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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

Tue, 27 May 2008 06:35:37 -0600

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/2008/May/27/t1211891783xl6pnebwql635ox.htm/, Retrieved Mon, 20 May 2024 01:08:40 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13344, Retrieved Mon, 20 May 2024 01:08:40 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

200

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

-       [Exponential Smoothing] [Exponential Smoot...] [2008-05-27 12:35:37] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Dataseries X:

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Histogram

Boxplots

1.43
1.43
1.43
1.43
1.43
1.43
1.43
1.43
1.43
1.43
1.43
1.43
1.43
1.43
1.43
1.43
1.43
1.43
1.44
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.57
1.58
1.58
1.58
1.58
1.59
1.6
1.6
1.61
1.61
1.61
1.62
1.63
1.63
1.64
1.64
1.64
1.64
1.64
1.65
1.65
1.65
1.65

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13344&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13344&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13344&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.0305775233429336
gamma	0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0305775233429336 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13344&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]0.0305775233429336[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13344&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13344&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	0.0305775233429336
gamma	0

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	1.43	1.43	0
4	1.43	1.43	0
5	1.43	1.43	0
6	1.43	1.43	0
7	1.43	1.43	0
8	1.43	1.43	0
9	1.43	1.43	0
10	1.43	1.43	0
11	1.43	1.43	0
12	1.43	1.43	0
13	1.43	1.43	0
14	1.43	1.43	0
15	1.43	1.43	0
16	1.43	1.43	0
17	1.43	1.43	0
18	1.43	1.43	0
19	1.44	1.43	0.01
20	1.48	1.44030577523343	0.0396942247665708
21	1.48	1.48151952631781	-0.00151952631780872
22	1.48	1.48147306296636	-0.00147306296635574
23	1.48	1.48142802034912	-0.00142802034911638
24	1.48	1.48138435502356	-0.00138435502355705
25	1.48	1.48134202487551	-0.00134202487550938
26	1.48	1.48130098907855	-0.00130098907855181
27	1.48	1.48126120805463	-0.00126120805463348
28	1.48	1.48122264343590	-0.00122264343590262
29	1.48	1.4811852580277	-0.00118525802770120
30	1.48	1.48114901577269	-0.00114901577269166
31	1.48	1.48111388171608	-0.00111388171608096
32	1.48	1.48107982197191	-0.00107982197190615
33	1.48	1.48104680369035	-0.00104680369035393
34	1.48	1.48101479502608	-0.00101479502607660
35	1.48	1.48098376510748	-0.00098376510747844
36	1.48	1.48095368400694	-0.000953684006940625
37	1.48	1.48092452271196	-0.000924522711956755
38	1.48	1.48089625309715	-0.000896253097150801
39	1.48	1.48086884789715	-0.00086884789715147
40	1.48	1.48084228068029	-0.000842280680294794
41	1.48	1.48081652582313	-0.000816525823131853
42	1.48	1.48079155848571	-0.000791558485714772
43	1.48	1.48076735458764	-0.000767354587640545
44	1.48	1.48074389078482	-0.00074389078482473
45	1.48	1.48072114444699	-0.000721144446987232
46	1.48	1.48069909363583	-0.000699093635825765
47	1.48	1.48067771708386	-0.000677717083857443
48	1.48	1.48065699417391	-0.000656994173905856
49	1.48	1.48063690491922	-0.000636904919217196
50	1.57	1.48061742994418	0.0893825700558175
51	1.58	1.57335052756652	0.00664947243348424
52	1.58	1.58355385196507	-0.00355385196506863
53	1.58	1.58344518397365	-0.00344518397364957
54	1.58	1.58333983878027	-0.00333983878027455
55	1.59	1.58323771478201	0.00676228521799094
56	1.6	1.59344448871611	0.0065555112838862
57	1.6	1.60364494001542	-0.00364494001542170
58	1.61	1.60353348677702	0.00646651322298353
59	1.61	1.61373121673604	-0.00373121673603971
60	1.61	1.61361712536920	-0.00361712536919589
61	1.62	1.61350652263379	0.00649347736621508
62	1.63	1.62370507708953	0.00629492291047251
63	1.63	1.63389756024176	-0.00389756024176413
64	1.64	1.63377838250249	0.00622161749750894
65	1.64	1.64396862415675	-0.00396862415675203
66	1.64	1.64384727345896	-0.00384727345895963
67	1.64	1.64372963336496	-0.00372963336496168
68	1.64	1.64361559041368	-0.00361559041368387
69	1.65	1.64350503461341	0.00649496538658911
70	1.65	1.65370363456913	-0.00370363456913103
71	1.65	1.65359038659664	-0.00359038659663957
72	1.65	1.65348060146667	-0.00348060146667084

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1.43 & 1.43 & 0 \tabularnewline
4 & 1.43 & 1.43 & 0 \tabularnewline
5 & 1.43 & 1.43 & 0 \tabularnewline
6 & 1.43 & 1.43 & 0 \tabularnewline
7 & 1.43 & 1.43 & 0 \tabularnewline
8 & 1.43 & 1.43 & 0 \tabularnewline
9 & 1.43 & 1.43 & 0 \tabularnewline
10 & 1.43 & 1.43 & 0 \tabularnewline
11 & 1.43 & 1.43 & 0 \tabularnewline
12 & 1.43 & 1.43 & 0 \tabularnewline
13 & 1.43 & 1.43 & 0 \tabularnewline
14 & 1.43 & 1.43 & 0 \tabularnewline
15 & 1.43 & 1.43 & 0 \tabularnewline
16 & 1.43 & 1.43 & 0 \tabularnewline
17 & 1.43 & 1.43 & 0 \tabularnewline
18 & 1.43 & 1.43 & 0 \tabularnewline
19 & 1.44 & 1.43 & 0.01 \tabularnewline
20 & 1.48 & 1.44030577523343 & 0.0396942247665708 \tabularnewline
21 & 1.48 & 1.48151952631781 & -0.00151952631780872 \tabularnewline
22 & 1.48 & 1.48147306296636 & -0.00147306296635574 \tabularnewline
23 & 1.48 & 1.48142802034912 & -0.00142802034911638 \tabularnewline
24 & 1.48 & 1.48138435502356 & -0.00138435502355705 \tabularnewline
25 & 1.48 & 1.48134202487551 & -0.00134202487550938 \tabularnewline
26 & 1.48 & 1.48130098907855 & -0.00130098907855181 \tabularnewline
27 & 1.48 & 1.48126120805463 & -0.00126120805463348 \tabularnewline
28 & 1.48 & 1.48122264343590 & -0.00122264343590262 \tabularnewline
29 & 1.48 & 1.4811852580277 & -0.00118525802770120 \tabularnewline
30 & 1.48 & 1.48114901577269 & -0.00114901577269166 \tabularnewline
31 & 1.48 & 1.48111388171608 & -0.00111388171608096 \tabularnewline
32 & 1.48 & 1.48107982197191 & -0.00107982197190615 \tabularnewline
33 & 1.48 & 1.48104680369035 & -0.00104680369035393 \tabularnewline
34 & 1.48 & 1.48101479502608 & -0.00101479502607660 \tabularnewline
35 & 1.48 & 1.48098376510748 & -0.00098376510747844 \tabularnewline
36 & 1.48 & 1.48095368400694 & -0.000953684006940625 \tabularnewline
37 & 1.48 & 1.48092452271196 & -0.000924522711956755 \tabularnewline
38 & 1.48 & 1.48089625309715 & -0.000896253097150801 \tabularnewline
39 & 1.48 & 1.48086884789715 & -0.00086884789715147 \tabularnewline
40 & 1.48 & 1.48084228068029 & -0.000842280680294794 \tabularnewline
41 & 1.48 & 1.48081652582313 & -0.000816525823131853 \tabularnewline
42 & 1.48 & 1.48079155848571 & -0.000791558485714772 \tabularnewline
43 & 1.48 & 1.48076735458764 & -0.000767354587640545 \tabularnewline
44 & 1.48 & 1.48074389078482 & -0.00074389078482473 \tabularnewline
45 & 1.48 & 1.48072114444699 & -0.000721144446987232 \tabularnewline
46 & 1.48 & 1.48069909363583 & -0.000699093635825765 \tabularnewline
47 & 1.48 & 1.48067771708386 & -0.000677717083857443 \tabularnewline
48 & 1.48 & 1.48065699417391 & -0.000656994173905856 \tabularnewline
49 & 1.48 & 1.48063690491922 & -0.000636904919217196 \tabularnewline
50 & 1.57 & 1.48061742994418 & 0.0893825700558175 \tabularnewline
51 & 1.58 & 1.57335052756652 & 0.00664947243348424 \tabularnewline
52 & 1.58 & 1.58355385196507 & -0.00355385196506863 \tabularnewline
53 & 1.58 & 1.58344518397365 & -0.00344518397364957 \tabularnewline
54 & 1.58 & 1.58333983878027 & -0.00333983878027455 \tabularnewline
55 & 1.59 & 1.58323771478201 & 0.00676228521799094 \tabularnewline
56 & 1.6 & 1.59344448871611 & 0.0065555112838862 \tabularnewline
57 & 1.6 & 1.60364494001542 & -0.00364494001542170 \tabularnewline
58 & 1.61 & 1.60353348677702 & 0.00646651322298353 \tabularnewline
59 & 1.61 & 1.61373121673604 & -0.00373121673603971 \tabularnewline
60 & 1.61 & 1.61361712536920 & -0.00361712536919589 \tabularnewline
61 & 1.62 & 1.61350652263379 & 0.00649347736621508 \tabularnewline
62 & 1.63 & 1.62370507708953 & 0.00629492291047251 \tabularnewline
63 & 1.63 & 1.63389756024176 & -0.00389756024176413 \tabularnewline
64 & 1.64 & 1.63377838250249 & 0.00622161749750894 \tabularnewline
65 & 1.64 & 1.64396862415675 & -0.00396862415675203 \tabularnewline
66 & 1.64 & 1.64384727345896 & -0.00384727345895963 \tabularnewline
67 & 1.64 & 1.64372963336496 & -0.00372963336496168 \tabularnewline
68 & 1.64 & 1.64361559041368 & -0.00361559041368387 \tabularnewline
69 & 1.65 & 1.64350503461341 & 0.00649496538658911 \tabularnewline
70 & 1.65 & 1.65370363456913 & -0.00370363456913103 \tabularnewline
71 & 1.65 & 1.65359038659664 & -0.00359038659663957 \tabularnewline
72 & 1.65 & 1.65348060146667 & -0.00348060146667084 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13344&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]1.43[/C][C]1.43[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]1.43[/C][C]1.43[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]1.43[/C][C]1.43[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]1.43[/C][C]1.43[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]1.43[/C][C]1.43[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]1.43[/C][C]1.43[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]1.43[/C][C]1.43[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]1.43[/C][C]1.43[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]1.43[/C][C]1.43[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]1.43[/C][C]1.43[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]1.43[/C][C]1.43[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]1.43[/C][C]1.43[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]1.43[/C][C]1.43[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]1.43[/C][C]1.43[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]1.43[/C][C]1.43[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]1.43[/C][C]1.43[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]1.44[/C][C]1.43[/C][C]0.01[/C][/ROW]
[ROW][C]20[/C][C]1.48[/C][C]1.44030577523343[/C][C]0.0396942247665708[/C][/ROW]
[ROW][C]21[/C][C]1.48[/C][C]1.48151952631781[/C][C]-0.00151952631780872[/C][/ROW]
[ROW][C]22[/C][C]1.48[/C][C]1.48147306296636[/C][C]-0.00147306296635574[/C][/ROW]
[ROW][C]23[/C][C]1.48[/C][C]1.48142802034912[/C][C]-0.00142802034911638[/C][/ROW]
[ROW][C]24[/C][C]1.48[/C][C]1.48138435502356[/C][C]-0.00138435502355705[/C][/ROW]
[ROW][C]25[/C][C]1.48[/C][C]1.48134202487551[/C][C]-0.00134202487550938[/C][/ROW]
[ROW][C]26[/C][C]1.48[/C][C]1.48130098907855[/C][C]-0.00130098907855181[/C][/ROW]
[ROW][C]27[/C][C]1.48[/C][C]1.48126120805463[/C][C]-0.00126120805463348[/C][/ROW]
[ROW][C]28[/C][C]1.48[/C][C]1.48122264343590[/C][C]-0.00122264343590262[/C][/ROW]
[ROW][C]29[/C][C]1.48[/C][C]1.4811852580277[/C][C]-0.00118525802770120[/C][/ROW]
[ROW][C]30[/C][C]1.48[/C][C]1.48114901577269[/C][C]-0.00114901577269166[/C][/ROW]
[ROW][C]31[/C][C]1.48[/C][C]1.48111388171608[/C][C]-0.00111388171608096[/C][/ROW]
[ROW][C]32[/C][C]1.48[/C][C]1.48107982197191[/C][C]-0.00107982197190615[/C][/ROW]
[ROW][C]33[/C][C]1.48[/C][C]1.48104680369035[/C][C]-0.00104680369035393[/C][/ROW]
[ROW][C]34[/C][C]1.48[/C][C]1.48101479502608[/C][C]-0.00101479502607660[/C][/ROW]
[ROW][C]35[/C][C]1.48[/C][C]1.48098376510748[/C][C]-0.00098376510747844[/C][/ROW]
[ROW][C]36[/C][C]1.48[/C][C]1.48095368400694[/C][C]-0.000953684006940625[/C][/ROW]
[ROW][C]37[/C][C]1.48[/C][C]1.48092452271196[/C][C]-0.000924522711956755[/C][/ROW]
[ROW][C]38[/C][C]1.48[/C][C]1.48089625309715[/C][C]-0.000896253097150801[/C][/ROW]
[ROW][C]39[/C][C]1.48[/C][C]1.48086884789715[/C][C]-0.00086884789715147[/C][/ROW]
[ROW][C]40[/C][C]1.48[/C][C]1.48084228068029[/C][C]-0.000842280680294794[/C][/ROW]
[ROW][C]41[/C][C]1.48[/C][C]1.48081652582313[/C][C]-0.000816525823131853[/C][/ROW]
[ROW][C]42[/C][C]1.48[/C][C]1.48079155848571[/C][C]-0.000791558485714772[/C][/ROW]
[ROW][C]43[/C][C]1.48[/C][C]1.48076735458764[/C][C]-0.000767354587640545[/C][/ROW]
[ROW][C]44[/C][C]1.48[/C][C]1.48074389078482[/C][C]-0.00074389078482473[/C][/ROW]
[ROW][C]45[/C][C]1.48[/C][C]1.48072114444699[/C][C]-0.000721144446987232[/C][/ROW]
[ROW][C]46[/C][C]1.48[/C][C]1.48069909363583[/C][C]-0.000699093635825765[/C][/ROW]
[ROW][C]47[/C][C]1.48[/C][C]1.48067771708386[/C][C]-0.000677717083857443[/C][/ROW]
[ROW][C]48[/C][C]1.48[/C][C]1.48065699417391[/C][C]-0.000656994173905856[/C][/ROW]
[ROW][C]49[/C][C]1.48[/C][C]1.48063690491922[/C][C]-0.000636904919217196[/C][/ROW]
[ROW][C]50[/C][C]1.57[/C][C]1.48061742994418[/C][C]0.0893825700558175[/C][/ROW]
[ROW][C]51[/C][C]1.58[/C][C]1.57335052756652[/C][C]0.00664947243348424[/C][/ROW]
[ROW][C]52[/C][C]1.58[/C][C]1.58355385196507[/C][C]-0.00355385196506863[/C][/ROW]
[ROW][C]53[/C][C]1.58[/C][C]1.58344518397365[/C][C]-0.00344518397364957[/C][/ROW]
[ROW][C]54[/C][C]1.58[/C][C]1.58333983878027[/C][C]-0.00333983878027455[/C][/ROW]
[ROW][C]55[/C][C]1.59[/C][C]1.58323771478201[/C][C]0.00676228521799094[/C][/ROW]
[ROW][C]56[/C][C]1.6[/C][C]1.59344448871611[/C][C]0.0065555112838862[/C][/ROW]
[ROW][C]57[/C][C]1.6[/C][C]1.60364494001542[/C][C]-0.00364494001542170[/C][/ROW]
[ROW][C]58[/C][C]1.61[/C][C]1.60353348677702[/C][C]0.00646651322298353[/C][/ROW]
[ROW][C]59[/C][C]1.61[/C][C]1.61373121673604[/C][C]-0.00373121673603971[/C][/ROW]
[ROW][C]60[/C][C]1.61[/C][C]1.61361712536920[/C][C]-0.00361712536919589[/C][/ROW]
[ROW][C]61[/C][C]1.62[/C][C]1.61350652263379[/C][C]0.00649347736621508[/C][/ROW]
[ROW][C]62[/C][C]1.63[/C][C]1.62370507708953[/C][C]0.00629492291047251[/C][/ROW]
[ROW][C]63[/C][C]1.63[/C][C]1.63389756024176[/C][C]-0.00389756024176413[/C][/ROW]
[ROW][C]64[/C][C]1.64[/C][C]1.63377838250249[/C][C]0.00622161749750894[/C][/ROW]
[ROW][C]65[/C][C]1.64[/C][C]1.64396862415675[/C][C]-0.00396862415675203[/C][/ROW]
[ROW][C]66[/C][C]1.64[/C][C]1.64384727345896[/C][C]-0.00384727345895963[/C][/ROW]
[ROW][C]67[/C][C]1.64[/C][C]1.64372963336496[/C][C]-0.00372963336496168[/C][/ROW]
[ROW][C]68[/C][C]1.64[/C][C]1.64361559041368[/C][C]-0.00361559041368387[/C][/ROW]
[ROW][C]69[/C][C]1.65[/C][C]1.64350503461341[/C][C]0.00649496538658911[/C][/ROW]
[ROW][C]70[/C][C]1.65[/C][C]1.65370363456913[/C][C]-0.00370363456913103[/C][/ROW]
[ROW][C]71[/C][C]1.65[/C][C]1.65359038659664[/C][C]-0.00359038659663957[/C][/ROW]
[ROW][C]72[/C][C]1.65[/C][C]1.65348060146667[/C][C]-0.00348060146667084[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13344&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13344&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	1.43	1.43	0
4	1.43	1.43	0
5	1.43	1.43	0
6	1.43	1.43	0
7	1.43	1.43	0
8	1.43	1.43	0
9	1.43	1.43	0
10	1.43	1.43	0
11	1.43	1.43	0
12	1.43	1.43	0
13	1.43	1.43	0
14	1.43	1.43	0
15	1.43	1.43	0
16	1.43	1.43	0
17	1.43	1.43	0
18	1.43	1.43	0
19	1.44	1.43	0.01
20	1.48	1.44030577523343	0.0396942247665708
21	1.48	1.48151952631781	-0.00151952631780872
22	1.48	1.48147306296636	-0.00147306296635574
23	1.48	1.48142802034912	-0.00142802034911638
24	1.48	1.48138435502356	-0.00138435502355705
25	1.48	1.48134202487551	-0.00134202487550938
26	1.48	1.48130098907855	-0.00130098907855181
27	1.48	1.48126120805463	-0.00126120805463348
28	1.48	1.48122264343590	-0.00122264343590262
29	1.48	1.4811852580277	-0.00118525802770120
30	1.48	1.48114901577269	-0.00114901577269166
31	1.48	1.48111388171608	-0.00111388171608096
32	1.48	1.48107982197191	-0.00107982197190615
33	1.48	1.48104680369035	-0.00104680369035393
34	1.48	1.48101479502608	-0.00101479502607660
35	1.48	1.48098376510748	-0.00098376510747844
36	1.48	1.48095368400694	-0.000953684006940625
37	1.48	1.48092452271196	-0.000924522711956755
38	1.48	1.48089625309715	-0.000896253097150801
39	1.48	1.48086884789715	-0.00086884789715147
40	1.48	1.48084228068029	-0.000842280680294794
41	1.48	1.48081652582313	-0.000816525823131853
42	1.48	1.48079155848571	-0.000791558485714772
43	1.48	1.48076735458764	-0.000767354587640545
44	1.48	1.48074389078482	-0.00074389078482473
45	1.48	1.48072114444699	-0.000721144446987232
46	1.48	1.48069909363583	-0.000699093635825765
47	1.48	1.48067771708386	-0.000677717083857443
48	1.48	1.48065699417391	-0.000656994173905856
49	1.48	1.48063690491922	-0.000636904919217196
50	1.57	1.48061742994418	0.0893825700558175
51	1.58	1.57335052756652	0.00664947243348424
52	1.58	1.58355385196507	-0.00355385196506863
53	1.58	1.58344518397365	-0.00344518397364957
54	1.58	1.58333983878027	-0.00333983878027455
55	1.59	1.58323771478201	0.00676228521799094
56	1.6	1.59344448871611	0.0065555112838862
57	1.6	1.60364494001542	-0.00364494001542170
58	1.61	1.60353348677702	0.00646651322298353
59	1.61	1.61373121673604	-0.00373121673603971
60	1.61	1.61361712536920	-0.00361712536919589
61	1.62	1.61350652263379	0.00649347736621508
62	1.63	1.62370507708953	0.00629492291047251
63	1.63	1.63389756024176	-0.00389756024176413
64	1.64	1.63377838250249	0.00622161749750894
65	1.64	1.64396862415675	-0.00396862415675203
66	1.64	1.64384727345896	-0.00384727345895963
67	1.64	1.64372963336496	-0.00372963336496168
68	1.64	1.64361559041368	-0.00361559041368387
69	1.65	1.64350503461341	0.00649496538658911
70	1.65	1.65370363456913	-0.00370363456913103
71	1.65	1.65359038659664	-0.00359038659663957
72	1.65	1.65348060146667	-0.00348060146667084

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	1.65337417329408	1.62972271901860	1.67702562756956
74	1.65674834658815	1.62278490739932	1.69071178577698
75	1.66012251988223	1.61789198849296	1.7023530512715
76	1.66349669317630	1.61399775304764	1.71299563330497
77	1.66687086647038	1.61070376645881	1.72303796648196
78	1.67024503976446	1.60780900869406	1.73268107083486
79	1.67361921305853	1.60519600299749	1.74204242311957
80	1.67699338635261	1.60278946282922	1.751197309876
81	1.68036755964669	1.60053796742486	1.76019715186851
82	1.68374173294076	1.59840471691591	1.76907874896562
83	1.68711590623484	1.59636241682374	1.77786939564593
84	1.69049007952891	1.59439024369165	1.78658991536618

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 1.65337417329408 & 1.62972271901860 & 1.67702562756956 \tabularnewline
74 & 1.65674834658815 & 1.62278490739932 & 1.69071178577698 \tabularnewline
75 & 1.66012251988223 & 1.61789198849296 & 1.7023530512715 \tabularnewline
76 & 1.66349669317630 & 1.61399775304764 & 1.71299563330497 \tabularnewline
77 & 1.66687086647038 & 1.61070376645881 & 1.72303796648196 \tabularnewline
78 & 1.67024503976446 & 1.60780900869406 & 1.73268107083486 \tabularnewline
79 & 1.67361921305853 & 1.60519600299749 & 1.74204242311957 \tabularnewline
80 & 1.67699338635261 & 1.60278946282922 & 1.751197309876 \tabularnewline
81 & 1.68036755964669 & 1.60053796742486 & 1.76019715186851 \tabularnewline
82 & 1.68374173294076 & 1.59840471691591 & 1.76907874896562 \tabularnewline
83 & 1.68711590623484 & 1.59636241682374 & 1.77786939564593 \tabularnewline
84 & 1.69049007952891 & 1.59439024369165 & 1.78658991536618 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13344&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]1.65337417329408[/C][C]1.62972271901860[/C][C]1.67702562756956[/C][/ROW]
[ROW][C]74[/C][C]1.65674834658815[/C][C]1.62278490739932[/C][C]1.69071178577698[/C][/ROW]
[ROW][C]75[/C][C]1.66012251988223[/C][C]1.61789198849296[/C][C]1.7023530512715[/C][/ROW]
[ROW][C]76[/C][C]1.66349669317630[/C][C]1.61399775304764[/C][C]1.71299563330497[/C][/ROW]
[ROW][C]77[/C][C]1.66687086647038[/C][C]1.61070376645881[/C][C]1.72303796648196[/C][/ROW]
[ROW][C]78[/C][C]1.67024503976446[/C][C]1.60780900869406[/C][C]1.73268107083486[/C][/ROW]
[ROW][C]79[/C][C]1.67361921305853[/C][C]1.60519600299749[/C][C]1.74204242311957[/C][/ROW]
[ROW][C]80[/C][C]1.67699338635261[/C][C]1.60278946282922[/C][C]1.751197309876[/C][/ROW]
[ROW][C]81[/C][C]1.68036755964669[/C][C]1.60053796742486[/C][C]1.76019715186851[/C][/ROW]
[ROW][C]82[/C][C]1.68374173294076[/C][C]1.59840471691591[/C][C]1.76907874896562[/C][/ROW]
[ROW][C]83[/C][C]1.68711590623484[/C][C]1.59636241682374[/C][C]1.77786939564593[/C][/ROW]
[ROW][C]84[/C][C]1.69049007952891[/C][C]1.59439024369165[/C][C]1.78658991536618[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13344&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13344&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	1.65337417329408	1.62972271901860	1.67702562756956
74	1.65674834658815	1.62278490739932	1.69071178577698
75	1.66012251988223	1.61789198849296	1.7023530512715
76	1.66349669317630	1.61399775304764	1.71299563330497
77	1.66687086647038	1.61070376645881	1.72303796648196
78	1.67024503976446	1.60780900869406	1.73268107083486
79	1.67361921305853	1.60519600299749	1.74204242311957
80	1.67699338635261	1.60278946282922	1.751197309876
81	1.68036755964669	1.60053796742486	1.76019715186851
82	1.68374173294076	1.59840471691591	1.76907874896562
83	1.68711590623484	1.59636241682374	1.77786939564593
84	1.69049007952891	1.59439024369165	1.78658991536618

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 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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