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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Wed, 21 May 2008 10:32:24 -0600

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/2008/May/21/t1211387645f1vbuubv2a7vgk2.htm/, Retrieved Wed, 15 May 2024 23:31:02 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=12997, Retrieved Wed, 15 May 2024 23:31:02 +0000

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Original text written by user:

Gem prijzen kattenvoeding Veronique Van Hoof 2MAR02

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

205

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

-       [Exponential Smoothing] [Exponential Smoot...] [2008-05-21 16:32:24] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Dataseries X:

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Boxplots

1,74
1,73
1,74
1,73
1,74
1,73
1,73
1,74
1,75
1,73
1,74
1,74
1,74
1,74
1,76
1,76
1,78
1,77
1,78
1,79
1,83
1,82
1,84
1,83
1,83
1,84
1,83
1,83
1,83
1,83
1,83
1,84
1,83
1,84
1,84
1,83
1,84
1,85
1,85
1,85
1,85
1,84
1,84
1,85
1,84
1,84
1,84
1,84
1,85
1,84
1,85
1,84
1,84
1,84
1,84
1,84
1,83
1,83
1,82
1,83
1,83
1,83
1,87
1,87
1,86
1,87
1,87
1,89
1,89
1,88
1,88
1,87

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 4 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12997&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12997&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12997&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	4 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.693896710109591
beta	0.271603477614666
gamma	0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.693896710109591 \tabularnewline
beta & 0.271603477614666 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12997&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]0.693896710109591[/C][/ROW]
[ROW][C]beta[/C][C]0.271603477614666[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12997&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12997&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	0.693896710109591
beta	0.271603477614666
gamma	0

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	1.74	1.72	0.02
4	1.73	1.72764722939361	0.0023527706063855
5	1.74	1.72349251871511	0.0165074812848909
6	1.73	1.73227079370045	-0.0022707937004538
7	1.73	1.72759092086314	0.00240907913685695
8	1.74	1.72661242291169	0.0133875770883110
9	1.75	1.73577495506788	0.0142250449321175
10	1.73	1.74819952307874	-0.0181995230787360
11	1.74	1.73469482127879	0.00530517872120995
12	1.74	1.73849979396211	0.00150020603789147
13	1.74	1.73994724458865	5.27554113460837e-05
14	1.74	1.74040025652331	-0.000400256523308773
15	1.76	1.74046349071743	0.0195365092825661
16	1.76	1.75804272463928	0.00195727536072088
17	1.78	1.76379266340678	0.0162073365932180
18	1.77	1.78248518457670	-0.0124851845767042
19	1.78	1.77891504239262	0.00108495760738236
20	1.79	1.78496565350041	0.00503434649959145
21	1.83	1.79470552947009	0.0352944705299103
22	1.82	1.83209456985453	-0.0120945698545276
23	1.84	1.83432111082120	0.00567888917879644
24	1.83	1.84995086702208	-0.0199508670220838
25	1.83	1.84403618435771	-0.0140361843577095
26	1.84	1.83958035442521	0.000419645574785132
27	1.83	1.84523446572714	-0.0152344657271390
28	1.83	1.83715508077651	-0.00715508077650862
29	1.83	1.83333347388457	-0.00333347388457295
30	1.83	1.83153542508809	-0.00153542508809079
31	1.83	1.83069566291604	-0.000695662916037731
32	1.84	1.83030750100823	0.00969249899176705
33	1.83	1.83895434496447	-0.00895434496446645
34	1.84	1.83297462677470	0.0070253732253025
35	1.84	1.83940721774109	0.000592782258908242
36	1.83	1.84148797356433	-0.0114879735643276
37	1.84	1.83302085449042	0.00697914550957779
38	1.85	1.83868333156758	0.0113166684324235
39	1.85	1.84948839472618	0.000511605273818549
40	1.85	1.85289227967143	-0.00289227967142947
41	1.85	1.85338912725869	-0.00338912725868989
42	1.84	1.85290248288576	-0.0129024828857593
43	1.84	1.84338288900617	-0.00338288900616757
44	1.85	1.839831354638	0.0101686453619994
45	1.84	1.84759961668816	-0.00759961668815512
46	1.84	1.84160628022538	-0.00160628022537623
47	1.84	1.83946897300022	0.000531026999779804
48	1.84	1.83891481610293	0.00108518389706735
49	1.85	1.83894970577581	0.0110502942241912
50	1.84	1.84798194376471	-0.00798194376470795
51	1.85	1.84230345931456	0.00769654068543923
52	1.84	1.84895475033369	-0.0089547503336862
53	1.84	1.84236411042691	-0.00236411042690521
54	1.84	1.83990114236575	9.88576342497716e-05
55	1.84	1.83916585091961	0.000834149080393587
56	1.84	1.83909798349480	0.000902016505203607
57	1.83	1.83924720737657	-0.00924720737656792
58	1.83	1.83061114548168	-0.000611145481683284
59	1.82	1.82785243913769	-0.00785243913769329
60	1.83	1.81858911489473	0.0114108851052719
61	1.83	1.82484309768759	0.00515690231241028
62	1.83	1.82772935674984	0.00227064325015691
63	1.87	1.82904078637849	0.0409592136215124
64	1.87	1.86491745605406	0.00508254394593965
65	1.86	1.87685730309485	-0.0168573030948458
66	1.87	1.87039615487893	-0.000396154878934629
67	1.87	1.87528268202066	-0.00528268202065929
68	1.89	1.87578286465797	0.0142171353420339
69	1.89	1.89249333540501	-0.00249333540500984
70	1.88	1.89713855961866	-0.0171385596186620
71	1.88	1.88839149641372	-0.00839149641371684
72	1.87	1.88413249023575	-0.0141324902357505

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1.74 & 1.72 & 0.02 \tabularnewline
4 & 1.73 & 1.72764722939361 & 0.0023527706063855 \tabularnewline
5 & 1.74 & 1.72349251871511 & 0.0165074812848909 \tabularnewline
6 & 1.73 & 1.73227079370045 & -0.0022707937004538 \tabularnewline
7 & 1.73 & 1.72759092086314 & 0.00240907913685695 \tabularnewline
8 & 1.74 & 1.72661242291169 & 0.0133875770883110 \tabularnewline
9 & 1.75 & 1.73577495506788 & 0.0142250449321175 \tabularnewline
10 & 1.73 & 1.74819952307874 & -0.0181995230787360 \tabularnewline
11 & 1.74 & 1.73469482127879 & 0.00530517872120995 \tabularnewline
12 & 1.74 & 1.73849979396211 & 0.00150020603789147 \tabularnewline
13 & 1.74 & 1.73994724458865 & 5.27554113460837e-05 \tabularnewline
14 & 1.74 & 1.74040025652331 & -0.000400256523308773 \tabularnewline
15 & 1.76 & 1.74046349071743 & 0.0195365092825661 \tabularnewline
16 & 1.76 & 1.75804272463928 & 0.00195727536072088 \tabularnewline
17 & 1.78 & 1.76379266340678 & 0.0162073365932180 \tabularnewline
18 & 1.77 & 1.78248518457670 & -0.0124851845767042 \tabularnewline
19 & 1.78 & 1.77891504239262 & 0.00108495760738236 \tabularnewline
20 & 1.79 & 1.78496565350041 & 0.00503434649959145 \tabularnewline
21 & 1.83 & 1.79470552947009 & 0.0352944705299103 \tabularnewline
22 & 1.82 & 1.83209456985453 & -0.0120945698545276 \tabularnewline
23 & 1.84 & 1.83432111082120 & 0.00567888917879644 \tabularnewline
24 & 1.83 & 1.84995086702208 & -0.0199508670220838 \tabularnewline
25 & 1.83 & 1.84403618435771 & -0.0140361843577095 \tabularnewline
26 & 1.84 & 1.83958035442521 & 0.000419645574785132 \tabularnewline
27 & 1.83 & 1.84523446572714 & -0.0152344657271390 \tabularnewline
28 & 1.83 & 1.83715508077651 & -0.00715508077650862 \tabularnewline
29 & 1.83 & 1.83333347388457 & -0.00333347388457295 \tabularnewline
30 & 1.83 & 1.83153542508809 & -0.00153542508809079 \tabularnewline
31 & 1.83 & 1.83069566291604 & -0.000695662916037731 \tabularnewline
32 & 1.84 & 1.83030750100823 & 0.00969249899176705 \tabularnewline
33 & 1.83 & 1.83895434496447 & -0.00895434496446645 \tabularnewline
34 & 1.84 & 1.83297462677470 & 0.0070253732253025 \tabularnewline
35 & 1.84 & 1.83940721774109 & 0.000592782258908242 \tabularnewline
36 & 1.83 & 1.84148797356433 & -0.0114879735643276 \tabularnewline
37 & 1.84 & 1.83302085449042 & 0.00697914550957779 \tabularnewline
38 & 1.85 & 1.83868333156758 & 0.0113166684324235 \tabularnewline
39 & 1.85 & 1.84948839472618 & 0.000511605273818549 \tabularnewline
40 & 1.85 & 1.85289227967143 & -0.00289227967142947 \tabularnewline
41 & 1.85 & 1.85338912725869 & -0.00338912725868989 \tabularnewline
42 & 1.84 & 1.85290248288576 & -0.0129024828857593 \tabularnewline
43 & 1.84 & 1.84338288900617 & -0.00338288900616757 \tabularnewline
44 & 1.85 & 1.839831354638 & 0.0101686453619994 \tabularnewline
45 & 1.84 & 1.84759961668816 & -0.00759961668815512 \tabularnewline
46 & 1.84 & 1.84160628022538 & -0.00160628022537623 \tabularnewline
47 & 1.84 & 1.83946897300022 & 0.000531026999779804 \tabularnewline
48 & 1.84 & 1.83891481610293 & 0.00108518389706735 \tabularnewline
49 & 1.85 & 1.83894970577581 & 0.0110502942241912 \tabularnewline
50 & 1.84 & 1.84798194376471 & -0.00798194376470795 \tabularnewline
51 & 1.85 & 1.84230345931456 & 0.00769654068543923 \tabularnewline
52 & 1.84 & 1.84895475033369 & -0.0089547503336862 \tabularnewline
53 & 1.84 & 1.84236411042691 & -0.00236411042690521 \tabularnewline
54 & 1.84 & 1.83990114236575 & 9.88576342497716e-05 \tabularnewline
55 & 1.84 & 1.83916585091961 & 0.000834149080393587 \tabularnewline
56 & 1.84 & 1.83909798349480 & 0.000902016505203607 \tabularnewline
57 & 1.83 & 1.83924720737657 & -0.00924720737656792 \tabularnewline
58 & 1.83 & 1.83061114548168 & -0.000611145481683284 \tabularnewline
59 & 1.82 & 1.82785243913769 & -0.00785243913769329 \tabularnewline
60 & 1.83 & 1.81858911489473 & 0.0114108851052719 \tabularnewline
61 & 1.83 & 1.82484309768759 & 0.00515690231241028 \tabularnewline
62 & 1.83 & 1.82772935674984 & 0.00227064325015691 \tabularnewline
63 & 1.87 & 1.82904078637849 & 0.0409592136215124 \tabularnewline
64 & 1.87 & 1.86491745605406 & 0.00508254394593965 \tabularnewline
65 & 1.86 & 1.87685730309485 & -0.0168573030948458 \tabularnewline
66 & 1.87 & 1.87039615487893 & -0.000396154878934629 \tabularnewline
67 & 1.87 & 1.87528268202066 & -0.00528268202065929 \tabularnewline
68 & 1.89 & 1.87578286465797 & 0.0142171353420339 \tabularnewline
69 & 1.89 & 1.89249333540501 & -0.00249333540500984 \tabularnewline
70 & 1.88 & 1.89713855961866 & -0.0171385596186620 \tabularnewline
71 & 1.88 & 1.88839149641372 & -0.00839149641371684 \tabularnewline
72 & 1.87 & 1.88413249023575 & -0.0141324902357505 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12997&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]3[/C][C]1.74[/C][C]1.72[/C][C]0.02[/C][/ROW]
[ROW][C]4[/C][C]1.73[/C][C]1.72764722939361[/C][C]0.0023527706063855[/C][/ROW]
[ROW][C]5[/C][C]1.74[/C][C]1.72349251871511[/C][C]0.0165074812848909[/C][/ROW]
[ROW][C]6[/C][C]1.73[/C][C]1.73227079370045[/C][C]-0.0022707937004538[/C][/ROW]
[ROW][C]7[/C][C]1.73[/C][C]1.72759092086314[/C][C]0.00240907913685695[/C][/ROW]
[ROW][C]8[/C][C]1.74[/C][C]1.72661242291169[/C][C]0.0133875770883110[/C][/ROW]
[ROW][C]9[/C][C]1.75[/C][C]1.73577495506788[/C][C]0.0142250449321175[/C][/ROW]
[ROW][C]10[/C][C]1.73[/C][C]1.74819952307874[/C][C]-0.0181995230787360[/C][/ROW]
[ROW][C]11[/C][C]1.74[/C][C]1.73469482127879[/C][C]0.00530517872120995[/C][/ROW]
[ROW][C]12[/C][C]1.74[/C][C]1.73849979396211[/C][C]0.00150020603789147[/C][/ROW]
[ROW][C]13[/C][C]1.74[/C][C]1.73994724458865[/C][C]5.27554113460837e-05[/C][/ROW]
[ROW][C]14[/C][C]1.74[/C][C]1.74040025652331[/C][C]-0.000400256523308773[/C][/ROW]
[ROW][C]15[/C][C]1.76[/C][C]1.74046349071743[/C][C]0.0195365092825661[/C][/ROW]
[ROW][C]16[/C][C]1.76[/C][C]1.75804272463928[/C][C]0.00195727536072088[/C][/ROW]
[ROW][C]17[/C][C]1.78[/C][C]1.76379266340678[/C][C]0.0162073365932180[/C][/ROW]
[ROW][C]18[/C][C]1.77[/C][C]1.78248518457670[/C][C]-0.0124851845767042[/C][/ROW]
[ROW][C]19[/C][C]1.78[/C][C]1.77891504239262[/C][C]0.00108495760738236[/C][/ROW]
[ROW][C]20[/C][C]1.79[/C][C]1.78496565350041[/C][C]0.00503434649959145[/C][/ROW]
[ROW][C]21[/C][C]1.83[/C][C]1.79470552947009[/C][C]0.0352944705299103[/C][/ROW]
[ROW][C]22[/C][C]1.82[/C][C]1.83209456985453[/C][C]-0.0120945698545276[/C][/ROW]
[ROW][C]23[/C][C]1.84[/C][C]1.83432111082120[/C][C]0.00567888917879644[/C][/ROW]
[ROW][C]24[/C][C]1.83[/C][C]1.84995086702208[/C][C]-0.0199508670220838[/C][/ROW]
[ROW][C]25[/C][C]1.83[/C][C]1.84403618435771[/C][C]-0.0140361843577095[/C][/ROW]
[ROW][C]26[/C][C]1.84[/C][C]1.83958035442521[/C][C]0.000419645574785132[/C][/ROW]
[ROW][C]27[/C][C]1.83[/C][C]1.84523446572714[/C][C]-0.0152344657271390[/C][/ROW]
[ROW][C]28[/C][C]1.83[/C][C]1.83715508077651[/C][C]-0.00715508077650862[/C][/ROW]
[ROW][C]29[/C][C]1.83[/C][C]1.83333347388457[/C][C]-0.00333347388457295[/C][/ROW]
[ROW][C]30[/C][C]1.83[/C][C]1.83153542508809[/C][C]-0.00153542508809079[/C][/ROW]
[ROW][C]31[/C][C]1.83[/C][C]1.83069566291604[/C][C]-0.000695662916037731[/C][/ROW]
[ROW][C]32[/C][C]1.84[/C][C]1.83030750100823[/C][C]0.00969249899176705[/C][/ROW]
[ROW][C]33[/C][C]1.83[/C][C]1.83895434496447[/C][C]-0.00895434496446645[/C][/ROW]
[ROW][C]34[/C][C]1.84[/C][C]1.83297462677470[/C][C]0.0070253732253025[/C][/ROW]
[ROW][C]35[/C][C]1.84[/C][C]1.83940721774109[/C][C]0.000592782258908242[/C][/ROW]
[ROW][C]36[/C][C]1.83[/C][C]1.84148797356433[/C][C]-0.0114879735643276[/C][/ROW]
[ROW][C]37[/C][C]1.84[/C][C]1.83302085449042[/C][C]0.00697914550957779[/C][/ROW]
[ROW][C]38[/C][C]1.85[/C][C]1.83868333156758[/C][C]0.0113166684324235[/C][/ROW]
[ROW][C]39[/C][C]1.85[/C][C]1.84948839472618[/C][C]0.000511605273818549[/C][/ROW]
[ROW][C]40[/C][C]1.85[/C][C]1.85289227967143[/C][C]-0.00289227967142947[/C][/ROW]
[ROW][C]41[/C][C]1.85[/C][C]1.85338912725869[/C][C]-0.00338912725868989[/C][/ROW]
[ROW][C]42[/C][C]1.84[/C][C]1.85290248288576[/C][C]-0.0129024828857593[/C][/ROW]
[ROW][C]43[/C][C]1.84[/C][C]1.84338288900617[/C][C]-0.00338288900616757[/C][/ROW]
[ROW][C]44[/C][C]1.85[/C][C]1.839831354638[/C][C]0.0101686453619994[/C][/ROW]
[ROW][C]45[/C][C]1.84[/C][C]1.84759961668816[/C][C]-0.00759961668815512[/C][/ROW]
[ROW][C]46[/C][C]1.84[/C][C]1.84160628022538[/C][C]-0.00160628022537623[/C][/ROW]
[ROW][C]47[/C][C]1.84[/C][C]1.83946897300022[/C][C]0.000531026999779804[/C][/ROW]
[ROW][C]48[/C][C]1.84[/C][C]1.83891481610293[/C][C]0.00108518389706735[/C][/ROW]
[ROW][C]49[/C][C]1.85[/C][C]1.83894970577581[/C][C]0.0110502942241912[/C][/ROW]
[ROW][C]50[/C][C]1.84[/C][C]1.84798194376471[/C][C]-0.00798194376470795[/C][/ROW]
[ROW][C]51[/C][C]1.85[/C][C]1.84230345931456[/C][C]0.00769654068543923[/C][/ROW]
[ROW][C]52[/C][C]1.84[/C][C]1.84895475033369[/C][C]-0.0089547503336862[/C][/ROW]
[ROW][C]53[/C][C]1.84[/C][C]1.84236411042691[/C][C]-0.00236411042690521[/C][/ROW]
[ROW][C]54[/C][C]1.84[/C][C]1.83990114236575[/C][C]9.88576342497716e-05[/C][/ROW]
[ROW][C]55[/C][C]1.84[/C][C]1.83916585091961[/C][C]0.000834149080393587[/C][/ROW]
[ROW][C]56[/C][C]1.84[/C][C]1.83909798349480[/C][C]0.000902016505203607[/C][/ROW]
[ROW][C]57[/C][C]1.83[/C][C]1.83924720737657[/C][C]-0.00924720737656792[/C][/ROW]
[ROW][C]58[/C][C]1.83[/C][C]1.83061114548168[/C][C]-0.000611145481683284[/C][/ROW]
[ROW][C]59[/C][C]1.82[/C][C]1.82785243913769[/C][C]-0.00785243913769329[/C][/ROW]
[ROW][C]60[/C][C]1.83[/C][C]1.81858911489473[/C][C]0.0114108851052719[/C][/ROW]
[ROW][C]61[/C][C]1.83[/C][C]1.82484309768759[/C][C]0.00515690231241028[/C][/ROW]
[ROW][C]62[/C][C]1.83[/C][C]1.82772935674984[/C][C]0.00227064325015691[/C][/ROW]
[ROW][C]63[/C][C]1.87[/C][C]1.82904078637849[/C][C]0.0409592136215124[/C][/ROW]
[ROW][C]64[/C][C]1.87[/C][C]1.86491745605406[/C][C]0.00508254394593965[/C][/ROW]
[ROW][C]65[/C][C]1.86[/C][C]1.87685730309485[/C][C]-0.0168573030948458[/C][/ROW]
[ROW][C]66[/C][C]1.87[/C][C]1.87039615487893[/C][C]-0.000396154878934629[/C][/ROW]
[ROW][C]67[/C][C]1.87[/C][C]1.87528268202066[/C][C]-0.00528268202065929[/C][/ROW]
[ROW][C]68[/C][C]1.89[/C][C]1.87578286465797[/C][C]0.0142171353420339[/C][/ROW]
[ROW][C]69[/C][C]1.89[/C][C]1.89249333540501[/C][C]-0.00249333540500984[/C][/ROW]
[ROW][C]70[/C][C]1.88[/C][C]1.89713855961866[/C][C]-0.0171385596186620[/C][/ROW]
[ROW][C]71[/C][C]1.88[/C][C]1.88839149641372[/C][C]-0.00839149641371684[/C][/ROW]
[ROW][C]72[/C][C]1.87[/C][C]1.88413249023575[/C][C]-0.0141324902357505[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12997&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12997&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
3	1.74	1.72	0.02
4	1.73	1.72764722939361	0.0023527706063855
5	1.74	1.72349251871511	0.0165074812848909
6	1.73	1.73227079370045	-0.0022707937004538
7	1.73	1.72759092086314	0.00240907913685695
8	1.74	1.72661242291169	0.0133875770883110
9	1.75	1.73577495506788	0.0142250449321175
10	1.73	1.74819952307874	-0.0181995230787360
11	1.74	1.73469482127879	0.00530517872120995
12	1.74	1.73849979396211	0.00150020603789147
13	1.74	1.73994724458865	5.27554113460837e-05
14	1.74	1.74040025652331	-0.000400256523308773
15	1.76	1.74046349071743	0.0195365092825661
16	1.76	1.75804272463928	0.00195727536072088
17	1.78	1.76379266340678	0.0162073365932180
18	1.77	1.78248518457670	-0.0124851845767042
19	1.78	1.77891504239262	0.00108495760738236
20	1.79	1.78496565350041	0.00503434649959145
21	1.83	1.79470552947009	0.0352944705299103
22	1.82	1.83209456985453	-0.0120945698545276
23	1.84	1.83432111082120	0.00567888917879644
24	1.83	1.84995086702208	-0.0199508670220838
25	1.83	1.84403618435771	-0.0140361843577095
26	1.84	1.83958035442521	0.000419645574785132
27	1.83	1.84523446572714	-0.0152344657271390
28	1.83	1.83715508077651	-0.00715508077650862
29	1.83	1.83333347388457	-0.00333347388457295
30	1.83	1.83153542508809	-0.00153542508809079
31	1.83	1.83069566291604	-0.000695662916037731
32	1.84	1.83030750100823	0.00969249899176705
33	1.83	1.83895434496447	-0.00895434496446645
34	1.84	1.83297462677470	0.0070253732253025
35	1.84	1.83940721774109	0.000592782258908242
36	1.83	1.84148797356433	-0.0114879735643276
37	1.84	1.83302085449042	0.00697914550957779
38	1.85	1.83868333156758	0.0113166684324235
39	1.85	1.84948839472618	0.000511605273818549
40	1.85	1.85289227967143	-0.00289227967142947
41	1.85	1.85338912725869	-0.00338912725868989
42	1.84	1.85290248288576	-0.0129024828857593
43	1.84	1.84338288900617	-0.00338288900616757
44	1.85	1.839831354638	0.0101686453619994
45	1.84	1.84759961668816	-0.00759961668815512
46	1.84	1.84160628022538	-0.00160628022537623
47	1.84	1.83946897300022	0.000531026999779804
48	1.84	1.83891481610293	0.00108518389706735
49	1.85	1.83894970577581	0.0110502942241912
50	1.84	1.84798194376471	-0.00798194376470795
51	1.85	1.84230345931456	0.00769654068543923
52	1.84	1.84895475033369	-0.0089547503336862
53	1.84	1.84236411042691	-0.00236411042690521
54	1.84	1.83990114236575	9.88576342497716e-05
55	1.84	1.83916585091961	0.000834149080393587
56	1.84	1.83909798349480	0.000902016505203607
57	1.83	1.83924720737657	-0.00924720737656792
58	1.83	1.83061114548168	-0.000611145481683284
59	1.82	1.82785243913769	-0.00785243913769329
60	1.83	1.81858911489473	0.0114108851052719
61	1.83	1.82484309768759	0.00515690231241028
62	1.83	1.82772935674984	0.00227064325015691
63	1.87	1.82904078637849	0.0409592136215124
64	1.87	1.86491745605406	0.00508254394593965
65	1.86	1.87685730309485	-0.0168573030948458
66	1.87	1.87039615487893	-0.000396154878934629
67	1.87	1.87528268202066	-0.00528268202065929
68	1.89	1.87578286465797	0.0142171353420339
69	1.89	1.89249333540501	-0.00249333540500984
70	1.88	1.89713855961866	-0.0171385596186620
71	1.88	1.88839149641372	-0.00839149641371684
72	1.87	1.88413249023575	-0.0141324902357505

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	1.87322635095749	1.85100001091685	1.89545269099813
74	1.87212670015948	1.84248504640327	1.90176835391569
75	1.87102704936147	1.83301266106515	1.90904143765778
76	1.86992739856345	1.82272038749492	1.91713440963198
77	1.86882774776544	1.81169679618181	1.92595869934907
78	1.86772809696742	1.80000425785574	1.93545193607911
79	1.86662844616941	1.78768977616825	1.94556711617057
80	1.86552879537140	1.77479057407830	1.95626701666449
81	1.86442914457338	1.76133721767474	1.96752107147202
82	1.86332949377537	1.74735549303263	1.97930349451811
83	1.86222984297735	1.73286760491986	1.99159208103485
84	1.86113019217934	1.71789298257730	2.00436740178139

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 1.87322635095749 & 1.85100001091685 & 1.89545269099813 \tabularnewline
74 & 1.87212670015948 & 1.84248504640327 & 1.90176835391569 \tabularnewline
75 & 1.87102704936147 & 1.83301266106515 & 1.90904143765778 \tabularnewline
76 & 1.86992739856345 & 1.82272038749492 & 1.91713440963198 \tabularnewline
77 & 1.86882774776544 & 1.81169679618181 & 1.92595869934907 \tabularnewline
78 & 1.86772809696742 & 1.80000425785574 & 1.93545193607911 \tabularnewline
79 & 1.86662844616941 & 1.78768977616825 & 1.94556711617057 \tabularnewline
80 & 1.86552879537140 & 1.77479057407830 & 1.95626701666449 \tabularnewline
81 & 1.86442914457338 & 1.76133721767474 & 1.96752107147202 \tabularnewline
82 & 1.86332949377537 & 1.74735549303263 & 1.97930349451811 \tabularnewline
83 & 1.86222984297735 & 1.73286760491986 & 1.99159208103485 \tabularnewline
84 & 1.86113019217934 & 1.71789298257730 & 2.00436740178139 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12997&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]1.87322635095749[/C][C]1.85100001091685[/C][C]1.89545269099813[/C][/ROW]
[ROW][C]74[/C][C]1.87212670015948[/C][C]1.84248504640327[/C][C]1.90176835391569[/C][/ROW]
[ROW][C]75[/C][C]1.87102704936147[/C][C]1.83301266106515[/C][C]1.90904143765778[/C][/ROW]
[ROW][C]76[/C][C]1.86992739856345[/C][C]1.82272038749492[/C][C]1.91713440963198[/C][/ROW]
[ROW][C]77[/C][C]1.86882774776544[/C][C]1.81169679618181[/C][C]1.92595869934907[/C][/ROW]
[ROW][C]78[/C][C]1.86772809696742[/C][C]1.80000425785574[/C][C]1.93545193607911[/C][/ROW]
[ROW][C]79[/C][C]1.86662844616941[/C][C]1.78768977616825[/C][C]1.94556711617057[/C][/ROW]
[ROW][C]80[/C][C]1.86552879537140[/C][C]1.77479057407830[/C][C]1.95626701666449[/C][/ROW]
[ROW][C]81[/C][C]1.86442914457338[/C][C]1.76133721767474[/C][C]1.96752107147202[/C][/ROW]
[ROW][C]82[/C][C]1.86332949377537[/C][C]1.74735549303263[/C][C]1.97930349451811[/C][/ROW]
[ROW][C]83[/C][C]1.86222984297735[/C][C]1.73286760491986[/C][C]1.99159208103485[/C][/ROW]
[ROW][C]84[/C][C]1.86113019217934[/C][C]1.71789298257730[/C][C]2.00436740178139[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12997&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12997&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	1.87322635095749	1.85100001091685	1.89545269099813
74	1.87212670015948	1.84248504640327	1.90176835391569
75	1.87102704936147	1.83301266106515	1.90904143765778
76	1.86992739856345	1.82272038749492	1.91713440963198
77	1.86882774776544	1.81169679618181	1.92595869934907
78	1.86772809696742	1.80000425785574	1.93545193607911
79	1.86662844616941	1.78768977616825	1.94556711617057
80	1.86552879537140	1.77479057407830	1.95626701666449
81	1.86442914457338	1.76133721767474	1.96752107147202
82	1.86332949377537	1.74735549303263	1.97930349451811
83	1.86222984297735	1.73286760491986	1.99159208103485
84	1.86113019217934	1.71789298257730	2.00436740178139

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 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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