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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sat, 24 Jan 2009 16:08:06 -0700

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jan/25/t1232838710l4x7bhzx9hrfsna.htm/, Retrieved Thu, 02 May 2024 07:49:42 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36954, Retrieved Thu, 02 May 2024 07:49:42 +0000

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No (this computation is public)

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Estimated Impact

206

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

-       [Exponential Smoothing] ["buitenlandse han...] [2009-01-24 23:08:06] [cd990bb7dd50d289d8ca88511d54b252] [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	'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 & 3 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=36954&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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36954&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36954&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	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.266577368862136
beta	0.0682753886454245
gamma	0.279348094072512

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.266577368862136 \tabularnewline
beta & 0.0682753886454245 \tabularnewline
gamma & 0.279348094072512 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36954&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]0.266577368862136[/C][/ROW]
[ROW][C]beta[/C][C]0.0682753886454245[/C][/ROW]
[ROW][C]gamma[/C][C]0.279348094072512[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36954&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36954&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	0.266577368862136
beta	0.0682753886454245
gamma	0.279348094072512

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	15.1	15.0510904319016	0.0489095680983951
14	14.8	14.7218457334219	0.0781542665781121
15	16.1	16.0604927489735	0.039507251026528
16	14.3	14.3076229186691	-0.00762291866908882
17	15.2	15.2941600733895	-0.0941600733894834
18	14.9	15.1018761801022	-0.201876180102206
19	13.1	13.3314071759306	-0.231407175930617
20	12.6	12.8350919636992	-0.235091963699235
21	13.6	13.8432201799708	-0.243220179970789
22	14.4	14.5879314602157	-0.187931460215712
23	14	14.1125515889085	-0.112551588908469
24	12.9	12.9894745519134	-0.0894745519134386
25	13.4	14.1309135595694	-0.730913559569382
26	13.5	13.5848823181235	-0.084882318123464
27	14.8	14.7186562461241	0.0813437538758617
28	14.3	13.0733741079052	1.22662589209479
29	14.3	14.2901835000978	0.00981649990220568
30	14	14.0976024736616	-0.0976024736615724
31	13.2	12.4418107420534	0.75818925794659
32	12.2	12.2315540256707	-0.0315540256707241
33	14.3	13.2585310220025	1.04146897799749
34	15.7	14.3806794583637	1.31932054163627
35	14.2	14.3788365009894	-0.178836500989384
36	14.6	13.2791630504391	1.32083694956095
37	14.5	14.8098294249884	-0.309829424988385
38	14.3	14.5940674775911	-0.294067477591062
39	15.3	15.8977698478695	-0.597769847869536
40	14.4	14.2891103299211	0.110889670078880
41	13.7	15.0552628038393	-1.35526280383933
42	14.2	14.5089933615323	-0.308993361532252
43	13.5	12.9618208886007	0.538179111399286
44	11.9	12.5426247199143	-0.642624719914297
45	14.6	13.6531844221941	0.946815577805864
46	15.6	14.8244809189694	0.775519081030598
47	14.1	14.3723696300227	-0.272369630022661
48	14.9	13.5489931782484	1.35100682175156
49	14.2	14.7550746433979	-0.55507464339788
50	14.6	14.4743531722819	0.125646827718073
51	17.2	15.8361691113066	1.36383088869342
52	15.4	14.8838474638876	0.516152536112399
53	14.3	15.5167558968915	-1.21675589689146
54	17.5	15.2720208546613	2.22797914533872
55	14.5	14.5264465189786	-0.0264465189785899
56	14.4	13.7054964295749	0.694503570425145
57	16.6	15.8223063816722	0.777693618327811
58	16.7	17.1442511662569	-0.44425116625694
59	16.6	16.1294199122416	0.470580087758428
60	16.9	15.8636879423913	1.03631205760869
61	15.7	16.7438684012890	-1.04386840128896
62	16.4	16.5526269241394	-0.152626924139422
63	18.4	18.3841775840748	0.0158224159251752
64	16.9	16.7746485185517	0.125351481448295
65	16.5	16.9996801903750	-0.499680190374963
66	18.3	17.7926949833589	0.507305016641119
67	15.1	15.9700598555965	-0.87005985559647
68	15.7	15.0196680688655	0.680331931134539
69	18.1	17.3149333319122	0.785066668087786
70	16.8	18.4633711045252	-1.66337110452524
71	18.9	17.2499346427579	1.65006535724208
72	19	17.3922641018335	1.60773589816653
73	18.1	18.0225203504535	0.0774796495464827
74	17.8	18.3745583776809	-0.57455837768094
75	21.5	20.3574683578654	1.14253164213463
76	17.1	18.9164907381066	-1.81649073810657
77	18.7	18.5103705737484	0.189629426251635
78	19	19.8369785657669	-0.836978565766941
79	16.4	17.1739811505324	-0.773981150532379
80	16.9	16.5310104796998	0.368989520300183
81	18.6	18.9374063800715	-0.337406380071517
82	19.3	19.2799460044787	0.0200539955213124
83	19.4	19.1817078872601	0.218292112739903
84	17.6	18.883431683516	-1.28343168351598
85	18.6	18.3579892625101	0.242010737489878
86	18.1	18.5571903147752	-0.457190314775193
87	20.4	20.8934680527554	-0.493468052755365
88	18.1	18.3292415303005	-0.229241530300495
89	19.6	18.7012296344698	0.898770365530236
90	19.9	19.9720871577415	-0.0720871577414677
91	19.2	17.4264096130320	1.77359038696803
92	17.8	17.6925799305669	0.107420069433115
93	19.2	20.0209176062141	-0.820917606214053
94	22.1	20.3325907812362	1.76740921876379
95	21.2	20.7621784986867	0.437821501313266
96	19.5	20.1831712973344	-0.683171297334415

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 15.1 & 15.0510904319016 & 0.0489095680983951 \tabularnewline
14 & 14.8 & 14.7218457334219 & 0.0781542665781121 \tabularnewline
15 & 16.1 & 16.0604927489735 & 0.039507251026528 \tabularnewline
16 & 14.3 & 14.3076229186691 & -0.00762291866908882 \tabularnewline
17 & 15.2 & 15.2941600733895 & -0.0941600733894834 \tabularnewline
18 & 14.9 & 15.1018761801022 & -0.201876180102206 \tabularnewline
19 & 13.1 & 13.3314071759306 & -0.231407175930617 \tabularnewline
20 & 12.6 & 12.8350919636992 & -0.235091963699235 \tabularnewline
21 & 13.6 & 13.8432201799708 & -0.243220179970789 \tabularnewline
22 & 14.4 & 14.5879314602157 & -0.187931460215712 \tabularnewline
23 & 14 & 14.1125515889085 & -0.112551588908469 \tabularnewline
24 & 12.9 & 12.9894745519134 & -0.0894745519134386 \tabularnewline
25 & 13.4 & 14.1309135595694 & -0.730913559569382 \tabularnewline
26 & 13.5 & 13.5848823181235 & -0.084882318123464 \tabularnewline
27 & 14.8 & 14.7186562461241 & 0.0813437538758617 \tabularnewline
28 & 14.3 & 13.0733741079052 & 1.22662589209479 \tabularnewline
29 & 14.3 & 14.2901835000978 & 0.00981649990220568 \tabularnewline
30 & 14 & 14.0976024736616 & -0.0976024736615724 \tabularnewline
31 & 13.2 & 12.4418107420534 & 0.75818925794659 \tabularnewline
32 & 12.2 & 12.2315540256707 & -0.0315540256707241 \tabularnewline
33 & 14.3 & 13.2585310220025 & 1.04146897799749 \tabularnewline
34 & 15.7 & 14.3806794583637 & 1.31932054163627 \tabularnewline
35 & 14.2 & 14.3788365009894 & -0.178836500989384 \tabularnewline
36 & 14.6 & 13.2791630504391 & 1.32083694956095 \tabularnewline
37 & 14.5 & 14.8098294249884 & -0.309829424988385 \tabularnewline
38 & 14.3 & 14.5940674775911 & -0.294067477591062 \tabularnewline
39 & 15.3 & 15.8977698478695 & -0.597769847869536 \tabularnewline
40 & 14.4 & 14.2891103299211 & 0.110889670078880 \tabularnewline
41 & 13.7 & 15.0552628038393 & -1.35526280383933 \tabularnewline
42 & 14.2 & 14.5089933615323 & -0.308993361532252 \tabularnewline
43 & 13.5 & 12.9618208886007 & 0.538179111399286 \tabularnewline
44 & 11.9 & 12.5426247199143 & -0.642624719914297 \tabularnewline
45 & 14.6 & 13.6531844221941 & 0.946815577805864 \tabularnewline
46 & 15.6 & 14.8244809189694 & 0.775519081030598 \tabularnewline
47 & 14.1 & 14.3723696300227 & -0.272369630022661 \tabularnewline
48 & 14.9 & 13.5489931782484 & 1.35100682175156 \tabularnewline
49 & 14.2 & 14.7550746433979 & -0.55507464339788 \tabularnewline
50 & 14.6 & 14.4743531722819 & 0.125646827718073 \tabularnewline
51 & 17.2 & 15.8361691113066 & 1.36383088869342 \tabularnewline
52 & 15.4 & 14.8838474638876 & 0.516152536112399 \tabularnewline
53 & 14.3 & 15.5167558968915 & -1.21675589689146 \tabularnewline
54 & 17.5 & 15.2720208546613 & 2.22797914533872 \tabularnewline
55 & 14.5 & 14.5264465189786 & -0.0264465189785899 \tabularnewline
56 & 14.4 & 13.7054964295749 & 0.694503570425145 \tabularnewline
57 & 16.6 & 15.8223063816722 & 0.777693618327811 \tabularnewline
58 & 16.7 & 17.1442511662569 & -0.44425116625694 \tabularnewline
59 & 16.6 & 16.1294199122416 & 0.470580087758428 \tabularnewline
60 & 16.9 & 15.8636879423913 & 1.03631205760869 \tabularnewline
61 & 15.7 & 16.7438684012890 & -1.04386840128896 \tabularnewline
62 & 16.4 & 16.5526269241394 & -0.152626924139422 \tabularnewline
63 & 18.4 & 18.3841775840748 & 0.0158224159251752 \tabularnewline
64 & 16.9 & 16.7746485185517 & 0.125351481448295 \tabularnewline
65 & 16.5 & 16.9996801903750 & -0.499680190374963 \tabularnewline
66 & 18.3 & 17.7926949833589 & 0.507305016641119 \tabularnewline
67 & 15.1 & 15.9700598555965 & -0.87005985559647 \tabularnewline
68 & 15.7 & 15.0196680688655 & 0.680331931134539 \tabularnewline
69 & 18.1 & 17.3149333319122 & 0.785066668087786 \tabularnewline
70 & 16.8 & 18.4633711045252 & -1.66337110452524 \tabularnewline
71 & 18.9 & 17.2499346427579 & 1.65006535724208 \tabularnewline
72 & 19 & 17.3922641018335 & 1.60773589816653 \tabularnewline
73 & 18.1 & 18.0225203504535 & 0.0774796495464827 \tabularnewline
74 & 17.8 & 18.3745583776809 & -0.57455837768094 \tabularnewline
75 & 21.5 & 20.3574683578654 & 1.14253164213463 \tabularnewline
76 & 17.1 & 18.9164907381066 & -1.81649073810657 \tabularnewline
77 & 18.7 & 18.5103705737484 & 0.189629426251635 \tabularnewline
78 & 19 & 19.8369785657669 & -0.836978565766941 \tabularnewline
79 & 16.4 & 17.1739811505324 & -0.773981150532379 \tabularnewline
80 & 16.9 & 16.5310104796998 & 0.368989520300183 \tabularnewline
81 & 18.6 & 18.9374063800715 & -0.337406380071517 \tabularnewline
82 & 19.3 & 19.2799460044787 & 0.0200539955213124 \tabularnewline
83 & 19.4 & 19.1817078872601 & 0.218292112739903 \tabularnewline
84 & 17.6 & 18.883431683516 & -1.28343168351598 \tabularnewline
85 & 18.6 & 18.3579892625101 & 0.242010737489878 \tabularnewline
86 & 18.1 & 18.5571903147752 & -0.457190314775193 \tabularnewline
87 & 20.4 & 20.8934680527554 & -0.493468052755365 \tabularnewline
88 & 18.1 & 18.3292415303005 & -0.229241530300495 \tabularnewline
89 & 19.6 & 18.7012296344698 & 0.898770365530236 \tabularnewline
90 & 19.9 & 19.9720871577415 & -0.0720871577414677 \tabularnewline
91 & 19.2 & 17.4264096130320 & 1.77359038696803 \tabularnewline
92 & 17.8 & 17.6925799305669 & 0.107420069433115 \tabularnewline
93 & 19.2 & 20.0209176062141 & -0.820917606214053 \tabularnewline
94 & 22.1 & 20.3325907812362 & 1.76740921876379 \tabularnewline
95 & 21.2 & 20.7621784986867 & 0.437821501313266 \tabularnewline
96 & 19.5 & 20.1831712973344 & -0.683171297334415 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36954&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]15.1[/C][C]15.0510904319016[/C][C]0.0489095680983951[/C][/ROW]
[ROW][C]14[/C][C]14.8[/C][C]14.7218457334219[/C][C]0.0781542665781121[/C][/ROW]
[ROW][C]15[/C][C]16.1[/C][C]16.0604927489735[/C][C]0.039507251026528[/C][/ROW]
[ROW][C]16[/C][C]14.3[/C][C]14.3076229186691[/C][C]-0.00762291866908882[/C][/ROW]
[ROW][C]17[/C][C]15.2[/C][C]15.2941600733895[/C][C]-0.0941600733894834[/C][/ROW]
[ROW][C]18[/C][C]14.9[/C][C]15.1018761801022[/C][C]-0.201876180102206[/C][/ROW]
[ROW][C]19[/C][C]13.1[/C][C]13.3314071759306[/C][C]-0.231407175930617[/C][/ROW]
[ROW][C]20[/C][C]12.6[/C][C]12.8350919636992[/C][C]-0.235091963699235[/C][/ROW]
[ROW][C]21[/C][C]13.6[/C][C]13.8432201799708[/C][C]-0.243220179970789[/C][/ROW]
[ROW][C]22[/C][C]14.4[/C][C]14.5879314602157[/C][C]-0.187931460215712[/C][/ROW]
[ROW][C]23[/C][C]14[/C][C]14.1125515889085[/C][C]-0.112551588908469[/C][/ROW]
[ROW][C]24[/C][C]12.9[/C][C]12.9894745519134[/C][C]-0.0894745519134386[/C][/ROW]
[ROW][C]25[/C][C]13.4[/C][C]14.1309135595694[/C][C]-0.730913559569382[/C][/ROW]
[ROW][C]26[/C][C]13.5[/C][C]13.5848823181235[/C][C]-0.084882318123464[/C][/ROW]
[ROW][C]27[/C][C]14.8[/C][C]14.7186562461241[/C][C]0.0813437538758617[/C][/ROW]
[ROW][C]28[/C][C]14.3[/C][C]13.0733741079052[/C][C]1.22662589209479[/C][/ROW]
[ROW][C]29[/C][C]14.3[/C][C]14.2901835000978[/C][C]0.00981649990220568[/C][/ROW]
[ROW][C]30[/C][C]14[/C][C]14.0976024736616[/C][C]-0.0976024736615724[/C][/ROW]
[ROW][C]31[/C][C]13.2[/C][C]12.4418107420534[/C][C]0.75818925794659[/C][/ROW]
[ROW][C]32[/C][C]12.2[/C][C]12.2315540256707[/C][C]-0.0315540256707241[/C][/ROW]
[ROW][C]33[/C][C]14.3[/C][C]13.2585310220025[/C][C]1.04146897799749[/C][/ROW]
[ROW][C]34[/C][C]15.7[/C][C]14.3806794583637[/C][C]1.31932054163627[/C][/ROW]
[ROW][C]35[/C][C]14.2[/C][C]14.3788365009894[/C][C]-0.178836500989384[/C][/ROW]
[ROW][C]36[/C][C]14.6[/C][C]13.2791630504391[/C][C]1.32083694956095[/C][/ROW]
[ROW][C]37[/C][C]14.5[/C][C]14.8098294249884[/C][C]-0.309829424988385[/C][/ROW]
[ROW][C]38[/C][C]14.3[/C][C]14.5940674775911[/C][C]-0.294067477591062[/C][/ROW]
[ROW][C]39[/C][C]15.3[/C][C]15.8977698478695[/C][C]-0.597769847869536[/C][/ROW]
[ROW][C]40[/C][C]14.4[/C][C]14.2891103299211[/C][C]0.110889670078880[/C][/ROW]
[ROW][C]41[/C][C]13.7[/C][C]15.0552628038393[/C][C]-1.35526280383933[/C][/ROW]
[ROW][C]42[/C][C]14.2[/C][C]14.5089933615323[/C][C]-0.308993361532252[/C][/ROW]
[ROW][C]43[/C][C]13.5[/C][C]12.9618208886007[/C][C]0.538179111399286[/C][/ROW]
[ROW][C]44[/C][C]11.9[/C][C]12.5426247199143[/C][C]-0.642624719914297[/C][/ROW]
[ROW][C]45[/C][C]14.6[/C][C]13.6531844221941[/C][C]0.946815577805864[/C][/ROW]
[ROW][C]46[/C][C]15.6[/C][C]14.8244809189694[/C][C]0.775519081030598[/C][/ROW]
[ROW][C]47[/C][C]14.1[/C][C]14.3723696300227[/C][C]-0.272369630022661[/C][/ROW]
[ROW][C]48[/C][C]14.9[/C][C]13.5489931782484[/C][C]1.35100682175156[/C][/ROW]
[ROW][C]49[/C][C]14.2[/C][C]14.7550746433979[/C][C]-0.55507464339788[/C][/ROW]
[ROW][C]50[/C][C]14.6[/C][C]14.4743531722819[/C][C]0.125646827718073[/C][/ROW]
[ROW][C]51[/C][C]17.2[/C][C]15.8361691113066[/C][C]1.36383088869342[/C][/ROW]
[ROW][C]52[/C][C]15.4[/C][C]14.8838474638876[/C][C]0.516152536112399[/C][/ROW]
[ROW][C]53[/C][C]14.3[/C][C]15.5167558968915[/C][C]-1.21675589689146[/C][/ROW]
[ROW][C]54[/C][C]17.5[/C][C]15.2720208546613[/C][C]2.22797914533872[/C][/ROW]
[ROW][C]55[/C][C]14.5[/C][C]14.5264465189786[/C][C]-0.0264465189785899[/C][/ROW]
[ROW][C]56[/C][C]14.4[/C][C]13.7054964295749[/C][C]0.694503570425145[/C][/ROW]
[ROW][C]57[/C][C]16.6[/C][C]15.8223063816722[/C][C]0.777693618327811[/C][/ROW]
[ROW][C]58[/C][C]16.7[/C][C]17.1442511662569[/C][C]-0.44425116625694[/C][/ROW]
[ROW][C]59[/C][C]16.6[/C][C]16.1294199122416[/C][C]0.470580087758428[/C][/ROW]
[ROW][C]60[/C][C]16.9[/C][C]15.8636879423913[/C][C]1.03631205760869[/C][/ROW]
[ROW][C]61[/C][C]15.7[/C][C]16.7438684012890[/C][C]-1.04386840128896[/C][/ROW]
[ROW][C]62[/C][C]16.4[/C][C]16.5526269241394[/C][C]-0.152626924139422[/C][/ROW]
[ROW][C]63[/C][C]18.4[/C][C]18.3841775840748[/C][C]0.0158224159251752[/C][/ROW]
[ROW][C]64[/C][C]16.9[/C][C]16.7746485185517[/C][C]0.125351481448295[/C][/ROW]
[ROW][C]65[/C][C]16.5[/C][C]16.9996801903750[/C][C]-0.499680190374963[/C][/ROW]
[ROW][C]66[/C][C]18.3[/C][C]17.7926949833589[/C][C]0.507305016641119[/C][/ROW]
[ROW][C]67[/C][C]15.1[/C][C]15.9700598555965[/C][C]-0.87005985559647[/C][/ROW]
[ROW][C]68[/C][C]15.7[/C][C]15.0196680688655[/C][C]0.680331931134539[/C][/ROW]
[ROW][C]69[/C][C]18.1[/C][C]17.3149333319122[/C][C]0.785066668087786[/C][/ROW]
[ROW][C]70[/C][C]16.8[/C][C]18.4633711045252[/C][C]-1.66337110452524[/C][/ROW]
[ROW][C]71[/C][C]18.9[/C][C]17.2499346427579[/C][C]1.65006535724208[/C][/ROW]
[ROW][C]72[/C][C]19[/C][C]17.3922641018335[/C][C]1.60773589816653[/C][/ROW]
[ROW][C]73[/C][C]18.1[/C][C]18.0225203504535[/C][C]0.0774796495464827[/C][/ROW]
[ROW][C]74[/C][C]17.8[/C][C]18.3745583776809[/C][C]-0.57455837768094[/C][/ROW]
[ROW][C]75[/C][C]21.5[/C][C]20.3574683578654[/C][C]1.14253164213463[/C][/ROW]
[ROW][C]76[/C][C]17.1[/C][C]18.9164907381066[/C][C]-1.81649073810657[/C][/ROW]
[ROW][C]77[/C][C]18.7[/C][C]18.5103705737484[/C][C]0.189629426251635[/C][/ROW]
[ROW][C]78[/C][C]19[/C][C]19.8369785657669[/C][C]-0.836978565766941[/C][/ROW]
[ROW][C]79[/C][C]16.4[/C][C]17.1739811505324[/C][C]-0.773981150532379[/C][/ROW]
[ROW][C]80[/C][C]16.9[/C][C]16.5310104796998[/C][C]0.368989520300183[/C][/ROW]
[ROW][C]81[/C][C]18.6[/C][C]18.9374063800715[/C][C]-0.337406380071517[/C][/ROW]
[ROW][C]82[/C][C]19.3[/C][C]19.2799460044787[/C][C]0.0200539955213124[/C][/ROW]
[ROW][C]83[/C][C]19.4[/C][C]19.1817078872601[/C][C]0.218292112739903[/C][/ROW]
[ROW][C]84[/C][C]17.6[/C][C]18.883431683516[/C][C]-1.28343168351598[/C][/ROW]
[ROW][C]85[/C][C]18.6[/C][C]18.3579892625101[/C][C]0.242010737489878[/C][/ROW]
[ROW][C]86[/C][C]18.1[/C][C]18.5571903147752[/C][C]-0.457190314775193[/C][/ROW]
[ROW][C]87[/C][C]20.4[/C][C]20.8934680527554[/C][C]-0.493468052755365[/C][/ROW]
[ROW][C]88[/C][C]18.1[/C][C]18.3292415303005[/C][C]-0.229241530300495[/C][/ROW]
[ROW][C]89[/C][C]19.6[/C][C]18.7012296344698[/C][C]0.898770365530236[/C][/ROW]
[ROW][C]90[/C][C]19.9[/C][C]19.9720871577415[/C][C]-0.0720871577414677[/C][/ROW]
[ROW][C]91[/C][C]19.2[/C][C]17.4264096130320[/C][C]1.77359038696803[/C][/ROW]
[ROW][C]92[/C][C]17.8[/C][C]17.6925799305669[/C][C]0.107420069433115[/C][/ROW]
[ROW][C]93[/C][C]19.2[/C][C]20.0209176062141[/C][C]-0.820917606214053[/C][/ROW]
[ROW][C]94[/C][C]22.1[/C][C]20.3325907812362[/C][C]1.76740921876379[/C][/ROW]
[ROW][C]95[/C][C]21.2[/C][C]20.7621784986867[/C][C]0.437821501313266[/C][/ROW]
[ROW][C]96[/C][C]19.5[/C][C]20.1831712973344[/C][C]-0.683171297334415[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36954&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36954&T=2

As an alternative you can also use a QR Code:

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

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	15.1	15.0510904319016	0.0489095680983951
14	14.8	14.7218457334219	0.0781542665781121
15	16.1	16.0604927489735	0.039507251026528
16	14.3	14.3076229186691	-0.00762291866908882
17	15.2	15.2941600733895	-0.0941600733894834
18	14.9	15.1018761801022	-0.201876180102206
19	13.1	13.3314071759306	-0.231407175930617
20	12.6	12.8350919636992	-0.235091963699235
21	13.6	13.8432201799708	-0.243220179970789
22	14.4	14.5879314602157	-0.187931460215712
23	14	14.1125515889085	-0.112551588908469
24	12.9	12.9894745519134	-0.0894745519134386
25	13.4	14.1309135595694	-0.730913559569382
26	13.5	13.5848823181235	-0.084882318123464
27	14.8	14.7186562461241	0.0813437538758617
28	14.3	13.0733741079052	1.22662589209479
29	14.3	14.2901835000978	0.00981649990220568
30	14	14.0976024736616	-0.0976024736615724
31	13.2	12.4418107420534	0.75818925794659
32	12.2	12.2315540256707	-0.0315540256707241
33	14.3	13.2585310220025	1.04146897799749
34	15.7	14.3806794583637	1.31932054163627
35	14.2	14.3788365009894	-0.178836500989384
36	14.6	13.2791630504391	1.32083694956095
37	14.5	14.8098294249884	-0.309829424988385
38	14.3	14.5940674775911	-0.294067477591062
39	15.3	15.8977698478695	-0.597769847869536
40	14.4	14.2891103299211	0.110889670078880
41	13.7	15.0552628038393	-1.35526280383933
42	14.2	14.5089933615323	-0.308993361532252
43	13.5	12.9618208886007	0.538179111399286
44	11.9	12.5426247199143	-0.642624719914297
45	14.6	13.6531844221941	0.946815577805864
46	15.6	14.8244809189694	0.775519081030598
47	14.1	14.3723696300227	-0.272369630022661
48	14.9	13.5489931782484	1.35100682175156
49	14.2	14.7550746433979	-0.55507464339788
50	14.6	14.4743531722819	0.125646827718073
51	17.2	15.8361691113066	1.36383088869342
52	15.4	14.8838474638876	0.516152536112399
53	14.3	15.5167558968915	-1.21675589689146
54	17.5	15.2720208546613	2.22797914533872
55	14.5	14.5264465189786	-0.0264465189785899
56	14.4	13.7054964295749	0.694503570425145
57	16.6	15.8223063816722	0.777693618327811
58	16.7	17.1442511662569	-0.44425116625694
59	16.6	16.1294199122416	0.470580087758428
60	16.9	15.8636879423913	1.03631205760869
61	15.7	16.7438684012890	-1.04386840128896
62	16.4	16.5526269241394	-0.152626924139422
63	18.4	18.3841775840748	0.0158224159251752
64	16.9	16.7746485185517	0.125351481448295
65	16.5	16.9996801903750	-0.499680190374963
66	18.3	17.7926949833589	0.507305016641119
67	15.1	15.9700598555965	-0.87005985559647
68	15.7	15.0196680688655	0.680331931134539
69	18.1	17.3149333319122	0.785066668087786
70	16.8	18.4633711045252	-1.66337110452524
71	18.9	17.2499346427579	1.65006535724208
72	19	17.3922641018335	1.60773589816653
73	18.1	18.0225203504535	0.0774796495464827
74	17.8	18.3745583776809	-0.57455837768094
75	21.5	20.3574683578654	1.14253164213463
76	17.1	18.9164907381066	-1.81649073810657
77	18.7	18.5103705737484	0.189629426251635
78	19	19.8369785657669	-0.836978565766941
79	16.4	17.1739811505324	-0.773981150532379
80	16.9	16.5310104796998	0.368989520300183
81	18.6	18.9374063800715	-0.337406380071517
82	19.3	19.2799460044787	0.0200539955213124
83	19.4	19.1817078872601	0.218292112739903
84	17.6	18.883431683516	-1.28343168351598
85	18.6	18.3579892625101	0.242010737489878
86	18.1	18.5571903147752	-0.457190314775193
87	20.4	20.8934680527554	-0.493468052755365
88	18.1	18.3292415303005	-0.229241530300495
89	19.6	18.7012296344698	0.898770365530236
90	19.9	19.9720871577415	-0.0720871577414677
91	19.2	17.4264096130320	1.77359038696803
92	17.8	17.6925799305669	0.107420069433115
93	19.2	20.0209176062141	-0.820917606214053
94	22.1	20.3325907812362	1.76740921876379
95	21.2	20.7621784986867	0.437821501313266
96	19.5	20.1831712973344	-0.683171297334415

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
97	20.1826384938025	19.4406408816069	20.9246361059980
98	20.208102658073	19.3423143244261	21.0738909917199
99	22.9571149449742	21.9110962133709	24.0031336765774
100	20.36591891948	19.2779674575882	21.4538703813717
101	21.1637063820843	19.9292688312401	22.3981439329286
102	22.1267332126768	20.7321522772812	23.5213141480724
103	19.7702903799787	18.3785769344365	21.162003825521
104	19.1813765160763	17.7075552083288	20.6551978238237
105	21.4625112667695	19.7231068813118	23.2019156522271
106	22.6315345544553	20.6868185891971	24.5762505197136
107	22.2813416920063	20.2417599111506	24.3209234728619
108	21.2761604223595	14.8738393541274	27.6784814905916

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 20.1826384938025 & 19.4406408816069 & 20.9246361059980 \tabularnewline
98 & 20.208102658073 & 19.3423143244261 & 21.0738909917199 \tabularnewline
99 & 22.9571149449742 & 21.9110962133709 & 24.0031336765774 \tabularnewline
100 & 20.36591891948 & 19.2779674575882 & 21.4538703813717 \tabularnewline
101 & 21.1637063820843 & 19.9292688312401 & 22.3981439329286 \tabularnewline
102 & 22.1267332126768 & 20.7321522772812 & 23.5213141480724 \tabularnewline
103 & 19.7702903799787 & 18.3785769344365 & 21.162003825521 \tabularnewline
104 & 19.1813765160763 & 17.7075552083288 & 20.6551978238237 \tabularnewline
105 & 21.4625112667695 & 19.7231068813118 & 23.2019156522271 \tabularnewline
106 & 22.6315345544553 & 20.6868185891971 & 24.5762505197136 \tabularnewline
107 & 22.2813416920063 & 20.2417599111506 & 24.3209234728619 \tabularnewline
108 & 21.2761604223595 & 14.8738393541274 & 27.6784814905916 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36954&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]20.1826384938025[/C][C]19.4406408816069[/C][C]20.9246361059980[/C][/ROW]
[ROW][C]98[/C][C]20.208102658073[/C][C]19.3423143244261[/C][C]21.0738909917199[/C][/ROW]
[ROW][C]99[/C][C]22.9571149449742[/C][C]21.9110962133709[/C][C]24.0031336765774[/C][/ROW]
[ROW][C]100[/C][C]20.36591891948[/C][C]19.2779674575882[/C][C]21.4538703813717[/C][/ROW]
[ROW][C]101[/C][C]21.1637063820843[/C][C]19.9292688312401[/C][C]22.3981439329286[/C][/ROW]
[ROW][C]102[/C][C]22.1267332126768[/C][C]20.7321522772812[/C][C]23.5213141480724[/C][/ROW]
[ROW][C]103[/C][C]19.7702903799787[/C][C]18.3785769344365[/C][C]21.162003825521[/C][/ROW]
[ROW][C]104[/C][C]19.1813765160763[/C][C]17.7075552083288[/C][C]20.6551978238237[/C][/ROW]
[ROW][C]105[/C][C]21.4625112667695[/C][C]19.7231068813118[/C][C]23.2019156522271[/C][/ROW]
[ROW][C]106[/C][C]22.6315345544553[/C][C]20.6868185891971[/C][C]24.5762505197136[/C][/ROW]
[ROW][C]107[/C][C]22.2813416920063[/C][C]20.2417599111506[/C][C]24.3209234728619[/C][/ROW]
[ROW][C]108[/C][C]21.2761604223595[/C][C]14.8738393541274[/C][C]27.6784814905916[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36954&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36954&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	20.1826384938025	19.4406408816069	20.9246361059980
98	20.208102658073	19.3423143244261	21.0738909917199
99	22.9571149449742	21.9110962133709	24.0031336765774
100	20.36591891948	19.2779674575882	21.4538703813717
101	21.1637063820843	19.9292688312401	22.3981439329286
102	22.1267332126768	20.7321522772812	23.5213141480724
103	19.7702903799787	18.3785769344365	21.162003825521
104	19.1813765160763	17.7075552083288	20.6551978238237
105	21.4625112667695	19.7231068813118	23.2019156522271
106	22.6315345544553	20.6868185891971	24.5762505197136
107	22.2813416920063	20.2417599111506	24.3209234728619
108	21.2761604223595	14.8738393541274	27.6784814905916

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

R code (references can be found in the software module):

par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code