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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Fri, 21 Dec 2012 04:10:27 -0500

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/21/t1356081145ovk9b51yhi03kqa.htm/, Retrieved Wed, 24 Apr 2024 03:16:45 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=203334, Retrieved Wed, 24 Apr 2024 03:16:45 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

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

-     [Exponential Smoothing] [] [2012-12-21 08:56:25] [2f0f353a58a70fd7baf0f5141860d820]
- R  D    [Exponential Smoothing] [] [2012-12-21 09:10:27] [492ce95363299443ae43b669aa70c778] [Current]

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Dataseries X:

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Histogram

Boxplots

1.26
1.26
1.28
1.34
1.39
1.47
1.57
1.63
1.72
1.43
1.35
1.41
1.44
1.43
1.43
1.42
1.45
1.51
1.48
1.48
1.45
1.38
1.46
1.45
1.41
1.45
1.47
1.47
1.53
1.56
1.66
1.79
1.78
1.46
1.41
1.43
1.43
1.45
1.35
1.35
1.29
1.29
1.26
1.3
1.3
1.16
1.24
1.15
1.21
1.22
1.17
1.13
1.15
1.2
1.23
1.25
1.38
1.28
1.26
1.25
1.26
1.28
1.31
1.22
1.23
1.36
1.54
1.58
1.44
1.29
1.28
1.23

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Gwilym Jenkins' @ 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203334&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203334&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203334&T=0

As an alternative you can also use a QR Code:

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

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

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.832244655997629
beta	0
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.832244655997629 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203334&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]0.832244655997629[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203334&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203334&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	0.832244655997629
beta	0
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	1.44	1.39936959226552	0.0406304077344832
14	1.43	1.43222568321503	-0.00222568321502603
15	1.43	1.44691747022395	-0.0169174702239521
16	1.42	1.43530576230229	-0.015305762302293
17	1.45	1.44938130942394	0.000618690576056791
18	1.51	1.50262285920117	0.00737714079883212
19	1.48	1.58252319248858	-0.102523192488575
20	1.48	1.53795611878566	-0.057956118785659
21	1.45	1.55679222519364	-0.106792225193637
22	1.38	1.21177116346434	0.168228836535661
23	1.46	1.27046016415022	0.189539835849779
24	1.45	1.48680177534671	-0.0368017753467114
25	1.41	1.49563469888821	-0.0856346988882077
26	1.45	1.41629842178247	0.0337015782175296
27	1.47	1.45854598942251	0.0114540105774863
28	1.47	1.47088473409143	-0.000884734091433304
29	1.53	1.5007001754095	0.0292998245905012
30	1.56	1.58176760510247	-0.0217676051024722
31	1.66	1.61995425313775	0.0400457468622526
32	1.79	1.70690503191163	0.083094968088373
33	1.78	1.84558002803356	-0.0655800280335641
34	1.46	1.52816210958135	-0.0681621095813516
35	1.41	1.38483969312771	0.0251603068722863
36	1.43	1.42549103602695	0.004508963973054
37	1.43	1.45934659492766	-0.0293465949276617
38	1.45	1.44698696732681	0.0030130326731892
39	1.35	1.45994564228532	-0.109945642285324
40	1.35	1.36908068409795	-0.0190806840979481
41	1.29	1.38585674663312	-0.0958567466331162
42	1.29	1.34700944070806	-0.0570094407080599
43	1.26	1.35486258901052	-0.0948625890105175
44	1.3	1.3220767259878	-0.022076725987803
45	1.3	1.33570274009453	-0.0357027400945258
46	1.16	1.11231498521556	0.0476850147844425
47	1.24	1.09583542815109	0.144164571848911
48	1.15	1.22973039949716	-0.0797303994971597
49	1.21	1.18304817440093	0.0269518255990722
50	1.22	1.22011424323695	-0.000114243236949196
51	1.17	1.2117209712668	-0.0417209712668005
52	1.13	1.19072093401558	-0.060720934015577
53	1.15	1.15594860160409	-0.0059486016040935
54	1.2	1.19294006045426	0.00705993954573625
55	1.23	1.24333525132073	-0.0133352513207263
56	1.25	1.28925535441567	-0.0392553544156653
57	1.38	1.285147235184	0.0948527648159991
58	1.28	1.17528990393289	0.104710096067112
59	1.26	1.21638665574786	0.04361334425214
60	1.25	1.22803314352468	0.0219668564753195
61	1.26	1.28699776635124	-0.0269977663512397
62	1.28	1.27511051411452	0.00488948588548244
63	1.31	1.26297770233438	0.0470222976656154
64	1.22	1.31341215481965	-0.0934121548196463
65	1.23	1.26301622025122	-0.033016220251219
66	1.36	1.28299389441997	0.0770061055800306
67	1.54	1.39328858503506	0.146711414964938
68	1.58	1.58025355685031	-0.000253556850313252
69	1.44	1.64363881379831	-0.203638813798306
70	1.29	1.27300141469087	0.0169985853091301
71	1.28	1.23032768216855	0.0496723178314482
72	1.23	1.24307519173348	-0.0130751917334806

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1.44 & 1.39936959226552 & 0.0406304077344832 \tabularnewline
14 & 1.43 & 1.43222568321503 & -0.00222568321502603 \tabularnewline
15 & 1.43 & 1.44691747022395 & -0.0169174702239521 \tabularnewline
16 & 1.42 & 1.43530576230229 & -0.015305762302293 \tabularnewline
17 & 1.45 & 1.44938130942394 & 0.000618690576056791 \tabularnewline
18 & 1.51 & 1.50262285920117 & 0.00737714079883212 \tabularnewline
19 & 1.48 & 1.58252319248858 & -0.102523192488575 \tabularnewline
20 & 1.48 & 1.53795611878566 & -0.057956118785659 \tabularnewline
21 & 1.45 & 1.55679222519364 & -0.106792225193637 \tabularnewline
22 & 1.38 & 1.21177116346434 & 0.168228836535661 \tabularnewline
23 & 1.46 & 1.27046016415022 & 0.189539835849779 \tabularnewline
24 & 1.45 & 1.48680177534671 & -0.0368017753467114 \tabularnewline
25 & 1.41 & 1.49563469888821 & -0.0856346988882077 \tabularnewline
26 & 1.45 & 1.41629842178247 & 0.0337015782175296 \tabularnewline
27 & 1.47 & 1.45854598942251 & 0.0114540105774863 \tabularnewline
28 & 1.47 & 1.47088473409143 & -0.000884734091433304 \tabularnewline
29 & 1.53 & 1.5007001754095 & 0.0292998245905012 \tabularnewline
30 & 1.56 & 1.58176760510247 & -0.0217676051024722 \tabularnewline
31 & 1.66 & 1.61995425313775 & 0.0400457468622526 \tabularnewline
32 & 1.79 & 1.70690503191163 & 0.083094968088373 \tabularnewline
33 & 1.78 & 1.84558002803356 & -0.0655800280335641 \tabularnewline
34 & 1.46 & 1.52816210958135 & -0.0681621095813516 \tabularnewline
35 & 1.41 & 1.38483969312771 & 0.0251603068722863 \tabularnewline
36 & 1.43 & 1.42549103602695 & 0.004508963973054 \tabularnewline
37 & 1.43 & 1.45934659492766 & -0.0293465949276617 \tabularnewline
38 & 1.45 & 1.44698696732681 & 0.0030130326731892 \tabularnewline
39 & 1.35 & 1.45994564228532 & -0.109945642285324 \tabularnewline
40 & 1.35 & 1.36908068409795 & -0.0190806840979481 \tabularnewline
41 & 1.29 & 1.38585674663312 & -0.0958567466331162 \tabularnewline
42 & 1.29 & 1.34700944070806 & -0.0570094407080599 \tabularnewline
43 & 1.26 & 1.35486258901052 & -0.0948625890105175 \tabularnewline
44 & 1.3 & 1.3220767259878 & -0.022076725987803 \tabularnewline
45 & 1.3 & 1.33570274009453 & -0.0357027400945258 \tabularnewline
46 & 1.16 & 1.11231498521556 & 0.0476850147844425 \tabularnewline
47 & 1.24 & 1.09583542815109 & 0.144164571848911 \tabularnewline
48 & 1.15 & 1.22973039949716 & -0.0797303994971597 \tabularnewline
49 & 1.21 & 1.18304817440093 & 0.0269518255990722 \tabularnewline
50 & 1.22 & 1.22011424323695 & -0.000114243236949196 \tabularnewline
51 & 1.17 & 1.2117209712668 & -0.0417209712668005 \tabularnewline
52 & 1.13 & 1.19072093401558 & -0.060720934015577 \tabularnewline
53 & 1.15 & 1.15594860160409 & -0.0059486016040935 \tabularnewline
54 & 1.2 & 1.19294006045426 & 0.00705993954573625 \tabularnewline
55 & 1.23 & 1.24333525132073 & -0.0133352513207263 \tabularnewline
56 & 1.25 & 1.28925535441567 & -0.0392553544156653 \tabularnewline
57 & 1.38 & 1.285147235184 & 0.0948527648159991 \tabularnewline
58 & 1.28 & 1.17528990393289 & 0.104710096067112 \tabularnewline
59 & 1.26 & 1.21638665574786 & 0.04361334425214 \tabularnewline
60 & 1.25 & 1.22803314352468 & 0.0219668564753195 \tabularnewline
61 & 1.26 & 1.28699776635124 & -0.0269977663512397 \tabularnewline
62 & 1.28 & 1.27511051411452 & 0.00488948588548244 \tabularnewline
63 & 1.31 & 1.26297770233438 & 0.0470222976656154 \tabularnewline
64 & 1.22 & 1.31341215481965 & -0.0934121548196463 \tabularnewline
65 & 1.23 & 1.26301622025122 & -0.033016220251219 \tabularnewline
66 & 1.36 & 1.28299389441997 & 0.0770061055800306 \tabularnewline
67 & 1.54 & 1.39328858503506 & 0.146711414964938 \tabularnewline
68 & 1.58 & 1.58025355685031 & -0.000253556850313252 \tabularnewline
69 & 1.44 & 1.64363881379831 & -0.203638813798306 \tabularnewline
70 & 1.29 & 1.27300141469087 & 0.0169985853091301 \tabularnewline
71 & 1.28 & 1.23032768216855 & 0.0496723178314482 \tabularnewline
72 & 1.23 & 1.24307519173348 & -0.0130751917334806 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203334&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]1.44[/C][C]1.39936959226552[/C][C]0.0406304077344832[/C][/ROW]
[ROW][C]14[/C][C]1.43[/C][C]1.43222568321503[/C][C]-0.00222568321502603[/C][/ROW]
[ROW][C]15[/C][C]1.43[/C][C]1.44691747022395[/C][C]-0.0169174702239521[/C][/ROW]
[ROW][C]16[/C][C]1.42[/C][C]1.43530576230229[/C][C]-0.015305762302293[/C][/ROW]
[ROW][C]17[/C][C]1.45[/C][C]1.44938130942394[/C][C]0.000618690576056791[/C][/ROW]
[ROW][C]18[/C][C]1.51[/C][C]1.50262285920117[/C][C]0.00737714079883212[/C][/ROW]
[ROW][C]19[/C][C]1.48[/C][C]1.58252319248858[/C][C]-0.102523192488575[/C][/ROW]
[ROW][C]20[/C][C]1.48[/C][C]1.53795611878566[/C][C]-0.057956118785659[/C][/ROW]
[ROW][C]21[/C][C]1.45[/C][C]1.55679222519364[/C][C]-0.106792225193637[/C][/ROW]
[ROW][C]22[/C][C]1.38[/C][C]1.21177116346434[/C][C]0.168228836535661[/C][/ROW]
[ROW][C]23[/C][C]1.46[/C][C]1.27046016415022[/C][C]0.189539835849779[/C][/ROW]
[ROW][C]24[/C][C]1.45[/C][C]1.48680177534671[/C][C]-0.0368017753467114[/C][/ROW]
[ROW][C]25[/C][C]1.41[/C][C]1.49563469888821[/C][C]-0.0856346988882077[/C][/ROW]
[ROW][C]26[/C][C]1.45[/C][C]1.41629842178247[/C][C]0.0337015782175296[/C][/ROW]
[ROW][C]27[/C][C]1.47[/C][C]1.45854598942251[/C][C]0.0114540105774863[/C][/ROW]
[ROW][C]28[/C][C]1.47[/C][C]1.47088473409143[/C][C]-0.000884734091433304[/C][/ROW]
[ROW][C]29[/C][C]1.53[/C][C]1.5007001754095[/C][C]0.0292998245905012[/C][/ROW]
[ROW][C]30[/C][C]1.56[/C][C]1.58176760510247[/C][C]-0.0217676051024722[/C][/ROW]
[ROW][C]31[/C][C]1.66[/C][C]1.61995425313775[/C][C]0.0400457468622526[/C][/ROW]
[ROW][C]32[/C][C]1.79[/C][C]1.70690503191163[/C][C]0.083094968088373[/C][/ROW]
[ROW][C]33[/C][C]1.78[/C][C]1.84558002803356[/C][C]-0.0655800280335641[/C][/ROW]
[ROW][C]34[/C][C]1.46[/C][C]1.52816210958135[/C][C]-0.0681621095813516[/C][/ROW]
[ROW][C]35[/C][C]1.41[/C][C]1.38483969312771[/C][C]0.0251603068722863[/C][/ROW]
[ROW][C]36[/C][C]1.43[/C][C]1.42549103602695[/C][C]0.004508963973054[/C][/ROW]
[ROW][C]37[/C][C]1.43[/C][C]1.45934659492766[/C][C]-0.0293465949276617[/C][/ROW]
[ROW][C]38[/C][C]1.45[/C][C]1.44698696732681[/C][C]0.0030130326731892[/C][/ROW]
[ROW][C]39[/C][C]1.35[/C][C]1.45994564228532[/C][C]-0.109945642285324[/C][/ROW]
[ROW][C]40[/C][C]1.35[/C][C]1.36908068409795[/C][C]-0.0190806840979481[/C][/ROW]
[ROW][C]41[/C][C]1.29[/C][C]1.38585674663312[/C][C]-0.0958567466331162[/C][/ROW]
[ROW][C]42[/C][C]1.29[/C][C]1.34700944070806[/C][C]-0.0570094407080599[/C][/ROW]
[ROW][C]43[/C][C]1.26[/C][C]1.35486258901052[/C][C]-0.0948625890105175[/C][/ROW]
[ROW][C]44[/C][C]1.3[/C][C]1.3220767259878[/C][C]-0.022076725987803[/C][/ROW]
[ROW][C]45[/C][C]1.3[/C][C]1.33570274009453[/C][C]-0.0357027400945258[/C][/ROW]
[ROW][C]46[/C][C]1.16[/C][C]1.11231498521556[/C][C]0.0476850147844425[/C][/ROW]
[ROW][C]47[/C][C]1.24[/C][C]1.09583542815109[/C][C]0.144164571848911[/C][/ROW]
[ROW][C]48[/C][C]1.15[/C][C]1.22973039949716[/C][C]-0.0797303994971597[/C][/ROW]
[ROW][C]49[/C][C]1.21[/C][C]1.18304817440093[/C][C]0.0269518255990722[/C][/ROW]
[ROW][C]50[/C][C]1.22[/C][C]1.22011424323695[/C][C]-0.000114243236949196[/C][/ROW]
[ROW][C]51[/C][C]1.17[/C][C]1.2117209712668[/C][C]-0.0417209712668005[/C][/ROW]
[ROW][C]52[/C][C]1.13[/C][C]1.19072093401558[/C][C]-0.060720934015577[/C][/ROW]
[ROW][C]53[/C][C]1.15[/C][C]1.15594860160409[/C][C]-0.0059486016040935[/C][/ROW]
[ROW][C]54[/C][C]1.2[/C][C]1.19294006045426[/C][C]0.00705993954573625[/C][/ROW]
[ROW][C]55[/C][C]1.23[/C][C]1.24333525132073[/C][C]-0.0133352513207263[/C][/ROW]
[ROW][C]56[/C][C]1.25[/C][C]1.28925535441567[/C][C]-0.0392553544156653[/C][/ROW]
[ROW][C]57[/C][C]1.38[/C][C]1.285147235184[/C][C]0.0948527648159991[/C][/ROW]
[ROW][C]58[/C][C]1.28[/C][C]1.17528990393289[/C][C]0.104710096067112[/C][/ROW]
[ROW][C]59[/C][C]1.26[/C][C]1.21638665574786[/C][C]0.04361334425214[/C][/ROW]
[ROW][C]60[/C][C]1.25[/C][C]1.22803314352468[/C][C]0.0219668564753195[/C][/ROW]
[ROW][C]61[/C][C]1.26[/C][C]1.28699776635124[/C][C]-0.0269977663512397[/C][/ROW]
[ROW][C]62[/C][C]1.28[/C][C]1.27511051411452[/C][C]0.00488948588548244[/C][/ROW]
[ROW][C]63[/C][C]1.31[/C][C]1.26297770233438[/C][C]0.0470222976656154[/C][/ROW]
[ROW][C]64[/C][C]1.22[/C][C]1.31341215481965[/C][C]-0.0934121548196463[/C][/ROW]
[ROW][C]65[/C][C]1.23[/C][C]1.26301622025122[/C][C]-0.033016220251219[/C][/ROW]
[ROW][C]66[/C][C]1.36[/C][C]1.28299389441997[/C][C]0.0770061055800306[/C][/ROW]
[ROW][C]67[/C][C]1.54[/C][C]1.39328858503506[/C][C]0.146711414964938[/C][/ROW]
[ROW][C]68[/C][C]1.58[/C][C]1.58025355685031[/C][C]-0.000253556850313252[/C][/ROW]
[ROW][C]69[/C][C]1.44[/C][C]1.64363881379831[/C][C]-0.203638813798306[/C][/ROW]
[ROW][C]70[/C][C]1.29[/C][C]1.27300141469087[/C][C]0.0169985853091301[/C][/ROW]
[ROW][C]71[/C][C]1.28[/C][C]1.23032768216855[/C][C]0.0496723178314482[/C][/ROW]
[ROW][C]72[/C][C]1.23[/C][C]1.24307519173348[/C][C]-0.0130751917334806[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203334&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203334&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	1.44	1.39936959226552	0.0406304077344832
14	1.43	1.43222568321503	-0.00222568321502603
15	1.43	1.44691747022395	-0.0169174702239521
16	1.42	1.43530576230229	-0.015305762302293
17	1.45	1.44938130942394	0.000618690576056791
18	1.51	1.50262285920117	0.00737714079883212
19	1.48	1.58252319248858	-0.102523192488575
20	1.48	1.53795611878566	-0.057956118785659
21	1.45	1.55679222519364	-0.106792225193637
22	1.38	1.21177116346434	0.168228836535661
23	1.46	1.27046016415022	0.189539835849779
24	1.45	1.48680177534671	-0.0368017753467114
25	1.41	1.49563469888821	-0.0856346988882077
26	1.45	1.41629842178247	0.0337015782175296
27	1.47	1.45854598942251	0.0114540105774863
28	1.47	1.47088473409143	-0.000884734091433304
29	1.53	1.5007001754095	0.0292998245905012
30	1.56	1.58176760510247	-0.0217676051024722
31	1.66	1.61995425313775	0.0400457468622526
32	1.79	1.70690503191163	0.083094968088373
33	1.78	1.84558002803356	-0.0655800280335641
34	1.46	1.52816210958135	-0.0681621095813516
35	1.41	1.38483969312771	0.0251603068722863
36	1.43	1.42549103602695	0.004508963973054
37	1.43	1.45934659492766	-0.0293465949276617
38	1.45	1.44698696732681	0.0030130326731892
39	1.35	1.45994564228532	-0.109945642285324
40	1.35	1.36908068409795	-0.0190806840979481
41	1.29	1.38585674663312	-0.0958567466331162
42	1.29	1.34700944070806	-0.0570094407080599
43	1.26	1.35486258901052	-0.0948625890105175
44	1.3	1.3220767259878	-0.022076725987803
45	1.3	1.33570274009453	-0.0357027400945258
46	1.16	1.11231498521556	0.0476850147844425
47	1.24	1.09583542815109	0.144164571848911
48	1.15	1.22973039949716	-0.0797303994971597
49	1.21	1.18304817440093	0.0269518255990722
50	1.22	1.22011424323695	-0.000114243236949196
51	1.17	1.2117209712668	-0.0417209712668005
52	1.13	1.19072093401558	-0.060720934015577
53	1.15	1.15594860160409	-0.0059486016040935
54	1.2	1.19294006045426	0.00705993954573625
55	1.23	1.24333525132073	-0.0133352513207263
56	1.25	1.28925535441567	-0.0392553544156653
57	1.38	1.285147235184	0.0948527648159991
58	1.28	1.17528990393289	0.104710096067112
59	1.26	1.21638665574786	0.04361334425214
60	1.25	1.22803314352468	0.0219668564753195
61	1.26	1.28699776635124	-0.0269977663512397
62	1.28	1.27511051411452	0.00488948588548244
63	1.31	1.26297770233438	0.0470222976656154
64	1.22	1.31341215481965	-0.0934121548196463
65	1.23	1.26301622025122	-0.033016220251219
66	1.36	1.28299389441997	0.0770061055800306
67	1.54	1.39328858503506	0.146711414964938
68	1.58	1.58025355685031	-0.000253556850313252
69	1.44	1.64363881379831	-0.203638813798306
70	1.29	1.27300141469087	0.0169985853091301
71	1.28	1.23032768216855	0.0496723178314482
72	1.23	1.24307519173348	-0.0130751917334806

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	1.26411049955603	1.12401926799567	1.40420173111638
74	1.28009288447999	1.09684456296017	1.4633412059998
75	1.27072112331431	1.05438573070373	1.48705651592489
76	1.25785348656667	1.01368864524161	1.50201832789172
77	1.29638889512768	1.01961190260455	1.57316588765082
78	1.36525112676719	1.05223183601853	1.67827041751585
79	1.42138720480066	1.07584352971242	1.76693087988889
80	1.45843957649238	1.08546229090608	1.83141686207867
81	1.48196127434101	1.08549786191597	1.87842468676606
82	1.31301981548836	0.940986193004238	1.68505343797248
83	1.26050077559271	0.883992850040376	1.63700870114505
84	1.22194915632537	-176.616407388419	179.06030570107

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 1.26411049955603 & 1.12401926799567 & 1.40420173111638 \tabularnewline
74 & 1.28009288447999 & 1.09684456296017 & 1.4633412059998 \tabularnewline
75 & 1.27072112331431 & 1.05438573070373 & 1.48705651592489 \tabularnewline
76 & 1.25785348656667 & 1.01368864524161 & 1.50201832789172 \tabularnewline
77 & 1.29638889512768 & 1.01961190260455 & 1.57316588765082 \tabularnewline
78 & 1.36525112676719 & 1.05223183601853 & 1.67827041751585 \tabularnewline
79 & 1.42138720480066 & 1.07584352971242 & 1.76693087988889 \tabularnewline
80 & 1.45843957649238 & 1.08546229090608 & 1.83141686207867 \tabularnewline
81 & 1.48196127434101 & 1.08549786191597 & 1.87842468676606 \tabularnewline
82 & 1.31301981548836 & 0.940986193004238 & 1.68505343797248 \tabularnewline
83 & 1.26050077559271 & 0.883992850040376 & 1.63700870114505 \tabularnewline
84 & 1.22194915632537 & -176.616407388419 & 179.06030570107 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203334&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]73[/C][C]1.26411049955603[/C][C]1.12401926799567[/C][C]1.40420173111638[/C][/ROW]
[ROW][C]74[/C][C]1.28009288447999[/C][C]1.09684456296017[/C][C]1.4633412059998[/C][/ROW]
[ROW][C]75[/C][C]1.27072112331431[/C][C]1.05438573070373[/C][C]1.48705651592489[/C][/ROW]
[ROW][C]76[/C][C]1.25785348656667[/C][C]1.01368864524161[/C][C]1.50201832789172[/C][/ROW]
[ROW][C]77[/C][C]1.29638889512768[/C][C]1.01961190260455[/C][C]1.57316588765082[/C][/ROW]
[ROW][C]78[/C][C]1.36525112676719[/C][C]1.05223183601853[/C][C]1.67827041751585[/C][/ROW]
[ROW][C]79[/C][C]1.42138720480066[/C][C]1.07584352971242[/C][C]1.76693087988889[/C][/ROW]
[ROW][C]80[/C][C]1.45843957649238[/C][C]1.08546229090608[/C][C]1.83141686207867[/C][/ROW]
[ROW][C]81[/C][C]1.48196127434101[/C][C]1.08549786191597[/C][C]1.87842468676606[/C][/ROW]
[ROW][C]82[/C][C]1.31301981548836[/C][C]0.940986193004238[/C][C]1.68505343797248[/C][/ROW]
[ROW][C]83[/C][C]1.26050077559271[/C][C]0.883992850040376[/C][C]1.63700870114505[/C][/ROW]
[ROW][C]84[/C][C]1.22194915632537[/C][C]-176.616407388419[/C][C]179.06030570107[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203334&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203334&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
73	1.26411049955603	1.12401926799567	1.40420173111638
74	1.28009288447999	1.09684456296017	1.4633412059998
75	1.27072112331431	1.05438573070373	1.48705651592489
76	1.25785348656667	1.01368864524161	1.50201832789172
77	1.29638889512768	1.01961190260455	1.57316588765082
78	1.36525112676719	1.05223183601853	1.67827041751585
79	1.42138720480066	1.07584352971242	1.76693087988889
80	1.45843957649238	1.08546229090608	1.83141686207867
81	1.48196127434101	1.08549786191597	1.87842468676606
82	1.31301981548836	0.940986193004238	1.68505343797248
83	1.26050077559271	0.883992850040376	1.63700870114505
84	1.22194915632537	-176.616407388419	179.06030570107

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=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