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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sun, 12 Dec 2010 19:21:34 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/12/t1292181576dllkoxmp7m39hu3.htm/, Retrieved Tue, 07 May 2024 12:32:53 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=108628, Retrieved Tue, 07 May 2024 12:32:53 +0000

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Estimated Impact

175

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] [Unemployment] [2010-11-30 13:37:23] [b98453cac15ba1066b407e146608df68]
-   PD      [Exponential Smoothing] [ws8] [2010-12-12 19:21:34] [c1f1b5e209adb4577289f490325e36f2] [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	2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108628&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108628&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108628&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	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.824124154937339
beta	0
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.824124154937339 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108628&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]0.824124154937339[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108628&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108628&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	0.824124154937339
beta	0
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	1.2159	1.21481549145299	0.00108450854700815
14	1.1922	1.19014760613116	0.00205239386883771
15	1.2114	1.20910237848226	0.0022976215177386
16	1.2614	1.25777591552895	0.00362408447105467
17	1.2812	1.27404678940275	0.00715321059724694
18	1.2786	1.26838443469631	0.0102155653036904
19	1.2772	1.23867917380777	0.0385208261922347
20	1.2815	1.30482596212927	-0.0233259621292741
21	1.2679	1.26379915162306	0.00410084837693625
22	1.2765	1.27232543814791	0.0041745618520892
23	1.3247	1.25737080706151	0.0673291929384907
24	1.3191	1.31476343294957	0.00433656705043250
25	1.3029	1.34844971978419	-0.045549719784195
26	1.3234	1.28551966809666	0.0378803319033416
27	1.3354	1.33404423922357	0.00135576077642630
28	1.3651	1.38217485887561	-0.0170748588756138
29	1.3453	1.38200792159553	-0.0367079215955290
30	1.3534	1.34073714260800	0.0126628573920033
31	1.3706	1.31802696592211	0.0525730340778903
32	1.3638	1.38487716203193	-0.0210771620319317
33	1.4268	1.35052735548072	0.0762726445192803
34	1.4485	1.41854512693142	0.029954873068579
35	1.4635	1.43594404715227	0.0275559528477276
36	1.4587	1.44947970385063	0.0092202961493677
37	1.4876	1.47841699694778	0.00918300305221598
38	1.5189	1.47526683505939	0.0436331649406088
39	1.5783	1.52210866503914	0.0561913349608576
40	1.5633	1.6121891051201	-0.0488891051200999
41	1.5554	1.58235029754178	-0.0269502975417761
42	1.5757	1.55780413970757	0.0178958602924271
43	1.5593	1.54642584316601	0.0128741568339867
44	1.466	1.56760594513540	-0.101605945135396
45	1.4065	1.48401190275479	-0.0775119027547904
46	1.2759	1.41714593694552	-0.141245936945515
47	1.2705	1.29303222216783	-0.0225322221678332
48	1.3954	1.26206420484254	0.133335795157462
49	1.2793	1.39328151971938	-0.113981519719385
50	1.2694	1.29468745091825	-0.0252874509182524
51	1.3282	1.28693881536031	0.0412611846396893
52	1.323	1.34623384672595	-0.0232338467259532
53	1.4135	1.34139666361391	0.0721033363860906
54	1.4042	1.40637035404089	-0.00217035404088617
55	1.4253	1.37757180922969	0.0477281907703144
56	1.4322	1.40734167778628	0.0248583222137231
57	1.4632	1.4322074529292	0.0309925470708017
58	1.4713	1.44355334801683	0.0277466519831659
59	1.5016	1.47958938268773	0.0220106173122729
60	1.4318	1.51274361457281	-0.0809436145728115

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1.2159 & 1.21481549145299 & 0.00108450854700815 \tabularnewline
14 & 1.1922 & 1.19014760613116 & 0.00205239386883771 \tabularnewline
15 & 1.2114 & 1.20910237848226 & 0.0022976215177386 \tabularnewline
16 & 1.2614 & 1.25777591552895 & 0.00362408447105467 \tabularnewline
17 & 1.2812 & 1.27404678940275 & 0.00715321059724694 \tabularnewline
18 & 1.2786 & 1.26838443469631 & 0.0102155653036904 \tabularnewline
19 & 1.2772 & 1.23867917380777 & 0.0385208261922347 \tabularnewline
20 & 1.2815 & 1.30482596212927 & -0.0233259621292741 \tabularnewline
21 & 1.2679 & 1.26379915162306 & 0.00410084837693625 \tabularnewline
22 & 1.2765 & 1.27232543814791 & 0.0041745618520892 \tabularnewline
23 & 1.3247 & 1.25737080706151 & 0.0673291929384907 \tabularnewline
24 & 1.3191 & 1.31476343294957 & 0.00433656705043250 \tabularnewline
25 & 1.3029 & 1.34844971978419 & -0.045549719784195 \tabularnewline
26 & 1.3234 & 1.28551966809666 & 0.0378803319033416 \tabularnewline
27 & 1.3354 & 1.33404423922357 & 0.00135576077642630 \tabularnewline
28 & 1.3651 & 1.38217485887561 & -0.0170748588756138 \tabularnewline
29 & 1.3453 & 1.38200792159553 & -0.0367079215955290 \tabularnewline
30 & 1.3534 & 1.34073714260800 & 0.0126628573920033 \tabularnewline
31 & 1.3706 & 1.31802696592211 & 0.0525730340778903 \tabularnewline
32 & 1.3638 & 1.38487716203193 & -0.0210771620319317 \tabularnewline
33 & 1.4268 & 1.35052735548072 & 0.0762726445192803 \tabularnewline
34 & 1.4485 & 1.41854512693142 & 0.029954873068579 \tabularnewline
35 & 1.4635 & 1.43594404715227 & 0.0275559528477276 \tabularnewline
36 & 1.4587 & 1.44947970385063 & 0.0092202961493677 \tabularnewline
37 & 1.4876 & 1.47841699694778 & 0.00918300305221598 \tabularnewline
38 & 1.5189 & 1.47526683505939 & 0.0436331649406088 \tabularnewline
39 & 1.5783 & 1.52210866503914 & 0.0561913349608576 \tabularnewline
40 & 1.5633 & 1.6121891051201 & -0.0488891051200999 \tabularnewline
41 & 1.5554 & 1.58235029754178 & -0.0269502975417761 \tabularnewline
42 & 1.5757 & 1.55780413970757 & 0.0178958602924271 \tabularnewline
43 & 1.5593 & 1.54642584316601 & 0.0128741568339867 \tabularnewline
44 & 1.466 & 1.56760594513540 & -0.101605945135396 \tabularnewline
45 & 1.4065 & 1.48401190275479 & -0.0775119027547904 \tabularnewline
46 & 1.2759 & 1.41714593694552 & -0.141245936945515 \tabularnewline
47 & 1.2705 & 1.29303222216783 & -0.0225322221678332 \tabularnewline
48 & 1.3954 & 1.26206420484254 & 0.133335795157462 \tabularnewline
49 & 1.2793 & 1.39328151971938 & -0.113981519719385 \tabularnewline
50 & 1.2694 & 1.29468745091825 & -0.0252874509182524 \tabularnewline
51 & 1.3282 & 1.28693881536031 & 0.0412611846396893 \tabularnewline
52 & 1.323 & 1.34623384672595 & -0.0232338467259532 \tabularnewline
53 & 1.4135 & 1.34139666361391 & 0.0721033363860906 \tabularnewline
54 & 1.4042 & 1.40637035404089 & -0.00217035404088617 \tabularnewline
55 & 1.4253 & 1.37757180922969 & 0.0477281907703144 \tabularnewline
56 & 1.4322 & 1.40734167778628 & 0.0248583222137231 \tabularnewline
57 & 1.4632 & 1.4322074529292 & 0.0309925470708017 \tabularnewline
58 & 1.4713 & 1.44355334801683 & 0.0277466519831659 \tabularnewline
59 & 1.5016 & 1.47958938268773 & 0.0220106173122729 \tabularnewline
60 & 1.4318 & 1.51274361457281 & -0.0809436145728115 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108628&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]1.2159[/C][C]1.21481549145299[/C][C]0.00108450854700815[/C][/ROW]
[ROW][C]14[/C][C]1.1922[/C][C]1.19014760613116[/C][C]0.00205239386883771[/C][/ROW]
[ROW][C]15[/C][C]1.2114[/C][C]1.20910237848226[/C][C]0.0022976215177386[/C][/ROW]
[ROW][C]16[/C][C]1.2614[/C][C]1.25777591552895[/C][C]0.00362408447105467[/C][/ROW]
[ROW][C]17[/C][C]1.2812[/C][C]1.27404678940275[/C][C]0.00715321059724694[/C][/ROW]
[ROW][C]18[/C][C]1.2786[/C][C]1.26838443469631[/C][C]0.0102155653036904[/C][/ROW]
[ROW][C]19[/C][C]1.2772[/C][C]1.23867917380777[/C][C]0.0385208261922347[/C][/ROW]
[ROW][C]20[/C][C]1.2815[/C][C]1.30482596212927[/C][C]-0.0233259621292741[/C][/ROW]
[ROW][C]21[/C][C]1.2679[/C][C]1.26379915162306[/C][C]0.00410084837693625[/C][/ROW]
[ROW][C]22[/C][C]1.2765[/C][C]1.27232543814791[/C][C]0.0041745618520892[/C][/ROW]
[ROW][C]23[/C][C]1.3247[/C][C]1.25737080706151[/C][C]0.0673291929384907[/C][/ROW]
[ROW][C]24[/C][C]1.3191[/C][C]1.31476343294957[/C][C]0.00433656705043250[/C][/ROW]
[ROW][C]25[/C][C]1.3029[/C][C]1.34844971978419[/C][C]-0.045549719784195[/C][/ROW]
[ROW][C]26[/C][C]1.3234[/C][C]1.28551966809666[/C][C]0.0378803319033416[/C][/ROW]
[ROW][C]27[/C][C]1.3354[/C][C]1.33404423922357[/C][C]0.00135576077642630[/C][/ROW]
[ROW][C]28[/C][C]1.3651[/C][C]1.38217485887561[/C][C]-0.0170748588756138[/C][/ROW]
[ROW][C]29[/C][C]1.3453[/C][C]1.38200792159553[/C][C]-0.0367079215955290[/C][/ROW]
[ROW][C]30[/C][C]1.3534[/C][C]1.34073714260800[/C][C]0.0126628573920033[/C][/ROW]
[ROW][C]31[/C][C]1.3706[/C][C]1.31802696592211[/C][C]0.0525730340778903[/C][/ROW]
[ROW][C]32[/C][C]1.3638[/C][C]1.38487716203193[/C][C]-0.0210771620319317[/C][/ROW]
[ROW][C]33[/C][C]1.4268[/C][C]1.35052735548072[/C][C]0.0762726445192803[/C][/ROW]
[ROW][C]34[/C][C]1.4485[/C][C]1.41854512693142[/C][C]0.029954873068579[/C][/ROW]
[ROW][C]35[/C][C]1.4635[/C][C]1.43594404715227[/C][C]0.0275559528477276[/C][/ROW]
[ROW][C]36[/C][C]1.4587[/C][C]1.44947970385063[/C][C]0.0092202961493677[/C][/ROW]
[ROW][C]37[/C][C]1.4876[/C][C]1.47841699694778[/C][C]0.00918300305221598[/C][/ROW]
[ROW][C]38[/C][C]1.5189[/C][C]1.47526683505939[/C][C]0.0436331649406088[/C][/ROW]
[ROW][C]39[/C][C]1.5783[/C][C]1.52210866503914[/C][C]0.0561913349608576[/C][/ROW]
[ROW][C]40[/C][C]1.5633[/C][C]1.6121891051201[/C][C]-0.0488891051200999[/C][/ROW]
[ROW][C]41[/C][C]1.5554[/C][C]1.58235029754178[/C][C]-0.0269502975417761[/C][/ROW]
[ROW][C]42[/C][C]1.5757[/C][C]1.55780413970757[/C][C]0.0178958602924271[/C][/ROW]
[ROW][C]43[/C][C]1.5593[/C][C]1.54642584316601[/C][C]0.0128741568339867[/C][/ROW]
[ROW][C]44[/C][C]1.466[/C][C]1.56760594513540[/C][C]-0.101605945135396[/C][/ROW]
[ROW][C]45[/C][C]1.4065[/C][C]1.48401190275479[/C][C]-0.0775119027547904[/C][/ROW]
[ROW][C]46[/C][C]1.2759[/C][C]1.41714593694552[/C][C]-0.141245936945515[/C][/ROW]
[ROW][C]47[/C][C]1.2705[/C][C]1.29303222216783[/C][C]-0.0225322221678332[/C][/ROW]
[ROW][C]48[/C][C]1.3954[/C][C]1.26206420484254[/C][C]0.133335795157462[/C][/ROW]
[ROW][C]49[/C][C]1.2793[/C][C]1.39328151971938[/C][C]-0.113981519719385[/C][/ROW]
[ROW][C]50[/C][C]1.2694[/C][C]1.29468745091825[/C][C]-0.0252874509182524[/C][/ROW]
[ROW][C]51[/C][C]1.3282[/C][C]1.28693881536031[/C][C]0.0412611846396893[/C][/ROW]
[ROW][C]52[/C][C]1.323[/C][C]1.34623384672595[/C][C]-0.0232338467259532[/C][/ROW]
[ROW][C]53[/C][C]1.4135[/C][C]1.34139666361391[/C][C]0.0721033363860906[/C][/ROW]
[ROW][C]54[/C][C]1.4042[/C][C]1.40637035404089[/C][C]-0.00217035404088617[/C][/ROW]
[ROW][C]55[/C][C]1.4253[/C][C]1.37757180922969[/C][C]0.0477281907703144[/C][/ROW]
[ROW][C]56[/C][C]1.4322[/C][C]1.40734167778628[/C][C]0.0248583222137231[/C][/ROW]
[ROW][C]57[/C][C]1.4632[/C][C]1.4322074529292[/C][C]0.0309925470708017[/C][/ROW]
[ROW][C]58[/C][C]1.4713[/C][C]1.44355334801683[/C][C]0.0277466519831659[/C][/ROW]
[ROW][C]59[/C][C]1.5016[/C][C]1.47958938268773[/C][C]0.0220106173122729[/C][/ROW]
[ROW][C]60[/C][C]1.4318[/C][C]1.51274361457281[/C][C]-0.0809436145728115[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108628&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108628&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	1.2159	1.21481549145299	0.00108450854700815
14	1.1922	1.19014760613116	0.00205239386883771
15	1.2114	1.20910237848226	0.0022976215177386
16	1.2614	1.25777591552895	0.00362408447105467
17	1.2812	1.27404678940275	0.00715321059724694
18	1.2786	1.26838443469631	0.0102155653036904
19	1.2772	1.23867917380777	0.0385208261922347
20	1.2815	1.30482596212927	-0.0233259621292741
21	1.2679	1.26379915162306	0.00410084837693625
22	1.2765	1.27232543814791	0.0041745618520892
23	1.3247	1.25737080706151	0.0673291929384907
24	1.3191	1.31476343294957	0.00433656705043250
25	1.3029	1.34844971978419	-0.045549719784195
26	1.3234	1.28551966809666	0.0378803319033416
27	1.3354	1.33404423922357	0.00135576077642630
28	1.3651	1.38217485887561	-0.0170748588756138
29	1.3453	1.38200792159553	-0.0367079215955290
30	1.3534	1.34073714260800	0.0126628573920033
31	1.3706	1.31802696592211	0.0525730340778903
32	1.3638	1.38487716203193	-0.0210771620319317
33	1.4268	1.35052735548072	0.0762726445192803
34	1.4485	1.41854512693142	0.029954873068579
35	1.4635	1.43594404715227	0.0275559528477276
36	1.4587	1.44947970385063	0.0092202961493677
37	1.4876	1.47841699694778	0.00918300305221598
38	1.5189	1.47526683505939	0.0436331649406088
39	1.5783	1.52210866503914	0.0561913349608576
40	1.5633	1.6121891051201	-0.0488891051200999
41	1.5554	1.58235029754178	-0.0269502975417761
42	1.5757	1.55780413970757	0.0178958602924271
43	1.5593	1.54642584316601	0.0128741568339867
44	1.466	1.56760594513540	-0.101605945135396
45	1.4065	1.48401190275479	-0.0775119027547904
46	1.2759	1.41714593694552	-0.141245936945515
47	1.2705	1.29303222216783	-0.0225322221678332
48	1.3954	1.26206420484254	0.133335795157462
49	1.2793	1.39328151971938	-0.113981519719385
50	1.2694	1.29468745091825	-0.0252874509182524
51	1.3282	1.28693881536031	0.0412611846396893
52	1.323	1.34623384672595	-0.0232338467259532
53	1.4135	1.34139666361391	0.0721033363860906
54	1.4042	1.40637035404089	-0.00217035404088617
55	1.4253	1.37757180922969	0.0477281907703144
56	1.4322	1.40734167778628	0.0248583222137231
57	1.4632	1.4322074529292	0.0309925470708017
58	1.4713	1.44355334801683	0.0277466519831659
59	1.5016	1.47958938268773	0.0220106173122729
60	1.4318	1.51274361457281	-0.0809436145728115

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	1.42387095023263	1.32541206914885	1.52232983131641
62	1.43481094935116	1.30722477863904	1.56239712006327
63	1.45960661042826	1.30840373132310	1.61080948953342
64	1.47355418472723	1.30195467906826	1.64515369038619
65	1.50463208355988	1.31481514534015	1.69444902177960
66	1.49712072474974	1.29068780652248	1.70355364297700
67	1.47888676986446	1.25707912928251	1.70069441044642
68	1.46530042607692	1.22911679177250	1.70148406038134
69	1.47075871941284	1.2210252839142	1.72049215491148
70	1.45599203329487	1.19340705943181	1.71857700715793
71	1.46815255190275	1.19331633123419	1.74298877257130
72	1.46506013986014	1.17849596225923	1.75162431746105

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 1.42387095023263 & 1.32541206914885 & 1.52232983131641 \tabularnewline
62 & 1.43481094935116 & 1.30722477863904 & 1.56239712006327 \tabularnewline
63 & 1.45960661042826 & 1.30840373132310 & 1.61080948953342 \tabularnewline
64 & 1.47355418472723 & 1.30195467906826 & 1.64515369038619 \tabularnewline
65 & 1.50463208355988 & 1.31481514534015 & 1.69444902177960 \tabularnewline
66 & 1.49712072474974 & 1.29068780652248 & 1.70355364297700 \tabularnewline
67 & 1.47888676986446 & 1.25707912928251 & 1.70069441044642 \tabularnewline
68 & 1.46530042607692 & 1.22911679177250 & 1.70148406038134 \tabularnewline
69 & 1.47075871941284 & 1.2210252839142 & 1.72049215491148 \tabularnewline
70 & 1.45599203329487 & 1.19340705943181 & 1.71857700715793 \tabularnewline
71 & 1.46815255190275 & 1.19331633123419 & 1.74298877257130 \tabularnewline
72 & 1.46506013986014 & 1.17849596225923 & 1.75162431746105 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108628&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]1.42387095023263[/C][C]1.32541206914885[/C][C]1.52232983131641[/C][/ROW]
[ROW][C]62[/C][C]1.43481094935116[/C][C]1.30722477863904[/C][C]1.56239712006327[/C][/ROW]
[ROW][C]63[/C][C]1.45960661042826[/C][C]1.30840373132310[/C][C]1.61080948953342[/C][/ROW]
[ROW][C]64[/C][C]1.47355418472723[/C][C]1.30195467906826[/C][C]1.64515369038619[/C][/ROW]
[ROW][C]65[/C][C]1.50463208355988[/C][C]1.31481514534015[/C][C]1.69444902177960[/C][/ROW]
[ROW][C]66[/C][C]1.49712072474974[/C][C]1.29068780652248[/C][C]1.70355364297700[/C][/ROW]
[ROW][C]67[/C][C]1.47888676986446[/C][C]1.25707912928251[/C][C]1.70069441044642[/C][/ROW]
[ROW][C]68[/C][C]1.46530042607692[/C][C]1.22911679177250[/C][C]1.70148406038134[/C][/ROW]
[ROW][C]69[/C][C]1.47075871941284[/C][C]1.2210252839142[/C][C]1.72049215491148[/C][/ROW]
[ROW][C]70[/C][C]1.45599203329487[/C][C]1.19340705943181[/C][C]1.71857700715793[/C][/ROW]
[ROW][C]71[/C][C]1.46815255190275[/C][C]1.19331633123419[/C][C]1.74298877257130[/C][/ROW]
[ROW][C]72[/C][C]1.46506013986014[/C][C]1.17849596225923[/C][C]1.75162431746105[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108628&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108628&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	1.42387095023263	1.32541206914885	1.52232983131641
62	1.43481094935116	1.30722477863904	1.56239712006327
63	1.45960661042826	1.30840373132310	1.61080948953342
64	1.47355418472723	1.30195467906826	1.64515369038619
65	1.50463208355988	1.31481514534015	1.69444902177960
66	1.49712072474974	1.29068780652248	1.70355364297700
67	1.47888676986446	1.25707912928251	1.70069441044642
68	1.46530042607692	1.22911679177250	1.70148406038134
69	1.47075871941284	1.2210252839142	1.72049215491148
70	1.45599203329487	1.19340705943181	1.71857700715793
71	1.46815255190275	1.19331633123419	1.74298877257130
72	1.46506013986014	1.17849596225923	1.75162431746105

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 = 1 ; par2 = 0 ; par3 = 0 ; par4 = 1 ; par5 = 1 ; par6 = 0 ; par7 = 0 ; par8 = 1 ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = additive ;

R code (references can be found in the software module):

par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code