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Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Wed, 26 Dec 2012 10:42:38 -0500

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/26/t1356536640hgotujzbh6284qz.htm/, Retrieved Fri, 19 Apr 2024 07:23:13 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=204735, Retrieved Fri, 19 Apr 2024 07:23:13 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

150

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Exponential Smoothing] [] [2012-12-26 13:21:24] [984faca3bcb6f67338b0016ae158a29e]
-   PD    [Exponential Smoothing] [] [2012-12-26 15:42:38] [f369ceac14ec552c853c67dff6d1d312] [Current]

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Dataseries X:

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Histogram

Boxplots

0,67
0,66
0,66
0,67
0,67
0,67
0,67
0,68
0,68
0,67
0,67
0,67
0,67
0,67
0,69
0,69
0,69
0,69
0,69
0,69
0,7
0,69
0,68
0,7
0,7
0,71
0,69
0,7
0,7
0,71
0,71
0,71
0,71
0,7
0,7
0,71
0,71
0,71
0,71
0,7
0,69
0,7
0,7
0,7
0,71
0,7
0,7
0,69
0,7
0,71
0,71
0,71
0,71
0,71
0,71
0,71
0,71
0,69
0,7
0,7
0,7
0,72
0,7
0,69
0,7
0,71
0,72
0,72
0,73
0,72
0,74
0,75

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'George Udny Yule' @ yule.wessa.net

\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 & 4 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204735&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204735&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204735&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'George Udny Yule' @ yule.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.787756634642108
beta	0.170864350599678
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.787756634642108 \tabularnewline
beta & 0.170864350599678 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204735&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]0.787756634642108[/C][/ROW]
[ROW][C]beta[/C][C]0.170864350599678[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204735&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204735&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
Parameter	Value
alpha	0.787756634642108
beta	0.170864350599678
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	0.66	0.65	0.01
4	0.67	0.649223561604508	0.0207764383954918
5	0.67	0.659732832808904	0.0102671671910959
6	0.67	0.663345311732104	0.00665468826789584
7	0.67	0.665007754301312	0.00499224569868784
8	0.68	0.666032550610679	0.0139674493893209
9	0.68	0.676007635239166	0.00399236476083364
10	0.67	0.67866215117411	-0.00866215117410984
11	0.67	0.670182066782599	-0.000182066782598689
12	0.67	0.668357719030222	0.00164228096977781
13	0.67	0.668191563563452	0.00180843643654849
14	0.67	0.668399712854826	0.00160028714517402
15	0.69	0.668659289051822	0.0213407109481775
16	0.69	0.687341964644327	0.00265803535567255
17	0.69	0.691665008884427	-0.00166500888442678
18	0.69	0.692358436936225	-0.00235843693622539
19	0.69	0.692188167946307	-0.00218816794630694
20	0.69	0.691857503114908	-0.00185750311490784
21	0.7	0.691537302659831	0.00846269734016858
22	0.69	0.700485983633127	-0.0104859836331272
23	0.68	0.693096307027336	-0.0130963070273357
24	0.7	0.68188757413347	0.0181124258665296
25	0.7	0.697701651568401	0.00229834843159882
26	0.71	0.701367441192258	0.00863255880774239
27	0.69	0.711184985387178	-0.0211849853871779
28	0.7	0.694662072326437	0.00533792767356311
29	0.7	0.699751242532993	0.00024875746700681
30	0.71	0.700864867781612	0.00913513221838769
31	0.71	0.710208378163343	-0.000208378163342737
32	0.71	0.712163428649043	-0.00216342864904273
33	0.71	0.71228717867329	-0.00228717867329009
34	0.7	0.712005590630035	-0.0120055906300349
35	0.7	0.702452312283813	-0.0024523122838126
36	0.71	0.700094612266874	0.00990538773312633
37	0.71	0.708805032919025	0.00119496708097455
38	0.71	0.710814603914377	-0.000814603914377265
39	0.71	0.711131476724759	-0.00113147672475922
40	0.7	0.711046434645809	-0.0110464346458089
41	0.69	0.701663973817152	-0.0116639738171516
42	0.7	0.690225077064284	0.00977492293571625
43	0.7	0.696990513459859	0.0030094865401411
44	0.7	0.698831507909801	0.00116849209019876
45	0.71	0.699379525248714	0.0106204747512858
46	0.7	0.708802915504807	-0.00880291550480705
47	0.7	0.701740532966739	-0.00174053296673882
48	0.69	0.700007314217437	-0.0100073142174368
49	0.7	0.690414903942477	0.00958509605752322
50	0.71	0.69754669423442	0.0124533057655797
51	0.71	0.708614144804228	0.00138585519577195
52	0.71	0.711149673211287	-0.00114967321128656
53	0.71	0.711533076824287	-0.00153307682428716
54	0.71	0.711408100283823	-0.00140810028382332
55	0.71	0.711192045211791	-0.00119204521179084
56	0.71	0.71098574023595	-0.000985740235950328
57	0.71	0.710809273205258	-0.000809273205258476
58	0.69	0.710662891459112	-0.0206628914591123
59	0.7	0.692095474819608	0.00790452518039231
60	0.7	0.697096175513482	0.00290382448651805
61	0.7	0.698548394456814	0.00145160554318546
62	0.72	0.699052003710358	0.0209479962896422
63	0.7	0.717733614493226	-0.017733614493226
64	0.69	0.703556593641583	-0.0135565936415833
65	0.7	0.690845337603122	0.00915466239687801
66	0.71	0.697257237407573	0.0127427625924271
67	0.72	0.708210856749262	0.0117891432507381
68	0.72	0.720000069218853	-6.92188526496551e-08
69	0.73	0.722502242031493	0.00749775796850694
70	0.72	0.731920072623566	-0.0119200726235655
71	0.74	0.724436942213639	0.0155630577863609
72	0.75	0.740698610323044	0.00930138967695582

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 0.66 & 0.65 & 0.01 \tabularnewline
4 & 0.67 & 0.649223561604508 & 0.0207764383954918 \tabularnewline
5 & 0.67 & 0.659732832808904 & 0.0102671671910959 \tabularnewline
6 & 0.67 & 0.663345311732104 & 0.00665468826789584 \tabularnewline
7 & 0.67 & 0.665007754301312 & 0.00499224569868784 \tabularnewline
8 & 0.68 & 0.666032550610679 & 0.0139674493893209 \tabularnewline
9 & 0.68 & 0.676007635239166 & 0.00399236476083364 \tabularnewline
10 & 0.67 & 0.67866215117411 & -0.00866215117410984 \tabularnewline
11 & 0.67 & 0.670182066782599 & -0.000182066782598689 \tabularnewline
12 & 0.67 & 0.668357719030222 & 0.00164228096977781 \tabularnewline
13 & 0.67 & 0.668191563563452 & 0.00180843643654849 \tabularnewline
14 & 0.67 & 0.668399712854826 & 0.00160028714517402 \tabularnewline
15 & 0.69 & 0.668659289051822 & 0.0213407109481775 \tabularnewline
16 & 0.69 & 0.687341964644327 & 0.00265803535567255 \tabularnewline
17 & 0.69 & 0.691665008884427 & -0.00166500888442678 \tabularnewline
18 & 0.69 & 0.692358436936225 & -0.00235843693622539 \tabularnewline
19 & 0.69 & 0.692188167946307 & -0.00218816794630694 \tabularnewline
20 & 0.69 & 0.691857503114908 & -0.00185750311490784 \tabularnewline
21 & 0.7 & 0.691537302659831 & 0.00846269734016858 \tabularnewline
22 & 0.69 & 0.700485983633127 & -0.0104859836331272 \tabularnewline
23 & 0.68 & 0.693096307027336 & -0.0130963070273357 \tabularnewline
24 & 0.7 & 0.68188757413347 & 0.0181124258665296 \tabularnewline
25 & 0.7 & 0.697701651568401 & 0.00229834843159882 \tabularnewline
26 & 0.71 & 0.701367441192258 & 0.00863255880774239 \tabularnewline
27 & 0.69 & 0.711184985387178 & -0.0211849853871779 \tabularnewline
28 & 0.7 & 0.694662072326437 & 0.00533792767356311 \tabularnewline
29 & 0.7 & 0.699751242532993 & 0.00024875746700681 \tabularnewline
30 & 0.71 & 0.700864867781612 & 0.00913513221838769 \tabularnewline
31 & 0.71 & 0.710208378163343 & -0.000208378163342737 \tabularnewline
32 & 0.71 & 0.712163428649043 & -0.00216342864904273 \tabularnewline
33 & 0.71 & 0.71228717867329 & -0.00228717867329009 \tabularnewline
34 & 0.7 & 0.712005590630035 & -0.0120055906300349 \tabularnewline
35 & 0.7 & 0.702452312283813 & -0.0024523122838126 \tabularnewline
36 & 0.71 & 0.700094612266874 & 0.00990538773312633 \tabularnewline
37 & 0.71 & 0.708805032919025 & 0.00119496708097455 \tabularnewline
38 & 0.71 & 0.710814603914377 & -0.000814603914377265 \tabularnewline
39 & 0.71 & 0.711131476724759 & -0.00113147672475922 \tabularnewline
40 & 0.7 & 0.711046434645809 & -0.0110464346458089 \tabularnewline
41 & 0.69 & 0.701663973817152 & -0.0116639738171516 \tabularnewline
42 & 0.7 & 0.690225077064284 & 0.00977492293571625 \tabularnewline
43 & 0.7 & 0.696990513459859 & 0.0030094865401411 \tabularnewline
44 & 0.7 & 0.698831507909801 & 0.00116849209019876 \tabularnewline
45 & 0.71 & 0.699379525248714 & 0.0106204747512858 \tabularnewline
46 & 0.7 & 0.708802915504807 & -0.00880291550480705 \tabularnewline
47 & 0.7 & 0.701740532966739 & -0.00174053296673882 \tabularnewline
48 & 0.69 & 0.700007314217437 & -0.0100073142174368 \tabularnewline
49 & 0.7 & 0.690414903942477 & 0.00958509605752322 \tabularnewline
50 & 0.71 & 0.69754669423442 & 0.0124533057655797 \tabularnewline
51 & 0.71 & 0.708614144804228 & 0.00138585519577195 \tabularnewline
52 & 0.71 & 0.711149673211287 & -0.00114967321128656 \tabularnewline
53 & 0.71 & 0.711533076824287 & -0.00153307682428716 \tabularnewline
54 & 0.71 & 0.711408100283823 & -0.00140810028382332 \tabularnewline
55 & 0.71 & 0.711192045211791 & -0.00119204521179084 \tabularnewline
56 & 0.71 & 0.71098574023595 & -0.000985740235950328 \tabularnewline
57 & 0.71 & 0.710809273205258 & -0.000809273205258476 \tabularnewline
58 & 0.69 & 0.710662891459112 & -0.0206628914591123 \tabularnewline
59 & 0.7 & 0.692095474819608 & 0.00790452518039231 \tabularnewline
60 & 0.7 & 0.697096175513482 & 0.00290382448651805 \tabularnewline
61 & 0.7 & 0.698548394456814 & 0.00145160554318546 \tabularnewline
62 & 0.72 & 0.699052003710358 & 0.0209479962896422 \tabularnewline
63 & 0.7 & 0.717733614493226 & -0.017733614493226 \tabularnewline
64 & 0.69 & 0.703556593641583 & -0.0135565936415833 \tabularnewline
65 & 0.7 & 0.690845337603122 & 0.00915466239687801 \tabularnewline
66 & 0.71 & 0.697257237407573 & 0.0127427625924271 \tabularnewline
67 & 0.72 & 0.708210856749262 & 0.0117891432507381 \tabularnewline
68 & 0.72 & 0.720000069218853 & -6.92188526496551e-08 \tabularnewline
69 & 0.73 & 0.722502242031493 & 0.00749775796850694 \tabularnewline
70 & 0.72 & 0.731920072623566 & -0.0119200726235655 \tabularnewline
71 & 0.74 & 0.724436942213639 & 0.0155630577863609 \tabularnewline
72 & 0.75 & 0.740698610323044 & 0.00930138967695582 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204735&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]3[/C][C]0.66[/C][C]0.65[/C][C]0.01[/C][/ROW]
[ROW][C]4[/C][C]0.67[/C][C]0.649223561604508[/C][C]0.0207764383954918[/C][/ROW]
[ROW][C]5[/C][C]0.67[/C][C]0.659732832808904[/C][C]0.0102671671910959[/C][/ROW]
[ROW][C]6[/C][C]0.67[/C][C]0.663345311732104[/C][C]0.00665468826789584[/C][/ROW]
[ROW][C]7[/C][C]0.67[/C][C]0.665007754301312[/C][C]0.00499224569868784[/C][/ROW]
[ROW][C]8[/C][C]0.68[/C][C]0.666032550610679[/C][C]0.0139674493893209[/C][/ROW]
[ROW][C]9[/C][C]0.68[/C][C]0.676007635239166[/C][C]0.00399236476083364[/C][/ROW]
[ROW][C]10[/C][C]0.67[/C][C]0.67866215117411[/C][C]-0.00866215117410984[/C][/ROW]
[ROW][C]11[/C][C]0.67[/C][C]0.670182066782599[/C][C]-0.000182066782598689[/C][/ROW]
[ROW][C]12[/C][C]0.67[/C][C]0.668357719030222[/C][C]0.00164228096977781[/C][/ROW]
[ROW][C]13[/C][C]0.67[/C][C]0.668191563563452[/C][C]0.00180843643654849[/C][/ROW]
[ROW][C]14[/C][C]0.67[/C][C]0.668399712854826[/C][C]0.00160028714517402[/C][/ROW]
[ROW][C]15[/C][C]0.69[/C][C]0.668659289051822[/C][C]0.0213407109481775[/C][/ROW]
[ROW][C]16[/C][C]0.69[/C][C]0.687341964644327[/C][C]0.00265803535567255[/C][/ROW]
[ROW][C]17[/C][C]0.69[/C][C]0.691665008884427[/C][C]-0.00166500888442678[/C][/ROW]
[ROW][C]18[/C][C]0.69[/C][C]0.692358436936225[/C][C]-0.00235843693622539[/C][/ROW]
[ROW][C]19[/C][C]0.69[/C][C]0.692188167946307[/C][C]-0.00218816794630694[/C][/ROW]
[ROW][C]20[/C][C]0.69[/C][C]0.691857503114908[/C][C]-0.00185750311490784[/C][/ROW]
[ROW][C]21[/C][C]0.7[/C][C]0.691537302659831[/C][C]0.00846269734016858[/C][/ROW]
[ROW][C]22[/C][C]0.69[/C][C]0.700485983633127[/C][C]-0.0104859836331272[/C][/ROW]
[ROW][C]23[/C][C]0.68[/C][C]0.693096307027336[/C][C]-0.0130963070273357[/C][/ROW]
[ROW][C]24[/C][C]0.7[/C][C]0.68188757413347[/C][C]0.0181124258665296[/C][/ROW]
[ROW][C]25[/C][C]0.7[/C][C]0.697701651568401[/C][C]0.00229834843159882[/C][/ROW]
[ROW][C]26[/C][C]0.71[/C][C]0.701367441192258[/C][C]0.00863255880774239[/C][/ROW]
[ROW][C]27[/C][C]0.69[/C][C]0.711184985387178[/C][C]-0.0211849853871779[/C][/ROW]
[ROW][C]28[/C][C]0.7[/C][C]0.694662072326437[/C][C]0.00533792767356311[/C][/ROW]
[ROW][C]29[/C][C]0.7[/C][C]0.699751242532993[/C][C]0.00024875746700681[/C][/ROW]
[ROW][C]30[/C][C]0.71[/C][C]0.700864867781612[/C][C]0.00913513221838769[/C][/ROW]
[ROW][C]31[/C][C]0.71[/C][C]0.710208378163343[/C][C]-0.000208378163342737[/C][/ROW]
[ROW][C]32[/C][C]0.71[/C][C]0.712163428649043[/C][C]-0.00216342864904273[/C][/ROW]
[ROW][C]33[/C][C]0.71[/C][C]0.71228717867329[/C][C]-0.00228717867329009[/C][/ROW]
[ROW][C]34[/C][C]0.7[/C][C]0.712005590630035[/C][C]-0.0120055906300349[/C][/ROW]
[ROW][C]35[/C][C]0.7[/C][C]0.702452312283813[/C][C]-0.0024523122838126[/C][/ROW]
[ROW][C]36[/C][C]0.71[/C][C]0.700094612266874[/C][C]0.00990538773312633[/C][/ROW]
[ROW][C]37[/C][C]0.71[/C][C]0.708805032919025[/C][C]0.00119496708097455[/C][/ROW]
[ROW][C]38[/C][C]0.71[/C][C]0.710814603914377[/C][C]-0.000814603914377265[/C][/ROW]
[ROW][C]39[/C][C]0.71[/C][C]0.711131476724759[/C][C]-0.00113147672475922[/C][/ROW]
[ROW][C]40[/C][C]0.7[/C][C]0.711046434645809[/C][C]-0.0110464346458089[/C][/ROW]
[ROW][C]41[/C][C]0.69[/C][C]0.701663973817152[/C][C]-0.0116639738171516[/C][/ROW]
[ROW][C]42[/C][C]0.7[/C][C]0.690225077064284[/C][C]0.00977492293571625[/C][/ROW]
[ROW][C]43[/C][C]0.7[/C][C]0.696990513459859[/C][C]0.0030094865401411[/C][/ROW]
[ROW][C]44[/C][C]0.7[/C][C]0.698831507909801[/C][C]0.00116849209019876[/C][/ROW]
[ROW][C]45[/C][C]0.71[/C][C]0.699379525248714[/C][C]0.0106204747512858[/C][/ROW]
[ROW][C]46[/C][C]0.7[/C][C]0.708802915504807[/C][C]-0.00880291550480705[/C][/ROW]
[ROW][C]47[/C][C]0.7[/C][C]0.701740532966739[/C][C]-0.00174053296673882[/C][/ROW]
[ROW][C]48[/C][C]0.69[/C][C]0.700007314217437[/C][C]-0.0100073142174368[/C][/ROW]
[ROW][C]49[/C][C]0.7[/C][C]0.690414903942477[/C][C]0.00958509605752322[/C][/ROW]
[ROW][C]50[/C][C]0.71[/C][C]0.69754669423442[/C][C]0.0124533057655797[/C][/ROW]
[ROW][C]51[/C][C]0.71[/C][C]0.708614144804228[/C][C]0.00138585519577195[/C][/ROW]
[ROW][C]52[/C][C]0.71[/C][C]0.711149673211287[/C][C]-0.00114967321128656[/C][/ROW]
[ROW][C]53[/C][C]0.71[/C][C]0.711533076824287[/C][C]-0.00153307682428716[/C][/ROW]
[ROW][C]54[/C][C]0.71[/C][C]0.711408100283823[/C][C]-0.00140810028382332[/C][/ROW]
[ROW][C]55[/C][C]0.71[/C][C]0.711192045211791[/C][C]-0.00119204521179084[/C][/ROW]
[ROW][C]56[/C][C]0.71[/C][C]0.71098574023595[/C][C]-0.000985740235950328[/C][/ROW]
[ROW][C]57[/C][C]0.71[/C][C]0.710809273205258[/C][C]-0.000809273205258476[/C][/ROW]
[ROW][C]58[/C][C]0.69[/C][C]0.710662891459112[/C][C]-0.0206628914591123[/C][/ROW]
[ROW][C]59[/C][C]0.7[/C][C]0.692095474819608[/C][C]0.00790452518039231[/C][/ROW]
[ROW][C]60[/C][C]0.7[/C][C]0.697096175513482[/C][C]0.00290382448651805[/C][/ROW]
[ROW][C]61[/C][C]0.7[/C][C]0.698548394456814[/C][C]0.00145160554318546[/C][/ROW]
[ROW][C]62[/C][C]0.72[/C][C]0.699052003710358[/C][C]0.0209479962896422[/C][/ROW]
[ROW][C]63[/C][C]0.7[/C][C]0.717733614493226[/C][C]-0.017733614493226[/C][/ROW]
[ROW][C]64[/C][C]0.69[/C][C]0.703556593641583[/C][C]-0.0135565936415833[/C][/ROW]
[ROW][C]65[/C][C]0.7[/C][C]0.690845337603122[/C][C]0.00915466239687801[/C][/ROW]
[ROW][C]66[/C][C]0.71[/C][C]0.697257237407573[/C][C]0.0127427625924271[/C][/ROW]
[ROW][C]67[/C][C]0.72[/C][C]0.708210856749262[/C][C]0.0117891432507381[/C][/ROW]
[ROW][C]68[/C][C]0.72[/C][C]0.720000069218853[/C][C]-6.92188526496551e-08[/C][/ROW]
[ROW][C]69[/C][C]0.73[/C][C]0.722502242031493[/C][C]0.00749775796850694[/C][/ROW]
[ROW][C]70[/C][C]0.72[/C][C]0.731920072623566[/C][C]-0.0119200726235655[/C][/ROW]
[ROW][C]71[/C][C]0.74[/C][C]0.724436942213639[/C][C]0.0155630577863609[/C][/ROW]
[ROW][C]72[/C][C]0.75[/C][C]0.740698610323044[/C][C]0.00930138967695582[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204735&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204735&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
t	Observed	Fitted	Residuals
3	0.66	0.65	0.01
4	0.67	0.649223561604508	0.0207764383954918
5	0.67	0.659732832808904	0.0102671671910959
6	0.67	0.663345311732104	0.00665468826789584
7	0.67	0.665007754301312	0.00499224569868784
8	0.68	0.666032550610679	0.0139674493893209
9	0.68	0.676007635239166	0.00399236476083364
10	0.67	0.67866215117411	-0.00866215117410984
11	0.67	0.670182066782599	-0.000182066782598689
12	0.67	0.668357719030222	0.00164228096977781
13	0.67	0.668191563563452	0.00180843643654849
14	0.67	0.668399712854826	0.00160028714517402
15	0.69	0.668659289051822	0.0213407109481775
16	0.69	0.687341964644327	0.00265803535567255
17	0.69	0.691665008884427	-0.00166500888442678
18	0.69	0.692358436936225	-0.00235843693622539
19	0.69	0.692188167946307	-0.00218816794630694
20	0.69	0.691857503114908	-0.00185750311490784
21	0.7	0.691537302659831	0.00846269734016858
22	0.69	0.700485983633127	-0.0104859836331272
23	0.68	0.693096307027336	-0.0130963070273357
24	0.7	0.68188757413347	0.0181124258665296
25	0.7	0.697701651568401	0.00229834843159882
26	0.71	0.701367441192258	0.00863255880774239
27	0.69	0.711184985387178	-0.0211849853871779
28	0.7	0.694662072326437	0.00533792767356311
29	0.7	0.699751242532993	0.00024875746700681
30	0.71	0.700864867781612	0.00913513221838769
31	0.71	0.710208378163343	-0.000208378163342737
32	0.71	0.712163428649043	-0.00216342864904273
33	0.71	0.71228717867329	-0.00228717867329009
34	0.7	0.712005590630035	-0.0120055906300349
35	0.7	0.702452312283813	-0.0024523122838126
36	0.71	0.700094612266874	0.00990538773312633
37	0.71	0.708805032919025	0.00119496708097455
38	0.71	0.710814603914377	-0.000814603914377265
39	0.71	0.711131476724759	-0.00113147672475922
40	0.7	0.711046434645809	-0.0110464346458089
41	0.69	0.701663973817152	-0.0116639738171516
42	0.7	0.690225077064284	0.00977492293571625
43	0.7	0.696990513459859	0.0030094865401411
44	0.7	0.698831507909801	0.00116849209019876
45	0.71	0.699379525248714	0.0106204747512858
46	0.7	0.708802915504807	-0.00880291550480705
47	0.7	0.701740532966739	-0.00174053296673882
48	0.69	0.700007314217437	-0.0100073142174368
49	0.7	0.690414903942477	0.00958509605752322
50	0.71	0.69754669423442	0.0124533057655797
51	0.71	0.708614144804228	0.00138585519577195
52	0.71	0.711149673211287	-0.00114967321128656
53	0.71	0.711533076824287	-0.00153307682428716
54	0.71	0.711408100283823	-0.00140810028382332
55	0.71	0.711192045211791	-0.00119204521179084
56	0.71	0.71098574023595	-0.000985740235950328
57	0.71	0.710809273205258	-0.000809273205258476
58	0.69	0.710662891459112	-0.0206628914591123
59	0.7	0.692095474819608	0.00790452518039231
60	0.7	0.697096175513482	0.00290382448651805
61	0.7	0.698548394456814	0.00145160554318546
62	0.72	0.699052003710358	0.0209479962896422
63	0.7	0.717733614493226	-0.017733614493226
64	0.69	0.703556593641583	-0.0135565936415833
65	0.7	0.690845337603122	0.00915466239687801
66	0.71	0.697257237407573	0.0127427625924271
67	0.72	0.708210856749262	0.0117891432507381
68	0.72	0.720000069218853	-6.92188526496551e-08
69	0.73	0.722502242031493	0.00749775796850694
70	0.72	0.731920072623566	-0.0119200726235655
71	0.74	0.724436942213639	0.0155630577863609
72	0.75	0.740698610323044	0.00930138967695582

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	0.753279570475219	0.734784501790855	0.771774639159583
74	0.75853329919798	0.733372249344088	0.783694349051872
75	0.763787027920741	0.731924494571482	0.79564956127
76	0.769040756643502	0.730299436725476	0.807782076561529
77	0.774294485366263	0.728441683481008	0.820147287251519
78	0.779548214089025	0.7263280652265	0.832768362951549
79	0.784801942811786	0.723949672681931	0.845654212941641
80	0.790055671534547	0.721304543950667	0.858806799118427
81	0.795309400257308	0.71839428447668	0.872224516037936
82	0.800563128980069	0.715222366429352	0.885903891530786
83	0.80581685770283	0.711793221345103	0.899840494060557
84	0.811070586425591	0.708111736114276	0.914029436736906

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 0.753279570475219 & 0.734784501790855 & 0.771774639159583 \tabularnewline
74 & 0.75853329919798 & 0.733372249344088 & 0.783694349051872 \tabularnewline
75 & 0.763787027920741 & 0.731924494571482 & 0.79564956127 \tabularnewline
76 & 0.769040756643502 & 0.730299436725476 & 0.807782076561529 \tabularnewline
77 & 0.774294485366263 & 0.728441683481008 & 0.820147287251519 \tabularnewline
78 & 0.779548214089025 & 0.7263280652265 & 0.832768362951549 \tabularnewline
79 & 0.784801942811786 & 0.723949672681931 & 0.845654212941641 \tabularnewline
80 & 0.790055671534547 & 0.721304543950667 & 0.858806799118427 \tabularnewline
81 & 0.795309400257308 & 0.71839428447668 & 0.872224516037936 \tabularnewline
82 & 0.800563128980069 & 0.715222366429352 & 0.885903891530786 \tabularnewline
83 & 0.80581685770283 & 0.711793221345103 & 0.899840494060557 \tabularnewline
84 & 0.811070586425591 & 0.708111736114276 & 0.914029436736906 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204735&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]73[/C][C]0.753279570475219[/C][C]0.734784501790855[/C][C]0.771774639159583[/C][/ROW]
[ROW][C]74[/C][C]0.75853329919798[/C][C]0.733372249344088[/C][C]0.783694349051872[/C][/ROW]
[ROW][C]75[/C][C]0.763787027920741[/C][C]0.731924494571482[/C][C]0.79564956127[/C][/ROW]
[ROW][C]76[/C][C]0.769040756643502[/C][C]0.730299436725476[/C][C]0.807782076561529[/C][/ROW]
[ROW][C]77[/C][C]0.774294485366263[/C][C]0.728441683481008[/C][C]0.820147287251519[/C][/ROW]
[ROW][C]78[/C][C]0.779548214089025[/C][C]0.7263280652265[/C][C]0.832768362951549[/C][/ROW]
[ROW][C]79[/C][C]0.784801942811786[/C][C]0.723949672681931[/C][C]0.845654212941641[/C][/ROW]
[ROW][C]80[/C][C]0.790055671534547[/C][C]0.721304543950667[/C][C]0.858806799118427[/C][/ROW]
[ROW][C]81[/C][C]0.795309400257308[/C][C]0.71839428447668[/C][C]0.872224516037936[/C][/ROW]
[ROW][C]82[/C][C]0.800563128980069[/C][C]0.715222366429352[/C][C]0.885903891530786[/C][/ROW]
[ROW][C]83[/C][C]0.80581685770283[/C][C]0.711793221345103[/C][C]0.899840494060557[/C][/ROW]
[ROW][C]84[/C][C]0.811070586425591[/C][C]0.708111736114276[/C][C]0.914029436736906[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204735&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204735&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
t	Forecast	95% Lower Bound	95% Upper Bound
73	0.753279570475219	0.734784501790855	0.771774639159583
74	0.75853329919798	0.733372249344088	0.783694349051872
75	0.763787027920741	0.731924494571482	0.79564956127
76	0.769040756643502	0.730299436725476	0.807782076561529
77	0.774294485366263	0.728441683481008	0.820147287251519
78	0.779548214089025	0.7263280652265	0.832768362951549
79	0.784801942811786	0.723949672681931	0.845654212941641
80	0.790055671534547	0.721304543950667	0.858806799118427
81	0.795309400257308	0.71839428447668	0.872224516037936
82	0.800563128980069	0.715222366429352	0.885903891530786
83	0.80581685770283	0.711793221345103	0.899840494060557
84	0.811070586425591	0.708111736114276	0.914029436736906

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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=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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code