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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 15 Aug 2008 07:13:44 -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/2008/Aug/15/t1218806078zc6z1a47mj0sf2v.htm/, Retrieved Wed, 15 May 2024 12:51:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=14575, Retrieved Wed, 15 May 2024 12:51:59 +0000
QR Codes:

Original text written by user:Triple multiplicative
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact250
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Opgave 10 - Super...] [2008-08-15 13:13:44] [f38aed22bcf737d6f431a6f90e40d4b2] [Current]
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Dataseries X:
0.91
0.9
0.89
0.89
0.89
0.89
0.89
0.89
0.88
0.88
0.88
0.86
0.85
0.85
0.86
0.9
0.92
0.91
0.93
0.96
0.96
0.97
0.98
1.01
0.99
1.03
1.08
1.06
1.1
1.17
1.16
1.12
1.17
1.13
1.12
1.07
1.04
1.08
1.06
1.12
1.18
1.13
1.08
1.06
1.09
1.02
1.01
1.01
1
1.01
1.03
1.09
1.07
1.05
1.06
1.06
1.08
1.07
1.04
1.04
1.06
1.09
1.09
1.05
1.01
1.02
1.03
1.06
1.08
1.05
1.05
1.05
1.04
1.05
1.07
1.1
1.16
1.16
1.17
1.17
1.18
1.21
1.18
1.13
1.12
1.17
1.19
1.26
1.25
1.28
1.35
1.39
1.45
1.41
1.32
1.31




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14575&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14575&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14575&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.799338468046928
beta0.0091143646723173
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.799338468046928 \tabularnewline
beta & 0.0091143646723173 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14575&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]0.799338468046928[/C][/ROW]
[ROW][C]beta[/C][C]0.0091143646723173[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14575&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14575&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
alpha0.799338468046928
beta0.0091143646723173
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
130.850.8103762374967240.0396237625032760
140.850.8480824745082080.00191752549179225
150.860.864043420959625-0.0040434209596254
160.90.904578457094851-0.00457845709485105
170.920.92383889187728-0.00383889187728059
180.910.9110934864036-0.00109348640359919
190.930.9288912654338260.00110873456617377
200.960.9571572611739130.0028427388260871
210.960.9535584335219620.00644156647803829
220.970.9637434695518140.0062565304481863
230.980.9754924821575640.00450751784243641
241.011.001651891453770.00834810854622758
250.990.990215789475333-0.000215789475333295
261.030.9866688887450070.043331111254993
271.081.035523241629650.0444767583703489
281.061.12360370959481-0.0636037095948134
291.11.098545633406060.00145436659393994
301.171.087132225963860.0828677740361419
311.161.17575854419085-0.0157585441908548
321.121.19602409819807-0.0760240981980698
331.171.127537309879770.0424626901202250
341.131.16586684933194-0.0358668493319356
351.121.14313613719794-0.0231361371979428
361.071.14988461978709-0.0798846197870884
371.041.06337914250779-0.0233791425077887
381.081.048761792355340.0312382076446582
391.061.08723326930132-0.0272332693013189
401.121.094114329456240.0258856705437613
411.181.154361128288910.0256388717110918
421.131.17656263174621-0.0465626317462124
431.081.14068107677332-0.0606810767733239
441.061.10984176849747-0.0498417684974661
451.091.083976435452160.00602356454783615
461.021.07700358520965-0.0570035852096511
471.011.03807194043097-0.0280719404309666
481.011.02630400488978-0.016304004889782
4911.00145034562005-0.00145034562005142
501.011.01357567832863-0.00357567832863293
511.031.011263264557660.0187367354423402
521.091.063172046205790.0268279537942113
531.071.12173910695277-0.0517391069527693
541.051.06738693496684-0.0173869349668403
551.061.050597185306510.00940281469348547
561.061.07619885060324-0.0161988506032447
571.081.08751901052413-0.00751901052413051
581.071.055811166135670.014188833864335
591.041.07911047634731-0.0391104763473056
601.041.06039957127836-0.020399571278358
611.061.034050677474730.0259493225252680
621.091.067467371961420.0225326280385840
631.091.089956516742274.34832577309585e-05
641.051.12978866779252-0.0797886677925153
651.011.08554664847600-0.0755466484760015
661.021.018310033723720.00168996627628260
671.031.021128519199730.008871480800267
681.061.039813594833010.0201864051669896
691.081.08094844970193-0.00094844970193364
701.051.05794900976268-0.0079490097626811
711.051.05173126496785-0.00173126496785181
721.051.06591575877450-0.0159157587745022
731.041.05152139264002-0.0115213926400182
741.051.05316961574409-0.00316961574409125
751.071.049728595856300.0202714041437018
761.11.087394976824810.0126050231751886
771.161.117111286767120.0428887132328801
781.161.16070035651934-0.000700356519342638
791.171.162884331063700.00711566893629678
801.171.18367679210897-0.0136767921089738
811.181.19509502285563-0.0150950228556337
821.211.156501510100830.0534984898991733
831.181.20033971905677-0.0203397190567707
841.131.19784906074891-0.0678490607489077
851.121.14211693226228-0.0221169322622847
861.171.137356685523740.0326433144762635
871.191.167029531694890.0229704683051053
881.261.206877904108270.0531220958917287
891.251.27776750084836-0.0277675008483582
901.281.255551764376350.0244482356236533
911.351.279254217692100.0707457823078963
921.391.347807503006960.0421924969930394
931.451.407216561998590.0427834380014096
941.411.42514909362493-0.0151490936249323
951.321.39656620503061-0.0765662050306122
961.311.33895995103608-0.0289599510360776

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 0.85 & 0.810376237496724 & 0.0396237625032760 \tabularnewline
14 & 0.85 & 0.848082474508208 & 0.00191752549179225 \tabularnewline
15 & 0.86 & 0.864043420959625 & -0.0040434209596254 \tabularnewline
16 & 0.9 & 0.904578457094851 & -0.00457845709485105 \tabularnewline
17 & 0.92 & 0.92383889187728 & -0.00383889187728059 \tabularnewline
18 & 0.91 & 0.9110934864036 & -0.00109348640359919 \tabularnewline
19 & 0.93 & 0.928891265433826 & 0.00110873456617377 \tabularnewline
20 & 0.96 & 0.957157261173913 & 0.0028427388260871 \tabularnewline
21 & 0.96 & 0.953558433521962 & 0.00644156647803829 \tabularnewline
22 & 0.97 & 0.963743469551814 & 0.0062565304481863 \tabularnewline
23 & 0.98 & 0.975492482157564 & 0.00450751784243641 \tabularnewline
24 & 1.01 & 1.00165189145377 & 0.00834810854622758 \tabularnewline
25 & 0.99 & 0.990215789475333 & -0.000215789475333295 \tabularnewline
26 & 1.03 & 0.986668888745007 & 0.043331111254993 \tabularnewline
27 & 1.08 & 1.03552324162965 & 0.0444767583703489 \tabularnewline
28 & 1.06 & 1.12360370959481 & -0.0636037095948134 \tabularnewline
29 & 1.1 & 1.09854563340606 & 0.00145436659393994 \tabularnewline
30 & 1.17 & 1.08713222596386 & 0.0828677740361419 \tabularnewline
31 & 1.16 & 1.17575854419085 & -0.0157585441908548 \tabularnewline
32 & 1.12 & 1.19602409819807 & -0.0760240981980698 \tabularnewline
33 & 1.17 & 1.12753730987977 & 0.0424626901202250 \tabularnewline
34 & 1.13 & 1.16586684933194 & -0.0358668493319356 \tabularnewline
35 & 1.12 & 1.14313613719794 & -0.0231361371979428 \tabularnewline
36 & 1.07 & 1.14988461978709 & -0.0798846197870884 \tabularnewline
37 & 1.04 & 1.06337914250779 & -0.0233791425077887 \tabularnewline
38 & 1.08 & 1.04876179235534 & 0.0312382076446582 \tabularnewline
39 & 1.06 & 1.08723326930132 & -0.0272332693013189 \tabularnewline
40 & 1.12 & 1.09411432945624 & 0.0258856705437613 \tabularnewline
41 & 1.18 & 1.15436112828891 & 0.0256388717110918 \tabularnewline
42 & 1.13 & 1.17656263174621 & -0.0465626317462124 \tabularnewline
43 & 1.08 & 1.14068107677332 & -0.0606810767733239 \tabularnewline
44 & 1.06 & 1.10984176849747 & -0.0498417684974661 \tabularnewline
45 & 1.09 & 1.08397643545216 & 0.00602356454783615 \tabularnewline
46 & 1.02 & 1.07700358520965 & -0.0570035852096511 \tabularnewline
47 & 1.01 & 1.03807194043097 & -0.0280719404309666 \tabularnewline
48 & 1.01 & 1.02630400488978 & -0.016304004889782 \tabularnewline
49 & 1 & 1.00145034562005 & -0.00145034562005142 \tabularnewline
50 & 1.01 & 1.01357567832863 & -0.00357567832863293 \tabularnewline
51 & 1.03 & 1.01126326455766 & 0.0187367354423402 \tabularnewline
52 & 1.09 & 1.06317204620579 & 0.0268279537942113 \tabularnewline
53 & 1.07 & 1.12173910695277 & -0.0517391069527693 \tabularnewline
54 & 1.05 & 1.06738693496684 & -0.0173869349668403 \tabularnewline
55 & 1.06 & 1.05059718530651 & 0.00940281469348547 \tabularnewline
56 & 1.06 & 1.07619885060324 & -0.0161988506032447 \tabularnewline
57 & 1.08 & 1.08751901052413 & -0.00751901052413051 \tabularnewline
58 & 1.07 & 1.05581116613567 & 0.014188833864335 \tabularnewline
59 & 1.04 & 1.07911047634731 & -0.0391104763473056 \tabularnewline
60 & 1.04 & 1.06039957127836 & -0.020399571278358 \tabularnewline
61 & 1.06 & 1.03405067747473 & 0.0259493225252680 \tabularnewline
62 & 1.09 & 1.06746737196142 & 0.0225326280385840 \tabularnewline
63 & 1.09 & 1.08995651674227 & 4.34832577309585e-05 \tabularnewline
64 & 1.05 & 1.12978866779252 & -0.0797886677925153 \tabularnewline
65 & 1.01 & 1.08554664847600 & -0.0755466484760015 \tabularnewline
66 & 1.02 & 1.01831003372372 & 0.00168996627628260 \tabularnewline
67 & 1.03 & 1.02112851919973 & 0.008871480800267 \tabularnewline
68 & 1.06 & 1.03981359483301 & 0.0201864051669896 \tabularnewline
69 & 1.08 & 1.08094844970193 & -0.00094844970193364 \tabularnewline
70 & 1.05 & 1.05794900976268 & -0.0079490097626811 \tabularnewline
71 & 1.05 & 1.05173126496785 & -0.00173126496785181 \tabularnewline
72 & 1.05 & 1.06591575877450 & -0.0159157587745022 \tabularnewline
73 & 1.04 & 1.05152139264002 & -0.0115213926400182 \tabularnewline
74 & 1.05 & 1.05316961574409 & -0.00316961574409125 \tabularnewline
75 & 1.07 & 1.04972859585630 & 0.0202714041437018 \tabularnewline
76 & 1.1 & 1.08739497682481 & 0.0126050231751886 \tabularnewline
77 & 1.16 & 1.11711128676712 & 0.0428887132328801 \tabularnewline
78 & 1.16 & 1.16070035651934 & -0.000700356519342638 \tabularnewline
79 & 1.17 & 1.16288433106370 & 0.00711566893629678 \tabularnewline
80 & 1.17 & 1.18367679210897 & -0.0136767921089738 \tabularnewline
81 & 1.18 & 1.19509502285563 & -0.0150950228556337 \tabularnewline
82 & 1.21 & 1.15650151010083 & 0.0534984898991733 \tabularnewline
83 & 1.18 & 1.20033971905677 & -0.0203397190567707 \tabularnewline
84 & 1.13 & 1.19784906074891 & -0.0678490607489077 \tabularnewline
85 & 1.12 & 1.14211693226228 & -0.0221169322622847 \tabularnewline
86 & 1.17 & 1.13735668552374 & 0.0326433144762635 \tabularnewline
87 & 1.19 & 1.16702953169489 & 0.0229704683051053 \tabularnewline
88 & 1.26 & 1.20687790410827 & 0.0531220958917287 \tabularnewline
89 & 1.25 & 1.27776750084836 & -0.0277675008483582 \tabularnewline
90 & 1.28 & 1.25555176437635 & 0.0244482356236533 \tabularnewline
91 & 1.35 & 1.27925421769210 & 0.0707457823078963 \tabularnewline
92 & 1.39 & 1.34780750300696 & 0.0421924969930394 \tabularnewline
93 & 1.45 & 1.40721656199859 & 0.0427834380014096 \tabularnewline
94 & 1.41 & 1.42514909362493 & -0.0151490936249323 \tabularnewline
95 & 1.32 & 1.39656620503061 & -0.0765662050306122 \tabularnewline
96 & 1.31 & 1.33895995103608 & -0.0289599510360776 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14575&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]0.85[/C][C]0.810376237496724[/C][C]0.0396237625032760[/C][/ROW]
[ROW][C]14[/C][C]0.85[/C][C]0.848082474508208[/C][C]0.00191752549179225[/C][/ROW]
[ROW][C]15[/C][C]0.86[/C][C]0.864043420959625[/C][C]-0.0040434209596254[/C][/ROW]
[ROW][C]16[/C][C]0.9[/C][C]0.904578457094851[/C][C]-0.00457845709485105[/C][/ROW]
[ROW][C]17[/C][C]0.92[/C][C]0.92383889187728[/C][C]-0.00383889187728059[/C][/ROW]
[ROW][C]18[/C][C]0.91[/C][C]0.9110934864036[/C][C]-0.00109348640359919[/C][/ROW]
[ROW][C]19[/C][C]0.93[/C][C]0.928891265433826[/C][C]0.00110873456617377[/C][/ROW]
[ROW][C]20[/C][C]0.96[/C][C]0.957157261173913[/C][C]0.0028427388260871[/C][/ROW]
[ROW][C]21[/C][C]0.96[/C][C]0.953558433521962[/C][C]0.00644156647803829[/C][/ROW]
[ROW][C]22[/C][C]0.97[/C][C]0.963743469551814[/C][C]0.0062565304481863[/C][/ROW]
[ROW][C]23[/C][C]0.98[/C][C]0.975492482157564[/C][C]0.00450751784243641[/C][/ROW]
[ROW][C]24[/C][C]1.01[/C][C]1.00165189145377[/C][C]0.00834810854622758[/C][/ROW]
[ROW][C]25[/C][C]0.99[/C][C]0.990215789475333[/C][C]-0.000215789475333295[/C][/ROW]
[ROW][C]26[/C][C]1.03[/C][C]0.986668888745007[/C][C]0.043331111254993[/C][/ROW]
[ROW][C]27[/C][C]1.08[/C][C]1.03552324162965[/C][C]0.0444767583703489[/C][/ROW]
[ROW][C]28[/C][C]1.06[/C][C]1.12360370959481[/C][C]-0.0636037095948134[/C][/ROW]
[ROW][C]29[/C][C]1.1[/C][C]1.09854563340606[/C][C]0.00145436659393994[/C][/ROW]
[ROW][C]30[/C][C]1.17[/C][C]1.08713222596386[/C][C]0.0828677740361419[/C][/ROW]
[ROW][C]31[/C][C]1.16[/C][C]1.17575854419085[/C][C]-0.0157585441908548[/C][/ROW]
[ROW][C]32[/C][C]1.12[/C][C]1.19602409819807[/C][C]-0.0760240981980698[/C][/ROW]
[ROW][C]33[/C][C]1.17[/C][C]1.12753730987977[/C][C]0.0424626901202250[/C][/ROW]
[ROW][C]34[/C][C]1.13[/C][C]1.16586684933194[/C][C]-0.0358668493319356[/C][/ROW]
[ROW][C]35[/C][C]1.12[/C][C]1.14313613719794[/C][C]-0.0231361371979428[/C][/ROW]
[ROW][C]36[/C][C]1.07[/C][C]1.14988461978709[/C][C]-0.0798846197870884[/C][/ROW]
[ROW][C]37[/C][C]1.04[/C][C]1.06337914250779[/C][C]-0.0233791425077887[/C][/ROW]
[ROW][C]38[/C][C]1.08[/C][C]1.04876179235534[/C][C]0.0312382076446582[/C][/ROW]
[ROW][C]39[/C][C]1.06[/C][C]1.08723326930132[/C][C]-0.0272332693013189[/C][/ROW]
[ROW][C]40[/C][C]1.12[/C][C]1.09411432945624[/C][C]0.0258856705437613[/C][/ROW]
[ROW][C]41[/C][C]1.18[/C][C]1.15436112828891[/C][C]0.0256388717110918[/C][/ROW]
[ROW][C]42[/C][C]1.13[/C][C]1.17656263174621[/C][C]-0.0465626317462124[/C][/ROW]
[ROW][C]43[/C][C]1.08[/C][C]1.14068107677332[/C][C]-0.0606810767733239[/C][/ROW]
[ROW][C]44[/C][C]1.06[/C][C]1.10984176849747[/C][C]-0.0498417684974661[/C][/ROW]
[ROW][C]45[/C][C]1.09[/C][C]1.08397643545216[/C][C]0.00602356454783615[/C][/ROW]
[ROW][C]46[/C][C]1.02[/C][C]1.07700358520965[/C][C]-0.0570035852096511[/C][/ROW]
[ROW][C]47[/C][C]1.01[/C][C]1.03807194043097[/C][C]-0.0280719404309666[/C][/ROW]
[ROW][C]48[/C][C]1.01[/C][C]1.02630400488978[/C][C]-0.016304004889782[/C][/ROW]
[ROW][C]49[/C][C]1[/C][C]1.00145034562005[/C][C]-0.00145034562005142[/C][/ROW]
[ROW][C]50[/C][C]1.01[/C][C]1.01357567832863[/C][C]-0.00357567832863293[/C][/ROW]
[ROW][C]51[/C][C]1.03[/C][C]1.01126326455766[/C][C]0.0187367354423402[/C][/ROW]
[ROW][C]52[/C][C]1.09[/C][C]1.06317204620579[/C][C]0.0268279537942113[/C][/ROW]
[ROW][C]53[/C][C]1.07[/C][C]1.12173910695277[/C][C]-0.0517391069527693[/C][/ROW]
[ROW][C]54[/C][C]1.05[/C][C]1.06738693496684[/C][C]-0.0173869349668403[/C][/ROW]
[ROW][C]55[/C][C]1.06[/C][C]1.05059718530651[/C][C]0.00940281469348547[/C][/ROW]
[ROW][C]56[/C][C]1.06[/C][C]1.07619885060324[/C][C]-0.0161988506032447[/C][/ROW]
[ROW][C]57[/C][C]1.08[/C][C]1.08751901052413[/C][C]-0.00751901052413051[/C][/ROW]
[ROW][C]58[/C][C]1.07[/C][C]1.05581116613567[/C][C]0.014188833864335[/C][/ROW]
[ROW][C]59[/C][C]1.04[/C][C]1.07911047634731[/C][C]-0.0391104763473056[/C][/ROW]
[ROW][C]60[/C][C]1.04[/C][C]1.06039957127836[/C][C]-0.020399571278358[/C][/ROW]
[ROW][C]61[/C][C]1.06[/C][C]1.03405067747473[/C][C]0.0259493225252680[/C][/ROW]
[ROW][C]62[/C][C]1.09[/C][C]1.06746737196142[/C][C]0.0225326280385840[/C][/ROW]
[ROW][C]63[/C][C]1.09[/C][C]1.08995651674227[/C][C]4.34832577309585e-05[/C][/ROW]
[ROW][C]64[/C][C]1.05[/C][C]1.12978866779252[/C][C]-0.0797886677925153[/C][/ROW]
[ROW][C]65[/C][C]1.01[/C][C]1.08554664847600[/C][C]-0.0755466484760015[/C][/ROW]
[ROW][C]66[/C][C]1.02[/C][C]1.01831003372372[/C][C]0.00168996627628260[/C][/ROW]
[ROW][C]67[/C][C]1.03[/C][C]1.02112851919973[/C][C]0.008871480800267[/C][/ROW]
[ROW][C]68[/C][C]1.06[/C][C]1.03981359483301[/C][C]0.0201864051669896[/C][/ROW]
[ROW][C]69[/C][C]1.08[/C][C]1.08094844970193[/C][C]-0.00094844970193364[/C][/ROW]
[ROW][C]70[/C][C]1.05[/C][C]1.05794900976268[/C][C]-0.0079490097626811[/C][/ROW]
[ROW][C]71[/C][C]1.05[/C][C]1.05173126496785[/C][C]-0.00173126496785181[/C][/ROW]
[ROW][C]72[/C][C]1.05[/C][C]1.06591575877450[/C][C]-0.0159157587745022[/C][/ROW]
[ROW][C]73[/C][C]1.04[/C][C]1.05152139264002[/C][C]-0.0115213926400182[/C][/ROW]
[ROW][C]74[/C][C]1.05[/C][C]1.05316961574409[/C][C]-0.00316961574409125[/C][/ROW]
[ROW][C]75[/C][C]1.07[/C][C]1.04972859585630[/C][C]0.0202714041437018[/C][/ROW]
[ROW][C]76[/C][C]1.1[/C][C]1.08739497682481[/C][C]0.0126050231751886[/C][/ROW]
[ROW][C]77[/C][C]1.16[/C][C]1.11711128676712[/C][C]0.0428887132328801[/C][/ROW]
[ROW][C]78[/C][C]1.16[/C][C]1.16070035651934[/C][C]-0.000700356519342638[/C][/ROW]
[ROW][C]79[/C][C]1.17[/C][C]1.16288433106370[/C][C]0.00711566893629678[/C][/ROW]
[ROW][C]80[/C][C]1.17[/C][C]1.18367679210897[/C][C]-0.0136767921089738[/C][/ROW]
[ROW][C]81[/C][C]1.18[/C][C]1.19509502285563[/C][C]-0.0150950228556337[/C][/ROW]
[ROW][C]82[/C][C]1.21[/C][C]1.15650151010083[/C][C]0.0534984898991733[/C][/ROW]
[ROW][C]83[/C][C]1.18[/C][C]1.20033971905677[/C][C]-0.0203397190567707[/C][/ROW]
[ROW][C]84[/C][C]1.13[/C][C]1.19784906074891[/C][C]-0.0678490607489077[/C][/ROW]
[ROW][C]85[/C][C]1.12[/C][C]1.14211693226228[/C][C]-0.0221169322622847[/C][/ROW]
[ROW][C]86[/C][C]1.17[/C][C]1.13735668552374[/C][C]0.0326433144762635[/C][/ROW]
[ROW][C]87[/C][C]1.19[/C][C]1.16702953169489[/C][C]0.0229704683051053[/C][/ROW]
[ROW][C]88[/C][C]1.26[/C][C]1.20687790410827[/C][C]0.0531220958917287[/C][/ROW]
[ROW][C]89[/C][C]1.25[/C][C]1.27776750084836[/C][C]-0.0277675008483582[/C][/ROW]
[ROW][C]90[/C][C]1.28[/C][C]1.25555176437635[/C][C]0.0244482356236533[/C][/ROW]
[ROW][C]91[/C][C]1.35[/C][C]1.27925421769210[/C][C]0.0707457823078963[/C][/ROW]
[ROW][C]92[/C][C]1.39[/C][C]1.34780750300696[/C][C]0.0421924969930394[/C][/ROW]
[ROW][C]93[/C][C]1.45[/C][C]1.40721656199859[/C][C]0.0427834380014096[/C][/ROW]
[ROW][C]94[/C][C]1.41[/C][C]1.42514909362493[/C][C]-0.0151490936249323[/C][/ROW]
[ROW][C]95[/C][C]1.32[/C][C]1.39656620503061[/C][C]-0.0765662050306122[/C][/ROW]
[ROW][C]96[/C][C]1.31[/C][C]1.33895995103608[/C][C]-0.0289599510360776[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14575&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14575&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
130.850.8103762374967240.0396237625032760
140.850.8480824745082080.00191752549179225
150.860.864043420959625-0.0040434209596254
160.90.904578457094851-0.00457845709485105
170.920.92383889187728-0.00383889187728059
180.910.9110934864036-0.00109348640359919
190.930.9288912654338260.00110873456617377
200.960.9571572611739130.0028427388260871
210.960.9535584335219620.00644156647803829
220.970.9637434695518140.0062565304481863
230.980.9754924821575640.00450751784243641
241.011.001651891453770.00834810854622758
250.990.990215789475333-0.000215789475333295
261.030.9866688887450070.043331111254993
271.081.035523241629650.0444767583703489
281.061.12360370959481-0.0636037095948134
291.11.098545633406060.00145436659393994
301.171.087132225963860.0828677740361419
311.161.17575854419085-0.0157585441908548
321.121.19602409819807-0.0760240981980698
331.171.127537309879770.0424626901202250
341.131.16586684933194-0.0358668493319356
351.121.14313613719794-0.0231361371979428
361.071.14988461978709-0.0798846197870884
371.041.06337914250779-0.0233791425077887
381.081.048761792355340.0312382076446582
391.061.08723326930132-0.0272332693013189
401.121.094114329456240.0258856705437613
411.181.154361128288910.0256388717110918
421.131.17656263174621-0.0465626317462124
431.081.14068107677332-0.0606810767733239
441.061.10984176849747-0.0498417684974661
451.091.083976435452160.00602356454783615
461.021.07700358520965-0.0570035852096511
471.011.03807194043097-0.0280719404309666
481.011.02630400488978-0.016304004889782
4911.00145034562005-0.00145034562005142
501.011.01357567832863-0.00357567832863293
511.031.011263264557660.0187367354423402
521.091.063172046205790.0268279537942113
531.071.12173910695277-0.0517391069527693
541.051.06738693496684-0.0173869349668403
551.061.050597185306510.00940281469348547
561.061.07619885060324-0.0161988506032447
571.081.08751901052413-0.00751901052413051
581.071.055811166135670.014188833864335
591.041.07911047634731-0.0391104763473056
601.041.06039957127836-0.020399571278358
611.061.034050677474730.0259493225252680
621.091.067467371961420.0225326280385840
631.091.089956516742274.34832577309585e-05
641.051.12978866779252-0.0797886677925153
651.011.08554664847600-0.0755466484760015
661.021.018310033723720.00168996627628260
671.031.021128519199730.008871480800267
681.061.039813594833010.0201864051669896
691.081.08094844970193-0.00094844970193364
701.051.05794900976268-0.0079490097626811
711.051.05173126496785-0.00173126496785181
721.051.06591575877450-0.0159157587745022
731.041.05152139264002-0.0115213926400182
741.051.05316961574409-0.00316961574409125
751.071.049728595856300.0202714041437018
761.11.087394976824810.0126050231751886
771.161.117111286767120.0428887132328801
781.161.16070035651934-0.000700356519342638
791.171.162884331063700.00711566893629678
801.171.18367679210897-0.0136767921089738
811.181.19509502285563-0.0150950228556337
821.211.156501510100830.0534984898991733
831.181.20033971905677-0.0203397190567707
841.131.19784906074891-0.0678490607489077
851.121.14211693226228-0.0221169322622847
861.171.137356685523740.0326433144762635
871.191.167029531694890.0229704683051053
881.261.206877904108270.0531220958917287
891.251.27776750084836-0.0277675008483582
901.281.255551764376350.0244482356236533
911.351.279254217692100.0707457823078963
921.391.347807503006960.0421924969930394
931.451.407216561998590.0427834380014096
941.411.42514909362493-0.0151490936249323
951.321.39656620503061-0.0765662050306122
961.311.33895995103608-0.0289599510360776







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
971.324311642062001.255898801191401.39272448293260
981.352101738130371.263690896057491.44051258020325
991.353526070689001.249329273506511.4577228678715
1001.383984294836921.264307616079401.50366097359445
1011.396688489212561.263935072860841.52944190556429
1021.407777086667461.262983190813961.55257098252096
1031.421336158818601.264981639170511.57769067846668
1041.426984308097341.260383636253721.59358497994095
1051.452421664785411.273969412319301.63087391725152
1061.423551042868421.239644897429961.60745718830689
1071.392921040775671.204169389567151.5816726919842
1081.40602462566043-6.658047120808399.47009637212924

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 1.32431164206200 & 1.25589880119140 & 1.39272448293260 \tabularnewline
98 & 1.35210173813037 & 1.26369089605749 & 1.44051258020325 \tabularnewline
99 & 1.35352607068900 & 1.24932927350651 & 1.4577228678715 \tabularnewline
100 & 1.38398429483692 & 1.26430761607940 & 1.50366097359445 \tabularnewline
101 & 1.39668848921256 & 1.26393507286084 & 1.52944190556429 \tabularnewline
102 & 1.40777708666746 & 1.26298319081396 & 1.55257098252096 \tabularnewline
103 & 1.42133615881860 & 1.26498163917051 & 1.57769067846668 \tabularnewline
104 & 1.42698430809734 & 1.26038363625372 & 1.59358497994095 \tabularnewline
105 & 1.45242166478541 & 1.27396941231930 & 1.63087391725152 \tabularnewline
106 & 1.42355104286842 & 1.23964489742996 & 1.60745718830689 \tabularnewline
107 & 1.39292104077567 & 1.20416938956715 & 1.5816726919842 \tabularnewline
108 & 1.40602462566043 & -6.65804712080839 & 9.47009637212924 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14575&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]97[/C][C]1.32431164206200[/C][C]1.25589880119140[/C][C]1.39272448293260[/C][/ROW]
[ROW][C]98[/C][C]1.35210173813037[/C][C]1.26369089605749[/C][C]1.44051258020325[/C][/ROW]
[ROW][C]99[/C][C]1.35352607068900[/C][C]1.24932927350651[/C][C]1.4577228678715[/C][/ROW]
[ROW][C]100[/C][C]1.38398429483692[/C][C]1.26430761607940[/C][C]1.50366097359445[/C][/ROW]
[ROW][C]101[/C][C]1.39668848921256[/C][C]1.26393507286084[/C][C]1.52944190556429[/C][/ROW]
[ROW][C]102[/C][C]1.40777708666746[/C][C]1.26298319081396[/C][C]1.55257098252096[/C][/ROW]
[ROW][C]103[/C][C]1.42133615881860[/C][C]1.26498163917051[/C][C]1.57769067846668[/C][/ROW]
[ROW][C]104[/C][C]1.42698430809734[/C][C]1.26038363625372[/C][C]1.59358497994095[/C][/ROW]
[ROW][C]105[/C][C]1.45242166478541[/C][C]1.27396941231930[/C][C]1.63087391725152[/C][/ROW]
[ROW][C]106[/C][C]1.42355104286842[/C][C]1.23964489742996[/C][C]1.60745718830689[/C][/ROW]
[ROW][C]107[/C][C]1.39292104077567[/C][C]1.20416938956715[/C][C]1.5816726919842[/C][/ROW]
[ROW][C]108[/C][C]1.40602462566043[/C][C]-6.65804712080839[/C][C]9.47009637212924[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14575&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14575&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
971.324311642062001.255898801191401.39272448293260
981.352101738130371.263690896057491.44051258020325
991.353526070689001.249329273506511.4577228678715
1001.383984294836921.264307616079401.50366097359445
1011.396688489212561.263935072860841.52944190556429
1021.407777086667461.262983190813961.55257098252096
1031.421336158818601.264981639170511.57769067846668
1041.426984308097341.260383636253721.59358497994095
1051.452421664785411.273969412319301.63087391725152
1061.423551042868421.239644897429961.60745718830689
1071.392921040775671.204169389567151.5816726919842
1081.40602462566043-6.658047120808399.47009637212924



Parameters (Session):
par2 = grey ; par3 = FALSE ; par4 = Unknown ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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')