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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

Sun, 07 Jun 2009 19:29:27 -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/2009/Jun/08/t12444251274657v0lwc7tzy3y.htm/, Retrieved Fri, 10 May 2024 15:05:22 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=42272, Retrieved Fri, 10 May 2024 15:05:22 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

215

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

-     [Exponential Smoothing] [Exponential Smoot...] [2009-06-02 07:41:47] [693e95349fa8389087a357753937cdd6]
-   PD    [Exponential Smoothing] [Opgave 10 OEFENIN...] [2009-06-08 01:29:27] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Dataseries X:

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Histogram

Boxplots

3.27
3.27
3.27
3.27
3.27
3.28
3.32
3.34
3.34
3.35
3.35
3.35
3.35
3.35
3.4
3.42
3.42
3.42
3.42
3.42
3.42
3.42
3.42
3.42
3.42
3.42
3.43
3.47
3.51
3.52
3.52
3.52
3.52
3.52
3.52
3.52
3.52
3.52
3.58
3.6
3.61
3.61
3.61
3.63
3.68
3.69
3.69
3.69
3.69
3.69
3.69
3.69
3.69
3.78
3.79
3.79
3.8
3.8
3.8
3.8
3.81
3.95
3.99
4
4.06
4.16
4.19
4.2
4.2
4.2
4.2
4.2
4.23
4.38
4.43
4.44
4.44
4.44
4.44
4.44
4.45
4.45
4.45
4.45
4.45
4.45
4.45
4.45
4.46
4.46
4.46
4.48
4.58
4.67
4.68
4.68
4.69
4.69
4.69
4.69
4.69
4.69
4.69
4.73
4.78
4.79
4.79
4.8
4.8
4.81
5.16
5.26
5.29
5.29
5.29
5.3
5.3
5.3
5.3
5.3
5.3
5.3
5.3
5.35
5.44
5.47
5.47
5.48
5.48
5.48
5.48

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42272&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42272&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42272&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.0339940381487946
gamma	0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0339940381487946 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42272&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0339940381487946[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42272&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42272&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	1
beta	0.0339940381487946
gamma	0

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	3.27	3.27	0
4	3.27	3.27	0
5	3.27	3.27	0
6	3.28	3.27	0.00999999999999979
7	3.32	3.28033994038149	0.0396600596185119
8	3.34	3.32168814596114	0.0183118540388567
9	3.34	3.34231063982591	-0.00231063982591495
10	3.35	3.34223209184752	0.0077679081524753
11	3.35	3.35249615441360	-0.00249615441359641
12	3.35	3.35241130004524	-0.00241130004523527
13	3.35	3.35232933021951	-0.00232933021950954
14	3.35	3.35225014687917	-0.00225014687916625
15	3.4	3.35217365530032	0.0478263446996841
16	3.42	3.40379946588655	0.0162005341134459
17	3.42	3.42435018746124	-0.00435018746123728
18	3.42	3.42420230702273	-0.00420230702272573
19	3.42	3.42405945363748	-0.00405945363748206
20	3.42	3.42392145641567	-0.00392145641566621
21	3.42	3.42378815027667	-0.00378815027667345
22	3.42	3.42365937575165	-0.00365937575165454
23	3.42	3.42353497879275	-0.00353497879275233
24	3.42	3.42341481058882	-0.00341481058881632
25	3.42	3.42329872738739	-0.00329872738738901
26	3.42	3.42318659032274	-0.00318659032273949
27	3.43	3.42307826524974	0.00692173475025637
28	3.47	3.4333135629649	0.0366864370351001
29	3.51	3.47456068310501	0.0354393168949851
30	3.52	3.51576540859551	0.00423459140449056
31	3.52	3.52590935945726	-0.00590935945725857
32	3.52	3.52570847646643	-0.00570847646643369
33	3.52	3.52551442229966	-0.00551442229966215
34	3.52	3.52532696481764	-0.00532696481763884
35	3.52	3.52514587977241	-0.00514587977241066
36	3.52	3.52497095053912	-0.00497095053911822
37	3.52	3.52480196785686	-0.00480196785685605
38	3.52	3.52463872957834	-0.00463872957834077
39	3.58	3.52448104042809	0.0555189595719074
40	3.6	3.58636835405776	0.0136316459422385
41	3.61	3.60683174874995	0.00316825125004705
42	3.61	3.61693945040381	-0.00693945040381161
43	3.61	3.61670355046205	-0.00670355046205273
44	3.63	3.61647566971191	0.0135243302880865
45	3.68	3.63693541631166	0.0430645836883365
46	3.69	3.68839935541243	0.00160064458757292
47	3.69	3.6984537677856	-0.00845376778559936
48	3.69	3.69816639008099	-0.00816639008099473
49	3.69	3.69788878150504	-0.00788878150504368
50	3.69	3.69762060996561	-0.00762060996561376
51	3.69	3.69736155465973	-0.00736155465972521
52	3.69	3.69711130568979	-0.00711130568978824
53	3.69	3.69686956369288	-0.00686956369288172
54	3.78	3.69663603948264	0.0833639605173593
55	3.79	3.7894699171367	0.00053008286329792
56	3.79	3.79948793679378	-0.00948793679377902
57	3.8	3.79916540350846	0.000834596491541717
58	3.8	3.80919377481343	-0.00919377481343053
59	3.8	3.80888124128169	-0.00888124128169121
60	3.8	3.80857933202675	-0.00857933202675287
61	3.81	3.80828768588654	0.00171231411345607
62	3.95	3.81834589435784	0.131654105642161
63	3.99	3.96282134904749	0.0271786509525151
64	4	4.0037452611448	-0.00374526114479767
65	4.06	4.01361794459456	0.0463820554054362
66	4.16	4.07519465795544	0.0848053420445645
67	4.19	4.17807753398812	0.0119224660118800
68	4.2	4.20848282675256	-0.00848282675255607
69	4.2	4.21819446121632	-0.0181944612163196
70	4.2	4.21757595800764	-0.0175759580076358
71	4.2	4.21697848022062	-0.0169784802206223
72	4.2	4.21640131311629	-0.0164013131162939
73	4.23	4.21584376625253	0.0141562337474719
74	4.38	4.24632499380258	0.133675006197416
75	4.43	4.4008691470628	0.0291308529372012
76	4.44	4.45185942238885	-0.0118594223888522
77	4.44	4.46145627273174	-0.0214562727317436
78	4.44	4.46072688737797	-0.0207268873779691
79	4.44	4.46002229677774	-0.0200222967777366
80	4.44	4.45934165805725	-0.0193416580572485
81	4.45	4.45868415699539	-0.00868415699538971
82	4.45	4.4683889474312	-0.0183889474311973
83	4.45	4.46776383285071	-0.0177638328507053
84	4.45	4.46715996843911	-0.0171599684391097
85	4.45	4.46657663181736	-0.0165766318173581
86	4.45	4.46601312516298	-0.0160131251629805
87	4.45	4.46546877437531	-0.0154687743753090
88	4.45	4.46494292826908	-0.0149429282690798
89	4.46	4.46443495779545	-0.00443495779544634
90	4.46	4.47428419567096	-0.0142841956709594
91	4.46	4.4737986181784	-0.013798618178396
92	4.48	4.47332954742564	0.00667045257436172
93	4.58	4.49355630304492	0.0864436969550786
94	4.67	4.59649487337694	0.0735051266230649
95	4.68	4.68899360945549	-0.00899360945549166
96	4.68	4.69868788035257	-0.0186878803525659
97	4.69	4.69805260383494	-0.00805260383494044
98	4.69	4.70777886331298	-0.0177788633129792
99	4.69	4.70717448795528	-0.0171744879552751
100	4.69	4.70659065775654	-0.0165906577565371
101	4.69	4.70602667430385	-0.0160266743038484
102	4.69	4.70548186292616	-0.0154818629261646
103	4.69	4.70495557188724	-0.0149555718872385
104	4.73	4.70444717160597	0.0255528283940336
105	4.78	4.7453158154292	0.0346841845707972
106	4.79	4.79649487092266	-0.00649487092266288
107	4.79	4.80627408403275	-0.0162740840327462
108	4.8	4.8057208621993	-0.00572086219930057
109	4.8	4.81552638699145	-0.0155263869914535
110	4.81	4.81499858239975	-0.00499858239975293
111	5.16	4.82482866039896	0.335171339601035
112	5.26	5.18622248770375	0.073777512296254
113	5.29	5.28873048327127	0.00126951672873243
114	5.29	5.31877363927137	-0.0287736392713747
115	5.29	5.3177955070803	-0.0277955070803042
116	5.3	5.31685062555225	-0.0168506255522516
117	5.3	5.3262778047444	-0.0262778047443968
118	5.3	5.32538451604745	-0.0253845160474491
119	5.3	5.32452159384054	-0.0245215938405439
120	5.3	5.32368800584406	-0.0236880058440585
121	5.3	5.32288275486973	-0.0228827548697268
122	5.3	5.32210487762774	-0.0221048776277364
123	5.3	5.32135344357438	-0.0213534435743847
124	5.35	5.32062755379891	0.0293724462010916
125	5.44	5.37162604185559	0.0683739581444085
126	5.47	5.46395034879714	0.00604965120286227
127	5.47	5.49415600087091	-0.0241560008709136
128	5.48	5.49333484085579	-0.0133348408557854
129	5.48	5.50288153576703	-0.0228815357670262
130	5.48	5.50210369996726	-0.0221036999672588
131	5.48	5.50135230594734	-0.0213523059473424

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 3.27 & 3.27 & 0 \tabularnewline
4 & 3.27 & 3.27 & 0 \tabularnewline
5 & 3.27 & 3.27 & 0 \tabularnewline
6 & 3.28 & 3.27 & 0.00999999999999979 \tabularnewline
7 & 3.32 & 3.28033994038149 & 0.0396600596185119 \tabularnewline
8 & 3.34 & 3.32168814596114 & 0.0183118540388567 \tabularnewline
9 & 3.34 & 3.34231063982591 & -0.00231063982591495 \tabularnewline
10 & 3.35 & 3.34223209184752 & 0.0077679081524753 \tabularnewline
11 & 3.35 & 3.35249615441360 & -0.00249615441359641 \tabularnewline
12 & 3.35 & 3.35241130004524 & -0.00241130004523527 \tabularnewline
13 & 3.35 & 3.35232933021951 & -0.00232933021950954 \tabularnewline
14 & 3.35 & 3.35225014687917 & -0.00225014687916625 \tabularnewline
15 & 3.4 & 3.35217365530032 & 0.0478263446996841 \tabularnewline
16 & 3.42 & 3.40379946588655 & 0.0162005341134459 \tabularnewline
17 & 3.42 & 3.42435018746124 & -0.00435018746123728 \tabularnewline
18 & 3.42 & 3.42420230702273 & -0.00420230702272573 \tabularnewline
19 & 3.42 & 3.42405945363748 & -0.00405945363748206 \tabularnewline
20 & 3.42 & 3.42392145641567 & -0.00392145641566621 \tabularnewline
21 & 3.42 & 3.42378815027667 & -0.00378815027667345 \tabularnewline
22 & 3.42 & 3.42365937575165 & -0.00365937575165454 \tabularnewline
23 & 3.42 & 3.42353497879275 & -0.00353497879275233 \tabularnewline
24 & 3.42 & 3.42341481058882 & -0.00341481058881632 \tabularnewline
25 & 3.42 & 3.42329872738739 & -0.00329872738738901 \tabularnewline
26 & 3.42 & 3.42318659032274 & -0.00318659032273949 \tabularnewline
27 & 3.43 & 3.42307826524974 & 0.00692173475025637 \tabularnewline
28 & 3.47 & 3.4333135629649 & 0.0366864370351001 \tabularnewline
29 & 3.51 & 3.47456068310501 & 0.0354393168949851 \tabularnewline
30 & 3.52 & 3.51576540859551 & 0.00423459140449056 \tabularnewline
31 & 3.52 & 3.52590935945726 & -0.00590935945725857 \tabularnewline
32 & 3.52 & 3.52570847646643 & -0.00570847646643369 \tabularnewline
33 & 3.52 & 3.52551442229966 & -0.00551442229966215 \tabularnewline
34 & 3.52 & 3.52532696481764 & -0.00532696481763884 \tabularnewline
35 & 3.52 & 3.52514587977241 & -0.00514587977241066 \tabularnewline
36 & 3.52 & 3.52497095053912 & -0.00497095053911822 \tabularnewline
37 & 3.52 & 3.52480196785686 & -0.00480196785685605 \tabularnewline
38 & 3.52 & 3.52463872957834 & -0.00463872957834077 \tabularnewline
39 & 3.58 & 3.52448104042809 & 0.0555189595719074 \tabularnewline
40 & 3.6 & 3.58636835405776 & 0.0136316459422385 \tabularnewline
41 & 3.61 & 3.60683174874995 & 0.00316825125004705 \tabularnewline
42 & 3.61 & 3.61693945040381 & -0.00693945040381161 \tabularnewline
43 & 3.61 & 3.61670355046205 & -0.00670355046205273 \tabularnewline
44 & 3.63 & 3.61647566971191 & 0.0135243302880865 \tabularnewline
45 & 3.68 & 3.63693541631166 & 0.0430645836883365 \tabularnewline
46 & 3.69 & 3.68839935541243 & 0.00160064458757292 \tabularnewline
47 & 3.69 & 3.6984537677856 & -0.00845376778559936 \tabularnewline
48 & 3.69 & 3.69816639008099 & -0.00816639008099473 \tabularnewline
49 & 3.69 & 3.69788878150504 & -0.00788878150504368 \tabularnewline
50 & 3.69 & 3.69762060996561 & -0.00762060996561376 \tabularnewline
51 & 3.69 & 3.69736155465973 & -0.00736155465972521 \tabularnewline
52 & 3.69 & 3.69711130568979 & -0.00711130568978824 \tabularnewline
53 & 3.69 & 3.69686956369288 & -0.00686956369288172 \tabularnewline
54 & 3.78 & 3.69663603948264 & 0.0833639605173593 \tabularnewline
55 & 3.79 & 3.7894699171367 & 0.00053008286329792 \tabularnewline
56 & 3.79 & 3.79948793679378 & -0.00948793679377902 \tabularnewline
57 & 3.8 & 3.79916540350846 & 0.000834596491541717 \tabularnewline
58 & 3.8 & 3.80919377481343 & -0.00919377481343053 \tabularnewline
59 & 3.8 & 3.80888124128169 & -0.00888124128169121 \tabularnewline
60 & 3.8 & 3.80857933202675 & -0.00857933202675287 \tabularnewline
61 & 3.81 & 3.80828768588654 & 0.00171231411345607 \tabularnewline
62 & 3.95 & 3.81834589435784 & 0.131654105642161 \tabularnewline
63 & 3.99 & 3.96282134904749 & 0.0271786509525151 \tabularnewline
64 & 4 & 4.0037452611448 & -0.00374526114479767 \tabularnewline
65 & 4.06 & 4.01361794459456 & 0.0463820554054362 \tabularnewline
66 & 4.16 & 4.07519465795544 & 0.0848053420445645 \tabularnewline
67 & 4.19 & 4.17807753398812 & 0.0119224660118800 \tabularnewline
68 & 4.2 & 4.20848282675256 & -0.00848282675255607 \tabularnewline
69 & 4.2 & 4.21819446121632 & -0.0181944612163196 \tabularnewline
70 & 4.2 & 4.21757595800764 & -0.0175759580076358 \tabularnewline
71 & 4.2 & 4.21697848022062 & -0.0169784802206223 \tabularnewline
72 & 4.2 & 4.21640131311629 & -0.0164013131162939 \tabularnewline
73 & 4.23 & 4.21584376625253 & 0.0141562337474719 \tabularnewline
74 & 4.38 & 4.24632499380258 & 0.133675006197416 \tabularnewline
75 & 4.43 & 4.4008691470628 & 0.0291308529372012 \tabularnewline
76 & 4.44 & 4.45185942238885 & -0.0118594223888522 \tabularnewline
77 & 4.44 & 4.46145627273174 & -0.0214562727317436 \tabularnewline
78 & 4.44 & 4.46072688737797 & -0.0207268873779691 \tabularnewline
79 & 4.44 & 4.46002229677774 & -0.0200222967777366 \tabularnewline
80 & 4.44 & 4.45934165805725 & -0.0193416580572485 \tabularnewline
81 & 4.45 & 4.45868415699539 & -0.00868415699538971 \tabularnewline
82 & 4.45 & 4.4683889474312 & -0.0183889474311973 \tabularnewline
83 & 4.45 & 4.46776383285071 & -0.0177638328507053 \tabularnewline
84 & 4.45 & 4.46715996843911 & -0.0171599684391097 \tabularnewline
85 & 4.45 & 4.46657663181736 & -0.0165766318173581 \tabularnewline
86 & 4.45 & 4.46601312516298 & -0.0160131251629805 \tabularnewline
87 & 4.45 & 4.46546877437531 & -0.0154687743753090 \tabularnewline
88 & 4.45 & 4.46494292826908 & -0.0149429282690798 \tabularnewline
89 & 4.46 & 4.46443495779545 & -0.00443495779544634 \tabularnewline
90 & 4.46 & 4.47428419567096 & -0.0142841956709594 \tabularnewline
91 & 4.46 & 4.4737986181784 & -0.013798618178396 \tabularnewline
92 & 4.48 & 4.47332954742564 & 0.00667045257436172 \tabularnewline
93 & 4.58 & 4.49355630304492 & 0.0864436969550786 \tabularnewline
94 & 4.67 & 4.59649487337694 & 0.0735051266230649 \tabularnewline
95 & 4.68 & 4.68899360945549 & -0.00899360945549166 \tabularnewline
96 & 4.68 & 4.69868788035257 & -0.0186878803525659 \tabularnewline
97 & 4.69 & 4.69805260383494 & -0.00805260383494044 \tabularnewline
98 & 4.69 & 4.70777886331298 & -0.0177788633129792 \tabularnewline
99 & 4.69 & 4.70717448795528 & -0.0171744879552751 \tabularnewline
100 & 4.69 & 4.70659065775654 & -0.0165906577565371 \tabularnewline
101 & 4.69 & 4.70602667430385 & -0.0160266743038484 \tabularnewline
102 & 4.69 & 4.70548186292616 & -0.0154818629261646 \tabularnewline
103 & 4.69 & 4.70495557188724 & -0.0149555718872385 \tabularnewline
104 & 4.73 & 4.70444717160597 & 0.0255528283940336 \tabularnewline
105 & 4.78 & 4.7453158154292 & 0.0346841845707972 \tabularnewline
106 & 4.79 & 4.79649487092266 & -0.00649487092266288 \tabularnewline
107 & 4.79 & 4.80627408403275 & -0.0162740840327462 \tabularnewline
108 & 4.8 & 4.8057208621993 & -0.00572086219930057 \tabularnewline
109 & 4.8 & 4.81552638699145 & -0.0155263869914535 \tabularnewline
110 & 4.81 & 4.81499858239975 & -0.00499858239975293 \tabularnewline
111 & 5.16 & 4.82482866039896 & 0.335171339601035 \tabularnewline
112 & 5.26 & 5.18622248770375 & 0.073777512296254 \tabularnewline
113 & 5.29 & 5.28873048327127 & 0.00126951672873243 \tabularnewline
114 & 5.29 & 5.31877363927137 & -0.0287736392713747 \tabularnewline
115 & 5.29 & 5.3177955070803 & -0.0277955070803042 \tabularnewline
116 & 5.3 & 5.31685062555225 & -0.0168506255522516 \tabularnewline
117 & 5.3 & 5.3262778047444 & -0.0262778047443968 \tabularnewline
118 & 5.3 & 5.32538451604745 & -0.0253845160474491 \tabularnewline
119 & 5.3 & 5.32452159384054 & -0.0245215938405439 \tabularnewline
120 & 5.3 & 5.32368800584406 & -0.0236880058440585 \tabularnewline
121 & 5.3 & 5.32288275486973 & -0.0228827548697268 \tabularnewline
122 & 5.3 & 5.32210487762774 & -0.0221048776277364 \tabularnewline
123 & 5.3 & 5.32135344357438 & -0.0213534435743847 \tabularnewline
124 & 5.35 & 5.32062755379891 & 0.0293724462010916 \tabularnewline
125 & 5.44 & 5.37162604185559 & 0.0683739581444085 \tabularnewline
126 & 5.47 & 5.46395034879714 & 0.00604965120286227 \tabularnewline
127 & 5.47 & 5.49415600087091 & -0.0241560008709136 \tabularnewline
128 & 5.48 & 5.49333484085579 & -0.0133348408557854 \tabularnewline
129 & 5.48 & 5.50288153576703 & -0.0228815357670262 \tabularnewline
130 & 5.48 & 5.50210369996726 & -0.0221036999672588 \tabularnewline
131 & 5.48 & 5.50135230594734 & -0.0213523059473424 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42272&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]3.27[/C][C]3.27[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]3.27[/C][C]3.27[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]3.27[/C][C]3.27[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]3.28[/C][C]3.27[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]7[/C][C]3.32[/C][C]3.28033994038149[/C][C]0.0396600596185119[/C][/ROW]
[ROW][C]8[/C][C]3.34[/C][C]3.32168814596114[/C][C]0.0183118540388567[/C][/ROW]
[ROW][C]9[/C][C]3.34[/C][C]3.34231063982591[/C][C]-0.00231063982591495[/C][/ROW]
[ROW][C]10[/C][C]3.35[/C][C]3.34223209184752[/C][C]0.0077679081524753[/C][/ROW]
[ROW][C]11[/C][C]3.35[/C][C]3.35249615441360[/C][C]-0.00249615441359641[/C][/ROW]
[ROW][C]12[/C][C]3.35[/C][C]3.35241130004524[/C][C]-0.00241130004523527[/C][/ROW]
[ROW][C]13[/C][C]3.35[/C][C]3.35232933021951[/C][C]-0.00232933021950954[/C][/ROW]
[ROW][C]14[/C][C]3.35[/C][C]3.35225014687917[/C][C]-0.00225014687916625[/C][/ROW]
[ROW][C]15[/C][C]3.4[/C][C]3.35217365530032[/C][C]0.0478263446996841[/C][/ROW]
[ROW][C]16[/C][C]3.42[/C][C]3.40379946588655[/C][C]0.0162005341134459[/C][/ROW]
[ROW][C]17[/C][C]3.42[/C][C]3.42435018746124[/C][C]-0.00435018746123728[/C][/ROW]
[ROW][C]18[/C][C]3.42[/C][C]3.42420230702273[/C][C]-0.00420230702272573[/C][/ROW]
[ROW][C]19[/C][C]3.42[/C][C]3.42405945363748[/C][C]-0.00405945363748206[/C][/ROW]
[ROW][C]20[/C][C]3.42[/C][C]3.42392145641567[/C][C]-0.00392145641566621[/C][/ROW]
[ROW][C]21[/C][C]3.42[/C][C]3.42378815027667[/C][C]-0.00378815027667345[/C][/ROW]
[ROW][C]22[/C][C]3.42[/C][C]3.42365937575165[/C][C]-0.00365937575165454[/C][/ROW]
[ROW][C]23[/C][C]3.42[/C][C]3.42353497879275[/C][C]-0.00353497879275233[/C][/ROW]
[ROW][C]24[/C][C]3.42[/C][C]3.42341481058882[/C][C]-0.00341481058881632[/C][/ROW]
[ROW][C]25[/C][C]3.42[/C][C]3.42329872738739[/C][C]-0.00329872738738901[/C][/ROW]
[ROW][C]26[/C][C]3.42[/C][C]3.42318659032274[/C][C]-0.00318659032273949[/C][/ROW]
[ROW][C]27[/C][C]3.43[/C][C]3.42307826524974[/C][C]0.00692173475025637[/C][/ROW]
[ROW][C]28[/C][C]3.47[/C][C]3.4333135629649[/C][C]0.0366864370351001[/C][/ROW]
[ROW][C]29[/C][C]3.51[/C][C]3.47456068310501[/C][C]0.0354393168949851[/C][/ROW]
[ROW][C]30[/C][C]3.52[/C][C]3.51576540859551[/C][C]0.00423459140449056[/C][/ROW]
[ROW][C]31[/C][C]3.52[/C][C]3.52590935945726[/C][C]-0.00590935945725857[/C][/ROW]
[ROW][C]32[/C][C]3.52[/C][C]3.52570847646643[/C][C]-0.00570847646643369[/C][/ROW]
[ROW][C]33[/C][C]3.52[/C][C]3.52551442229966[/C][C]-0.00551442229966215[/C][/ROW]
[ROW][C]34[/C][C]3.52[/C][C]3.52532696481764[/C][C]-0.00532696481763884[/C][/ROW]
[ROW][C]35[/C][C]3.52[/C][C]3.52514587977241[/C][C]-0.00514587977241066[/C][/ROW]
[ROW][C]36[/C][C]3.52[/C][C]3.52497095053912[/C][C]-0.00497095053911822[/C][/ROW]
[ROW][C]37[/C][C]3.52[/C][C]3.52480196785686[/C][C]-0.00480196785685605[/C][/ROW]
[ROW][C]38[/C][C]3.52[/C][C]3.52463872957834[/C][C]-0.00463872957834077[/C][/ROW]
[ROW][C]39[/C][C]3.58[/C][C]3.52448104042809[/C][C]0.0555189595719074[/C][/ROW]
[ROW][C]40[/C][C]3.6[/C][C]3.58636835405776[/C][C]0.0136316459422385[/C][/ROW]
[ROW][C]41[/C][C]3.61[/C][C]3.60683174874995[/C][C]0.00316825125004705[/C][/ROW]
[ROW][C]42[/C][C]3.61[/C][C]3.61693945040381[/C][C]-0.00693945040381161[/C][/ROW]
[ROW][C]43[/C][C]3.61[/C][C]3.61670355046205[/C][C]-0.00670355046205273[/C][/ROW]
[ROW][C]44[/C][C]3.63[/C][C]3.61647566971191[/C][C]0.0135243302880865[/C][/ROW]
[ROW][C]45[/C][C]3.68[/C][C]3.63693541631166[/C][C]0.0430645836883365[/C][/ROW]
[ROW][C]46[/C][C]3.69[/C][C]3.68839935541243[/C][C]0.00160064458757292[/C][/ROW]
[ROW][C]47[/C][C]3.69[/C][C]3.6984537677856[/C][C]-0.00845376778559936[/C][/ROW]
[ROW][C]48[/C][C]3.69[/C][C]3.69816639008099[/C][C]-0.00816639008099473[/C][/ROW]
[ROW][C]49[/C][C]3.69[/C][C]3.69788878150504[/C][C]-0.00788878150504368[/C][/ROW]
[ROW][C]50[/C][C]3.69[/C][C]3.69762060996561[/C][C]-0.00762060996561376[/C][/ROW]
[ROW][C]51[/C][C]3.69[/C][C]3.69736155465973[/C][C]-0.00736155465972521[/C][/ROW]
[ROW][C]52[/C][C]3.69[/C][C]3.69711130568979[/C][C]-0.00711130568978824[/C][/ROW]
[ROW][C]53[/C][C]3.69[/C][C]3.69686956369288[/C][C]-0.00686956369288172[/C][/ROW]
[ROW][C]54[/C][C]3.78[/C][C]3.69663603948264[/C][C]0.0833639605173593[/C][/ROW]
[ROW][C]55[/C][C]3.79[/C][C]3.7894699171367[/C][C]0.00053008286329792[/C][/ROW]
[ROW][C]56[/C][C]3.79[/C][C]3.79948793679378[/C][C]-0.00948793679377902[/C][/ROW]
[ROW][C]57[/C][C]3.8[/C][C]3.79916540350846[/C][C]0.000834596491541717[/C][/ROW]
[ROW][C]58[/C][C]3.8[/C][C]3.80919377481343[/C][C]-0.00919377481343053[/C][/ROW]
[ROW][C]59[/C][C]3.8[/C][C]3.80888124128169[/C][C]-0.00888124128169121[/C][/ROW]
[ROW][C]60[/C][C]3.8[/C][C]3.80857933202675[/C][C]-0.00857933202675287[/C][/ROW]
[ROW][C]61[/C][C]3.81[/C][C]3.80828768588654[/C][C]0.00171231411345607[/C][/ROW]
[ROW][C]62[/C][C]3.95[/C][C]3.81834589435784[/C][C]0.131654105642161[/C][/ROW]
[ROW][C]63[/C][C]3.99[/C][C]3.96282134904749[/C][C]0.0271786509525151[/C][/ROW]
[ROW][C]64[/C][C]4[/C][C]4.0037452611448[/C][C]-0.00374526114479767[/C][/ROW]
[ROW][C]65[/C][C]4.06[/C][C]4.01361794459456[/C][C]0.0463820554054362[/C][/ROW]
[ROW][C]66[/C][C]4.16[/C][C]4.07519465795544[/C][C]0.0848053420445645[/C][/ROW]
[ROW][C]67[/C][C]4.19[/C][C]4.17807753398812[/C][C]0.0119224660118800[/C][/ROW]
[ROW][C]68[/C][C]4.2[/C][C]4.20848282675256[/C][C]-0.00848282675255607[/C][/ROW]
[ROW][C]69[/C][C]4.2[/C][C]4.21819446121632[/C][C]-0.0181944612163196[/C][/ROW]
[ROW][C]70[/C][C]4.2[/C][C]4.21757595800764[/C][C]-0.0175759580076358[/C][/ROW]
[ROW][C]71[/C][C]4.2[/C][C]4.21697848022062[/C][C]-0.0169784802206223[/C][/ROW]
[ROW][C]72[/C][C]4.2[/C][C]4.21640131311629[/C][C]-0.0164013131162939[/C][/ROW]
[ROW][C]73[/C][C]4.23[/C][C]4.21584376625253[/C][C]0.0141562337474719[/C][/ROW]
[ROW][C]74[/C][C]4.38[/C][C]4.24632499380258[/C][C]0.133675006197416[/C][/ROW]
[ROW][C]75[/C][C]4.43[/C][C]4.4008691470628[/C][C]0.0291308529372012[/C][/ROW]
[ROW][C]76[/C][C]4.44[/C][C]4.45185942238885[/C][C]-0.0118594223888522[/C][/ROW]
[ROW][C]77[/C][C]4.44[/C][C]4.46145627273174[/C][C]-0.0214562727317436[/C][/ROW]
[ROW][C]78[/C][C]4.44[/C][C]4.46072688737797[/C][C]-0.0207268873779691[/C][/ROW]
[ROW][C]79[/C][C]4.44[/C][C]4.46002229677774[/C][C]-0.0200222967777366[/C][/ROW]
[ROW][C]80[/C][C]4.44[/C][C]4.45934165805725[/C][C]-0.0193416580572485[/C][/ROW]
[ROW][C]81[/C][C]4.45[/C][C]4.45868415699539[/C][C]-0.00868415699538971[/C][/ROW]
[ROW][C]82[/C][C]4.45[/C][C]4.4683889474312[/C][C]-0.0183889474311973[/C][/ROW]
[ROW][C]83[/C][C]4.45[/C][C]4.46776383285071[/C][C]-0.0177638328507053[/C][/ROW]
[ROW][C]84[/C][C]4.45[/C][C]4.46715996843911[/C][C]-0.0171599684391097[/C][/ROW]
[ROW][C]85[/C][C]4.45[/C][C]4.46657663181736[/C][C]-0.0165766318173581[/C][/ROW]
[ROW][C]86[/C][C]4.45[/C][C]4.46601312516298[/C][C]-0.0160131251629805[/C][/ROW]
[ROW][C]87[/C][C]4.45[/C][C]4.46546877437531[/C][C]-0.0154687743753090[/C][/ROW]
[ROW][C]88[/C][C]4.45[/C][C]4.46494292826908[/C][C]-0.0149429282690798[/C][/ROW]
[ROW][C]89[/C][C]4.46[/C][C]4.46443495779545[/C][C]-0.00443495779544634[/C][/ROW]
[ROW][C]90[/C][C]4.46[/C][C]4.47428419567096[/C][C]-0.0142841956709594[/C][/ROW]
[ROW][C]91[/C][C]4.46[/C][C]4.4737986181784[/C][C]-0.013798618178396[/C][/ROW]
[ROW][C]92[/C][C]4.48[/C][C]4.47332954742564[/C][C]0.00667045257436172[/C][/ROW]
[ROW][C]93[/C][C]4.58[/C][C]4.49355630304492[/C][C]0.0864436969550786[/C][/ROW]
[ROW][C]94[/C][C]4.67[/C][C]4.59649487337694[/C][C]0.0735051266230649[/C][/ROW]
[ROW][C]95[/C][C]4.68[/C][C]4.68899360945549[/C][C]-0.00899360945549166[/C][/ROW]
[ROW][C]96[/C][C]4.68[/C][C]4.69868788035257[/C][C]-0.0186878803525659[/C][/ROW]
[ROW][C]97[/C][C]4.69[/C][C]4.69805260383494[/C][C]-0.00805260383494044[/C][/ROW]
[ROW][C]98[/C][C]4.69[/C][C]4.70777886331298[/C][C]-0.0177788633129792[/C][/ROW]
[ROW][C]99[/C][C]4.69[/C][C]4.70717448795528[/C][C]-0.0171744879552751[/C][/ROW]
[ROW][C]100[/C][C]4.69[/C][C]4.70659065775654[/C][C]-0.0165906577565371[/C][/ROW]
[ROW][C]101[/C][C]4.69[/C][C]4.70602667430385[/C][C]-0.0160266743038484[/C][/ROW]
[ROW][C]102[/C][C]4.69[/C][C]4.70548186292616[/C][C]-0.0154818629261646[/C][/ROW]
[ROW][C]103[/C][C]4.69[/C][C]4.70495557188724[/C][C]-0.0149555718872385[/C][/ROW]
[ROW][C]104[/C][C]4.73[/C][C]4.70444717160597[/C][C]0.0255528283940336[/C][/ROW]
[ROW][C]105[/C][C]4.78[/C][C]4.7453158154292[/C][C]0.0346841845707972[/C][/ROW]
[ROW][C]106[/C][C]4.79[/C][C]4.79649487092266[/C][C]-0.00649487092266288[/C][/ROW]
[ROW][C]107[/C][C]4.79[/C][C]4.80627408403275[/C][C]-0.0162740840327462[/C][/ROW]
[ROW][C]108[/C][C]4.8[/C][C]4.8057208621993[/C][C]-0.00572086219930057[/C][/ROW]
[ROW][C]109[/C][C]4.8[/C][C]4.81552638699145[/C][C]-0.0155263869914535[/C][/ROW]
[ROW][C]110[/C][C]4.81[/C][C]4.81499858239975[/C][C]-0.00499858239975293[/C][/ROW]
[ROW][C]111[/C][C]5.16[/C][C]4.82482866039896[/C][C]0.335171339601035[/C][/ROW]
[ROW][C]112[/C][C]5.26[/C][C]5.18622248770375[/C][C]0.073777512296254[/C][/ROW]
[ROW][C]113[/C][C]5.29[/C][C]5.28873048327127[/C][C]0.00126951672873243[/C][/ROW]
[ROW][C]114[/C][C]5.29[/C][C]5.31877363927137[/C][C]-0.0287736392713747[/C][/ROW]
[ROW][C]115[/C][C]5.29[/C][C]5.3177955070803[/C][C]-0.0277955070803042[/C][/ROW]
[ROW][C]116[/C][C]5.3[/C][C]5.31685062555225[/C][C]-0.0168506255522516[/C][/ROW]
[ROW][C]117[/C][C]5.3[/C][C]5.3262778047444[/C][C]-0.0262778047443968[/C][/ROW]
[ROW][C]118[/C][C]5.3[/C][C]5.32538451604745[/C][C]-0.0253845160474491[/C][/ROW]
[ROW][C]119[/C][C]5.3[/C][C]5.32452159384054[/C][C]-0.0245215938405439[/C][/ROW]
[ROW][C]120[/C][C]5.3[/C][C]5.32368800584406[/C][C]-0.0236880058440585[/C][/ROW]
[ROW][C]121[/C][C]5.3[/C][C]5.32288275486973[/C][C]-0.0228827548697268[/C][/ROW]
[ROW][C]122[/C][C]5.3[/C][C]5.32210487762774[/C][C]-0.0221048776277364[/C][/ROW]
[ROW][C]123[/C][C]5.3[/C][C]5.32135344357438[/C][C]-0.0213534435743847[/C][/ROW]
[ROW][C]124[/C][C]5.35[/C][C]5.32062755379891[/C][C]0.0293724462010916[/C][/ROW]
[ROW][C]125[/C][C]5.44[/C][C]5.37162604185559[/C][C]0.0683739581444085[/C][/ROW]
[ROW][C]126[/C][C]5.47[/C][C]5.46395034879714[/C][C]0.00604965120286227[/C][/ROW]
[ROW][C]127[/C][C]5.47[/C][C]5.49415600087091[/C][C]-0.0241560008709136[/C][/ROW]
[ROW][C]128[/C][C]5.48[/C][C]5.49333484085579[/C][C]-0.0133348408557854[/C][/ROW]
[ROW][C]129[/C][C]5.48[/C][C]5.50288153576703[/C][C]-0.0228815357670262[/C][/ROW]
[ROW][C]130[/C][C]5.48[/C][C]5.50210369996726[/C][C]-0.0221036999672588[/C][/ROW]
[ROW][C]131[/C][C]5.48[/C][C]5.50135230594734[/C][C]-0.0213523059473424[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42272&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42272&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	3.27	3.27	0
4	3.27	3.27	0
5	3.27	3.27	0
6	3.28	3.27	0.00999999999999979
7	3.32	3.28033994038149	0.0396600596185119
8	3.34	3.32168814596114	0.0183118540388567
9	3.34	3.34231063982591	-0.00231063982591495
10	3.35	3.34223209184752	0.0077679081524753
11	3.35	3.35249615441360	-0.00249615441359641
12	3.35	3.35241130004524	-0.00241130004523527
13	3.35	3.35232933021951	-0.00232933021950954
14	3.35	3.35225014687917	-0.00225014687916625
15	3.4	3.35217365530032	0.0478263446996841
16	3.42	3.40379946588655	0.0162005341134459
17	3.42	3.42435018746124	-0.00435018746123728
18	3.42	3.42420230702273	-0.00420230702272573
19	3.42	3.42405945363748	-0.00405945363748206
20	3.42	3.42392145641567	-0.00392145641566621
21	3.42	3.42378815027667	-0.00378815027667345
22	3.42	3.42365937575165	-0.00365937575165454
23	3.42	3.42353497879275	-0.00353497879275233
24	3.42	3.42341481058882	-0.00341481058881632
25	3.42	3.42329872738739	-0.00329872738738901
26	3.42	3.42318659032274	-0.00318659032273949
27	3.43	3.42307826524974	0.00692173475025637
28	3.47	3.4333135629649	0.0366864370351001
29	3.51	3.47456068310501	0.0354393168949851
30	3.52	3.51576540859551	0.00423459140449056
31	3.52	3.52590935945726	-0.00590935945725857
32	3.52	3.52570847646643	-0.00570847646643369
33	3.52	3.52551442229966	-0.00551442229966215
34	3.52	3.52532696481764	-0.00532696481763884
35	3.52	3.52514587977241	-0.00514587977241066
36	3.52	3.52497095053912	-0.00497095053911822
37	3.52	3.52480196785686	-0.00480196785685605
38	3.52	3.52463872957834	-0.00463872957834077
39	3.58	3.52448104042809	0.0555189595719074
40	3.6	3.58636835405776	0.0136316459422385
41	3.61	3.60683174874995	0.00316825125004705
42	3.61	3.61693945040381	-0.00693945040381161
43	3.61	3.61670355046205	-0.00670355046205273
44	3.63	3.61647566971191	0.0135243302880865
45	3.68	3.63693541631166	0.0430645836883365
46	3.69	3.68839935541243	0.00160064458757292
47	3.69	3.6984537677856	-0.00845376778559936
48	3.69	3.69816639008099	-0.00816639008099473
49	3.69	3.69788878150504	-0.00788878150504368
50	3.69	3.69762060996561	-0.00762060996561376
51	3.69	3.69736155465973	-0.00736155465972521
52	3.69	3.69711130568979	-0.00711130568978824
53	3.69	3.69686956369288	-0.00686956369288172
54	3.78	3.69663603948264	0.0833639605173593
55	3.79	3.7894699171367	0.00053008286329792
56	3.79	3.79948793679378	-0.00948793679377902
57	3.8	3.79916540350846	0.000834596491541717
58	3.8	3.80919377481343	-0.00919377481343053
59	3.8	3.80888124128169	-0.00888124128169121
60	3.8	3.80857933202675	-0.00857933202675287
61	3.81	3.80828768588654	0.00171231411345607
62	3.95	3.81834589435784	0.131654105642161
63	3.99	3.96282134904749	0.0271786509525151
64	4	4.0037452611448	-0.00374526114479767
65	4.06	4.01361794459456	0.0463820554054362
66	4.16	4.07519465795544	0.0848053420445645
67	4.19	4.17807753398812	0.0119224660118800
68	4.2	4.20848282675256	-0.00848282675255607
69	4.2	4.21819446121632	-0.0181944612163196
70	4.2	4.21757595800764	-0.0175759580076358
71	4.2	4.21697848022062	-0.0169784802206223
72	4.2	4.21640131311629	-0.0164013131162939
73	4.23	4.21584376625253	0.0141562337474719
74	4.38	4.24632499380258	0.133675006197416
75	4.43	4.4008691470628	0.0291308529372012
76	4.44	4.45185942238885	-0.0118594223888522
77	4.44	4.46145627273174	-0.0214562727317436
78	4.44	4.46072688737797	-0.0207268873779691
79	4.44	4.46002229677774	-0.0200222967777366
80	4.44	4.45934165805725	-0.0193416580572485
81	4.45	4.45868415699539	-0.00868415699538971
82	4.45	4.4683889474312	-0.0183889474311973
83	4.45	4.46776383285071	-0.0177638328507053
84	4.45	4.46715996843911	-0.0171599684391097
85	4.45	4.46657663181736	-0.0165766318173581
86	4.45	4.46601312516298	-0.0160131251629805
87	4.45	4.46546877437531	-0.0154687743753090
88	4.45	4.46494292826908	-0.0149429282690798
89	4.46	4.46443495779545	-0.00443495779544634
90	4.46	4.47428419567096	-0.0142841956709594
91	4.46	4.4737986181784	-0.013798618178396
92	4.48	4.47332954742564	0.00667045257436172
93	4.58	4.49355630304492	0.0864436969550786
94	4.67	4.59649487337694	0.0735051266230649
95	4.68	4.68899360945549	-0.00899360945549166
96	4.68	4.69868788035257	-0.0186878803525659
97	4.69	4.69805260383494	-0.00805260383494044
98	4.69	4.70777886331298	-0.0177788633129792
99	4.69	4.70717448795528	-0.0171744879552751
100	4.69	4.70659065775654	-0.0165906577565371
101	4.69	4.70602667430385	-0.0160266743038484
102	4.69	4.70548186292616	-0.0154818629261646
103	4.69	4.70495557188724	-0.0149555718872385
104	4.73	4.70444717160597	0.0255528283940336
105	4.78	4.7453158154292	0.0346841845707972
106	4.79	4.79649487092266	-0.00649487092266288
107	4.79	4.80627408403275	-0.0162740840327462
108	4.8	4.8057208621993	-0.00572086219930057
109	4.8	4.81552638699145	-0.0155263869914535
110	4.81	4.81499858239975	-0.00499858239975293
111	5.16	4.82482866039896	0.335171339601035
112	5.26	5.18622248770375	0.073777512296254
113	5.29	5.28873048327127	0.00126951672873243
114	5.29	5.31877363927137	-0.0287736392713747
115	5.29	5.3177955070803	-0.0277955070803042
116	5.3	5.31685062555225	-0.0168506255522516
117	5.3	5.3262778047444	-0.0262778047443968
118	5.3	5.32538451604745	-0.0253845160474491
119	5.3	5.32452159384054	-0.0245215938405439
120	5.3	5.32368800584406	-0.0236880058440585
121	5.3	5.32288275486973	-0.0228827548697268
122	5.3	5.32210487762774	-0.0221048776277364
123	5.3	5.32135344357438	-0.0213534435743847
124	5.35	5.32062755379891	0.0293724462010916
125	5.44	5.37162604185559	0.0683739581444085
126	5.47	5.46395034879714	0.00604965120286227
127	5.47	5.49415600087091	-0.0241560008709136
128	5.48	5.49333484085579	-0.0133348408557854
129	5.48	5.50288153576703	-0.0228815357670262
130	5.48	5.50210369996726	-0.0221036999672588
131	5.48	5.50135230594734	-0.0213523059473424

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
132	5.5006264548444	5.41958471087874	5.58166819881007
133	5.52125290968881	5.40467826467087	5.63782755470675
134	5.54187936453321	5.39668697446261	5.68707175460381
135	5.56250581937762	5.39204617479483	5.7329654639604
136	5.58313227422202	5.3894009961642	5.77686355227984
137	5.60375872906642	5.38806922426724	5.8194482338656
138	5.62438518391083	5.38765298727227	5.86111738054938
139	5.64501163875523	5.38789785309109	5.90212542441937
140	5.66563809359963	5.38863044138325	5.94264574581601
141	5.68626454844404	5.38972697224972	5.98280212463835
142	5.70689100328844	5.39109587626607	6.02268613031081
143	5.72751745813285	5.39266748695128	6.06236742931441

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
132 & 5.5006264548444 & 5.41958471087874 & 5.58166819881007 \tabularnewline
133 & 5.52125290968881 & 5.40467826467087 & 5.63782755470675 \tabularnewline
134 & 5.54187936453321 & 5.39668697446261 & 5.68707175460381 \tabularnewline
135 & 5.56250581937762 & 5.39204617479483 & 5.7329654639604 \tabularnewline
136 & 5.58313227422202 & 5.3894009961642 & 5.77686355227984 \tabularnewline
137 & 5.60375872906642 & 5.38806922426724 & 5.8194482338656 \tabularnewline
138 & 5.62438518391083 & 5.38765298727227 & 5.86111738054938 \tabularnewline
139 & 5.64501163875523 & 5.38789785309109 & 5.90212542441937 \tabularnewline
140 & 5.66563809359963 & 5.38863044138325 & 5.94264574581601 \tabularnewline
141 & 5.68626454844404 & 5.38972697224972 & 5.98280212463835 \tabularnewline
142 & 5.70689100328844 & 5.39109587626607 & 6.02268613031081 \tabularnewline
143 & 5.72751745813285 & 5.39266748695128 & 6.06236742931441 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42272&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]132[/C][C]5.5006264548444[/C][C]5.41958471087874[/C][C]5.58166819881007[/C][/ROW]
[ROW][C]133[/C][C]5.52125290968881[/C][C]5.40467826467087[/C][C]5.63782755470675[/C][/ROW]
[ROW][C]134[/C][C]5.54187936453321[/C][C]5.39668697446261[/C][C]5.68707175460381[/C][/ROW]
[ROW][C]135[/C][C]5.56250581937762[/C][C]5.39204617479483[/C][C]5.7329654639604[/C][/ROW]
[ROW][C]136[/C][C]5.58313227422202[/C][C]5.3894009961642[/C][C]5.77686355227984[/C][/ROW]
[ROW][C]137[/C][C]5.60375872906642[/C][C]5.38806922426724[/C][C]5.8194482338656[/C][/ROW]
[ROW][C]138[/C][C]5.62438518391083[/C][C]5.38765298727227[/C][C]5.86111738054938[/C][/ROW]
[ROW][C]139[/C][C]5.64501163875523[/C][C]5.38789785309109[/C][C]5.90212542441937[/C][/ROW]
[ROW][C]140[/C][C]5.66563809359963[/C][C]5.38863044138325[/C][C]5.94264574581601[/C][/ROW]
[ROW][C]141[/C][C]5.68626454844404[/C][C]5.38972697224972[/C][C]5.98280212463835[/C][/ROW]
[ROW][C]142[/C][C]5.70689100328844[/C][C]5.39109587626607[/C][C]6.02268613031081[/C][/ROW]
[ROW][C]143[/C][C]5.72751745813285[/C][C]5.39266748695128[/C][C]6.06236742931441[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42272&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42272&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
132	5.5006264548444	5.41958471087874	5.58166819881007
133	5.52125290968881	5.40467826467087	5.63782755470675
134	5.54187936453321	5.39668697446261	5.68707175460381
135	5.56250581937762	5.39204617479483	5.7329654639604
136	5.58313227422202	5.3894009961642	5.77686355227984
137	5.60375872906642	5.38806922426724	5.8194482338656
138	5.62438518391083	5.38765298727227	5.86111738054938
139	5.64501163875523	5.38789785309109	5.90212542441937
140	5.66563809359963	5.38863044138325	5.94264574581601
141	5.68626454844404	5.38972697224972	5.98280212463835
142	5.70689100328844	5.39109587626607	6.02268613031081
143	5.72751745813285	5.39266748695128	6.06236742931441

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