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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Tue, 02 Jun 2009 12:36:57 -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/2009/Jun/02/t1243967862u5wrfe2ld9wfmvc.htm/, Retrieved Thu, 09 May 2024 21:58:43 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41364, Retrieved Thu, 09 May 2024 21:58:43 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

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

-       [Exponential Smoothing] [Exponential Smoot...] [2009-06-02 18:36:57] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Dataseries X:

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4.2
4.19
4.19
4.19
4.19
4.18
4.2
4.19
4.17
4.21
4.22
4.23
4.21
4.23
4.23
4.22
4.25
4.28
4.3
4.32
4.33
4.32
4.34
4.33
4.31
4.31
4.3
4.3
4.29
4.33
4.32
4.32
4.35
4.37
4.39
4.4
4.41
4.44
4.47
4.47
4.47
4.48
4.47
4.48
4.46
4.44
4.43
4.41
4.41
4.38
4.35
4.37
4.4
4.39
4.36
4.34
4.33
4.33
4.34
4.34
4.35
4.37
4.39
4.4
4.38
4.37
4.36
4.33
4.33
4.33
4.32
4.33
4.34

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41364&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41364&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41364&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.187080608713926
gamma	0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.187080608713926 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41364&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.187080608713926[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41364&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41364&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	1
beta	0.187080608713926
gamma	0

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	4.19	4.18	0.00999999999999979
4	4.19	4.18187080608714	0.00812919391286027
5	4.19	4.18339162063271	0.00660837936728864
6	4.18	4.18462792026736	-0.0046279202673567
7	4.2	4.17376212612666	0.0262378738733409
8	4.19	4.19867072354224	-0.0086707235422434
9	4.17	4.18704859930397	-0.0170485993039708
10	4.21	4.16385913696846	0.0461408630315363
11	4.22	4.21249119771099	0.00750880228901085
12	4.23	4.22389594901393	0.00610405098607103
13	4.21	4.23503789858803	-0.0250378985880255
14	4.23	4.21035379327926	0.0196462067207408
15	4.23	4.23402921759150	-0.00402921759149510
16	4.22	4.23327542911184	-0.0132754291118387
17	4.25	4.22079185375266	0.0292081462473437
18	4.28	4.25625613153202	0.0237438684679852
19	4.3	4.29069814889823	0.00930185110177106
20	4.32	4.31243834486451	0.00756165513548623
21	4.33	4.33385298391015	-0.00385298391014643
22	4.32	4.34313216533487	-0.0231321653348706
23	4.34	4.32880458576315	0.0111954142368473
24	4.33	4.35089903067339	-0.0208990306733856
25	4.31	4.33698922729348	-0.0269892272934786
26	4.31	4.31194006622269	-0.00194006622269516
27	4.3	4.31157711745281	-0.0115771174528083
28	4.3	4.29941126327258	0.000588736727415551
29	4.29	4.29952140449792	-0.00952140449792171
30	4.33	4.28774013434864	0.0422598656513609
31	4.32	4.33564613573886	-0.0156461357388640
32	4.32	4.32271904714082	-0.0027190471408165
33	4.35	4.32221036614659	0.0277896338534083
34	4.37	4.35740926776382	0.0125907322361769
35	4.39	4.37976474961472	0.0102352503852776
36	4.4	4.40167956648714	-0.00167956648713830
37	4.41	4.41136535216635	-0.00136535216635014
38	4.44	4.42110992125196	0.0188900787480399
39	4.47	4.4546438886828	0.0153561113172023
40	4.47	4.4875167193355	-0.0175167193354984
41	4.47	4.48423968081954	-0.0142396808195420
42	4.48	4.48157571266393	-0.00157571266392953
43	4.47	4.49128092737960	-0.0212809273796051
44	4.48	4.47729967853143	0.00270032146856991
45	4.46	4.48780485631549	-0.0278048563154947
46	4.44	4.46260310687079	-0.0226031068707879
47	4.43	4.43837450387858	-0.00837450387857608
48	4.41	4.42680779659529	-0.0168077965952937
49	4.41	4.40366338377711	0.00633661622289328
50	4.38	4.40484884179727	-0.0248488417972723
51	4.35	4.370200105348	-0.0202001053480023
52	4.37	4.33642105734341	0.0335789426565878
53	4.4	4.36270302637558	0.0372969736244233
54	4.39	4.39968056690442	-0.00968056690442243
55	4.36	4.38786952055525	-0.0278695205552459
56	4.34	4.35265567368521	-0.0126556736852059
57	4.33	4.33028804254849	-0.000288042548492129
58	4.33	4.32023415537318	0.0097658446268154
59	4.34	4.32206115553058	0.0179388444694242
60	4.34	4.33541716547354	0.00458283452646047
61	4.35	4.33627452494638	0.0137254750536151
62	4.37	4.3488422951743	0.021157704825697
63	4.39	4.37280049147208	0.0171995085279155
64	4.4	4.39601818599707	0.00398181400293396
65	4.38	4.40676310618452	-0.0267631061845215
66	4.37	4.38175624798845	-0.011756247988445
67	4.36	4.36955688195858	-0.0095568819585754
68	4.33	4.35776897466436	-0.0277689746643581
69	4.33	4.32257393798079	0.0074260620192117
70	4.33	4.32396321018369	0.00603678981631006
71	4.32	4.3250925764972	-0.00509257649720318
72	4.33	4.31413985418618	0.0158601458138152
73	4.34	4.32710697991932	0.0128930200806749

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 4.19 & 4.18 & 0.00999999999999979 \tabularnewline
4 & 4.19 & 4.18187080608714 & 0.00812919391286027 \tabularnewline
5 & 4.19 & 4.18339162063271 & 0.00660837936728864 \tabularnewline
6 & 4.18 & 4.18462792026736 & -0.0046279202673567 \tabularnewline
7 & 4.2 & 4.17376212612666 & 0.0262378738733409 \tabularnewline
8 & 4.19 & 4.19867072354224 & -0.0086707235422434 \tabularnewline
9 & 4.17 & 4.18704859930397 & -0.0170485993039708 \tabularnewline
10 & 4.21 & 4.16385913696846 & 0.0461408630315363 \tabularnewline
11 & 4.22 & 4.21249119771099 & 0.00750880228901085 \tabularnewline
12 & 4.23 & 4.22389594901393 & 0.00610405098607103 \tabularnewline
13 & 4.21 & 4.23503789858803 & -0.0250378985880255 \tabularnewline
14 & 4.23 & 4.21035379327926 & 0.0196462067207408 \tabularnewline
15 & 4.23 & 4.23402921759150 & -0.00402921759149510 \tabularnewline
16 & 4.22 & 4.23327542911184 & -0.0132754291118387 \tabularnewline
17 & 4.25 & 4.22079185375266 & 0.0292081462473437 \tabularnewline
18 & 4.28 & 4.25625613153202 & 0.0237438684679852 \tabularnewline
19 & 4.3 & 4.29069814889823 & 0.00930185110177106 \tabularnewline
20 & 4.32 & 4.31243834486451 & 0.00756165513548623 \tabularnewline
21 & 4.33 & 4.33385298391015 & -0.00385298391014643 \tabularnewline
22 & 4.32 & 4.34313216533487 & -0.0231321653348706 \tabularnewline
23 & 4.34 & 4.32880458576315 & 0.0111954142368473 \tabularnewline
24 & 4.33 & 4.35089903067339 & -0.0208990306733856 \tabularnewline
25 & 4.31 & 4.33698922729348 & -0.0269892272934786 \tabularnewline
26 & 4.31 & 4.31194006622269 & -0.00194006622269516 \tabularnewline
27 & 4.3 & 4.31157711745281 & -0.0115771174528083 \tabularnewline
28 & 4.3 & 4.29941126327258 & 0.000588736727415551 \tabularnewline
29 & 4.29 & 4.29952140449792 & -0.00952140449792171 \tabularnewline
30 & 4.33 & 4.28774013434864 & 0.0422598656513609 \tabularnewline
31 & 4.32 & 4.33564613573886 & -0.0156461357388640 \tabularnewline
32 & 4.32 & 4.32271904714082 & -0.0027190471408165 \tabularnewline
33 & 4.35 & 4.32221036614659 & 0.0277896338534083 \tabularnewline
34 & 4.37 & 4.35740926776382 & 0.0125907322361769 \tabularnewline
35 & 4.39 & 4.37976474961472 & 0.0102352503852776 \tabularnewline
36 & 4.4 & 4.40167956648714 & -0.00167956648713830 \tabularnewline
37 & 4.41 & 4.41136535216635 & -0.00136535216635014 \tabularnewline
38 & 4.44 & 4.42110992125196 & 0.0188900787480399 \tabularnewline
39 & 4.47 & 4.4546438886828 & 0.0153561113172023 \tabularnewline
40 & 4.47 & 4.4875167193355 & -0.0175167193354984 \tabularnewline
41 & 4.47 & 4.48423968081954 & -0.0142396808195420 \tabularnewline
42 & 4.48 & 4.48157571266393 & -0.00157571266392953 \tabularnewline
43 & 4.47 & 4.49128092737960 & -0.0212809273796051 \tabularnewline
44 & 4.48 & 4.47729967853143 & 0.00270032146856991 \tabularnewline
45 & 4.46 & 4.48780485631549 & -0.0278048563154947 \tabularnewline
46 & 4.44 & 4.46260310687079 & -0.0226031068707879 \tabularnewline
47 & 4.43 & 4.43837450387858 & -0.00837450387857608 \tabularnewline
48 & 4.41 & 4.42680779659529 & -0.0168077965952937 \tabularnewline
49 & 4.41 & 4.40366338377711 & 0.00633661622289328 \tabularnewline
50 & 4.38 & 4.40484884179727 & -0.0248488417972723 \tabularnewline
51 & 4.35 & 4.370200105348 & -0.0202001053480023 \tabularnewline
52 & 4.37 & 4.33642105734341 & 0.0335789426565878 \tabularnewline
53 & 4.4 & 4.36270302637558 & 0.0372969736244233 \tabularnewline
54 & 4.39 & 4.39968056690442 & -0.00968056690442243 \tabularnewline
55 & 4.36 & 4.38786952055525 & -0.0278695205552459 \tabularnewline
56 & 4.34 & 4.35265567368521 & -0.0126556736852059 \tabularnewline
57 & 4.33 & 4.33028804254849 & -0.000288042548492129 \tabularnewline
58 & 4.33 & 4.32023415537318 & 0.0097658446268154 \tabularnewline
59 & 4.34 & 4.32206115553058 & 0.0179388444694242 \tabularnewline
60 & 4.34 & 4.33541716547354 & 0.00458283452646047 \tabularnewline
61 & 4.35 & 4.33627452494638 & 0.0137254750536151 \tabularnewline
62 & 4.37 & 4.3488422951743 & 0.021157704825697 \tabularnewline
63 & 4.39 & 4.37280049147208 & 0.0171995085279155 \tabularnewline
64 & 4.4 & 4.39601818599707 & 0.00398181400293396 \tabularnewline
65 & 4.38 & 4.40676310618452 & -0.0267631061845215 \tabularnewline
66 & 4.37 & 4.38175624798845 & -0.011756247988445 \tabularnewline
67 & 4.36 & 4.36955688195858 & -0.0095568819585754 \tabularnewline
68 & 4.33 & 4.35776897466436 & -0.0277689746643581 \tabularnewline
69 & 4.33 & 4.32257393798079 & 0.0074260620192117 \tabularnewline
70 & 4.33 & 4.32396321018369 & 0.00603678981631006 \tabularnewline
71 & 4.32 & 4.3250925764972 & -0.00509257649720318 \tabularnewline
72 & 4.33 & 4.31413985418618 & 0.0158601458138152 \tabularnewline
73 & 4.34 & 4.32710697991932 & 0.0128930200806749 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41364&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]4.19[/C][C]4.18[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]4[/C][C]4.19[/C][C]4.18187080608714[/C][C]0.00812919391286027[/C][/ROW]
[ROW][C]5[/C][C]4.19[/C][C]4.18339162063271[/C][C]0.00660837936728864[/C][/ROW]
[ROW][C]6[/C][C]4.18[/C][C]4.18462792026736[/C][C]-0.0046279202673567[/C][/ROW]
[ROW][C]7[/C][C]4.2[/C][C]4.17376212612666[/C][C]0.0262378738733409[/C][/ROW]
[ROW][C]8[/C][C]4.19[/C][C]4.19867072354224[/C][C]-0.0086707235422434[/C][/ROW]
[ROW][C]9[/C][C]4.17[/C][C]4.18704859930397[/C][C]-0.0170485993039708[/C][/ROW]
[ROW][C]10[/C][C]4.21[/C][C]4.16385913696846[/C][C]0.0461408630315363[/C][/ROW]
[ROW][C]11[/C][C]4.22[/C][C]4.21249119771099[/C][C]0.00750880228901085[/C][/ROW]
[ROW][C]12[/C][C]4.23[/C][C]4.22389594901393[/C][C]0.00610405098607103[/C][/ROW]
[ROW][C]13[/C][C]4.21[/C][C]4.23503789858803[/C][C]-0.0250378985880255[/C][/ROW]
[ROW][C]14[/C][C]4.23[/C][C]4.21035379327926[/C][C]0.0196462067207408[/C][/ROW]
[ROW][C]15[/C][C]4.23[/C][C]4.23402921759150[/C][C]-0.00402921759149510[/C][/ROW]
[ROW][C]16[/C][C]4.22[/C][C]4.23327542911184[/C][C]-0.0132754291118387[/C][/ROW]
[ROW][C]17[/C][C]4.25[/C][C]4.22079185375266[/C][C]0.0292081462473437[/C][/ROW]
[ROW][C]18[/C][C]4.28[/C][C]4.25625613153202[/C][C]0.0237438684679852[/C][/ROW]
[ROW][C]19[/C][C]4.3[/C][C]4.29069814889823[/C][C]0.00930185110177106[/C][/ROW]
[ROW][C]20[/C][C]4.32[/C][C]4.31243834486451[/C][C]0.00756165513548623[/C][/ROW]
[ROW][C]21[/C][C]4.33[/C][C]4.33385298391015[/C][C]-0.00385298391014643[/C][/ROW]
[ROW][C]22[/C][C]4.32[/C][C]4.34313216533487[/C][C]-0.0231321653348706[/C][/ROW]
[ROW][C]23[/C][C]4.34[/C][C]4.32880458576315[/C][C]0.0111954142368473[/C][/ROW]
[ROW][C]24[/C][C]4.33[/C][C]4.35089903067339[/C][C]-0.0208990306733856[/C][/ROW]
[ROW][C]25[/C][C]4.31[/C][C]4.33698922729348[/C][C]-0.0269892272934786[/C][/ROW]
[ROW][C]26[/C][C]4.31[/C][C]4.31194006622269[/C][C]-0.00194006622269516[/C][/ROW]
[ROW][C]27[/C][C]4.3[/C][C]4.31157711745281[/C][C]-0.0115771174528083[/C][/ROW]
[ROW][C]28[/C][C]4.3[/C][C]4.29941126327258[/C][C]0.000588736727415551[/C][/ROW]
[ROW][C]29[/C][C]4.29[/C][C]4.29952140449792[/C][C]-0.00952140449792171[/C][/ROW]
[ROW][C]30[/C][C]4.33[/C][C]4.28774013434864[/C][C]0.0422598656513609[/C][/ROW]
[ROW][C]31[/C][C]4.32[/C][C]4.33564613573886[/C][C]-0.0156461357388640[/C][/ROW]
[ROW][C]32[/C][C]4.32[/C][C]4.32271904714082[/C][C]-0.0027190471408165[/C][/ROW]
[ROW][C]33[/C][C]4.35[/C][C]4.32221036614659[/C][C]0.0277896338534083[/C][/ROW]
[ROW][C]34[/C][C]4.37[/C][C]4.35740926776382[/C][C]0.0125907322361769[/C][/ROW]
[ROW][C]35[/C][C]4.39[/C][C]4.37976474961472[/C][C]0.0102352503852776[/C][/ROW]
[ROW][C]36[/C][C]4.4[/C][C]4.40167956648714[/C][C]-0.00167956648713830[/C][/ROW]
[ROW][C]37[/C][C]4.41[/C][C]4.41136535216635[/C][C]-0.00136535216635014[/C][/ROW]
[ROW][C]38[/C][C]4.44[/C][C]4.42110992125196[/C][C]0.0188900787480399[/C][/ROW]
[ROW][C]39[/C][C]4.47[/C][C]4.4546438886828[/C][C]0.0153561113172023[/C][/ROW]
[ROW][C]40[/C][C]4.47[/C][C]4.4875167193355[/C][C]-0.0175167193354984[/C][/ROW]
[ROW][C]41[/C][C]4.47[/C][C]4.48423968081954[/C][C]-0.0142396808195420[/C][/ROW]
[ROW][C]42[/C][C]4.48[/C][C]4.48157571266393[/C][C]-0.00157571266392953[/C][/ROW]
[ROW][C]43[/C][C]4.47[/C][C]4.49128092737960[/C][C]-0.0212809273796051[/C][/ROW]
[ROW][C]44[/C][C]4.48[/C][C]4.47729967853143[/C][C]0.00270032146856991[/C][/ROW]
[ROW][C]45[/C][C]4.46[/C][C]4.48780485631549[/C][C]-0.0278048563154947[/C][/ROW]
[ROW][C]46[/C][C]4.44[/C][C]4.46260310687079[/C][C]-0.0226031068707879[/C][/ROW]
[ROW][C]47[/C][C]4.43[/C][C]4.43837450387858[/C][C]-0.00837450387857608[/C][/ROW]
[ROW][C]48[/C][C]4.41[/C][C]4.42680779659529[/C][C]-0.0168077965952937[/C][/ROW]
[ROW][C]49[/C][C]4.41[/C][C]4.40366338377711[/C][C]0.00633661622289328[/C][/ROW]
[ROW][C]50[/C][C]4.38[/C][C]4.40484884179727[/C][C]-0.0248488417972723[/C][/ROW]
[ROW][C]51[/C][C]4.35[/C][C]4.370200105348[/C][C]-0.0202001053480023[/C][/ROW]
[ROW][C]52[/C][C]4.37[/C][C]4.33642105734341[/C][C]0.0335789426565878[/C][/ROW]
[ROW][C]53[/C][C]4.4[/C][C]4.36270302637558[/C][C]0.0372969736244233[/C][/ROW]
[ROW][C]54[/C][C]4.39[/C][C]4.39968056690442[/C][C]-0.00968056690442243[/C][/ROW]
[ROW][C]55[/C][C]4.36[/C][C]4.38786952055525[/C][C]-0.0278695205552459[/C][/ROW]
[ROW][C]56[/C][C]4.34[/C][C]4.35265567368521[/C][C]-0.0126556736852059[/C][/ROW]
[ROW][C]57[/C][C]4.33[/C][C]4.33028804254849[/C][C]-0.000288042548492129[/C][/ROW]
[ROW][C]58[/C][C]4.33[/C][C]4.32023415537318[/C][C]0.0097658446268154[/C][/ROW]
[ROW][C]59[/C][C]4.34[/C][C]4.32206115553058[/C][C]0.0179388444694242[/C][/ROW]
[ROW][C]60[/C][C]4.34[/C][C]4.33541716547354[/C][C]0.00458283452646047[/C][/ROW]
[ROW][C]61[/C][C]4.35[/C][C]4.33627452494638[/C][C]0.0137254750536151[/C][/ROW]
[ROW][C]62[/C][C]4.37[/C][C]4.3488422951743[/C][C]0.021157704825697[/C][/ROW]
[ROW][C]63[/C][C]4.39[/C][C]4.37280049147208[/C][C]0.0171995085279155[/C][/ROW]
[ROW][C]64[/C][C]4.4[/C][C]4.39601818599707[/C][C]0.00398181400293396[/C][/ROW]
[ROW][C]65[/C][C]4.38[/C][C]4.40676310618452[/C][C]-0.0267631061845215[/C][/ROW]
[ROW][C]66[/C][C]4.37[/C][C]4.38175624798845[/C][C]-0.011756247988445[/C][/ROW]
[ROW][C]67[/C][C]4.36[/C][C]4.36955688195858[/C][C]-0.0095568819585754[/C][/ROW]
[ROW][C]68[/C][C]4.33[/C][C]4.35776897466436[/C][C]-0.0277689746643581[/C][/ROW]
[ROW][C]69[/C][C]4.33[/C][C]4.32257393798079[/C][C]0.0074260620192117[/C][/ROW]
[ROW][C]70[/C][C]4.33[/C][C]4.32396321018369[/C][C]0.00603678981631006[/C][/ROW]
[ROW][C]71[/C][C]4.32[/C][C]4.3250925764972[/C][C]-0.00509257649720318[/C][/ROW]
[ROW][C]72[/C][C]4.33[/C][C]4.31413985418618[/C][C]0.0158601458138152[/C][/ROW]
[ROW][C]73[/C][C]4.34[/C][C]4.32710697991932[/C][C]0.0128930200806749[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41364&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41364&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	4.19	4.18	0.00999999999999979
4	4.19	4.18187080608714	0.00812919391286027
5	4.19	4.18339162063271	0.00660837936728864
6	4.18	4.18462792026736	-0.0046279202673567
7	4.2	4.17376212612666	0.0262378738733409
8	4.19	4.19867072354224	-0.0086707235422434
9	4.17	4.18704859930397	-0.0170485993039708
10	4.21	4.16385913696846	0.0461408630315363
11	4.22	4.21249119771099	0.00750880228901085
12	4.23	4.22389594901393	0.00610405098607103
13	4.21	4.23503789858803	-0.0250378985880255
14	4.23	4.21035379327926	0.0196462067207408
15	4.23	4.23402921759150	-0.00402921759149510
16	4.22	4.23327542911184	-0.0132754291118387
17	4.25	4.22079185375266	0.0292081462473437
18	4.28	4.25625613153202	0.0237438684679852
19	4.3	4.29069814889823	0.00930185110177106
20	4.32	4.31243834486451	0.00756165513548623
21	4.33	4.33385298391015	-0.00385298391014643
22	4.32	4.34313216533487	-0.0231321653348706
23	4.34	4.32880458576315	0.0111954142368473
24	4.33	4.35089903067339	-0.0208990306733856
25	4.31	4.33698922729348	-0.0269892272934786
26	4.31	4.31194006622269	-0.00194006622269516
27	4.3	4.31157711745281	-0.0115771174528083
28	4.3	4.29941126327258	0.000588736727415551
29	4.29	4.29952140449792	-0.00952140449792171
30	4.33	4.28774013434864	0.0422598656513609
31	4.32	4.33564613573886	-0.0156461357388640
32	4.32	4.32271904714082	-0.0027190471408165
33	4.35	4.32221036614659	0.0277896338534083
34	4.37	4.35740926776382	0.0125907322361769
35	4.39	4.37976474961472	0.0102352503852776
36	4.4	4.40167956648714	-0.00167956648713830
37	4.41	4.41136535216635	-0.00136535216635014
38	4.44	4.42110992125196	0.0188900787480399
39	4.47	4.4546438886828	0.0153561113172023
40	4.47	4.4875167193355	-0.0175167193354984
41	4.47	4.48423968081954	-0.0142396808195420
42	4.48	4.48157571266393	-0.00157571266392953
43	4.47	4.49128092737960	-0.0212809273796051
44	4.48	4.47729967853143	0.00270032146856991
45	4.46	4.48780485631549	-0.0278048563154947
46	4.44	4.46260310687079	-0.0226031068707879
47	4.43	4.43837450387858	-0.00837450387857608
48	4.41	4.42680779659529	-0.0168077965952937
49	4.41	4.40366338377711	0.00633661622289328
50	4.38	4.40484884179727	-0.0248488417972723
51	4.35	4.370200105348	-0.0202001053480023
52	4.37	4.33642105734341	0.0335789426565878
53	4.4	4.36270302637558	0.0372969736244233
54	4.39	4.39968056690442	-0.00968056690442243
55	4.36	4.38786952055525	-0.0278695205552459
56	4.34	4.35265567368521	-0.0126556736852059
57	4.33	4.33028804254849	-0.000288042548492129
58	4.33	4.32023415537318	0.0097658446268154
59	4.34	4.32206115553058	0.0179388444694242
60	4.34	4.33541716547354	0.00458283452646047
61	4.35	4.33627452494638	0.0137254750536151
62	4.37	4.3488422951743	0.021157704825697
63	4.39	4.37280049147208	0.0171995085279155
64	4.4	4.39601818599707	0.00398181400293396
65	4.38	4.40676310618452	-0.0267631061845215
66	4.37	4.38175624798845	-0.011756247988445
67	4.36	4.36955688195858	-0.0095568819585754
68	4.33	4.35776897466436	-0.0277689746643581
69	4.33	4.32257393798079	0.0074260620192117
70	4.33	4.32396321018369	0.00603678981631006
71	4.32	4.3250925764972	-0.00509257649720318
72	4.33	4.31413985418618	0.0158601458138152
73	4.34	4.32710697991932	0.0128930200806749

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
74	4.33951901396418	4.30411565811095	4.37492236981741
75	4.33903802792836	4.28408681464403	4.39398924121269
76	4.33855704189253	4.26516460073345	4.41194948305162
77	4.33807605585671	4.24619800052617	4.42995411118725
78	4.33759506982089	4.22681261882094	4.44837752082084
79	4.33711408378507	4.20685392362074	4.46737424394939
80	4.33663309774925	4.18625295812702	4.48701323737147
81	4.33615211171342	4.16497992249482	4.50732430093203
82	4.3356711256776	4.14302471137059	4.52831753998461
83	4.33519013964178	4.12038769585863	4.54999258342493
84	4.33470915360596	4.09707497928852	4.5723433279234
85	4.33422816757014	4.07309580744918	4.59536052769109

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
74 & 4.33951901396418 & 4.30411565811095 & 4.37492236981741 \tabularnewline
75 & 4.33903802792836 & 4.28408681464403 & 4.39398924121269 \tabularnewline
76 & 4.33855704189253 & 4.26516460073345 & 4.41194948305162 \tabularnewline
77 & 4.33807605585671 & 4.24619800052617 & 4.42995411118725 \tabularnewline
78 & 4.33759506982089 & 4.22681261882094 & 4.44837752082084 \tabularnewline
79 & 4.33711408378507 & 4.20685392362074 & 4.46737424394939 \tabularnewline
80 & 4.33663309774925 & 4.18625295812702 & 4.48701323737147 \tabularnewline
81 & 4.33615211171342 & 4.16497992249482 & 4.50732430093203 \tabularnewline
82 & 4.3356711256776 & 4.14302471137059 & 4.52831753998461 \tabularnewline
83 & 4.33519013964178 & 4.12038769585863 & 4.54999258342493 \tabularnewline
84 & 4.33470915360596 & 4.09707497928852 & 4.5723433279234 \tabularnewline
85 & 4.33422816757014 & 4.07309580744918 & 4.59536052769109 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41364&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]74[/C][C]4.33951901396418[/C][C]4.30411565811095[/C][C]4.37492236981741[/C][/ROW]
[ROW][C]75[/C][C]4.33903802792836[/C][C]4.28408681464403[/C][C]4.39398924121269[/C][/ROW]
[ROW][C]76[/C][C]4.33855704189253[/C][C]4.26516460073345[/C][C]4.41194948305162[/C][/ROW]
[ROW][C]77[/C][C]4.33807605585671[/C][C]4.24619800052617[/C][C]4.42995411118725[/C][/ROW]
[ROW][C]78[/C][C]4.33759506982089[/C][C]4.22681261882094[/C][C]4.44837752082084[/C][/ROW]
[ROW][C]79[/C][C]4.33711408378507[/C][C]4.20685392362074[/C][C]4.46737424394939[/C][/ROW]
[ROW][C]80[/C][C]4.33663309774925[/C][C]4.18625295812702[/C][C]4.48701323737147[/C][/ROW]
[ROW][C]81[/C][C]4.33615211171342[/C][C]4.16497992249482[/C][C]4.50732430093203[/C][/ROW]
[ROW][C]82[/C][C]4.3356711256776[/C][C]4.14302471137059[/C][C]4.52831753998461[/C][/ROW]
[ROW][C]83[/C][C]4.33519013964178[/C][C]4.12038769585863[/C][C]4.54999258342493[/C][/ROW]
[ROW][C]84[/C][C]4.33470915360596[/C][C]4.09707497928852[/C][C]4.5723433279234[/C][/ROW]
[ROW][C]85[/C][C]4.33422816757014[/C][C]4.07309580744918[/C][C]4.59536052769109[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41364&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41364&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
74	4.33951901396418	4.30411565811095	4.37492236981741
75	4.33903802792836	4.28408681464403	4.39398924121269
76	4.33855704189253	4.26516460073345	4.41194948305162
77	4.33807605585671	4.24619800052617	4.42995411118725
78	4.33759506982089	4.22681261882094	4.44837752082084
79	4.33711408378507	4.20685392362074	4.46737424394939
80	4.33663309774925	4.18625295812702	4.48701323737147
81	4.33615211171342	4.16497992249482	4.50732430093203
82	4.3356711256776	4.14302471137059	4.52831753998461
83	4.33519013964178	4.12038769585863	4.54999258342493
84	4.33470915360596	4.09707497928852	4.5723433279234
85	4.33422816757014	4.07309580744918	4.59536052769109

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=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