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

Thu, 06 Aug 2009 16:31:35 -0600

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/2009/Aug/07/t1249598307npx0907kppw63us.htm/, Retrieved Fri, 03 May 2024 22:54:54 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=42529, Retrieved Fri, 03 May 2024 22:54:54 +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

269

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

-     [Bootstrap Plot - Central Tendency] [Bootstrap plot ma...] [2009-08-05 15:54:55] [b61406873bd841e2047c054f7ebec102]
- RMPD  [Blocked Bootstrap Plot - Central Tendency] [Bootstrap plot ge...] [2009-08-05 18:54:30] [b61406873bd841e2047c054f7ebec102]
- RMP     [Classical Decomposition] [Classical decompo...] [2009-08-06 12:26:35] [b61406873bd841e2047c054f7ebec102]
- RMP         [Exponential Smoothing] [Exponential smoot...] [2009-08-06 22:31:35] [d41d8cd98f00b204e9800998ecf8427e] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42529&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42529&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42529&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.569865562830892
beta	0
gamma	0.691729797158563

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.569865562830892 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.691729797158563 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42529&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]0.569865562830892[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.691729797158563[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42529&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42529&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	0.569865562830892
beta	0
gamma	0.691729797158563

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	11.63	11.6445738636364	-0.0145738636363664
14	11.46	11.4671020539659	-0.00710205396594432
15	11.35	11.3543048379854	-0.00430483798538539
16	11.7	11.6993516590639	0.000648340936052705
17	11.52	11.4963877929030	0.0236122070969564
18	11.64	11.5960935765900	0.0439064234099718
19	11.9	11.8261143352784	0.0738856647215602
20	11.73	11.8940525645235	-0.164052564523459
21	11.7	11.6247313241741	0.0752686758258854
22	11.54	11.5867910171538	-0.0467910171538382
23	11.97	11.3972097611614	0.572790238838632
24	11.64	11.7286231930012	-0.088623193001185
25	11.98	11.9050336263901	0.0749663736099428
26	11.79	11.7808108528057	0.00918914719433062
27	11.66	11.6781297060548	-0.0181297060547720
28	11.96	12.0167719639506	-0.056771963950565
29	11.83	11.7879188388408	0.0420811611591798
30	12.36	11.9041877197512	0.455812280248814
31	12.53	12.3778593691158	0.152140630884244
32	12.55	12.4195970277108	0.130402972289204
33	12.53	12.3892827352705	0.140717264729549
34	12.24	12.3523220738928	-0.112322073892846
35	12.34	12.3097451539378	0.0302548460622223
36	12.05	12.1351915082181	-0.0851915082181183
37	12.22	12.3622314578911	-0.142231457891070
38	12.23	12.0946639738934	0.135336026106593
39	11.92	12.0557412249273	-0.135741224927282
40	12.13	12.3158632343968	-0.185863234396820
41	12.1	12.0428578830022	0.0571421169977899
42	12.15	12.2908097201080	-0.140809720107981
43	12.23	12.3341335445215	-0.104133544521501
44	12.08	12.2233616223805	-0.143361622380468
45	12.02	12.0401071967544	-0.0201071967544113
46	11.93	11.8362096962638	0.0937903037362187
47	12.16	11.9535110039043	0.206488996095683
48	11.87	11.8450375916541	0.0249624083458500
49	11.93	12.1178789804922	-0.187878980492211
50	11.79	11.9068850882441	-0.116885088244057
51	11.43	11.6435747522748	-0.213574752274779
52	11.63	11.8444289722186	-0.214428972218641
53	11.93	11.6274480268940	0.302551973105956
54	11.89	11.9563525322281	-0.0663525322280751
55	11.83	12.0530194560956	-0.223019456095601
56	11.59	11.8628267500128	-0.272826750012849
57	12.04	11.6424673348078	0.397532665192228
58	11.81	11.7104571079243	0.099542892075732
59	11.9	11.8645686266314	0.0354313733685956
60	11.72	11.6046045246294	0.115395475370603
61	11.91	11.8656524568793	0.0443475431207219
62	11.94	11.8081197592282	0.131880240771766
63	11.91	11.6578034835883	0.252196516411709
64	11.84	12.1238305478381	-0.283830547838088
65	12.01	12.0211208943	-0.0111208942999923
66	11.89	12.0615113659096	-0.171511365909579
67	11.8	12.0516377155486	-0.251637715548586
68	11.7	11.8303169457393	-0.130316945739272
69	11.5	11.8906255602805	-0.390625560280485
70	11.76	11.4208081770342	0.339191822965780
71	11.61	11.6924118320585	-0.0824118320584653
72	11.27	11.3890852090522	-0.119085209052182
73	11.64	11.4953712991968	0.144628700803230
74	11.39	11.5210295792747	-0.131029579274706
75	11.54	11.2566885715411	0.283311428458886
76	11.62	11.5809591715086	0.0390408284913697
77	11.59	11.7433839561092	-0.153383956109188
78	11.44	11.6549815391391	-0.214981539139078
79	11.31	11.5964951958182	-0.286495195818235
80	11.56	11.3914077428649	0.168592257135131
81	11.4	11.5446030245390	-0.144603024539045
82	11.51	11.4321329459773	0.0778670540227004
83	11.5	11.4293740091417	0.0706259908582947
84	11.24	11.2023466917346	0.0376533082653623
85	11.8	11.4764172599606	0.323582740039351

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 11.63 & 11.6445738636364 & -0.0145738636363664 \tabularnewline
14 & 11.46 & 11.4671020539659 & -0.00710205396594432 \tabularnewline
15 & 11.35 & 11.3543048379854 & -0.00430483798538539 \tabularnewline
16 & 11.7 & 11.6993516590639 & 0.000648340936052705 \tabularnewline
17 & 11.52 & 11.4963877929030 & 0.0236122070969564 \tabularnewline
18 & 11.64 & 11.5960935765900 & 0.0439064234099718 \tabularnewline
19 & 11.9 & 11.8261143352784 & 0.0738856647215602 \tabularnewline
20 & 11.73 & 11.8940525645235 & -0.164052564523459 \tabularnewline
21 & 11.7 & 11.6247313241741 & 0.0752686758258854 \tabularnewline
22 & 11.54 & 11.5867910171538 & -0.0467910171538382 \tabularnewline
23 & 11.97 & 11.3972097611614 & 0.572790238838632 \tabularnewline
24 & 11.64 & 11.7286231930012 & -0.088623193001185 \tabularnewline
25 & 11.98 & 11.9050336263901 & 0.0749663736099428 \tabularnewline
26 & 11.79 & 11.7808108528057 & 0.00918914719433062 \tabularnewline
27 & 11.66 & 11.6781297060548 & -0.0181297060547720 \tabularnewline
28 & 11.96 & 12.0167719639506 & -0.056771963950565 \tabularnewline
29 & 11.83 & 11.7879188388408 & 0.0420811611591798 \tabularnewline
30 & 12.36 & 11.9041877197512 & 0.455812280248814 \tabularnewline
31 & 12.53 & 12.3778593691158 & 0.152140630884244 \tabularnewline
32 & 12.55 & 12.4195970277108 & 0.130402972289204 \tabularnewline
33 & 12.53 & 12.3892827352705 & 0.140717264729549 \tabularnewline
34 & 12.24 & 12.3523220738928 & -0.112322073892846 \tabularnewline
35 & 12.34 & 12.3097451539378 & 0.0302548460622223 \tabularnewline
36 & 12.05 & 12.1351915082181 & -0.0851915082181183 \tabularnewline
37 & 12.22 & 12.3622314578911 & -0.142231457891070 \tabularnewline
38 & 12.23 & 12.0946639738934 & 0.135336026106593 \tabularnewline
39 & 11.92 & 12.0557412249273 & -0.135741224927282 \tabularnewline
40 & 12.13 & 12.3158632343968 & -0.185863234396820 \tabularnewline
41 & 12.1 & 12.0428578830022 & 0.0571421169977899 \tabularnewline
42 & 12.15 & 12.2908097201080 & -0.140809720107981 \tabularnewline
43 & 12.23 & 12.3341335445215 & -0.104133544521501 \tabularnewline
44 & 12.08 & 12.2233616223805 & -0.143361622380468 \tabularnewline
45 & 12.02 & 12.0401071967544 & -0.0201071967544113 \tabularnewline
46 & 11.93 & 11.8362096962638 & 0.0937903037362187 \tabularnewline
47 & 12.16 & 11.9535110039043 & 0.206488996095683 \tabularnewline
48 & 11.87 & 11.8450375916541 & 0.0249624083458500 \tabularnewline
49 & 11.93 & 12.1178789804922 & -0.187878980492211 \tabularnewline
50 & 11.79 & 11.9068850882441 & -0.116885088244057 \tabularnewline
51 & 11.43 & 11.6435747522748 & -0.213574752274779 \tabularnewline
52 & 11.63 & 11.8444289722186 & -0.214428972218641 \tabularnewline
53 & 11.93 & 11.6274480268940 & 0.302551973105956 \tabularnewline
54 & 11.89 & 11.9563525322281 & -0.0663525322280751 \tabularnewline
55 & 11.83 & 12.0530194560956 & -0.223019456095601 \tabularnewline
56 & 11.59 & 11.8628267500128 & -0.272826750012849 \tabularnewline
57 & 12.04 & 11.6424673348078 & 0.397532665192228 \tabularnewline
58 & 11.81 & 11.7104571079243 & 0.099542892075732 \tabularnewline
59 & 11.9 & 11.8645686266314 & 0.0354313733685956 \tabularnewline
60 & 11.72 & 11.6046045246294 & 0.115395475370603 \tabularnewline
61 & 11.91 & 11.8656524568793 & 0.0443475431207219 \tabularnewline
62 & 11.94 & 11.8081197592282 & 0.131880240771766 \tabularnewline
63 & 11.91 & 11.6578034835883 & 0.252196516411709 \tabularnewline
64 & 11.84 & 12.1238305478381 & -0.283830547838088 \tabularnewline
65 & 12.01 & 12.0211208943 & -0.0111208942999923 \tabularnewline
66 & 11.89 & 12.0615113659096 & -0.171511365909579 \tabularnewline
67 & 11.8 & 12.0516377155486 & -0.251637715548586 \tabularnewline
68 & 11.7 & 11.8303169457393 & -0.130316945739272 \tabularnewline
69 & 11.5 & 11.8906255602805 & -0.390625560280485 \tabularnewline
70 & 11.76 & 11.4208081770342 & 0.339191822965780 \tabularnewline
71 & 11.61 & 11.6924118320585 & -0.0824118320584653 \tabularnewline
72 & 11.27 & 11.3890852090522 & -0.119085209052182 \tabularnewline
73 & 11.64 & 11.4953712991968 & 0.144628700803230 \tabularnewline
74 & 11.39 & 11.5210295792747 & -0.131029579274706 \tabularnewline
75 & 11.54 & 11.2566885715411 & 0.283311428458886 \tabularnewline
76 & 11.62 & 11.5809591715086 & 0.0390408284913697 \tabularnewline
77 & 11.59 & 11.7433839561092 & -0.153383956109188 \tabularnewline
78 & 11.44 & 11.6549815391391 & -0.214981539139078 \tabularnewline
79 & 11.31 & 11.5964951958182 & -0.286495195818235 \tabularnewline
80 & 11.56 & 11.3914077428649 & 0.168592257135131 \tabularnewline
81 & 11.4 & 11.5446030245390 & -0.144603024539045 \tabularnewline
82 & 11.51 & 11.4321329459773 & 0.0778670540227004 \tabularnewline
83 & 11.5 & 11.4293740091417 & 0.0706259908582947 \tabularnewline
84 & 11.24 & 11.2023466917346 & 0.0376533082653623 \tabularnewline
85 & 11.8 & 11.4764172599606 & 0.323582740039351 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42529&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]11.63[/C][C]11.6445738636364[/C][C]-0.0145738636363664[/C][/ROW]
[ROW][C]14[/C][C]11.46[/C][C]11.4671020539659[/C][C]-0.00710205396594432[/C][/ROW]
[ROW][C]15[/C][C]11.35[/C][C]11.3543048379854[/C][C]-0.00430483798538539[/C][/ROW]
[ROW][C]16[/C][C]11.7[/C][C]11.6993516590639[/C][C]0.000648340936052705[/C][/ROW]
[ROW][C]17[/C][C]11.52[/C][C]11.4963877929030[/C][C]0.0236122070969564[/C][/ROW]
[ROW][C]18[/C][C]11.64[/C][C]11.5960935765900[/C][C]0.0439064234099718[/C][/ROW]
[ROW][C]19[/C][C]11.9[/C][C]11.8261143352784[/C][C]0.0738856647215602[/C][/ROW]
[ROW][C]20[/C][C]11.73[/C][C]11.8940525645235[/C][C]-0.164052564523459[/C][/ROW]
[ROW][C]21[/C][C]11.7[/C][C]11.6247313241741[/C][C]0.0752686758258854[/C][/ROW]
[ROW][C]22[/C][C]11.54[/C][C]11.5867910171538[/C][C]-0.0467910171538382[/C][/ROW]
[ROW][C]23[/C][C]11.97[/C][C]11.3972097611614[/C][C]0.572790238838632[/C][/ROW]
[ROW][C]24[/C][C]11.64[/C][C]11.7286231930012[/C][C]-0.088623193001185[/C][/ROW]
[ROW][C]25[/C][C]11.98[/C][C]11.9050336263901[/C][C]0.0749663736099428[/C][/ROW]
[ROW][C]26[/C][C]11.79[/C][C]11.7808108528057[/C][C]0.00918914719433062[/C][/ROW]
[ROW][C]27[/C][C]11.66[/C][C]11.6781297060548[/C][C]-0.0181297060547720[/C][/ROW]
[ROW][C]28[/C][C]11.96[/C][C]12.0167719639506[/C][C]-0.056771963950565[/C][/ROW]
[ROW][C]29[/C][C]11.83[/C][C]11.7879188388408[/C][C]0.0420811611591798[/C][/ROW]
[ROW][C]30[/C][C]12.36[/C][C]11.9041877197512[/C][C]0.455812280248814[/C][/ROW]
[ROW][C]31[/C][C]12.53[/C][C]12.3778593691158[/C][C]0.152140630884244[/C][/ROW]
[ROW][C]32[/C][C]12.55[/C][C]12.4195970277108[/C][C]0.130402972289204[/C][/ROW]
[ROW][C]33[/C][C]12.53[/C][C]12.3892827352705[/C][C]0.140717264729549[/C][/ROW]
[ROW][C]34[/C][C]12.24[/C][C]12.3523220738928[/C][C]-0.112322073892846[/C][/ROW]
[ROW][C]35[/C][C]12.34[/C][C]12.3097451539378[/C][C]0.0302548460622223[/C][/ROW]
[ROW][C]36[/C][C]12.05[/C][C]12.1351915082181[/C][C]-0.0851915082181183[/C][/ROW]
[ROW][C]37[/C][C]12.22[/C][C]12.3622314578911[/C][C]-0.142231457891070[/C][/ROW]
[ROW][C]38[/C][C]12.23[/C][C]12.0946639738934[/C][C]0.135336026106593[/C][/ROW]
[ROW][C]39[/C][C]11.92[/C][C]12.0557412249273[/C][C]-0.135741224927282[/C][/ROW]
[ROW][C]40[/C][C]12.13[/C][C]12.3158632343968[/C][C]-0.185863234396820[/C][/ROW]
[ROW][C]41[/C][C]12.1[/C][C]12.0428578830022[/C][C]0.0571421169977899[/C][/ROW]
[ROW][C]42[/C][C]12.15[/C][C]12.2908097201080[/C][C]-0.140809720107981[/C][/ROW]
[ROW][C]43[/C][C]12.23[/C][C]12.3341335445215[/C][C]-0.104133544521501[/C][/ROW]
[ROW][C]44[/C][C]12.08[/C][C]12.2233616223805[/C][C]-0.143361622380468[/C][/ROW]
[ROW][C]45[/C][C]12.02[/C][C]12.0401071967544[/C][C]-0.0201071967544113[/C][/ROW]
[ROW][C]46[/C][C]11.93[/C][C]11.8362096962638[/C][C]0.0937903037362187[/C][/ROW]
[ROW][C]47[/C][C]12.16[/C][C]11.9535110039043[/C][C]0.206488996095683[/C][/ROW]
[ROW][C]48[/C][C]11.87[/C][C]11.8450375916541[/C][C]0.0249624083458500[/C][/ROW]
[ROW][C]49[/C][C]11.93[/C][C]12.1178789804922[/C][C]-0.187878980492211[/C][/ROW]
[ROW][C]50[/C][C]11.79[/C][C]11.9068850882441[/C][C]-0.116885088244057[/C][/ROW]
[ROW][C]51[/C][C]11.43[/C][C]11.6435747522748[/C][C]-0.213574752274779[/C][/ROW]
[ROW][C]52[/C][C]11.63[/C][C]11.8444289722186[/C][C]-0.214428972218641[/C][/ROW]
[ROW][C]53[/C][C]11.93[/C][C]11.6274480268940[/C][C]0.302551973105956[/C][/ROW]
[ROW][C]54[/C][C]11.89[/C][C]11.9563525322281[/C][C]-0.0663525322280751[/C][/ROW]
[ROW][C]55[/C][C]11.83[/C][C]12.0530194560956[/C][C]-0.223019456095601[/C][/ROW]
[ROW][C]56[/C][C]11.59[/C][C]11.8628267500128[/C][C]-0.272826750012849[/C][/ROW]
[ROW][C]57[/C][C]12.04[/C][C]11.6424673348078[/C][C]0.397532665192228[/C][/ROW]
[ROW][C]58[/C][C]11.81[/C][C]11.7104571079243[/C][C]0.099542892075732[/C][/ROW]
[ROW][C]59[/C][C]11.9[/C][C]11.8645686266314[/C][C]0.0354313733685956[/C][/ROW]
[ROW][C]60[/C][C]11.72[/C][C]11.6046045246294[/C][C]0.115395475370603[/C][/ROW]
[ROW][C]61[/C][C]11.91[/C][C]11.8656524568793[/C][C]0.0443475431207219[/C][/ROW]
[ROW][C]62[/C][C]11.94[/C][C]11.8081197592282[/C][C]0.131880240771766[/C][/ROW]
[ROW][C]63[/C][C]11.91[/C][C]11.6578034835883[/C][C]0.252196516411709[/C][/ROW]
[ROW][C]64[/C][C]11.84[/C][C]12.1238305478381[/C][C]-0.283830547838088[/C][/ROW]
[ROW][C]65[/C][C]12.01[/C][C]12.0211208943[/C][C]-0.0111208942999923[/C][/ROW]
[ROW][C]66[/C][C]11.89[/C][C]12.0615113659096[/C][C]-0.171511365909579[/C][/ROW]
[ROW][C]67[/C][C]11.8[/C][C]12.0516377155486[/C][C]-0.251637715548586[/C][/ROW]
[ROW][C]68[/C][C]11.7[/C][C]11.8303169457393[/C][C]-0.130316945739272[/C][/ROW]
[ROW][C]69[/C][C]11.5[/C][C]11.8906255602805[/C][C]-0.390625560280485[/C][/ROW]
[ROW][C]70[/C][C]11.76[/C][C]11.4208081770342[/C][C]0.339191822965780[/C][/ROW]
[ROW][C]71[/C][C]11.61[/C][C]11.6924118320585[/C][C]-0.0824118320584653[/C][/ROW]
[ROW][C]72[/C][C]11.27[/C][C]11.3890852090522[/C][C]-0.119085209052182[/C][/ROW]
[ROW][C]73[/C][C]11.64[/C][C]11.4953712991968[/C][C]0.144628700803230[/C][/ROW]
[ROW][C]74[/C][C]11.39[/C][C]11.5210295792747[/C][C]-0.131029579274706[/C][/ROW]
[ROW][C]75[/C][C]11.54[/C][C]11.2566885715411[/C][C]0.283311428458886[/C][/ROW]
[ROW][C]76[/C][C]11.62[/C][C]11.5809591715086[/C][C]0.0390408284913697[/C][/ROW]
[ROW][C]77[/C][C]11.59[/C][C]11.7433839561092[/C][C]-0.153383956109188[/C][/ROW]
[ROW][C]78[/C][C]11.44[/C][C]11.6549815391391[/C][C]-0.214981539139078[/C][/ROW]
[ROW][C]79[/C][C]11.31[/C][C]11.5964951958182[/C][C]-0.286495195818235[/C][/ROW]
[ROW][C]80[/C][C]11.56[/C][C]11.3914077428649[/C][C]0.168592257135131[/C][/ROW]
[ROW][C]81[/C][C]11.4[/C][C]11.5446030245390[/C][C]-0.144603024539045[/C][/ROW]
[ROW][C]82[/C][C]11.51[/C][C]11.4321329459773[/C][C]0.0778670540227004[/C][/ROW]
[ROW][C]83[/C][C]11.5[/C][C]11.4293740091417[/C][C]0.0706259908582947[/C][/ROW]
[ROW][C]84[/C][C]11.24[/C][C]11.2023466917346[/C][C]0.0376533082653623[/C][/ROW]
[ROW][C]85[/C][C]11.8[/C][C]11.4764172599606[/C][C]0.323582740039351[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42529&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42529&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	11.63	11.6445738636364	-0.0145738636363664
14	11.46	11.4671020539659	-0.00710205396594432
15	11.35	11.3543048379854	-0.00430483798538539
16	11.7	11.6993516590639	0.000648340936052705
17	11.52	11.4963877929030	0.0236122070969564
18	11.64	11.5960935765900	0.0439064234099718
19	11.9	11.8261143352784	0.0738856647215602
20	11.73	11.8940525645235	-0.164052564523459
21	11.7	11.6247313241741	0.0752686758258854
22	11.54	11.5867910171538	-0.0467910171538382
23	11.97	11.3972097611614	0.572790238838632
24	11.64	11.7286231930012	-0.088623193001185
25	11.98	11.9050336263901	0.0749663736099428
26	11.79	11.7808108528057	0.00918914719433062
27	11.66	11.6781297060548	-0.0181297060547720
28	11.96	12.0167719639506	-0.056771963950565
29	11.83	11.7879188388408	0.0420811611591798
30	12.36	11.9041877197512	0.455812280248814
31	12.53	12.3778593691158	0.152140630884244
32	12.55	12.4195970277108	0.130402972289204
33	12.53	12.3892827352705	0.140717264729549
34	12.24	12.3523220738928	-0.112322073892846
35	12.34	12.3097451539378	0.0302548460622223
36	12.05	12.1351915082181	-0.0851915082181183
37	12.22	12.3622314578911	-0.142231457891070
38	12.23	12.0946639738934	0.135336026106593
39	11.92	12.0557412249273	-0.135741224927282
40	12.13	12.3158632343968	-0.185863234396820
41	12.1	12.0428578830022	0.0571421169977899
42	12.15	12.2908097201080	-0.140809720107981
43	12.23	12.3341335445215	-0.104133544521501
44	12.08	12.2233616223805	-0.143361622380468
45	12.02	12.0401071967544	-0.0201071967544113
46	11.93	11.8362096962638	0.0937903037362187
47	12.16	11.9535110039043	0.206488996095683
48	11.87	11.8450375916541	0.0249624083458500
49	11.93	12.1178789804922	-0.187878980492211
50	11.79	11.9068850882441	-0.116885088244057
51	11.43	11.6435747522748	-0.213574752274779
52	11.63	11.8444289722186	-0.214428972218641
53	11.93	11.6274480268940	0.302551973105956
54	11.89	11.9563525322281	-0.0663525322280751
55	11.83	12.0530194560956	-0.223019456095601
56	11.59	11.8628267500128	-0.272826750012849
57	12.04	11.6424673348078	0.397532665192228
58	11.81	11.7104571079243	0.099542892075732
59	11.9	11.8645686266314	0.0354313733685956
60	11.72	11.6046045246294	0.115395475370603
61	11.91	11.8656524568793	0.0443475431207219
62	11.94	11.8081197592282	0.131880240771766
63	11.91	11.6578034835883	0.252196516411709
64	11.84	12.1238305478381	-0.283830547838088
65	12.01	12.0211208943	-0.0111208942999923
66	11.89	12.0615113659096	-0.171511365909579
67	11.8	12.0516377155486	-0.251637715548586
68	11.7	11.8303169457393	-0.130316945739272
69	11.5	11.8906255602805	-0.390625560280485
70	11.76	11.4208081770342	0.339191822965780
71	11.61	11.6924118320585	-0.0824118320584653
72	11.27	11.3890852090522	-0.119085209052182
73	11.64	11.4953712991968	0.144628700803230
74	11.39	11.5210295792747	-0.131029579274706
75	11.54	11.2566885715411	0.283311428458886
76	11.62	11.5809591715086	0.0390408284913697
77	11.59	11.7433839561092	-0.153383956109188
78	11.44	11.6549815391391	-0.214981539139078
79	11.31	11.5964951958182	-0.286495195818235
80	11.56	11.3914077428649	0.168592257135131
81	11.4	11.5446030245390	-0.144603024539045
82	11.51	11.4321329459773	0.0778670540227004
83	11.5	11.4293740091417	0.0706259908582947
84	11.24	11.2023466917346	0.0376533082653623
85	11.8	11.4764172599606	0.323582740039351

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
86	11.5220367998584	11.1626926397749	11.8813809599419
87	11.4556467375051	11.0420500762926	11.8692433987176
88	11.5457884164856	11.0842733344501	12.0073034985210
89	11.6287117213918	11.1238056472293	12.1336177955543
90	11.6093899907271	11.0645376102549	12.1542423711992
91	11.6521362781426	11.0700726310333	12.2341999252520
92	11.7457178388482	11.1286829435090	12.3627527341874
93	11.7096510749525	11.0595233683853	12.3597787815197
94	11.7457783171792	11.0641625840669	12.4273940502916
95	11.6964911449640	10.9847791383164	12.4082031516116
96	11.4194059208299	10.6788196981749	12.1599921434849
97	11.7570936954987	10.9887175337352	12.5254698572622

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
86 & 11.5220367998584 & 11.1626926397749 & 11.8813809599419 \tabularnewline
87 & 11.4556467375051 & 11.0420500762926 & 11.8692433987176 \tabularnewline
88 & 11.5457884164856 & 11.0842733344501 & 12.0073034985210 \tabularnewline
89 & 11.6287117213918 & 11.1238056472293 & 12.1336177955543 \tabularnewline
90 & 11.6093899907271 & 11.0645376102549 & 12.1542423711992 \tabularnewline
91 & 11.6521362781426 & 11.0700726310333 & 12.2341999252520 \tabularnewline
92 & 11.7457178388482 & 11.1286829435090 & 12.3627527341874 \tabularnewline
93 & 11.7096510749525 & 11.0595233683853 & 12.3597787815197 \tabularnewline
94 & 11.7457783171792 & 11.0641625840669 & 12.4273940502916 \tabularnewline
95 & 11.6964911449640 & 10.9847791383164 & 12.4082031516116 \tabularnewline
96 & 11.4194059208299 & 10.6788196981749 & 12.1599921434849 \tabularnewline
97 & 11.7570936954987 & 10.9887175337352 & 12.5254698572622 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42529&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]86[/C][C]11.5220367998584[/C][C]11.1626926397749[/C][C]11.8813809599419[/C][/ROW]
[ROW][C]87[/C][C]11.4556467375051[/C][C]11.0420500762926[/C][C]11.8692433987176[/C][/ROW]
[ROW][C]88[/C][C]11.5457884164856[/C][C]11.0842733344501[/C][C]12.0073034985210[/C][/ROW]
[ROW][C]89[/C][C]11.6287117213918[/C][C]11.1238056472293[/C][C]12.1336177955543[/C][/ROW]
[ROW][C]90[/C][C]11.6093899907271[/C][C]11.0645376102549[/C][C]12.1542423711992[/C][/ROW]
[ROW][C]91[/C][C]11.6521362781426[/C][C]11.0700726310333[/C][C]12.2341999252520[/C][/ROW]
[ROW][C]92[/C][C]11.7457178388482[/C][C]11.1286829435090[/C][C]12.3627527341874[/C][/ROW]
[ROW][C]93[/C][C]11.7096510749525[/C][C]11.0595233683853[/C][C]12.3597787815197[/C][/ROW]
[ROW][C]94[/C][C]11.7457783171792[/C][C]11.0641625840669[/C][C]12.4273940502916[/C][/ROW]
[ROW][C]95[/C][C]11.6964911449640[/C][C]10.9847791383164[/C][C]12.4082031516116[/C][/ROW]
[ROW][C]96[/C][C]11.4194059208299[/C][C]10.6788196981749[/C][C]12.1599921434849[/C][/ROW]
[ROW][C]97[/C][C]11.7570936954987[/C][C]10.9887175337352[/C][C]12.5254698572622[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42529&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42529&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
86	11.5220367998584	11.1626926397749	11.8813809599419
87	11.4556467375051	11.0420500762926	11.8692433987176
88	11.5457884164856	11.0842733344501	12.0073034985210
89	11.6287117213918	11.1238056472293	12.1336177955543
90	11.6093899907271	11.0645376102549	12.1542423711992
91	11.6521362781426	11.0700726310333	12.2341999252520
92	11.7457178388482	11.1286829435090	12.3627527341874
93	11.7096510749525	11.0595233683853	12.3597787815197
94	11.7457783171792	11.0641625840669	12.4273940502916
95	11.6964911449640	10.9847791383164	12.4082031516116
96	11.4194059208299	10.6788196981749	12.1599921434849
97	11.7570936954987	10.9887175337352	12.5254698572622

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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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