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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sun, 08 Jan 2017 21:34:18 +0000

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/2017/Jan/08/t1483911353fhi27pyr9chk3zx.htm/, Retrieved Tue, 14 May 2024 01:40:53 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 14 May 2024 01:40:53 +0200

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Estimated Impact

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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	1 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	1 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.283915505806246
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.283915505806246 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.283915505806246[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	0.283915505806246
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	1.3999	1.3938	0.00609999999999999
4	1.4442	1.43053188458542	0.0136681154145819
5	1.4349	1.47871247448677	-0.0438124744867672
6	1.4388	1.45697343363223	-0.0181734336322334
7	1.4264	1.4557137140303	-0.0293137140303019
8	1.4343	1.43499109608433	-0.000691096084328935
9	1.377	1.44269488318999	-0.0656948831899857
10	1.3706	1.36674308720022	0.00385691279978118
11	1.3556	1.36143812454862	-0.00583812454861943
12	1.3179	1.34478059046444	-0.026880590464438
13	1.2905	1.29944877402636	-0.00894877402635674
14	1.3224	1.26950807832232	0.0528919216776822
15	1.3201	1.3164249150185	0.00367508498149882
16	1.3162	1.3151683286299	0.00103167137009552
17	1.2789	1.31156123612877	-0.032661236128771
18	1.2526	1.26498820475301	-0.0123882047530137
19	1.2288	1.23517100133453	-0.00637100133453061
20	1.24	1.20956217526814	0.0304378247318551
21	1.2856	1.22940394567253	0.0561960543274687
22	1.2974	1.29095887686123	0.00644112313876999
23	1.2828	1.30458761159513	-0.0217876115951343
24	1.3119	1.28380177082879	0.0280982291712084
25	1.3288	1.3208792937762	0.00792070622380492
26	1.3359	1.34002810509007	-0.00412810509006922
27	1.2964	1.3459560720454	-0.0495560720454011
28	1.3026	1.29238633478486	0.0102136652151399
29	1.2982	1.30148615271055	-0.0032861527105521
30	1.3189	1.29615316300158	0.0227468369984207
31	1.308	1.32331134273348	-0.0153113427334779
32	1.331	1.30806421511673	0.0229357848832701
33	1.3348	1.33757604008293	-0.00277604008292665
34	1.3635	1.34058787925864	0.0229121207413558
35	1.3493	1.37579298560802	-0.02649298560802
36	1.3704	1.3540712161988	0.0163287838011987
37	1.361	1.37980721111092	-0.0188072111109197
38	1.3658	1.36506755225556	0.000732447744441922
39	1.3823	1.3700755055274	0.0122244944726024
40	1.3812	1.39004622905881	-0.00884622905881249
41	1.3732	1.3864346474611	-0.0132346474611018
42	1.3592	1.37467712583302	-0.0154771258330157
43	1.3539	1.35628292982371	-0.00238292982370791
44	1.3316	1.35030637909751	-0.0187063790975095
45	1.2901	1.32269534801424	-0.0325953480142365
46	1.2673	1.27194102329584	-0.00464102329584382
47	1.2472	1.24782336481935	-0.000623364819345884
48	1.2331	1.22754638188136	0.00555361811864064
49	1.1621	1.21502314017857	-0.0529231401785681
50	1.135	1.12899744006591	0.00600255993408516
51	1.0838	1.10360165990573	-0.0198016599057329
52	1.0779	1.04677966161779	0.0311203383822063
53	1.115	1.04971520823044	0.0652847917695607
54	1.1213	1.10535057290715	0.0159494270928504
55	1.0996	1.11617886256754	-0.016578862567536
56	1.1139	1.08977186641598	0.0241281335840182
57	1.1221	1.11092221766665	0.0111777823333512
58	1.1235	1.12229576339161	0.00120423660838531
59	1.0736	1.12403766483739	-0.0504376648373945
60	1.0877	1.0598176297134	0.0278823702866

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1.3999 & 1.3938 & 0.00609999999999999 \tabularnewline
4 & 1.4442 & 1.43053188458542 & 0.0136681154145819 \tabularnewline
5 & 1.4349 & 1.47871247448677 & -0.0438124744867672 \tabularnewline
6 & 1.4388 & 1.45697343363223 & -0.0181734336322334 \tabularnewline
7 & 1.4264 & 1.4557137140303 & -0.0293137140303019 \tabularnewline
8 & 1.4343 & 1.43499109608433 & -0.000691096084328935 \tabularnewline
9 & 1.377 & 1.44269488318999 & -0.0656948831899857 \tabularnewline
10 & 1.3706 & 1.36674308720022 & 0.00385691279978118 \tabularnewline
11 & 1.3556 & 1.36143812454862 & -0.00583812454861943 \tabularnewline
12 & 1.3179 & 1.34478059046444 & -0.026880590464438 \tabularnewline
13 & 1.2905 & 1.29944877402636 & -0.00894877402635674 \tabularnewline
14 & 1.3224 & 1.26950807832232 & 0.0528919216776822 \tabularnewline
15 & 1.3201 & 1.3164249150185 & 0.00367508498149882 \tabularnewline
16 & 1.3162 & 1.3151683286299 & 0.00103167137009552 \tabularnewline
17 & 1.2789 & 1.31156123612877 & -0.032661236128771 \tabularnewline
18 & 1.2526 & 1.26498820475301 & -0.0123882047530137 \tabularnewline
19 & 1.2288 & 1.23517100133453 & -0.00637100133453061 \tabularnewline
20 & 1.24 & 1.20956217526814 & 0.0304378247318551 \tabularnewline
21 & 1.2856 & 1.22940394567253 & 0.0561960543274687 \tabularnewline
22 & 1.2974 & 1.29095887686123 & 0.00644112313876999 \tabularnewline
23 & 1.2828 & 1.30458761159513 & -0.0217876115951343 \tabularnewline
24 & 1.3119 & 1.28380177082879 & 0.0280982291712084 \tabularnewline
25 & 1.3288 & 1.3208792937762 & 0.00792070622380492 \tabularnewline
26 & 1.3359 & 1.34002810509007 & -0.00412810509006922 \tabularnewline
27 & 1.2964 & 1.3459560720454 & -0.0495560720454011 \tabularnewline
28 & 1.3026 & 1.29238633478486 & 0.0102136652151399 \tabularnewline
29 & 1.2982 & 1.30148615271055 & -0.0032861527105521 \tabularnewline
30 & 1.3189 & 1.29615316300158 & 0.0227468369984207 \tabularnewline
31 & 1.308 & 1.32331134273348 & -0.0153113427334779 \tabularnewline
32 & 1.331 & 1.30806421511673 & 0.0229357848832701 \tabularnewline
33 & 1.3348 & 1.33757604008293 & -0.00277604008292665 \tabularnewline
34 & 1.3635 & 1.34058787925864 & 0.0229121207413558 \tabularnewline
35 & 1.3493 & 1.37579298560802 & -0.02649298560802 \tabularnewline
36 & 1.3704 & 1.3540712161988 & 0.0163287838011987 \tabularnewline
37 & 1.361 & 1.37980721111092 & -0.0188072111109197 \tabularnewline
38 & 1.3658 & 1.36506755225556 & 0.000732447744441922 \tabularnewline
39 & 1.3823 & 1.3700755055274 & 0.0122244944726024 \tabularnewline
40 & 1.3812 & 1.39004622905881 & -0.00884622905881249 \tabularnewline
41 & 1.3732 & 1.3864346474611 & -0.0132346474611018 \tabularnewline
42 & 1.3592 & 1.37467712583302 & -0.0154771258330157 \tabularnewline
43 & 1.3539 & 1.35628292982371 & -0.00238292982370791 \tabularnewline
44 & 1.3316 & 1.35030637909751 & -0.0187063790975095 \tabularnewline
45 & 1.2901 & 1.32269534801424 & -0.0325953480142365 \tabularnewline
46 & 1.2673 & 1.27194102329584 & -0.00464102329584382 \tabularnewline
47 & 1.2472 & 1.24782336481935 & -0.000623364819345884 \tabularnewline
48 & 1.2331 & 1.22754638188136 & 0.00555361811864064 \tabularnewline
49 & 1.1621 & 1.21502314017857 & -0.0529231401785681 \tabularnewline
50 & 1.135 & 1.12899744006591 & 0.00600255993408516 \tabularnewline
51 & 1.0838 & 1.10360165990573 & -0.0198016599057329 \tabularnewline
52 & 1.0779 & 1.04677966161779 & 0.0311203383822063 \tabularnewline
53 & 1.115 & 1.04971520823044 & 0.0652847917695607 \tabularnewline
54 & 1.1213 & 1.10535057290715 & 0.0159494270928504 \tabularnewline
55 & 1.0996 & 1.11617886256754 & -0.016578862567536 \tabularnewline
56 & 1.1139 & 1.08977186641598 & 0.0241281335840182 \tabularnewline
57 & 1.1221 & 1.11092221766665 & 0.0111777823333512 \tabularnewline
58 & 1.1235 & 1.12229576339161 & 0.00120423660838531 \tabularnewline
59 & 1.0736 & 1.12403766483739 & -0.0504376648373945 \tabularnewline
60 & 1.0877 & 1.0598176297134 & 0.0278823702866 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]1.3999[/C][C]1.3938[/C][C]0.00609999999999999[/C][/ROW]
[ROW][C]4[/C][C]1.4442[/C][C]1.43053188458542[/C][C]0.0136681154145819[/C][/ROW]
[ROW][C]5[/C][C]1.4349[/C][C]1.47871247448677[/C][C]-0.0438124744867672[/C][/ROW]
[ROW][C]6[/C][C]1.4388[/C][C]1.45697343363223[/C][C]-0.0181734336322334[/C][/ROW]
[ROW][C]7[/C][C]1.4264[/C][C]1.4557137140303[/C][C]-0.0293137140303019[/C][/ROW]
[ROW][C]8[/C][C]1.4343[/C][C]1.43499109608433[/C][C]-0.000691096084328935[/C][/ROW]
[ROW][C]9[/C][C]1.377[/C][C]1.44269488318999[/C][C]-0.0656948831899857[/C][/ROW]
[ROW][C]10[/C][C]1.3706[/C][C]1.36674308720022[/C][C]0.00385691279978118[/C][/ROW]
[ROW][C]11[/C][C]1.3556[/C][C]1.36143812454862[/C][C]-0.00583812454861943[/C][/ROW]
[ROW][C]12[/C][C]1.3179[/C][C]1.34478059046444[/C][C]-0.026880590464438[/C][/ROW]
[ROW][C]13[/C][C]1.2905[/C][C]1.29944877402636[/C][C]-0.00894877402635674[/C][/ROW]
[ROW][C]14[/C][C]1.3224[/C][C]1.26950807832232[/C][C]0.0528919216776822[/C][/ROW]
[ROW][C]15[/C][C]1.3201[/C][C]1.3164249150185[/C][C]0.00367508498149882[/C][/ROW]
[ROW][C]16[/C][C]1.3162[/C][C]1.3151683286299[/C][C]0.00103167137009552[/C][/ROW]
[ROW][C]17[/C][C]1.2789[/C][C]1.31156123612877[/C][C]-0.032661236128771[/C][/ROW]
[ROW][C]18[/C][C]1.2526[/C][C]1.26498820475301[/C][C]-0.0123882047530137[/C][/ROW]
[ROW][C]19[/C][C]1.2288[/C][C]1.23517100133453[/C][C]-0.00637100133453061[/C][/ROW]
[ROW][C]20[/C][C]1.24[/C][C]1.20956217526814[/C][C]0.0304378247318551[/C][/ROW]
[ROW][C]21[/C][C]1.2856[/C][C]1.22940394567253[/C][C]0.0561960543274687[/C][/ROW]
[ROW][C]22[/C][C]1.2974[/C][C]1.29095887686123[/C][C]0.00644112313876999[/C][/ROW]
[ROW][C]23[/C][C]1.2828[/C][C]1.30458761159513[/C][C]-0.0217876115951343[/C][/ROW]
[ROW][C]24[/C][C]1.3119[/C][C]1.28380177082879[/C][C]0.0280982291712084[/C][/ROW]
[ROW][C]25[/C][C]1.3288[/C][C]1.3208792937762[/C][C]0.00792070622380492[/C][/ROW]
[ROW][C]26[/C][C]1.3359[/C][C]1.34002810509007[/C][C]-0.00412810509006922[/C][/ROW]
[ROW][C]27[/C][C]1.2964[/C][C]1.3459560720454[/C][C]-0.0495560720454011[/C][/ROW]
[ROW][C]28[/C][C]1.3026[/C][C]1.29238633478486[/C][C]0.0102136652151399[/C][/ROW]
[ROW][C]29[/C][C]1.2982[/C][C]1.30148615271055[/C][C]-0.0032861527105521[/C][/ROW]
[ROW][C]30[/C][C]1.3189[/C][C]1.29615316300158[/C][C]0.0227468369984207[/C][/ROW]
[ROW][C]31[/C][C]1.308[/C][C]1.32331134273348[/C][C]-0.0153113427334779[/C][/ROW]
[ROW][C]32[/C][C]1.331[/C][C]1.30806421511673[/C][C]0.0229357848832701[/C][/ROW]
[ROW][C]33[/C][C]1.3348[/C][C]1.33757604008293[/C][C]-0.00277604008292665[/C][/ROW]
[ROW][C]34[/C][C]1.3635[/C][C]1.34058787925864[/C][C]0.0229121207413558[/C][/ROW]
[ROW][C]35[/C][C]1.3493[/C][C]1.37579298560802[/C][C]-0.02649298560802[/C][/ROW]
[ROW][C]36[/C][C]1.3704[/C][C]1.3540712161988[/C][C]0.0163287838011987[/C][/ROW]
[ROW][C]37[/C][C]1.361[/C][C]1.37980721111092[/C][C]-0.0188072111109197[/C][/ROW]
[ROW][C]38[/C][C]1.3658[/C][C]1.36506755225556[/C][C]0.000732447744441922[/C][/ROW]
[ROW][C]39[/C][C]1.3823[/C][C]1.3700755055274[/C][C]0.0122244944726024[/C][/ROW]
[ROW][C]40[/C][C]1.3812[/C][C]1.39004622905881[/C][C]-0.00884622905881249[/C][/ROW]
[ROW][C]41[/C][C]1.3732[/C][C]1.3864346474611[/C][C]-0.0132346474611018[/C][/ROW]
[ROW][C]42[/C][C]1.3592[/C][C]1.37467712583302[/C][C]-0.0154771258330157[/C][/ROW]
[ROW][C]43[/C][C]1.3539[/C][C]1.35628292982371[/C][C]-0.00238292982370791[/C][/ROW]
[ROW][C]44[/C][C]1.3316[/C][C]1.35030637909751[/C][C]-0.0187063790975095[/C][/ROW]
[ROW][C]45[/C][C]1.2901[/C][C]1.32269534801424[/C][C]-0.0325953480142365[/C][/ROW]
[ROW][C]46[/C][C]1.2673[/C][C]1.27194102329584[/C][C]-0.00464102329584382[/C][/ROW]
[ROW][C]47[/C][C]1.2472[/C][C]1.24782336481935[/C][C]-0.000623364819345884[/C][/ROW]
[ROW][C]48[/C][C]1.2331[/C][C]1.22754638188136[/C][C]0.00555361811864064[/C][/ROW]
[ROW][C]49[/C][C]1.1621[/C][C]1.21502314017857[/C][C]-0.0529231401785681[/C][/ROW]
[ROW][C]50[/C][C]1.135[/C][C]1.12899744006591[/C][C]0.00600255993408516[/C][/ROW]
[ROW][C]51[/C][C]1.0838[/C][C]1.10360165990573[/C][C]-0.0198016599057329[/C][/ROW]
[ROW][C]52[/C][C]1.0779[/C][C]1.04677966161779[/C][C]0.0311203383822063[/C][/ROW]
[ROW][C]53[/C][C]1.115[/C][C]1.04971520823044[/C][C]0.0652847917695607[/C][/ROW]
[ROW][C]54[/C][C]1.1213[/C][C]1.10535057290715[/C][C]0.0159494270928504[/C][/ROW]
[ROW][C]55[/C][C]1.0996[/C][C]1.11617886256754[/C][C]-0.016578862567536[/C][/ROW]
[ROW][C]56[/C][C]1.1139[/C][C]1.08977186641598[/C][C]0.0241281335840182[/C][/ROW]
[ROW][C]57[/C][C]1.1221[/C][C]1.11092221766665[/C][C]0.0111777823333512[/C][/ROW]
[ROW][C]58[/C][C]1.1235[/C][C]1.12229576339161[/C][C]0.00120423660838531[/C][/ROW]
[ROW][C]59[/C][C]1.0736[/C][C]1.12403766483739[/C][C]-0.0504376648373945[/C][/ROW]
[ROW][C]60[/C][C]1.0877[/C][C]1.0598176297134[/C][C]0.0278823702866[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	1.3999	1.3938	0.00609999999999999
4	1.4442	1.43053188458542	0.0136681154145819
5	1.4349	1.47871247448677	-0.0438124744867672
6	1.4388	1.45697343363223	-0.0181734336322334
7	1.4264	1.4557137140303	-0.0293137140303019
8	1.4343	1.43499109608433	-0.000691096084328935
9	1.377	1.44269488318999	-0.0656948831899857
10	1.3706	1.36674308720022	0.00385691279978118
11	1.3556	1.36143812454862	-0.00583812454861943
12	1.3179	1.34478059046444	-0.026880590464438
13	1.2905	1.29944877402636	-0.00894877402635674
14	1.3224	1.26950807832232	0.0528919216776822
15	1.3201	1.3164249150185	0.00367508498149882
16	1.3162	1.3151683286299	0.00103167137009552
17	1.2789	1.31156123612877	-0.032661236128771
18	1.2526	1.26498820475301	-0.0123882047530137
19	1.2288	1.23517100133453	-0.00637100133453061
20	1.24	1.20956217526814	0.0304378247318551
21	1.2856	1.22940394567253	0.0561960543274687
22	1.2974	1.29095887686123	0.00644112313876999
23	1.2828	1.30458761159513	-0.0217876115951343
24	1.3119	1.28380177082879	0.0280982291712084
25	1.3288	1.3208792937762	0.00792070622380492
26	1.3359	1.34002810509007	-0.00412810509006922
27	1.2964	1.3459560720454	-0.0495560720454011
28	1.3026	1.29238633478486	0.0102136652151399
29	1.2982	1.30148615271055	-0.0032861527105521
30	1.3189	1.29615316300158	0.0227468369984207
31	1.308	1.32331134273348	-0.0153113427334779
32	1.331	1.30806421511673	0.0229357848832701
33	1.3348	1.33757604008293	-0.00277604008292665
34	1.3635	1.34058787925864	0.0229121207413558
35	1.3493	1.37579298560802	-0.02649298560802
36	1.3704	1.3540712161988	0.0163287838011987
37	1.361	1.37980721111092	-0.0188072111109197
38	1.3658	1.36506755225556	0.000732447744441922
39	1.3823	1.3700755055274	0.0122244944726024
40	1.3812	1.39004622905881	-0.00884622905881249
41	1.3732	1.3864346474611	-0.0132346474611018
42	1.3592	1.37467712583302	-0.0154771258330157
43	1.3539	1.35628292982371	-0.00238292982370791
44	1.3316	1.35030637909751	-0.0187063790975095
45	1.2901	1.32269534801424	-0.0325953480142365
46	1.2673	1.27194102329584	-0.00464102329584382
47	1.2472	1.24782336481935	-0.000623364819345884
48	1.2331	1.22754638188136	0.00555361811864064
49	1.1621	1.21502314017857	-0.0529231401785681
50	1.135	1.12899744006591	0.00600255993408516
51	1.0838	1.10360165990573	-0.0198016599057329
52	1.0779	1.04677966161779	0.0311203383822063
53	1.115	1.04971520823044	0.0652847917695607
54	1.1213	1.10535057290715	0.0159494270928504
55	1.0996	1.11617886256754	-0.016578862567536
56	1.1139	1.08977186641598	0.0241281335840182
57	1.1221	1.11092221766665	0.0111777823333512
58	1.1235	1.12229576339161	0.00120423660838531
59	1.0736	1.12403766483739	-0.0504376648373945
60	1.0877	1.0598176297134	0.0278823702866

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	1.0818338669764	1.03081557669418	1.13285215725861
62	1.07596773395279	0.992940438779063	1.15899502912652
63	1.07010160092919	0.954812307789235	1.18539089406915
64	1.06423546790559	0.915182598892847	1.21328833691833
65	1.05836933488198	0.873738445268148	1.24300022449582
66	1.05250320185838	0.830407124135727	1.27459927958104
67	1.04663706883478	0.785197422850134	1.30807671481942
68	1.04077093581118	0.738148644218112	1.34339322740424
69	1.03490480278757	0.689311139535125	1.38049846604002
70	1.02903866976397	0.638738146657381	1.41933919287056
71	1.02317253674037	0.586482223301651	1.45986285017908
72	1.01730640371676	0.532593707026135	1.50201910040739

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 1.0818338669764 & 1.03081557669418 & 1.13285215725861 \tabularnewline
62 & 1.07596773395279 & 0.992940438779063 & 1.15899502912652 \tabularnewline
63 & 1.07010160092919 & 0.954812307789235 & 1.18539089406915 \tabularnewline
64 & 1.06423546790559 & 0.915182598892847 & 1.21328833691833 \tabularnewline
65 & 1.05836933488198 & 0.873738445268148 & 1.24300022449582 \tabularnewline
66 & 1.05250320185838 & 0.830407124135727 & 1.27459927958104 \tabularnewline
67 & 1.04663706883478 & 0.785197422850134 & 1.30807671481942 \tabularnewline
68 & 1.04077093581118 & 0.738148644218112 & 1.34339322740424 \tabularnewline
69 & 1.03490480278757 & 0.689311139535125 & 1.38049846604002 \tabularnewline
70 & 1.02903866976397 & 0.638738146657381 & 1.41933919287056 \tabularnewline
71 & 1.02317253674037 & 0.586482223301651 & 1.45986285017908 \tabularnewline
72 & 1.01730640371676 & 0.532593707026135 & 1.50201910040739 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]1.0818338669764[/C][C]1.03081557669418[/C][C]1.13285215725861[/C][/ROW]
[ROW][C]62[/C][C]1.07596773395279[/C][C]0.992940438779063[/C][C]1.15899502912652[/C][/ROW]
[ROW][C]63[/C][C]1.07010160092919[/C][C]0.954812307789235[/C][C]1.18539089406915[/C][/ROW]
[ROW][C]64[/C][C]1.06423546790559[/C][C]0.915182598892847[/C][C]1.21328833691833[/C][/ROW]
[ROW][C]65[/C][C]1.05836933488198[/C][C]0.873738445268148[/C][C]1.24300022449582[/C][/ROW]
[ROW][C]66[/C][C]1.05250320185838[/C][C]0.830407124135727[/C][C]1.27459927958104[/C][/ROW]
[ROW][C]67[/C][C]1.04663706883478[/C][C]0.785197422850134[/C][C]1.30807671481942[/C][/ROW]
[ROW][C]68[/C][C]1.04077093581118[/C][C]0.738148644218112[/C][C]1.34339322740424[/C][/ROW]
[ROW][C]69[/C][C]1.03490480278757[/C][C]0.689311139535125[/C][C]1.38049846604002[/C][/ROW]
[ROW][C]70[/C][C]1.02903866976397[/C][C]0.638738146657381[/C][C]1.41933919287056[/C][/ROW]
[ROW][C]71[/C][C]1.02317253674037[/C][C]0.586482223301651[/C][C]1.45986285017908[/C][/ROW]
[ROW][C]72[/C][C]1.01730640371676[/C][C]0.532593707026135[/C][C]1.50201910040739[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	1.0818338669764	1.03081557669418	1.13285215725861
62	1.07596773395279	0.992940438779063	1.15899502912652
63	1.07010160092919	0.954812307789235	1.18539089406915
64	1.06423546790559	0.915182598892847	1.21328833691833
65	1.05836933488198	0.873738445268148	1.24300022449582
66	1.05250320185838	0.830407124135727	1.27459927958104
67	1.04663706883478	0.785197422850134	1.30807671481942
68	1.04077093581118	0.738148644218112	1.34339322740424
69	1.03490480278757	0.689311139535125	1.38049846604002
70	1.02903866976397	0.638738146657381	1.41933919287056
71	1.02317253674037	0.586482223301651	1.45986285017908
72	1.01730640371676	0.532593707026135	1.50201910040739

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