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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Tue, 26 Apr 2016 21:50:42 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Apr/26/t1461703866hsgj07p0np0vunl.htm/, Retrieved Sat, 04 May 2024 01:45:19 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294982, Retrieved Sat, 04 May 2024 01:45:19 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

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

-       [Exponential Smoothing] [Opgave 10 oef 2] [2016-04-26 20:50:42] [76c30f62b7052b57088120e90a652e05] [Current]
- RMPD    [Bootstrap Plot - Central Tendency] [Opgave 11 oef 1 5...] [2016-05-02 22:34:44] [2f0f353a58a70fd7baf0f5141860d820] 
- R P       [Bootstrap Plot - Central Tendency] [Opgave 11 oef 1 2...] [2016-05-02 22:39:46] [2f0f353a58a70fd7baf0f5141860d820] 
- R P       [Bootstrap Plot - Central Tendency] [Opgave 11 oef 1 7...] [2016-05-02 22:43:32] [2f0f353a58a70fd7baf0f5141860d820] 
- R  D      [Bootstrap Plot - Central Tendency] [Opgave 11 oef 2 5...] [2016-05-02 22:50:23] [2f0f353a58a70fd7baf0f5141860d820] 
- R PD      [Bootstrap Plot - Central Tendency] [Opgave 11 oef 2 2...] [2016-05-02 22:53:23] [2f0f353a58a70fd7baf0f5141860d820] 
- R PD      [Bootstrap Plot - Central Tendency] [Opgave 11 oef 2 7...] [2016-05-02 22:55:53] [2f0f353a58a70fd7baf0f5141860d820] 

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Dataseries X:

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Histogram

Boxplots

96,86
96,89
96,9
96,94
96,88
96,89
96,89
96,95
97,03
97,29
97,11733333
97,14739394
97,17745455
97,20751515
97,23757576
97,26763636
97,29769697
97,32775758
97,35781818
97,38787879
97,41793939
97,9
97,98
98,03
98,03
97,94
98,12
98,19
98,34
98,42
98,43
98,45
98,77
99,24
99,46
99,54
99,55
99,24
99,43
99,47
99,57
99,62
99,64
99,75
99,85
100,28
100,52
100,57
100,57
100,27
100,27
100,18
100,16
100,18
100,18
100,59
100,69
101,06
101,15
101,16
101,16
100,81
100,94
101,13
101,29
101,34
101,35
101,7
102,05
102,48
102,66
102,72
102,73
102,18
102,22
102,37
102,53
102,61
102,62
103
103,17
103,52
103,69
103,73
99,57
99,09
99,14
99,36
99,6
99,65
99,8
100,15
100,45
100,89
101,13
101,17
101,21
101,1
101,17
101,11
101,2
101,15
100,92
101,1
101,22
101,25
101,39
101,43

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294982&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294982&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294982&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	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.935465964560229
beta	0
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.935465964560229 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294982&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]0.935465964560229[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294982&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294982&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	0.935465964560229
beta	0
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	97.17745455	96.9823327385524	0.195121811447621
14	97.20751515	97.1947966157646	0.0127185342353755
15	97.23757576	97.2399567282372	-0.00238096823723311
16	97.26763636	97.2638200429816	0.00381631701839069
17	97.29769697	97.273700413822	0.0239965561780338
18	97.32775758	97.2911001257195	0.0366574542804869
19	97.35781818	97.358954780206	-0.00113660020599582
20	97.38787879	97.4290452959743	-0.0411665059743171
21	97.41793939	97.4808508135818	-0.0629114235818236
22	97.9	97.691892983782	0.208107016218008
23	97.98	97.7204586264331	0.25954137356689
24	98.03	97.9952782556265	0.0347217443734849
25	98.03	98.0702903876895	-0.0402903876894527
26	97.94	98.0507629454108	-0.110762945410769
27	98.12	97.9794359045932	0.140564095406816
28	98.19	98.1374193970048	0.0525806029952207
29	98.34	98.1942194099316	0.145780590068355
30	98.42	98.3263609994073	0.0936390005927166
31	98.43	98.4450809482252	-0.0150809482252185
32	98.45	98.4995437096661	-0.0495437096660822
33	98.77	98.5421093510582	0.227890648941766
34	99.24	99.0426768761267	0.197323123873318
35	99.46	99.0644738211638	0.395526178836178
36	99.54	99.4519940894661	0.088005910533937
37	99.55	99.5720109098331	-0.0220109098331136
38	99.24	99.5650354184014	-0.325035418401441
39	99.43	99.309482920118	0.120517079881964
40	99.47	99.4430351819977	0.0269648180022841
41	99.57	99.481887071177	0.0881129288230369
42	99.62	99.5567176191187	0.0632823808813043
43	99.64	99.6400238463675	-2.38463674975264e-05
44	99.75	99.706347993053	0.0436520069469992
45	99.85	99.8539990141101	-0.00399901411009296
46	100.28	100.135669006114	0.144330993885887
47	100.52	100.120684460132	0.399315539868297
48	100.57	100.491904022814	0.0780959771861234
49	100.57	100.595550608438	-0.0255506084384365
50	100.27	100.565708455062	-0.2957084550616
51	100.27	100.366343633541	-0.0963436335410393
52	100.18	100.29099277398	-0.110992773979632
53	100.16	100.204736165658	-0.0447361656578948
54	100.18	100.153688491829	0.0263115081707923
55	100.18	100.198324319664	-0.0183243196644014
56	100.59	100.250347575511	0.339652424489032
57	100.69	100.671821799993	0.018178200007398
58	101.06	100.983810154985	0.0761898450148948
59	101.15	100.921537065175	0.228462934825146
60	101.16	101.112200236241	0.0477997637593575
61	101.16	101.18081701292	-0.0208170129195082
62	100.81	101.137968600992	-0.327968600992321
63	100.94	100.921291327399	0.0187086726007237
64	101.13	100.952622616229	0.177377383770562
65	101.29	101.140402281987	0.1495977180126
66	101.34	101.275732335194	0.0642676648059535
67	101.35	101.352994325612	-0.00299432561156721
68	101.7	101.442459953025	0.257540046974711
69	102.05	101.766374814077	0.283625185922517
70	102.48	102.330423515344	0.149576484656478
71	102.66	102.346627926146	0.313372073854239
72	102.72	102.605061783369	0.114938216630861
73	102.73	102.732056180125	-0.00205618012455488
74	102.18	102.686936157274	-0.506936157273785
75	102.22	102.325213309479	-0.105213309479126
76	102.37	102.250859334043	0.119140665957445
77	102.53	102.382367798464	0.14763220153587
78	102.61	102.510352485226	0.0996475147737073
79	102.62	102.616370433447	0.00362956655348512
80	103	102.728845820967	0.271154179032663
81	103.17	103.067179618478	0.102820381521937
82	103.52	103.45344087536	0.0665591246397526
83	103.69	103.402555761757	0.287444238242642
84	103.73	103.623929273657	0.106070726343134
85	99.57	103.735078314511	-4.16507831451059
86	99.09	99.7630108328926	-0.673010832892629
87	99.14	99.2718555749777	-0.131855574977706
88	99.36	99.1870571343503	0.172942865649674
89	99.6	99.3707343991692	0.229265600830786
90	99.65	99.571987707067	0.0780122929329679
91	99.8	99.6515702159463	0.148429784053747
92	100.15	99.9167657214222	0.233234278577783
93	100.45	100.208763483424	0.241236516576379
94	100.89	100.722168238358	0.167831761641523
95	101.13	100.780274837561	0.349725162438631
96	101.17	101.048205269643	0.12179473035718
97	101.21	100.898429097507	0.311570902492704
98	101.1	101.339471800288	-0.23947180028793
99	101.17	101.288800484276	-0.118800484275766
100	101.11	101.235884510034	-0.125884510033714
101	101.2	101.14365366901	0.0563463309898253
102	101.15	101.173385899023	-0.0233858990229123
103	100.92	101.162658175327	-0.242658175327037
104	101.1	101.067476981908	0.0325230180919363
105	101.22	101.172232607732	0.0477673922684261
106	101.25	101.499916476627	-0.249916476626666
107	101.39	101.178972132348	0.211027867652035
108	101.43	101.302446695198	0.127553304801779

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 97.17745455 & 96.9823327385524 & 0.195121811447621 \tabularnewline
14 & 97.20751515 & 97.1947966157646 & 0.0127185342353755 \tabularnewline
15 & 97.23757576 & 97.2399567282372 & -0.00238096823723311 \tabularnewline
16 & 97.26763636 & 97.2638200429816 & 0.00381631701839069 \tabularnewline
17 & 97.29769697 & 97.273700413822 & 0.0239965561780338 \tabularnewline
18 & 97.32775758 & 97.2911001257195 & 0.0366574542804869 \tabularnewline
19 & 97.35781818 & 97.358954780206 & -0.00113660020599582 \tabularnewline
20 & 97.38787879 & 97.4290452959743 & -0.0411665059743171 \tabularnewline
21 & 97.41793939 & 97.4808508135818 & -0.0629114235818236 \tabularnewline
22 & 97.9 & 97.691892983782 & 0.208107016218008 \tabularnewline
23 & 97.98 & 97.7204586264331 & 0.25954137356689 \tabularnewline
24 & 98.03 & 97.9952782556265 & 0.0347217443734849 \tabularnewline
25 & 98.03 & 98.0702903876895 & -0.0402903876894527 \tabularnewline
26 & 97.94 & 98.0507629454108 & -0.110762945410769 \tabularnewline
27 & 98.12 & 97.9794359045932 & 0.140564095406816 \tabularnewline
28 & 98.19 & 98.1374193970048 & 0.0525806029952207 \tabularnewline
29 & 98.34 & 98.1942194099316 & 0.145780590068355 \tabularnewline
30 & 98.42 & 98.3263609994073 & 0.0936390005927166 \tabularnewline
31 & 98.43 & 98.4450809482252 & -0.0150809482252185 \tabularnewline
32 & 98.45 & 98.4995437096661 & -0.0495437096660822 \tabularnewline
33 & 98.77 & 98.5421093510582 & 0.227890648941766 \tabularnewline
34 & 99.24 & 99.0426768761267 & 0.197323123873318 \tabularnewline
35 & 99.46 & 99.0644738211638 & 0.395526178836178 \tabularnewline
36 & 99.54 & 99.4519940894661 & 0.088005910533937 \tabularnewline
37 & 99.55 & 99.5720109098331 & -0.0220109098331136 \tabularnewline
38 & 99.24 & 99.5650354184014 & -0.325035418401441 \tabularnewline
39 & 99.43 & 99.309482920118 & 0.120517079881964 \tabularnewline
40 & 99.47 & 99.4430351819977 & 0.0269648180022841 \tabularnewline
41 & 99.57 & 99.481887071177 & 0.0881129288230369 \tabularnewline
42 & 99.62 & 99.5567176191187 & 0.0632823808813043 \tabularnewline
43 & 99.64 & 99.6400238463675 & -2.38463674975264e-05 \tabularnewline
44 & 99.75 & 99.706347993053 & 0.0436520069469992 \tabularnewline
45 & 99.85 & 99.8539990141101 & -0.00399901411009296 \tabularnewline
46 & 100.28 & 100.135669006114 & 0.144330993885887 \tabularnewline
47 & 100.52 & 100.120684460132 & 0.399315539868297 \tabularnewline
48 & 100.57 & 100.491904022814 & 0.0780959771861234 \tabularnewline
49 & 100.57 & 100.595550608438 & -0.0255506084384365 \tabularnewline
50 & 100.27 & 100.565708455062 & -0.2957084550616 \tabularnewline
51 & 100.27 & 100.366343633541 & -0.0963436335410393 \tabularnewline
52 & 100.18 & 100.29099277398 & -0.110992773979632 \tabularnewline
53 & 100.16 & 100.204736165658 & -0.0447361656578948 \tabularnewline
54 & 100.18 & 100.153688491829 & 0.0263115081707923 \tabularnewline
55 & 100.18 & 100.198324319664 & -0.0183243196644014 \tabularnewline
56 & 100.59 & 100.250347575511 & 0.339652424489032 \tabularnewline
57 & 100.69 & 100.671821799993 & 0.018178200007398 \tabularnewline
58 & 101.06 & 100.983810154985 & 0.0761898450148948 \tabularnewline
59 & 101.15 & 100.921537065175 & 0.228462934825146 \tabularnewline
60 & 101.16 & 101.112200236241 & 0.0477997637593575 \tabularnewline
61 & 101.16 & 101.18081701292 & -0.0208170129195082 \tabularnewline
62 & 100.81 & 101.137968600992 & -0.327968600992321 \tabularnewline
63 & 100.94 & 100.921291327399 & 0.0187086726007237 \tabularnewline
64 & 101.13 & 100.952622616229 & 0.177377383770562 \tabularnewline
65 & 101.29 & 101.140402281987 & 0.1495977180126 \tabularnewline
66 & 101.34 & 101.275732335194 & 0.0642676648059535 \tabularnewline
67 & 101.35 & 101.352994325612 & -0.00299432561156721 \tabularnewline
68 & 101.7 & 101.442459953025 & 0.257540046974711 \tabularnewline
69 & 102.05 & 101.766374814077 & 0.283625185922517 \tabularnewline
70 & 102.48 & 102.330423515344 & 0.149576484656478 \tabularnewline
71 & 102.66 & 102.346627926146 & 0.313372073854239 \tabularnewline
72 & 102.72 & 102.605061783369 & 0.114938216630861 \tabularnewline
73 & 102.73 & 102.732056180125 & -0.00205618012455488 \tabularnewline
74 & 102.18 & 102.686936157274 & -0.506936157273785 \tabularnewline
75 & 102.22 & 102.325213309479 & -0.105213309479126 \tabularnewline
76 & 102.37 & 102.250859334043 & 0.119140665957445 \tabularnewline
77 & 102.53 & 102.382367798464 & 0.14763220153587 \tabularnewline
78 & 102.61 & 102.510352485226 & 0.0996475147737073 \tabularnewline
79 & 102.62 & 102.616370433447 & 0.00362956655348512 \tabularnewline
80 & 103 & 102.728845820967 & 0.271154179032663 \tabularnewline
81 & 103.17 & 103.067179618478 & 0.102820381521937 \tabularnewline
82 & 103.52 & 103.45344087536 & 0.0665591246397526 \tabularnewline
83 & 103.69 & 103.402555761757 & 0.287444238242642 \tabularnewline
84 & 103.73 & 103.623929273657 & 0.106070726343134 \tabularnewline
85 & 99.57 & 103.735078314511 & -4.16507831451059 \tabularnewline
86 & 99.09 & 99.7630108328926 & -0.673010832892629 \tabularnewline
87 & 99.14 & 99.2718555749777 & -0.131855574977706 \tabularnewline
88 & 99.36 & 99.1870571343503 & 0.172942865649674 \tabularnewline
89 & 99.6 & 99.3707343991692 & 0.229265600830786 \tabularnewline
90 & 99.65 & 99.571987707067 & 0.0780122929329679 \tabularnewline
91 & 99.8 & 99.6515702159463 & 0.148429784053747 \tabularnewline
92 & 100.15 & 99.9167657214222 & 0.233234278577783 \tabularnewline
93 & 100.45 & 100.208763483424 & 0.241236516576379 \tabularnewline
94 & 100.89 & 100.722168238358 & 0.167831761641523 \tabularnewline
95 & 101.13 & 100.780274837561 & 0.349725162438631 \tabularnewline
96 & 101.17 & 101.048205269643 & 0.12179473035718 \tabularnewline
97 & 101.21 & 100.898429097507 & 0.311570902492704 \tabularnewline
98 & 101.1 & 101.339471800288 & -0.23947180028793 \tabularnewline
99 & 101.17 & 101.288800484276 & -0.118800484275766 \tabularnewline
100 & 101.11 & 101.235884510034 & -0.125884510033714 \tabularnewline
101 & 101.2 & 101.14365366901 & 0.0563463309898253 \tabularnewline
102 & 101.15 & 101.173385899023 & -0.0233858990229123 \tabularnewline
103 & 100.92 & 101.162658175327 & -0.242658175327037 \tabularnewline
104 & 101.1 & 101.067476981908 & 0.0325230180919363 \tabularnewline
105 & 101.22 & 101.172232607732 & 0.0477673922684261 \tabularnewline
106 & 101.25 & 101.499916476627 & -0.249916476626666 \tabularnewline
107 & 101.39 & 101.178972132348 & 0.211027867652035 \tabularnewline
108 & 101.43 & 101.302446695198 & 0.127553304801779 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294982&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]97.17745455[/C][C]96.9823327385524[/C][C]0.195121811447621[/C][/ROW]
[ROW][C]14[/C][C]97.20751515[/C][C]97.1947966157646[/C][C]0.0127185342353755[/C][/ROW]
[ROW][C]15[/C][C]97.23757576[/C][C]97.2399567282372[/C][C]-0.00238096823723311[/C][/ROW]
[ROW][C]16[/C][C]97.26763636[/C][C]97.2638200429816[/C][C]0.00381631701839069[/C][/ROW]
[ROW][C]17[/C][C]97.29769697[/C][C]97.273700413822[/C][C]0.0239965561780338[/C][/ROW]
[ROW][C]18[/C][C]97.32775758[/C][C]97.2911001257195[/C][C]0.0366574542804869[/C][/ROW]
[ROW][C]19[/C][C]97.35781818[/C][C]97.358954780206[/C][C]-0.00113660020599582[/C][/ROW]
[ROW][C]20[/C][C]97.38787879[/C][C]97.4290452959743[/C][C]-0.0411665059743171[/C][/ROW]
[ROW][C]21[/C][C]97.41793939[/C][C]97.4808508135818[/C][C]-0.0629114235818236[/C][/ROW]
[ROW][C]22[/C][C]97.9[/C][C]97.691892983782[/C][C]0.208107016218008[/C][/ROW]
[ROW][C]23[/C][C]97.98[/C][C]97.7204586264331[/C][C]0.25954137356689[/C][/ROW]
[ROW][C]24[/C][C]98.03[/C][C]97.9952782556265[/C][C]0.0347217443734849[/C][/ROW]
[ROW][C]25[/C][C]98.03[/C][C]98.0702903876895[/C][C]-0.0402903876894527[/C][/ROW]
[ROW][C]26[/C][C]97.94[/C][C]98.0507629454108[/C][C]-0.110762945410769[/C][/ROW]
[ROW][C]27[/C][C]98.12[/C][C]97.9794359045932[/C][C]0.140564095406816[/C][/ROW]
[ROW][C]28[/C][C]98.19[/C][C]98.1374193970048[/C][C]0.0525806029952207[/C][/ROW]
[ROW][C]29[/C][C]98.34[/C][C]98.1942194099316[/C][C]0.145780590068355[/C][/ROW]
[ROW][C]30[/C][C]98.42[/C][C]98.3263609994073[/C][C]0.0936390005927166[/C][/ROW]
[ROW][C]31[/C][C]98.43[/C][C]98.4450809482252[/C][C]-0.0150809482252185[/C][/ROW]
[ROW][C]32[/C][C]98.45[/C][C]98.4995437096661[/C][C]-0.0495437096660822[/C][/ROW]
[ROW][C]33[/C][C]98.77[/C][C]98.5421093510582[/C][C]0.227890648941766[/C][/ROW]
[ROW][C]34[/C][C]99.24[/C][C]99.0426768761267[/C][C]0.197323123873318[/C][/ROW]
[ROW][C]35[/C][C]99.46[/C][C]99.0644738211638[/C][C]0.395526178836178[/C][/ROW]
[ROW][C]36[/C][C]99.54[/C][C]99.4519940894661[/C][C]0.088005910533937[/C][/ROW]
[ROW][C]37[/C][C]99.55[/C][C]99.5720109098331[/C][C]-0.0220109098331136[/C][/ROW]
[ROW][C]38[/C][C]99.24[/C][C]99.5650354184014[/C][C]-0.325035418401441[/C][/ROW]
[ROW][C]39[/C][C]99.43[/C][C]99.309482920118[/C][C]0.120517079881964[/C][/ROW]
[ROW][C]40[/C][C]99.47[/C][C]99.4430351819977[/C][C]0.0269648180022841[/C][/ROW]
[ROW][C]41[/C][C]99.57[/C][C]99.481887071177[/C][C]0.0881129288230369[/C][/ROW]
[ROW][C]42[/C][C]99.62[/C][C]99.5567176191187[/C][C]0.0632823808813043[/C][/ROW]
[ROW][C]43[/C][C]99.64[/C][C]99.6400238463675[/C][C]-2.38463674975264e-05[/C][/ROW]
[ROW][C]44[/C][C]99.75[/C][C]99.706347993053[/C][C]0.0436520069469992[/C][/ROW]
[ROW][C]45[/C][C]99.85[/C][C]99.8539990141101[/C][C]-0.00399901411009296[/C][/ROW]
[ROW][C]46[/C][C]100.28[/C][C]100.135669006114[/C][C]0.144330993885887[/C][/ROW]
[ROW][C]47[/C][C]100.52[/C][C]100.120684460132[/C][C]0.399315539868297[/C][/ROW]
[ROW][C]48[/C][C]100.57[/C][C]100.491904022814[/C][C]0.0780959771861234[/C][/ROW]
[ROW][C]49[/C][C]100.57[/C][C]100.595550608438[/C][C]-0.0255506084384365[/C][/ROW]
[ROW][C]50[/C][C]100.27[/C][C]100.565708455062[/C][C]-0.2957084550616[/C][/ROW]
[ROW][C]51[/C][C]100.27[/C][C]100.366343633541[/C][C]-0.0963436335410393[/C][/ROW]
[ROW][C]52[/C][C]100.18[/C][C]100.29099277398[/C][C]-0.110992773979632[/C][/ROW]
[ROW][C]53[/C][C]100.16[/C][C]100.204736165658[/C][C]-0.0447361656578948[/C][/ROW]
[ROW][C]54[/C][C]100.18[/C][C]100.153688491829[/C][C]0.0263115081707923[/C][/ROW]
[ROW][C]55[/C][C]100.18[/C][C]100.198324319664[/C][C]-0.0183243196644014[/C][/ROW]
[ROW][C]56[/C][C]100.59[/C][C]100.250347575511[/C][C]0.339652424489032[/C][/ROW]
[ROW][C]57[/C][C]100.69[/C][C]100.671821799993[/C][C]0.018178200007398[/C][/ROW]
[ROW][C]58[/C][C]101.06[/C][C]100.983810154985[/C][C]0.0761898450148948[/C][/ROW]
[ROW][C]59[/C][C]101.15[/C][C]100.921537065175[/C][C]0.228462934825146[/C][/ROW]
[ROW][C]60[/C][C]101.16[/C][C]101.112200236241[/C][C]0.0477997637593575[/C][/ROW]
[ROW][C]61[/C][C]101.16[/C][C]101.18081701292[/C][C]-0.0208170129195082[/C][/ROW]
[ROW][C]62[/C][C]100.81[/C][C]101.137968600992[/C][C]-0.327968600992321[/C][/ROW]
[ROW][C]63[/C][C]100.94[/C][C]100.921291327399[/C][C]0.0187086726007237[/C][/ROW]
[ROW][C]64[/C][C]101.13[/C][C]100.952622616229[/C][C]0.177377383770562[/C][/ROW]
[ROW][C]65[/C][C]101.29[/C][C]101.140402281987[/C][C]0.1495977180126[/C][/ROW]
[ROW][C]66[/C][C]101.34[/C][C]101.275732335194[/C][C]0.0642676648059535[/C][/ROW]
[ROW][C]67[/C][C]101.35[/C][C]101.352994325612[/C][C]-0.00299432561156721[/C][/ROW]
[ROW][C]68[/C][C]101.7[/C][C]101.442459953025[/C][C]0.257540046974711[/C][/ROW]
[ROW][C]69[/C][C]102.05[/C][C]101.766374814077[/C][C]0.283625185922517[/C][/ROW]
[ROW][C]70[/C][C]102.48[/C][C]102.330423515344[/C][C]0.149576484656478[/C][/ROW]
[ROW][C]71[/C][C]102.66[/C][C]102.346627926146[/C][C]0.313372073854239[/C][/ROW]
[ROW][C]72[/C][C]102.72[/C][C]102.605061783369[/C][C]0.114938216630861[/C][/ROW]
[ROW][C]73[/C][C]102.73[/C][C]102.732056180125[/C][C]-0.00205618012455488[/C][/ROW]
[ROW][C]74[/C][C]102.18[/C][C]102.686936157274[/C][C]-0.506936157273785[/C][/ROW]
[ROW][C]75[/C][C]102.22[/C][C]102.325213309479[/C][C]-0.105213309479126[/C][/ROW]
[ROW][C]76[/C][C]102.37[/C][C]102.250859334043[/C][C]0.119140665957445[/C][/ROW]
[ROW][C]77[/C][C]102.53[/C][C]102.382367798464[/C][C]0.14763220153587[/C][/ROW]
[ROW][C]78[/C][C]102.61[/C][C]102.510352485226[/C][C]0.0996475147737073[/C][/ROW]
[ROW][C]79[/C][C]102.62[/C][C]102.616370433447[/C][C]0.00362956655348512[/C][/ROW]
[ROW][C]80[/C][C]103[/C][C]102.728845820967[/C][C]0.271154179032663[/C][/ROW]
[ROW][C]81[/C][C]103.17[/C][C]103.067179618478[/C][C]0.102820381521937[/C][/ROW]
[ROW][C]82[/C][C]103.52[/C][C]103.45344087536[/C][C]0.0665591246397526[/C][/ROW]
[ROW][C]83[/C][C]103.69[/C][C]103.402555761757[/C][C]0.287444238242642[/C][/ROW]
[ROW][C]84[/C][C]103.73[/C][C]103.623929273657[/C][C]0.106070726343134[/C][/ROW]
[ROW][C]85[/C][C]99.57[/C][C]103.735078314511[/C][C]-4.16507831451059[/C][/ROW]
[ROW][C]86[/C][C]99.09[/C][C]99.7630108328926[/C][C]-0.673010832892629[/C][/ROW]
[ROW][C]87[/C][C]99.14[/C][C]99.2718555749777[/C][C]-0.131855574977706[/C][/ROW]
[ROW][C]88[/C][C]99.36[/C][C]99.1870571343503[/C][C]0.172942865649674[/C][/ROW]
[ROW][C]89[/C][C]99.6[/C][C]99.3707343991692[/C][C]0.229265600830786[/C][/ROW]
[ROW][C]90[/C][C]99.65[/C][C]99.571987707067[/C][C]0.0780122929329679[/C][/ROW]
[ROW][C]91[/C][C]99.8[/C][C]99.6515702159463[/C][C]0.148429784053747[/C][/ROW]
[ROW][C]92[/C][C]100.15[/C][C]99.9167657214222[/C][C]0.233234278577783[/C][/ROW]
[ROW][C]93[/C][C]100.45[/C][C]100.208763483424[/C][C]0.241236516576379[/C][/ROW]
[ROW][C]94[/C][C]100.89[/C][C]100.722168238358[/C][C]0.167831761641523[/C][/ROW]
[ROW][C]95[/C][C]101.13[/C][C]100.780274837561[/C][C]0.349725162438631[/C][/ROW]
[ROW][C]96[/C][C]101.17[/C][C]101.048205269643[/C][C]0.12179473035718[/C][/ROW]
[ROW][C]97[/C][C]101.21[/C][C]100.898429097507[/C][C]0.311570902492704[/C][/ROW]
[ROW][C]98[/C][C]101.1[/C][C]101.339471800288[/C][C]-0.23947180028793[/C][/ROW]
[ROW][C]99[/C][C]101.17[/C][C]101.288800484276[/C][C]-0.118800484275766[/C][/ROW]
[ROW][C]100[/C][C]101.11[/C][C]101.235884510034[/C][C]-0.125884510033714[/C][/ROW]
[ROW][C]101[/C][C]101.2[/C][C]101.14365366901[/C][C]0.0563463309898253[/C][/ROW]
[ROW][C]102[/C][C]101.15[/C][C]101.173385899023[/C][C]-0.0233858990229123[/C][/ROW]
[ROW][C]103[/C][C]100.92[/C][C]101.162658175327[/C][C]-0.242658175327037[/C][/ROW]
[ROW][C]104[/C][C]101.1[/C][C]101.067476981908[/C][C]0.0325230180919363[/C][/ROW]
[ROW][C]105[/C][C]101.22[/C][C]101.172232607732[/C][C]0.0477673922684261[/C][/ROW]
[ROW][C]106[/C][C]101.25[/C][C]101.499916476627[/C][C]-0.249916476626666[/C][/ROW]
[ROW][C]107[/C][C]101.39[/C][C]101.178972132348[/C][C]0.211027867652035[/C][/ROW]
[ROW][C]108[/C][C]101.43[/C][C]101.302446695198[/C][C]0.127553304801779[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294982&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294982&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	97.17745455	96.9823327385524	0.195121811447621
14	97.20751515	97.1947966157646	0.0127185342353755
15	97.23757576	97.2399567282372	-0.00238096823723311
16	97.26763636	97.2638200429816	0.00381631701839069
17	97.29769697	97.273700413822	0.0239965561780338
18	97.32775758	97.2911001257195	0.0366574542804869
19	97.35781818	97.358954780206	-0.00113660020599582
20	97.38787879	97.4290452959743	-0.0411665059743171
21	97.41793939	97.4808508135818	-0.0629114235818236
22	97.9	97.691892983782	0.208107016218008
23	97.98	97.7204586264331	0.25954137356689
24	98.03	97.9952782556265	0.0347217443734849
25	98.03	98.0702903876895	-0.0402903876894527
26	97.94	98.0507629454108	-0.110762945410769
27	98.12	97.9794359045932	0.140564095406816
28	98.19	98.1374193970048	0.0525806029952207
29	98.34	98.1942194099316	0.145780590068355
30	98.42	98.3263609994073	0.0936390005927166
31	98.43	98.4450809482252	-0.0150809482252185
32	98.45	98.4995437096661	-0.0495437096660822
33	98.77	98.5421093510582	0.227890648941766
34	99.24	99.0426768761267	0.197323123873318
35	99.46	99.0644738211638	0.395526178836178
36	99.54	99.4519940894661	0.088005910533937
37	99.55	99.5720109098331	-0.0220109098331136
38	99.24	99.5650354184014	-0.325035418401441
39	99.43	99.309482920118	0.120517079881964
40	99.47	99.4430351819977	0.0269648180022841
41	99.57	99.481887071177	0.0881129288230369
42	99.62	99.5567176191187	0.0632823808813043
43	99.64	99.6400238463675	-2.38463674975264e-05
44	99.75	99.706347993053	0.0436520069469992
45	99.85	99.8539990141101	-0.00399901411009296
46	100.28	100.135669006114	0.144330993885887
47	100.52	100.120684460132	0.399315539868297
48	100.57	100.491904022814	0.0780959771861234
49	100.57	100.595550608438	-0.0255506084384365
50	100.27	100.565708455062	-0.2957084550616
51	100.27	100.366343633541	-0.0963436335410393
52	100.18	100.29099277398	-0.110992773979632
53	100.16	100.204736165658	-0.0447361656578948
54	100.18	100.153688491829	0.0263115081707923
55	100.18	100.198324319664	-0.0183243196644014
56	100.59	100.250347575511	0.339652424489032
57	100.69	100.671821799993	0.018178200007398
58	101.06	100.983810154985	0.0761898450148948
59	101.15	100.921537065175	0.228462934825146
60	101.16	101.112200236241	0.0477997637593575
61	101.16	101.18081701292	-0.0208170129195082
62	100.81	101.137968600992	-0.327968600992321
63	100.94	100.921291327399	0.0187086726007237
64	101.13	100.952622616229	0.177377383770562
65	101.29	101.140402281987	0.1495977180126
66	101.34	101.275732335194	0.0642676648059535
67	101.35	101.352994325612	-0.00299432561156721
68	101.7	101.442459953025	0.257540046974711
69	102.05	101.766374814077	0.283625185922517
70	102.48	102.330423515344	0.149576484656478
71	102.66	102.346627926146	0.313372073854239
72	102.72	102.605061783369	0.114938216630861
73	102.73	102.732056180125	-0.00205618012455488
74	102.18	102.686936157274	-0.506936157273785
75	102.22	102.325213309479	-0.105213309479126
76	102.37	102.250859334043	0.119140665957445
77	102.53	102.382367798464	0.14763220153587
78	102.61	102.510352485226	0.0996475147737073
79	102.62	102.616370433447	0.00362956655348512
80	103	102.728845820967	0.271154179032663
81	103.17	103.067179618478	0.102820381521937
82	103.52	103.45344087536	0.0665591246397526
83	103.69	103.402555761757	0.287444238242642
84	103.73	103.623929273657	0.106070726343134
85	99.57	103.735078314511	-4.16507831451059
86	99.09	99.7630108328926	-0.673010832892629
87	99.14	99.2718555749777	-0.131855574977706
88	99.36	99.1870571343503	0.172942865649674
89	99.6	99.3707343991692	0.229265600830786
90	99.65	99.571987707067	0.0780122929329679
91	99.8	99.6515702159463	0.148429784053747
92	100.15	99.9167657214222	0.233234278577783
93	100.45	100.208763483424	0.241236516576379
94	100.89	100.722168238358	0.167831761641523
95	101.13	100.780274837561	0.349725162438631
96	101.17	101.048205269643	0.12179473035718
97	101.21	100.898429097507	0.311570902492704
98	101.1	101.339471800288	-0.23947180028793
99	101.17	101.288800484276	-0.118800484275766
100	101.11	101.235884510034	-0.125884510033714
101	101.2	101.14365366901	0.0563463309898253
102	101.15	101.173385899023	-0.0233858990229123
103	100.92	101.162658175327	-0.242658175327037
104	101.1	101.067476981908	0.0325230180919363
105	101.22	101.172232607732	0.0477673922684261
106	101.25	101.499916476627	-0.249916476626666
107	101.39	101.178972132348	0.211027867652035
108	101.43	101.302446695198	0.127553304801779

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
109	101.170304495678	100.257453490671	102.083155500686
110	101.28432221432	100.034317307443	102.534327121196
111	101.465456023933	99.9516107289685	102.979301318897
112	101.523216698535	99.7851307147707	103.261302682299
113	101.560506623666	99.6239741047476	103.497039142584
114	101.532383336252	99.4159302877066	103.648836384798
115	101.529381800293	99.2471485044686	103.811615096118
116	101.678957623803	99.2421966329712	104.115718614636
117	101.75427285412	99.1722156440043	104.336330064237
118	102.018061211988	99.2984592657123	104.737663158263
119	101.960651824225	99.1101343175162	104.811169330934
120	101.881330048916	98.9056510732995	104.857009024533

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 101.170304495678 & 100.257453490671 & 102.083155500686 \tabularnewline
110 & 101.28432221432 & 100.034317307443 & 102.534327121196 \tabularnewline
111 & 101.465456023933 & 99.9516107289685 & 102.979301318897 \tabularnewline
112 & 101.523216698535 & 99.7851307147707 & 103.261302682299 \tabularnewline
113 & 101.560506623666 & 99.6239741047476 & 103.497039142584 \tabularnewline
114 & 101.532383336252 & 99.4159302877066 & 103.648836384798 \tabularnewline
115 & 101.529381800293 & 99.2471485044686 & 103.811615096118 \tabularnewline
116 & 101.678957623803 & 99.2421966329712 & 104.115718614636 \tabularnewline
117 & 101.75427285412 & 99.1722156440043 & 104.336330064237 \tabularnewline
118 & 102.018061211988 & 99.2984592657123 & 104.737663158263 \tabularnewline
119 & 101.960651824225 & 99.1101343175162 & 104.811169330934 \tabularnewline
120 & 101.881330048916 & 98.9056510732995 & 104.857009024533 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294982&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]109[/C][C]101.170304495678[/C][C]100.257453490671[/C][C]102.083155500686[/C][/ROW]
[ROW][C]110[/C][C]101.28432221432[/C][C]100.034317307443[/C][C]102.534327121196[/C][/ROW]
[ROW][C]111[/C][C]101.465456023933[/C][C]99.9516107289685[/C][C]102.979301318897[/C][/ROW]
[ROW][C]112[/C][C]101.523216698535[/C][C]99.7851307147707[/C][C]103.261302682299[/C][/ROW]
[ROW][C]113[/C][C]101.560506623666[/C][C]99.6239741047476[/C][C]103.497039142584[/C][/ROW]
[ROW][C]114[/C][C]101.532383336252[/C][C]99.4159302877066[/C][C]103.648836384798[/C][/ROW]
[ROW][C]115[/C][C]101.529381800293[/C][C]99.2471485044686[/C][C]103.811615096118[/C][/ROW]
[ROW][C]116[/C][C]101.678957623803[/C][C]99.2421966329712[/C][C]104.115718614636[/C][/ROW]
[ROW][C]117[/C][C]101.75427285412[/C][C]99.1722156440043[/C][C]104.336330064237[/C][/ROW]
[ROW][C]118[/C][C]102.018061211988[/C][C]99.2984592657123[/C][C]104.737663158263[/C][/ROW]
[ROW][C]119[/C][C]101.960651824225[/C][C]99.1101343175162[/C][C]104.811169330934[/C][/ROW]
[ROW][C]120[/C][C]101.881330048916[/C][C]98.9056510732995[/C][C]104.857009024533[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294982&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294982&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
109	101.170304495678	100.257453490671	102.083155500686
110	101.28432221432	100.034317307443	102.534327121196
111	101.465456023933	99.9516107289685	102.979301318897
112	101.523216698535	99.7851307147707	103.261302682299
113	101.560506623666	99.6239741047476	103.497039142584
114	101.532383336252	99.4159302877066	103.648836384798
115	101.529381800293	99.2471485044686	103.811615096118
116	101.678957623803	99.2421966329712	104.115718614636
117	101.75427285412	99.1722156440043	104.336330064237
118	102.018061211988	99.2984592657123	104.737663158263
119	101.960651824225	99.1101343175162	104.811169330934
120	101.881330048916	98.9056510732995	104.857009024533

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

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

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

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