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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

Wed, 20 Jan 2010 09:18:29 -0700

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/2010/Jan/20/t1264004344wv5t925aazpiqkb.htm/, Retrieved Sun, 05 May 2024 23:36:27 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72313, Retrieved Sun, 05 May 2024 23:36:27 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W62

Estimated Impact

176

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

-       [Exponential Smoothing] [] [2010-01-20 16:18:29] [d7e29fbdd9c070952bc7bcf8a141229f] [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	'Gwilym Jenkins' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72313&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72313&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72313&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' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.72568966705914
beta	0.184950675591331
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.72568966705914 \tabularnewline
beta & 0.184950675591331 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72313&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]0.72568966705914[/C][/ROW]
[ROW][C]beta[/C][C]0.184950675591331[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72313&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72313&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	0.72568966705914
beta	0.184950675591331
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	103.8	103.8	-1.4210854715202e-14
4	104	103.9	0.09999999999998
5	104	104.085990646125	-0.085990646125154
6	104.1	104.125468413334	-0.0254684133341812
7	104.2	104.205448250716	-0.00544825071608557
8	104.3	104.299225266498	0.000774733502282743
9	104.4	104.397622219872	0.00237778012808576
10	104.5	104.497501625644	0.00249837435563904
11	104.7	104.597803869198	0.102196130801644
12	104.7	104.784172181489	-0.0841721814892509
13	104.9	104.823997614924	0.0760023850762792
14	105	104.990260872716	0.00973912728359494
15	105.2	105.109744723465	0.0902552765345206
16	105.3	105.299772085633	0.000227914367258109
17	105.4	105.424498111258	-0.0244981112583389
18	105.5	105.527992657623	-0.0279926576231446
19	105.7	105.625194163033	0.0748058369671298
20	105.8	105.807035673381	-0.00703567338057098
21	105.9	105.928541339806	-0.0285413398062957
22	106	106.030609839193	-0.0306098391929055
23	106.1	106.127068895461	-0.0270688954611416
24	106.2	106.222464477636	-0.022464477636035
25	106.6	106.318186328078	0.28181367192208
26	106.8	106.672543815171	0.127456184829086
27	107	106.931992429375	0.0680075706249568
28	107.1	107.157427556640	-0.0574275566403486
29	107.3	107.284127965612	0.0158720343876126
30	107.4	107.466151423966	-0.0661514239658914
31	107.6	107.579772674080	0.0202273259201178
32	107.7	107.758792937280	-0.0587929372796907
33	107.9	107.872578012424	0.0274219875757069
34	108.2	108.052608858946	0.14739114105447
35	108.3	108.339482446957	-0.0394824469567965
36	108.5	108.485444595645	0.0145554043553915
37	108.92	108.672575034371	0.247424965629492
38	109.23	109.061905093176	0.168094906824464
39	109.41	109.416227307533	-0.00622730753259759
40	109.65	109.643209882938	0.00679011706162669
41	109.91	109.880550416608	0.029449583391866
42	110.01	110.138287319528	-0.128287319527942
43	110.2	110.264337869122	-0.0643378691223973
44	110.49	110.428160651551	0.0618393484485011
45	110.57	110.691848816094	-0.121848816093760
46	110.72	110.805882220194	-0.0858822201944065
47	110.94	110.934489375026	0.00551062497409305
48	111.09	111.130158991657	-0.0401589916573357
49	111.28	111.287296628283	-0.00729662828256039
50	111.41	111.467302812387	-0.0573028123874906
51	111.62	111.603329025622	0.0166709743784281
52	111.76	111.795274776282	-0.0352747762820513
53	111.89	111.944789565052	-0.0547895650521752
54	112.04	112.072788993480	-0.0327889934804801
55	112.12	112.212353175778	-0.0923531757780154
56	112.3	112.296296899269	0.00370310073097357
57	112.47	112.450444688387	0.0195553116125495
58	112.59	112.618720914377	-0.0287209143767484
59	112.78	112.748108752947	0.0318912470529256
60	112.73	112.925762551707	-0.195762551707276
61	112.99	112.911935718927	0.0780642810725851
62	113.1	113.107299726806	-0.00729972680589697
63	113.33	113.239736210298	0.0902637897021634
64	113.38	113.455088446087	-0.0750884460871077
65	113.68	113.540368142424	0.139631857575708
66	113.65	113.800209084728	-0.150209084728303
67	113.81	113.829554868301	-0.0195548683008155
68	113.88	113.951090474958	-0.0710904749582966
69	114.02	114.025685688732	-0.00568568873229935
70	114.25	114.146981365132	0.103018634867709
71	114.28	114.360989476847	-0.0809894768474777
72	114.38	114.43059465529	-0.0505946552901122
73	114.73	114.515466389233	0.214533610767276
74	114.97	114.821532979782	0.148467020217836
75	115.05	115.099582495729	-0.0495824957289557
76	115.29	115.227254720762	0.0627452792376886
77	115.37	115.444863521643	-0.0748635216426834
78	115.54	115.552563095751	-0.0125630957509486
79	115.76	115.703787266745	0.056212733254597
80	115.92	115.912466039043	0.00753396095716141
81	116.02	116.086830313366	-0.0668303133661396
82	116.21	116.198259451800	0.0117405482001942
83	116.26	116.368282431346	-0.108282431345572
84	116.51	116.436672654023	0.0733273459772192

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 103.8 & 103.8 & -1.4210854715202e-14 \tabularnewline
4 & 104 & 103.9 & 0.09999999999998 \tabularnewline
5 & 104 & 104.085990646125 & -0.085990646125154 \tabularnewline
6 & 104.1 & 104.125468413334 & -0.0254684133341812 \tabularnewline
7 & 104.2 & 104.205448250716 & -0.00544825071608557 \tabularnewline
8 & 104.3 & 104.299225266498 & 0.000774733502282743 \tabularnewline
9 & 104.4 & 104.397622219872 & 0.00237778012808576 \tabularnewline
10 & 104.5 & 104.497501625644 & 0.00249837435563904 \tabularnewline
11 & 104.7 & 104.597803869198 & 0.102196130801644 \tabularnewline
12 & 104.7 & 104.784172181489 & -0.0841721814892509 \tabularnewline
13 & 104.9 & 104.823997614924 & 0.0760023850762792 \tabularnewline
14 & 105 & 104.990260872716 & 0.00973912728359494 \tabularnewline
15 & 105.2 & 105.109744723465 & 0.0902552765345206 \tabularnewline
16 & 105.3 & 105.299772085633 & 0.000227914367258109 \tabularnewline
17 & 105.4 & 105.424498111258 & -0.0244981112583389 \tabularnewline
18 & 105.5 & 105.527992657623 & -0.0279926576231446 \tabularnewline
19 & 105.7 & 105.625194163033 & 0.0748058369671298 \tabularnewline
20 & 105.8 & 105.807035673381 & -0.00703567338057098 \tabularnewline
21 & 105.9 & 105.928541339806 & -0.0285413398062957 \tabularnewline
22 & 106 & 106.030609839193 & -0.0306098391929055 \tabularnewline
23 & 106.1 & 106.127068895461 & -0.0270688954611416 \tabularnewline
24 & 106.2 & 106.222464477636 & -0.022464477636035 \tabularnewline
25 & 106.6 & 106.318186328078 & 0.28181367192208 \tabularnewline
26 & 106.8 & 106.672543815171 & 0.127456184829086 \tabularnewline
27 & 107 & 106.931992429375 & 0.0680075706249568 \tabularnewline
28 & 107.1 & 107.157427556640 & -0.0574275566403486 \tabularnewline
29 & 107.3 & 107.284127965612 & 0.0158720343876126 \tabularnewline
30 & 107.4 & 107.466151423966 & -0.0661514239658914 \tabularnewline
31 & 107.6 & 107.579772674080 & 0.0202273259201178 \tabularnewline
32 & 107.7 & 107.758792937280 & -0.0587929372796907 \tabularnewline
33 & 107.9 & 107.872578012424 & 0.0274219875757069 \tabularnewline
34 & 108.2 & 108.052608858946 & 0.14739114105447 \tabularnewline
35 & 108.3 & 108.339482446957 & -0.0394824469567965 \tabularnewline
36 & 108.5 & 108.485444595645 & 0.0145554043553915 \tabularnewline
37 & 108.92 & 108.672575034371 & 0.247424965629492 \tabularnewline
38 & 109.23 & 109.061905093176 & 0.168094906824464 \tabularnewline
39 & 109.41 & 109.416227307533 & -0.00622730753259759 \tabularnewline
40 & 109.65 & 109.643209882938 & 0.00679011706162669 \tabularnewline
41 & 109.91 & 109.880550416608 & 0.029449583391866 \tabularnewline
42 & 110.01 & 110.138287319528 & -0.128287319527942 \tabularnewline
43 & 110.2 & 110.264337869122 & -0.0643378691223973 \tabularnewline
44 & 110.49 & 110.428160651551 & 0.0618393484485011 \tabularnewline
45 & 110.57 & 110.691848816094 & -0.121848816093760 \tabularnewline
46 & 110.72 & 110.805882220194 & -0.0858822201944065 \tabularnewline
47 & 110.94 & 110.934489375026 & 0.00551062497409305 \tabularnewline
48 & 111.09 & 111.130158991657 & -0.0401589916573357 \tabularnewline
49 & 111.28 & 111.287296628283 & -0.00729662828256039 \tabularnewline
50 & 111.41 & 111.467302812387 & -0.0573028123874906 \tabularnewline
51 & 111.62 & 111.603329025622 & 0.0166709743784281 \tabularnewline
52 & 111.76 & 111.795274776282 & -0.0352747762820513 \tabularnewline
53 & 111.89 & 111.944789565052 & -0.0547895650521752 \tabularnewline
54 & 112.04 & 112.072788993480 & -0.0327889934804801 \tabularnewline
55 & 112.12 & 112.212353175778 & -0.0923531757780154 \tabularnewline
56 & 112.3 & 112.296296899269 & 0.00370310073097357 \tabularnewline
57 & 112.47 & 112.450444688387 & 0.0195553116125495 \tabularnewline
58 & 112.59 & 112.618720914377 & -0.0287209143767484 \tabularnewline
59 & 112.78 & 112.748108752947 & 0.0318912470529256 \tabularnewline
60 & 112.73 & 112.925762551707 & -0.195762551707276 \tabularnewline
61 & 112.99 & 112.911935718927 & 0.0780642810725851 \tabularnewline
62 & 113.1 & 113.107299726806 & -0.00729972680589697 \tabularnewline
63 & 113.33 & 113.239736210298 & 0.0902637897021634 \tabularnewline
64 & 113.38 & 113.455088446087 & -0.0750884460871077 \tabularnewline
65 & 113.68 & 113.540368142424 & 0.139631857575708 \tabularnewline
66 & 113.65 & 113.800209084728 & -0.150209084728303 \tabularnewline
67 & 113.81 & 113.829554868301 & -0.0195548683008155 \tabularnewline
68 & 113.88 & 113.951090474958 & -0.0710904749582966 \tabularnewline
69 & 114.02 & 114.025685688732 & -0.00568568873229935 \tabularnewline
70 & 114.25 & 114.146981365132 & 0.103018634867709 \tabularnewline
71 & 114.28 & 114.360989476847 & -0.0809894768474777 \tabularnewline
72 & 114.38 & 114.43059465529 & -0.0505946552901122 \tabularnewline
73 & 114.73 & 114.515466389233 & 0.214533610767276 \tabularnewline
74 & 114.97 & 114.821532979782 & 0.148467020217836 \tabularnewline
75 & 115.05 & 115.099582495729 & -0.0495824957289557 \tabularnewline
76 & 115.29 & 115.227254720762 & 0.0627452792376886 \tabularnewline
77 & 115.37 & 115.444863521643 & -0.0748635216426834 \tabularnewline
78 & 115.54 & 115.552563095751 & -0.0125630957509486 \tabularnewline
79 & 115.76 & 115.703787266745 & 0.056212733254597 \tabularnewline
80 & 115.92 & 115.912466039043 & 0.00753396095716141 \tabularnewline
81 & 116.02 & 116.086830313366 & -0.0668303133661396 \tabularnewline
82 & 116.21 & 116.198259451800 & 0.0117405482001942 \tabularnewline
83 & 116.26 & 116.368282431346 & -0.108282431345572 \tabularnewline
84 & 116.51 & 116.436672654023 & 0.0733273459772192 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72313&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]103.8[/C][C]103.8[/C][C]-1.4210854715202e-14[/C][/ROW]
[ROW][C]4[/C][C]104[/C][C]103.9[/C][C]0.09999999999998[/C][/ROW]
[ROW][C]5[/C][C]104[/C][C]104.085990646125[/C][C]-0.085990646125154[/C][/ROW]
[ROW][C]6[/C][C]104.1[/C][C]104.125468413334[/C][C]-0.0254684133341812[/C][/ROW]
[ROW][C]7[/C][C]104.2[/C][C]104.205448250716[/C][C]-0.00544825071608557[/C][/ROW]
[ROW][C]8[/C][C]104.3[/C][C]104.299225266498[/C][C]0.000774733502282743[/C][/ROW]
[ROW][C]9[/C][C]104.4[/C][C]104.397622219872[/C][C]0.00237778012808576[/C][/ROW]
[ROW][C]10[/C][C]104.5[/C][C]104.497501625644[/C][C]0.00249837435563904[/C][/ROW]
[ROW][C]11[/C][C]104.7[/C][C]104.597803869198[/C][C]0.102196130801644[/C][/ROW]
[ROW][C]12[/C][C]104.7[/C][C]104.784172181489[/C][C]-0.0841721814892509[/C][/ROW]
[ROW][C]13[/C][C]104.9[/C][C]104.823997614924[/C][C]0.0760023850762792[/C][/ROW]
[ROW][C]14[/C][C]105[/C][C]104.990260872716[/C][C]0.00973912728359494[/C][/ROW]
[ROW][C]15[/C][C]105.2[/C][C]105.109744723465[/C][C]0.0902552765345206[/C][/ROW]
[ROW][C]16[/C][C]105.3[/C][C]105.299772085633[/C][C]0.000227914367258109[/C][/ROW]
[ROW][C]17[/C][C]105.4[/C][C]105.424498111258[/C][C]-0.0244981112583389[/C][/ROW]
[ROW][C]18[/C][C]105.5[/C][C]105.527992657623[/C][C]-0.0279926576231446[/C][/ROW]
[ROW][C]19[/C][C]105.7[/C][C]105.625194163033[/C][C]0.0748058369671298[/C][/ROW]
[ROW][C]20[/C][C]105.8[/C][C]105.807035673381[/C][C]-0.00703567338057098[/C][/ROW]
[ROW][C]21[/C][C]105.9[/C][C]105.928541339806[/C][C]-0.0285413398062957[/C][/ROW]
[ROW][C]22[/C][C]106[/C][C]106.030609839193[/C][C]-0.0306098391929055[/C][/ROW]
[ROW][C]23[/C][C]106.1[/C][C]106.127068895461[/C][C]-0.0270688954611416[/C][/ROW]
[ROW][C]24[/C][C]106.2[/C][C]106.222464477636[/C][C]-0.022464477636035[/C][/ROW]
[ROW][C]25[/C][C]106.6[/C][C]106.318186328078[/C][C]0.28181367192208[/C][/ROW]
[ROW][C]26[/C][C]106.8[/C][C]106.672543815171[/C][C]0.127456184829086[/C][/ROW]
[ROW][C]27[/C][C]107[/C][C]106.931992429375[/C][C]0.0680075706249568[/C][/ROW]
[ROW][C]28[/C][C]107.1[/C][C]107.157427556640[/C][C]-0.0574275566403486[/C][/ROW]
[ROW][C]29[/C][C]107.3[/C][C]107.284127965612[/C][C]0.0158720343876126[/C][/ROW]
[ROW][C]30[/C][C]107.4[/C][C]107.466151423966[/C][C]-0.0661514239658914[/C][/ROW]
[ROW][C]31[/C][C]107.6[/C][C]107.579772674080[/C][C]0.0202273259201178[/C][/ROW]
[ROW][C]32[/C][C]107.7[/C][C]107.758792937280[/C][C]-0.0587929372796907[/C][/ROW]
[ROW][C]33[/C][C]107.9[/C][C]107.872578012424[/C][C]0.0274219875757069[/C][/ROW]
[ROW][C]34[/C][C]108.2[/C][C]108.052608858946[/C][C]0.14739114105447[/C][/ROW]
[ROW][C]35[/C][C]108.3[/C][C]108.339482446957[/C][C]-0.0394824469567965[/C][/ROW]
[ROW][C]36[/C][C]108.5[/C][C]108.485444595645[/C][C]0.0145554043553915[/C][/ROW]
[ROW][C]37[/C][C]108.92[/C][C]108.672575034371[/C][C]0.247424965629492[/C][/ROW]
[ROW][C]38[/C][C]109.23[/C][C]109.061905093176[/C][C]0.168094906824464[/C][/ROW]
[ROW][C]39[/C][C]109.41[/C][C]109.416227307533[/C][C]-0.00622730753259759[/C][/ROW]
[ROW][C]40[/C][C]109.65[/C][C]109.643209882938[/C][C]0.00679011706162669[/C][/ROW]
[ROW][C]41[/C][C]109.91[/C][C]109.880550416608[/C][C]0.029449583391866[/C][/ROW]
[ROW][C]42[/C][C]110.01[/C][C]110.138287319528[/C][C]-0.128287319527942[/C][/ROW]
[ROW][C]43[/C][C]110.2[/C][C]110.264337869122[/C][C]-0.0643378691223973[/C][/ROW]
[ROW][C]44[/C][C]110.49[/C][C]110.428160651551[/C][C]0.0618393484485011[/C][/ROW]
[ROW][C]45[/C][C]110.57[/C][C]110.691848816094[/C][C]-0.121848816093760[/C][/ROW]
[ROW][C]46[/C][C]110.72[/C][C]110.805882220194[/C][C]-0.0858822201944065[/C][/ROW]
[ROW][C]47[/C][C]110.94[/C][C]110.934489375026[/C][C]0.00551062497409305[/C][/ROW]
[ROW][C]48[/C][C]111.09[/C][C]111.130158991657[/C][C]-0.0401589916573357[/C][/ROW]
[ROW][C]49[/C][C]111.28[/C][C]111.287296628283[/C][C]-0.00729662828256039[/C][/ROW]
[ROW][C]50[/C][C]111.41[/C][C]111.467302812387[/C][C]-0.0573028123874906[/C][/ROW]
[ROW][C]51[/C][C]111.62[/C][C]111.603329025622[/C][C]0.0166709743784281[/C][/ROW]
[ROW][C]52[/C][C]111.76[/C][C]111.795274776282[/C][C]-0.0352747762820513[/C][/ROW]
[ROW][C]53[/C][C]111.89[/C][C]111.944789565052[/C][C]-0.0547895650521752[/C][/ROW]
[ROW][C]54[/C][C]112.04[/C][C]112.072788993480[/C][C]-0.0327889934804801[/C][/ROW]
[ROW][C]55[/C][C]112.12[/C][C]112.212353175778[/C][C]-0.0923531757780154[/C][/ROW]
[ROW][C]56[/C][C]112.3[/C][C]112.296296899269[/C][C]0.00370310073097357[/C][/ROW]
[ROW][C]57[/C][C]112.47[/C][C]112.450444688387[/C][C]0.0195553116125495[/C][/ROW]
[ROW][C]58[/C][C]112.59[/C][C]112.618720914377[/C][C]-0.0287209143767484[/C][/ROW]
[ROW][C]59[/C][C]112.78[/C][C]112.748108752947[/C][C]0.0318912470529256[/C][/ROW]
[ROW][C]60[/C][C]112.73[/C][C]112.925762551707[/C][C]-0.195762551707276[/C][/ROW]
[ROW][C]61[/C][C]112.99[/C][C]112.911935718927[/C][C]0.0780642810725851[/C][/ROW]
[ROW][C]62[/C][C]113.1[/C][C]113.107299726806[/C][C]-0.00729972680589697[/C][/ROW]
[ROW][C]63[/C][C]113.33[/C][C]113.239736210298[/C][C]0.0902637897021634[/C][/ROW]
[ROW][C]64[/C][C]113.38[/C][C]113.455088446087[/C][C]-0.0750884460871077[/C][/ROW]
[ROW][C]65[/C][C]113.68[/C][C]113.540368142424[/C][C]0.139631857575708[/C][/ROW]
[ROW][C]66[/C][C]113.65[/C][C]113.800209084728[/C][C]-0.150209084728303[/C][/ROW]
[ROW][C]67[/C][C]113.81[/C][C]113.829554868301[/C][C]-0.0195548683008155[/C][/ROW]
[ROW][C]68[/C][C]113.88[/C][C]113.951090474958[/C][C]-0.0710904749582966[/C][/ROW]
[ROW][C]69[/C][C]114.02[/C][C]114.025685688732[/C][C]-0.00568568873229935[/C][/ROW]
[ROW][C]70[/C][C]114.25[/C][C]114.146981365132[/C][C]0.103018634867709[/C][/ROW]
[ROW][C]71[/C][C]114.28[/C][C]114.360989476847[/C][C]-0.0809894768474777[/C][/ROW]
[ROW][C]72[/C][C]114.38[/C][C]114.43059465529[/C][C]-0.0505946552901122[/C][/ROW]
[ROW][C]73[/C][C]114.73[/C][C]114.515466389233[/C][C]0.214533610767276[/C][/ROW]
[ROW][C]74[/C][C]114.97[/C][C]114.821532979782[/C][C]0.148467020217836[/C][/ROW]
[ROW][C]75[/C][C]115.05[/C][C]115.099582495729[/C][C]-0.0495824957289557[/C][/ROW]
[ROW][C]76[/C][C]115.29[/C][C]115.227254720762[/C][C]0.0627452792376886[/C][/ROW]
[ROW][C]77[/C][C]115.37[/C][C]115.444863521643[/C][C]-0.0748635216426834[/C][/ROW]
[ROW][C]78[/C][C]115.54[/C][C]115.552563095751[/C][C]-0.0125630957509486[/C][/ROW]
[ROW][C]79[/C][C]115.76[/C][C]115.703787266745[/C][C]0.056212733254597[/C][/ROW]
[ROW][C]80[/C][C]115.92[/C][C]115.912466039043[/C][C]0.00753396095716141[/C][/ROW]
[ROW][C]81[/C][C]116.02[/C][C]116.086830313366[/C][C]-0.0668303133661396[/C][/ROW]
[ROW][C]82[/C][C]116.21[/C][C]116.198259451800[/C][C]0.0117405482001942[/C][/ROW]
[ROW][C]83[/C][C]116.26[/C][C]116.368282431346[/C][C]-0.108282431345572[/C][/ROW]
[ROW][C]84[/C][C]116.51[/C][C]116.436672654023[/C][C]0.0733273459772192[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72313&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72313&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	103.8	103.8	-1.4210854715202e-14
4	104	103.9	0.09999999999998
5	104	104.085990646125	-0.085990646125154
6	104.1	104.125468413334	-0.0254684133341812
7	104.2	104.205448250716	-0.00544825071608557
8	104.3	104.299225266498	0.000774733502282743
9	104.4	104.397622219872	0.00237778012808576
10	104.5	104.497501625644	0.00249837435563904
11	104.7	104.597803869198	0.102196130801644
12	104.7	104.784172181489	-0.0841721814892509
13	104.9	104.823997614924	0.0760023850762792
14	105	104.990260872716	0.00973912728359494
15	105.2	105.109744723465	0.0902552765345206
16	105.3	105.299772085633	0.000227914367258109
17	105.4	105.424498111258	-0.0244981112583389
18	105.5	105.527992657623	-0.0279926576231446
19	105.7	105.625194163033	0.0748058369671298
20	105.8	105.807035673381	-0.00703567338057098
21	105.9	105.928541339806	-0.0285413398062957
22	106	106.030609839193	-0.0306098391929055
23	106.1	106.127068895461	-0.0270688954611416
24	106.2	106.222464477636	-0.022464477636035
25	106.6	106.318186328078	0.28181367192208
26	106.8	106.672543815171	0.127456184829086
27	107	106.931992429375	0.0680075706249568
28	107.1	107.157427556640	-0.0574275566403486
29	107.3	107.284127965612	0.0158720343876126
30	107.4	107.466151423966	-0.0661514239658914
31	107.6	107.579772674080	0.0202273259201178
32	107.7	107.758792937280	-0.0587929372796907
33	107.9	107.872578012424	0.0274219875757069
34	108.2	108.052608858946	0.14739114105447
35	108.3	108.339482446957	-0.0394824469567965
36	108.5	108.485444595645	0.0145554043553915
37	108.92	108.672575034371	0.247424965629492
38	109.23	109.061905093176	0.168094906824464
39	109.41	109.416227307533	-0.00622730753259759
40	109.65	109.643209882938	0.00679011706162669
41	109.91	109.880550416608	0.029449583391866
42	110.01	110.138287319528	-0.128287319527942
43	110.2	110.264337869122	-0.0643378691223973
44	110.49	110.428160651551	0.0618393484485011
45	110.57	110.691848816094	-0.121848816093760
46	110.72	110.805882220194	-0.0858822201944065
47	110.94	110.934489375026	0.00551062497409305
48	111.09	111.130158991657	-0.0401589916573357
49	111.28	111.287296628283	-0.00729662828256039
50	111.41	111.467302812387	-0.0573028123874906
51	111.62	111.603329025622	0.0166709743784281
52	111.76	111.795274776282	-0.0352747762820513
53	111.89	111.944789565052	-0.0547895650521752
54	112.04	112.072788993480	-0.0327889934804801
55	112.12	112.212353175778	-0.0923531757780154
56	112.3	112.296296899269	0.00370310073097357
57	112.47	112.450444688387	0.0195553116125495
58	112.59	112.618720914377	-0.0287209143767484
59	112.78	112.748108752947	0.0318912470529256
60	112.73	112.925762551707	-0.195762551707276
61	112.99	112.911935718927	0.0780642810725851
62	113.1	113.107299726806	-0.00729972680589697
63	113.33	113.239736210298	0.0902637897021634
64	113.38	113.455088446087	-0.0750884460871077
65	113.68	113.540368142424	0.139631857575708
66	113.65	113.800209084728	-0.150209084728303
67	113.81	113.829554868301	-0.0195548683008155
68	113.88	113.951090474958	-0.0710904749582966
69	114.02	114.025685688732	-0.00568568873229935
70	114.25	114.146981365132	0.103018634867709
71	114.28	114.360989476847	-0.0809894768474777
72	114.38	114.43059465529	-0.0505946552901122
73	114.73	114.515466389233	0.214533610767276
74	114.97	114.821532979782	0.148467020217836
75	115.05	115.099582495729	-0.0495824957289557
76	115.29	115.227254720762	0.0627452792376886
77	115.37	115.444863521643	-0.0748635216426834
78	115.54	115.552563095751	-0.0125630957509486
79	115.76	115.703787266745	0.056212733254597
80	115.92	115.912466039043	0.00753396095716141
81	116.02	116.086830313366	-0.0668303133661396
82	116.21	116.198259451800	0.0117405482001942
83	116.26	116.368282431346	-0.108282431345572
84	116.51	116.436672654023	0.0733273459772192

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	116.646696976844	116.480435032221	116.812958921466
86	116.803508402376	116.584229184955	117.022787619797
87	116.960319827909	116.685724740546	117.234914915271
88	117.117131253441	116.784571144477	117.449691362405
89	117.273942678973	116.880673561429	117.667211796517
90	117.430754104506	116.974035907327	117.887472301685
91	117.587565530038	117.064703314969	118.110427745108
92	117.744376955571	117.152737975142	118.336015935999
93	117.901188381103	117.238208136533	118.564168625674
94	118.057999806636	117.321182874186	118.794816739085
95	118.214811232168	117.401729578008	119.027892886328
96	118.371622657700	117.479912789376	119.263332526024

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 116.646696976844 & 116.480435032221 & 116.812958921466 \tabularnewline
86 & 116.803508402376 & 116.584229184955 & 117.022787619797 \tabularnewline
87 & 116.960319827909 & 116.685724740546 & 117.234914915271 \tabularnewline
88 & 117.117131253441 & 116.784571144477 & 117.449691362405 \tabularnewline
89 & 117.273942678973 & 116.880673561429 & 117.667211796517 \tabularnewline
90 & 117.430754104506 & 116.974035907327 & 117.887472301685 \tabularnewline
91 & 117.587565530038 & 117.064703314969 & 118.110427745108 \tabularnewline
92 & 117.744376955571 & 117.152737975142 & 118.336015935999 \tabularnewline
93 & 117.901188381103 & 117.238208136533 & 118.564168625674 \tabularnewline
94 & 118.057999806636 & 117.321182874186 & 118.794816739085 \tabularnewline
95 & 118.214811232168 & 117.401729578008 & 119.027892886328 \tabularnewline
96 & 118.371622657700 & 117.479912789376 & 119.263332526024 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72313&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]85[/C][C]116.646696976844[/C][C]116.480435032221[/C][C]116.812958921466[/C][/ROW]
[ROW][C]86[/C][C]116.803508402376[/C][C]116.584229184955[/C][C]117.022787619797[/C][/ROW]
[ROW][C]87[/C][C]116.960319827909[/C][C]116.685724740546[/C][C]117.234914915271[/C][/ROW]
[ROW][C]88[/C][C]117.117131253441[/C][C]116.784571144477[/C][C]117.449691362405[/C][/ROW]
[ROW][C]89[/C][C]117.273942678973[/C][C]116.880673561429[/C][C]117.667211796517[/C][/ROW]
[ROW][C]90[/C][C]117.430754104506[/C][C]116.974035907327[/C][C]117.887472301685[/C][/ROW]
[ROW][C]91[/C][C]117.587565530038[/C][C]117.064703314969[/C][C]118.110427745108[/C][/ROW]
[ROW][C]92[/C][C]117.744376955571[/C][C]117.152737975142[/C][C]118.336015935999[/C][/ROW]
[ROW][C]93[/C][C]117.901188381103[/C][C]117.238208136533[/C][C]118.564168625674[/C][/ROW]
[ROW][C]94[/C][C]118.057999806636[/C][C]117.321182874186[/C][C]118.794816739085[/C][/ROW]
[ROW][C]95[/C][C]118.214811232168[/C][C]117.401729578008[/C][C]119.027892886328[/C][/ROW]
[ROW][C]96[/C][C]118.371622657700[/C][C]117.479912789376[/C][C]119.263332526024[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72313&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72313&T=3

As an alternative you can also use a QR Code:

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

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	116.646696976844	116.480435032221	116.812958921466
86	116.803508402376	116.584229184955	117.022787619797
87	116.960319827909	116.685724740546	117.234914915271
88	117.117131253441	116.784571144477	117.449691362405
89	117.273942678973	116.880673561429	117.667211796517
90	117.430754104506	116.974035907327	117.887472301685
91	117.587565530038	117.064703314969	118.110427745108
92	117.744376955571	117.152737975142	118.336015935999
93	117.901188381103	117.238208136533	118.564168625674
94	118.057999806636	117.321182874186	118.794816739085
95	118.214811232168	117.401729578008	119.027892886328
96	118.371622657700	117.479912789376	119.263332526024

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