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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sun, 15 Jan 2012 13:43:43 -0500

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/Jan/15/t1326653078s44w88rm077cqu4.htm/, Retrieved Fri, 03 May 2024 05:49:31 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=161115, Retrieved Fri, 03 May 2024 05:49:31 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W102

Estimated Impact

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

-       [Exponential Smoothing] [] [2012-01-15 18:43:43] [618e20b48371a4632e04cdc6ff96552f] [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	2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161115&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]2 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=161115&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161115&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	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.964788833633748
beta	1
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.964788833633748 \tabularnewline
beta & 1 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161115&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]0.964788833633748[/C][/ROW]
[ROW][C]beta[/C][C]1[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161115&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161115&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	0.964788833633748
beta	1
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	99.8	99.6726228632479	0.127377136752116
14	99.9	99.986894703883	-0.0868947038830328
15	100	99.9897710919696	0.0102289080303564
16	100.2	100.192053325894	0.00794667410625038
17	100.2	100.228967215121	-0.0289672151210425
18	100.2	100.243986417192	-0.0439864171922721
19	100.2	99.7937443233431	0.406255676656883
20	100.1	100.38234171451	-0.282341714510395
21	100.2	100.109187898381	0.0908121016185106
22	100.1	100.541996552215	-0.441996552215301
23	99.9	100.200990694952	-0.300990694951523
24	99.8	99.7889665860693	0.0110334139307326
25	99.9	99.4764431987051	0.423556801294907
26	99.8	99.8418641157333	-0.0418641157333326
27	99.8	99.7079933614357	0.0920066385642855
28	99.9	99.8843797310993	0.0156202689006903
29	99.9	99.8300868909737	0.069913109026345
30	99.9	99.9380641677994	-0.0380641677993765
31	99.9	99.5131913491642	0.386808650835818
32	100	100.043819882171	-0.0438198821706806
33	100.1	100.229091380479	-0.12909138047867
34	100.2	100.43398130507	-0.233981305069619
35	100.4	100.502324512761	-0.102324512761228
36	100.6	100.688322261668	-0.0883222616677273
37	101	100.593974021958	0.40602597804228
38	101.3	101.208686805016	0.0913131949836981
39	101.5	101.619099182555	-0.119099182554862
40	101.6	101.796532225348	-0.196532225348321
41	101.7	101.542195249722	0.157804750278146
42	102.1	101.81869077654	0.281309223459502
43	102.6	102.112557370501	0.487442629499114
44	102.8	103.217855311834	-0.417855311834415
45	102.8	103.17113569173	-0.371135691729521
46	102.5	103.03716561868	-0.537165618680092
47	102.1	102.423481882664	-0.323481882664268
48	101.8	101.789078452627	0.0109215473733855
49	101.5	101.29611137499	0.203888625010435
50	101.3	100.997928296947	0.302071703053031
51	101.5	101.100812123738	0.399187876262204
52	101.7	101.772136652011	-0.0721366520110678
53	101.9	101.76688764107	0.133112358930106
54	102	102.116681903922	-0.116681903921631
55	101.9	101.7426248473	0.157375152700297
56	102	101.887950907634	0.112049092365794
57	102.3	102.255718175362	0.0442818246377357
58	102.8	102.819078340558	-0.0190783405583375
59	103.6	103.514994464218	0.0850055357815762
60	104.2	104.4828049543	-0.282804954299834
61	104.4	104.626199459938	-0.226199459937561
62	104.6	104.414536195274	0.1854638047257
63	104.8	104.793842453878	0.00615754612181263
64	105.2	105.075693404477	0.124306595522697
65	105.8	105.463037536436	0.336962463564234
66	106.1	106.393220695479	-0.293220695478581
67	106.2	106.080680336728	0.119319663271867
68	106.4	106.373168875148	0.0268311248523077
69	106.9	106.759589264169	0.140410735831097
70	107.4	107.609463273578	-0.209463273577995
71	108	108.137682526407	-0.137682526406977
72	108.5	108.675167540517	-0.175167540517293
73	108.9	108.825722457601	0.0742775423990452

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 99.8 & 99.6726228632479 & 0.127377136752116 \tabularnewline
14 & 99.9 & 99.986894703883 & -0.0868947038830328 \tabularnewline
15 & 100 & 99.9897710919696 & 0.0102289080303564 \tabularnewline
16 & 100.2 & 100.192053325894 & 0.00794667410625038 \tabularnewline
17 & 100.2 & 100.228967215121 & -0.0289672151210425 \tabularnewline
18 & 100.2 & 100.243986417192 & -0.0439864171922721 \tabularnewline
19 & 100.2 & 99.7937443233431 & 0.406255676656883 \tabularnewline
20 & 100.1 & 100.38234171451 & -0.282341714510395 \tabularnewline
21 & 100.2 & 100.109187898381 & 0.0908121016185106 \tabularnewline
22 & 100.1 & 100.541996552215 & -0.441996552215301 \tabularnewline
23 & 99.9 & 100.200990694952 & -0.300990694951523 \tabularnewline
24 & 99.8 & 99.7889665860693 & 0.0110334139307326 \tabularnewline
25 & 99.9 & 99.4764431987051 & 0.423556801294907 \tabularnewline
26 & 99.8 & 99.8418641157333 & -0.0418641157333326 \tabularnewline
27 & 99.8 & 99.7079933614357 & 0.0920066385642855 \tabularnewline
28 & 99.9 & 99.8843797310993 & 0.0156202689006903 \tabularnewline
29 & 99.9 & 99.8300868909737 & 0.069913109026345 \tabularnewline
30 & 99.9 & 99.9380641677994 & -0.0380641677993765 \tabularnewline
31 & 99.9 & 99.5131913491642 & 0.386808650835818 \tabularnewline
32 & 100 & 100.043819882171 & -0.0438198821706806 \tabularnewline
33 & 100.1 & 100.229091380479 & -0.12909138047867 \tabularnewline
34 & 100.2 & 100.43398130507 & -0.233981305069619 \tabularnewline
35 & 100.4 & 100.502324512761 & -0.102324512761228 \tabularnewline
36 & 100.6 & 100.688322261668 & -0.0883222616677273 \tabularnewline
37 & 101 & 100.593974021958 & 0.40602597804228 \tabularnewline
38 & 101.3 & 101.208686805016 & 0.0913131949836981 \tabularnewline
39 & 101.5 & 101.619099182555 & -0.119099182554862 \tabularnewline
40 & 101.6 & 101.796532225348 & -0.196532225348321 \tabularnewline
41 & 101.7 & 101.542195249722 & 0.157804750278146 \tabularnewline
42 & 102.1 & 101.81869077654 & 0.281309223459502 \tabularnewline
43 & 102.6 & 102.112557370501 & 0.487442629499114 \tabularnewline
44 & 102.8 & 103.217855311834 & -0.417855311834415 \tabularnewline
45 & 102.8 & 103.17113569173 & -0.371135691729521 \tabularnewline
46 & 102.5 & 103.03716561868 & -0.537165618680092 \tabularnewline
47 & 102.1 & 102.423481882664 & -0.323481882664268 \tabularnewline
48 & 101.8 & 101.789078452627 & 0.0109215473733855 \tabularnewline
49 & 101.5 & 101.29611137499 & 0.203888625010435 \tabularnewline
50 & 101.3 & 100.997928296947 & 0.302071703053031 \tabularnewline
51 & 101.5 & 101.100812123738 & 0.399187876262204 \tabularnewline
52 & 101.7 & 101.772136652011 & -0.0721366520110678 \tabularnewline
53 & 101.9 & 101.76688764107 & 0.133112358930106 \tabularnewline
54 & 102 & 102.116681903922 & -0.116681903921631 \tabularnewline
55 & 101.9 & 101.7426248473 & 0.157375152700297 \tabularnewline
56 & 102 & 101.887950907634 & 0.112049092365794 \tabularnewline
57 & 102.3 & 102.255718175362 & 0.0442818246377357 \tabularnewline
58 & 102.8 & 102.819078340558 & -0.0190783405583375 \tabularnewline
59 & 103.6 & 103.514994464218 & 0.0850055357815762 \tabularnewline
60 & 104.2 & 104.4828049543 & -0.282804954299834 \tabularnewline
61 & 104.4 & 104.626199459938 & -0.226199459937561 \tabularnewline
62 & 104.6 & 104.414536195274 & 0.1854638047257 \tabularnewline
63 & 104.8 & 104.793842453878 & 0.00615754612181263 \tabularnewline
64 & 105.2 & 105.075693404477 & 0.124306595522697 \tabularnewline
65 & 105.8 & 105.463037536436 & 0.336962463564234 \tabularnewline
66 & 106.1 & 106.393220695479 & -0.293220695478581 \tabularnewline
67 & 106.2 & 106.080680336728 & 0.119319663271867 \tabularnewline
68 & 106.4 & 106.373168875148 & 0.0268311248523077 \tabularnewline
69 & 106.9 & 106.759589264169 & 0.140410735831097 \tabularnewline
70 & 107.4 & 107.609463273578 & -0.209463273577995 \tabularnewline
71 & 108 & 108.137682526407 & -0.137682526406977 \tabularnewline
72 & 108.5 & 108.675167540517 & -0.175167540517293 \tabularnewline
73 & 108.9 & 108.825722457601 & 0.0742775423990452 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161115&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]99.8[/C][C]99.6726228632479[/C][C]0.127377136752116[/C][/ROW]
[ROW][C]14[/C][C]99.9[/C][C]99.986894703883[/C][C]-0.0868947038830328[/C][/ROW]
[ROW][C]15[/C][C]100[/C][C]99.9897710919696[/C][C]0.0102289080303564[/C][/ROW]
[ROW][C]16[/C][C]100.2[/C][C]100.192053325894[/C][C]0.00794667410625038[/C][/ROW]
[ROW][C]17[/C][C]100.2[/C][C]100.228967215121[/C][C]-0.0289672151210425[/C][/ROW]
[ROW][C]18[/C][C]100.2[/C][C]100.243986417192[/C][C]-0.0439864171922721[/C][/ROW]
[ROW][C]19[/C][C]100.2[/C][C]99.7937443233431[/C][C]0.406255676656883[/C][/ROW]
[ROW][C]20[/C][C]100.1[/C][C]100.38234171451[/C][C]-0.282341714510395[/C][/ROW]
[ROW][C]21[/C][C]100.2[/C][C]100.109187898381[/C][C]0.0908121016185106[/C][/ROW]
[ROW][C]22[/C][C]100.1[/C][C]100.541996552215[/C][C]-0.441996552215301[/C][/ROW]
[ROW][C]23[/C][C]99.9[/C][C]100.200990694952[/C][C]-0.300990694951523[/C][/ROW]
[ROW][C]24[/C][C]99.8[/C][C]99.7889665860693[/C][C]0.0110334139307326[/C][/ROW]
[ROW][C]25[/C][C]99.9[/C][C]99.4764431987051[/C][C]0.423556801294907[/C][/ROW]
[ROW][C]26[/C][C]99.8[/C][C]99.8418641157333[/C][C]-0.0418641157333326[/C][/ROW]
[ROW][C]27[/C][C]99.8[/C][C]99.7079933614357[/C][C]0.0920066385642855[/C][/ROW]
[ROW][C]28[/C][C]99.9[/C][C]99.8843797310993[/C][C]0.0156202689006903[/C][/ROW]
[ROW][C]29[/C][C]99.9[/C][C]99.8300868909737[/C][C]0.069913109026345[/C][/ROW]
[ROW][C]30[/C][C]99.9[/C][C]99.9380641677994[/C][C]-0.0380641677993765[/C][/ROW]
[ROW][C]31[/C][C]99.9[/C][C]99.5131913491642[/C][C]0.386808650835818[/C][/ROW]
[ROW][C]32[/C][C]100[/C][C]100.043819882171[/C][C]-0.0438198821706806[/C][/ROW]
[ROW][C]33[/C][C]100.1[/C][C]100.229091380479[/C][C]-0.12909138047867[/C][/ROW]
[ROW][C]34[/C][C]100.2[/C][C]100.43398130507[/C][C]-0.233981305069619[/C][/ROW]
[ROW][C]35[/C][C]100.4[/C][C]100.502324512761[/C][C]-0.102324512761228[/C][/ROW]
[ROW][C]36[/C][C]100.6[/C][C]100.688322261668[/C][C]-0.0883222616677273[/C][/ROW]
[ROW][C]37[/C][C]101[/C][C]100.593974021958[/C][C]0.40602597804228[/C][/ROW]
[ROW][C]38[/C][C]101.3[/C][C]101.208686805016[/C][C]0.0913131949836981[/C][/ROW]
[ROW][C]39[/C][C]101.5[/C][C]101.619099182555[/C][C]-0.119099182554862[/C][/ROW]
[ROW][C]40[/C][C]101.6[/C][C]101.796532225348[/C][C]-0.196532225348321[/C][/ROW]
[ROW][C]41[/C][C]101.7[/C][C]101.542195249722[/C][C]0.157804750278146[/C][/ROW]
[ROW][C]42[/C][C]102.1[/C][C]101.81869077654[/C][C]0.281309223459502[/C][/ROW]
[ROW][C]43[/C][C]102.6[/C][C]102.112557370501[/C][C]0.487442629499114[/C][/ROW]
[ROW][C]44[/C][C]102.8[/C][C]103.217855311834[/C][C]-0.417855311834415[/C][/ROW]
[ROW][C]45[/C][C]102.8[/C][C]103.17113569173[/C][C]-0.371135691729521[/C][/ROW]
[ROW][C]46[/C][C]102.5[/C][C]103.03716561868[/C][C]-0.537165618680092[/C][/ROW]
[ROW][C]47[/C][C]102.1[/C][C]102.423481882664[/C][C]-0.323481882664268[/C][/ROW]
[ROW][C]48[/C][C]101.8[/C][C]101.789078452627[/C][C]0.0109215473733855[/C][/ROW]
[ROW][C]49[/C][C]101.5[/C][C]101.29611137499[/C][C]0.203888625010435[/C][/ROW]
[ROW][C]50[/C][C]101.3[/C][C]100.997928296947[/C][C]0.302071703053031[/C][/ROW]
[ROW][C]51[/C][C]101.5[/C][C]101.100812123738[/C][C]0.399187876262204[/C][/ROW]
[ROW][C]52[/C][C]101.7[/C][C]101.772136652011[/C][C]-0.0721366520110678[/C][/ROW]
[ROW][C]53[/C][C]101.9[/C][C]101.76688764107[/C][C]0.133112358930106[/C][/ROW]
[ROW][C]54[/C][C]102[/C][C]102.116681903922[/C][C]-0.116681903921631[/C][/ROW]
[ROW][C]55[/C][C]101.9[/C][C]101.7426248473[/C][C]0.157375152700297[/C][/ROW]
[ROW][C]56[/C][C]102[/C][C]101.887950907634[/C][C]0.112049092365794[/C][/ROW]
[ROW][C]57[/C][C]102.3[/C][C]102.255718175362[/C][C]0.0442818246377357[/C][/ROW]
[ROW][C]58[/C][C]102.8[/C][C]102.819078340558[/C][C]-0.0190783405583375[/C][/ROW]
[ROW][C]59[/C][C]103.6[/C][C]103.514994464218[/C][C]0.0850055357815762[/C][/ROW]
[ROW][C]60[/C][C]104.2[/C][C]104.4828049543[/C][C]-0.282804954299834[/C][/ROW]
[ROW][C]61[/C][C]104.4[/C][C]104.626199459938[/C][C]-0.226199459937561[/C][/ROW]
[ROW][C]62[/C][C]104.6[/C][C]104.414536195274[/C][C]0.1854638047257[/C][/ROW]
[ROW][C]63[/C][C]104.8[/C][C]104.793842453878[/C][C]0.00615754612181263[/C][/ROW]
[ROW][C]64[/C][C]105.2[/C][C]105.075693404477[/C][C]0.124306595522697[/C][/ROW]
[ROW][C]65[/C][C]105.8[/C][C]105.463037536436[/C][C]0.336962463564234[/C][/ROW]
[ROW][C]66[/C][C]106.1[/C][C]106.393220695479[/C][C]-0.293220695478581[/C][/ROW]
[ROW][C]67[/C][C]106.2[/C][C]106.080680336728[/C][C]0.119319663271867[/C][/ROW]
[ROW][C]68[/C][C]106.4[/C][C]106.373168875148[/C][C]0.0268311248523077[/C][/ROW]
[ROW][C]69[/C][C]106.9[/C][C]106.759589264169[/C][C]0.140410735831097[/C][/ROW]
[ROW][C]70[/C][C]107.4[/C][C]107.609463273578[/C][C]-0.209463273577995[/C][/ROW]
[ROW][C]71[/C][C]108[/C][C]108.137682526407[/C][C]-0.137682526406977[/C][/ROW]
[ROW][C]72[/C][C]108.5[/C][C]108.675167540517[/C][C]-0.175167540517293[/C][/ROW]
[ROW][C]73[/C][C]108.9[/C][C]108.825722457601[/C][C]0.0742775423990452[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161115&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161115&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	99.8	99.6726228632479	0.127377136752116
14	99.9	99.986894703883	-0.0868947038830328
15	100	99.9897710919696	0.0102289080303564
16	100.2	100.192053325894	0.00794667410625038
17	100.2	100.228967215121	-0.0289672151210425
18	100.2	100.243986417192	-0.0439864171922721
19	100.2	99.7937443233431	0.406255676656883
20	100.1	100.38234171451	-0.282341714510395
21	100.2	100.109187898381	0.0908121016185106
22	100.1	100.541996552215	-0.441996552215301
23	99.9	100.200990694952	-0.300990694951523
24	99.8	99.7889665860693	0.0110334139307326
25	99.9	99.4764431987051	0.423556801294907
26	99.8	99.8418641157333	-0.0418641157333326
27	99.8	99.7079933614357	0.0920066385642855
28	99.9	99.8843797310993	0.0156202689006903
29	99.9	99.8300868909737	0.069913109026345
30	99.9	99.9380641677994	-0.0380641677993765
31	99.9	99.5131913491642	0.386808650835818
32	100	100.043819882171	-0.0438198821706806
33	100.1	100.229091380479	-0.12909138047867
34	100.2	100.43398130507	-0.233981305069619
35	100.4	100.502324512761	-0.102324512761228
36	100.6	100.688322261668	-0.0883222616677273
37	101	100.593974021958	0.40602597804228
38	101.3	101.208686805016	0.0913131949836981
39	101.5	101.619099182555	-0.119099182554862
40	101.6	101.796532225348	-0.196532225348321
41	101.7	101.542195249722	0.157804750278146
42	102.1	101.81869077654	0.281309223459502
43	102.6	102.112557370501	0.487442629499114
44	102.8	103.217855311834	-0.417855311834415
45	102.8	103.17113569173	-0.371135691729521
46	102.5	103.03716561868	-0.537165618680092
47	102.1	102.423481882664	-0.323481882664268
48	101.8	101.789078452627	0.0109215473733855
49	101.5	101.29611137499	0.203888625010435
50	101.3	100.997928296947	0.302071703053031
51	101.5	101.100812123738	0.399187876262204
52	101.7	101.772136652011	-0.0721366520110678
53	101.9	101.76688764107	0.133112358930106
54	102	102.116681903922	-0.116681903921631
55	101.9	101.7426248473	0.157375152700297
56	102	101.887950907634	0.112049092365794
57	102.3	102.255718175362	0.0442818246377357
58	102.8	102.819078340558	-0.0190783405583375
59	103.6	103.514994464218	0.0850055357815762
60	104.2	104.4828049543	-0.282804954299834
61	104.4	104.626199459938	-0.226199459937561
62	104.6	104.414536195274	0.1854638047257
63	104.8	104.793842453878	0.00615754612181263
64	105.2	105.075693404477	0.124306595522697
65	105.8	105.463037536436	0.336962463564234
66	106.1	106.393220695479	-0.293220695478581
67	106.2	106.080680336728	0.119319663271867
68	106.4	106.373168875148	0.0268311248523077
69	106.9	106.759589264169	0.140410735831097
70	107.4	107.609463273578	-0.209463273577995
71	108	108.137682526407	-0.137682526406977
72	108.5	108.675167540517	-0.175167540517293
73	108.9	108.825722457601	0.0742775423990452

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
74	109.109667940941	108.659451740171	109.55988414171
75	109.316010549044	108.337551838796	110.294469259291
76	109.602423541839	107.972875508437	111.231971575241
77	109.763738912434	107.381686420556	112.145791404312
78	109.907950335817	106.684448094393	113.131452577241
79	109.737043480442	105.591787386727	113.882299574158
80	109.640250255416	104.499427205531	114.781073305302
81	109.707990320338	103.502907665463	115.913072975212
82	109.977818212664	102.643961187649	117.31167523768
83	110.480480669054	101.956829493122	119.004131844987
84	111.052142812551	101.280658499471	120.823627125631
85	111.452142812551	100.377368268171	122.526917356931

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
74 & 109.109667940941 & 108.659451740171 & 109.55988414171 \tabularnewline
75 & 109.316010549044 & 108.337551838796 & 110.294469259291 \tabularnewline
76 & 109.602423541839 & 107.972875508437 & 111.231971575241 \tabularnewline
77 & 109.763738912434 & 107.381686420556 & 112.145791404312 \tabularnewline
78 & 109.907950335817 & 106.684448094393 & 113.131452577241 \tabularnewline
79 & 109.737043480442 & 105.591787386727 & 113.882299574158 \tabularnewline
80 & 109.640250255416 & 104.499427205531 & 114.781073305302 \tabularnewline
81 & 109.707990320338 & 103.502907665463 & 115.913072975212 \tabularnewline
82 & 109.977818212664 & 102.643961187649 & 117.31167523768 \tabularnewline
83 & 110.480480669054 & 101.956829493122 & 119.004131844987 \tabularnewline
84 & 111.052142812551 & 101.280658499471 & 120.823627125631 \tabularnewline
85 & 111.452142812551 & 100.377368268171 & 122.526917356931 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161115&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]109.109667940941[/C][C]108.659451740171[/C][C]109.55988414171[/C][/ROW]
[ROW][C]75[/C][C]109.316010549044[/C][C]108.337551838796[/C][C]110.294469259291[/C][/ROW]
[ROW][C]76[/C][C]109.602423541839[/C][C]107.972875508437[/C][C]111.231971575241[/C][/ROW]
[ROW][C]77[/C][C]109.763738912434[/C][C]107.381686420556[/C][C]112.145791404312[/C][/ROW]
[ROW][C]78[/C][C]109.907950335817[/C][C]106.684448094393[/C][C]113.131452577241[/C][/ROW]
[ROW][C]79[/C][C]109.737043480442[/C][C]105.591787386727[/C][C]113.882299574158[/C][/ROW]
[ROW][C]80[/C][C]109.640250255416[/C][C]104.499427205531[/C][C]114.781073305302[/C][/ROW]
[ROW][C]81[/C][C]109.707990320338[/C][C]103.502907665463[/C][C]115.913072975212[/C][/ROW]
[ROW][C]82[/C][C]109.977818212664[/C][C]102.643961187649[/C][C]117.31167523768[/C][/ROW]
[ROW][C]83[/C][C]110.480480669054[/C][C]101.956829493122[/C][C]119.004131844987[/C][/ROW]
[ROW][C]84[/C][C]111.052142812551[/C][C]101.280658499471[/C][C]120.823627125631[/C][/ROW]
[ROW][C]85[/C][C]111.452142812551[/C][C]100.377368268171[/C][C]122.526917356931[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161115&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161115&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	109.109667940941	108.659451740171	109.55988414171
75	109.316010549044	108.337551838796	110.294469259291
76	109.602423541839	107.972875508437	111.231971575241
77	109.763738912434	107.381686420556	112.145791404312
78	109.907950335817	106.684448094393	113.131452577241
79	109.737043480442	105.591787386727	113.882299574158
80	109.640250255416	104.499427205531	114.781073305302
81	109.707990320338	103.502907665463	115.913072975212
82	109.977818212664	102.643961187649	117.31167523768
83	110.480480669054	101.956829493122	119.004131844987
84	111.052142812551	101.280658499471	120.823627125631
85	111.452142812551	100.377368268171	122.526917356931

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):

par2 = grey ; par3 = FALSE ; par4 = Unknown ;

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