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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 28 May 2012 11:17:59 -0400

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/May/28/t1338218316ain88nllux0qv1o.htm/, Retrieved Thu, 02 May 2024 00:20:25 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167815, Retrieved Thu, 02 May 2024 00:20:25 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

109

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

-     [Standard Deviation-Mean Plot] [] [2012-05-02 16:05:10] [2e3d5d2fadc43e8101372c775eeeade1]
- RMPD  [Exponential Smoothing] [] [2012-05-21 16:27:15] [2f0f353a58a70fd7baf0f5141860d820]
- R PD      [Exponential Smoothing] [] [2012-05-28 15:17:59] [e0b098c2bb79809f51906d3408b0bcc0] [Current]

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Dataseries X:

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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	12 seconds
R Server	'AstonUniversity' @ aston.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 & 12 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167815&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]12 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167815&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167815&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	12 seconds
R Server	'AstonUniversity' @ aston.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.390930173502102
gamma	0.0255606071067017

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.390930173502102 \tabularnewline
gamma & 0.0255606071067017 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167815&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]0.390930173502102[/C][/ROW]
[ROW][C]gamma[/C][C]0.0255606071067017[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167815&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167815&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	0.390930173502102
gamma	0.0255606071067017

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	23.74	23.3455128205128	0.394487179487168
14	23.87	24.0316994590038	-0.161699459003788
15	24.13	24.2355695947736	-0.105569594773581
16	24.23	24.2951325881055	-0.0651325881055271
17	24.27	24.3055036274701	-0.0355036274701277
18	24.41	24.4245408548899	-0.0145408548899404
19	24.39	24.427606395965	-0.0376063959649535
20	24.34	24.4324882543989	-0.092488254398912
21	24.31	24.3271651383932	-0.0171651383931746
22	24.34	24.2233714345296	0.116628565470389
23	24.41	24.3377150598643	0.0722849401357486
24	24.39	24.2801400907198	0.109859909280225
25	24.54	24.4818376441156	0.0581623558843738
26	24.9	24.7641583973261	0.135841602673874
27	25.63	25.3143463119616	0.315653688038442
28	26.7	26.0085781963263	0.691421803673663
29	27.12	27.284709175333	-0.164709175332952
30	27.68	27.7332360555093	-0.0532360555093199
31	27.84	28.1411744750925	-0.301174475092498
32	27.84	28.2230196186235	-0.383019618623511
33	27.77	28.0541190259936	-0.28411902599365
34	27.8	27.8059649925334	-0.00596499253337157
35	27.82	27.8723830969674	-0.0523830969673647
36	27.72	27.716071630448	0.00392836955199982
37	27.87	27.7963573486385	0.0736426513614532
38	27.83	28.0847298164458	-0.254729816445767
39	28.07	28.0822315784398	-0.0122315784397955
40	28.05	28.1582832186915	-0.108283218691454
41	28.15	28.0317853745544	0.118214625445624
42	28.3	28.270915705257	0.0290842947430185
43	28.41	28.3010356336471	0.108964366352936
44	28.43	28.4932164256243	-0.0632164256242902
45	28.43	28.4693365507201	-0.0393365507201402
46	28.29	28.3868753727888	-0.0968753727888085
47	28.19	28.2477538664964	-0.0577538664963981
48	27.53	27.9693428041132	-0.439342804113213
49	27.92	27.3163404454743	0.603659554525663
50	27.98	28.0519125131946	-0.0719125131945866
51	27.92	28.2208830752678	-0.300883075267787
52	27.89	27.8840921357828	0.00590786421716061
53	27.95	27.7922350314996	0.157764968500384
54	28.02	28.0068267846747	0.0131732153253132
55	27.97	27.9507265920274	0.0192734079726016
56	27.81	27.9478444820834	-0.13784448208343
57	27.78	27.7147902481196	0.0652097518804169
58	27.56	27.6431993744029	-0.083199374402895
59	27.52	27.4294242285323	0.090575771467698
60	27.18	27.2689996972539	-0.0889996972539215

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 23.74 & 23.3455128205128 & 0.394487179487168 \tabularnewline
14 & 23.87 & 24.0316994590038 & -0.161699459003788 \tabularnewline
15 & 24.13 & 24.2355695947736 & -0.105569594773581 \tabularnewline
16 & 24.23 & 24.2951325881055 & -0.0651325881055271 \tabularnewline
17 & 24.27 & 24.3055036274701 & -0.0355036274701277 \tabularnewline
18 & 24.41 & 24.4245408548899 & -0.0145408548899404 \tabularnewline
19 & 24.39 & 24.427606395965 & -0.0376063959649535 \tabularnewline
20 & 24.34 & 24.4324882543989 & -0.092488254398912 \tabularnewline
21 & 24.31 & 24.3271651383932 & -0.0171651383931746 \tabularnewline
22 & 24.34 & 24.2233714345296 & 0.116628565470389 \tabularnewline
23 & 24.41 & 24.3377150598643 & 0.0722849401357486 \tabularnewline
24 & 24.39 & 24.2801400907198 & 0.109859909280225 \tabularnewline
25 & 24.54 & 24.4818376441156 & 0.0581623558843738 \tabularnewline
26 & 24.9 & 24.7641583973261 & 0.135841602673874 \tabularnewline
27 & 25.63 & 25.3143463119616 & 0.315653688038442 \tabularnewline
28 & 26.7 & 26.0085781963263 & 0.691421803673663 \tabularnewline
29 & 27.12 & 27.284709175333 & -0.164709175332952 \tabularnewline
30 & 27.68 & 27.7332360555093 & -0.0532360555093199 \tabularnewline
31 & 27.84 & 28.1411744750925 & -0.301174475092498 \tabularnewline
32 & 27.84 & 28.2230196186235 & -0.383019618623511 \tabularnewline
33 & 27.77 & 28.0541190259936 & -0.28411902599365 \tabularnewline
34 & 27.8 & 27.8059649925334 & -0.00596499253337157 \tabularnewline
35 & 27.82 & 27.8723830969674 & -0.0523830969673647 \tabularnewline
36 & 27.72 & 27.716071630448 & 0.00392836955199982 \tabularnewline
37 & 27.87 & 27.7963573486385 & 0.0736426513614532 \tabularnewline
38 & 27.83 & 28.0847298164458 & -0.254729816445767 \tabularnewline
39 & 28.07 & 28.0822315784398 & -0.0122315784397955 \tabularnewline
40 & 28.05 & 28.1582832186915 & -0.108283218691454 \tabularnewline
41 & 28.15 & 28.0317853745544 & 0.118214625445624 \tabularnewline
42 & 28.3 & 28.270915705257 & 0.0290842947430185 \tabularnewline
43 & 28.41 & 28.3010356336471 & 0.108964366352936 \tabularnewline
44 & 28.43 & 28.4932164256243 & -0.0632164256242902 \tabularnewline
45 & 28.43 & 28.4693365507201 & -0.0393365507201402 \tabularnewline
46 & 28.29 & 28.3868753727888 & -0.0968753727888085 \tabularnewline
47 & 28.19 & 28.2477538664964 & -0.0577538664963981 \tabularnewline
48 & 27.53 & 27.9693428041132 & -0.439342804113213 \tabularnewline
49 & 27.92 & 27.3163404454743 & 0.603659554525663 \tabularnewline
50 & 27.98 & 28.0519125131946 & -0.0719125131945866 \tabularnewline
51 & 27.92 & 28.2208830752678 & -0.300883075267787 \tabularnewline
52 & 27.89 & 27.8840921357828 & 0.00590786421716061 \tabularnewline
53 & 27.95 & 27.7922350314996 & 0.157764968500384 \tabularnewline
54 & 28.02 & 28.0068267846747 & 0.0131732153253132 \tabularnewline
55 & 27.97 & 27.9507265920274 & 0.0192734079726016 \tabularnewline
56 & 27.81 & 27.9478444820834 & -0.13784448208343 \tabularnewline
57 & 27.78 & 27.7147902481196 & 0.0652097518804169 \tabularnewline
58 & 27.56 & 27.6431993744029 & -0.083199374402895 \tabularnewline
59 & 27.52 & 27.4294242285323 & 0.090575771467698 \tabularnewline
60 & 27.18 & 27.2689996972539 & -0.0889996972539215 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167815&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]23.74[/C][C]23.3455128205128[/C][C]0.394487179487168[/C][/ROW]
[ROW][C]14[/C][C]23.87[/C][C]24.0316994590038[/C][C]-0.161699459003788[/C][/ROW]
[ROW][C]15[/C][C]24.13[/C][C]24.2355695947736[/C][C]-0.105569594773581[/C][/ROW]
[ROW][C]16[/C][C]24.23[/C][C]24.2951325881055[/C][C]-0.0651325881055271[/C][/ROW]
[ROW][C]17[/C][C]24.27[/C][C]24.3055036274701[/C][C]-0.0355036274701277[/C][/ROW]
[ROW][C]18[/C][C]24.41[/C][C]24.4245408548899[/C][C]-0.0145408548899404[/C][/ROW]
[ROW][C]19[/C][C]24.39[/C][C]24.427606395965[/C][C]-0.0376063959649535[/C][/ROW]
[ROW][C]20[/C][C]24.34[/C][C]24.4324882543989[/C][C]-0.092488254398912[/C][/ROW]
[ROW][C]21[/C][C]24.31[/C][C]24.3271651383932[/C][C]-0.0171651383931746[/C][/ROW]
[ROW][C]22[/C][C]24.34[/C][C]24.2233714345296[/C][C]0.116628565470389[/C][/ROW]
[ROW][C]23[/C][C]24.41[/C][C]24.3377150598643[/C][C]0.0722849401357486[/C][/ROW]
[ROW][C]24[/C][C]24.39[/C][C]24.2801400907198[/C][C]0.109859909280225[/C][/ROW]
[ROW][C]25[/C][C]24.54[/C][C]24.4818376441156[/C][C]0.0581623558843738[/C][/ROW]
[ROW][C]26[/C][C]24.9[/C][C]24.7641583973261[/C][C]0.135841602673874[/C][/ROW]
[ROW][C]27[/C][C]25.63[/C][C]25.3143463119616[/C][C]0.315653688038442[/C][/ROW]
[ROW][C]28[/C][C]26.7[/C][C]26.0085781963263[/C][C]0.691421803673663[/C][/ROW]
[ROW][C]29[/C][C]27.12[/C][C]27.284709175333[/C][C]-0.164709175332952[/C][/ROW]
[ROW][C]30[/C][C]27.68[/C][C]27.7332360555093[/C][C]-0.0532360555093199[/C][/ROW]
[ROW][C]31[/C][C]27.84[/C][C]28.1411744750925[/C][C]-0.301174475092498[/C][/ROW]
[ROW][C]32[/C][C]27.84[/C][C]28.2230196186235[/C][C]-0.383019618623511[/C][/ROW]
[ROW][C]33[/C][C]27.77[/C][C]28.0541190259936[/C][C]-0.28411902599365[/C][/ROW]
[ROW][C]34[/C][C]27.8[/C][C]27.8059649925334[/C][C]-0.00596499253337157[/C][/ROW]
[ROW][C]35[/C][C]27.82[/C][C]27.8723830969674[/C][C]-0.0523830969673647[/C][/ROW]
[ROW][C]36[/C][C]27.72[/C][C]27.716071630448[/C][C]0.00392836955199982[/C][/ROW]
[ROW][C]37[/C][C]27.87[/C][C]27.7963573486385[/C][C]0.0736426513614532[/C][/ROW]
[ROW][C]38[/C][C]27.83[/C][C]28.0847298164458[/C][C]-0.254729816445767[/C][/ROW]
[ROW][C]39[/C][C]28.07[/C][C]28.0822315784398[/C][C]-0.0122315784397955[/C][/ROW]
[ROW][C]40[/C][C]28.05[/C][C]28.1582832186915[/C][C]-0.108283218691454[/C][/ROW]
[ROW][C]41[/C][C]28.15[/C][C]28.0317853745544[/C][C]0.118214625445624[/C][/ROW]
[ROW][C]42[/C][C]28.3[/C][C]28.270915705257[/C][C]0.0290842947430185[/C][/ROW]
[ROW][C]43[/C][C]28.41[/C][C]28.3010356336471[/C][C]0.108964366352936[/C][/ROW]
[ROW][C]44[/C][C]28.43[/C][C]28.4932164256243[/C][C]-0.0632164256242902[/C][/ROW]
[ROW][C]45[/C][C]28.43[/C][C]28.4693365507201[/C][C]-0.0393365507201402[/C][/ROW]
[ROW][C]46[/C][C]28.29[/C][C]28.3868753727888[/C][C]-0.0968753727888085[/C][/ROW]
[ROW][C]47[/C][C]28.19[/C][C]28.2477538664964[/C][C]-0.0577538664963981[/C][/ROW]
[ROW][C]48[/C][C]27.53[/C][C]27.9693428041132[/C][C]-0.439342804113213[/C][/ROW]
[ROW][C]49[/C][C]27.92[/C][C]27.3163404454743[/C][C]0.603659554525663[/C][/ROW]
[ROW][C]50[/C][C]27.98[/C][C]28.0519125131946[/C][C]-0.0719125131945866[/C][/ROW]
[ROW][C]51[/C][C]27.92[/C][C]28.2208830752678[/C][C]-0.300883075267787[/C][/ROW]
[ROW][C]52[/C][C]27.89[/C][C]27.8840921357828[/C][C]0.00590786421716061[/C][/ROW]
[ROW][C]53[/C][C]27.95[/C][C]27.7922350314996[/C][C]0.157764968500384[/C][/ROW]
[ROW][C]54[/C][C]28.02[/C][C]28.0068267846747[/C][C]0.0131732153253132[/C][/ROW]
[ROW][C]55[/C][C]27.97[/C][C]27.9507265920274[/C][C]0.0192734079726016[/C][/ROW]
[ROW][C]56[/C][C]27.81[/C][C]27.9478444820834[/C][C]-0.13784448208343[/C][/ROW]
[ROW][C]57[/C][C]27.78[/C][C]27.7147902481196[/C][C]0.0652097518804169[/C][/ROW]
[ROW][C]58[/C][C]27.56[/C][C]27.6431993744029[/C][C]-0.083199374402895[/C][/ROW]
[ROW][C]59[/C][C]27.52[/C][C]27.4294242285323[/C][C]0.090575771467698[/C][/ROW]
[ROW][C]60[/C][C]27.18[/C][C]27.2689996972539[/C][C]-0.0889996972539215[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167815&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167815&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	23.74	23.3455128205128	0.394487179487168
14	23.87	24.0316994590038	-0.161699459003788
15	24.13	24.2355695947736	-0.105569594773581
16	24.23	24.2951325881055	-0.0651325881055271
17	24.27	24.3055036274701	-0.0355036274701277
18	24.41	24.4245408548899	-0.0145408548899404
19	24.39	24.427606395965	-0.0376063959649535
20	24.34	24.4324882543989	-0.092488254398912
21	24.31	24.3271651383932	-0.0171651383931746
22	24.34	24.2233714345296	0.116628565470389
23	24.41	24.3377150598643	0.0722849401357486
24	24.39	24.2801400907198	0.109859909280225
25	24.54	24.4818376441156	0.0581623558843738
26	24.9	24.7641583973261	0.135841602673874
27	25.63	25.3143463119616	0.315653688038442
28	26.7	26.0085781963263	0.691421803673663
29	27.12	27.284709175333	-0.164709175332952
30	27.68	27.7332360555093	-0.0532360555093199
31	27.84	28.1411744750925	-0.301174475092498
32	27.84	28.2230196186235	-0.383019618623511
33	27.77	28.0541190259936	-0.28411902599365
34	27.8	27.8059649925334	-0.00596499253337157
35	27.82	27.8723830969674	-0.0523830969673647
36	27.72	27.716071630448	0.00392836955199982
37	27.87	27.7963573486385	0.0736426513614532
38	27.83	28.0847298164458	-0.254729816445767
39	28.07	28.0822315784398	-0.0122315784397955
40	28.05	28.1582832186915	-0.108283218691454
41	28.15	28.0317853745544	0.118214625445624
42	28.3	28.270915705257	0.0290842947430185
43	28.41	28.3010356336471	0.108964366352936
44	28.43	28.4932164256243	-0.0632164256242902
45	28.43	28.4693365507201	-0.0393365507201402
46	28.29	28.3868753727888	-0.0968753727888085
47	28.19	28.2477538664964	-0.0577538664963981
48	27.53	27.9693428041132	-0.439342804113213
49	27.92	27.3163404454743	0.603659554525663
50	27.98	28.0519125131946	-0.0719125131945866
51	27.92	28.2208830752678	-0.300883075267787
52	27.89	27.8840921357828	0.00590786421716061
53	27.95	27.7922350314996	0.157764968500384
54	28.02	28.0068267846747	0.0131732153253132
55	27.97	27.9507265920274	0.0192734079726016
56	27.81	27.9478444820834	-0.13784448208343
57	27.78	27.7147902481196	0.0652097518804169
58	27.56	27.6431993744029	-0.083199374402895
59	27.52	27.4294242285323	0.090575771467698
60	27.18	27.2689996972539	-0.0889996972539215

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	27.0729570301648	26.6646468062822	27.4812672540474
62	27.075497393663	26.3760241120655	27.7749706752605
63	27.2151210904944	26.205866668014	28.2243755129749
64	27.1955781206593	25.8518260293564	28.5393302119622
65	27.1118684841574	25.4085053274895	28.8152316408253
66	27.1210755143222	25.0337611723493	29.2083898562951
67	26.999032544487	24.5044518923355	29.4936131966385
68	26.9165729079852	23.9924391835784	29.8407066323919
69	26.8149466048167	23.4399332748207	30.1899599348126
70	26.6462369683148	22.7998931148	30.4925808218296
71	26.5162773318129	22.1789447627392	30.8536099008867
72	26.2304843619778	21.3832221558916	31.0777465680639

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 27.0729570301648 & 26.6646468062822 & 27.4812672540474 \tabularnewline
62 & 27.075497393663 & 26.3760241120655 & 27.7749706752605 \tabularnewline
63 & 27.2151210904944 & 26.205866668014 & 28.2243755129749 \tabularnewline
64 & 27.1955781206593 & 25.8518260293564 & 28.5393302119622 \tabularnewline
65 & 27.1118684841574 & 25.4085053274895 & 28.8152316408253 \tabularnewline
66 & 27.1210755143222 & 25.0337611723493 & 29.2083898562951 \tabularnewline
67 & 26.999032544487 & 24.5044518923355 & 29.4936131966385 \tabularnewline
68 & 26.9165729079852 & 23.9924391835784 & 29.8407066323919 \tabularnewline
69 & 26.8149466048167 & 23.4399332748207 & 30.1899599348126 \tabularnewline
70 & 26.6462369683148 & 22.7998931148 & 30.4925808218296 \tabularnewline
71 & 26.5162773318129 & 22.1789447627392 & 30.8536099008867 \tabularnewline
72 & 26.2304843619778 & 21.3832221558916 & 31.0777465680639 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167815&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]61[/C][C]27.0729570301648[/C][C]26.6646468062822[/C][C]27.4812672540474[/C][/ROW]
[ROW][C]62[/C][C]27.075497393663[/C][C]26.3760241120655[/C][C]27.7749706752605[/C][/ROW]
[ROW][C]63[/C][C]27.2151210904944[/C][C]26.205866668014[/C][C]28.2243755129749[/C][/ROW]
[ROW][C]64[/C][C]27.1955781206593[/C][C]25.8518260293564[/C][C]28.5393302119622[/C][/ROW]
[ROW][C]65[/C][C]27.1118684841574[/C][C]25.4085053274895[/C][C]28.8152316408253[/C][/ROW]
[ROW][C]66[/C][C]27.1210755143222[/C][C]25.0337611723493[/C][C]29.2083898562951[/C][/ROW]
[ROW][C]67[/C][C]26.999032544487[/C][C]24.5044518923355[/C][C]29.4936131966385[/C][/ROW]
[ROW][C]68[/C][C]26.9165729079852[/C][C]23.9924391835784[/C][C]29.8407066323919[/C][/ROW]
[ROW][C]69[/C][C]26.8149466048167[/C][C]23.4399332748207[/C][C]30.1899599348126[/C][/ROW]
[ROW][C]70[/C][C]26.6462369683148[/C][C]22.7998931148[/C][C]30.4925808218296[/C][/ROW]
[ROW][C]71[/C][C]26.5162773318129[/C][C]22.1789447627392[/C][C]30.8536099008867[/C][/ROW]
[ROW][C]72[/C][C]26.2304843619778[/C][C]21.3832221558916[/C][C]31.0777465680639[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167815&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167815&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
61	27.0729570301648	26.6646468062822	27.4812672540474
62	27.075497393663	26.3760241120655	27.7749706752605
63	27.2151210904944	26.205866668014	28.2243755129749
64	27.1955781206593	25.8518260293564	28.5393302119622
65	27.1118684841574	25.4085053274895	28.8152316408253
66	27.1210755143222	25.0337611723493	29.2083898562951
67	26.999032544487	24.5044518923355	29.4936131966385
68	26.9165729079852	23.9924391835784	29.8407066323919
69	26.8149466048167	23.4399332748207	30.1899599348126
70	26.6462369683148	22.7998931148	30.4925808218296
71	26.5162773318129	22.1789447627392	30.8536099008867
72	26.2304843619778	21.3832221558916	31.0777465680639

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):

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