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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sat, 26 May 2012 09:30:30 -0400

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/2012/May/26/t1338039060x22aaoac81k1nwg.htm/, Retrieved Thu, 02 May 2024 14:53:25 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167603, Retrieved Thu, 02 May 2024 14:53:25 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W102

Estimated Impact

114

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

-     [Classical Decomposition] [jens vanpachtenbe...] [2012-05-26 12:41:30] [6c12ae1bbd1f05ed2de376c80d275927]
- RMPD    [Exponential Smoothing] [jens vanpachtenbe...] [2012-05-26 13:30:30] [76c30f62b7052b57088120e90a652e05] [Current]

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Dataseries X:

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Boxplots

2,31
2,31
2,32
2,33
2,34
2,36
2,37
2,37
2,38
2,39
2,4
2,4
2,39
2,4
2,42
2,42
2,44
2,44
2,44
2,45
2,46
2,47
2,48
2,48
2,49
2,5
2,51
2,52
2,52
2,52
2,54
2,54
2,54
2,56
2,57
2,58
2,58
2,58
2,58
2,59
2,6
2,61
2,61
2,62
2,63
2,65
2,67
2,68
2,67
2,68
2,68
2,68
2,68
2,69
2,69
2,69
2,7
2,71
2,72
2,71
2,72
2,73
2,74
2,74
2,75
2,75
2,76
2,75
2,78
2,79
2,8
2,81
2,81
2,82
2,82
2,83
2,83
2,84
2,84
2,84
2,86
2,87
2,88
2,88

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	'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167603&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167603&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167603&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	'Gertrude Mary Cox' @ cox.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.928320581576317
beta	0.0868906738479239
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.928320581576317 \tabularnewline
beta & 0.0868906738479239 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167603&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]0.928320581576317[/C][/ROW]
[ROW][C]beta[/C][C]0.0868906738479239[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167603&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167603&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	0.928320581576317
beta	0.0868906738479239
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	2.32	2.31	0.00999999999999979
4	2.33	2.32008982982456	0.00991017017543649
5	2.34	2.33089564689363	0.00910435310637325
6	2.36	2.34168778637251	0.0183122136274876
7	2.37	2.36250487940205	0.00749512059794588
8	2.37	2.37388481676176	-0.00388481676176289
9	2.38	2.37438716540642	0.00561283459357798
10	2.39	2.38415912399494	0.00584087600505967
11	2.4	2.394613917201	0.00538608279899977
12	2.4	2.40508097088342	-0.00508097088341941
13	2.39	2.40542139989373	-0.015421399893726
14	2.4	2.39491866869108	0.00508133130892263
15	2.42	2.40385891722542	0.0161410827745807
16	2.42	2.42436813916185	-0.00436813916185175
17	2.44	2.4254858836704	0.0145141163295959
18	2.44	2.44530315804805	-0.0053031580480476
19	2.44	2.44629588328978	-0.00629588328977748
20	2.45	2.44585920019595	0.00414079980405502
21	2.46	2.45544511167527	0.00455488832473394
22	2.47	2.46578283827894	0.00421716172105935
23	2.48	2.4761472127148	0.00385278728520122
24	2.48	2.48648410593495	-0.00648410593495408
25	2.49	2.48670202487701	0.00329797512299201
26	2.5	2.49626687358727	0.00373312641273493
27	2.51	2.50653680513513	0.00346319486487001
28	2.52	2.51683550328401	0.00316449671598917
29	2.52	2.5271121696963	-0.00711216969629547
30	2.52	2.52727511048489	-0.00727511048489271
31	2.54	2.52669996210748	0.0133000378925225
32	2.54	2.54629796042601	-0.00629796042601027
33	2.54	2.54719472493914	-0.00719472493914175
34	2.56	2.54667866071064	0.013321339289357
35	2.57	2.56628261236842	0.00371738763158103
36	2.58	2.57727087144918	0.00272912855081797
37	2.58	2.58756184734656	-0.00756184734656262
38	2.58	2.58768954175184	-0.00768954175183678
39	2.58	2.58707843791317	-0.00707843791317231
40	2.59	2.58646367054886	0.00353632945113658
41	2.6	2.59598805902132	0.00401194097868185
42	2.61	2.60627758025516	0.00372241974484178
43	2.61	2.61659859228252	-0.00659859228252291
44	2.62	2.61680613812625	0.00319386187374882
45	2.63	2.62636184527421	0.00363815472579443
46	2.65	2.63662346091592	0.0133765390840832
47	2.67	2.65700440294672	0.0129955970532838
48	2.68	2.67807996470912	0.00192003529087525
49	2.67	2.68902872919131	-0.0190287291913065
50	2.68	2.67899542146382	0.00100457853618341
51	2.68	2.68764047733341	-0.00764047733340867
52	2.68	2.6876438506648	-0.00764385066479889
53	2.68	2.68702752111664	-0.00702752111663951
54	2.69	2.68641648624757	0.00358351375243293
55	2.69	2.69594494826214	-0.00594494826213587
56	2.69	2.69614840907788	-0.00614840907788095
57	2.7	2.69566704759301	0.0043329524069895
58	2.71	2.70526525604153	0.00473474395846596
59	2.72	2.71561837167204	0.00438162832796163
60	2.71	2.72599711545577	-0.0159971154557672
61	2.72	2.71616748621857	0.00383251378142813
62	2.73	2.72505524969031	0.00494475030969133
63	2.74	2.73537438065455	0.0046256193454548
64	2.74	2.74577036933842	-0.00577036933842479
65	2.75	2.74605009591642	0.00394990408357776
66	2.75	2.75567196111724	-0.00567196111724133
67	2.76	2.75590413681757	0.00409586318242816
68	2.75	2.76553436701048	-0.0155343670104777
69	2.78	2.75568841115501	0.0243115888449887
70	2.79	2.7847933073382	0.00520669266179885
71	2.8	2.7965827195164	0.00341728048359746
72	2.81	2.80698662958894	0.00301337041105665
73	2.81	2.81725864732014	-0.00725864732013592
74	2.82	2.81740943965716	0.002590560342838
75	2.82	2.82691241499682	-0.00691241499682338
76	2.83	2.82703601075294	0.00296398924705832
77	2.83	2.83656715832947	-0.00656715832947397
78	2.84	2.83672062268686	0.00327937731314476
79	2.84	2.84627935118597	-0.00627935118597378
80	2.84	2.84645800774303	-0.00645800774303096
81	2.86	2.84594989533168	0.0140501046683168
82	2.87	2.86561320093623	0.00438679906376693
83	2.88	2.87665971080668	0.00334028919332052
84	2.88	2.88700415977153	-0.00700415977153446

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 2.32 & 2.31 & 0.00999999999999979 \tabularnewline
4 & 2.33 & 2.32008982982456 & 0.00991017017543649 \tabularnewline
5 & 2.34 & 2.33089564689363 & 0.00910435310637325 \tabularnewline
6 & 2.36 & 2.34168778637251 & 0.0183122136274876 \tabularnewline
7 & 2.37 & 2.36250487940205 & 0.00749512059794588 \tabularnewline
8 & 2.37 & 2.37388481676176 & -0.00388481676176289 \tabularnewline
9 & 2.38 & 2.37438716540642 & 0.00561283459357798 \tabularnewline
10 & 2.39 & 2.38415912399494 & 0.00584087600505967 \tabularnewline
11 & 2.4 & 2.394613917201 & 0.00538608279899977 \tabularnewline
12 & 2.4 & 2.40508097088342 & -0.00508097088341941 \tabularnewline
13 & 2.39 & 2.40542139989373 & -0.015421399893726 \tabularnewline
14 & 2.4 & 2.39491866869108 & 0.00508133130892263 \tabularnewline
15 & 2.42 & 2.40385891722542 & 0.0161410827745807 \tabularnewline
16 & 2.42 & 2.42436813916185 & -0.00436813916185175 \tabularnewline
17 & 2.44 & 2.4254858836704 & 0.0145141163295959 \tabularnewline
18 & 2.44 & 2.44530315804805 & -0.0053031580480476 \tabularnewline
19 & 2.44 & 2.44629588328978 & -0.00629588328977748 \tabularnewline
20 & 2.45 & 2.44585920019595 & 0.00414079980405502 \tabularnewline
21 & 2.46 & 2.45544511167527 & 0.00455488832473394 \tabularnewline
22 & 2.47 & 2.46578283827894 & 0.00421716172105935 \tabularnewline
23 & 2.48 & 2.4761472127148 & 0.00385278728520122 \tabularnewline
24 & 2.48 & 2.48648410593495 & -0.00648410593495408 \tabularnewline
25 & 2.49 & 2.48670202487701 & 0.00329797512299201 \tabularnewline
26 & 2.5 & 2.49626687358727 & 0.00373312641273493 \tabularnewline
27 & 2.51 & 2.50653680513513 & 0.00346319486487001 \tabularnewline
28 & 2.52 & 2.51683550328401 & 0.00316449671598917 \tabularnewline
29 & 2.52 & 2.5271121696963 & -0.00711216969629547 \tabularnewline
30 & 2.52 & 2.52727511048489 & -0.00727511048489271 \tabularnewline
31 & 2.54 & 2.52669996210748 & 0.0133000378925225 \tabularnewline
32 & 2.54 & 2.54629796042601 & -0.00629796042601027 \tabularnewline
33 & 2.54 & 2.54719472493914 & -0.00719472493914175 \tabularnewline
34 & 2.56 & 2.54667866071064 & 0.013321339289357 \tabularnewline
35 & 2.57 & 2.56628261236842 & 0.00371738763158103 \tabularnewline
36 & 2.58 & 2.57727087144918 & 0.00272912855081797 \tabularnewline
37 & 2.58 & 2.58756184734656 & -0.00756184734656262 \tabularnewline
38 & 2.58 & 2.58768954175184 & -0.00768954175183678 \tabularnewline
39 & 2.58 & 2.58707843791317 & -0.00707843791317231 \tabularnewline
40 & 2.59 & 2.58646367054886 & 0.00353632945113658 \tabularnewline
41 & 2.6 & 2.59598805902132 & 0.00401194097868185 \tabularnewline
42 & 2.61 & 2.60627758025516 & 0.00372241974484178 \tabularnewline
43 & 2.61 & 2.61659859228252 & -0.00659859228252291 \tabularnewline
44 & 2.62 & 2.61680613812625 & 0.00319386187374882 \tabularnewline
45 & 2.63 & 2.62636184527421 & 0.00363815472579443 \tabularnewline
46 & 2.65 & 2.63662346091592 & 0.0133765390840832 \tabularnewline
47 & 2.67 & 2.65700440294672 & 0.0129955970532838 \tabularnewline
48 & 2.68 & 2.67807996470912 & 0.00192003529087525 \tabularnewline
49 & 2.67 & 2.68902872919131 & -0.0190287291913065 \tabularnewline
50 & 2.68 & 2.67899542146382 & 0.00100457853618341 \tabularnewline
51 & 2.68 & 2.68764047733341 & -0.00764047733340867 \tabularnewline
52 & 2.68 & 2.6876438506648 & -0.00764385066479889 \tabularnewline
53 & 2.68 & 2.68702752111664 & -0.00702752111663951 \tabularnewline
54 & 2.69 & 2.68641648624757 & 0.00358351375243293 \tabularnewline
55 & 2.69 & 2.69594494826214 & -0.00594494826213587 \tabularnewline
56 & 2.69 & 2.69614840907788 & -0.00614840907788095 \tabularnewline
57 & 2.7 & 2.69566704759301 & 0.0043329524069895 \tabularnewline
58 & 2.71 & 2.70526525604153 & 0.00473474395846596 \tabularnewline
59 & 2.72 & 2.71561837167204 & 0.00438162832796163 \tabularnewline
60 & 2.71 & 2.72599711545577 & -0.0159971154557672 \tabularnewline
61 & 2.72 & 2.71616748621857 & 0.00383251378142813 \tabularnewline
62 & 2.73 & 2.72505524969031 & 0.00494475030969133 \tabularnewline
63 & 2.74 & 2.73537438065455 & 0.0046256193454548 \tabularnewline
64 & 2.74 & 2.74577036933842 & -0.00577036933842479 \tabularnewline
65 & 2.75 & 2.74605009591642 & 0.00394990408357776 \tabularnewline
66 & 2.75 & 2.75567196111724 & -0.00567196111724133 \tabularnewline
67 & 2.76 & 2.75590413681757 & 0.00409586318242816 \tabularnewline
68 & 2.75 & 2.76553436701048 & -0.0155343670104777 \tabularnewline
69 & 2.78 & 2.75568841115501 & 0.0243115888449887 \tabularnewline
70 & 2.79 & 2.7847933073382 & 0.00520669266179885 \tabularnewline
71 & 2.8 & 2.7965827195164 & 0.00341728048359746 \tabularnewline
72 & 2.81 & 2.80698662958894 & 0.00301337041105665 \tabularnewline
73 & 2.81 & 2.81725864732014 & -0.00725864732013592 \tabularnewline
74 & 2.82 & 2.81740943965716 & 0.002590560342838 \tabularnewline
75 & 2.82 & 2.82691241499682 & -0.00691241499682338 \tabularnewline
76 & 2.83 & 2.82703601075294 & 0.00296398924705832 \tabularnewline
77 & 2.83 & 2.83656715832947 & -0.00656715832947397 \tabularnewline
78 & 2.84 & 2.83672062268686 & 0.00327937731314476 \tabularnewline
79 & 2.84 & 2.84627935118597 & -0.00627935118597378 \tabularnewline
80 & 2.84 & 2.84645800774303 & -0.00645800774303096 \tabularnewline
81 & 2.86 & 2.84594989533168 & 0.0140501046683168 \tabularnewline
82 & 2.87 & 2.86561320093623 & 0.00438679906376693 \tabularnewline
83 & 2.88 & 2.87665971080668 & 0.00334028919332052 \tabularnewline
84 & 2.88 & 2.88700415977153 & -0.00700415977153446 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167603&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]2.32[/C][C]2.31[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]4[/C][C]2.33[/C][C]2.32008982982456[/C][C]0.00991017017543649[/C][/ROW]
[ROW][C]5[/C][C]2.34[/C][C]2.33089564689363[/C][C]0.00910435310637325[/C][/ROW]
[ROW][C]6[/C][C]2.36[/C][C]2.34168778637251[/C][C]0.0183122136274876[/C][/ROW]
[ROW][C]7[/C][C]2.37[/C][C]2.36250487940205[/C][C]0.00749512059794588[/C][/ROW]
[ROW][C]8[/C][C]2.37[/C][C]2.37388481676176[/C][C]-0.00388481676176289[/C][/ROW]
[ROW][C]9[/C][C]2.38[/C][C]2.37438716540642[/C][C]0.00561283459357798[/C][/ROW]
[ROW][C]10[/C][C]2.39[/C][C]2.38415912399494[/C][C]0.00584087600505967[/C][/ROW]
[ROW][C]11[/C][C]2.4[/C][C]2.394613917201[/C][C]0.00538608279899977[/C][/ROW]
[ROW][C]12[/C][C]2.4[/C][C]2.40508097088342[/C][C]-0.00508097088341941[/C][/ROW]
[ROW][C]13[/C][C]2.39[/C][C]2.40542139989373[/C][C]-0.015421399893726[/C][/ROW]
[ROW][C]14[/C][C]2.4[/C][C]2.39491866869108[/C][C]0.00508133130892263[/C][/ROW]
[ROW][C]15[/C][C]2.42[/C][C]2.40385891722542[/C][C]0.0161410827745807[/C][/ROW]
[ROW][C]16[/C][C]2.42[/C][C]2.42436813916185[/C][C]-0.00436813916185175[/C][/ROW]
[ROW][C]17[/C][C]2.44[/C][C]2.4254858836704[/C][C]0.0145141163295959[/C][/ROW]
[ROW][C]18[/C][C]2.44[/C][C]2.44530315804805[/C][C]-0.0053031580480476[/C][/ROW]
[ROW][C]19[/C][C]2.44[/C][C]2.44629588328978[/C][C]-0.00629588328977748[/C][/ROW]
[ROW][C]20[/C][C]2.45[/C][C]2.44585920019595[/C][C]0.00414079980405502[/C][/ROW]
[ROW][C]21[/C][C]2.46[/C][C]2.45544511167527[/C][C]0.00455488832473394[/C][/ROW]
[ROW][C]22[/C][C]2.47[/C][C]2.46578283827894[/C][C]0.00421716172105935[/C][/ROW]
[ROW][C]23[/C][C]2.48[/C][C]2.4761472127148[/C][C]0.00385278728520122[/C][/ROW]
[ROW][C]24[/C][C]2.48[/C][C]2.48648410593495[/C][C]-0.00648410593495408[/C][/ROW]
[ROW][C]25[/C][C]2.49[/C][C]2.48670202487701[/C][C]0.00329797512299201[/C][/ROW]
[ROW][C]26[/C][C]2.5[/C][C]2.49626687358727[/C][C]0.00373312641273493[/C][/ROW]
[ROW][C]27[/C][C]2.51[/C][C]2.50653680513513[/C][C]0.00346319486487001[/C][/ROW]
[ROW][C]28[/C][C]2.52[/C][C]2.51683550328401[/C][C]0.00316449671598917[/C][/ROW]
[ROW][C]29[/C][C]2.52[/C][C]2.5271121696963[/C][C]-0.00711216969629547[/C][/ROW]
[ROW][C]30[/C][C]2.52[/C][C]2.52727511048489[/C][C]-0.00727511048489271[/C][/ROW]
[ROW][C]31[/C][C]2.54[/C][C]2.52669996210748[/C][C]0.0133000378925225[/C][/ROW]
[ROW][C]32[/C][C]2.54[/C][C]2.54629796042601[/C][C]-0.00629796042601027[/C][/ROW]
[ROW][C]33[/C][C]2.54[/C][C]2.54719472493914[/C][C]-0.00719472493914175[/C][/ROW]
[ROW][C]34[/C][C]2.56[/C][C]2.54667866071064[/C][C]0.013321339289357[/C][/ROW]
[ROW][C]35[/C][C]2.57[/C][C]2.56628261236842[/C][C]0.00371738763158103[/C][/ROW]
[ROW][C]36[/C][C]2.58[/C][C]2.57727087144918[/C][C]0.00272912855081797[/C][/ROW]
[ROW][C]37[/C][C]2.58[/C][C]2.58756184734656[/C][C]-0.00756184734656262[/C][/ROW]
[ROW][C]38[/C][C]2.58[/C][C]2.58768954175184[/C][C]-0.00768954175183678[/C][/ROW]
[ROW][C]39[/C][C]2.58[/C][C]2.58707843791317[/C][C]-0.00707843791317231[/C][/ROW]
[ROW][C]40[/C][C]2.59[/C][C]2.58646367054886[/C][C]0.00353632945113658[/C][/ROW]
[ROW][C]41[/C][C]2.6[/C][C]2.59598805902132[/C][C]0.00401194097868185[/C][/ROW]
[ROW][C]42[/C][C]2.61[/C][C]2.60627758025516[/C][C]0.00372241974484178[/C][/ROW]
[ROW][C]43[/C][C]2.61[/C][C]2.61659859228252[/C][C]-0.00659859228252291[/C][/ROW]
[ROW][C]44[/C][C]2.62[/C][C]2.61680613812625[/C][C]0.00319386187374882[/C][/ROW]
[ROW][C]45[/C][C]2.63[/C][C]2.62636184527421[/C][C]0.00363815472579443[/C][/ROW]
[ROW][C]46[/C][C]2.65[/C][C]2.63662346091592[/C][C]0.0133765390840832[/C][/ROW]
[ROW][C]47[/C][C]2.67[/C][C]2.65700440294672[/C][C]0.0129955970532838[/C][/ROW]
[ROW][C]48[/C][C]2.68[/C][C]2.67807996470912[/C][C]0.00192003529087525[/C][/ROW]
[ROW][C]49[/C][C]2.67[/C][C]2.68902872919131[/C][C]-0.0190287291913065[/C][/ROW]
[ROW][C]50[/C][C]2.68[/C][C]2.67899542146382[/C][C]0.00100457853618341[/C][/ROW]
[ROW][C]51[/C][C]2.68[/C][C]2.68764047733341[/C][C]-0.00764047733340867[/C][/ROW]
[ROW][C]52[/C][C]2.68[/C][C]2.6876438506648[/C][C]-0.00764385066479889[/C][/ROW]
[ROW][C]53[/C][C]2.68[/C][C]2.68702752111664[/C][C]-0.00702752111663951[/C][/ROW]
[ROW][C]54[/C][C]2.69[/C][C]2.68641648624757[/C][C]0.00358351375243293[/C][/ROW]
[ROW][C]55[/C][C]2.69[/C][C]2.69594494826214[/C][C]-0.00594494826213587[/C][/ROW]
[ROW][C]56[/C][C]2.69[/C][C]2.69614840907788[/C][C]-0.00614840907788095[/C][/ROW]
[ROW][C]57[/C][C]2.7[/C][C]2.69566704759301[/C][C]0.0043329524069895[/C][/ROW]
[ROW][C]58[/C][C]2.71[/C][C]2.70526525604153[/C][C]0.00473474395846596[/C][/ROW]
[ROW][C]59[/C][C]2.72[/C][C]2.71561837167204[/C][C]0.00438162832796163[/C][/ROW]
[ROW][C]60[/C][C]2.71[/C][C]2.72599711545577[/C][C]-0.0159971154557672[/C][/ROW]
[ROW][C]61[/C][C]2.72[/C][C]2.71616748621857[/C][C]0.00383251378142813[/C][/ROW]
[ROW][C]62[/C][C]2.73[/C][C]2.72505524969031[/C][C]0.00494475030969133[/C][/ROW]
[ROW][C]63[/C][C]2.74[/C][C]2.73537438065455[/C][C]0.0046256193454548[/C][/ROW]
[ROW][C]64[/C][C]2.74[/C][C]2.74577036933842[/C][C]-0.00577036933842479[/C][/ROW]
[ROW][C]65[/C][C]2.75[/C][C]2.74605009591642[/C][C]0.00394990408357776[/C][/ROW]
[ROW][C]66[/C][C]2.75[/C][C]2.75567196111724[/C][C]-0.00567196111724133[/C][/ROW]
[ROW][C]67[/C][C]2.76[/C][C]2.75590413681757[/C][C]0.00409586318242816[/C][/ROW]
[ROW][C]68[/C][C]2.75[/C][C]2.76553436701048[/C][C]-0.0155343670104777[/C][/ROW]
[ROW][C]69[/C][C]2.78[/C][C]2.75568841115501[/C][C]0.0243115888449887[/C][/ROW]
[ROW][C]70[/C][C]2.79[/C][C]2.7847933073382[/C][C]0.00520669266179885[/C][/ROW]
[ROW][C]71[/C][C]2.8[/C][C]2.7965827195164[/C][C]0.00341728048359746[/C][/ROW]
[ROW][C]72[/C][C]2.81[/C][C]2.80698662958894[/C][C]0.00301337041105665[/C][/ROW]
[ROW][C]73[/C][C]2.81[/C][C]2.81725864732014[/C][C]-0.00725864732013592[/C][/ROW]
[ROW][C]74[/C][C]2.82[/C][C]2.81740943965716[/C][C]0.002590560342838[/C][/ROW]
[ROW][C]75[/C][C]2.82[/C][C]2.82691241499682[/C][C]-0.00691241499682338[/C][/ROW]
[ROW][C]76[/C][C]2.83[/C][C]2.82703601075294[/C][C]0.00296398924705832[/C][/ROW]
[ROW][C]77[/C][C]2.83[/C][C]2.83656715832947[/C][C]-0.00656715832947397[/C][/ROW]
[ROW][C]78[/C][C]2.84[/C][C]2.83672062268686[/C][C]0.00327937731314476[/C][/ROW]
[ROW][C]79[/C][C]2.84[/C][C]2.84627935118597[/C][C]-0.00627935118597378[/C][/ROW]
[ROW][C]80[/C][C]2.84[/C][C]2.84645800774303[/C][C]-0.00645800774303096[/C][/ROW]
[ROW][C]81[/C][C]2.86[/C][C]2.84594989533168[/C][C]0.0140501046683168[/C][/ROW]
[ROW][C]82[/C][C]2.87[/C][C]2.86561320093623[/C][C]0.00438679906376693[/C][/ROW]
[ROW][C]83[/C][C]2.88[/C][C]2.87665971080668[/C][C]0.00334028919332052[/C][/ROW]
[ROW][C]84[/C][C]2.88[/C][C]2.88700415977153[/C][C]-0.00700415977153446[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167603&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167603&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	2.32	2.31	0.00999999999999979
4	2.33	2.32008982982456	0.00991017017543649
5	2.34	2.33089564689363	0.00910435310637325
6	2.36	2.34168778637251	0.0183122136274876
7	2.37	2.36250487940205	0.00749512059794588
8	2.37	2.37388481676176	-0.00388481676176289
9	2.38	2.37438716540642	0.00561283459357798
10	2.39	2.38415912399494	0.00584087600505967
11	2.4	2.394613917201	0.00538608279899977
12	2.4	2.40508097088342	-0.00508097088341941
13	2.39	2.40542139989373	-0.015421399893726
14	2.4	2.39491866869108	0.00508133130892263
15	2.42	2.40385891722542	0.0161410827745807
16	2.42	2.42436813916185	-0.00436813916185175
17	2.44	2.4254858836704	0.0145141163295959
18	2.44	2.44530315804805	-0.0053031580480476
19	2.44	2.44629588328978	-0.00629588328977748
20	2.45	2.44585920019595	0.00414079980405502
21	2.46	2.45544511167527	0.00455488832473394
22	2.47	2.46578283827894	0.00421716172105935
23	2.48	2.4761472127148	0.00385278728520122
24	2.48	2.48648410593495	-0.00648410593495408
25	2.49	2.48670202487701	0.00329797512299201
26	2.5	2.49626687358727	0.00373312641273493
27	2.51	2.50653680513513	0.00346319486487001
28	2.52	2.51683550328401	0.00316449671598917
29	2.52	2.5271121696963	-0.00711216969629547
30	2.52	2.52727511048489	-0.00727511048489271
31	2.54	2.52669996210748	0.0133000378925225
32	2.54	2.54629796042601	-0.00629796042601027
33	2.54	2.54719472493914	-0.00719472493914175
34	2.56	2.54667866071064	0.013321339289357
35	2.57	2.56628261236842	0.00371738763158103
36	2.58	2.57727087144918	0.00272912855081797
37	2.58	2.58756184734656	-0.00756184734656262
38	2.58	2.58768954175184	-0.00768954175183678
39	2.58	2.58707843791317	-0.00707843791317231
40	2.59	2.58646367054886	0.00353632945113658
41	2.6	2.59598805902132	0.00401194097868185
42	2.61	2.60627758025516	0.00372241974484178
43	2.61	2.61659859228252	-0.00659859228252291
44	2.62	2.61680613812625	0.00319386187374882
45	2.63	2.62636184527421	0.00363815472579443
46	2.65	2.63662346091592	0.0133765390840832
47	2.67	2.65700440294672	0.0129955970532838
48	2.68	2.67807996470912	0.00192003529087525
49	2.67	2.68902872919131	-0.0190287291913065
50	2.68	2.67899542146382	0.00100457853618341
51	2.68	2.68764047733341	-0.00764047733340867
52	2.68	2.6876438506648	-0.00764385066479889
53	2.68	2.68702752111664	-0.00702752111663951
54	2.69	2.68641648624757	0.00358351375243293
55	2.69	2.69594494826214	-0.00594494826213587
56	2.69	2.69614840907788	-0.00614840907788095
57	2.7	2.69566704759301	0.0043329524069895
58	2.71	2.70526525604153	0.00473474395846596
59	2.72	2.71561837167204	0.00438162832796163
60	2.71	2.72599711545577	-0.0159971154557672
61	2.72	2.71616748621857	0.00383251378142813
62	2.73	2.72505524969031	0.00494475030969133
63	2.74	2.73537438065455	0.0046256193454548
64	2.74	2.74577036933842	-0.00577036933842479
65	2.75	2.74605009591642	0.00394990408357776
66	2.75	2.75567196111724	-0.00567196111724133
67	2.76	2.75590413681757	0.00409586318242816
68	2.75	2.76553436701048	-0.0155343670104777
69	2.78	2.75568841115501	0.0243115888449887
70	2.79	2.7847933073382	0.00520669266179885
71	2.8	2.7965827195164	0.00341728048359746
72	2.81	2.80698662958894	0.00301337041105665
73	2.81	2.81725864732014	-0.00725864732013592
74	2.82	2.81740943965716	0.002590560342838
75	2.82	2.82691241499682	-0.00691241499682338
76	2.83	2.82703601075294	0.00296398924705832
77	2.83	2.83656715832947	-0.00656715832947397
78	2.84	2.83672062268686	0.00327937731314476
79	2.84	2.84627935118597	-0.00627935118597378
80	2.84	2.84645800774303	-0.00645800774303096
81	2.86	2.84594989533168	0.0140501046683168
82	2.87	2.86561320093623	0.00438679906376693
83	2.88	2.87665971080668	0.00334028919332052
84	2.88	2.88700415977153	-0.00700415977153446

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	2.88718067151393	2.87117530891994	2.90318603410792
86	2.89385928892889	2.87112239587849	2.91659618197929
87	2.90053790634385	2.87188261335373	2.92919319933397
88	2.90721652375881	2.87298227649077	2.94145077102685
89	2.91389514117377	2.87423567273917	2.95355460960836
90	2.92057375858873	2.87555011380273	2.96559740337473
91	2.92725237600368	2.87687298867251	2.97763176333485
92	2.93393099341864	2.87817196551634	2.98969002132094
93	2.9406096108336	2.87942610254908	3.00179311911813
94	2.94728822824856	2.88062134239063	3.01395511410649
95	2.95396684566352	2.88174802078708	3.02618567053997
96	2.96064546307848	2.88279939575601	3.03849153040095

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 2.88718067151393 & 2.87117530891994 & 2.90318603410792 \tabularnewline
86 & 2.89385928892889 & 2.87112239587849 & 2.91659618197929 \tabularnewline
87 & 2.90053790634385 & 2.87188261335373 & 2.92919319933397 \tabularnewline
88 & 2.90721652375881 & 2.87298227649077 & 2.94145077102685 \tabularnewline
89 & 2.91389514117377 & 2.87423567273917 & 2.95355460960836 \tabularnewline
90 & 2.92057375858873 & 2.87555011380273 & 2.96559740337473 \tabularnewline
91 & 2.92725237600368 & 2.87687298867251 & 2.97763176333485 \tabularnewline
92 & 2.93393099341864 & 2.87817196551634 & 2.98969002132094 \tabularnewline
93 & 2.9406096108336 & 2.87942610254908 & 3.00179311911813 \tabularnewline
94 & 2.94728822824856 & 2.88062134239063 & 3.01395511410649 \tabularnewline
95 & 2.95396684566352 & 2.88174802078708 & 3.02618567053997 \tabularnewline
96 & 2.96064546307848 & 2.88279939575601 & 3.03849153040095 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167603&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]85[/C][C]2.88718067151393[/C][C]2.87117530891994[/C][C]2.90318603410792[/C][/ROW]
[ROW][C]86[/C][C]2.89385928892889[/C][C]2.87112239587849[/C][C]2.91659618197929[/C][/ROW]
[ROW][C]87[/C][C]2.90053790634385[/C][C]2.87188261335373[/C][C]2.92919319933397[/C][/ROW]
[ROW][C]88[/C][C]2.90721652375881[/C][C]2.87298227649077[/C][C]2.94145077102685[/C][/ROW]
[ROW][C]89[/C][C]2.91389514117377[/C][C]2.87423567273917[/C][C]2.95355460960836[/C][/ROW]
[ROW][C]90[/C][C]2.92057375858873[/C][C]2.87555011380273[/C][C]2.96559740337473[/C][/ROW]
[ROW][C]91[/C][C]2.92725237600368[/C][C]2.87687298867251[/C][C]2.97763176333485[/C][/ROW]
[ROW][C]92[/C][C]2.93393099341864[/C][C]2.87817196551634[/C][C]2.98969002132094[/C][/ROW]
[ROW][C]93[/C][C]2.9406096108336[/C][C]2.87942610254908[/C][C]3.00179311911813[/C][/ROW]
[ROW][C]94[/C][C]2.94728822824856[/C][C]2.88062134239063[/C][C]3.01395511410649[/C][/ROW]
[ROW][C]95[/C][C]2.95396684566352[/C][C]2.88174802078708[/C][C]3.02618567053997[/C][/ROW]
[ROW][C]96[/C][C]2.96064546307848[/C][C]2.88279939575601[/C][C]3.03849153040095[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167603&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167603&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
85	2.88718067151393	2.87117530891994	2.90318603410792
86	2.89385928892889	2.87112239587849	2.91659618197929
87	2.90053790634385	2.87188261335373	2.92919319933397
88	2.90721652375881	2.87298227649077	2.94145077102685
89	2.91389514117377	2.87423567273917	2.95355460960836
90	2.92057375858873	2.87555011380273	2.96559740337473
91	2.92725237600368	2.87687298867251	2.97763176333485
92	2.93393099341864	2.87817196551634	2.98969002132094
93	2.9406096108336	2.87942610254908	3.00179311911813
94	2.94728822824856	2.88062134239063	3.01395511410649
95	2.95396684566352	2.88174802078708	3.02618567053997
96	2.96064546307848	2.88279939575601	3.03849153040095

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=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code