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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Fri, 21 Dec 2012 06:34:02 -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/21/t13560896567evnhoo75n033zt.htm/, Retrieved Tue, 30 Apr 2024 20:10:11 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=203499, Retrieved Tue, 30 Apr 2024 20:10:11 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

110

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

-     [Exponential Smoothing] [HPC Retail Sales] [2008-03-10 17:43:04] [74be16979710d4c4e7c6647856088456]
- RM D  [Exponential Smoothing] [...] [2012-11-24 22:27:08] [0883bf8f4217d775edf6393676d58a73]
-    D    [Exponential Smoothing] [Single] [2012-12-21 11:31:18] [0604709baf8ca89a71bc0fcadc3cdffd]
- R PD      [Exponential Smoothing] [double] [2012-12-21 11:32:59] [0604709baf8ca89a71bc0fcadc3cdffd]
-   P           [Exponential Smoothing] [triple] [2012-12-21 11:34:02] [b650a28572edc4a1d205c228043a3295] [Current]

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Dataseries X:

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Boxplots

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	'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 & 3 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203499&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203499&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203499&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	'Gertrude Mary Cox' @ cox.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.690931889653249
beta	0
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.690931889653249 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203499&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]0.690931889653249[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203499&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203499&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	0.690931889653249
beta	0
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	1.2727	1.3790280715812	-0.106328071581196
14	1.3917	1.42402632536787	-0.0323263253678738
15	1.2816	1.29131724550336	-0.0097172455033625
16	1.2644	1.26226699991296	0.00213300008704098
17	1.3308	1.31745030023452	0.0133496997654787
18	1.3275	1.30024190939391	0.0272580906060869
19	1.4098	1.40599326931884	0.00380673068115822
20	1.4134	1.43284550348257	-0.0194455034825682
21	1.4138	1.40281536089022	0.0109846391097754
22	1.4272	1.32867287422163	0.0985271257783733
23	1.4643	1.36129128329191	0.103008716708093
24	1.48	1.28453116645191	0.195468833548088
25	1.5023	1.38583374336399	0.116466256636013
26	1.4406	1.60763928321432	-0.167039283214318
27	1.3966	1.38884047041459	0.00775952958541182
28	1.357	1.37552801907309	-0.0185280190730872
29	1.3479	1.41990268655812	-0.0720026865581216
30	1.3315	1.3480202502236	-0.016520250223605
31	1.2307	1.41627569089613	-0.185575690896131
32	1.2271	1.30509104657803	-0.0779910465780296
33	1.3028	1.24401490793256	0.0587850920674391
34	1.268	1.229955869482	0.0380441305179982
35	1.3648	1.22216976518514	0.142630234814862
36	1.3857	1.20136189231576	0.18433810768424
37	1.2998	1.27055671861478	0.0292432813852248
38	1.3362	1.34447460187952	-0.00827460187952345
39	1.3692	1.28939610912751	0.0798038908724927
40	1.3834	1.31773676147942	0.06566323852058
41	1.4207	1.40375453923491	0.0169454607650901
42	1.486	1.41047706616692	0.0755229338330816
43	1.4385	1.49007843233694	-0.0515784323369382
44	1.4453	1.50472774980522	-0.0594277498052178
45	1.426	1.49875072758886	-0.0727507275888624
46	1.445	1.38739902691323	0.0576009730867744
47	1.3503	1.42544959843162	-0.0751495984316177
48	1.4001	1.2670612673032	0.133038732696798
49	1.3418	1.25287685461532	0.088923145384681
50	1.2939	1.35643387780261	-0.0625338778026145
51	1.3176	1.2910881743229	0.0265118256771046
52	1.3443	1.27823721466436	0.0660627853356415
53	1.3356	1.3494739405446	-0.0138739405446018
54	1.3214	1.35300678920173	-0.0316067892017349
55	1.2403	1.31930583433262	-0.0790058343326212
56	1.259	1.31257871139431	-0.0535787113943116
57	1.2284	1.30652526877207	-0.078125268772075
58	1.2611	1.23174768000901	0.0293523199909937
59	1.293	1.20925138797713	0.083748612022869
60	1.2993	1.22499527175866	0.0743047282413438
61	1.2986	1.15659494117807	0.142005058821929

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1.2727 & 1.3790280715812 & -0.106328071581196 \tabularnewline
14 & 1.3917 & 1.42402632536787 & -0.0323263253678738 \tabularnewline
15 & 1.2816 & 1.29131724550336 & -0.0097172455033625 \tabularnewline
16 & 1.2644 & 1.26226699991296 & 0.00213300008704098 \tabularnewline
17 & 1.3308 & 1.31745030023452 & 0.0133496997654787 \tabularnewline
18 & 1.3275 & 1.30024190939391 & 0.0272580906060869 \tabularnewline
19 & 1.4098 & 1.40599326931884 & 0.00380673068115822 \tabularnewline
20 & 1.4134 & 1.43284550348257 & -0.0194455034825682 \tabularnewline
21 & 1.4138 & 1.40281536089022 & 0.0109846391097754 \tabularnewline
22 & 1.4272 & 1.32867287422163 & 0.0985271257783733 \tabularnewline
23 & 1.4643 & 1.36129128329191 & 0.103008716708093 \tabularnewline
24 & 1.48 & 1.28453116645191 & 0.195468833548088 \tabularnewline
25 & 1.5023 & 1.38583374336399 & 0.116466256636013 \tabularnewline
26 & 1.4406 & 1.60763928321432 & -0.167039283214318 \tabularnewline
27 & 1.3966 & 1.38884047041459 & 0.00775952958541182 \tabularnewline
28 & 1.357 & 1.37552801907309 & -0.0185280190730872 \tabularnewline
29 & 1.3479 & 1.41990268655812 & -0.0720026865581216 \tabularnewline
30 & 1.3315 & 1.3480202502236 & -0.016520250223605 \tabularnewline
31 & 1.2307 & 1.41627569089613 & -0.185575690896131 \tabularnewline
32 & 1.2271 & 1.30509104657803 & -0.0779910465780296 \tabularnewline
33 & 1.3028 & 1.24401490793256 & 0.0587850920674391 \tabularnewline
34 & 1.268 & 1.229955869482 & 0.0380441305179982 \tabularnewline
35 & 1.3648 & 1.22216976518514 & 0.142630234814862 \tabularnewline
36 & 1.3857 & 1.20136189231576 & 0.18433810768424 \tabularnewline
37 & 1.2998 & 1.27055671861478 & 0.0292432813852248 \tabularnewline
38 & 1.3362 & 1.34447460187952 & -0.00827460187952345 \tabularnewline
39 & 1.3692 & 1.28939610912751 & 0.0798038908724927 \tabularnewline
40 & 1.3834 & 1.31773676147942 & 0.06566323852058 \tabularnewline
41 & 1.4207 & 1.40375453923491 & 0.0169454607650901 \tabularnewline
42 & 1.486 & 1.41047706616692 & 0.0755229338330816 \tabularnewline
43 & 1.4385 & 1.49007843233694 & -0.0515784323369382 \tabularnewline
44 & 1.4453 & 1.50472774980522 & -0.0594277498052178 \tabularnewline
45 & 1.426 & 1.49875072758886 & -0.0727507275888624 \tabularnewline
46 & 1.445 & 1.38739902691323 & 0.0576009730867744 \tabularnewline
47 & 1.3503 & 1.42544959843162 & -0.0751495984316177 \tabularnewline
48 & 1.4001 & 1.2670612673032 & 0.133038732696798 \tabularnewline
49 & 1.3418 & 1.25287685461532 & 0.088923145384681 \tabularnewline
50 & 1.2939 & 1.35643387780261 & -0.0625338778026145 \tabularnewline
51 & 1.3176 & 1.2910881743229 & 0.0265118256771046 \tabularnewline
52 & 1.3443 & 1.27823721466436 & 0.0660627853356415 \tabularnewline
53 & 1.3356 & 1.3494739405446 & -0.0138739405446018 \tabularnewline
54 & 1.3214 & 1.35300678920173 & -0.0316067892017349 \tabularnewline
55 & 1.2403 & 1.31930583433262 & -0.0790058343326212 \tabularnewline
56 & 1.259 & 1.31257871139431 & -0.0535787113943116 \tabularnewline
57 & 1.2284 & 1.30652526877207 & -0.078125268772075 \tabularnewline
58 & 1.2611 & 1.23174768000901 & 0.0293523199909937 \tabularnewline
59 & 1.293 & 1.20925138797713 & 0.083748612022869 \tabularnewline
60 & 1.2993 & 1.22499527175866 & 0.0743047282413438 \tabularnewline
61 & 1.2986 & 1.15659494117807 & 0.142005058821929 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203499&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]1.2727[/C][C]1.3790280715812[/C][C]-0.106328071581196[/C][/ROW]
[ROW][C]14[/C][C]1.3917[/C][C]1.42402632536787[/C][C]-0.0323263253678738[/C][/ROW]
[ROW][C]15[/C][C]1.2816[/C][C]1.29131724550336[/C][C]-0.0097172455033625[/C][/ROW]
[ROW][C]16[/C][C]1.2644[/C][C]1.26226699991296[/C][C]0.00213300008704098[/C][/ROW]
[ROW][C]17[/C][C]1.3308[/C][C]1.31745030023452[/C][C]0.0133496997654787[/C][/ROW]
[ROW][C]18[/C][C]1.3275[/C][C]1.30024190939391[/C][C]0.0272580906060869[/C][/ROW]
[ROW][C]19[/C][C]1.4098[/C][C]1.40599326931884[/C][C]0.00380673068115822[/C][/ROW]
[ROW][C]20[/C][C]1.4134[/C][C]1.43284550348257[/C][C]-0.0194455034825682[/C][/ROW]
[ROW][C]21[/C][C]1.4138[/C][C]1.40281536089022[/C][C]0.0109846391097754[/C][/ROW]
[ROW][C]22[/C][C]1.4272[/C][C]1.32867287422163[/C][C]0.0985271257783733[/C][/ROW]
[ROW][C]23[/C][C]1.4643[/C][C]1.36129128329191[/C][C]0.103008716708093[/C][/ROW]
[ROW][C]24[/C][C]1.48[/C][C]1.28453116645191[/C][C]0.195468833548088[/C][/ROW]
[ROW][C]25[/C][C]1.5023[/C][C]1.38583374336399[/C][C]0.116466256636013[/C][/ROW]
[ROW][C]26[/C][C]1.4406[/C][C]1.60763928321432[/C][C]-0.167039283214318[/C][/ROW]
[ROW][C]27[/C][C]1.3966[/C][C]1.38884047041459[/C][C]0.00775952958541182[/C][/ROW]
[ROW][C]28[/C][C]1.357[/C][C]1.37552801907309[/C][C]-0.0185280190730872[/C][/ROW]
[ROW][C]29[/C][C]1.3479[/C][C]1.41990268655812[/C][C]-0.0720026865581216[/C][/ROW]
[ROW][C]30[/C][C]1.3315[/C][C]1.3480202502236[/C][C]-0.016520250223605[/C][/ROW]
[ROW][C]31[/C][C]1.2307[/C][C]1.41627569089613[/C][C]-0.185575690896131[/C][/ROW]
[ROW][C]32[/C][C]1.2271[/C][C]1.30509104657803[/C][C]-0.0779910465780296[/C][/ROW]
[ROW][C]33[/C][C]1.3028[/C][C]1.24401490793256[/C][C]0.0587850920674391[/C][/ROW]
[ROW][C]34[/C][C]1.268[/C][C]1.229955869482[/C][C]0.0380441305179982[/C][/ROW]
[ROW][C]35[/C][C]1.3648[/C][C]1.22216976518514[/C][C]0.142630234814862[/C][/ROW]
[ROW][C]36[/C][C]1.3857[/C][C]1.20136189231576[/C][C]0.18433810768424[/C][/ROW]
[ROW][C]37[/C][C]1.2998[/C][C]1.27055671861478[/C][C]0.0292432813852248[/C][/ROW]
[ROW][C]38[/C][C]1.3362[/C][C]1.34447460187952[/C][C]-0.00827460187952345[/C][/ROW]
[ROW][C]39[/C][C]1.3692[/C][C]1.28939610912751[/C][C]0.0798038908724927[/C][/ROW]
[ROW][C]40[/C][C]1.3834[/C][C]1.31773676147942[/C][C]0.06566323852058[/C][/ROW]
[ROW][C]41[/C][C]1.4207[/C][C]1.40375453923491[/C][C]0.0169454607650901[/C][/ROW]
[ROW][C]42[/C][C]1.486[/C][C]1.41047706616692[/C][C]0.0755229338330816[/C][/ROW]
[ROW][C]43[/C][C]1.4385[/C][C]1.49007843233694[/C][C]-0.0515784323369382[/C][/ROW]
[ROW][C]44[/C][C]1.4453[/C][C]1.50472774980522[/C][C]-0.0594277498052178[/C][/ROW]
[ROW][C]45[/C][C]1.426[/C][C]1.49875072758886[/C][C]-0.0727507275888624[/C][/ROW]
[ROW][C]46[/C][C]1.445[/C][C]1.38739902691323[/C][C]0.0576009730867744[/C][/ROW]
[ROW][C]47[/C][C]1.3503[/C][C]1.42544959843162[/C][C]-0.0751495984316177[/C][/ROW]
[ROW][C]48[/C][C]1.4001[/C][C]1.2670612673032[/C][C]0.133038732696798[/C][/ROW]
[ROW][C]49[/C][C]1.3418[/C][C]1.25287685461532[/C][C]0.088923145384681[/C][/ROW]
[ROW][C]50[/C][C]1.2939[/C][C]1.35643387780261[/C][C]-0.0625338778026145[/C][/ROW]
[ROW][C]51[/C][C]1.3176[/C][C]1.2910881743229[/C][C]0.0265118256771046[/C][/ROW]
[ROW][C]52[/C][C]1.3443[/C][C]1.27823721466436[/C][C]0.0660627853356415[/C][/ROW]
[ROW][C]53[/C][C]1.3356[/C][C]1.3494739405446[/C][C]-0.0138739405446018[/C][/ROW]
[ROW][C]54[/C][C]1.3214[/C][C]1.35300678920173[/C][C]-0.0316067892017349[/C][/ROW]
[ROW][C]55[/C][C]1.2403[/C][C]1.31930583433262[/C][C]-0.0790058343326212[/C][/ROW]
[ROW][C]56[/C][C]1.259[/C][C]1.31257871139431[/C][C]-0.0535787113943116[/C][/ROW]
[ROW][C]57[/C][C]1.2284[/C][C]1.30652526877207[/C][C]-0.078125268772075[/C][/ROW]
[ROW][C]58[/C][C]1.2611[/C][C]1.23174768000901[/C][C]0.0293523199909937[/C][/ROW]
[ROW][C]59[/C][C]1.293[/C][C]1.20925138797713[/C][C]0.083748612022869[/C][/ROW]
[ROW][C]60[/C][C]1.2993[/C][C]1.22499527175866[/C][C]0.0743047282413438[/C][/ROW]
[ROW][C]61[/C][C]1.2986[/C][C]1.15659494117807[/C][C]0.142005058821929[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203499&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203499&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	1.2727	1.3790280715812	-0.106328071581196
14	1.3917	1.42402632536787	-0.0323263253678738
15	1.2816	1.29131724550336	-0.0097172455033625
16	1.2644	1.26226699991296	0.00213300008704098
17	1.3308	1.31745030023452	0.0133496997654787
18	1.3275	1.30024190939391	0.0272580906060869
19	1.4098	1.40599326931884	0.00380673068115822
20	1.4134	1.43284550348257	-0.0194455034825682
21	1.4138	1.40281536089022	0.0109846391097754
22	1.4272	1.32867287422163	0.0985271257783733
23	1.4643	1.36129128329191	0.103008716708093
24	1.48	1.28453116645191	0.195468833548088
25	1.5023	1.38583374336399	0.116466256636013
26	1.4406	1.60763928321432	-0.167039283214318
27	1.3966	1.38884047041459	0.00775952958541182
28	1.357	1.37552801907309	-0.0185280190730872
29	1.3479	1.41990268655812	-0.0720026865581216
30	1.3315	1.3480202502236	-0.016520250223605
31	1.2307	1.41627569089613	-0.185575690896131
32	1.2271	1.30509104657803	-0.0779910465780296
33	1.3028	1.24401490793256	0.0587850920674391
34	1.268	1.229955869482	0.0380441305179982
35	1.3648	1.22216976518514	0.142630234814862
36	1.3857	1.20136189231576	0.18433810768424
37	1.2998	1.27055671861478	0.0292432813852248
38	1.3362	1.34447460187952	-0.00827460187952345
39	1.3692	1.28939610912751	0.0798038908724927
40	1.3834	1.31773676147942	0.06566323852058
41	1.4207	1.40375453923491	0.0169454607650901
42	1.486	1.41047706616692	0.0755229338330816
43	1.4385	1.49007843233694	-0.0515784323369382
44	1.4453	1.50472774980522	-0.0594277498052178
45	1.426	1.49875072758886	-0.0727507275888624
46	1.445	1.38739902691323	0.0576009730867744
47	1.3503	1.42544959843162	-0.0751495984316177
48	1.4001	1.2670612673032	0.133038732696798
49	1.3418	1.25287685461532	0.088923145384681
50	1.2939	1.35643387780261	-0.0625338778026145
51	1.3176	1.2910881743229	0.0265118256771046
52	1.3443	1.27823721466436	0.0660627853356415
53	1.3356	1.3494739405446	-0.0138739405446018
54	1.3214	1.35300678920173	-0.0316067892017349
55	1.2403	1.31930583433262	-0.0790058343326212
56	1.259	1.31257871139431	-0.0535787113943116
57	1.2284	1.30652526877207	-0.078125268772075
58	1.2611	1.23174768000901	0.0293523199909937
59	1.293	1.20925138797713	0.083748612022869
60	1.2993	1.22499527175866	0.0743047282413438
61	1.2986	1.15659494117807	0.142005058821929

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
62	1.25001741516773	1.08685448855302	1.41318034178245
63	1.25539954935449	1.05707859441296	1.45372050429603
64	1.23645466424678	1.00833131665526	1.46457801183831
65	1.2373406122042	0.982881730921181	1.49179949348722
66	1.24497875079323	0.96666528936664	1.52329221221981
67	1.2184664012023	0.91818745861942	1.51874534378517
68	1.27418564151115	0.953441968298208	1.5949293147241
69	1.29756488109351	0.95758611050103	1.63754365168599
70	1.30998442717643	0.95180203648557	1.66816681786728
71	1.28401984041563	0.908515265811724	1.65952441501953
72	1.23898033412167	0.846918162909112	1.63104250533422
73	1.14016451048951	0.732216221311403	1.54811279966762

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
62 & 1.25001741516773 & 1.08685448855302 & 1.41318034178245 \tabularnewline
63 & 1.25539954935449 & 1.05707859441296 & 1.45372050429603 \tabularnewline
64 & 1.23645466424678 & 1.00833131665526 & 1.46457801183831 \tabularnewline
65 & 1.2373406122042 & 0.982881730921181 & 1.49179949348722 \tabularnewline
66 & 1.24497875079323 & 0.96666528936664 & 1.52329221221981 \tabularnewline
67 & 1.2184664012023 & 0.91818745861942 & 1.51874534378517 \tabularnewline
68 & 1.27418564151115 & 0.953441968298208 & 1.5949293147241 \tabularnewline
69 & 1.29756488109351 & 0.95758611050103 & 1.63754365168599 \tabularnewline
70 & 1.30998442717643 & 0.95180203648557 & 1.66816681786728 \tabularnewline
71 & 1.28401984041563 & 0.908515265811724 & 1.65952441501953 \tabularnewline
72 & 1.23898033412167 & 0.846918162909112 & 1.63104250533422 \tabularnewline
73 & 1.14016451048951 & 0.732216221311403 & 1.54811279966762 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203499&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]62[/C][C]1.25001741516773[/C][C]1.08685448855302[/C][C]1.41318034178245[/C][/ROW]
[ROW][C]63[/C][C]1.25539954935449[/C][C]1.05707859441296[/C][C]1.45372050429603[/C][/ROW]
[ROW][C]64[/C][C]1.23645466424678[/C][C]1.00833131665526[/C][C]1.46457801183831[/C][/ROW]
[ROW][C]65[/C][C]1.2373406122042[/C][C]0.982881730921181[/C][C]1.49179949348722[/C][/ROW]
[ROW][C]66[/C][C]1.24497875079323[/C][C]0.96666528936664[/C][C]1.52329221221981[/C][/ROW]
[ROW][C]67[/C][C]1.2184664012023[/C][C]0.91818745861942[/C][C]1.51874534378517[/C][/ROW]
[ROW][C]68[/C][C]1.27418564151115[/C][C]0.953441968298208[/C][C]1.5949293147241[/C][/ROW]
[ROW][C]69[/C][C]1.29756488109351[/C][C]0.95758611050103[/C][C]1.63754365168599[/C][/ROW]
[ROW][C]70[/C][C]1.30998442717643[/C][C]0.95180203648557[/C][C]1.66816681786728[/C][/ROW]
[ROW][C]71[/C][C]1.28401984041563[/C][C]0.908515265811724[/C][C]1.65952441501953[/C][/ROW]
[ROW][C]72[/C][C]1.23898033412167[/C][C]0.846918162909112[/C][C]1.63104250533422[/C][/ROW]
[ROW][C]73[/C][C]1.14016451048951[/C][C]0.732216221311403[/C][C]1.54811279966762[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203499&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203499&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
62	1.25001741516773	1.08685448855302	1.41318034178245
63	1.25539954935449	1.05707859441296	1.45372050429603
64	1.23645466424678	1.00833131665526	1.46457801183831
65	1.2373406122042	0.982881730921181	1.49179949348722
66	1.24497875079323	0.96666528936664	1.52329221221981
67	1.2184664012023	0.91818745861942	1.51874534378517
68	1.27418564151115	0.953441968298208	1.5949293147241
69	1.29756488109351	0.95758611050103	1.63754365168599
70	1.30998442717643	0.95180203648557	1.66816681786728
71	1.28401984041563	0.908515265811724	1.65952441501953
72	1.23898033412167	0.846918162909112	1.63104250533422
73	1.14016451048951	0.732216221311403	1.54811279966762

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