.05754138288[/C][C]863.942458617124[/C][/ROW]
[ROW][C]53[/C][C]7080[/C][C]7020.86083743278[/C][C]59.139162567224[/C][/ROW]
[ROW][C]54[/C][C]8226[/C][C]9378.15604810974[/C][C]-1152.15604810974[/C][/ROW]
[ROW][C]55[/C][C]7614[/C][C]8233.25657712064[/C][C]-619.256577120645[/C][/ROW]
[ROW][C]56[/C][C]7326[/C][C]7720.33209796971[/C][C]-394.332097969706[/C][/ROW]
[ROW][C]57[/C][C]7422[/C][C]6448.32371584858[/C][C]973.676284151424[/C][/ROW]
[ROW][C]58[/C][C]8886[/C][C]8489.93513777731[/C][C]396.064862222685[/C][/ROW]
[ROW][C]59[/C][C]7698[/C][C]10313.1900120309[/C][C]-2615.19001203092[/C][/ROW]
[ROW][C]60[/C][C]8634[/C][C]8395.55200375036[/C][C]238.447996249639[/C][/ROW]
[ROW][C]61[/C][C]5460[/C][C]9213.06871836828[/C][C]-3753.06871836828[/C][/ROW]
[ROW][C]62[/C][C]9744[/C][C]6516.82324370215[/C][C]3227.17675629785[/C][/ROW]
[ROW][C]63[/C][C]12330[/C][C]9031.20723644439[/C][C]3298.79276355561[/C][/ROW]
[ROW][C]64[/C][C]12870[/C][C]10796.0481976484[/C][C]2073.95180235163[/C][/ROW]
[ROW][C]65[/C][C]9264[/C][C]12418.9378865679[/C][C]-3154.93788656788[/C][/ROW]
[ROW][C]66[/C][C]9822[/C][C]12463.7728177463[/C][C]-2641.77281774626[/C][/ROW]
[ROW][C]67[/C][C]21126[/C][C]10286.1642460354[/C][C]10839.8357539646[/C][/ROW]
[ROW][C]68[/C][C]13050[/C][C]17844.2498008698[/C][C]-4794.24980086976[/C][/ROW]
[ROW][C]69[/C][C]13938[/C][C]13578.6834231258[/C][C]359.316576874198[/C][/ROW]
[ROW][C]70[/C][C]10764[/C][C]15181.5854801323[/C][C]-4417.58548013233[/C][/ROW]
[ROW][C]71[/C][C]8886[/C][C]13490.4562988629[/C][C]-4604.45629886289[/C][/ROW]
[ROW][C]72[/C][C]10830[/C][C]10296.4860471616[/C][C]533.513952838362[/C][/ROW]
[ROW][C]73[/C][C]7308[/C][C]11119.4111188841[/C][C]-3811.41111888412[/C][/ROW]
[ROW][C]74[/C][C]18336[/C][C]8690.57430057063[/C][C]9645.42569942937[/C][/ROW]
[ROW][C]75[/C][C]17484[/C][C]15715.6478487437[/C][C]1768.35215125628[/C][/ROW]
[ROW][C]76[/C][C]20082[/C][C]16362.1736366201[/C][C]3719.82636337991[/C][/ROW]
[ROW][C]77[/C][C]16308[/C][C]18911.4329234638[/C][C]-2603.43292346376[/C][/ROW]
[ROW][C]78[/C][C]18600[/C][C]19386.5315243065[/C][C]-786.53152430648[/C][/ROW]
[ROW][C]79[/C][C]19794[/C][C]19163.1245786483[/C][C]630.875421351673[/C][/ROW]
[ROW][C]80[/C][C]24114[/C][C]18830.4615346642[/C][C]5283.53846533582[/C][/ROW]
[ROW][C]81[/C][C]24708[/C][C]21884.1444126325[/C][C]2823.85558736745[/C][/ROW]
[ROW][C]82[/C][C]22482[/C][C]25031.595192728[/C][C]-2549.59519272805[/C][/ROW]
[ROW][C]83[/C][C]21288[/C][C]24690.4731538005[/C][C]-3402.47315380045[/C][/ROW]
[ROW][C]84[/C][C]15870[/C][C]22634.0656458565[/C][C]-6764.06564585654[/C][/ROW]
[ROW][C]85[/C][C]10734[/C][C]18170.2187646763[/C][C]-7436.21876467627[/C][/ROW]
[ROW][C]86[/C][C]11142[/C][C]13832.1238685553[/C][C]-2690.12386855533[/C][/ROW]
[ROW][C]87[/C][C]13080[/C][C]11799.4971267556[/C][C]1280.50287324443[/C][/ROW]
[ROW][C]88[/C][C]13098[/C][C]12130.9067615228[/C][C]967.093238477217[/C][/ROW]
[ROW][C]89[/C][C]18282[/C][C]12382.0470902537[/C][C]5899.95290974634[/C][/ROW]
[ROW][C]90[/C][C]15678[/C][C]18855.70852038[/C][C]-3177.70852037995[/C][/ROW]
[ROW][C]91[/C][C]6096[/C][C]16978.1440365078[/C][C]-10882.1440365078[/C][/ROW]
[ROW][C]92[/C][C]7854[/C][C]8700.54838326357[/C][C]-846.548383263573[/C][/ROW]
[ROW][C]93[/C][C]9342[/C][C]7213.26779893937[/C][C]2128.73220106063[/C][/ROW]
[ROW][C]94[/C][C]9162[/C][C]9483.1484263639[/C][C]-321.148426363899[/C][/ROW]
[ROW][C]95[/C][C]7092[/C][C]10531.2223457971[/C][C]-3439.22234579705[/C][/ROW]
[ROW][C]96[/C][C]4692[/C][C]8162.58222600823[/C][C]-3470.58222600823[/C][/ROW]
[ROW][C]97[/C][C]4764[/C][C]5858.22283795226[/C][C]-1094.22283795226[/C][/ROW]
[ROW][C]98[/C][C]3852[/C][C]6096.69934240443[/C][C]-2244.69934240443[/C][/ROW]
[ROW][C]99[/C][C]9456[/C][C]4481.68806902806[/C][C]4974.31193097194[/C][/ROW]
[ROW][C]100[/C][C]5490[/C][C]7323.37835389298[/C][C]-1833.37835389298[/C][/ROW]
[ROW][C]101[/C][C]6528[/C][C]5770.60183878165[/C][C]757.398161218352[/C][/ROW]
[ROW][C]102[/C][C]9306[/C][C]8124.62883815121[/C][C]1181.37116184879[/C][/ROW]
[ROW][C]103[/C][C]9018[/C][C]8861.03053749803[/C][C]156.969462501975[/C][/ROW]
[ROW][C]104[/C][C]5964[/C][C]8751.56782797102[/C][C]-2787.56782797102[/C][/ROW]
[ROW][C]105[/C][C]5856[/C][C]6013.61878986015[/C][C]-157.618789860154[/C][/ROW]
[ROW][C]106[/C][C]20574[/C][C]6527.49064663901[/C][C]14046.509353361[/C][/ROW]
[ROW][C]107[/C][C]7704[/C][C]17513.7755077965[/C][C]-9809.77550779653[/C][/ROW]
[ROW][C]108[/C][C]4464[/C][C]10685.3909443768[/C][C]-6221.39094437678[/C][/ROW]
[ROW][C]109[/C][C]9258[/C][C]6551.28809014735[/C][C]2706.71190985265[/C][/ROW]
[ROW][C]110[/C][C]6240[/C][C]9399.4333860212[/C][C]-3159.4333860212[/C][/ROW]
[ROW][C]111[/C][C]9354[/C][C]7478.98395682169[/C][C]1875.01604317831[/C][/ROW]
[ROW][C]112[/C][C]11916[/C][C]7819.50856725187[/C][C]4096.49143274813[/C][/ROW]
[ROW][C]113[/C][C]13026[/C][C]10549.4351400496[/C][C]2476.56485995035[/C][/ROW]
[ROW][C]114[/C][C]10062[/C][C]14148.5967854144[/C][C]-4086.59678541438[/C][/ROW]
[ROW][C]115[/C][C]7638[/C][C]11147.4975170951[/C][C]-3509.49751709514[/C][/ROW]
[ROW][C]116[/C][C]8844[/C][C]8312.8567995254[/C][C]531.143200474604[/C][/ROW]
[ROW][C]117[/C][C]13476[/C][C]8012.56475249915[/C][C]5463.43524750085[/C][/ROW]
[ROW][C]118[/C][C]19074[/C][C]13141.3297184495[/C][C]5932.6702815505[/C][/ROW]
[ROW][C]119[/C][C]16896[/C][C]17324.1427719758[/C][C]-428.142771975788[/C][/ROW]
[ROW][C]120[/C][C]21162[/C][C]17255.0790929017[/C][C]3906.92090709833[/C][/ROW]
[ROW][C]121[/C][C]16014[/C][C]20702.9028141856[/C][C]-4688.90281418557[/C][/ROW]
[ROW][C]122[/C][C]13746[/C][C]18148.0245875772[/C][C]-4402.02458757721[/C][/ROW]
[ROW][C]123[/C][C]14550[/C][C]15629.0359642913[/C][C]-1079.03596429131[/C][/ROW]
[ROW][C]124[/C][C]13146[/C][C]14027.8072837962[/C][C]-881.807283796237[/C][/ROW]
[ROW][C]125[/C][C]11022[/C][C]13195.7381773534[/C][C]-2173.73817735335[/C][/ROW]
[ROW][C]126[/C][C]10386[/C][C]13208.8108821894[/C][C]-2822.81088218936[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297998&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297998&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
1361623177.607371794872984.39262820513
1461325284.10473051446847.89526948554
1562406055.28283068104184.717169318958
1659045912.45454688901-8.45454688900918
1759226017.93977699975-95.9397769997522
1884608641.22548421066-181.225484210659
1978968119.4105286488-223.410528648804
2072907676.43051998712-386.430519987121
2165526686.65846648402-134.658466484024
2284428240.83146423235201.168535767654
23957010460.2366118317-890.236611831744
24931210029.5029741341-717.50297413414
25658810005.512489772-3417.51248977203
2660847509.14568644808-1425.14568644808
27112986622.710070732544675.28992926746
2897989599.08156590497198.918434095025
29144009833.219206341154566.78079365885
301373415726.2708284923-1992.27082849234
311348213937.8369006245-455.836900624494
321481413325.82860805951488.17139194055
331354813670.0378932844-122.037893284405
341551615259.5193793512256.480620648807
351548017478.1024268929-1998.10242689295
361048816285.781683351-5797.78168335104
371426212561.48519560061700.51480439938
381494613743.86555856591202.1344414341
391416614997.9883884978-831.988388497821
401154413904.3724049083-2360.37240490826
411019412528.4721731589-2334.47217315886
421185013230.7892760367-1380.78927603668
431270211886.6487340501815.351265949923
441822212205.94987659926016.05012340083
451956015618.14093642923941.85906357076
461949420064.3249012866-570.324901286636
471528221591.5262356663-6309.52623566626
481103417175.9897738422-6141.98977384218
49877213526.8604836667-4754.86048366669
50711010104.3607556046-2994.36075560458
5163128240.94648505984-1928.94648505984
5270806216.05754138288863.942458617124
5370807020.8608374327859.139162567224
5482269378.15604810974-1152.15604810974
5576148233.25657712064-619.256577120645
5673267720.33209796971-394.332097969706
5774226448.32371584858973.676284151424
5888868489.93513777731396.064862222685
59769810313.1900120309-2615.19001203092
6086348395.55200375036238.447996249639
6154609213.06871836828-3753.06871836828
6297446516.823243702153227.17675629785
63123309031.207236444393298.79276355561
641287010796.04819764842073.95180235163
65926412418.9378865679-3154.93788656788
66982212463.7728177463-2641.77281774626
672112610286.164246035410839.8357539646
681305017844.2498008698-4794.24980086976
691393813578.6834231258359.316576874198
701076415181.5854801323-4417.58548013233
71888613490.4562988629-4604.45629886289
721083010296.4860471616533.513952838362
73730811119.4111188841-3811.41111888412
74183368690.574300570639645.42569942937
751748415715.64784874371768.35215125628
762008216362.17363662013719.82636337991
771630818911.4329234638-2603.43292346376
781860019386.5315243065-786.53152430648
791979419163.1245786483630.875421351673
802411418830.46153466425283.53846533582
812470821884.14441263252823.85558736745
822248225031.595192728-2549.59519272805
832128824690.4731538005-3402.47315380045
841587022634.0656458565-6764.06564585654
851073418170.2187646763-7436.21876467627
861114213832.1238685553-2690.12386855533
871308011799.49712675561280.50287324443
881309812130.9067615228967.093238477217
891828212382.04709025375899.95290974634
901567818855.70852038-3177.70852037995
91609616978.1440365078-10882.1440365078
9278548700.54838326357-846.548383263573
9393427213.267798939372128.73220106063
9491629483.1484263639-321.148426363899
95709210531.2223457971-3439.22234579705
9646928162.58222600823-3470.58222600823
9747645858.22283795226-1094.22283795226
9838526096.69934240443-2244.69934240443
9994564481.688069028064974.31193097194
10054907323.37835389298-1833.37835389298
10165285770.60183878165757.398161218352
10293068124.628838151211181.37116184879
10390188861.03053749803156.969462501975
10459648751.56782797102-2787.56782797102
10558566013.61878986015-157.618789860154
106205746527.4906466390114046.509353361
107770417513.7755077965-9809.77550779653
108446410685.3909443768-6221.39094437678
10992586551.288090147352706.71190985265
11062409399.4333860212-3159.4333860212
11193547478.983956821691875.01604317831
112119167819.508567251874096.49143274813
1131302610549.43514004962476.56485995035
1141006214148.5967854144-4086.59678541438
115763811147.4975170951-3509.49751709514
11688448312.8567995254531.143200474604
117134768012.564752499155463.43524750085
1181907413141.32971844955932.6702815505
1191689617324.1427719758-428.142771975788
1202116217255.07909290173906.92090709833
1211601420702.9028141856-4688.90281418557
1221374618148.0245875772-4402.02458757721
1231455015629.0359642913-1079.03596429131
1241314614027.8072837962-881.807283796237
1251102213195.7381773534-2173.73817735335
1261038613208.8108821894-2822.81088218936







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12711097.24124658053717.4372779708518477.0452151901
12810902.18445301141873.8039999884919930.5649060343
12910453.315178270414.961867321184420891.6684892196
13011747.41979072350.962912089524323443.8766693566
13111419.495563134-1428.0023564107424266.9934826787
13211788.6590772556-2129.5094754209525706.8276299321
13312021.217397458-2904.6541314461826947.0889263621
13412701.4224874405-3181.265448869628584.1104237507
13513380.5256929302-3416.8764751101230177.9278609705
13612513.0277963776-5163.6056391770130189.6612319323
13712212.0980578571-6313.4147372601530737.6108529742
13813701.2126267032-5646.8979243487533049.3231777551

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
127 & 11097.2412465805 & 3717.43727797085 & 18477.0452151901 \tabularnewline
128 & 10902.1844530114 & 1873.80399998849 & 19930.5649060343 \tabularnewline
129 & 10453.3151782704 & 14.9618673211844 & 20891.6684892196 \tabularnewline
130 & 11747.419790723 & 50.9629120895243 & 23443.8766693566 \tabularnewline
131 & 11419.495563134 & -1428.00235641074 & 24266.9934826787 \tabularnewline
132 & 11788.6590772556 & -2129.50947542095 & 25706.8276299321 \tabularnewline
133 & 12021.217397458 & -2904.65413144618 & 26947.0889263621 \tabularnewline
134 & 12701.4224874405 & -3181.2654488696 & 28584.1104237507 \tabularnewline
135 & 13380.5256929302 & -3416.87647511012 & 30177.9278609705 \tabularnewline
136 & 12513.0277963776 & -5163.60563917701 & 30189.6612319323 \tabularnewline
137 & 12212.0980578571 & -6313.41473726015 & 30737.6108529742 \tabularnewline
138 & 13701.2126267032 & -5646.89792434875 & 33049.3231777551 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297998&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]11097.2412465805[/C][C]3717.43727797085[/C][C]18477.0452151901[/C][/ROW]
[ROW][C]128[/C][C]10902.1844530114[/C][C]1873.80399998849[/C][C]19930.5649060343[/C][/ROW]
[ROW][C]129[/C][C]10453.3151782704[/C][C]14.9618673211844[/C][C]20891.6684892196[/C][/ROW]
[ROW][C]130[/C][C]11747.419790723[/C][C]50.9629120895243[/C][C]23443.8766693566[/C][/ROW]
[ROW][C]131[/C][C]11419.495563134[/C][C]-1428.00235641074[/C][C]24266.9934826787[/C][/ROW]
[ROW][C]132[/C][C]11788.6590772556[/C][C]-2129.50947542095[/C][C]25706.8276299321[/C][/ROW]
[ROW][C]133[/C][C]12021.217397458[/C][C]-2904.65413144618[/C][C]26947.0889263621[/C][/ROW]
[ROW][C]134[/C][C]12701.4224874405[/C][C]-3181.2654488696[/C][C]28584.1104237507[/C][/ROW]
[ROW][C]135[/C][C]13380.5256929302[/C][C]-3416.87647511012[/C][C]30177.9278609705[/C][/ROW]
[ROW][C]136[/C][C]12513.0277963776[/C][C]-5163.60563917701[/C][C]30189.6612319323[/C][/ROW]
[ROW][C]137[/C][C]12212.0980578571[/C][C]-6313.41473726015[/C][C]30737.6108529742[/C][/ROW]
[ROW][C]138[/C][C]13701.2126267032[/C][C]-5646.89792434875[/C][C]33049.3231777551[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297998&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297998&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
12711097.24124658053717.4372779708518477.0452151901
12810902.18445301141873.8039999884919930.5649060343
12910453.315178270414.961867321184420891.6684892196
13011747.41979072350.962912089524323443.8766693566
13111419.495563134-1428.0023564107424266.9934826787
13211788.6590772556-2129.5094754209525706.8276299321
13312021.217397458-2904.6541314461826947.0889263621
13412701.4224874405-3181.265448869628584.1104237507
13513380.5256929302-3416.8764751101230177.9278609705
13612513.0277963776-5163.6056391770130189.6612319323
13712212.0980578571-6313.4147372601530737.6108529742
13813701.2126267032-5646.8979243487533049.3231777551



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
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')