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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Tue, 15 Jan 2013 20:26:26 -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/2013/Jan/15/t13582996014z1gpdnepsvosii.htm/, Retrieved Sat, 27 Apr 2024 15:13:36 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=205587, Retrieved Sat, 27 Apr 2024 15:13:36 +0000

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No (this computation is public)

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Estimated Impact

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

-     [Bootstrap Plot - Central Tendency] [] [2012-12-29 21:04:13] [8ed3f4120f64b138d86c2354ccf260c2]
- RMPD    [Exponential Smoothing] [] [2013-01-16 01:26:26] [3f9aa5867cfe47c4a12580af2904c765] [Current]

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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=205587&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=205587&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205587&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	1
beta	0.0366240380602464
gamma	0.251276247363328

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0366240380602464 \tabularnewline
gamma & 0.251276247363328 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205587&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]0.0366240380602464[/C][/ROW]
[ROW][C]gamma[/C][C]0.251276247363328[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205587&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205587&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	0.0366240380602464
gamma	0.251276247363328

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	105.38	101.715742521368	3.66425747863248
14	105.38	105.402865406525	-0.0228654065254688
15	108.37	108.452444649673	-0.0824446496732918
16	112.21	112.380258527019	-0.170258527019143
17	112.05	112.268189638912	-0.21818963891215
18	112.05	112.284365319939	-0.234365319938959
19	112.06	110.248281915541	1.81171808445851
20	112.05	112.680884347621	-0.630884347621162
21	111.36	113.281112148596	-1.9211121485956
22	111.36	112.226169930814	-0.86616993081411
23	111.36	111.856113956968	-0.496113956968003
24	111.36	111.299610927192	0.0603890728075527
25	111.78	111.281405952227	0.49859404777331
26	111.89	111.719666479609	0.17033352039104
27	111.89	114.886321447609	-2.99632144760938
28	111.89	115.717417390205	-3.82741739020473
29	112.02	111.6314085767	0.388591423299914
30	112.02	111.959807030444	0.0601929695564252
31	112.02	109.934511540052	2.08548845994845
32	112.02	112.367140548783	-0.347140548782917
33	112.02	112.987760193445	-0.967760193445372
34	112.02	112.657733573954	-0.637733573954108
35	112.02	112.296043861936	-0.276043861935989
36	111.28	111.747600687697	-0.467600687696802
37	111.28	110.970058595647	0.309941404353069
38	111.28	110.981409901436	0.298590098563594
39	111.28	114.042762143237	-2.76276214323728
40	110.56	114.882411970685	-4.32241197068528
41	110.56	110.058274456826	0.501725543174501
42	110.56	110.260816338881	0.299183661118803
43	110.56	108.244273652673	2.315726347327
44	110.56	110.685334902555	-0.125334902554627
45	111.37	111.314077965647	0.0559220343534719
46	109.43	111.831542723028	-2.40154272302776
47	109.43	109.465255197603	-0.0352551976029645
48	109.57	108.925630676571	0.644369323429203
49	109.57	109.06881341653	0.50118658346976
50	109.57	109.087168893039	0.482831106961484
51	109.57	112.155268784543	-2.58526878454323
52	109.57	113.001419135515	-3.43141913551548
53	109.39	108.929913377162	0.46008662283765
54	111.68	108.950930273815	2.72906972618516
55	111.68	109.313379827336	2.3666201726643
56	111.68	111.756305014614	-0.0763050146135242
57	111.93	112.386843750187	-0.456843750187474
58	111.93	112.32552895396	-0.395528953959683
59	111.93	111.972709753163	-0.0427097531626117
60	111.93	111.432812216204	0.497187783796107
61	111.56	111.430604573854	0.129395426145933
62	111.89	111.065343556866	0.824656443133946
63	111.89	114.475962472493	-2.5859624724927
64	111.89	115.322087417811	-3.43208741781108
65	110.82	111.250557184262	-0.430557184261744
66	110.82	110.348955108225	0.471044891775108
67	110.82	108.338706674269	2.48129332573068
68	110.82	110.78583165547	0.0341683445304568
69	110.98	111.420416371553	-0.440416371553411
70	110.98	111.269703212266	-0.289703212265962
71	111.78	110.92075977746	0.859240222539569
72	111.78	111.21389529074	0.566104709259733

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 105.38 & 101.715742521368 & 3.66425747863248 \tabularnewline
14 & 105.38 & 105.402865406525 & -0.0228654065254688 \tabularnewline
15 & 108.37 & 108.452444649673 & -0.0824446496732918 \tabularnewline
16 & 112.21 & 112.380258527019 & -0.170258527019143 \tabularnewline
17 & 112.05 & 112.268189638912 & -0.21818963891215 \tabularnewline
18 & 112.05 & 112.284365319939 & -0.234365319938959 \tabularnewline
19 & 112.06 & 110.248281915541 & 1.81171808445851 \tabularnewline
20 & 112.05 & 112.680884347621 & -0.630884347621162 \tabularnewline
21 & 111.36 & 113.281112148596 & -1.9211121485956 \tabularnewline
22 & 111.36 & 112.226169930814 & -0.86616993081411 \tabularnewline
23 & 111.36 & 111.856113956968 & -0.496113956968003 \tabularnewline
24 & 111.36 & 111.299610927192 & 0.0603890728075527 \tabularnewline
25 & 111.78 & 111.281405952227 & 0.49859404777331 \tabularnewline
26 & 111.89 & 111.719666479609 & 0.17033352039104 \tabularnewline
27 & 111.89 & 114.886321447609 & -2.99632144760938 \tabularnewline
28 & 111.89 & 115.717417390205 & -3.82741739020473 \tabularnewline
29 & 112.02 & 111.6314085767 & 0.388591423299914 \tabularnewline
30 & 112.02 & 111.959807030444 & 0.0601929695564252 \tabularnewline
31 & 112.02 & 109.934511540052 & 2.08548845994845 \tabularnewline
32 & 112.02 & 112.367140548783 & -0.347140548782917 \tabularnewline
33 & 112.02 & 112.987760193445 & -0.967760193445372 \tabularnewline
34 & 112.02 & 112.657733573954 & -0.637733573954108 \tabularnewline
35 & 112.02 & 112.296043861936 & -0.276043861935989 \tabularnewline
36 & 111.28 & 111.747600687697 & -0.467600687696802 \tabularnewline
37 & 111.28 & 110.970058595647 & 0.309941404353069 \tabularnewline
38 & 111.28 & 110.981409901436 & 0.298590098563594 \tabularnewline
39 & 111.28 & 114.042762143237 & -2.76276214323728 \tabularnewline
40 & 110.56 & 114.882411970685 & -4.32241197068528 \tabularnewline
41 & 110.56 & 110.058274456826 & 0.501725543174501 \tabularnewline
42 & 110.56 & 110.260816338881 & 0.299183661118803 \tabularnewline
43 & 110.56 & 108.244273652673 & 2.315726347327 \tabularnewline
44 & 110.56 & 110.685334902555 & -0.125334902554627 \tabularnewline
45 & 111.37 & 111.314077965647 & 0.0559220343534719 \tabularnewline
46 & 109.43 & 111.831542723028 & -2.40154272302776 \tabularnewline
47 & 109.43 & 109.465255197603 & -0.0352551976029645 \tabularnewline
48 & 109.57 & 108.925630676571 & 0.644369323429203 \tabularnewline
49 & 109.57 & 109.06881341653 & 0.50118658346976 \tabularnewline
50 & 109.57 & 109.087168893039 & 0.482831106961484 \tabularnewline
51 & 109.57 & 112.155268784543 & -2.58526878454323 \tabularnewline
52 & 109.57 & 113.001419135515 & -3.43141913551548 \tabularnewline
53 & 109.39 & 108.929913377162 & 0.46008662283765 \tabularnewline
54 & 111.68 & 108.950930273815 & 2.72906972618516 \tabularnewline
55 & 111.68 & 109.313379827336 & 2.3666201726643 \tabularnewline
56 & 111.68 & 111.756305014614 & -0.0763050146135242 \tabularnewline
57 & 111.93 & 112.386843750187 & -0.456843750187474 \tabularnewline
58 & 111.93 & 112.32552895396 & -0.395528953959683 \tabularnewline
59 & 111.93 & 111.972709753163 & -0.0427097531626117 \tabularnewline
60 & 111.93 & 111.432812216204 & 0.497187783796107 \tabularnewline
61 & 111.56 & 111.430604573854 & 0.129395426145933 \tabularnewline
62 & 111.89 & 111.065343556866 & 0.824656443133946 \tabularnewline
63 & 111.89 & 114.475962472493 & -2.5859624724927 \tabularnewline
64 & 111.89 & 115.322087417811 & -3.43208741781108 \tabularnewline
65 & 110.82 & 111.250557184262 & -0.430557184261744 \tabularnewline
66 & 110.82 & 110.348955108225 & 0.471044891775108 \tabularnewline
67 & 110.82 & 108.338706674269 & 2.48129332573068 \tabularnewline
68 & 110.82 & 110.78583165547 & 0.0341683445304568 \tabularnewline
69 & 110.98 & 111.420416371553 & -0.440416371553411 \tabularnewline
70 & 110.98 & 111.269703212266 & -0.289703212265962 \tabularnewline
71 & 111.78 & 110.92075977746 & 0.859240222539569 \tabularnewline
72 & 111.78 & 111.21389529074 & 0.566104709259733 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205587&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]105.38[/C][C]101.715742521368[/C][C]3.66425747863248[/C][/ROW]
[ROW][C]14[/C][C]105.38[/C][C]105.402865406525[/C][C]-0.0228654065254688[/C][/ROW]
[ROW][C]15[/C][C]108.37[/C][C]108.452444649673[/C][C]-0.0824446496732918[/C][/ROW]
[ROW][C]16[/C][C]112.21[/C][C]112.380258527019[/C][C]-0.170258527019143[/C][/ROW]
[ROW][C]17[/C][C]112.05[/C][C]112.268189638912[/C][C]-0.21818963891215[/C][/ROW]
[ROW][C]18[/C][C]112.05[/C][C]112.284365319939[/C][C]-0.234365319938959[/C][/ROW]
[ROW][C]19[/C][C]112.06[/C][C]110.248281915541[/C][C]1.81171808445851[/C][/ROW]
[ROW][C]20[/C][C]112.05[/C][C]112.680884347621[/C][C]-0.630884347621162[/C][/ROW]
[ROW][C]21[/C][C]111.36[/C][C]113.281112148596[/C][C]-1.9211121485956[/C][/ROW]
[ROW][C]22[/C][C]111.36[/C][C]112.226169930814[/C][C]-0.86616993081411[/C][/ROW]
[ROW][C]23[/C][C]111.36[/C][C]111.856113956968[/C][C]-0.496113956968003[/C][/ROW]
[ROW][C]24[/C][C]111.36[/C][C]111.299610927192[/C][C]0.0603890728075527[/C][/ROW]
[ROW][C]25[/C][C]111.78[/C][C]111.281405952227[/C][C]0.49859404777331[/C][/ROW]
[ROW][C]26[/C][C]111.89[/C][C]111.719666479609[/C][C]0.17033352039104[/C][/ROW]
[ROW][C]27[/C][C]111.89[/C][C]114.886321447609[/C][C]-2.99632144760938[/C][/ROW]
[ROW][C]28[/C][C]111.89[/C][C]115.717417390205[/C][C]-3.82741739020473[/C][/ROW]
[ROW][C]29[/C][C]112.02[/C][C]111.6314085767[/C][C]0.388591423299914[/C][/ROW]
[ROW][C]30[/C][C]112.02[/C][C]111.959807030444[/C][C]0.0601929695564252[/C][/ROW]
[ROW][C]31[/C][C]112.02[/C][C]109.934511540052[/C][C]2.08548845994845[/C][/ROW]
[ROW][C]32[/C][C]112.02[/C][C]112.367140548783[/C][C]-0.347140548782917[/C][/ROW]
[ROW][C]33[/C][C]112.02[/C][C]112.987760193445[/C][C]-0.967760193445372[/C][/ROW]
[ROW][C]34[/C][C]112.02[/C][C]112.657733573954[/C][C]-0.637733573954108[/C][/ROW]
[ROW][C]35[/C][C]112.02[/C][C]112.296043861936[/C][C]-0.276043861935989[/C][/ROW]
[ROW][C]36[/C][C]111.28[/C][C]111.747600687697[/C][C]-0.467600687696802[/C][/ROW]
[ROW][C]37[/C][C]111.28[/C][C]110.970058595647[/C][C]0.309941404353069[/C][/ROW]
[ROW][C]38[/C][C]111.28[/C][C]110.981409901436[/C][C]0.298590098563594[/C][/ROW]
[ROW][C]39[/C][C]111.28[/C][C]114.042762143237[/C][C]-2.76276214323728[/C][/ROW]
[ROW][C]40[/C][C]110.56[/C][C]114.882411970685[/C][C]-4.32241197068528[/C][/ROW]
[ROW][C]41[/C][C]110.56[/C][C]110.058274456826[/C][C]0.501725543174501[/C][/ROW]
[ROW][C]42[/C][C]110.56[/C][C]110.260816338881[/C][C]0.299183661118803[/C][/ROW]
[ROW][C]43[/C][C]110.56[/C][C]108.244273652673[/C][C]2.315726347327[/C][/ROW]
[ROW][C]44[/C][C]110.56[/C][C]110.685334902555[/C][C]-0.125334902554627[/C][/ROW]
[ROW][C]45[/C][C]111.37[/C][C]111.314077965647[/C][C]0.0559220343534719[/C][/ROW]
[ROW][C]46[/C][C]109.43[/C][C]111.831542723028[/C][C]-2.40154272302776[/C][/ROW]
[ROW][C]47[/C][C]109.43[/C][C]109.465255197603[/C][C]-0.0352551976029645[/C][/ROW]
[ROW][C]48[/C][C]109.57[/C][C]108.925630676571[/C][C]0.644369323429203[/C][/ROW]
[ROW][C]49[/C][C]109.57[/C][C]109.06881341653[/C][C]0.50118658346976[/C][/ROW]
[ROW][C]50[/C][C]109.57[/C][C]109.087168893039[/C][C]0.482831106961484[/C][/ROW]
[ROW][C]51[/C][C]109.57[/C][C]112.155268784543[/C][C]-2.58526878454323[/C][/ROW]
[ROW][C]52[/C][C]109.57[/C][C]113.001419135515[/C][C]-3.43141913551548[/C][/ROW]
[ROW][C]53[/C][C]109.39[/C][C]108.929913377162[/C][C]0.46008662283765[/C][/ROW]
[ROW][C]54[/C][C]111.68[/C][C]108.950930273815[/C][C]2.72906972618516[/C][/ROW]
[ROW][C]55[/C][C]111.68[/C][C]109.313379827336[/C][C]2.3666201726643[/C][/ROW]
[ROW][C]56[/C][C]111.68[/C][C]111.756305014614[/C][C]-0.0763050146135242[/C][/ROW]
[ROW][C]57[/C][C]111.93[/C][C]112.386843750187[/C][C]-0.456843750187474[/C][/ROW]
[ROW][C]58[/C][C]111.93[/C][C]112.32552895396[/C][C]-0.395528953959683[/C][/ROW]
[ROW][C]59[/C][C]111.93[/C][C]111.972709753163[/C][C]-0.0427097531626117[/C][/ROW]
[ROW][C]60[/C][C]111.93[/C][C]111.432812216204[/C][C]0.497187783796107[/C][/ROW]
[ROW][C]61[/C][C]111.56[/C][C]111.430604573854[/C][C]0.129395426145933[/C][/ROW]
[ROW][C]62[/C][C]111.89[/C][C]111.065343556866[/C][C]0.824656443133946[/C][/ROW]
[ROW][C]63[/C][C]111.89[/C][C]114.475962472493[/C][C]-2.5859624724927[/C][/ROW]
[ROW][C]64[/C][C]111.89[/C][C]115.322087417811[/C][C]-3.43208741781108[/C][/ROW]
[ROW][C]65[/C][C]110.82[/C][C]111.250557184262[/C][C]-0.430557184261744[/C][/ROW]
[ROW][C]66[/C][C]110.82[/C][C]110.348955108225[/C][C]0.471044891775108[/C][/ROW]
[ROW][C]67[/C][C]110.82[/C][C]108.338706674269[/C][C]2.48129332573068[/C][/ROW]
[ROW][C]68[/C][C]110.82[/C][C]110.78583165547[/C][C]0.0341683445304568[/C][/ROW]
[ROW][C]69[/C][C]110.98[/C][C]111.420416371553[/C][C]-0.440416371553411[/C][/ROW]
[ROW][C]70[/C][C]110.98[/C][C]111.269703212266[/C][C]-0.289703212265962[/C][/ROW]
[ROW][C]71[/C][C]111.78[/C][C]110.92075977746[/C][C]0.859240222539569[/C][/ROW]
[ROW][C]72[/C][C]111.78[/C][C]111.21389529074[/C][C]0.566104709259733[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205587&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205587&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	105.38	101.715742521368	3.66425747863248
14	105.38	105.402865406525	-0.0228654065254688
15	108.37	108.452444649673	-0.0824446496732918
16	112.21	112.380258527019	-0.170258527019143
17	112.05	112.268189638912	-0.21818963891215
18	112.05	112.284365319939	-0.234365319938959
19	112.06	110.248281915541	1.81171808445851
20	112.05	112.680884347621	-0.630884347621162
21	111.36	113.281112148596	-1.9211121485956
22	111.36	112.226169930814	-0.86616993081411
23	111.36	111.856113956968	-0.496113956968003
24	111.36	111.299610927192	0.0603890728075527
25	111.78	111.281405952227	0.49859404777331
26	111.89	111.719666479609	0.17033352039104
27	111.89	114.886321447609	-2.99632144760938
28	111.89	115.717417390205	-3.82741739020473
29	112.02	111.6314085767	0.388591423299914
30	112.02	111.959807030444	0.0601929695564252
31	112.02	109.934511540052	2.08548845994845
32	112.02	112.367140548783	-0.347140548782917
33	112.02	112.987760193445	-0.967760193445372
34	112.02	112.657733573954	-0.637733573954108
35	112.02	112.296043861936	-0.276043861935989
36	111.28	111.747600687697	-0.467600687696802
37	111.28	110.970058595647	0.309941404353069
38	111.28	110.981409901436	0.298590098563594
39	111.28	114.042762143237	-2.76276214323728
40	110.56	114.882411970685	-4.32241197068528
41	110.56	110.058274456826	0.501725543174501
42	110.56	110.260816338881	0.299183661118803
43	110.56	108.244273652673	2.315726347327
44	110.56	110.685334902555	-0.125334902554627
45	111.37	111.314077965647	0.0559220343534719
46	109.43	111.831542723028	-2.40154272302776
47	109.43	109.465255197603	-0.0352551976029645
48	109.57	108.925630676571	0.644369323429203
49	109.57	109.06881341653	0.50118658346976
50	109.57	109.087168893039	0.482831106961484
51	109.57	112.155268784543	-2.58526878454323
52	109.57	113.001419135515	-3.43141913551548
53	109.39	108.929913377162	0.46008662283765
54	111.68	108.950930273815	2.72906972618516
55	111.68	109.313379827336	2.3666201726643
56	111.68	111.756305014614	-0.0763050146135242
57	111.93	112.386843750187	-0.456843750187474
58	111.93	112.32552895396	-0.395528953959683
59	111.93	111.972709753163	-0.0427097531626117
60	111.93	111.432812216204	0.497187783796107
61	111.56	111.430604573854	0.129395426145933
62	111.89	111.065343556866	0.824656443133946
63	111.89	114.475962472493	-2.5859624724927
64	111.89	115.322087417811	-3.43208741781108
65	110.82	111.250557184262	-0.430557184261744
66	110.82	110.348955108225	0.471044891775108
67	110.82	108.338706674269	2.48129332573068
68	110.82	110.78583165547	0.0341683445304568
69	110.98	111.420416371553	-0.440416371553411
70	110.98	111.269703212266	-0.289703212265962
71	111.78	110.92075977746	0.859240222539569
72	111.78	111.21389529074	0.566104709259733

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	111.214211664492	108.111734574197	114.316688754786
74	110.648423328983	106.179790619918	115.117056038049
75	113.133051660142	107.560281795158	118.705821525125
76	116.558513324633	110.007754397278	123.109272251988
77	116.038141655791	108.583979372398	123.492303939185
78	115.701936653616	107.393033968755	124.010839338478
79	113.338231651441	104.208157755123	122.468305547759
80	113.330776649266	103.403465164568	123.258088133964
81	113.956654980425	103.24948555511	124.663824405739
82	114.287949978249	102.813632477561	125.762267478938
83	114.280911642741	102.048708663851	126.513114621631
84	113.735539973899	100.752097390255	126.718982557544

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 111.214211664492 & 108.111734574197 & 114.316688754786 \tabularnewline
74 & 110.648423328983 & 106.179790619918 & 115.117056038049 \tabularnewline
75 & 113.133051660142 & 107.560281795158 & 118.705821525125 \tabularnewline
76 & 116.558513324633 & 110.007754397278 & 123.109272251988 \tabularnewline
77 & 116.038141655791 & 108.583979372398 & 123.492303939185 \tabularnewline
78 & 115.701936653616 & 107.393033968755 & 124.010839338478 \tabularnewline
79 & 113.338231651441 & 104.208157755123 & 122.468305547759 \tabularnewline
80 & 113.330776649266 & 103.403465164568 & 123.258088133964 \tabularnewline
81 & 113.956654980425 & 103.24948555511 & 124.663824405739 \tabularnewline
82 & 114.287949978249 & 102.813632477561 & 125.762267478938 \tabularnewline
83 & 114.280911642741 & 102.048708663851 & 126.513114621631 \tabularnewline
84 & 113.735539973899 & 100.752097390255 & 126.718982557544 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205587&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]111.214211664492[/C][C]108.111734574197[/C][C]114.316688754786[/C][/ROW]
[ROW][C]74[/C][C]110.648423328983[/C][C]106.179790619918[/C][C]115.117056038049[/C][/ROW]
[ROW][C]75[/C][C]113.133051660142[/C][C]107.560281795158[/C][C]118.705821525125[/C][/ROW]
[ROW][C]76[/C][C]116.558513324633[/C][C]110.007754397278[/C][C]123.109272251988[/C][/ROW]
[ROW][C]77[/C][C]116.038141655791[/C][C]108.583979372398[/C][C]123.492303939185[/C][/ROW]
[ROW][C]78[/C][C]115.701936653616[/C][C]107.393033968755[/C][C]124.010839338478[/C][/ROW]
[ROW][C]79[/C][C]113.338231651441[/C][C]104.208157755123[/C][C]122.468305547759[/C][/ROW]
[ROW][C]80[/C][C]113.330776649266[/C][C]103.403465164568[/C][C]123.258088133964[/C][/ROW]
[ROW][C]81[/C][C]113.956654980425[/C][C]103.24948555511[/C][C]124.663824405739[/C][/ROW]
[ROW][C]82[/C][C]114.287949978249[/C][C]102.813632477561[/C][C]125.762267478938[/C][/ROW]
[ROW][C]83[/C][C]114.280911642741[/C][C]102.048708663851[/C][C]126.513114621631[/C][/ROW]
[ROW][C]84[/C][C]113.735539973899[/C][C]100.752097390255[/C][C]126.718982557544[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205587&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205587&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	111.214211664492	108.111734574197	114.316688754786
74	110.648423328983	106.179790619918	115.117056038049
75	113.133051660142	107.560281795158	118.705821525125
76	116.558513324633	110.007754397278	123.109272251988
77	116.038141655791	108.583979372398	123.492303939185
78	115.701936653616	107.393033968755	124.010839338478
79	113.338231651441	104.208157755123	122.468305547759
80	113.330776649266	103.403465164568	123.258088133964
81	113.956654980425	103.24948555511	124.663824405739
82	114.287949978249	102.813632477561	125.762267478938
83	114.280911642741	102.048708663851	126.513114621631
84	113.735539973899	100.752097390255	126.718982557544

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 = 200 ; par2 = 5 ; par3 = 0 ;

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