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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, 28 May 2008 13:02:50 -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/28/t1212001464csym1luerd2f1sk.htm/, Retrieved Mon, 13 May 2024 22:21:50 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13471, Retrieved Mon, 13 May 2024 22:21:50 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

174

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

-       [Exponential Smoothing] [ExponentialSmooth...] [2008-05-28 19:02:50] [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
1.43
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=13471&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=13471&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13471&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=13471&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=13471&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13471&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	1.43	1.43	0
20	1.44	1.43	0.01
21	1.48	1.44030577523343	0.0396942247665708
22	1.48	1.48151952631781	-0.00151952631780872
23	1.48	1.48147306296636	-0.00147306296635574
24	1.48	1.48142802034912	-0.00142802034911638
25	1.48	1.48138435502356	-0.00138435502355705
26	1.48	1.48134202487551	-0.00134202487550938
27	1.48	1.48130098907855	-0.00130098907855181
28	1.48	1.48126120805463	-0.00126120805463348
29	1.48	1.48122264343590	-0.00122264343590262
30	1.48	1.4811852580277	-0.00118525802770120
31	1.48	1.48114901577269	-0.00114901577269166
32	1.48	1.48111388171608	-0.00111388171608096
33	1.48	1.48107982197191	-0.00107982197190615
34	1.48	1.48104680369035	-0.00104680369035393
35	1.48	1.48101479502608	-0.00101479502607660
36	1.48	1.48098376510748	-0.00098376510747844
37	1.48	1.48095368400694	-0.000953684006940625
38	1.48	1.48092452271196	-0.000924522711956755
39	1.48	1.48089625309715	-0.000896253097150801
40	1.48	1.48086884789715	-0.00086884789715147
41	1.48	1.48084228068029	-0.000842280680294794
42	1.48	1.48081652582313	-0.000816525823131853
43	1.48	1.48079155848571	-0.000791558485714772
44	1.48	1.48076735458764	-0.000767354587640545
45	1.48	1.48074389078482	-0.00074389078482473
46	1.48	1.48072114444699	-0.000721144446987232
47	1.48	1.48069909363583	-0.000699093635825765
48	1.48	1.48067771708386	-0.000677717083857443
49	1.48	1.48065699417391	-0.000656994173905856
50	1.48	1.48063690491922	-0.000636904919217196
51	1.57	1.48061742994418	0.0893825700558175
52	1.58	1.57335052756652	0.00664947243348424
53	1.58	1.58355385196507	-0.00355385196506863
54	1.58	1.58344518397365	-0.00344518397364957
55	1.58	1.58333983878027	-0.00333983878027455
56	1.59	1.58323771478201	0.00676228521799094
57	1.6	1.59344448871611	0.0065555112838862
58	1.6	1.60364494001542	-0.00364494001542170
59	1.61	1.60353348677702	0.00646651322298353
60	1.61	1.61373121673604	-0.00373121673603971
61	1.61	1.61361712536920	-0.00361712536919589
62	1.62	1.61350652263379	0.00649347736621508
63	1.63	1.62370507708953	0.00629492291047251
64	1.63	1.63389756024176	-0.00389756024176413
65	1.64	1.63377838250249	0.00622161749750894
66	1.64	1.64396862415675	-0.00396862415675203
67	1.64	1.64384727345896	-0.00384727345895963
68	1.64	1.64372963336496	-0.00372963336496168
69	1.64	1.64361559041368	-0.00361559041368387
70	1.65	1.64350503461341	0.00649496538658911
71	1.65	1.65370363456913	-0.00370363456913103
72	1.65	1.65359038659664	-0.00359038659663957
73	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 & 1.43 & 1.43 & 0 \tabularnewline
20 & 1.44 & 1.43 & 0.01 \tabularnewline
21 & 1.48 & 1.44030577523343 & 0.0396942247665708 \tabularnewline
22 & 1.48 & 1.48151952631781 & -0.00151952631780872 \tabularnewline
23 & 1.48 & 1.48147306296636 & -0.00147306296635574 \tabularnewline
24 & 1.48 & 1.48142802034912 & -0.00142802034911638 \tabularnewline
25 & 1.48 & 1.48138435502356 & -0.00138435502355705 \tabularnewline
26 & 1.48 & 1.48134202487551 & -0.00134202487550938 \tabularnewline
27 & 1.48 & 1.48130098907855 & -0.00130098907855181 \tabularnewline
28 & 1.48 & 1.48126120805463 & -0.00126120805463348 \tabularnewline
29 & 1.48 & 1.48122264343590 & -0.00122264343590262 \tabularnewline
30 & 1.48 & 1.4811852580277 & -0.00118525802770120 \tabularnewline
31 & 1.48 & 1.48114901577269 & -0.00114901577269166 \tabularnewline
32 & 1.48 & 1.48111388171608 & -0.00111388171608096 \tabularnewline
33 & 1.48 & 1.48107982197191 & -0.00107982197190615 \tabularnewline
34 & 1.48 & 1.48104680369035 & -0.00104680369035393 \tabularnewline
35 & 1.48 & 1.48101479502608 & -0.00101479502607660 \tabularnewline
36 & 1.48 & 1.48098376510748 & -0.00098376510747844 \tabularnewline
37 & 1.48 & 1.48095368400694 & -0.000953684006940625 \tabularnewline
38 & 1.48 & 1.48092452271196 & -0.000924522711956755 \tabularnewline
39 & 1.48 & 1.48089625309715 & -0.000896253097150801 \tabularnewline
40 & 1.48 & 1.48086884789715 & -0.00086884789715147 \tabularnewline
41 & 1.48 & 1.48084228068029 & -0.000842280680294794 \tabularnewline
42 & 1.48 & 1.48081652582313 & -0.000816525823131853 \tabularnewline
43 & 1.48 & 1.48079155848571 & -0.000791558485714772 \tabularnewline
44 & 1.48 & 1.48076735458764 & -0.000767354587640545 \tabularnewline
45 & 1.48 & 1.48074389078482 & -0.00074389078482473 \tabularnewline
46 & 1.48 & 1.48072114444699 & -0.000721144446987232 \tabularnewline
47 & 1.48 & 1.48069909363583 & -0.000699093635825765 \tabularnewline
48 & 1.48 & 1.48067771708386 & -0.000677717083857443 \tabularnewline
49 & 1.48 & 1.48065699417391 & -0.000656994173905856 \tabularnewline
50 & 1.48 & 1.48063690491922 & -0.000636904919217196 \tabularnewline
51 & 1.57 & 1.48061742994418 & 0.0893825700558175 \tabularnewline
52 & 1.58 & 1.57335052756652 & 0.00664947243348424 \tabularnewline
53 & 1.58 & 1.58355385196507 & -0.00355385196506863 \tabularnewline
54 & 1.58 & 1.58344518397365 & -0.00344518397364957 \tabularnewline
55 & 1.58 & 1.58333983878027 & -0.00333983878027455 \tabularnewline
56 & 1.59 & 1.58323771478201 & 0.00676228521799094 \tabularnewline
57 & 1.6 & 1.59344448871611 & 0.0065555112838862 \tabularnewline
58 & 1.6 & 1.60364494001542 & -0.00364494001542170 \tabularnewline
59 & 1.61 & 1.60353348677702 & 0.00646651322298353 \tabularnewline
60 & 1.61 & 1.61373121673604 & -0.00373121673603971 \tabularnewline
61 & 1.61 & 1.61361712536920 & -0.00361712536919589 \tabularnewline
62 & 1.62 & 1.61350652263379 & 0.00649347736621508 \tabularnewline
63 & 1.63 & 1.62370507708953 & 0.00629492291047251 \tabularnewline
64 & 1.63 & 1.63389756024176 & -0.00389756024176413 \tabularnewline
65 & 1.64 & 1.63377838250249 & 0.00622161749750894 \tabularnewline
66 & 1.64 & 1.64396862415675 & -0.00396862415675203 \tabularnewline
67 & 1.64 & 1.64384727345896 & -0.00384727345895963 \tabularnewline
68 & 1.64 & 1.64372963336496 & -0.00372963336496168 \tabularnewline
69 & 1.64 & 1.64361559041368 & -0.00361559041368387 \tabularnewline
70 & 1.65 & 1.64350503461341 & 0.00649496538658911 \tabularnewline
71 & 1.65 & 1.65370363456913 & -0.00370363456913103 \tabularnewline
72 & 1.65 & 1.65359038659664 & -0.00359038659663957 \tabularnewline
73 & 1.65 & 1.65348060146667 & -0.00348060146667084 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13471&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]1.43[/C][C]1.43[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]1.44[/C][C]1.43[/C][C]0.01[/C][/ROW]
[ROW][C]21[/C][C]1.48[/C][C]1.44030577523343[/C][C]0.0396942247665708[/C][/ROW]
[ROW][C]22[/C][C]1.48[/C][C]1.48151952631781[/C][C]-0.00151952631780872[/C][/ROW]
[ROW][C]23[/C][C]1.48[/C][C]1.48147306296636[/C][C]-0.00147306296635574[/C][/ROW]
[ROW][C]24[/C][C]1.48[/C][C]1.48142802034912[/C][C]-0.00142802034911638[/C][/ROW]
[ROW][C]25[/C][C]1.48[/C][C]1.48138435502356[/C][C]-0.00138435502355705[/C][/ROW]
[ROW][C]26[/C][C]1.48[/C][C]1.48134202487551[/C][C]-0.00134202487550938[/C][/ROW]
[ROW][C]27[/C][C]1.48[/C][C]1.48130098907855[/C][C]-0.00130098907855181[/C][/ROW]
[ROW][C]28[/C][C]1.48[/C][C]1.48126120805463[/C][C]-0.00126120805463348[/C][/ROW]
[ROW][C]29[/C][C]1.48[/C][C]1.48122264343590[/C][C]-0.00122264343590262[/C][/ROW]
[ROW][C]30[/C][C]1.48[/C][C]1.4811852580277[/C][C]-0.00118525802770120[/C][/ROW]
[ROW][C]31[/C][C]1.48[/C][C]1.48114901577269[/C][C]-0.00114901577269166[/C][/ROW]
[ROW][C]32[/C][C]1.48[/C][C]1.48111388171608[/C][C]-0.00111388171608096[/C][/ROW]
[ROW][C]33[/C][C]1.48[/C][C]1.48107982197191[/C][C]-0.00107982197190615[/C][/ROW]
[ROW][C]34[/C][C]1.48[/C][C]1.48104680369035[/C][C]-0.00104680369035393[/C][/ROW]
[ROW][C]35[/C][C]1.48[/C][C]1.48101479502608[/C][C]-0.00101479502607660[/C][/ROW]
[ROW][C]36[/C][C]1.48[/C][C]1.48098376510748[/C][C]-0.00098376510747844[/C][/ROW]
[ROW][C]37[/C][C]1.48[/C][C]1.48095368400694[/C][C]-0.000953684006940625[/C][/ROW]
[ROW][C]38[/C][C]1.48[/C][C]1.48092452271196[/C][C]-0.000924522711956755[/C][/ROW]
[ROW][C]39[/C][C]1.48[/C][C]1.48089625309715[/C][C]-0.000896253097150801[/C][/ROW]
[ROW][C]40[/C][C]1.48[/C][C]1.48086884789715[/C][C]-0.00086884789715147[/C][/ROW]
[ROW][C]41[/C][C]1.48[/C][C]1.48084228068029[/C][C]-0.000842280680294794[/C][/ROW]
[ROW][C]42[/C][C]1.48[/C][C]1.48081652582313[/C][C]-0.000816525823131853[/C][/ROW]
[ROW][C]43[/C][C]1.48[/C][C]1.48079155848571[/C][C]-0.000791558485714772[/C][/ROW]
[ROW][C]44[/C][C]1.48[/C][C]1.48076735458764[/C][C]-0.000767354587640545[/C][/ROW]
[ROW][C]45[/C][C]1.48[/C][C]1.48074389078482[/C][C]-0.00074389078482473[/C][/ROW]
[ROW][C]46[/C][C]1.48[/C][C]1.48072114444699[/C][C]-0.000721144446987232[/C][/ROW]
[ROW][C]47[/C][C]1.48[/C][C]1.48069909363583[/C][C]-0.000699093635825765[/C][/ROW]
[ROW][C]48[/C][C]1.48[/C][C]1.48067771708386[/C][C]-0.000677717083857443[/C][/ROW]
[ROW][C]49[/C][C]1.48[/C][C]1.48065699417391[/C][C]-0.000656994173905856[/C][/ROW]
[ROW][C]50[/C][C]1.48[/C][C]1.48063690491922[/C][C]-0.000636904919217196[/C][/ROW]
[ROW][C]51[/C][C]1.57[/C][C]1.48061742994418[/C][C]0.0893825700558175[/C][/ROW]
[ROW][C]52[/C][C]1.58[/C][C]1.57335052756652[/C][C]0.00664947243348424[/C][/ROW]
[ROW][C]53[/C][C]1.58[/C][C]1.58355385196507[/C][C]-0.00355385196506863[/C][/ROW]
[ROW][C]54[/C][C]1.58[/C][C]1.58344518397365[/C][C]-0.00344518397364957[/C][/ROW]
[ROW][C]55[/C][C]1.58[/C][C]1.58333983878027[/C][C]-0.00333983878027455[/C][/ROW]
[ROW][C]56[/C][C]1.59[/C][C]1.58323771478201[/C][C]0.00676228521799094[/C][/ROW]
[ROW][C]57[/C][C]1.6[/C][C]1.59344448871611[/C][C]0.0065555112838862[/C][/ROW]
[ROW][C]58[/C][C]1.6[/C][C]1.60364494001542[/C][C]-0.00364494001542170[/C][/ROW]
[ROW][C]59[/C][C]1.61[/C][C]1.60353348677702[/C][C]0.00646651322298353[/C][/ROW]
[ROW][C]60[/C][C]1.61[/C][C]1.61373121673604[/C][C]-0.00373121673603971[/C][/ROW]
[ROW][C]61[/C][C]1.61[/C][C]1.61361712536920[/C][C]-0.00361712536919589[/C][/ROW]
[ROW][C]62[/C][C]1.62[/C][C]1.61350652263379[/C][C]0.00649347736621508[/C][/ROW]
[ROW][C]63[/C][C]1.63[/C][C]1.62370507708953[/C][C]0.00629492291047251[/C][/ROW]
[ROW][C]64[/C][C]1.63[/C][C]1.63389756024176[/C][C]-0.00389756024176413[/C][/ROW]
[ROW][C]65[/C][C]1.64[/C][C]1.63377838250249[/C][C]0.00622161749750894[/C][/ROW]
[ROW][C]66[/C][C]1.64[/C][C]1.64396862415675[/C][C]-0.00396862415675203[/C][/ROW]
[ROW][C]67[/C][C]1.64[/C][C]1.64384727345896[/C][C]-0.00384727345895963[/C][/ROW]
[ROW][C]68[/C][C]1.64[/C][C]1.64372963336496[/C][C]-0.00372963336496168[/C][/ROW]
[ROW][C]69[/C][C]1.64[/C][C]1.64361559041368[/C][C]-0.00361559041368387[/C][/ROW]
[ROW][C]70[/C][C]1.65[/C][C]1.64350503461341[/C][C]0.00649496538658911[/C][/ROW]
[ROW][C]71[/C][C]1.65[/C][C]1.65370363456913[/C][C]-0.00370363456913103[/C][/ROW]
[ROW][C]72[/C][C]1.65[/C][C]1.65359038659664[/C][C]-0.00359038659663957[/C][/ROW]
[ROW][C]73[/C][C]1.65[/C][C]1.65348060146667[/C][C]-0.00348060146667084[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13471&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13471&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	1.43	1.43	0
20	1.44	1.43	0.01
21	1.48	1.44030577523343	0.0396942247665708
22	1.48	1.48151952631781	-0.00151952631780872
23	1.48	1.48147306296636	-0.00147306296635574
24	1.48	1.48142802034912	-0.00142802034911638
25	1.48	1.48138435502356	-0.00138435502355705
26	1.48	1.48134202487551	-0.00134202487550938
27	1.48	1.48130098907855	-0.00130098907855181
28	1.48	1.48126120805463	-0.00126120805463348
29	1.48	1.48122264343590	-0.00122264343590262
30	1.48	1.4811852580277	-0.00118525802770120
31	1.48	1.48114901577269	-0.00114901577269166
32	1.48	1.48111388171608	-0.00111388171608096
33	1.48	1.48107982197191	-0.00107982197190615
34	1.48	1.48104680369035	-0.00104680369035393
35	1.48	1.48101479502608	-0.00101479502607660
36	1.48	1.48098376510748	-0.00098376510747844
37	1.48	1.48095368400694	-0.000953684006940625
38	1.48	1.48092452271196	-0.000924522711956755
39	1.48	1.48089625309715	-0.000896253097150801
40	1.48	1.48086884789715	-0.00086884789715147
41	1.48	1.48084228068029	-0.000842280680294794
42	1.48	1.48081652582313	-0.000816525823131853
43	1.48	1.48079155848571	-0.000791558485714772
44	1.48	1.48076735458764	-0.000767354587640545
45	1.48	1.48074389078482	-0.00074389078482473
46	1.48	1.48072114444699	-0.000721144446987232
47	1.48	1.48069909363583	-0.000699093635825765
48	1.48	1.48067771708386	-0.000677717083857443
49	1.48	1.48065699417391	-0.000656994173905856
50	1.48	1.48063690491922	-0.000636904919217196
51	1.57	1.48061742994418	0.0893825700558175
52	1.58	1.57335052756652	0.00664947243348424
53	1.58	1.58355385196507	-0.00355385196506863
54	1.58	1.58344518397365	-0.00344518397364957
55	1.58	1.58333983878027	-0.00333983878027455
56	1.59	1.58323771478201	0.00676228521799094
57	1.6	1.59344448871611	0.0065555112838862
58	1.6	1.60364494001542	-0.00364494001542170
59	1.61	1.60353348677702	0.00646651322298353
60	1.61	1.61373121673604	-0.00373121673603971
61	1.61	1.61361712536920	-0.00361712536919589
62	1.62	1.61350652263379	0.00649347736621508
63	1.63	1.62370507708953	0.00629492291047251
64	1.63	1.63389756024176	-0.00389756024176413
65	1.64	1.63377838250249	0.00622161749750894
66	1.64	1.64396862415675	-0.00396862415675203
67	1.64	1.64384727345896	-0.00384727345895963
68	1.64	1.64372963336496	-0.00372963336496168
69	1.64	1.64361559041368	-0.00361559041368387
70	1.65	1.64350503461341	0.00649496538658911
71	1.65	1.65370363456913	-0.00370363456913103
72	1.65	1.65359038659664	-0.00359038659663957
73	1.65	1.65348060146667	-0.00348060146667084

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
74	1.65337417329408	1.62988940293862	1.67685894364953
75	1.65674834658815	1.62302426516209	1.69047242801422
76	1.66012251988223	1.61818960869147	1.70205543107298
77	1.66349669317630	1.61434659744772	1.71264678890489
78	1.66687086647038	1.61109960479912	1.72264212814164
79	1.67024503976446	1.60824902740447	1.73224105212445
80	1.67361921305853	1.60567821642677	1.74156020969029
81	1.67699338635261	1.60331241590898	1.75067435679624
82	1.68036755964669	1.60110056747518	1.75963455181819
83	1.68374173294076	1.59900613060441	1.76847733527712
84	1.68711590623484	1.59700200317622	1.77722980929345
85	1.69049007952891	1.59506750848748	1.78591265057035

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
74 & 1.65337417329408 & 1.62988940293862 & 1.67685894364953 \tabularnewline
75 & 1.65674834658815 & 1.62302426516209 & 1.69047242801422 \tabularnewline
76 & 1.66012251988223 & 1.61818960869147 & 1.70205543107298 \tabularnewline
77 & 1.66349669317630 & 1.61434659744772 & 1.71264678890489 \tabularnewline
78 & 1.66687086647038 & 1.61109960479912 & 1.72264212814164 \tabularnewline
79 & 1.67024503976446 & 1.60824902740447 & 1.73224105212445 \tabularnewline
80 & 1.67361921305853 & 1.60567821642677 & 1.74156020969029 \tabularnewline
81 & 1.67699338635261 & 1.60331241590898 & 1.75067435679624 \tabularnewline
82 & 1.68036755964669 & 1.60110056747518 & 1.75963455181819 \tabularnewline
83 & 1.68374173294076 & 1.59900613060441 & 1.76847733527712 \tabularnewline
84 & 1.68711590623484 & 1.59700200317622 & 1.77722980929345 \tabularnewline
85 & 1.69049007952891 & 1.59506750848748 & 1.78591265057035 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13471&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]74[/C][C]1.65337417329408[/C][C]1.62988940293862[/C][C]1.67685894364953[/C][/ROW]
[ROW][C]75[/C][C]1.65674834658815[/C][C]1.62302426516209[/C][C]1.69047242801422[/C][/ROW]
[ROW][C]76[/C][C]1.66012251988223[/C][C]1.61818960869147[/C][C]1.70205543107298[/C][/ROW]
[ROW][C]77[/C][C]1.66349669317630[/C][C]1.61434659744772[/C][C]1.71264678890489[/C][/ROW]
[ROW][C]78[/C][C]1.66687086647038[/C][C]1.61109960479912[/C][C]1.72264212814164[/C][/ROW]
[ROW][C]79[/C][C]1.67024503976446[/C][C]1.60824902740447[/C][C]1.73224105212445[/C][/ROW]
[ROW][C]80[/C][C]1.67361921305853[/C][C]1.60567821642677[/C][C]1.74156020969029[/C][/ROW]
[ROW][C]81[/C][C]1.67699338635261[/C][C]1.60331241590898[/C][C]1.75067435679624[/C][/ROW]
[ROW][C]82[/C][C]1.68036755964669[/C][C]1.60110056747518[/C][C]1.75963455181819[/C][/ROW]
[ROW][C]83[/C][C]1.68374173294076[/C][C]1.59900613060441[/C][C]1.76847733527712[/C][/ROW]
[ROW][C]84[/C][C]1.68711590623484[/C][C]1.59700200317622[/C][C]1.77722980929345[/C][/ROW]
[ROW][C]85[/C][C]1.69049007952891[/C][C]1.59506750848748[/C][C]1.78591265057035[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13471&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13471&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
74	1.65337417329408	1.62988940293862	1.67685894364953
75	1.65674834658815	1.62302426516209	1.69047242801422
76	1.66012251988223	1.61818960869147	1.70205543107298
77	1.66349669317630	1.61434659744772	1.71264678890489
78	1.66687086647038	1.61109960479912	1.72264212814164
79	1.67024503976446	1.60824902740447	1.73224105212445
80	1.67361921305853	1.60567821642677	1.74156020969029
81	1.67699338635261	1.60331241590898	1.75067435679624
82	1.68036755964669	1.60110056747518	1.75963455181819
83	1.68374173294076	1.59900613060441	1.76847733527712
84	1.68711590623484	1.59700200317622	1.77722980929345
85	1.69049007952891	1.59506750848748	1.78591265057035

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=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