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Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Wed, 26 Dec 2012 08:19:59 -0500

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/26/t1356528008w4k70wyzlc7hgzl.htm/, Retrieved Tue, 16 Apr 2024 22:49:01 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=204728, Retrieved Tue, 16 Apr 2024 22:49:01 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

125

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

-       [Exponential Smoothing] [] [2012-12-26 13:19:59] [76c30f62b7052b57088120e90a652e05] [Current]

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Dataseries X:

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Histogram

Boxplots

0.67
0.66
0.66
0.67
0.67
0.67
0.67
0.68
0.68
0.67
0.67
0.67
0.67
0.67
0.69
0.69
0.69
0.69
0.69
0.69
0.7
0.69
0.68
0.7
0.7
0.71
0.69
0.7
0.7
0.71
0.71
0.71
0.71
0.7
0.7
0.71
0.71
0.71
0.71
0.7
0.69
0.7
0.7
0.7
0.71
0.7
0.7
0.69
0.7
0.71
0.71
0.71
0.71
0.71
0.71
0.71
0.71
0.69
0.7
0.7
0.7
0.72
0.7
0.69
0.7
0.71
0.72
0.72
0.73
0.72
0.74
0.75

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Gwilym Jenkins' @ jenkins.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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204728&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204728&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204728&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	3 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.694725004533896
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.694725004533896 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204728&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]0.694725004533896[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204728&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204728&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	0.694725004533896
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	0.66	0.67	-0.01
3	0.66	0.663052749954661	-0.00305274995466109
4	0.67	0.660931928228568	0.00906807177143165
5	0.67	0.66723174443109	0.00276825556891014
6	0.67	0.669154920793752	0.000845079206248101
7	0.67	0.669742018449144	0.000257981550855879
8	0.68	0.669921244683232	0.0100787553167678
9	0.68	0.67692320801637	0.00307679198363031
10	0.67	0.679060732341147	-0.00906073234114713
11	0.67	0.672766015024363	-0.00276601502436324
12	0.67	0.670844395224022	-0.000844395224021688
13	0.67	0.670257772748185	-0.000257772748184837
14	0.67	0.670078691574533	-7.86915745334404e-05
15	0.69	0.670024022570059	0.0199759774299409
16	0.69	0.683901833580644	0.00609816641935623
17	0.69	0.688138382273979	0.00186161772602056
18	0.69	0.689431694657129	0.000568305342870556
19	0.69	0.689826510589032	0.000173489410968175
20	0.69	0.689947038020853	5.29619791467262e-05
21	0.7	0.689983832032056	0.0100161679679439
22	0.69	0.696942314368998	-0.00694231436899817
23	0.68	0.69211931498752	-0.0121193149875201
24	0.7	0.683699723827867	0.0163002761721325
25	0.7	0.695023933265456	0.00497606673454398
26	0.71	0.698480931250173	0.011519068749827
27	0.69	0.706483516339623	-0.0164835163396229
28	0.7	0.695032005375844	0.0049679946241562
29	0.7	0.698483395463635	0.00151660453636493
30	0.71	0.699537018557037	0.0104629814429626
31	0.71	0.706805913387438	0.00319408661256237
32	0.71	0.709024925223832	0.000975074776168317
33	0.71	0.709702334052126	0.000297665947873949
34	0.7	0.709909130029112	-0.00990913002911242
35	0.7	0.70302500962471	-0.00302500962471031
36	0.71	0.700923459799468	0.00907654020053161
37	0.71	0.707229159231435	0.00277084076856515
38	0.71	0.709154131596939	0.000845868403061001
39	0.71	0.709741777527091	0.000258222472909408
40	0.7	0.709921171135753	-0.0099211711357533
41	0.69	0.703028685473486	-0.0130286854734856
42	0.7	0.693977331898848	0.00602266810115237
43	0.7	0.698161430022727	0.00183856997727316
44	0.7	0.699438730558524	0.000561269441476164
45	0.71	0.699828658473798	0.0101713415262019
46	0.7	0.706894943761704	-0.00689494376170452
47	0.7	0.702104853925593	-0.00210485392559334
48	0.69	0.700642559272592	-0.0106425592725923
49	0.7	0.693248907233688	0.00675109276631169
50	0.71	0.697939060186373	0.0120609398136271
51	0.71	0.706318096653078	0.00368190334692198
52	0.71	0.708876006972462	0.00112399302753829
53	0.71	0.709656873033614	0.000343126966385721
54	0.71	0.709895251916892	0.000104748083107675
55	0.71	0.709968023029404	3.19769705957595e-05
56	0.71	0.709990238230446	9.76176955369557e-06
57	0.71	0.709997019975844	2.98002415621834e-06
58	0.69	0.709999090273139	-0.0199990902731393
59	0.7	0.696105222192459	0.00389477780754122
60	0.7	0.698811021722461	0.00118897827753861
61	0.7	0.699637034661715	0.000362965338284948
62	0.72	0.699889195758001	0.0201108042419993
63	0.7	0.713860674326204	-0.013860674326204
64	0.69	0.704231317292089	-0.014231317292089
65	0.7	0.694344465321819	0.00565553467818081
66	0.71	0.69827350667676	0.0117264933232401
67	0.72	0.706420194803915	0.0135798051960854
68	0.72	0.715854425030334	0.0041455749696655
69	0.73	0.718734459619931	0.011265540380069
70	0.72	0.726560912211551	-0.0065609122115512
71	0.74	0.722002882445635	0.0179971175543652
72	0.75	0.734505930020188	0.0154940699798117

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 0.66 & 0.67 & -0.01 \tabularnewline
3 & 0.66 & 0.663052749954661 & -0.00305274995466109 \tabularnewline
4 & 0.67 & 0.660931928228568 & 0.00906807177143165 \tabularnewline
5 & 0.67 & 0.66723174443109 & 0.00276825556891014 \tabularnewline
6 & 0.67 & 0.669154920793752 & 0.000845079206248101 \tabularnewline
7 & 0.67 & 0.669742018449144 & 0.000257981550855879 \tabularnewline
8 & 0.68 & 0.669921244683232 & 0.0100787553167678 \tabularnewline
9 & 0.68 & 0.67692320801637 & 0.00307679198363031 \tabularnewline
10 & 0.67 & 0.679060732341147 & -0.00906073234114713 \tabularnewline
11 & 0.67 & 0.672766015024363 & -0.00276601502436324 \tabularnewline
12 & 0.67 & 0.670844395224022 & -0.000844395224021688 \tabularnewline
13 & 0.67 & 0.670257772748185 & -0.000257772748184837 \tabularnewline
14 & 0.67 & 0.670078691574533 & -7.86915745334404e-05 \tabularnewline
15 & 0.69 & 0.670024022570059 & 0.0199759774299409 \tabularnewline
16 & 0.69 & 0.683901833580644 & 0.00609816641935623 \tabularnewline
17 & 0.69 & 0.688138382273979 & 0.00186161772602056 \tabularnewline
18 & 0.69 & 0.689431694657129 & 0.000568305342870556 \tabularnewline
19 & 0.69 & 0.689826510589032 & 0.000173489410968175 \tabularnewline
20 & 0.69 & 0.689947038020853 & 5.29619791467262e-05 \tabularnewline
21 & 0.7 & 0.689983832032056 & 0.0100161679679439 \tabularnewline
22 & 0.69 & 0.696942314368998 & -0.00694231436899817 \tabularnewline
23 & 0.68 & 0.69211931498752 & -0.0121193149875201 \tabularnewline
24 & 0.7 & 0.683699723827867 & 0.0163002761721325 \tabularnewline
25 & 0.7 & 0.695023933265456 & 0.00497606673454398 \tabularnewline
26 & 0.71 & 0.698480931250173 & 0.011519068749827 \tabularnewline
27 & 0.69 & 0.706483516339623 & -0.0164835163396229 \tabularnewline
28 & 0.7 & 0.695032005375844 & 0.0049679946241562 \tabularnewline
29 & 0.7 & 0.698483395463635 & 0.00151660453636493 \tabularnewline
30 & 0.71 & 0.699537018557037 & 0.0104629814429626 \tabularnewline
31 & 0.71 & 0.706805913387438 & 0.00319408661256237 \tabularnewline
32 & 0.71 & 0.709024925223832 & 0.000975074776168317 \tabularnewline
33 & 0.71 & 0.709702334052126 & 0.000297665947873949 \tabularnewline
34 & 0.7 & 0.709909130029112 & -0.00990913002911242 \tabularnewline
35 & 0.7 & 0.70302500962471 & -0.00302500962471031 \tabularnewline
36 & 0.71 & 0.700923459799468 & 0.00907654020053161 \tabularnewline
37 & 0.71 & 0.707229159231435 & 0.00277084076856515 \tabularnewline
38 & 0.71 & 0.709154131596939 & 0.000845868403061001 \tabularnewline
39 & 0.71 & 0.709741777527091 & 0.000258222472909408 \tabularnewline
40 & 0.7 & 0.709921171135753 & -0.0099211711357533 \tabularnewline
41 & 0.69 & 0.703028685473486 & -0.0130286854734856 \tabularnewline
42 & 0.7 & 0.693977331898848 & 0.00602266810115237 \tabularnewline
43 & 0.7 & 0.698161430022727 & 0.00183856997727316 \tabularnewline
44 & 0.7 & 0.699438730558524 & 0.000561269441476164 \tabularnewline
45 & 0.71 & 0.699828658473798 & 0.0101713415262019 \tabularnewline
46 & 0.7 & 0.706894943761704 & -0.00689494376170452 \tabularnewline
47 & 0.7 & 0.702104853925593 & -0.00210485392559334 \tabularnewline
48 & 0.69 & 0.700642559272592 & -0.0106425592725923 \tabularnewline
49 & 0.7 & 0.693248907233688 & 0.00675109276631169 \tabularnewline
50 & 0.71 & 0.697939060186373 & 0.0120609398136271 \tabularnewline
51 & 0.71 & 0.706318096653078 & 0.00368190334692198 \tabularnewline
52 & 0.71 & 0.708876006972462 & 0.00112399302753829 \tabularnewline
53 & 0.71 & 0.709656873033614 & 0.000343126966385721 \tabularnewline
54 & 0.71 & 0.709895251916892 & 0.000104748083107675 \tabularnewline
55 & 0.71 & 0.709968023029404 & 3.19769705957595e-05 \tabularnewline
56 & 0.71 & 0.709990238230446 & 9.76176955369557e-06 \tabularnewline
57 & 0.71 & 0.709997019975844 & 2.98002415621834e-06 \tabularnewline
58 & 0.69 & 0.709999090273139 & -0.0199990902731393 \tabularnewline
59 & 0.7 & 0.696105222192459 & 0.00389477780754122 \tabularnewline
60 & 0.7 & 0.698811021722461 & 0.00118897827753861 \tabularnewline
61 & 0.7 & 0.699637034661715 & 0.000362965338284948 \tabularnewline
62 & 0.72 & 0.699889195758001 & 0.0201108042419993 \tabularnewline
63 & 0.7 & 0.713860674326204 & -0.013860674326204 \tabularnewline
64 & 0.69 & 0.704231317292089 & -0.014231317292089 \tabularnewline
65 & 0.7 & 0.694344465321819 & 0.00565553467818081 \tabularnewline
66 & 0.71 & 0.69827350667676 & 0.0117264933232401 \tabularnewline
67 & 0.72 & 0.706420194803915 & 0.0135798051960854 \tabularnewline
68 & 0.72 & 0.715854425030334 & 0.0041455749696655 \tabularnewline
69 & 0.73 & 0.718734459619931 & 0.011265540380069 \tabularnewline
70 & 0.72 & 0.726560912211551 & -0.0065609122115512 \tabularnewline
71 & 0.74 & 0.722002882445635 & 0.0179971175543652 \tabularnewline
72 & 0.75 & 0.734505930020188 & 0.0154940699798117 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204728&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]2[/C][C]0.66[/C][C]0.67[/C][C]-0.01[/C][/ROW]
[ROW][C]3[/C][C]0.66[/C][C]0.663052749954661[/C][C]-0.00305274995466109[/C][/ROW]
[ROW][C]4[/C][C]0.67[/C][C]0.660931928228568[/C][C]0.00906807177143165[/C][/ROW]
[ROW][C]5[/C][C]0.67[/C][C]0.66723174443109[/C][C]0.00276825556891014[/C][/ROW]
[ROW][C]6[/C][C]0.67[/C][C]0.669154920793752[/C][C]0.000845079206248101[/C][/ROW]
[ROW][C]7[/C][C]0.67[/C][C]0.669742018449144[/C][C]0.000257981550855879[/C][/ROW]
[ROW][C]8[/C][C]0.68[/C][C]0.669921244683232[/C][C]0.0100787553167678[/C][/ROW]
[ROW][C]9[/C][C]0.68[/C][C]0.67692320801637[/C][C]0.00307679198363031[/C][/ROW]
[ROW][C]10[/C][C]0.67[/C][C]0.679060732341147[/C][C]-0.00906073234114713[/C][/ROW]
[ROW][C]11[/C][C]0.67[/C][C]0.672766015024363[/C][C]-0.00276601502436324[/C][/ROW]
[ROW][C]12[/C][C]0.67[/C][C]0.670844395224022[/C][C]-0.000844395224021688[/C][/ROW]
[ROW][C]13[/C][C]0.67[/C][C]0.670257772748185[/C][C]-0.000257772748184837[/C][/ROW]
[ROW][C]14[/C][C]0.67[/C][C]0.670078691574533[/C][C]-7.86915745334404e-05[/C][/ROW]
[ROW][C]15[/C][C]0.69[/C][C]0.670024022570059[/C][C]0.0199759774299409[/C][/ROW]
[ROW][C]16[/C][C]0.69[/C][C]0.683901833580644[/C][C]0.00609816641935623[/C][/ROW]
[ROW][C]17[/C][C]0.69[/C][C]0.688138382273979[/C][C]0.00186161772602056[/C][/ROW]
[ROW][C]18[/C][C]0.69[/C][C]0.689431694657129[/C][C]0.000568305342870556[/C][/ROW]
[ROW][C]19[/C][C]0.69[/C][C]0.689826510589032[/C][C]0.000173489410968175[/C][/ROW]
[ROW][C]20[/C][C]0.69[/C][C]0.689947038020853[/C][C]5.29619791467262e-05[/C][/ROW]
[ROW][C]21[/C][C]0.7[/C][C]0.689983832032056[/C][C]0.0100161679679439[/C][/ROW]
[ROW][C]22[/C][C]0.69[/C][C]0.696942314368998[/C][C]-0.00694231436899817[/C][/ROW]
[ROW][C]23[/C][C]0.68[/C][C]0.69211931498752[/C][C]-0.0121193149875201[/C][/ROW]
[ROW][C]24[/C][C]0.7[/C][C]0.683699723827867[/C][C]0.0163002761721325[/C][/ROW]
[ROW][C]25[/C][C]0.7[/C][C]0.695023933265456[/C][C]0.00497606673454398[/C][/ROW]
[ROW][C]26[/C][C]0.71[/C][C]0.698480931250173[/C][C]0.011519068749827[/C][/ROW]
[ROW][C]27[/C][C]0.69[/C][C]0.706483516339623[/C][C]-0.0164835163396229[/C][/ROW]
[ROW][C]28[/C][C]0.7[/C][C]0.695032005375844[/C][C]0.0049679946241562[/C][/ROW]
[ROW][C]29[/C][C]0.7[/C][C]0.698483395463635[/C][C]0.00151660453636493[/C][/ROW]
[ROW][C]30[/C][C]0.71[/C][C]0.699537018557037[/C][C]0.0104629814429626[/C][/ROW]
[ROW][C]31[/C][C]0.71[/C][C]0.706805913387438[/C][C]0.00319408661256237[/C][/ROW]
[ROW][C]32[/C][C]0.71[/C][C]0.709024925223832[/C][C]0.000975074776168317[/C][/ROW]
[ROW][C]33[/C][C]0.71[/C][C]0.709702334052126[/C][C]0.000297665947873949[/C][/ROW]
[ROW][C]34[/C][C]0.7[/C][C]0.709909130029112[/C][C]-0.00990913002911242[/C][/ROW]
[ROW][C]35[/C][C]0.7[/C][C]0.70302500962471[/C][C]-0.00302500962471031[/C][/ROW]
[ROW][C]36[/C][C]0.71[/C][C]0.700923459799468[/C][C]0.00907654020053161[/C][/ROW]
[ROW][C]37[/C][C]0.71[/C][C]0.707229159231435[/C][C]0.00277084076856515[/C][/ROW]
[ROW][C]38[/C][C]0.71[/C][C]0.709154131596939[/C][C]0.000845868403061001[/C][/ROW]
[ROW][C]39[/C][C]0.71[/C][C]0.709741777527091[/C][C]0.000258222472909408[/C][/ROW]
[ROW][C]40[/C][C]0.7[/C][C]0.709921171135753[/C][C]-0.0099211711357533[/C][/ROW]
[ROW][C]41[/C][C]0.69[/C][C]0.703028685473486[/C][C]-0.0130286854734856[/C][/ROW]
[ROW][C]42[/C][C]0.7[/C][C]0.693977331898848[/C][C]0.00602266810115237[/C][/ROW]
[ROW][C]43[/C][C]0.7[/C][C]0.698161430022727[/C][C]0.00183856997727316[/C][/ROW]
[ROW][C]44[/C][C]0.7[/C][C]0.699438730558524[/C][C]0.000561269441476164[/C][/ROW]
[ROW][C]45[/C][C]0.71[/C][C]0.699828658473798[/C][C]0.0101713415262019[/C][/ROW]
[ROW][C]46[/C][C]0.7[/C][C]0.706894943761704[/C][C]-0.00689494376170452[/C][/ROW]
[ROW][C]47[/C][C]0.7[/C][C]0.702104853925593[/C][C]-0.00210485392559334[/C][/ROW]
[ROW][C]48[/C][C]0.69[/C][C]0.700642559272592[/C][C]-0.0106425592725923[/C][/ROW]
[ROW][C]49[/C][C]0.7[/C][C]0.693248907233688[/C][C]0.00675109276631169[/C][/ROW]
[ROW][C]50[/C][C]0.71[/C][C]0.697939060186373[/C][C]0.0120609398136271[/C][/ROW]
[ROW][C]51[/C][C]0.71[/C][C]0.706318096653078[/C][C]0.00368190334692198[/C][/ROW]
[ROW][C]52[/C][C]0.71[/C][C]0.708876006972462[/C][C]0.00112399302753829[/C][/ROW]
[ROW][C]53[/C][C]0.71[/C][C]0.709656873033614[/C][C]0.000343126966385721[/C][/ROW]
[ROW][C]54[/C][C]0.71[/C][C]0.709895251916892[/C][C]0.000104748083107675[/C][/ROW]
[ROW][C]55[/C][C]0.71[/C][C]0.709968023029404[/C][C]3.19769705957595e-05[/C][/ROW]
[ROW][C]56[/C][C]0.71[/C][C]0.709990238230446[/C][C]9.76176955369557e-06[/C][/ROW]
[ROW][C]57[/C][C]0.71[/C][C]0.709997019975844[/C][C]2.98002415621834e-06[/C][/ROW]
[ROW][C]58[/C][C]0.69[/C][C]0.709999090273139[/C][C]-0.0199990902731393[/C][/ROW]
[ROW][C]59[/C][C]0.7[/C][C]0.696105222192459[/C][C]0.00389477780754122[/C][/ROW]
[ROW][C]60[/C][C]0.7[/C][C]0.698811021722461[/C][C]0.00118897827753861[/C][/ROW]
[ROW][C]61[/C][C]0.7[/C][C]0.699637034661715[/C][C]0.000362965338284948[/C][/ROW]
[ROW][C]62[/C][C]0.72[/C][C]0.699889195758001[/C][C]0.0201108042419993[/C][/ROW]
[ROW][C]63[/C][C]0.7[/C][C]0.713860674326204[/C][C]-0.013860674326204[/C][/ROW]
[ROW][C]64[/C][C]0.69[/C][C]0.704231317292089[/C][C]-0.014231317292089[/C][/ROW]
[ROW][C]65[/C][C]0.7[/C][C]0.694344465321819[/C][C]0.00565553467818081[/C][/ROW]
[ROW][C]66[/C][C]0.71[/C][C]0.69827350667676[/C][C]0.0117264933232401[/C][/ROW]
[ROW][C]67[/C][C]0.72[/C][C]0.706420194803915[/C][C]0.0135798051960854[/C][/ROW]
[ROW][C]68[/C][C]0.72[/C][C]0.715854425030334[/C][C]0.0041455749696655[/C][/ROW]
[ROW][C]69[/C][C]0.73[/C][C]0.718734459619931[/C][C]0.011265540380069[/C][/ROW]
[ROW][C]70[/C][C]0.72[/C][C]0.726560912211551[/C][C]-0.0065609122115512[/C][/ROW]
[ROW][C]71[/C][C]0.74[/C][C]0.722002882445635[/C][C]0.0179971175543652[/C][/ROW]
[ROW][C]72[/C][C]0.75[/C][C]0.734505930020188[/C][C]0.0154940699798117[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204728&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204728&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
2	0.66	0.67	-0.01
3	0.66	0.663052749954661	-0.00305274995466109
4	0.67	0.660931928228568	0.00906807177143165
5	0.67	0.66723174443109	0.00276825556891014
6	0.67	0.669154920793752	0.000845079206248101
7	0.67	0.669742018449144	0.000257981550855879
8	0.68	0.669921244683232	0.0100787553167678
9	0.68	0.67692320801637	0.00307679198363031
10	0.67	0.679060732341147	-0.00906073234114713
11	0.67	0.672766015024363	-0.00276601502436324
12	0.67	0.670844395224022	-0.000844395224021688
13	0.67	0.670257772748185	-0.000257772748184837
14	0.67	0.670078691574533	-7.86915745334404e-05
15	0.69	0.670024022570059	0.0199759774299409
16	0.69	0.683901833580644	0.00609816641935623
17	0.69	0.688138382273979	0.00186161772602056
18	0.69	0.689431694657129	0.000568305342870556
19	0.69	0.689826510589032	0.000173489410968175
20	0.69	0.689947038020853	5.29619791467262e-05
21	0.7	0.689983832032056	0.0100161679679439
22	0.69	0.696942314368998	-0.00694231436899817
23	0.68	0.69211931498752	-0.0121193149875201
24	0.7	0.683699723827867	0.0163002761721325
25	0.7	0.695023933265456	0.00497606673454398
26	0.71	0.698480931250173	0.011519068749827
27	0.69	0.706483516339623	-0.0164835163396229
28	0.7	0.695032005375844	0.0049679946241562
29	0.7	0.698483395463635	0.00151660453636493
30	0.71	0.699537018557037	0.0104629814429626
31	0.71	0.706805913387438	0.00319408661256237
32	0.71	0.709024925223832	0.000975074776168317
33	0.71	0.709702334052126	0.000297665947873949
34	0.7	0.709909130029112	-0.00990913002911242
35	0.7	0.70302500962471	-0.00302500962471031
36	0.71	0.700923459799468	0.00907654020053161
37	0.71	0.707229159231435	0.00277084076856515
38	0.71	0.709154131596939	0.000845868403061001
39	0.71	0.709741777527091	0.000258222472909408
40	0.7	0.709921171135753	-0.0099211711357533
41	0.69	0.703028685473486	-0.0130286854734856
42	0.7	0.693977331898848	0.00602266810115237
43	0.7	0.698161430022727	0.00183856997727316
44	0.7	0.699438730558524	0.000561269441476164
45	0.71	0.699828658473798	0.0101713415262019
46	0.7	0.706894943761704	-0.00689494376170452
47	0.7	0.702104853925593	-0.00210485392559334
48	0.69	0.700642559272592	-0.0106425592725923
49	0.7	0.693248907233688	0.00675109276631169
50	0.71	0.697939060186373	0.0120609398136271
51	0.71	0.706318096653078	0.00368190334692198
52	0.71	0.708876006972462	0.00112399302753829
53	0.71	0.709656873033614	0.000343126966385721
54	0.71	0.709895251916892	0.000104748083107675
55	0.71	0.709968023029404	3.19769705957595e-05
56	0.71	0.709990238230446	9.76176955369557e-06
57	0.71	0.709997019975844	2.98002415621834e-06
58	0.69	0.709999090273139	-0.0199990902731393
59	0.7	0.696105222192459	0.00389477780754122
60	0.7	0.698811021722461	0.00118897827753861
61	0.7	0.699637034661715	0.000362965338284948
62	0.72	0.699889195758001	0.0201108042419993
63	0.7	0.713860674326204	-0.013860674326204
64	0.69	0.704231317292089	-0.014231317292089
65	0.7	0.694344465321819	0.00565553467818081
66	0.71	0.69827350667676	0.0117264933232401
67	0.72	0.706420194803915	0.0135798051960854
68	0.72	0.715854425030334	0.0041455749696655
69	0.73	0.718734459619931	0.011265540380069
70	0.72	0.726560912211551	-0.0065609122115512
71	0.74	0.722002882445635	0.0179971175543652
72	0.75	0.734505930020188	0.0154940699798117

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	0.745270047857161	0.728514219506286	0.762025876208037
74	0.745270047857161	0.724867510869192	0.765672584845131
75	0.745270047857161	0.721780278863685	0.768759816850638
76	0.745270047857161	0.719054117982592	0.77148597773173
77	0.745270047857161	0.716585893503063	0.77395420221126
78	0.745270047857161	0.714313845848013	0.77622624986631
79	0.745270047857161	0.712197518854186	0.778342576860137
80	0.745270047857161	0.710208702953207	0.780331392761116
81	0.745270047857161	0.708326798970585	0.782213296743738
82	0.745270047857161	0.706536220649965	0.784003875064358
83	0.745270047857161	0.704824836744616	0.785715258969707
84	0.745270047857161	0.703182985311056	0.787357110403267

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 0.745270047857161 & 0.728514219506286 & 0.762025876208037 \tabularnewline
74 & 0.745270047857161 & 0.724867510869192 & 0.765672584845131 \tabularnewline
75 & 0.745270047857161 & 0.721780278863685 & 0.768759816850638 \tabularnewline
76 & 0.745270047857161 & 0.719054117982592 & 0.77148597773173 \tabularnewline
77 & 0.745270047857161 & 0.716585893503063 & 0.77395420221126 \tabularnewline
78 & 0.745270047857161 & 0.714313845848013 & 0.77622624986631 \tabularnewline
79 & 0.745270047857161 & 0.712197518854186 & 0.778342576860137 \tabularnewline
80 & 0.745270047857161 & 0.710208702953207 & 0.780331392761116 \tabularnewline
81 & 0.745270047857161 & 0.708326798970585 & 0.782213296743738 \tabularnewline
82 & 0.745270047857161 & 0.706536220649965 & 0.784003875064358 \tabularnewline
83 & 0.745270047857161 & 0.704824836744616 & 0.785715258969707 \tabularnewline
84 & 0.745270047857161 & 0.703182985311056 & 0.787357110403267 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204728&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]73[/C][C]0.745270047857161[/C][C]0.728514219506286[/C][C]0.762025876208037[/C][/ROW]
[ROW][C]74[/C][C]0.745270047857161[/C][C]0.724867510869192[/C][C]0.765672584845131[/C][/ROW]
[ROW][C]75[/C][C]0.745270047857161[/C][C]0.721780278863685[/C][C]0.768759816850638[/C][/ROW]
[ROW][C]76[/C][C]0.745270047857161[/C][C]0.719054117982592[/C][C]0.77148597773173[/C][/ROW]
[ROW][C]77[/C][C]0.745270047857161[/C][C]0.716585893503063[/C][C]0.77395420221126[/C][/ROW]
[ROW][C]78[/C][C]0.745270047857161[/C][C]0.714313845848013[/C][C]0.77622624986631[/C][/ROW]
[ROW][C]79[/C][C]0.745270047857161[/C][C]0.712197518854186[/C][C]0.778342576860137[/C][/ROW]
[ROW][C]80[/C][C]0.745270047857161[/C][C]0.710208702953207[/C][C]0.780331392761116[/C][/ROW]
[ROW][C]81[/C][C]0.745270047857161[/C][C]0.708326798970585[/C][C]0.782213296743738[/C][/ROW]
[ROW][C]82[/C][C]0.745270047857161[/C][C]0.706536220649965[/C][C]0.784003875064358[/C][/ROW]
[ROW][C]83[/C][C]0.745270047857161[/C][C]0.704824836744616[/C][C]0.785715258969707[/C][/ROW]
[ROW][C]84[/C][C]0.745270047857161[/C][C]0.703182985311056[/C][C]0.787357110403267[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204728&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204728&T=3

As an alternative you can also use a QR Code:

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

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	0.745270047857161	0.728514219506286	0.762025876208037
74	0.745270047857161	0.724867510869192	0.765672584845131
75	0.745270047857161	0.721780278863685	0.768759816850638
76	0.745270047857161	0.719054117982592	0.77148597773173
77	0.745270047857161	0.716585893503063	0.77395420221126
78	0.745270047857161	0.714313845848013	0.77622624986631
79	0.745270047857161	0.712197518854186	0.778342576860137
80	0.745270047857161	0.710208702953207	0.780331392761116
81	0.745270047857161	0.708326798970585	0.782213296743738
82	0.745270047857161	0.706536220649965	0.784003875064358
83	0.745270047857161	0.704824836744616	0.785715258969707
84	0.745270047857161	0.703182985311056	0.787357110403267

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 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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