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Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Tue, 27 May 2008 06:03:46 -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/27/t1211889904lzvqkz7bn9spdy7.htm/, Retrieved Mon, 20 May 2024 02:21:56 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13339, Retrieved Mon, 20 May 2024 02:21:56 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

exponential smoothing - Bisocoop - Evy Heynen

Estimated Impact

209

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

-       [Exponential Smoothing] [exponential smoot...] [2008-05-27 12:03:46] [e5d4dd27997f361fc44e43a7aa346cdf] [Current]

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Dataseries X:

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Boxplots

5,44
5,44
5,44
5,44
5,49
5,49
5,49
5,49
5,49
5,49
5,6
5,6
5,6
5,6
5,6
5,6
5,6
5,67
5,67
5,67
5,67
5,67
5,67
5,67
5,67
5,67
5,82
5,82
5,95
5,95
5,95
5,95
5,95
5,95
6,02
6,02
6,05
6,05
6,05
6,12
6,12
6,12
6,12
6,12
6,12
6,12
6,12
6,17
6,17
6,17
6,17
6,17
6,28
6,27
6,28
6,28
6,27
6,27
6,28
6,59
6,59
6,59
6,59
6,59
6,63
6,63
6,63
6,63
6,63
6,63
6,63
6,63
6,63
6,63
6,63
6,63
6,63
6,63
6,63
6,63
6,63
6,79
6,79
6,79

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	'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 & 3 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=13339&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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13339&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13339&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	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.91195083019207
beta	0.0325127367673738
gamma	0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.91195083019207 \tabularnewline
beta & 0.0325127367673738 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13339&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]0.91195083019207[/C][/ROW]
[ROW][C]beta[/C][C]0.0325127367673738[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13339&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13339&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	0.91195083019207
beta	0.0325127367673738
gamma	0

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	5.44	5.44	0
4	5.44	5.44	0
5	5.49	5.44	0.0499999999999998
6	5.49	5.48708004237394	0.00291995762605524
7	5.49	5.49131197781358	-0.00131197781358239
8	5.49	5.49164569605087	-0.00164569605087017
9	5.49	5.49162628474826	-0.00162628474825599
10	5.49	5.49157635622828	-0.00157635622827712
11	5.6	5.49152522107412	0.108474778925875
12	5.6	5.59505158905772	0.0049484109422826
13	5.6	5.60431372028188	-0.00431372028188459
14	5.6	5.6050013413659	-0.00500134136589558
15	5.6	5.60491359597353	-0.00491359597352936
16	5.6	5.60476018185902	-0.00476018185902127
17	5.6	5.60460553439919	-0.00460553439919398
18	5.67	5.60445536364419	0.065544636355809
19	5.67	5.67022209894834	-0.000222098948337468
20	5.67	5.67600622015519	-0.00600622015518759
21	5.67	5.67633742269409	-0.00633742269408888
22	5.67	5.67617868011024	-0.0061786801102448
23	5.67	5.67598150498544	-0.00598150498544481
24	5.67	5.67578679215318	-0.00578679215318001
25	5.67	5.67559806936257	-0.00559806936257168
26	5.67	5.67541546962416	-0.00541546962416195
27	5.82	5.67523882310082	0.144761176899185
28	5.82	5.81630806544742	0.00369193455258365
29	5.95	5.82883856104477	0.121161438955226
30	5.95	5.95208790746389	-0.00208790746389109
31	5.95	5.96287800360307	-0.0128780036030669
32	5.95	5.96344622958082	-0.0134462295808184
33	5.95	5.96309758046691	-0.0130975804669085
34	5.95	5.96267853871462	-0.0126785387146153
35	6.02	5.96226572354415	0.0577342764558484
36	6.02	6.02777775591951	-0.00777775591951091
37	6.05	6.03331542538513	0.0166845746148745
38	6.05	6.06165623541576	-0.0116562354157601
39	6.05	6.06380601262907	-0.0138060126290656
40	6.12	6.06358595021485	0.056414049785146
41	6.12	6.12907580956677	-0.00907580956677112
42	6.12	6.134573039403	-0.0145730394029986
43	6.12	6.1346249750561	-0.0146249750561012
44	6.12	6.13419591718401	-0.0141959171840087
45	6.12	6.13373722980466	-0.0137372298046632
46	6.12	6.13328953366053	-0.0132895336605294
47	6.12	6.13285607948394	-0.0128560794839432
48	6.17	6.1324367312246	0.0375632687753944
49	6.17	6.17911110103665	-0.00911110103665358
50	6.17	6.18295059624667	-0.0129505962466743
51	6.17	6.18290467520981	-0.0129046752098096
52	6.17	6.18251800805758	-0.0125180080575849
53	6.28	6.18211280318054	0.0978871968194639
54	6.27	6.28529407362649	-0.0152940736264933
55	6.28	6.28480612097965	-0.00480612097965416
56	6.28	6.29374016388599	-0.0137401638859860
57	6.27	6.29411940285017	-0.0241194028501743
58	6.27	6.28431814551275	-0.0143181455127532
59	6.28	6.28303061967915	-0.00303061967915053
60	6.59	6.29194690447444	0.298053095525558
61	6.59	6.5842740127427	0.00572598725729812
62	6.59	6.61018294755924	-0.0201829475592383
63	6.59	6.61186578301641	-0.0218657830164117
64	6.59	6.61136563443691	-0.0213656344369131
65	6.63	6.61068810533931	0.0193118946606905
66	6.63	6.64767908068296	-0.0176790806829583
67	6.63	6.65041192030449	-0.020411920304487
68	6.63	6.6500473307745	-0.0200473307744948
69	6.63	6.64942082526504	-0.0194208252650405
70	6.63	6.64878983417022	-0.0187898341702208
71	6.63	6.6481771570202	-0.0181771570202010
72	6.63	6.64758425828591	-0.0175842582859076
73	6.63	6.64701068048242	-0.0170106804824197
74	6.63	6.64645581046264	-0.016455810462638
75	6.63	6.64591903955336	-0.0159190395533590
76	6.63	6.64539977752247	-0.0153997775224735
77	6.63	6.64489745326199	-0.0148974532619865
78	6.63	6.64441151428113	-0.0144115142811287
79	6.63	6.64394142610972	-0.0139414261097217
80	6.63	6.64348667171134	-0.0134866717113376
81	6.63	6.64304675091471	-0.0130467509147101
82	6.79	6.64262117986363	0.147378820136373
83	6.79	6.79286562608137	-0.00286562608137153
84	6.79	6.80600955897625	-0.0160095589762461

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 5.44 & 5.44 & 0 \tabularnewline
4 & 5.44 & 5.44 & 0 \tabularnewline
5 & 5.49 & 5.44 & 0.0499999999999998 \tabularnewline
6 & 5.49 & 5.48708004237394 & 0.00291995762605524 \tabularnewline
7 & 5.49 & 5.49131197781358 & -0.00131197781358239 \tabularnewline
8 & 5.49 & 5.49164569605087 & -0.00164569605087017 \tabularnewline
9 & 5.49 & 5.49162628474826 & -0.00162628474825599 \tabularnewline
10 & 5.49 & 5.49157635622828 & -0.00157635622827712 \tabularnewline
11 & 5.6 & 5.49152522107412 & 0.108474778925875 \tabularnewline
12 & 5.6 & 5.59505158905772 & 0.0049484109422826 \tabularnewline
13 & 5.6 & 5.60431372028188 & -0.00431372028188459 \tabularnewline
14 & 5.6 & 5.6050013413659 & -0.00500134136589558 \tabularnewline
15 & 5.6 & 5.60491359597353 & -0.00491359597352936 \tabularnewline
16 & 5.6 & 5.60476018185902 & -0.00476018185902127 \tabularnewline
17 & 5.6 & 5.60460553439919 & -0.00460553439919398 \tabularnewline
18 & 5.67 & 5.60445536364419 & 0.065544636355809 \tabularnewline
19 & 5.67 & 5.67022209894834 & -0.000222098948337468 \tabularnewline
20 & 5.67 & 5.67600622015519 & -0.00600622015518759 \tabularnewline
21 & 5.67 & 5.67633742269409 & -0.00633742269408888 \tabularnewline
22 & 5.67 & 5.67617868011024 & -0.0061786801102448 \tabularnewline
23 & 5.67 & 5.67598150498544 & -0.00598150498544481 \tabularnewline
24 & 5.67 & 5.67578679215318 & -0.00578679215318001 \tabularnewline
25 & 5.67 & 5.67559806936257 & -0.00559806936257168 \tabularnewline
26 & 5.67 & 5.67541546962416 & -0.00541546962416195 \tabularnewline
27 & 5.82 & 5.67523882310082 & 0.144761176899185 \tabularnewline
28 & 5.82 & 5.81630806544742 & 0.00369193455258365 \tabularnewline
29 & 5.95 & 5.82883856104477 & 0.121161438955226 \tabularnewline
30 & 5.95 & 5.95208790746389 & -0.00208790746389109 \tabularnewline
31 & 5.95 & 5.96287800360307 & -0.0128780036030669 \tabularnewline
32 & 5.95 & 5.96344622958082 & -0.0134462295808184 \tabularnewline
33 & 5.95 & 5.96309758046691 & -0.0130975804669085 \tabularnewline
34 & 5.95 & 5.96267853871462 & -0.0126785387146153 \tabularnewline
35 & 6.02 & 5.96226572354415 & 0.0577342764558484 \tabularnewline
36 & 6.02 & 6.02777775591951 & -0.00777775591951091 \tabularnewline
37 & 6.05 & 6.03331542538513 & 0.0166845746148745 \tabularnewline
38 & 6.05 & 6.06165623541576 & -0.0116562354157601 \tabularnewline
39 & 6.05 & 6.06380601262907 & -0.0138060126290656 \tabularnewline
40 & 6.12 & 6.06358595021485 & 0.056414049785146 \tabularnewline
41 & 6.12 & 6.12907580956677 & -0.00907580956677112 \tabularnewline
42 & 6.12 & 6.134573039403 & -0.0145730394029986 \tabularnewline
43 & 6.12 & 6.1346249750561 & -0.0146249750561012 \tabularnewline
44 & 6.12 & 6.13419591718401 & -0.0141959171840087 \tabularnewline
45 & 6.12 & 6.13373722980466 & -0.0137372298046632 \tabularnewline
46 & 6.12 & 6.13328953366053 & -0.0132895336605294 \tabularnewline
47 & 6.12 & 6.13285607948394 & -0.0128560794839432 \tabularnewline
48 & 6.17 & 6.1324367312246 & 0.0375632687753944 \tabularnewline
49 & 6.17 & 6.17911110103665 & -0.00911110103665358 \tabularnewline
50 & 6.17 & 6.18295059624667 & -0.0129505962466743 \tabularnewline
51 & 6.17 & 6.18290467520981 & -0.0129046752098096 \tabularnewline
52 & 6.17 & 6.18251800805758 & -0.0125180080575849 \tabularnewline
53 & 6.28 & 6.18211280318054 & 0.0978871968194639 \tabularnewline
54 & 6.27 & 6.28529407362649 & -0.0152940736264933 \tabularnewline
55 & 6.28 & 6.28480612097965 & -0.00480612097965416 \tabularnewline
56 & 6.28 & 6.29374016388599 & -0.0137401638859860 \tabularnewline
57 & 6.27 & 6.29411940285017 & -0.0241194028501743 \tabularnewline
58 & 6.27 & 6.28431814551275 & -0.0143181455127532 \tabularnewline
59 & 6.28 & 6.28303061967915 & -0.00303061967915053 \tabularnewline
60 & 6.59 & 6.29194690447444 & 0.298053095525558 \tabularnewline
61 & 6.59 & 6.5842740127427 & 0.00572598725729812 \tabularnewline
62 & 6.59 & 6.61018294755924 & -0.0201829475592383 \tabularnewline
63 & 6.59 & 6.61186578301641 & -0.0218657830164117 \tabularnewline
64 & 6.59 & 6.61136563443691 & -0.0213656344369131 \tabularnewline
65 & 6.63 & 6.61068810533931 & 0.0193118946606905 \tabularnewline
66 & 6.63 & 6.64767908068296 & -0.0176790806829583 \tabularnewline
67 & 6.63 & 6.65041192030449 & -0.020411920304487 \tabularnewline
68 & 6.63 & 6.6500473307745 & -0.0200473307744948 \tabularnewline
69 & 6.63 & 6.64942082526504 & -0.0194208252650405 \tabularnewline
70 & 6.63 & 6.64878983417022 & -0.0187898341702208 \tabularnewline
71 & 6.63 & 6.6481771570202 & -0.0181771570202010 \tabularnewline
72 & 6.63 & 6.64758425828591 & -0.0175842582859076 \tabularnewline
73 & 6.63 & 6.64701068048242 & -0.0170106804824197 \tabularnewline
74 & 6.63 & 6.64645581046264 & -0.016455810462638 \tabularnewline
75 & 6.63 & 6.64591903955336 & -0.0159190395533590 \tabularnewline
76 & 6.63 & 6.64539977752247 & -0.0153997775224735 \tabularnewline
77 & 6.63 & 6.64489745326199 & -0.0148974532619865 \tabularnewline
78 & 6.63 & 6.64441151428113 & -0.0144115142811287 \tabularnewline
79 & 6.63 & 6.64394142610972 & -0.0139414261097217 \tabularnewline
80 & 6.63 & 6.64348667171134 & -0.0134866717113376 \tabularnewline
81 & 6.63 & 6.64304675091471 & -0.0130467509147101 \tabularnewline
82 & 6.79 & 6.64262117986363 & 0.147378820136373 \tabularnewline
83 & 6.79 & 6.79286562608137 & -0.00286562608137153 \tabularnewline
84 & 6.79 & 6.80600955897625 & -0.0160095589762461 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13339&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]5.44[/C][C]5.44[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]5.44[/C][C]5.44[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]5.49[/C][C]5.44[/C][C]0.0499999999999998[/C][/ROW]
[ROW][C]6[/C][C]5.49[/C][C]5.48708004237394[/C][C]0.00291995762605524[/C][/ROW]
[ROW][C]7[/C][C]5.49[/C][C]5.49131197781358[/C][C]-0.00131197781358239[/C][/ROW]
[ROW][C]8[/C][C]5.49[/C][C]5.49164569605087[/C][C]-0.00164569605087017[/C][/ROW]
[ROW][C]9[/C][C]5.49[/C][C]5.49162628474826[/C][C]-0.00162628474825599[/C][/ROW]
[ROW][C]10[/C][C]5.49[/C][C]5.49157635622828[/C][C]-0.00157635622827712[/C][/ROW]
[ROW][C]11[/C][C]5.6[/C][C]5.49152522107412[/C][C]0.108474778925875[/C][/ROW]
[ROW][C]12[/C][C]5.6[/C][C]5.59505158905772[/C][C]0.0049484109422826[/C][/ROW]
[ROW][C]13[/C][C]5.6[/C][C]5.60431372028188[/C][C]-0.00431372028188459[/C][/ROW]
[ROW][C]14[/C][C]5.6[/C][C]5.6050013413659[/C][C]-0.00500134136589558[/C][/ROW]
[ROW][C]15[/C][C]5.6[/C][C]5.60491359597353[/C][C]-0.00491359597352936[/C][/ROW]
[ROW][C]16[/C][C]5.6[/C][C]5.60476018185902[/C][C]-0.00476018185902127[/C][/ROW]
[ROW][C]17[/C][C]5.6[/C][C]5.60460553439919[/C][C]-0.00460553439919398[/C][/ROW]
[ROW][C]18[/C][C]5.67[/C][C]5.60445536364419[/C][C]0.065544636355809[/C][/ROW]
[ROW][C]19[/C][C]5.67[/C][C]5.67022209894834[/C][C]-0.000222098948337468[/C][/ROW]
[ROW][C]20[/C][C]5.67[/C][C]5.67600622015519[/C][C]-0.00600622015518759[/C][/ROW]
[ROW][C]21[/C][C]5.67[/C][C]5.67633742269409[/C][C]-0.00633742269408888[/C][/ROW]
[ROW][C]22[/C][C]5.67[/C][C]5.67617868011024[/C][C]-0.0061786801102448[/C][/ROW]
[ROW][C]23[/C][C]5.67[/C][C]5.67598150498544[/C][C]-0.00598150498544481[/C][/ROW]
[ROW][C]24[/C][C]5.67[/C][C]5.67578679215318[/C][C]-0.00578679215318001[/C][/ROW]
[ROW][C]25[/C][C]5.67[/C][C]5.67559806936257[/C][C]-0.00559806936257168[/C][/ROW]
[ROW][C]26[/C][C]5.67[/C][C]5.67541546962416[/C][C]-0.00541546962416195[/C][/ROW]
[ROW][C]27[/C][C]5.82[/C][C]5.67523882310082[/C][C]0.144761176899185[/C][/ROW]
[ROW][C]28[/C][C]5.82[/C][C]5.81630806544742[/C][C]0.00369193455258365[/C][/ROW]
[ROW][C]29[/C][C]5.95[/C][C]5.82883856104477[/C][C]0.121161438955226[/C][/ROW]
[ROW][C]30[/C][C]5.95[/C][C]5.95208790746389[/C][C]-0.00208790746389109[/C][/ROW]
[ROW][C]31[/C][C]5.95[/C][C]5.96287800360307[/C][C]-0.0128780036030669[/C][/ROW]
[ROW][C]32[/C][C]5.95[/C][C]5.96344622958082[/C][C]-0.0134462295808184[/C][/ROW]
[ROW][C]33[/C][C]5.95[/C][C]5.96309758046691[/C][C]-0.0130975804669085[/C][/ROW]
[ROW][C]34[/C][C]5.95[/C][C]5.96267853871462[/C][C]-0.0126785387146153[/C][/ROW]
[ROW][C]35[/C][C]6.02[/C][C]5.96226572354415[/C][C]0.0577342764558484[/C][/ROW]
[ROW][C]36[/C][C]6.02[/C][C]6.02777775591951[/C][C]-0.00777775591951091[/C][/ROW]
[ROW][C]37[/C][C]6.05[/C][C]6.03331542538513[/C][C]0.0166845746148745[/C][/ROW]
[ROW][C]38[/C][C]6.05[/C][C]6.06165623541576[/C][C]-0.0116562354157601[/C][/ROW]
[ROW][C]39[/C][C]6.05[/C][C]6.06380601262907[/C][C]-0.0138060126290656[/C][/ROW]
[ROW][C]40[/C][C]6.12[/C][C]6.06358595021485[/C][C]0.056414049785146[/C][/ROW]
[ROW][C]41[/C][C]6.12[/C][C]6.12907580956677[/C][C]-0.00907580956677112[/C][/ROW]
[ROW][C]42[/C][C]6.12[/C][C]6.134573039403[/C][C]-0.0145730394029986[/C][/ROW]
[ROW][C]43[/C][C]6.12[/C][C]6.1346249750561[/C][C]-0.0146249750561012[/C][/ROW]
[ROW][C]44[/C][C]6.12[/C][C]6.13419591718401[/C][C]-0.0141959171840087[/C][/ROW]
[ROW][C]45[/C][C]6.12[/C][C]6.13373722980466[/C][C]-0.0137372298046632[/C][/ROW]
[ROW][C]46[/C][C]6.12[/C][C]6.13328953366053[/C][C]-0.0132895336605294[/C][/ROW]
[ROW][C]47[/C][C]6.12[/C][C]6.13285607948394[/C][C]-0.0128560794839432[/C][/ROW]
[ROW][C]48[/C][C]6.17[/C][C]6.1324367312246[/C][C]0.0375632687753944[/C][/ROW]
[ROW][C]49[/C][C]6.17[/C][C]6.17911110103665[/C][C]-0.00911110103665358[/C][/ROW]
[ROW][C]50[/C][C]6.17[/C][C]6.18295059624667[/C][C]-0.0129505962466743[/C][/ROW]
[ROW][C]51[/C][C]6.17[/C][C]6.18290467520981[/C][C]-0.0129046752098096[/C][/ROW]
[ROW][C]52[/C][C]6.17[/C][C]6.18251800805758[/C][C]-0.0125180080575849[/C][/ROW]
[ROW][C]53[/C][C]6.28[/C][C]6.18211280318054[/C][C]0.0978871968194639[/C][/ROW]
[ROW][C]54[/C][C]6.27[/C][C]6.28529407362649[/C][C]-0.0152940736264933[/C][/ROW]
[ROW][C]55[/C][C]6.28[/C][C]6.28480612097965[/C][C]-0.00480612097965416[/C][/ROW]
[ROW][C]56[/C][C]6.28[/C][C]6.29374016388599[/C][C]-0.0137401638859860[/C][/ROW]
[ROW][C]57[/C][C]6.27[/C][C]6.29411940285017[/C][C]-0.0241194028501743[/C][/ROW]
[ROW][C]58[/C][C]6.27[/C][C]6.28431814551275[/C][C]-0.0143181455127532[/C][/ROW]
[ROW][C]59[/C][C]6.28[/C][C]6.28303061967915[/C][C]-0.00303061967915053[/C][/ROW]
[ROW][C]60[/C][C]6.59[/C][C]6.29194690447444[/C][C]0.298053095525558[/C][/ROW]
[ROW][C]61[/C][C]6.59[/C][C]6.5842740127427[/C][C]0.00572598725729812[/C][/ROW]
[ROW][C]62[/C][C]6.59[/C][C]6.61018294755924[/C][C]-0.0201829475592383[/C][/ROW]
[ROW][C]63[/C][C]6.59[/C][C]6.61186578301641[/C][C]-0.0218657830164117[/C][/ROW]
[ROW][C]64[/C][C]6.59[/C][C]6.61136563443691[/C][C]-0.0213656344369131[/C][/ROW]
[ROW][C]65[/C][C]6.63[/C][C]6.61068810533931[/C][C]0.0193118946606905[/C][/ROW]
[ROW][C]66[/C][C]6.63[/C][C]6.64767908068296[/C][C]-0.0176790806829583[/C][/ROW]
[ROW][C]67[/C][C]6.63[/C][C]6.65041192030449[/C][C]-0.020411920304487[/C][/ROW]
[ROW][C]68[/C][C]6.63[/C][C]6.6500473307745[/C][C]-0.0200473307744948[/C][/ROW]
[ROW][C]69[/C][C]6.63[/C][C]6.64942082526504[/C][C]-0.0194208252650405[/C][/ROW]
[ROW][C]70[/C][C]6.63[/C][C]6.64878983417022[/C][C]-0.0187898341702208[/C][/ROW]
[ROW][C]71[/C][C]6.63[/C][C]6.6481771570202[/C][C]-0.0181771570202010[/C][/ROW]
[ROW][C]72[/C][C]6.63[/C][C]6.64758425828591[/C][C]-0.0175842582859076[/C][/ROW]
[ROW][C]73[/C][C]6.63[/C][C]6.64701068048242[/C][C]-0.0170106804824197[/C][/ROW]
[ROW][C]74[/C][C]6.63[/C][C]6.64645581046264[/C][C]-0.016455810462638[/C][/ROW]
[ROW][C]75[/C][C]6.63[/C][C]6.64591903955336[/C][C]-0.0159190395533590[/C][/ROW]
[ROW][C]76[/C][C]6.63[/C][C]6.64539977752247[/C][C]-0.0153997775224735[/C][/ROW]
[ROW][C]77[/C][C]6.63[/C][C]6.64489745326199[/C][C]-0.0148974532619865[/C][/ROW]
[ROW][C]78[/C][C]6.63[/C][C]6.64441151428113[/C][C]-0.0144115142811287[/C][/ROW]
[ROW][C]79[/C][C]6.63[/C][C]6.64394142610972[/C][C]-0.0139414261097217[/C][/ROW]
[ROW][C]80[/C][C]6.63[/C][C]6.64348667171134[/C][C]-0.0134866717113376[/C][/ROW]
[ROW][C]81[/C][C]6.63[/C][C]6.64304675091471[/C][C]-0.0130467509147101[/C][/ROW]
[ROW][C]82[/C][C]6.79[/C][C]6.64262117986363[/C][C]0.147378820136373[/C][/ROW]
[ROW][C]83[/C][C]6.79[/C][C]6.79286562608137[/C][C]-0.00286562608137153[/C][/ROW]
[ROW][C]84[/C][C]6.79[/C][C]6.80600955897625[/C][C]-0.0160095589762461[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13339&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13339&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	5.44	5.44	0
4	5.44	5.44	0
5	5.49	5.44	0.0499999999999998
6	5.49	5.48708004237394	0.00291995762605524
7	5.49	5.49131197781358	-0.00131197781358239
8	5.49	5.49164569605087	-0.00164569605087017
9	5.49	5.49162628474826	-0.00162628474825599
10	5.49	5.49157635622828	-0.00157635622827712
11	5.6	5.49152522107412	0.108474778925875
12	5.6	5.59505158905772	0.0049484109422826
13	5.6	5.60431372028188	-0.00431372028188459
14	5.6	5.6050013413659	-0.00500134136589558
15	5.6	5.60491359597353	-0.00491359597352936
16	5.6	5.60476018185902	-0.00476018185902127
17	5.6	5.60460553439919	-0.00460553439919398
18	5.67	5.60445536364419	0.065544636355809
19	5.67	5.67022209894834	-0.000222098948337468
20	5.67	5.67600622015519	-0.00600622015518759
21	5.67	5.67633742269409	-0.00633742269408888
22	5.67	5.67617868011024	-0.0061786801102448
23	5.67	5.67598150498544	-0.00598150498544481
24	5.67	5.67578679215318	-0.00578679215318001
25	5.67	5.67559806936257	-0.00559806936257168
26	5.67	5.67541546962416	-0.00541546962416195
27	5.82	5.67523882310082	0.144761176899185
28	5.82	5.81630806544742	0.00369193455258365
29	5.95	5.82883856104477	0.121161438955226
30	5.95	5.95208790746389	-0.00208790746389109
31	5.95	5.96287800360307	-0.0128780036030669
32	5.95	5.96344622958082	-0.0134462295808184
33	5.95	5.96309758046691	-0.0130975804669085
34	5.95	5.96267853871462	-0.0126785387146153
35	6.02	5.96226572354415	0.0577342764558484
36	6.02	6.02777775591951	-0.00777775591951091
37	6.05	6.03331542538513	0.0166845746148745
38	6.05	6.06165623541576	-0.0116562354157601
39	6.05	6.06380601262907	-0.0138060126290656
40	6.12	6.06358595021485	0.056414049785146
41	6.12	6.12907580956677	-0.00907580956677112
42	6.12	6.134573039403	-0.0145730394029986
43	6.12	6.1346249750561	-0.0146249750561012
44	6.12	6.13419591718401	-0.0141959171840087
45	6.12	6.13373722980466	-0.0137372298046632
46	6.12	6.13328953366053	-0.0132895336605294
47	6.12	6.13285607948394	-0.0128560794839432
48	6.17	6.1324367312246	0.0375632687753944
49	6.17	6.17911110103665	-0.00911110103665358
50	6.17	6.18295059624667	-0.0129505962466743
51	6.17	6.18290467520981	-0.0129046752098096
52	6.17	6.18251800805758	-0.0125180080575849
53	6.28	6.18211280318054	0.0978871968194639
54	6.27	6.28529407362649	-0.0152940736264933
55	6.28	6.28480612097965	-0.00480612097965416
56	6.28	6.29374016388599	-0.0137401638859860
57	6.27	6.29411940285017	-0.0241194028501743
58	6.27	6.28431814551275	-0.0143181455127532
59	6.28	6.28303061967915	-0.00303061967915053
60	6.59	6.29194690447444	0.298053095525558
61	6.59	6.5842740127427	0.00572598725729812
62	6.59	6.61018294755924	-0.0201829475592383
63	6.59	6.61186578301641	-0.0218657830164117
64	6.59	6.61136563443691	-0.0213656344369131
65	6.63	6.61068810533931	0.0193118946606905
66	6.63	6.64767908068296	-0.0176790806829583
67	6.63	6.65041192030449	-0.020411920304487
68	6.63	6.6500473307745	-0.0200473307744948
69	6.63	6.64942082526504	-0.0194208252650405
70	6.63	6.64878983417022	-0.0187898341702208
71	6.63	6.6481771570202	-0.0181771570202010
72	6.63	6.64758425828591	-0.0175842582859076
73	6.63	6.64701068048242	-0.0170106804824197
74	6.63	6.64645581046264	-0.016455810462638
75	6.63	6.64591903955336	-0.0159190395533590
76	6.63	6.64539977752247	-0.0153997775224735
77	6.63	6.64489745326199	-0.0148974532619865
78	6.63	6.64441151428113	-0.0144115142811287
79	6.63	6.64394142610972	-0.0139414261097217
80	6.63	6.64348667171134	-0.0134866717113376
81	6.63	6.64304675091471	-0.0130467509147101
82	6.79	6.64262117986363	0.147378820136373
83	6.79	6.79286562608137	-0.00286562608137153
84	6.79	6.80600955897625	-0.0160095589762461

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	6.80669218765525	6.71167166030342	6.90171271500708
86	6.82197474693365	6.69146025095177	6.95248924291554
87	6.83725730621205	6.67740972064516	6.99710489177895
88	6.85253986549045	6.66653871897092	7.03854101200999
89	6.86782242476886	6.6576191032339	7.07802574630381
90	6.88310498404726	6.6500081044399	7.11620186365461
91	6.89838754332566	6.64332194737134	7.15345313927997
92	6.91367010260406	6.6373112411707	7.19002896403742
93	6.92895266188246	6.63180401813626	7.22610130562866
94	6.94423522116086	6.6266763733235	7.26179406899823
95	6.95951778043926	6.62183596066007	7.29719960021845
96	6.97480033971766	6.61721208455978	7.33238859487555

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 6.80669218765525 & 6.71167166030342 & 6.90171271500708 \tabularnewline
86 & 6.82197474693365 & 6.69146025095177 & 6.95248924291554 \tabularnewline
87 & 6.83725730621205 & 6.67740972064516 & 6.99710489177895 \tabularnewline
88 & 6.85253986549045 & 6.66653871897092 & 7.03854101200999 \tabularnewline
89 & 6.86782242476886 & 6.6576191032339 & 7.07802574630381 \tabularnewline
90 & 6.88310498404726 & 6.6500081044399 & 7.11620186365461 \tabularnewline
91 & 6.89838754332566 & 6.64332194737134 & 7.15345313927997 \tabularnewline
92 & 6.91367010260406 & 6.6373112411707 & 7.19002896403742 \tabularnewline
93 & 6.92895266188246 & 6.63180401813626 & 7.22610130562866 \tabularnewline
94 & 6.94423522116086 & 6.6266763733235 & 7.26179406899823 \tabularnewline
95 & 6.95951778043926 & 6.62183596066007 & 7.29719960021845 \tabularnewline
96 & 6.97480033971766 & 6.61721208455978 & 7.33238859487555 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13339&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]6.80669218765525[/C][C]6.71167166030342[/C][C]6.90171271500708[/C][/ROW]
[ROW][C]86[/C][C]6.82197474693365[/C][C]6.69146025095177[/C][C]6.95248924291554[/C][/ROW]
[ROW][C]87[/C][C]6.83725730621205[/C][C]6.67740972064516[/C][C]6.99710489177895[/C][/ROW]
[ROW][C]88[/C][C]6.85253986549045[/C][C]6.66653871897092[/C][C]7.03854101200999[/C][/ROW]
[ROW][C]89[/C][C]6.86782242476886[/C][C]6.6576191032339[/C][C]7.07802574630381[/C][/ROW]
[ROW][C]90[/C][C]6.88310498404726[/C][C]6.6500081044399[/C][C]7.11620186365461[/C][/ROW]
[ROW][C]91[/C][C]6.89838754332566[/C][C]6.64332194737134[/C][C]7.15345313927997[/C][/ROW]
[ROW][C]92[/C][C]6.91367010260406[/C][C]6.6373112411707[/C][C]7.19002896403742[/C][/ROW]
[ROW][C]93[/C][C]6.92895266188246[/C][C]6.63180401813626[/C][C]7.22610130562866[/C][/ROW]
[ROW][C]94[/C][C]6.94423522116086[/C][C]6.6266763733235[/C][C]7.26179406899823[/C][/ROW]
[ROW][C]95[/C][C]6.95951778043926[/C][C]6.62183596066007[/C][C]7.29719960021845[/C][/ROW]
[ROW][C]96[/C][C]6.97480033971766[/C][C]6.61721208455978[/C][C]7.33238859487555[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13339&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13339&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	6.80669218765525	6.71167166030342	6.90171271500708
86	6.82197474693365	6.69146025095177	6.95248924291554
87	6.83725730621205	6.67740972064516	6.99710489177895
88	6.85253986549045	6.66653871897092	7.03854101200999
89	6.86782242476886	6.6576191032339	7.07802574630381
90	6.88310498404726	6.6500081044399	7.11620186365461
91	6.89838754332566	6.64332194737134	7.15345313927997
92	6.91367010260406	6.6373112411707	7.19002896403742
93	6.92895266188246	6.63180401813626	7.22610130562866
94	6.94423522116086	6.6266763733235	7.26179406899823
95	6.95951778043926	6.62183596066007	7.29719960021845
96	6.97480033971766	6.61721208455978	7.33238859487555

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