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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sat, 17 Jan 2009 04:19:26 -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/17/t1232191200inio8cfokuwz9dc.htm/, Retrieved Wed, 11 Feb 2026 14:04:36 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36925, Retrieved Wed, 11 Feb 2026 14:04:36 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

536

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

-     [Harrell-Davis Quantiles] [Harrel davis deci...] [2008-10-18 16:19:32] [ea79f99c5895b39ae8bb6e8c563d0f54]
-   PD  [Harrell-Davis Quantiles] [Harrel davis deci...] [2008-10-18 17:17:36] [ea79f99c5895b39ae8bb6e8c563d0f54]
- RMPD    [(Partial) Autocorrelation Function] [OEF 2 deel 1 De L...] [2008-12-11 08:24:21] [ea79f99c5895b39ae8bb6e8c563d0f54]
- RMP       [Bootstrap Plot - Central Tendency] [Oef 2 opg. 7 De L...] [2008-12-18 22:45:41] [ea79f99c5895b39ae8bb6e8c563d0f54]
- RMP         [Blocked Bootstrap Plot - Central Tendency] [VERbetering Block...] [2009-01-04 16:07:05] [ea79f99c5895b39ae8bb6e8c563d0f54]
- RMP           [Variability] [SDL OPG 8 OEF3 va...] [2009-01-06 10:22:38] [ea79f99c5895b39ae8bb6e8c563d0f54]
- RMP             [Classical Decomposition] [SDL OPG 9 OEF2] [2009-01-15 22:26:39] [74be16979710d4c4e7c6647856088456]
- RMP                 [Exponential Smoothing] [SDL OPG 10 OEF2] [2009-01-17 11:19:26] [d41d8cd98f00b204e9800998ecf8427e] [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	1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36925&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]1 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=36925&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36925&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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.723508762606638
beta	0.0203107142670814
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.723508762606638 \tabularnewline
beta & 0.0203107142670814 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36925&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]0.723508762606638[/C][/ROW]
[ROW][C]beta[/C][C]0.0203107142670814[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36925&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36925&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	0.723508762606638
beta	0.0203107142670814
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	104.7	103.722943376068	0.97705662393156
14	104.7	104.428548810435	0.271451189565269
15	104.7	104.627631499827	0.0723685001728711
16	104.7	104.683739572605	0.0162604273948261
17	106	105.999491909727	0.000508090273399375
18	107	107.003854759285	-0.00385475928538881
19	107	106.817504403349	0.182495596651194
20	107	106.997828598611	0.00217140138936145
21	107	107.04771856719	-0.0477185671899747
22	107	107.060811482958	-0.0608114829575896
23	107	107.063537935929	-0.0635379359288066
24	107	107.042524754270	-0.0425247542695502
25	107	107.285404154889	-0.28540415488915
26	107	106.883122858014	0.116877141985654
27	107	106.913662212221	0.0863377877786746
28	107	106.962906036762	0.0370939632384619
29	107.6	108.288224625069	-0.688224625068827
30	109.9	108.781804505637	1.11819549436304
31	109.9	109.464007561881	0.435992438119499
32	109.9	109.786821995388	0.113178004611939
33	109.9	109.913804426776	-0.0138044267764599
34	109.9	109.958885163251	-0.0588851632507073
35	109.9	109.973350511706	-0.0733505117056694
36	109.9	109.962002637136	-0.0620026371362883
37	109.9	110.134304196766	-0.234304196765507
38	109.9	109.891640937720	0.00835906227978
39	109.9	109.845047492347	0.0549525076534962
40	109.9	109.867331945484	0.0326680545159803
41	110.6	110.998202717189	-0.398202717189406
42	114.3	112.214635790719	2.08536420928051
43	114.3	113.435743711817	0.864256288182531
44	114.3	114.013221751854	0.286778248145623
45	114.3	114.267313323581	0.0326866764189475
46	114.3	114.370866910343	-0.0708669103427582
47	114.3	114.409788304513	-0.109788304513486
48	114.3	114.411803989634	-0.111803989633586
49	114.3	114.536291167243	-0.236291167242825
50	114.3	114.395112588247	-0.0951125882467636
51	114.3	114.320846668430	-0.0208466684299111
52	114.3	114.315321922121	-0.0153219221210890
53	114.3	115.324827945323	-1.02482794532304
54	119.01	116.797856835977	2.21214316402320
55	119.01	117.798207983722	1.21179201627787
56	119.01	118.497713763055	0.512286236944519
57	119.01	118.878272295524	0.131727704475907
58	119.01	119.059870728390	-0.0498707283898057
59	119.01	119.138549612006	-0.1285496120055
60	119.01	119.161486302707	-0.151486302706573
61	119.01	119.257312529746	-0.247312529745741
62	119.01	119.181501744140	-0.171501744139761
63	119.01	119.105686145371	-0.0956861453705216
64	119.01	119.079626829690	-0.0696268296895681
65	121.27	119.802010101425	1.46798989857476
66	123.54	124.041527495403	-0.50152749540328
67	123.54	122.829967282429	0.710032717570996
68	123.54	122.993706718076	0.546293281923582
69	123.54	123.314816403012	0.225183596988316
70	123.54	123.53636180704	0.00363819295989742
71	123.54	123.655328344182	-0.115328344182302
72	123.54	123.705010732215	-0.165010732215478
73	123.54	123.787879850892	-0.247879850892076
74	123.54	123.755934331598	-0.215934331597879
75	123.54	123.691595489414	-0.151595489414461
76	123.54	123.654130633406	-0.114130633405594
77	123.54	124.790638770085	-1.25063877008486
78	125.24	126.499886210527	-1.25988621052662
79	125.24	125.044724550305	0.195275449695103
80	125.24	124.753287671112	0.486712328888103
81	125.24	124.904158057672	0.335841942327889
82	125.24	125.107788560812	0.132211439188438
83	125.24	125.252053323924	-0.0120533239243201
84	125.24	125.329404534210	-0.0894045342098764
85	125.24	125.411859031116	-0.171859031116099
86	125.24	125.412661238266	-0.172661238265917
87	125.24	125.366969222648	-0.126969222647844
88	125.24	125.327591511590	-0.0875915115898067
89	125.24	126.139367507052	-0.899367507052418
90	128.35	128.075668984811	0.274331015188665
91	128.35	128.13087470695	0.219125293050041
92	128.35	127.935631942497	0.414368057502514
93	128.35	127.989741978053	0.360258021946734
94	128.35	128.152390175890	0.197609824109662
95	128.35	128.302698825560	0.0473011744404914
96	128.35	128.401094341689	-0.051094341688696

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 104.7 & 103.722943376068 & 0.97705662393156 \tabularnewline
14 & 104.7 & 104.428548810435 & 0.271451189565269 \tabularnewline
15 & 104.7 & 104.627631499827 & 0.0723685001728711 \tabularnewline
16 & 104.7 & 104.683739572605 & 0.0162604273948261 \tabularnewline
17 & 106 & 105.999491909727 & 0.000508090273399375 \tabularnewline
18 & 107 & 107.003854759285 & -0.00385475928538881 \tabularnewline
19 & 107 & 106.817504403349 & 0.182495596651194 \tabularnewline
20 & 107 & 106.997828598611 & 0.00217140138936145 \tabularnewline
21 & 107 & 107.04771856719 & -0.0477185671899747 \tabularnewline
22 & 107 & 107.060811482958 & -0.0608114829575896 \tabularnewline
23 & 107 & 107.063537935929 & -0.0635379359288066 \tabularnewline
24 & 107 & 107.042524754270 & -0.0425247542695502 \tabularnewline
25 & 107 & 107.285404154889 & -0.28540415488915 \tabularnewline
26 & 107 & 106.883122858014 & 0.116877141985654 \tabularnewline
27 & 107 & 106.913662212221 & 0.0863377877786746 \tabularnewline
28 & 107 & 106.962906036762 & 0.0370939632384619 \tabularnewline
29 & 107.6 & 108.288224625069 & -0.688224625068827 \tabularnewline
30 & 109.9 & 108.781804505637 & 1.11819549436304 \tabularnewline
31 & 109.9 & 109.464007561881 & 0.435992438119499 \tabularnewline
32 & 109.9 & 109.786821995388 & 0.113178004611939 \tabularnewline
33 & 109.9 & 109.913804426776 & -0.0138044267764599 \tabularnewline
34 & 109.9 & 109.958885163251 & -0.0588851632507073 \tabularnewline
35 & 109.9 & 109.973350511706 & -0.0733505117056694 \tabularnewline
36 & 109.9 & 109.962002637136 & -0.0620026371362883 \tabularnewline
37 & 109.9 & 110.134304196766 & -0.234304196765507 \tabularnewline
38 & 109.9 & 109.891640937720 & 0.00835906227978 \tabularnewline
39 & 109.9 & 109.845047492347 & 0.0549525076534962 \tabularnewline
40 & 109.9 & 109.867331945484 & 0.0326680545159803 \tabularnewline
41 & 110.6 & 110.998202717189 & -0.398202717189406 \tabularnewline
42 & 114.3 & 112.214635790719 & 2.08536420928051 \tabularnewline
43 & 114.3 & 113.435743711817 & 0.864256288182531 \tabularnewline
44 & 114.3 & 114.013221751854 & 0.286778248145623 \tabularnewline
45 & 114.3 & 114.267313323581 & 0.0326866764189475 \tabularnewline
46 & 114.3 & 114.370866910343 & -0.0708669103427582 \tabularnewline
47 & 114.3 & 114.409788304513 & -0.109788304513486 \tabularnewline
48 & 114.3 & 114.411803989634 & -0.111803989633586 \tabularnewline
49 & 114.3 & 114.536291167243 & -0.236291167242825 \tabularnewline
50 & 114.3 & 114.395112588247 & -0.0951125882467636 \tabularnewline
51 & 114.3 & 114.320846668430 & -0.0208466684299111 \tabularnewline
52 & 114.3 & 114.315321922121 & -0.0153219221210890 \tabularnewline
53 & 114.3 & 115.324827945323 & -1.02482794532304 \tabularnewline
54 & 119.01 & 116.797856835977 & 2.21214316402320 \tabularnewline
55 & 119.01 & 117.798207983722 & 1.21179201627787 \tabularnewline
56 & 119.01 & 118.497713763055 & 0.512286236944519 \tabularnewline
57 & 119.01 & 118.878272295524 & 0.131727704475907 \tabularnewline
58 & 119.01 & 119.059870728390 & -0.0498707283898057 \tabularnewline
59 & 119.01 & 119.138549612006 & -0.1285496120055 \tabularnewline
60 & 119.01 & 119.161486302707 & -0.151486302706573 \tabularnewline
61 & 119.01 & 119.257312529746 & -0.247312529745741 \tabularnewline
62 & 119.01 & 119.181501744140 & -0.171501744139761 \tabularnewline
63 & 119.01 & 119.105686145371 & -0.0956861453705216 \tabularnewline
64 & 119.01 & 119.079626829690 & -0.0696268296895681 \tabularnewline
65 & 121.27 & 119.802010101425 & 1.46798989857476 \tabularnewline
66 & 123.54 & 124.041527495403 & -0.50152749540328 \tabularnewline
67 & 123.54 & 122.829967282429 & 0.710032717570996 \tabularnewline
68 & 123.54 & 122.993706718076 & 0.546293281923582 \tabularnewline
69 & 123.54 & 123.314816403012 & 0.225183596988316 \tabularnewline
70 & 123.54 & 123.53636180704 & 0.00363819295989742 \tabularnewline
71 & 123.54 & 123.655328344182 & -0.115328344182302 \tabularnewline
72 & 123.54 & 123.705010732215 & -0.165010732215478 \tabularnewline
73 & 123.54 & 123.787879850892 & -0.247879850892076 \tabularnewline
74 & 123.54 & 123.755934331598 & -0.215934331597879 \tabularnewline
75 & 123.54 & 123.691595489414 & -0.151595489414461 \tabularnewline
76 & 123.54 & 123.654130633406 & -0.114130633405594 \tabularnewline
77 & 123.54 & 124.790638770085 & -1.25063877008486 \tabularnewline
78 & 125.24 & 126.499886210527 & -1.25988621052662 \tabularnewline
79 & 125.24 & 125.044724550305 & 0.195275449695103 \tabularnewline
80 & 125.24 & 124.753287671112 & 0.486712328888103 \tabularnewline
81 & 125.24 & 124.904158057672 & 0.335841942327889 \tabularnewline
82 & 125.24 & 125.107788560812 & 0.132211439188438 \tabularnewline
83 & 125.24 & 125.252053323924 & -0.0120533239243201 \tabularnewline
84 & 125.24 & 125.329404534210 & -0.0894045342098764 \tabularnewline
85 & 125.24 & 125.411859031116 & -0.171859031116099 \tabularnewline
86 & 125.24 & 125.412661238266 & -0.172661238265917 \tabularnewline
87 & 125.24 & 125.366969222648 & -0.126969222647844 \tabularnewline
88 & 125.24 & 125.327591511590 & -0.0875915115898067 \tabularnewline
89 & 125.24 & 126.139367507052 & -0.899367507052418 \tabularnewline
90 & 128.35 & 128.075668984811 & 0.274331015188665 \tabularnewline
91 & 128.35 & 128.13087470695 & 0.219125293050041 \tabularnewline
92 & 128.35 & 127.935631942497 & 0.414368057502514 \tabularnewline
93 & 128.35 & 127.989741978053 & 0.360258021946734 \tabularnewline
94 & 128.35 & 128.152390175890 & 0.197609824109662 \tabularnewline
95 & 128.35 & 128.302698825560 & 0.0473011744404914 \tabularnewline
96 & 128.35 & 128.401094341689 & -0.051094341688696 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36925&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]104.7[/C][C]103.722943376068[/C][C]0.97705662393156[/C][/ROW]
[ROW][C]14[/C][C]104.7[/C][C]104.428548810435[/C][C]0.271451189565269[/C][/ROW]
[ROW][C]15[/C][C]104.7[/C][C]104.627631499827[/C][C]0.0723685001728711[/C][/ROW]
[ROW][C]16[/C][C]104.7[/C][C]104.683739572605[/C][C]0.0162604273948261[/C][/ROW]
[ROW][C]17[/C][C]106[/C][C]105.999491909727[/C][C]0.000508090273399375[/C][/ROW]
[ROW][C]18[/C][C]107[/C][C]107.003854759285[/C][C]-0.00385475928538881[/C][/ROW]
[ROW][C]19[/C][C]107[/C][C]106.817504403349[/C][C]0.182495596651194[/C][/ROW]
[ROW][C]20[/C][C]107[/C][C]106.997828598611[/C][C]0.00217140138936145[/C][/ROW]
[ROW][C]21[/C][C]107[/C][C]107.04771856719[/C][C]-0.0477185671899747[/C][/ROW]
[ROW][C]22[/C][C]107[/C][C]107.060811482958[/C][C]-0.0608114829575896[/C][/ROW]
[ROW][C]23[/C][C]107[/C][C]107.063537935929[/C][C]-0.0635379359288066[/C][/ROW]
[ROW][C]24[/C][C]107[/C][C]107.042524754270[/C][C]-0.0425247542695502[/C][/ROW]
[ROW][C]25[/C][C]107[/C][C]107.285404154889[/C][C]-0.28540415488915[/C][/ROW]
[ROW][C]26[/C][C]107[/C][C]106.883122858014[/C][C]0.116877141985654[/C][/ROW]
[ROW][C]27[/C][C]107[/C][C]106.913662212221[/C][C]0.0863377877786746[/C][/ROW]
[ROW][C]28[/C][C]107[/C][C]106.962906036762[/C][C]0.0370939632384619[/C][/ROW]
[ROW][C]29[/C][C]107.6[/C][C]108.288224625069[/C][C]-0.688224625068827[/C][/ROW]
[ROW][C]30[/C][C]109.9[/C][C]108.781804505637[/C][C]1.11819549436304[/C][/ROW]
[ROW][C]31[/C][C]109.9[/C][C]109.464007561881[/C][C]0.435992438119499[/C][/ROW]
[ROW][C]32[/C][C]109.9[/C][C]109.786821995388[/C][C]0.113178004611939[/C][/ROW]
[ROW][C]33[/C][C]109.9[/C][C]109.913804426776[/C][C]-0.0138044267764599[/C][/ROW]
[ROW][C]34[/C][C]109.9[/C][C]109.958885163251[/C][C]-0.0588851632507073[/C][/ROW]
[ROW][C]35[/C][C]109.9[/C][C]109.973350511706[/C][C]-0.0733505117056694[/C][/ROW]
[ROW][C]36[/C][C]109.9[/C][C]109.962002637136[/C][C]-0.0620026371362883[/C][/ROW]
[ROW][C]37[/C][C]109.9[/C][C]110.134304196766[/C][C]-0.234304196765507[/C][/ROW]
[ROW][C]38[/C][C]109.9[/C][C]109.891640937720[/C][C]0.00835906227978[/C][/ROW]
[ROW][C]39[/C][C]109.9[/C][C]109.845047492347[/C][C]0.0549525076534962[/C][/ROW]
[ROW][C]40[/C][C]109.9[/C][C]109.867331945484[/C][C]0.0326680545159803[/C][/ROW]
[ROW][C]41[/C][C]110.6[/C][C]110.998202717189[/C][C]-0.398202717189406[/C][/ROW]
[ROW][C]42[/C][C]114.3[/C][C]112.214635790719[/C][C]2.08536420928051[/C][/ROW]
[ROW][C]43[/C][C]114.3[/C][C]113.435743711817[/C][C]0.864256288182531[/C][/ROW]
[ROW][C]44[/C][C]114.3[/C][C]114.013221751854[/C][C]0.286778248145623[/C][/ROW]
[ROW][C]45[/C][C]114.3[/C][C]114.267313323581[/C][C]0.0326866764189475[/C][/ROW]
[ROW][C]46[/C][C]114.3[/C][C]114.370866910343[/C][C]-0.0708669103427582[/C][/ROW]
[ROW][C]47[/C][C]114.3[/C][C]114.409788304513[/C][C]-0.109788304513486[/C][/ROW]
[ROW][C]48[/C][C]114.3[/C][C]114.411803989634[/C][C]-0.111803989633586[/C][/ROW]
[ROW][C]49[/C][C]114.3[/C][C]114.536291167243[/C][C]-0.236291167242825[/C][/ROW]
[ROW][C]50[/C][C]114.3[/C][C]114.395112588247[/C][C]-0.0951125882467636[/C][/ROW]
[ROW][C]51[/C][C]114.3[/C][C]114.320846668430[/C][C]-0.0208466684299111[/C][/ROW]
[ROW][C]52[/C][C]114.3[/C][C]114.315321922121[/C][C]-0.0153219221210890[/C][/ROW]
[ROW][C]53[/C][C]114.3[/C][C]115.324827945323[/C][C]-1.02482794532304[/C][/ROW]
[ROW][C]54[/C][C]119.01[/C][C]116.797856835977[/C][C]2.21214316402320[/C][/ROW]
[ROW][C]55[/C][C]119.01[/C][C]117.798207983722[/C][C]1.21179201627787[/C][/ROW]
[ROW][C]56[/C][C]119.01[/C][C]118.497713763055[/C][C]0.512286236944519[/C][/ROW]
[ROW][C]57[/C][C]119.01[/C][C]118.878272295524[/C][C]0.131727704475907[/C][/ROW]
[ROW][C]58[/C][C]119.01[/C][C]119.059870728390[/C][C]-0.0498707283898057[/C][/ROW]
[ROW][C]59[/C][C]119.01[/C][C]119.138549612006[/C][C]-0.1285496120055[/C][/ROW]
[ROW][C]60[/C][C]119.01[/C][C]119.161486302707[/C][C]-0.151486302706573[/C][/ROW]
[ROW][C]61[/C][C]119.01[/C][C]119.257312529746[/C][C]-0.247312529745741[/C][/ROW]
[ROW][C]62[/C][C]119.01[/C][C]119.181501744140[/C][C]-0.171501744139761[/C][/ROW]
[ROW][C]63[/C][C]119.01[/C][C]119.105686145371[/C][C]-0.0956861453705216[/C][/ROW]
[ROW][C]64[/C][C]119.01[/C][C]119.079626829690[/C][C]-0.0696268296895681[/C][/ROW]
[ROW][C]65[/C][C]121.27[/C][C]119.802010101425[/C][C]1.46798989857476[/C][/ROW]
[ROW][C]66[/C][C]123.54[/C][C]124.041527495403[/C][C]-0.50152749540328[/C][/ROW]
[ROW][C]67[/C][C]123.54[/C][C]122.829967282429[/C][C]0.710032717570996[/C][/ROW]
[ROW][C]68[/C][C]123.54[/C][C]122.993706718076[/C][C]0.546293281923582[/C][/ROW]
[ROW][C]69[/C][C]123.54[/C][C]123.314816403012[/C][C]0.225183596988316[/C][/ROW]
[ROW][C]70[/C][C]123.54[/C][C]123.53636180704[/C][C]0.00363819295989742[/C][/ROW]
[ROW][C]71[/C][C]123.54[/C][C]123.655328344182[/C][C]-0.115328344182302[/C][/ROW]
[ROW][C]72[/C][C]123.54[/C][C]123.705010732215[/C][C]-0.165010732215478[/C][/ROW]
[ROW][C]73[/C][C]123.54[/C][C]123.787879850892[/C][C]-0.247879850892076[/C][/ROW]
[ROW][C]74[/C][C]123.54[/C][C]123.755934331598[/C][C]-0.215934331597879[/C][/ROW]
[ROW][C]75[/C][C]123.54[/C][C]123.691595489414[/C][C]-0.151595489414461[/C][/ROW]
[ROW][C]76[/C][C]123.54[/C][C]123.654130633406[/C][C]-0.114130633405594[/C][/ROW]
[ROW][C]77[/C][C]123.54[/C][C]124.790638770085[/C][C]-1.25063877008486[/C][/ROW]
[ROW][C]78[/C][C]125.24[/C][C]126.499886210527[/C][C]-1.25988621052662[/C][/ROW]
[ROW][C]79[/C][C]125.24[/C][C]125.044724550305[/C][C]0.195275449695103[/C][/ROW]
[ROW][C]80[/C][C]125.24[/C][C]124.753287671112[/C][C]0.486712328888103[/C][/ROW]
[ROW][C]81[/C][C]125.24[/C][C]124.904158057672[/C][C]0.335841942327889[/C][/ROW]
[ROW][C]82[/C][C]125.24[/C][C]125.107788560812[/C][C]0.132211439188438[/C][/ROW]
[ROW][C]83[/C][C]125.24[/C][C]125.252053323924[/C][C]-0.0120533239243201[/C][/ROW]
[ROW][C]84[/C][C]125.24[/C][C]125.329404534210[/C][C]-0.0894045342098764[/C][/ROW]
[ROW][C]85[/C][C]125.24[/C][C]125.411859031116[/C][C]-0.171859031116099[/C][/ROW]
[ROW][C]86[/C][C]125.24[/C][C]125.412661238266[/C][C]-0.172661238265917[/C][/ROW]
[ROW][C]87[/C][C]125.24[/C][C]125.366969222648[/C][C]-0.126969222647844[/C][/ROW]
[ROW][C]88[/C][C]125.24[/C][C]125.327591511590[/C][C]-0.0875915115898067[/C][/ROW]
[ROW][C]89[/C][C]125.24[/C][C]126.139367507052[/C][C]-0.899367507052418[/C][/ROW]
[ROW][C]90[/C][C]128.35[/C][C]128.075668984811[/C][C]0.274331015188665[/C][/ROW]
[ROW][C]91[/C][C]128.35[/C][C]128.13087470695[/C][C]0.219125293050041[/C][/ROW]
[ROW][C]92[/C][C]128.35[/C][C]127.935631942497[/C][C]0.414368057502514[/C][/ROW]
[ROW][C]93[/C][C]128.35[/C][C]127.989741978053[/C][C]0.360258021946734[/C][/ROW]
[ROW][C]94[/C][C]128.35[/C][C]128.152390175890[/C][C]0.197609824109662[/C][/ROW]
[ROW][C]95[/C][C]128.35[/C][C]128.302698825560[/C][C]0.0473011744404914[/C][/ROW]
[ROW][C]96[/C][C]128.35[/C][C]128.401094341689[/C][C]-0.051094341688696[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36925&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36925&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	104.7	103.722943376068	0.97705662393156
14	104.7	104.428548810435	0.271451189565269
15	104.7	104.627631499827	0.0723685001728711
16	104.7	104.683739572605	0.0162604273948261
17	106	105.999491909727	0.000508090273399375
18	107	107.003854759285	-0.00385475928538881
19	107	106.817504403349	0.182495596651194
20	107	106.997828598611	0.00217140138936145
21	107	107.04771856719	-0.0477185671899747
22	107	107.060811482958	-0.0608114829575896
23	107	107.063537935929	-0.0635379359288066
24	107	107.042524754270	-0.0425247542695502
25	107	107.285404154889	-0.28540415488915
26	107	106.883122858014	0.116877141985654
27	107	106.913662212221	0.0863377877786746
28	107	106.962906036762	0.0370939632384619
29	107.6	108.288224625069	-0.688224625068827
30	109.9	108.781804505637	1.11819549436304
31	109.9	109.464007561881	0.435992438119499
32	109.9	109.786821995388	0.113178004611939
33	109.9	109.913804426776	-0.0138044267764599
34	109.9	109.958885163251	-0.0588851632507073
35	109.9	109.973350511706	-0.0733505117056694
36	109.9	109.962002637136	-0.0620026371362883
37	109.9	110.134304196766	-0.234304196765507
38	109.9	109.891640937720	0.00835906227978
39	109.9	109.845047492347	0.0549525076534962
40	109.9	109.867331945484	0.0326680545159803
41	110.6	110.998202717189	-0.398202717189406
42	114.3	112.214635790719	2.08536420928051
43	114.3	113.435743711817	0.864256288182531
44	114.3	114.013221751854	0.286778248145623
45	114.3	114.267313323581	0.0326866764189475
46	114.3	114.370866910343	-0.0708669103427582
47	114.3	114.409788304513	-0.109788304513486
48	114.3	114.411803989634	-0.111803989633586
49	114.3	114.536291167243	-0.236291167242825
50	114.3	114.395112588247	-0.0951125882467636
51	114.3	114.320846668430	-0.0208466684299111
52	114.3	114.315321922121	-0.0153219221210890
53	114.3	115.324827945323	-1.02482794532304
54	119.01	116.797856835977	2.21214316402320
55	119.01	117.798207983722	1.21179201627787
56	119.01	118.497713763055	0.512286236944519
57	119.01	118.878272295524	0.131727704475907
58	119.01	119.059870728390	-0.0498707283898057
59	119.01	119.138549612006	-0.1285496120055
60	119.01	119.161486302707	-0.151486302706573
61	119.01	119.257312529746	-0.247312529745741
62	119.01	119.181501744140	-0.171501744139761
63	119.01	119.105686145371	-0.0956861453705216
64	119.01	119.079626829690	-0.0696268296895681
65	121.27	119.802010101425	1.46798989857476
66	123.54	124.041527495403	-0.50152749540328
67	123.54	122.829967282429	0.710032717570996
68	123.54	122.993706718076	0.546293281923582
69	123.54	123.314816403012	0.225183596988316
70	123.54	123.53636180704	0.00363819295989742
71	123.54	123.655328344182	-0.115328344182302
72	123.54	123.705010732215	-0.165010732215478
73	123.54	123.787879850892	-0.247879850892076
74	123.54	123.755934331598	-0.215934331597879
75	123.54	123.691595489414	-0.151595489414461
76	123.54	123.654130633406	-0.114130633405594
77	123.54	124.790638770085	-1.25063877008486
78	125.24	126.499886210527	-1.25988621052662
79	125.24	125.044724550305	0.195275449695103
80	125.24	124.753287671112	0.486712328888103
81	125.24	124.904158057672	0.335841942327889
82	125.24	125.107788560812	0.132211439188438
83	125.24	125.252053323924	-0.0120533239243201
84	125.24	125.329404534210	-0.0894045342098764
85	125.24	125.411859031116	-0.171859031116099
86	125.24	125.412661238266	-0.172661238265917
87	125.24	125.366969222648	-0.126969222647844
88	125.24	125.327591511590	-0.0875915115898067
89	125.24	126.139367507052	-0.899367507052418
90	128.35	128.075668984811	0.274331015188665
91	128.35	128.13087470695	0.219125293050041
92	128.35	127.935631942497	0.414368057502514
93	128.35	127.989741978053	0.360258021946734
94	128.35	128.152390175890	0.197609824109662
95	128.35	128.302698825560	0.0473011744404914
96	128.35	128.401094341689	-0.051094341688696

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
97	128.488519358228	127.426637182674	129.550401533783
98	128.616017447583	127.296142427470	129.935892467696
99	128.712994216657	127.169863016180	130.256125417134
100	128.783346676884	127.038172689875	130.528520663893
101	129.442313338590	127.509519482916	131.375107194264
102	132.375315022099	130.265357576236	134.485272467961
103	132.234227240608	129.955015920861	134.513438560354
104	131.948659566457	129.506359312734	134.390959820179
105	131.696151846962	129.095673759795	134.296629934129
106	131.556027539489	128.801348159190	134.310706919788
107	131.521748984784	128.616127856828	134.427370112740
108	131.557965358399	128.504098919694	134.611831797103

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 128.488519358228 & 127.426637182674 & 129.550401533783 \tabularnewline
98 & 128.616017447583 & 127.296142427470 & 129.935892467696 \tabularnewline
99 & 128.712994216657 & 127.169863016180 & 130.256125417134 \tabularnewline
100 & 128.783346676884 & 127.038172689875 & 130.528520663893 \tabularnewline
101 & 129.442313338590 & 127.509519482916 & 131.375107194264 \tabularnewline
102 & 132.375315022099 & 130.265357576236 & 134.485272467961 \tabularnewline
103 & 132.234227240608 & 129.955015920861 & 134.513438560354 \tabularnewline
104 & 131.948659566457 & 129.506359312734 & 134.390959820179 \tabularnewline
105 & 131.696151846962 & 129.095673759795 & 134.296629934129 \tabularnewline
106 & 131.556027539489 & 128.801348159190 & 134.310706919788 \tabularnewline
107 & 131.521748984784 & 128.616127856828 & 134.427370112740 \tabularnewline
108 & 131.557965358399 & 128.504098919694 & 134.611831797103 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36925&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]128.488519358228[/C][C]127.426637182674[/C][C]129.550401533783[/C][/ROW]
[ROW][C]98[/C][C]128.616017447583[/C][C]127.296142427470[/C][C]129.935892467696[/C][/ROW]
[ROW][C]99[/C][C]128.712994216657[/C][C]127.169863016180[/C][C]130.256125417134[/C][/ROW]
[ROW][C]100[/C][C]128.783346676884[/C][C]127.038172689875[/C][C]130.528520663893[/C][/ROW]
[ROW][C]101[/C][C]129.442313338590[/C][C]127.509519482916[/C][C]131.375107194264[/C][/ROW]
[ROW][C]102[/C][C]132.375315022099[/C][C]130.265357576236[/C][C]134.485272467961[/C][/ROW]
[ROW][C]103[/C][C]132.234227240608[/C][C]129.955015920861[/C][C]134.513438560354[/C][/ROW]
[ROW][C]104[/C][C]131.948659566457[/C][C]129.506359312734[/C][C]134.390959820179[/C][/ROW]
[ROW][C]105[/C][C]131.696151846962[/C][C]129.095673759795[/C][C]134.296629934129[/C][/ROW]
[ROW][C]106[/C][C]131.556027539489[/C][C]128.801348159190[/C][C]134.310706919788[/C][/ROW]
[ROW][C]107[/C][C]131.521748984784[/C][C]128.616127856828[/C][C]134.427370112740[/C][/ROW]
[ROW][C]108[/C][C]131.557965358399[/C][C]128.504098919694[/C][C]134.611831797103[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36925&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36925&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	128.488519358228	127.426637182674	129.550401533783
98	128.616017447583	127.296142427470	129.935892467696
99	128.712994216657	127.169863016180	130.256125417134
100	128.783346676884	127.038172689875	130.528520663893
101	129.442313338590	127.509519482916	131.375107194264
102	132.375315022099	130.265357576236	134.485272467961
103	132.234227240608	129.955015920861	134.513438560354
104	131.948659566457	129.506359312734	134.390959820179
105	131.696151846962	129.095673759795	134.296629934129
106	131.556027539489	128.801348159190	134.310706919788
107	131.521748984784	128.616127856828	134.427370112740
108	131.557965358399	128.504098919694	134.611831797103

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 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = additive ;

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

par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=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