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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sun, 01 Jun 2008 13:17:09 -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/Jun/01/t1212347986nbtjqldv37y5ocq.htm/, Retrieved Sat, 18 May 2024 15:30:51 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13743, Retrieved Sat, 18 May 2024 15:30:51 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

226

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

-       [Exponential Smoothing] [Opgave 10 oef 2 w...] [2008-06-01 19:17:09] [2819b14941a6d5fb28b80112328b56ca] [Current]

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Dataseries X:

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3,35
3,35
3,35
3,4
3,42
3,42
3,42
3,42
3,42
3,42
3,42
3,42
3,42
3,42
3,42
3,43
3,47
3,51
3,52
3,52
3,52
3,52
3,52
3,52
3,52
3,52
3,52
3,58
3,6
3,61
3,61
3,61
3,63
3,68
3,69
3,69
3,69
3,69
3,69
3,69
3,69
3,69
3,78
3,79
3,79
3,8
3,8
3,8
3,8
3,81
3,95
3,99
4
4,06
4,16
4,19
4,2
4,2
4,2
4,2
4,2
4,23
4,38
4,43
4,44
4,44
4,44
4,44
4,44
4,45
4,45
4,45
4,45
4,45
4,45
4,45
4,45
4,46
4,46
4,46
4,48
4,58
4,67
4,68
4,68

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	5 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13743&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13743&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13743&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	5 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.0267594807601861
gamma	0.189768133478781

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0267594807601861 \tabularnewline
gamma & 0.189768133478781 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13743&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]0.0267594807601861[/C][/ROW]
[ROW][C]gamma[/C][C]0.189768133478781[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13743&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13743&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	0.0267594807601861
gamma	0.189768133478781

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	3.42	3.37588856275748	0.0441114372425191
14	3.42	3.42125663406065	-0.00125663406064991
15	3.42	3.42122005591351	-0.00122005591351426
16	3.43	3.43118801297687	-0.00118801297686932
17	3.47	3.47116689691699	-0.00116689691698868
18	3.51	3.51114601048734	-0.00114601048734286
19	3.52	3.52111584812909	-0.00111584812909182
20	3.52	3.52108339922625	-0.00108339922625289
21	3.52	3.52105189991888	-0.00105189991887711
22	3.52	3.51893367765305	0.00106632234695114
23	3.52	3.51771756681591	0.00228243318409271
24	3.52	3.51985915877127	0.000140841228727151
25	3.52	3.52725631854992	-0.00725631854992326
26	3.52	3.52066866925353	-0.000668669253534926
27	3.52	3.52064920560608	-0.000649205606076286
28	3.58	3.53092455285644	0.0490754471435606
29	3.6	3.62359185338927	-0.0235918533892709
30	3.61	3.64277357021164	-0.0327735702116403
31	3.61	3.62075858549629	-0.0107585854962853
32	3.61	3.61020987094782	-0.000209870947822655
33	3.63	3.61020376905174	0.0197962309482604
34	3.68	3.62853163971491	0.0514683602850878
35	3.69	3.67845666078794	0.0115433392120616
36	3.69	3.69091057956862	-0.000910579568619063
37	3.69	3.6986360438745	-0.00863604387450012
38	3.69	3.69170027495085	-0.00170027495085101
39	3.69	3.69165078328954	-0.00165078328953872
40	3.69	3.70239690162931	-0.0123969016293137
41	3.69	3.73434575429593	-0.0443457542959322
42	3.69	3.73276847830309	-0.0427684783030871
43	3.78	3.69970235431219	0.0802976456878097
44	3.79	3.78114554027880	0.00885445972120502
45	3.79	3.79135540566411	-0.00135540566411008
46	3.8	3.78906810068412	0.0109318993158816
47	3.8	3.79798584268982	0.00201415731017551
48	3.8	3.80028456439374	-0.000284564393736364
49	3.8	3.80825819241790	-0.00825819241789638
50	3.81	3.80113416193817	0.0088658380618285
51	3.95	3.81134396650686	0.138656033493137
52	3.99	3.96626860334788	0.0237313966521153
53	4	4.0418648555755	-0.041864855575497
54	4.06	4.05045036373338	0.0095496362666152
55	4.16	4.07613213306740	0.0838678669325965
56	4.19	4.16658234981999	0.0234176501800070
57	4.2	4.19712048543048	0.00287951456951863
58	4.2	4.20466226896450	-0.00466226896450372
59	4.2	4.20303330740683	-0.00303330740683005
60	4.2	4.2054193819983	-0.00541938199829772
61	4.2	4.21409271030591	-0.0140927103059125
62	4.23	4.20607422545851	0.0239257745414916
63	4.38	4.23662587007582	0.143374129924178
64	4.43	4.40291268319916	0.0270873168008423
65	4.44	4.4925019439234	-0.0525019439233958
66	4.44	4.50080362897636	-0.0608036289763598
67	4.44	4.46077086208357	-0.0207708620835731
68	4.44	4.44757759426897	-0.00757759426896687
69	4.44	4.44735727938848	-0.00735727938848019
70	4.45	4.44450665996467	0.00549334003532742
71	4.45	4.45303088351653	-0.00303088351652914
72	4.45	4.45556436552752	-0.0055643655275226
73	4.45	4.46475882108412	-0.0147588210841247
74	4.45	4.45626807460502	-0.00626807460502032
75	4.45	4.45608562327545	-0.00608562327544604
76	4.45	4.46893748942416	-0.0189374894241565
77	4.45	4.50739572231754	-0.0573957223175423
78	4.46	4.50542348674352	-0.0454234867435153
79	4.46	4.47571799978883	-0.0157179997888264
80	4.46	4.46261496105226	-0.00261496105225678
81	4.48	4.46253893232714	0.0174610676728584
82	4.58	4.48029360529785	0.0997063947021504
83	4.67	4.58103250063080	0.088967499369196
84	4.68	4.67585918132283	0.00414081867717453
85	4.68	4.69576899697257	-0.0157689969725654

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 3.42 & 3.37588856275748 & 0.0441114372425191 \tabularnewline
14 & 3.42 & 3.42125663406065 & -0.00125663406064991 \tabularnewline
15 & 3.42 & 3.42122005591351 & -0.00122005591351426 \tabularnewline
16 & 3.43 & 3.43118801297687 & -0.00118801297686932 \tabularnewline
17 & 3.47 & 3.47116689691699 & -0.00116689691698868 \tabularnewline
18 & 3.51 & 3.51114601048734 & -0.00114601048734286 \tabularnewline
19 & 3.52 & 3.52111584812909 & -0.00111584812909182 \tabularnewline
20 & 3.52 & 3.52108339922625 & -0.00108339922625289 \tabularnewline
21 & 3.52 & 3.52105189991888 & -0.00105189991887711 \tabularnewline
22 & 3.52 & 3.51893367765305 & 0.00106632234695114 \tabularnewline
23 & 3.52 & 3.51771756681591 & 0.00228243318409271 \tabularnewline
24 & 3.52 & 3.51985915877127 & 0.000140841228727151 \tabularnewline
25 & 3.52 & 3.52725631854992 & -0.00725631854992326 \tabularnewline
26 & 3.52 & 3.52066866925353 & -0.000668669253534926 \tabularnewline
27 & 3.52 & 3.52064920560608 & -0.000649205606076286 \tabularnewline
28 & 3.58 & 3.53092455285644 & 0.0490754471435606 \tabularnewline
29 & 3.6 & 3.62359185338927 & -0.0235918533892709 \tabularnewline
30 & 3.61 & 3.64277357021164 & -0.0327735702116403 \tabularnewline
31 & 3.61 & 3.62075858549629 & -0.0107585854962853 \tabularnewline
32 & 3.61 & 3.61020987094782 & -0.000209870947822655 \tabularnewline
33 & 3.63 & 3.61020376905174 & 0.0197962309482604 \tabularnewline
34 & 3.68 & 3.62853163971491 & 0.0514683602850878 \tabularnewline
35 & 3.69 & 3.67845666078794 & 0.0115433392120616 \tabularnewline
36 & 3.69 & 3.69091057956862 & -0.000910579568619063 \tabularnewline
37 & 3.69 & 3.6986360438745 & -0.00863604387450012 \tabularnewline
38 & 3.69 & 3.69170027495085 & -0.00170027495085101 \tabularnewline
39 & 3.69 & 3.69165078328954 & -0.00165078328953872 \tabularnewline
40 & 3.69 & 3.70239690162931 & -0.0123969016293137 \tabularnewline
41 & 3.69 & 3.73434575429593 & -0.0443457542959322 \tabularnewline
42 & 3.69 & 3.73276847830309 & -0.0427684783030871 \tabularnewline
43 & 3.78 & 3.69970235431219 & 0.0802976456878097 \tabularnewline
44 & 3.79 & 3.78114554027880 & 0.00885445972120502 \tabularnewline
45 & 3.79 & 3.79135540566411 & -0.00135540566411008 \tabularnewline
46 & 3.8 & 3.78906810068412 & 0.0109318993158816 \tabularnewline
47 & 3.8 & 3.79798584268982 & 0.00201415731017551 \tabularnewline
48 & 3.8 & 3.80028456439374 & -0.000284564393736364 \tabularnewline
49 & 3.8 & 3.80825819241790 & -0.00825819241789638 \tabularnewline
50 & 3.81 & 3.80113416193817 & 0.0088658380618285 \tabularnewline
51 & 3.95 & 3.81134396650686 & 0.138656033493137 \tabularnewline
52 & 3.99 & 3.96626860334788 & 0.0237313966521153 \tabularnewline
53 & 4 & 4.0418648555755 & -0.041864855575497 \tabularnewline
54 & 4.06 & 4.05045036373338 & 0.0095496362666152 \tabularnewline
55 & 4.16 & 4.07613213306740 & 0.0838678669325965 \tabularnewline
56 & 4.19 & 4.16658234981999 & 0.0234176501800070 \tabularnewline
57 & 4.2 & 4.19712048543048 & 0.00287951456951863 \tabularnewline
58 & 4.2 & 4.20466226896450 & -0.00466226896450372 \tabularnewline
59 & 4.2 & 4.20303330740683 & -0.00303330740683005 \tabularnewline
60 & 4.2 & 4.2054193819983 & -0.00541938199829772 \tabularnewline
61 & 4.2 & 4.21409271030591 & -0.0140927103059125 \tabularnewline
62 & 4.23 & 4.20607422545851 & 0.0239257745414916 \tabularnewline
63 & 4.38 & 4.23662587007582 & 0.143374129924178 \tabularnewline
64 & 4.43 & 4.40291268319916 & 0.0270873168008423 \tabularnewline
65 & 4.44 & 4.4925019439234 & -0.0525019439233958 \tabularnewline
66 & 4.44 & 4.50080362897636 & -0.0608036289763598 \tabularnewline
67 & 4.44 & 4.46077086208357 & -0.0207708620835731 \tabularnewline
68 & 4.44 & 4.44757759426897 & -0.00757759426896687 \tabularnewline
69 & 4.44 & 4.44735727938848 & -0.00735727938848019 \tabularnewline
70 & 4.45 & 4.44450665996467 & 0.00549334003532742 \tabularnewline
71 & 4.45 & 4.45303088351653 & -0.00303088351652914 \tabularnewline
72 & 4.45 & 4.45556436552752 & -0.0055643655275226 \tabularnewline
73 & 4.45 & 4.46475882108412 & -0.0147588210841247 \tabularnewline
74 & 4.45 & 4.45626807460502 & -0.00626807460502032 \tabularnewline
75 & 4.45 & 4.45608562327545 & -0.00608562327544604 \tabularnewline
76 & 4.45 & 4.46893748942416 & -0.0189374894241565 \tabularnewline
77 & 4.45 & 4.50739572231754 & -0.0573957223175423 \tabularnewline
78 & 4.46 & 4.50542348674352 & -0.0454234867435153 \tabularnewline
79 & 4.46 & 4.47571799978883 & -0.0157179997888264 \tabularnewline
80 & 4.46 & 4.46261496105226 & -0.00261496105225678 \tabularnewline
81 & 4.48 & 4.46253893232714 & 0.0174610676728584 \tabularnewline
82 & 4.58 & 4.48029360529785 & 0.0997063947021504 \tabularnewline
83 & 4.67 & 4.58103250063080 & 0.088967499369196 \tabularnewline
84 & 4.68 & 4.67585918132283 & 0.00414081867717453 \tabularnewline
85 & 4.68 & 4.69576899697257 & -0.0157689969725654 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13743&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]3.42[/C][C]3.37588856275748[/C][C]0.0441114372425191[/C][/ROW]
[ROW][C]14[/C][C]3.42[/C][C]3.42125663406065[/C][C]-0.00125663406064991[/C][/ROW]
[ROW][C]15[/C][C]3.42[/C][C]3.42122005591351[/C][C]-0.00122005591351426[/C][/ROW]
[ROW][C]16[/C][C]3.43[/C][C]3.43118801297687[/C][C]-0.00118801297686932[/C][/ROW]
[ROW][C]17[/C][C]3.47[/C][C]3.47116689691699[/C][C]-0.00116689691698868[/C][/ROW]
[ROW][C]18[/C][C]3.51[/C][C]3.51114601048734[/C][C]-0.00114601048734286[/C][/ROW]
[ROW][C]19[/C][C]3.52[/C][C]3.52111584812909[/C][C]-0.00111584812909182[/C][/ROW]
[ROW][C]20[/C][C]3.52[/C][C]3.52108339922625[/C][C]-0.00108339922625289[/C][/ROW]
[ROW][C]21[/C][C]3.52[/C][C]3.52105189991888[/C][C]-0.00105189991887711[/C][/ROW]
[ROW][C]22[/C][C]3.52[/C][C]3.51893367765305[/C][C]0.00106632234695114[/C][/ROW]
[ROW][C]23[/C][C]3.52[/C][C]3.51771756681591[/C][C]0.00228243318409271[/C][/ROW]
[ROW][C]24[/C][C]3.52[/C][C]3.51985915877127[/C][C]0.000140841228727151[/C][/ROW]
[ROW][C]25[/C][C]3.52[/C][C]3.52725631854992[/C][C]-0.00725631854992326[/C][/ROW]
[ROW][C]26[/C][C]3.52[/C][C]3.52066866925353[/C][C]-0.000668669253534926[/C][/ROW]
[ROW][C]27[/C][C]3.52[/C][C]3.52064920560608[/C][C]-0.000649205606076286[/C][/ROW]
[ROW][C]28[/C][C]3.58[/C][C]3.53092455285644[/C][C]0.0490754471435606[/C][/ROW]
[ROW][C]29[/C][C]3.6[/C][C]3.62359185338927[/C][C]-0.0235918533892709[/C][/ROW]
[ROW][C]30[/C][C]3.61[/C][C]3.64277357021164[/C][C]-0.0327735702116403[/C][/ROW]
[ROW][C]31[/C][C]3.61[/C][C]3.62075858549629[/C][C]-0.0107585854962853[/C][/ROW]
[ROW][C]32[/C][C]3.61[/C][C]3.61020987094782[/C][C]-0.000209870947822655[/C][/ROW]
[ROW][C]33[/C][C]3.63[/C][C]3.61020376905174[/C][C]0.0197962309482604[/C][/ROW]
[ROW][C]34[/C][C]3.68[/C][C]3.62853163971491[/C][C]0.0514683602850878[/C][/ROW]
[ROW][C]35[/C][C]3.69[/C][C]3.67845666078794[/C][C]0.0115433392120616[/C][/ROW]
[ROW][C]36[/C][C]3.69[/C][C]3.69091057956862[/C][C]-0.000910579568619063[/C][/ROW]
[ROW][C]37[/C][C]3.69[/C][C]3.6986360438745[/C][C]-0.00863604387450012[/C][/ROW]
[ROW][C]38[/C][C]3.69[/C][C]3.69170027495085[/C][C]-0.00170027495085101[/C][/ROW]
[ROW][C]39[/C][C]3.69[/C][C]3.69165078328954[/C][C]-0.00165078328953872[/C][/ROW]
[ROW][C]40[/C][C]3.69[/C][C]3.70239690162931[/C][C]-0.0123969016293137[/C][/ROW]
[ROW][C]41[/C][C]3.69[/C][C]3.73434575429593[/C][C]-0.0443457542959322[/C][/ROW]
[ROW][C]42[/C][C]3.69[/C][C]3.73276847830309[/C][C]-0.0427684783030871[/C][/ROW]
[ROW][C]43[/C][C]3.78[/C][C]3.69970235431219[/C][C]0.0802976456878097[/C][/ROW]
[ROW][C]44[/C][C]3.79[/C][C]3.78114554027880[/C][C]0.00885445972120502[/C][/ROW]
[ROW][C]45[/C][C]3.79[/C][C]3.79135540566411[/C][C]-0.00135540566411008[/C][/ROW]
[ROW][C]46[/C][C]3.8[/C][C]3.78906810068412[/C][C]0.0109318993158816[/C][/ROW]
[ROW][C]47[/C][C]3.8[/C][C]3.79798584268982[/C][C]0.00201415731017551[/C][/ROW]
[ROW][C]48[/C][C]3.8[/C][C]3.80028456439374[/C][C]-0.000284564393736364[/C][/ROW]
[ROW][C]49[/C][C]3.8[/C][C]3.80825819241790[/C][C]-0.00825819241789638[/C][/ROW]
[ROW][C]50[/C][C]3.81[/C][C]3.80113416193817[/C][C]0.0088658380618285[/C][/ROW]
[ROW][C]51[/C][C]3.95[/C][C]3.81134396650686[/C][C]0.138656033493137[/C][/ROW]
[ROW][C]52[/C][C]3.99[/C][C]3.96626860334788[/C][C]0.0237313966521153[/C][/ROW]
[ROW][C]53[/C][C]4[/C][C]4.0418648555755[/C][C]-0.041864855575497[/C][/ROW]
[ROW][C]54[/C][C]4.06[/C][C]4.05045036373338[/C][C]0.0095496362666152[/C][/ROW]
[ROW][C]55[/C][C]4.16[/C][C]4.07613213306740[/C][C]0.0838678669325965[/C][/ROW]
[ROW][C]56[/C][C]4.19[/C][C]4.16658234981999[/C][C]0.0234176501800070[/C][/ROW]
[ROW][C]57[/C][C]4.2[/C][C]4.19712048543048[/C][C]0.00287951456951863[/C][/ROW]
[ROW][C]58[/C][C]4.2[/C][C]4.20466226896450[/C][C]-0.00466226896450372[/C][/ROW]
[ROW][C]59[/C][C]4.2[/C][C]4.20303330740683[/C][C]-0.00303330740683005[/C][/ROW]
[ROW][C]60[/C][C]4.2[/C][C]4.2054193819983[/C][C]-0.00541938199829772[/C][/ROW]
[ROW][C]61[/C][C]4.2[/C][C]4.21409271030591[/C][C]-0.0140927103059125[/C][/ROW]
[ROW][C]62[/C][C]4.23[/C][C]4.20607422545851[/C][C]0.0239257745414916[/C][/ROW]
[ROW][C]63[/C][C]4.38[/C][C]4.23662587007582[/C][C]0.143374129924178[/C][/ROW]
[ROW][C]64[/C][C]4.43[/C][C]4.40291268319916[/C][C]0.0270873168008423[/C][/ROW]
[ROW][C]65[/C][C]4.44[/C][C]4.4925019439234[/C][C]-0.0525019439233958[/C][/ROW]
[ROW][C]66[/C][C]4.44[/C][C]4.50080362897636[/C][C]-0.0608036289763598[/C][/ROW]
[ROW][C]67[/C][C]4.44[/C][C]4.46077086208357[/C][C]-0.0207708620835731[/C][/ROW]
[ROW][C]68[/C][C]4.44[/C][C]4.44757759426897[/C][C]-0.00757759426896687[/C][/ROW]
[ROW][C]69[/C][C]4.44[/C][C]4.44735727938848[/C][C]-0.00735727938848019[/C][/ROW]
[ROW][C]70[/C][C]4.45[/C][C]4.44450665996467[/C][C]0.00549334003532742[/C][/ROW]
[ROW][C]71[/C][C]4.45[/C][C]4.45303088351653[/C][C]-0.00303088351652914[/C][/ROW]
[ROW][C]72[/C][C]4.45[/C][C]4.45556436552752[/C][C]-0.0055643655275226[/C][/ROW]
[ROW][C]73[/C][C]4.45[/C][C]4.46475882108412[/C][C]-0.0147588210841247[/C][/ROW]
[ROW][C]74[/C][C]4.45[/C][C]4.45626807460502[/C][C]-0.00626807460502032[/C][/ROW]
[ROW][C]75[/C][C]4.45[/C][C]4.45608562327545[/C][C]-0.00608562327544604[/C][/ROW]
[ROW][C]76[/C][C]4.45[/C][C]4.46893748942416[/C][C]-0.0189374894241565[/C][/ROW]
[ROW][C]77[/C][C]4.45[/C][C]4.50739572231754[/C][C]-0.0573957223175423[/C][/ROW]
[ROW][C]78[/C][C]4.46[/C][C]4.50542348674352[/C][C]-0.0454234867435153[/C][/ROW]
[ROW][C]79[/C][C]4.46[/C][C]4.47571799978883[/C][C]-0.0157179997888264[/C][/ROW]
[ROW][C]80[/C][C]4.46[/C][C]4.46261496105226[/C][C]-0.00261496105225678[/C][/ROW]
[ROW][C]81[/C][C]4.48[/C][C]4.46253893232714[/C][C]0.0174610676728584[/C][/ROW]
[ROW][C]82[/C][C]4.58[/C][C]4.48029360529785[/C][C]0.0997063947021504[/C][/ROW]
[ROW][C]83[/C][C]4.67[/C][C]4.58103250063080[/C][C]0.088967499369196[/C][/ROW]
[ROW][C]84[/C][C]4.68[/C][C]4.67585918132283[/C][C]0.00414081867717453[/C][/ROW]
[ROW][C]85[/C][C]4.68[/C][C]4.69576899697257[/C][C]-0.0157689969725654[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13743&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13743&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	3.42	3.37588856275748	0.0441114372425191
14	3.42	3.42125663406065	-0.00125663406064991
15	3.42	3.42122005591351	-0.00122005591351426
16	3.43	3.43118801297687	-0.00118801297686932
17	3.47	3.47116689691699	-0.00116689691698868
18	3.51	3.51114601048734	-0.00114601048734286
19	3.52	3.52111584812909	-0.00111584812909182
20	3.52	3.52108339922625	-0.00108339922625289
21	3.52	3.52105189991888	-0.00105189991887711
22	3.52	3.51893367765305	0.00106632234695114
23	3.52	3.51771756681591	0.00228243318409271
24	3.52	3.51985915877127	0.000140841228727151
25	3.52	3.52725631854992	-0.00725631854992326
26	3.52	3.52066866925353	-0.000668669253534926
27	3.52	3.52064920560608	-0.000649205606076286
28	3.58	3.53092455285644	0.0490754471435606
29	3.6	3.62359185338927	-0.0235918533892709
30	3.61	3.64277357021164	-0.0327735702116403
31	3.61	3.62075858549629	-0.0107585854962853
32	3.61	3.61020987094782	-0.000209870947822655
33	3.63	3.61020376905174	0.0197962309482604
34	3.68	3.62853163971491	0.0514683602850878
35	3.69	3.67845666078794	0.0115433392120616
36	3.69	3.69091057956862	-0.000910579568619063
37	3.69	3.6986360438745	-0.00863604387450012
38	3.69	3.69170027495085	-0.00170027495085101
39	3.69	3.69165078328954	-0.00165078328953872
40	3.69	3.70239690162931	-0.0123969016293137
41	3.69	3.73434575429593	-0.0443457542959322
42	3.69	3.73276847830309	-0.0427684783030871
43	3.78	3.69970235431219	0.0802976456878097
44	3.79	3.78114554027880	0.00885445972120502
45	3.79	3.79135540566411	-0.00135540566411008
46	3.8	3.78906810068412	0.0109318993158816
47	3.8	3.79798584268982	0.00201415731017551
48	3.8	3.80028456439374	-0.000284564393736364
49	3.8	3.80825819241790	-0.00825819241789638
50	3.81	3.80113416193817	0.0088658380618285
51	3.95	3.81134396650686	0.138656033493137
52	3.99	3.96626860334788	0.0237313966521153
53	4	4.0418648555755	-0.041864855575497
54	4.06	4.05045036373338	0.0095496362666152
55	4.16	4.07613213306740	0.0838678669325965
56	4.19	4.16658234981999	0.0234176501800070
57	4.2	4.19712048543048	0.00287951456951863
58	4.2	4.20466226896450	-0.00466226896450372
59	4.2	4.20303330740683	-0.00303330740683005
60	4.2	4.2054193819983	-0.00541938199829772
61	4.2	4.21409271030591	-0.0140927103059125
62	4.23	4.20607422545851	0.0239257745414916
63	4.38	4.23662587007582	0.143374129924178
64	4.43	4.40291268319916	0.0270873168008423
65	4.44	4.4925019439234	-0.0525019439233958
66	4.44	4.50080362897636	-0.0608036289763598
67	4.44	4.46077086208357	-0.0207708620835731
68	4.44	4.44757759426897	-0.00757759426896687
69	4.44	4.44735727938848	-0.00735727938848019
70	4.45	4.44450665996467	0.00549334003532742
71	4.45	4.45303088351653	-0.00303088351652914
72	4.45	4.45556436552752	-0.0055643655275226
73	4.45	4.46475882108412	-0.0147588210841247
74	4.45	4.45626807460502	-0.00626807460502032
75	4.45	4.45608562327545	-0.00608562327544604
76	4.45	4.46893748942416	-0.0189374894241565
77	4.45	4.50739572231754	-0.0573957223175423
78	4.46	4.50542348674352	-0.0454234867435153
79	4.46	4.47571799978883	-0.0157179997888264
80	4.46	4.46261496105226	-0.00261496105225678
81	4.48	4.46253893232714	0.0174610676728584
82	4.58	4.48029360529785	0.0997063947021504
83	4.67	4.58103250063080	0.088967499369196
84	4.68	4.67585918132283	0.00414081867717453
85	4.68	4.69576899697257	-0.0157689969725654

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
86	4.68683220134191	4.61326257311618	4.76040182956764
87	4.69363142873911	4.58831751033437	4.79894534714385
88	4.71414177389617	4.5833411009018	4.84494244689053
89	4.77594962996827	4.62181187770708	4.93008738222946
90	4.83788189082637	4.66219720044024	5.01356658121249
91	4.85852974054167	4.66387081020305	5.05318867088028
92	4.86536171510408	4.65314750974865	5.07757592045951
93	4.87216118740882	4.64308854197157	5.10123383284608
94	4.87603562921543	4.63078061142329	5.12129064700757
95	4.87815691509444	4.61724439068912	5.13906943949976
96	4.88314036492862	4.60678045330341	5.15950027655383
97	4.89836368675299	0.881671161459107	8.91505621204688

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
86 & 4.68683220134191 & 4.61326257311618 & 4.76040182956764 \tabularnewline
87 & 4.69363142873911 & 4.58831751033437 & 4.79894534714385 \tabularnewline
88 & 4.71414177389617 & 4.5833411009018 & 4.84494244689053 \tabularnewline
89 & 4.77594962996827 & 4.62181187770708 & 4.93008738222946 \tabularnewline
90 & 4.83788189082637 & 4.66219720044024 & 5.01356658121249 \tabularnewline
91 & 4.85852974054167 & 4.66387081020305 & 5.05318867088028 \tabularnewline
92 & 4.86536171510408 & 4.65314750974865 & 5.07757592045951 \tabularnewline
93 & 4.87216118740882 & 4.64308854197157 & 5.10123383284608 \tabularnewline
94 & 4.87603562921543 & 4.63078061142329 & 5.12129064700757 \tabularnewline
95 & 4.87815691509444 & 4.61724439068912 & 5.13906943949976 \tabularnewline
96 & 4.88314036492862 & 4.60678045330341 & 5.15950027655383 \tabularnewline
97 & 4.89836368675299 & 0.881671161459107 & 8.91505621204688 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13743&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]86[/C][C]4.68683220134191[/C][C]4.61326257311618[/C][C]4.76040182956764[/C][/ROW]
[ROW][C]87[/C][C]4.69363142873911[/C][C]4.58831751033437[/C][C]4.79894534714385[/C][/ROW]
[ROW][C]88[/C][C]4.71414177389617[/C][C]4.5833411009018[/C][C]4.84494244689053[/C][/ROW]
[ROW][C]89[/C][C]4.77594962996827[/C][C]4.62181187770708[/C][C]4.93008738222946[/C][/ROW]
[ROW][C]90[/C][C]4.83788189082637[/C][C]4.66219720044024[/C][C]5.01356658121249[/C][/ROW]
[ROW][C]91[/C][C]4.85852974054167[/C][C]4.66387081020305[/C][C]5.05318867088028[/C][/ROW]
[ROW][C]92[/C][C]4.86536171510408[/C][C]4.65314750974865[/C][C]5.07757592045951[/C][/ROW]
[ROW][C]93[/C][C]4.87216118740882[/C][C]4.64308854197157[/C][C]5.10123383284608[/C][/ROW]
[ROW][C]94[/C][C]4.87603562921543[/C][C]4.63078061142329[/C][C]5.12129064700757[/C][/ROW]
[ROW][C]95[/C][C]4.87815691509444[/C][C]4.61724439068912[/C][C]5.13906943949976[/C][/ROW]
[ROW][C]96[/C][C]4.88314036492862[/C][C]4.60678045330341[/C][C]5.15950027655383[/C][/ROW]
[ROW][C]97[/C][C]4.89836368675299[/C][C]0.881671161459107[/C][C]8.91505621204688[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13743&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13743&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
86	4.68683220134191	4.61326257311618	4.76040182956764
87	4.69363142873911	4.58831751033437	4.79894534714385
88	4.71414177389617	4.5833411009018	4.84494244689053
89	4.77594962996827	4.62181187770708	4.93008738222946
90	4.83788189082637	4.66219720044024	5.01356658121249
91	4.85852974054167	4.66387081020305	5.05318867088028
92	4.86536171510408	4.65314750974865	5.07757592045951
93	4.87216118740882	4.64308854197157	5.10123383284608
94	4.87603562921543	4.63078061142329	5.12129064700757
95	4.87815691509444	4.61724439068912	5.13906943949976
96	4.88314036492862	4.60678045330341	5.15950027655383
97	4.89836368675299	0.881671161459107	8.91505621204688

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