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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

Mon, 17 Dec 2012 02:53:57 -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/17/t1355730919rymi86v2q16eo0s.htm/, Retrieved Thu, 18 Apr 2024 23:31:37 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=200682, Retrieved Thu, 18 Apr 2024 23:31:37 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

146

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

-       [Exponential Smoothing] [] [2012-12-17 07:53:57] [946b987ea445738c2c70467dba74cc4f] [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

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	'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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200682&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200682&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200682&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	'Gwilym Jenkins' @ jenkins.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.002012910036564
gamma	0.0982581635507916

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.002012910036564 \tabularnewline
gamma & 0.0982581635507916 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200682&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]0.002012910036564[/C][/ROW]
[ROW][C]gamma[/C][C]0.0982581635507916[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200682&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200682&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	0.002012910036564
gamma	0.0982581635507916

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	3.53	3.48032585470085	0.049674145299146
14	3.53	3.52940943014507	0.000590569854928891
15	3.53	3.53024395224239	-0.000243952242392709
16	3.53	3.53191012785514	-0.00191012785514255
17	3.53	3.53273961627294	-0.00273961627294472
18	3.53	3.53273410167185	-0.00273410167185206
19	3.53	3.51939526483782	0.0106047351621767
20	3.53	3.52941661121567	0.000583388784333838
21	3.58	3.59941778552481	-0.019417785524805
22	3.58	3.59937869926943	-0.0193786992694345
23	3.59	3.58933969169118	0.000660308308821023
24	3.59	3.5893410208324	0.000658979167598606
25	3.59	3.58934234729818	0.000657652701818279
26	3.59	3.58934367109391	0.000656328906094128
27	3.59	3.59017832555828	-0.000178325558281678
28	3.59	3.59184463327164	-0.00184463327164286
29	3.59	3.59267425352415	-0.00267425352414952
30	3.59	3.59266887049239	-0.00266887049239006
31	3.59	3.57933016496286	0.0106698350371435
32	3.61	3.58935164238089	0.0206483576191085
33	3.71	3.67939320566718	0.0306067943328188
34	3.83	3.72945481439068	0.100545185609319
35	3.83	3.83965720280392	-0.00965720280392146
36	3.83	3.82963776372347	0.000362236276527206
37	3.83	3.82963849287251	0.000361507127490501
38	3.83	3.82963922055383	0.000360779446165083
39	3.83	3.83047328010374	-0.000473280103736595
40	3.83	3.83213899410013	-0.00213899410013241
41	3.83	3.83296802183077	-0.00296802183077327
42	3.83	3.83296204746984	-0.00296204746984063
43	3.83	3.81962275180143	0.0103772481985729
44	3.83	3.82964364026848	0.000356359731521927
45	3.92	3.89964435758856	0.0203556424114422
46	3.92	3.93968533166547	-0.0196853316654688
47	3.92	3.92964570686379	-0.00964570686378563
48	3.92	3.91962629092363	0.000373709076369799
49	3.92	3.91962704316638	0.000372956833619043
50	3.92	3.91962779389493	0.000372206105065498
51	3.92	3.92046187644567	-0.000461876445672527
52	3.92	3.92212761339661	-0.00212761339660616
53	3.92	3.92295666403558	-0.00295666403557959
54	3.92	3.92295071253687	-0.00295071253686707
55	3.92	3.90961143968465	0.0103885603153464
56	3.92	3.91963235092198	0.000367649078022225
57	3.98	3.9896330909665	-0.00963309096649656
58	3.98	3.99961370042101	-0.0196137004210071
59	3.98	3.98957421980657	-0.00957421980657491
60	3.98	3.97955494776343	0.000445052236565324
61	3.98	3.97955584361355	0.000444156386451677
62	3.98	3.9795567376604	0.000443262339603567
63	3.98	3.98039096324094	-0.000390963240942455
64	3.98	3.98205684293378	-0.0020568429337775
65	3.98	3.98288603602733	-0.00288603602732573
66	3.98	3.98288022669644	-0.00288022669643961
67	3.98	3.96954109572588	0.0104589042741181
68	3.98	3.97956214855927	0.000437851440732828
69	4.09	4.04956302991483	0.0404369700851737
70	4.09	4.10964442589776	-0.0196444258977593
71	4.09	4.09960488343571	-0.00960488343570631
72	4.09	4.08958554966944	0.000414450330560534

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 3.53 & 3.48032585470085 & 0.049674145299146 \tabularnewline
14 & 3.53 & 3.52940943014507 & 0.000590569854928891 \tabularnewline
15 & 3.53 & 3.53024395224239 & -0.000243952242392709 \tabularnewline
16 & 3.53 & 3.53191012785514 & -0.00191012785514255 \tabularnewline
17 & 3.53 & 3.53273961627294 & -0.00273961627294472 \tabularnewline
18 & 3.53 & 3.53273410167185 & -0.00273410167185206 \tabularnewline
19 & 3.53 & 3.51939526483782 & 0.0106047351621767 \tabularnewline
20 & 3.53 & 3.52941661121567 & 0.000583388784333838 \tabularnewline
21 & 3.58 & 3.59941778552481 & -0.019417785524805 \tabularnewline
22 & 3.58 & 3.59937869926943 & -0.0193786992694345 \tabularnewline
23 & 3.59 & 3.58933969169118 & 0.000660308308821023 \tabularnewline
24 & 3.59 & 3.5893410208324 & 0.000658979167598606 \tabularnewline
25 & 3.59 & 3.58934234729818 & 0.000657652701818279 \tabularnewline
26 & 3.59 & 3.58934367109391 & 0.000656328906094128 \tabularnewline
27 & 3.59 & 3.59017832555828 & -0.000178325558281678 \tabularnewline
28 & 3.59 & 3.59184463327164 & -0.00184463327164286 \tabularnewline
29 & 3.59 & 3.59267425352415 & -0.00267425352414952 \tabularnewline
30 & 3.59 & 3.59266887049239 & -0.00266887049239006 \tabularnewline
31 & 3.59 & 3.57933016496286 & 0.0106698350371435 \tabularnewline
32 & 3.61 & 3.58935164238089 & 0.0206483576191085 \tabularnewline
33 & 3.71 & 3.67939320566718 & 0.0306067943328188 \tabularnewline
34 & 3.83 & 3.72945481439068 & 0.100545185609319 \tabularnewline
35 & 3.83 & 3.83965720280392 & -0.00965720280392146 \tabularnewline
36 & 3.83 & 3.82963776372347 & 0.000362236276527206 \tabularnewline
37 & 3.83 & 3.82963849287251 & 0.000361507127490501 \tabularnewline
38 & 3.83 & 3.82963922055383 & 0.000360779446165083 \tabularnewline
39 & 3.83 & 3.83047328010374 & -0.000473280103736595 \tabularnewline
40 & 3.83 & 3.83213899410013 & -0.00213899410013241 \tabularnewline
41 & 3.83 & 3.83296802183077 & -0.00296802183077327 \tabularnewline
42 & 3.83 & 3.83296204746984 & -0.00296204746984063 \tabularnewline
43 & 3.83 & 3.81962275180143 & 0.0103772481985729 \tabularnewline
44 & 3.83 & 3.82964364026848 & 0.000356359731521927 \tabularnewline
45 & 3.92 & 3.89964435758856 & 0.0203556424114422 \tabularnewline
46 & 3.92 & 3.93968533166547 & -0.0196853316654688 \tabularnewline
47 & 3.92 & 3.92964570686379 & -0.00964570686378563 \tabularnewline
48 & 3.92 & 3.91962629092363 & 0.000373709076369799 \tabularnewline
49 & 3.92 & 3.91962704316638 & 0.000372956833619043 \tabularnewline
50 & 3.92 & 3.91962779389493 & 0.000372206105065498 \tabularnewline
51 & 3.92 & 3.92046187644567 & -0.000461876445672527 \tabularnewline
52 & 3.92 & 3.92212761339661 & -0.00212761339660616 \tabularnewline
53 & 3.92 & 3.92295666403558 & -0.00295666403557959 \tabularnewline
54 & 3.92 & 3.92295071253687 & -0.00295071253686707 \tabularnewline
55 & 3.92 & 3.90961143968465 & 0.0103885603153464 \tabularnewline
56 & 3.92 & 3.91963235092198 & 0.000367649078022225 \tabularnewline
57 & 3.98 & 3.9896330909665 & -0.00963309096649656 \tabularnewline
58 & 3.98 & 3.99961370042101 & -0.0196137004210071 \tabularnewline
59 & 3.98 & 3.98957421980657 & -0.00957421980657491 \tabularnewline
60 & 3.98 & 3.97955494776343 & 0.000445052236565324 \tabularnewline
61 & 3.98 & 3.97955584361355 & 0.000444156386451677 \tabularnewline
62 & 3.98 & 3.9795567376604 & 0.000443262339603567 \tabularnewline
63 & 3.98 & 3.98039096324094 & -0.000390963240942455 \tabularnewline
64 & 3.98 & 3.98205684293378 & -0.0020568429337775 \tabularnewline
65 & 3.98 & 3.98288603602733 & -0.00288603602732573 \tabularnewline
66 & 3.98 & 3.98288022669644 & -0.00288022669643961 \tabularnewline
67 & 3.98 & 3.96954109572588 & 0.0104589042741181 \tabularnewline
68 & 3.98 & 3.97956214855927 & 0.000437851440732828 \tabularnewline
69 & 4.09 & 4.04956302991483 & 0.0404369700851737 \tabularnewline
70 & 4.09 & 4.10964442589776 & -0.0196444258977593 \tabularnewline
71 & 4.09 & 4.09960488343571 & -0.00960488343570631 \tabularnewline
72 & 4.09 & 4.08958554966944 & 0.000414450330560534 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200682&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]3.53[/C][C]3.48032585470085[/C][C]0.049674145299146[/C][/ROW]
[ROW][C]14[/C][C]3.53[/C][C]3.52940943014507[/C][C]0.000590569854928891[/C][/ROW]
[ROW][C]15[/C][C]3.53[/C][C]3.53024395224239[/C][C]-0.000243952242392709[/C][/ROW]
[ROW][C]16[/C][C]3.53[/C][C]3.53191012785514[/C][C]-0.00191012785514255[/C][/ROW]
[ROW][C]17[/C][C]3.53[/C][C]3.53273961627294[/C][C]-0.00273961627294472[/C][/ROW]
[ROW][C]18[/C][C]3.53[/C][C]3.53273410167185[/C][C]-0.00273410167185206[/C][/ROW]
[ROW][C]19[/C][C]3.53[/C][C]3.51939526483782[/C][C]0.0106047351621767[/C][/ROW]
[ROW][C]20[/C][C]3.53[/C][C]3.52941661121567[/C][C]0.000583388784333838[/C][/ROW]
[ROW][C]21[/C][C]3.58[/C][C]3.59941778552481[/C][C]-0.019417785524805[/C][/ROW]
[ROW][C]22[/C][C]3.58[/C][C]3.59937869926943[/C][C]-0.0193786992694345[/C][/ROW]
[ROW][C]23[/C][C]3.59[/C][C]3.58933969169118[/C][C]0.000660308308821023[/C][/ROW]
[ROW][C]24[/C][C]3.59[/C][C]3.5893410208324[/C][C]0.000658979167598606[/C][/ROW]
[ROW][C]25[/C][C]3.59[/C][C]3.58934234729818[/C][C]0.000657652701818279[/C][/ROW]
[ROW][C]26[/C][C]3.59[/C][C]3.58934367109391[/C][C]0.000656328906094128[/C][/ROW]
[ROW][C]27[/C][C]3.59[/C][C]3.59017832555828[/C][C]-0.000178325558281678[/C][/ROW]
[ROW][C]28[/C][C]3.59[/C][C]3.59184463327164[/C][C]-0.00184463327164286[/C][/ROW]
[ROW][C]29[/C][C]3.59[/C][C]3.59267425352415[/C][C]-0.00267425352414952[/C][/ROW]
[ROW][C]30[/C][C]3.59[/C][C]3.59266887049239[/C][C]-0.00266887049239006[/C][/ROW]
[ROW][C]31[/C][C]3.59[/C][C]3.57933016496286[/C][C]0.0106698350371435[/C][/ROW]
[ROW][C]32[/C][C]3.61[/C][C]3.58935164238089[/C][C]0.0206483576191085[/C][/ROW]
[ROW][C]33[/C][C]3.71[/C][C]3.67939320566718[/C][C]0.0306067943328188[/C][/ROW]
[ROW][C]34[/C][C]3.83[/C][C]3.72945481439068[/C][C]0.100545185609319[/C][/ROW]
[ROW][C]35[/C][C]3.83[/C][C]3.83965720280392[/C][C]-0.00965720280392146[/C][/ROW]
[ROW][C]36[/C][C]3.83[/C][C]3.82963776372347[/C][C]0.000362236276527206[/C][/ROW]
[ROW][C]37[/C][C]3.83[/C][C]3.82963849287251[/C][C]0.000361507127490501[/C][/ROW]
[ROW][C]38[/C][C]3.83[/C][C]3.82963922055383[/C][C]0.000360779446165083[/C][/ROW]
[ROW][C]39[/C][C]3.83[/C][C]3.83047328010374[/C][C]-0.000473280103736595[/C][/ROW]
[ROW][C]40[/C][C]3.83[/C][C]3.83213899410013[/C][C]-0.00213899410013241[/C][/ROW]
[ROW][C]41[/C][C]3.83[/C][C]3.83296802183077[/C][C]-0.00296802183077327[/C][/ROW]
[ROW][C]42[/C][C]3.83[/C][C]3.83296204746984[/C][C]-0.00296204746984063[/C][/ROW]
[ROW][C]43[/C][C]3.83[/C][C]3.81962275180143[/C][C]0.0103772481985729[/C][/ROW]
[ROW][C]44[/C][C]3.83[/C][C]3.82964364026848[/C][C]0.000356359731521927[/C][/ROW]
[ROW][C]45[/C][C]3.92[/C][C]3.89964435758856[/C][C]0.0203556424114422[/C][/ROW]
[ROW][C]46[/C][C]3.92[/C][C]3.93968533166547[/C][C]-0.0196853316654688[/C][/ROW]
[ROW][C]47[/C][C]3.92[/C][C]3.92964570686379[/C][C]-0.00964570686378563[/C][/ROW]
[ROW][C]48[/C][C]3.92[/C][C]3.91962629092363[/C][C]0.000373709076369799[/C][/ROW]
[ROW][C]49[/C][C]3.92[/C][C]3.91962704316638[/C][C]0.000372956833619043[/C][/ROW]
[ROW][C]50[/C][C]3.92[/C][C]3.91962779389493[/C][C]0.000372206105065498[/C][/ROW]
[ROW][C]51[/C][C]3.92[/C][C]3.92046187644567[/C][C]-0.000461876445672527[/C][/ROW]
[ROW][C]52[/C][C]3.92[/C][C]3.92212761339661[/C][C]-0.00212761339660616[/C][/ROW]
[ROW][C]53[/C][C]3.92[/C][C]3.92295666403558[/C][C]-0.00295666403557959[/C][/ROW]
[ROW][C]54[/C][C]3.92[/C][C]3.92295071253687[/C][C]-0.00295071253686707[/C][/ROW]
[ROW][C]55[/C][C]3.92[/C][C]3.90961143968465[/C][C]0.0103885603153464[/C][/ROW]
[ROW][C]56[/C][C]3.92[/C][C]3.91963235092198[/C][C]0.000367649078022225[/C][/ROW]
[ROW][C]57[/C][C]3.98[/C][C]3.9896330909665[/C][C]-0.00963309096649656[/C][/ROW]
[ROW][C]58[/C][C]3.98[/C][C]3.99961370042101[/C][C]-0.0196137004210071[/C][/ROW]
[ROW][C]59[/C][C]3.98[/C][C]3.98957421980657[/C][C]-0.00957421980657491[/C][/ROW]
[ROW][C]60[/C][C]3.98[/C][C]3.97955494776343[/C][C]0.000445052236565324[/C][/ROW]
[ROW][C]61[/C][C]3.98[/C][C]3.97955584361355[/C][C]0.000444156386451677[/C][/ROW]
[ROW][C]62[/C][C]3.98[/C][C]3.9795567376604[/C][C]0.000443262339603567[/C][/ROW]
[ROW][C]63[/C][C]3.98[/C][C]3.98039096324094[/C][C]-0.000390963240942455[/C][/ROW]
[ROW][C]64[/C][C]3.98[/C][C]3.98205684293378[/C][C]-0.0020568429337775[/C][/ROW]
[ROW][C]65[/C][C]3.98[/C][C]3.98288603602733[/C][C]-0.00288603602732573[/C][/ROW]
[ROW][C]66[/C][C]3.98[/C][C]3.98288022669644[/C][C]-0.00288022669643961[/C][/ROW]
[ROW][C]67[/C][C]3.98[/C][C]3.96954109572588[/C][C]0.0104589042741181[/C][/ROW]
[ROW][C]68[/C][C]3.98[/C][C]3.97956214855927[/C][C]0.000437851440732828[/C][/ROW]
[ROW][C]69[/C][C]4.09[/C][C]4.04956302991483[/C][C]0.0404369700851737[/C][/ROW]
[ROW][C]70[/C][C]4.09[/C][C]4.10964442589776[/C][C]-0.0196444258977593[/C][/ROW]
[ROW][C]71[/C][C]4.09[/C][C]4.09960488343571[/C][C]-0.00960488343570631[/C][/ROW]
[ROW][C]72[/C][C]4.09[/C][C]4.08958554966944[/C][C]0.000414450330560534[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200682&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200682&T=2

As an alternative you can also use a QR Code:

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

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	3.53	3.48032585470085	0.049674145299146
14	3.53	3.52940943014507	0.000590569854928891
15	3.53	3.53024395224239	-0.000243952242392709
16	3.53	3.53191012785514	-0.00191012785514255
17	3.53	3.53273961627294	-0.00273961627294472
18	3.53	3.53273410167185	-0.00273410167185206
19	3.53	3.51939526483782	0.0106047351621767
20	3.53	3.52941661121567	0.000583388784333838
21	3.58	3.59941778552481	-0.019417785524805
22	3.58	3.59937869926943	-0.0193786992694345
23	3.59	3.58933969169118	0.000660308308821023
24	3.59	3.5893410208324	0.000658979167598606
25	3.59	3.58934234729818	0.000657652701818279
26	3.59	3.58934367109391	0.000656328906094128
27	3.59	3.59017832555828	-0.000178325558281678
28	3.59	3.59184463327164	-0.00184463327164286
29	3.59	3.59267425352415	-0.00267425352414952
30	3.59	3.59266887049239	-0.00266887049239006
31	3.59	3.57933016496286	0.0106698350371435
32	3.61	3.58935164238089	0.0206483576191085
33	3.71	3.67939320566718	0.0306067943328188
34	3.83	3.72945481439068	0.100545185609319
35	3.83	3.83965720280392	-0.00965720280392146
36	3.83	3.82963776372347	0.000362236276527206
37	3.83	3.82963849287251	0.000361507127490501
38	3.83	3.82963922055383	0.000360779446165083
39	3.83	3.83047328010374	-0.000473280103736595
40	3.83	3.83213899410013	-0.00213899410013241
41	3.83	3.83296802183077	-0.00296802183077327
42	3.83	3.83296204746984	-0.00296204746984063
43	3.83	3.81962275180143	0.0103772481985729
44	3.83	3.82964364026848	0.000356359731521927
45	3.92	3.89964435758856	0.0203556424114422
46	3.92	3.93968533166547	-0.0196853316654688
47	3.92	3.92964570686379	-0.00964570686378563
48	3.92	3.91962629092363	0.000373709076369799
49	3.92	3.91962704316638	0.000372956833619043
50	3.92	3.91962779389493	0.000372206105065498
51	3.92	3.92046187644567	-0.000461876445672527
52	3.92	3.92212761339661	-0.00212761339660616
53	3.92	3.92295666403558	-0.00295666403557959
54	3.92	3.92295071253687	-0.00295071253686707
55	3.92	3.90961143968465	0.0103885603153464
56	3.92	3.91963235092198	0.000367649078022225
57	3.98	3.9896330909665	-0.00963309096649656
58	3.98	3.99961370042101	-0.0196137004210071
59	3.98	3.98957421980657	-0.00957421980657491
60	3.98	3.97955494776343	0.000445052236565324
61	3.98	3.97955584361355	0.000444156386451677
62	3.98	3.9795567376604	0.000443262339603567
63	3.98	3.98039096324094	-0.000390963240942455
64	3.98	3.98205684293378	-0.0020568429337775
65	3.98	3.98288603602733	-0.00288603602732573
66	3.98	3.98288022669644	-0.00288022669643961
67	3.98	3.96954109572588	0.0104589042741181
68	3.98	3.97956214855927	0.000437851440732828
69	4.09	4.04956302991483	0.0404369700851737
70	4.09	4.10964442589776	-0.0196444258977593
71	4.09	4.09960488343571	-0.00960488343570631
72	4.09	4.08958554966944	0.000414450330560534

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	4.08958638392067	4.05468793738193	4.1244848304594
74	4.08917276784134	4.03976921403267	4.13857632165001
75	4.08959248509534	4.02902484898716	4.15016012120352
76	4.09167886901601	4.02167105741874	4.16168668061328
77	4.09459858627001	4.01624881651254	4.17294835602749
78	4.09751830352402	4.01160423818912	4.18343236885891
79	4.08710468744469	3.99421376131087	4.1799956135785
80	4.08669107136535	3.98728690194906	4.18609524078165
81	4.15627745528602	4.05073774375615	4.26181716681589
82	4.17586383920669	4.06450379491434	4.28722388349905
83	4.18545022312736	4.06853792680354	4.30236251945119
84	4.18503660704803	4.06280356208901	4.30726965200705

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 4.08958638392067 & 4.05468793738193 & 4.1244848304594 \tabularnewline
74 & 4.08917276784134 & 4.03976921403267 & 4.13857632165001 \tabularnewline
75 & 4.08959248509534 & 4.02902484898716 & 4.15016012120352 \tabularnewline
76 & 4.09167886901601 & 4.02167105741874 & 4.16168668061328 \tabularnewline
77 & 4.09459858627001 & 4.01624881651254 & 4.17294835602749 \tabularnewline
78 & 4.09751830352402 & 4.01160423818912 & 4.18343236885891 \tabularnewline
79 & 4.08710468744469 & 3.99421376131087 & 4.1799956135785 \tabularnewline
80 & 4.08669107136535 & 3.98728690194906 & 4.18609524078165 \tabularnewline
81 & 4.15627745528602 & 4.05073774375615 & 4.26181716681589 \tabularnewline
82 & 4.17586383920669 & 4.06450379491434 & 4.28722388349905 \tabularnewline
83 & 4.18545022312736 & 4.06853792680354 & 4.30236251945119 \tabularnewline
84 & 4.18503660704803 & 4.06280356208901 & 4.30726965200705 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200682&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]4.08958638392067[/C][C]4.05468793738193[/C][C]4.1244848304594[/C][/ROW]
[ROW][C]74[/C][C]4.08917276784134[/C][C]4.03976921403267[/C][C]4.13857632165001[/C][/ROW]
[ROW][C]75[/C][C]4.08959248509534[/C][C]4.02902484898716[/C][C]4.15016012120352[/C][/ROW]
[ROW][C]76[/C][C]4.09167886901601[/C][C]4.02167105741874[/C][C]4.16168668061328[/C][/ROW]
[ROW][C]77[/C][C]4.09459858627001[/C][C]4.01624881651254[/C][C]4.17294835602749[/C][/ROW]
[ROW][C]78[/C][C]4.09751830352402[/C][C]4.01160423818912[/C][C]4.18343236885891[/C][/ROW]
[ROW][C]79[/C][C]4.08710468744469[/C][C]3.99421376131087[/C][C]4.1799956135785[/C][/ROW]
[ROW][C]80[/C][C]4.08669107136535[/C][C]3.98728690194906[/C][C]4.18609524078165[/C][/ROW]
[ROW][C]81[/C][C]4.15627745528602[/C][C]4.05073774375615[/C][C]4.26181716681589[/C][/ROW]
[ROW][C]82[/C][C]4.17586383920669[/C][C]4.06450379491434[/C][C]4.28722388349905[/C][/ROW]
[ROW][C]83[/C][C]4.18545022312736[/C][C]4.06853792680354[/C][C]4.30236251945119[/C][/ROW]
[ROW][C]84[/C][C]4.18503660704803[/C][C]4.06280356208901[/C][C]4.30726965200705[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200682&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200682&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	4.08958638392067	4.05468793738193	4.1244848304594
74	4.08917276784134	4.03976921403267	4.13857632165001
75	4.08959248509534	4.02902484898716	4.15016012120352
76	4.09167886901601	4.02167105741874	4.16168668061328
77	4.09459858627001	4.01624881651254	4.17294835602749
78	4.09751830352402	4.01160423818912	4.18343236885891
79	4.08710468744469	3.99421376131087	4.1799956135785
80	4.08669107136535	3.98728690194906	4.18609524078165
81	4.15627745528602	4.05073774375615	4.26181716681589
82	4.17586383920669	4.06450379491434	4.28722388349905
83	4.18545022312736	4.06853792680354	4.30236251945119
84	4.18503660704803	4.06280356208901	4.30726965200705

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