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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sat, 11 Jan 2014 06:20:13 -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/2014/Jan/11/t1389439227j1nt0wmmeita1wo.htm/, Retrieved Thu, 02 May 2024 06:55:04 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232896, Retrieved Thu, 02 May 2024 06:55:04 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

131

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

-     [Exponential Smoothing] [] [2013-12-16 10:10:01] [ac3e2d6dc43fcca5a6f32f298845dec8]
- R PD    [Exponential Smoothing] [] [2014-01-11 11:20:13] [c3373c0d5a698012d591c0e2feefe9b5] [Current]

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Dataseries X:

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2,57
2,58
2,58
2,58
2,57
2,57
2,57
2,57
2,59
2,62
2,66
2,67
2,67
2,69
2,69
2,69
2,69
2,71
2,71
2,71
2,74
2,77
2,82
2,82
2,82
2,8
2,82
2,82
2,82
2,82
2,82
2,82
2,85
2,93
2,94
2,94
2,95
2,95
2,96
2,96
2,97
2,97
2,97
2,97
2,98
3,03
3,03
3,03
3,03
3,04
3,05
3,06
3,06
3,07
3,07
3,07
3,04
3,06
3,09
3,09
3,09
3,09
3,1
3,1
3,1
3,1
3,1
3,11
3,11
3,17
3,19
3,19
3,19
3,19
3,19
3,19
3,19
3,19
3,19
3,19
3,25
3,23
3,24
3,24

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	'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232896&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232896&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232896&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	'Gertrude Mary Cox' @ cox.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.824541566618982
beta	0.0379751225973511
gamma	0.568089976016938

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.824541566618982 \tabularnewline
beta & 0.0379751225973511 \tabularnewline
gamma & 0.568089976016938 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232896&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]0.824541566618982[/C][/ROW]
[ROW][C]beta[/C][C]0.0379751225973511[/C][/ROW]
[ROW][C]gamma[/C][C]0.568089976016938[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232896&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232896&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	0.824541566618982
beta	0.0379751225973511
gamma	0.568089976016938

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	2.67	2.60925747863248	0.0607425213675215
14	2.69	2.68064686691753	0.00935313308247165
15	2.69	2.68953976774224	0.000460232257759152
16	2.69	2.69069784634582	-0.000697846345818487
17	2.69	2.69046252332508	-0.000462523325076347
18	2.71	2.71040675135514	-0.000406751355138457
19	2.71	2.70455089613362	0.00544910386638309
20	2.71	2.71369405965613	-0.00369405965612657
21	2.74	2.73476596949352	0.00523403050648108
22	2.77	2.77336334909482	-0.00336334909481684
23	2.82	2.81434985177171	0.00565014822829157
24	2.82	2.83169527547244	-0.0116952754724426
25	2.82	2.82959372208197	-0.00959372208196552
26	2.8	2.83774770744946	-0.0377477074494572
27	2.82	2.80532482361603	0.0146751763839745
28	2.82	2.81694060749637	0.00305939250362641
29	2.82	2.81879671292237	0.00120328707762818
30	2.82	2.83914216271594	-0.0191421627159398
31	2.82	2.81685735957285	0.0031426404271544
32	2.82	2.82155066064269	-0.00155066064268672
33	2.85	2.84371019232381	0.00628980767619192
34	2.93	2.88078459108558	0.0492154089144239
35	2.94	2.96613268674812	-0.0261326867481233
36	2.94	2.95465752064783	-0.0146575206478321
37	2.95	2.94934479803688	0.000655201963116525
38	2.95	2.96248593090414	-0.0124859309041421
39	2.96	2.95625150822577	0.00374849177423053
40	2.96	2.95749159613398	0.00250840386601725
41	2.97	2.95848275304543	0.0115172469545661
42	2.97	2.98540186023169	-0.0154018602316861
43	2.97	2.96863679796486	0.00136320203513973
44	2.97	2.97155379193087	-0.00155379193087057
45	2.98	2.99465087572196	-0.0146508757219617
46	3.03	3.01824040041889	0.0117595995811097
47	3.03	3.06352432541904	-0.0335243254190405
48	3.03	3.04519691037308	-0.0151969103730822
49	3.03	3.03904752645255	-0.00904752645254625
50	3.04	3.04065646034697	-0.000656460346970533
51	3.05	3.04394248002542	0.00605751997457871
52	3.06	3.04518351786664	0.0148164821333578
53	3.06	3.05582722275262	0.00417277724737852
54	3.07	3.07238340395187	-0.0023834039518662
55	3.07	3.06680740038434	0.00319259961565832
56	3.07	3.06978305915555	0.000216940844453894
57	3.04	3.09193116904746	-0.051931169047458
58	3.06	3.08514316502209	-0.0251431650220857
59	3.09	3.09205912383372	-0.00205912383372242
60	3.09	3.09906174825266	-0.00906174825266426
61	3.09	3.09633497839343	-0.00633497839343056
62	3.09	3.09885281658663	-0.00885281658662818
63	3.1	3.09362908516706	0.00637091483294228
64	3.1	3.09359066442499	0.00640933557501322
65	3.1	3.09356723303047	0.00643276696952855
66	3.1	3.10872996889441	-0.00872996889441069
67	3.1	3.09567462365673	0.00432537634326646
68	3.11	3.09652104142593	0.0134789585740744
69	3.11	3.12205491293045	-0.0120549129304499
70	3.17	3.14971387441759	0.0202861255824112
71	3.19	3.19670879463617	-0.00670879463617124
72	3.19	3.19935368055209	-0.00935368055208974
73	3.19	3.19682295654652	-0.00682295654651988
74	3.19	3.19883715055177	-0.00883715055177081
75	3.19	3.19529395288467	-0.00529395288466761
76	3.19	3.18542611545732	0.00457388454268326
77	3.19	3.18361906416345	0.00638093583655452
78	3.19	3.19695352683537	-0.00695352683536843
79	3.19	3.18644569017299	0.00355430982700788
80	3.19	3.18732603329844	0.00267396670155806
81	3.25	3.2008246022108	0.049175397789198
82	3.23	3.2835303597405	-0.053530359740499
83	3.24	3.26599465094835	-0.0259946509483462
84	3.24	3.25089491643449	-0.0108949164344936

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 2.67 & 2.60925747863248 & 0.0607425213675215 \tabularnewline
14 & 2.69 & 2.68064686691753 & 0.00935313308247165 \tabularnewline
15 & 2.69 & 2.68953976774224 & 0.000460232257759152 \tabularnewline
16 & 2.69 & 2.69069784634582 & -0.000697846345818487 \tabularnewline
17 & 2.69 & 2.69046252332508 & -0.000462523325076347 \tabularnewline
18 & 2.71 & 2.71040675135514 & -0.000406751355138457 \tabularnewline
19 & 2.71 & 2.70455089613362 & 0.00544910386638309 \tabularnewline
20 & 2.71 & 2.71369405965613 & -0.00369405965612657 \tabularnewline
21 & 2.74 & 2.73476596949352 & 0.00523403050648108 \tabularnewline
22 & 2.77 & 2.77336334909482 & -0.00336334909481684 \tabularnewline
23 & 2.82 & 2.81434985177171 & 0.00565014822829157 \tabularnewline
24 & 2.82 & 2.83169527547244 & -0.0116952754724426 \tabularnewline
25 & 2.82 & 2.82959372208197 & -0.00959372208196552 \tabularnewline
26 & 2.8 & 2.83774770744946 & -0.0377477074494572 \tabularnewline
27 & 2.82 & 2.80532482361603 & 0.0146751763839745 \tabularnewline
28 & 2.82 & 2.81694060749637 & 0.00305939250362641 \tabularnewline
29 & 2.82 & 2.81879671292237 & 0.00120328707762818 \tabularnewline
30 & 2.82 & 2.83914216271594 & -0.0191421627159398 \tabularnewline
31 & 2.82 & 2.81685735957285 & 0.0031426404271544 \tabularnewline
32 & 2.82 & 2.82155066064269 & -0.00155066064268672 \tabularnewline
33 & 2.85 & 2.84371019232381 & 0.00628980767619192 \tabularnewline
34 & 2.93 & 2.88078459108558 & 0.0492154089144239 \tabularnewline
35 & 2.94 & 2.96613268674812 & -0.0261326867481233 \tabularnewline
36 & 2.94 & 2.95465752064783 & -0.0146575206478321 \tabularnewline
37 & 2.95 & 2.94934479803688 & 0.000655201963116525 \tabularnewline
38 & 2.95 & 2.96248593090414 & -0.0124859309041421 \tabularnewline
39 & 2.96 & 2.95625150822577 & 0.00374849177423053 \tabularnewline
40 & 2.96 & 2.95749159613398 & 0.00250840386601725 \tabularnewline
41 & 2.97 & 2.95848275304543 & 0.0115172469545661 \tabularnewline
42 & 2.97 & 2.98540186023169 & -0.0154018602316861 \tabularnewline
43 & 2.97 & 2.96863679796486 & 0.00136320203513973 \tabularnewline
44 & 2.97 & 2.97155379193087 & -0.00155379193087057 \tabularnewline
45 & 2.98 & 2.99465087572196 & -0.0146508757219617 \tabularnewline
46 & 3.03 & 3.01824040041889 & 0.0117595995811097 \tabularnewline
47 & 3.03 & 3.06352432541904 & -0.0335243254190405 \tabularnewline
48 & 3.03 & 3.04519691037308 & -0.0151969103730822 \tabularnewline
49 & 3.03 & 3.03904752645255 & -0.00904752645254625 \tabularnewline
50 & 3.04 & 3.04065646034697 & -0.000656460346970533 \tabularnewline
51 & 3.05 & 3.04394248002542 & 0.00605751997457871 \tabularnewline
52 & 3.06 & 3.04518351786664 & 0.0148164821333578 \tabularnewline
53 & 3.06 & 3.05582722275262 & 0.00417277724737852 \tabularnewline
54 & 3.07 & 3.07238340395187 & -0.0023834039518662 \tabularnewline
55 & 3.07 & 3.06680740038434 & 0.00319259961565832 \tabularnewline
56 & 3.07 & 3.06978305915555 & 0.000216940844453894 \tabularnewline
57 & 3.04 & 3.09193116904746 & -0.051931169047458 \tabularnewline
58 & 3.06 & 3.08514316502209 & -0.0251431650220857 \tabularnewline
59 & 3.09 & 3.09205912383372 & -0.00205912383372242 \tabularnewline
60 & 3.09 & 3.09906174825266 & -0.00906174825266426 \tabularnewline
61 & 3.09 & 3.09633497839343 & -0.00633497839343056 \tabularnewline
62 & 3.09 & 3.09885281658663 & -0.00885281658662818 \tabularnewline
63 & 3.1 & 3.09362908516706 & 0.00637091483294228 \tabularnewline
64 & 3.1 & 3.09359066442499 & 0.00640933557501322 \tabularnewline
65 & 3.1 & 3.09356723303047 & 0.00643276696952855 \tabularnewline
66 & 3.1 & 3.10872996889441 & -0.00872996889441069 \tabularnewline
67 & 3.1 & 3.09567462365673 & 0.00432537634326646 \tabularnewline
68 & 3.11 & 3.09652104142593 & 0.0134789585740744 \tabularnewline
69 & 3.11 & 3.12205491293045 & -0.0120549129304499 \tabularnewline
70 & 3.17 & 3.14971387441759 & 0.0202861255824112 \tabularnewline
71 & 3.19 & 3.19670879463617 & -0.00670879463617124 \tabularnewline
72 & 3.19 & 3.19935368055209 & -0.00935368055208974 \tabularnewline
73 & 3.19 & 3.19682295654652 & -0.00682295654651988 \tabularnewline
74 & 3.19 & 3.19883715055177 & -0.00883715055177081 \tabularnewline
75 & 3.19 & 3.19529395288467 & -0.00529395288466761 \tabularnewline
76 & 3.19 & 3.18542611545732 & 0.00457388454268326 \tabularnewline
77 & 3.19 & 3.18361906416345 & 0.00638093583655452 \tabularnewline
78 & 3.19 & 3.19695352683537 & -0.00695352683536843 \tabularnewline
79 & 3.19 & 3.18644569017299 & 0.00355430982700788 \tabularnewline
80 & 3.19 & 3.18732603329844 & 0.00267396670155806 \tabularnewline
81 & 3.25 & 3.2008246022108 & 0.049175397789198 \tabularnewline
82 & 3.23 & 3.2835303597405 & -0.053530359740499 \tabularnewline
83 & 3.24 & 3.26599465094835 & -0.0259946509483462 \tabularnewline
84 & 3.24 & 3.25089491643449 & -0.0108949164344936 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232896&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]2.67[/C][C]2.60925747863248[/C][C]0.0607425213675215[/C][/ROW]
[ROW][C]14[/C][C]2.69[/C][C]2.68064686691753[/C][C]0.00935313308247165[/C][/ROW]
[ROW][C]15[/C][C]2.69[/C][C]2.68953976774224[/C][C]0.000460232257759152[/C][/ROW]
[ROW][C]16[/C][C]2.69[/C][C]2.69069784634582[/C][C]-0.000697846345818487[/C][/ROW]
[ROW][C]17[/C][C]2.69[/C][C]2.69046252332508[/C][C]-0.000462523325076347[/C][/ROW]
[ROW][C]18[/C][C]2.71[/C][C]2.71040675135514[/C][C]-0.000406751355138457[/C][/ROW]
[ROW][C]19[/C][C]2.71[/C][C]2.70455089613362[/C][C]0.00544910386638309[/C][/ROW]
[ROW][C]20[/C][C]2.71[/C][C]2.71369405965613[/C][C]-0.00369405965612657[/C][/ROW]
[ROW][C]21[/C][C]2.74[/C][C]2.73476596949352[/C][C]0.00523403050648108[/C][/ROW]
[ROW][C]22[/C][C]2.77[/C][C]2.77336334909482[/C][C]-0.00336334909481684[/C][/ROW]
[ROW][C]23[/C][C]2.82[/C][C]2.81434985177171[/C][C]0.00565014822829157[/C][/ROW]
[ROW][C]24[/C][C]2.82[/C][C]2.83169527547244[/C][C]-0.0116952754724426[/C][/ROW]
[ROW][C]25[/C][C]2.82[/C][C]2.82959372208197[/C][C]-0.00959372208196552[/C][/ROW]
[ROW][C]26[/C][C]2.8[/C][C]2.83774770744946[/C][C]-0.0377477074494572[/C][/ROW]
[ROW][C]27[/C][C]2.82[/C][C]2.80532482361603[/C][C]0.0146751763839745[/C][/ROW]
[ROW][C]28[/C][C]2.82[/C][C]2.81694060749637[/C][C]0.00305939250362641[/C][/ROW]
[ROW][C]29[/C][C]2.82[/C][C]2.81879671292237[/C][C]0.00120328707762818[/C][/ROW]
[ROW][C]30[/C][C]2.82[/C][C]2.83914216271594[/C][C]-0.0191421627159398[/C][/ROW]
[ROW][C]31[/C][C]2.82[/C][C]2.81685735957285[/C][C]0.0031426404271544[/C][/ROW]
[ROW][C]32[/C][C]2.82[/C][C]2.82155066064269[/C][C]-0.00155066064268672[/C][/ROW]
[ROW][C]33[/C][C]2.85[/C][C]2.84371019232381[/C][C]0.00628980767619192[/C][/ROW]
[ROW][C]34[/C][C]2.93[/C][C]2.88078459108558[/C][C]0.0492154089144239[/C][/ROW]
[ROW][C]35[/C][C]2.94[/C][C]2.96613268674812[/C][C]-0.0261326867481233[/C][/ROW]
[ROW][C]36[/C][C]2.94[/C][C]2.95465752064783[/C][C]-0.0146575206478321[/C][/ROW]
[ROW][C]37[/C][C]2.95[/C][C]2.94934479803688[/C][C]0.000655201963116525[/C][/ROW]
[ROW][C]38[/C][C]2.95[/C][C]2.96248593090414[/C][C]-0.0124859309041421[/C][/ROW]
[ROW][C]39[/C][C]2.96[/C][C]2.95625150822577[/C][C]0.00374849177423053[/C][/ROW]
[ROW][C]40[/C][C]2.96[/C][C]2.95749159613398[/C][C]0.00250840386601725[/C][/ROW]
[ROW][C]41[/C][C]2.97[/C][C]2.95848275304543[/C][C]0.0115172469545661[/C][/ROW]
[ROW][C]42[/C][C]2.97[/C][C]2.98540186023169[/C][C]-0.0154018602316861[/C][/ROW]
[ROW][C]43[/C][C]2.97[/C][C]2.96863679796486[/C][C]0.00136320203513973[/C][/ROW]
[ROW][C]44[/C][C]2.97[/C][C]2.97155379193087[/C][C]-0.00155379193087057[/C][/ROW]
[ROW][C]45[/C][C]2.98[/C][C]2.99465087572196[/C][C]-0.0146508757219617[/C][/ROW]
[ROW][C]46[/C][C]3.03[/C][C]3.01824040041889[/C][C]0.0117595995811097[/C][/ROW]
[ROW][C]47[/C][C]3.03[/C][C]3.06352432541904[/C][C]-0.0335243254190405[/C][/ROW]
[ROW][C]48[/C][C]3.03[/C][C]3.04519691037308[/C][C]-0.0151969103730822[/C][/ROW]
[ROW][C]49[/C][C]3.03[/C][C]3.03904752645255[/C][C]-0.00904752645254625[/C][/ROW]
[ROW][C]50[/C][C]3.04[/C][C]3.04065646034697[/C][C]-0.000656460346970533[/C][/ROW]
[ROW][C]51[/C][C]3.05[/C][C]3.04394248002542[/C][C]0.00605751997457871[/C][/ROW]
[ROW][C]52[/C][C]3.06[/C][C]3.04518351786664[/C][C]0.0148164821333578[/C][/ROW]
[ROW][C]53[/C][C]3.06[/C][C]3.05582722275262[/C][C]0.00417277724737852[/C][/ROW]
[ROW][C]54[/C][C]3.07[/C][C]3.07238340395187[/C][C]-0.0023834039518662[/C][/ROW]
[ROW][C]55[/C][C]3.07[/C][C]3.06680740038434[/C][C]0.00319259961565832[/C][/ROW]
[ROW][C]56[/C][C]3.07[/C][C]3.06978305915555[/C][C]0.000216940844453894[/C][/ROW]
[ROW][C]57[/C][C]3.04[/C][C]3.09193116904746[/C][C]-0.051931169047458[/C][/ROW]
[ROW][C]58[/C][C]3.06[/C][C]3.08514316502209[/C][C]-0.0251431650220857[/C][/ROW]
[ROW][C]59[/C][C]3.09[/C][C]3.09205912383372[/C][C]-0.00205912383372242[/C][/ROW]
[ROW][C]60[/C][C]3.09[/C][C]3.09906174825266[/C][C]-0.00906174825266426[/C][/ROW]
[ROW][C]61[/C][C]3.09[/C][C]3.09633497839343[/C][C]-0.00633497839343056[/C][/ROW]
[ROW][C]62[/C][C]3.09[/C][C]3.09885281658663[/C][C]-0.00885281658662818[/C][/ROW]
[ROW][C]63[/C][C]3.1[/C][C]3.09362908516706[/C][C]0.00637091483294228[/C][/ROW]
[ROW][C]64[/C][C]3.1[/C][C]3.09359066442499[/C][C]0.00640933557501322[/C][/ROW]
[ROW][C]65[/C][C]3.1[/C][C]3.09356723303047[/C][C]0.00643276696952855[/C][/ROW]
[ROW][C]66[/C][C]3.1[/C][C]3.10872996889441[/C][C]-0.00872996889441069[/C][/ROW]
[ROW][C]67[/C][C]3.1[/C][C]3.09567462365673[/C][C]0.00432537634326646[/C][/ROW]
[ROW][C]68[/C][C]3.11[/C][C]3.09652104142593[/C][C]0.0134789585740744[/C][/ROW]
[ROW][C]69[/C][C]3.11[/C][C]3.12205491293045[/C][C]-0.0120549129304499[/C][/ROW]
[ROW][C]70[/C][C]3.17[/C][C]3.14971387441759[/C][C]0.0202861255824112[/C][/ROW]
[ROW][C]71[/C][C]3.19[/C][C]3.19670879463617[/C][C]-0.00670879463617124[/C][/ROW]
[ROW][C]72[/C][C]3.19[/C][C]3.19935368055209[/C][C]-0.00935368055208974[/C][/ROW]
[ROW][C]73[/C][C]3.19[/C][C]3.19682295654652[/C][C]-0.00682295654651988[/C][/ROW]
[ROW][C]74[/C][C]3.19[/C][C]3.19883715055177[/C][C]-0.00883715055177081[/C][/ROW]
[ROW][C]75[/C][C]3.19[/C][C]3.19529395288467[/C][C]-0.00529395288466761[/C][/ROW]
[ROW][C]76[/C][C]3.19[/C][C]3.18542611545732[/C][C]0.00457388454268326[/C][/ROW]
[ROW][C]77[/C][C]3.19[/C][C]3.18361906416345[/C][C]0.00638093583655452[/C][/ROW]
[ROW][C]78[/C][C]3.19[/C][C]3.19695352683537[/C][C]-0.00695352683536843[/C][/ROW]
[ROW][C]79[/C][C]3.19[/C][C]3.18644569017299[/C][C]0.00355430982700788[/C][/ROW]
[ROW][C]80[/C][C]3.19[/C][C]3.18732603329844[/C][C]0.00267396670155806[/C][/ROW]
[ROW][C]81[/C][C]3.25[/C][C]3.2008246022108[/C][C]0.049175397789198[/C][/ROW]
[ROW][C]82[/C][C]3.23[/C][C]3.2835303597405[/C][C]-0.053530359740499[/C][/ROW]
[ROW][C]83[/C][C]3.24[/C][C]3.26599465094835[/C][C]-0.0259946509483462[/C][/ROW]
[ROW][C]84[/C][C]3.24[/C][C]3.25089491643449[/C][C]-0.0108949164344936[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232896&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232896&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	2.67	2.60925747863248	0.0607425213675215
14	2.69	2.68064686691753	0.00935313308247165
15	2.69	2.68953976774224	0.000460232257759152
16	2.69	2.69069784634582	-0.000697846345818487
17	2.69	2.69046252332508	-0.000462523325076347
18	2.71	2.71040675135514	-0.000406751355138457
19	2.71	2.70455089613362	0.00544910386638309
20	2.71	2.71369405965613	-0.00369405965612657
21	2.74	2.73476596949352	0.00523403050648108
22	2.77	2.77336334909482	-0.00336334909481684
23	2.82	2.81434985177171	0.00565014822829157
24	2.82	2.83169527547244	-0.0116952754724426
25	2.82	2.82959372208197	-0.00959372208196552
26	2.8	2.83774770744946	-0.0377477074494572
27	2.82	2.80532482361603	0.0146751763839745
28	2.82	2.81694060749637	0.00305939250362641
29	2.82	2.81879671292237	0.00120328707762818
30	2.82	2.83914216271594	-0.0191421627159398
31	2.82	2.81685735957285	0.0031426404271544
32	2.82	2.82155066064269	-0.00155066064268672
33	2.85	2.84371019232381	0.00628980767619192
34	2.93	2.88078459108558	0.0492154089144239
35	2.94	2.96613268674812	-0.0261326867481233
36	2.94	2.95465752064783	-0.0146575206478321
37	2.95	2.94934479803688	0.000655201963116525
38	2.95	2.96248593090414	-0.0124859309041421
39	2.96	2.95625150822577	0.00374849177423053
40	2.96	2.95749159613398	0.00250840386601725
41	2.97	2.95848275304543	0.0115172469545661
42	2.97	2.98540186023169	-0.0154018602316861
43	2.97	2.96863679796486	0.00136320203513973
44	2.97	2.97155379193087	-0.00155379193087057
45	2.98	2.99465087572196	-0.0146508757219617
46	3.03	3.01824040041889	0.0117595995811097
47	3.03	3.06352432541904	-0.0335243254190405
48	3.03	3.04519691037308	-0.0151969103730822
49	3.03	3.03904752645255	-0.00904752645254625
50	3.04	3.04065646034697	-0.000656460346970533
51	3.05	3.04394248002542	0.00605751997457871
52	3.06	3.04518351786664	0.0148164821333578
53	3.06	3.05582722275262	0.00417277724737852
54	3.07	3.07238340395187	-0.0023834039518662
55	3.07	3.06680740038434	0.00319259961565832
56	3.07	3.06978305915555	0.000216940844453894
57	3.04	3.09193116904746	-0.051931169047458
58	3.06	3.08514316502209	-0.0251431650220857
59	3.09	3.09205912383372	-0.00205912383372242
60	3.09	3.09906174825266	-0.00906174825266426
61	3.09	3.09633497839343	-0.00633497839343056
62	3.09	3.09885281658663	-0.00885281658662818
63	3.1	3.09362908516706	0.00637091483294228
64	3.1	3.09359066442499	0.00640933557501322
65	3.1	3.09356723303047	0.00643276696952855
66	3.1	3.10872996889441	-0.00872996889441069
67	3.1	3.09567462365673	0.00432537634326646
68	3.11	3.09652104142593	0.0134789585740744
69	3.11	3.12205491293045	-0.0120549129304499
70	3.17	3.14971387441759	0.0202861255824112
71	3.19	3.19670879463617	-0.00670879463617124
72	3.19	3.19935368055209	-0.00935368055208974
73	3.19	3.19682295654652	-0.00682295654651988
74	3.19	3.19883715055177	-0.00883715055177081
75	3.19	3.19529395288467	-0.00529395288466761
76	3.19	3.18542611545732	0.00457388454268326
77	3.19	3.18361906416345	0.00638093583655452
78	3.19	3.19695352683537	-0.00695352683536843
79	3.19	3.18644569017299	0.00355430982700788
80	3.19	3.18732603329844	0.00267396670155806
81	3.25	3.2008246022108	0.049175397789198
82	3.23	3.2835303597405	-0.053530359740499
83	3.24	3.26599465094835	-0.0259946509483462
84	3.24	3.25089491643449	-0.0108949164344936

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	3.24571837485775	3.21056939886885	3.28086735084666
86	3.25174399644068	3.20547953893181	3.29800845394956
87	3.25470366203985	3.19891139203913	3.31049593204057
88	3.24921335464488	3.1847540249346	3.31367268435517
89	3.24270070512518	3.1701093420226	3.31529206822777
90	3.24813053214623	3.16776447956859	3.32849658472387
91	3.24330711712678	3.15541504126061	3.33119919299294
92	3.23996131077741	3.14472018331428	3.33520243824055
93	3.25459871641311	3.15213559586737	3.35706183695885
94	3.28368876229907	3.17409453015826	3.39328299443987
95	3.31188062576983	3.19521911161869	3.42854213992096
96	3.31937850293167	3.19569279982746	3.44306420603587

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 3.24571837485775 & 3.21056939886885 & 3.28086735084666 \tabularnewline
86 & 3.25174399644068 & 3.20547953893181 & 3.29800845394956 \tabularnewline
87 & 3.25470366203985 & 3.19891139203913 & 3.31049593204057 \tabularnewline
88 & 3.24921335464488 & 3.1847540249346 & 3.31367268435517 \tabularnewline
89 & 3.24270070512518 & 3.1701093420226 & 3.31529206822777 \tabularnewline
90 & 3.24813053214623 & 3.16776447956859 & 3.32849658472387 \tabularnewline
91 & 3.24330711712678 & 3.15541504126061 & 3.33119919299294 \tabularnewline
92 & 3.23996131077741 & 3.14472018331428 & 3.33520243824055 \tabularnewline
93 & 3.25459871641311 & 3.15213559586737 & 3.35706183695885 \tabularnewline
94 & 3.28368876229907 & 3.17409453015826 & 3.39328299443987 \tabularnewline
95 & 3.31188062576983 & 3.19521911161869 & 3.42854213992096 \tabularnewline
96 & 3.31937850293167 & 3.19569279982746 & 3.44306420603587 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232896&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]85[/C][C]3.24571837485775[/C][C]3.21056939886885[/C][C]3.28086735084666[/C][/ROW]
[ROW][C]86[/C][C]3.25174399644068[/C][C]3.20547953893181[/C][C]3.29800845394956[/C][/ROW]
[ROW][C]87[/C][C]3.25470366203985[/C][C]3.19891139203913[/C][C]3.31049593204057[/C][/ROW]
[ROW][C]88[/C][C]3.24921335464488[/C][C]3.1847540249346[/C][C]3.31367268435517[/C][/ROW]
[ROW][C]89[/C][C]3.24270070512518[/C][C]3.1701093420226[/C][C]3.31529206822777[/C][/ROW]
[ROW][C]90[/C][C]3.24813053214623[/C][C]3.16776447956859[/C][C]3.32849658472387[/C][/ROW]
[ROW][C]91[/C][C]3.24330711712678[/C][C]3.15541504126061[/C][C]3.33119919299294[/C][/ROW]
[ROW][C]92[/C][C]3.23996131077741[/C][C]3.14472018331428[/C][C]3.33520243824055[/C][/ROW]
[ROW][C]93[/C][C]3.25459871641311[/C][C]3.15213559586737[/C][C]3.35706183695885[/C][/ROW]
[ROW][C]94[/C][C]3.28368876229907[/C][C]3.17409453015826[/C][C]3.39328299443987[/C][/ROW]
[ROW][C]95[/C][C]3.31188062576983[/C][C]3.19521911161869[/C][C]3.42854213992096[/C][/ROW]
[ROW][C]96[/C][C]3.31937850293167[/C][C]3.19569279982746[/C][C]3.44306420603587[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232896&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232896&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
85	3.24571837485775	3.21056939886885	3.28086735084666
86	3.25174399644068	3.20547953893181	3.29800845394956
87	3.25470366203985	3.19891139203913	3.31049593204057
88	3.24921335464488	3.1847540249346	3.31367268435517
89	3.24270070512518	3.1701093420226	3.31529206822777
90	3.24813053214623	3.16776447956859	3.32849658472387
91	3.24330711712678	3.15541504126061	3.33119919299294
92	3.23996131077741	3.14472018331428	3.33520243824055
93	3.25459871641311	3.15213559586737	3.35706183695885
94	3.28368876229907	3.17409453015826	3.39328299443987
95	3.31188062576983	3.19521911161869	3.42854213992096
96	3.31937850293167	3.19569279982746	3.44306420603587

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 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = additive ;

R code (references can be found in the software module):

par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=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