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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sun, 01 Jun 2008 15:42:51 -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/Jun/01/t1212356983igag30s9h7a8l2f.htm/, Retrieved Sat, 18 May 2024 14:46:49 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13753, Retrieved Sat, 18 May 2024 14:46:49 +0000

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IsPrivate?

No (this computation is public)

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Estimated Impact

186

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

-       [Exponential Smoothing] [Ruts Wouter: expo...] [2008-06-01 21:42:51] [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	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13753&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13753&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13753&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.740672708482406
beta	0
gamma	0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.740672708482406 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13753&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]0.740672708482406[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13753&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13753&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	0.740672708482406
beta	0
gamma	0

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	6.54	6.53	0.00999999999999979
3	6.54	6.53740672708482	0.00259327291517586
4	6.51	6.53932749355874	-0.0293274935587418
5	6.51	6.51760541947159	-0.007605419471588
6	6.49	6.51197229283242	-0.0219722928324213
7	6.46	6.49569801518866	-0.0356980151886637
8	6.46	6.46925746959143	-0.00925746959143048
9	6.52	6.46240071451545	0.0575992854845477
10	6.48	6.50506293330194	-0.0250629333019425
11	6.49	6.48649950261068	0.00350049738932068
12	6.48	6.48909222549306	-0.00909222549306321
13	6.53	6.48235786221098	0.0476421377890164
14	6.49	6.51764509344507	-0.0276450934450665
15	6.48	6.49716912720686	-0.0171691272068593
16	6.57	6.48445242325628	0.085547576743724
17	6.53	6.54781517862716	-0.0178151786271563
18	6.57	6.53461996202128	0.035380037978717
19	6.55	6.56082499057719	-0.0108249905771904
20	6.57	6.55280721548709	0.0171927845129138
21	6.62	6.56554144175862	0.0544585582413797
22	6.56	6.60587740959131	-0.0458774095913101
23	6.65	6.57189726437116	0.0781027356288426
24	6.59	6.62974582910926	-0.0397458291092576
25	6.68	6.60030717821202	0.0796928217879751
26	6.75	6.65933347637233	0.0906665236276698
27	6.77	6.72648769599632	0.0435123040036789
28	6.82	6.75871607205504	0.0612839279449648
29	6.88	6.80410740495247	0.0758925950475264
30	6.81	6.86031897888008	-0.0503189788800835
31	6.87	6.8230490845049	0.0469509154950973
32	6.91	6.85782434625038	0.0521756537496154
33	6.98	6.89646942902995	0.0835305709700478
34	7.04	6.95833824327142	0.0816617567285807
35	6.99	7.01882287780701	-0.0288228778070083
36	7.08	6.99747455883543	0.0825254411645657
37	7.13	7.0585989008615	0.0714010991385008
38	7.1	7.11148374634903	-0.0114837463490334
39	7.02	7.10297804883717	-0.0829780488371696
40	7.03	7.04151847266036	-0.0115184726603568
41	7.12	7.03298705431743	0.0870129456825701
42	7.11	7.09743516846917	0.0125648315308284
43	7.09	7.10674159627074	-0.0167415962707356
44	7.02	7.09434155281657	-0.0743415528165716
45	7.03	7.03927879353913	-0.00927879353913319
46	7.06	7.03240624439705	0.0275937556029451
47	7.05	7.05284418609669	-0.00284418609668968
48	7.11	7.05073757507703	0.0592624249229736
49	7.06	7.09463163585596	-0.0346316358559609
50	7.05	7.06898092832735	-0.0189809283273501
51	7.11	7.05492227273362	0.0550777272663794
52	7.09	7.09571684216507	-0.0057168421650653
53	7.13	7.0914825331947	0.0385174668052999
54	7.03	7.12001136965726	-0.0900113696572626
55	7.06	7.05334240469901	0.00665759530099219
56	7.11	7.05827350384257	0.0517264961574275
57	7.08	7.0965859078518	-0.0165859078517991
58	7.13	7.08430117856057	0.0456988214394327
59	7	7.11814904841057	-0.118149048410566
60	7.02	7.03063927271969	-0.0106392727196933
61	6.96	7.02275905377812	-0.0627590537781151
62	6.98	6.97627513543449	0.00372486456551524
63	7.02	6.97903404096096	0.0409659590390437
64	7.02	7.00937640879798	0.0106235912020161
65	7.06	7.01724501286739	0.0427549871326089
66	7.02	7.04891246498803	-0.0289124649880312
67	6.94	7.02749779123644	-0.0874977912364425
68	6.97	6.96269056521512	0.00730943478488122
69	6.97	6.96810446407471	0.00189553592528746
70	6.94	6.96950843580252	-0.0295084358025202
71	6.93	6.94765234273359	-0.0176523427335891
72	7	6.93457773423004	0.0654222657699579
73	6.97	6.98303422101293	-0.0130342210129326
74	6.97	6.97338012923232	-0.00338012923232522
75	6.98	6.9708765597588	0.00912344024120237
76	6.92	6.97763404295293	-0.0576340429529267
77	7	6.93494608025819	0.0650539197418087
78	6.94	6.98312974319075	-0.0431297431907538
79	6.97	6.95118471948551	0.0188152805144917
80	6.93	6.96512068426503	-0.0351206842650331
81	6.92	6.9391077519267	-0.0191077519266951
82	6.84	6.92495516155414	-0.0849551615541397
83	6.86	6.86203119194627	-0.00203119194627455
84	6.86	6.86052674350598	-0.000526743505980143
85	6.84	6.86013659896673	-0.0201365989667304

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 6.54 & 6.53 & 0.00999999999999979 \tabularnewline
3 & 6.54 & 6.53740672708482 & 0.00259327291517586 \tabularnewline
4 & 6.51 & 6.53932749355874 & -0.0293274935587418 \tabularnewline
5 & 6.51 & 6.51760541947159 & -0.007605419471588 \tabularnewline
6 & 6.49 & 6.51197229283242 & -0.0219722928324213 \tabularnewline
7 & 6.46 & 6.49569801518866 & -0.0356980151886637 \tabularnewline
8 & 6.46 & 6.46925746959143 & -0.00925746959143048 \tabularnewline
9 & 6.52 & 6.46240071451545 & 0.0575992854845477 \tabularnewline
10 & 6.48 & 6.50506293330194 & -0.0250629333019425 \tabularnewline
11 & 6.49 & 6.48649950261068 & 0.00350049738932068 \tabularnewline
12 & 6.48 & 6.48909222549306 & -0.00909222549306321 \tabularnewline
13 & 6.53 & 6.48235786221098 & 0.0476421377890164 \tabularnewline
14 & 6.49 & 6.51764509344507 & -0.0276450934450665 \tabularnewline
15 & 6.48 & 6.49716912720686 & -0.0171691272068593 \tabularnewline
16 & 6.57 & 6.48445242325628 & 0.085547576743724 \tabularnewline
17 & 6.53 & 6.54781517862716 & -0.0178151786271563 \tabularnewline
18 & 6.57 & 6.53461996202128 & 0.035380037978717 \tabularnewline
19 & 6.55 & 6.56082499057719 & -0.0108249905771904 \tabularnewline
20 & 6.57 & 6.55280721548709 & 0.0171927845129138 \tabularnewline
21 & 6.62 & 6.56554144175862 & 0.0544585582413797 \tabularnewline
22 & 6.56 & 6.60587740959131 & -0.0458774095913101 \tabularnewline
23 & 6.65 & 6.57189726437116 & 0.0781027356288426 \tabularnewline
24 & 6.59 & 6.62974582910926 & -0.0397458291092576 \tabularnewline
25 & 6.68 & 6.60030717821202 & 0.0796928217879751 \tabularnewline
26 & 6.75 & 6.65933347637233 & 0.0906665236276698 \tabularnewline
27 & 6.77 & 6.72648769599632 & 0.0435123040036789 \tabularnewline
28 & 6.82 & 6.75871607205504 & 0.0612839279449648 \tabularnewline
29 & 6.88 & 6.80410740495247 & 0.0758925950475264 \tabularnewline
30 & 6.81 & 6.86031897888008 & -0.0503189788800835 \tabularnewline
31 & 6.87 & 6.8230490845049 & 0.0469509154950973 \tabularnewline
32 & 6.91 & 6.85782434625038 & 0.0521756537496154 \tabularnewline
33 & 6.98 & 6.89646942902995 & 0.0835305709700478 \tabularnewline
34 & 7.04 & 6.95833824327142 & 0.0816617567285807 \tabularnewline
35 & 6.99 & 7.01882287780701 & -0.0288228778070083 \tabularnewline
36 & 7.08 & 6.99747455883543 & 0.0825254411645657 \tabularnewline
37 & 7.13 & 7.0585989008615 & 0.0714010991385008 \tabularnewline
38 & 7.1 & 7.11148374634903 & -0.0114837463490334 \tabularnewline
39 & 7.02 & 7.10297804883717 & -0.0829780488371696 \tabularnewline
40 & 7.03 & 7.04151847266036 & -0.0115184726603568 \tabularnewline
41 & 7.12 & 7.03298705431743 & 0.0870129456825701 \tabularnewline
42 & 7.11 & 7.09743516846917 & 0.0125648315308284 \tabularnewline
43 & 7.09 & 7.10674159627074 & -0.0167415962707356 \tabularnewline
44 & 7.02 & 7.09434155281657 & -0.0743415528165716 \tabularnewline
45 & 7.03 & 7.03927879353913 & -0.00927879353913319 \tabularnewline
46 & 7.06 & 7.03240624439705 & 0.0275937556029451 \tabularnewline
47 & 7.05 & 7.05284418609669 & -0.00284418609668968 \tabularnewline
48 & 7.11 & 7.05073757507703 & 0.0592624249229736 \tabularnewline
49 & 7.06 & 7.09463163585596 & -0.0346316358559609 \tabularnewline
50 & 7.05 & 7.06898092832735 & -0.0189809283273501 \tabularnewline
51 & 7.11 & 7.05492227273362 & 0.0550777272663794 \tabularnewline
52 & 7.09 & 7.09571684216507 & -0.0057168421650653 \tabularnewline
53 & 7.13 & 7.0914825331947 & 0.0385174668052999 \tabularnewline
54 & 7.03 & 7.12001136965726 & -0.0900113696572626 \tabularnewline
55 & 7.06 & 7.05334240469901 & 0.00665759530099219 \tabularnewline
56 & 7.11 & 7.05827350384257 & 0.0517264961574275 \tabularnewline
57 & 7.08 & 7.0965859078518 & -0.0165859078517991 \tabularnewline
58 & 7.13 & 7.08430117856057 & 0.0456988214394327 \tabularnewline
59 & 7 & 7.11814904841057 & -0.118149048410566 \tabularnewline
60 & 7.02 & 7.03063927271969 & -0.0106392727196933 \tabularnewline
61 & 6.96 & 7.02275905377812 & -0.0627590537781151 \tabularnewline
62 & 6.98 & 6.97627513543449 & 0.00372486456551524 \tabularnewline
63 & 7.02 & 6.97903404096096 & 0.0409659590390437 \tabularnewline
64 & 7.02 & 7.00937640879798 & 0.0106235912020161 \tabularnewline
65 & 7.06 & 7.01724501286739 & 0.0427549871326089 \tabularnewline
66 & 7.02 & 7.04891246498803 & -0.0289124649880312 \tabularnewline
67 & 6.94 & 7.02749779123644 & -0.0874977912364425 \tabularnewline
68 & 6.97 & 6.96269056521512 & 0.00730943478488122 \tabularnewline
69 & 6.97 & 6.96810446407471 & 0.00189553592528746 \tabularnewline
70 & 6.94 & 6.96950843580252 & -0.0295084358025202 \tabularnewline
71 & 6.93 & 6.94765234273359 & -0.0176523427335891 \tabularnewline
72 & 7 & 6.93457773423004 & 0.0654222657699579 \tabularnewline
73 & 6.97 & 6.98303422101293 & -0.0130342210129326 \tabularnewline
74 & 6.97 & 6.97338012923232 & -0.00338012923232522 \tabularnewline
75 & 6.98 & 6.9708765597588 & 0.00912344024120237 \tabularnewline
76 & 6.92 & 6.97763404295293 & -0.0576340429529267 \tabularnewline
77 & 7 & 6.93494608025819 & 0.0650539197418087 \tabularnewline
78 & 6.94 & 6.98312974319075 & -0.0431297431907538 \tabularnewline
79 & 6.97 & 6.95118471948551 & 0.0188152805144917 \tabularnewline
80 & 6.93 & 6.96512068426503 & -0.0351206842650331 \tabularnewline
81 & 6.92 & 6.9391077519267 & -0.0191077519266951 \tabularnewline
82 & 6.84 & 6.92495516155414 & -0.0849551615541397 \tabularnewline
83 & 6.86 & 6.86203119194627 & -0.00203119194627455 \tabularnewline
84 & 6.86 & 6.86052674350598 & -0.000526743505980143 \tabularnewline
85 & 6.84 & 6.86013659896673 & -0.0201365989667304 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13753&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]2[/C][C]6.54[/C][C]6.53[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]3[/C][C]6.54[/C][C]6.53740672708482[/C][C]0.00259327291517586[/C][/ROW]
[ROW][C]4[/C][C]6.51[/C][C]6.53932749355874[/C][C]-0.0293274935587418[/C][/ROW]
[ROW][C]5[/C][C]6.51[/C][C]6.51760541947159[/C][C]-0.007605419471588[/C][/ROW]
[ROW][C]6[/C][C]6.49[/C][C]6.51197229283242[/C][C]-0.0219722928324213[/C][/ROW]
[ROW][C]7[/C][C]6.46[/C][C]6.49569801518866[/C][C]-0.0356980151886637[/C][/ROW]
[ROW][C]8[/C][C]6.46[/C][C]6.46925746959143[/C][C]-0.00925746959143048[/C][/ROW]
[ROW][C]9[/C][C]6.52[/C][C]6.46240071451545[/C][C]0.0575992854845477[/C][/ROW]
[ROW][C]10[/C][C]6.48[/C][C]6.50506293330194[/C][C]-0.0250629333019425[/C][/ROW]
[ROW][C]11[/C][C]6.49[/C][C]6.48649950261068[/C][C]0.00350049738932068[/C][/ROW]
[ROW][C]12[/C][C]6.48[/C][C]6.48909222549306[/C][C]-0.00909222549306321[/C][/ROW]
[ROW][C]13[/C][C]6.53[/C][C]6.48235786221098[/C][C]0.0476421377890164[/C][/ROW]
[ROW][C]14[/C][C]6.49[/C][C]6.51764509344507[/C][C]-0.0276450934450665[/C][/ROW]
[ROW][C]15[/C][C]6.48[/C][C]6.49716912720686[/C][C]-0.0171691272068593[/C][/ROW]
[ROW][C]16[/C][C]6.57[/C][C]6.48445242325628[/C][C]0.085547576743724[/C][/ROW]
[ROW][C]17[/C][C]6.53[/C][C]6.54781517862716[/C][C]-0.0178151786271563[/C][/ROW]
[ROW][C]18[/C][C]6.57[/C][C]6.53461996202128[/C][C]0.035380037978717[/C][/ROW]
[ROW][C]19[/C][C]6.55[/C][C]6.56082499057719[/C][C]-0.0108249905771904[/C][/ROW]
[ROW][C]20[/C][C]6.57[/C][C]6.55280721548709[/C][C]0.0171927845129138[/C][/ROW]
[ROW][C]21[/C][C]6.62[/C][C]6.56554144175862[/C][C]0.0544585582413797[/C][/ROW]
[ROW][C]22[/C][C]6.56[/C][C]6.60587740959131[/C][C]-0.0458774095913101[/C][/ROW]
[ROW][C]23[/C][C]6.65[/C][C]6.57189726437116[/C][C]0.0781027356288426[/C][/ROW]
[ROW][C]24[/C][C]6.59[/C][C]6.62974582910926[/C][C]-0.0397458291092576[/C][/ROW]
[ROW][C]25[/C][C]6.68[/C][C]6.60030717821202[/C][C]0.0796928217879751[/C][/ROW]
[ROW][C]26[/C][C]6.75[/C][C]6.65933347637233[/C][C]0.0906665236276698[/C][/ROW]
[ROW][C]27[/C][C]6.77[/C][C]6.72648769599632[/C][C]0.0435123040036789[/C][/ROW]
[ROW][C]28[/C][C]6.82[/C][C]6.75871607205504[/C][C]0.0612839279449648[/C][/ROW]
[ROW][C]29[/C][C]6.88[/C][C]6.80410740495247[/C][C]0.0758925950475264[/C][/ROW]
[ROW][C]30[/C][C]6.81[/C][C]6.86031897888008[/C][C]-0.0503189788800835[/C][/ROW]
[ROW][C]31[/C][C]6.87[/C][C]6.8230490845049[/C][C]0.0469509154950973[/C][/ROW]
[ROW][C]32[/C][C]6.91[/C][C]6.85782434625038[/C][C]0.0521756537496154[/C][/ROW]
[ROW][C]33[/C][C]6.98[/C][C]6.89646942902995[/C][C]0.0835305709700478[/C][/ROW]
[ROW][C]34[/C][C]7.04[/C][C]6.95833824327142[/C][C]0.0816617567285807[/C][/ROW]
[ROW][C]35[/C][C]6.99[/C][C]7.01882287780701[/C][C]-0.0288228778070083[/C][/ROW]
[ROW][C]36[/C][C]7.08[/C][C]6.99747455883543[/C][C]0.0825254411645657[/C][/ROW]
[ROW][C]37[/C][C]7.13[/C][C]7.0585989008615[/C][C]0.0714010991385008[/C][/ROW]
[ROW][C]38[/C][C]7.1[/C][C]7.11148374634903[/C][C]-0.0114837463490334[/C][/ROW]
[ROW][C]39[/C][C]7.02[/C][C]7.10297804883717[/C][C]-0.0829780488371696[/C][/ROW]
[ROW][C]40[/C][C]7.03[/C][C]7.04151847266036[/C][C]-0.0115184726603568[/C][/ROW]
[ROW][C]41[/C][C]7.12[/C][C]7.03298705431743[/C][C]0.0870129456825701[/C][/ROW]
[ROW][C]42[/C][C]7.11[/C][C]7.09743516846917[/C][C]0.0125648315308284[/C][/ROW]
[ROW][C]43[/C][C]7.09[/C][C]7.10674159627074[/C][C]-0.0167415962707356[/C][/ROW]
[ROW][C]44[/C][C]7.02[/C][C]7.09434155281657[/C][C]-0.0743415528165716[/C][/ROW]
[ROW][C]45[/C][C]7.03[/C][C]7.03927879353913[/C][C]-0.00927879353913319[/C][/ROW]
[ROW][C]46[/C][C]7.06[/C][C]7.03240624439705[/C][C]0.0275937556029451[/C][/ROW]
[ROW][C]47[/C][C]7.05[/C][C]7.05284418609669[/C][C]-0.00284418609668968[/C][/ROW]
[ROW][C]48[/C][C]7.11[/C][C]7.05073757507703[/C][C]0.0592624249229736[/C][/ROW]
[ROW][C]49[/C][C]7.06[/C][C]7.09463163585596[/C][C]-0.0346316358559609[/C][/ROW]
[ROW][C]50[/C][C]7.05[/C][C]7.06898092832735[/C][C]-0.0189809283273501[/C][/ROW]
[ROW][C]51[/C][C]7.11[/C][C]7.05492227273362[/C][C]0.0550777272663794[/C][/ROW]
[ROW][C]52[/C][C]7.09[/C][C]7.09571684216507[/C][C]-0.0057168421650653[/C][/ROW]
[ROW][C]53[/C][C]7.13[/C][C]7.0914825331947[/C][C]0.0385174668052999[/C][/ROW]
[ROW][C]54[/C][C]7.03[/C][C]7.12001136965726[/C][C]-0.0900113696572626[/C][/ROW]
[ROW][C]55[/C][C]7.06[/C][C]7.05334240469901[/C][C]0.00665759530099219[/C][/ROW]
[ROW][C]56[/C][C]7.11[/C][C]7.05827350384257[/C][C]0.0517264961574275[/C][/ROW]
[ROW][C]57[/C][C]7.08[/C][C]7.0965859078518[/C][C]-0.0165859078517991[/C][/ROW]
[ROW][C]58[/C][C]7.13[/C][C]7.08430117856057[/C][C]0.0456988214394327[/C][/ROW]
[ROW][C]59[/C][C]7[/C][C]7.11814904841057[/C][C]-0.118149048410566[/C][/ROW]
[ROW][C]60[/C][C]7.02[/C][C]7.03063927271969[/C][C]-0.0106392727196933[/C][/ROW]
[ROW][C]61[/C][C]6.96[/C][C]7.02275905377812[/C][C]-0.0627590537781151[/C][/ROW]
[ROW][C]62[/C][C]6.98[/C][C]6.97627513543449[/C][C]0.00372486456551524[/C][/ROW]
[ROW][C]63[/C][C]7.02[/C][C]6.97903404096096[/C][C]0.0409659590390437[/C][/ROW]
[ROW][C]64[/C][C]7.02[/C][C]7.00937640879798[/C][C]0.0106235912020161[/C][/ROW]
[ROW][C]65[/C][C]7.06[/C][C]7.01724501286739[/C][C]0.0427549871326089[/C][/ROW]
[ROW][C]66[/C][C]7.02[/C][C]7.04891246498803[/C][C]-0.0289124649880312[/C][/ROW]
[ROW][C]67[/C][C]6.94[/C][C]7.02749779123644[/C][C]-0.0874977912364425[/C][/ROW]
[ROW][C]68[/C][C]6.97[/C][C]6.96269056521512[/C][C]0.00730943478488122[/C][/ROW]
[ROW][C]69[/C][C]6.97[/C][C]6.96810446407471[/C][C]0.00189553592528746[/C][/ROW]
[ROW][C]70[/C][C]6.94[/C][C]6.96950843580252[/C][C]-0.0295084358025202[/C][/ROW]
[ROW][C]71[/C][C]6.93[/C][C]6.94765234273359[/C][C]-0.0176523427335891[/C][/ROW]
[ROW][C]72[/C][C]7[/C][C]6.93457773423004[/C][C]0.0654222657699579[/C][/ROW]
[ROW][C]73[/C][C]6.97[/C][C]6.98303422101293[/C][C]-0.0130342210129326[/C][/ROW]
[ROW][C]74[/C][C]6.97[/C][C]6.97338012923232[/C][C]-0.00338012923232522[/C][/ROW]
[ROW][C]75[/C][C]6.98[/C][C]6.9708765597588[/C][C]0.00912344024120237[/C][/ROW]
[ROW][C]76[/C][C]6.92[/C][C]6.97763404295293[/C][C]-0.0576340429529267[/C][/ROW]
[ROW][C]77[/C][C]7[/C][C]6.93494608025819[/C][C]0.0650539197418087[/C][/ROW]
[ROW][C]78[/C][C]6.94[/C][C]6.98312974319075[/C][C]-0.0431297431907538[/C][/ROW]
[ROW][C]79[/C][C]6.97[/C][C]6.95118471948551[/C][C]0.0188152805144917[/C][/ROW]
[ROW][C]80[/C][C]6.93[/C][C]6.96512068426503[/C][C]-0.0351206842650331[/C][/ROW]
[ROW][C]81[/C][C]6.92[/C][C]6.9391077519267[/C][C]-0.0191077519266951[/C][/ROW]
[ROW][C]82[/C][C]6.84[/C][C]6.92495516155414[/C][C]-0.0849551615541397[/C][/ROW]
[ROW][C]83[/C][C]6.86[/C][C]6.86203119194627[/C][C]-0.00203119194627455[/C][/ROW]
[ROW][C]84[/C][C]6.86[/C][C]6.86052674350598[/C][C]-0.000526743505980143[/C][/ROW]
[ROW][C]85[/C][C]6.84[/C][C]6.86013659896673[/C][C]-0.0201365989667304[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13753&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13753&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
2	6.54	6.53	0.00999999999999979
3	6.54	6.53740672708482	0.00259327291517586
4	6.51	6.53932749355874	-0.0293274935587418
5	6.51	6.51760541947159	-0.007605419471588
6	6.49	6.51197229283242	-0.0219722928324213
7	6.46	6.49569801518866	-0.0356980151886637
8	6.46	6.46925746959143	-0.00925746959143048
9	6.52	6.46240071451545	0.0575992854845477
10	6.48	6.50506293330194	-0.0250629333019425
11	6.49	6.48649950261068	0.00350049738932068
12	6.48	6.48909222549306	-0.00909222549306321
13	6.53	6.48235786221098	0.0476421377890164
14	6.49	6.51764509344507	-0.0276450934450665
15	6.48	6.49716912720686	-0.0171691272068593
16	6.57	6.48445242325628	0.085547576743724
17	6.53	6.54781517862716	-0.0178151786271563
18	6.57	6.53461996202128	0.035380037978717
19	6.55	6.56082499057719	-0.0108249905771904
20	6.57	6.55280721548709	0.0171927845129138
21	6.62	6.56554144175862	0.0544585582413797
22	6.56	6.60587740959131	-0.0458774095913101
23	6.65	6.57189726437116	0.0781027356288426
24	6.59	6.62974582910926	-0.0397458291092576
25	6.68	6.60030717821202	0.0796928217879751
26	6.75	6.65933347637233	0.0906665236276698
27	6.77	6.72648769599632	0.0435123040036789
28	6.82	6.75871607205504	0.0612839279449648
29	6.88	6.80410740495247	0.0758925950475264
30	6.81	6.86031897888008	-0.0503189788800835
31	6.87	6.8230490845049	0.0469509154950973
32	6.91	6.85782434625038	0.0521756537496154
33	6.98	6.89646942902995	0.0835305709700478
34	7.04	6.95833824327142	0.0816617567285807
35	6.99	7.01882287780701	-0.0288228778070083
36	7.08	6.99747455883543	0.0825254411645657
37	7.13	7.0585989008615	0.0714010991385008
38	7.1	7.11148374634903	-0.0114837463490334
39	7.02	7.10297804883717	-0.0829780488371696
40	7.03	7.04151847266036	-0.0115184726603568
41	7.12	7.03298705431743	0.0870129456825701
42	7.11	7.09743516846917	0.0125648315308284
43	7.09	7.10674159627074	-0.0167415962707356
44	7.02	7.09434155281657	-0.0743415528165716
45	7.03	7.03927879353913	-0.00927879353913319
46	7.06	7.03240624439705	0.0275937556029451
47	7.05	7.05284418609669	-0.00284418609668968
48	7.11	7.05073757507703	0.0592624249229736
49	7.06	7.09463163585596	-0.0346316358559609
50	7.05	7.06898092832735	-0.0189809283273501
51	7.11	7.05492227273362	0.0550777272663794
52	7.09	7.09571684216507	-0.0057168421650653
53	7.13	7.0914825331947	0.0385174668052999
54	7.03	7.12001136965726	-0.0900113696572626
55	7.06	7.05334240469901	0.00665759530099219
56	7.11	7.05827350384257	0.0517264961574275
57	7.08	7.0965859078518	-0.0165859078517991
58	7.13	7.08430117856057	0.0456988214394327
59	7	7.11814904841057	-0.118149048410566
60	7.02	7.03063927271969	-0.0106392727196933
61	6.96	7.02275905377812	-0.0627590537781151
62	6.98	6.97627513543449	0.00372486456551524
63	7.02	6.97903404096096	0.0409659590390437
64	7.02	7.00937640879798	0.0106235912020161
65	7.06	7.01724501286739	0.0427549871326089
66	7.02	7.04891246498803	-0.0289124649880312
67	6.94	7.02749779123644	-0.0874977912364425
68	6.97	6.96269056521512	0.00730943478488122
69	6.97	6.96810446407471	0.00189553592528746
70	6.94	6.96950843580252	-0.0295084358025202
71	6.93	6.94765234273359	-0.0176523427335891
72	7	6.93457773423004	0.0654222657699579
73	6.97	6.98303422101293	-0.0130342210129326
74	6.97	6.97338012923232	-0.00338012923232522
75	6.98	6.9708765597588	0.00912344024120237
76	6.92	6.97763404295293	-0.0576340429529267
77	7	6.93494608025819	0.0650539197418087
78	6.94	6.98312974319075	-0.0431297431907538
79	6.97	6.95118471948551	0.0188152805144917
80	6.93	6.96512068426503	-0.0351206842650331
81	6.92	6.9391077519267	-0.0191077519266951
82	6.84	6.92495516155414	-0.0849551615541397
83	6.86	6.86203119194627	-0.00203119194627455
84	6.86	6.86052674350598	-0.000526743505980143
85	6.84	6.86013659896673	-0.0201365989667304

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
86	6.84522196967042	6.75164053250602	6.93880340683482
87	6.84522196967042	6.72876679646096	6.96167714287987
88	6.84522196967042	6.70970027637841	6.98074366296243
89	6.84522196967042	6.6930035366926	6.99744040264824
90	6.84522196967042	6.67796536046255	7.01247857887828
91	6.84522196967042	6.66417198952902	7.02627194981182
92	6.84522196967042	6.65135753947578	7.03908639986506
93	6.84522196967042	6.6393391406628	7.05110479867804
94	6.84522196967042	6.62798463110803	7.06245930823281
95	6.84522196967042	6.61719481503492	7.07324912430591
96	6.84522196967042	6.60689298436513	7.08355095497571
97	6.84522196967042	6.59701836932961	7.09342557001123

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
86 & 6.84522196967042 & 6.75164053250602 & 6.93880340683482 \tabularnewline
87 & 6.84522196967042 & 6.72876679646096 & 6.96167714287987 \tabularnewline
88 & 6.84522196967042 & 6.70970027637841 & 6.98074366296243 \tabularnewline
89 & 6.84522196967042 & 6.6930035366926 & 6.99744040264824 \tabularnewline
90 & 6.84522196967042 & 6.67796536046255 & 7.01247857887828 \tabularnewline
91 & 6.84522196967042 & 6.66417198952902 & 7.02627194981182 \tabularnewline
92 & 6.84522196967042 & 6.65135753947578 & 7.03908639986506 \tabularnewline
93 & 6.84522196967042 & 6.6393391406628 & 7.05110479867804 \tabularnewline
94 & 6.84522196967042 & 6.62798463110803 & 7.06245930823281 \tabularnewline
95 & 6.84522196967042 & 6.61719481503492 & 7.07324912430591 \tabularnewline
96 & 6.84522196967042 & 6.60689298436513 & 7.08355095497571 \tabularnewline
97 & 6.84522196967042 & 6.59701836932961 & 7.09342557001123 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13753&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]86[/C][C]6.84522196967042[/C][C]6.75164053250602[/C][C]6.93880340683482[/C][/ROW]
[ROW][C]87[/C][C]6.84522196967042[/C][C]6.72876679646096[/C][C]6.96167714287987[/C][/ROW]
[ROW][C]88[/C][C]6.84522196967042[/C][C]6.70970027637841[/C][C]6.98074366296243[/C][/ROW]
[ROW][C]89[/C][C]6.84522196967042[/C][C]6.6930035366926[/C][C]6.99744040264824[/C][/ROW]
[ROW][C]90[/C][C]6.84522196967042[/C][C]6.67796536046255[/C][C]7.01247857887828[/C][/ROW]
[ROW][C]91[/C][C]6.84522196967042[/C][C]6.66417198952902[/C][C]7.02627194981182[/C][/ROW]
[ROW][C]92[/C][C]6.84522196967042[/C][C]6.65135753947578[/C][C]7.03908639986506[/C][/ROW]
[ROW][C]93[/C][C]6.84522196967042[/C][C]6.6393391406628[/C][C]7.05110479867804[/C][/ROW]
[ROW][C]94[/C][C]6.84522196967042[/C][C]6.62798463110803[/C][C]7.06245930823281[/C][/ROW]
[ROW][C]95[/C][C]6.84522196967042[/C][C]6.61719481503492[/C][C]7.07324912430591[/C][/ROW]
[ROW][C]96[/C][C]6.84522196967042[/C][C]6.60689298436513[/C][C]7.08355095497571[/C][/ROW]
[ROW][C]97[/C][C]6.84522196967042[/C][C]6.59701836932961[/C][C]7.09342557001123[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13753&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13753&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
86	6.84522196967042	6.75164053250602	6.93880340683482
87	6.84522196967042	6.72876679646096	6.96167714287987
88	6.84522196967042	6.70970027637841	6.98074366296243
89	6.84522196967042	6.6930035366926	6.99744040264824
90	6.84522196967042	6.67796536046255	7.01247857887828
91	6.84522196967042	6.66417198952902	7.02627194981182
92	6.84522196967042	6.65135753947578	7.03908639986506
93	6.84522196967042	6.6393391406628	7.05110479867804
94	6.84522196967042	6.62798463110803	7.06245930823281
95	6.84522196967042	6.61719481503492	7.07324912430591
96	6.84522196967042	6.60689298436513	7.08355095497571
97	6.84522196967042	6.59701836932961	7.09342557001123

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 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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