Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 23 Dec 2013 05:00:39 -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/2013/Dec/23/t13877928807kq8ibingaxxy3l.htm/, Retrieved Tue, 26 May 2026 10:58:26 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232582, Retrieved Tue, 26 May 2026 10:58:26 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

501

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

-       [Exponential Smoothing] [] [2013-12-23 10:00:39] [54d14d1b7b5a29bb4ce37619db20eed6] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

0,43
0,45
0,44
0,44
0,44
0,48
0,47
0,47
0,47
0,49
0,49
0,46
0,45
0,44
0,42
0,43
0,43
0,47
0,47
0,47
0,47
0,48
0,48
0,48
0,49
0,49
0,47
0,5
0,51
0,5
0,49
0,5
0,51
0,51
0,5
0,53
0,5
0,49
0,46
0,46
0,47
0,49
0,5
0,5
0,51
0,5
0,52
0,5
0,48
0,47
0,43
0,42
0,45
0,5
0,52
0,52
0,51
0,52
0,52
0,51
0,51
0,51
0,48
0,49
0,47
0,51
0,5
0,51
0,51
0,52
0,51
0,52
0,48
0,49
0,47
0,44
0,44
0,47
0,51
0,51
0,52
0,52
0,52
0,52

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 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 & 4 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232582&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]4 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=232582&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232582&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	4 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.665667454192795
beta	0
gamma	0.606758105817834

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.665667454192795 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.606758105817834 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232582&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]0.665667454192795[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.606758105817834[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232582&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232582&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	0.665667454192795
beta	0
gamma	0.606758105817834

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	0.45	0.455074786324786	-0.00507478632478625
14	0.44	0.441178018212745	-0.00117801821274538
15	0.42	0.419875201809426	0.000124798190573538
16	0.43	0.429856294551252	0.000143705448747866
17	0.43	0.430266639906159	-0.000266639906159105
18	0.47	0.469153831713325	0.000846168286674776
19	0.47	0.464198450383887	0.0058015496161134
20	0.47	0.467125038461903	0.00287496153809669
21	0.47	0.469770158771222	0.000229841228777727
22	0.48	0.490654508578203	-0.0106545085782033
23	0.48	0.483876834291961	-0.00387683429196073
24	0.48	0.451610837193189	0.0283891628068108
25	0.49	0.459377131584717	0.030622868415283
26	0.49	0.470033624837258	0.0199663751627425
27	0.47	0.463070230952231	0.00692976904776921
28	0.5	0.477585006827572	0.0224149931724283
29	0.51	0.492737381342046	0.0172626186579536
30	0.5	0.543518973208863	-0.0435189732088628
31	0.49	0.510036404698125	-0.0200364046981252
32	0.5	0.495169822827387	0.00483017717261336
33	0.51	0.498579880136768	0.0114201198632319
34	0.51	0.524705246110223	-0.0147052461102226
35	0.5	0.516606039790877	-0.0166060397908768
36	0.53	0.482412072205103	0.0475879277948968
37	0.5	0.503411486856181	-0.00341148685618131
38	0.49	0.489250652104965	0.000749347895035446
39	0.46	0.46685051595357	-0.00685051595356961
40	0.46	0.475333521399197	-0.0153335213991973
41	0.47	0.464312732869262	0.00568726713073847
42	0.49	0.495058898090532	-0.00505889809053206
43	0.5	0.491941599819577	0.00805840018042281
44	0.5	0.500821224677656	-0.000821224677655885
45	0.51	0.501806156771771	0.00819384322822891
46	0.5	0.520484130239915	-0.020484130239915
47	0.52	0.508152515762438	0.0118474842375617
48	0.5	0.505921456007783	-0.00592145600778315
49	0.48	0.480955726018224	-0.00095572601822369
50	0.47	0.469273674034881	0.000726325965119179
51	0.43	0.445316512288766	-0.0153165122887663
52	0.42	0.44644312565598	-0.0264431256559797
53	0.45	0.432291290909718	0.0177087090902817
54	0.5	0.468859782656507	0.0311402173434933
55	0.52	0.492500019177105	0.0274999808228948
56	0.52	0.51251995986585	0.00748004013414971
57	0.51	0.520859561273737	-0.0108595612737372
58	0.52	0.521036718963838	-0.00103671896383806
59	0.52	0.528209371647165	-0.0082093716471654
60	0.51	0.50902252656354	0.000977473436459708
61	0.51	0.489656532305384	0.0203434676946164
62	0.51	0.492493879730587	0.0175061202694132
63	0.48	0.476452047100992	0.00354795289900794
64	0.49	0.487878987521373	0.00212101247862662
65	0.47	0.501697966147595	-0.0316979661475955
66	0.51	0.508102744262411	0.00189725573758948
67	0.5	0.511538438302187	-0.0115384383021871
68	0.51	0.50151054912426	0.00848945087574038
69	0.51	0.506801729535046	0.00319827046495424
70	0.52	0.51832938008348	0.00167061991651973
71	0.51	0.525849183123867	-0.0158491831238667
72	0.52	0.503440398227393	0.0165596017726074
73	0.48	0.498375485554306	-0.0183754855543057
74	0.49	0.474863304530444	0.015136695469556
75	0.47	0.454412683300188	0.0155873166998116
76	0.44	0.473564368690603	-0.0335643686906026
77	0.44	0.456768266898601	-0.0167682668986006
78	0.47	0.479926352423013	-0.00992635242301304
79	0.51	0.472765904100991	0.0372340958990087
80	0.51	0.499267140813698	0.0107328591863015
81	0.52	0.504978321650484	0.0150216783495162
82	0.52	0.524066532389894	-0.00406653238989396
83	0.52	0.52421325044691	-0.00421325044690968
84	0.52	0.516124540351336	0.00387545964866365

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 0.45 & 0.455074786324786 & -0.00507478632478625 \tabularnewline
14 & 0.44 & 0.441178018212745 & -0.00117801821274538 \tabularnewline
15 & 0.42 & 0.419875201809426 & 0.000124798190573538 \tabularnewline
16 & 0.43 & 0.429856294551252 & 0.000143705448747866 \tabularnewline
17 & 0.43 & 0.430266639906159 & -0.000266639906159105 \tabularnewline
18 & 0.47 & 0.469153831713325 & 0.000846168286674776 \tabularnewline
19 & 0.47 & 0.464198450383887 & 0.0058015496161134 \tabularnewline
20 & 0.47 & 0.467125038461903 & 0.00287496153809669 \tabularnewline
21 & 0.47 & 0.469770158771222 & 0.000229841228777727 \tabularnewline
22 & 0.48 & 0.490654508578203 & -0.0106545085782033 \tabularnewline
23 & 0.48 & 0.483876834291961 & -0.00387683429196073 \tabularnewline
24 & 0.48 & 0.451610837193189 & 0.0283891628068108 \tabularnewline
25 & 0.49 & 0.459377131584717 & 0.030622868415283 \tabularnewline
26 & 0.49 & 0.470033624837258 & 0.0199663751627425 \tabularnewline
27 & 0.47 & 0.463070230952231 & 0.00692976904776921 \tabularnewline
28 & 0.5 & 0.477585006827572 & 0.0224149931724283 \tabularnewline
29 & 0.51 & 0.492737381342046 & 0.0172626186579536 \tabularnewline
30 & 0.5 & 0.543518973208863 & -0.0435189732088628 \tabularnewline
31 & 0.49 & 0.510036404698125 & -0.0200364046981252 \tabularnewline
32 & 0.5 & 0.495169822827387 & 0.00483017717261336 \tabularnewline
33 & 0.51 & 0.498579880136768 & 0.0114201198632319 \tabularnewline
34 & 0.51 & 0.524705246110223 & -0.0147052461102226 \tabularnewline
35 & 0.5 & 0.516606039790877 & -0.0166060397908768 \tabularnewline
36 & 0.53 & 0.482412072205103 & 0.0475879277948968 \tabularnewline
37 & 0.5 & 0.503411486856181 & -0.00341148685618131 \tabularnewline
38 & 0.49 & 0.489250652104965 & 0.000749347895035446 \tabularnewline
39 & 0.46 & 0.46685051595357 & -0.00685051595356961 \tabularnewline
40 & 0.46 & 0.475333521399197 & -0.0153335213991973 \tabularnewline
41 & 0.47 & 0.464312732869262 & 0.00568726713073847 \tabularnewline
42 & 0.49 & 0.495058898090532 & -0.00505889809053206 \tabularnewline
43 & 0.5 & 0.491941599819577 & 0.00805840018042281 \tabularnewline
44 & 0.5 & 0.500821224677656 & -0.000821224677655885 \tabularnewline
45 & 0.51 & 0.501806156771771 & 0.00819384322822891 \tabularnewline
46 & 0.5 & 0.520484130239915 & -0.020484130239915 \tabularnewline
47 & 0.52 & 0.508152515762438 & 0.0118474842375617 \tabularnewline
48 & 0.5 & 0.505921456007783 & -0.00592145600778315 \tabularnewline
49 & 0.48 & 0.480955726018224 & -0.00095572601822369 \tabularnewline
50 & 0.47 & 0.469273674034881 & 0.000726325965119179 \tabularnewline
51 & 0.43 & 0.445316512288766 & -0.0153165122887663 \tabularnewline
52 & 0.42 & 0.44644312565598 & -0.0264431256559797 \tabularnewline
53 & 0.45 & 0.432291290909718 & 0.0177087090902817 \tabularnewline
54 & 0.5 & 0.468859782656507 & 0.0311402173434933 \tabularnewline
55 & 0.52 & 0.492500019177105 & 0.0274999808228948 \tabularnewline
56 & 0.52 & 0.51251995986585 & 0.00748004013414971 \tabularnewline
57 & 0.51 & 0.520859561273737 & -0.0108595612737372 \tabularnewline
58 & 0.52 & 0.521036718963838 & -0.00103671896383806 \tabularnewline
59 & 0.52 & 0.528209371647165 & -0.0082093716471654 \tabularnewline
60 & 0.51 & 0.50902252656354 & 0.000977473436459708 \tabularnewline
61 & 0.51 & 0.489656532305384 & 0.0203434676946164 \tabularnewline
62 & 0.51 & 0.492493879730587 & 0.0175061202694132 \tabularnewline
63 & 0.48 & 0.476452047100992 & 0.00354795289900794 \tabularnewline
64 & 0.49 & 0.487878987521373 & 0.00212101247862662 \tabularnewline
65 & 0.47 & 0.501697966147595 & -0.0316979661475955 \tabularnewline
66 & 0.51 & 0.508102744262411 & 0.00189725573758948 \tabularnewline
67 & 0.5 & 0.511538438302187 & -0.0115384383021871 \tabularnewline
68 & 0.51 & 0.50151054912426 & 0.00848945087574038 \tabularnewline
69 & 0.51 & 0.506801729535046 & 0.00319827046495424 \tabularnewline
70 & 0.52 & 0.51832938008348 & 0.00167061991651973 \tabularnewline
71 & 0.51 & 0.525849183123867 & -0.0158491831238667 \tabularnewline
72 & 0.52 & 0.503440398227393 & 0.0165596017726074 \tabularnewline
73 & 0.48 & 0.498375485554306 & -0.0183754855543057 \tabularnewline
74 & 0.49 & 0.474863304530444 & 0.015136695469556 \tabularnewline
75 & 0.47 & 0.454412683300188 & 0.0155873166998116 \tabularnewline
76 & 0.44 & 0.473564368690603 & -0.0335643686906026 \tabularnewline
77 & 0.44 & 0.456768266898601 & -0.0167682668986006 \tabularnewline
78 & 0.47 & 0.479926352423013 & -0.00992635242301304 \tabularnewline
79 & 0.51 & 0.472765904100991 & 0.0372340958990087 \tabularnewline
80 & 0.51 & 0.499267140813698 & 0.0107328591863015 \tabularnewline
81 & 0.52 & 0.504978321650484 & 0.0150216783495162 \tabularnewline
82 & 0.52 & 0.524066532389894 & -0.00406653238989396 \tabularnewline
83 & 0.52 & 0.52421325044691 & -0.00421325044690968 \tabularnewline
84 & 0.52 & 0.516124540351336 & 0.00387545964866365 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232582&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]0.45[/C][C]0.455074786324786[/C][C]-0.00507478632478625[/C][/ROW]
[ROW][C]14[/C][C]0.44[/C][C]0.441178018212745[/C][C]-0.00117801821274538[/C][/ROW]
[ROW][C]15[/C][C]0.42[/C][C]0.419875201809426[/C][C]0.000124798190573538[/C][/ROW]
[ROW][C]16[/C][C]0.43[/C][C]0.429856294551252[/C][C]0.000143705448747866[/C][/ROW]
[ROW][C]17[/C][C]0.43[/C][C]0.430266639906159[/C][C]-0.000266639906159105[/C][/ROW]
[ROW][C]18[/C][C]0.47[/C][C]0.469153831713325[/C][C]0.000846168286674776[/C][/ROW]
[ROW][C]19[/C][C]0.47[/C][C]0.464198450383887[/C][C]0.0058015496161134[/C][/ROW]
[ROW][C]20[/C][C]0.47[/C][C]0.467125038461903[/C][C]0.00287496153809669[/C][/ROW]
[ROW][C]21[/C][C]0.47[/C][C]0.469770158771222[/C][C]0.000229841228777727[/C][/ROW]
[ROW][C]22[/C][C]0.48[/C][C]0.490654508578203[/C][C]-0.0106545085782033[/C][/ROW]
[ROW][C]23[/C][C]0.48[/C][C]0.483876834291961[/C][C]-0.00387683429196073[/C][/ROW]
[ROW][C]24[/C][C]0.48[/C][C]0.451610837193189[/C][C]0.0283891628068108[/C][/ROW]
[ROW][C]25[/C][C]0.49[/C][C]0.459377131584717[/C][C]0.030622868415283[/C][/ROW]
[ROW][C]26[/C][C]0.49[/C][C]0.470033624837258[/C][C]0.0199663751627425[/C][/ROW]
[ROW][C]27[/C][C]0.47[/C][C]0.463070230952231[/C][C]0.00692976904776921[/C][/ROW]
[ROW][C]28[/C][C]0.5[/C][C]0.477585006827572[/C][C]0.0224149931724283[/C][/ROW]
[ROW][C]29[/C][C]0.51[/C][C]0.492737381342046[/C][C]0.0172626186579536[/C][/ROW]
[ROW][C]30[/C][C]0.5[/C][C]0.543518973208863[/C][C]-0.0435189732088628[/C][/ROW]
[ROW][C]31[/C][C]0.49[/C][C]0.510036404698125[/C][C]-0.0200364046981252[/C][/ROW]
[ROW][C]32[/C][C]0.5[/C][C]0.495169822827387[/C][C]0.00483017717261336[/C][/ROW]
[ROW][C]33[/C][C]0.51[/C][C]0.498579880136768[/C][C]0.0114201198632319[/C][/ROW]
[ROW][C]34[/C][C]0.51[/C][C]0.524705246110223[/C][C]-0.0147052461102226[/C][/ROW]
[ROW][C]35[/C][C]0.5[/C][C]0.516606039790877[/C][C]-0.0166060397908768[/C][/ROW]
[ROW][C]36[/C][C]0.53[/C][C]0.482412072205103[/C][C]0.0475879277948968[/C][/ROW]
[ROW][C]37[/C][C]0.5[/C][C]0.503411486856181[/C][C]-0.00341148685618131[/C][/ROW]
[ROW][C]38[/C][C]0.49[/C][C]0.489250652104965[/C][C]0.000749347895035446[/C][/ROW]
[ROW][C]39[/C][C]0.46[/C][C]0.46685051595357[/C][C]-0.00685051595356961[/C][/ROW]
[ROW][C]40[/C][C]0.46[/C][C]0.475333521399197[/C][C]-0.0153335213991973[/C][/ROW]
[ROW][C]41[/C][C]0.47[/C][C]0.464312732869262[/C][C]0.00568726713073847[/C][/ROW]
[ROW][C]42[/C][C]0.49[/C][C]0.495058898090532[/C][C]-0.00505889809053206[/C][/ROW]
[ROW][C]43[/C][C]0.5[/C][C]0.491941599819577[/C][C]0.00805840018042281[/C][/ROW]
[ROW][C]44[/C][C]0.5[/C][C]0.500821224677656[/C][C]-0.000821224677655885[/C][/ROW]
[ROW][C]45[/C][C]0.51[/C][C]0.501806156771771[/C][C]0.00819384322822891[/C][/ROW]
[ROW][C]46[/C][C]0.5[/C][C]0.520484130239915[/C][C]-0.020484130239915[/C][/ROW]
[ROW][C]47[/C][C]0.52[/C][C]0.508152515762438[/C][C]0.0118474842375617[/C][/ROW]
[ROW][C]48[/C][C]0.5[/C][C]0.505921456007783[/C][C]-0.00592145600778315[/C][/ROW]
[ROW][C]49[/C][C]0.48[/C][C]0.480955726018224[/C][C]-0.00095572601822369[/C][/ROW]
[ROW][C]50[/C][C]0.47[/C][C]0.469273674034881[/C][C]0.000726325965119179[/C][/ROW]
[ROW][C]51[/C][C]0.43[/C][C]0.445316512288766[/C][C]-0.0153165122887663[/C][/ROW]
[ROW][C]52[/C][C]0.42[/C][C]0.44644312565598[/C][C]-0.0264431256559797[/C][/ROW]
[ROW][C]53[/C][C]0.45[/C][C]0.432291290909718[/C][C]0.0177087090902817[/C][/ROW]
[ROW][C]54[/C][C]0.5[/C][C]0.468859782656507[/C][C]0.0311402173434933[/C][/ROW]
[ROW][C]55[/C][C]0.52[/C][C]0.492500019177105[/C][C]0.0274999808228948[/C][/ROW]
[ROW][C]56[/C][C]0.52[/C][C]0.51251995986585[/C][C]0.00748004013414971[/C][/ROW]
[ROW][C]57[/C][C]0.51[/C][C]0.520859561273737[/C][C]-0.0108595612737372[/C][/ROW]
[ROW][C]58[/C][C]0.52[/C][C]0.521036718963838[/C][C]-0.00103671896383806[/C][/ROW]
[ROW][C]59[/C][C]0.52[/C][C]0.528209371647165[/C][C]-0.0082093716471654[/C][/ROW]
[ROW][C]60[/C][C]0.51[/C][C]0.50902252656354[/C][C]0.000977473436459708[/C][/ROW]
[ROW][C]61[/C][C]0.51[/C][C]0.489656532305384[/C][C]0.0203434676946164[/C][/ROW]
[ROW][C]62[/C][C]0.51[/C][C]0.492493879730587[/C][C]0.0175061202694132[/C][/ROW]
[ROW][C]63[/C][C]0.48[/C][C]0.476452047100992[/C][C]0.00354795289900794[/C][/ROW]
[ROW][C]64[/C][C]0.49[/C][C]0.487878987521373[/C][C]0.00212101247862662[/C][/ROW]
[ROW][C]65[/C][C]0.47[/C][C]0.501697966147595[/C][C]-0.0316979661475955[/C][/ROW]
[ROW][C]66[/C][C]0.51[/C][C]0.508102744262411[/C][C]0.00189725573758948[/C][/ROW]
[ROW][C]67[/C][C]0.5[/C][C]0.511538438302187[/C][C]-0.0115384383021871[/C][/ROW]
[ROW][C]68[/C][C]0.51[/C][C]0.50151054912426[/C][C]0.00848945087574038[/C][/ROW]
[ROW][C]69[/C][C]0.51[/C][C]0.506801729535046[/C][C]0.00319827046495424[/C][/ROW]
[ROW][C]70[/C][C]0.52[/C][C]0.51832938008348[/C][C]0.00167061991651973[/C][/ROW]
[ROW][C]71[/C][C]0.51[/C][C]0.525849183123867[/C][C]-0.0158491831238667[/C][/ROW]
[ROW][C]72[/C][C]0.52[/C][C]0.503440398227393[/C][C]0.0165596017726074[/C][/ROW]
[ROW][C]73[/C][C]0.48[/C][C]0.498375485554306[/C][C]-0.0183754855543057[/C][/ROW]
[ROW][C]74[/C][C]0.49[/C][C]0.474863304530444[/C][C]0.015136695469556[/C][/ROW]
[ROW][C]75[/C][C]0.47[/C][C]0.454412683300188[/C][C]0.0155873166998116[/C][/ROW]
[ROW][C]76[/C][C]0.44[/C][C]0.473564368690603[/C][C]-0.0335643686906026[/C][/ROW]
[ROW][C]77[/C][C]0.44[/C][C]0.456768266898601[/C][C]-0.0167682668986006[/C][/ROW]
[ROW][C]78[/C][C]0.47[/C][C]0.479926352423013[/C][C]-0.00992635242301304[/C][/ROW]
[ROW][C]79[/C][C]0.51[/C][C]0.472765904100991[/C][C]0.0372340958990087[/C][/ROW]
[ROW][C]80[/C][C]0.51[/C][C]0.499267140813698[/C][C]0.0107328591863015[/C][/ROW]
[ROW][C]81[/C][C]0.52[/C][C]0.504978321650484[/C][C]0.0150216783495162[/C][/ROW]
[ROW][C]82[/C][C]0.52[/C][C]0.524066532389894[/C][C]-0.00406653238989396[/C][/ROW]
[ROW][C]83[/C][C]0.52[/C][C]0.52421325044691[/C][C]-0.00421325044690968[/C][/ROW]
[ROW][C]84[/C][C]0.52[/C][C]0.516124540351336[/C][C]0.00387545964866365[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232582&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232582&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	0.45	0.455074786324786	-0.00507478632478625
14	0.44	0.441178018212745	-0.00117801821274538
15	0.42	0.419875201809426	0.000124798190573538
16	0.43	0.429856294551252	0.000143705448747866
17	0.43	0.430266639906159	-0.000266639906159105
18	0.47	0.469153831713325	0.000846168286674776
19	0.47	0.464198450383887	0.0058015496161134
20	0.47	0.467125038461903	0.00287496153809669
21	0.47	0.469770158771222	0.000229841228777727
22	0.48	0.490654508578203	-0.0106545085782033
23	0.48	0.483876834291961	-0.00387683429196073
24	0.48	0.451610837193189	0.0283891628068108
25	0.49	0.459377131584717	0.030622868415283
26	0.49	0.470033624837258	0.0199663751627425
27	0.47	0.463070230952231	0.00692976904776921
28	0.5	0.477585006827572	0.0224149931724283
29	0.51	0.492737381342046	0.0172626186579536
30	0.5	0.543518973208863	-0.0435189732088628
31	0.49	0.510036404698125	-0.0200364046981252
32	0.5	0.495169822827387	0.00483017717261336
33	0.51	0.498579880136768	0.0114201198632319
34	0.51	0.524705246110223	-0.0147052461102226
35	0.5	0.516606039790877	-0.0166060397908768
36	0.53	0.482412072205103	0.0475879277948968
37	0.5	0.503411486856181	-0.00341148685618131
38	0.49	0.489250652104965	0.000749347895035446
39	0.46	0.46685051595357	-0.00685051595356961
40	0.46	0.475333521399197	-0.0153335213991973
41	0.47	0.464312732869262	0.00568726713073847
42	0.49	0.495058898090532	-0.00505889809053206
43	0.5	0.491941599819577	0.00805840018042281
44	0.5	0.500821224677656	-0.000821224677655885
45	0.51	0.501806156771771	0.00819384322822891
46	0.5	0.520484130239915	-0.020484130239915
47	0.52	0.508152515762438	0.0118474842375617
48	0.5	0.505921456007783	-0.00592145600778315
49	0.48	0.480955726018224	-0.00095572601822369
50	0.47	0.469273674034881	0.000726325965119179
51	0.43	0.445316512288766	-0.0153165122887663
52	0.42	0.44644312565598	-0.0264431256559797
53	0.45	0.432291290909718	0.0177087090902817
54	0.5	0.468859782656507	0.0311402173434933
55	0.52	0.492500019177105	0.0274999808228948
56	0.52	0.51251995986585	0.00748004013414971
57	0.51	0.520859561273737	-0.0108595612737372
58	0.52	0.521036718963838	-0.00103671896383806
59	0.52	0.528209371647165	-0.0082093716471654
60	0.51	0.50902252656354	0.000977473436459708
61	0.51	0.489656532305384	0.0203434676946164
62	0.51	0.492493879730587	0.0175061202694132
63	0.48	0.476452047100992	0.00354795289900794
64	0.49	0.487878987521373	0.00212101247862662
65	0.47	0.501697966147595	-0.0316979661475955
66	0.51	0.508102744262411	0.00189725573758948
67	0.5	0.511538438302187	-0.0115384383021871
68	0.51	0.50151054912426	0.00848945087574038
69	0.51	0.506801729535046	0.00319827046495424
70	0.52	0.51832938008348	0.00167061991651973
71	0.51	0.525849183123867	-0.0158491831238667
72	0.52	0.503440398227393	0.0165596017726074
73	0.48	0.498375485554306	-0.0183754855543057
74	0.49	0.474863304530444	0.015136695469556
75	0.47	0.454412683300188	0.0155873166998116
76	0.44	0.473564368690603	-0.0335643686906026
77	0.44	0.456768266898601	-0.0167682668986006
78	0.47	0.479926352423013	-0.00992635242301304
79	0.51	0.472765904100991	0.0372340958990087
80	0.51	0.499267140813698	0.0107328591863015
81	0.52	0.504978321650484	0.0150216783495162
82	0.52	0.524066532389894	-0.00406653238989396
83	0.52	0.52421325044691	-0.00421325044690968
84	0.52	0.516124540351336	0.00387545964866365

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	0.495529310823526	0.463376282569216	0.527682339077835
86	0.4910473394222	0.452422020739756	0.529672658104644
87	0.460612125217964	0.416453170738512	0.504771079697416
88	0.459416980311049	0.410344469899248	0.508489490722849
89	0.468370826491483	0.414833836517128	0.521907816465838
90	0.504078945360379	0.446422139058676	0.561735751662082
91	0.513093067332247	0.451591804497163	0.574594330167331
92	0.509432764311918	0.444313616991732	0.574551911632103
93	0.508869455588269	0.440323110936596	0.577415800239942
94	0.5140860089403	0.442275846828632	0.585896171051967
95	0.516909922184971	0.441977970389346	0.591841873980596
96	0.513266703285626	0.435337919018837	0.591195487552415

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 0.495529310823526 & 0.463376282569216 & 0.527682339077835 \tabularnewline
86 & 0.4910473394222 & 0.452422020739756 & 0.529672658104644 \tabularnewline
87 & 0.460612125217964 & 0.416453170738512 & 0.504771079697416 \tabularnewline
88 & 0.459416980311049 & 0.410344469899248 & 0.508489490722849 \tabularnewline
89 & 0.468370826491483 & 0.414833836517128 & 0.521907816465838 \tabularnewline
90 & 0.504078945360379 & 0.446422139058676 & 0.561735751662082 \tabularnewline
91 & 0.513093067332247 & 0.451591804497163 & 0.574594330167331 \tabularnewline
92 & 0.509432764311918 & 0.444313616991732 & 0.574551911632103 \tabularnewline
93 & 0.508869455588269 & 0.440323110936596 & 0.577415800239942 \tabularnewline
94 & 0.5140860089403 & 0.442275846828632 & 0.585896171051967 \tabularnewline
95 & 0.516909922184971 & 0.441977970389346 & 0.591841873980596 \tabularnewline
96 & 0.513266703285626 & 0.435337919018837 & 0.591195487552415 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232582&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]85[/C][C]0.495529310823526[/C][C]0.463376282569216[/C][C]0.527682339077835[/C][/ROW]
[ROW][C]86[/C][C]0.4910473394222[/C][C]0.452422020739756[/C][C]0.529672658104644[/C][/ROW]
[ROW][C]87[/C][C]0.460612125217964[/C][C]0.416453170738512[/C][C]0.504771079697416[/C][/ROW]
[ROW][C]88[/C][C]0.459416980311049[/C][C]0.410344469899248[/C][C]0.508489490722849[/C][/ROW]
[ROW][C]89[/C][C]0.468370826491483[/C][C]0.414833836517128[/C][C]0.521907816465838[/C][/ROW]
[ROW][C]90[/C][C]0.504078945360379[/C][C]0.446422139058676[/C][C]0.561735751662082[/C][/ROW]
[ROW][C]91[/C][C]0.513093067332247[/C][C]0.451591804497163[/C][C]0.574594330167331[/C][/ROW]
[ROW][C]92[/C][C]0.509432764311918[/C][C]0.444313616991732[/C][C]0.574551911632103[/C][/ROW]
[ROW][C]93[/C][C]0.508869455588269[/C][C]0.440323110936596[/C][C]0.577415800239942[/C][/ROW]
[ROW][C]94[/C][C]0.5140860089403[/C][C]0.442275846828632[/C][C]0.585896171051967[/C][/ROW]
[ROW][C]95[/C][C]0.516909922184971[/C][C]0.441977970389346[/C][C]0.591841873980596[/C][/ROW]
[ROW][C]96[/C][C]0.513266703285626[/C][C]0.435337919018837[/C][C]0.591195487552415[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232582&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232582&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
85	0.495529310823526	0.463376282569216	0.527682339077835
86	0.4910473394222	0.452422020739756	0.529672658104644
87	0.460612125217964	0.416453170738512	0.504771079697416
88	0.459416980311049	0.410344469899248	0.508489490722849
89	0.468370826491483	0.414833836517128	0.521907816465838
90	0.504078945360379	0.446422139058676	0.561735751662082
91	0.513093067332247	0.451591804497163	0.574594330167331
92	0.509432764311918	0.444313616991732	0.574551911632103
93	0.508869455588269	0.440323110936596	0.577415800239942
94	0.5140860089403	0.442275846828632	0.585896171051967
95	0.516909922184971	0.441977970389346	0.591841873980596
96	0.513266703285626	0.435337919018837	0.591195487552415

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):

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