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*The author of this computation has been verified*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Thu, 03 Dec 2009 11:54:20 -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/Dec/03/t1259866671szocf0f1yp5ygh1.htm/, Retrieved Sat, 20 Apr 2024 11:47:55 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=63065, Retrieved Sat, 20 Apr 2024 11:47:55 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

162

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [] [2009-11-27 15:04:36] [b98453cac15ba1066b407e146608df68]
-    D      [Exponential Smoothing] [SHW WS9] [2009-12-03 18:54:20] [b7e46d23597387652ca7420fdeb9acca] [Current]
-   PD        [Exponential Smoothing] [Exponential Smoot...] [2009-12-04 15:53:12] [ba905ddf7cdf9ecb063c35348c4dab2e] 
-   PD          [Exponential Smoothing] [exponential smoot...] [2009-12-06 20:13:50] [ba905ddf7cdf9ecb063c35348c4dab2e] 
-    D        [Exponential Smoothing] [SHW  WS9] [2009-12-06 10:49:38] [253127ae8da904b75450fbd69fe4eb21] 
-    D          [Exponential Smoothing] [ws9 techniek 4 fo...] [2009-12-11 10:43:22] [95cead3ebb75668735f848316249436a] 

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Dataseries X:

Download CSV

Histogram

Boxplots

1.59
1.26
1.13
1.92
2.61
2.26
2.41
2.26
2.03
2.86
2.55
2.27
2.26
2.57
3.07
2.76
2.51
2.87
3.14
3.11
3.16
2.47
2.57
2.89
2.63
2.38
1.69
1.96
2.19
1.87
1.6
1.63
1.22
1.21
1.49
1.64
1.66
1.77
1.82
1.78
1.28
1.29
1.37
1.12
1.51
2.24
2.94
3.09
3.46
3.64
4.39
4.15
5.21
5.8
5.91
5.39
5.46
4.72
3.14
2.63

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' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63065&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63065&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63065&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' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.888966488320276
beta	0
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.888966488320276 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63065&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]0.888966488320276[/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=63065&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63065&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	0.888966488320276
beta	0
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	2.26	1.93469425938856	0.325305740611437
14	2.57	2.52078854176534	0.0492114582346606
15	3.07	3.03420164067502	0.0357983593249784
16	2.76	2.78222736468926	-0.0222273646892632
17	2.51	2.57835260397630	-0.0683526039763032
18	2.87	2.90961127396768	-0.0396112739676839
19	3.14	3.19612999117814	-0.0561299911781408
20	3.11	2.89790720766739	0.212092792332605
21	3.16	2.66095729753223	0.499042702467769
22	2.47	4.23348483147476	-1.76348483147476
23	2.57	2.40525201288053	0.164747987119474
24	2.89	2.30334674674196	0.586653253258037
25	2.63	2.8464304290902	-0.2164304290902
26	2.38	2.95696193075564	-0.576961930755638
27	1.69	2.89239067395073	-1.20239067395073
28	1.96	1.67412754061246	0.285872459387537
29	2.19	1.81151962604167	0.378480373958327
30	1.87	2.49460661561066	-0.624606615610657
31	1.6	2.17618175811147	-0.576181758111474
32	1.63	1.57479023769102	0.0552097623089802
33	1.22	1.43800469373072	-0.218004693730717
34	1.21	1.58134542110573	-0.371345421105732
35	1.49	1.25591593674353	0.234084063256472
36	1.64	1.36484532354974	0.275154676450262
37	1.66	1.59302168861610	0.0669783113839038
38	1.77	1.82930579339221	-0.0593057933922083
39	1.82	2.01601796141711	-0.196017961417114
40	1.78	1.84932255172931	-0.0693225517293077
41	1.28	1.68923463784740	-0.409234637847403
42	1.29	1.47814694140706	-0.188146941407060
43	1.37	1.48525488635487	-0.115254886354868
44	1.12	1.37408714745063	-0.254087147450625
45	1.51	1.00769512144109	0.502304878558914
46	2.24	1.81153135781857	0.428468642181429
47	2.94	2.26787632094682	0.672123679053183
48	3.09	2.62537908394678	0.464620916053222
49	3.46	2.92176232499024	0.53823767500976
50	3.64	3.67694736369968	-0.0369473636996784
51	4.39	4.03955325347355	0.350446746526447
52	4.15	4.32232514268676	-0.172325142686762
53	5.21	3.75249973923036	1.45750026076964
54	5.8	5.57276717316195	0.227232826838049
55	5.91	6.37556886689363	-0.465568866893626
56	5.39	5.64135319843935	-0.251353198439354
57	5.46	4.86698354118025	0.593016458819752
58	4.72	6.45703392550234	-1.73703392550234
59	3.14	5.03095591214422	-1.89095591214422
60	2.63	3.03471010365082	-0.404710103650824

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 2.26 & 1.93469425938856 & 0.325305740611437 \tabularnewline
14 & 2.57 & 2.52078854176534 & 0.0492114582346606 \tabularnewline
15 & 3.07 & 3.03420164067502 & 0.0357983593249784 \tabularnewline
16 & 2.76 & 2.78222736468926 & -0.0222273646892632 \tabularnewline
17 & 2.51 & 2.57835260397630 & -0.0683526039763032 \tabularnewline
18 & 2.87 & 2.90961127396768 & -0.0396112739676839 \tabularnewline
19 & 3.14 & 3.19612999117814 & -0.0561299911781408 \tabularnewline
20 & 3.11 & 2.89790720766739 & 0.212092792332605 \tabularnewline
21 & 3.16 & 2.66095729753223 & 0.499042702467769 \tabularnewline
22 & 2.47 & 4.23348483147476 & -1.76348483147476 \tabularnewline
23 & 2.57 & 2.40525201288053 & 0.164747987119474 \tabularnewline
24 & 2.89 & 2.30334674674196 & 0.586653253258037 \tabularnewline
25 & 2.63 & 2.8464304290902 & -0.2164304290902 \tabularnewline
26 & 2.38 & 2.95696193075564 & -0.576961930755638 \tabularnewline
27 & 1.69 & 2.89239067395073 & -1.20239067395073 \tabularnewline
28 & 1.96 & 1.67412754061246 & 0.285872459387537 \tabularnewline
29 & 2.19 & 1.81151962604167 & 0.378480373958327 \tabularnewline
30 & 1.87 & 2.49460661561066 & -0.624606615610657 \tabularnewline
31 & 1.6 & 2.17618175811147 & -0.576181758111474 \tabularnewline
32 & 1.63 & 1.57479023769102 & 0.0552097623089802 \tabularnewline
33 & 1.22 & 1.43800469373072 & -0.218004693730717 \tabularnewline
34 & 1.21 & 1.58134542110573 & -0.371345421105732 \tabularnewline
35 & 1.49 & 1.25591593674353 & 0.234084063256472 \tabularnewline
36 & 1.64 & 1.36484532354974 & 0.275154676450262 \tabularnewline
37 & 1.66 & 1.59302168861610 & 0.0669783113839038 \tabularnewline
38 & 1.77 & 1.82930579339221 & -0.0593057933922083 \tabularnewline
39 & 1.82 & 2.01601796141711 & -0.196017961417114 \tabularnewline
40 & 1.78 & 1.84932255172931 & -0.0693225517293077 \tabularnewline
41 & 1.28 & 1.68923463784740 & -0.409234637847403 \tabularnewline
42 & 1.29 & 1.47814694140706 & -0.188146941407060 \tabularnewline
43 & 1.37 & 1.48525488635487 & -0.115254886354868 \tabularnewline
44 & 1.12 & 1.37408714745063 & -0.254087147450625 \tabularnewline
45 & 1.51 & 1.00769512144109 & 0.502304878558914 \tabularnewline
46 & 2.24 & 1.81153135781857 & 0.428468642181429 \tabularnewline
47 & 2.94 & 2.26787632094682 & 0.672123679053183 \tabularnewline
48 & 3.09 & 2.62537908394678 & 0.464620916053222 \tabularnewline
49 & 3.46 & 2.92176232499024 & 0.53823767500976 \tabularnewline
50 & 3.64 & 3.67694736369968 & -0.0369473636996784 \tabularnewline
51 & 4.39 & 4.03955325347355 & 0.350446746526447 \tabularnewline
52 & 4.15 & 4.32232514268676 & -0.172325142686762 \tabularnewline
53 & 5.21 & 3.75249973923036 & 1.45750026076964 \tabularnewline
54 & 5.8 & 5.57276717316195 & 0.227232826838049 \tabularnewline
55 & 5.91 & 6.37556886689363 & -0.465568866893626 \tabularnewline
56 & 5.39 & 5.64135319843935 & -0.251353198439354 \tabularnewline
57 & 5.46 & 4.86698354118025 & 0.593016458819752 \tabularnewline
58 & 4.72 & 6.45703392550234 & -1.73703392550234 \tabularnewline
59 & 3.14 & 5.03095591214422 & -1.89095591214422 \tabularnewline
60 & 2.63 & 3.03471010365082 & -0.404710103650824 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63065&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]2.26[/C][C]1.93469425938856[/C][C]0.325305740611437[/C][/ROW]
[ROW][C]14[/C][C]2.57[/C][C]2.52078854176534[/C][C]0.0492114582346606[/C][/ROW]
[ROW][C]15[/C][C]3.07[/C][C]3.03420164067502[/C][C]0.0357983593249784[/C][/ROW]
[ROW][C]16[/C][C]2.76[/C][C]2.78222736468926[/C][C]-0.0222273646892632[/C][/ROW]
[ROW][C]17[/C][C]2.51[/C][C]2.57835260397630[/C][C]-0.0683526039763032[/C][/ROW]
[ROW][C]18[/C][C]2.87[/C][C]2.90961127396768[/C][C]-0.0396112739676839[/C][/ROW]
[ROW][C]19[/C][C]3.14[/C][C]3.19612999117814[/C][C]-0.0561299911781408[/C][/ROW]
[ROW][C]20[/C][C]3.11[/C][C]2.89790720766739[/C][C]0.212092792332605[/C][/ROW]
[ROW][C]21[/C][C]3.16[/C][C]2.66095729753223[/C][C]0.499042702467769[/C][/ROW]
[ROW][C]22[/C][C]2.47[/C][C]4.23348483147476[/C][C]-1.76348483147476[/C][/ROW]
[ROW][C]23[/C][C]2.57[/C][C]2.40525201288053[/C][C]0.164747987119474[/C][/ROW]
[ROW][C]24[/C][C]2.89[/C][C]2.30334674674196[/C][C]0.586653253258037[/C][/ROW]
[ROW][C]25[/C][C]2.63[/C][C]2.8464304290902[/C][C]-0.2164304290902[/C][/ROW]
[ROW][C]26[/C][C]2.38[/C][C]2.95696193075564[/C][C]-0.576961930755638[/C][/ROW]
[ROW][C]27[/C][C]1.69[/C][C]2.89239067395073[/C][C]-1.20239067395073[/C][/ROW]
[ROW][C]28[/C][C]1.96[/C][C]1.67412754061246[/C][C]0.285872459387537[/C][/ROW]
[ROW][C]29[/C][C]2.19[/C][C]1.81151962604167[/C][C]0.378480373958327[/C][/ROW]
[ROW][C]30[/C][C]1.87[/C][C]2.49460661561066[/C][C]-0.624606615610657[/C][/ROW]
[ROW][C]31[/C][C]1.6[/C][C]2.17618175811147[/C][C]-0.576181758111474[/C][/ROW]
[ROW][C]32[/C][C]1.63[/C][C]1.57479023769102[/C][C]0.0552097623089802[/C][/ROW]
[ROW][C]33[/C][C]1.22[/C][C]1.43800469373072[/C][C]-0.218004693730717[/C][/ROW]
[ROW][C]34[/C][C]1.21[/C][C]1.58134542110573[/C][C]-0.371345421105732[/C][/ROW]
[ROW][C]35[/C][C]1.49[/C][C]1.25591593674353[/C][C]0.234084063256472[/C][/ROW]
[ROW][C]36[/C][C]1.64[/C][C]1.36484532354974[/C][C]0.275154676450262[/C][/ROW]
[ROW][C]37[/C][C]1.66[/C][C]1.59302168861610[/C][C]0.0669783113839038[/C][/ROW]
[ROW][C]38[/C][C]1.77[/C][C]1.82930579339221[/C][C]-0.0593057933922083[/C][/ROW]
[ROW][C]39[/C][C]1.82[/C][C]2.01601796141711[/C][C]-0.196017961417114[/C][/ROW]
[ROW][C]40[/C][C]1.78[/C][C]1.84932255172931[/C][C]-0.0693225517293077[/C][/ROW]
[ROW][C]41[/C][C]1.28[/C][C]1.68923463784740[/C][C]-0.409234637847403[/C][/ROW]
[ROW][C]42[/C][C]1.29[/C][C]1.47814694140706[/C][C]-0.188146941407060[/C][/ROW]
[ROW][C]43[/C][C]1.37[/C][C]1.48525488635487[/C][C]-0.115254886354868[/C][/ROW]
[ROW][C]44[/C][C]1.12[/C][C]1.37408714745063[/C][C]-0.254087147450625[/C][/ROW]
[ROW][C]45[/C][C]1.51[/C][C]1.00769512144109[/C][C]0.502304878558914[/C][/ROW]
[ROW][C]46[/C][C]2.24[/C][C]1.81153135781857[/C][C]0.428468642181429[/C][/ROW]
[ROW][C]47[/C][C]2.94[/C][C]2.26787632094682[/C][C]0.672123679053183[/C][/ROW]
[ROW][C]48[/C][C]3.09[/C][C]2.62537908394678[/C][C]0.464620916053222[/C][/ROW]
[ROW][C]49[/C][C]3.46[/C][C]2.92176232499024[/C][C]0.53823767500976[/C][/ROW]
[ROW][C]50[/C][C]3.64[/C][C]3.67694736369968[/C][C]-0.0369473636996784[/C][/ROW]
[ROW][C]51[/C][C]4.39[/C][C]4.03955325347355[/C][C]0.350446746526447[/C][/ROW]
[ROW][C]52[/C][C]4.15[/C][C]4.32232514268676[/C][C]-0.172325142686762[/C][/ROW]
[ROW][C]53[/C][C]5.21[/C][C]3.75249973923036[/C][C]1.45750026076964[/C][/ROW]
[ROW][C]54[/C][C]5.8[/C][C]5.57276717316195[/C][C]0.227232826838049[/C][/ROW]
[ROW][C]55[/C][C]5.91[/C][C]6.37556886689363[/C][C]-0.465568866893626[/C][/ROW]
[ROW][C]56[/C][C]5.39[/C][C]5.64135319843935[/C][C]-0.251353198439354[/C][/ROW]
[ROW][C]57[/C][C]5.46[/C][C]4.86698354118025[/C][C]0.593016458819752[/C][/ROW]
[ROW][C]58[/C][C]4.72[/C][C]6.45703392550234[/C][C]-1.73703392550234[/C][/ROW]
[ROW][C]59[/C][C]3.14[/C][C]5.03095591214422[/C][C]-1.89095591214422[/C][/ROW]
[ROW][C]60[/C][C]2.63[/C][C]3.03471010365082[/C][C]-0.404710103650824[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63065&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63065&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	2.26	1.93469425938856	0.325305740611437
14	2.57	2.52078854176534	0.0492114582346606
15	3.07	3.03420164067502	0.0357983593249784
16	2.76	2.78222736468926	-0.0222273646892632
17	2.51	2.57835260397630	-0.0683526039763032
18	2.87	2.90961127396768	-0.0396112739676839
19	3.14	3.19612999117814	-0.0561299911781408
20	3.11	2.89790720766739	0.212092792332605
21	3.16	2.66095729753223	0.499042702467769
22	2.47	4.23348483147476	-1.76348483147476
23	2.57	2.40525201288053	0.164747987119474
24	2.89	2.30334674674196	0.586653253258037
25	2.63	2.8464304290902	-0.2164304290902
26	2.38	2.95696193075564	-0.576961930755638
27	1.69	2.89239067395073	-1.20239067395073
28	1.96	1.67412754061246	0.285872459387537
29	2.19	1.81151962604167	0.378480373958327
30	1.87	2.49460661561066	-0.624606615610657
31	1.6	2.17618175811147	-0.576181758111474
32	1.63	1.57479023769102	0.0552097623089802
33	1.22	1.43800469373072	-0.218004693730717
34	1.21	1.58134542110573	-0.371345421105732
35	1.49	1.25591593674353	0.234084063256472
36	1.64	1.36484532354974	0.275154676450262
37	1.66	1.59302168861610	0.0669783113839038
38	1.77	1.82930579339221	-0.0593057933922083
39	1.82	2.01601796141711	-0.196017961417114
40	1.78	1.84932255172931	-0.0693225517293077
41	1.28	1.68923463784740	-0.409234637847403
42	1.29	1.47814694140706	-0.188146941407060
43	1.37	1.48525488635487	-0.115254886354868
44	1.12	1.37408714745063	-0.254087147450625
45	1.51	1.00769512144109	0.502304878558914
46	2.24	1.81153135781857	0.428468642181429
47	2.94	2.26787632094682	0.672123679053183
48	3.09	2.62537908394678	0.464620916053222
49	3.46	2.92176232499024	0.53823767500976
50	3.64	3.67694736369968	-0.0369473636996784
51	4.39	4.03955325347355	0.350446746526447
52	4.15	4.32232514268676	-0.172325142686762
53	5.21	3.75249973923036	1.45750026076964
54	5.8	5.57276717316195	0.227232826838049
55	5.91	6.37556886689363	-0.465568866893626
56	5.39	5.64135319843935	-0.251353198439354
57	5.46	4.86698354118025	0.593016458819752
58	4.72	6.45703392550234	-1.73703392550234
59	3.14	5.03095591214422	-1.89095591214422
60	2.63	3.03471010365082	-0.404710103650824

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	2.58062800055381	1.36225236851070	3.79900363259691
62	2.75295883243842	1.08922390814993	4.41669375672691
63	3.09686438962256	0.981270518214004	5.21245826103111
64	3.05196134635758	0.732711312332134	5.37121138038303
65	2.86201824786779	0.4581515401765	5.26588495555908
66	3.09988366620187	0.330621930310382	5.86914540209336
67	3.40606501472994	0.235105566147667	6.57702446331222
68	3.25853623848574	0.0813760710131928	6.43569640595828
69	2.99856143897777	-0.0816123929101518	6.07873527086569
70	3.43295465304555	-0.187862690392194	7.0537719964833
71	3.44533392960542	-0.289989914068904	7.18065777327974
72	3.26869252487611	-17.1231856882811	23.6605707380333

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 2.58062800055381 & 1.36225236851070 & 3.79900363259691 \tabularnewline
62 & 2.75295883243842 & 1.08922390814993 & 4.41669375672691 \tabularnewline
63 & 3.09686438962256 & 0.981270518214004 & 5.21245826103111 \tabularnewline
64 & 3.05196134635758 & 0.732711312332134 & 5.37121138038303 \tabularnewline
65 & 2.86201824786779 & 0.4581515401765 & 5.26588495555908 \tabularnewline
66 & 3.09988366620187 & 0.330621930310382 & 5.86914540209336 \tabularnewline
67 & 3.40606501472994 & 0.235105566147667 & 6.57702446331222 \tabularnewline
68 & 3.25853623848574 & 0.0813760710131928 & 6.43569640595828 \tabularnewline
69 & 2.99856143897777 & -0.0816123929101518 & 6.07873527086569 \tabularnewline
70 & 3.43295465304555 & -0.187862690392194 & 7.0537719964833 \tabularnewline
71 & 3.44533392960542 & -0.289989914068904 & 7.18065777327974 \tabularnewline
72 & 3.26869252487611 & -17.1231856882811 & 23.6605707380333 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63065&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]61[/C][C]2.58062800055381[/C][C]1.36225236851070[/C][C]3.79900363259691[/C][/ROW]
[ROW][C]62[/C][C]2.75295883243842[/C][C]1.08922390814993[/C][C]4.41669375672691[/C][/ROW]
[ROW][C]63[/C][C]3.09686438962256[/C][C]0.981270518214004[/C][C]5.21245826103111[/C][/ROW]
[ROW][C]64[/C][C]3.05196134635758[/C][C]0.732711312332134[/C][C]5.37121138038303[/C][/ROW]
[ROW][C]65[/C][C]2.86201824786779[/C][C]0.4581515401765[/C][C]5.26588495555908[/C][/ROW]
[ROW][C]66[/C][C]3.09988366620187[/C][C]0.330621930310382[/C][C]5.86914540209336[/C][/ROW]
[ROW][C]67[/C][C]3.40606501472994[/C][C]0.235105566147667[/C][C]6.57702446331222[/C][/ROW]
[ROW][C]68[/C][C]3.25853623848574[/C][C]0.0813760710131928[/C][C]6.43569640595828[/C][/ROW]
[ROW][C]69[/C][C]2.99856143897777[/C][C]-0.0816123929101518[/C][C]6.07873527086569[/C][/ROW]
[ROW][C]70[/C][C]3.43295465304555[/C][C]-0.187862690392194[/C][C]7.0537719964833[/C][/ROW]
[ROW][C]71[/C][C]3.44533392960542[/C][C]-0.289989914068904[/C][C]7.18065777327974[/C][/ROW]
[ROW][C]72[/C][C]3.26869252487611[/C][C]-17.1231856882811[/C][C]23.6605707380333[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63065&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63065&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
61	2.58062800055381	1.36225236851070	3.79900363259691
62	2.75295883243842	1.08922390814993	4.41669375672691
63	3.09686438962256	0.981270518214004	5.21245826103111
64	3.05196134635758	0.732711312332134	5.37121138038303
65	2.86201824786779	0.4581515401765	5.26588495555908
66	3.09988366620187	0.330621930310382	5.86914540209336
67	3.40606501472994	0.235105566147667	6.57702446331222
68	3.25853623848574	0.0813760710131928	6.43569640595828
69	2.99856143897777	-0.0816123929101518	6.07873527086569
70	3.43295465304555	-0.187862690392194	7.0537719964833
71	3.44533392960542	-0.289989914068904	7.18065777327974
72	3.26869252487611	-17.1231856882811	23.6605707380333

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