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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sun, 12 Jan 2014 15:34:30 -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/12/t1389559059izlwxhn4e4uaa05.htm/, Retrieved Sat, 02 May 2026 18:34:44 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=233061, Retrieved Sat, 02 May 2026 18:34:44 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

394

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

-     [Univariate Data Series] [] [2013-10-16 14:31:33] [520d9ebc87bc557903715fb12897748b]
- RMPD    [Exponential Smoothing] [] [2014-01-12 20:34:30] [17e53cb7c94beab0adf1165deaf51c6f] [Current]

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Dataseries X:

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Boxplots

3,43
3,43
3,43
3,43
3,43
3,43
3,43
3,43
3,5
3,52
3,53
3,53
3,53
3,53
3,53
3,53
3,53
3,53
3,53
3,53
3,58
3,58
3,59
3,59
3,59
3,59
3,59
3,59
3,59
3,59
3,59
3,61
3,71
3,83
3,83
3,83
3,83
3,83
3,83
3,83
3,83
3,83
3,83
3,83
3,92
3,92
3,92
3,92
3,92
3,92
3,92
3,92
3,92
3,92
3,92
3,92
3,98
3,98
3,98
3,98
3,98
3,98
3,98
3,98
3,98
3,98
3,98
3,98
4,09
4,09
4,09
4,09
4,09
4,09
4,09
4,09
4,09
4,09
4,09
4,09
4,21
4,21
4,21
4,21

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=233061&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=233061&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233061&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	1
beta	0.0287479142360522
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0287479142360522 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233061&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]0.0287479142360522[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233061&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233061&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	0.0287479142360522
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	3.43	3.43	0
4	3.43	3.43	0
5	3.43	3.43	0
6	3.43	3.43	0
7	3.43	3.43	0
8	3.43	3.43	0
9	3.5	3.43	0.0699999999999998
10	3.52	3.50201235399652	0.0179876460034762
11	3.53	3.52252946130114	0.00747053869885983
12	3.53	3.53274422370695	-0.00274422370695193
13	3.53	3.53266533299918	-0.00266533299918015
14	3.53	3.53258871023471	-0.00258871023470908
15	3.53	3.5325142902149	-0.00251429021489979
16	3.53	3.53244200961544	-0.00244200961543717
17	3.53	3.53237180693245	-0.00237180693244898
18	3.53	3.53230362243017	-0.00230362243017046
19	3.53	3.53223739809012	-0.00223739809011558
20	3.53	3.53217307756171	-0.00217307756170904
21	3.58	3.53211060611434	0.0478893938856633
22	3.58	3.58348732630258	-0.00348732630257853
23	3.59	3.58338707294512	0.00661292705488092
24	3.59	3.59357718080494	-0.00357718080494163
25	3.59	3.59347434431795	-0.00347434431795435
26	3.59	3.59337446416548	-0.00337446416547538
27	3.59	3.59327745535905	-0.00327745535905377
28	3.59	3.59318323535348	-0.00318323535347886
29	3.59	3.59309172397654	-0.003091723976544
30	3.59	3.59300284336082	-0.00300284336082468
31	3.59	3.59291651787742	-0.00291651787742353
32	3.61	3.59283267407162	0.0171673259283844
33	3.71	3.61332619888507	0.0966738011149331
34	3.83	3.71610536902839	0.113894630971608
35	3.83	3.83937960211151	-0.0093796021115109
36	3.83	3.83910995811444	-0.00910995811444071
37	3.83	3.83884806581987	-0.00884806581987307
38	3.83	3.83859370238253	-0.00859370238252843
39	3.83	3.83834665136347	-0.00834665136346535
40	3.83	3.83810670254591	-0.00810670254591006
41	3.83	3.83787365175638	-0.0078736517563831
42	3.83	3.83764730069097	-0.00764730069096586
43	3.83	3.83742745674656	-0.00742745674656486
44	3.83	3.83721393285702	-0.00721393285702243
45	3.92	3.83700654733394	0.0829934526660558
46	3.92	3.92939243599334	-0.00939243599334194
47	3.92	3.92912242304894	-0.00912242304893773
48	3.92	3.9288601724135	-0.00886017241350201
49	3.92	3.92860546093684	-0.00860546093684178
50	3.92	3.92835807188387	-0.00835807188386761
51	3.92	3.92811779475017	-0.00811779475017183
52	3.92	3.92788442508291	-0.00788442508290776
53	3.92	3.92765776430682	-0.00765776430682363
54	3.92	3.92743761955529	-0.00743761955529143
55	3.92	3.9272238035062	-0.00722380350619556
56	3.92	3.92701613422254	-0.00701613422254121
57	3.98	3.92681443499764	0.0531855650023569
58	3.98	3.98834340905893	-0.00834340905892672
59	3.98	3.98810355345086	-0.00810355345086444
60	3.98	3.98787059319125	-0.00787059319125172
61	3.98	3.9876443300532	-0.00764433005320253
62	3.98	3.98742457150844	-0.00742457150844134
63	3.98	3.98721113056348	-0.00721113056347722
64	3.98	3.98700382560049	-0.0070038256004934
65	3.98	3.98680248022281	-0.00680248022280594
66	3.98	3.98660692310477	-0.00660692310476829
67	3.98	3.98641698784599	-0.00641698784598832
68	3.98	3.98623251282974	-0.00623251282973802
69	4.09	3.98605334108543	0.103946658914566
70	4.09	4.09904159072103	-0.00904159072103372
71	4.09	4.09878166384643	-0.00878166384642753
72	4.09	4.09852920932732	-0.00852920932732104
73	4.09	4.09828401234908	-0.00828401234907794
74	4.09	4.09804586427254	-0.00804586427253629
75	4.09	4.09781456245647	-0.00781456245647405
76	4.09	4.09758991008518	-0.0075899100851835
77	4.09	4.097371716001	-0.0073717160009954
78	4.09	4.09715979454163	-0.00715979454162596
79	4.09	4.0969539653822	-0.00695396538219573
80	4.09	4.09675405338179	-0.00675405338178781
81	4.21	4.09655988843442	0.113440111565578
82	4.21	4.21982105503264	-0.00982105503263764
83	4.21	4.21953872018485	-0.00953872018485225
84	4.21	4.21926450187506	-0.00926450187505612

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 3.43 & 3.43 & 0 \tabularnewline
4 & 3.43 & 3.43 & 0 \tabularnewline
5 & 3.43 & 3.43 & 0 \tabularnewline
6 & 3.43 & 3.43 & 0 \tabularnewline
7 & 3.43 & 3.43 & 0 \tabularnewline
8 & 3.43 & 3.43 & 0 \tabularnewline
9 & 3.5 & 3.43 & 0.0699999999999998 \tabularnewline
10 & 3.52 & 3.50201235399652 & 0.0179876460034762 \tabularnewline
11 & 3.53 & 3.52252946130114 & 0.00747053869885983 \tabularnewline
12 & 3.53 & 3.53274422370695 & -0.00274422370695193 \tabularnewline
13 & 3.53 & 3.53266533299918 & -0.00266533299918015 \tabularnewline
14 & 3.53 & 3.53258871023471 & -0.00258871023470908 \tabularnewline
15 & 3.53 & 3.5325142902149 & -0.00251429021489979 \tabularnewline
16 & 3.53 & 3.53244200961544 & -0.00244200961543717 \tabularnewline
17 & 3.53 & 3.53237180693245 & -0.00237180693244898 \tabularnewline
18 & 3.53 & 3.53230362243017 & -0.00230362243017046 \tabularnewline
19 & 3.53 & 3.53223739809012 & -0.00223739809011558 \tabularnewline
20 & 3.53 & 3.53217307756171 & -0.00217307756170904 \tabularnewline
21 & 3.58 & 3.53211060611434 & 0.0478893938856633 \tabularnewline
22 & 3.58 & 3.58348732630258 & -0.00348732630257853 \tabularnewline
23 & 3.59 & 3.58338707294512 & 0.00661292705488092 \tabularnewline
24 & 3.59 & 3.59357718080494 & -0.00357718080494163 \tabularnewline
25 & 3.59 & 3.59347434431795 & -0.00347434431795435 \tabularnewline
26 & 3.59 & 3.59337446416548 & -0.00337446416547538 \tabularnewline
27 & 3.59 & 3.59327745535905 & -0.00327745535905377 \tabularnewline
28 & 3.59 & 3.59318323535348 & -0.00318323535347886 \tabularnewline
29 & 3.59 & 3.59309172397654 & -0.003091723976544 \tabularnewline
30 & 3.59 & 3.59300284336082 & -0.00300284336082468 \tabularnewline
31 & 3.59 & 3.59291651787742 & -0.00291651787742353 \tabularnewline
32 & 3.61 & 3.59283267407162 & 0.0171673259283844 \tabularnewline
33 & 3.71 & 3.61332619888507 & 0.0966738011149331 \tabularnewline
34 & 3.83 & 3.71610536902839 & 0.113894630971608 \tabularnewline
35 & 3.83 & 3.83937960211151 & -0.0093796021115109 \tabularnewline
36 & 3.83 & 3.83910995811444 & -0.00910995811444071 \tabularnewline
37 & 3.83 & 3.83884806581987 & -0.00884806581987307 \tabularnewline
38 & 3.83 & 3.83859370238253 & -0.00859370238252843 \tabularnewline
39 & 3.83 & 3.83834665136347 & -0.00834665136346535 \tabularnewline
40 & 3.83 & 3.83810670254591 & -0.00810670254591006 \tabularnewline
41 & 3.83 & 3.83787365175638 & -0.0078736517563831 \tabularnewline
42 & 3.83 & 3.83764730069097 & -0.00764730069096586 \tabularnewline
43 & 3.83 & 3.83742745674656 & -0.00742745674656486 \tabularnewline
44 & 3.83 & 3.83721393285702 & -0.00721393285702243 \tabularnewline
45 & 3.92 & 3.83700654733394 & 0.0829934526660558 \tabularnewline
46 & 3.92 & 3.92939243599334 & -0.00939243599334194 \tabularnewline
47 & 3.92 & 3.92912242304894 & -0.00912242304893773 \tabularnewline
48 & 3.92 & 3.9288601724135 & -0.00886017241350201 \tabularnewline
49 & 3.92 & 3.92860546093684 & -0.00860546093684178 \tabularnewline
50 & 3.92 & 3.92835807188387 & -0.00835807188386761 \tabularnewline
51 & 3.92 & 3.92811779475017 & -0.00811779475017183 \tabularnewline
52 & 3.92 & 3.92788442508291 & -0.00788442508290776 \tabularnewline
53 & 3.92 & 3.92765776430682 & -0.00765776430682363 \tabularnewline
54 & 3.92 & 3.92743761955529 & -0.00743761955529143 \tabularnewline
55 & 3.92 & 3.9272238035062 & -0.00722380350619556 \tabularnewline
56 & 3.92 & 3.92701613422254 & -0.00701613422254121 \tabularnewline
57 & 3.98 & 3.92681443499764 & 0.0531855650023569 \tabularnewline
58 & 3.98 & 3.98834340905893 & -0.00834340905892672 \tabularnewline
59 & 3.98 & 3.98810355345086 & -0.00810355345086444 \tabularnewline
60 & 3.98 & 3.98787059319125 & -0.00787059319125172 \tabularnewline
61 & 3.98 & 3.9876443300532 & -0.00764433005320253 \tabularnewline
62 & 3.98 & 3.98742457150844 & -0.00742457150844134 \tabularnewline
63 & 3.98 & 3.98721113056348 & -0.00721113056347722 \tabularnewline
64 & 3.98 & 3.98700382560049 & -0.0070038256004934 \tabularnewline
65 & 3.98 & 3.98680248022281 & -0.00680248022280594 \tabularnewline
66 & 3.98 & 3.98660692310477 & -0.00660692310476829 \tabularnewline
67 & 3.98 & 3.98641698784599 & -0.00641698784598832 \tabularnewline
68 & 3.98 & 3.98623251282974 & -0.00623251282973802 \tabularnewline
69 & 4.09 & 3.98605334108543 & 0.103946658914566 \tabularnewline
70 & 4.09 & 4.09904159072103 & -0.00904159072103372 \tabularnewline
71 & 4.09 & 4.09878166384643 & -0.00878166384642753 \tabularnewline
72 & 4.09 & 4.09852920932732 & -0.00852920932732104 \tabularnewline
73 & 4.09 & 4.09828401234908 & -0.00828401234907794 \tabularnewline
74 & 4.09 & 4.09804586427254 & -0.00804586427253629 \tabularnewline
75 & 4.09 & 4.09781456245647 & -0.00781456245647405 \tabularnewline
76 & 4.09 & 4.09758991008518 & -0.0075899100851835 \tabularnewline
77 & 4.09 & 4.097371716001 & -0.0073717160009954 \tabularnewline
78 & 4.09 & 4.09715979454163 & -0.00715979454162596 \tabularnewline
79 & 4.09 & 4.0969539653822 & -0.00695396538219573 \tabularnewline
80 & 4.09 & 4.09675405338179 & -0.00675405338178781 \tabularnewline
81 & 4.21 & 4.09655988843442 & 0.113440111565578 \tabularnewline
82 & 4.21 & 4.21982105503264 & -0.00982105503263764 \tabularnewline
83 & 4.21 & 4.21953872018485 & -0.00953872018485225 \tabularnewline
84 & 4.21 & 4.21926450187506 & -0.00926450187505612 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233061&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]3.43[/C][C]3.43[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]3.43[/C][C]3.43[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]3.43[/C][C]3.43[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]3.43[/C][C]3.43[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]3.43[/C][C]3.43[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]3.43[/C][C]3.43[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]3.5[/C][C]3.43[/C][C]0.0699999999999998[/C][/ROW]
[ROW][C]10[/C][C]3.52[/C][C]3.50201235399652[/C][C]0.0179876460034762[/C][/ROW]
[ROW][C]11[/C][C]3.53[/C][C]3.52252946130114[/C][C]0.00747053869885983[/C][/ROW]
[ROW][C]12[/C][C]3.53[/C][C]3.53274422370695[/C][C]-0.00274422370695193[/C][/ROW]
[ROW][C]13[/C][C]3.53[/C][C]3.53266533299918[/C][C]-0.00266533299918015[/C][/ROW]
[ROW][C]14[/C][C]3.53[/C][C]3.53258871023471[/C][C]-0.00258871023470908[/C][/ROW]
[ROW][C]15[/C][C]3.53[/C][C]3.5325142902149[/C][C]-0.00251429021489979[/C][/ROW]
[ROW][C]16[/C][C]3.53[/C][C]3.53244200961544[/C][C]-0.00244200961543717[/C][/ROW]
[ROW][C]17[/C][C]3.53[/C][C]3.53237180693245[/C][C]-0.00237180693244898[/C][/ROW]
[ROW][C]18[/C][C]3.53[/C][C]3.53230362243017[/C][C]-0.00230362243017046[/C][/ROW]
[ROW][C]19[/C][C]3.53[/C][C]3.53223739809012[/C][C]-0.00223739809011558[/C][/ROW]
[ROW][C]20[/C][C]3.53[/C][C]3.53217307756171[/C][C]-0.00217307756170904[/C][/ROW]
[ROW][C]21[/C][C]3.58[/C][C]3.53211060611434[/C][C]0.0478893938856633[/C][/ROW]
[ROW][C]22[/C][C]3.58[/C][C]3.58348732630258[/C][C]-0.00348732630257853[/C][/ROW]
[ROW][C]23[/C][C]3.59[/C][C]3.58338707294512[/C][C]0.00661292705488092[/C][/ROW]
[ROW][C]24[/C][C]3.59[/C][C]3.59357718080494[/C][C]-0.00357718080494163[/C][/ROW]
[ROW][C]25[/C][C]3.59[/C][C]3.59347434431795[/C][C]-0.00347434431795435[/C][/ROW]
[ROW][C]26[/C][C]3.59[/C][C]3.59337446416548[/C][C]-0.00337446416547538[/C][/ROW]
[ROW][C]27[/C][C]3.59[/C][C]3.59327745535905[/C][C]-0.00327745535905377[/C][/ROW]
[ROW][C]28[/C][C]3.59[/C][C]3.59318323535348[/C][C]-0.00318323535347886[/C][/ROW]
[ROW][C]29[/C][C]3.59[/C][C]3.59309172397654[/C][C]-0.003091723976544[/C][/ROW]
[ROW][C]30[/C][C]3.59[/C][C]3.59300284336082[/C][C]-0.00300284336082468[/C][/ROW]
[ROW][C]31[/C][C]3.59[/C][C]3.59291651787742[/C][C]-0.00291651787742353[/C][/ROW]
[ROW][C]32[/C][C]3.61[/C][C]3.59283267407162[/C][C]0.0171673259283844[/C][/ROW]
[ROW][C]33[/C][C]3.71[/C][C]3.61332619888507[/C][C]0.0966738011149331[/C][/ROW]
[ROW][C]34[/C][C]3.83[/C][C]3.71610536902839[/C][C]0.113894630971608[/C][/ROW]
[ROW][C]35[/C][C]3.83[/C][C]3.83937960211151[/C][C]-0.0093796021115109[/C][/ROW]
[ROW][C]36[/C][C]3.83[/C][C]3.83910995811444[/C][C]-0.00910995811444071[/C][/ROW]
[ROW][C]37[/C][C]3.83[/C][C]3.83884806581987[/C][C]-0.00884806581987307[/C][/ROW]
[ROW][C]38[/C][C]3.83[/C][C]3.83859370238253[/C][C]-0.00859370238252843[/C][/ROW]
[ROW][C]39[/C][C]3.83[/C][C]3.83834665136347[/C][C]-0.00834665136346535[/C][/ROW]
[ROW][C]40[/C][C]3.83[/C][C]3.83810670254591[/C][C]-0.00810670254591006[/C][/ROW]
[ROW][C]41[/C][C]3.83[/C][C]3.83787365175638[/C][C]-0.0078736517563831[/C][/ROW]
[ROW][C]42[/C][C]3.83[/C][C]3.83764730069097[/C][C]-0.00764730069096586[/C][/ROW]
[ROW][C]43[/C][C]3.83[/C][C]3.83742745674656[/C][C]-0.00742745674656486[/C][/ROW]
[ROW][C]44[/C][C]3.83[/C][C]3.83721393285702[/C][C]-0.00721393285702243[/C][/ROW]
[ROW][C]45[/C][C]3.92[/C][C]3.83700654733394[/C][C]0.0829934526660558[/C][/ROW]
[ROW][C]46[/C][C]3.92[/C][C]3.92939243599334[/C][C]-0.00939243599334194[/C][/ROW]
[ROW][C]47[/C][C]3.92[/C][C]3.92912242304894[/C][C]-0.00912242304893773[/C][/ROW]
[ROW][C]48[/C][C]3.92[/C][C]3.9288601724135[/C][C]-0.00886017241350201[/C][/ROW]
[ROW][C]49[/C][C]3.92[/C][C]3.92860546093684[/C][C]-0.00860546093684178[/C][/ROW]
[ROW][C]50[/C][C]3.92[/C][C]3.92835807188387[/C][C]-0.00835807188386761[/C][/ROW]
[ROW][C]51[/C][C]3.92[/C][C]3.92811779475017[/C][C]-0.00811779475017183[/C][/ROW]
[ROW][C]52[/C][C]3.92[/C][C]3.92788442508291[/C][C]-0.00788442508290776[/C][/ROW]
[ROW][C]53[/C][C]3.92[/C][C]3.92765776430682[/C][C]-0.00765776430682363[/C][/ROW]
[ROW][C]54[/C][C]3.92[/C][C]3.92743761955529[/C][C]-0.00743761955529143[/C][/ROW]
[ROW][C]55[/C][C]3.92[/C][C]3.9272238035062[/C][C]-0.00722380350619556[/C][/ROW]
[ROW][C]56[/C][C]3.92[/C][C]3.92701613422254[/C][C]-0.00701613422254121[/C][/ROW]
[ROW][C]57[/C][C]3.98[/C][C]3.92681443499764[/C][C]0.0531855650023569[/C][/ROW]
[ROW][C]58[/C][C]3.98[/C][C]3.98834340905893[/C][C]-0.00834340905892672[/C][/ROW]
[ROW][C]59[/C][C]3.98[/C][C]3.98810355345086[/C][C]-0.00810355345086444[/C][/ROW]
[ROW][C]60[/C][C]3.98[/C][C]3.98787059319125[/C][C]-0.00787059319125172[/C][/ROW]
[ROW][C]61[/C][C]3.98[/C][C]3.9876443300532[/C][C]-0.00764433005320253[/C][/ROW]
[ROW][C]62[/C][C]3.98[/C][C]3.98742457150844[/C][C]-0.00742457150844134[/C][/ROW]
[ROW][C]63[/C][C]3.98[/C][C]3.98721113056348[/C][C]-0.00721113056347722[/C][/ROW]
[ROW][C]64[/C][C]3.98[/C][C]3.98700382560049[/C][C]-0.0070038256004934[/C][/ROW]
[ROW][C]65[/C][C]3.98[/C][C]3.98680248022281[/C][C]-0.00680248022280594[/C][/ROW]
[ROW][C]66[/C][C]3.98[/C][C]3.98660692310477[/C][C]-0.00660692310476829[/C][/ROW]
[ROW][C]67[/C][C]3.98[/C][C]3.98641698784599[/C][C]-0.00641698784598832[/C][/ROW]
[ROW][C]68[/C][C]3.98[/C][C]3.98623251282974[/C][C]-0.00623251282973802[/C][/ROW]
[ROW][C]69[/C][C]4.09[/C][C]3.98605334108543[/C][C]0.103946658914566[/C][/ROW]
[ROW][C]70[/C][C]4.09[/C][C]4.09904159072103[/C][C]-0.00904159072103372[/C][/ROW]
[ROW][C]71[/C][C]4.09[/C][C]4.09878166384643[/C][C]-0.00878166384642753[/C][/ROW]
[ROW][C]72[/C][C]4.09[/C][C]4.09852920932732[/C][C]-0.00852920932732104[/C][/ROW]
[ROW][C]73[/C][C]4.09[/C][C]4.09828401234908[/C][C]-0.00828401234907794[/C][/ROW]
[ROW][C]74[/C][C]4.09[/C][C]4.09804586427254[/C][C]-0.00804586427253629[/C][/ROW]
[ROW][C]75[/C][C]4.09[/C][C]4.09781456245647[/C][C]-0.00781456245647405[/C][/ROW]
[ROW][C]76[/C][C]4.09[/C][C]4.09758991008518[/C][C]-0.0075899100851835[/C][/ROW]
[ROW][C]77[/C][C]4.09[/C][C]4.097371716001[/C][C]-0.0073717160009954[/C][/ROW]
[ROW][C]78[/C][C]4.09[/C][C]4.09715979454163[/C][C]-0.00715979454162596[/C][/ROW]
[ROW][C]79[/C][C]4.09[/C][C]4.0969539653822[/C][C]-0.00695396538219573[/C][/ROW]
[ROW][C]80[/C][C]4.09[/C][C]4.09675405338179[/C][C]-0.00675405338178781[/C][/ROW]
[ROW][C]81[/C][C]4.21[/C][C]4.09655988843442[/C][C]0.113440111565578[/C][/ROW]
[ROW][C]82[/C][C]4.21[/C][C]4.21982105503264[/C][C]-0.00982105503263764[/C][/ROW]
[ROW][C]83[/C][C]4.21[/C][C]4.21953872018485[/C][C]-0.00953872018485225[/C][/ROW]
[ROW][C]84[/C][C]4.21[/C][C]4.21926450187506[/C][C]-0.00926450187505612[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233061&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233061&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	3.43	3.43	0
4	3.43	3.43	0
5	3.43	3.43	0
6	3.43	3.43	0
7	3.43	3.43	0
8	3.43	3.43	0
9	3.5	3.43	0.0699999999999998
10	3.52	3.50201235399652	0.0179876460034762
11	3.53	3.52252946130114	0.00747053869885983
12	3.53	3.53274422370695	-0.00274422370695193
13	3.53	3.53266533299918	-0.00266533299918015
14	3.53	3.53258871023471	-0.00258871023470908
15	3.53	3.5325142902149	-0.00251429021489979
16	3.53	3.53244200961544	-0.00244200961543717
17	3.53	3.53237180693245	-0.00237180693244898
18	3.53	3.53230362243017	-0.00230362243017046
19	3.53	3.53223739809012	-0.00223739809011558
20	3.53	3.53217307756171	-0.00217307756170904
21	3.58	3.53211060611434	0.0478893938856633
22	3.58	3.58348732630258	-0.00348732630257853
23	3.59	3.58338707294512	0.00661292705488092
24	3.59	3.59357718080494	-0.00357718080494163
25	3.59	3.59347434431795	-0.00347434431795435
26	3.59	3.59337446416548	-0.00337446416547538
27	3.59	3.59327745535905	-0.00327745535905377
28	3.59	3.59318323535348	-0.00318323535347886
29	3.59	3.59309172397654	-0.003091723976544
30	3.59	3.59300284336082	-0.00300284336082468
31	3.59	3.59291651787742	-0.00291651787742353
32	3.61	3.59283267407162	0.0171673259283844
33	3.71	3.61332619888507	0.0966738011149331
34	3.83	3.71610536902839	0.113894630971608
35	3.83	3.83937960211151	-0.0093796021115109
36	3.83	3.83910995811444	-0.00910995811444071
37	3.83	3.83884806581987	-0.00884806581987307
38	3.83	3.83859370238253	-0.00859370238252843
39	3.83	3.83834665136347	-0.00834665136346535
40	3.83	3.83810670254591	-0.00810670254591006
41	3.83	3.83787365175638	-0.0078736517563831
42	3.83	3.83764730069097	-0.00764730069096586
43	3.83	3.83742745674656	-0.00742745674656486
44	3.83	3.83721393285702	-0.00721393285702243
45	3.92	3.83700654733394	0.0829934526660558
46	3.92	3.92939243599334	-0.00939243599334194
47	3.92	3.92912242304894	-0.00912242304893773
48	3.92	3.9288601724135	-0.00886017241350201
49	3.92	3.92860546093684	-0.00860546093684178
50	3.92	3.92835807188387	-0.00835807188386761
51	3.92	3.92811779475017	-0.00811779475017183
52	3.92	3.92788442508291	-0.00788442508290776
53	3.92	3.92765776430682	-0.00765776430682363
54	3.92	3.92743761955529	-0.00743761955529143
55	3.92	3.9272238035062	-0.00722380350619556
56	3.92	3.92701613422254	-0.00701613422254121
57	3.98	3.92681443499764	0.0531855650023569
58	3.98	3.98834340905893	-0.00834340905892672
59	3.98	3.98810355345086	-0.00810355345086444
60	3.98	3.98787059319125	-0.00787059319125172
61	3.98	3.9876443300532	-0.00764433005320253
62	3.98	3.98742457150844	-0.00742457150844134
63	3.98	3.98721113056348	-0.00721113056347722
64	3.98	3.98700382560049	-0.0070038256004934
65	3.98	3.98680248022281	-0.00680248022280594
66	3.98	3.98660692310477	-0.00660692310476829
67	3.98	3.98641698784599	-0.00641698784598832
68	3.98	3.98623251282974	-0.00623251282973802
69	4.09	3.98605334108543	0.103946658914566
70	4.09	4.09904159072103	-0.00904159072103372
71	4.09	4.09878166384643	-0.00878166384642753
72	4.09	4.09852920932732	-0.00852920932732104
73	4.09	4.09828401234908	-0.00828401234907794
74	4.09	4.09804586427254	-0.00804586427253629
75	4.09	4.09781456245647	-0.00781456245647405
76	4.09	4.09758991008518	-0.0075899100851835
77	4.09	4.097371716001	-0.0073717160009954
78	4.09	4.09715979454163	-0.00715979454162596
79	4.09	4.0969539653822	-0.00695396538219573
80	4.09	4.09675405338179	-0.00675405338178781
81	4.21	4.09655988843442	0.113440111565578
82	4.21	4.21982105503264	-0.00982105503263764
83	4.21	4.21953872018485	-0.00953872018485225
84	4.21	4.21926450187506	-0.00926450187505612

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	4.21899816676971	4.16324772241075	4.27474861112867
86	4.22799633353942	4.14801198353493	4.30798068354392
87	4.23699450030914	4.13763007030277	4.33635893031551
88	4.24599266707885	4.1296284521629	4.3623568819948
89	4.25499083384856	4.12306412963211	4.38691753806502
90	4.26398900061827	4.11746084079923	4.41051716043732
91	4.27298716738799	4.1125399584099	4.43343437636607
92	4.2819853341577	4.10812272062519	4.45584794769021
93	4.29098350092741	4.10408688908364	4.47788011277118
94	4.29998166769712	4.10034487343298	4.49961846196127
95	4.30897983446684	4.09683162200031	4.52112804693337
96	4.31797800123655	4.09349743602666	4.54245856644643

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 4.21899816676971 & 4.16324772241075 & 4.27474861112867 \tabularnewline
86 & 4.22799633353942 & 4.14801198353493 & 4.30798068354392 \tabularnewline
87 & 4.23699450030914 & 4.13763007030277 & 4.33635893031551 \tabularnewline
88 & 4.24599266707885 & 4.1296284521629 & 4.3623568819948 \tabularnewline
89 & 4.25499083384856 & 4.12306412963211 & 4.38691753806502 \tabularnewline
90 & 4.26398900061827 & 4.11746084079923 & 4.41051716043732 \tabularnewline
91 & 4.27298716738799 & 4.1125399584099 & 4.43343437636607 \tabularnewline
92 & 4.2819853341577 & 4.10812272062519 & 4.45584794769021 \tabularnewline
93 & 4.29098350092741 & 4.10408688908364 & 4.47788011277118 \tabularnewline
94 & 4.29998166769712 & 4.10034487343298 & 4.49961846196127 \tabularnewline
95 & 4.30897983446684 & 4.09683162200031 & 4.52112804693337 \tabularnewline
96 & 4.31797800123655 & 4.09349743602666 & 4.54245856644643 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233061&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]4.21899816676971[/C][C]4.16324772241075[/C][C]4.27474861112867[/C][/ROW]
[ROW][C]86[/C][C]4.22799633353942[/C][C]4.14801198353493[/C][C]4.30798068354392[/C][/ROW]
[ROW][C]87[/C][C]4.23699450030914[/C][C]4.13763007030277[/C][C]4.33635893031551[/C][/ROW]
[ROW][C]88[/C][C]4.24599266707885[/C][C]4.1296284521629[/C][C]4.3623568819948[/C][/ROW]
[ROW][C]89[/C][C]4.25499083384856[/C][C]4.12306412963211[/C][C]4.38691753806502[/C][/ROW]
[ROW][C]90[/C][C]4.26398900061827[/C][C]4.11746084079923[/C][C]4.41051716043732[/C][/ROW]
[ROW][C]91[/C][C]4.27298716738799[/C][C]4.1125399584099[/C][C]4.43343437636607[/C][/ROW]
[ROW][C]92[/C][C]4.2819853341577[/C][C]4.10812272062519[/C][C]4.45584794769021[/C][/ROW]
[ROW][C]93[/C][C]4.29098350092741[/C][C]4.10408688908364[/C][C]4.47788011277118[/C][/ROW]
[ROW][C]94[/C][C]4.29998166769712[/C][C]4.10034487343298[/C][C]4.49961846196127[/C][/ROW]
[ROW][C]95[/C][C]4.30897983446684[/C][C]4.09683162200031[/C][C]4.52112804693337[/C][/ROW]
[ROW][C]96[/C][C]4.31797800123655[/C][C]4.09349743602666[/C][C]4.54245856644643[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233061&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233061&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	4.21899816676971	4.16324772241075	4.27474861112867
86	4.22799633353942	4.14801198353493	4.30798068354392
87	4.23699450030914	4.13763007030277	4.33635893031551
88	4.24599266707885	4.1296284521629	4.3623568819948
89	4.25499083384856	4.12306412963211	4.38691753806502
90	4.26398900061827	4.11746084079923	4.41051716043732
91	4.27298716738799	4.1125399584099	4.43343437636607
92	4.2819853341577	4.10812272062519	4.45584794769021
93	4.29098350092741	4.10408688908364	4.47788011277118
94	4.29998166769712	4.10034487343298	4.49961846196127
95	4.30897983446684	4.09683162200031	4.52112804693337
96	4.31797800123655	4.09349743602666	4.54245856644643

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 = grey ;

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=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