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Description of Statistical Computation

Author's title

exponential smoothing(triple&add)-aantal geboortes per maand (2000-2006)-Ol...

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 06 Jun 2009 08:30:23 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jun/06/t1244298717eemma6hys0p1u4g.htm/, Retrieved Sun, 28 Apr 2024 22:18:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=42011, Retrieved Sun, 28 Apr 2024 22:18:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact185

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Classical Decomposition] [Nieuwe personenwa...] [2009-01-13 17:37:29] [74be16979710d4c4e7c6647856088456]
-       [Classical Decomposition] [roger dirkx oefen...] [2009-01-14 16:39:03] [74be16979710d4c4e7c6647856088456]
- RMP     [Exponential Smoothing] [roger dirkx oef 10] [2009-01-24 20:53:30] [74be16979710d4c4e7c6647856088456]
-           [Exponential Smoothing] [Dennis Collin oef 10] [2009-01-25 12:25:31] [2097edf1f094fab6879a8cb46df74ec2]
-             [Exponential Smoothing] [Dennis Collin oef 2] [2009-01-25 12:34:26] [2097edf1f094fab6879a8cb46df74ec2]
-               [Exponential Smoothing] [Dennis Collin oef 10] [2009-01-25 12:39:06] [2097edf1f094fab6879a8cb46df74ec2]
-    D            [Exponential Smoothing] [tripple exponenti...] [2009-06-06 14:18:33] [74be16979710d4c4e7c6647856088456]
-   PD                [Exponential Smoothing] [exponential smoot...] [2009-06-06 14:30:23] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9.733
9.259
9.864
9.215
10.103
9.380
9.896
10.117
9.451
9.700
9.081
9.084
9.743
8.587
9.731
9.563
9.998
9.437
10.038
9.918
9.252
9.737
9.035
9.133
9.487
8.700
9.627
8.947
9.283
8.829
9.947
9.628
9.318
9.605
8.640
9.214
9.567
8.547
9.185
9.470
9.123
9.278
10.170
9.434
9.655
9.429
8.739
9.552
9.687
9.019
9.672
9.206
9.069
9.788
10.312
10.105
9.863
9.656
9.295
9.946
9.701
9.049
10.190
9.706
9.765
9.893
9.994
10.433
10.073
10.112
9.266
9.820
10.097
9.115
10.411
9.678
10.408
10.153
10.368
10.581
10.597
10.680
9.738
9.556

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=42011&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=42011&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42011&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
alpha0.10425711833567
beta0.130348249108125
gamma0.727179362888915

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.10425711833567 \tabularnewline
beta & 0.130348249108125 \tabularnewline
gamma & 0.727179362888915 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42011&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]0.10425711833567[/C][/ROW]
[ROW][C]beta[/C][C]0.130348249108125[/C][/ROW]
[ROW][C]gamma[/C][C]0.727179362888915[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42011&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42011&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
alpha0.10425711833567
beta0.130348249108125
gamma0.727179362888915






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
139.7439.74921180555556-0.00621180555555689
148.5878.59142105170956-0.00442105170955998
159.7319.74796524912095-0.016965249120954
169.5639.58113773812208-0.0181377381220837
179.99810.0105664997834-0.0125664997834232
189.4379.44390532732481-0.00690532732481053
1910.0389.836157197506350.201842802493651
209.91810.1042072025874-0.186207202587356
219.2529.44822805956723-0.196228059567231
229.7379.661037483971450.0759625160285538
239.0359.034090357056820.000909642943176081
249.1339.033455795676080.099544204323923
259.4879.68611954459826-0.199119544598256
268.78.50581874997090.194181250029102
279.6279.67403227136777-0.0470322713677724
288.9479.50203221802548-0.555032218025485
299.2839.87054444750937-0.587544447509369
308.8299.23124105357236-0.402241053572357
319.9479.696491061578620.250508938421376
329.6289.69575706137927-0.0677570613792717
339.3189.026114333186950.291885666813053
349.6059.45425642574780.150743574252209
358.648.77438286347976-0.134382863479759
369.2148.810215657173090.403784342826912
379.5679.290519203245840.276480796754155
388.5478.412909003869030.134090996130967
399.1859.41384606651053-0.228846066510531
409.478.885632671089240.584367328910757
419.1239.36087799748514-0.237877997485139
429.2788.892601911455660.38539808854434
4310.179.889723501985460.280276498014537
449.4349.70976556212332-0.275765562123317
459.6559.274848786362740.380151213637262
469.4299.6436109406425-0.214610940642499
478.7398.75831278013992-0.0193127801399235
489.5529.17663770351850.375362296481507
499.6879.59062220757360.0963777924263916
509.0198.618604925553530.400395074446468
519.6729.431638092780550.240361907219448
529.2069.5091554995017-0.303155499501692
539.0699.37133980882434-0.302339808824335
549.7889.316499778382750.471500221617255
5510.31210.26947160230460.0425283976953832
5610.1059.714655126098080.390344873901917
579.8639.79759422480950.0654057751904986
589.6569.76302433589962-0.107024335899615
599.2959.034505547229390.260494452770612
609.9469.761234866498880.184765133501118
619.7019.99319182522465-0.29219182522465
629.0499.19297379159361-0.143973791593615
6310.199.851898635738650.338101364261345
649.7069.593791841240230.112208158759774
659.7659.513671144125380.251328855874622
669.89310.0419911674629-0.148991167462865
679.99410.6638057580960-0.669805758095981
6810.43310.26454963992260.168450360077351
6910.07310.1129555017458-0.0399555017458297
7010.1129.953909093085320.158090906914678
719.2669.49484565791946-0.228845657919457
729.8210.1170063573100-0.297006357310037
7310.0979.977290695328180.119709304671821
749.1159.31138696974474-0.196386969744744
7510.41110.27296885989460.138031140105372
769.6789.83825957821236-0.160259578212356
7710.4089.808043224160320.599956775839683
7810.15310.10438579126860.0486142087313794
7910.36810.4026771219723-0.0346771219723347
8010.58110.6193959818708-0.0383959818707975
8110.59710.31142419727890.28557580272107
8210.6810.32067726806690.359322731933105
839.7389.638651027302580.099348972697424
849.55610.2631854515408-0.707185451540758

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 9.743 & 9.74921180555556 & -0.00621180555555689 \tabularnewline
14 & 8.587 & 8.59142105170956 & -0.00442105170955998 \tabularnewline
15 & 9.731 & 9.74796524912095 & -0.016965249120954 \tabularnewline
16 & 9.563 & 9.58113773812208 & -0.0181377381220837 \tabularnewline
17 & 9.998 & 10.0105664997834 & -0.0125664997834232 \tabularnewline
18 & 9.437 & 9.44390532732481 & -0.00690532732481053 \tabularnewline
19 & 10.038 & 9.83615719750635 & 0.201842802493651 \tabularnewline
20 & 9.918 & 10.1042072025874 & -0.186207202587356 \tabularnewline
21 & 9.252 & 9.44822805956723 & -0.196228059567231 \tabularnewline
22 & 9.737 & 9.66103748397145 & 0.0759625160285538 \tabularnewline
23 & 9.035 & 9.03409035705682 & 0.000909642943176081 \tabularnewline
24 & 9.133 & 9.03345579567608 & 0.099544204323923 \tabularnewline
25 & 9.487 & 9.68611954459826 & -0.199119544598256 \tabularnewline
26 & 8.7 & 8.5058187499709 & 0.194181250029102 \tabularnewline
27 & 9.627 & 9.67403227136777 & -0.0470322713677724 \tabularnewline
28 & 8.947 & 9.50203221802548 & -0.555032218025485 \tabularnewline
29 & 9.283 & 9.87054444750937 & -0.587544447509369 \tabularnewline
30 & 8.829 & 9.23124105357236 & -0.402241053572357 \tabularnewline
31 & 9.947 & 9.69649106157862 & 0.250508938421376 \tabularnewline
32 & 9.628 & 9.69575706137927 & -0.0677570613792717 \tabularnewline
33 & 9.318 & 9.02611433318695 & 0.291885666813053 \tabularnewline
34 & 9.605 & 9.4542564257478 & 0.150743574252209 \tabularnewline
35 & 8.64 & 8.77438286347976 & -0.134382863479759 \tabularnewline
36 & 9.214 & 8.81021565717309 & 0.403784342826912 \tabularnewline
37 & 9.567 & 9.29051920324584 & 0.276480796754155 \tabularnewline
38 & 8.547 & 8.41290900386903 & 0.134090996130967 \tabularnewline
39 & 9.185 & 9.41384606651053 & -0.228846066510531 \tabularnewline
40 & 9.47 & 8.88563267108924 & 0.584367328910757 \tabularnewline
41 & 9.123 & 9.36087799748514 & -0.237877997485139 \tabularnewline
42 & 9.278 & 8.89260191145566 & 0.38539808854434 \tabularnewline
43 & 10.17 & 9.88972350198546 & 0.280276498014537 \tabularnewline
44 & 9.434 & 9.70976556212332 & -0.275765562123317 \tabularnewline
45 & 9.655 & 9.27484878636274 & 0.380151213637262 \tabularnewline
46 & 9.429 & 9.6436109406425 & -0.214610940642499 \tabularnewline
47 & 8.739 & 8.75831278013992 & -0.0193127801399235 \tabularnewline
48 & 9.552 & 9.1766377035185 & 0.375362296481507 \tabularnewline
49 & 9.687 & 9.5906222075736 & 0.0963777924263916 \tabularnewline
50 & 9.019 & 8.61860492555353 & 0.400395074446468 \tabularnewline
51 & 9.672 & 9.43163809278055 & 0.240361907219448 \tabularnewline
52 & 9.206 & 9.5091554995017 & -0.303155499501692 \tabularnewline
53 & 9.069 & 9.37133980882434 & -0.302339808824335 \tabularnewline
54 & 9.788 & 9.31649977838275 & 0.471500221617255 \tabularnewline
55 & 10.312 & 10.2694716023046 & 0.0425283976953832 \tabularnewline
56 & 10.105 & 9.71465512609808 & 0.390344873901917 \tabularnewline
57 & 9.863 & 9.7975942248095 & 0.0654057751904986 \tabularnewline
58 & 9.656 & 9.76302433589962 & -0.107024335899615 \tabularnewline
59 & 9.295 & 9.03450554722939 & 0.260494452770612 \tabularnewline
60 & 9.946 & 9.76123486649888 & 0.184765133501118 \tabularnewline
61 & 9.701 & 9.99319182522465 & -0.29219182522465 \tabularnewline
62 & 9.049 & 9.19297379159361 & -0.143973791593615 \tabularnewline
63 & 10.19 & 9.85189863573865 & 0.338101364261345 \tabularnewline
64 & 9.706 & 9.59379184124023 & 0.112208158759774 \tabularnewline
65 & 9.765 & 9.51367114412538 & 0.251328855874622 \tabularnewline
66 & 9.893 & 10.0419911674629 & -0.148991167462865 \tabularnewline
67 & 9.994 & 10.6638057580960 & -0.669805758095981 \tabularnewline
68 & 10.433 & 10.2645496399226 & 0.168450360077351 \tabularnewline
69 & 10.073 & 10.1129555017458 & -0.0399555017458297 \tabularnewline
70 & 10.112 & 9.95390909308532 & 0.158090906914678 \tabularnewline
71 & 9.266 & 9.49484565791946 & -0.228845657919457 \tabularnewline
72 & 9.82 & 10.1170063573100 & -0.297006357310037 \tabularnewline
73 & 10.097 & 9.97729069532818 & 0.119709304671821 \tabularnewline
74 & 9.115 & 9.31138696974474 & -0.196386969744744 \tabularnewline
75 & 10.411 & 10.2729688598946 & 0.138031140105372 \tabularnewline
76 & 9.678 & 9.83825957821236 & -0.160259578212356 \tabularnewline
77 & 10.408 & 9.80804322416032 & 0.599956775839683 \tabularnewline
78 & 10.153 & 10.1043857912686 & 0.0486142087313794 \tabularnewline
79 & 10.368 & 10.4026771219723 & -0.0346771219723347 \tabularnewline
80 & 10.581 & 10.6193959818708 & -0.0383959818707975 \tabularnewline
81 & 10.597 & 10.3114241972789 & 0.28557580272107 \tabularnewline
82 & 10.68 & 10.3206772680669 & 0.359322731933105 \tabularnewline
83 & 9.738 & 9.63865102730258 & 0.099348972697424 \tabularnewline
84 & 9.556 & 10.2631854515408 & -0.707185451540758 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42011&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]9.743[/C][C]9.74921180555556[/C][C]-0.00621180555555689[/C][/ROW]
[ROW][C]14[/C][C]8.587[/C][C]8.59142105170956[/C][C]-0.00442105170955998[/C][/ROW]
[ROW][C]15[/C][C]9.731[/C][C]9.74796524912095[/C][C]-0.016965249120954[/C][/ROW]
[ROW][C]16[/C][C]9.563[/C][C]9.58113773812208[/C][C]-0.0181377381220837[/C][/ROW]
[ROW][C]17[/C][C]9.998[/C][C]10.0105664997834[/C][C]-0.0125664997834232[/C][/ROW]
[ROW][C]18[/C][C]9.437[/C][C]9.44390532732481[/C][C]-0.00690532732481053[/C][/ROW]
[ROW][C]19[/C][C]10.038[/C][C]9.83615719750635[/C][C]0.201842802493651[/C][/ROW]
[ROW][C]20[/C][C]9.918[/C][C]10.1042072025874[/C][C]-0.186207202587356[/C][/ROW]
[ROW][C]21[/C][C]9.252[/C][C]9.44822805956723[/C][C]-0.196228059567231[/C][/ROW]
[ROW][C]22[/C][C]9.737[/C][C]9.66103748397145[/C][C]0.0759625160285538[/C][/ROW]
[ROW][C]23[/C][C]9.035[/C][C]9.03409035705682[/C][C]0.000909642943176081[/C][/ROW]
[ROW][C]24[/C][C]9.133[/C][C]9.03345579567608[/C][C]0.099544204323923[/C][/ROW]
[ROW][C]25[/C][C]9.487[/C][C]9.68611954459826[/C][C]-0.199119544598256[/C][/ROW]
[ROW][C]26[/C][C]8.7[/C][C]8.5058187499709[/C][C]0.194181250029102[/C][/ROW]
[ROW][C]27[/C][C]9.627[/C][C]9.67403227136777[/C][C]-0.0470322713677724[/C][/ROW]
[ROW][C]28[/C][C]8.947[/C][C]9.50203221802548[/C][C]-0.555032218025485[/C][/ROW]
[ROW][C]29[/C][C]9.283[/C][C]9.87054444750937[/C][C]-0.587544447509369[/C][/ROW]
[ROW][C]30[/C][C]8.829[/C][C]9.23124105357236[/C][C]-0.402241053572357[/C][/ROW]
[ROW][C]31[/C][C]9.947[/C][C]9.69649106157862[/C][C]0.250508938421376[/C][/ROW]
[ROW][C]32[/C][C]9.628[/C][C]9.69575706137927[/C][C]-0.0677570613792717[/C][/ROW]
[ROW][C]33[/C][C]9.318[/C][C]9.02611433318695[/C][C]0.291885666813053[/C][/ROW]
[ROW][C]34[/C][C]9.605[/C][C]9.4542564257478[/C][C]0.150743574252209[/C][/ROW]
[ROW][C]35[/C][C]8.64[/C][C]8.77438286347976[/C][C]-0.134382863479759[/C][/ROW]
[ROW][C]36[/C][C]9.214[/C][C]8.81021565717309[/C][C]0.403784342826912[/C][/ROW]
[ROW][C]37[/C][C]9.567[/C][C]9.29051920324584[/C][C]0.276480796754155[/C][/ROW]
[ROW][C]38[/C][C]8.547[/C][C]8.41290900386903[/C][C]0.134090996130967[/C][/ROW]
[ROW][C]39[/C][C]9.185[/C][C]9.41384606651053[/C][C]-0.228846066510531[/C][/ROW]
[ROW][C]40[/C][C]9.47[/C][C]8.88563267108924[/C][C]0.584367328910757[/C][/ROW]
[ROW][C]41[/C][C]9.123[/C][C]9.36087799748514[/C][C]-0.237877997485139[/C][/ROW]
[ROW][C]42[/C][C]9.278[/C][C]8.89260191145566[/C][C]0.38539808854434[/C][/ROW]
[ROW][C]43[/C][C]10.17[/C][C]9.88972350198546[/C][C]0.280276498014537[/C][/ROW]
[ROW][C]44[/C][C]9.434[/C][C]9.70976556212332[/C][C]-0.275765562123317[/C][/ROW]
[ROW][C]45[/C][C]9.655[/C][C]9.27484878636274[/C][C]0.380151213637262[/C][/ROW]
[ROW][C]46[/C][C]9.429[/C][C]9.6436109406425[/C][C]-0.214610940642499[/C][/ROW]
[ROW][C]47[/C][C]8.739[/C][C]8.75831278013992[/C][C]-0.0193127801399235[/C][/ROW]
[ROW][C]48[/C][C]9.552[/C][C]9.1766377035185[/C][C]0.375362296481507[/C][/ROW]
[ROW][C]49[/C][C]9.687[/C][C]9.5906222075736[/C][C]0.0963777924263916[/C][/ROW]
[ROW][C]50[/C][C]9.019[/C][C]8.61860492555353[/C][C]0.400395074446468[/C][/ROW]
[ROW][C]51[/C][C]9.672[/C][C]9.43163809278055[/C][C]0.240361907219448[/C][/ROW]
[ROW][C]52[/C][C]9.206[/C][C]9.5091554995017[/C][C]-0.303155499501692[/C][/ROW]
[ROW][C]53[/C][C]9.069[/C][C]9.37133980882434[/C][C]-0.302339808824335[/C][/ROW]
[ROW][C]54[/C][C]9.788[/C][C]9.31649977838275[/C][C]0.471500221617255[/C][/ROW]
[ROW][C]55[/C][C]10.312[/C][C]10.2694716023046[/C][C]0.0425283976953832[/C][/ROW]
[ROW][C]56[/C][C]10.105[/C][C]9.71465512609808[/C][C]0.390344873901917[/C][/ROW]
[ROW][C]57[/C][C]9.863[/C][C]9.7975942248095[/C][C]0.0654057751904986[/C][/ROW]
[ROW][C]58[/C][C]9.656[/C][C]9.76302433589962[/C][C]-0.107024335899615[/C][/ROW]
[ROW][C]59[/C][C]9.295[/C][C]9.03450554722939[/C][C]0.260494452770612[/C][/ROW]
[ROW][C]60[/C][C]9.946[/C][C]9.76123486649888[/C][C]0.184765133501118[/C][/ROW]
[ROW][C]61[/C][C]9.701[/C][C]9.99319182522465[/C][C]-0.29219182522465[/C][/ROW]
[ROW][C]62[/C][C]9.049[/C][C]9.19297379159361[/C][C]-0.143973791593615[/C][/ROW]
[ROW][C]63[/C][C]10.19[/C][C]9.85189863573865[/C][C]0.338101364261345[/C][/ROW]
[ROW][C]64[/C][C]9.706[/C][C]9.59379184124023[/C][C]0.112208158759774[/C][/ROW]
[ROW][C]65[/C][C]9.765[/C][C]9.51367114412538[/C][C]0.251328855874622[/C][/ROW]
[ROW][C]66[/C][C]9.893[/C][C]10.0419911674629[/C][C]-0.148991167462865[/C][/ROW]
[ROW][C]67[/C][C]9.994[/C][C]10.6638057580960[/C][C]-0.669805758095981[/C][/ROW]
[ROW][C]68[/C][C]10.433[/C][C]10.2645496399226[/C][C]0.168450360077351[/C][/ROW]
[ROW][C]69[/C][C]10.073[/C][C]10.1129555017458[/C][C]-0.0399555017458297[/C][/ROW]
[ROW][C]70[/C][C]10.112[/C][C]9.95390909308532[/C][C]0.158090906914678[/C][/ROW]
[ROW][C]71[/C][C]9.266[/C][C]9.49484565791946[/C][C]-0.228845657919457[/C][/ROW]
[ROW][C]72[/C][C]9.82[/C][C]10.1170063573100[/C][C]-0.297006357310037[/C][/ROW]
[ROW][C]73[/C][C]10.097[/C][C]9.97729069532818[/C][C]0.119709304671821[/C][/ROW]
[ROW][C]74[/C][C]9.115[/C][C]9.31138696974474[/C][C]-0.196386969744744[/C][/ROW]
[ROW][C]75[/C][C]10.411[/C][C]10.2729688598946[/C][C]0.138031140105372[/C][/ROW]
[ROW][C]76[/C][C]9.678[/C][C]9.83825957821236[/C][C]-0.160259578212356[/C][/ROW]
[ROW][C]77[/C][C]10.408[/C][C]9.80804322416032[/C][C]0.599956775839683[/C][/ROW]
[ROW][C]78[/C][C]10.153[/C][C]10.1043857912686[/C][C]0.0486142087313794[/C][/ROW]
[ROW][C]79[/C][C]10.368[/C][C]10.4026771219723[/C][C]-0.0346771219723347[/C][/ROW]
[ROW][C]80[/C][C]10.581[/C][C]10.6193959818708[/C][C]-0.0383959818707975[/C][/ROW]
[ROW][C]81[/C][C]10.597[/C][C]10.3114241972789[/C][C]0.28557580272107[/C][/ROW]
[ROW][C]82[/C][C]10.68[/C][C]10.3206772680669[/C][C]0.359322731933105[/C][/ROW]
[ROW][C]83[/C][C]9.738[/C][C]9.63865102730258[/C][C]0.099348972697424[/C][/ROW]
[ROW][C]84[/C][C]9.556[/C][C]10.2631854515408[/C][C]-0.707185451540758[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42011&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42011&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
139.7439.74921180555556-0.00621180555555689
148.5878.59142105170956-0.00442105170955998
159.7319.74796524912095-0.016965249120954
169.5639.58113773812208-0.0181377381220837
179.99810.0105664997834-0.0125664997834232
189.4379.44390532732481-0.00690532732481053
1910.0389.836157197506350.201842802493651
209.91810.1042072025874-0.186207202587356
219.2529.44822805956723-0.196228059567231
229.7379.661037483971450.0759625160285538
239.0359.034090357056820.000909642943176081
249.1339.033455795676080.099544204323923
259.4879.68611954459826-0.199119544598256
268.78.50581874997090.194181250029102
279.6279.67403227136777-0.0470322713677724
288.9479.50203221802548-0.555032218025485
299.2839.87054444750937-0.587544447509369
308.8299.23124105357236-0.402241053572357
319.9479.696491061578620.250508938421376
329.6289.69575706137927-0.0677570613792717
339.3189.026114333186950.291885666813053
349.6059.45425642574780.150743574252209
358.648.77438286347976-0.134382863479759
369.2148.810215657173090.403784342826912
379.5679.290519203245840.276480796754155
388.5478.412909003869030.134090996130967
399.1859.41384606651053-0.228846066510531
409.478.885632671089240.584367328910757
419.1239.36087799748514-0.237877997485139
429.2788.892601911455660.38539808854434
4310.179.889723501985460.280276498014537
449.4349.70976556212332-0.275765562123317
459.6559.274848786362740.380151213637262
469.4299.6436109406425-0.214610940642499
478.7398.75831278013992-0.0193127801399235
489.5529.17663770351850.375362296481507
499.6879.59062220757360.0963777924263916
509.0198.618604925553530.400395074446468
519.6729.431638092780550.240361907219448
529.2069.5091554995017-0.303155499501692
539.0699.37133980882434-0.302339808824335
549.7889.316499778382750.471500221617255
5510.31210.26947160230460.0425283976953832
5610.1059.714655126098080.390344873901917
579.8639.79759422480950.0654057751904986
589.6569.76302433589962-0.107024335899615
599.2959.034505547229390.260494452770612
609.9469.761234866498880.184765133501118
619.7019.99319182522465-0.29219182522465
629.0499.19297379159361-0.143973791593615
6310.199.851898635738650.338101364261345
649.7069.593791841240230.112208158759774
659.7659.513671144125380.251328855874622
669.89310.0419911674629-0.148991167462865
679.99410.6638057580960-0.669805758095981
6810.43310.26454963992260.168450360077351
6910.07310.1129555017458-0.0399555017458297
7010.1129.953909093085320.158090906914678
719.2669.49484565791946-0.228845657919457
729.8210.1170063573100-0.297006357310037
7310.0979.977290695328180.119709304671821
749.1159.31138696974474-0.196386969744744
7510.41110.27296885989460.138031140105372
769.6789.83825957821236-0.160259578212356
7710.4089.808043224160320.599956775839683
7810.15310.10438579126860.0486142087313794
7910.36810.4026771219723-0.0346771219723347
8010.58110.6193959818708-0.0383959818707975
8110.59710.31142419727890.28557580272107
8210.6810.32067726806690.359322731933105
839.7389.638651027302580.099348972697424
849.55610.2631854515408-0.707185451540758






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8510.35912042225989.8103701484564610.9078706960631
869.480195467364128.9276478433200610.0327430914082
8710.688103043327710.130867889440511.245338197215
8810.05085331989129.487963892565210.6137427472171
8910.54084858002799.9712692847910511.1104278752648
9010.41568699803219.8383219142658210.9930520817985
9110.654167451808710.067869463335111.2404654402823
9210.872061182895110.275641471372411.4684808944178
9310.779620236727610.171857875529311.3873825979259
9410.803758984803410.183410371360111.4241075982466
959.906672456556669.2724803401198910.5408645729934
969.985889691375539.3365915876809510.6351877950701

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 10.3591204222598 & 9.81037014845646 & 10.9078706960631 \tabularnewline
86 & 9.48019546736412 & 8.92764784332006 & 10.0327430914082 \tabularnewline
87 & 10.6881030433277 & 10.1308678894405 & 11.245338197215 \tabularnewline
88 & 10.0508533198912 & 9.4879638925652 & 10.6137427472171 \tabularnewline
89 & 10.5408485800279 & 9.97126928479105 & 11.1104278752648 \tabularnewline
90 & 10.4156869980321 & 9.83832191426582 & 10.9930520817985 \tabularnewline
91 & 10.6541674518087 & 10.0678694633351 & 11.2404654402823 \tabularnewline
92 & 10.8720611828951 & 10.2756414713724 & 11.4684808944178 \tabularnewline
93 & 10.7796202367276 & 10.1718578755293 & 11.3873825979259 \tabularnewline
94 & 10.8037589848034 & 10.1834103713601 & 11.4241075982466 \tabularnewline
95 & 9.90667245655666 & 9.27248034011989 & 10.5408645729934 \tabularnewline
96 & 9.98588969137553 & 9.33659158768095 & 10.6351877950701 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42011&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]85[/C][C]10.3591204222598[/C][C]9.81037014845646[/C][C]10.9078706960631[/C][/ROW]
[ROW][C]86[/C][C]9.48019546736412[/C][C]8.92764784332006[/C][C]10.0327430914082[/C][/ROW]
[ROW][C]87[/C][C]10.6881030433277[/C][C]10.1308678894405[/C][C]11.245338197215[/C][/ROW]
[ROW][C]88[/C][C]10.0508533198912[/C][C]9.4879638925652[/C][C]10.6137427472171[/C][/ROW]
[ROW][C]89[/C][C]10.5408485800279[/C][C]9.97126928479105[/C][C]11.1104278752648[/C][/ROW]
[ROW][C]90[/C][C]10.4156869980321[/C][C]9.83832191426582[/C][C]10.9930520817985[/C][/ROW]
[ROW][C]91[/C][C]10.6541674518087[/C][C]10.0678694633351[/C][C]11.2404654402823[/C][/ROW]
[ROW][C]92[/C][C]10.8720611828951[/C][C]10.2756414713724[/C][C]11.4684808944178[/C][/ROW]
[ROW][C]93[/C][C]10.7796202367276[/C][C]10.1718578755293[/C][C]11.3873825979259[/C][/ROW]
[ROW][C]94[/C][C]10.8037589848034[/C][C]10.1834103713601[/C][C]11.4241075982466[/C][/ROW]
[ROW][C]95[/C][C]9.90667245655666[/C][C]9.27248034011989[/C][C]10.5408645729934[/C][/ROW]
[ROW][C]96[/C][C]9.98588969137553[/C][C]9.33659158768095[/C][C]10.6351877950701[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42011&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42011&T=3

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


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

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8510.35912042225989.8103701484564610.9078706960631
869.480195467364128.9276478433200610.0327430914082
8710.688103043327710.130867889440511.245338197215
8810.05085331989129.487963892565210.6137427472171
8910.54084858002799.9712692847910511.1104278752648
9010.41568699803219.8383219142658210.9930520817985
9110.654167451808710.067869463335111.2404654402823
9210.872061182895110.275641471372411.4684808944178
9310.779620236727610.171857875529311.3873825979259
9410.803758984803410.183410371360111.4241075982466
959.906672456556669.2724803401198910.5408645729934
969.985889691375539.3365915876809510.6351877950701


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 ;
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')