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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Tue, 10 Jan 2017 03:56:33 +0000

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/2017/Jan/10/t1484020618u1jtelgt2uvi0pq.htm/, Retrieved Thu, 16 May 2024 01:11:03 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Thu, 16 May 2024 01:11:03 +0200

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

Dataseries X:

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Boxplots

2,32
1,93
0,62
0,6
-0,37
-1,1
-1,68
-0,77
-1,2
-0,97
-0,12
0,26
0,62
0,7
1,65
1,79
2,28
2,46
2,57
2,32
2,91
3,01
2,87
3,11
3,22
3,38
3,52
3,41
3,35
3,68
3,75
3,6
3,56
3,57
3,85
3,48
3,65
3,66
3,36
3,19
2,81
2,25
2,32
2,85
2,75
2,78
2,26
2,23
1,46
1,19
1,11
1
1,18
1,59
1,51
1,01
0,9
0,63
0,81
0,97
1,14
0,97
0,89
0,62
0,36
0,27
0,34
0,02
-0,12
0,09
-0,11
-0,38
-0,65
-0,4
-0,4
0,29
0,56
0,63
0,46
0,91
1,06
1,28
1,52
1,5

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	'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.134779015206886
beta	0
gamma	0.728955179481844

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.134779015206886 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.728955179481844 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.134779015206886[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.728955179481844[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	0.134779015206886
beta	0
gamma	0.728955179481844

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	0.62	-0.279618279511905	0.899618279511905
14	0.7	-0.040079302472917	0.740079302472917
15	1.65	0.243546836428045	1.40645316357196
16	1.79	0.483826275771695	1.30617372422831
17	2.28	0.832311302782549	1.44768869721745
18	2.46	1.09766089624567	1.36233910375433
19	2.57	17.8820527792069	-15.3120527792069
20	2.32	3.78213905877996	-1.46213905877996
21	2.91	5.89396732363298	-2.98396732363298
22	3.01	7.85498472259071	-4.84498472259071
23	2.87	-12.8524248816207	15.7224248816207
24	3.11	1.06575033302018	2.04424966697982
25	3.22	-4.01619204105793	7.23619204105793
26	3.38	8.43699673136926	-5.05699673136926
27	3.52	5.15907214927376	-1.63907214927376
28	3.41	3.34869006162678	0.0613099383732232
29	3.35	3.25797590948511	0.0920240905148852
30	3.68	2.95391001669643	0.726089983303566
31	3.75	9.67711117485926	-5.92711117485926
32	3.6	3.93951313282296	-0.339513132822963
33	3.56	5.51300404464268	-1.95300404464268
34	3.57	6.40526870475644	-2.83526870475644
35	3.85	-1.3844315504024	5.2344315504024
36	3.48	1.76884011579745	1.71115988420255
37	3.65	1.56136259553516	2.08863740446484
38	3.66	5.92524432160331	-2.26524432160331
39	3.36	4.94387207042073	-1.58387207042073
40	3.19	4.04761485433573	-0.857614854335726
41	2.81	3.80154826075335	-0.991548260753355
42	2.25	3.72029849809463	-1.47029849809463
43	2.32	5.62107269511623	-3.30107269511623
44	2.85	3.74741924557449	-0.897419245574492
45	2.75	4.16214842386953	-1.41214842386953
46	2.78	4.45487253027512	-1.67487253027512
47	2.26	5.34060399337656	-3.08060399337656
48	2.23	4.8587463329076	-2.6287463329076
49	1.46	3.8098879628016	-2.3498879628016
50	1.19	4.85268291609852	-3.66268291609852
51	1.11	4.04545910380877	-2.93545910380877
52	1	3.4194712517819	-2.4194712517819
53	1.18	2.89405364118289	-1.71405364118289
54	1.59	2.41999777189907	-0.829997771899065
55	1.51	3.01156174883309	-1.50156174883309
56	1.01	2.88939371678574	-1.87939371678574
57	0.9	2.80815367387424	-1.90815367387424
58	0.63	2.80127572452501	-2.17127572452501
59	0.81	2.59687556068638	-1.78687556068638
60	0.97	2.46428445869139	-1.49428445869139
61	1.14	1.77111653188567	-0.631116531885667
62	0.97	1.93531048252427	-0.965310482524273
63	0.89	1.77160358827122	-0.881603588271224
64	0.62	1.60174197901574	-0.981741979015737
65	0.36	1.61915814136115	-1.25915814136115
66	0.27	1.72533552155596	-1.45533552155596
67	0.34	1.7300151300828	-1.3900151300828
68	0.02	1.3359215711986	-1.3159215711986
69	-0.12	1.20534397212416	-1.32534397212416
70	0.09	0.990773916597287	-0.900773916597287
71	-0.11	1.05739610403744	-1.16739610403744
72	-0.38	1.08188241989128	-1.46188241989128
73	-0.65	0.940340914144965	-1.59034091414497
74	-0.4	0.764048749920463	-1.16404874992046
75	-0.4	0.638866851456836	-1.03886685145684
76	0.29	0.458203251343418	-0.168203251343418
77	0.56	0.401142727258745	0.158857272741255
78	0.63	0.463284043492505	0.166715956507495
79	0.46	0.605538896420503	-0.145538896420503
80	0.91	0.337051303316096	0.572948696683904
81	1.06	0.277418467721465	0.782581532278535
82	1.28	0.657390794208236	0.622609205791764
83	1.52	0.446996038557938	1.07300396144206
84	1.5	-0.152343742974665	1.65234374297467

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 0.62 & -0.279618279511905 & 0.899618279511905 \tabularnewline
14 & 0.7 & -0.040079302472917 & 0.740079302472917 \tabularnewline
15 & 1.65 & 0.243546836428045 & 1.40645316357196 \tabularnewline
16 & 1.79 & 0.483826275771695 & 1.30617372422831 \tabularnewline
17 & 2.28 & 0.832311302782549 & 1.44768869721745 \tabularnewline
18 & 2.46 & 1.09766089624567 & 1.36233910375433 \tabularnewline
19 & 2.57 & 17.8820527792069 & -15.3120527792069 \tabularnewline
20 & 2.32 & 3.78213905877996 & -1.46213905877996 \tabularnewline
21 & 2.91 & 5.89396732363298 & -2.98396732363298 \tabularnewline
22 & 3.01 & 7.85498472259071 & -4.84498472259071 \tabularnewline
23 & 2.87 & -12.8524248816207 & 15.7224248816207 \tabularnewline
24 & 3.11 & 1.06575033302018 & 2.04424966697982 \tabularnewline
25 & 3.22 & -4.01619204105793 & 7.23619204105793 \tabularnewline
26 & 3.38 & 8.43699673136926 & -5.05699673136926 \tabularnewline
27 & 3.52 & 5.15907214927376 & -1.63907214927376 \tabularnewline
28 & 3.41 & 3.34869006162678 & 0.0613099383732232 \tabularnewline
29 & 3.35 & 3.25797590948511 & 0.0920240905148852 \tabularnewline
30 & 3.68 & 2.95391001669643 & 0.726089983303566 \tabularnewline
31 & 3.75 & 9.67711117485926 & -5.92711117485926 \tabularnewline
32 & 3.6 & 3.93951313282296 & -0.339513132822963 \tabularnewline
33 & 3.56 & 5.51300404464268 & -1.95300404464268 \tabularnewline
34 & 3.57 & 6.40526870475644 & -2.83526870475644 \tabularnewline
35 & 3.85 & -1.3844315504024 & 5.2344315504024 \tabularnewline
36 & 3.48 & 1.76884011579745 & 1.71115988420255 \tabularnewline
37 & 3.65 & 1.56136259553516 & 2.08863740446484 \tabularnewline
38 & 3.66 & 5.92524432160331 & -2.26524432160331 \tabularnewline
39 & 3.36 & 4.94387207042073 & -1.58387207042073 \tabularnewline
40 & 3.19 & 4.04761485433573 & -0.857614854335726 \tabularnewline
41 & 2.81 & 3.80154826075335 & -0.991548260753355 \tabularnewline
42 & 2.25 & 3.72029849809463 & -1.47029849809463 \tabularnewline
43 & 2.32 & 5.62107269511623 & -3.30107269511623 \tabularnewline
44 & 2.85 & 3.74741924557449 & -0.897419245574492 \tabularnewline
45 & 2.75 & 4.16214842386953 & -1.41214842386953 \tabularnewline
46 & 2.78 & 4.45487253027512 & -1.67487253027512 \tabularnewline
47 & 2.26 & 5.34060399337656 & -3.08060399337656 \tabularnewline
48 & 2.23 & 4.8587463329076 & -2.6287463329076 \tabularnewline
49 & 1.46 & 3.8098879628016 & -2.3498879628016 \tabularnewline
50 & 1.19 & 4.85268291609852 & -3.66268291609852 \tabularnewline
51 & 1.11 & 4.04545910380877 & -2.93545910380877 \tabularnewline
52 & 1 & 3.4194712517819 & -2.4194712517819 \tabularnewline
53 & 1.18 & 2.89405364118289 & -1.71405364118289 \tabularnewline
54 & 1.59 & 2.41999777189907 & -0.829997771899065 \tabularnewline
55 & 1.51 & 3.01156174883309 & -1.50156174883309 \tabularnewline
56 & 1.01 & 2.88939371678574 & -1.87939371678574 \tabularnewline
57 & 0.9 & 2.80815367387424 & -1.90815367387424 \tabularnewline
58 & 0.63 & 2.80127572452501 & -2.17127572452501 \tabularnewline
59 & 0.81 & 2.59687556068638 & -1.78687556068638 \tabularnewline
60 & 0.97 & 2.46428445869139 & -1.49428445869139 \tabularnewline
61 & 1.14 & 1.77111653188567 & -0.631116531885667 \tabularnewline
62 & 0.97 & 1.93531048252427 & -0.965310482524273 \tabularnewline
63 & 0.89 & 1.77160358827122 & -0.881603588271224 \tabularnewline
64 & 0.62 & 1.60174197901574 & -0.981741979015737 \tabularnewline
65 & 0.36 & 1.61915814136115 & -1.25915814136115 \tabularnewline
66 & 0.27 & 1.72533552155596 & -1.45533552155596 \tabularnewline
67 & 0.34 & 1.7300151300828 & -1.3900151300828 \tabularnewline
68 & 0.02 & 1.3359215711986 & -1.3159215711986 \tabularnewline
69 & -0.12 & 1.20534397212416 & -1.32534397212416 \tabularnewline
70 & 0.09 & 0.990773916597287 & -0.900773916597287 \tabularnewline
71 & -0.11 & 1.05739610403744 & -1.16739610403744 \tabularnewline
72 & -0.38 & 1.08188241989128 & -1.46188241989128 \tabularnewline
73 & -0.65 & 0.940340914144965 & -1.59034091414497 \tabularnewline
74 & -0.4 & 0.764048749920463 & -1.16404874992046 \tabularnewline
75 & -0.4 & 0.638866851456836 & -1.03886685145684 \tabularnewline
76 & 0.29 & 0.458203251343418 & -0.168203251343418 \tabularnewline
77 & 0.56 & 0.401142727258745 & 0.158857272741255 \tabularnewline
78 & 0.63 & 0.463284043492505 & 0.166715956507495 \tabularnewline
79 & 0.46 & 0.605538896420503 & -0.145538896420503 \tabularnewline
80 & 0.91 & 0.337051303316096 & 0.572948696683904 \tabularnewline
81 & 1.06 & 0.277418467721465 & 0.782581532278535 \tabularnewline
82 & 1.28 & 0.657390794208236 & 0.622609205791764 \tabularnewline
83 & 1.52 & 0.446996038557938 & 1.07300396144206 \tabularnewline
84 & 1.5 & -0.152343742974665 & 1.65234374297467 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.62[/C][C]-0.279618279511905[/C][C]0.899618279511905[/C][/ROW]
[ROW][C]14[/C][C]0.7[/C][C]-0.040079302472917[/C][C]0.740079302472917[/C][/ROW]
[ROW][C]15[/C][C]1.65[/C][C]0.243546836428045[/C][C]1.40645316357196[/C][/ROW]
[ROW][C]16[/C][C]1.79[/C][C]0.483826275771695[/C][C]1.30617372422831[/C][/ROW]
[ROW][C]17[/C][C]2.28[/C][C]0.832311302782549[/C][C]1.44768869721745[/C][/ROW]
[ROW][C]18[/C][C]2.46[/C][C]1.09766089624567[/C][C]1.36233910375433[/C][/ROW]
[ROW][C]19[/C][C]2.57[/C][C]17.8820527792069[/C][C]-15.3120527792069[/C][/ROW]
[ROW][C]20[/C][C]2.32[/C][C]3.78213905877996[/C][C]-1.46213905877996[/C][/ROW]
[ROW][C]21[/C][C]2.91[/C][C]5.89396732363298[/C][C]-2.98396732363298[/C][/ROW]
[ROW][C]22[/C][C]3.01[/C][C]7.85498472259071[/C][C]-4.84498472259071[/C][/ROW]
[ROW][C]23[/C][C]2.87[/C][C]-12.8524248816207[/C][C]15.7224248816207[/C][/ROW]
[ROW][C]24[/C][C]3.11[/C][C]1.06575033302018[/C][C]2.04424966697982[/C][/ROW]
[ROW][C]25[/C][C]3.22[/C][C]-4.01619204105793[/C][C]7.23619204105793[/C][/ROW]
[ROW][C]26[/C][C]3.38[/C][C]8.43699673136926[/C][C]-5.05699673136926[/C][/ROW]
[ROW][C]27[/C][C]3.52[/C][C]5.15907214927376[/C][C]-1.63907214927376[/C][/ROW]
[ROW][C]28[/C][C]3.41[/C][C]3.34869006162678[/C][C]0.0613099383732232[/C][/ROW]
[ROW][C]29[/C][C]3.35[/C][C]3.25797590948511[/C][C]0.0920240905148852[/C][/ROW]
[ROW][C]30[/C][C]3.68[/C][C]2.95391001669643[/C][C]0.726089983303566[/C][/ROW]
[ROW][C]31[/C][C]3.75[/C][C]9.67711117485926[/C][C]-5.92711117485926[/C][/ROW]
[ROW][C]32[/C][C]3.6[/C][C]3.93951313282296[/C][C]-0.339513132822963[/C][/ROW]
[ROW][C]33[/C][C]3.56[/C][C]5.51300404464268[/C][C]-1.95300404464268[/C][/ROW]
[ROW][C]34[/C][C]3.57[/C][C]6.40526870475644[/C][C]-2.83526870475644[/C][/ROW]
[ROW][C]35[/C][C]3.85[/C][C]-1.3844315504024[/C][C]5.2344315504024[/C][/ROW]
[ROW][C]36[/C][C]3.48[/C][C]1.76884011579745[/C][C]1.71115988420255[/C][/ROW]
[ROW][C]37[/C][C]3.65[/C][C]1.56136259553516[/C][C]2.08863740446484[/C][/ROW]
[ROW][C]38[/C][C]3.66[/C][C]5.92524432160331[/C][C]-2.26524432160331[/C][/ROW]
[ROW][C]39[/C][C]3.36[/C][C]4.94387207042073[/C][C]-1.58387207042073[/C][/ROW]
[ROW][C]40[/C][C]3.19[/C][C]4.04761485433573[/C][C]-0.857614854335726[/C][/ROW]
[ROW][C]41[/C][C]2.81[/C][C]3.80154826075335[/C][C]-0.991548260753355[/C][/ROW]
[ROW][C]42[/C][C]2.25[/C][C]3.72029849809463[/C][C]-1.47029849809463[/C][/ROW]
[ROW][C]43[/C][C]2.32[/C][C]5.62107269511623[/C][C]-3.30107269511623[/C][/ROW]
[ROW][C]44[/C][C]2.85[/C][C]3.74741924557449[/C][C]-0.897419245574492[/C][/ROW]
[ROW][C]45[/C][C]2.75[/C][C]4.16214842386953[/C][C]-1.41214842386953[/C][/ROW]
[ROW][C]46[/C][C]2.78[/C][C]4.45487253027512[/C][C]-1.67487253027512[/C][/ROW]
[ROW][C]47[/C][C]2.26[/C][C]5.34060399337656[/C][C]-3.08060399337656[/C][/ROW]
[ROW][C]48[/C][C]2.23[/C][C]4.8587463329076[/C][C]-2.6287463329076[/C][/ROW]
[ROW][C]49[/C][C]1.46[/C][C]3.8098879628016[/C][C]-2.3498879628016[/C][/ROW]
[ROW][C]50[/C][C]1.19[/C][C]4.85268291609852[/C][C]-3.66268291609852[/C][/ROW]
[ROW][C]51[/C][C]1.11[/C][C]4.04545910380877[/C][C]-2.93545910380877[/C][/ROW]
[ROW][C]52[/C][C]1[/C][C]3.4194712517819[/C][C]-2.4194712517819[/C][/ROW]
[ROW][C]53[/C][C]1.18[/C][C]2.89405364118289[/C][C]-1.71405364118289[/C][/ROW]
[ROW][C]54[/C][C]1.59[/C][C]2.41999777189907[/C][C]-0.829997771899065[/C][/ROW]
[ROW][C]55[/C][C]1.51[/C][C]3.01156174883309[/C][C]-1.50156174883309[/C][/ROW]
[ROW][C]56[/C][C]1.01[/C][C]2.88939371678574[/C][C]-1.87939371678574[/C][/ROW]
[ROW][C]57[/C][C]0.9[/C][C]2.80815367387424[/C][C]-1.90815367387424[/C][/ROW]
[ROW][C]58[/C][C]0.63[/C][C]2.80127572452501[/C][C]-2.17127572452501[/C][/ROW]
[ROW][C]59[/C][C]0.81[/C][C]2.59687556068638[/C][C]-1.78687556068638[/C][/ROW]
[ROW][C]60[/C][C]0.97[/C][C]2.46428445869139[/C][C]-1.49428445869139[/C][/ROW]
[ROW][C]61[/C][C]1.14[/C][C]1.77111653188567[/C][C]-0.631116531885667[/C][/ROW]
[ROW][C]62[/C][C]0.97[/C][C]1.93531048252427[/C][C]-0.965310482524273[/C][/ROW]
[ROW][C]63[/C][C]0.89[/C][C]1.77160358827122[/C][C]-0.881603588271224[/C][/ROW]
[ROW][C]64[/C][C]0.62[/C][C]1.60174197901574[/C][C]-0.981741979015737[/C][/ROW]
[ROW][C]65[/C][C]0.36[/C][C]1.61915814136115[/C][C]-1.25915814136115[/C][/ROW]
[ROW][C]66[/C][C]0.27[/C][C]1.72533552155596[/C][C]-1.45533552155596[/C][/ROW]
[ROW][C]67[/C][C]0.34[/C][C]1.7300151300828[/C][C]-1.3900151300828[/C][/ROW]
[ROW][C]68[/C][C]0.02[/C][C]1.3359215711986[/C][C]-1.3159215711986[/C][/ROW]
[ROW][C]69[/C][C]-0.12[/C][C]1.20534397212416[/C][C]-1.32534397212416[/C][/ROW]
[ROW][C]70[/C][C]0.09[/C][C]0.990773916597287[/C][C]-0.900773916597287[/C][/ROW]
[ROW][C]71[/C][C]-0.11[/C][C]1.05739610403744[/C][C]-1.16739610403744[/C][/ROW]
[ROW][C]72[/C][C]-0.38[/C][C]1.08188241989128[/C][C]-1.46188241989128[/C][/ROW]
[ROW][C]73[/C][C]-0.65[/C][C]0.940340914144965[/C][C]-1.59034091414497[/C][/ROW]
[ROW][C]74[/C][C]-0.4[/C][C]0.764048749920463[/C][C]-1.16404874992046[/C][/ROW]
[ROW][C]75[/C][C]-0.4[/C][C]0.638866851456836[/C][C]-1.03886685145684[/C][/ROW]
[ROW][C]76[/C][C]0.29[/C][C]0.458203251343418[/C][C]-0.168203251343418[/C][/ROW]
[ROW][C]77[/C][C]0.56[/C][C]0.401142727258745[/C][C]0.158857272741255[/C][/ROW]
[ROW][C]78[/C][C]0.63[/C][C]0.463284043492505[/C][C]0.166715956507495[/C][/ROW]
[ROW][C]79[/C][C]0.46[/C][C]0.605538896420503[/C][C]-0.145538896420503[/C][/ROW]
[ROW][C]80[/C][C]0.91[/C][C]0.337051303316096[/C][C]0.572948696683904[/C][/ROW]
[ROW][C]81[/C][C]1.06[/C][C]0.277418467721465[/C][C]0.782581532278535[/C][/ROW]
[ROW][C]82[/C][C]1.28[/C][C]0.657390794208236[/C][C]0.622609205791764[/C][/ROW]
[ROW][C]83[/C][C]1.52[/C][C]0.446996038557938[/C][C]1.07300396144206[/C][/ROW]
[ROW][C]84[/C][C]1.5[/C][C]-0.152343742974665[/C][C]1.65234374297467[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	0.62	-0.279618279511905	0.899618279511905
14	0.7	-0.040079302472917	0.740079302472917
15	1.65	0.243546836428045	1.40645316357196
16	1.79	0.483826275771695	1.30617372422831
17	2.28	0.832311302782549	1.44768869721745
18	2.46	1.09766089624567	1.36233910375433
19	2.57	17.8820527792069	-15.3120527792069
20	2.32	3.78213905877996	-1.46213905877996
21	2.91	5.89396732363298	-2.98396732363298
22	3.01	7.85498472259071	-4.84498472259071
23	2.87	-12.8524248816207	15.7224248816207
24	3.11	1.06575033302018	2.04424966697982
25	3.22	-4.01619204105793	7.23619204105793
26	3.38	8.43699673136926	-5.05699673136926
27	3.52	5.15907214927376	-1.63907214927376
28	3.41	3.34869006162678	0.0613099383732232
29	3.35	3.25797590948511	0.0920240905148852
30	3.68	2.95391001669643	0.726089983303566
31	3.75	9.67711117485926	-5.92711117485926
32	3.6	3.93951313282296	-0.339513132822963
33	3.56	5.51300404464268	-1.95300404464268
34	3.57	6.40526870475644	-2.83526870475644
35	3.85	-1.3844315504024	5.2344315504024
36	3.48	1.76884011579745	1.71115988420255
37	3.65	1.56136259553516	2.08863740446484
38	3.66	5.92524432160331	-2.26524432160331
39	3.36	4.94387207042073	-1.58387207042073
40	3.19	4.04761485433573	-0.857614854335726
41	2.81	3.80154826075335	-0.991548260753355
42	2.25	3.72029849809463	-1.47029849809463
43	2.32	5.62107269511623	-3.30107269511623
44	2.85	3.74741924557449	-0.897419245574492
45	2.75	4.16214842386953	-1.41214842386953
46	2.78	4.45487253027512	-1.67487253027512
47	2.26	5.34060399337656	-3.08060399337656
48	2.23	4.8587463329076	-2.6287463329076
49	1.46	3.8098879628016	-2.3498879628016
50	1.19	4.85268291609852	-3.66268291609852
51	1.11	4.04545910380877	-2.93545910380877
52	1	3.4194712517819	-2.4194712517819
53	1.18	2.89405364118289	-1.71405364118289
54	1.59	2.41999777189907	-0.829997771899065
55	1.51	3.01156174883309	-1.50156174883309
56	1.01	2.88939371678574	-1.87939371678574
57	0.9	2.80815367387424	-1.90815367387424
58	0.63	2.80127572452501	-2.17127572452501
59	0.81	2.59687556068638	-1.78687556068638
60	0.97	2.46428445869139	-1.49428445869139
61	1.14	1.77111653188567	-0.631116531885667
62	0.97	1.93531048252427	-0.965310482524273
63	0.89	1.77160358827122	-0.881603588271224
64	0.62	1.60174197901574	-0.981741979015737
65	0.36	1.61915814136115	-1.25915814136115
66	0.27	1.72533552155596	-1.45533552155596
67	0.34	1.7300151300828	-1.3900151300828
68	0.02	1.3359215711986	-1.3159215711986
69	-0.12	1.20534397212416	-1.32534397212416
70	0.09	0.990773916597287	-0.900773916597287
71	-0.11	1.05739610403744	-1.16739610403744
72	-0.38	1.08188241989128	-1.46188241989128
73	-0.65	0.940340914144965	-1.59034091414497
74	-0.4	0.764048749920463	-1.16404874992046
75	-0.4	0.638866851456836	-1.03886685145684
76	0.29	0.458203251343418	-0.168203251343418
77	0.56	0.401142727258745	0.158857272741255
78	0.63	0.463284043492505	0.166715956507495
79	0.46	0.605538896420503	-0.145538896420503
80	0.91	0.337051303316096	0.572948696683904
81	1.06	0.277418467721465	0.782581532278535
82	1.28	0.657390794208236	0.622609205791764
83	1.52	0.446996038557938	1.07300396144206
84	1.5	-0.152343742974665	1.65234374297467

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	0.566563937250131	-4.38559805672447	5.51872593122473
86	0.266871178088932	-4.70489069584199	5.23863305201985
87	0.337370295750515	-4.79124567338681	5.46598626488784
88	-0.587176662372754	-6.38418344093189	5.20983011618638
89	-0.69982820989148	-7.12489563018443	5.72523921040147
90	-0.605989546942622	-6.97430245088853	5.76232335700329
91	-0.423352287766446	-6.31825314285063	5.47154856731774
92	-0.433881153669947	-6.70485974492298	5.83709743758309
93	-0.286873752270904	-6.08036968046395	5.50662217592215
94	-0.265569212085904	-6.28439142339509	5.75325299922328
95	-0.176495317360992	-5.89641568026871	5.54342504554673
96	0.253671620450943	-8.58719741881967	9.09454065972156

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 0.566563937250131 & -4.38559805672447 & 5.51872593122473 \tabularnewline
86 & 0.266871178088932 & -4.70489069584199 & 5.23863305201985 \tabularnewline
87 & 0.337370295750515 & -4.79124567338681 & 5.46598626488784 \tabularnewline
88 & -0.587176662372754 & -6.38418344093189 & 5.20983011618638 \tabularnewline
89 & -0.69982820989148 & -7.12489563018443 & 5.72523921040147 \tabularnewline
90 & -0.605989546942622 & -6.97430245088853 & 5.76232335700329 \tabularnewline
91 & -0.423352287766446 & -6.31825314285063 & 5.47154856731774 \tabularnewline
92 & -0.433881153669947 & -6.70485974492298 & 5.83709743758309 \tabularnewline
93 & -0.286873752270904 & -6.08036968046395 & 5.50662217592215 \tabularnewline
94 & -0.265569212085904 & -6.28439142339509 & 5.75325299922328 \tabularnewline
95 & -0.176495317360992 & -5.89641568026871 & 5.54342504554673 \tabularnewline
96 & 0.253671620450943 & -8.58719741881967 & 9.09454065972156 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]85[/C][C]0.566563937250131[/C][C]-4.38559805672447[/C][C]5.51872593122473[/C][/ROW]
[ROW][C]86[/C][C]0.266871178088932[/C][C]-4.70489069584199[/C][C]5.23863305201985[/C][/ROW]
[ROW][C]87[/C][C]0.337370295750515[/C][C]-4.79124567338681[/C][C]5.46598626488784[/C][/ROW]
[ROW][C]88[/C][C]-0.587176662372754[/C][C]-6.38418344093189[/C][C]5.20983011618638[/C][/ROW]
[ROW][C]89[/C][C]-0.69982820989148[/C][C]-7.12489563018443[/C][C]5.72523921040147[/C][/ROW]
[ROW][C]90[/C][C]-0.605989546942622[/C][C]-6.97430245088853[/C][C]5.76232335700329[/C][/ROW]
[ROW][C]91[/C][C]-0.423352287766446[/C][C]-6.31825314285063[/C][C]5.47154856731774[/C][/ROW]
[ROW][C]92[/C][C]-0.433881153669947[/C][C]-6.70485974492298[/C][C]5.83709743758309[/C][/ROW]
[ROW][C]93[/C][C]-0.286873752270904[/C][C]-6.08036968046395[/C][C]5.50662217592215[/C][/ROW]
[ROW][C]94[/C][C]-0.265569212085904[/C][C]-6.28439142339509[/C][C]5.75325299922328[/C][/ROW]
[ROW][C]95[/C][C]-0.176495317360992[/C][C]-5.89641568026871[/C][C]5.54342504554673[/C][/ROW]
[ROW][C]96[/C][C]0.253671620450943[/C][C]-8.58719741881967[/C][C]9.09454065972156[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
85	0.566563937250131	-4.38559805672447	5.51872593122473
86	0.266871178088932	-4.70489069584199	5.23863305201985
87	0.337370295750515	-4.79124567338681	5.46598626488784
88	-0.587176662372754	-6.38418344093189	5.20983011618638
89	-0.69982820989148	-7.12489563018443	5.72523921040147
90	-0.605989546942622	-6.97430245088853	5.76232335700329
91	-0.423352287766446	-6.31825314285063	5.47154856731774
92	-0.433881153669947	-6.70485974492298	5.83709743758309
93	-0.286873752270904	-6.08036968046395	5.50662217592215
94	-0.265569212085904	-6.28439142339509	5.75325299922328
95	-0.176495317360992	-5.89641568026871	5.54342504554673
96	0.253671620450943	-8.58719741881967	9.09454065972156

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 ;

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=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