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Author

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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Fri, 04 Dec 2009 02:11:49 -0700

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/Dec/04/t1259917970c3ny0l2t4eumnjw.htm/, Retrieved Sun, 28 Apr 2024 16:55:32 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=63195, Retrieved Sun, 28 Apr 2024 16:55:32 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

132

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] [expo smoothing] [2009-12-04 09:11:49] [87085ce7f5378f281469a8b1f0969170] [Current]
-             [Exponential Smoothing] [Workshop 9-10] [2009-12-04 22:11:18] [aba88da643e3763d32ff92bd8f92a385] 
-             [Exponential Smoothing] [Workshop 9] [2009-12-05 14:19:14] [b6394cb5c2dcec6d17418d3cdf42d699] 

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Dataseries X:

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Histogram

Boxplots

5.7
6.1
6
5.9
5.8
5.7
5.6
5.4
5.4
5.5
5.6
5.7
5.9
6.1
6
5.8
5.8
5.7
5.5
5.3
5.2
5.2
5
5.1
5.1
5.2
4.9
4.8
4.5
4.5
4.4
4.4
4.2
4.1
3.9
3.8
3.9
4.2
4.1
3.8
3.6
3.7
3.5
3.4
3.1
3.1
3.1
3.2
3.3
3.5
3.6
3.5
3.3
3.2
3.1
3.2
3
3
3.1
3.4

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63195&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]3 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=63195&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63195&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	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.795617759934405
beta	0.115622092346912
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.795617759934405 \tabularnewline
beta & 0.115622092346912 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63195&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]0.795617759934405[/C][/ROW]
[ROW][C]beta[/C][C]0.115622092346912[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63195&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63195&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	0.795617759934405
beta	0.115622092346912
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	5.9	5.91141206844105	-0.0114120684410484
14	6.1	6.09959501506799	0.000404984932013797
15	6	6.00157408438233	-0.00157408438233375
16	5.8	5.81031371087173	-0.0103137108717304
17	5.8	5.82842033663677	-0.028420336636767
18	5.7	5.74202426512985	-0.0420242651298519
19	5.5	5.45947408374793	0.0405259162520668
20	5.3	5.27415719418642	0.0258428058135802
21	5.2	5.28338773530909	-0.0833877353090866
22	5.2	5.29816326227001	-0.0981632622700124
23	5	5.28991767617873	-0.289917676178727
24	5.1	5.09300016320327	0.00699983679672567
25	5.1	5.22129803504218	-0.121298035042178
26	5.2	5.23686392003097	-0.0368639200309691
27	4.9	5.05919557120876	-0.159195571208759
28	4.8	4.69830756726449	0.101692432735510
29	4.5	4.73103257316789	-0.231032573167893
30	4.5	4.40926848263627	0.0907315173637349
31	4.4	4.22730752354078	0.172692476459217
32	4.4	4.13339342179269	0.266606578207315
33	4.2	4.28455429904767	-0.0845542990476673
34	4.1	4.24486578898424	-0.14486578898424
35	3.9	4.10933651747807	-0.209336517478072
36	3.8	3.97489505508343	-0.174895055083426
37	3.9	3.84515059473186	0.0548494052681359
38	4.2	3.93673989363645	0.263260106363548
39	4.1	3.98650169833447	0.113498301665525
40	3.8	3.93018633909184	-0.130186339091839
41	3.6	3.71434602817831	-0.114346028178310
42	3.7	3.55385174913284	0.146148250867164
43	3.5	3.47219720812245	0.0278027918775474
44	3.4	3.30884476441603	0.0911552355839738
45	3.1	3.25237280793271	-0.152372807932715
46	3.1	3.10534363273615	-0.00534363273615002
47	3.1	3.04774695106348	0.0522530489365201
48	3.2	3.11468517381809	0.0853148261819148
49	3.3	3.25102718156222	0.0489728184377793
50	3.5	3.38743863026519	0.112561369734810
51	3.6	3.33044526200662	0.269554737993377
52	3.5	3.4035720801344	0.0964279198655986
53	3.3	3.43178898730854	-0.131788987308539
54	3.2	3.36210769613620	-0.162107696136195
55	3.1	3.05799001604015	0.0420099839598529
56	3.2	2.95932910718225	0.240670892817750
57	3	3.02065973935298	-0.0206597393529750
58	3	3.06029592031758	-0.060295920317579
59	3.1	3.01938236342738	0.0806176365726174
60	3.4	3.1688183551414	0.231181644858601

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 5.9 & 5.91141206844105 & -0.0114120684410484 \tabularnewline
14 & 6.1 & 6.09959501506799 & 0.000404984932013797 \tabularnewline
15 & 6 & 6.00157408438233 & -0.00157408438233375 \tabularnewline
16 & 5.8 & 5.81031371087173 & -0.0103137108717304 \tabularnewline
17 & 5.8 & 5.82842033663677 & -0.028420336636767 \tabularnewline
18 & 5.7 & 5.74202426512985 & -0.0420242651298519 \tabularnewline
19 & 5.5 & 5.45947408374793 & 0.0405259162520668 \tabularnewline
20 & 5.3 & 5.27415719418642 & 0.0258428058135802 \tabularnewline
21 & 5.2 & 5.28338773530909 & -0.0833877353090866 \tabularnewline
22 & 5.2 & 5.29816326227001 & -0.0981632622700124 \tabularnewline
23 & 5 & 5.28991767617873 & -0.289917676178727 \tabularnewline
24 & 5.1 & 5.09300016320327 & 0.00699983679672567 \tabularnewline
25 & 5.1 & 5.22129803504218 & -0.121298035042178 \tabularnewline
26 & 5.2 & 5.23686392003097 & -0.0368639200309691 \tabularnewline
27 & 4.9 & 5.05919557120876 & -0.159195571208759 \tabularnewline
28 & 4.8 & 4.69830756726449 & 0.101692432735510 \tabularnewline
29 & 4.5 & 4.73103257316789 & -0.231032573167893 \tabularnewline
30 & 4.5 & 4.40926848263627 & 0.0907315173637349 \tabularnewline
31 & 4.4 & 4.22730752354078 & 0.172692476459217 \tabularnewline
32 & 4.4 & 4.13339342179269 & 0.266606578207315 \tabularnewline
33 & 4.2 & 4.28455429904767 & -0.0845542990476673 \tabularnewline
34 & 4.1 & 4.24486578898424 & -0.14486578898424 \tabularnewline
35 & 3.9 & 4.10933651747807 & -0.209336517478072 \tabularnewline
36 & 3.8 & 3.97489505508343 & -0.174895055083426 \tabularnewline
37 & 3.9 & 3.84515059473186 & 0.0548494052681359 \tabularnewline
38 & 4.2 & 3.93673989363645 & 0.263260106363548 \tabularnewline
39 & 4.1 & 3.98650169833447 & 0.113498301665525 \tabularnewline
40 & 3.8 & 3.93018633909184 & -0.130186339091839 \tabularnewline
41 & 3.6 & 3.71434602817831 & -0.114346028178310 \tabularnewline
42 & 3.7 & 3.55385174913284 & 0.146148250867164 \tabularnewline
43 & 3.5 & 3.47219720812245 & 0.0278027918775474 \tabularnewline
44 & 3.4 & 3.30884476441603 & 0.0911552355839738 \tabularnewline
45 & 3.1 & 3.25237280793271 & -0.152372807932715 \tabularnewline
46 & 3.1 & 3.10534363273615 & -0.00534363273615002 \tabularnewline
47 & 3.1 & 3.04774695106348 & 0.0522530489365201 \tabularnewline
48 & 3.2 & 3.11468517381809 & 0.0853148261819148 \tabularnewline
49 & 3.3 & 3.25102718156222 & 0.0489728184377793 \tabularnewline
50 & 3.5 & 3.38743863026519 & 0.112561369734810 \tabularnewline
51 & 3.6 & 3.33044526200662 & 0.269554737993377 \tabularnewline
52 & 3.5 & 3.4035720801344 & 0.0964279198655986 \tabularnewline
53 & 3.3 & 3.43178898730854 & -0.131788987308539 \tabularnewline
54 & 3.2 & 3.36210769613620 & -0.162107696136195 \tabularnewline
55 & 3.1 & 3.05799001604015 & 0.0420099839598529 \tabularnewline
56 & 3.2 & 2.95932910718225 & 0.240670892817750 \tabularnewline
57 & 3 & 3.02065973935298 & -0.0206597393529750 \tabularnewline
58 & 3 & 3.06029592031758 & -0.060295920317579 \tabularnewline
59 & 3.1 & 3.01938236342738 & 0.0806176365726174 \tabularnewline
60 & 3.4 & 3.1688183551414 & 0.231181644858601 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63195&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]5.9[/C][C]5.91141206844105[/C][C]-0.0114120684410484[/C][/ROW]
[ROW][C]14[/C][C]6.1[/C][C]6.09959501506799[/C][C]0.000404984932013797[/C][/ROW]
[ROW][C]15[/C][C]6[/C][C]6.00157408438233[/C][C]-0.00157408438233375[/C][/ROW]
[ROW][C]16[/C][C]5.8[/C][C]5.81031371087173[/C][C]-0.0103137108717304[/C][/ROW]
[ROW][C]17[/C][C]5.8[/C][C]5.82842033663677[/C][C]-0.028420336636767[/C][/ROW]
[ROW][C]18[/C][C]5.7[/C][C]5.74202426512985[/C][C]-0.0420242651298519[/C][/ROW]
[ROW][C]19[/C][C]5.5[/C][C]5.45947408374793[/C][C]0.0405259162520668[/C][/ROW]
[ROW][C]20[/C][C]5.3[/C][C]5.27415719418642[/C][C]0.0258428058135802[/C][/ROW]
[ROW][C]21[/C][C]5.2[/C][C]5.28338773530909[/C][C]-0.0833877353090866[/C][/ROW]
[ROW][C]22[/C][C]5.2[/C][C]5.29816326227001[/C][C]-0.0981632622700124[/C][/ROW]
[ROW][C]23[/C][C]5[/C][C]5.28991767617873[/C][C]-0.289917676178727[/C][/ROW]
[ROW][C]24[/C][C]5.1[/C][C]5.09300016320327[/C][C]0.00699983679672567[/C][/ROW]
[ROW][C]25[/C][C]5.1[/C][C]5.22129803504218[/C][C]-0.121298035042178[/C][/ROW]
[ROW][C]26[/C][C]5.2[/C][C]5.23686392003097[/C][C]-0.0368639200309691[/C][/ROW]
[ROW][C]27[/C][C]4.9[/C][C]5.05919557120876[/C][C]-0.159195571208759[/C][/ROW]
[ROW][C]28[/C][C]4.8[/C][C]4.69830756726449[/C][C]0.101692432735510[/C][/ROW]
[ROW][C]29[/C][C]4.5[/C][C]4.73103257316789[/C][C]-0.231032573167893[/C][/ROW]
[ROW][C]30[/C][C]4.5[/C][C]4.40926848263627[/C][C]0.0907315173637349[/C][/ROW]
[ROW][C]31[/C][C]4.4[/C][C]4.22730752354078[/C][C]0.172692476459217[/C][/ROW]
[ROW][C]32[/C][C]4.4[/C][C]4.13339342179269[/C][C]0.266606578207315[/C][/ROW]
[ROW][C]33[/C][C]4.2[/C][C]4.28455429904767[/C][C]-0.0845542990476673[/C][/ROW]
[ROW][C]34[/C][C]4.1[/C][C]4.24486578898424[/C][C]-0.14486578898424[/C][/ROW]
[ROW][C]35[/C][C]3.9[/C][C]4.10933651747807[/C][C]-0.209336517478072[/C][/ROW]
[ROW][C]36[/C][C]3.8[/C][C]3.97489505508343[/C][C]-0.174895055083426[/C][/ROW]
[ROW][C]37[/C][C]3.9[/C][C]3.84515059473186[/C][C]0.0548494052681359[/C][/ROW]
[ROW][C]38[/C][C]4.2[/C][C]3.93673989363645[/C][C]0.263260106363548[/C][/ROW]
[ROW][C]39[/C][C]4.1[/C][C]3.98650169833447[/C][C]0.113498301665525[/C][/ROW]
[ROW][C]40[/C][C]3.8[/C][C]3.93018633909184[/C][C]-0.130186339091839[/C][/ROW]
[ROW][C]41[/C][C]3.6[/C][C]3.71434602817831[/C][C]-0.114346028178310[/C][/ROW]
[ROW][C]42[/C][C]3.7[/C][C]3.55385174913284[/C][C]0.146148250867164[/C][/ROW]
[ROW][C]43[/C][C]3.5[/C][C]3.47219720812245[/C][C]0.0278027918775474[/C][/ROW]
[ROW][C]44[/C][C]3.4[/C][C]3.30884476441603[/C][C]0.0911552355839738[/C][/ROW]
[ROW][C]45[/C][C]3.1[/C][C]3.25237280793271[/C][C]-0.152372807932715[/C][/ROW]
[ROW][C]46[/C][C]3.1[/C][C]3.10534363273615[/C][C]-0.00534363273615002[/C][/ROW]
[ROW][C]47[/C][C]3.1[/C][C]3.04774695106348[/C][C]0.0522530489365201[/C][/ROW]
[ROW][C]48[/C][C]3.2[/C][C]3.11468517381809[/C][C]0.0853148261819148[/C][/ROW]
[ROW][C]49[/C][C]3.3[/C][C]3.25102718156222[/C][C]0.0489728184377793[/C][/ROW]
[ROW][C]50[/C][C]3.5[/C][C]3.38743863026519[/C][C]0.112561369734810[/C][/ROW]
[ROW][C]51[/C][C]3.6[/C][C]3.33044526200662[/C][C]0.269554737993377[/C][/ROW]
[ROW][C]52[/C][C]3.5[/C][C]3.4035720801344[/C][C]0.0964279198655986[/C][/ROW]
[ROW][C]53[/C][C]3.3[/C][C]3.43178898730854[/C][C]-0.131788987308539[/C][/ROW]
[ROW][C]54[/C][C]3.2[/C][C]3.36210769613620[/C][C]-0.162107696136195[/C][/ROW]
[ROW][C]55[/C][C]3.1[/C][C]3.05799001604015[/C][C]0.0420099839598529[/C][/ROW]
[ROW][C]56[/C][C]3.2[/C][C]2.95932910718225[/C][C]0.240670892817750[/C][/ROW]
[ROW][C]57[/C][C]3[/C][C]3.02065973935298[/C][C]-0.0206597393529750[/C][/ROW]
[ROW][C]58[/C][C]3[/C][C]3.06029592031758[/C][C]-0.060295920317579[/C][/ROW]
[ROW][C]59[/C][C]3.1[/C][C]3.01938236342738[/C][C]0.0806176365726174[/C][/ROW]
[ROW][C]60[/C][C]3.4[/C][C]3.1688183551414[/C][C]0.231181644858601[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63195&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63195&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	5.9	5.91141206844105	-0.0114120684410484
14	6.1	6.09959501506799	0.000404984932013797
15	6	6.00157408438233	-0.00157408438233375
16	5.8	5.81031371087173	-0.0103137108717304
17	5.8	5.82842033663677	-0.028420336636767
18	5.7	5.74202426512985	-0.0420242651298519
19	5.5	5.45947408374793	0.0405259162520668
20	5.3	5.27415719418642	0.0258428058135802
21	5.2	5.28338773530909	-0.0833877353090866
22	5.2	5.29816326227001	-0.0981632622700124
23	5	5.28991767617873	-0.289917676178727
24	5.1	5.09300016320327	0.00699983679672567
25	5.1	5.22129803504218	-0.121298035042178
26	5.2	5.23686392003097	-0.0368639200309691
27	4.9	5.05919557120876	-0.159195571208759
28	4.8	4.69830756726449	0.101692432735510
29	4.5	4.73103257316789	-0.231032573167893
30	4.5	4.40926848263627	0.0907315173637349
31	4.4	4.22730752354078	0.172692476459217
32	4.4	4.13339342179269	0.266606578207315
33	4.2	4.28455429904767	-0.0845542990476673
34	4.1	4.24486578898424	-0.14486578898424
35	3.9	4.10933651747807	-0.209336517478072
36	3.8	3.97489505508343	-0.174895055083426
37	3.9	3.84515059473186	0.0548494052681359
38	4.2	3.93673989363645	0.263260106363548
39	4.1	3.98650169833447	0.113498301665525
40	3.8	3.93018633909184	-0.130186339091839
41	3.6	3.71434602817831	-0.114346028178310
42	3.7	3.55385174913284	0.146148250867164
43	3.5	3.47219720812245	0.0278027918775474
44	3.4	3.30884476441603	0.0911552355839738
45	3.1	3.25237280793271	-0.152372807932715
46	3.1	3.10534363273615	-0.00534363273615002
47	3.1	3.04774695106348	0.0522530489365201
48	3.2	3.11468517381809	0.0853148261819148
49	3.3	3.25102718156222	0.0489728184377793
50	3.5	3.38743863026519	0.112561369734810
51	3.6	3.33044526200662	0.269554737993377
52	3.5	3.4035720801344	0.0964279198655986
53	3.3	3.43178898730854	-0.131788987308539
54	3.2	3.36210769613620	-0.162107696136195
55	3.1	3.05799001604015	0.0420099839598529
56	3.2	2.95932910718225	0.240670892817750
57	3	3.02065973935298	-0.0206597393529750
58	3	3.06029592031758	-0.060295920317579
59	3.1	3.01938236342738	0.0806176365726174
60	3.4	3.1688183551414	0.231181644858601

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	3.49002179107176	3.22406804667539	3.75597553546813
62	3.67924954757116	3.31512459120152	4.04337450394081
63	3.61599089835826	3.17194885142785	4.06003294528867
64	3.46938596262686	2.95739418129983	3.9813777439539
65	3.39585861786705	2.81026355476833	3.98145368096577
66	3.45969461501472	2.77920701553256	4.14018221449687
67	3.36690773552337	2.61838644778714	4.11542902325959
68	3.31106711822	2.48810996930822	4.13402426713179
69	3.14138399121592	2.27297395993347	4.00979402249837
70	3.21440228855856	2.23757635421557	4.19122822290154
71	3.28245842628467	2.19353601591677	4.37138083665256
72	3.42532446035466	-123.777322913226	130.627971833935

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 3.49002179107176 & 3.22406804667539 & 3.75597553546813 \tabularnewline
62 & 3.67924954757116 & 3.31512459120152 & 4.04337450394081 \tabularnewline
63 & 3.61599089835826 & 3.17194885142785 & 4.06003294528867 \tabularnewline
64 & 3.46938596262686 & 2.95739418129983 & 3.9813777439539 \tabularnewline
65 & 3.39585861786705 & 2.81026355476833 & 3.98145368096577 \tabularnewline
66 & 3.45969461501472 & 2.77920701553256 & 4.14018221449687 \tabularnewline
67 & 3.36690773552337 & 2.61838644778714 & 4.11542902325959 \tabularnewline
68 & 3.31106711822 & 2.48810996930822 & 4.13402426713179 \tabularnewline
69 & 3.14138399121592 & 2.27297395993347 & 4.00979402249837 \tabularnewline
70 & 3.21440228855856 & 2.23757635421557 & 4.19122822290154 \tabularnewline
71 & 3.28245842628467 & 2.19353601591677 & 4.37138083665256 \tabularnewline
72 & 3.42532446035466 & -123.777322913226 & 130.627971833935 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63195&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]3.49002179107176[/C][C]3.22406804667539[/C][C]3.75597553546813[/C][/ROW]
[ROW][C]62[/C][C]3.67924954757116[/C][C]3.31512459120152[/C][C]4.04337450394081[/C][/ROW]
[ROW][C]63[/C][C]3.61599089835826[/C][C]3.17194885142785[/C][C]4.06003294528867[/C][/ROW]
[ROW][C]64[/C][C]3.46938596262686[/C][C]2.95739418129983[/C][C]3.9813777439539[/C][/ROW]
[ROW][C]65[/C][C]3.39585861786705[/C][C]2.81026355476833[/C][C]3.98145368096577[/C][/ROW]
[ROW][C]66[/C][C]3.45969461501472[/C][C]2.77920701553256[/C][C]4.14018221449687[/C][/ROW]
[ROW][C]67[/C][C]3.36690773552337[/C][C]2.61838644778714[/C][C]4.11542902325959[/C][/ROW]
[ROW][C]68[/C][C]3.31106711822[/C][C]2.48810996930822[/C][C]4.13402426713179[/C][/ROW]
[ROW][C]69[/C][C]3.14138399121592[/C][C]2.27297395993347[/C][C]4.00979402249837[/C][/ROW]
[ROW][C]70[/C][C]3.21440228855856[/C][C]2.23757635421557[/C][C]4.19122822290154[/C][/ROW]
[ROW][C]71[/C][C]3.28245842628467[/C][C]2.19353601591677[/C][C]4.37138083665256[/C][/ROW]
[ROW][C]72[/C][C]3.42532446035466[/C][C]-123.777322913226[/C][C]130.627971833935[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63195&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63195&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	3.49002179107176	3.22406804667539	3.75597553546813
62	3.67924954757116	3.31512459120152	4.04337450394081
63	3.61599089835826	3.17194885142785	4.06003294528867
64	3.46938596262686	2.95739418129983	3.9813777439539
65	3.39585861786705	2.81026355476833	3.98145368096577
66	3.45969461501472	2.77920701553256	4.14018221449687
67	3.36690773552337	2.61838644778714	4.11542902325959
68	3.31106711822	2.48810996930822	4.13402426713179
69	3.14138399121592	2.27297395993347	4.00979402249837
70	3.21440228855856	2.23757635421557	4.19122822290154
71	3.28245842628467	2.19353601591677	4.37138083665256
72	3.42532446035466	-123.777322913226	130.627971833935

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