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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Fri, 04 Dec 2009 07:33:11 -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/t1259937249ucvtvexbopqk74x.htm/, Retrieved Sun, 28 Apr 2024 15:24:25 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=63614, Retrieved Sun, 28 Apr 2024 15:24:25 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

WS9,ES

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]
-   PD      [Exponential Smoothing] [] [2009-12-04 14:33:11] [30f5b608e5a1bbbae86b1702c0071566] [Current]

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Dataseries X:

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Histogram

Boxplots

1.3
1.2
1.1
1.4
1.2
1.5
1.1
1.3
1.5
1.1
1.4
1.3
1.5
1.6
1.7
1.1
1.6
1.3
1.7
1.6
1.7
1.9
1.8
1.9
1.6
1.5
1.6
1.6
1.7
2
2
1.9
1.7
1.8
1.9
1.7
2
2.1
2.4
2.5
2.5
2.6
2.2
2.5
2.8
2.8
2.9
3
3.1
2.9
2.7
2.2
2.5
2.3
2.6
2.3
2.2
1.8
1.8

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=63614&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=63614&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63614&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	0.553341713987221
beta	0
gamma	0.844083465078655

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.553341713987221 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.844083465078655 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63614&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]0.553341713987221[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.844083465078655[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63614&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63614&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	0.553341713987221
beta	0
gamma	0.844083465078655

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	1.5	1.41893876910371	0.0810612308962884
14	1.6	1.54887584608295	0.0511241539170475
15	1.7	1.68136239390808	0.0186376060919151
16	1.1	1.08280563043064	0.0171943695693588
17	1.6	1.56375566213877	0.0362443378612345
18	1.3	1.27387321470486	0.0261267852951392
19	1.7	1.36491384724107	0.335086152758934
20	1.6	1.82246058015649	-0.222460580156485
21	1.7	1.92866313091967	-0.228663130919671
22	1.9	1.32986489075222	0.57013510924778
23	1.8	2.11355119233864	-0.313551192338636
24	1.9	1.81445622294131	0.0855437770586895
25	1.6	2.19470352895315	-0.594703528953154
26	1.5	1.95022904457696	-0.45022904457696
27	1.6	1.79708414577162	-0.197084145771615
28	1.6	1.08250573695895	0.517494263041052
29	1.7	1.95840018769848	-0.258400187698482
30	2	1.45588632182518	0.544113678174821
31	2	1.98956097184463	0.0104390281553715
32	1.9	2.05727768595704	-0.157277685957041
33	1.7	2.23381218056110	-0.533812180561104
34	1.8	1.69559181661626	0.104408183383736
35	1.9	1.87207458653634	0.0279254134636573
36	1.7	1.91157141539358	-0.211571415393579
37	2	1.83074270791164	0.169257292088362
38	2.1	2.05386497901739	0.0461350209826064
39	2.4	2.32265111717495	0.077348882825051
40	2.5	1.8029790458527	0.697020954147298
41	2.5	2.58360963788585	-0.0836096378858513
42	2.6	2.39017044505937	0.209829554940633
43	2.2	2.53986759559519	-0.339867595595188
44	2.5	2.34313315453827	0.156866845461731
45	2.8	2.53907562490880	0.260924375091197
46	2.8	2.66520817257876	0.134791827421243
47	2.9	2.86413366372172	0.0358663362782807
48	3	2.76337592284359	0.236624077156410
49	3.1	3.1752437055419	-0.0752437055418973
50	2.9	3.24921777324037	-0.349217773240373
51	2.7	3.41375905686105	-0.71375905686105
52	2.2	2.53962118754568	-0.339621187545684
53	2.5	2.44868127014259	0.0513187298574125
54	2.3	2.43760728189445	-0.137607281894450
55	2.6	2.19540617847323	0.404593821526769
56	2.3	2.60922356027274	-0.309223560272744
57	2.2	2.57877530788985	-0.378775307889845
58	1.8	2.31551823875185	-0.515518238751847
59	1.8	2.10019434842643	-0.300194348426426

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1.5 & 1.41893876910371 & 0.0810612308962884 \tabularnewline
14 & 1.6 & 1.54887584608295 & 0.0511241539170475 \tabularnewline
15 & 1.7 & 1.68136239390808 & 0.0186376060919151 \tabularnewline
16 & 1.1 & 1.08280563043064 & 0.0171943695693588 \tabularnewline
17 & 1.6 & 1.56375566213877 & 0.0362443378612345 \tabularnewline
18 & 1.3 & 1.27387321470486 & 0.0261267852951392 \tabularnewline
19 & 1.7 & 1.36491384724107 & 0.335086152758934 \tabularnewline
20 & 1.6 & 1.82246058015649 & -0.222460580156485 \tabularnewline
21 & 1.7 & 1.92866313091967 & -0.228663130919671 \tabularnewline
22 & 1.9 & 1.32986489075222 & 0.57013510924778 \tabularnewline
23 & 1.8 & 2.11355119233864 & -0.313551192338636 \tabularnewline
24 & 1.9 & 1.81445622294131 & 0.0855437770586895 \tabularnewline
25 & 1.6 & 2.19470352895315 & -0.594703528953154 \tabularnewline
26 & 1.5 & 1.95022904457696 & -0.45022904457696 \tabularnewline
27 & 1.6 & 1.79708414577162 & -0.197084145771615 \tabularnewline
28 & 1.6 & 1.08250573695895 & 0.517494263041052 \tabularnewline
29 & 1.7 & 1.95840018769848 & -0.258400187698482 \tabularnewline
30 & 2 & 1.45588632182518 & 0.544113678174821 \tabularnewline
31 & 2 & 1.98956097184463 & 0.0104390281553715 \tabularnewline
32 & 1.9 & 2.05727768595704 & -0.157277685957041 \tabularnewline
33 & 1.7 & 2.23381218056110 & -0.533812180561104 \tabularnewline
34 & 1.8 & 1.69559181661626 & 0.104408183383736 \tabularnewline
35 & 1.9 & 1.87207458653634 & 0.0279254134636573 \tabularnewline
36 & 1.7 & 1.91157141539358 & -0.211571415393579 \tabularnewline
37 & 2 & 1.83074270791164 & 0.169257292088362 \tabularnewline
38 & 2.1 & 2.05386497901739 & 0.0461350209826064 \tabularnewline
39 & 2.4 & 2.32265111717495 & 0.077348882825051 \tabularnewline
40 & 2.5 & 1.8029790458527 & 0.697020954147298 \tabularnewline
41 & 2.5 & 2.58360963788585 & -0.0836096378858513 \tabularnewline
42 & 2.6 & 2.39017044505937 & 0.209829554940633 \tabularnewline
43 & 2.2 & 2.53986759559519 & -0.339867595595188 \tabularnewline
44 & 2.5 & 2.34313315453827 & 0.156866845461731 \tabularnewline
45 & 2.8 & 2.53907562490880 & 0.260924375091197 \tabularnewline
46 & 2.8 & 2.66520817257876 & 0.134791827421243 \tabularnewline
47 & 2.9 & 2.86413366372172 & 0.0358663362782807 \tabularnewline
48 & 3 & 2.76337592284359 & 0.236624077156410 \tabularnewline
49 & 3.1 & 3.1752437055419 & -0.0752437055418973 \tabularnewline
50 & 2.9 & 3.24921777324037 & -0.349217773240373 \tabularnewline
51 & 2.7 & 3.41375905686105 & -0.71375905686105 \tabularnewline
52 & 2.2 & 2.53962118754568 & -0.339621187545684 \tabularnewline
53 & 2.5 & 2.44868127014259 & 0.0513187298574125 \tabularnewline
54 & 2.3 & 2.43760728189445 & -0.137607281894450 \tabularnewline
55 & 2.6 & 2.19540617847323 & 0.404593821526769 \tabularnewline
56 & 2.3 & 2.60922356027274 & -0.309223560272744 \tabularnewline
57 & 2.2 & 2.57877530788985 & -0.378775307889845 \tabularnewline
58 & 1.8 & 2.31551823875185 & -0.515518238751847 \tabularnewline
59 & 1.8 & 2.10019434842643 & -0.300194348426426 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63614&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]1.5[/C][C]1.41893876910371[/C][C]0.0810612308962884[/C][/ROW]
[ROW][C]14[/C][C]1.6[/C][C]1.54887584608295[/C][C]0.0511241539170475[/C][/ROW]
[ROW][C]15[/C][C]1.7[/C][C]1.68136239390808[/C][C]0.0186376060919151[/C][/ROW]
[ROW][C]16[/C][C]1.1[/C][C]1.08280563043064[/C][C]0.0171943695693588[/C][/ROW]
[ROW][C]17[/C][C]1.6[/C][C]1.56375566213877[/C][C]0.0362443378612345[/C][/ROW]
[ROW][C]18[/C][C]1.3[/C][C]1.27387321470486[/C][C]0.0261267852951392[/C][/ROW]
[ROW][C]19[/C][C]1.7[/C][C]1.36491384724107[/C][C]0.335086152758934[/C][/ROW]
[ROW][C]20[/C][C]1.6[/C][C]1.82246058015649[/C][C]-0.222460580156485[/C][/ROW]
[ROW][C]21[/C][C]1.7[/C][C]1.92866313091967[/C][C]-0.228663130919671[/C][/ROW]
[ROW][C]22[/C][C]1.9[/C][C]1.32986489075222[/C][C]0.57013510924778[/C][/ROW]
[ROW][C]23[/C][C]1.8[/C][C]2.11355119233864[/C][C]-0.313551192338636[/C][/ROW]
[ROW][C]24[/C][C]1.9[/C][C]1.81445622294131[/C][C]0.0855437770586895[/C][/ROW]
[ROW][C]25[/C][C]1.6[/C][C]2.19470352895315[/C][C]-0.594703528953154[/C][/ROW]
[ROW][C]26[/C][C]1.5[/C][C]1.95022904457696[/C][C]-0.45022904457696[/C][/ROW]
[ROW][C]27[/C][C]1.6[/C][C]1.79708414577162[/C][C]-0.197084145771615[/C][/ROW]
[ROW][C]28[/C][C]1.6[/C][C]1.08250573695895[/C][C]0.517494263041052[/C][/ROW]
[ROW][C]29[/C][C]1.7[/C][C]1.95840018769848[/C][C]-0.258400187698482[/C][/ROW]
[ROW][C]30[/C][C]2[/C][C]1.45588632182518[/C][C]0.544113678174821[/C][/ROW]
[ROW][C]31[/C][C]2[/C][C]1.98956097184463[/C][C]0.0104390281553715[/C][/ROW]
[ROW][C]32[/C][C]1.9[/C][C]2.05727768595704[/C][C]-0.157277685957041[/C][/ROW]
[ROW][C]33[/C][C]1.7[/C][C]2.23381218056110[/C][C]-0.533812180561104[/C][/ROW]
[ROW][C]34[/C][C]1.8[/C][C]1.69559181661626[/C][C]0.104408183383736[/C][/ROW]
[ROW][C]35[/C][C]1.9[/C][C]1.87207458653634[/C][C]0.0279254134636573[/C][/ROW]
[ROW][C]36[/C][C]1.7[/C][C]1.91157141539358[/C][C]-0.211571415393579[/C][/ROW]
[ROW][C]37[/C][C]2[/C][C]1.83074270791164[/C][C]0.169257292088362[/C][/ROW]
[ROW][C]38[/C][C]2.1[/C][C]2.05386497901739[/C][C]0.0461350209826064[/C][/ROW]
[ROW][C]39[/C][C]2.4[/C][C]2.32265111717495[/C][C]0.077348882825051[/C][/ROW]
[ROW][C]40[/C][C]2.5[/C][C]1.8029790458527[/C][C]0.697020954147298[/C][/ROW]
[ROW][C]41[/C][C]2.5[/C][C]2.58360963788585[/C][C]-0.0836096378858513[/C][/ROW]
[ROW][C]42[/C][C]2.6[/C][C]2.39017044505937[/C][C]0.209829554940633[/C][/ROW]
[ROW][C]43[/C][C]2.2[/C][C]2.53986759559519[/C][C]-0.339867595595188[/C][/ROW]
[ROW][C]44[/C][C]2.5[/C][C]2.34313315453827[/C][C]0.156866845461731[/C][/ROW]
[ROW][C]45[/C][C]2.8[/C][C]2.53907562490880[/C][C]0.260924375091197[/C][/ROW]
[ROW][C]46[/C][C]2.8[/C][C]2.66520817257876[/C][C]0.134791827421243[/C][/ROW]
[ROW][C]47[/C][C]2.9[/C][C]2.86413366372172[/C][C]0.0358663362782807[/C][/ROW]
[ROW][C]48[/C][C]3[/C][C]2.76337592284359[/C][C]0.236624077156410[/C][/ROW]
[ROW][C]49[/C][C]3.1[/C][C]3.1752437055419[/C][C]-0.0752437055418973[/C][/ROW]
[ROW][C]50[/C][C]2.9[/C][C]3.24921777324037[/C][C]-0.349217773240373[/C][/ROW]
[ROW][C]51[/C][C]2.7[/C][C]3.41375905686105[/C][C]-0.71375905686105[/C][/ROW]
[ROW][C]52[/C][C]2.2[/C][C]2.53962118754568[/C][C]-0.339621187545684[/C][/ROW]
[ROW][C]53[/C][C]2.5[/C][C]2.44868127014259[/C][C]0.0513187298574125[/C][/ROW]
[ROW][C]54[/C][C]2.3[/C][C]2.43760728189445[/C][C]-0.137607281894450[/C][/ROW]
[ROW][C]55[/C][C]2.6[/C][C]2.19540617847323[/C][C]0.404593821526769[/C][/ROW]
[ROW][C]56[/C][C]2.3[/C][C]2.60922356027274[/C][C]-0.309223560272744[/C][/ROW]
[ROW][C]57[/C][C]2.2[/C][C]2.57877530788985[/C][C]-0.378775307889845[/C][/ROW]
[ROW][C]58[/C][C]1.8[/C][C]2.31551823875185[/C][C]-0.515518238751847[/C][/ROW]
[ROW][C]59[/C][C]1.8[/C][C]2.10019434842643[/C][C]-0.300194348426426[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63614&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63614&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	1.5	1.41893876910371	0.0810612308962884
14	1.6	1.54887584608295	0.0511241539170475
15	1.7	1.68136239390808	0.0186376060919151
16	1.1	1.08280563043064	0.0171943695693588
17	1.6	1.56375566213877	0.0362443378612345
18	1.3	1.27387321470486	0.0261267852951392
19	1.7	1.36491384724107	0.335086152758934
20	1.6	1.82246058015649	-0.222460580156485
21	1.7	1.92866313091967	-0.228663130919671
22	1.9	1.32986489075222	0.57013510924778
23	1.8	2.11355119233864	-0.313551192338636
24	1.9	1.81445622294131	0.0855437770586895
25	1.6	2.19470352895315	-0.594703528953154
26	1.5	1.95022904457696	-0.45022904457696
27	1.6	1.79708414577162	-0.197084145771615
28	1.6	1.08250573695895	0.517494263041052
29	1.7	1.95840018769848	-0.258400187698482
30	2	1.45588632182518	0.544113678174821
31	2	1.98956097184463	0.0104390281553715
32	1.9	2.05727768595704	-0.157277685957041
33	1.7	2.23381218056110	-0.533812180561104
34	1.8	1.69559181661626	0.104408183383736
35	1.9	1.87207458653634	0.0279254134636573
36	1.7	1.91157141539358	-0.211571415393579
37	2	1.83074270791164	0.169257292088362
38	2.1	2.05386497901739	0.0461350209826064
39	2.4	2.32265111717495	0.077348882825051
40	2.5	1.8029790458527	0.697020954147298
41	2.5	2.58360963788585	-0.0836096378858513
42	2.6	2.39017044505937	0.209829554940633
43	2.2	2.53986759559519	-0.339867595595188
44	2.5	2.34313315453827	0.156866845461731
45	2.8	2.53907562490880	0.260924375091197
46	2.8	2.66520817257876	0.134791827421243
47	2.9	2.86413366372172	0.0358663362782807
48	3	2.76337592284359	0.236624077156410
49	3.1	3.1752437055419	-0.0752437055418973
50	2.9	3.24921777324037	-0.349217773240373
51	2.7	3.41375905686105	-0.71375905686105
52	2.2	2.53962118754568	-0.339621187545684
53	2.5	2.44868127014259	0.0513187298574125
54	2.3	2.43760728189445	-0.137607281894450
55	2.6	2.19540617847323	0.404593821526769
56	2.3	2.60922356027274	-0.309223560272744
57	2.2	2.57877530788985	-0.378775307889845
58	1.8	2.31551823875185	-0.515518238751847
59	1.8	2.10019434842643	-0.300194348426426

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
60	1.90935052329672	1.33464623585302	2.48405481074042
61	2.02264668970715	1.34575824426485	2.69953513514946
62	2.03389952170057	1.27776359334414	2.79003545005699
63	2.17063004510033	1.31705579025328	3.02420429994738
64	1.90039992486478	1.05435390254632	2.74644594718325
65	2.11267824041330	1.1449013696028	3.08045511122381
66	2.02119494632359	1.03284060000782	3.00954929263936
67	2.04535069926650	0.999331002665473	3.09137039586754
68	1.98048045358057	0.91401774264963	3.04694316451151
69	2.07074736656975	0.922821646960254	3.21867308617925
70	1.94899880761724	0.814580887873234	3.08341672736124
71	2.09768248461301	-19.8481061927748	24.0434711620008

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
60 & 1.90935052329672 & 1.33464623585302 & 2.48405481074042 \tabularnewline
61 & 2.02264668970715 & 1.34575824426485 & 2.69953513514946 \tabularnewline
62 & 2.03389952170057 & 1.27776359334414 & 2.79003545005699 \tabularnewline
63 & 2.17063004510033 & 1.31705579025328 & 3.02420429994738 \tabularnewline
64 & 1.90039992486478 & 1.05435390254632 & 2.74644594718325 \tabularnewline
65 & 2.11267824041330 & 1.1449013696028 & 3.08045511122381 \tabularnewline
66 & 2.02119494632359 & 1.03284060000782 & 3.00954929263936 \tabularnewline
67 & 2.04535069926650 & 0.999331002665473 & 3.09137039586754 \tabularnewline
68 & 1.98048045358057 & 0.91401774264963 & 3.04694316451151 \tabularnewline
69 & 2.07074736656975 & 0.922821646960254 & 3.21867308617925 \tabularnewline
70 & 1.94899880761724 & 0.814580887873234 & 3.08341672736124 \tabularnewline
71 & 2.09768248461301 & -19.8481061927748 & 24.0434711620008 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63614&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]60[/C][C]1.90935052329672[/C][C]1.33464623585302[/C][C]2.48405481074042[/C][/ROW]
[ROW][C]61[/C][C]2.02264668970715[/C][C]1.34575824426485[/C][C]2.69953513514946[/C][/ROW]
[ROW][C]62[/C][C]2.03389952170057[/C][C]1.27776359334414[/C][C]2.79003545005699[/C][/ROW]
[ROW][C]63[/C][C]2.17063004510033[/C][C]1.31705579025328[/C][C]3.02420429994738[/C][/ROW]
[ROW][C]64[/C][C]1.90039992486478[/C][C]1.05435390254632[/C][C]2.74644594718325[/C][/ROW]
[ROW][C]65[/C][C]2.11267824041330[/C][C]1.1449013696028[/C][C]3.08045511122381[/C][/ROW]
[ROW][C]66[/C][C]2.02119494632359[/C][C]1.03284060000782[/C][C]3.00954929263936[/C][/ROW]
[ROW][C]67[/C][C]2.04535069926650[/C][C]0.999331002665473[/C][C]3.09137039586754[/C][/ROW]
[ROW][C]68[/C][C]1.98048045358057[/C][C]0.91401774264963[/C][C]3.04694316451151[/C][/ROW]
[ROW][C]69[/C][C]2.07074736656975[/C][C]0.922821646960254[/C][C]3.21867308617925[/C][/ROW]
[ROW][C]70[/C][C]1.94899880761724[/C][C]0.814580887873234[/C][C]3.08341672736124[/C][/ROW]
[ROW][C]71[/C][C]2.09768248461301[/C][C]-19.8481061927748[/C][C]24.0434711620008[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63614&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63614&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
60	1.90935052329672	1.33464623585302	2.48405481074042
61	2.02264668970715	1.34575824426485	2.69953513514946
62	2.03389952170057	1.27776359334414	2.79003545005699
63	2.17063004510033	1.31705579025328	3.02420429994738
64	1.90039992486478	1.05435390254632	2.74644594718325
65	2.11267824041330	1.1449013696028	3.08045511122381
66	2.02119494632359	1.03284060000782	3.00954929263936
67	2.04535069926650	0.999331002665473	3.09137039586754
68	1.98048045358057	0.91401774264963	3.04694316451151
69	2.07074736656975	0.922821646960254	3.21867308617925
70	1.94899880761724	0.814580887873234	3.08341672736124
71	2.09768248461301	-19.8481061927748	24.0434711620008

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 = 36 ; par2 = 0.0 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

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