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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Wed, 13 Aug 2008 07:54:47 -0600

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/2008/Aug/13/t1218635811hpmgacyij5zn9cj.htm/, Retrieved Tue, 14 May 2024 03:34:09 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=14037, Retrieved Tue, 14 May 2024 03:34:09 +0000

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IsPrivate?

No (this computation is public)

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Estimated Impact

291

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

-       [Exponential Smoothing] [Raf Mattheussen e...] [2008-08-13 13:54:47] [3b0a90e6bea50e83b08189298324fe13] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 4 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14037&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14037&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14037&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.914696945069777
beta	0
gamma	0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.914696945069777 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14037&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]0.914696945069777[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14037&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14037&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	0.914696945069777
beta	0
gamma	0

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	16.91	16.91	0
4	17.16	16.91	0.25
5	17.02	17.1386742362674	-0.118674236267445
6	17.23	17.0301232748951	0.199876725104875
7	17.22	17.2129499047391	0.00705009526089384
8	17.29	17.2193986053367	0.0706013946633028
9	17.3	17.2839774853529	0.0160225146471156
10	17.22	17.2986332305529	-0.0786332305529385
11	17.19	17.2267076547852	-0.0367076547851966
12	17.23	17.1931312750925	0.0368687249074995
13	17.36	17.226854985134	0.133145014865992
14	17.39	17.3486423234832	0.0413576765167996
15	17.29	17.3864720638483	-0.096472063848303
16	17.28	17.2982293617617	-0.0182293617616835
17	17.4	17.2815550202477	0.118444979752297
18	17.51	17.3898962813860	0.120103718614022
19	17.54	17.4997547858937	0.0402452141062533
20	17.64	17.5365669602904	0.103433039709586
21	17.65	17.6311768457321	0.0188231542679453
22	17.5	17.6483943274375	-0.148394327437519
23	17.37	17.5126584894647	-0.142658489464736
24	17.56	17.3821692049631	0.177830795036925
25	17.49	17.5448304899227	-0.0548304899226792
26	17.61	17.4946772082937	0.115322791706276
27	17.79	17.6001626135644	0.189837386435627
28	17.83	17.7738062909971	0.0561937090029261
29	17.56	17.8252065049542	-0.265206504954190
30	17.95	17.5826229250600	0.367377074940041
31	18.09	17.9186616131963	0.171338386803715
32	18.38	18.0753843121788	0.304615687821173
33	18.38	18.3540153512492	0.0259846487508177
34	18.44	18.3777834300803	0.0622165699197375
35	18.84	18.4346927365186	0.405307263481433
36	19.01	18.8054260522396	0.204573947760377
37	19.06	18.9925492172969	0.0674507827030943
38	19.06	19.054246242178	0.00575375782200993
39	18.97	19.0595091868805	-0.089509186880452
40	18.98	18.9776354070852	0.00236459291478042
41	19.41	18.9797982930007	0.430201706999298
42	19.55	19.3733024801568	0.176697519843238
43	19.64	19.5349271617588	0.105072838241220
44	19.71	19.6310369659078	0.0789630340921654
45	19.48	19.7032642119654	-0.223264211965379
46	19.48	19.4990451193372	-0.0190451193372354
47	19.41	19.4816246068610	-0.0716246068609756
48	19.25	19.4161097977734	-0.166109797773416
49	19.14	19.2641696732039	-0.124169673203912
50	19.21	19.1505920524540	0.0594079475460205
51	19.3	19.2049323205872	0.0950676794128107
52	19.53	19.2918904365210	0.238109563479039
53	19.14	19.5096885268271	-0.369688526827137
54	19.16	19.171535560711	-0.0115355607110104
55	19.24	19.160984018569	0.0790159814310165
56	19.38	19.2332596953956	0.146740304604375
57	19.27	19.3674826037359	-0.0974826037358554
58	19.27	19.2783155639012	-0.00831556390122046
59	19.07	19.2707093430042	-0.200709343004242
60	19.15	19.0871211201113	0.0628788798887001
61	19.24	19.1446362394549	0.0953637605450979
62	19.36	19.2318651798959	0.128134820104133
63	19.57	19.3490697084022	0.220930291597817
64	19.59	19.5511539712001	0.0388460287999202
65	19.36	19.5866863150715	-0.226686315071461
66	19.46	19.3793370351865	0.0806629648135306
67	19.65	19.4531192026817	0.196880797318322
68	19.46	19.6332054665316	-0.173205466531648
69	19.51	19.4747749554258	0.0352250445742364
70	19.64	19.5069951960878	0.133004803912236
71	19.64	19.6286542839059	0.0113457160941088
72	19.69	19.6390321757568	0.0509678242431981
73	19.28	19.6856522888889	-0.405652288888909
74	19.67	19.3146033794817	0.355396620518338
75	19.65	19.6396835825579	0.0103164174420876
76	19.6	19.6491199780763	-0.0491199780762521
77	19.53	19.604190084188	-0.074190084188011
78	19.64	19.5363286408268	0.103671359173230
79	19.67	19.6311565163538	0.0388434836462466
80	19.81	19.6666865321808	0.143313467819155
81	19.73	19.7977749233824	-0.0677749233823803
82	19.87	19.7357814080122	0.134218591987821
83	19.97	19.858550744075	0.111449255924992
84	20.12	19.9604930379999	0.159506962000105
85	19.94	20.1063935688588	-0.166393568858751
86	20.31	19.9541938797444	0.355806120255604
87	20.13	20.2796486509793	-0.149648650979326
88	20.22	20.1427654870947	0.077234512905278
89	20.38	20.2134116601031	0.166588339896869
90	20.44	20.3657895056910	0.0742104943089608
91	20.34	20.4336696181276	-0.0936696181275636
92	20.14	20.3479903045804	-0.207990304580427
93	19.97	20.1577422083766	-0.18774220837658
94	19.82	19.9860149839139	-0.166014983913868
95	19.98	19.8341615852920	0.145838414707956
96	20.12	19.9675595376992	0.152440462300770

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 16.91 & 16.91 & 0 \tabularnewline
4 & 17.16 & 16.91 & 0.25 \tabularnewline
5 & 17.02 & 17.1386742362674 & -0.118674236267445 \tabularnewline
6 & 17.23 & 17.0301232748951 & 0.199876725104875 \tabularnewline
7 & 17.22 & 17.2129499047391 & 0.00705009526089384 \tabularnewline
8 & 17.29 & 17.2193986053367 & 0.0706013946633028 \tabularnewline
9 & 17.3 & 17.2839774853529 & 0.0160225146471156 \tabularnewline
10 & 17.22 & 17.2986332305529 & -0.0786332305529385 \tabularnewline
11 & 17.19 & 17.2267076547852 & -0.0367076547851966 \tabularnewline
12 & 17.23 & 17.1931312750925 & 0.0368687249074995 \tabularnewline
13 & 17.36 & 17.226854985134 & 0.133145014865992 \tabularnewline
14 & 17.39 & 17.3486423234832 & 0.0413576765167996 \tabularnewline
15 & 17.29 & 17.3864720638483 & -0.096472063848303 \tabularnewline
16 & 17.28 & 17.2982293617617 & -0.0182293617616835 \tabularnewline
17 & 17.4 & 17.2815550202477 & 0.118444979752297 \tabularnewline
18 & 17.51 & 17.3898962813860 & 0.120103718614022 \tabularnewline
19 & 17.54 & 17.4997547858937 & 0.0402452141062533 \tabularnewline
20 & 17.64 & 17.5365669602904 & 0.103433039709586 \tabularnewline
21 & 17.65 & 17.6311768457321 & 0.0188231542679453 \tabularnewline
22 & 17.5 & 17.6483943274375 & -0.148394327437519 \tabularnewline
23 & 17.37 & 17.5126584894647 & -0.142658489464736 \tabularnewline
24 & 17.56 & 17.3821692049631 & 0.177830795036925 \tabularnewline
25 & 17.49 & 17.5448304899227 & -0.0548304899226792 \tabularnewline
26 & 17.61 & 17.4946772082937 & 0.115322791706276 \tabularnewline
27 & 17.79 & 17.6001626135644 & 0.189837386435627 \tabularnewline
28 & 17.83 & 17.7738062909971 & 0.0561937090029261 \tabularnewline
29 & 17.56 & 17.8252065049542 & -0.265206504954190 \tabularnewline
30 & 17.95 & 17.5826229250600 & 0.367377074940041 \tabularnewline
31 & 18.09 & 17.9186616131963 & 0.171338386803715 \tabularnewline
32 & 18.38 & 18.0753843121788 & 0.304615687821173 \tabularnewline
33 & 18.38 & 18.3540153512492 & 0.0259846487508177 \tabularnewline
34 & 18.44 & 18.3777834300803 & 0.0622165699197375 \tabularnewline
35 & 18.84 & 18.4346927365186 & 0.405307263481433 \tabularnewline
36 & 19.01 & 18.8054260522396 & 0.204573947760377 \tabularnewline
37 & 19.06 & 18.9925492172969 & 0.0674507827030943 \tabularnewline
38 & 19.06 & 19.054246242178 & 0.00575375782200993 \tabularnewline
39 & 18.97 & 19.0595091868805 & -0.089509186880452 \tabularnewline
40 & 18.98 & 18.9776354070852 & 0.00236459291478042 \tabularnewline
41 & 19.41 & 18.9797982930007 & 0.430201706999298 \tabularnewline
42 & 19.55 & 19.3733024801568 & 0.176697519843238 \tabularnewline
43 & 19.64 & 19.5349271617588 & 0.105072838241220 \tabularnewline
44 & 19.71 & 19.6310369659078 & 0.0789630340921654 \tabularnewline
45 & 19.48 & 19.7032642119654 & -0.223264211965379 \tabularnewline
46 & 19.48 & 19.4990451193372 & -0.0190451193372354 \tabularnewline
47 & 19.41 & 19.4816246068610 & -0.0716246068609756 \tabularnewline
48 & 19.25 & 19.4161097977734 & -0.166109797773416 \tabularnewline
49 & 19.14 & 19.2641696732039 & -0.124169673203912 \tabularnewline
50 & 19.21 & 19.1505920524540 & 0.0594079475460205 \tabularnewline
51 & 19.3 & 19.2049323205872 & 0.0950676794128107 \tabularnewline
52 & 19.53 & 19.2918904365210 & 0.238109563479039 \tabularnewline
53 & 19.14 & 19.5096885268271 & -0.369688526827137 \tabularnewline
54 & 19.16 & 19.171535560711 & -0.0115355607110104 \tabularnewline
55 & 19.24 & 19.160984018569 & 0.0790159814310165 \tabularnewline
56 & 19.38 & 19.2332596953956 & 0.146740304604375 \tabularnewline
57 & 19.27 & 19.3674826037359 & -0.0974826037358554 \tabularnewline
58 & 19.27 & 19.2783155639012 & -0.00831556390122046 \tabularnewline
59 & 19.07 & 19.2707093430042 & -0.200709343004242 \tabularnewline
60 & 19.15 & 19.0871211201113 & 0.0628788798887001 \tabularnewline
61 & 19.24 & 19.1446362394549 & 0.0953637605450979 \tabularnewline
62 & 19.36 & 19.2318651798959 & 0.128134820104133 \tabularnewline
63 & 19.57 & 19.3490697084022 & 0.220930291597817 \tabularnewline
64 & 19.59 & 19.5511539712001 & 0.0388460287999202 \tabularnewline
65 & 19.36 & 19.5866863150715 & -0.226686315071461 \tabularnewline
66 & 19.46 & 19.3793370351865 & 0.0806629648135306 \tabularnewline
67 & 19.65 & 19.4531192026817 & 0.196880797318322 \tabularnewline
68 & 19.46 & 19.6332054665316 & -0.173205466531648 \tabularnewline
69 & 19.51 & 19.4747749554258 & 0.0352250445742364 \tabularnewline
70 & 19.64 & 19.5069951960878 & 0.133004803912236 \tabularnewline
71 & 19.64 & 19.6286542839059 & 0.0113457160941088 \tabularnewline
72 & 19.69 & 19.6390321757568 & 0.0509678242431981 \tabularnewline
73 & 19.28 & 19.6856522888889 & -0.405652288888909 \tabularnewline
74 & 19.67 & 19.3146033794817 & 0.355396620518338 \tabularnewline
75 & 19.65 & 19.6396835825579 & 0.0103164174420876 \tabularnewline
76 & 19.6 & 19.6491199780763 & -0.0491199780762521 \tabularnewline
77 & 19.53 & 19.604190084188 & -0.074190084188011 \tabularnewline
78 & 19.64 & 19.5363286408268 & 0.103671359173230 \tabularnewline
79 & 19.67 & 19.6311565163538 & 0.0388434836462466 \tabularnewline
80 & 19.81 & 19.6666865321808 & 0.143313467819155 \tabularnewline
81 & 19.73 & 19.7977749233824 & -0.0677749233823803 \tabularnewline
82 & 19.87 & 19.7357814080122 & 0.134218591987821 \tabularnewline
83 & 19.97 & 19.858550744075 & 0.111449255924992 \tabularnewline
84 & 20.12 & 19.9604930379999 & 0.159506962000105 \tabularnewline
85 & 19.94 & 20.1063935688588 & -0.166393568858751 \tabularnewline
86 & 20.31 & 19.9541938797444 & 0.355806120255604 \tabularnewline
87 & 20.13 & 20.2796486509793 & -0.149648650979326 \tabularnewline
88 & 20.22 & 20.1427654870947 & 0.077234512905278 \tabularnewline
89 & 20.38 & 20.2134116601031 & 0.166588339896869 \tabularnewline
90 & 20.44 & 20.3657895056910 & 0.0742104943089608 \tabularnewline
91 & 20.34 & 20.4336696181276 & -0.0936696181275636 \tabularnewline
92 & 20.14 & 20.3479903045804 & -0.207990304580427 \tabularnewline
93 & 19.97 & 20.1577422083766 & -0.18774220837658 \tabularnewline
94 & 19.82 & 19.9860149839139 & -0.166014983913868 \tabularnewline
95 & 19.98 & 19.8341615852920 & 0.145838414707956 \tabularnewline
96 & 20.12 & 19.9675595376992 & 0.152440462300770 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14037&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]3[/C][C]16.91[/C][C]16.91[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]17.16[/C][C]16.91[/C][C]0.25[/C][/ROW]
[ROW][C]5[/C][C]17.02[/C][C]17.1386742362674[/C][C]-0.118674236267445[/C][/ROW]
[ROW][C]6[/C][C]17.23[/C][C]17.0301232748951[/C][C]0.199876725104875[/C][/ROW]
[ROW][C]7[/C][C]17.22[/C][C]17.2129499047391[/C][C]0.00705009526089384[/C][/ROW]
[ROW][C]8[/C][C]17.29[/C][C]17.2193986053367[/C][C]0.0706013946633028[/C][/ROW]
[ROW][C]9[/C][C]17.3[/C][C]17.2839774853529[/C][C]0.0160225146471156[/C][/ROW]
[ROW][C]10[/C][C]17.22[/C][C]17.2986332305529[/C][C]-0.0786332305529385[/C][/ROW]
[ROW][C]11[/C][C]17.19[/C][C]17.2267076547852[/C][C]-0.0367076547851966[/C][/ROW]
[ROW][C]12[/C][C]17.23[/C][C]17.1931312750925[/C][C]0.0368687249074995[/C][/ROW]
[ROW][C]13[/C][C]17.36[/C][C]17.226854985134[/C][C]0.133145014865992[/C][/ROW]
[ROW][C]14[/C][C]17.39[/C][C]17.3486423234832[/C][C]0.0413576765167996[/C][/ROW]
[ROW][C]15[/C][C]17.29[/C][C]17.3864720638483[/C][C]-0.096472063848303[/C][/ROW]
[ROW][C]16[/C][C]17.28[/C][C]17.2982293617617[/C][C]-0.0182293617616835[/C][/ROW]
[ROW][C]17[/C][C]17.4[/C][C]17.2815550202477[/C][C]0.118444979752297[/C][/ROW]
[ROW][C]18[/C][C]17.51[/C][C]17.3898962813860[/C][C]0.120103718614022[/C][/ROW]
[ROW][C]19[/C][C]17.54[/C][C]17.4997547858937[/C][C]0.0402452141062533[/C][/ROW]
[ROW][C]20[/C][C]17.64[/C][C]17.5365669602904[/C][C]0.103433039709586[/C][/ROW]
[ROW][C]21[/C][C]17.65[/C][C]17.6311768457321[/C][C]0.0188231542679453[/C][/ROW]
[ROW][C]22[/C][C]17.5[/C][C]17.6483943274375[/C][C]-0.148394327437519[/C][/ROW]
[ROW][C]23[/C][C]17.37[/C][C]17.5126584894647[/C][C]-0.142658489464736[/C][/ROW]
[ROW][C]24[/C][C]17.56[/C][C]17.3821692049631[/C][C]0.177830795036925[/C][/ROW]
[ROW][C]25[/C][C]17.49[/C][C]17.5448304899227[/C][C]-0.0548304899226792[/C][/ROW]
[ROW][C]26[/C][C]17.61[/C][C]17.4946772082937[/C][C]0.115322791706276[/C][/ROW]
[ROW][C]27[/C][C]17.79[/C][C]17.6001626135644[/C][C]0.189837386435627[/C][/ROW]
[ROW][C]28[/C][C]17.83[/C][C]17.7738062909971[/C][C]0.0561937090029261[/C][/ROW]
[ROW][C]29[/C][C]17.56[/C][C]17.8252065049542[/C][C]-0.265206504954190[/C][/ROW]
[ROW][C]30[/C][C]17.95[/C][C]17.5826229250600[/C][C]0.367377074940041[/C][/ROW]
[ROW][C]31[/C][C]18.09[/C][C]17.9186616131963[/C][C]0.171338386803715[/C][/ROW]
[ROW][C]32[/C][C]18.38[/C][C]18.0753843121788[/C][C]0.304615687821173[/C][/ROW]
[ROW][C]33[/C][C]18.38[/C][C]18.3540153512492[/C][C]0.0259846487508177[/C][/ROW]
[ROW][C]34[/C][C]18.44[/C][C]18.3777834300803[/C][C]0.0622165699197375[/C][/ROW]
[ROW][C]35[/C][C]18.84[/C][C]18.4346927365186[/C][C]0.405307263481433[/C][/ROW]
[ROW][C]36[/C][C]19.01[/C][C]18.8054260522396[/C][C]0.204573947760377[/C][/ROW]
[ROW][C]37[/C][C]19.06[/C][C]18.9925492172969[/C][C]0.0674507827030943[/C][/ROW]
[ROW][C]38[/C][C]19.06[/C][C]19.054246242178[/C][C]0.00575375782200993[/C][/ROW]
[ROW][C]39[/C][C]18.97[/C][C]19.0595091868805[/C][C]-0.089509186880452[/C][/ROW]
[ROW][C]40[/C][C]18.98[/C][C]18.9776354070852[/C][C]0.00236459291478042[/C][/ROW]
[ROW][C]41[/C][C]19.41[/C][C]18.9797982930007[/C][C]0.430201706999298[/C][/ROW]
[ROW][C]42[/C][C]19.55[/C][C]19.3733024801568[/C][C]0.176697519843238[/C][/ROW]
[ROW][C]43[/C][C]19.64[/C][C]19.5349271617588[/C][C]0.105072838241220[/C][/ROW]
[ROW][C]44[/C][C]19.71[/C][C]19.6310369659078[/C][C]0.0789630340921654[/C][/ROW]
[ROW][C]45[/C][C]19.48[/C][C]19.7032642119654[/C][C]-0.223264211965379[/C][/ROW]
[ROW][C]46[/C][C]19.48[/C][C]19.4990451193372[/C][C]-0.0190451193372354[/C][/ROW]
[ROW][C]47[/C][C]19.41[/C][C]19.4816246068610[/C][C]-0.0716246068609756[/C][/ROW]
[ROW][C]48[/C][C]19.25[/C][C]19.4161097977734[/C][C]-0.166109797773416[/C][/ROW]
[ROW][C]49[/C][C]19.14[/C][C]19.2641696732039[/C][C]-0.124169673203912[/C][/ROW]
[ROW][C]50[/C][C]19.21[/C][C]19.1505920524540[/C][C]0.0594079475460205[/C][/ROW]
[ROW][C]51[/C][C]19.3[/C][C]19.2049323205872[/C][C]0.0950676794128107[/C][/ROW]
[ROW][C]52[/C][C]19.53[/C][C]19.2918904365210[/C][C]0.238109563479039[/C][/ROW]
[ROW][C]53[/C][C]19.14[/C][C]19.5096885268271[/C][C]-0.369688526827137[/C][/ROW]
[ROW][C]54[/C][C]19.16[/C][C]19.171535560711[/C][C]-0.0115355607110104[/C][/ROW]
[ROW][C]55[/C][C]19.24[/C][C]19.160984018569[/C][C]0.0790159814310165[/C][/ROW]
[ROW][C]56[/C][C]19.38[/C][C]19.2332596953956[/C][C]0.146740304604375[/C][/ROW]
[ROW][C]57[/C][C]19.27[/C][C]19.3674826037359[/C][C]-0.0974826037358554[/C][/ROW]
[ROW][C]58[/C][C]19.27[/C][C]19.2783155639012[/C][C]-0.00831556390122046[/C][/ROW]
[ROW][C]59[/C][C]19.07[/C][C]19.2707093430042[/C][C]-0.200709343004242[/C][/ROW]
[ROW][C]60[/C][C]19.15[/C][C]19.0871211201113[/C][C]0.0628788798887001[/C][/ROW]
[ROW][C]61[/C][C]19.24[/C][C]19.1446362394549[/C][C]0.0953637605450979[/C][/ROW]
[ROW][C]62[/C][C]19.36[/C][C]19.2318651798959[/C][C]0.128134820104133[/C][/ROW]
[ROW][C]63[/C][C]19.57[/C][C]19.3490697084022[/C][C]0.220930291597817[/C][/ROW]
[ROW][C]64[/C][C]19.59[/C][C]19.5511539712001[/C][C]0.0388460287999202[/C][/ROW]
[ROW][C]65[/C][C]19.36[/C][C]19.5866863150715[/C][C]-0.226686315071461[/C][/ROW]
[ROW][C]66[/C][C]19.46[/C][C]19.3793370351865[/C][C]0.0806629648135306[/C][/ROW]
[ROW][C]67[/C][C]19.65[/C][C]19.4531192026817[/C][C]0.196880797318322[/C][/ROW]
[ROW][C]68[/C][C]19.46[/C][C]19.6332054665316[/C][C]-0.173205466531648[/C][/ROW]
[ROW][C]69[/C][C]19.51[/C][C]19.4747749554258[/C][C]0.0352250445742364[/C][/ROW]
[ROW][C]70[/C][C]19.64[/C][C]19.5069951960878[/C][C]0.133004803912236[/C][/ROW]
[ROW][C]71[/C][C]19.64[/C][C]19.6286542839059[/C][C]0.0113457160941088[/C][/ROW]
[ROW][C]72[/C][C]19.69[/C][C]19.6390321757568[/C][C]0.0509678242431981[/C][/ROW]
[ROW][C]73[/C][C]19.28[/C][C]19.6856522888889[/C][C]-0.405652288888909[/C][/ROW]
[ROW][C]74[/C][C]19.67[/C][C]19.3146033794817[/C][C]0.355396620518338[/C][/ROW]
[ROW][C]75[/C][C]19.65[/C][C]19.6396835825579[/C][C]0.0103164174420876[/C][/ROW]
[ROW][C]76[/C][C]19.6[/C][C]19.6491199780763[/C][C]-0.0491199780762521[/C][/ROW]
[ROW][C]77[/C][C]19.53[/C][C]19.604190084188[/C][C]-0.074190084188011[/C][/ROW]
[ROW][C]78[/C][C]19.64[/C][C]19.5363286408268[/C][C]0.103671359173230[/C][/ROW]
[ROW][C]79[/C][C]19.67[/C][C]19.6311565163538[/C][C]0.0388434836462466[/C][/ROW]
[ROW][C]80[/C][C]19.81[/C][C]19.6666865321808[/C][C]0.143313467819155[/C][/ROW]
[ROW][C]81[/C][C]19.73[/C][C]19.7977749233824[/C][C]-0.0677749233823803[/C][/ROW]
[ROW][C]82[/C][C]19.87[/C][C]19.7357814080122[/C][C]0.134218591987821[/C][/ROW]
[ROW][C]83[/C][C]19.97[/C][C]19.858550744075[/C][C]0.111449255924992[/C][/ROW]
[ROW][C]84[/C][C]20.12[/C][C]19.9604930379999[/C][C]0.159506962000105[/C][/ROW]
[ROW][C]85[/C][C]19.94[/C][C]20.1063935688588[/C][C]-0.166393568858751[/C][/ROW]
[ROW][C]86[/C][C]20.31[/C][C]19.9541938797444[/C][C]0.355806120255604[/C][/ROW]
[ROW][C]87[/C][C]20.13[/C][C]20.2796486509793[/C][C]-0.149648650979326[/C][/ROW]
[ROW][C]88[/C][C]20.22[/C][C]20.1427654870947[/C][C]0.077234512905278[/C][/ROW]
[ROW][C]89[/C][C]20.38[/C][C]20.2134116601031[/C][C]0.166588339896869[/C][/ROW]
[ROW][C]90[/C][C]20.44[/C][C]20.3657895056910[/C][C]0.0742104943089608[/C][/ROW]
[ROW][C]91[/C][C]20.34[/C][C]20.4336696181276[/C][C]-0.0936696181275636[/C][/ROW]
[ROW][C]92[/C][C]20.14[/C][C]20.3479903045804[/C][C]-0.207990304580427[/C][/ROW]
[ROW][C]93[/C][C]19.97[/C][C]20.1577422083766[/C][C]-0.18774220837658[/C][/ROW]
[ROW][C]94[/C][C]19.82[/C][C]19.9860149839139[/C][C]-0.166014983913868[/C][/ROW]
[ROW][C]95[/C][C]19.98[/C][C]19.8341615852920[/C][C]0.145838414707956[/C][/ROW]
[ROW][C]96[/C][C]20.12[/C][C]19.9675595376992[/C][C]0.152440462300770[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14037&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14037&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
3	16.91	16.91	0
4	17.16	16.91	0.25
5	17.02	17.1386742362674	-0.118674236267445
6	17.23	17.0301232748951	0.199876725104875
7	17.22	17.2129499047391	0.00705009526089384
8	17.29	17.2193986053367	0.0706013946633028
9	17.3	17.2839774853529	0.0160225146471156
10	17.22	17.2986332305529	-0.0786332305529385
11	17.19	17.2267076547852	-0.0367076547851966
12	17.23	17.1931312750925	0.0368687249074995
13	17.36	17.226854985134	0.133145014865992
14	17.39	17.3486423234832	0.0413576765167996
15	17.29	17.3864720638483	-0.096472063848303
16	17.28	17.2982293617617	-0.0182293617616835
17	17.4	17.2815550202477	0.118444979752297
18	17.51	17.3898962813860	0.120103718614022
19	17.54	17.4997547858937	0.0402452141062533
20	17.64	17.5365669602904	0.103433039709586
21	17.65	17.6311768457321	0.0188231542679453
22	17.5	17.6483943274375	-0.148394327437519
23	17.37	17.5126584894647	-0.142658489464736
24	17.56	17.3821692049631	0.177830795036925
25	17.49	17.5448304899227	-0.0548304899226792
26	17.61	17.4946772082937	0.115322791706276
27	17.79	17.6001626135644	0.189837386435627
28	17.83	17.7738062909971	0.0561937090029261
29	17.56	17.8252065049542	-0.265206504954190
30	17.95	17.5826229250600	0.367377074940041
31	18.09	17.9186616131963	0.171338386803715
32	18.38	18.0753843121788	0.304615687821173
33	18.38	18.3540153512492	0.0259846487508177
34	18.44	18.3777834300803	0.0622165699197375
35	18.84	18.4346927365186	0.405307263481433
36	19.01	18.8054260522396	0.204573947760377
37	19.06	18.9925492172969	0.0674507827030943
38	19.06	19.054246242178	0.00575375782200993
39	18.97	19.0595091868805	-0.089509186880452
40	18.98	18.9776354070852	0.00236459291478042
41	19.41	18.9797982930007	0.430201706999298
42	19.55	19.3733024801568	0.176697519843238
43	19.64	19.5349271617588	0.105072838241220
44	19.71	19.6310369659078	0.0789630340921654
45	19.48	19.7032642119654	-0.223264211965379
46	19.48	19.4990451193372	-0.0190451193372354
47	19.41	19.4816246068610	-0.0716246068609756
48	19.25	19.4161097977734	-0.166109797773416
49	19.14	19.2641696732039	-0.124169673203912
50	19.21	19.1505920524540	0.0594079475460205
51	19.3	19.2049323205872	0.0950676794128107
52	19.53	19.2918904365210	0.238109563479039
53	19.14	19.5096885268271	-0.369688526827137
54	19.16	19.171535560711	-0.0115355607110104
55	19.24	19.160984018569	0.0790159814310165
56	19.38	19.2332596953956	0.146740304604375
57	19.27	19.3674826037359	-0.0974826037358554
58	19.27	19.2783155639012	-0.00831556390122046
59	19.07	19.2707093430042	-0.200709343004242
60	19.15	19.0871211201113	0.0628788798887001
61	19.24	19.1446362394549	0.0953637605450979
62	19.36	19.2318651798959	0.128134820104133
63	19.57	19.3490697084022	0.220930291597817
64	19.59	19.5511539712001	0.0388460287999202
65	19.36	19.5866863150715	-0.226686315071461
66	19.46	19.3793370351865	0.0806629648135306
67	19.65	19.4531192026817	0.196880797318322
68	19.46	19.6332054665316	-0.173205466531648
69	19.51	19.4747749554258	0.0352250445742364
70	19.64	19.5069951960878	0.133004803912236
71	19.64	19.6286542839059	0.0113457160941088
72	19.69	19.6390321757568	0.0509678242431981
73	19.28	19.6856522888889	-0.405652288888909
74	19.67	19.3146033794817	0.355396620518338
75	19.65	19.6396835825579	0.0103164174420876
76	19.6	19.6491199780763	-0.0491199780762521
77	19.53	19.604190084188	-0.074190084188011
78	19.64	19.5363286408268	0.103671359173230
79	19.67	19.6311565163538	0.0388434836462466
80	19.81	19.6666865321808	0.143313467819155
81	19.73	19.7977749233824	-0.0677749233823803
82	19.87	19.7357814080122	0.134218591987821
83	19.97	19.858550744075	0.111449255924992
84	20.12	19.9604930379999	0.159506962000105
85	19.94	20.1063935688588	-0.166393568858751
86	20.31	19.9541938797444	0.355806120255604
87	20.13	20.2796486509793	-0.149648650979326
88	20.22	20.1427654870947	0.077234512905278
89	20.38	20.2134116601031	0.166588339896869
90	20.44	20.3657895056910	0.0742104943089608
91	20.34	20.4336696181276	-0.0936696181275636
92	20.14	20.3479903045804	-0.207990304580427
93	19.97	20.1577422083766	-0.18774220837658
94	19.82	19.9860149839139	-0.166014983913868
95	19.98	19.8341615852920	0.145838414707956
96	20.12	19.9675595376992	0.152440462300770

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
97	20.1069963628708	19.7946229267090	20.4193697990326
98	20.1069963628708	19.6836559584413	20.5303367673002
99	20.1069963628708	19.5962547134771	20.6177380122645
100	20.1069963628708	19.5217639587540	20.6922287669876
101	20.1069963628708	19.4557384253136	20.758254300428
102	20.1069963628708	19.3958164730860	20.8181762526555
103	20.1069963628708	19.3405651721973	20.8734275535442
104	20.1069963628708	19.2890374981104	20.9249552276311
105	20.1069963628708	19.2405688478166	20.973423877925
106	20.1069963628708	19.1946715450312	21.0193211807103
107	20.1069963628708	19.1509751770967	21.0630175486449
108	20.1069963628708	19.1091905490714	21.1048021766701

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 20.1069963628708 & 19.7946229267090 & 20.4193697990326 \tabularnewline
98 & 20.1069963628708 & 19.6836559584413 & 20.5303367673002 \tabularnewline
99 & 20.1069963628708 & 19.5962547134771 & 20.6177380122645 \tabularnewline
100 & 20.1069963628708 & 19.5217639587540 & 20.6922287669876 \tabularnewline
101 & 20.1069963628708 & 19.4557384253136 & 20.758254300428 \tabularnewline
102 & 20.1069963628708 & 19.3958164730860 & 20.8181762526555 \tabularnewline
103 & 20.1069963628708 & 19.3405651721973 & 20.8734275535442 \tabularnewline
104 & 20.1069963628708 & 19.2890374981104 & 20.9249552276311 \tabularnewline
105 & 20.1069963628708 & 19.2405688478166 & 20.973423877925 \tabularnewline
106 & 20.1069963628708 & 19.1946715450312 & 21.0193211807103 \tabularnewline
107 & 20.1069963628708 & 19.1509751770967 & 21.0630175486449 \tabularnewline
108 & 20.1069963628708 & 19.1091905490714 & 21.1048021766701 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14037&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]97[/C][C]20.1069963628708[/C][C]19.7946229267090[/C][C]20.4193697990326[/C][/ROW]
[ROW][C]98[/C][C]20.1069963628708[/C][C]19.6836559584413[/C][C]20.5303367673002[/C][/ROW]
[ROW][C]99[/C][C]20.1069963628708[/C][C]19.5962547134771[/C][C]20.6177380122645[/C][/ROW]
[ROW][C]100[/C][C]20.1069963628708[/C][C]19.5217639587540[/C][C]20.6922287669876[/C][/ROW]
[ROW][C]101[/C][C]20.1069963628708[/C][C]19.4557384253136[/C][C]20.758254300428[/C][/ROW]
[ROW][C]102[/C][C]20.1069963628708[/C][C]19.3958164730860[/C][C]20.8181762526555[/C][/ROW]
[ROW][C]103[/C][C]20.1069963628708[/C][C]19.3405651721973[/C][C]20.8734275535442[/C][/ROW]
[ROW][C]104[/C][C]20.1069963628708[/C][C]19.2890374981104[/C][C]20.9249552276311[/C][/ROW]
[ROW][C]105[/C][C]20.1069963628708[/C][C]19.2405688478166[/C][C]20.973423877925[/C][/ROW]
[ROW][C]106[/C][C]20.1069963628708[/C][C]19.1946715450312[/C][C]21.0193211807103[/C][/ROW]
[ROW][C]107[/C][C]20.1069963628708[/C][C]19.1509751770967[/C][C]21.0630175486449[/C][/ROW]
[ROW][C]108[/C][C]20.1069963628708[/C][C]19.1091905490714[/C][C]21.1048021766701[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14037&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14037&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
97	20.1069963628708	19.7946229267090	20.4193697990326
98	20.1069963628708	19.6836559584413	20.5303367673002
99	20.1069963628708	19.5962547134771	20.6177380122645
100	20.1069963628708	19.5217639587540	20.6922287669876
101	20.1069963628708	19.4557384253136	20.758254300428
102	20.1069963628708	19.3958164730860	20.8181762526555
103	20.1069963628708	19.3405651721973	20.8734275535442
104	20.1069963628708	19.2890374981104	20.9249552276311
105	20.1069963628708	19.2405688478166	20.973423877925
106	20.1069963628708	19.1946715450312	21.0193211807103
107	20.1069963628708	19.1509751770967	21.0630175486449
108	20.1069963628708	19.1091905490714	21.1048021766701

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 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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=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