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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

Sat, 17 Dec 2011 09:16:28 -0500

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/2011/Dec/17/t13241314407j6w7cxudfq9gbr.htm/, Retrieved Thu, 25 Apr 2024 21:41:27 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=156324, Retrieved Thu, 25 Apr 2024 21:41:27 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W102

Estimated Impact

104

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

-       [Exponential Smoothing] [Evolutie gemiddel...] [2011-12-17 14:16:28] [9b00bb73e1719a6b710100764835da33] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'AstonUniversity' @ aston.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 & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156324&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=156324&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156324&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	'AstonUniversity' @ aston.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.107590001844371
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.107590001844371 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156324&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]0.107590001844371[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=156324&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156324&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	0.107590001844371
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	10.89	10.91	-0.0199999999999996
4	10.94	10.8778481999631	0.0621518000368866
5	10.98	10.9345351122437	0.0454648877562889
6	10.99	10.9794266796013	0.0105733203987342
7	11.02	10.9905642631625	0.0294357368375326
8	11.04	11.0237312541431	0.0162687458568929
9	11.05	11.0454816085399	0.00451839146014521
10	11.05	11.0559677422854	-0.00596774228538699
11	11.02	11.0553256728819	-0.0353256728818963
12	10.91	11.0215249836714	-0.111524983671378
13	11.01	10.8995260104725	0.110473989527518
14	11.02	11.0114119072095	0.00858809279049844
15	11.03	11.0223359001287	0.0076640998713291
16	11.04	11.033160480648	0.0068395193520363
17	11.06	11.0438963445477	0.0161036554523388
18	11.08	11.0656289368675	0.0143710631325185
19	11.06	11.0871751195764	-0.0271751195764143
20	11.06	11.0642513484111	-0.00425134841106711
21	11.09	11.0637939458277	0.0262060541723201
22	11.07	11.0966134552444	-0.0266134552444122
23	11.06	11.0737501135456	-0.0137501135455818
24	11.08	11.0622707388039	0.0177292611961466
25	11.08	11.0841782300486	-0.00417823004864459
26	11.08	11.08372869427	-0.00372869427000566
27	11.11	11.0833275240466	0.0266724759533812
28	11.09	11.1161972157836	-0.0261972157836361
29	11.08	11.0933786572892	-0.0133786572891577
30	11.05	11.0819392475267	-0.0319392475267417
31	11.07	11.0485029038264	0.021497096173567
32	11.06	11.0708157764434	-0.010815776443394
33	11.06	11.0596521070359	0.000347892964098762
34	11.07	11.0596895368406	0.0103104631594491
35	11.02	11.0707988395909	-0.0507988395908932
36	11.01	11.0153333923456	-0.00533339234561581
37	11.04	11.0047595726533	0.0352404273466842
38	11.02	11.0385510902965	-0.0185510902965405
39	11.03	11.0165551784573	0.013444821542679
40	11.17	11.0280017068319	0.141998293168106
41	11.19	11.1832793034557	0.00672069654425123
42	11.15	11.2040023832093	-0.0540023832093386
43	11.13	11.1581922667002	-0.0281922667002465
44	11.06	11.135159060674	-0.07515906067397
45	11.01	11.0570726971974	-0.0470726971974376
46	11.03	11.0020081456191	0.0279918543808542
47	10.99	11.0250197892836	-0.0350197892836075
48	10.94	10.98125201009	-0.0412520100899965
49	11	10.9268137062483	0.0731862937516716
50	11.06	10.9946878197281	0.0653121802719472
51	11.06	11.061714757324	-0.00171475732397219
52	11.05	11.0615302665803	-0.0115302665803227
53	11.04	11.0502897251777	-0.0102897251776817
54	11.15	11.0391826536268	0.110817346373166
55	11.2	11.1611054921275	0.0388945078724863
56	11.16	11.2152901523012	-0.0552901523012483
57	11.3	11.1693414847132	0.130658515286818
58	11.23	11.3233990346139	-0.0933990346138742
59	11.25	11.2433502323075	0.00664976769249392
60	11.25	11.2640656808258	-0.0140656808258051
61	11.12	11.2625523541998	-0.142552354199815
62	11.14	11.1172151461485	0.0227848538514639
63	11.17	11.1396665686164	0.0303334313835588
64	11.25	11.1729301425549	0.077069857445057
65	11.27	11.2612220886596	0.00877791134039718
66	11.34	11.2821665041569	0.0578334958430951
67	11.39	11.3583888100813	0.0316111899186708
68	11.44	11.411789858063	0.0282101419370164
69	11.46	11.464824987286	-0.00482498728601399
70	11.49	11.484305866895	0.0056941331049849
71	11.51	11.5149184986863	-0.00491849868628336
72	11.48	11.5343893174036	-0.0543893174035528
73	11.49	11.4985375706438	-0.00853757064379224
74	11.52	11.5076190134025	0.0123809865975204
75	11.56	11.5389510837733	0.0210489162266594
76	11.58	11.581215736709	-0.00121573670899089
77	11.58	11.6010849355942	-0.021084935594228
78	11.58	11.5988164073348	-0.0188164073347554
79	11.6	11.5967919500349	0.00320804996509416
80	11.62	11.6171371041366	0.00286289586343358
81	11.62	11.6374451231078	-0.0174451231077928
82	11.64	11.6355682022804	0.00443179771955116
83	11.67	11.6560450194053	0.013954980594729
84	11.66	11.6875464357932	-0.0275464357931963
85	11.72	11.6745827147154	0.0454172852846
86	11.82	11.7394691605229	0.0805308394770634
87	11.9	11.8481334736908	0.0518665263091975
88	12.04	11.9337137933521	0.106286206647928
89	12.08	12.0851491265214	-0.00514912652135102
90	12.15	12.1245951319894	0.0254048680105772
91	12.19	12.1973284417855	-0.00732844178553727
92	12.22	12.2365399747203	-0.0165399747203132
93	12.23	12.2647604388097	-0.0347604388096503
94	12.25	12.271020563134	-0.0210205631340088
95	12.26	12.2887589607077	-0.0287589607076519
96	12.27	12.2956647840721	-0.0256647840720721
97	12.34	12.3029035099064	0.0370964900935782
98	12.38	12.376894721344	0.00310527865599042
99	12.42	12.4172288182803	0.00277118171966251
100	12.43	12.4575269697267	-0.0275269697266651
101	12.48	12.464565343003	0.0154346569969963
102	12.5	12.5162259577778	-0.0162259577777775
103	12.5	12.5344802069505	-0.0344802069505405
104	12.49	12.5307704814211	-0.040770481421136
105	12.46	12.5163839852498	-0.0563839852498411
106	12.45	12.4803176321728	-0.0303176321728191
107	12.45	12.4670557580714	-0.017055758071427
108	12.38	12.4652207290291	-0.0852207290290643
109	12.42	12.3860518306357	0.0339481693643489
110	12.37	12.4297043142402	-0.0597043142401734
111	12.35	12.373280726961	-0.0232807269609552
112	12.35	12.3507759535043	-0.00077595350428794
113	12.36	12.3506924686653	0.00930753133466844
114	12.32	12.3616938659788	-0.0416938659787931
115	12.32	12.3172080228612	0.002791977138763
116	12.34	12.3175084116867	0.0224915883132528
117	12.35	12.3399282817149	0.0100717182851486
118	12.34	12.3510118979037	-0.0110118979037264
119	12.31	12.339827127788	-0.0298271277879536
120	12.24	12.3066180270542	-0.0666180270542363

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 10.89 & 10.91 & -0.0199999999999996 \tabularnewline
4 & 10.94 & 10.8778481999631 & 0.0621518000368866 \tabularnewline
5 & 10.98 & 10.9345351122437 & 0.0454648877562889 \tabularnewline
6 & 10.99 & 10.9794266796013 & 0.0105733203987342 \tabularnewline
7 & 11.02 & 10.9905642631625 & 0.0294357368375326 \tabularnewline
8 & 11.04 & 11.0237312541431 & 0.0162687458568929 \tabularnewline
9 & 11.05 & 11.0454816085399 & 0.00451839146014521 \tabularnewline
10 & 11.05 & 11.0559677422854 & -0.00596774228538699 \tabularnewline
11 & 11.02 & 11.0553256728819 & -0.0353256728818963 \tabularnewline
12 & 10.91 & 11.0215249836714 & -0.111524983671378 \tabularnewline
13 & 11.01 & 10.8995260104725 & 0.110473989527518 \tabularnewline
14 & 11.02 & 11.0114119072095 & 0.00858809279049844 \tabularnewline
15 & 11.03 & 11.0223359001287 & 0.0076640998713291 \tabularnewline
16 & 11.04 & 11.033160480648 & 0.0068395193520363 \tabularnewline
17 & 11.06 & 11.0438963445477 & 0.0161036554523388 \tabularnewline
18 & 11.08 & 11.0656289368675 & 0.0143710631325185 \tabularnewline
19 & 11.06 & 11.0871751195764 & -0.0271751195764143 \tabularnewline
20 & 11.06 & 11.0642513484111 & -0.00425134841106711 \tabularnewline
21 & 11.09 & 11.0637939458277 & 0.0262060541723201 \tabularnewline
22 & 11.07 & 11.0966134552444 & -0.0266134552444122 \tabularnewline
23 & 11.06 & 11.0737501135456 & -0.0137501135455818 \tabularnewline
24 & 11.08 & 11.0622707388039 & 0.0177292611961466 \tabularnewline
25 & 11.08 & 11.0841782300486 & -0.00417823004864459 \tabularnewline
26 & 11.08 & 11.08372869427 & -0.00372869427000566 \tabularnewline
27 & 11.11 & 11.0833275240466 & 0.0266724759533812 \tabularnewline
28 & 11.09 & 11.1161972157836 & -0.0261972157836361 \tabularnewline
29 & 11.08 & 11.0933786572892 & -0.0133786572891577 \tabularnewline
30 & 11.05 & 11.0819392475267 & -0.0319392475267417 \tabularnewline
31 & 11.07 & 11.0485029038264 & 0.021497096173567 \tabularnewline
32 & 11.06 & 11.0708157764434 & -0.010815776443394 \tabularnewline
33 & 11.06 & 11.0596521070359 & 0.000347892964098762 \tabularnewline
34 & 11.07 & 11.0596895368406 & 0.0103104631594491 \tabularnewline
35 & 11.02 & 11.0707988395909 & -0.0507988395908932 \tabularnewline
36 & 11.01 & 11.0153333923456 & -0.00533339234561581 \tabularnewline
37 & 11.04 & 11.0047595726533 & 0.0352404273466842 \tabularnewline
38 & 11.02 & 11.0385510902965 & -0.0185510902965405 \tabularnewline
39 & 11.03 & 11.0165551784573 & 0.013444821542679 \tabularnewline
40 & 11.17 & 11.0280017068319 & 0.141998293168106 \tabularnewline
41 & 11.19 & 11.1832793034557 & 0.00672069654425123 \tabularnewline
42 & 11.15 & 11.2040023832093 & -0.0540023832093386 \tabularnewline
43 & 11.13 & 11.1581922667002 & -0.0281922667002465 \tabularnewline
44 & 11.06 & 11.135159060674 & -0.07515906067397 \tabularnewline
45 & 11.01 & 11.0570726971974 & -0.0470726971974376 \tabularnewline
46 & 11.03 & 11.0020081456191 & 0.0279918543808542 \tabularnewline
47 & 10.99 & 11.0250197892836 & -0.0350197892836075 \tabularnewline
48 & 10.94 & 10.98125201009 & -0.0412520100899965 \tabularnewline
49 & 11 & 10.9268137062483 & 0.0731862937516716 \tabularnewline
50 & 11.06 & 10.9946878197281 & 0.0653121802719472 \tabularnewline
51 & 11.06 & 11.061714757324 & -0.00171475732397219 \tabularnewline
52 & 11.05 & 11.0615302665803 & -0.0115302665803227 \tabularnewline
53 & 11.04 & 11.0502897251777 & -0.0102897251776817 \tabularnewline
54 & 11.15 & 11.0391826536268 & 0.110817346373166 \tabularnewline
55 & 11.2 & 11.1611054921275 & 0.0388945078724863 \tabularnewline
56 & 11.16 & 11.2152901523012 & -0.0552901523012483 \tabularnewline
57 & 11.3 & 11.1693414847132 & 0.130658515286818 \tabularnewline
58 & 11.23 & 11.3233990346139 & -0.0933990346138742 \tabularnewline
59 & 11.25 & 11.2433502323075 & 0.00664976769249392 \tabularnewline
60 & 11.25 & 11.2640656808258 & -0.0140656808258051 \tabularnewline
61 & 11.12 & 11.2625523541998 & -0.142552354199815 \tabularnewline
62 & 11.14 & 11.1172151461485 & 0.0227848538514639 \tabularnewline
63 & 11.17 & 11.1396665686164 & 0.0303334313835588 \tabularnewline
64 & 11.25 & 11.1729301425549 & 0.077069857445057 \tabularnewline
65 & 11.27 & 11.2612220886596 & 0.00877791134039718 \tabularnewline
66 & 11.34 & 11.2821665041569 & 0.0578334958430951 \tabularnewline
67 & 11.39 & 11.3583888100813 & 0.0316111899186708 \tabularnewline
68 & 11.44 & 11.411789858063 & 0.0282101419370164 \tabularnewline
69 & 11.46 & 11.464824987286 & -0.00482498728601399 \tabularnewline
70 & 11.49 & 11.484305866895 & 0.0056941331049849 \tabularnewline
71 & 11.51 & 11.5149184986863 & -0.00491849868628336 \tabularnewline
72 & 11.48 & 11.5343893174036 & -0.0543893174035528 \tabularnewline
73 & 11.49 & 11.4985375706438 & -0.00853757064379224 \tabularnewline
74 & 11.52 & 11.5076190134025 & 0.0123809865975204 \tabularnewline
75 & 11.56 & 11.5389510837733 & 0.0210489162266594 \tabularnewline
76 & 11.58 & 11.581215736709 & -0.00121573670899089 \tabularnewline
77 & 11.58 & 11.6010849355942 & -0.021084935594228 \tabularnewline
78 & 11.58 & 11.5988164073348 & -0.0188164073347554 \tabularnewline
79 & 11.6 & 11.5967919500349 & 0.00320804996509416 \tabularnewline
80 & 11.62 & 11.6171371041366 & 0.00286289586343358 \tabularnewline
81 & 11.62 & 11.6374451231078 & -0.0174451231077928 \tabularnewline
82 & 11.64 & 11.6355682022804 & 0.00443179771955116 \tabularnewline
83 & 11.67 & 11.6560450194053 & 0.013954980594729 \tabularnewline
84 & 11.66 & 11.6875464357932 & -0.0275464357931963 \tabularnewline
85 & 11.72 & 11.6745827147154 & 0.0454172852846 \tabularnewline
86 & 11.82 & 11.7394691605229 & 0.0805308394770634 \tabularnewline
87 & 11.9 & 11.8481334736908 & 0.0518665263091975 \tabularnewline
88 & 12.04 & 11.9337137933521 & 0.106286206647928 \tabularnewline
89 & 12.08 & 12.0851491265214 & -0.00514912652135102 \tabularnewline
90 & 12.15 & 12.1245951319894 & 0.0254048680105772 \tabularnewline
91 & 12.19 & 12.1973284417855 & -0.00732844178553727 \tabularnewline
92 & 12.22 & 12.2365399747203 & -0.0165399747203132 \tabularnewline
93 & 12.23 & 12.2647604388097 & -0.0347604388096503 \tabularnewline
94 & 12.25 & 12.271020563134 & -0.0210205631340088 \tabularnewline
95 & 12.26 & 12.2887589607077 & -0.0287589607076519 \tabularnewline
96 & 12.27 & 12.2956647840721 & -0.0256647840720721 \tabularnewline
97 & 12.34 & 12.3029035099064 & 0.0370964900935782 \tabularnewline
98 & 12.38 & 12.376894721344 & 0.00310527865599042 \tabularnewline
99 & 12.42 & 12.4172288182803 & 0.00277118171966251 \tabularnewline
100 & 12.43 & 12.4575269697267 & -0.0275269697266651 \tabularnewline
101 & 12.48 & 12.464565343003 & 0.0154346569969963 \tabularnewline
102 & 12.5 & 12.5162259577778 & -0.0162259577777775 \tabularnewline
103 & 12.5 & 12.5344802069505 & -0.0344802069505405 \tabularnewline
104 & 12.49 & 12.5307704814211 & -0.040770481421136 \tabularnewline
105 & 12.46 & 12.5163839852498 & -0.0563839852498411 \tabularnewline
106 & 12.45 & 12.4803176321728 & -0.0303176321728191 \tabularnewline
107 & 12.45 & 12.4670557580714 & -0.017055758071427 \tabularnewline
108 & 12.38 & 12.4652207290291 & -0.0852207290290643 \tabularnewline
109 & 12.42 & 12.3860518306357 & 0.0339481693643489 \tabularnewline
110 & 12.37 & 12.4297043142402 & -0.0597043142401734 \tabularnewline
111 & 12.35 & 12.373280726961 & -0.0232807269609552 \tabularnewline
112 & 12.35 & 12.3507759535043 & -0.00077595350428794 \tabularnewline
113 & 12.36 & 12.3506924686653 & 0.00930753133466844 \tabularnewline
114 & 12.32 & 12.3616938659788 & -0.0416938659787931 \tabularnewline
115 & 12.32 & 12.3172080228612 & 0.002791977138763 \tabularnewline
116 & 12.34 & 12.3175084116867 & 0.0224915883132528 \tabularnewline
117 & 12.35 & 12.3399282817149 & 0.0100717182851486 \tabularnewline
118 & 12.34 & 12.3510118979037 & -0.0110118979037264 \tabularnewline
119 & 12.31 & 12.339827127788 & -0.0298271277879536 \tabularnewline
120 & 12.24 & 12.3066180270542 & -0.0666180270542363 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156324&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]10.89[/C][C]10.91[/C][C]-0.0199999999999996[/C][/ROW]
[ROW][C]4[/C][C]10.94[/C][C]10.8778481999631[/C][C]0.0621518000368866[/C][/ROW]
[ROW][C]5[/C][C]10.98[/C][C]10.9345351122437[/C][C]0.0454648877562889[/C][/ROW]
[ROW][C]6[/C][C]10.99[/C][C]10.9794266796013[/C][C]0.0105733203987342[/C][/ROW]
[ROW][C]7[/C][C]11.02[/C][C]10.9905642631625[/C][C]0.0294357368375326[/C][/ROW]
[ROW][C]8[/C][C]11.04[/C][C]11.0237312541431[/C][C]0.0162687458568929[/C][/ROW]
[ROW][C]9[/C][C]11.05[/C][C]11.0454816085399[/C][C]0.00451839146014521[/C][/ROW]
[ROW][C]10[/C][C]11.05[/C][C]11.0559677422854[/C][C]-0.00596774228538699[/C][/ROW]
[ROW][C]11[/C][C]11.02[/C][C]11.0553256728819[/C][C]-0.0353256728818963[/C][/ROW]
[ROW][C]12[/C][C]10.91[/C][C]11.0215249836714[/C][C]-0.111524983671378[/C][/ROW]
[ROW][C]13[/C][C]11.01[/C][C]10.8995260104725[/C][C]0.110473989527518[/C][/ROW]
[ROW][C]14[/C][C]11.02[/C][C]11.0114119072095[/C][C]0.00858809279049844[/C][/ROW]
[ROW][C]15[/C][C]11.03[/C][C]11.0223359001287[/C][C]0.0076640998713291[/C][/ROW]
[ROW][C]16[/C][C]11.04[/C][C]11.033160480648[/C][C]0.0068395193520363[/C][/ROW]
[ROW][C]17[/C][C]11.06[/C][C]11.0438963445477[/C][C]0.0161036554523388[/C][/ROW]
[ROW][C]18[/C][C]11.08[/C][C]11.0656289368675[/C][C]0.0143710631325185[/C][/ROW]
[ROW][C]19[/C][C]11.06[/C][C]11.0871751195764[/C][C]-0.0271751195764143[/C][/ROW]
[ROW][C]20[/C][C]11.06[/C][C]11.0642513484111[/C][C]-0.00425134841106711[/C][/ROW]
[ROW][C]21[/C][C]11.09[/C][C]11.0637939458277[/C][C]0.0262060541723201[/C][/ROW]
[ROW][C]22[/C][C]11.07[/C][C]11.0966134552444[/C][C]-0.0266134552444122[/C][/ROW]
[ROW][C]23[/C][C]11.06[/C][C]11.0737501135456[/C][C]-0.0137501135455818[/C][/ROW]
[ROW][C]24[/C][C]11.08[/C][C]11.0622707388039[/C][C]0.0177292611961466[/C][/ROW]
[ROW][C]25[/C][C]11.08[/C][C]11.0841782300486[/C][C]-0.00417823004864459[/C][/ROW]
[ROW][C]26[/C][C]11.08[/C][C]11.08372869427[/C][C]-0.00372869427000566[/C][/ROW]
[ROW][C]27[/C][C]11.11[/C][C]11.0833275240466[/C][C]0.0266724759533812[/C][/ROW]
[ROW][C]28[/C][C]11.09[/C][C]11.1161972157836[/C][C]-0.0261972157836361[/C][/ROW]
[ROW][C]29[/C][C]11.08[/C][C]11.0933786572892[/C][C]-0.0133786572891577[/C][/ROW]
[ROW][C]30[/C][C]11.05[/C][C]11.0819392475267[/C][C]-0.0319392475267417[/C][/ROW]
[ROW][C]31[/C][C]11.07[/C][C]11.0485029038264[/C][C]0.021497096173567[/C][/ROW]
[ROW][C]32[/C][C]11.06[/C][C]11.0708157764434[/C][C]-0.010815776443394[/C][/ROW]
[ROW][C]33[/C][C]11.06[/C][C]11.0596521070359[/C][C]0.000347892964098762[/C][/ROW]
[ROW][C]34[/C][C]11.07[/C][C]11.0596895368406[/C][C]0.0103104631594491[/C][/ROW]
[ROW][C]35[/C][C]11.02[/C][C]11.0707988395909[/C][C]-0.0507988395908932[/C][/ROW]
[ROW][C]36[/C][C]11.01[/C][C]11.0153333923456[/C][C]-0.00533339234561581[/C][/ROW]
[ROW][C]37[/C][C]11.04[/C][C]11.0047595726533[/C][C]0.0352404273466842[/C][/ROW]
[ROW][C]38[/C][C]11.02[/C][C]11.0385510902965[/C][C]-0.0185510902965405[/C][/ROW]
[ROW][C]39[/C][C]11.03[/C][C]11.0165551784573[/C][C]0.013444821542679[/C][/ROW]
[ROW][C]40[/C][C]11.17[/C][C]11.0280017068319[/C][C]0.141998293168106[/C][/ROW]
[ROW][C]41[/C][C]11.19[/C][C]11.1832793034557[/C][C]0.00672069654425123[/C][/ROW]
[ROW][C]42[/C][C]11.15[/C][C]11.2040023832093[/C][C]-0.0540023832093386[/C][/ROW]
[ROW][C]43[/C][C]11.13[/C][C]11.1581922667002[/C][C]-0.0281922667002465[/C][/ROW]
[ROW][C]44[/C][C]11.06[/C][C]11.135159060674[/C][C]-0.07515906067397[/C][/ROW]
[ROW][C]45[/C][C]11.01[/C][C]11.0570726971974[/C][C]-0.0470726971974376[/C][/ROW]
[ROW][C]46[/C][C]11.03[/C][C]11.0020081456191[/C][C]0.0279918543808542[/C][/ROW]
[ROW][C]47[/C][C]10.99[/C][C]11.0250197892836[/C][C]-0.0350197892836075[/C][/ROW]
[ROW][C]48[/C][C]10.94[/C][C]10.98125201009[/C][C]-0.0412520100899965[/C][/ROW]
[ROW][C]49[/C][C]11[/C][C]10.9268137062483[/C][C]0.0731862937516716[/C][/ROW]
[ROW][C]50[/C][C]11.06[/C][C]10.9946878197281[/C][C]0.0653121802719472[/C][/ROW]
[ROW][C]51[/C][C]11.06[/C][C]11.061714757324[/C][C]-0.00171475732397219[/C][/ROW]
[ROW][C]52[/C][C]11.05[/C][C]11.0615302665803[/C][C]-0.0115302665803227[/C][/ROW]
[ROW][C]53[/C][C]11.04[/C][C]11.0502897251777[/C][C]-0.0102897251776817[/C][/ROW]
[ROW][C]54[/C][C]11.15[/C][C]11.0391826536268[/C][C]0.110817346373166[/C][/ROW]
[ROW][C]55[/C][C]11.2[/C][C]11.1611054921275[/C][C]0.0388945078724863[/C][/ROW]
[ROW][C]56[/C][C]11.16[/C][C]11.2152901523012[/C][C]-0.0552901523012483[/C][/ROW]
[ROW][C]57[/C][C]11.3[/C][C]11.1693414847132[/C][C]0.130658515286818[/C][/ROW]
[ROW][C]58[/C][C]11.23[/C][C]11.3233990346139[/C][C]-0.0933990346138742[/C][/ROW]
[ROW][C]59[/C][C]11.25[/C][C]11.2433502323075[/C][C]0.00664976769249392[/C][/ROW]
[ROW][C]60[/C][C]11.25[/C][C]11.2640656808258[/C][C]-0.0140656808258051[/C][/ROW]
[ROW][C]61[/C][C]11.12[/C][C]11.2625523541998[/C][C]-0.142552354199815[/C][/ROW]
[ROW][C]62[/C][C]11.14[/C][C]11.1172151461485[/C][C]0.0227848538514639[/C][/ROW]
[ROW][C]63[/C][C]11.17[/C][C]11.1396665686164[/C][C]0.0303334313835588[/C][/ROW]
[ROW][C]64[/C][C]11.25[/C][C]11.1729301425549[/C][C]0.077069857445057[/C][/ROW]
[ROW][C]65[/C][C]11.27[/C][C]11.2612220886596[/C][C]0.00877791134039718[/C][/ROW]
[ROW][C]66[/C][C]11.34[/C][C]11.2821665041569[/C][C]0.0578334958430951[/C][/ROW]
[ROW][C]67[/C][C]11.39[/C][C]11.3583888100813[/C][C]0.0316111899186708[/C][/ROW]
[ROW][C]68[/C][C]11.44[/C][C]11.411789858063[/C][C]0.0282101419370164[/C][/ROW]
[ROW][C]69[/C][C]11.46[/C][C]11.464824987286[/C][C]-0.00482498728601399[/C][/ROW]
[ROW][C]70[/C][C]11.49[/C][C]11.484305866895[/C][C]0.0056941331049849[/C][/ROW]
[ROW][C]71[/C][C]11.51[/C][C]11.5149184986863[/C][C]-0.00491849868628336[/C][/ROW]
[ROW][C]72[/C][C]11.48[/C][C]11.5343893174036[/C][C]-0.0543893174035528[/C][/ROW]
[ROW][C]73[/C][C]11.49[/C][C]11.4985375706438[/C][C]-0.00853757064379224[/C][/ROW]
[ROW][C]74[/C][C]11.52[/C][C]11.5076190134025[/C][C]0.0123809865975204[/C][/ROW]
[ROW][C]75[/C][C]11.56[/C][C]11.5389510837733[/C][C]0.0210489162266594[/C][/ROW]
[ROW][C]76[/C][C]11.58[/C][C]11.581215736709[/C][C]-0.00121573670899089[/C][/ROW]
[ROW][C]77[/C][C]11.58[/C][C]11.6010849355942[/C][C]-0.021084935594228[/C][/ROW]
[ROW][C]78[/C][C]11.58[/C][C]11.5988164073348[/C][C]-0.0188164073347554[/C][/ROW]
[ROW][C]79[/C][C]11.6[/C][C]11.5967919500349[/C][C]0.00320804996509416[/C][/ROW]
[ROW][C]80[/C][C]11.62[/C][C]11.6171371041366[/C][C]0.00286289586343358[/C][/ROW]
[ROW][C]81[/C][C]11.62[/C][C]11.6374451231078[/C][C]-0.0174451231077928[/C][/ROW]
[ROW][C]82[/C][C]11.64[/C][C]11.6355682022804[/C][C]0.00443179771955116[/C][/ROW]
[ROW][C]83[/C][C]11.67[/C][C]11.6560450194053[/C][C]0.013954980594729[/C][/ROW]
[ROW][C]84[/C][C]11.66[/C][C]11.6875464357932[/C][C]-0.0275464357931963[/C][/ROW]
[ROW][C]85[/C][C]11.72[/C][C]11.6745827147154[/C][C]0.0454172852846[/C][/ROW]
[ROW][C]86[/C][C]11.82[/C][C]11.7394691605229[/C][C]0.0805308394770634[/C][/ROW]
[ROW][C]87[/C][C]11.9[/C][C]11.8481334736908[/C][C]0.0518665263091975[/C][/ROW]
[ROW][C]88[/C][C]12.04[/C][C]11.9337137933521[/C][C]0.106286206647928[/C][/ROW]
[ROW][C]89[/C][C]12.08[/C][C]12.0851491265214[/C][C]-0.00514912652135102[/C][/ROW]
[ROW][C]90[/C][C]12.15[/C][C]12.1245951319894[/C][C]0.0254048680105772[/C][/ROW]
[ROW][C]91[/C][C]12.19[/C][C]12.1973284417855[/C][C]-0.00732844178553727[/C][/ROW]
[ROW][C]92[/C][C]12.22[/C][C]12.2365399747203[/C][C]-0.0165399747203132[/C][/ROW]
[ROW][C]93[/C][C]12.23[/C][C]12.2647604388097[/C][C]-0.0347604388096503[/C][/ROW]
[ROW][C]94[/C][C]12.25[/C][C]12.271020563134[/C][C]-0.0210205631340088[/C][/ROW]
[ROW][C]95[/C][C]12.26[/C][C]12.2887589607077[/C][C]-0.0287589607076519[/C][/ROW]
[ROW][C]96[/C][C]12.27[/C][C]12.2956647840721[/C][C]-0.0256647840720721[/C][/ROW]
[ROW][C]97[/C][C]12.34[/C][C]12.3029035099064[/C][C]0.0370964900935782[/C][/ROW]
[ROW][C]98[/C][C]12.38[/C][C]12.376894721344[/C][C]0.00310527865599042[/C][/ROW]
[ROW][C]99[/C][C]12.42[/C][C]12.4172288182803[/C][C]0.00277118171966251[/C][/ROW]
[ROW][C]100[/C][C]12.43[/C][C]12.4575269697267[/C][C]-0.0275269697266651[/C][/ROW]
[ROW][C]101[/C][C]12.48[/C][C]12.464565343003[/C][C]0.0154346569969963[/C][/ROW]
[ROW][C]102[/C][C]12.5[/C][C]12.5162259577778[/C][C]-0.0162259577777775[/C][/ROW]
[ROW][C]103[/C][C]12.5[/C][C]12.5344802069505[/C][C]-0.0344802069505405[/C][/ROW]
[ROW][C]104[/C][C]12.49[/C][C]12.5307704814211[/C][C]-0.040770481421136[/C][/ROW]
[ROW][C]105[/C][C]12.46[/C][C]12.5163839852498[/C][C]-0.0563839852498411[/C][/ROW]
[ROW][C]106[/C][C]12.45[/C][C]12.4803176321728[/C][C]-0.0303176321728191[/C][/ROW]
[ROW][C]107[/C][C]12.45[/C][C]12.4670557580714[/C][C]-0.017055758071427[/C][/ROW]
[ROW][C]108[/C][C]12.38[/C][C]12.4652207290291[/C][C]-0.0852207290290643[/C][/ROW]
[ROW][C]109[/C][C]12.42[/C][C]12.3860518306357[/C][C]0.0339481693643489[/C][/ROW]
[ROW][C]110[/C][C]12.37[/C][C]12.4297043142402[/C][C]-0.0597043142401734[/C][/ROW]
[ROW][C]111[/C][C]12.35[/C][C]12.373280726961[/C][C]-0.0232807269609552[/C][/ROW]
[ROW][C]112[/C][C]12.35[/C][C]12.3507759535043[/C][C]-0.00077595350428794[/C][/ROW]
[ROW][C]113[/C][C]12.36[/C][C]12.3506924686653[/C][C]0.00930753133466844[/C][/ROW]
[ROW][C]114[/C][C]12.32[/C][C]12.3616938659788[/C][C]-0.0416938659787931[/C][/ROW]
[ROW][C]115[/C][C]12.32[/C][C]12.3172080228612[/C][C]0.002791977138763[/C][/ROW]
[ROW][C]116[/C][C]12.34[/C][C]12.3175084116867[/C][C]0.0224915883132528[/C][/ROW]
[ROW][C]117[/C][C]12.35[/C][C]12.3399282817149[/C][C]0.0100717182851486[/C][/ROW]
[ROW][C]118[/C][C]12.34[/C][C]12.3510118979037[/C][C]-0.0110118979037264[/C][/ROW]
[ROW][C]119[/C][C]12.31[/C][C]12.339827127788[/C][C]-0.0298271277879536[/C][/ROW]
[ROW][C]120[/C][C]12.24[/C][C]12.3066180270542[/C][C]-0.0666180270542363[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=156324&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156324&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	10.89	10.91	-0.0199999999999996
4	10.94	10.8778481999631	0.0621518000368866
5	10.98	10.9345351122437	0.0454648877562889
6	10.99	10.9794266796013	0.0105733203987342
7	11.02	10.9905642631625	0.0294357368375326
8	11.04	11.0237312541431	0.0162687458568929
9	11.05	11.0454816085399	0.00451839146014521
10	11.05	11.0559677422854	-0.00596774228538699
11	11.02	11.0553256728819	-0.0353256728818963
12	10.91	11.0215249836714	-0.111524983671378
13	11.01	10.8995260104725	0.110473989527518
14	11.02	11.0114119072095	0.00858809279049844
15	11.03	11.0223359001287	0.0076640998713291
16	11.04	11.033160480648	0.0068395193520363
17	11.06	11.0438963445477	0.0161036554523388
18	11.08	11.0656289368675	0.0143710631325185
19	11.06	11.0871751195764	-0.0271751195764143
20	11.06	11.0642513484111	-0.00425134841106711
21	11.09	11.0637939458277	0.0262060541723201
22	11.07	11.0966134552444	-0.0266134552444122
23	11.06	11.0737501135456	-0.0137501135455818
24	11.08	11.0622707388039	0.0177292611961466
25	11.08	11.0841782300486	-0.00417823004864459
26	11.08	11.08372869427	-0.00372869427000566
27	11.11	11.0833275240466	0.0266724759533812
28	11.09	11.1161972157836	-0.0261972157836361
29	11.08	11.0933786572892	-0.0133786572891577
30	11.05	11.0819392475267	-0.0319392475267417
31	11.07	11.0485029038264	0.021497096173567
32	11.06	11.0708157764434	-0.010815776443394
33	11.06	11.0596521070359	0.000347892964098762
34	11.07	11.0596895368406	0.0103104631594491
35	11.02	11.0707988395909	-0.0507988395908932
36	11.01	11.0153333923456	-0.00533339234561581
37	11.04	11.0047595726533	0.0352404273466842
38	11.02	11.0385510902965	-0.0185510902965405
39	11.03	11.0165551784573	0.013444821542679
40	11.17	11.0280017068319	0.141998293168106
41	11.19	11.1832793034557	0.00672069654425123
42	11.15	11.2040023832093	-0.0540023832093386
43	11.13	11.1581922667002	-0.0281922667002465
44	11.06	11.135159060674	-0.07515906067397
45	11.01	11.0570726971974	-0.0470726971974376
46	11.03	11.0020081456191	0.0279918543808542
47	10.99	11.0250197892836	-0.0350197892836075
48	10.94	10.98125201009	-0.0412520100899965
49	11	10.9268137062483	0.0731862937516716
50	11.06	10.9946878197281	0.0653121802719472
51	11.06	11.061714757324	-0.00171475732397219
52	11.05	11.0615302665803	-0.0115302665803227
53	11.04	11.0502897251777	-0.0102897251776817
54	11.15	11.0391826536268	0.110817346373166
55	11.2	11.1611054921275	0.0388945078724863
56	11.16	11.2152901523012	-0.0552901523012483
57	11.3	11.1693414847132	0.130658515286818
58	11.23	11.3233990346139	-0.0933990346138742
59	11.25	11.2433502323075	0.00664976769249392
60	11.25	11.2640656808258	-0.0140656808258051
61	11.12	11.2625523541998	-0.142552354199815
62	11.14	11.1172151461485	0.0227848538514639
63	11.17	11.1396665686164	0.0303334313835588
64	11.25	11.1729301425549	0.077069857445057
65	11.27	11.2612220886596	0.00877791134039718
66	11.34	11.2821665041569	0.0578334958430951
67	11.39	11.3583888100813	0.0316111899186708
68	11.44	11.411789858063	0.0282101419370164
69	11.46	11.464824987286	-0.00482498728601399
70	11.49	11.484305866895	0.0056941331049849
71	11.51	11.5149184986863	-0.00491849868628336
72	11.48	11.5343893174036	-0.0543893174035528
73	11.49	11.4985375706438	-0.00853757064379224
74	11.52	11.5076190134025	0.0123809865975204
75	11.56	11.5389510837733	0.0210489162266594
76	11.58	11.581215736709	-0.00121573670899089
77	11.58	11.6010849355942	-0.021084935594228
78	11.58	11.5988164073348	-0.0188164073347554
79	11.6	11.5967919500349	0.00320804996509416
80	11.62	11.6171371041366	0.00286289586343358
81	11.62	11.6374451231078	-0.0174451231077928
82	11.64	11.6355682022804	0.00443179771955116
83	11.67	11.6560450194053	0.013954980594729
84	11.66	11.6875464357932	-0.0275464357931963
85	11.72	11.6745827147154	0.0454172852846
86	11.82	11.7394691605229	0.0805308394770634
87	11.9	11.8481334736908	0.0518665263091975
88	12.04	11.9337137933521	0.106286206647928
89	12.08	12.0851491265214	-0.00514912652135102
90	12.15	12.1245951319894	0.0254048680105772
91	12.19	12.1973284417855	-0.00732844178553727
92	12.22	12.2365399747203	-0.0165399747203132
93	12.23	12.2647604388097	-0.0347604388096503
94	12.25	12.271020563134	-0.0210205631340088
95	12.26	12.2887589607077	-0.0287589607076519
96	12.27	12.2956647840721	-0.0256647840720721
97	12.34	12.3029035099064	0.0370964900935782
98	12.38	12.376894721344	0.00310527865599042
99	12.42	12.4172288182803	0.00277118171966251
100	12.43	12.4575269697267	-0.0275269697266651
101	12.48	12.464565343003	0.0154346569969963
102	12.5	12.5162259577778	-0.0162259577777775
103	12.5	12.5344802069505	-0.0344802069505405
104	12.49	12.5307704814211	-0.040770481421136
105	12.46	12.5163839852498	-0.0563839852498411
106	12.45	12.4803176321728	-0.0303176321728191
107	12.45	12.4670557580714	-0.017055758071427
108	12.38	12.4652207290291	-0.0852207290290643
109	12.42	12.3860518306357	0.0339481693643489
110	12.37	12.4297043142402	-0.0597043142401734
111	12.35	12.373280726961	-0.0232807269609552
112	12.35	12.3507759535043	-0.00077595350428794
113	12.36	12.3506924686653	0.00930753133466844
114	12.32	12.3616938659788	-0.0416938659787931
115	12.32	12.3172080228612	0.002791977138763
116	12.34	12.3175084116867	0.0224915883132528
117	12.35	12.3399282817149	0.0100717182851486
118	12.34	12.3510118979037	-0.0110118979037264
119	12.31	12.339827127788	-0.0298271277879536
120	12.24	12.3066180270542	-0.0666180270542363

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
121	12.2294505934006	12.142843975568	12.3160572112332
122	12.2189011868012	12.0896640414331	12.3481383321693
123	12.2083517802018	12.0416836940259	12.3750198663777
124	12.1978023736024	11.9955589797663	12.4000457674386
125	12.187252967003	11.9500857086737	12.4244202253324
126	12.1767035604036	11.9046931641926	12.4487139566146
127	12.1661541538042	11.8590709688223	12.4732373387861
128	12.1556047472048	11.8130361563258	12.4981733380838
129	12.1450553406054	11.7664753926427	12.5236352885682
130	12.134505934006	11.7193164042673	12.5496954637448
131	12.1239565274066	11.6715125024151	12.5764005523981
132	12.1134071208072	11.6230336122294	12.6037806293851

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 12.2294505934006 & 12.142843975568 & 12.3160572112332 \tabularnewline
122 & 12.2189011868012 & 12.0896640414331 & 12.3481383321693 \tabularnewline
123 & 12.2083517802018 & 12.0416836940259 & 12.3750198663777 \tabularnewline
124 & 12.1978023736024 & 11.9955589797663 & 12.4000457674386 \tabularnewline
125 & 12.187252967003 & 11.9500857086737 & 12.4244202253324 \tabularnewline
126 & 12.1767035604036 & 11.9046931641926 & 12.4487139566146 \tabularnewline
127 & 12.1661541538042 & 11.8590709688223 & 12.4732373387861 \tabularnewline
128 & 12.1556047472048 & 11.8130361563258 & 12.4981733380838 \tabularnewline
129 & 12.1450553406054 & 11.7664753926427 & 12.5236352885682 \tabularnewline
130 & 12.134505934006 & 11.7193164042673 & 12.5496954637448 \tabularnewline
131 & 12.1239565274066 & 11.6715125024151 & 12.5764005523981 \tabularnewline
132 & 12.1134071208072 & 11.6230336122294 & 12.6037806293851 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156324&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]121[/C][C]12.2294505934006[/C][C]12.142843975568[/C][C]12.3160572112332[/C][/ROW]
[ROW][C]122[/C][C]12.2189011868012[/C][C]12.0896640414331[/C][C]12.3481383321693[/C][/ROW]
[ROW][C]123[/C][C]12.2083517802018[/C][C]12.0416836940259[/C][C]12.3750198663777[/C][/ROW]
[ROW][C]124[/C][C]12.1978023736024[/C][C]11.9955589797663[/C][C]12.4000457674386[/C][/ROW]
[ROW][C]125[/C][C]12.187252967003[/C][C]11.9500857086737[/C][C]12.4244202253324[/C][/ROW]
[ROW][C]126[/C][C]12.1767035604036[/C][C]11.9046931641926[/C][C]12.4487139566146[/C][/ROW]
[ROW][C]127[/C][C]12.1661541538042[/C][C]11.8590709688223[/C][C]12.4732373387861[/C][/ROW]
[ROW][C]128[/C][C]12.1556047472048[/C][C]11.8130361563258[/C][C]12.4981733380838[/C][/ROW]
[ROW][C]129[/C][C]12.1450553406054[/C][C]11.7664753926427[/C][C]12.5236352885682[/C][/ROW]
[ROW][C]130[/C][C]12.134505934006[/C][C]11.7193164042673[/C][C]12.5496954637448[/C][/ROW]
[ROW][C]131[/C][C]12.1239565274066[/C][C]11.6715125024151[/C][C]12.5764005523981[/C][/ROW]
[ROW][C]132[/C][C]12.1134071208072[/C][C]11.6230336122294[/C][C]12.6037806293851[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=156324&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156324&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
121	12.2294505934006	12.142843975568	12.3160572112332
122	12.2189011868012	12.0896640414331	12.3481383321693
123	12.2083517802018	12.0416836940259	12.3750198663777
124	12.1978023736024	11.9955589797663	12.4000457674386
125	12.187252967003	11.9500857086737	12.4244202253324
126	12.1767035604036	11.9046931641926	12.4487139566146
127	12.1661541538042	11.8590709688223	12.4732373387861
128	12.1556047472048	11.8130361563258	12.4981733380838
129	12.1450553406054	11.7664753926427	12.5236352885682
130	12.134505934006	11.7193164042673	12.5496954637448
131	12.1239565274066	11.6715125024151	12.5764005523981
132	12.1134071208072	11.6230336122294	12.6037806293851

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; par3 = additive ;

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

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

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code