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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Thu, 02 Apr 2015 16:20:08 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Apr/02/t1427988034vtnc6r8lhr0nlcb.htm/, Retrieved Thu, 09 May 2024 12:09:58 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278574, Retrieved Thu, 09 May 2024 12:09:58 +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] [] [2015-04-02 15:20:08] [8a8c4bd73c288c653fbb494901d06130] [Current]

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Dataseries X:

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2
2,2
1,9
2,3
2,2
2,3
2,1
2,4
2,3
1,9
1,6
1,8
1,8
2
2,3
2,2
2,2
2
2
1,9
1,5
1,6
1,5
2
1,5
1,5
1,9
1,1
1,5
2,1
2,3
2,6
2,9
3,2
3,2
3,1
3
3,3
2,7
3,6
3,1
2,7
2,6
2,2
2,7
2,1
1,8
1,7
1,7
1,2
1,2
1,2
1,5
1,3
1,1
1,2
1,3
1,6
1,9
1,6
2,1
2,2
2,3
2,1
1,7
1,7
2,2
2
1,5
1,5
1,7
2,2
2,6
2,6
2,3
2,3
2,7
2,7
2,5
2,5
2,7
2,6
2,6
2,4
1,4
1,8
2,1
1,7
1,6
1,7
1,8
2
1,9
2
2,1
2,3

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=278574&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=278574&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278574&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	0.804574804859477
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.804574804859477 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278574&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]0.804574804859477[/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=278574&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278574&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	0.804574804859477
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	2.2	2	0.2
3	1.9	2.1609149609719	-0.260914960971896
4	2.3	1.95098935716301	0.349010642836985
5	2.2	2.23179452701746	-0.0317945270174622
6	2.3	2.20621345164679	0.0937865483532114
7	2.1	2.28167174548652	-0.181671745486517
8	2.4	2.13550323631322	0.264496763686778
9	2.3	2.34831066834247	-0.0483106683424745
10	1.9	2.3094411217882	-0.409441121788197
11	1.6	1.98001511112401	-0.380015111124013
12	1.8	1.67426452724776	0.125735472752242
13	1.8	1.77542812070131	0.0245718792986929
14	2	1.79519803569308	0.204801964306916
15	2.3	1.95997653616016	0.340023463839841
16	2.2	2.23355084822674	-0.0335508482267421
17	2.2	2.20655668106184	-0.00655668106184137
18	2	2.20128134067599	-0.201281340675985
19	2	2.03933544527975	-0.0393354452797503
20	1.9	2.00768713706973	-0.107687137069735
21	1.5	1.92104477977598	-0.421044779775977
22	1.6	1.58228275825062	0.0177172417493812
23	1.5	1.59653760457378	-0.0965376045737756
24	2	1.51886588021223	0.481134119787771
25	1.5	1.90597427075171	-0.405974270751711
26	1.5	1.57933760108368	-0.0793376010836846
27	1.9	1.51550456617376	0.38449543382624
28	1.1	1.82485990481387	-0.724859904813867
29	1.5	1.24165588834779	0.258344111652209
30	2.1	1.44951305156696	0.650486948433038
31	2.3	1.97287846116611	0.32712153883389
32	2.6	2.23607220943872	0.363927790561281
33	2.9	2.5288793405125	0.371120659487497
34	3.2	2.82747367269898	0.372526327301024
35	3.2	3.12719896979222	0.0728010302077848
36	3.1	3.18577284446521	-0.0857728444652128
37	3	3.11676217486737	-0.116762174867372
38	3.3	3.02281827080849	0.277181729191512
39	2.7	3.24583170648336	-0.54583170648336
40	3.6	2.8066692677534	0.793330732246604
41	3.1	3.44496318683973	-0.344963186839733
42	2.7	3.16741449810445	-0.467414498104452
43	2.6	2.79134456950357	-0.191344569503572
44	2.2	2.63739354983432	-0.437393549834315
45	2.7	2.28547771982958	0.414522280170423
46	2.1	2.6189919025076	-0.5189919025076
47	1.8	2.2014240938239	-0.401424093823899
48	1.7	1.87844838186964	-0.178448381869643
49	1.7	1.73487330984939	-0.0348733098493856
50	1.2	1.70681512338251	-0.506815123382512
51	1.2	1.2990444443872	-0.0990444443871956
52	1.2	1.21935577987195	-0.0193557798719524
53	1.5	1.20378260705857	0.296217392941427
54	1.3	1.4421116581804	-0.142111658180404
55	1.1	1.32777219853165	-0.227772198531649
56	1.2	1.14451242634563	0.0554875736543663
57	1.3	1.18915633009072	0.110843669909279
58	1.6	1.27833835417789	0.321661645822112
59	1.9	1.53713921009599	0.362860789904008
60	1.6	1.82908785932416	-0.229087859324165
61	2.1	1.64476953961275	0.45523046038725
62	2.2	2.01103649844491	0.188963501555089
63	2.3	2.16307177083416	0.136928229165839
64	2.1	2.27324077409502	-0.173240774095019
65	1.7	2.13385561208381	-0.433855612083814
66	1.7	1.78478631765429	-0.0847863176542905
67	2.2	1.71656938267284	0.483430617327164
68	2	2.10552547727194	-0.105525477271936
69	1.5	2.02062233698816	-0.520622336988165
70	1.5	1.60174272180043	-0.101742721800427
71	1.7	1.51988309126198	0.180116908738024
72	2.2	1.66480061796176	0.535199382038236
73	2.6	2.09540855632609	0.50459144367391
74	2.6	2.50139011865379	0.0986098813462117
75	2.3	2.58072914469513	-0.280729144695133
76	2.3	2.35486154788368	-0.0548615478836787
77	2.7	2.31072132870088	0.389278671299121
78	2.7	2.62392513969733	0.0760748603026746
79	2.5	2.68513305558006	-0.185133055580062
80	2.5	2.53617966351369	-0.0361796635136948
81	2.7	2.50707041780228	0.192929582197718
82	2.6	2.66229669875063	-0.0622966987506315
83	2.6	2.61217434450995	-0.0121743445099529
84	2.4	2.60237917365157	-0.202379173651566
85	1.4	2.43954998950323	-1.03954998950323
86	1.8	1.603154259557	0.196845740443002
87	2.1	1.76153138276135	0.338468617238654
88	1.7	2.03385470442719	-0.333854704427193
89	1.6	1.76524362076127	-0.165243620761266
90	1.7	1.632292766833	0.0677072331670028
91	1.8	1.68676830074591	0.113231699254086
92	2	1.77787167307718	0.222128326922823
93	1.9	1.95659052836487	-0.0565905283648696
94	2	1.91105921504881	0.0889407849511901
95	2.1	1.98261872974496	0.117381270255038
96	2.3	2.07706074235457	0.222939257645433

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 2.2 & 2 & 0.2 \tabularnewline
3 & 1.9 & 2.1609149609719 & -0.260914960971896 \tabularnewline
4 & 2.3 & 1.95098935716301 & 0.349010642836985 \tabularnewline
5 & 2.2 & 2.23179452701746 & -0.0317945270174622 \tabularnewline
6 & 2.3 & 2.20621345164679 & 0.0937865483532114 \tabularnewline
7 & 2.1 & 2.28167174548652 & -0.181671745486517 \tabularnewline
8 & 2.4 & 2.13550323631322 & 0.264496763686778 \tabularnewline
9 & 2.3 & 2.34831066834247 & -0.0483106683424745 \tabularnewline
10 & 1.9 & 2.3094411217882 & -0.409441121788197 \tabularnewline
11 & 1.6 & 1.98001511112401 & -0.380015111124013 \tabularnewline
12 & 1.8 & 1.67426452724776 & 0.125735472752242 \tabularnewline
13 & 1.8 & 1.77542812070131 & 0.0245718792986929 \tabularnewline
14 & 2 & 1.79519803569308 & 0.204801964306916 \tabularnewline
15 & 2.3 & 1.95997653616016 & 0.340023463839841 \tabularnewline
16 & 2.2 & 2.23355084822674 & -0.0335508482267421 \tabularnewline
17 & 2.2 & 2.20655668106184 & -0.00655668106184137 \tabularnewline
18 & 2 & 2.20128134067599 & -0.201281340675985 \tabularnewline
19 & 2 & 2.03933544527975 & -0.0393354452797503 \tabularnewline
20 & 1.9 & 2.00768713706973 & -0.107687137069735 \tabularnewline
21 & 1.5 & 1.92104477977598 & -0.421044779775977 \tabularnewline
22 & 1.6 & 1.58228275825062 & 0.0177172417493812 \tabularnewline
23 & 1.5 & 1.59653760457378 & -0.0965376045737756 \tabularnewline
24 & 2 & 1.51886588021223 & 0.481134119787771 \tabularnewline
25 & 1.5 & 1.90597427075171 & -0.405974270751711 \tabularnewline
26 & 1.5 & 1.57933760108368 & -0.0793376010836846 \tabularnewline
27 & 1.9 & 1.51550456617376 & 0.38449543382624 \tabularnewline
28 & 1.1 & 1.82485990481387 & -0.724859904813867 \tabularnewline
29 & 1.5 & 1.24165588834779 & 0.258344111652209 \tabularnewline
30 & 2.1 & 1.44951305156696 & 0.650486948433038 \tabularnewline
31 & 2.3 & 1.97287846116611 & 0.32712153883389 \tabularnewline
32 & 2.6 & 2.23607220943872 & 0.363927790561281 \tabularnewline
33 & 2.9 & 2.5288793405125 & 0.371120659487497 \tabularnewline
34 & 3.2 & 2.82747367269898 & 0.372526327301024 \tabularnewline
35 & 3.2 & 3.12719896979222 & 0.0728010302077848 \tabularnewline
36 & 3.1 & 3.18577284446521 & -0.0857728444652128 \tabularnewline
37 & 3 & 3.11676217486737 & -0.116762174867372 \tabularnewline
38 & 3.3 & 3.02281827080849 & 0.277181729191512 \tabularnewline
39 & 2.7 & 3.24583170648336 & -0.54583170648336 \tabularnewline
40 & 3.6 & 2.8066692677534 & 0.793330732246604 \tabularnewline
41 & 3.1 & 3.44496318683973 & -0.344963186839733 \tabularnewline
42 & 2.7 & 3.16741449810445 & -0.467414498104452 \tabularnewline
43 & 2.6 & 2.79134456950357 & -0.191344569503572 \tabularnewline
44 & 2.2 & 2.63739354983432 & -0.437393549834315 \tabularnewline
45 & 2.7 & 2.28547771982958 & 0.414522280170423 \tabularnewline
46 & 2.1 & 2.6189919025076 & -0.5189919025076 \tabularnewline
47 & 1.8 & 2.2014240938239 & -0.401424093823899 \tabularnewline
48 & 1.7 & 1.87844838186964 & -0.178448381869643 \tabularnewline
49 & 1.7 & 1.73487330984939 & -0.0348733098493856 \tabularnewline
50 & 1.2 & 1.70681512338251 & -0.506815123382512 \tabularnewline
51 & 1.2 & 1.2990444443872 & -0.0990444443871956 \tabularnewline
52 & 1.2 & 1.21935577987195 & -0.0193557798719524 \tabularnewline
53 & 1.5 & 1.20378260705857 & 0.296217392941427 \tabularnewline
54 & 1.3 & 1.4421116581804 & -0.142111658180404 \tabularnewline
55 & 1.1 & 1.32777219853165 & -0.227772198531649 \tabularnewline
56 & 1.2 & 1.14451242634563 & 0.0554875736543663 \tabularnewline
57 & 1.3 & 1.18915633009072 & 0.110843669909279 \tabularnewline
58 & 1.6 & 1.27833835417789 & 0.321661645822112 \tabularnewline
59 & 1.9 & 1.53713921009599 & 0.362860789904008 \tabularnewline
60 & 1.6 & 1.82908785932416 & -0.229087859324165 \tabularnewline
61 & 2.1 & 1.64476953961275 & 0.45523046038725 \tabularnewline
62 & 2.2 & 2.01103649844491 & 0.188963501555089 \tabularnewline
63 & 2.3 & 2.16307177083416 & 0.136928229165839 \tabularnewline
64 & 2.1 & 2.27324077409502 & -0.173240774095019 \tabularnewline
65 & 1.7 & 2.13385561208381 & -0.433855612083814 \tabularnewline
66 & 1.7 & 1.78478631765429 & -0.0847863176542905 \tabularnewline
67 & 2.2 & 1.71656938267284 & 0.483430617327164 \tabularnewline
68 & 2 & 2.10552547727194 & -0.105525477271936 \tabularnewline
69 & 1.5 & 2.02062233698816 & -0.520622336988165 \tabularnewline
70 & 1.5 & 1.60174272180043 & -0.101742721800427 \tabularnewline
71 & 1.7 & 1.51988309126198 & 0.180116908738024 \tabularnewline
72 & 2.2 & 1.66480061796176 & 0.535199382038236 \tabularnewline
73 & 2.6 & 2.09540855632609 & 0.50459144367391 \tabularnewline
74 & 2.6 & 2.50139011865379 & 0.0986098813462117 \tabularnewline
75 & 2.3 & 2.58072914469513 & -0.280729144695133 \tabularnewline
76 & 2.3 & 2.35486154788368 & -0.0548615478836787 \tabularnewline
77 & 2.7 & 2.31072132870088 & 0.389278671299121 \tabularnewline
78 & 2.7 & 2.62392513969733 & 0.0760748603026746 \tabularnewline
79 & 2.5 & 2.68513305558006 & -0.185133055580062 \tabularnewline
80 & 2.5 & 2.53617966351369 & -0.0361796635136948 \tabularnewline
81 & 2.7 & 2.50707041780228 & 0.192929582197718 \tabularnewline
82 & 2.6 & 2.66229669875063 & -0.0622966987506315 \tabularnewline
83 & 2.6 & 2.61217434450995 & -0.0121743445099529 \tabularnewline
84 & 2.4 & 2.60237917365157 & -0.202379173651566 \tabularnewline
85 & 1.4 & 2.43954998950323 & -1.03954998950323 \tabularnewline
86 & 1.8 & 1.603154259557 & 0.196845740443002 \tabularnewline
87 & 2.1 & 1.76153138276135 & 0.338468617238654 \tabularnewline
88 & 1.7 & 2.03385470442719 & -0.333854704427193 \tabularnewline
89 & 1.6 & 1.76524362076127 & -0.165243620761266 \tabularnewline
90 & 1.7 & 1.632292766833 & 0.0677072331670028 \tabularnewline
91 & 1.8 & 1.68676830074591 & 0.113231699254086 \tabularnewline
92 & 2 & 1.77787167307718 & 0.222128326922823 \tabularnewline
93 & 1.9 & 1.95659052836487 & -0.0565905283648696 \tabularnewline
94 & 2 & 1.91105921504881 & 0.0889407849511901 \tabularnewline
95 & 2.1 & 1.98261872974496 & 0.117381270255038 \tabularnewline
96 & 2.3 & 2.07706074235457 & 0.222939257645433 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278574&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]2.2[/C][C]2[/C][C]0.2[/C][/ROW]
[ROW][C]3[/C][C]1.9[/C][C]2.1609149609719[/C][C]-0.260914960971896[/C][/ROW]
[ROW][C]4[/C][C]2.3[/C][C]1.95098935716301[/C][C]0.349010642836985[/C][/ROW]
[ROW][C]5[/C][C]2.2[/C][C]2.23179452701746[/C][C]-0.0317945270174622[/C][/ROW]
[ROW][C]6[/C][C]2.3[/C][C]2.20621345164679[/C][C]0.0937865483532114[/C][/ROW]
[ROW][C]7[/C][C]2.1[/C][C]2.28167174548652[/C][C]-0.181671745486517[/C][/ROW]
[ROW][C]8[/C][C]2.4[/C][C]2.13550323631322[/C][C]0.264496763686778[/C][/ROW]
[ROW][C]9[/C][C]2.3[/C][C]2.34831066834247[/C][C]-0.0483106683424745[/C][/ROW]
[ROW][C]10[/C][C]1.9[/C][C]2.3094411217882[/C][C]-0.409441121788197[/C][/ROW]
[ROW][C]11[/C][C]1.6[/C][C]1.98001511112401[/C][C]-0.380015111124013[/C][/ROW]
[ROW][C]12[/C][C]1.8[/C][C]1.67426452724776[/C][C]0.125735472752242[/C][/ROW]
[ROW][C]13[/C][C]1.8[/C][C]1.77542812070131[/C][C]0.0245718792986929[/C][/ROW]
[ROW][C]14[/C][C]2[/C][C]1.79519803569308[/C][C]0.204801964306916[/C][/ROW]
[ROW][C]15[/C][C]2.3[/C][C]1.95997653616016[/C][C]0.340023463839841[/C][/ROW]
[ROW][C]16[/C][C]2.2[/C][C]2.23355084822674[/C][C]-0.0335508482267421[/C][/ROW]
[ROW][C]17[/C][C]2.2[/C][C]2.20655668106184[/C][C]-0.00655668106184137[/C][/ROW]
[ROW][C]18[/C][C]2[/C][C]2.20128134067599[/C][C]-0.201281340675985[/C][/ROW]
[ROW][C]19[/C][C]2[/C][C]2.03933544527975[/C][C]-0.0393354452797503[/C][/ROW]
[ROW][C]20[/C][C]1.9[/C][C]2.00768713706973[/C][C]-0.107687137069735[/C][/ROW]
[ROW][C]21[/C][C]1.5[/C][C]1.92104477977598[/C][C]-0.421044779775977[/C][/ROW]
[ROW][C]22[/C][C]1.6[/C][C]1.58228275825062[/C][C]0.0177172417493812[/C][/ROW]
[ROW][C]23[/C][C]1.5[/C][C]1.59653760457378[/C][C]-0.0965376045737756[/C][/ROW]
[ROW][C]24[/C][C]2[/C][C]1.51886588021223[/C][C]0.481134119787771[/C][/ROW]
[ROW][C]25[/C][C]1.5[/C][C]1.90597427075171[/C][C]-0.405974270751711[/C][/ROW]
[ROW][C]26[/C][C]1.5[/C][C]1.57933760108368[/C][C]-0.0793376010836846[/C][/ROW]
[ROW][C]27[/C][C]1.9[/C][C]1.51550456617376[/C][C]0.38449543382624[/C][/ROW]
[ROW][C]28[/C][C]1.1[/C][C]1.82485990481387[/C][C]-0.724859904813867[/C][/ROW]
[ROW][C]29[/C][C]1.5[/C][C]1.24165588834779[/C][C]0.258344111652209[/C][/ROW]
[ROW][C]30[/C][C]2.1[/C][C]1.44951305156696[/C][C]0.650486948433038[/C][/ROW]
[ROW][C]31[/C][C]2.3[/C][C]1.97287846116611[/C][C]0.32712153883389[/C][/ROW]
[ROW][C]32[/C][C]2.6[/C][C]2.23607220943872[/C][C]0.363927790561281[/C][/ROW]
[ROW][C]33[/C][C]2.9[/C][C]2.5288793405125[/C][C]0.371120659487497[/C][/ROW]
[ROW][C]34[/C][C]3.2[/C][C]2.82747367269898[/C][C]0.372526327301024[/C][/ROW]
[ROW][C]35[/C][C]3.2[/C][C]3.12719896979222[/C][C]0.0728010302077848[/C][/ROW]
[ROW][C]36[/C][C]3.1[/C][C]3.18577284446521[/C][C]-0.0857728444652128[/C][/ROW]
[ROW][C]37[/C][C]3[/C][C]3.11676217486737[/C][C]-0.116762174867372[/C][/ROW]
[ROW][C]38[/C][C]3.3[/C][C]3.02281827080849[/C][C]0.277181729191512[/C][/ROW]
[ROW][C]39[/C][C]2.7[/C][C]3.24583170648336[/C][C]-0.54583170648336[/C][/ROW]
[ROW][C]40[/C][C]3.6[/C][C]2.8066692677534[/C][C]0.793330732246604[/C][/ROW]
[ROW][C]41[/C][C]3.1[/C][C]3.44496318683973[/C][C]-0.344963186839733[/C][/ROW]
[ROW][C]42[/C][C]2.7[/C][C]3.16741449810445[/C][C]-0.467414498104452[/C][/ROW]
[ROW][C]43[/C][C]2.6[/C][C]2.79134456950357[/C][C]-0.191344569503572[/C][/ROW]
[ROW][C]44[/C][C]2.2[/C][C]2.63739354983432[/C][C]-0.437393549834315[/C][/ROW]
[ROW][C]45[/C][C]2.7[/C][C]2.28547771982958[/C][C]0.414522280170423[/C][/ROW]
[ROW][C]46[/C][C]2.1[/C][C]2.6189919025076[/C][C]-0.5189919025076[/C][/ROW]
[ROW][C]47[/C][C]1.8[/C][C]2.2014240938239[/C][C]-0.401424093823899[/C][/ROW]
[ROW][C]48[/C][C]1.7[/C][C]1.87844838186964[/C][C]-0.178448381869643[/C][/ROW]
[ROW][C]49[/C][C]1.7[/C][C]1.73487330984939[/C][C]-0.0348733098493856[/C][/ROW]
[ROW][C]50[/C][C]1.2[/C][C]1.70681512338251[/C][C]-0.506815123382512[/C][/ROW]
[ROW][C]51[/C][C]1.2[/C][C]1.2990444443872[/C][C]-0.0990444443871956[/C][/ROW]
[ROW][C]52[/C][C]1.2[/C][C]1.21935577987195[/C][C]-0.0193557798719524[/C][/ROW]
[ROW][C]53[/C][C]1.5[/C][C]1.20378260705857[/C][C]0.296217392941427[/C][/ROW]
[ROW][C]54[/C][C]1.3[/C][C]1.4421116581804[/C][C]-0.142111658180404[/C][/ROW]
[ROW][C]55[/C][C]1.1[/C][C]1.32777219853165[/C][C]-0.227772198531649[/C][/ROW]
[ROW][C]56[/C][C]1.2[/C][C]1.14451242634563[/C][C]0.0554875736543663[/C][/ROW]
[ROW][C]57[/C][C]1.3[/C][C]1.18915633009072[/C][C]0.110843669909279[/C][/ROW]
[ROW][C]58[/C][C]1.6[/C][C]1.27833835417789[/C][C]0.321661645822112[/C][/ROW]
[ROW][C]59[/C][C]1.9[/C][C]1.53713921009599[/C][C]0.362860789904008[/C][/ROW]
[ROW][C]60[/C][C]1.6[/C][C]1.82908785932416[/C][C]-0.229087859324165[/C][/ROW]
[ROW][C]61[/C][C]2.1[/C][C]1.64476953961275[/C][C]0.45523046038725[/C][/ROW]
[ROW][C]62[/C][C]2.2[/C][C]2.01103649844491[/C][C]0.188963501555089[/C][/ROW]
[ROW][C]63[/C][C]2.3[/C][C]2.16307177083416[/C][C]0.136928229165839[/C][/ROW]
[ROW][C]64[/C][C]2.1[/C][C]2.27324077409502[/C][C]-0.173240774095019[/C][/ROW]
[ROW][C]65[/C][C]1.7[/C][C]2.13385561208381[/C][C]-0.433855612083814[/C][/ROW]
[ROW][C]66[/C][C]1.7[/C][C]1.78478631765429[/C][C]-0.0847863176542905[/C][/ROW]
[ROW][C]67[/C][C]2.2[/C][C]1.71656938267284[/C][C]0.483430617327164[/C][/ROW]
[ROW][C]68[/C][C]2[/C][C]2.10552547727194[/C][C]-0.105525477271936[/C][/ROW]
[ROW][C]69[/C][C]1.5[/C][C]2.02062233698816[/C][C]-0.520622336988165[/C][/ROW]
[ROW][C]70[/C][C]1.5[/C][C]1.60174272180043[/C][C]-0.101742721800427[/C][/ROW]
[ROW][C]71[/C][C]1.7[/C][C]1.51988309126198[/C][C]0.180116908738024[/C][/ROW]
[ROW][C]72[/C][C]2.2[/C][C]1.66480061796176[/C][C]0.535199382038236[/C][/ROW]
[ROW][C]73[/C][C]2.6[/C][C]2.09540855632609[/C][C]0.50459144367391[/C][/ROW]
[ROW][C]74[/C][C]2.6[/C][C]2.50139011865379[/C][C]0.0986098813462117[/C][/ROW]
[ROW][C]75[/C][C]2.3[/C][C]2.58072914469513[/C][C]-0.280729144695133[/C][/ROW]
[ROW][C]76[/C][C]2.3[/C][C]2.35486154788368[/C][C]-0.0548615478836787[/C][/ROW]
[ROW][C]77[/C][C]2.7[/C][C]2.31072132870088[/C][C]0.389278671299121[/C][/ROW]
[ROW][C]78[/C][C]2.7[/C][C]2.62392513969733[/C][C]0.0760748603026746[/C][/ROW]
[ROW][C]79[/C][C]2.5[/C][C]2.68513305558006[/C][C]-0.185133055580062[/C][/ROW]
[ROW][C]80[/C][C]2.5[/C][C]2.53617966351369[/C][C]-0.0361796635136948[/C][/ROW]
[ROW][C]81[/C][C]2.7[/C][C]2.50707041780228[/C][C]0.192929582197718[/C][/ROW]
[ROW][C]82[/C][C]2.6[/C][C]2.66229669875063[/C][C]-0.0622966987506315[/C][/ROW]
[ROW][C]83[/C][C]2.6[/C][C]2.61217434450995[/C][C]-0.0121743445099529[/C][/ROW]
[ROW][C]84[/C][C]2.4[/C][C]2.60237917365157[/C][C]-0.202379173651566[/C][/ROW]
[ROW][C]85[/C][C]1.4[/C][C]2.43954998950323[/C][C]-1.03954998950323[/C][/ROW]
[ROW][C]86[/C][C]1.8[/C][C]1.603154259557[/C][C]0.196845740443002[/C][/ROW]
[ROW][C]87[/C][C]2.1[/C][C]1.76153138276135[/C][C]0.338468617238654[/C][/ROW]
[ROW][C]88[/C][C]1.7[/C][C]2.03385470442719[/C][C]-0.333854704427193[/C][/ROW]
[ROW][C]89[/C][C]1.6[/C][C]1.76524362076127[/C][C]-0.165243620761266[/C][/ROW]
[ROW][C]90[/C][C]1.7[/C][C]1.632292766833[/C][C]0.0677072331670028[/C][/ROW]
[ROW][C]91[/C][C]1.8[/C][C]1.68676830074591[/C][C]0.113231699254086[/C][/ROW]
[ROW][C]92[/C][C]2[/C][C]1.77787167307718[/C][C]0.222128326922823[/C][/ROW]
[ROW][C]93[/C][C]1.9[/C][C]1.95659052836487[/C][C]-0.0565905283648696[/C][/ROW]
[ROW][C]94[/C][C]2[/C][C]1.91105921504881[/C][C]0.0889407849511901[/C][/ROW]
[ROW][C]95[/C][C]2.1[/C][C]1.98261872974496[/C][C]0.117381270255038[/C][/ROW]
[ROW][C]96[/C][C]2.3[/C][C]2.07706074235457[/C][C]0.222939257645433[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278574&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278574&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	2.2	2	0.2
3	1.9	2.1609149609719	-0.260914960971896
4	2.3	1.95098935716301	0.349010642836985
5	2.2	2.23179452701746	-0.0317945270174622
6	2.3	2.20621345164679	0.0937865483532114
7	2.1	2.28167174548652	-0.181671745486517
8	2.4	2.13550323631322	0.264496763686778
9	2.3	2.34831066834247	-0.0483106683424745
10	1.9	2.3094411217882	-0.409441121788197
11	1.6	1.98001511112401	-0.380015111124013
12	1.8	1.67426452724776	0.125735472752242
13	1.8	1.77542812070131	0.0245718792986929
14	2	1.79519803569308	0.204801964306916
15	2.3	1.95997653616016	0.340023463839841
16	2.2	2.23355084822674	-0.0335508482267421
17	2.2	2.20655668106184	-0.00655668106184137
18	2	2.20128134067599	-0.201281340675985
19	2	2.03933544527975	-0.0393354452797503
20	1.9	2.00768713706973	-0.107687137069735
21	1.5	1.92104477977598	-0.421044779775977
22	1.6	1.58228275825062	0.0177172417493812
23	1.5	1.59653760457378	-0.0965376045737756
24	2	1.51886588021223	0.481134119787771
25	1.5	1.90597427075171	-0.405974270751711
26	1.5	1.57933760108368	-0.0793376010836846
27	1.9	1.51550456617376	0.38449543382624
28	1.1	1.82485990481387	-0.724859904813867
29	1.5	1.24165588834779	0.258344111652209
30	2.1	1.44951305156696	0.650486948433038
31	2.3	1.97287846116611	0.32712153883389
32	2.6	2.23607220943872	0.363927790561281
33	2.9	2.5288793405125	0.371120659487497
34	3.2	2.82747367269898	0.372526327301024
35	3.2	3.12719896979222	0.0728010302077848
36	3.1	3.18577284446521	-0.0857728444652128
37	3	3.11676217486737	-0.116762174867372
38	3.3	3.02281827080849	0.277181729191512
39	2.7	3.24583170648336	-0.54583170648336
40	3.6	2.8066692677534	0.793330732246604
41	3.1	3.44496318683973	-0.344963186839733
42	2.7	3.16741449810445	-0.467414498104452
43	2.6	2.79134456950357	-0.191344569503572
44	2.2	2.63739354983432	-0.437393549834315
45	2.7	2.28547771982958	0.414522280170423
46	2.1	2.6189919025076	-0.5189919025076
47	1.8	2.2014240938239	-0.401424093823899
48	1.7	1.87844838186964	-0.178448381869643
49	1.7	1.73487330984939	-0.0348733098493856
50	1.2	1.70681512338251	-0.506815123382512
51	1.2	1.2990444443872	-0.0990444443871956
52	1.2	1.21935577987195	-0.0193557798719524
53	1.5	1.20378260705857	0.296217392941427
54	1.3	1.4421116581804	-0.142111658180404
55	1.1	1.32777219853165	-0.227772198531649
56	1.2	1.14451242634563	0.0554875736543663
57	1.3	1.18915633009072	0.110843669909279
58	1.6	1.27833835417789	0.321661645822112
59	1.9	1.53713921009599	0.362860789904008
60	1.6	1.82908785932416	-0.229087859324165
61	2.1	1.64476953961275	0.45523046038725
62	2.2	2.01103649844491	0.188963501555089
63	2.3	2.16307177083416	0.136928229165839
64	2.1	2.27324077409502	-0.173240774095019
65	1.7	2.13385561208381	-0.433855612083814
66	1.7	1.78478631765429	-0.0847863176542905
67	2.2	1.71656938267284	0.483430617327164
68	2	2.10552547727194	-0.105525477271936
69	1.5	2.02062233698816	-0.520622336988165
70	1.5	1.60174272180043	-0.101742721800427
71	1.7	1.51988309126198	0.180116908738024
72	2.2	1.66480061796176	0.535199382038236
73	2.6	2.09540855632609	0.50459144367391
74	2.6	2.50139011865379	0.0986098813462117
75	2.3	2.58072914469513	-0.280729144695133
76	2.3	2.35486154788368	-0.0548615478836787
77	2.7	2.31072132870088	0.389278671299121
78	2.7	2.62392513969733	0.0760748603026746
79	2.5	2.68513305558006	-0.185133055580062
80	2.5	2.53617966351369	-0.0361796635136948
81	2.7	2.50707041780228	0.192929582197718
82	2.6	2.66229669875063	-0.0622966987506315
83	2.6	2.61217434450995	-0.0121743445099529
84	2.4	2.60237917365157	-0.202379173651566
85	1.4	2.43954998950323	-1.03954998950323
86	1.8	1.603154259557	0.196845740443002
87	2.1	1.76153138276135	0.338468617238654
88	1.7	2.03385470442719	-0.333854704427193
89	1.6	1.76524362076127	-0.165243620761266
90	1.7	1.632292766833	0.0677072331670028
91	1.8	1.68676830074591	0.113231699254086
92	2	1.77787167307718	0.222128326922823
93	1.9	1.95659052836487	-0.0565905283648696
94	2	1.91105921504881	0.0889407849511901
95	2.1	1.98261872974496	0.117381270255038
96	2.3	2.07706074235457	0.222939257645433

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
97	2.25643205207016	1.63066475446827	2.88219934967204
98	2.25643205207016	1.45326743702513	3.05959666711518
99	2.25643205207016	1.30850690366819	3.20435720047212
100	2.25643205207016	1.18309576968455	3.32976833445576
101	2.25643205207016	1.07087755598075	3.44198654815957
102	2.25643205207016	0.968399385050306	3.54446471909001
103	2.25643205207016	0.873494295183488	3.63936980895683
104	2.25643205207016	0.78469650261326	3.72816760152706
105	2.25643205207016	0.700959707202638	3.81190439693768
106	2.25643205207016	0.621506089293824	3.89135801484649
107	2.25643205207016	0.545738744702474	3.96712535943784
108	2.25643205207016	0.473187739031407	4.03967636510891

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 2.25643205207016 & 1.63066475446827 & 2.88219934967204 \tabularnewline
98 & 2.25643205207016 & 1.45326743702513 & 3.05959666711518 \tabularnewline
99 & 2.25643205207016 & 1.30850690366819 & 3.20435720047212 \tabularnewline
100 & 2.25643205207016 & 1.18309576968455 & 3.32976833445576 \tabularnewline
101 & 2.25643205207016 & 1.07087755598075 & 3.44198654815957 \tabularnewline
102 & 2.25643205207016 & 0.968399385050306 & 3.54446471909001 \tabularnewline
103 & 2.25643205207016 & 0.873494295183488 & 3.63936980895683 \tabularnewline
104 & 2.25643205207016 & 0.78469650261326 & 3.72816760152706 \tabularnewline
105 & 2.25643205207016 & 0.700959707202638 & 3.81190439693768 \tabularnewline
106 & 2.25643205207016 & 0.621506089293824 & 3.89135801484649 \tabularnewline
107 & 2.25643205207016 & 0.545738744702474 & 3.96712535943784 \tabularnewline
108 & 2.25643205207016 & 0.473187739031407 & 4.03967636510891 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278574&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]2.25643205207016[/C][C]1.63066475446827[/C][C]2.88219934967204[/C][/ROW]
[ROW][C]98[/C][C]2.25643205207016[/C][C]1.45326743702513[/C][C]3.05959666711518[/C][/ROW]
[ROW][C]99[/C][C]2.25643205207016[/C][C]1.30850690366819[/C][C]3.20435720047212[/C][/ROW]
[ROW][C]100[/C][C]2.25643205207016[/C][C]1.18309576968455[/C][C]3.32976833445576[/C][/ROW]
[ROW][C]101[/C][C]2.25643205207016[/C][C]1.07087755598075[/C][C]3.44198654815957[/C][/ROW]
[ROW][C]102[/C][C]2.25643205207016[/C][C]0.968399385050306[/C][C]3.54446471909001[/C][/ROW]
[ROW][C]103[/C][C]2.25643205207016[/C][C]0.873494295183488[/C][C]3.63936980895683[/C][/ROW]
[ROW][C]104[/C][C]2.25643205207016[/C][C]0.78469650261326[/C][C]3.72816760152706[/C][/ROW]
[ROW][C]105[/C][C]2.25643205207016[/C][C]0.700959707202638[/C][C]3.81190439693768[/C][/ROW]
[ROW][C]106[/C][C]2.25643205207016[/C][C]0.621506089293824[/C][C]3.89135801484649[/C][/ROW]
[ROW][C]107[/C][C]2.25643205207016[/C][C]0.545738744702474[/C][C]3.96712535943784[/C][/ROW]
[ROW][C]108[/C][C]2.25643205207016[/C][C]0.473187739031407[/C][C]4.03967636510891[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278574&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278574&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	2.25643205207016	1.63066475446827	2.88219934967204
98	2.25643205207016	1.45326743702513	3.05959666711518
99	2.25643205207016	1.30850690366819	3.20435720047212
100	2.25643205207016	1.18309576968455	3.32976833445576
101	2.25643205207016	1.07087755598075	3.44198654815957
102	2.25643205207016	0.968399385050306	3.54446471909001
103	2.25643205207016	0.873494295183488	3.63936980895683
104	2.25643205207016	0.78469650261326	3.72816760152706
105	2.25643205207016	0.700959707202638	3.81190439693768
106	2.25643205207016	0.621506089293824	3.89135801484649
107	2.25643205207016	0.545738744702474	3.96712535943784
108	2.25643205207016	0.473187739031407	4.03967636510891

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