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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Wed, 18 May 2011 14:40:51 +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/2011/May/18/t1305729403zi7klyeqjdaiu7g.htm/, Retrieved Tue, 21 May 2024 21:09:17 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=121875, Retrieved Tue, 21 May 2024 21:09:17 +0000

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No (this computation is public)

User-defined keywords

KDGP2W102

Estimated Impact

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

-       [Exponential Smoothing] [gemiddelde temper...] [2011-05-18 14:40:51] [8408ae72b9c03ee1c59e868ccc07a80d] [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	3 seconds
R Server	'Gwilym Jenkins' @ www.wessa.org

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121875&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121875&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121875&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Gwilym Jenkins' @ www.wessa.org

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.171048148072183
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.171048148072183 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121875&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]0.171048148072183[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121875&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121875&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	0.171048148072183
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	16.7	17	-0.300000000000001
3	15.4	16.9486855555783	-1.54868555557834
4	15.1	16.6837857593505	-1.58378575935053
5	16.1	16.4128821382705	-0.31288213827052
6	17	16.3593642279545	0.640635772045517
7	16.1	16.4689437903517	-0.368943790351661
8	14.3	16.4058366382693	-2.10583663826928
9	16.1	16.0456371811508	0.0543628188492349
10	14.8	16.0549358406389	-1.25493584063891
11	15.9	15.8402813891482	0.0597186108517835
12	17.6	15.8504961469399	1.74950385306014
13	15.9	16.1497455410509	-0.249745541050943
14	14.8	16.1070270287649	-1.3070270287649
15	16.5	15.8834624760144	0.616537523985627
16	15.6	15.9889200777091	-0.388920077709125
17	14.6	15.9223960186689	-1.32239601866889
18	17.1	15.6962026286575	1.40379737134245
19	15.2	15.9363195692943	-0.736319569294274
20	14.8	15.8103734705772	-1.01037347057718
21	15.4	15.6375509595737	-0.237550959573687
22	16.6	15.5969183078658	1.00308169213416
23	15.1	15.7684935736705	-0.668493573670498
24	15.4	15.654148985896	-0.254148985896004
25	15.2	15.6106772725241	-0.410677272524071
26	16.6	15.5404316856035	1.05956831439651
27	16.1	15.721668883537	0.378331116463023
28	15.7	15.7863817203661	-0.0863817203660613
29	15.8	15.7716062870702	0.0283937129298444
30	15.7	15.7764629790837	-0.0764629790837006
31	16.9	15.7633841281154	1.13661587188465
32	15.9	15.9578001680707	-0.0578001680706688
33	17.1	15.9479135563639	1.15208644363608
34	17	16.1449758089669	0.85502419103306
35	16.6	16.2912261134001	0.308773886599941
36	17.1	16.344041314876	0.755958685123971
37	16.6	16.4733466479856	0.126653352014433
38	16.6	16.4950104692948	0.104989530705229
39	16.5	16.5129687340889	-0.0129687340888687
40	17	16.5107504561401	0.489249543859874
41	15.9	16.5944356845625	-0.694435684562519
42	17	16.4756537467629	0.524346253237137
43	16.1	16.5653422023277	-0.465342202327662
44	16.1	16.4857462803997	-0.385746280399683
45	16.8	16.4197650935116	0.380234906488415
46	16.7	16.4848035700988	0.215196429901169
47	15.7	16.5216125209052	-0.821612520905173
48	18.7	16.3810772207714	2.31892277922858
49	16.1	16.7777246676809	-0.67772466768087
50	16.3	16.6618011183712	-0.361801118371222
51	17.2	16.5999157071034	0.600084292896618
52	16.1	16.7025590140906	-0.602559014090552
53	16.5	16.5994924106262	-0.099492410626162
54	16.5	16.5824744180413	-0.0824744180413184
55	15.1	16.568367321572	-1.46836732157202
56	16.7	16.3172058105274	0.382794189472587
57	14.4	16.3826820477295	-1.98268204772949
58	16.2	16.0435479552494	0.156452044750605
59	15.9	16.0703087877661	-0.170308787766091
60	17.3	16.0411777850183	1.25882221498172
61	15.6	16.256496993643	-0.65649699364303
62	15.6	16.1442043986654	-0.544204398665434
63	14.7	16.051119244101	-1.35111924410097
64	15.8	15.8200127995728	-0.0200127995728145
65	15.8	15.8165896472681	-0.0165896472681446
66	14.8	15.8137520188258	-1.01375201882576
67	16.1	15.6403516134012	0.459648386598825
68	16.3	15.7189736186933	0.581026381306728
69	16.1	15.8183571051969	0.281642894803131
70	17.4	15.8665316007706	1.53346839922936
71	16.7	16.128828530586	0.571171469413969
72	16.1	16.226526352661	-0.126526352660957
73	15.4	16.204884254356	-0.804884254355974
74	16.9	16.0672102932359	0.832789706764075
75	15.5	16.2096574303115	-0.709657430311495
76	17.6	16.088271841091	1.51172815890895
77	18.4	16.346850143061	2.053149856939
78	15.9	16.6980376238051	-0.798037623805081
79	15.2	16.5615347661613	-1.3615347661613
80	15.5	16.3286467658735	-0.828646765873515
81	15.9	16.1869082711648	-0.286908271164846
82	15.8	16.1378331427155	-0.337833142715507
83	17.6	16.0800474092966	1.51995259070339
84	18.2	16.3400324850939	1.85996751490605
85	15.9	16.658176483993	-0.758176483993045
86	15.7	16.5284918004942	-0.828491800494156
87	16.4	16.3867798123266	0.0132201876733582
88	15.6	16.3890411009453	-0.789041100945335
89	15.8	16.2540770818758	-0.454077081875798
90	17	16.1764080379389	0.823591962061077
91	16.8	16.3172819178166	0.482718082183393
92	16.6	16.399849951815	0.20015004818497
93	17.7	16.4340852468936	1.26591475310637
94	15.7	16.6506176210297	-0.950617621029732
95	18	16.4880162374278	1.51198376257219
96	18.2	16.746638259931	1.453361740069
97	16.4	16.9952330940488	-0.595233094048766
98	18	16.8934195756404	1.10658042435955
99	16.3	17.0826981079201	-0.78269810792008

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 16.7 & 17 & -0.300000000000001 \tabularnewline
3 & 15.4 & 16.9486855555783 & -1.54868555557834 \tabularnewline
4 & 15.1 & 16.6837857593505 & -1.58378575935053 \tabularnewline
5 & 16.1 & 16.4128821382705 & -0.31288213827052 \tabularnewline
6 & 17 & 16.3593642279545 & 0.640635772045517 \tabularnewline
7 & 16.1 & 16.4689437903517 & -0.368943790351661 \tabularnewline
8 & 14.3 & 16.4058366382693 & -2.10583663826928 \tabularnewline
9 & 16.1 & 16.0456371811508 & 0.0543628188492349 \tabularnewline
10 & 14.8 & 16.0549358406389 & -1.25493584063891 \tabularnewline
11 & 15.9 & 15.8402813891482 & 0.0597186108517835 \tabularnewline
12 & 17.6 & 15.8504961469399 & 1.74950385306014 \tabularnewline
13 & 15.9 & 16.1497455410509 & -0.249745541050943 \tabularnewline
14 & 14.8 & 16.1070270287649 & -1.3070270287649 \tabularnewline
15 & 16.5 & 15.8834624760144 & 0.616537523985627 \tabularnewline
16 & 15.6 & 15.9889200777091 & -0.388920077709125 \tabularnewline
17 & 14.6 & 15.9223960186689 & -1.32239601866889 \tabularnewline
18 & 17.1 & 15.6962026286575 & 1.40379737134245 \tabularnewline
19 & 15.2 & 15.9363195692943 & -0.736319569294274 \tabularnewline
20 & 14.8 & 15.8103734705772 & -1.01037347057718 \tabularnewline
21 & 15.4 & 15.6375509595737 & -0.237550959573687 \tabularnewline
22 & 16.6 & 15.5969183078658 & 1.00308169213416 \tabularnewline
23 & 15.1 & 15.7684935736705 & -0.668493573670498 \tabularnewline
24 & 15.4 & 15.654148985896 & -0.254148985896004 \tabularnewline
25 & 15.2 & 15.6106772725241 & -0.410677272524071 \tabularnewline
26 & 16.6 & 15.5404316856035 & 1.05956831439651 \tabularnewline
27 & 16.1 & 15.721668883537 & 0.378331116463023 \tabularnewline
28 & 15.7 & 15.7863817203661 & -0.0863817203660613 \tabularnewline
29 & 15.8 & 15.7716062870702 & 0.0283937129298444 \tabularnewline
30 & 15.7 & 15.7764629790837 & -0.0764629790837006 \tabularnewline
31 & 16.9 & 15.7633841281154 & 1.13661587188465 \tabularnewline
32 & 15.9 & 15.9578001680707 & -0.0578001680706688 \tabularnewline
33 & 17.1 & 15.9479135563639 & 1.15208644363608 \tabularnewline
34 & 17 & 16.1449758089669 & 0.85502419103306 \tabularnewline
35 & 16.6 & 16.2912261134001 & 0.308773886599941 \tabularnewline
36 & 17.1 & 16.344041314876 & 0.755958685123971 \tabularnewline
37 & 16.6 & 16.4733466479856 & 0.126653352014433 \tabularnewline
38 & 16.6 & 16.4950104692948 & 0.104989530705229 \tabularnewline
39 & 16.5 & 16.5129687340889 & -0.0129687340888687 \tabularnewline
40 & 17 & 16.5107504561401 & 0.489249543859874 \tabularnewline
41 & 15.9 & 16.5944356845625 & -0.694435684562519 \tabularnewline
42 & 17 & 16.4756537467629 & 0.524346253237137 \tabularnewline
43 & 16.1 & 16.5653422023277 & -0.465342202327662 \tabularnewline
44 & 16.1 & 16.4857462803997 & -0.385746280399683 \tabularnewline
45 & 16.8 & 16.4197650935116 & 0.380234906488415 \tabularnewline
46 & 16.7 & 16.4848035700988 & 0.215196429901169 \tabularnewline
47 & 15.7 & 16.5216125209052 & -0.821612520905173 \tabularnewline
48 & 18.7 & 16.3810772207714 & 2.31892277922858 \tabularnewline
49 & 16.1 & 16.7777246676809 & -0.67772466768087 \tabularnewline
50 & 16.3 & 16.6618011183712 & -0.361801118371222 \tabularnewline
51 & 17.2 & 16.5999157071034 & 0.600084292896618 \tabularnewline
52 & 16.1 & 16.7025590140906 & -0.602559014090552 \tabularnewline
53 & 16.5 & 16.5994924106262 & -0.099492410626162 \tabularnewline
54 & 16.5 & 16.5824744180413 & -0.0824744180413184 \tabularnewline
55 & 15.1 & 16.568367321572 & -1.46836732157202 \tabularnewline
56 & 16.7 & 16.3172058105274 & 0.382794189472587 \tabularnewline
57 & 14.4 & 16.3826820477295 & -1.98268204772949 \tabularnewline
58 & 16.2 & 16.0435479552494 & 0.156452044750605 \tabularnewline
59 & 15.9 & 16.0703087877661 & -0.170308787766091 \tabularnewline
60 & 17.3 & 16.0411777850183 & 1.25882221498172 \tabularnewline
61 & 15.6 & 16.256496993643 & -0.65649699364303 \tabularnewline
62 & 15.6 & 16.1442043986654 & -0.544204398665434 \tabularnewline
63 & 14.7 & 16.051119244101 & -1.35111924410097 \tabularnewline
64 & 15.8 & 15.8200127995728 & -0.0200127995728145 \tabularnewline
65 & 15.8 & 15.8165896472681 & -0.0165896472681446 \tabularnewline
66 & 14.8 & 15.8137520188258 & -1.01375201882576 \tabularnewline
67 & 16.1 & 15.6403516134012 & 0.459648386598825 \tabularnewline
68 & 16.3 & 15.7189736186933 & 0.581026381306728 \tabularnewline
69 & 16.1 & 15.8183571051969 & 0.281642894803131 \tabularnewline
70 & 17.4 & 15.8665316007706 & 1.53346839922936 \tabularnewline
71 & 16.7 & 16.128828530586 & 0.571171469413969 \tabularnewline
72 & 16.1 & 16.226526352661 & -0.126526352660957 \tabularnewline
73 & 15.4 & 16.204884254356 & -0.804884254355974 \tabularnewline
74 & 16.9 & 16.0672102932359 & 0.832789706764075 \tabularnewline
75 & 15.5 & 16.2096574303115 & -0.709657430311495 \tabularnewline
76 & 17.6 & 16.088271841091 & 1.51172815890895 \tabularnewline
77 & 18.4 & 16.346850143061 & 2.053149856939 \tabularnewline
78 & 15.9 & 16.6980376238051 & -0.798037623805081 \tabularnewline
79 & 15.2 & 16.5615347661613 & -1.3615347661613 \tabularnewline
80 & 15.5 & 16.3286467658735 & -0.828646765873515 \tabularnewline
81 & 15.9 & 16.1869082711648 & -0.286908271164846 \tabularnewline
82 & 15.8 & 16.1378331427155 & -0.337833142715507 \tabularnewline
83 & 17.6 & 16.0800474092966 & 1.51995259070339 \tabularnewline
84 & 18.2 & 16.3400324850939 & 1.85996751490605 \tabularnewline
85 & 15.9 & 16.658176483993 & -0.758176483993045 \tabularnewline
86 & 15.7 & 16.5284918004942 & -0.828491800494156 \tabularnewline
87 & 16.4 & 16.3867798123266 & 0.0132201876733582 \tabularnewline
88 & 15.6 & 16.3890411009453 & -0.789041100945335 \tabularnewline
89 & 15.8 & 16.2540770818758 & -0.454077081875798 \tabularnewline
90 & 17 & 16.1764080379389 & 0.823591962061077 \tabularnewline
91 & 16.8 & 16.3172819178166 & 0.482718082183393 \tabularnewline
92 & 16.6 & 16.399849951815 & 0.20015004818497 \tabularnewline
93 & 17.7 & 16.4340852468936 & 1.26591475310637 \tabularnewline
94 & 15.7 & 16.6506176210297 & -0.950617621029732 \tabularnewline
95 & 18 & 16.4880162374278 & 1.51198376257219 \tabularnewline
96 & 18.2 & 16.746638259931 & 1.453361740069 \tabularnewline
97 & 16.4 & 16.9952330940488 & -0.595233094048766 \tabularnewline
98 & 18 & 16.8934195756404 & 1.10658042435955 \tabularnewline
99 & 16.3 & 17.0826981079201 & -0.78269810792008 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121875&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]2[/C][C]16.7[/C][C]17[/C][C]-0.300000000000001[/C][/ROW]
[ROW][C]3[/C][C]15.4[/C][C]16.9486855555783[/C][C]-1.54868555557834[/C][/ROW]
[ROW][C]4[/C][C]15.1[/C][C]16.6837857593505[/C][C]-1.58378575935053[/C][/ROW]
[ROW][C]5[/C][C]16.1[/C][C]16.4128821382705[/C][C]-0.31288213827052[/C][/ROW]
[ROW][C]6[/C][C]17[/C][C]16.3593642279545[/C][C]0.640635772045517[/C][/ROW]
[ROW][C]7[/C][C]16.1[/C][C]16.4689437903517[/C][C]-0.368943790351661[/C][/ROW]
[ROW][C]8[/C][C]14.3[/C][C]16.4058366382693[/C][C]-2.10583663826928[/C][/ROW]
[ROW][C]9[/C][C]16.1[/C][C]16.0456371811508[/C][C]0.0543628188492349[/C][/ROW]
[ROW][C]10[/C][C]14.8[/C][C]16.0549358406389[/C][C]-1.25493584063891[/C][/ROW]
[ROW][C]11[/C][C]15.9[/C][C]15.8402813891482[/C][C]0.0597186108517835[/C][/ROW]
[ROW][C]12[/C][C]17.6[/C][C]15.8504961469399[/C][C]1.74950385306014[/C][/ROW]
[ROW][C]13[/C][C]15.9[/C][C]16.1497455410509[/C][C]-0.249745541050943[/C][/ROW]
[ROW][C]14[/C][C]14.8[/C][C]16.1070270287649[/C][C]-1.3070270287649[/C][/ROW]
[ROW][C]15[/C][C]16.5[/C][C]15.8834624760144[/C][C]0.616537523985627[/C][/ROW]
[ROW][C]16[/C][C]15.6[/C][C]15.9889200777091[/C][C]-0.388920077709125[/C][/ROW]
[ROW][C]17[/C][C]14.6[/C][C]15.9223960186689[/C][C]-1.32239601866889[/C][/ROW]
[ROW][C]18[/C][C]17.1[/C][C]15.6962026286575[/C][C]1.40379737134245[/C][/ROW]
[ROW][C]19[/C][C]15.2[/C][C]15.9363195692943[/C][C]-0.736319569294274[/C][/ROW]
[ROW][C]20[/C][C]14.8[/C][C]15.8103734705772[/C][C]-1.01037347057718[/C][/ROW]
[ROW][C]21[/C][C]15.4[/C][C]15.6375509595737[/C][C]-0.237550959573687[/C][/ROW]
[ROW][C]22[/C][C]16.6[/C][C]15.5969183078658[/C][C]1.00308169213416[/C][/ROW]
[ROW][C]23[/C][C]15.1[/C][C]15.7684935736705[/C][C]-0.668493573670498[/C][/ROW]
[ROW][C]24[/C][C]15.4[/C][C]15.654148985896[/C][C]-0.254148985896004[/C][/ROW]
[ROW][C]25[/C][C]15.2[/C][C]15.6106772725241[/C][C]-0.410677272524071[/C][/ROW]
[ROW][C]26[/C][C]16.6[/C][C]15.5404316856035[/C][C]1.05956831439651[/C][/ROW]
[ROW][C]27[/C][C]16.1[/C][C]15.721668883537[/C][C]0.378331116463023[/C][/ROW]
[ROW][C]28[/C][C]15.7[/C][C]15.7863817203661[/C][C]-0.0863817203660613[/C][/ROW]
[ROW][C]29[/C][C]15.8[/C][C]15.7716062870702[/C][C]0.0283937129298444[/C][/ROW]
[ROW][C]30[/C][C]15.7[/C][C]15.7764629790837[/C][C]-0.0764629790837006[/C][/ROW]
[ROW][C]31[/C][C]16.9[/C][C]15.7633841281154[/C][C]1.13661587188465[/C][/ROW]
[ROW][C]32[/C][C]15.9[/C][C]15.9578001680707[/C][C]-0.0578001680706688[/C][/ROW]
[ROW][C]33[/C][C]17.1[/C][C]15.9479135563639[/C][C]1.15208644363608[/C][/ROW]
[ROW][C]34[/C][C]17[/C][C]16.1449758089669[/C][C]0.85502419103306[/C][/ROW]
[ROW][C]35[/C][C]16.6[/C][C]16.2912261134001[/C][C]0.308773886599941[/C][/ROW]
[ROW][C]36[/C][C]17.1[/C][C]16.344041314876[/C][C]0.755958685123971[/C][/ROW]
[ROW][C]37[/C][C]16.6[/C][C]16.4733466479856[/C][C]0.126653352014433[/C][/ROW]
[ROW][C]38[/C][C]16.6[/C][C]16.4950104692948[/C][C]0.104989530705229[/C][/ROW]
[ROW][C]39[/C][C]16.5[/C][C]16.5129687340889[/C][C]-0.0129687340888687[/C][/ROW]
[ROW][C]40[/C][C]17[/C][C]16.5107504561401[/C][C]0.489249543859874[/C][/ROW]
[ROW][C]41[/C][C]15.9[/C][C]16.5944356845625[/C][C]-0.694435684562519[/C][/ROW]
[ROW][C]42[/C][C]17[/C][C]16.4756537467629[/C][C]0.524346253237137[/C][/ROW]
[ROW][C]43[/C][C]16.1[/C][C]16.5653422023277[/C][C]-0.465342202327662[/C][/ROW]
[ROW][C]44[/C][C]16.1[/C][C]16.4857462803997[/C][C]-0.385746280399683[/C][/ROW]
[ROW][C]45[/C][C]16.8[/C][C]16.4197650935116[/C][C]0.380234906488415[/C][/ROW]
[ROW][C]46[/C][C]16.7[/C][C]16.4848035700988[/C][C]0.215196429901169[/C][/ROW]
[ROW][C]47[/C][C]15.7[/C][C]16.5216125209052[/C][C]-0.821612520905173[/C][/ROW]
[ROW][C]48[/C][C]18.7[/C][C]16.3810772207714[/C][C]2.31892277922858[/C][/ROW]
[ROW][C]49[/C][C]16.1[/C][C]16.7777246676809[/C][C]-0.67772466768087[/C][/ROW]
[ROW][C]50[/C][C]16.3[/C][C]16.6618011183712[/C][C]-0.361801118371222[/C][/ROW]
[ROW][C]51[/C][C]17.2[/C][C]16.5999157071034[/C][C]0.600084292896618[/C][/ROW]
[ROW][C]52[/C][C]16.1[/C][C]16.7025590140906[/C][C]-0.602559014090552[/C][/ROW]
[ROW][C]53[/C][C]16.5[/C][C]16.5994924106262[/C][C]-0.099492410626162[/C][/ROW]
[ROW][C]54[/C][C]16.5[/C][C]16.5824744180413[/C][C]-0.0824744180413184[/C][/ROW]
[ROW][C]55[/C][C]15.1[/C][C]16.568367321572[/C][C]-1.46836732157202[/C][/ROW]
[ROW][C]56[/C][C]16.7[/C][C]16.3172058105274[/C][C]0.382794189472587[/C][/ROW]
[ROW][C]57[/C][C]14.4[/C][C]16.3826820477295[/C][C]-1.98268204772949[/C][/ROW]
[ROW][C]58[/C][C]16.2[/C][C]16.0435479552494[/C][C]0.156452044750605[/C][/ROW]
[ROW][C]59[/C][C]15.9[/C][C]16.0703087877661[/C][C]-0.170308787766091[/C][/ROW]
[ROW][C]60[/C][C]17.3[/C][C]16.0411777850183[/C][C]1.25882221498172[/C][/ROW]
[ROW][C]61[/C][C]15.6[/C][C]16.256496993643[/C][C]-0.65649699364303[/C][/ROW]
[ROW][C]62[/C][C]15.6[/C][C]16.1442043986654[/C][C]-0.544204398665434[/C][/ROW]
[ROW][C]63[/C][C]14.7[/C][C]16.051119244101[/C][C]-1.35111924410097[/C][/ROW]
[ROW][C]64[/C][C]15.8[/C][C]15.8200127995728[/C][C]-0.0200127995728145[/C][/ROW]
[ROW][C]65[/C][C]15.8[/C][C]15.8165896472681[/C][C]-0.0165896472681446[/C][/ROW]
[ROW][C]66[/C][C]14.8[/C][C]15.8137520188258[/C][C]-1.01375201882576[/C][/ROW]
[ROW][C]67[/C][C]16.1[/C][C]15.6403516134012[/C][C]0.459648386598825[/C][/ROW]
[ROW][C]68[/C][C]16.3[/C][C]15.7189736186933[/C][C]0.581026381306728[/C][/ROW]
[ROW][C]69[/C][C]16.1[/C][C]15.8183571051969[/C][C]0.281642894803131[/C][/ROW]
[ROW][C]70[/C][C]17.4[/C][C]15.8665316007706[/C][C]1.53346839922936[/C][/ROW]
[ROW][C]71[/C][C]16.7[/C][C]16.128828530586[/C][C]0.571171469413969[/C][/ROW]
[ROW][C]72[/C][C]16.1[/C][C]16.226526352661[/C][C]-0.126526352660957[/C][/ROW]
[ROW][C]73[/C][C]15.4[/C][C]16.204884254356[/C][C]-0.804884254355974[/C][/ROW]
[ROW][C]74[/C][C]16.9[/C][C]16.0672102932359[/C][C]0.832789706764075[/C][/ROW]
[ROW][C]75[/C][C]15.5[/C][C]16.2096574303115[/C][C]-0.709657430311495[/C][/ROW]
[ROW][C]76[/C][C]17.6[/C][C]16.088271841091[/C][C]1.51172815890895[/C][/ROW]
[ROW][C]77[/C][C]18.4[/C][C]16.346850143061[/C][C]2.053149856939[/C][/ROW]
[ROW][C]78[/C][C]15.9[/C][C]16.6980376238051[/C][C]-0.798037623805081[/C][/ROW]
[ROW][C]79[/C][C]15.2[/C][C]16.5615347661613[/C][C]-1.3615347661613[/C][/ROW]
[ROW][C]80[/C][C]15.5[/C][C]16.3286467658735[/C][C]-0.828646765873515[/C][/ROW]
[ROW][C]81[/C][C]15.9[/C][C]16.1869082711648[/C][C]-0.286908271164846[/C][/ROW]
[ROW][C]82[/C][C]15.8[/C][C]16.1378331427155[/C][C]-0.337833142715507[/C][/ROW]
[ROW][C]83[/C][C]17.6[/C][C]16.0800474092966[/C][C]1.51995259070339[/C][/ROW]
[ROW][C]84[/C][C]18.2[/C][C]16.3400324850939[/C][C]1.85996751490605[/C][/ROW]
[ROW][C]85[/C][C]15.9[/C][C]16.658176483993[/C][C]-0.758176483993045[/C][/ROW]
[ROW][C]86[/C][C]15.7[/C][C]16.5284918004942[/C][C]-0.828491800494156[/C][/ROW]
[ROW][C]87[/C][C]16.4[/C][C]16.3867798123266[/C][C]0.0132201876733582[/C][/ROW]
[ROW][C]88[/C][C]15.6[/C][C]16.3890411009453[/C][C]-0.789041100945335[/C][/ROW]
[ROW][C]89[/C][C]15.8[/C][C]16.2540770818758[/C][C]-0.454077081875798[/C][/ROW]
[ROW][C]90[/C][C]17[/C][C]16.1764080379389[/C][C]0.823591962061077[/C][/ROW]
[ROW][C]91[/C][C]16.8[/C][C]16.3172819178166[/C][C]0.482718082183393[/C][/ROW]
[ROW][C]92[/C][C]16.6[/C][C]16.399849951815[/C][C]0.20015004818497[/C][/ROW]
[ROW][C]93[/C][C]17.7[/C][C]16.4340852468936[/C][C]1.26591475310637[/C][/ROW]
[ROW][C]94[/C][C]15.7[/C][C]16.6506176210297[/C][C]-0.950617621029732[/C][/ROW]
[ROW][C]95[/C][C]18[/C][C]16.4880162374278[/C][C]1.51198376257219[/C][/ROW]
[ROW][C]96[/C][C]18.2[/C][C]16.746638259931[/C][C]1.453361740069[/C][/ROW]
[ROW][C]97[/C][C]16.4[/C][C]16.9952330940488[/C][C]-0.595233094048766[/C][/ROW]
[ROW][C]98[/C][C]18[/C][C]16.8934195756404[/C][C]1.10658042435955[/C][/ROW]
[ROW][C]99[/C][C]16.3[/C][C]17.0826981079201[/C][C]-0.78269810792008[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121875&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121875&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
2	16.7	17	-0.300000000000001
3	15.4	16.9486855555783	-1.54868555557834
4	15.1	16.6837857593505	-1.58378575935053
5	16.1	16.4128821382705	-0.31288213827052
6	17	16.3593642279545	0.640635772045517
7	16.1	16.4689437903517	-0.368943790351661
8	14.3	16.4058366382693	-2.10583663826928
9	16.1	16.0456371811508	0.0543628188492349
10	14.8	16.0549358406389	-1.25493584063891
11	15.9	15.8402813891482	0.0597186108517835
12	17.6	15.8504961469399	1.74950385306014
13	15.9	16.1497455410509	-0.249745541050943
14	14.8	16.1070270287649	-1.3070270287649
15	16.5	15.8834624760144	0.616537523985627
16	15.6	15.9889200777091	-0.388920077709125
17	14.6	15.9223960186689	-1.32239601866889
18	17.1	15.6962026286575	1.40379737134245
19	15.2	15.9363195692943	-0.736319569294274
20	14.8	15.8103734705772	-1.01037347057718
21	15.4	15.6375509595737	-0.237550959573687
22	16.6	15.5969183078658	1.00308169213416
23	15.1	15.7684935736705	-0.668493573670498
24	15.4	15.654148985896	-0.254148985896004
25	15.2	15.6106772725241	-0.410677272524071
26	16.6	15.5404316856035	1.05956831439651
27	16.1	15.721668883537	0.378331116463023
28	15.7	15.7863817203661	-0.0863817203660613
29	15.8	15.7716062870702	0.0283937129298444
30	15.7	15.7764629790837	-0.0764629790837006
31	16.9	15.7633841281154	1.13661587188465
32	15.9	15.9578001680707	-0.0578001680706688
33	17.1	15.9479135563639	1.15208644363608
34	17	16.1449758089669	0.85502419103306
35	16.6	16.2912261134001	0.308773886599941
36	17.1	16.344041314876	0.755958685123971
37	16.6	16.4733466479856	0.126653352014433
38	16.6	16.4950104692948	0.104989530705229
39	16.5	16.5129687340889	-0.0129687340888687
40	17	16.5107504561401	0.489249543859874
41	15.9	16.5944356845625	-0.694435684562519
42	17	16.4756537467629	0.524346253237137
43	16.1	16.5653422023277	-0.465342202327662
44	16.1	16.4857462803997	-0.385746280399683
45	16.8	16.4197650935116	0.380234906488415
46	16.7	16.4848035700988	0.215196429901169
47	15.7	16.5216125209052	-0.821612520905173
48	18.7	16.3810772207714	2.31892277922858
49	16.1	16.7777246676809	-0.67772466768087
50	16.3	16.6618011183712	-0.361801118371222
51	17.2	16.5999157071034	0.600084292896618
52	16.1	16.7025590140906	-0.602559014090552
53	16.5	16.5994924106262	-0.099492410626162
54	16.5	16.5824744180413	-0.0824744180413184
55	15.1	16.568367321572	-1.46836732157202
56	16.7	16.3172058105274	0.382794189472587
57	14.4	16.3826820477295	-1.98268204772949
58	16.2	16.0435479552494	0.156452044750605
59	15.9	16.0703087877661	-0.170308787766091
60	17.3	16.0411777850183	1.25882221498172
61	15.6	16.256496993643	-0.65649699364303
62	15.6	16.1442043986654	-0.544204398665434
63	14.7	16.051119244101	-1.35111924410097
64	15.8	15.8200127995728	-0.0200127995728145
65	15.8	15.8165896472681	-0.0165896472681446
66	14.8	15.8137520188258	-1.01375201882576
67	16.1	15.6403516134012	0.459648386598825
68	16.3	15.7189736186933	0.581026381306728
69	16.1	15.8183571051969	0.281642894803131
70	17.4	15.8665316007706	1.53346839922936
71	16.7	16.128828530586	0.571171469413969
72	16.1	16.226526352661	-0.126526352660957
73	15.4	16.204884254356	-0.804884254355974
74	16.9	16.0672102932359	0.832789706764075
75	15.5	16.2096574303115	-0.709657430311495
76	17.6	16.088271841091	1.51172815890895
77	18.4	16.346850143061	2.053149856939
78	15.9	16.6980376238051	-0.798037623805081
79	15.2	16.5615347661613	-1.3615347661613
80	15.5	16.3286467658735	-0.828646765873515
81	15.9	16.1869082711648	-0.286908271164846
82	15.8	16.1378331427155	-0.337833142715507
83	17.6	16.0800474092966	1.51995259070339
84	18.2	16.3400324850939	1.85996751490605
85	15.9	16.658176483993	-0.758176483993045
86	15.7	16.5284918004942	-0.828491800494156
87	16.4	16.3867798123266	0.0132201876733582
88	15.6	16.3890411009453	-0.789041100945335
89	15.8	16.2540770818758	-0.454077081875798
90	17	16.1764080379389	0.823591962061077
91	16.8	16.3172819178166	0.482718082183393
92	16.6	16.399849951815	0.20015004818497
93	17.7	16.4340852468936	1.26591475310637
94	15.7	16.6506176210297	-0.950617621029732
95	18	16.4880162374278	1.51198376257219
96	18.2	16.746638259931	1.453361740069
97	16.4	16.9952330940488	-0.595233094048766
98	18	16.8934195756404	1.10658042435955
99	16.3	17.0826981079201	-0.78269810792008

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
100	16.9488190460607	15.1389890486533	18.7586490434682
101	16.9488190460607	15.112704395747	18.7849336963745
102	16.9488190460607	15.0867907437308	18.8108473483907
103	16.9488190460607	15.0612328127303	18.8364052793912
104	16.9488190460607	15.0360163437834	18.8616217483381
105	16.9488190460607	15.0111280058223	18.8865100862992
106	16.9488190460607	14.9865553132762	18.9110827788452
107	16.9488190460607	14.96228655285	18.9353515392715
108	16.9488190460607	14.9383107182583	18.9593273738632
109	16.9488190460607	14.9146174518857	18.9830206402358
110	16.9488190460607	14.8911969924938	19.0064410996277
111	16.9488190460607	14.8680401282259	19.0295979638956

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
100 & 16.9488190460607 & 15.1389890486533 & 18.7586490434682 \tabularnewline
101 & 16.9488190460607 & 15.112704395747 & 18.7849336963745 \tabularnewline
102 & 16.9488190460607 & 15.0867907437308 & 18.8108473483907 \tabularnewline
103 & 16.9488190460607 & 15.0612328127303 & 18.8364052793912 \tabularnewline
104 & 16.9488190460607 & 15.0360163437834 & 18.8616217483381 \tabularnewline
105 & 16.9488190460607 & 15.0111280058223 & 18.8865100862992 \tabularnewline
106 & 16.9488190460607 & 14.9865553132762 & 18.9110827788452 \tabularnewline
107 & 16.9488190460607 & 14.96228655285 & 18.9353515392715 \tabularnewline
108 & 16.9488190460607 & 14.9383107182583 & 18.9593273738632 \tabularnewline
109 & 16.9488190460607 & 14.9146174518857 & 18.9830206402358 \tabularnewline
110 & 16.9488190460607 & 14.8911969924938 & 19.0064410996277 \tabularnewline
111 & 16.9488190460607 & 14.8680401282259 & 19.0295979638956 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121875&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]100[/C][C]16.9488190460607[/C][C]15.1389890486533[/C][C]18.7586490434682[/C][/ROW]
[ROW][C]101[/C][C]16.9488190460607[/C][C]15.112704395747[/C][C]18.7849336963745[/C][/ROW]
[ROW][C]102[/C][C]16.9488190460607[/C][C]15.0867907437308[/C][C]18.8108473483907[/C][/ROW]
[ROW][C]103[/C][C]16.9488190460607[/C][C]15.0612328127303[/C][C]18.8364052793912[/C][/ROW]
[ROW][C]104[/C][C]16.9488190460607[/C][C]15.0360163437834[/C][C]18.8616217483381[/C][/ROW]
[ROW][C]105[/C][C]16.9488190460607[/C][C]15.0111280058223[/C][C]18.8865100862992[/C][/ROW]
[ROW][C]106[/C][C]16.9488190460607[/C][C]14.9865553132762[/C][C]18.9110827788452[/C][/ROW]
[ROW][C]107[/C][C]16.9488190460607[/C][C]14.96228655285[/C][C]18.9353515392715[/C][/ROW]
[ROW][C]108[/C][C]16.9488190460607[/C][C]14.9383107182583[/C][C]18.9593273738632[/C][/ROW]
[ROW][C]109[/C][C]16.9488190460607[/C][C]14.9146174518857[/C][C]18.9830206402358[/C][/ROW]
[ROW][C]110[/C][C]16.9488190460607[/C][C]14.8911969924938[/C][C]19.0064410996277[/C][/ROW]
[ROW][C]111[/C][C]16.9488190460607[/C][C]14.8680401282259[/C][C]19.0295979638956[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121875&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121875&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
100	16.9488190460607	15.1389890486533	18.7586490434682
101	16.9488190460607	15.112704395747	18.7849336963745
102	16.9488190460607	15.0867907437308	18.8108473483907
103	16.9488190460607	15.0612328127303	18.8364052793912
104	16.9488190460607	15.0360163437834	18.8616217483381
105	16.9488190460607	15.0111280058223	18.8865100862992
106	16.9488190460607	14.9865553132762	18.9110827788452
107	16.9488190460607	14.96228655285	18.9353515392715
108	16.9488190460607	14.9383107182583	18.9593273738632
109	16.9488190460607	14.9146174518857	18.9830206402358
110	16.9488190460607	14.8911969924938	19.0064410996277
111	16.9488190460607	14.8680401282259	19.0295979638956

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 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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