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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Fri, 21 Dec 2012 06:32:59 -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/21/t1356089586pch47igwiodkj9l.htm/, Retrieved Fri, 26 Apr 2024 23:36:50 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=203498, Retrieved Fri, 26 Apr 2024 23:36:50 +0000

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IsPrivate?

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User-defined keywords

Estimated Impact

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] [b650a28572edc4a1d205c228043a3295] [Current]
-   P           [Exponential Smoothing] [triple] [2012-12-21 11:34:02] [0604709baf8ca89a71bc0fcadc3cdffd] 
- RMPD          [Histogram] [] [2012-12-21 13:41:38] [0604709baf8ca89a71bc0fcadc3cdffd] 

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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	2 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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203498&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]2 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=203498&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203498&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	2 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.929242079750219
beta	0
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.929242079750219 \tabularnewline
beta & 0 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203498&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]0.929242079750219[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203498&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203498&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	0.929242079750219
beta	0
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	1.487	1.4681	0.0189000000000001
4	1.5167	1.48166267530728	0.0350373246927207
5	1.5812	1.51022083177363	0.0709791682263732
6	1.554	1.57217766167524	-0.0181776616752423
7	1.5508	1.55128621353514	-0.000486213535144442
8	1.5764	1.54683440345854	0.0295655965414559
9	1.5611	1.57030799987778	-0.00920799987778254
10	1.4735	1.55775153892101	-0.0842515389210121
11	1.4303	1.47546146367189	-0.0451614636718944
12	1.2757	1.42949553124486	-0.153795531244859
13	1.2727	1.2825822519346	-0.00988225193459669
14	1.3917	1.26939924759428	0.122300752405724
15	1.2816	1.37904625311479	-0.0974462531147875
16	1.2644	1.28449509420654	-0.0200950942065363
17	1.3308	1.26182188707328	0.0689781129267222
18	1.3275	1.32191925218655	0.0055807478134493
19	1.4098	1.32310511789128	0.0866948821087183
20	1.4134	1.39966565044569	0.013734349554313
21	1.4138	1.40842818598955	0.00537181401044662
22	1.4272	1.40941990161265	0.017780098387348
23	1.4643	1.42194191721627	0.0423580827837251
24	1.48	1.45730283015646	0.0226971698435445
25	1.5023	1.47439399546631	0.0279060045336852
26	1.4406	1.49632542915672	-0.0557254291567153
27	1.3966	1.44054301547216	-0.0439430154721558
28	1.357	1.39570931638431	-0.0387093163843137
29	1.3479	1.35573899072164	-0.00783899072164473
30	1.3315	1.34445467068032	-0.0129546706803212
31	1.2307	1.32841664555486	-0.0977166455548604
32	1.2271	1.23361422661325	-0.00651422661324674
33	1.3028	1.22356093312719	0.0792390668728107
34	1.268	1.29319320842555	-0.0251932084255466
35	1.3648	1.26578261903261	0.0990173809673891
36	1.3857	1.35379373605417	0.0319062639458327
37	1.2998	1.37944237912025	-0.0796423791202521
38	1.3362	1.30143532911029	0.0347646708897063
39	1.3692	1.32974012418968	0.0394598758103237
40	1.3834	1.36240790125435	0.0209920987456531
41	1.4207	1.37791464275108	0.0427853572489205
42	1.486	1.41367259710392	0.0723274028960774
43	1.4385	1.47688226339401	-0.0383822633940056
44	1.4453	1.43721584913224	0.00808415086776093
45	1.426	1.44072798229761	-0.0147279822976119
46	1.445	1.42304212139685	0.0219578786031456
47	1.3503	1.43944630617694	-0.0891463061769442
48	1.4001	1.35260780722303	0.0474921927769691
49	1.3418	1.392739551211	-0.0509395512109998
50	1.2939	1.34140437670215	-0.0475043767021477
51	1.3176	1.29326131089821	0.0243386891017938
52	1.3443	1.31187784497755	0.0324221550224488
53	1.3356	1.3380058757406	-0.00240587574059559
54	1.3214	1.33177023476378	-0.010370234763784
55	1.2403	1.31813377624439	-0.0778337762443873
56	1.259	1.24180735613224	0.0171926438677603
57	1.2284	1.25378348427632	-0.0253834842763221
58	1.2611	1.22619608255609	0.0349039174439145
59	1.293	1.2546302713931	0.0383697286069014
60	1.2993	1.28628503780323	0.0130149621967728
61	1.2986	1.29437908834283	0.0042209116571732

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1.487 & 1.4681 & 0.0189000000000001 \tabularnewline
4 & 1.5167 & 1.48166267530728 & 0.0350373246927207 \tabularnewline
5 & 1.5812 & 1.51022083177363 & 0.0709791682263732 \tabularnewline
6 & 1.554 & 1.57217766167524 & -0.0181776616752423 \tabularnewline
7 & 1.5508 & 1.55128621353514 & -0.000486213535144442 \tabularnewline
8 & 1.5764 & 1.54683440345854 & 0.0295655965414559 \tabularnewline
9 & 1.5611 & 1.57030799987778 & -0.00920799987778254 \tabularnewline
10 & 1.4735 & 1.55775153892101 & -0.0842515389210121 \tabularnewline
11 & 1.4303 & 1.47546146367189 & -0.0451614636718944 \tabularnewline
12 & 1.2757 & 1.42949553124486 & -0.153795531244859 \tabularnewline
13 & 1.2727 & 1.2825822519346 & -0.00988225193459669 \tabularnewline
14 & 1.3917 & 1.26939924759428 & 0.122300752405724 \tabularnewline
15 & 1.2816 & 1.37904625311479 & -0.0974462531147875 \tabularnewline
16 & 1.2644 & 1.28449509420654 & -0.0200950942065363 \tabularnewline
17 & 1.3308 & 1.26182188707328 & 0.0689781129267222 \tabularnewline
18 & 1.3275 & 1.32191925218655 & 0.0055807478134493 \tabularnewline
19 & 1.4098 & 1.32310511789128 & 0.0866948821087183 \tabularnewline
20 & 1.4134 & 1.39966565044569 & 0.013734349554313 \tabularnewline
21 & 1.4138 & 1.40842818598955 & 0.00537181401044662 \tabularnewline
22 & 1.4272 & 1.40941990161265 & 0.017780098387348 \tabularnewline
23 & 1.4643 & 1.42194191721627 & 0.0423580827837251 \tabularnewline
24 & 1.48 & 1.45730283015646 & 0.0226971698435445 \tabularnewline
25 & 1.5023 & 1.47439399546631 & 0.0279060045336852 \tabularnewline
26 & 1.4406 & 1.49632542915672 & -0.0557254291567153 \tabularnewline
27 & 1.3966 & 1.44054301547216 & -0.0439430154721558 \tabularnewline
28 & 1.357 & 1.39570931638431 & -0.0387093163843137 \tabularnewline
29 & 1.3479 & 1.35573899072164 & -0.00783899072164473 \tabularnewline
30 & 1.3315 & 1.34445467068032 & -0.0129546706803212 \tabularnewline
31 & 1.2307 & 1.32841664555486 & -0.0977166455548604 \tabularnewline
32 & 1.2271 & 1.23361422661325 & -0.00651422661324674 \tabularnewline
33 & 1.3028 & 1.22356093312719 & 0.0792390668728107 \tabularnewline
34 & 1.268 & 1.29319320842555 & -0.0251932084255466 \tabularnewline
35 & 1.3648 & 1.26578261903261 & 0.0990173809673891 \tabularnewline
36 & 1.3857 & 1.35379373605417 & 0.0319062639458327 \tabularnewline
37 & 1.2998 & 1.37944237912025 & -0.0796423791202521 \tabularnewline
38 & 1.3362 & 1.30143532911029 & 0.0347646708897063 \tabularnewline
39 & 1.3692 & 1.32974012418968 & 0.0394598758103237 \tabularnewline
40 & 1.3834 & 1.36240790125435 & 0.0209920987456531 \tabularnewline
41 & 1.4207 & 1.37791464275108 & 0.0427853572489205 \tabularnewline
42 & 1.486 & 1.41367259710392 & 0.0723274028960774 \tabularnewline
43 & 1.4385 & 1.47688226339401 & -0.0383822633940056 \tabularnewline
44 & 1.4453 & 1.43721584913224 & 0.00808415086776093 \tabularnewline
45 & 1.426 & 1.44072798229761 & -0.0147279822976119 \tabularnewline
46 & 1.445 & 1.42304212139685 & 0.0219578786031456 \tabularnewline
47 & 1.3503 & 1.43944630617694 & -0.0891463061769442 \tabularnewline
48 & 1.4001 & 1.35260780722303 & 0.0474921927769691 \tabularnewline
49 & 1.3418 & 1.392739551211 & -0.0509395512109998 \tabularnewline
50 & 1.2939 & 1.34140437670215 & -0.0475043767021477 \tabularnewline
51 & 1.3176 & 1.29326131089821 & 0.0243386891017938 \tabularnewline
52 & 1.3443 & 1.31187784497755 & 0.0324221550224488 \tabularnewline
53 & 1.3356 & 1.3380058757406 & -0.00240587574059559 \tabularnewline
54 & 1.3214 & 1.33177023476378 & -0.010370234763784 \tabularnewline
55 & 1.2403 & 1.31813377624439 & -0.0778337762443873 \tabularnewline
56 & 1.259 & 1.24180735613224 & 0.0171926438677603 \tabularnewline
57 & 1.2284 & 1.25378348427632 & -0.0253834842763221 \tabularnewline
58 & 1.2611 & 1.22619608255609 & 0.0349039174439145 \tabularnewline
59 & 1.293 & 1.2546302713931 & 0.0383697286069014 \tabularnewline
60 & 1.2993 & 1.28628503780323 & 0.0130149621967728 \tabularnewline
61 & 1.2986 & 1.29437908834283 & 0.0042209116571732 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203498&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]1.487[/C][C]1.4681[/C][C]0.0189000000000001[/C][/ROW]
[ROW][C]4[/C][C]1.5167[/C][C]1.48166267530728[/C][C]0.0350373246927207[/C][/ROW]
[ROW][C]5[/C][C]1.5812[/C][C]1.51022083177363[/C][C]0.0709791682263732[/C][/ROW]
[ROW][C]6[/C][C]1.554[/C][C]1.57217766167524[/C][C]-0.0181776616752423[/C][/ROW]
[ROW][C]7[/C][C]1.5508[/C][C]1.55128621353514[/C][C]-0.000486213535144442[/C][/ROW]
[ROW][C]8[/C][C]1.5764[/C][C]1.54683440345854[/C][C]0.0295655965414559[/C][/ROW]
[ROW][C]9[/C][C]1.5611[/C][C]1.57030799987778[/C][C]-0.00920799987778254[/C][/ROW]
[ROW][C]10[/C][C]1.4735[/C][C]1.55775153892101[/C][C]-0.0842515389210121[/C][/ROW]
[ROW][C]11[/C][C]1.4303[/C][C]1.47546146367189[/C][C]-0.0451614636718944[/C][/ROW]
[ROW][C]12[/C][C]1.2757[/C][C]1.42949553124486[/C][C]-0.153795531244859[/C][/ROW]
[ROW][C]13[/C][C]1.2727[/C][C]1.2825822519346[/C][C]-0.00988225193459669[/C][/ROW]
[ROW][C]14[/C][C]1.3917[/C][C]1.26939924759428[/C][C]0.122300752405724[/C][/ROW]
[ROW][C]15[/C][C]1.2816[/C][C]1.37904625311479[/C][C]-0.0974462531147875[/C][/ROW]
[ROW][C]16[/C][C]1.2644[/C][C]1.28449509420654[/C][C]-0.0200950942065363[/C][/ROW]
[ROW][C]17[/C][C]1.3308[/C][C]1.26182188707328[/C][C]0.0689781129267222[/C][/ROW]
[ROW][C]18[/C][C]1.3275[/C][C]1.32191925218655[/C][C]0.0055807478134493[/C][/ROW]
[ROW][C]19[/C][C]1.4098[/C][C]1.32310511789128[/C][C]0.0866948821087183[/C][/ROW]
[ROW][C]20[/C][C]1.4134[/C][C]1.39966565044569[/C][C]0.013734349554313[/C][/ROW]
[ROW][C]21[/C][C]1.4138[/C][C]1.40842818598955[/C][C]0.00537181401044662[/C][/ROW]
[ROW][C]22[/C][C]1.4272[/C][C]1.40941990161265[/C][C]0.017780098387348[/C][/ROW]
[ROW][C]23[/C][C]1.4643[/C][C]1.42194191721627[/C][C]0.0423580827837251[/C][/ROW]
[ROW][C]24[/C][C]1.48[/C][C]1.45730283015646[/C][C]0.0226971698435445[/C][/ROW]
[ROW][C]25[/C][C]1.5023[/C][C]1.47439399546631[/C][C]0.0279060045336852[/C][/ROW]
[ROW][C]26[/C][C]1.4406[/C][C]1.49632542915672[/C][C]-0.0557254291567153[/C][/ROW]
[ROW][C]27[/C][C]1.3966[/C][C]1.44054301547216[/C][C]-0.0439430154721558[/C][/ROW]
[ROW][C]28[/C][C]1.357[/C][C]1.39570931638431[/C][C]-0.0387093163843137[/C][/ROW]
[ROW][C]29[/C][C]1.3479[/C][C]1.35573899072164[/C][C]-0.00783899072164473[/C][/ROW]
[ROW][C]30[/C][C]1.3315[/C][C]1.34445467068032[/C][C]-0.0129546706803212[/C][/ROW]
[ROW][C]31[/C][C]1.2307[/C][C]1.32841664555486[/C][C]-0.0977166455548604[/C][/ROW]
[ROW][C]32[/C][C]1.2271[/C][C]1.23361422661325[/C][C]-0.00651422661324674[/C][/ROW]
[ROW][C]33[/C][C]1.3028[/C][C]1.22356093312719[/C][C]0.0792390668728107[/C][/ROW]
[ROW][C]34[/C][C]1.268[/C][C]1.29319320842555[/C][C]-0.0251932084255466[/C][/ROW]
[ROW][C]35[/C][C]1.3648[/C][C]1.26578261903261[/C][C]0.0990173809673891[/C][/ROW]
[ROW][C]36[/C][C]1.3857[/C][C]1.35379373605417[/C][C]0.0319062639458327[/C][/ROW]
[ROW][C]37[/C][C]1.2998[/C][C]1.37944237912025[/C][C]-0.0796423791202521[/C][/ROW]
[ROW][C]38[/C][C]1.3362[/C][C]1.30143532911029[/C][C]0.0347646708897063[/C][/ROW]
[ROW][C]39[/C][C]1.3692[/C][C]1.32974012418968[/C][C]0.0394598758103237[/C][/ROW]
[ROW][C]40[/C][C]1.3834[/C][C]1.36240790125435[/C][C]0.0209920987456531[/C][/ROW]
[ROW][C]41[/C][C]1.4207[/C][C]1.37791464275108[/C][C]0.0427853572489205[/C][/ROW]
[ROW][C]42[/C][C]1.486[/C][C]1.41367259710392[/C][C]0.0723274028960774[/C][/ROW]
[ROW][C]43[/C][C]1.4385[/C][C]1.47688226339401[/C][C]-0.0383822633940056[/C][/ROW]
[ROW][C]44[/C][C]1.4453[/C][C]1.43721584913224[/C][C]0.00808415086776093[/C][/ROW]
[ROW][C]45[/C][C]1.426[/C][C]1.44072798229761[/C][C]-0.0147279822976119[/C][/ROW]
[ROW][C]46[/C][C]1.445[/C][C]1.42304212139685[/C][C]0.0219578786031456[/C][/ROW]
[ROW][C]47[/C][C]1.3503[/C][C]1.43944630617694[/C][C]-0.0891463061769442[/C][/ROW]
[ROW][C]48[/C][C]1.4001[/C][C]1.35260780722303[/C][C]0.0474921927769691[/C][/ROW]
[ROW][C]49[/C][C]1.3418[/C][C]1.392739551211[/C][C]-0.0509395512109998[/C][/ROW]
[ROW][C]50[/C][C]1.2939[/C][C]1.34140437670215[/C][C]-0.0475043767021477[/C][/ROW]
[ROW][C]51[/C][C]1.3176[/C][C]1.29326131089821[/C][C]0.0243386891017938[/C][/ROW]
[ROW][C]52[/C][C]1.3443[/C][C]1.31187784497755[/C][C]0.0324221550224488[/C][/ROW]
[ROW][C]53[/C][C]1.3356[/C][C]1.3380058757406[/C][C]-0.00240587574059559[/C][/ROW]
[ROW][C]54[/C][C]1.3214[/C][C]1.33177023476378[/C][C]-0.010370234763784[/C][/ROW]
[ROW][C]55[/C][C]1.2403[/C][C]1.31813377624439[/C][C]-0.0778337762443873[/C][/ROW]
[ROW][C]56[/C][C]1.259[/C][C]1.24180735613224[/C][C]0.0171926438677603[/C][/ROW]
[ROW][C]57[/C][C]1.2284[/C][C]1.25378348427632[/C][C]-0.0253834842763221[/C][/ROW]
[ROW][C]58[/C][C]1.2611[/C][C]1.22619608255609[/C][C]0.0349039174439145[/C][/ROW]
[ROW][C]59[/C][C]1.293[/C][C]1.2546302713931[/C][C]0.0383697286069014[/C][/ROW]
[ROW][C]60[/C][C]1.2993[/C][C]1.28628503780323[/C][C]0.0130149621967728[/C][/ROW]
[ROW][C]61[/C][C]1.2986[/C][C]1.29437908834283[/C][C]0.0042209116571732[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203498&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203498&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	1.487	1.4681	0.0189000000000001
4	1.5167	1.48166267530728	0.0350373246927207
5	1.5812	1.51022083177363	0.0709791682263732
6	1.554	1.57217766167524	-0.0181776616752423
7	1.5508	1.55128621353514	-0.000486213535144442
8	1.5764	1.54683440345854	0.0295655965414559
9	1.5611	1.57030799987778	-0.00920799987778254
10	1.4735	1.55775153892101	-0.0842515389210121
11	1.4303	1.47546146367189	-0.0451614636718944
12	1.2757	1.42949553124486	-0.153795531244859
13	1.2727	1.2825822519346	-0.00988225193459669
14	1.3917	1.26939924759428	0.122300752405724
15	1.2816	1.37904625311479	-0.0974462531147875
16	1.2644	1.28449509420654	-0.0200950942065363
17	1.3308	1.26182188707328	0.0689781129267222
18	1.3275	1.32191925218655	0.0055807478134493
19	1.4098	1.32310511789128	0.0866948821087183
20	1.4134	1.39966565044569	0.013734349554313
21	1.4138	1.40842818598955	0.00537181401044662
22	1.4272	1.40941990161265	0.017780098387348
23	1.4643	1.42194191721627	0.0423580827837251
24	1.48	1.45730283015646	0.0226971698435445
25	1.5023	1.47439399546631	0.0279060045336852
26	1.4406	1.49632542915672	-0.0557254291567153
27	1.3966	1.44054301547216	-0.0439430154721558
28	1.357	1.39570931638431	-0.0387093163843137
29	1.3479	1.35573899072164	-0.00783899072164473
30	1.3315	1.34445467068032	-0.0129546706803212
31	1.2307	1.32841664555486	-0.0977166455548604
32	1.2271	1.23361422661325	-0.00651422661324674
33	1.3028	1.22356093312719	0.0792390668728107
34	1.268	1.29319320842555	-0.0251932084255466
35	1.3648	1.26578261903261	0.0990173809673891
36	1.3857	1.35379373605417	0.0319062639458327
37	1.2998	1.37944237912025	-0.0796423791202521
38	1.3362	1.30143532911029	0.0347646708897063
39	1.3692	1.32974012418968	0.0394598758103237
40	1.3834	1.36240790125435	0.0209920987456531
41	1.4207	1.37791464275108	0.0427853572489205
42	1.486	1.41367259710392	0.0723274028960774
43	1.4385	1.47688226339401	-0.0383822633940056
44	1.4453	1.43721584913224	0.00808415086776093
45	1.426	1.44072798229761	-0.0147279822976119
46	1.445	1.42304212139685	0.0219578786031456
47	1.3503	1.43944630617694	-0.0891463061769442
48	1.4001	1.35260780722303	0.0474921927769691
49	1.3418	1.392739551211	-0.0509395512109998
50	1.2939	1.34140437670215	-0.0475043767021477
51	1.3176	1.29326131089821	0.0243386891017938
52	1.3443	1.31187784497755	0.0324221550224488
53	1.3356	1.3380058757406	-0.00240587574059559
54	1.3214	1.33177023476378	-0.010370234763784
55	1.2403	1.31813377624439	-0.0778337762443873
56	1.259	1.24180735613224	0.0171926438677603
57	1.2284	1.25378348427632	-0.0253834842763221
58	1.2611	1.22619608255609	0.0349039174439145
59	1.293	1.2546302713931	0.0383697286069014
60	1.2993	1.28628503780323	0.0130149621967728
61	1.2986	1.29437908834283	0.0042209116571732

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
62	1.29430133706958	1.19099438668386	1.3976082874553
63	1.29030133706958	1.14927729029593	1.43132538384323
64	1.28630133706958	1.1157046268468	1.45689804729236
65	1.28230133706958	1.08654972581375	1.47805294832541
66	1.27830133706958	1.06027806060656	1.4963246135326
67	1.27430133706958	1.03607958145081	1.51252309268835
68	1.27030133706958	1.0134646951734	1.52713797896576
69	1.26630133706958	0.992110680060762	1.5404919940784
70	1.26230133706958	0.971791488421818	1.55281118571734
71	1.25830133706958	0.952341490142301	1.56426118399686
72	1.25430133706958	0.933635024990836	1.57496764914832
73	1.25030133706958	0.915574075746871	1.58502859839229

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
62 & 1.29430133706958 & 1.19099438668386 & 1.3976082874553 \tabularnewline
63 & 1.29030133706958 & 1.14927729029593 & 1.43132538384323 \tabularnewline
64 & 1.28630133706958 & 1.1157046268468 & 1.45689804729236 \tabularnewline
65 & 1.28230133706958 & 1.08654972581375 & 1.47805294832541 \tabularnewline
66 & 1.27830133706958 & 1.06027806060656 & 1.4963246135326 \tabularnewline
67 & 1.27430133706958 & 1.03607958145081 & 1.51252309268835 \tabularnewline
68 & 1.27030133706958 & 1.0134646951734 & 1.52713797896576 \tabularnewline
69 & 1.26630133706958 & 0.992110680060762 & 1.5404919940784 \tabularnewline
70 & 1.26230133706958 & 0.971791488421818 & 1.55281118571734 \tabularnewline
71 & 1.25830133706958 & 0.952341490142301 & 1.56426118399686 \tabularnewline
72 & 1.25430133706958 & 0.933635024990836 & 1.57496764914832 \tabularnewline
73 & 1.25030133706958 & 0.915574075746871 & 1.58502859839229 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203498&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]1.29430133706958[/C][C]1.19099438668386[/C][C]1.3976082874553[/C][/ROW]
[ROW][C]63[/C][C]1.29030133706958[/C][C]1.14927729029593[/C][C]1.43132538384323[/C][/ROW]
[ROW][C]64[/C][C]1.28630133706958[/C][C]1.1157046268468[/C][C]1.45689804729236[/C][/ROW]
[ROW][C]65[/C][C]1.28230133706958[/C][C]1.08654972581375[/C][C]1.47805294832541[/C][/ROW]
[ROW][C]66[/C][C]1.27830133706958[/C][C]1.06027806060656[/C][C]1.4963246135326[/C][/ROW]
[ROW][C]67[/C][C]1.27430133706958[/C][C]1.03607958145081[/C][C]1.51252309268835[/C][/ROW]
[ROW][C]68[/C][C]1.27030133706958[/C][C]1.0134646951734[/C][C]1.52713797896576[/C][/ROW]
[ROW][C]69[/C][C]1.26630133706958[/C][C]0.992110680060762[/C][C]1.5404919940784[/C][/ROW]
[ROW][C]70[/C][C]1.26230133706958[/C][C]0.971791488421818[/C][C]1.55281118571734[/C][/ROW]
[ROW][C]71[/C][C]1.25830133706958[/C][C]0.952341490142301[/C][C]1.56426118399686[/C][/ROW]
[ROW][C]72[/C][C]1.25430133706958[/C][C]0.933635024990836[/C][C]1.57496764914832[/C][/ROW]
[ROW][C]73[/C][C]1.25030133706958[/C][C]0.915574075746871[/C][C]1.58502859839229[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203498&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203498&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	1.29430133706958	1.19099438668386	1.3976082874553
63	1.29030133706958	1.14927729029593	1.43132538384323
64	1.28630133706958	1.1157046268468	1.45689804729236
65	1.28230133706958	1.08654972581375	1.47805294832541
66	1.27830133706958	1.06027806060656	1.4963246135326
67	1.27430133706958	1.03607958145081	1.51252309268835
68	1.27030133706958	1.0134646951734	1.52713797896576
69	1.26630133706958	0.992110680060762	1.5404919940784
70	1.26230133706958	0.971791488421818	1.55281118571734
71	1.25830133706958	0.952341490142301	1.56426118399686
72	1.25430133706958	0.933635024990836	1.57496764914832
73	1.25030133706958	0.915574075746871	1.58502859839229

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 = Double ; par3 = additive ;

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