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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Thu, 28 Apr 2016 11:15:04 +0100

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/2016/Apr/28/t1461838518x523dbld6n83wgs.htm/, Retrieved Sat, 04 May 2024 17:58:19 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=295013, Retrieved Sat, 04 May 2024 17:58:19 +0000

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No (this computation is public)

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Estimated Impact

133

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

-       [Exponential Smoothing] [] [2016-04-28 10:15:04] [aeeb828bd20a6dc3c22e186b82add773] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295013&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295013&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295013&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	'Gwilym Jenkins' @ jenkins.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0
gamma	0.468873000282372

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.468873000282372 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295013&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[/C][/ROW]
[ROW][C]gamma[/C][C]0.468873000282372[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295013&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295013&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
gamma	0.468873000282372

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	0.8766	0.853247676282052	0.0233523237179483
14	0.9188	0.910075422494172	0.00872457750582767
15	0.9838	0.970621255827506	0.0131787441724941
16	0.9994	0.985746255827506	0.0136537441724943
17	1.0731	1.05922958916084	0.013870410839161
18	1.1372	1.12042542249417	0.0167745775058277
19	1.1248	1.05716292249417	0.0676370775058277
20	1.189	1.11765042249417	0.0713495775058277
21	1.2497	1.26614208916084	-0.0164420891608392
22	1.2046	1.21709625582751	-0.0124962558275059
23	1.222	1.23418792249417	-0.0121879224941721
24	1.2977	1.22927958916084	0.0684204108391611
25	1.3113	1.27453792249417	0.0367620775058271
26	1.2594	1.34477542249417	-0.0853754224941718
27	1.2199	1.31122125582751	-0.0913212558275061
28	1.1884	1.22184625582751	-0.0334462558275055
29	1.2023	1.24822958916084	-0.0459295891608391
30	1.2582	1.24962542249417	0.00857457750582769
31	1.2743	1.17816292249417	0.0961370775058277
32	1.2887	1.26715042249417	0.0215495775058276
33	1.3106	1.36584208916084	-0.0552420891608392
34	1.3481	1.27799625582751	0.0701037441724943
35	1.3738	1.37768792249417	-0.00388792249417236
36	1.4486	1.38107958916084	0.0675204108391612
37	1.4976	1.42543792249417	0.0721620775058271
38	1.5622	1.53107542249417	0.031124577505828
39	1.505	1.61402125582751	-0.109021255827506
40	1.318	1.50694625582751	-0.188946255827505
41	1.3029	1.37782958916084	-0.0749295891608392
42	1.3632	1.35022542249417	0.0129745775058276
43	1.4303	1.28316292249417	0.147137077505828
44	1.4779	1.42315042249417	0.0547495775058278
45	1.3829	1.55504208916084	-0.172142089160839
46	1.2708	1.35029625582751	-0.0794962558275059
47	1.291	1.30038792249417	-0.0093879224941722
48	1.3583	1.29827958916084	0.0600204108391611
49	1.368	1.33513792249417	0.0328620775058273
50	1.4391	1.40147542249417	0.0376245775058279
51	1.4127	1.49092125582751	-0.0782212558275059
52	1.3482	1.41464625582751	-0.0664462558275054
53	1.3108	1.40802958916084	-0.0972295891608392
54	1.2814	1.35812542249417	-0.0767254224941722
55	1.2502	1.20136292249417	0.0488370775058276
56	1.2967	1.24305042249417	0.0536495775058277
57	1.3206	1.37384208916084	-0.0532420891608392
58	1.3062	1.28799625582751	0.0182037441724943
59	1.3242	1.33578792249417	-0.0115879224941722
60	1.361	1.33147958916084	0.0295204108391609
61	1.3696	1.33783792249417	0.0317620775058272
62	1.3711	1.40307542249417	-0.031975422494172
63	1.3256	1.42292125582751	-0.0973212558275061
64	1.2498	1.32754625582751	-0.0777462558275053
65	1.1261	1.30962958916084	-0.183529589160839
66	1.1053	1.17342542249417	-0.0681254224941725
67	1.1117	1.02526292249417	0.0864370775058276
68	1.0953	1.10455042249417	-0.00925042249417229

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 0.8766 & 0.853247676282052 & 0.0233523237179483 \tabularnewline
14 & 0.9188 & 0.910075422494172 & 0.00872457750582767 \tabularnewline
15 & 0.9838 & 0.970621255827506 & 0.0131787441724941 \tabularnewline
16 & 0.9994 & 0.985746255827506 & 0.0136537441724943 \tabularnewline
17 & 1.0731 & 1.05922958916084 & 0.013870410839161 \tabularnewline
18 & 1.1372 & 1.12042542249417 & 0.0167745775058277 \tabularnewline
19 & 1.1248 & 1.05716292249417 & 0.0676370775058277 \tabularnewline
20 & 1.189 & 1.11765042249417 & 0.0713495775058277 \tabularnewline
21 & 1.2497 & 1.26614208916084 & -0.0164420891608392 \tabularnewline
22 & 1.2046 & 1.21709625582751 & -0.0124962558275059 \tabularnewline
23 & 1.222 & 1.23418792249417 & -0.0121879224941721 \tabularnewline
24 & 1.2977 & 1.22927958916084 & 0.0684204108391611 \tabularnewline
25 & 1.3113 & 1.27453792249417 & 0.0367620775058271 \tabularnewline
26 & 1.2594 & 1.34477542249417 & -0.0853754224941718 \tabularnewline
27 & 1.2199 & 1.31122125582751 & -0.0913212558275061 \tabularnewline
28 & 1.1884 & 1.22184625582751 & -0.0334462558275055 \tabularnewline
29 & 1.2023 & 1.24822958916084 & -0.0459295891608391 \tabularnewline
30 & 1.2582 & 1.24962542249417 & 0.00857457750582769 \tabularnewline
31 & 1.2743 & 1.17816292249417 & 0.0961370775058277 \tabularnewline
32 & 1.2887 & 1.26715042249417 & 0.0215495775058276 \tabularnewline
33 & 1.3106 & 1.36584208916084 & -0.0552420891608392 \tabularnewline
34 & 1.3481 & 1.27799625582751 & 0.0701037441724943 \tabularnewline
35 & 1.3738 & 1.37768792249417 & -0.00388792249417236 \tabularnewline
36 & 1.4486 & 1.38107958916084 & 0.0675204108391612 \tabularnewline
37 & 1.4976 & 1.42543792249417 & 0.0721620775058271 \tabularnewline
38 & 1.5622 & 1.53107542249417 & 0.031124577505828 \tabularnewline
39 & 1.505 & 1.61402125582751 & -0.109021255827506 \tabularnewline
40 & 1.318 & 1.50694625582751 & -0.188946255827505 \tabularnewline
41 & 1.3029 & 1.37782958916084 & -0.0749295891608392 \tabularnewline
42 & 1.3632 & 1.35022542249417 & 0.0129745775058276 \tabularnewline
43 & 1.4303 & 1.28316292249417 & 0.147137077505828 \tabularnewline
44 & 1.4779 & 1.42315042249417 & 0.0547495775058278 \tabularnewline
45 & 1.3829 & 1.55504208916084 & -0.172142089160839 \tabularnewline
46 & 1.2708 & 1.35029625582751 & -0.0794962558275059 \tabularnewline
47 & 1.291 & 1.30038792249417 & -0.0093879224941722 \tabularnewline
48 & 1.3583 & 1.29827958916084 & 0.0600204108391611 \tabularnewline
49 & 1.368 & 1.33513792249417 & 0.0328620775058273 \tabularnewline
50 & 1.4391 & 1.40147542249417 & 0.0376245775058279 \tabularnewline
51 & 1.4127 & 1.49092125582751 & -0.0782212558275059 \tabularnewline
52 & 1.3482 & 1.41464625582751 & -0.0664462558275054 \tabularnewline
53 & 1.3108 & 1.40802958916084 & -0.0972295891608392 \tabularnewline
54 & 1.2814 & 1.35812542249417 & -0.0767254224941722 \tabularnewline
55 & 1.2502 & 1.20136292249417 & 0.0488370775058276 \tabularnewline
56 & 1.2967 & 1.24305042249417 & 0.0536495775058277 \tabularnewline
57 & 1.3206 & 1.37384208916084 & -0.0532420891608392 \tabularnewline
58 & 1.3062 & 1.28799625582751 & 0.0182037441724943 \tabularnewline
59 & 1.3242 & 1.33578792249417 & -0.0115879224941722 \tabularnewline
60 & 1.361 & 1.33147958916084 & 0.0295204108391609 \tabularnewline
61 & 1.3696 & 1.33783792249417 & 0.0317620775058272 \tabularnewline
62 & 1.3711 & 1.40307542249417 & -0.031975422494172 \tabularnewline
63 & 1.3256 & 1.42292125582751 & -0.0973212558275061 \tabularnewline
64 & 1.2498 & 1.32754625582751 & -0.0777462558275053 \tabularnewline
65 & 1.1261 & 1.30962958916084 & -0.183529589160839 \tabularnewline
66 & 1.1053 & 1.17342542249417 & -0.0681254224941725 \tabularnewline
67 & 1.1117 & 1.02526292249417 & 0.0864370775058276 \tabularnewline
68 & 1.0953 & 1.10455042249417 & -0.00925042249417229 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295013&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]0.8766[/C][C]0.853247676282052[/C][C]0.0233523237179483[/C][/ROW]
[ROW][C]14[/C][C]0.9188[/C][C]0.910075422494172[/C][C]0.00872457750582767[/C][/ROW]
[ROW][C]15[/C][C]0.9838[/C][C]0.970621255827506[/C][C]0.0131787441724941[/C][/ROW]
[ROW][C]16[/C][C]0.9994[/C][C]0.985746255827506[/C][C]0.0136537441724943[/C][/ROW]
[ROW][C]17[/C][C]1.0731[/C][C]1.05922958916084[/C][C]0.013870410839161[/C][/ROW]
[ROW][C]18[/C][C]1.1372[/C][C]1.12042542249417[/C][C]0.0167745775058277[/C][/ROW]
[ROW][C]19[/C][C]1.1248[/C][C]1.05716292249417[/C][C]0.0676370775058277[/C][/ROW]
[ROW][C]20[/C][C]1.189[/C][C]1.11765042249417[/C][C]0.0713495775058277[/C][/ROW]
[ROW][C]21[/C][C]1.2497[/C][C]1.26614208916084[/C][C]-0.0164420891608392[/C][/ROW]
[ROW][C]22[/C][C]1.2046[/C][C]1.21709625582751[/C][C]-0.0124962558275059[/C][/ROW]
[ROW][C]23[/C][C]1.222[/C][C]1.23418792249417[/C][C]-0.0121879224941721[/C][/ROW]
[ROW][C]24[/C][C]1.2977[/C][C]1.22927958916084[/C][C]0.0684204108391611[/C][/ROW]
[ROW][C]25[/C][C]1.3113[/C][C]1.27453792249417[/C][C]0.0367620775058271[/C][/ROW]
[ROW][C]26[/C][C]1.2594[/C][C]1.34477542249417[/C][C]-0.0853754224941718[/C][/ROW]
[ROW][C]27[/C][C]1.2199[/C][C]1.31122125582751[/C][C]-0.0913212558275061[/C][/ROW]
[ROW][C]28[/C][C]1.1884[/C][C]1.22184625582751[/C][C]-0.0334462558275055[/C][/ROW]
[ROW][C]29[/C][C]1.2023[/C][C]1.24822958916084[/C][C]-0.0459295891608391[/C][/ROW]
[ROW][C]30[/C][C]1.2582[/C][C]1.24962542249417[/C][C]0.00857457750582769[/C][/ROW]
[ROW][C]31[/C][C]1.2743[/C][C]1.17816292249417[/C][C]0.0961370775058277[/C][/ROW]
[ROW][C]32[/C][C]1.2887[/C][C]1.26715042249417[/C][C]0.0215495775058276[/C][/ROW]
[ROW][C]33[/C][C]1.3106[/C][C]1.36584208916084[/C][C]-0.0552420891608392[/C][/ROW]
[ROW][C]34[/C][C]1.3481[/C][C]1.27799625582751[/C][C]0.0701037441724943[/C][/ROW]
[ROW][C]35[/C][C]1.3738[/C][C]1.37768792249417[/C][C]-0.00388792249417236[/C][/ROW]
[ROW][C]36[/C][C]1.4486[/C][C]1.38107958916084[/C][C]0.0675204108391612[/C][/ROW]
[ROW][C]37[/C][C]1.4976[/C][C]1.42543792249417[/C][C]0.0721620775058271[/C][/ROW]
[ROW][C]38[/C][C]1.5622[/C][C]1.53107542249417[/C][C]0.031124577505828[/C][/ROW]
[ROW][C]39[/C][C]1.505[/C][C]1.61402125582751[/C][C]-0.109021255827506[/C][/ROW]
[ROW][C]40[/C][C]1.318[/C][C]1.50694625582751[/C][C]-0.188946255827505[/C][/ROW]
[ROW][C]41[/C][C]1.3029[/C][C]1.37782958916084[/C][C]-0.0749295891608392[/C][/ROW]
[ROW][C]42[/C][C]1.3632[/C][C]1.35022542249417[/C][C]0.0129745775058276[/C][/ROW]
[ROW][C]43[/C][C]1.4303[/C][C]1.28316292249417[/C][C]0.147137077505828[/C][/ROW]
[ROW][C]44[/C][C]1.4779[/C][C]1.42315042249417[/C][C]0.0547495775058278[/C][/ROW]
[ROW][C]45[/C][C]1.3829[/C][C]1.55504208916084[/C][C]-0.172142089160839[/C][/ROW]
[ROW][C]46[/C][C]1.2708[/C][C]1.35029625582751[/C][C]-0.0794962558275059[/C][/ROW]
[ROW][C]47[/C][C]1.291[/C][C]1.30038792249417[/C][C]-0.0093879224941722[/C][/ROW]
[ROW][C]48[/C][C]1.3583[/C][C]1.29827958916084[/C][C]0.0600204108391611[/C][/ROW]
[ROW][C]49[/C][C]1.368[/C][C]1.33513792249417[/C][C]0.0328620775058273[/C][/ROW]
[ROW][C]50[/C][C]1.4391[/C][C]1.40147542249417[/C][C]0.0376245775058279[/C][/ROW]
[ROW][C]51[/C][C]1.4127[/C][C]1.49092125582751[/C][C]-0.0782212558275059[/C][/ROW]
[ROW][C]52[/C][C]1.3482[/C][C]1.41464625582751[/C][C]-0.0664462558275054[/C][/ROW]
[ROW][C]53[/C][C]1.3108[/C][C]1.40802958916084[/C][C]-0.0972295891608392[/C][/ROW]
[ROW][C]54[/C][C]1.2814[/C][C]1.35812542249417[/C][C]-0.0767254224941722[/C][/ROW]
[ROW][C]55[/C][C]1.2502[/C][C]1.20136292249417[/C][C]0.0488370775058276[/C][/ROW]
[ROW][C]56[/C][C]1.2967[/C][C]1.24305042249417[/C][C]0.0536495775058277[/C][/ROW]
[ROW][C]57[/C][C]1.3206[/C][C]1.37384208916084[/C][C]-0.0532420891608392[/C][/ROW]
[ROW][C]58[/C][C]1.3062[/C][C]1.28799625582751[/C][C]0.0182037441724943[/C][/ROW]
[ROW][C]59[/C][C]1.3242[/C][C]1.33578792249417[/C][C]-0.0115879224941722[/C][/ROW]
[ROW][C]60[/C][C]1.361[/C][C]1.33147958916084[/C][C]0.0295204108391609[/C][/ROW]
[ROW][C]61[/C][C]1.3696[/C][C]1.33783792249417[/C][C]0.0317620775058272[/C][/ROW]
[ROW][C]62[/C][C]1.3711[/C][C]1.40307542249417[/C][C]-0.031975422494172[/C][/ROW]
[ROW][C]63[/C][C]1.3256[/C][C]1.42292125582751[/C][C]-0.0973212558275061[/C][/ROW]
[ROW][C]64[/C][C]1.2498[/C][C]1.32754625582751[/C][C]-0.0777462558275053[/C][/ROW]
[ROW][C]65[/C][C]1.1261[/C][C]1.30962958916084[/C][C]-0.183529589160839[/C][/ROW]
[ROW][C]66[/C][C]1.1053[/C][C]1.17342542249417[/C][C]-0.0681254224941725[/C][/ROW]
[ROW][C]67[/C][C]1.1117[/C][C]1.02526292249417[/C][C]0.0864370775058276[/C][/ROW]
[ROW][C]68[/C][C]1.0953[/C][C]1.10455042249417[/C][C]-0.00925042249417229[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295013&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295013&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	0.8766	0.853247676282052	0.0233523237179483
14	0.9188	0.910075422494172	0.00872457750582767
15	0.9838	0.970621255827506	0.0131787441724941
16	0.9994	0.985746255827506	0.0136537441724943
17	1.0731	1.05922958916084	0.013870410839161
18	1.1372	1.12042542249417	0.0167745775058277
19	1.1248	1.05716292249417	0.0676370775058277
20	1.189	1.11765042249417	0.0713495775058277
21	1.2497	1.26614208916084	-0.0164420891608392
22	1.2046	1.21709625582751	-0.0124962558275059
23	1.222	1.23418792249417	-0.0121879224941721
24	1.2977	1.22927958916084	0.0684204108391611
25	1.3113	1.27453792249417	0.0367620775058271
26	1.2594	1.34477542249417	-0.0853754224941718
27	1.2199	1.31122125582751	-0.0913212558275061
28	1.1884	1.22184625582751	-0.0334462558275055
29	1.2023	1.24822958916084	-0.0459295891608391
30	1.2582	1.24962542249417	0.00857457750582769
31	1.2743	1.17816292249417	0.0961370775058277
32	1.2887	1.26715042249417	0.0215495775058276
33	1.3106	1.36584208916084	-0.0552420891608392
34	1.3481	1.27799625582751	0.0701037441724943
35	1.3738	1.37768792249417	-0.00388792249417236
36	1.4486	1.38107958916084	0.0675204108391612
37	1.4976	1.42543792249417	0.0721620775058271
38	1.5622	1.53107542249417	0.031124577505828
39	1.505	1.61402125582751	-0.109021255827506
40	1.318	1.50694625582751	-0.188946255827505
41	1.3029	1.37782958916084	-0.0749295891608392
42	1.3632	1.35022542249417	0.0129745775058276
43	1.4303	1.28316292249417	0.147137077505828
44	1.4779	1.42315042249417	0.0547495775058278
45	1.3829	1.55504208916084	-0.172142089160839
46	1.2708	1.35029625582751	-0.0794962558275059
47	1.291	1.30038792249417	-0.0093879224941722
48	1.3583	1.29827958916084	0.0600204108391611
49	1.368	1.33513792249417	0.0328620775058273
50	1.4391	1.40147542249417	0.0376245775058279
51	1.4127	1.49092125582751	-0.0782212558275059
52	1.3482	1.41464625582751	-0.0664462558275054
53	1.3108	1.40802958916084	-0.0972295891608392
54	1.2814	1.35812542249417	-0.0767254224941722
55	1.2502	1.20136292249417	0.0488370775058276
56	1.2967	1.24305042249417	0.0536495775058277
57	1.3206	1.37384208916084	-0.0532420891608392
58	1.3062	1.28799625582751	0.0182037441724943
59	1.3242	1.33578792249417	-0.0115879224941722
60	1.361	1.33147958916084	0.0295204108391609
61	1.3696	1.33783792249417	0.0317620775058272
62	1.3711	1.40307542249417	-0.031975422494172
63	1.3256	1.42292125582751	-0.0973212558275061
64	1.2498	1.32754625582751	-0.0777462558275053
65	1.1261	1.30962958916084	-0.183529589160839
66	1.1053	1.17342542249417	-0.0681254224941725
67	1.1117	1.02526292249417	0.0864370775058276
68	1.0953	1.10455042249417	-0.00925042249417229

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
69	1.17244208916084	1.03284361928772	1.31204055903396
70	1.13983834498835	0.942416295607242	1.33726039436945
71	1.16942626748252	0.927634625003394	1.41121790996164
72	1.17670585664336	0.897508916897109	1.4559027963896
73	1.15354377913753	0.841392110946268	1.46569544732879
74	1.1870192016317	0.845074181569258	1.52896422169414
75	1.23884045745921	0.86949762276978	1.60818329214864
76	1.24078671328671	0.845942614524506	1.63563081204892
77	1.30061630244755	0.881820892828181	1.71941171206692
78	1.34794172494172	0.906492602268257	1.78939084761519
79	1.2679046474359	0.804908901559013	1.73090039331278
80	1.26075506993007	0.777171784971822	1.74433835488832

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
69 & 1.17244208916084 & 1.03284361928772 & 1.31204055903396 \tabularnewline
70 & 1.13983834498835 & 0.942416295607242 & 1.33726039436945 \tabularnewline
71 & 1.16942626748252 & 0.927634625003394 & 1.41121790996164 \tabularnewline
72 & 1.17670585664336 & 0.897508916897109 & 1.4559027963896 \tabularnewline
73 & 1.15354377913753 & 0.841392110946268 & 1.46569544732879 \tabularnewline
74 & 1.1870192016317 & 0.845074181569258 & 1.52896422169414 \tabularnewline
75 & 1.23884045745921 & 0.86949762276978 & 1.60818329214864 \tabularnewline
76 & 1.24078671328671 & 0.845942614524506 & 1.63563081204892 \tabularnewline
77 & 1.30061630244755 & 0.881820892828181 & 1.71941171206692 \tabularnewline
78 & 1.34794172494172 & 0.906492602268257 & 1.78939084761519 \tabularnewline
79 & 1.2679046474359 & 0.804908901559013 & 1.73090039331278 \tabularnewline
80 & 1.26075506993007 & 0.777171784971822 & 1.74433835488832 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295013&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]69[/C][C]1.17244208916084[/C][C]1.03284361928772[/C][C]1.31204055903396[/C][/ROW]
[ROW][C]70[/C][C]1.13983834498835[/C][C]0.942416295607242[/C][C]1.33726039436945[/C][/ROW]
[ROW][C]71[/C][C]1.16942626748252[/C][C]0.927634625003394[/C][C]1.41121790996164[/C][/ROW]
[ROW][C]72[/C][C]1.17670585664336[/C][C]0.897508916897109[/C][C]1.4559027963896[/C][/ROW]
[ROW][C]73[/C][C]1.15354377913753[/C][C]0.841392110946268[/C][C]1.46569544732879[/C][/ROW]
[ROW][C]74[/C][C]1.1870192016317[/C][C]0.845074181569258[/C][C]1.52896422169414[/C][/ROW]
[ROW][C]75[/C][C]1.23884045745921[/C][C]0.86949762276978[/C][C]1.60818329214864[/C][/ROW]
[ROW][C]76[/C][C]1.24078671328671[/C][C]0.845942614524506[/C][C]1.63563081204892[/C][/ROW]
[ROW][C]77[/C][C]1.30061630244755[/C][C]0.881820892828181[/C][C]1.71941171206692[/C][/ROW]
[ROW][C]78[/C][C]1.34794172494172[/C][C]0.906492602268257[/C][C]1.78939084761519[/C][/ROW]
[ROW][C]79[/C][C]1.2679046474359[/C][C]0.804908901559013[/C][C]1.73090039331278[/C][/ROW]
[ROW][C]80[/C][C]1.26075506993007[/C][C]0.777171784971822[/C][C]1.74433835488832[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295013&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295013&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
69	1.17244208916084	1.03284361928772	1.31204055903396
70	1.13983834498835	0.942416295607242	1.33726039436945
71	1.16942626748252	0.927634625003394	1.41121790996164
72	1.17670585664336	0.897508916897109	1.4559027963896
73	1.15354377913753	0.841392110946268	1.46569544732879
74	1.1870192016317	0.845074181569258	1.52896422169414
75	1.23884045745921	0.86949762276978	1.60818329214864
76	1.24078671328671	0.845942614524506	1.63563081204892
77	1.30061630244755	0.881820892828181	1.71941171206692
78	1.34794172494172	0.906492602268257	1.78939084761519
79	1.2679046474359	0.804908901559013	1.73090039331278
80	1.26075506993007	0.777171784971822	1.74433835488832

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 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = additive ;

R code (references can be found in the software module):

par3 <- 'additive'
par2 <- 'Single'
par1 <- '12'
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