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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Thu, 22 May 2008 08:03:16 -0600

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/2008/May/22/t1211465149intazvhe49fkqg0.htm/, Retrieved Tue, 14 May 2024 03:11:33 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13021, Retrieved Tue, 14 May 2024 03:11:33 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

224

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

-       [Exponential Smoothing] [Gemiddelde prijs ...] [2008-05-22 14:03:16] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Dataseries X:

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Boxplots

0,33
0,35
0,35
0,34
0,37
0,38
0,39
0,37
0,37
0,37
0,37
0,38
0,36
0,36
0,36
0,36
0,38
0,37
0,39
0,39
0,4
0,42
0,42
0,4
0,36
0,36
0,36
0,36
0,35
0,38
0,4
0,39
0,39
0,39
0,36
0,35
0,35
0,33
0,33
0,32
0,36
0,37
0,38
0,38
0,38
0,38
0,39
0,4
0,38
0,41
0,41
0,43
0,42
0,41
0,41
0,43
0,44
0,46
0,44
0,43
0,43
0,42
0,42
0,42
0,43
0,44
0,45
0,44
0,47
0,48
0,48
0,45
0,44
0,44
0,45
0,46
0,45
0,46
0,47
0,48
0,48
0,46
0,47
0,47
0,43
0,41
0,39
0,41
0,44
0,45
0,45
0,46
0,45
0,45
0,46
0,46

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13021&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13021&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13021&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	2 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.841006539333911
beta	0
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.841006539333911 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13021&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]0.841006539333911[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13021&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13021&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	0.841006539333911
beta	0
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	0.36	0.354168721864335	0.00583127813566497
14	0.36	0.358265959594702	0.00173404040529840
15	0.36	0.357714665960194	0.00228533403980585
16	0.36	0.356450497137153	0.00354950286284744
17	0.38	0.375248721294845	0.00475127870515524
18	0.37	0.366454836418137	0.00354516358186269
19	0.39	0.388561175974231	0.00143882402576945
20	0.39	0.389771236388853	0.000228763611146654
21	0.4	0.399962695468502	3.73045314979725e-05
22	0.42	0.41999377226461	6.22773538955235e-06
23	0.42	0.421370062093576	-0.00137006209357576
24	0.4	0.401080320516783	-0.00108032051678314
25	0.36	0.37287669013049	-0.0128766901304904
26	0.36	0.360579552610568	-0.000579552610567746
27	0.36	0.358167729915886	0.00183227008411407
28	0.36	0.356721258383452	0.0032787416165479
29	0.35	0.375451722368071	-0.025451722368071
30	0.38	0.341947527779654	0.0380524722203462
31	0.4	0.392939718067491	0.00706028193250913
32	0.39	0.398680671937991	-0.00868067193799055
33	0.39	0.401384074199658	-0.0113840741996585
34	0.39	0.411395362682129	-0.0213953626821292
35	0.36	0.394480424556518	-0.0344804245565176
36	0.35	0.348868532187066	0.00113146781293416
37	0.35	0.324255375431368	0.0257446245686317
38	0.33	0.346374979781771	-0.016374979781771
39	0.33	0.331178679034397	-0.001178679034397
40	0.32	0.327654643061797	-0.00765464306179681
41	0.36	0.331175132966034	0.0288248670339658
42	0.37	0.352857888890978	0.0171421111090218
43	0.38	0.380849704025799	-0.000849704025799314
44	0.38	0.377545196333015	0.00245480366698503
45	0.38	0.388885662661695	-0.0088856626616951
46	0.38	0.398858044040577	-0.0188580440405772
47	0.39	0.38158739313176	0.00841260686823964
48	0.4	0.376838409032491	0.0231615909675089
49	0.38	0.371510696837184	0.00848930316281599
50	0.41	0.371795243930462	0.0382047560695378
51	0.41	0.405138344847736	0.00486165515226394
52	0.43	0.404779120023733	0.0252208799762673
53	0.42	0.446551397531768	-0.0265513975317682
54	0.41	0.418890906862472	-0.00889090686247168
55	0.41	0.423327191628258	-0.0133271916282584
56	0.43	0.409877629034235	0.0201223709657654
57	0.44	0.43516284611313	0.00483715388687
58	0.46	0.457419222733862	0.0025807772661377
59	0.44	0.463097787048965	-0.0230977870489652
60	0.43	0.432682919853982	-0.002682919853982
61	0.43	0.401195212514832	0.0288047874851679
62	0.42	0.422494194554144	-0.00249419455414446
63	0.42	0.416196279419709	0.00380372058029144
64	0.42	0.41795232043303	0.00204767956696966
65	0.43	0.431491381418336	-0.00149138141833588
66	0.44	0.427626624570958	0.0123733754290418
67	0.45	0.449945737531405	5.42624685953008e-05
68	0.44	0.453229223192051	-0.0132292231920506
69	0.47	0.448194926265441	0.0218050737345586
70	0.48	0.485435798511558	-0.00543579851155845
71	0.48	0.480095501569868	-9.55015698678174e-05
72	0.45	0.471564862662166	-0.0215648626621663
73	0.44	0.427608752169333	0.0123912478306673
74	0.44	0.429977921153402	0.0100220788465976
75	0.45	0.435062591504202	0.0149374084957979
76	0.46	0.445788243938788	0.0142117560612118
77	0.45	0.470005218999662	-0.0200052189996620
78	0.46	0.452703462501075	0.00729653749892489
79	0.47	0.469220487753507	0.000779512246492975
80	0.48	0.470996383531979	0.00900361646802111
81	0.48	0.491104277428729	-0.0111042774287292
82	0.46	0.496693396821315	-0.0366933968213146
83	0.47	0.465911954756431	0.00408804524356932
84	0.47	0.457615348774467	0.0123846512255326
85	0.43	0.446742803797396	-0.0167428037973964
86	0.41	0.424343805119414	-0.0143438051194145
87	0.39	0.409817091292825	-0.0198170912928252
88	0.41	0.391393683328863	0.0186063166711372
89	0.44	0.412976062794227	0.0270239372057733
90	0.45	0.439429166345048	0.0105708336549523
91	0.45	0.457426281922807	-0.00742628192280742
92	0.46	0.453489671319325	0.0065103286806748
93	0.45	0.46786169251636	-0.0178616925163598
94	0.45	0.462720207810253	-0.0127202078102533
95	0.46	0.458465877973486	0.00153412202651398
96	0.46	0.449524660402054	0.0104753395979463

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 0.36 & 0.354168721864335 & 0.00583127813566497 \tabularnewline
14 & 0.36 & 0.358265959594702 & 0.00173404040529840 \tabularnewline
15 & 0.36 & 0.357714665960194 & 0.00228533403980585 \tabularnewline
16 & 0.36 & 0.356450497137153 & 0.00354950286284744 \tabularnewline
17 & 0.38 & 0.375248721294845 & 0.00475127870515524 \tabularnewline
18 & 0.37 & 0.366454836418137 & 0.00354516358186269 \tabularnewline
19 & 0.39 & 0.388561175974231 & 0.00143882402576945 \tabularnewline
20 & 0.39 & 0.389771236388853 & 0.000228763611146654 \tabularnewline
21 & 0.4 & 0.399962695468502 & 3.73045314979725e-05 \tabularnewline
22 & 0.42 & 0.41999377226461 & 6.22773538955235e-06 \tabularnewline
23 & 0.42 & 0.421370062093576 & -0.00137006209357576 \tabularnewline
24 & 0.4 & 0.401080320516783 & -0.00108032051678314 \tabularnewline
25 & 0.36 & 0.37287669013049 & -0.0128766901304904 \tabularnewline
26 & 0.36 & 0.360579552610568 & -0.000579552610567746 \tabularnewline
27 & 0.36 & 0.358167729915886 & 0.00183227008411407 \tabularnewline
28 & 0.36 & 0.356721258383452 & 0.0032787416165479 \tabularnewline
29 & 0.35 & 0.375451722368071 & -0.025451722368071 \tabularnewline
30 & 0.38 & 0.341947527779654 & 0.0380524722203462 \tabularnewline
31 & 0.4 & 0.392939718067491 & 0.00706028193250913 \tabularnewline
32 & 0.39 & 0.398680671937991 & -0.00868067193799055 \tabularnewline
33 & 0.39 & 0.401384074199658 & -0.0113840741996585 \tabularnewline
34 & 0.39 & 0.411395362682129 & -0.0213953626821292 \tabularnewline
35 & 0.36 & 0.394480424556518 & -0.0344804245565176 \tabularnewline
36 & 0.35 & 0.348868532187066 & 0.00113146781293416 \tabularnewline
37 & 0.35 & 0.324255375431368 & 0.0257446245686317 \tabularnewline
38 & 0.33 & 0.346374979781771 & -0.016374979781771 \tabularnewline
39 & 0.33 & 0.331178679034397 & -0.001178679034397 \tabularnewline
40 & 0.32 & 0.327654643061797 & -0.00765464306179681 \tabularnewline
41 & 0.36 & 0.331175132966034 & 0.0288248670339658 \tabularnewline
42 & 0.37 & 0.352857888890978 & 0.0171421111090218 \tabularnewline
43 & 0.38 & 0.380849704025799 & -0.000849704025799314 \tabularnewline
44 & 0.38 & 0.377545196333015 & 0.00245480366698503 \tabularnewline
45 & 0.38 & 0.388885662661695 & -0.0088856626616951 \tabularnewline
46 & 0.38 & 0.398858044040577 & -0.0188580440405772 \tabularnewline
47 & 0.39 & 0.38158739313176 & 0.00841260686823964 \tabularnewline
48 & 0.4 & 0.376838409032491 & 0.0231615909675089 \tabularnewline
49 & 0.38 & 0.371510696837184 & 0.00848930316281599 \tabularnewline
50 & 0.41 & 0.371795243930462 & 0.0382047560695378 \tabularnewline
51 & 0.41 & 0.405138344847736 & 0.00486165515226394 \tabularnewline
52 & 0.43 & 0.404779120023733 & 0.0252208799762673 \tabularnewline
53 & 0.42 & 0.446551397531768 & -0.0265513975317682 \tabularnewline
54 & 0.41 & 0.418890906862472 & -0.00889090686247168 \tabularnewline
55 & 0.41 & 0.423327191628258 & -0.0133271916282584 \tabularnewline
56 & 0.43 & 0.409877629034235 & 0.0201223709657654 \tabularnewline
57 & 0.44 & 0.43516284611313 & 0.00483715388687 \tabularnewline
58 & 0.46 & 0.457419222733862 & 0.0025807772661377 \tabularnewline
59 & 0.44 & 0.463097787048965 & -0.0230977870489652 \tabularnewline
60 & 0.43 & 0.432682919853982 & -0.002682919853982 \tabularnewline
61 & 0.43 & 0.401195212514832 & 0.0288047874851679 \tabularnewline
62 & 0.42 & 0.422494194554144 & -0.00249419455414446 \tabularnewline
63 & 0.42 & 0.416196279419709 & 0.00380372058029144 \tabularnewline
64 & 0.42 & 0.41795232043303 & 0.00204767956696966 \tabularnewline
65 & 0.43 & 0.431491381418336 & -0.00149138141833588 \tabularnewline
66 & 0.44 & 0.427626624570958 & 0.0123733754290418 \tabularnewline
67 & 0.45 & 0.449945737531405 & 5.42624685953008e-05 \tabularnewline
68 & 0.44 & 0.453229223192051 & -0.0132292231920506 \tabularnewline
69 & 0.47 & 0.448194926265441 & 0.0218050737345586 \tabularnewline
70 & 0.48 & 0.485435798511558 & -0.00543579851155845 \tabularnewline
71 & 0.48 & 0.480095501569868 & -9.55015698678174e-05 \tabularnewline
72 & 0.45 & 0.471564862662166 & -0.0215648626621663 \tabularnewline
73 & 0.44 & 0.427608752169333 & 0.0123912478306673 \tabularnewline
74 & 0.44 & 0.429977921153402 & 0.0100220788465976 \tabularnewline
75 & 0.45 & 0.435062591504202 & 0.0149374084957979 \tabularnewline
76 & 0.46 & 0.445788243938788 & 0.0142117560612118 \tabularnewline
77 & 0.45 & 0.470005218999662 & -0.0200052189996620 \tabularnewline
78 & 0.46 & 0.452703462501075 & 0.00729653749892489 \tabularnewline
79 & 0.47 & 0.469220487753507 & 0.000779512246492975 \tabularnewline
80 & 0.48 & 0.470996383531979 & 0.00900361646802111 \tabularnewline
81 & 0.48 & 0.491104277428729 & -0.0111042774287292 \tabularnewline
82 & 0.46 & 0.496693396821315 & -0.0366933968213146 \tabularnewline
83 & 0.47 & 0.465911954756431 & 0.00408804524356932 \tabularnewline
84 & 0.47 & 0.457615348774467 & 0.0123846512255326 \tabularnewline
85 & 0.43 & 0.446742803797396 & -0.0167428037973964 \tabularnewline
86 & 0.41 & 0.424343805119414 & -0.0143438051194145 \tabularnewline
87 & 0.39 & 0.409817091292825 & -0.0198170912928252 \tabularnewline
88 & 0.41 & 0.391393683328863 & 0.0186063166711372 \tabularnewline
89 & 0.44 & 0.412976062794227 & 0.0270239372057733 \tabularnewline
90 & 0.45 & 0.439429166345048 & 0.0105708336549523 \tabularnewline
91 & 0.45 & 0.457426281922807 & -0.00742628192280742 \tabularnewline
92 & 0.46 & 0.453489671319325 & 0.0065103286806748 \tabularnewline
93 & 0.45 & 0.46786169251636 & -0.0178616925163598 \tabularnewline
94 & 0.45 & 0.462720207810253 & -0.0127202078102533 \tabularnewline
95 & 0.46 & 0.458465877973486 & 0.00153412202651398 \tabularnewline
96 & 0.46 & 0.449524660402054 & 0.0104753395979463 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13021&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]0.36[/C][C]0.354168721864335[/C][C]0.00583127813566497[/C][/ROW]
[ROW][C]14[/C][C]0.36[/C][C]0.358265959594702[/C][C]0.00173404040529840[/C][/ROW]
[ROW][C]15[/C][C]0.36[/C][C]0.357714665960194[/C][C]0.00228533403980585[/C][/ROW]
[ROW][C]16[/C][C]0.36[/C][C]0.356450497137153[/C][C]0.00354950286284744[/C][/ROW]
[ROW][C]17[/C][C]0.38[/C][C]0.375248721294845[/C][C]0.00475127870515524[/C][/ROW]
[ROW][C]18[/C][C]0.37[/C][C]0.366454836418137[/C][C]0.00354516358186269[/C][/ROW]
[ROW][C]19[/C][C]0.39[/C][C]0.388561175974231[/C][C]0.00143882402576945[/C][/ROW]
[ROW][C]20[/C][C]0.39[/C][C]0.389771236388853[/C][C]0.000228763611146654[/C][/ROW]
[ROW][C]21[/C][C]0.4[/C][C]0.399962695468502[/C][C]3.73045314979725e-05[/C][/ROW]
[ROW][C]22[/C][C]0.42[/C][C]0.41999377226461[/C][C]6.22773538955235e-06[/C][/ROW]
[ROW][C]23[/C][C]0.42[/C][C]0.421370062093576[/C][C]-0.00137006209357576[/C][/ROW]
[ROW][C]24[/C][C]0.4[/C][C]0.401080320516783[/C][C]-0.00108032051678314[/C][/ROW]
[ROW][C]25[/C][C]0.36[/C][C]0.37287669013049[/C][C]-0.0128766901304904[/C][/ROW]
[ROW][C]26[/C][C]0.36[/C][C]0.360579552610568[/C][C]-0.000579552610567746[/C][/ROW]
[ROW][C]27[/C][C]0.36[/C][C]0.358167729915886[/C][C]0.00183227008411407[/C][/ROW]
[ROW][C]28[/C][C]0.36[/C][C]0.356721258383452[/C][C]0.0032787416165479[/C][/ROW]
[ROW][C]29[/C][C]0.35[/C][C]0.375451722368071[/C][C]-0.025451722368071[/C][/ROW]
[ROW][C]30[/C][C]0.38[/C][C]0.341947527779654[/C][C]0.0380524722203462[/C][/ROW]
[ROW][C]31[/C][C]0.4[/C][C]0.392939718067491[/C][C]0.00706028193250913[/C][/ROW]
[ROW][C]32[/C][C]0.39[/C][C]0.398680671937991[/C][C]-0.00868067193799055[/C][/ROW]
[ROW][C]33[/C][C]0.39[/C][C]0.401384074199658[/C][C]-0.0113840741996585[/C][/ROW]
[ROW][C]34[/C][C]0.39[/C][C]0.411395362682129[/C][C]-0.0213953626821292[/C][/ROW]
[ROW][C]35[/C][C]0.36[/C][C]0.394480424556518[/C][C]-0.0344804245565176[/C][/ROW]
[ROW][C]36[/C][C]0.35[/C][C]0.348868532187066[/C][C]0.00113146781293416[/C][/ROW]
[ROW][C]37[/C][C]0.35[/C][C]0.324255375431368[/C][C]0.0257446245686317[/C][/ROW]
[ROW][C]38[/C][C]0.33[/C][C]0.346374979781771[/C][C]-0.016374979781771[/C][/ROW]
[ROW][C]39[/C][C]0.33[/C][C]0.331178679034397[/C][C]-0.001178679034397[/C][/ROW]
[ROW][C]40[/C][C]0.32[/C][C]0.327654643061797[/C][C]-0.00765464306179681[/C][/ROW]
[ROW][C]41[/C][C]0.36[/C][C]0.331175132966034[/C][C]0.0288248670339658[/C][/ROW]
[ROW][C]42[/C][C]0.37[/C][C]0.352857888890978[/C][C]0.0171421111090218[/C][/ROW]
[ROW][C]43[/C][C]0.38[/C][C]0.380849704025799[/C][C]-0.000849704025799314[/C][/ROW]
[ROW][C]44[/C][C]0.38[/C][C]0.377545196333015[/C][C]0.00245480366698503[/C][/ROW]
[ROW][C]45[/C][C]0.38[/C][C]0.388885662661695[/C][C]-0.0088856626616951[/C][/ROW]
[ROW][C]46[/C][C]0.38[/C][C]0.398858044040577[/C][C]-0.0188580440405772[/C][/ROW]
[ROW][C]47[/C][C]0.39[/C][C]0.38158739313176[/C][C]0.00841260686823964[/C][/ROW]
[ROW][C]48[/C][C]0.4[/C][C]0.376838409032491[/C][C]0.0231615909675089[/C][/ROW]
[ROW][C]49[/C][C]0.38[/C][C]0.371510696837184[/C][C]0.00848930316281599[/C][/ROW]
[ROW][C]50[/C][C]0.41[/C][C]0.371795243930462[/C][C]0.0382047560695378[/C][/ROW]
[ROW][C]51[/C][C]0.41[/C][C]0.405138344847736[/C][C]0.00486165515226394[/C][/ROW]
[ROW][C]52[/C][C]0.43[/C][C]0.404779120023733[/C][C]0.0252208799762673[/C][/ROW]
[ROW][C]53[/C][C]0.42[/C][C]0.446551397531768[/C][C]-0.0265513975317682[/C][/ROW]
[ROW][C]54[/C][C]0.41[/C][C]0.418890906862472[/C][C]-0.00889090686247168[/C][/ROW]
[ROW][C]55[/C][C]0.41[/C][C]0.423327191628258[/C][C]-0.0133271916282584[/C][/ROW]
[ROW][C]56[/C][C]0.43[/C][C]0.409877629034235[/C][C]0.0201223709657654[/C][/ROW]
[ROW][C]57[/C][C]0.44[/C][C]0.43516284611313[/C][C]0.00483715388687[/C][/ROW]
[ROW][C]58[/C][C]0.46[/C][C]0.457419222733862[/C][C]0.0025807772661377[/C][/ROW]
[ROW][C]59[/C][C]0.44[/C][C]0.463097787048965[/C][C]-0.0230977870489652[/C][/ROW]
[ROW][C]60[/C][C]0.43[/C][C]0.432682919853982[/C][C]-0.002682919853982[/C][/ROW]
[ROW][C]61[/C][C]0.43[/C][C]0.401195212514832[/C][C]0.0288047874851679[/C][/ROW]
[ROW][C]62[/C][C]0.42[/C][C]0.422494194554144[/C][C]-0.00249419455414446[/C][/ROW]
[ROW][C]63[/C][C]0.42[/C][C]0.416196279419709[/C][C]0.00380372058029144[/C][/ROW]
[ROW][C]64[/C][C]0.42[/C][C]0.41795232043303[/C][C]0.00204767956696966[/C][/ROW]
[ROW][C]65[/C][C]0.43[/C][C]0.431491381418336[/C][C]-0.00149138141833588[/C][/ROW]
[ROW][C]66[/C][C]0.44[/C][C]0.427626624570958[/C][C]0.0123733754290418[/C][/ROW]
[ROW][C]67[/C][C]0.45[/C][C]0.449945737531405[/C][C]5.42624685953008e-05[/C][/ROW]
[ROW][C]68[/C][C]0.44[/C][C]0.453229223192051[/C][C]-0.0132292231920506[/C][/ROW]
[ROW][C]69[/C][C]0.47[/C][C]0.448194926265441[/C][C]0.0218050737345586[/C][/ROW]
[ROW][C]70[/C][C]0.48[/C][C]0.485435798511558[/C][C]-0.00543579851155845[/C][/ROW]
[ROW][C]71[/C][C]0.48[/C][C]0.480095501569868[/C][C]-9.55015698678174e-05[/C][/ROW]
[ROW][C]72[/C][C]0.45[/C][C]0.471564862662166[/C][C]-0.0215648626621663[/C][/ROW]
[ROW][C]73[/C][C]0.44[/C][C]0.427608752169333[/C][C]0.0123912478306673[/C][/ROW]
[ROW][C]74[/C][C]0.44[/C][C]0.429977921153402[/C][C]0.0100220788465976[/C][/ROW]
[ROW][C]75[/C][C]0.45[/C][C]0.435062591504202[/C][C]0.0149374084957979[/C][/ROW]
[ROW][C]76[/C][C]0.46[/C][C]0.445788243938788[/C][C]0.0142117560612118[/C][/ROW]
[ROW][C]77[/C][C]0.45[/C][C]0.470005218999662[/C][C]-0.0200052189996620[/C][/ROW]
[ROW][C]78[/C][C]0.46[/C][C]0.452703462501075[/C][C]0.00729653749892489[/C][/ROW]
[ROW][C]79[/C][C]0.47[/C][C]0.469220487753507[/C][C]0.000779512246492975[/C][/ROW]
[ROW][C]80[/C][C]0.48[/C][C]0.470996383531979[/C][C]0.00900361646802111[/C][/ROW]
[ROW][C]81[/C][C]0.48[/C][C]0.491104277428729[/C][C]-0.0111042774287292[/C][/ROW]
[ROW][C]82[/C][C]0.46[/C][C]0.496693396821315[/C][C]-0.0366933968213146[/C][/ROW]
[ROW][C]83[/C][C]0.47[/C][C]0.465911954756431[/C][C]0.00408804524356932[/C][/ROW]
[ROW][C]84[/C][C]0.47[/C][C]0.457615348774467[/C][C]0.0123846512255326[/C][/ROW]
[ROW][C]85[/C][C]0.43[/C][C]0.446742803797396[/C][C]-0.0167428037973964[/C][/ROW]
[ROW][C]86[/C][C]0.41[/C][C]0.424343805119414[/C][C]-0.0143438051194145[/C][/ROW]
[ROW][C]87[/C][C]0.39[/C][C]0.409817091292825[/C][C]-0.0198170912928252[/C][/ROW]
[ROW][C]88[/C][C]0.41[/C][C]0.391393683328863[/C][C]0.0186063166711372[/C][/ROW]
[ROW][C]89[/C][C]0.44[/C][C]0.412976062794227[/C][C]0.0270239372057733[/C][/ROW]
[ROW][C]90[/C][C]0.45[/C][C]0.439429166345048[/C][C]0.0105708336549523[/C][/ROW]
[ROW][C]91[/C][C]0.45[/C][C]0.457426281922807[/C][C]-0.00742628192280742[/C][/ROW]
[ROW][C]92[/C][C]0.46[/C][C]0.453489671319325[/C][C]0.0065103286806748[/C][/ROW]
[ROW][C]93[/C][C]0.45[/C][C]0.46786169251636[/C][C]-0.0178616925163598[/C][/ROW]
[ROW][C]94[/C][C]0.45[/C][C]0.462720207810253[/C][C]-0.0127202078102533[/C][/ROW]
[ROW][C]95[/C][C]0.46[/C][C]0.458465877973486[/C][C]0.00153412202651398[/C][/ROW]
[ROW][C]96[/C][C]0.46[/C][C]0.449524660402054[/C][C]0.0104753395979463[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13021&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13021&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
13	0.36	0.354168721864335	0.00583127813566497
14	0.36	0.358265959594702	0.00173404040529840
15	0.36	0.357714665960194	0.00228533403980585
16	0.36	0.356450497137153	0.00354950286284744
17	0.38	0.375248721294845	0.00475127870515524
18	0.37	0.366454836418137	0.00354516358186269
19	0.39	0.388561175974231	0.00143882402576945
20	0.39	0.389771236388853	0.000228763611146654
21	0.4	0.399962695468502	3.73045314979725e-05
22	0.42	0.41999377226461	6.22773538955235e-06
23	0.42	0.421370062093576	-0.00137006209357576
24	0.4	0.401080320516783	-0.00108032051678314
25	0.36	0.37287669013049	-0.0128766901304904
26	0.36	0.360579552610568	-0.000579552610567746
27	0.36	0.358167729915886	0.00183227008411407
28	0.36	0.356721258383452	0.0032787416165479
29	0.35	0.375451722368071	-0.025451722368071
30	0.38	0.341947527779654	0.0380524722203462
31	0.4	0.392939718067491	0.00706028193250913
32	0.39	0.398680671937991	-0.00868067193799055
33	0.39	0.401384074199658	-0.0113840741996585
34	0.39	0.411395362682129	-0.0213953626821292
35	0.36	0.394480424556518	-0.0344804245565176
36	0.35	0.348868532187066	0.00113146781293416
37	0.35	0.324255375431368	0.0257446245686317
38	0.33	0.346374979781771	-0.016374979781771
39	0.33	0.331178679034397	-0.001178679034397
40	0.32	0.327654643061797	-0.00765464306179681
41	0.36	0.331175132966034	0.0288248670339658
42	0.37	0.352857888890978	0.0171421111090218
43	0.38	0.380849704025799	-0.000849704025799314
44	0.38	0.377545196333015	0.00245480366698503
45	0.38	0.388885662661695	-0.0088856626616951
46	0.38	0.398858044040577	-0.0188580440405772
47	0.39	0.38158739313176	0.00841260686823964
48	0.4	0.376838409032491	0.0231615909675089
49	0.38	0.371510696837184	0.00848930316281599
50	0.41	0.371795243930462	0.0382047560695378
51	0.41	0.405138344847736	0.00486165515226394
52	0.43	0.404779120023733	0.0252208799762673
53	0.42	0.446551397531768	-0.0265513975317682
54	0.41	0.418890906862472	-0.00889090686247168
55	0.41	0.423327191628258	-0.0133271916282584
56	0.43	0.409877629034235	0.0201223709657654
57	0.44	0.43516284611313	0.00483715388687
58	0.46	0.457419222733862	0.0025807772661377
59	0.44	0.463097787048965	-0.0230977870489652
60	0.43	0.432682919853982	-0.002682919853982
61	0.43	0.401195212514832	0.0288047874851679
62	0.42	0.422494194554144	-0.00249419455414446
63	0.42	0.416196279419709	0.00380372058029144
64	0.42	0.41795232043303	0.00204767956696966
65	0.43	0.431491381418336	-0.00149138141833588
66	0.44	0.427626624570958	0.0123733754290418
67	0.45	0.449945737531405	5.42624685953008e-05
68	0.44	0.453229223192051	-0.0132292231920506
69	0.47	0.448194926265441	0.0218050737345586
70	0.48	0.485435798511558	-0.00543579851155845
71	0.48	0.480095501569868	-9.55015698678174e-05
72	0.45	0.471564862662166	-0.0215648626621663
73	0.44	0.427608752169333	0.0123912478306673
74	0.44	0.429977921153402	0.0100220788465976
75	0.45	0.435062591504202	0.0149374084957979
76	0.46	0.445788243938788	0.0142117560612118
77	0.45	0.470005218999662	-0.0200052189996620
78	0.46	0.452703462501075	0.00729653749892489
79	0.47	0.469220487753507	0.000779512246492975
80	0.48	0.470996383531979	0.00900361646802111
81	0.48	0.491104277428729	-0.0111042774287292
82	0.46	0.496693396821315	-0.0366933968213146
83	0.47	0.465911954756431	0.00408804524356932
84	0.47	0.457615348774467	0.0123846512255326
85	0.43	0.446742803797396	-0.0167428037973964
86	0.41	0.424343805119414	-0.0143438051194145
87	0.39	0.409817091292825	-0.0198170912928252
88	0.41	0.391393683328863	0.0186063166711372
89	0.44	0.412976062794227	0.0270239372057733
90	0.45	0.439429166345048	0.0105708336549523
91	0.45	0.457426281922807	-0.00742628192280742
92	0.46	0.453489671319325	0.0065103286806748
93	0.45	0.46786169251636	-0.0178616925163598
94	0.45	0.462720207810253	-0.0127202078102533
95	0.46	0.458465877973486	0.00153412202651398
96	0.46	0.449524660402054	0.0104753395979463

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
97	0.432974134123719	0.403102192962413	0.462846075285025
98	0.424915282141273	0.386019997961423	0.463810566321122
99	0.421321883795095	0.374724298914723	0.467919468675467
100	0.4259005073314	0.372340108865994	0.479460905796805
101	0.433222432878028	0.373954977615026	0.492489888141030
102	0.43428238219294	0.369210026705203	0.499354737680677
103	0.440294015383573	0.369968809332606	0.51061922143454
104	0.444709110360873	0.369358775041915	0.520059445679832
105	0.449472905966086	0.368428321304057	0.530517490628115
106	0.460110345670358	0.373820982507095	0.546399708833621
107	0.469015125853249	0.380677986977151	0.557352264729347
108	0.46	NA	NA

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 0.432974134123719 & 0.403102192962413 & 0.462846075285025 \tabularnewline
98 & 0.424915282141273 & 0.386019997961423 & 0.463810566321122 \tabularnewline
99 & 0.421321883795095 & 0.374724298914723 & 0.467919468675467 \tabularnewline
100 & 0.4259005073314 & 0.372340108865994 & 0.479460905796805 \tabularnewline
101 & 0.433222432878028 & 0.373954977615026 & 0.492489888141030 \tabularnewline
102 & 0.43428238219294 & 0.369210026705203 & 0.499354737680677 \tabularnewline
103 & 0.440294015383573 & 0.369968809332606 & 0.51061922143454 \tabularnewline
104 & 0.444709110360873 & 0.369358775041915 & 0.520059445679832 \tabularnewline
105 & 0.449472905966086 & 0.368428321304057 & 0.530517490628115 \tabularnewline
106 & 0.460110345670358 & 0.373820982507095 & 0.546399708833621 \tabularnewline
107 & 0.469015125853249 & 0.380677986977151 & 0.557352264729347 \tabularnewline
108 & 0.46 & NA & NA \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13021&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]0.432974134123719[/C][C]0.403102192962413[/C][C]0.462846075285025[/C][/ROW]
[ROW][C]98[/C][C]0.424915282141273[/C][C]0.386019997961423[/C][C]0.463810566321122[/C][/ROW]
[ROW][C]99[/C][C]0.421321883795095[/C][C]0.374724298914723[/C][C]0.467919468675467[/C][/ROW]
[ROW][C]100[/C][C]0.4259005073314[/C][C]0.372340108865994[/C][C]0.479460905796805[/C][/ROW]
[ROW][C]101[/C][C]0.433222432878028[/C][C]0.373954977615026[/C][C]0.492489888141030[/C][/ROW]
[ROW][C]102[/C][C]0.43428238219294[/C][C]0.369210026705203[/C][C]0.499354737680677[/C][/ROW]
[ROW][C]103[/C][C]0.440294015383573[/C][C]0.369968809332606[/C][C]0.51061922143454[/C][/ROW]
[ROW][C]104[/C][C]0.444709110360873[/C][C]0.369358775041915[/C][C]0.520059445679832[/C][/ROW]
[ROW][C]105[/C][C]0.449472905966086[/C][C]0.368428321304057[/C][C]0.530517490628115[/C][/ROW]
[ROW][C]106[/C][C]0.460110345670358[/C][C]0.373820982507095[/C][C]0.546399708833621[/C][/ROW]
[ROW][C]107[/C][C]0.469015125853249[/C][C]0.380677986977151[/C][C]0.557352264729347[/C][/ROW]
[ROW][C]108[/C][C]0.46[/C][C]NA[/C][C]NA[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13021&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13021&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
97	0.432974134123719	0.403102192962413	0.462846075285025
98	0.424915282141273	0.386019997961423	0.463810566321122
99	0.421321883795095	0.374724298914723	0.467919468675467
100	0.4259005073314	0.372340108865994	0.479460905796805
101	0.433222432878028	0.373954977615026	0.492489888141030
102	0.43428238219294	0.369210026705203	0.499354737680677
103	0.440294015383573	0.369968809332606	0.51061922143454
104	0.444709110360873	0.369358775041915	0.520059445679832
105	0.449472905966086	0.368428321304057	0.530517490628115
106	0.460110345670358	0.373820982507095	0.546399708833621
107	0.469015125853249	0.380677986977151	0.557352264729347
108	0.46	NA	NA

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 = Triple ; par3 = multiplicative ;

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code