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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Tue, 29 Nov 2011 10:13:08 -0500

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/29/t1322579624ftf2t8xn4xupaw9.htm/, Retrieved Fri, 26 Apr 2024 01:19:04 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=148498, Retrieved Fri, 26 Apr 2024 01:19:04 +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)

-       [Exponential Smoothing] [] [2011-11-29 15:13:08] [75a32e1bc492240bc1028714aca23077] [Current]
- R PD    [Exponential Smoothing] [] [2011-12-21 21:46:01] [493236dcc414c5f9e1823f06b33a5ad6] 

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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' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148498&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148498&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148498&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' @ jenkins.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.86146509347809
beta	0
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.86146509347809 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148498&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]0.86146509347809[/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=148498&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148498&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	0.86146509347809
beta	0
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	1.2613	1.21500972222222	0.0462902777777783
14	1.2646	1.25828755948306	0.00631244051693902
15	1.2262	1.22500088543094	0.00119911456906041
16	1.1985	1.19900509289648	-0.000505092896478043
17	1.2007	1.20022035178508	0.000479648214922523
18	1.2138	1.21183393076726	0.00196606923273923
19	1.2266	1.24453634290384	-0.0179363429038391
20	1.2176	1.19783102170874	0.0197689782912598
21	1.2218	1.21744085189493	0.00435914810506777
22	1.249	1.26554231794596	-0.0165423179459612
23	1.2991	1.25392956725818	0.0451704327418216
24	1.3408	1.35563853044377	-0.014838530443769
25	1.3119	1.38441051918731	-0.0725105191873137
26	1.3014	1.31980729083747	-0.0184072908374699
27	1.3201	1.26451705697116	0.0555829430288362
28	1.2938	1.28513494208257	0.00866505791743299
29	1.2694	1.2943863868171	-0.024986386817097
30	1.2165	1.28426778674666	-0.0677677867466608
31	1.2037	1.25413973731846	-0.050439737318456
32	1.2292	1.18465737956276	0.0445426204372443
33	1.2256	1.22347403831167	0.00212596168833157
34	1.2015	1.2667561095719	-0.0652561095718995
35	1.1786	1.22172749797515	-0.0431274979751475
36	1.1856	1.23905753991633	-0.0534575399163302
37	1.2103	1.22657101648504	-0.0162710164850444
38	1.1938	1.21791134226975	-0.0241113422697514
39	1.202	1.16795749733533	0.0340425026646656
40	1.2271	1.16351928014674	0.0635807198532559
41	1.277	1.2154167509736	0.0615832490263963
42	1.265	1.27394815309733	-0.00894815309732788
43	1.2684	1.29689170457694	-0.028491704576936
44	1.2811	1.25947518295149	0.0216248170485138
45	1.2727	1.27267276620706	2.72337929385635e-05
46	1.2611	1.30481208770141	-0.0437120877014137
47	1.2881	1.28140848405823	0.00669151594177042
48	1.3213	1.34022479608565	-0.0189247960856469
49	1.2999	1.36263865759394	-0.0627386575939433
50	1.3074	1.31286257378738	-0.0054625737873808
51	1.3242	1.28703032940876	0.0371696705912405
52	1.3516	1.2893781323874	0.0622218676125967
53	1.3511	1.33982828000746	0.011271719992539
54	1.3419	1.34524699486894	-0.00334699486893819
55	1.3716	1.37030828456802	0.00129171543198181
56	1.3622	1.36549202728323	-0.00329202728323263
57	1.3896	1.35423259972997	0.0353674002700293
58	1.4227	1.41075681822749	0.0119431817725106
59	1.4684	1.44228094502328	0.0261190549767163
60	1.457	1.51428465038934	-0.0572846503893354

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1.2613 & 1.21500972222222 & 0.0462902777777783 \tabularnewline
14 & 1.2646 & 1.25828755948306 & 0.00631244051693902 \tabularnewline
15 & 1.2262 & 1.22500088543094 & 0.00119911456906041 \tabularnewline
16 & 1.1985 & 1.19900509289648 & -0.000505092896478043 \tabularnewline
17 & 1.2007 & 1.20022035178508 & 0.000479648214922523 \tabularnewline
18 & 1.2138 & 1.21183393076726 & 0.00196606923273923 \tabularnewline
19 & 1.2266 & 1.24453634290384 & -0.0179363429038391 \tabularnewline
20 & 1.2176 & 1.19783102170874 & 0.0197689782912598 \tabularnewline
21 & 1.2218 & 1.21744085189493 & 0.00435914810506777 \tabularnewline
22 & 1.249 & 1.26554231794596 & -0.0165423179459612 \tabularnewline
23 & 1.2991 & 1.25392956725818 & 0.0451704327418216 \tabularnewline
24 & 1.3408 & 1.35563853044377 & -0.014838530443769 \tabularnewline
25 & 1.3119 & 1.38441051918731 & -0.0725105191873137 \tabularnewline
26 & 1.3014 & 1.31980729083747 & -0.0184072908374699 \tabularnewline
27 & 1.3201 & 1.26451705697116 & 0.0555829430288362 \tabularnewline
28 & 1.2938 & 1.28513494208257 & 0.00866505791743299 \tabularnewline
29 & 1.2694 & 1.2943863868171 & -0.024986386817097 \tabularnewline
30 & 1.2165 & 1.28426778674666 & -0.0677677867466608 \tabularnewline
31 & 1.2037 & 1.25413973731846 & -0.050439737318456 \tabularnewline
32 & 1.2292 & 1.18465737956276 & 0.0445426204372443 \tabularnewline
33 & 1.2256 & 1.22347403831167 & 0.00212596168833157 \tabularnewline
34 & 1.2015 & 1.2667561095719 & -0.0652561095718995 \tabularnewline
35 & 1.1786 & 1.22172749797515 & -0.0431274979751475 \tabularnewline
36 & 1.1856 & 1.23905753991633 & -0.0534575399163302 \tabularnewline
37 & 1.2103 & 1.22657101648504 & -0.0162710164850444 \tabularnewline
38 & 1.1938 & 1.21791134226975 & -0.0241113422697514 \tabularnewline
39 & 1.202 & 1.16795749733533 & 0.0340425026646656 \tabularnewline
40 & 1.2271 & 1.16351928014674 & 0.0635807198532559 \tabularnewline
41 & 1.277 & 1.2154167509736 & 0.0615832490263963 \tabularnewline
42 & 1.265 & 1.27394815309733 & -0.00894815309732788 \tabularnewline
43 & 1.2684 & 1.29689170457694 & -0.028491704576936 \tabularnewline
44 & 1.2811 & 1.25947518295149 & 0.0216248170485138 \tabularnewline
45 & 1.2727 & 1.27267276620706 & 2.72337929385635e-05 \tabularnewline
46 & 1.2611 & 1.30481208770141 & -0.0437120877014137 \tabularnewline
47 & 1.2881 & 1.28140848405823 & 0.00669151594177042 \tabularnewline
48 & 1.3213 & 1.34022479608565 & -0.0189247960856469 \tabularnewline
49 & 1.2999 & 1.36263865759394 & -0.0627386575939433 \tabularnewline
50 & 1.3074 & 1.31286257378738 & -0.0054625737873808 \tabularnewline
51 & 1.3242 & 1.28703032940876 & 0.0371696705912405 \tabularnewline
52 & 1.3516 & 1.2893781323874 & 0.0622218676125967 \tabularnewline
53 & 1.3511 & 1.33982828000746 & 0.011271719992539 \tabularnewline
54 & 1.3419 & 1.34524699486894 & -0.00334699486893819 \tabularnewline
55 & 1.3716 & 1.37030828456802 & 0.00129171543198181 \tabularnewline
56 & 1.3622 & 1.36549202728323 & -0.00329202728323263 \tabularnewline
57 & 1.3896 & 1.35423259972997 & 0.0353674002700293 \tabularnewline
58 & 1.4227 & 1.41075681822749 & 0.0119431817725106 \tabularnewline
59 & 1.4684 & 1.44228094502328 & 0.0261190549767163 \tabularnewline
60 & 1.457 & 1.51428465038934 & -0.0572846503893354 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148498&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]1.2613[/C][C]1.21500972222222[/C][C]0.0462902777777783[/C][/ROW]
[ROW][C]14[/C][C]1.2646[/C][C]1.25828755948306[/C][C]0.00631244051693902[/C][/ROW]
[ROW][C]15[/C][C]1.2262[/C][C]1.22500088543094[/C][C]0.00119911456906041[/C][/ROW]
[ROW][C]16[/C][C]1.1985[/C][C]1.19900509289648[/C][C]-0.000505092896478043[/C][/ROW]
[ROW][C]17[/C][C]1.2007[/C][C]1.20022035178508[/C][C]0.000479648214922523[/C][/ROW]
[ROW][C]18[/C][C]1.2138[/C][C]1.21183393076726[/C][C]0.00196606923273923[/C][/ROW]
[ROW][C]19[/C][C]1.2266[/C][C]1.24453634290384[/C][C]-0.0179363429038391[/C][/ROW]
[ROW][C]20[/C][C]1.2176[/C][C]1.19783102170874[/C][C]0.0197689782912598[/C][/ROW]
[ROW][C]21[/C][C]1.2218[/C][C]1.21744085189493[/C][C]0.00435914810506777[/C][/ROW]
[ROW][C]22[/C][C]1.249[/C][C]1.26554231794596[/C][C]-0.0165423179459612[/C][/ROW]
[ROW][C]23[/C][C]1.2991[/C][C]1.25392956725818[/C][C]0.0451704327418216[/C][/ROW]
[ROW][C]24[/C][C]1.3408[/C][C]1.35563853044377[/C][C]-0.014838530443769[/C][/ROW]
[ROW][C]25[/C][C]1.3119[/C][C]1.38441051918731[/C][C]-0.0725105191873137[/C][/ROW]
[ROW][C]26[/C][C]1.3014[/C][C]1.31980729083747[/C][C]-0.0184072908374699[/C][/ROW]
[ROW][C]27[/C][C]1.3201[/C][C]1.26451705697116[/C][C]0.0555829430288362[/C][/ROW]
[ROW][C]28[/C][C]1.2938[/C][C]1.28513494208257[/C][C]0.00866505791743299[/C][/ROW]
[ROW][C]29[/C][C]1.2694[/C][C]1.2943863868171[/C][C]-0.024986386817097[/C][/ROW]
[ROW][C]30[/C][C]1.2165[/C][C]1.28426778674666[/C][C]-0.0677677867466608[/C][/ROW]
[ROW][C]31[/C][C]1.2037[/C][C]1.25413973731846[/C][C]-0.050439737318456[/C][/ROW]
[ROW][C]32[/C][C]1.2292[/C][C]1.18465737956276[/C][C]0.0445426204372443[/C][/ROW]
[ROW][C]33[/C][C]1.2256[/C][C]1.22347403831167[/C][C]0.00212596168833157[/C][/ROW]
[ROW][C]34[/C][C]1.2015[/C][C]1.2667561095719[/C][C]-0.0652561095718995[/C][/ROW]
[ROW][C]35[/C][C]1.1786[/C][C]1.22172749797515[/C][C]-0.0431274979751475[/C][/ROW]
[ROW][C]36[/C][C]1.1856[/C][C]1.23905753991633[/C][C]-0.0534575399163302[/C][/ROW]
[ROW][C]37[/C][C]1.2103[/C][C]1.22657101648504[/C][C]-0.0162710164850444[/C][/ROW]
[ROW][C]38[/C][C]1.1938[/C][C]1.21791134226975[/C][C]-0.0241113422697514[/C][/ROW]
[ROW][C]39[/C][C]1.202[/C][C]1.16795749733533[/C][C]0.0340425026646656[/C][/ROW]
[ROW][C]40[/C][C]1.2271[/C][C]1.16351928014674[/C][C]0.0635807198532559[/C][/ROW]
[ROW][C]41[/C][C]1.277[/C][C]1.2154167509736[/C][C]0.0615832490263963[/C][/ROW]
[ROW][C]42[/C][C]1.265[/C][C]1.27394815309733[/C][C]-0.00894815309732788[/C][/ROW]
[ROW][C]43[/C][C]1.2684[/C][C]1.29689170457694[/C][C]-0.028491704576936[/C][/ROW]
[ROW][C]44[/C][C]1.2811[/C][C]1.25947518295149[/C][C]0.0216248170485138[/C][/ROW]
[ROW][C]45[/C][C]1.2727[/C][C]1.27267276620706[/C][C]2.72337929385635e-05[/C][/ROW]
[ROW][C]46[/C][C]1.2611[/C][C]1.30481208770141[/C][C]-0.0437120877014137[/C][/ROW]
[ROW][C]47[/C][C]1.2881[/C][C]1.28140848405823[/C][C]0.00669151594177042[/C][/ROW]
[ROW][C]48[/C][C]1.3213[/C][C]1.34022479608565[/C][C]-0.0189247960856469[/C][/ROW]
[ROW][C]49[/C][C]1.2999[/C][C]1.36263865759394[/C][C]-0.0627386575939433[/C][/ROW]
[ROW][C]50[/C][C]1.3074[/C][C]1.31286257378738[/C][C]-0.0054625737873808[/C][/ROW]
[ROW][C]51[/C][C]1.3242[/C][C]1.28703032940876[/C][C]0.0371696705912405[/C][/ROW]
[ROW][C]52[/C][C]1.3516[/C][C]1.2893781323874[/C][C]0.0622218676125967[/C][/ROW]
[ROW][C]53[/C][C]1.3511[/C][C]1.33982828000746[/C][C]0.011271719992539[/C][/ROW]
[ROW][C]54[/C][C]1.3419[/C][C]1.34524699486894[/C][C]-0.00334699486893819[/C][/ROW]
[ROW][C]55[/C][C]1.3716[/C][C]1.37030828456802[/C][C]0.00129171543198181[/C][/ROW]
[ROW][C]56[/C][C]1.3622[/C][C]1.36549202728323[/C][C]-0.00329202728323263[/C][/ROW]
[ROW][C]57[/C][C]1.3896[/C][C]1.35423259972997[/C][C]0.0353674002700293[/C][/ROW]
[ROW][C]58[/C][C]1.4227[/C][C]1.41075681822749[/C][C]0.0119431817725106[/C][/ROW]
[ROW][C]59[/C][C]1.4684[/C][C]1.44228094502328[/C][C]0.0261190549767163[/C][/ROW]
[ROW][C]60[/C][C]1.457[/C][C]1.51428465038934[/C][C]-0.0572846503893354[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148498&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148498&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	1.2613	1.21500972222222	0.0462902777777783
14	1.2646	1.25828755948306	0.00631244051693902
15	1.2262	1.22500088543094	0.00119911456906041
16	1.1985	1.19900509289648	-0.000505092896478043
17	1.2007	1.20022035178508	0.000479648214922523
18	1.2138	1.21183393076726	0.00196606923273923
19	1.2266	1.24453634290384	-0.0179363429038391
20	1.2176	1.19783102170874	0.0197689782912598
21	1.2218	1.21744085189493	0.00435914810506777
22	1.249	1.26554231794596	-0.0165423179459612
23	1.2991	1.25392956725818	0.0451704327418216
24	1.3408	1.35563853044377	-0.014838530443769
25	1.3119	1.38441051918731	-0.0725105191873137
26	1.3014	1.31980729083747	-0.0184072908374699
27	1.3201	1.26451705697116	0.0555829430288362
28	1.2938	1.28513494208257	0.00866505791743299
29	1.2694	1.2943863868171	-0.024986386817097
30	1.2165	1.28426778674666	-0.0677677867466608
31	1.2037	1.25413973731846	-0.050439737318456
32	1.2292	1.18465737956276	0.0445426204372443
33	1.2256	1.22347403831167	0.00212596168833157
34	1.2015	1.2667561095719	-0.0652561095718995
35	1.1786	1.22172749797515	-0.0431274979751475
36	1.1856	1.23905753991633	-0.0534575399163302
37	1.2103	1.22657101648504	-0.0162710164850444
38	1.1938	1.21791134226975	-0.0241113422697514
39	1.202	1.16795749733533	0.0340425026646656
40	1.2271	1.16351928014674	0.0635807198532559
41	1.277	1.2154167509736	0.0615832490263963
42	1.265	1.27394815309733	-0.00894815309732788
43	1.2684	1.29689170457694	-0.028491704576936
44	1.2811	1.25947518295149	0.0216248170485138
45	1.2727	1.27267276620706	2.72337929385635e-05
46	1.2611	1.30481208770141	-0.0437120877014137
47	1.2881	1.28140848405823	0.00669151594177042
48	1.3213	1.34022479608565	-0.0189247960856469
49	1.2999	1.36263865759394	-0.0627386575939433
50	1.3074	1.31286257378738	-0.0054625737873808
51	1.3242	1.28703032940876	0.0371696705912405
52	1.3516	1.2893781323874	0.0622218676125967
53	1.3511	1.33982828000746	0.011271719992539
54	1.3419	1.34524699486894	-0.00334699486893819
55	1.3716	1.37030828456802	0.00129171543198181
56	1.3622	1.36549202728323	-0.00329202728323263
57	1.3896	1.35423259972997	0.0353674002700293
58	1.4227	1.41075681822749	0.0119431817725106
59	1.4684	1.44228094502328	0.0261190549767163
60	1.457	1.51428465038934	-0.0572846503893354

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	1.49758308721568	1.4270117640726	1.56815441035877
62	1.50978890385406	1.41664218610779	1.60293562160033
63	1.49456853010363	1.38333764229075	1.60579941791651
64	1.46836656310436	1.34160572616968	1.59512740003904
65	1.45815636978733	1.31757077608329	1.59874196349137
66	1.45183968903497	1.29867210586589	1.60500727220405
67	1.48042692127961	1.31563521059429	1.64521863196493
68	1.47386288787089	1.29821463912547	1.64951113661631
69	1.47079510709119	1.28492335920015	1.65666685498224
70	1.49360647288911	1.29804495816597	1.68916798761225
71	1.51680581875204	1.31201249508755	1.72159914241652
72	1.55475454545455	1.34112799093876	1.76838109997033

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 1.49758308721568 & 1.4270117640726 & 1.56815441035877 \tabularnewline
62 & 1.50978890385406 & 1.41664218610779 & 1.60293562160033 \tabularnewline
63 & 1.49456853010363 & 1.38333764229075 & 1.60579941791651 \tabularnewline
64 & 1.46836656310436 & 1.34160572616968 & 1.59512740003904 \tabularnewline
65 & 1.45815636978733 & 1.31757077608329 & 1.59874196349137 \tabularnewline
66 & 1.45183968903497 & 1.29867210586589 & 1.60500727220405 \tabularnewline
67 & 1.48042692127961 & 1.31563521059429 & 1.64521863196493 \tabularnewline
68 & 1.47386288787089 & 1.29821463912547 & 1.64951113661631 \tabularnewline
69 & 1.47079510709119 & 1.28492335920015 & 1.65666685498224 \tabularnewline
70 & 1.49360647288911 & 1.29804495816597 & 1.68916798761225 \tabularnewline
71 & 1.51680581875204 & 1.31201249508755 & 1.72159914241652 \tabularnewline
72 & 1.55475454545455 & 1.34112799093876 & 1.76838109997033 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148498&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]1.49758308721568[/C][C]1.4270117640726[/C][C]1.56815441035877[/C][/ROW]
[ROW][C]62[/C][C]1.50978890385406[/C][C]1.41664218610779[/C][C]1.60293562160033[/C][/ROW]
[ROW][C]63[/C][C]1.49456853010363[/C][C]1.38333764229075[/C][C]1.60579941791651[/C][/ROW]
[ROW][C]64[/C][C]1.46836656310436[/C][C]1.34160572616968[/C][C]1.59512740003904[/C][/ROW]
[ROW][C]65[/C][C]1.45815636978733[/C][C]1.31757077608329[/C][C]1.59874196349137[/C][/ROW]
[ROW][C]66[/C][C]1.45183968903497[/C][C]1.29867210586589[/C][C]1.60500727220405[/C][/ROW]
[ROW][C]67[/C][C]1.48042692127961[/C][C]1.31563521059429[/C][C]1.64521863196493[/C][/ROW]
[ROW][C]68[/C][C]1.47386288787089[/C][C]1.29821463912547[/C][C]1.64951113661631[/C][/ROW]
[ROW][C]69[/C][C]1.47079510709119[/C][C]1.28492335920015[/C][C]1.65666685498224[/C][/ROW]
[ROW][C]70[/C][C]1.49360647288911[/C][C]1.29804495816597[/C][C]1.68916798761225[/C][/ROW]
[ROW][C]71[/C][C]1.51680581875204[/C][C]1.31201249508755[/C][C]1.72159914241652[/C][/ROW]
[ROW][C]72[/C][C]1.55475454545455[/C][C]1.34112799093876[/C][C]1.76838109997033[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148498&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148498&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	1.49758308721568	1.4270117640726	1.56815441035877
62	1.50978890385406	1.41664218610779	1.60293562160033
63	1.49456853010363	1.38333764229075	1.60579941791651
64	1.46836656310436	1.34160572616968	1.59512740003904
65	1.45815636978733	1.31757077608329	1.59874196349137
66	1.45183968903497	1.29867210586589	1.60500727220405
67	1.48042692127961	1.31563521059429	1.64521863196493
68	1.47386288787089	1.29821463912547	1.64951113661631
69	1.47079510709119	1.28492335920015	1.65666685498224
70	1.49360647288911	1.29804495816597	1.68916798761225
71	1.51680581875204	1.31201249508755	1.72159914241652
72	1.55475454545455	1.34112799093876	1.76838109997033

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 = additive ;

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