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Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sun, 27 May 2012 05:23:27 -0400

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/May/27/t1338110723oq7jmfwkw3o33hc.htm/, Retrieved Thu, 09 May 2024 00:04:58 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167661, Retrieved Thu, 09 May 2024 00:04:58 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W102

Estimated Impact

126

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

-       [Exponential Smoothing] [exponential smoot...] [2012-05-27 09:23:27] [a2709f7ab86902c8a6d752383a828f6c] [Current]

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Dataseries X:

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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	'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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167661&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167661&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167661&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	'Gertrude Mary Cox' @ cox.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.544845042486155
beta	0.135929694087167
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.544845042486155 \tabularnewline
beta & 0.135929694087167 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167661&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]0.544845042486155[/C][/ROW]
[ROW][C]beta[/C][C]0.135929694087167[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167661&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167661&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	0.544845042486155
beta	0.135929694087167
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	68.98	68.3825049381052	0.59749506189479
14	68.94	68.7152800839447	0.224719916055307
15	69.21	69.1721992988999	0.0378007011000676
16	69.21	69.2511083283824	-0.0411083283824354
17	69.67	69.7384745774128	-0.0684745774128004
18	69.66	69.7327092881544	-0.0727092881543996
19	69.66	69.7007462670907	-0.0407462670907108
20	69.66	69.8839829511605	-0.223982951160522
21	69.77	69.7933614557467	-0.0233614557466666
22	70.32	70.2719973460174	0.0480026539826213
23	70.34	70.311423567835	0.0285764321649538
24	70.38	70.3660381739325	0.0139618260674581
25	70.38	70.6820898040141	-0.302089804014102
26	70.29	70.3171074119522	-0.0271074119522297
27	70.42	70.5038157355684	-0.0838157355684359
28	70.29	70.419443099423	-0.129443099422986
29	70.59	70.786329239954	-0.196329239954039
30	70.64	70.6323862729729	0.00761372702707774
31	70.64	70.5882678316021	0.0517321683979048
32	70.68	70.676169802842	0.00383019715799549
33	70.78	70.7559265454912	0.024073454508752
34	70.9	71.2568641481657	-0.356864148165684
35	71.04	70.9939882315442	0.0460117684557844
36	71.15	70.9803450454738	0.169654954526237
37	71.15	71.1787229546433	-0.0287229546432997
38	71.15	71.047438731576	0.102561268423997
39	71.07	71.2509770075831	-0.180977007583138
40	71.17	71.0552889949983	0.114711005001652
41	71.24	71.5104395467084	-0.27043954670836
42	71.23	71.385215891376	-0.155215891376031
43	71.23	71.2360824524713	-0.00608245247124728
44	71.23	71.2306860415333	-0.000686041533271009
45	71.24	71.2772724056362	-0.0372724056362443
46	71.28	71.5278658861246	-0.247865886124572
47	71.52	71.4714827178971	0.0485172821029067
48	71.52	71.4786561150071	0.0413438849928838
49	71.52	71.4706304605739	0.0493695394261238
50	71.6	71.4009365722162	0.199063427783841
51	71.61	71.4946975901271	0.115302409872882
52	71.78	71.583822348827	0.196177651173016
53	71.66	71.9039044042756	-0.243904404275611
54	71.86	71.8426362155823	0.0173637844177108
55	71.86	71.8648105131592	-0.00481051315924219
56	71.82	71.8720228215472	-0.0520228215471832
57	71.8	71.8799078450693	-0.0799078450692576
58	72.22	72.0152155622297	0.2047844377703
59	72.51	72.3790844150694	0.130915584930648
60	72.56	72.4697812343179	0.0902187656820672

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 68.98 & 68.3825049381052 & 0.59749506189479 \tabularnewline
14 & 68.94 & 68.7152800839447 & 0.224719916055307 \tabularnewline
15 & 69.21 & 69.1721992988999 & 0.0378007011000676 \tabularnewline
16 & 69.21 & 69.2511083283824 & -0.0411083283824354 \tabularnewline
17 & 69.67 & 69.7384745774128 & -0.0684745774128004 \tabularnewline
18 & 69.66 & 69.7327092881544 & -0.0727092881543996 \tabularnewline
19 & 69.66 & 69.7007462670907 & -0.0407462670907108 \tabularnewline
20 & 69.66 & 69.8839829511605 & -0.223982951160522 \tabularnewline
21 & 69.77 & 69.7933614557467 & -0.0233614557466666 \tabularnewline
22 & 70.32 & 70.2719973460174 & 0.0480026539826213 \tabularnewline
23 & 70.34 & 70.311423567835 & 0.0285764321649538 \tabularnewline
24 & 70.38 & 70.3660381739325 & 0.0139618260674581 \tabularnewline
25 & 70.38 & 70.6820898040141 & -0.302089804014102 \tabularnewline
26 & 70.29 & 70.3171074119522 & -0.0271074119522297 \tabularnewline
27 & 70.42 & 70.5038157355684 & -0.0838157355684359 \tabularnewline
28 & 70.29 & 70.419443099423 & -0.129443099422986 \tabularnewline
29 & 70.59 & 70.786329239954 & -0.196329239954039 \tabularnewline
30 & 70.64 & 70.6323862729729 & 0.00761372702707774 \tabularnewline
31 & 70.64 & 70.5882678316021 & 0.0517321683979048 \tabularnewline
32 & 70.68 & 70.676169802842 & 0.00383019715799549 \tabularnewline
33 & 70.78 & 70.7559265454912 & 0.024073454508752 \tabularnewline
34 & 70.9 & 71.2568641481657 & -0.356864148165684 \tabularnewline
35 & 71.04 & 70.9939882315442 & 0.0460117684557844 \tabularnewline
36 & 71.15 & 70.9803450454738 & 0.169654954526237 \tabularnewline
37 & 71.15 & 71.1787229546433 & -0.0287229546432997 \tabularnewline
38 & 71.15 & 71.047438731576 & 0.102561268423997 \tabularnewline
39 & 71.07 & 71.2509770075831 & -0.180977007583138 \tabularnewline
40 & 71.17 & 71.0552889949983 & 0.114711005001652 \tabularnewline
41 & 71.24 & 71.5104395467084 & -0.27043954670836 \tabularnewline
42 & 71.23 & 71.385215891376 & -0.155215891376031 \tabularnewline
43 & 71.23 & 71.2360824524713 & -0.00608245247124728 \tabularnewline
44 & 71.23 & 71.2306860415333 & -0.000686041533271009 \tabularnewline
45 & 71.24 & 71.2772724056362 & -0.0372724056362443 \tabularnewline
46 & 71.28 & 71.5278658861246 & -0.247865886124572 \tabularnewline
47 & 71.52 & 71.4714827178971 & 0.0485172821029067 \tabularnewline
48 & 71.52 & 71.4786561150071 & 0.0413438849928838 \tabularnewline
49 & 71.52 & 71.4706304605739 & 0.0493695394261238 \tabularnewline
50 & 71.6 & 71.4009365722162 & 0.199063427783841 \tabularnewline
51 & 71.61 & 71.4946975901271 & 0.115302409872882 \tabularnewline
52 & 71.78 & 71.583822348827 & 0.196177651173016 \tabularnewline
53 & 71.66 & 71.9039044042756 & -0.243904404275611 \tabularnewline
54 & 71.86 & 71.8426362155823 & 0.0173637844177108 \tabularnewline
55 & 71.86 & 71.8648105131592 & -0.00481051315924219 \tabularnewline
56 & 71.82 & 71.8720228215472 & -0.0520228215471832 \tabularnewline
57 & 71.8 & 71.8799078450693 & -0.0799078450692576 \tabularnewline
58 & 72.22 & 72.0152155622297 & 0.2047844377703 \tabularnewline
59 & 72.51 & 72.3790844150694 & 0.130915584930648 \tabularnewline
60 & 72.56 & 72.4697812343179 & 0.0902187656820672 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167661&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]68.98[/C][C]68.3825049381052[/C][C]0.59749506189479[/C][/ROW]
[ROW][C]14[/C][C]68.94[/C][C]68.7152800839447[/C][C]0.224719916055307[/C][/ROW]
[ROW][C]15[/C][C]69.21[/C][C]69.1721992988999[/C][C]0.0378007011000676[/C][/ROW]
[ROW][C]16[/C][C]69.21[/C][C]69.2511083283824[/C][C]-0.0411083283824354[/C][/ROW]
[ROW][C]17[/C][C]69.67[/C][C]69.7384745774128[/C][C]-0.0684745774128004[/C][/ROW]
[ROW][C]18[/C][C]69.66[/C][C]69.7327092881544[/C][C]-0.0727092881543996[/C][/ROW]
[ROW][C]19[/C][C]69.66[/C][C]69.7007462670907[/C][C]-0.0407462670907108[/C][/ROW]
[ROW][C]20[/C][C]69.66[/C][C]69.8839829511605[/C][C]-0.223982951160522[/C][/ROW]
[ROW][C]21[/C][C]69.77[/C][C]69.7933614557467[/C][C]-0.0233614557466666[/C][/ROW]
[ROW][C]22[/C][C]70.32[/C][C]70.2719973460174[/C][C]0.0480026539826213[/C][/ROW]
[ROW][C]23[/C][C]70.34[/C][C]70.311423567835[/C][C]0.0285764321649538[/C][/ROW]
[ROW][C]24[/C][C]70.38[/C][C]70.3660381739325[/C][C]0.0139618260674581[/C][/ROW]
[ROW][C]25[/C][C]70.38[/C][C]70.6820898040141[/C][C]-0.302089804014102[/C][/ROW]
[ROW][C]26[/C][C]70.29[/C][C]70.3171074119522[/C][C]-0.0271074119522297[/C][/ROW]
[ROW][C]27[/C][C]70.42[/C][C]70.5038157355684[/C][C]-0.0838157355684359[/C][/ROW]
[ROW][C]28[/C][C]70.29[/C][C]70.419443099423[/C][C]-0.129443099422986[/C][/ROW]
[ROW][C]29[/C][C]70.59[/C][C]70.786329239954[/C][C]-0.196329239954039[/C][/ROW]
[ROW][C]30[/C][C]70.64[/C][C]70.6323862729729[/C][C]0.00761372702707774[/C][/ROW]
[ROW][C]31[/C][C]70.64[/C][C]70.5882678316021[/C][C]0.0517321683979048[/C][/ROW]
[ROW][C]32[/C][C]70.68[/C][C]70.676169802842[/C][C]0.00383019715799549[/C][/ROW]
[ROW][C]33[/C][C]70.78[/C][C]70.7559265454912[/C][C]0.024073454508752[/C][/ROW]
[ROW][C]34[/C][C]70.9[/C][C]71.2568641481657[/C][C]-0.356864148165684[/C][/ROW]
[ROW][C]35[/C][C]71.04[/C][C]70.9939882315442[/C][C]0.0460117684557844[/C][/ROW]
[ROW][C]36[/C][C]71.15[/C][C]70.9803450454738[/C][C]0.169654954526237[/C][/ROW]
[ROW][C]37[/C][C]71.15[/C][C]71.1787229546433[/C][C]-0.0287229546432997[/C][/ROW]
[ROW][C]38[/C][C]71.15[/C][C]71.047438731576[/C][C]0.102561268423997[/C][/ROW]
[ROW][C]39[/C][C]71.07[/C][C]71.2509770075831[/C][C]-0.180977007583138[/C][/ROW]
[ROW][C]40[/C][C]71.17[/C][C]71.0552889949983[/C][C]0.114711005001652[/C][/ROW]
[ROW][C]41[/C][C]71.24[/C][C]71.5104395467084[/C][C]-0.27043954670836[/C][/ROW]
[ROW][C]42[/C][C]71.23[/C][C]71.385215891376[/C][C]-0.155215891376031[/C][/ROW]
[ROW][C]43[/C][C]71.23[/C][C]71.2360824524713[/C][C]-0.00608245247124728[/C][/ROW]
[ROW][C]44[/C][C]71.23[/C][C]71.2306860415333[/C][C]-0.000686041533271009[/C][/ROW]
[ROW][C]45[/C][C]71.24[/C][C]71.2772724056362[/C][C]-0.0372724056362443[/C][/ROW]
[ROW][C]46[/C][C]71.28[/C][C]71.5278658861246[/C][C]-0.247865886124572[/C][/ROW]
[ROW][C]47[/C][C]71.52[/C][C]71.4714827178971[/C][C]0.0485172821029067[/C][/ROW]
[ROW][C]48[/C][C]71.52[/C][C]71.4786561150071[/C][C]0.0413438849928838[/C][/ROW]
[ROW][C]49[/C][C]71.52[/C][C]71.4706304605739[/C][C]0.0493695394261238[/C][/ROW]
[ROW][C]50[/C][C]71.6[/C][C]71.4009365722162[/C][C]0.199063427783841[/C][/ROW]
[ROW][C]51[/C][C]71.61[/C][C]71.4946975901271[/C][C]0.115302409872882[/C][/ROW]
[ROW][C]52[/C][C]71.78[/C][C]71.583822348827[/C][C]0.196177651173016[/C][/ROW]
[ROW][C]53[/C][C]71.66[/C][C]71.9039044042756[/C][C]-0.243904404275611[/C][/ROW]
[ROW][C]54[/C][C]71.86[/C][C]71.8426362155823[/C][C]0.0173637844177108[/C][/ROW]
[ROW][C]55[/C][C]71.86[/C][C]71.8648105131592[/C][C]-0.00481051315924219[/C][/ROW]
[ROW][C]56[/C][C]71.82[/C][C]71.8720228215472[/C][C]-0.0520228215471832[/C][/ROW]
[ROW][C]57[/C][C]71.8[/C][C]71.8799078450693[/C][C]-0.0799078450692576[/C][/ROW]
[ROW][C]58[/C][C]72.22[/C][C]72.0152155622297[/C][C]0.2047844377703[/C][/ROW]
[ROW][C]59[/C][C]72.51[/C][C]72.3790844150694[/C][C]0.130915584930648[/C][/ROW]
[ROW][C]60[/C][C]72.56[/C][C]72.4697812343179[/C][C]0.0902187656820672[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167661&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167661&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	68.98	68.3825049381052	0.59749506189479
14	68.94	68.7152800839447	0.224719916055307
15	69.21	69.1721992988999	0.0378007011000676
16	69.21	69.2511083283824	-0.0411083283824354
17	69.67	69.7384745774128	-0.0684745774128004
18	69.66	69.7327092881544	-0.0727092881543996
19	69.66	69.7007462670907	-0.0407462670907108
20	69.66	69.8839829511605	-0.223982951160522
21	69.77	69.7933614557467	-0.0233614557466666
22	70.32	70.2719973460174	0.0480026539826213
23	70.34	70.311423567835	0.0285764321649538
24	70.38	70.3660381739325	0.0139618260674581
25	70.38	70.6820898040141	-0.302089804014102
26	70.29	70.3171074119522	-0.0271074119522297
27	70.42	70.5038157355684	-0.0838157355684359
28	70.29	70.419443099423	-0.129443099422986
29	70.59	70.786329239954	-0.196329239954039
30	70.64	70.6323862729729	0.00761372702707774
31	70.64	70.5882678316021	0.0517321683979048
32	70.68	70.676169802842	0.00383019715799549
33	70.78	70.7559265454912	0.024073454508752
34	70.9	71.2568641481657	-0.356864148165684
35	71.04	70.9939882315442	0.0460117684557844
36	71.15	70.9803450454738	0.169654954526237
37	71.15	71.1787229546433	-0.0287229546432997
38	71.15	71.047438731576	0.102561268423997
39	71.07	71.2509770075831	-0.180977007583138
40	71.17	71.0552889949983	0.114711005001652
41	71.24	71.5104395467084	-0.27043954670836
42	71.23	71.385215891376	-0.155215891376031
43	71.23	71.2360824524713	-0.00608245247124728
44	71.23	71.2306860415333	-0.000686041533271009
45	71.24	71.2772724056362	-0.0372724056362443
46	71.28	71.5278658861246	-0.247865886124572
47	71.52	71.4714827178971	0.0485172821029067
48	71.52	71.4786561150071	0.0413438849928838
49	71.52	71.4706304605739	0.0493695394261238
50	71.6	71.4009365722162	0.199063427783841
51	71.61	71.4946975901271	0.115302409872882
52	71.78	71.583822348827	0.196177651173016
53	71.66	71.9039044042756	-0.243904404275611
54	71.86	71.8426362155823	0.0173637844177108
55	71.86	71.8648105131592	-0.00481051315924219
56	71.82	71.8720228215472	-0.0520228215471832
57	71.8	71.8799078450693	-0.0799078450692576
58	72.22	72.0152155622297	0.2047844377703
59	72.51	72.3790844150694	0.130915584930648
60	72.56	72.4697812343179	0.0902187656820672

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	72.5373564293533	72.2188030230879	72.8559098356186
62	72.550300551992	72.1757664573514	72.9248346466325
63	72.5237158374336	72.0892809570223	72.9581507178449
64	72.6058572113686	72.1074901868345	73.1042242359027
65	72.6224018744604	72.0569827223825	73.1878210265382
66	72.8373901571206	72.2004819795928	73.4742983346484
67	72.8606088281538	72.1504145551618	73.5708031011458
68	72.869666366051	72.0835099401659	73.6558227919361
69	72.9182688110156	72.0530977810523	73.7834398409788
70	73.2621616371634	72.3119675617556	74.2123557125711
71	73.4994225545667	72.4624609194899	74.5363841896435
72	73.5059516352304	69.3047027800952	77.7072004903656

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 72.5373564293533 & 72.2188030230879 & 72.8559098356186 \tabularnewline
62 & 72.550300551992 & 72.1757664573514 & 72.9248346466325 \tabularnewline
63 & 72.5237158374336 & 72.0892809570223 & 72.9581507178449 \tabularnewline
64 & 72.6058572113686 & 72.1074901868345 & 73.1042242359027 \tabularnewline
65 & 72.6224018744604 & 72.0569827223825 & 73.1878210265382 \tabularnewline
66 & 72.8373901571206 & 72.2004819795928 & 73.4742983346484 \tabularnewline
67 & 72.8606088281538 & 72.1504145551618 & 73.5708031011458 \tabularnewline
68 & 72.869666366051 & 72.0835099401659 & 73.6558227919361 \tabularnewline
69 & 72.9182688110156 & 72.0530977810523 & 73.7834398409788 \tabularnewline
70 & 73.2621616371634 & 72.3119675617556 & 74.2123557125711 \tabularnewline
71 & 73.4994225545667 & 72.4624609194899 & 74.5363841896435 \tabularnewline
72 & 73.5059516352304 & 69.3047027800952 & 77.7072004903656 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167661&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]61[/C][C]72.5373564293533[/C][C]72.2188030230879[/C][C]72.8559098356186[/C][/ROW]
[ROW][C]62[/C][C]72.550300551992[/C][C]72.1757664573514[/C][C]72.9248346466325[/C][/ROW]
[ROW][C]63[/C][C]72.5237158374336[/C][C]72.0892809570223[/C][C]72.9581507178449[/C][/ROW]
[ROW][C]64[/C][C]72.6058572113686[/C][C]72.1074901868345[/C][C]73.1042242359027[/C][/ROW]
[ROW][C]65[/C][C]72.6224018744604[/C][C]72.0569827223825[/C][C]73.1878210265382[/C][/ROW]
[ROW][C]66[/C][C]72.8373901571206[/C][C]72.2004819795928[/C][C]73.4742983346484[/C][/ROW]
[ROW][C]67[/C][C]72.8606088281538[/C][C]72.1504145551618[/C][C]73.5708031011458[/C][/ROW]
[ROW][C]68[/C][C]72.869666366051[/C][C]72.0835099401659[/C][C]73.6558227919361[/C][/ROW]
[ROW][C]69[/C][C]72.9182688110156[/C][C]72.0530977810523[/C][C]73.7834398409788[/C][/ROW]
[ROW][C]70[/C][C]73.2621616371634[/C][C]72.3119675617556[/C][C]74.2123557125711[/C][/ROW]
[ROW][C]71[/C][C]73.4994225545667[/C][C]72.4624609194899[/C][C]74.5363841896435[/C][/ROW]
[ROW][C]72[/C][C]73.5059516352304[/C][C]69.3047027800952[/C][C]77.7072004903656[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167661&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167661&T=3

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	72.5373564293533	72.2188030230879	72.8559098356186
62	72.550300551992	72.1757664573514	72.9248346466325
63	72.5237158374336	72.0892809570223	72.9581507178449
64	72.6058572113686	72.1074901868345	73.1042242359027
65	72.6224018744604	72.0569827223825	73.1878210265382
66	72.8373901571206	72.2004819795928	73.4742983346484
67	72.8606088281538	72.1504145551618	73.5708031011458
68	72.869666366051	72.0835099401659	73.6558227919361
69	72.9182688110156	72.0530977810523	73.7834398409788
70	73.2621616371634	72.3119675617556	74.2123557125711
71	73.4994225545667	72.4624609194899	74.5363841896435
72	73.5059516352304	69.3047027800952	77.7072004903656

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 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

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