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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Fri, 04 Dec 2009 05:30:03 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/04/t1259929874pfmt8jcn53ng6ap.htm/, Retrieved Sat, 27 Apr 2024 13:48:24 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=63410, Retrieved Sat, 27 Apr 2024 13:48:24 +0000

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Estimated Impact

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [] [2009-11-27 15:04:36] [b98453cac15ba1066b407e146608df68]
-    D      [Exponential Smoothing] [] [2009-12-04 12:30:03] [1c773da0103d9327c2f1f790e2d74438] [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	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63410&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63410&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63410&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	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.0339504410338378
gamma	0.266247991357555

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0339504410338378 \tabularnewline
gamma & 0.266247991357555 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63410&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0339504410338378[/C][/ROW]
[ROW][C]gamma[/C][C]0.266247991357555[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63410&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63410&T=1

As an alternative you can also use a QR Code:

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

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.0339504410338378
gamma	0.266247991357555

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	1.3322	1.27138682727723	0.060813172722769
14	1.4369	1.43185763494778	0.00504236505221511
15	1.4975	1.49505700178949	0.00244299821050853
16	1.577	1.57901700119157	-0.00201700119156634
17	1.5553	1.56090629104503	-0.00560629104503274
18	1.5557	1.55901031353179	-0.00331031353178934
19	1.575	1.45949475928585	0.115505240714154
20	1.5527	1.58559394354555	-0.0328939435455491
21	1.4748	1.53646247493622	-0.0616624749362209
22	1.4718	1.53206827304489	-0.0602682730448914
23	1.457	1.49466759529134	-0.0376675952913359
24	1.4684	1.37709622807195	0.0913037719280496
25	1.4227	1.53175532803572	-0.109055328035721
26	1.3896	1.52464227472821	-0.13504227472821
27	1.3622	1.43800281111357	-0.0758028111135665
28	1.3716	1.42641234790238	-0.0548123479023817
29	1.3419	1.34679016706208	-0.00489016706207801
30	1.3511	1.33449496993768	0.0166050300623219
31	1.3516	1.25822760853177	0.0933723914682347
32	1.3242	1.35138650493592	-0.0271865049359226
33	1.3074	1.30137939946158	0.00602060053842113
34	1.2999	1.35045000608958	-0.0505500060895849
35	1.3213	1.31247731831248	0.00882268168751876
36	1.2881	1.24275447667677	0.0453455233232307
37	1.2611	1.33654356203417	-0.075443562034172
38	1.2727	1.34449608090303	-0.0717960809030334
39	1.2811	1.31129252311742	-0.0301925231174185
40	1.2684	1.33674834225979	-0.068348342259788
41	1.265	1.24031980361613	0.0246801963838688
42	1.277	1.25384017144358	0.0231598285564221
43	1.2271	1.18556834906526	0.0415316509347436
44	1.202	1.22196351579028	-0.0199635157902824
45	1.1938	1.17660844155495	0.0171915584450475
46	1.2103	1.22867594897188	-0.0183759489718773
47	1.1856	1.21841282635249	-0.0328128263524943
48	1.1786	1.11060737748961	0.0679926225103893
49	1.2015	1.21910619052557	-0.0176061905255722
50	1.2256	1.27859172630983	-0.0529917263098263
51	1.2292	1.26085249615482	-0.031652496154819
52	1.2037	1.28051206921857	-0.0768120692185719
53	1.2165	1.17462556555472	0.0418744344452815
54	1.2694	1.20399054661212	0.0654094533878815
55	1.2938	1.17821632266330	0.115583677336695
56	1.3201	1.29050337417145	0.0295966258285536
57	1.3014	1.29592964727458	0.00547035272541962
58	1.3119	1.34278347696348	-0.0308834769634840
59	1.3408	1.32371290342279	0.0170870965772083
60	1.2991	1.26050411274305	0.0385958872569487

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1.3322 & 1.27138682727723 & 0.060813172722769 \tabularnewline
14 & 1.4369 & 1.43185763494778 & 0.00504236505221511 \tabularnewline
15 & 1.4975 & 1.49505700178949 & 0.00244299821050853 \tabularnewline
16 & 1.577 & 1.57901700119157 & -0.00201700119156634 \tabularnewline
17 & 1.5553 & 1.56090629104503 & -0.00560629104503274 \tabularnewline
18 & 1.5557 & 1.55901031353179 & -0.00331031353178934 \tabularnewline
19 & 1.575 & 1.45949475928585 & 0.115505240714154 \tabularnewline
20 & 1.5527 & 1.58559394354555 & -0.0328939435455491 \tabularnewline
21 & 1.4748 & 1.53646247493622 & -0.0616624749362209 \tabularnewline
22 & 1.4718 & 1.53206827304489 & -0.0602682730448914 \tabularnewline
23 & 1.457 & 1.49466759529134 & -0.0376675952913359 \tabularnewline
24 & 1.4684 & 1.37709622807195 & 0.0913037719280496 \tabularnewline
25 & 1.4227 & 1.53175532803572 & -0.109055328035721 \tabularnewline
26 & 1.3896 & 1.52464227472821 & -0.13504227472821 \tabularnewline
27 & 1.3622 & 1.43800281111357 & -0.0758028111135665 \tabularnewline
28 & 1.3716 & 1.42641234790238 & -0.0548123479023817 \tabularnewline
29 & 1.3419 & 1.34679016706208 & -0.00489016706207801 \tabularnewline
30 & 1.3511 & 1.33449496993768 & 0.0166050300623219 \tabularnewline
31 & 1.3516 & 1.25822760853177 & 0.0933723914682347 \tabularnewline
32 & 1.3242 & 1.35138650493592 & -0.0271865049359226 \tabularnewline
33 & 1.3074 & 1.30137939946158 & 0.00602060053842113 \tabularnewline
34 & 1.2999 & 1.35045000608958 & -0.0505500060895849 \tabularnewline
35 & 1.3213 & 1.31247731831248 & 0.00882268168751876 \tabularnewline
36 & 1.2881 & 1.24275447667677 & 0.0453455233232307 \tabularnewline
37 & 1.2611 & 1.33654356203417 & -0.075443562034172 \tabularnewline
38 & 1.2727 & 1.34449608090303 & -0.0717960809030334 \tabularnewline
39 & 1.2811 & 1.31129252311742 & -0.0301925231174185 \tabularnewline
40 & 1.2684 & 1.33674834225979 & -0.068348342259788 \tabularnewline
41 & 1.265 & 1.24031980361613 & 0.0246801963838688 \tabularnewline
42 & 1.277 & 1.25384017144358 & 0.0231598285564221 \tabularnewline
43 & 1.2271 & 1.18556834906526 & 0.0415316509347436 \tabularnewline
44 & 1.202 & 1.22196351579028 & -0.0199635157902824 \tabularnewline
45 & 1.1938 & 1.17660844155495 & 0.0171915584450475 \tabularnewline
46 & 1.2103 & 1.22867594897188 & -0.0183759489718773 \tabularnewline
47 & 1.1856 & 1.21841282635249 & -0.0328128263524943 \tabularnewline
48 & 1.1786 & 1.11060737748961 & 0.0679926225103893 \tabularnewline
49 & 1.2015 & 1.21910619052557 & -0.0176061905255722 \tabularnewline
50 & 1.2256 & 1.27859172630983 & -0.0529917263098263 \tabularnewline
51 & 1.2292 & 1.26085249615482 & -0.031652496154819 \tabularnewline
52 & 1.2037 & 1.28051206921857 & -0.0768120692185719 \tabularnewline
53 & 1.2165 & 1.17462556555472 & 0.0418744344452815 \tabularnewline
54 & 1.2694 & 1.20399054661212 & 0.0654094533878815 \tabularnewline
55 & 1.2938 & 1.17821632266330 & 0.115583677336695 \tabularnewline
56 & 1.3201 & 1.29050337417145 & 0.0295966258285536 \tabularnewline
57 & 1.3014 & 1.29592964727458 & 0.00547035272541962 \tabularnewline
58 & 1.3119 & 1.34278347696348 & -0.0308834769634840 \tabularnewline
59 & 1.3408 & 1.32371290342279 & 0.0170870965772083 \tabularnewline
60 & 1.2991 & 1.26050411274305 & 0.0385958872569487 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63410&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]1.3322[/C][C]1.27138682727723[/C][C]0.060813172722769[/C][/ROW]
[ROW][C]14[/C][C]1.4369[/C][C]1.43185763494778[/C][C]0.00504236505221511[/C][/ROW]
[ROW][C]15[/C][C]1.4975[/C][C]1.49505700178949[/C][C]0.00244299821050853[/C][/ROW]
[ROW][C]16[/C][C]1.577[/C][C]1.57901700119157[/C][C]-0.00201700119156634[/C][/ROW]
[ROW][C]17[/C][C]1.5553[/C][C]1.56090629104503[/C][C]-0.00560629104503274[/C][/ROW]
[ROW][C]18[/C][C]1.5557[/C][C]1.55901031353179[/C][C]-0.00331031353178934[/C][/ROW]
[ROW][C]19[/C][C]1.575[/C][C]1.45949475928585[/C][C]0.115505240714154[/C][/ROW]
[ROW][C]20[/C][C]1.5527[/C][C]1.58559394354555[/C][C]-0.0328939435455491[/C][/ROW]
[ROW][C]21[/C][C]1.4748[/C][C]1.53646247493622[/C][C]-0.0616624749362209[/C][/ROW]
[ROW][C]22[/C][C]1.4718[/C][C]1.53206827304489[/C][C]-0.0602682730448914[/C][/ROW]
[ROW][C]23[/C][C]1.457[/C][C]1.49466759529134[/C][C]-0.0376675952913359[/C][/ROW]
[ROW][C]24[/C][C]1.4684[/C][C]1.37709622807195[/C][C]0.0913037719280496[/C][/ROW]
[ROW][C]25[/C][C]1.4227[/C][C]1.53175532803572[/C][C]-0.109055328035721[/C][/ROW]
[ROW][C]26[/C][C]1.3896[/C][C]1.52464227472821[/C][C]-0.13504227472821[/C][/ROW]
[ROW][C]27[/C][C]1.3622[/C][C]1.43800281111357[/C][C]-0.0758028111135665[/C][/ROW]
[ROW][C]28[/C][C]1.3716[/C][C]1.42641234790238[/C][C]-0.0548123479023817[/C][/ROW]
[ROW][C]29[/C][C]1.3419[/C][C]1.34679016706208[/C][C]-0.00489016706207801[/C][/ROW]
[ROW][C]30[/C][C]1.3511[/C][C]1.33449496993768[/C][C]0.0166050300623219[/C][/ROW]
[ROW][C]31[/C][C]1.3516[/C][C]1.25822760853177[/C][C]0.0933723914682347[/C][/ROW]
[ROW][C]32[/C][C]1.3242[/C][C]1.35138650493592[/C][C]-0.0271865049359226[/C][/ROW]
[ROW][C]33[/C][C]1.3074[/C][C]1.30137939946158[/C][C]0.00602060053842113[/C][/ROW]
[ROW][C]34[/C][C]1.2999[/C][C]1.35045000608958[/C][C]-0.0505500060895849[/C][/ROW]
[ROW][C]35[/C][C]1.3213[/C][C]1.31247731831248[/C][C]0.00882268168751876[/C][/ROW]
[ROW][C]36[/C][C]1.2881[/C][C]1.24275447667677[/C][C]0.0453455233232307[/C][/ROW]
[ROW][C]37[/C][C]1.2611[/C][C]1.33654356203417[/C][C]-0.075443562034172[/C][/ROW]
[ROW][C]38[/C][C]1.2727[/C][C]1.34449608090303[/C][C]-0.0717960809030334[/C][/ROW]
[ROW][C]39[/C][C]1.2811[/C][C]1.31129252311742[/C][C]-0.0301925231174185[/C][/ROW]
[ROW][C]40[/C][C]1.2684[/C][C]1.33674834225979[/C][C]-0.068348342259788[/C][/ROW]
[ROW][C]41[/C][C]1.265[/C][C]1.24031980361613[/C][C]0.0246801963838688[/C][/ROW]
[ROW][C]42[/C][C]1.277[/C][C]1.25384017144358[/C][C]0.0231598285564221[/C][/ROW]
[ROW][C]43[/C][C]1.2271[/C][C]1.18556834906526[/C][C]0.0415316509347436[/C][/ROW]
[ROW][C]44[/C][C]1.202[/C][C]1.22196351579028[/C][C]-0.0199635157902824[/C][/ROW]
[ROW][C]45[/C][C]1.1938[/C][C]1.17660844155495[/C][C]0.0171915584450475[/C][/ROW]
[ROW][C]46[/C][C]1.2103[/C][C]1.22867594897188[/C][C]-0.0183759489718773[/C][/ROW]
[ROW][C]47[/C][C]1.1856[/C][C]1.21841282635249[/C][C]-0.0328128263524943[/C][/ROW]
[ROW][C]48[/C][C]1.1786[/C][C]1.11060737748961[/C][C]0.0679926225103893[/C][/ROW]
[ROW][C]49[/C][C]1.2015[/C][C]1.21910619052557[/C][C]-0.0176061905255722[/C][/ROW]
[ROW][C]50[/C][C]1.2256[/C][C]1.27859172630983[/C][C]-0.0529917263098263[/C][/ROW]
[ROW][C]51[/C][C]1.2292[/C][C]1.26085249615482[/C][C]-0.031652496154819[/C][/ROW]
[ROW][C]52[/C][C]1.2037[/C][C]1.28051206921857[/C][C]-0.0768120692185719[/C][/ROW]
[ROW][C]53[/C][C]1.2165[/C][C]1.17462556555472[/C][C]0.0418744344452815[/C][/ROW]
[ROW][C]54[/C][C]1.2694[/C][C]1.20399054661212[/C][C]0.0654094533878815[/C][/ROW]
[ROW][C]55[/C][C]1.2938[/C][C]1.17821632266330[/C][C]0.115583677336695[/C][/ROW]
[ROW][C]56[/C][C]1.3201[/C][C]1.29050337417145[/C][C]0.0295966258285536[/C][/ROW]
[ROW][C]57[/C][C]1.3014[/C][C]1.29592964727458[/C][C]0.00547035272541962[/C][/ROW]
[ROW][C]58[/C][C]1.3119[/C][C]1.34278347696348[/C][C]-0.0308834769634840[/C][/ROW]
[ROW][C]59[/C][C]1.3408[/C][C]1.32371290342279[/C][C]0.0170870965772083[/C][/ROW]
[ROW][C]60[/C][C]1.2991[/C][C]1.26050411274305[/C][C]0.0385958872569487[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63410&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63410&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	1.3322	1.27138682727723	0.060813172722769
14	1.4369	1.43185763494778	0.00504236505221511
15	1.4975	1.49505700178949	0.00244299821050853
16	1.577	1.57901700119157	-0.00201700119156634
17	1.5553	1.56090629104503	-0.00560629104503274
18	1.5557	1.55901031353179	-0.00331031353178934
19	1.575	1.45949475928585	0.115505240714154
20	1.5527	1.58559394354555	-0.0328939435455491
21	1.4748	1.53646247493622	-0.0616624749362209
22	1.4718	1.53206827304489	-0.0602682730448914
23	1.457	1.49466759529134	-0.0376675952913359
24	1.4684	1.37709622807195	0.0913037719280496
25	1.4227	1.53175532803572	-0.109055328035721
26	1.3896	1.52464227472821	-0.13504227472821
27	1.3622	1.43800281111357	-0.0758028111135665
28	1.3716	1.42641234790238	-0.0548123479023817
29	1.3419	1.34679016706208	-0.00489016706207801
30	1.3511	1.33449496993768	0.0166050300623219
31	1.3516	1.25822760853177	0.0933723914682347
32	1.3242	1.35138650493592	-0.0271865049359226
33	1.3074	1.30137939946158	0.00602060053842113
34	1.2999	1.35045000608958	-0.0505500060895849
35	1.3213	1.31247731831248	0.00882268168751876
36	1.2881	1.24275447667677	0.0453455233232307
37	1.2611	1.33654356203417	-0.075443562034172
38	1.2727	1.34449608090303	-0.0717960809030334
39	1.2811	1.31129252311742	-0.0301925231174185
40	1.2684	1.33674834225979	-0.068348342259788
41	1.265	1.24031980361613	0.0246801963838688
42	1.277	1.25384017144358	0.0231598285564221
43	1.2271	1.18556834906526	0.0415316509347436
44	1.202	1.22196351579028	-0.0199635157902824
45	1.1938	1.17660844155495	0.0171915584450475
46	1.2103	1.22867594897188	-0.0183759489718773
47	1.1856	1.21841282635249	-0.0328128263524943
48	1.1786	1.11060737748961	0.0679926225103893
49	1.2015	1.21910619052557	-0.0176061905255722
50	1.2256	1.27859172630983	-0.0529917263098263
51	1.2292	1.26085249615482	-0.031652496154819
52	1.2037	1.28051206921857	-0.0768120692185719
53	1.2165	1.17462556555472	0.0418744344452815
54	1.2694	1.20399054661212	0.0654094533878815
55	1.2938	1.17821632266330	0.115583677336695
56	1.3201	1.29050337417145	0.0295966258285536
57	1.3014	1.29592964727458	0.00547035272541962
58	1.3119	1.34278347696348	-0.0308834769634840
59	1.3408	1.32371290342279	0.0170870965772083
60	1.2991	1.26050411274305	0.0385958872569487

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	1.34712743112759	1.23770582167322	1.45654904058196
62	1.43782379706115	1.27524907360653	1.60039852051578
63	1.48564709302681	1.28107682356050	1.69021736249312
64	1.55576704515589	1.30978316007633	1.80175093023546
65	1.52952500416283	1.2579452945092	1.80110471381646
66	1.52313345509329	1.22453751327517	1.82172939691141
67	1.41979176332391	1.11376843279392	1.72581509385389
68	1.41791397404660	1.08570265652350	1.75012529156970
69	1.39268497884431	1.04049507761551	1.74487488007311
70	1.43753871237516	1.04900386545718	1.82607355929314
71	1.45208058454113	1.03515680804109	1.86900436104118
72	1.36607635851613	-15.3216613736994	18.0538140907316

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 1.34712743112759 & 1.23770582167322 & 1.45654904058196 \tabularnewline
62 & 1.43782379706115 & 1.27524907360653 & 1.60039852051578 \tabularnewline
63 & 1.48564709302681 & 1.28107682356050 & 1.69021736249312 \tabularnewline
64 & 1.55576704515589 & 1.30978316007633 & 1.80175093023546 \tabularnewline
65 & 1.52952500416283 & 1.2579452945092 & 1.80110471381646 \tabularnewline
66 & 1.52313345509329 & 1.22453751327517 & 1.82172939691141 \tabularnewline
67 & 1.41979176332391 & 1.11376843279392 & 1.72581509385389 \tabularnewline
68 & 1.41791397404660 & 1.08570265652350 & 1.75012529156970 \tabularnewline
69 & 1.39268497884431 & 1.04049507761551 & 1.74487488007311 \tabularnewline
70 & 1.43753871237516 & 1.04900386545718 & 1.82607355929314 \tabularnewline
71 & 1.45208058454113 & 1.03515680804109 & 1.86900436104118 \tabularnewline
72 & 1.36607635851613 & -15.3216613736994 & 18.0538140907316 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63410&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]1.34712743112759[/C][C]1.23770582167322[/C][C]1.45654904058196[/C][/ROW]
[ROW][C]62[/C][C]1.43782379706115[/C][C]1.27524907360653[/C][C]1.60039852051578[/C][/ROW]
[ROW][C]63[/C][C]1.48564709302681[/C][C]1.28107682356050[/C][C]1.69021736249312[/C][/ROW]
[ROW][C]64[/C][C]1.55576704515589[/C][C]1.30978316007633[/C][C]1.80175093023546[/C][/ROW]
[ROW][C]65[/C][C]1.52952500416283[/C][C]1.2579452945092[/C][C]1.80110471381646[/C][/ROW]
[ROW][C]66[/C][C]1.52313345509329[/C][C]1.22453751327517[/C][C]1.82172939691141[/C][/ROW]
[ROW][C]67[/C][C]1.41979176332391[/C][C]1.11376843279392[/C][C]1.72581509385389[/C][/ROW]
[ROW][C]68[/C][C]1.41791397404660[/C][C]1.08570265652350[/C][C]1.75012529156970[/C][/ROW]
[ROW][C]69[/C][C]1.39268497884431[/C][C]1.04049507761551[/C][C]1.74487488007311[/C][/ROW]
[ROW][C]70[/C][C]1.43753871237516[/C][C]1.04900386545718[/C][C]1.82607355929314[/C][/ROW]
[ROW][C]71[/C][C]1.45208058454113[/C][C]1.03515680804109[/C][C]1.86900436104118[/C][/ROW]
[ROW][C]72[/C][C]1.36607635851613[/C][C]-15.3216613736994[/C][C]18.0538140907316[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63410&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63410&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	1.34712743112759	1.23770582167322	1.45654904058196
62	1.43782379706115	1.27524907360653	1.60039852051578
63	1.48564709302681	1.28107682356050	1.69021736249312
64	1.55576704515589	1.30978316007633	1.80175093023546
65	1.52952500416283	1.2579452945092	1.80110471381646
66	1.52313345509329	1.22453751327517	1.82172939691141
67	1.41979176332391	1.11376843279392	1.72581509385389
68	1.41791397404660	1.08570265652350	1.75012529156970
69	1.39268497884431	1.04049507761551	1.74487488007311
70	1.43753871237516	1.04900386545718	1.82607355929314
71	1.45208058454113	1.03515680804109	1.86900436104118
72	1.36607635851613	-15.3216613736994	18.0538140907316

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=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