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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, 07 Dec 2010 17:44:26 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/07/t12917437465j7t1qir1iq2mgf.htm/, Retrieved Fri, 03 May 2024 21:14:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=106556, Retrieved Fri, 03 May 2024 21:14:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact171
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [HPC Retail Sales] [2008-03-10 17:56:43] [74be16979710d4c4e7c6647856088456]
-  M D    [Exponential Smoothing] [Paper Triple Expo...] [2010-12-07 17:44:26] [59f7d3e7fcb6374015f4e6b9053b0f01] [Current]
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Dataseries X:
17.848
19.592
21.092
20.899
25.890
24.965
22.225
20.977
22.897
22.785
22.769
19.637
20.203
20.450
23.083
21.738
26.766
25.280
22.574
22.729
21.378
22.902
24.989
21.116
15.169
15.846
20.927
18.273
22.538
15.596
14.034
11.366
14.861
15.149
13.577
13.026
13.190
13.196
15.826
14.733
16.307
15.703
14.589
12.043
15.057
14.053
12.698
10.888
10.045
11.549
13.767
12.434
13.116
14.211
12.266
12.602
15.714
13.742
12.745
10.491
10.057
10.900
11.771
11.992
11.933
14.504
11.727
11.477
13.578
11.555
11.846
11.397
10.066
10.269
14.279
13.870
13.695
14.420
11.424
9.704
12.464
14.301
13.464
9.893
11.572
12.380
16.692
16.052
16.459
14.761
13.654
13.480
18.068
16.560
14.530
10.650
11.651
13.735
13.360
17.818
20.613
16.231
13.862
12.004
17.734
15.034
12.609
12.320
10.833
11.350
13.648
14.890
16.325
18.045
15.616
11.926
16.855
15.083
12.520
12.355




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106556&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106556&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106556&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.473971450972799
beta0.0065615366876307
gamma0.328170676425391

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.473971450972799 \tabularnewline
beta & 0.0065615366876307 \tabularnewline
gamma & 0.328170676425391 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106556&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]0.473971450972799[/C][/ROW]
[ROW][C]beta[/C][C]0.0065615366876307[/C][/ROW]
[ROW][C]gamma[/C][C]0.328170676425391[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106556&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106556&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
alpha0.473971450972799
beta0.0065615366876307
gamma0.328170676425391







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1320.20319.75205021367520.450949786324788
1420.4520.18780332850030.262196671499719
1523.08322.99874161563290.0842583843670681
1621.73821.8157292766096-0.0777292766096025
1726.76626.7729060076284-0.00690600762840177
1825.2825.19287946865590.0871205313440981
1922.57423.0523981013263-0.478398101326281
2022.72921.5059309047481.22306909525199
2121.37823.9528809725080-2.57488097250796
2222.90222.56049497152850.341505028471538
2324.98922.69391308253532.29508691746474
2421.11620.66624424625030.449755753749734
2515.16921.5631443600254-6.39414436002542
2615.84618.7070404533627-2.86104045336273
2720.92719.98232941630290.944670583697079
2818.27319.1572331801393-0.884233180139319
2922.53823.7199366443331-1.18193664433310
3015.59621.5711168793076-5.97511687930761
3114.03416.4127369567014-2.37873695670139
3211.36614.2064255749357-2.84042557493574
3314.86114.00627126565170.854728734348273
3415.14914.68804112721390.46095887278606
3513.57715.1608610980324-1.58386109803237
3613.02610.90960682215842.11639317784157
3713.1911.35366519876901.83633480123103
3813.19612.97274235654620.223257643453822
3915.82616.340720977083-0.514720977083002
4014.73314.47750907375170.255490926248314
4116.30719.5018747509537-3.19487475095367
4215.70315.53814379676950.164856203230496
4314.58913.89646084674480.69253915325517
4412.04313.0613905059975-1.01839050599748
4515.05714.36362306923430.693376930765746
4614.05314.9013499437283-0.84834994372828
4712.69814.3969400845724-1.69894008457240
4810.88810.72588469416540.162115305834634
4910.04510.1852264162700-0.140226416269973
5011.54910.57276295589040.976237044109611
5113.76714.1563327990870-0.389332799086965
5212.43412.4719963747322-0.0379963747322165
5313.11616.7472035154773-3.63120351547726
5414.21113.14086181187641.07013818812356
5512.26612.00638035504540.259619644954562
5612.60210.65645052964721.94554947035279
5715.71413.65390625116712.06009374883288
5813.74214.5724271360866-0.830427136086591
5912.74513.9288861337279-1.1838861337279
6010.49110.8240310030629-0.333031003062949
6110.0579.995765939881310.0612340601186876
6210.910.67141824887540.228581751124628
6311.77113.6624585669115-1.89145856691147
6411.99211.31970819580250.672291804197467
6511.93315.3063961280774-3.37339612807743
6614.50412.62973829881721.87426170118276
6711.72711.7348830753153-0.00788307531533405
6811.47710.54678206802980.930217931970176
6913.57813.07719563553270.500804364467331
7011.55512.7472486974918-1.19224869749179
7111.84611.8596459251731-0.0136459251731296
7211.3979.448419298881161.94858070111884
7310.0669.76881702994870.297182970051301
7410.26910.5851080689890-0.316108068989035
7514.27912.95022740953531.32877259046466
7613.8712.58458539064731.28541460935272
7713.69516.1736250841754-2.47862508417542
7814.4214.8398787055740-0.419878705573966
7911.42412.5385497457272-1.11454974572725
809.70410.9902129166719-1.28621291667189
8112.46412.39143093018730.0725690698126975
8214.30111.56037179792252.7406282020775
8313.46412.74665642600350.71734357399654
849.89311.0292620950649-1.13626209506491
8511.5729.601493094083381.97050690591662
8612.3811.10926199098361.27073800901636
8716.69214.51962794755162.17237205244843
8816.05214.55814262982841.49385737017159
8916.45917.6086504737641-1.14965047376408
9014.76117.2767763721974-2.51577637219739
9113.65413.8721952174728-0.218195217472841
9213.4812.73192130877740.748078691222647
9318.06815.35107491751412.71692508248591
9416.5616.26134516408430.298654835915684
9514.5315.9607364858548-1.43073648585482
9610.6512.9183565913382-2.26835659133818
9711.65111.49992470226470.151075297735261
9813.73512.02848237627841.70651762372159
9913.3615.8063437290606-2.44634372906059
10017.81813.52952660924544.28847339075461
10120.61317.44789032581883.16510967418117
10216.23118.9383066349928-2.70730663499282
10313.86215.8520225188341-1.99002251883408
10412.00414.0456998503392-2.04169985033923
10517.73415.68071993957482.05328006042518
10615.03415.8551839135026-0.821183913502637
10712.60914.7179826843134-2.10898268431336
10812.3211.20014708696071.11985291303927
10910.83311.8064362583755-0.97343625837554
11011.3512.0681687829837-0.71816878298368
11113.64813.9700103316430-0.322010331642952
11214.8913.85939440912621.03060559087377
11316.32516.02628238417790.298717615822106
11418.04515.12204146269112.92295853730894
11515.61614.82334425918500.792655740815043
11611.92614.3308440601420-2.40484406014198
11716.85516.50335280686800.351647193131967
11815.08315.3724927828561-0.289492782856074
11912.5214.2640544045649-1.74405440456491
12012.35511.47676944261250.878230557387475

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 20.203 & 19.7520502136752 & 0.450949786324788 \tabularnewline
14 & 20.45 & 20.1878033285003 & 0.262196671499719 \tabularnewline
15 & 23.083 & 22.9987416156329 & 0.0842583843670681 \tabularnewline
16 & 21.738 & 21.8157292766096 & -0.0777292766096025 \tabularnewline
17 & 26.766 & 26.7729060076284 & -0.00690600762840177 \tabularnewline
18 & 25.28 & 25.1928794686559 & 0.0871205313440981 \tabularnewline
19 & 22.574 & 23.0523981013263 & -0.478398101326281 \tabularnewline
20 & 22.729 & 21.505930904748 & 1.22306909525199 \tabularnewline
21 & 21.378 & 23.9528809725080 & -2.57488097250796 \tabularnewline
22 & 22.902 & 22.5604949715285 & 0.341505028471538 \tabularnewline
23 & 24.989 & 22.6939130825353 & 2.29508691746474 \tabularnewline
24 & 21.116 & 20.6662442462503 & 0.449755753749734 \tabularnewline
25 & 15.169 & 21.5631443600254 & -6.39414436002542 \tabularnewline
26 & 15.846 & 18.7070404533627 & -2.86104045336273 \tabularnewline
27 & 20.927 & 19.9823294163029 & 0.944670583697079 \tabularnewline
28 & 18.273 & 19.1572331801393 & -0.884233180139319 \tabularnewline
29 & 22.538 & 23.7199366443331 & -1.18193664433310 \tabularnewline
30 & 15.596 & 21.5711168793076 & -5.97511687930761 \tabularnewline
31 & 14.034 & 16.4127369567014 & -2.37873695670139 \tabularnewline
32 & 11.366 & 14.2064255749357 & -2.84042557493574 \tabularnewline
33 & 14.861 & 14.0062712656517 & 0.854728734348273 \tabularnewline
34 & 15.149 & 14.6880411272139 & 0.46095887278606 \tabularnewline
35 & 13.577 & 15.1608610980324 & -1.58386109803237 \tabularnewline
36 & 13.026 & 10.9096068221584 & 2.11639317784157 \tabularnewline
37 & 13.19 & 11.3536651987690 & 1.83633480123103 \tabularnewline
38 & 13.196 & 12.9727423565462 & 0.223257643453822 \tabularnewline
39 & 15.826 & 16.340720977083 & -0.514720977083002 \tabularnewline
40 & 14.733 & 14.4775090737517 & 0.255490926248314 \tabularnewline
41 & 16.307 & 19.5018747509537 & -3.19487475095367 \tabularnewline
42 & 15.703 & 15.5381437967695 & 0.164856203230496 \tabularnewline
43 & 14.589 & 13.8964608467448 & 0.69253915325517 \tabularnewline
44 & 12.043 & 13.0613905059975 & -1.01839050599748 \tabularnewline
45 & 15.057 & 14.3636230692343 & 0.693376930765746 \tabularnewline
46 & 14.053 & 14.9013499437283 & -0.84834994372828 \tabularnewline
47 & 12.698 & 14.3969400845724 & -1.69894008457240 \tabularnewline
48 & 10.888 & 10.7258846941654 & 0.162115305834634 \tabularnewline
49 & 10.045 & 10.1852264162700 & -0.140226416269973 \tabularnewline
50 & 11.549 & 10.5727629558904 & 0.976237044109611 \tabularnewline
51 & 13.767 & 14.1563327990870 & -0.389332799086965 \tabularnewline
52 & 12.434 & 12.4719963747322 & -0.0379963747322165 \tabularnewline
53 & 13.116 & 16.7472035154773 & -3.63120351547726 \tabularnewline
54 & 14.211 & 13.1408618118764 & 1.07013818812356 \tabularnewline
55 & 12.266 & 12.0063803550454 & 0.259619644954562 \tabularnewline
56 & 12.602 & 10.6564505296472 & 1.94554947035279 \tabularnewline
57 & 15.714 & 13.6539062511671 & 2.06009374883288 \tabularnewline
58 & 13.742 & 14.5724271360866 & -0.830427136086591 \tabularnewline
59 & 12.745 & 13.9288861337279 & -1.1838861337279 \tabularnewline
60 & 10.491 & 10.8240310030629 & -0.333031003062949 \tabularnewline
61 & 10.057 & 9.99576593988131 & 0.0612340601186876 \tabularnewline
62 & 10.9 & 10.6714182488754 & 0.228581751124628 \tabularnewline
63 & 11.771 & 13.6624585669115 & -1.89145856691147 \tabularnewline
64 & 11.992 & 11.3197081958025 & 0.672291804197467 \tabularnewline
65 & 11.933 & 15.3063961280774 & -3.37339612807743 \tabularnewline
66 & 14.504 & 12.6297382988172 & 1.87426170118276 \tabularnewline
67 & 11.727 & 11.7348830753153 & -0.00788307531533405 \tabularnewline
68 & 11.477 & 10.5467820680298 & 0.930217931970176 \tabularnewline
69 & 13.578 & 13.0771956355327 & 0.500804364467331 \tabularnewline
70 & 11.555 & 12.7472486974918 & -1.19224869749179 \tabularnewline
71 & 11.846 & 11.8596459251731 & -0.0136459251731296 \tabularnewline
72 & 11.397 & 9.44841929888116 & 1.94858070111884 \tabularnewline
73 & 10.066 & 9.7688170299487 & 0.297182970051301 \tabularnewline
74 & 10.269 & 10.5851080689890 & -0.316108068989035 \tabularnewline
75 & 14.279 & 12.9502274095353 & 1.32877259046466 \tabularnewline
76 & 13.87 & 12.5845853906473 & 1.28541460935272 \tabularnewline
77 & 13.695 & 16.1736250841754 & -2.47862508417542 \tabularnewline
78 & 14.42 & 14.8398787055740 & -0.419878705573966 \tabularnewline
79 & 11.424 & 12.5385497457272 & -1.11454974572725 \tabularnewline
80 & 9.704 & 10.9902129166719 & -1.28621291667189 \tabularnewline
81 & 12.464 & 12.3914309301873 & 0.0725690698126975 \tabularnewline
82 & 14.301 & 11.5603717979225 & 2.7406282020775 \tabularnewline
83 & 13.464 & 12.7466564260035 & 0.71734357399654 \tabularnewline
84 & 9.893 & 11.0292620950649 & -1.13626209506491 \tabularnewline
85 & 11.572 & 9.60149309408338 & 1.97050690591662 \tabularnewline
86 & 12.38 & 11.1092619909836 & 1.27073800901636 \tabularnewline
87 & 16.692 & 14.5196279475516 & 2.17237205244843 \tabularnewline
88 & 16.052 & 14.5581426298284 & 1.49385737017159 \tabularnewline
89 & 16.459 & 17.6086504737641 & -1.14965047376408 \tabularnewline
90 & 14.761 & 17.2767763721974 & -2.51577637219739 \tabularnewline
91 & 13.654 & 13.8721952174728 & -0.218195217472841 \tabularnewline
92 & 13.48 & 12.7319213087774 & 0.748078691222647 \tabularnewline
93 & 18.068 & 15.3510749175141 & 2.71692508248591 \tabularnewline
94 & 16.56 & 16.2613451640843 & 0.298654835915684 \tabularnewline
95 & 14.53 & 15.9607364858548 & -1.43073648585482 \tabularnewline
96 & 10.65 & 12.9183565913382 & -2.26835659133818 \tabularnewline
97 & 11.651 & 11.4999247022647 & 0.151075297735261 \tabularnewline
98 & 13.735 & 12.0284823762784 & 1.70651762372159 \tabularnewline
99 & 13.36 & 15.8063437290606 & -2.44634372906059 \tabularnewline
100 & 17.818 & 13.5295266092454 & 4.28847339075461 \tabularnewline
101 & 20.613 & 17.4478903258188 & 3.16510967418117 \tabularnewline
102 & 16.231 & 18.9383066349928 & -2.70730663499282 \tabularnewline
103 & 13.862 & 15.8520225188341 & -1.99002251883408 \tabularnewline
104 & 12.004 & 14.0456998503392 & -2.04169985033923 \tabularnewline
105 & 17.734 & 15.6807199395748 & 2.05328006042518 \tabularnewline
106 & 15.034 & 15.8551839135026 & -0.821183913502637 \tabularnewline
107 & 12.609 & 14.7179826843134 & -2.10898268431336 \tabularnewline
108 & 12.32 & 11.2001470869607 & 1.11985291303927 \tabularnewline
109 & 10.833 & 11.8064362583755 & -0.97343625837554 \tabularnewline
110 & 11.35 & 12.0681687829837 & -0.71816878298368 \tabularnewline
111 & 13.648 & 13.9700103316430 & -0.322010331642952 \tabularnewline
112 & 14.89 & 13.8593944091262 & 1.03060559087377 \tabularnewline
113 & 16.325 & 16.0262823841779 & 0.298717615822106 \tabularnewline
114 & 18.045 & 15.1220414626911 & 2.92295853730894 \tabularnewline
115 & 15.616 & 14.8233442591850 & 0.792655740815043 \tabularnewline
116 & 11.926 & 14.3308440601420 & -2.40484406014198 \tabularnewline
117 & 16.855 & 16.5033528068680 & 0.351647193131967 \tabularnewline
118 & 15.083 & 15.3724927828561 & -0.289492782856074 \tabularnewline
119 & 12.52 & 14.2640544045649 & -1.74405440456491 \tabularnewline
120 & 12.355 & 11.4767694426125 & 0.878230557387475 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106556&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]20.203[/C][C]19.7520502136752[/C][C]0.450949786324788[/C][/ROW]
[ROW][C]14[/C][C]20.45[/C][C]20.1878033285003[/C][C]0.262196671499719[/C][/ROW]
[ROW][C]15[/C][C]23.083[/C][C]22.9987416156329[/C][C]0.0842583843670681[/C][/ROW]
[ROW][C]16[/C][C]21.738[/C][C]21.8157292766096[/C][C]-0.0777292766096025[/C][/ROW]
[ROW][C]17[/C][C]26.766[/C][C]26.7729060076284[/C][C]-0.00690600762840177[/C][/ROW]
[ROW][C]18[/C][C]25.28[/C][C]25.1928794686559[/C][C]0.0871205313440981[/C][/ROW]
[ROW][C]19[/C][C]22.574[/C][C]23.0523981013263[/C][C]-0.478398101326281[/C][/ROW]
[ROW][C]20[/C][C]22.729[/C][C]21.505930904748[/C][C]1.22306909525199[/C][/ROW]
[ROW][C]21[/C][C]21.378[/C][C]23.9528809725080[/C][C]-2.57488097250796[/C][/ROW]
[ROW][C]22[/C][C]22.902[/C][C]22.5604949715285[/C][C]0.341505028471538[/C][/ROW]
[ROW][C]23[/C][C]24.989[/C][C]22.6939130825353[/C][C]2.29508691746474[/C][/ROW]
[ROW][C]24[/C][C]21.116[/C][C]20.6662442462503[/C][C]0.449755753749734[/C][/ROW]
[ROW][C]25[/C][C]15.169[/C][C]21.5631443600254[/C][C]-6.39414436002542[/C][/ROW]
[ROW][C]26[/C][C]15.846[/C][C]18.7070404533627[/C][C]-2.86104045336273[/C][/ROW]
[ROW][C]27[/C][C]20.927[/C][C]19.9823294163029[/C][C]0.944670583697079[/C][/ROW]
[ROW][C]28[/C][C]18.273[/C][C]19.1572331801393[/C][C]-0.884233180139319[/C][/ROW]
[ROW][C]29[/C][C]22.538[/C][C]23.7199366443331[/C][C]-1.18193664433310[/C][/ROW]
[ROW][C]30[/C][C]15.596[/C][C]21.5711168793076[/C][C]-5.97511687930761[/C][/ROW]
[ROW][C]31[/C][C]14.034[/C][C]16.4127369567014[/C][C]-2.37873695670139[/C][/ROW]
[ROW][C]32[/C][C]11.366[/C][C]14.2064255749357[/C][C]-2.84042557493574[/C][/ROW]
[ROW][C]33[/C][C]14.861[/C][C]14.0062712656517[/C][C]0.854728734348273[/C][/ROW]
[ROW][C]34[/C][C]15.149[/C][C]14.6880411272139[/C][C]0.46095887278606[/C][/ROW]
[ROW][C]35[/C][C]13.577[/C][C]15.1608610980324[/C][C]-1.58386109803237[/C][/ROW]
[ROW][C]36[/C][C]13.026[/C][C]10.9096068221584[/C][C]2.11639317784157[/C][/ROW]
[ROW][C]37[/C][C]13.19[/C][C]11.3536651987690[/C][C]1.83633480123103[/C][/ROW]
[ROW][C]38[/C][C]13.196[/C][C]12.9727423565462[/C][C]0.223257643453822[/C][/ROW]
[ROW][C]39[/C][C]15.826[/C][C]16.340720977083[/C][C]-0.514720977083002[/C][/ROW]
[ROW][C]40[/C][C]14.733[/C][C]14.4775090737517[/C][C]0.255490926248314[/C][/ROW]
[ROW][C]41[/C][C]16.307[/C][C]19.5018747509537[/C][C]-3.19487475095367[/C][/ROW]
[ROW][C]42[/C][C]15.703[/C][C]15.5381437967695[/C][C]0.164856203230496[/C][/ROW]
[ROW][C]43[/C][C]14.589[/C][C]13.8964608467448[/C][C]0.69253915325517[/C][/ROW]
[ROW][C]44[/C][C]12.043[/C][C]13.0613905059975[/C][C]-1.01839050599748[/C][/ROW]
[ROW][C]45[/C][C]15.057[/C][C]14.3636230692343[/C][C]0.693376930765746[/C][/ROW]
[ROW][C]46[/C][C]14.053[/C][C]14.9013499437283[/C][C]-0.84834994372828[/C][/ROW]
[ROW][C]47[/C][C]12.698[/C][C]14.3969400845724[/C][C]-1.69894008457240[/C][/ROW]
[ROW][C]48[/C][C]10.888[/C][C]10.7258846941654[/C][C]0.162115305834634[/C][/ROW]
[ROW][C]49[/C][C]10.045[/C][C]10.1852264162700[/C][C]-0.140226416269973[/C][/ROW]
[ROW][C]50[/C][C]11.549[/C][C]10.5727629558904[/C][C]0.976237044109611[/C][/ROW]
[ROW][C]51[/C][C]13.767[/C][C]14.1563327990870[/C][C]-0.389332799086965[/C][/ROW]
[ROW][C]52[/C][C]12.434[/C][C]12.4719963747322[/C][C]-0.0379963747322165[/C][/ROW]
[ROW][C]53[/C][C]13.116[/C][C]16.7472035154773[/C][C]-3.63120351547726[/C][/ROW]
[ROW][C]54[/C][C]14.211[/C][C]13.1408618118764[/C][C]1.07013818812356[/C][/ROW]
[ROW][C]55[/C][C]12.266[/C][C]12.0063803550454[/C][C]0.259619644954562[/C][/ROW]
[ROW][C]56[/C][C]12.602[/C][C]10.6564505296472[/C][C]1.94554947035279[/C][/ROW]
[ROW][C]57[/C][C]15.714[/C][C]13.6539062511671[/C][C]2.06009374883288[/C][/ROW]
[ROW][C]58[/C][C]13.742[/C][C]14.5724271360866[/C][C]-0.830427136086591[/C][/ROW]
[ROW][C]59[/C][C]12.745[/C][C]13.9288861337279[/C][C]-1.1838861337279[/C][/ROW]
[ROW][C]60[/C][C]10.491[/C][C]10.8240310030629[/C][C]-0.333031003062949[/C][/ROW]
[ROW][C]61[/C][C]10.057[/C][C]9.99576593988131[/C][C]0.0612340601186876[/C][/ROW]
[ROW][C]62[/C][C]10.9[/C][C]10.6714182488754[/C][C]0.228581751124628[/C][/ROW]
[ROW][C]63[/C][C]11.771[/C][C]13.6624585669115[/C][C]-1.89145856691147[/C][/ROW]
[ROW][C]64[/C][C]11.992[/C][C]11.3197081958025[/C][C]0.672291804197467[/C][/ROW]
[ROW][C]65[/C][C]11.933[/C][C]15.3063961280774[/C][C]-3.37339612807743[/C][/ROW]
[ROW][C]66[/C][C]14.504[/C][C]12.6297382988172[/C][C]1.87426170118276[/C][/ROW]
[ROW][C]67[/C][C]11.727[/C][C]11.7348830753153[/C][C]-0.00788307531533405[/C][/ROW]
[ROW][C]68[/C][C]11.477[/C][C]10.5467820680298[/C][C]0.930217931970176[/C][/ROW]
[ROW][C]69[/C][C]13.578[/C][C]13.0771956355327[/C][C]0.500804364467331[/C][/ROW]
[ROW][C]70[/C][C]11.555[/C][C]12.7472486974918[/C][C]-1.19224869749179[/C][/ROW]
[ROW][C]71[/C][C]11.846[/C][C]11.8596459251731[/C][C]-0.0136459251731296[/C][/ROW]
[ROW][C]72[/C][C]11.397[/C][C]9.44841929888116[/C][C]1.94858070111884[/C][/ROW]
[ROW][C]73[/C][C]10.066[/C][C]9.7688170299487[/C][C]0.297182970051301[/C][/ROW]
[ROW][C]74[/C][C]10.269[/C][C]10.5851080689890[/C][C]-0.316108068989035[/C][/ROW]
[ROW][C]75[/C][C]14.279[/C][C]12.9502274095353[/C][C]1.32877259046466[/C][/ROW]
[ROW][C]76[/C][C]13.87[/C][C]12.5845853906473[/C][C]1.28541460935272[/C][/ROW]
[ROW][C]77[/C][C]13.695[/C][C]16.1736250841754[/C][C]-2.47862508417542[/C][/ROW]
[ROW][C]78[/C][C]14.42[/C][C]14.8398787055740[/C][C]-0.419878705573966[/C][/ROW]
[ROW][C]79[/C][C]11.424[/C][C]12.5385497457272[/C][C]-1.11454974572725[/C][/ROW]
[ROW][C]80[/C][C]9.704[/C][C]10.9902129166719[/C][C]-1.28621291667189[/C][/ROW]
[ROW][C]81[/C][C]12.464[/C][C]12.3914309301873[/C][C]0.0725690698126975[/C][/ROW]
[ROW][C]82[/C][C]14.301[/C][C]11.5603717979225[/C][C]2.7406282020775[/C][/ROW]
[ROW][C]83[/C][C]13.464[/C][C]12.7466564260035[/C][C]0.71734357399654[/C][/ROW]
[ROW][C]84[/C][C]9.893[/C][C]11.0292620950649[/C][C]-1.13626209506491[/C][/ROW]
[ROW][C]85[/C][C]11.572[/C][C]9.60149309408338[/C][C]1.97050690591662[/C][/ROW]
[ROW][C]86[/C][C]12.38[/C][C]11.1092619909836[/C][C]1.27073800901636[/C][/ROW]
[ROW][C]87[/C][C]16.692[/C][C]14.5196279475516[/C][C]2.17237205244843[/C][/ROW]
[ROW][C]88[/C][C]16.052[/C][C]14.5581426298284[/C][C]1.49385737017159[/C][/ROW]
[ROW][C]89[/C][C]16.459[/C][C]17.6086504737641[/C][C]-1.14965047376408[/C][/ROW]
[ROW][C]90[/C][C]14.761[/C][C]17.2767763721974[/C][C]-2.51577637219739[/C][/ROW]
[ROW][C]91[/C][C]13.654[/C][C]13.8721952174728[/C][C]-0.218195217472841[/C][/ROW]
[ROW][C]92[/C][C]13.48[/C][C]12.7319213087774[/C][C]0.748078691222647[/C][/ROW]
[ROW][C]93[/C][C]18.068[/C][C]15.3510749175141[/C][C]2.71692508248591[/C][/ROW]
[ROW][C]94[/C][C]16.56[/C][C]16.2613451640843[/C][C]0.298654835915684[/C][/ROW]
[ROW][C]95[/C][C]14.53[/C][C]15.9607364858548[/C][C]-1.43073648585482[/C][/ROW]
[ROW][C]96[/C][C]10.65[/C][C]12.9183565913382[/C][C]-2.26835659133818[/C][/ROW]
[ROW][C]97[/C][C]11.651[/C][C]11.4999247022647[/C][C]0.151075297735261[/C][/ROW]
[ROW][C]98[/C][C]13.735[/C][C]12.0284823762784[/C][C]1.70651762372159[/C][/ROW]
[ROW][C]99[/C][C]13.36[/C][C]15.8063437290606[/C][C]-2.44634372906059[/C][/ROW]
[ROW][C]100[/C][C]17.818[/C][C]13.5295266092454[/C][C]4.28847339075461[/C][/ROW]
[ROW][C]101[/C][C]20.613[/C][C]17.4478903258188[/C][C]3.16510967418117[/C][/ROW]
[ROW][C]102[/C][C]16.231[/C][C]18.9383066349928[/C][C]-2.70730663499282[/C][/ROW]
[ROW][C]103[/C][C]13.862[/C][C]15.8520225188341[/C][C]-1.99002251883408[/C][/ROW]
[ROW][C]104[/C][C]12.004[/C][C]14.0456998503392[/C][C]-2.04169985033923[/C][/ROW]
[ROW][C]105[/C][C]17.734[/C][C]15.6807199395748[/C][C]2.05328006042518[/C][/ROW]
[ROW][C]106[/C][C]15.034[/C][C]15.8551839135026[/C][C]-0.821183913502637[/C][/ROW]
[ROW][C]107[/C][C]12.609[/C][C]14.7179826843134[/C][C]-2.10898268431336[/C][/ROW]
[ROW][C]108[/C][C]12.32[/C][C]11.2001470869607[/C][C]1.11985291303927[/C][/ROW]
[ROW][C]109[/C][C]10.833[/C][C]11.8064362583755[/C][C]-0.97343625837554[/C][/ROW]
[ROW][C]110[/C][C]11.35[/C][C]12.0681687829837[/C][C]-0.71816878298368[/C][/ROW]
[ROW][C]111[/C][C]13.648[/C][C]13.9700103316430[/C][C]-0.322010331642952[/C][/ROW]
[ROW][C]112[/C][C]14.89[/C][C]13.8593944091262[/C][C]1.03060559087377[/C][/ROW]
[ROW][C]113[/C][C]16.325[/C][C]16.0262823841779[/C][C]0.298717615822106[/C][/ROW]
[ROW][C]114[/C][C]18.045[/C][C]15.1220414626911[/C][C]2.92295853730894[/C][/ROW]
[ROW][C]115[/C][C]15.616[/C][C]14.8233442591850[/C][C]0.792655740815043[/C][/ROW]
[ROW][C]116[/C][C]11.926[/C][C]14.3308440601420[/C][C]-2.40484406014198[/C][/ROW]
[ROW][C]117[/C][C]16.855[/C][C]16.5033528068680[/C][C]0.351647193131967[/C][/ROW]
[ROW][C]118[/C][C]15.083[/C][C]15.3724927828561[/C][C]-0.289492782856074[/C][/ROW]
[ROW][C]119[/C][C]12.52[/C][C]14.2640544045649[/C][C]-1.74405440456491[/C][/ROW]
[ROW][C]120[/C][C]12.355[/C][C]11.4767694426125[/C][C]0.878230557387475[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106556&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106556&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
1320.20319.75205021367520.450949786324788
1420.4520.18780332850030.262196671499719
1523.08322.99874161563290.0842583843670681
1621.73821.8157292766096-0.0777292766096025
1726.76626.7729060076284-0.00690600762840177
1825.2825.19287946865590.0871205313440981
1922.57423.0523981013263-0.478398101326281
2022.72921.5059309047481.22306909525199
2121.37823.9528809725080-2.57488097250796
2222.90222.56049497152850.341505028471538
2324.98922.69391308253532.29508691746474
2421.11620.66624424625030.449755753749734
2515.16921.5631443600254-6.39414436002542
2615.84618.7070404533627-2.86104045336273
2720.92719.98232941630290.944670583697079
2818.27319.1572331801393-0.884233180139319
2922.53823.7199366443331-1.18193664433310
3015.59621.5711168793076-5.97511687930761
3114.03416.4127369567014-2.37873695670139
3211.36614.2064255749357-2.84042557493574
3314.86114.00627126565170.854728734348273
3415.14914.68804112721390.46095887278606
3513.57715.1608610980324-1.58386109803237
3613.02610.90960682215842.11639317784157
3713.1911.35366519876901.83633480123103
3813.19612.97274235654620.223257643453822
3915.82616.340720977083-0.514720977083002
4014.73314.47750907375170.255490926248314
4116.30719.5018747509537-3.19487475095367
4215.70315.53814379676950.164856203230496
4314.58913.89646084674480.69253915325517
4412.04313.0613905059975-1.01839050599748
4515.05714.36362306923430.693376930765746
4614.05314.9013499437283-0.84834994372828
4712.69814.3969400845724-1.69894008457240
4810.88810.72588469416540.162115305834634
4910.04510.1852264162700-0.140226416269973
5011.54910.57276295589040.976237044109611
5113.76714.1563327990870-0.389332799086965
5212.43412.4719963747322-0.0379963747322165
5313.11616.7472035154773-3.63120351547726
5414.21113.14086181187641.07013818812356
5512.26612.00638035504540.259619644954562
5612.60210.65645052964721.94554947035279
5715.71413.65390625116712.06009374883288
5813.74214.5724271360866-0.830427136086591
5912.74513.9288861337279-1.1838861337279
6010.49110.8240310030629-0.333031003062949
6110.0579.995765939881310.0612340601186876
6210.910.67141824887540.228581751124628
6311.77113.6624585669115-1.89145856691147
6411.99211.31970819580250.672291804197467
6511.93315.3063961280774-3.37339612807743
6614.50412.62973829881721.87426170118276
6711.72711.7348830753153-0.00788307531533405
6811.47710.54678206802980.930217931970176
6913.57813.07719563553270.500804364467331
7011.55512.7472486974918-1.19224869749179
7111.84611.8596459251731-0.0136459251731296
7211.3979.448419298881161.94858070111884
7310.0669.76881702994870.297182970051301
7410.26910.5851080689890-0.316108068989035
7514.27912.95022740953531.32877259046466
7613.8712.58458539064731.28541460935272
7713.69516.1736250841754-2.47862508417542
7814.4214.8398787055740-0.419878705573966
7911.42412.5385497457272-1.11454974572725
809.70410.9902129166719-1.28621291667189
8112.46412.39143093018730.0725690698126975
8214.30111.56037179792252.7406282020775
8313.46412.74665642600350.71734357399654
849.89311.0292620950649-1.13626209506491
8511.5729.601493094083381.97050690591662
8612.3811.10926199098361.27073800901636
8716.69214.51962794755162.17237205244843
8816.05214.55814262982841.49385737017159
8916.45917.6086504737641-1.14965047376408
9014.76117.2767763721974-2.51577637219739
9113.65413.8721952174728-0.218195217472841
9213.4812.73192130877740.748078691222647
9318.06815.35107491751412.71692508248591
9416.5616.26134516408430.298654835915684
9514.5315.9607364858548-1.43073648585482
9610.6512.9183565913382-2.26835659133818
9711.65111.49992470226470.151075297735261
9813.73512.02848237627841.70651762372159
9913.3615.8063437290606-2.44634372906059
10017.81813.52952660924544.28847339075461
10120.61317.44789032581883.16510967418117
10216.23118.9383066349928-2.70730663499282
10313.86215.8520225188341-1.99002251883408
10412.00414.0456998503392-2.04169985033923
10517.73415.68071993957482.05328006042518
10615.03415.8551839135026-0.821183913502637
10712.60914.7179826843134-2.10898268431336
10812.3211.20014708696071.11985291303927
10910.83311.8064362583755-0.97343625837554
11011.3512.0681687829837-0.71816878298368
11113.64813.9700103316430-0.322010331642952
11214.8913.85939440912621.03060559087377
11316.32516.02628238417790.298717615822106
11418.04515.12204146269112.92295853730894
11515.61614.82334425918500.792655740815043
11611.92614.3308440601420-2.40484406014198
11716.85516.50335280686800.351647193131967
11815.08315.3724927828561-0.289492782856074
11912.5214.2640544045649-1.74405440456491
12012.35511.47676944261250.878230557387475







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12111.60662692087448.1445437707280815.0687100710206
12212.37628284319778.5403842456087716.2121814407867
12314.691613392090310.510955555354118.8722712288265
12414.972830642170910.469765321047719.4758959632940
12516.527403338478711.719759224836321.3350474521211
12615.936171086437610.838557358778521.0337848140966
12713.87681362277488.5014531211549719.2521741243946
12812.44666355492646.8039533728907318.0893737369621
12916.232345548060610.331249836094722.1334412600265
13014.82054361740458.668878022664120.9722092121449
13113.59552703805667.2001703616247519.9908837144884
13212.09028291892645.4573382676628418.7232275701900

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 11.6066269208744 & 8.14454377072808 & 15.0687100710206 \tabularnewline
122 & 12.3762828431977 & 8.54038424560877 & 16.2121814407867 \tabularnewline
123 & 14.6916133920903 & 10.5109555553541 & 18.8722712288265 \tabularnewline
124 & 14.9728306421709 & 10.4697653210477 & 19.4758959632940 \tabularnewline
125 & 16.5274033384787 & 11.7197592248363 & 21.3350474521211 \tabularnewline
126 & 15.9361710864376 & 10.8385573587785 & 21.0337848140966 \tabularnewline
127 & 13.8768136227748 & 8.50145312115497 & 19.2521741243946 \tabularnewline
128 & 12.4466635549264 & 6.80395337289073 & 18.0893737369621 \tabularnewline
129 & 16.2323455480606 & 10.3312498360947 & 22.1334412600265 \tabularnewline
130 & 14.8205436174045 & 8.6688780226641 & 20.9722092121449 \tabularnewline
131 & 13.5955270380566 & 7.20017036162475 & 19.9908837144884 \tabularnewline
132 & 12.0902829189264 & 5.45733826766284 & 18.7232275701900 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106556&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]121[/C][C]11.6066269208744[/C][C]8.14454377072808[/C][C]15.0687100710206[/C][/ROW]
[ROW][C]122[/C][C]12.3762828431977[/C][C]8.54038424560877[/C][C]16.2121814407867[/C][/ROW]
[ROW][C]123[/C][C]14.6916133920903[/C][C]10.5109555553541[/C][C]18.8722712288265[/C][/ROW]
[ROW][C]124[/C][C]14.9728306421709[/C][C]10.4697653210477[/C][C]19.4758959632940[/C][/ROW]
[ROW][C]125[/C][C]16.5274033384787[/C][C]11.7197592248363[/C][C]21.3350474521211[/C][/ROW]
[ROW][C]126[/C][C]15.9361710864376[/C][C]10.8385573587785[/C][C]21.0337848140966[/C][/ROW]
[ROW][C]127[/C][C]13.8768136227748[/C][C]8.50145312115497[/C][C]19.2521741243946[/C][/ROW]
[ROW][C]128[/C][C]12.4466635549264[/C][C]6.80395337289073[/C][C]18.0893737369621[/C][/ROW]
[ROW][C]129[/C][C]16.2323455480606[/C][C]10.3312498360947[/C][C]22.1334412600265[/C][/ROW]
[ROW][C]130[/C][C]14.8205436174045[/C][C]8.6688780226641[/C][C]20.9722092121449[/C][/ROW]
[ROW][C]131[/C][C]13.5955270380566[/C][C]7.20017036162475[/C][C]19.9908837144884[/C][/ROW]
[ROW][C]132[/C][C]12.0902829189264[/C][C]5.45733826766284[/C][C]18.7232275701900[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106556&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106556&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
12111.60662692087448.1445437707280815.0687100710206
12212.37628284319778.5403842456087716.2121814407867
12314.691613392090310.510955555354118.8722712288265
12414.972830642170910.469765321047719.4758959632940
12516.527403338478711.719759224836321.3350474521211
12615.936171086437610.838557358778521.0337848140966
12713.87681362277488.5014531211549719.2521741243946
12812.44666355492646.8039533728907318.0893737369621
12916.232345548060610.331249836094722.1334412600265
13014.82054361740458.668878022664120.9722092121449
13113.59552703805667.2001703616247519.9908837144884
13212.09028291892645.4573382676628418.7232275701900



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')