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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 24 Dec 2010 16:04:11 +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/24/t1293206515saocbugbdf498vu.htm/, Retrieved Tue, 30 Apr 2024 05:15:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115167, Retrieved Tue, 30 Apr 2024 05:15:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact177

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Multiple Regressi...] [2010-12-17 13:46:43] [1251ac2db27b84d4a3ba43449388906b]
-   PD  [Multiple Regression] [Multiple Regressi...] [2010-12-17 15:41:32] [1251ac2db27b84d4a3ba43449388906b]
-   P     [Multiple Regression] [MR Paper (monthly...] [2010-12-17 16:35:58] [1251ac2db27b84d4a3ba43449388906b]
-   PD      [Multiple Regression] [MR Paper (month)] [2010-12-17 16:45:18] [1251ac2db27b84d4a3ba43449388906b]
-   P         [Multiple Regression] [MR Paper (trend)b] [2010-12-18 12:41:58] [1251ac2db27b84d4a3ba43449388906b]
- RMPD          [Classical Decomposition] [CD] [2010-12-18 14:47:46] [1251ac2db27b84d4a3ba43449388906b]
- RM              [Exponential Smoothing] [Exponential Smoot...] [2010-12-18 18:46:08] [1251ac2db27b84d4a3ba43449388906b]
-   P                 [Exponential Smoothing] [] [2010-12-24 16:04:11] [4f70e6cd0867f10d298e58e8e27859b5] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
14.458
13.594
17.814
20.235
21.811
21.439
21.393
19.831
20.468
21.080
21.600
17.390
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

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115167&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115167&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115167&T=0

As an alternative you can also use a QR Code:  
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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.447201661696798
beta0
gamma0.474929455987073

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.447201661696798 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.474929455987073 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115167&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]0.447201661696798[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.474929455987073[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115167&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115167&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.447201661696798
beta0
gamma0.474929455987073






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1317.84816.05864362373741.78935637626262
1419.59218.52043010190311.07156989809688
1521.09220.35067960762300.74132039237702
1620.89920.31694931894370.582050681056295
1725.8925.44849335070380.441506649296159
1824.96524.57860252458590.386397475414068
1922.22523.4831084509999-1.25810845099988
2020.97720.96731359445130.00968640554871314
2122.89721.22214537110851.67485462889146
2222.78522.41889314424940.36610685575063
2322.76922.9049917384996-0.135991738499648
2419.63718.31730100706561.31969899293444
2520.20319.65366726240310.549332737596895
2620.4521.3724652931722-0.922465293172213
2723.08322.22427517194280.858724828057163
2821.73822.2012336378836-0.463233637883551
2926.76626.8284263250821-0.0624263250820825
3025.2825.7187074611296-0.438707461129585
3122.57423.8224761508690-1.24847615086896
3222.72921.64383600799381.08516399200619
3321.37822.8167967702696-1.43879677026962
3422.90222.27751554322280.624484456777235
3524.98922.74733995757322.24166004242681
3621.11619.60511640977211.51088359022795
3715.16920.8247286131131-5.65572861311307
3815.84619.3822067268321-3.53620672683214
3920.92719.53278112897061.39421887102939
4018.27319.4021461621031-1.12914616210312
4122.53823.8367696996340-1.29876969963403
4215.59622.0753670941416-6.47936709414157
4314.03417.2651459130930-3.23114591309303
4411.36614.8125269406535-3.44652694065349
4514.86113.29626678868791.56473321131210
4615.14914.64186345541850.507136544581474
4713.57715.4837833129012-1.90678331290119
4813.02610.29451079693682.73148920306324
4913.1910.17845595651423.01154404348576
5013.19613.16841253441690.0275874655831316
5115.82616.2071566133214-0.381156613321352
5214.73314.62008598371360.112914016286412
5316.30719.5656278970912-3.2586278970912
5415.70315.56765829998480.135341700015152
5514.58914.56833456757820.0206654324217919
5612.04313.5133848512927-1.47038485129271
5715.05714.19651603855040.860483961449637
5814.05314.9495096151991-0.896509615199067
5912.69814.5299655414359-1.83196554143592
6010.88810.59188471650210.296115283497945
6110.0459.46025227015580.584747729844194
6211.54910.58153290522760.967467094772395
6313.76713.9332809581206-0.166280958120614
6412.43412.5720164874451-0.138016487445114
6513.11616.5201765268627-3.40417652686269
6614.21113.34817084527320.862829154726803
6712.26612.6440735796332-0.378073579633224
6812.60211.01934645388161.58265354611840
6915.71413.67974828277752.03425171722251
7013.74214.4963712805018-0.754371280501832
7112.74513.8947969070686-1.14979690706864
7210.49110.8204898243408-0.329489824340847
7310.0579.484863358457520.572136641542476
7410.910.70098351788610.199016482113857
7511.77113.411424723346-1.640424723346
7611.99211.39834127146380.593658728536237
7711.93314.8162093273194-2.8832093273194
7814.50412.99744162818411.50655837181589
7911.72712.2554342685767-0.528434268576699
8011.47711.07823531222470.398764687775271
8113.57813.32776275692550.250237243074533
8211.55512.6144458385062-1.05944583850623
8311.84611.77262648714010.0733735128598703
8411.3979.460686845854171.93631315414583
8510.0669.375044442401650.690955557598347
8610.26910.5463415719972-0.277341571997182
8714.27912.56082737622531.71817262377473
8813.8712.63625098667761.23374901332236
8913.69515.4275507978102-1.73255079781023
9014.4215.2758500566134-0.855850056613422
9111.42412.9431023187442-1.51910231874418
929.70411.5663019766636-1.86230197666362
9312.46412.7656822246914-0.301682224691426
9414.30111.46170152654812.83929847345190
9513.46412.66081774504330.803182254956747
969.89311.1643463581869-1.27134635818687
9711.5729.317276840656782.25472315934321
9812.3810.93367650456231.44632349543769
9916.69214.24289091531542.44910908468457
10016.05214.51800984728741.53399015271255
10116.45916.6648050074222-0.205805007422200
10214.76117.4260367209542-2.6650367209542
10313.65414.1100873095826-0.456087309582628
10413.4813.11856533434510.361434665654912
10518.06815.72212974777552.34587025222454
10616.5616.42677266165290.133227338347059
10714.5315.8811669839622-1.35116698396216
10810.6512.8766198513743-2.22661985137434
10911.65111.52808548631240.122914513687613
11013.73511.97889936063641.75610063936356
11113.3615.689918168187-2.32991816818701
11217.81813.58759265107124.23040734892884
11320.61316.48346386818304.12953613181703
11416.23118.5378201226600-2.30682012266002
11513.86215.9620038206483-2.10000382064834
11612.00414.4499520443661-2.44595204436612
11717.73416.31904259977731.41495740022269
11815.03416.0264719950507-0.992471995050687
11912.60914.5877385017339-1.97873850173393
12012.3211.07269876033691.24730123966314
12110.83311.8945549349842-1.06155493498421
12211.3512.2444491387021-0.894449138702052
12313.64813.6973934286187-0.0493934286186999
12414.8914.33727163028240.552728369717578
12516.32515.56199594576840.763004054231564
12618.04514.42103111204243.62396888795764
12715.61614.55177110695761.06422889304242
12811.92614.3639441375175-2.43794413751746
12916.85517.2502598343074-0.395259834307392
13015.08315.516110045447-0.433110045447014
13112.5214.0685895256775-1.54858952567754
13212.35511.59287828548990.762121714510064

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 17.848 & 16.0586436237374 & 1.78935637626262 \tabularnewline
14 & 19.592 & 18.5204301019031 & 1.07156989809688 \tabularnewline
15 & 21.092 & 20.3506796076230 & 0.74132039237702 \tabularnewline
16 & 20.899 & 20.3169493189437 & 0.582050681056295 \tabularnewline
17 & 25.89 & 25.4484933507038 & 0.441506649296159 \tabularnewline
18 & 24.965 & 24.5786025245859 & 0.386397475414068 \tabularnewline
19 & 22.225 & 23.4831084509999 & -1.25810845099988 \tabularnewline
20 & 20.977 & 20.9673135944513 & 0.00968640554871314 \tabularnewline
21 & 22.897 & 21.2221453711085 & 1.67485462889146 \tabularnewline
22 & 22.785 & 22.4188931442494 & 0.36610685575063 \tabularnewline
23 & 22.769 & 22.9049917384996 & -0.135991738499648 \tabularnewline
24 & 19.637 & 18.3173010070656 & 1.31969899293444 \tabularnewline
25 & 20.203 & 19.6536672624031 & 0.549332737596895 \tabularnewline
26 & 20.45 & 21.3724652931722 & -0.922465293172213 \tabularnewline
27 & 23.083 & 22.2242751719428 & 0.858724828057163 \tabularnewline
28 & 21.738 & 22.2012336378836 & -0.463233637883551 \tabularnewline
29 & 26.766 & 26.8284263250821 & -0.0624263250820825 \tabularnewline
30 & 25.28 & 25.7187074611296 & -0.438707461129585 \tabularnewline
31 & 22.574 & 23.8224761508690 & -1.24847615086896 \tabularnewline
32 & 22.729 & 21.6438360079938 & 1.08516399200619 \tabularnewline
33 & 21.378 & 22.8167967702696 & -1.43879677026962 \tabularnewline
34 & 22.902 & 22.2775155432228 & 0.624484456777235 \tabularnewline
35 & 24.989 & 22.7473399575732 & 2.24166004242681 \tabularnewline
36 & 21.116 & 19.6051164097721 & 1.51088359022795 \tabularnewline
37 & 15.169 & 20.8247286131131 & -5.65572861311307 \tabularnewline
38 & 15.846 & 19.3822067268321 & -3.53620672683214 \tabularnewline
39 & 20.927 & 19.5327811289706 & 1.39421887102939 \tabularnewline
40 & 18.273 & 19.4021461621031 & -1.12914616210312 \tabularnewline
41 & 22.538 & 23.8367696996340 & -1.29876969963403 \tabularnewline
42 & 15.596 & 22.0753670941416 & -6.47936709414157 \tabularnewline
43 & 14.034 & 17.2651459130930 & -3.23114591309303 \tabularnewline
44 & 11.366 & 14.8125269406535 & -3.44652694065349 \tabularnewline
45 & 14.861 & 13.2962667886879 & 1.56473321131210 \tabularnewline
46 & 15.149 & 14.6418634554185 & 0.507136544581474 \tabularnewline
47 & 13.577 & 15.4837833129012 & -1.90678331290119 \tabularnewline
48 & 13.026 & 10.2945107969368 & 2.73148920306324 \tabularnewline
49 & 13.19 & 10.1784559565142 & 3.01154404348576 \tabularnewline
50 & 13.196 & 13.1684125344169 & 0.0275874655831316 \tabularnewline
51 & 15.826 & 16.2071566133214 & -0.381156613321352 \tabularnewline
52 & 14.733 & 14.6200859837136 & 0.112914016286412 \tabularnewline
53 & 16.307 & 19.5656278970912 & -3.2586278970912 \tabularnewline
54 & 15.703 & 15.5676582999848 & 0.135341700015152 \tabularnewline
55 & 14.589 & 14.5683345675782 & 0.0206654324217919 \tabularnewline
56 & 12.043 & 13.5133848512927 & -1.47038485129271 \tabularnewline
57 & 15.057 & 14.1965160385504 & 0.860483961449637 \tabularnewline
58 & 14.053 & 14.9495096151991 & -0.896509615199067 \tabularnewline
59 & 12.698 & 14.5299655414359 & -1.83196554143592 \tabularnewline
60 & 10.888 & 10.5918847165021 & 0.296115283497945 \tabularnewline
61 & 10.045 & 9.4602522701558 & 0.584747729844194 \tabularnewline
62 & 11.549 & 10.5815329052276 & 0.967467094772395 \tabularnewline
63 & 13.767 & 13.9332809581206 & -0.166280958120614 \tabularnewline
64 & 12.434 & 12.5720164874451 & -0.138016487445114 \tabularnewline
65 & 13.116 & 16.5201765268627 & -3.40417652686269 \tabularnewline
66 & 14.211 & 13.3481708452732 & 0.862829154726803 \tabularnewline
67 & 12.266 & 12.6440735796332 & -0.378073579633224 \tabularnewline
68 & 12.602 & 11.0193464538816 & 1.58265354611840 \tabularnewline
69 & 15.714 & 13.6797482827775 & 2.03425171722251 \tabularnewline
70 & 13.742 & 14.4963712805018 & -0.754371280501832 \tabularnewline
71 & 12.745 & 13.8947969070686 & -1.14979690706864 \tabularnewline
72 & 10.491 & 10.8204898243408 & -0.329489824340847 \tabularnewline
73 & 10.057 & 9.48486335845752 & 0.572136641542476 \tabularnewline
74 & 10.9 & 10.7009835178861 & 0.199016482113857 \tabularnewline
75 & 11.771 & 13.411424723346 & -1.640424723346 \tabularnewline
76 & 11.992 & 11.3983412714638 & 0.593658728536237 \tabularnewline
77 & 11.933 & 14.8162093273194 & -2.8832093273194 \tabularnewline
78 & 14.504 & 12.9974416281841 & 1.50655837181589 \tabularnewline
79 & 11.727 & 12.2554342685767 & -0.528434268576699 \tabularnewline
80 & 11.477 & 11.0782353122247 & 0.398764687775271 \tabularnewline
81 & 13.578 & 13.3277627569255 & 0.250237243074533 \tabularnewline
82 & 11.555 & 12.6144458385062 & -1.05944583850623 \tabularnewline
83 & 11.846 & 11.7726264871401 & 0.0733735128598703 \tabularnewline
84 & 11.397 & 9.46068684585417 & 1.93631315414583 \tabularnewline
85 & 10.066 & 9.37504444240165 & 0.690955557598347 \tabularnewline
86 & 10.269 & 10.5463415719972 & -0.277341571997182 \tabularnewline
87 & 14.279 & 12.5608273762253 & 1.71817262377473 \tabularnewline
88 & 13.87 & 12.6362509866776 & 1.23374901332236 \tabularnewline
89 & 13.695 & 15.4275507978102 & -1.73255079781023 \tabularnewline
90 & 14.42 & 15.2758500566134 & -0.855850056613422 \tabularnewline
91 & 11.424 & 12.9431023187442 & -1.51910231874418 \tabularnewline
92 & 9.704 & 11.5663019766636 & -1.86230197666362 \tabularnewline
93 & 12.464 & 12.7656822246914 & -0.301682224691426 \tabularnewline
94 & 14.301 & 11.4617015265481 & 2.83929847345190 \tabularnewline
95 & 13.464 & 12.6608177450433 & 0.803182254956747 \tabularnewline
96 & 9.893 & 11.1643463581869 & -1.27134635818687 \tabularnewline
97 & 11.572 & 9.31727684065678 & 2.25472315934321 \tabularnewline
98 & 12.38 & 10.9336765045623 & 1.44632349543769 \tabularnewline
99 & 16.692 & 14.2428909153154 & 2.44910908468457 \tabularnewline
100 & 16.052 & 14.5180098472874 & 1.53399015271255 \tabularnewline
101 & 16.459 & 16.6648050074222 & -0.205805007422200 \tabularnewline
102 & 14.761 & 17.4260367209542 & -2.6650367209542 \tabularnewline
103 & 13.654 & 14.1100873095826 & -0.456087309582628 \tabularnewline
104 & 13.48 & 13.1185653343451 & 0.361434665654912 \tabularnewline
105 & 18.068 & 15.7221297477755 & 2.34587025222454 \tabularnewline
106 & 16.56 & 16.4267726616529 & 0.133227338347059 \tabularnewline
107 & 14.53 & 15.8811669839622 & -1.35116698396216 \tabularnewline
108 & 10.65 & 12.8766198513743 & -2.22661985137434 \tabularnewline
109 & 11.651 & 11.5280854863124 & 0.122914513687613 \tabularnewline
110 & 13.735 & 11.9788993606364 & 1.75610063936356 \tabularnewline
111 & 13.36 & 15.689918168187 & -2.32991816818701 \tabularnewline
112 & 17.818 & 13.5875926510712 & 4.23040734892884 \tabularnewline
113 & 20.613 & 16.4834638681830 & 4.12953613181703 \tabularnewline
114 & 16.231 & 18.5378201226600 & -2.30682012266002 \tabularnewline
115 & 13.862 & 15.9620038206483 & -2.10000382064834 \tabularnewline
116 & 12.004 & 14.4499520443661 & -2.44595204436612 \tabularnewline
117 & 17.734 & 16.3190425997773 & 1.41495740022269 \tabularnewline
118 & 15.034 & 16.0264719950507 & -0.992471995050687 \tabularnewline
119 & 12.609 & 14.5877385017339 & -1.97873850173393 \tabularnewline
120 & 12.32 & 11.0726987603369 & 1.24730123966314 \tabularnewline
121 & 10.833 & 11.8945549349842 & -1.06155493498421 \tabularnewline
122 & 11.35 & 12.2444491387021 & -0.894449138702052 \tabularnewline
123 & 13.648 & 13.6973934286187 & -0.0493934286186999 \tabularnewline
124 & 14.89 & 14.3372716302824 & 0.552728369717578 \tabularnewline
125 & 16.325 & 15.5619959457684 & 0.763004054231564 \tabularnewline
126 & 18.045 & 14.4210311120424 & 3.62396888795764 \tabularnewline
127 & 15.616 & 14.5517711069576 & 1.06422889304242 \tabularnewline
128 & 11.926 & 14.3639441375175 & -2.43794413751746 \tabularnewline
129 & 16.855 & 17.2502598343074 & -0.395259834307392 \tabularnewline
130 & 15.083 & 15.516110045447 & -0.433110045447014 \tabularnewline
131 & 12.52 & 14.0685895256775 & -1.54858952567754 \tabularnewline
132 & 12.355 & 11.5928782854899 & 0.762121714510064 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115167&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]17.848[/C][C]16.0586436237374[/C][C]1.78935637626262[/C][/ROW]
[ROW][C]14[/C][C]19.592[/C][C]18.5204301019031[/C][C]1.07156989809688[/C][/ROW]
[ROW][C]15[/C][C]21.092[/C][C]20.3506796076230[/C][C]0.74132039237702[/C][/ROW]
[ROW][C]16[/C][C]20.899[/C][C]20.3169493189437[/C][C]0.582050681056295[/C][/ROW]
[ROW][C]17[/C][C]25.89[/C][C]25.4484933507038[/C][C]0.441506649296159[/C][/ROW]
[ROW][C]18[/C][C]24.965[/C][C]24.5786025245859[/C][C]0.386397475414068[/C][/ROW]
[ROW][C]19[/C][C]22.225[/C][C]23.4831084509999[/C][C]-1.25810845099988[/C][/ROW]
[ROW][C]20[/C][C]20.977[/C][C]20.9673135944513[/C][C]0.00968640554871314[/C][/ROW]
[ROW][C]21[/C][C]22.897[/C][C]21.2221453711085[/C][C]1.67485462889146[/C][/ROW]
[ROW][C]22[/C][C]22.785[/C][C]22.4188931442494[/C][C]0.36610685575063[/C][/ROW]
[ROW][C]23[/C][C]22.769[/C][C]22.9049917384996[/C][C]-0.135991738499648[/C][/ROW]
[ROW][C]24[/C][C]19.637[/C][C]18.3173010070656[/C][C]1.31969899293444[/C][/ROW]
[ROW][C]25[/C][C]20.203[/C][C]19.6536672624031[/C][C]0.549332737596895[/C][/ROW]
[ROW][C]26[/C][C]20.45[/C][C]21.3724652931722[/C][C]-0.922465293172213[/C][/ROW]
[ROW][C]27[/C][C]23.083[/C][C]22.2242751719428[/C][C]0.858724828057163[/C][/ROW]
[ROW][C]28[/C][C]21.738[/C][C]22.2012336378836[/C][C]-0.463233637883551[/C][/ROW]
[ROW][C]29[/C][C]26.766[/C][C]26.8284263250821[/C][C]-0.0624263250820825[/C][/ROW]
[ROW][C]30[/C][C]25.28[/C][C]25.7187074611296[/C][C]-0.438707461129585[/C][/ROW]
[ROW][C]31[/C][C]22.574[/C][C]23.8224761508690[/C][C]-1.24847615086896[/C][/ROW]
[ROW][C]32[/C][C]22.729[/C][C]21.6438360079938[/C][C]1.08516399200619[/C][/ROW]
[ROW][C]33[/C][C]21.378[/C][C]22.8167967702696[/C][C]-1.43879677026962[/C][/ROW]
[ROW][C]34[/C][C]22.902[/C][C]22.2775155432228[/C][C]0.624484456777235[/C][/ROW]
[ROW][C]35[/C][C]24.989[/C][C]22.7473399575732[/C][C]2.24166004242681[/C][/ROW]
[ROW][C]36[/C][C]21.116[/C][C]19.6051164097721[/C][C]1.51088359022795[/C][/ROW]
[ROW][C]37[/C][C]15.169[/C][C]20.8247286131131[/C][C]-5.65572861311307[/C][/ROW]
[ROW][C]38[/C][C]15.846[/C][C]19.3822067268321[/C][C]-3.53620672683214[/C][/ROW]
[ROW][C]39[/C][C]20.927[/C][C]19.5327811289706[/C][C]1.39421887102939[/C][/ROW]
[ROW][C]40[/C][C]18.273[/C][C]19.4021461621031[/C][C]-1.12914616210312[/C][/ROW]
[ROW][C]41[/C][C]22.538[/C][C]23.8367696996340[/C][C]-1.29876969963403[/C][/ROW]
[ROW][C]42[/C][C]15.596[/C][C]22.0753670941416[/C][C]-6.47936709414157[/C][/ROW]
[ROW][C]43[/C][C]14.034[/C][C]17.2651459130930[/C][C]-3.23114591309303[/C][/ROW]
[ROW][C]44[/C][C]11.366[/C][C]14.8125269406535[/C][C]-3.44652694065349[/C][/ROW]
[ROW][C]45[/C][C]14.861[/C][C]13.2962667886879[/C][C]1.56473321131210[/C][/ROW]
[ROW][C]46[/C][C]15.149[/C][C]14.6418634554185[/C][C]0.507136544581474[/C][/ROW]
[ROW][C]47[/C][C]13.577[/C][C]15.4837833129012[/C][C]-1.90678331290119[/C][/ROW]
[ROW][C]48[/C][C]13.026[/C][C]10.2945107969368[/C][C]2.73148920306324[/C][/ROW]
[ROW][C]49[/C][C]13.19[/C][C]10.1784559565142[/C][C]3.01154404348576[/C][/ROW]
[ROW][C]50[/C][C]13.196[/C][C]13.1684125344169[/C][C]0.0275874655831316[/C][/ROW]
[ROW][C]51[/C][C]15.826[/C][C]16.2071566133214[/C][C]-0.381156613321352[/C][/ROW]
[ROW][C]52[/C][C]14.733[/C][C]14.6200859837136[/C][C]0.112914016286412[/C][/ROW]
[ROW][C]53[/C][C]16.307[/C][C]19.5656278970912[/C][C]-3.2586278970912[/C][/ROW]
[ROW][C]54[/C][C]15.703[/C][C]15.5676582999848[/C][C]0.135341700015152[/C][/ROW]
[ROW][C]55[/C][C]14.589[/C][C]14.5683345675782[/C][C]0.0206654324217919[/C][/ROW]
[ROW][C]56[/C][C]12.043[/C][C]13.5133848512927[/C][C]-1.47038485129271[/C][/ROW]
[ROW][C]57[/C][C]15.057[/C][C]14.1965160385504[/C][C]0.860483961449637[/C][/ROW]
[ROW][C]58[/C][C]14.053[/C][C]14.9495096151991[/C][C]-0.896509615199067[/C][/ROW]
[ROW][C]59[/C][C]12.698[/C][C]14.5299655414359[/C][C]-1.83196554143592[/C][/ROW]
[ROW][C]60[/C][C]10.888[/C][C]10.5918847165021[/C][C]0.296115283497945[/C][/ROW]
[ROW][C]61[/C][C]10.045[/C][C]9.4602522701558[/C][C]0.584747729844194[/C][/ROW]
[ROW][C]62[/C][C]11.549[/C][C]10.5815329052276[/C][C]0.967467094772395[/C][/ROW]
[ROW][C]63[/C][C]13.767[/C][C]13.9332809581206[/C][C]-0.166280958120614[/C][/ROW]
[ROW][C]64[/C][C]12.434[/C][C]12.5720164874451[/C][C]-0.138016487445114[/C][/ROW]
[ROW][C]65[/C][C]13.116[/C][C]16.5201765268627[/C][C]-3.40417652686269[/C][/ROW]
[ROW][C]66[/C][C]14.211[/C][C]13.3481708452732[/C][C]0.862829154726803[/C][/ROW]
[ROW][C]67[/C][C]12.266[/C][C]12.6440735796332[/C][C]-0.378073579633224[/C][/ROW]
[ROW][C]68[/C][C]12.602[/C][C]11.0193464538816[/C][C]1.58265354611840[/C][/ROW]
[ROW][C]69[/C][C]15.714[/C][C]13.6797482827775[/C][C]2.03425171722251[/C][/ROW]
[ROW][C]70[/C][C]13.742[/C][C]14.4963712805018[/C][C]-0.754371280501832[/C][/ROW]
[ROW][C]71[/C][C]12.745[/C][C]13.8947969070686[/C][C]-1.14979690706864[/C][/ROW]
[ROW][C]72[/C][C]10.491[/C][C]10.8204898243408[/C][C]-0.329489824340847[/C][/ROW]
[ROW][C]73[/C][C]10.057[/C][C]9.48486335845752[/C][C]0.572136641542476[/C][/ROW]
[ROW][C]74[/C][C]10.9[/C][C]10.7009835178861[/C][C]0.199016482113857[/C][/ROW]
[ROW][C]75[/C][C]11.771[/C][C]13.411424723346[/C][C]-1.640424723346[/C][/ROW]
[ROW][C]76[/C][C]11.992[/C][C]11.3983412714638[/C][C]0.593658728536237[/C][/ROW]
[ROW][C]77[/C][C]11.933[/C][C]14.8162093273194[/C][C]-2.8832093273194[/C][/ROW]
[ROW][C]78[/C][C]14.504[/C][C]12.9974416281841[/C][C]1.50655837181589[/C][/ROW]
[ROW][C]79[/C][C]11.727[/C][C]12.2554342685767[/C][C]-0.528434268576699[/C][/ROW]
[ROW][C]80[/C][C]11.477[/C][C]11.0782353122247[/C][C]0.398764687775271[/C][/ROW]
[ROW][C]81[/C][C]13.578[/C][C]13.3277627569255[/C][C]0.250237243074533[/C][/ROW]
[ROW][C]82[/C][C]11.555[/C][C]12.6144458385062[/C][C]-1.05944583850623[/C][/ROW]
[ROW][C]83[/C][C]11.846[/C][C]11.7726264871401[/C][C]0.0733735128598703[/C][/ROW]
[ROW][C]84[/C][C]11.397[/C][C]9.46068684585417[/C][C]1.93631315414583[/C][/ROW]
[ROW][C]85[/C][C]10.066[/C][C]9.37504444240165[/C][C]0.690955557598347[/C][/ROW]
[ROW][C]86[/C][C]10.269[/C][C]10.5463415719972[/C][C]-0.277341571997182[/C][/ROW]
[ROW][C]87[/C][C]14.279[/C][C]12.5608273762253[/C][C]1.71817262377473[/C][/ROW]
[ROW][C]88[/C][C]13.87[/C][C]12.6362509866776[/C][C]1.23374901332236[/C][/ROW]
[ROW][C]89[/C][C]13.695[/C][C]15.4275507978102[/C][C]-1.73255079781023[/C][/ROW]
[ROW][C]90[/C][C]14.42[/C][C]15.2758500566134[/C][C]-0.855850056613422[/C][/ROW]
[ROW][C]91[/C][C]11.424[/C][C]12.9431023187442[/C][C]-1.51910231874418[/C][/ROW]
[ROW][C]92[/C][C]9.704[/C][C]11.5663019766636[/C][C]-1.86230197666362[/C][/ROW]
[ROW][C]93[/C][C]12.464[/C][C]12.7656822246914[/C][C]-0.301682224691426[/C][/ROW]
[ROW][C]94[/C][C]14.301[/C][C]11.4617015265481[/C][C]2.83929847345190[/C][/ROW]
[ROW][C]95[/C][C]13.464[/C][C]12.6608177450433[/C][C]0.803182254956747[/C][/ROW]
[ROW][C]96[/C][C]9.893[/C][C]11.1643463581869[/C][C]-1.27134635818687[/C][/ROW]
[ROW][C]97[/C][C]11.572[/C][C]9.31727684065678[/C][C]2.25472315934321[/C][/ROW]
[ROW][C]98[/C][C]12.38[/C][C]10.9336765045623[/C][C]1.44632349543769[/C][/ROW]
[ROW][C]99[/C][C]16.692[/C][C]14.2428909153154[/C][C]2.44910908468457[/C][/ROW]
[ROW][C]100[/C][C]16.052[/C][C]14.5180098472874[/C][C]1.53399015271255[/C][/ROW]
[ROW][C]101[/C][C]16.459[/C][C]16.6648050074222[/C][C]-0.205805007422200[/C][/ROW]
[ROW][C]102[/C][C]14.761[/C][C]17.4260367209542[/C][C]-2.6650367209542[/C][/ROW]
[ROW][C]103[/C][C]13.654[/C][C]14.1100873095826[/C][C]-0.456087309582628[/C][/ROW]
[ROW][C]104[/C][C]13.48[/C][C]13.1185653343451[/C][C]0.361434665654912[/C][/ROW]
[ROW][C]105[/C][C]18.068[/C][C]15.7221297477755[/C][C]2.34587025222454[/C][/ROW]
[ROW][C]106[/C][C]16.56[/C][C]16.4267726616529[/C][C]0.133227338347059[/C][/ROW]
[ROW][C]107[/C][C]14.53[/C][C]15.8811669839622[/C][C]-1.35116698396216[/C][/ROW]
[ROW][C]108[/C][C]10.65[/C][C]12.8766198513743[/C][C]-2.22661985137434[/C][/ROW]
[ROW][C]109[/C][C]11.651[/C][C]11.5280854863124[/C][C]0.122914513687613[/C][/ROW]
[ROW][C]110[/C][C]13.735[/C][C]11.9788993606364[/C][C]1.75610063936356[/C][/ROW]
[ROW][C]111[/C][C]13.36[/C][C]15.689918168187[/C][C]-2.32991816818701[/C][/ROW]
[ROW][C]112[/C][C]17.818[/C][C]13.5875926510712[/C][C]4.23040734892884[/C][/ROW]
[ROW][C]113[/C][C]20.613[/C][C]16.4834638681830[/C][C]4.12953613181703[/C][/ROW]
[ROW][C]114[/C][C]16.231[/C][C]18.5378201226600[/C][C]-2.30682012266002[/C][/ROW]
[ROW][C]115[/C][C]13.862[/C][C]15.9620038206483[/C][C]-2.10000382064834[/C][/ROW]
[ROW][C]116[/C][C]12.004[/C][C]14.4499520443661[/C][C]-2.44595204436612[/C][/ROW]
[ROW][C]117[/C][C]17.734[/C][C]16.3190425997773[/C][C]1.41495740022269[/C][/ROW]
[ROW][C]118[/C][C]15.034[/C][C]16.0264719950507[/C][C]-0.992471995050687[/C][/ROW]
[ROW][C]119[/C][C]12.609[/C][C]14.5877385017339[/C][C]-1.97873850173393[/C][/ROW]
[ROW][C]120[/C][C]12.32[/C][C]11.0726987603369[/C][C]1.24730123966314[/C][/ROW]
[ROW][C]121[/C][C]10.833[/C][C]11.8945549349842[/C][C]-1.06155493498421[/C][/ROW]
[ROW][C]122[/C][C]11.35[/C][C]12.2444491387021[/C][C]-0.894449138702052[/C][/ROW]
[ROW][C]123[/C][C]13.648[/C][C]13.6973934286187[/C][C]-0.0493934286186999[/C][/ROW]
[ROW][C]124[/C][C]14.89[/C][C]14.3372716302824[/C][C]0.552728369717578[/C][/ROW]
[ROW][C]125[/C][C]16.325[/C][C]15.5619959457684[/C][C]0.763004054231564[/C][/ROW]
[ROW][C]126[/C][C]18.045[/C][C]14.4210311120424[/C][C]3.62396888795764[/C][/ROW]
[ROW][C]127[/C][C]15.616[/C][C]14.5517711069576[/C][C]1.06422889304242[/C][/ROW]
[ROW][C]128[/C][C]11.926[/C][C]14.3639441375175[/C][C]-2.43794413751746[/C][/ROW]
[ROW][C]129[/C][C]16.855[/C][C]17.2502598343074[/C][C]-0.395259834307392[/C][/ROW]
[ROW][C]130[/C][C]15.083[/C][C]15.516110045447[/C][C]-0.433110045447014[/C][/ROW]
[ROW][C]131[/C][C]12.52[/C][C]14.0685895256775[/C][C]-1.54858952567754[/C][/ROW]
[ROW][C]132[/C][C]12.355[/C][C]11.5928782854899[/C][C]0.762121714510064[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115167&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115167&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1317.84816.05864362373741.78935637626262
1419.59218.52043010190311.07156989809688
1521.09220.35067960762300.74132039237702
1620.89920.31694931894370.582050681056295
1725.8925.44849335070380.441506649296159
1824.96524.57860252458590.386397475414068
1922.22523.4831084509999-1.25810845099988
2020.97720.96731359445130.00968640554871314
2122.89721.22214537110851.67485462889146
2222.78522.41889314424940.36610685575063
2322.76922.9049917384996-0.135991738499648
2419.63718.31730100706561.31969899293444
2520.20319.65366726240310.549332737596895
2620.4521.3724652931722-0.922465293172213
2723.08322.22427517194280.858724828057163
2821.73822.2012336378836-0.463233637883551
2926.76626.8284263250821-0.0624263250820825
3025.2825.7187074611296-0.438707461129585
3122.57423.8224761508690-1.24847615086896
3222.72921.64383600799381.08516399200619
3321.37822.8167967702696-1.43879677026962
3422.90222.27751554322280.624484456777235
3524.98922.74733995757322.24166004242681
3621.11619.60511640977211.51088359022795
3715.16920.8247286131131-5.65572861311307
3815.84619.3822067268321-3.53620672683214
3920.92719.53278112897061.39421887102939
4018.27319.4021461621031-1.12914616210312
4122.53823.8367696996340-1.29876969963403
4215.59622.0753670941416-6.47936709414157
4314.03417.2651459130930-3.23114591309303
4411.36614.8125269406535-3.44652694065349
4514.86113.29626678868791.56473321131210
4615.14914.64186345541850.507136544581474
4713.57715.4837833129012-1.90678331290119
4813.02610.29451079693682.73148920306324
4913.1910.17845595651423.01154404348576
5013.19613.16841253441690.0275874655831316
5115.82616.2071566133214-0.381156613321352
5214.73314.62008598371360.112914016286412
5316.30719.5656278970912-3.2586278970912
5415.70315.56765829998480.135341700015152
5514.58914.56833456757820.0206654324217919
5612.04313.5133848512927-1.47038485129271
5715.05714.19651603855040.860483961449637
5814.05314.9495096151991-0.896509615199067
5912.69814.5299655414359-1.83196554143592
6010.88810.59188471650210.296115283497945
6110.0459.46025227015580.584747729844194
6211.54910.58153290522760.967467094772395
6313.76713.9332809581206-0.166280958120614
6412.43412.5720164874451-0.138016487445114
6513.11616.5201765268627-3.40417652686269
6614.21113.34817084527320.862829154726803
6712.26612.6440735796332-0.378073579633224
6812.60211.01934645388161.58265354611840
6915.71413.67974828277752.03425171722251
7013.74214.4963712805018-0.754371280501832
7112.74513.8947969070686-1.14979690706864
7210.49110.8204898243408-0.329489824340847
7310.0579.484863358457520.572136641542476
7410.910.70098351788610.199016482113857
7511.77113.411424723346-1.640424723346
7611.99211.39834127146380.593658728536237
7711.93314.8162093273194-2.8832093273194
7814.50412.99744162818411.50655837181589
7911.72712.2554342685767-0.528434268576699
8011.47711.07823531222470.398764687775271
8113.57813.32776275692550.250237243074533
8211.55512.6144458385062-1.05944583850623
8311.84611.77262648714010.0733735128598703
8411.3979.460686845854171.93631315414583
8510.0669.375044442401650.690955557598347
8610.26910.5463415719972-0.277341571997182
8714.27912.56082737622531.71817262377473
8813.8712.63625098667761.23374901332236
8913.69515.4275507978102-1.73255079781023
9014.4215.2758500566134-0.855850056613422
9111.42412.9431023187442-1.51910231874418
929.70411.5663019766636-1.86230197666362
9312.46412.7656822246914-0.301682224691426
9414.30111.46170152654812.83929847345190
9513.46412.66081774504330.803182254956747
969.89311.1643463581869-1.27134635818687
9711.5729.317276840656782.25472315934321
9812.3810.93367650456231.44632349543769
9916.69214.24289091531542.44910908468457
10016.05214.51800984728741.53399015271255
10116.45916.6648050074222-0.205805007422200
10214.76117.4260367209542-2.6650367209542
10313.65414.1100873095826-0.456087309582628
10413.4813.11856533434510.361434665654912
10518.06815.72212974777552.34587025222454
10616.5616.42677266165290.133227338347059
10714.5315.8811669839622-1.35116698396216
10810.6512.8766198513743-2.22661985137434
10911.65111.52808548631240.122914513687613
11013.73511.97889936063641.75610063936356
11113.3615.689918168187-2.32991816818701
11217.81813.58759265107124.23040734892884
11320.61316.48346386818304.12953613181703
11416.23118.5378201226600-2.30682012266002
11513.86215.9620038206483-2.10000382064834
11612.00414.4499520443661-2.44595204436612
11717.73416.31904259977731.41495740022269
11815.03416.0264719950507-0.992471995050687
11912.60914.5877385017339-1.97873850173393
12012.3211.07269876033691.24730123966314
12110.83311.8945549349842-1.06155493498421
12211.3512.2444491387021-0.894449138702052
12313.64813.6973934286187-0.0493934286186999
12414.8914.33727163028240.552728369717578
12516.32515.56199594576840.763004054231564
12618.04514.42103111204243.62396888795764
12715.61614.55177110695761.06422889304242
12811.92614.3639441375175-2.43794413751746
12916.85517.2502598343074-0.395259834307392
13015.08315.516110045447-0.433110045447014
13112.5214.0685895256775-1.54858952567754
13212.35511.59287828548990.762121714510064






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
13311.59159377589378.1070577759371415.0761297758502
13412.46008910204898.6429881391318616.2771900649660
13514.53489364013210.411966477640318.6578208026237
13615.354941850988910.947357817380219.7625258845975
13716.387690944298511.712750769341121.062631119256
13815.656627749563110.728815429116920.5844400700092
13913.49468814958978.3263612547763618.6630150444030
14011.91147499356376.5133390636560317.3096109234714
14116.424330134039910.805776926685722.0428833413940
14214.85700399734819.0263600560686520.6876479386276
14313.31031278805767.2750267636765619.3455988124386
14412.13378798071725.9005748428405418.3670011185939

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
133 & 11.5915937758937 & 8.10705777593714 & 15.0761297758502 \tabularnewline
134 & 12.4600891020489 & 8.64298813913186 & 16.2771900649660 \tabularnewline
135 & 14.534893640132 & 10.4119664776403 & 18.6578208026237 \tabularnewline
136 & 15.3549418509889 & 10.9473578173802 & 19.7625258845975 \tabularnewline
137 & 16.3876909442985 & 11.7127507693411 & 21.062631119256 \tabularnewline
138 & 15.6566277495631 & 10.7288154291169 & 20.5844400700092 \tabularnewline
139 & 13.4946881495897 & 8.32636125477636 & 18.6630150444030 \tabularnewline
140 & 11.9114749935637 & 6.51333906365603 & 17.3096109234714 \tabularnewline
141 & 16.4243301340399 & 10.8057769266857 & 22.0428833413940 \tabularnewline
142 & 14.8570039973481 & 9.02636005606865 & 20.6876479386276 \tabularnewline
143 & 13.3103127880576 & 7.27502676367656 & 19.3455988124386 \tabularnewline
144 & 12.1337879807172 & 5.90057484284054 & 18.3670011185939 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115167&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]133[/C][C]11.5915937758937[/C][C]8.10705777593714[/C][C]15.0761297758502[/C][/ROW]
[ROW][C]134[/C][C]12.4600891020489[/C][C]8.64298813913186[/C][C]16.2771900649660[/C][/ROW]
[ROW][C]135[/C][C]14.534893640132[/C][C]10.4119664776403[/C][C]18.6578208026237[/C][/ROW]
[ROW][C]136[/C][C]15.3549418509889[/C][C]10.9473578173802[/C][C]19.7625258845975[/C][/ROW]
[ROW][C]137[/C][C]16.3876909442985[/C][C]11.7127507693411[/C][C]21.062631119256[/C][/ROW]
[ROW][C]138[/C][C]15.6566277495631[/C][C]10.7288154291169[/C][C]20.5844400700092[/C][/ROW]
[ROW][C]139[/C][C]13.4946881495897[/C][C]8.32636125477636[/C][C]18.6630150444030[/C][/ROW]
[ROW][C]140[/C][C]11.9114749935637[/C][C]6.51333906365603[/C][C]17.3096109234714[/C][/ROW]
[ROW][C]141[/C][C]16.4243301340399[/C][C]10.8057769266857[/C][C]22.0428833413940[/C][/ROW]
[ROW][C]142[/C][C]14.8570039973481[/C][C]9.02636005606865[/C][C]20.6876479386276[/C][/ROW]
[ROW][C]143[/C][C]13.3103127880576[/C][C]7.27502676367656[/C][C]19.3455988124386[/C][/ROW]
[ROW][C]144[/C][C]12.1337879807172[/C][C]5.90057484284054[/C][C]18.3670011185939[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115167&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115167&T=3

As an alternative you can also use a QR Code:  
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The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
13311.59159377589378.1070577759371415.0761297758502
13412.46008910204898.6429881391318616.2771900649660
13514.53489364013210.411966477640318.6578208026237
13615.354941850988910.947357817380219.7625258845975
13716.387690944298511.712750769341121.062631119256
13815.656627749563110.728815429116920.5844400700092
13913.49468814958978.3263612547763618.6630150444030
14011.91147499356376.5133390636560317.3096109234714
14116.424330134039910.805776926685722.0428833413940
14214.85700399734819.0263600560686520.6876479386276
14313.31031278805767.2750267636765619.3455988124386
14412.13378798071725.9005748428405418.3670011185939


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = ; par5 = ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;
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=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')