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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, 24 Apr 2016 12:30:18 +0100

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/2016/Apr/24/t1461497549lun7izmxuuvwold.htm/, Retrieved Tue, 30 Apr 2024 19:09:20 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294628, Retrieved Tue, 30 Apr 2024 19:09:20 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

107

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

-       [Exponential Smoothing] [opgave 10 oef 2] [2016-04-24 11:30:18] [3b4b14340a49fc08510bf0d59f03d4db] [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	'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294628&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294628&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294628&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	'Gertrude Mary Cox' @ cox.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.988821404765565
beta	0.0840238422818096
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.988821404765565 \tabularnewline
beta & 0.0840238422818096 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294628&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]0.988821404765565[/C][/ROW]
[ROW][C]beta[/C][C]0.0840238422818096[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294628&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294628&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	0.988821404765565
beta	0.0840238422818096
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	96.4	96.26	0.140000000000015
4	96.66	96.3200668369934	0.339933163006563
5	96.95	96.6060750670451	0.343924932954863
6	97.14	96.9246053011242	0.215394698875755
7	97.27	97.1339380653324	0.13606193466758
8	97.34	97.276129542039	0.0638704579610163
9	97.42	97.3522431911119	0.0677568088880633
10	97.47	97.4378292927537	0.0321707072462658
11	97.29	97.490899984879	-0.20089998487903
12	97.36	97.2968136981955	0.0631863018045351
13	97.47	97.3691113914425	0.100888608557497
14	97.48	97.487072219655	-0.00707221965501503
15	97.84	97.4976914776992	0.342308522300783
16	97.9	97.8822264494716	0.0177735505284176
17	97.53	97.9473310024303	-0.417331002430302
18	97.61	97.5475210916592	0.0624789083408217
19	97.73	97.6273485243456	0.102651475654383
20	97.76	97.7554282055766	0.00457179442344113
21	97.87	97.7869044442247	0.0830955557752588
22	97.85	97.9029306177132	-0.0529306177131588
23	98.13	97.8800534814364	0.249946518563632
24	98.21	98.1774344404816	0.0325655595184315
25	98.3	98.2625701498662	0.0374298501338046
26	98.34	98.3556256170745	-0.0156256170745337
27	98.38	98.3949204549331	-0.0149204549330904
28	98.42	98.4336729125725	-0.0136729125725026
29	98.16	98.4725229586883	-0.312522958688305
30	98.18	98.1898978455771	-0.00989784557712881
31	98.22	98.205692563649	0.0143074363510038
32	98.29	98.2466107098506	0.0433892901494346
33	98.45	98.3198905962561	0.130109403743916
34	98.54	98.4897312715596	0.0502687284404004
35	98.54	98.5848003340279	-0.0448003340279257
36	98.78	98.5821408559396	0.197859144060374
37	98.84	98.8358673065028	0.00413269349716927
38	99.14	98.8983762591576	0.241623740842428
39	99.2	99.2157966483854	-0.0157966483854182
40	99.33	99.2773617889238	0.0526382110762285
41	98.56	99.4109702066606	-0.850970206660605
42	98.65	98.580368782511	0.0696312174890039
43	98.77	98.6658630318436	0.104136968156411
44	98.82	98.7941294816354	0.0258705183645702
45	98.9	98.8471538315893	0.0528461684106816
46	98.89	98.9312429830935	-0.0412429830934684
47	98.9	98.9188681119632	-0.018868111963215
48	99.07	98.9270503432953	0.142949656704658
49	99.09	99.1071183592539	-0.0171183592539279
50	99.12	99.1274854232323	-0.00748542323226786
51	99.03	99.1567558173409	-0.126755817340893
52	99	99.0575576397449	-0.0575576397448714
53	99.21	99.0220019493618	0.187998050638214
54	99.35	99.2448767195963	0.105123280403731
55	99.37	99.3945372660523	-0.0245372660523202
56	99.39	99.4139480205279	-0.0239480205278824
57	99.41	99.4319517225127	-0.021951722512739
58	99.43	99.450105557197	-0.0201055571969988
59	99.6	99.4684144580123	0.131585541987675
60	99.73	99.6476514932827	0.0823485067172669
61	99.78	99.7850437847509	-0.00504378475085332
62	99.8	99.8356016470976	-0.0356016470976357
63	99.88	99.8529852933978	0.0270147066021877
64	99.74	99.934529835908	-0.194529835908028
65	100.15	99.7808439641753	0.369156035824687
66	100.27	100.215213919863	0.0547860801371058
67	100.26	100.343280012467	-0.0832800124674691
68	100.36	100.327904113094	0.0320958869061769
69	100.37	100.429281045698	-0.0592810456979151
70	100.54	100.435377171027	0.104622828972524
71	99.8	100.612237499106	-0.812237499105819
72	99.82	99.8150023031957	0.00499769680429551
73	99.82	99.8262819932381	-0.006281993238062
74	99.82	99.8258861475969	-0.00588614759688255
75	99.67	99.8253926745345	-0.155392674534511
76	99.78	99.6641532133551	0.115846786644923
77	99.44	99.7807462180967	-0.340746218096683
78	99.61	99.417539532193	0.192460467806953
79	99.71	99.5975695264082	0.112430473591772
80	99.71	99.707805387296	0.00219461270394561
81	99.77	99.7092200078263	0.0607799921736927
82	99.77	99.7736149853254	-0.00361498532538462
83	99.89	99.7740344811991	0.11596551880092
84	99.96	99.9023326848458	0.0576673151541769
85	100.02	99.9777756411667	0.0422243588333373
86	100	100.041456464581	-0.04145646458052
87	100.04	100.018947505945	0.0210524940548709
88	99.99	100.059997881093	-0.0699978810931441
89	99.97	100.005199952268	-0.0351999522682007
90	99.77	99.9818863872763	-0.211886387276337
91	99.93	99.7662570032445	0.16374299675546
92	99.9	99.9356625114937	-0.0356625114937259
93	100.01	99.9049285803913	0.105071419608677
94	100.08	100.022085186852	0.0579148131477893
95	100.21	100.097424159033	0.112575840966826
96	100.28	100.23616644129	0.0438335587096361
97	100.48	100.310576775981	0.16942322401907
98	100.72	100.523249316299	0.196750683700699
99	100.74	100.779290780381	-0.0392907803807816
100	100.88	100.798664934626	0.0813350653743043
101	101.03	100.944074196359	0.085925803640535
102	101.47	101.101161987125	0.368838012875059
103	101.46	101.568644175137	-0.108644175136831
104	101.46	101.554955100266	-0.0949551002656221
105	101.45	101.546912771607	-0.0969127716066964
106	101.74	101.528882699301	0.211117300698518
107	102.41	101.832979946745	0.577020053255168
108	102.54	102.546831133154	-0.00683113315386663
109	102.67	102.682790207458	-0.0127902074575132
110	102.87	102.811794152602	0.0582058473977725
111	102.9	103.015836524463	-0.115836524463063
112	102.88	103.038157845431	-0.158157845431035
113	102.82	103.005490461174	-0.185490461173657
114	102.94	102.930384605519	0.00961539448123006
115	102.97	103.049002487083	-0.0790024870825334
116	103.01	103.073429222546	-0.0634292225459205
117	103.11	103.107985145406	0.00201485459388095
118	103.21	103.207420975892	0.0025790241076038
119	104.66	103.307628946388	1.35237105361156
120	104.79	104.854901340193	-0.0649013401931313

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 96.4 & 96.26 & 0.140000000000015 \tabularnewline
4 & 96.66 & 96.3200668369934 & 0.339933163006563 \tabularnewline
5 & 96.95 & 96.6060750670451 & 0.343924932954863 \tabularnewline
6 & 97.14 & 96.9246053011242 & 0.215394698875755 \tabularnewline
7 & 97.27 & 97.1339380653324 & 0.13606193466758 \tabularnewline
8 & 97.34 & 97.276129542039 & 0.0638704579610163 \tabularnewline
9 & 97.42 & 97.3522431911119 & 0.0677568088880633 \tabularnewline
10 & 97.47 & 97.4378292927537 & 0.0321707072462658 \tabularnewline
11 & 97.29 & 97.490899984879 & -0.20089998487903 \tabularnewline
12 & 97.36 & 97.2968136981955 & 0.0631863018045351 \tabularnewline
13 & 97.47 & 97.3691113914425 & 0.100888608557497 \tabularnewline
14 & 97.48 & 97.487072219655 & -0.00707221965501503 \tabularnewline
15 & 97.84 & 97.4976914776992 & 0.342308522300783 \tabularnewline
16 & 97.9 & 97.8822264494716 & 0.0177735505284176 \tabularnewline
17 & 97.53 & 97.9473310024303 & -0.417331002430302 \tabularnewline
18 & 97.61 & 97.5475210916592 & 0.0624789083408217 \tabularnewline
19 & 97.73 & 97.6273485243456 & 0.102651475654383 \tabularnewline
20 & 97.76 & 97.7554282055766 & 0.00457179442344113 \tabularnewline
21 & 97.87 & 97.7869044442247 & 0.0830955557752588 \tabularnewline
22 & 97.85 & 97.9029306177132 & -0.0529306177131588 \tabularnewline
23 & 98.13 & 97.8800534814364 & 0.249946518563632 \tabularnewline
24 & 98.21 & 98.1774344404816 & 0.0325655595184315 \tabularnewline
25 & 98.3 & 98.2625701498662 & 0.0374298501338046 \tabularnewline
26 & 98.34 & 98.3556256170745 & -0.0156256170745337 \tabularnewline
27 & 98.38 & 98.3949204549331 & -0.0149204549330904 \tabularnewline
28 & 98.42 & 98.4336729125725 & -0.0136729125725026 \tabularnewline
29 & 98.16 & 98.4725229586883 & -0.312522958688305 \tabularnewline
30 & 98.18 & 98.1898978455771 & -0.00989784557712881 \tabularnewline
31 & 98.22 & 98.205692563649 & 0.0143074363510038 \tabularnewline
32 & 98.29 & 98.2466107098506 & 0.0433892901494346 \tabularnewline
33 & 98.45 & 98.3198905962561 & 0.130109403743916 \tabularnewline
34 & 98.54 & 98.4897312715596 & 0.0502687284404004 \tabularnewline
35 & 98.54 & 98.5848003340279 & -0.0448003340279257 \tabularnewline
36 & 98.78 & 98.5821408559396 & 0.197859144060374 \tabularnewline
37 & 98.84 & 98.8358673065028 & 0.00413269349716927 \tabularnewline
38 & 99.14 & 98.8983762591576 & 0.241623740842428 \tabularnewline
39 & 99.2 & 99.2157966483854 & -0.0157966483854182 \tabularnewline
40 & 99.33 & 99.2773617889238 & 0.0526382110762285 \tabularnewline
41 & 98.56 & 99.4109702066606 & -0.850970206660605 \tabularnewline
42 & 98.65 & 98.580368782511 & 0.0696312174890039 \tabularnewline
43 & 98.77 & 98.6658630318436 & 0.104136968156411 \tabularnewline
44 & 98.82 & 98.7941294816354 & 0.0258705183645702 \tabularnewline
45 & 98.9 & 98.8471538315893 & 0.0528461684106816 \tabularnewline
46 & 98.89 & 98.9312429830935 & -0.0412429830934684 \tabularnewline
47 & 98.9 & 98.9188681119632 & -0.018868111963215 \tabularnewline
48 & 99.07 & 98.9270503432953 & 0.142949656704658 \tabularnewline
49 & 99.09 & 99.1071183592539 & -0.0171183592539279 \tabularnewline
50 & 99.12 & 99.1274854232323 & -0.00748542323226786 \tabularnewline
51 & 99.03 & 99.1567558173409 & -0.126755817340893 \tabularnewline
52 & 99 & 99.0575576397449 & -0.0575576397448714 \tabularnewline
53 & 99.21 & 99.0220019493618 & 0.187998050638214 \tabularnewline
54 & 99.35 & 99.2448767195963 & 0.105123280403731 \tabularnewline
55 & 99.37 & 99.3945372660523 & -0.0245372660523202 \tabularnewline
56 & 99.39 & 99.4139480205279 & -0.0239480205278824 \tabularnewline
57 & 99.41 & 99.4319517225127 & -0.021951722512739 \tabularnewline
58 & 99.43 & 99.450105557197 & -0.0201055571969988 \tabularnewline
59 & 99.6 & 99.4684144580123 & 0.131585541987675 \tabularnewline
60 & 99.73 & 99.6476514932827 & 0.0823485067172669 \tabularnewline
61 & 99.78 & 99.7850437847509 & -0.00504378475085332 \tabularnewline
62 & 99.8 & 99.8356016470976 & -0.0356016470976357 \tabularnewline
63 & 99.88 & 99.8529852933978 & 0.0270147066021877 \tabularnewline
64 & 99.74 & 99.934529835908 & -0.194529835908028 \tabularnewline
65 & 100.15 & 99.7808439641753 & 0.369156035824687 \tabularnewline
66 & 100.27 & 100.215213919863 & 0.0547860801371058 \tabularnewline
67 & 100.26 & 100.343280012467 & -0.0832800124674691 \tabularnewline
68 & 100.36 & 100.327904113094 & 0.0320958869061769 \tabularnewline
69 & 100.37 & 100.429281045698 & -0.0592810456979151 \tabularnewline
70 & 100.54 & 100.435377171027 & 0.104622828972524 \tabularnewline
71 & 99.8 & 100.612237499106 & -0.812237499105819 \tabularnewline
72 & 99.82 & 99.8150023031957 & 0.00499769680429551 \tabularnewline
73 & 99.82 & 99.8262819932381 & -0.006281993238062 \tabularnewline
74 & 99.82 & 99.8258861475969 & -0.00588614759688255 \tabularnewline
75 & 99.67 & 99.8253926745345 & -0.155392674534511 \tabularnewline
76 & 99.78 & 99.6641532133551 & 0.115846786644923 \tabularnewline
77 & 99.44 & 99.7807462180967 & -0.340746218096683 \tabularnewline
78 & 99.61 & 99.417539532193 & 0.192460467806953 \tabularnewline
79 & 99.71 & 99.5975695264082 & 0.112430473591772 \tabularnewline
80 & 99.71 & 99.707805387296 & 0.00219461270394561 \tabularnewline
81 & 99.77 & 99.7092200078263 & 0.0607799921736927 \tabularnewline
82 & 99.77 & 99.7736149853254 & -0.00361498532538462 \tabularnewline
83 & 99.89 & 99.7740344811991 & 0.11596551880092 \tabularnewline
84 & 99.96 & 99.9023326848458 & 0.0576673151541769 \tabularnewline
85 & 100.02 & 99.9777756411667 & 0.0422243588333373 \tabularnewline
86 & 100 & 100.041456464581 & -0.04145646458052 \tabularnewline
87 & 100.04 & 100.018947505945 & 0.0210524940548709 \tabularnewline
88 & 99.99 & 100.059997881093 & -0.0699978810931441 \tabularnewline
89 & 99.97 & 100.005199952268 & -0.0351999522682007 \tabularnewline
90 & 99.77 & 99.9818863872763 & -0.211886387276337 \tabularnewline
91 & 99.93 & 99.7662570032445 & 0.16374299675546 \tabularnewline
92 & 99.9 & 99.9356625114937 & -0.0356625114937259 \tabularnewline
93 & 100.01 & 99.9049285803913 & 0.105071419608677 \tabularnewline
94 & 100.08 & 100.022085186852 & 0.0579148131477893 \tabularnewline
95 & 100.21 & 100.097424159033 & 0.112575840966826 \tabularnewline
96 & 100.28 & 100.23616644129 & 0.0438335587096361 \tabularnewline
97 & 100.48 & 100.310576775981 & 0.16942322401907 \tabularnewline
98 & 100.72 & 100.523249316299 & 0.196750683700699 \tabularnewline
99 & 100.74 & 100.779290780381 & -0.0392907803807816 \tabularnewline
100 & 100.88 & 100.798664934626 & 0.0813350653743043 \tabularnewline
101 & 101.03 & 100.944074196359 & 0.085925803640535 \tabularnewline
102 & 101.47 & 101.101161987125 & 0.368838012875059 \tabularnewline
103 & 101.46 & 101.568644175137 & -0.108644175136831 \tabularnewline
104 & 101.46 & 101.554955100266 & -0.0949551002656221 \tabularnewline
105 & 101.45 & 101.546912771607 & -0.0969127716066964 \tabularnewline
106 & 101.74 & 101.528882699301 & 0.211117300698518 \tabularnewline
107 & 102.41 & 101.832979946745 & 0.577020053255168 \tabularnewline
108 & 102.54 & 102.546831133154 & -0.00683113315386663 \tabularnewline
109 & 102.67 & 102.682790207458 & -0.0127902074575132 \tabularnewline
110 & 102.87 & 102.811794152602 & 0.0582058473977725 \tabularnewline
111 & 102.9 & 103.015836524463 & -0.115836524463063 \tabularnewline
112 & 102.88 & 103.038157845431 & -0.158157845431035 \tabularnewline
113 & 102.82 & 103.005490461174 & -0.185490461173657 \tabularnewline
114 & 102.94 & 102.930384605519 & 0.00961539448123006 \tabularnewline
115 & 102.97 & 103.049002487083 & -0.0790024870825334 \tabularnewline
116 & 103.01 & 103.073429222546 & -0.0634292225459205 \tabularnewline
117 & 103.11 & 103.107985145406 & 0.00201485459388095 \tabularnewline
118 & 103.21 & 103.207420975892 & 0.0025790241076038 \tabularnewline
119 & 104.66 & 103.307628946388 & 1.35237105361156 \tabularnewline
120 & 104.79 & 104.854901340193 & -0.0649013401931313 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294628&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]96.4[/C][C]96.26[/C][C]0.140000000000015[/C][/ROW]
[ROW][C]4[/C][C]96.66[/C][C]96.3200668369934[/C][C]0.339933163006563[/C][/ROW]
[ROW][C]5[/C][C]96.95[/C][C]96.6060750670451[/C][C]0.343924932954863[/C][/ROW]
[ROW][C]6[/C][C]97.14[/C][C]96.9246053011242[/C][C]0.215394698875755[/C][/ROW]
[ROW][C]7[/C][C]97.27[/C][C]97.1339380653324[/C][C]0.13606193466758[/C][/ROW]
[ROW][C]8[/C][C]97.34[/C][C]97.276129542039[/C][C]0.0638704579610163[/C][/ROW]
[ROW][C]9[/C][C]97.42[/C][C]97.3522431911119[/C][C]0.0677568088880633[/C][/ROW]
[ROW][C]10[/C][C]97.47[/C][C]97.4378292927537[/C][C]0.0321707072462658[/C][/ROW]
[ROW][C]11[/C][C]97.29[/C][C]97.490899984879[/C][C]-0.20089998487903[/C][/ROW]
[ROW][C]12[/C][C]97.36[/C][C]97.2968136981955[/C][C]0.0631863018045351[/C][/ROW]
[ROW][C]13[/C][C]97.47[/C][C]97.3691113914425[/C][C]0.100888608557497[/C][/ROW]
[ROW][C]14[/C][C]97.48[/C][C]97.487072219655[/C][C]-0.00707221965501503[/C][/ROW]
[ROW][C]15[/C][C]97.84[/C][C]97.4976914776992[/C][C]0.342308522300783[/C][/ROW]
[ROW][C]16[/C][C]97.9[/C][C]97.8822264494716[/C][C]0.0177735505284176[/C][/ROW]
[ROW][C]17[/C][C]97.53[/C][C]97.9473310024303[/C][C]-0.417331002430302[/C][/ROW]
[ROW][C]18[/C][C]97.61[/C][C]97.5475210916592[/C][C]0.0624789083408217[/C][/ROW]
[ROW][C]19[/C][C]97.73[/C][C]97.6273485243456[/C][C]0.102651475654383[/C][/ROW]
[ROW][C]20[/C][C]97.76[/C][C]97.7554282055766[/C][C]0.00457179442344113[/C][/ROW]
[ROW][C]21[/C][C]97.87[/C][C]97.7869044442247[/C][C]0.0830955557752588[/C][/ROW]
[ROW][C]22[/C][C]97.85[/C][C]97.9029306177132[/C][C]-0.0529306177131588[/C][/ROW]
[ROW][C]23[/C][C]98.13[/C][C]97.8800534814364[/C][C]0.249946518563632[/C][/ROW]
[ROW][C]24[/C][C]98.21[/C][C]98.1774344404816[/C][C]0.0325655595184315[/C][/ROW]
[ROW][C]25[/C][C]98.3[/C][C]98.2625701498662[/C][C]0.0374298501338046[/C][/ROW]
[ROW][C]26[/C][C]98.34[/C][C]98.3556256170745[/C][C]-0.0156256170745337[/C][/ROW]
[ROW][C]27[/C][C]98.38[/C][C]98.3949204549331[/C][C]-0.0149204549330904[/C][/ROW]
[ROW][C]28[/C][C]98.42[/C][C]98.4336729125725[/C][C]-0.0136729125725026[/C][/ROW]
[ROW][C]29[/C][C]98.16[/C][C]98.4725229586883[/C][C]-0.312522958688305[/C][/ROW]
[ROW][C]30[/C][C]98.18[/C][C]98.1898978455771[/C][C]-0.00989784557712881[/C][/ROW]
[ROW][C]31[/C][C]98.22[/C][C]98.205692563649[/C][C]0.0143074363510038[/C][/ROW]
[ROW][C]32[/C][C]98.29[/C][C]98.2466107098506[/C][C]0.0433892901494346[/C][/ROW]
[ROW][C]33[/C][C]98.45[/C][C]98.3198905962561[/C][C]0.130109403743916[/C][/ROW]
[ROW][C]34[/C][C]98.54[/C][C]98.4897312715596[/C][C]0.0502687284404004[/C][/ROW]
[ROW][C]35[/C][C]98.54[/C][C]98.5848003340279[/C][C]-0.0448003340279257[/C][/ROW]
[ROW][C]36[/C][C]98.78[/C][C]98.5821408559396[/C][C]0.197859144060374[/C][/ROW]
[ROW][C]37[/C][C]98.84[/C][C]98.8358673065028[/C][C]0.00413269349716927[/C][/ROW]
[ROW][C]38[/C][C]99.14[/C][C]98.8983762591576[/C][C]0.241623740842428[/C][/ROW]
[ROW][C]39[/C][C]99.2[/C][C]99.2157966483854[/C][C]-0.0157966483854182[/C][/ROW]
[ROW][C]40[/C][C]99.33[/C][C]99.2773617889238[/C][C]0.0526382110762285[/C][/ROW]
[ROW][C]41[/C][C]98.56[/C][C]99.4109702066606[/C][C]-0.850970206660605[/C][/ROW]
[ROW][C]42[/C][C]98.65[/C][C]98.580368782511[/C][C]0.0696312174890039[/C][/ROW]
[ROW][C]43[/C][C]98.77[/C][C]98.6658630318436[/C][C]0.104136968156411[/C][/ROW]
[ROW][C]44[/C][C]98.82[/C][C]98.7941294816354[/C][C]0.0258705183645702[/C][/ROW]
[ROW][C]45[/C][C]98.9[/C][C]98.8471538315893[/C][C]0.0528461684106816[/C][/ROW]
[ROW][C]46[/C][C]98.89[/C][C]98.9312429830935[/C][C]-0.0412429830934684[/C][/ROW]
[ROW][C]47[/C][C]98.9[/C][C]98.9188681119632[/C][C]-0.018868111963215[/C][/ROW]
[ROW][C]48[/C][C]99.07[/C][C]98.9270503432953[/C][C]0.142949656704658[/C][/ROW]
[ROW][C]49[/C][C]99.09[/C][C]99.1071183592539[/C][C]-0.0171183592539279[/C][/ROW]
[ROW][C]50[/C][C]99.12[/C][C]99.1274854232323[/C][C]-0.00748542323226786[/C][/ROW]
[ROW][C]51[/C][C]99.03[/C][C]99.1567558173409[/C][C]-0.126755817340893[/C][/ROW]
[ROW][C]52[/C][C]99[/C][C]99.0575576397449[/C][C]-0.0575576397448714[/C][/ROW]
[ROW][C]53[/C][C]99.21[/C][C]99.0220019493618[/C][C]0.187998050638214[/C][/ROW]
[ROW][C]54[/C][C]99.35[/C][C]99.2448767195963[/C][C]0.105123280403731[/C][/ROW]
[ROW][C]55[/C][C]99.37[/C][C]99.3945372660523[/C][C]-0.0245372660523202[/C][/ROW]
[ROW][C]56[/C][C]99.39[/C][C]99.4139480205279[/C][C]-0.0239480205278824[/C][/ROW]
[ROW][C]57[/C][C]99.41[/C][C]99.4319517225127[/C][C]-0.021951722512739[/C][/ROW]
[ROW][C]58[/C][C]99.43[/C][C]99.450105557197[/C][C]-0.0201055571969988[/C][/ROW]
[ROW][C]59[/C][C]99.6[/C][C]99.4684144580123[/C][C]0.131585541987675[/C][/ROW]
[ROW][C]60[/C][C]99.73[/C][C]99.6476514932827[/C][C]0.0823485067172669[/C][/ROW]
[ROW][C]61[/C][C]99.78[/C][C]99.7850437847509[/C][C]-0.00504378475085332[/C][/ROW]
[ROW][C]62[/C][C]99.8[/C][C]99.8356016470976[/C][C]-0.0356016470976357[/C][/ROW]
[ROW][C]63[/C][C]99.88[/C][C]99.8529852933978[/C][C]0.0270147066021877[/C][/ROW]
[ROW][C]64[/C][C]99.74[/C][C]99.934529835908[/C][C]-0.194529835908028[/C][/ROW]
[ROW][C]65[/C][C]100.15[/C][C]99.7808439641753[/C][C]0.369156035824687[/C][/ROW]
[ROW][C]66[/C][C]100.27[/C][C]100.215213919863[/C][C]0.0547860801371058[/C][/ROW]
[ROW][C]67[/C][C]100.26[/C][C]100.343280012467[/C][C]-0.0832800124674691[/C][/ROW]
[ROW][C]68[/C][C]100.36[/C][C]100.327904113094[/C][C]0.0320958869061769[/C][/ROW]
[ROW][C]69[/C][C]100.37[/C][C]100.429281045698[/C][C]-0.0592810456979151[/C][/ROW]
[ROW][C]70[/C][C]100.54[/C][C]100.435377171027[/C][C]0.104622828972524[/C][/ROW]
[ROW][C]71[/C][C]99.8[/C][C]100.612237499106[/C][C]-0.812237499105819[/C][/ROW]
[ROW][C]72[/C][C]99.82[/C][C]99.8150023031957[/C][C]0.00499769680429551[/C][/ROW]
[ROW][C]73[/C][C]99.82[/C][C]99.8262819932381[/C][C]-0.006281993238062[/C][/ROW]
[ROW][C]74[/C][C]99.82[/C][C]99.8258861475969[/C][C]-0.00588614759688255[/C][/ROW]
[ROW][C]75[/C][C]99.67[/C][C]99.8253926745345[/C][C]-0.155392674534511[/C][/ROW]
[ROW][C]76[/C][C]99.78[/C][C]99.6641532133551[/C][C]0.115846786644923[/C][/ROW]
[ROW][C]77[/C][C]99.44[/C][C]99.7807462180967[/C][C]-0.340746218096683[/C][/ROW]
[ROW][C]78[/C][C]99.61[/C][C]99.417539532193[/C][C]0.192460467806953[/C][/ROW]
[ROW][C]79[/C][C]99.71[/C][C]99.5975695264082[/C][C]0.112430473591772[/C][/ROW]
[ROW][C]80[/C][C]99.71[/C][C]99.707805387296[/C][C]0.00219461270394561[/C][/ROW]
[ROW][C]81[/C][C]99.77[/C][C]99.7092200078263[/C][C]0.0607799921736927[/C][/ROW]
[ROW][C]82[/C][C]99.77[/C][C]99.7736149853254[/C][C]-0.00361498532538462[/C][/ROW]
[ROW][C]83[/C][C]99.89[/C][C]99.7740344811991[/C][C]0.11596551880092[/C][/ROW]
[ROW][C]84[/C][C]99.96[/C][C]99.9023326848458[/C][C]0.0576673151541769[/C][/ROW]
[ROW][C]85[/C][C]100.02[/C][C]99.9777756411667[/C][C]0.0422243588333373[/C][/ROW]
[ROW][C]86[/C][C]100[/C][C]100.041456464581[/C][C]-0.04145646458052[/C][/ROW]
[ROW][C]87[/C][C]100.04[/C][C]100.018947505945[/C][C]0.0210524940548709[/C][/ROW]
[ROW][C]88[/C][C]99.99[/C][C]100.059997881093[/C][C]-0.0699978810931441[/C][/ROW]
[ROW][C]89[/C][C]99.97[/C][C]100.005199952268[/C][C]-0.0351999522682007[/C][/ROW]
[ROW][C]90[/C][C]99.77[/C][C]99.9818863872763[/C][C]-0.211886387276337[/C][/ROW]
[ROW][C]91[/C][C]99.93[/C][C]99.7662570032445[/C][C]0.16374299675546[/C][/ROW]
[ROW][C]92[/C][C]99.9[/C][C]99.9356625114937[/C][C]-0.0356625114937259[/C][/ROW]
[ROW][C]93[/C][C]100.01[/C][C]99.9049285803913[/C][C]0.105071419608677[/C][/ROW]
[ROW][C]94[/C][C]100.08[/C][C]100.022085186852[/C][C]0.0579148131477893[/C][/ROW]
[ROW][C]95[/C][C]100.21[/C][C]100.097424159033[/C][C]0.112575840966826[/C][/ROW]
[ROW][C]96[/C][C]100.28[/C][C]100.23616644129[/C][C]0.0438335587096361[/C][/ROW]
[ROW][C]97[/C][C]100.48[/C][C]100.310576775981[/C][C]0.16942322401907[/C][/ROW]
[ROW][C]98[/C][C]100.72[/C][C]100.523249316299[/C][C]0.196750683700699[/C][/ROW]
[ROW][C]99[/C][C]100.74[/C][C]100.779290780381[/C][C]-0.0392907803807816[/C][/ROW]
[ROW][C]100[/C][C]100.88[/C][C]100.798664934626[/C][C]0.0813350653743043[/C][/ROW]
[ROW][C]101[/C][C]101.03[/C][C]100.944074196359[/C][C]0.085925803640535[/C][/ROW]
[ROW][C]102[/C][C]101.47[/C][C]101.101161987125[/C][C]0.368838012875059[/C][/ROW]
[ROW][C]103[/C][C]101.46[/C][C]101.568644175137[/C][C]-0.108644175136831[/C][/ROW]
[ROW][C]104[/C][C]101.46[/C][C]101.554955100266[/C][C]-0.0949551002656221[/C][/ROW]
[ROW][C]105[/C][C]101.45[/C][C]101.546912771607[/C][C]-0.0969127716066964[/C][/ROW]
[ROW][C]106[/C][C]101.74[/C][C]101.528882699301[/C][C]0.211117300698518[/C][/ROW]
[ROW][C]107[/C][C]102.41[/C][C]101.832979946745[/C][C]0.577020053255168[/C][/ROW]
[ROW][C]108[/C][C]102.54[/C][C]102.546831133154[/C][C]-0.00683113315386663[/C][/ROW]
[ROW][C]109[/C][C]102.67[/C][C]102.682790207458[/C][C]-0.0127902074575132[/C][/ROW]
[ROW][C]110[/C][C]102.87[/C][C]102.811794152602[/C][C]0.0582058473977725[/C][/ROW]
[ROW][C]111[/C][C]102.9[/C][C]103.015836524463[/C][C]-0.115836524463063[/C][/ROW]
[ROW][C]112[/C][C]102.88[/C][C]103.038157845431[/C][C]-0.158157845431035[/C][/ROW]
[ROW][C]113[/C][C]102.82[/C][C]103.005490461174[/C][C]-0.185490461173657[/C][/ROW]
[ROW][C]114[/C][C]102.94[/C][C]102.930384605519[/C][C]0.00961539448123006[/C][/ROW]
[ROW][C]115[/C][C]102.97[/C][C]103.049002487083[/C][C]-0.0790024870825334[/C][/ROW]
[ROW][C]116[/C][C]103.01[/C][C]103.073429222546[/C][C]-0.0634292225459205[/C][/ROW]
[ROW][C]117[/C][C]103.11[/C][C]103.107985145406[/C][C]0.00201485459388095[/C][/ROW]
[ROW][C]118[/C][C]103.21[/C][C]103.207420975892[/C][C]0.0025790241076038[/C][/ROW]
[ROW][C]119[/C][C]104.66[/C][C]103.307628946388[/C][C]1.35237105361156[/C][/ROW]
[ROW][C]120[/C][C]104.79[/C][C]104.854901340193[/C][C]-0.0649013401931313[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294628&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294628&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	96.4	96.26	0.140000000000015
4	96.66	96.3200668369934	0.339933163006563
5	96.95	96.6060750670451	0.343924932954863
6	97.14	96.9246053011242	0.215394698875755
7	97.27	97.1339380653324	0.13606193466758
8	97.34	97.276129542039	0.0638704579610163
9	97.42	97.3522431911119	0.0677568088880633
10	97.47	97.4378292927537	0.0321707072462658
11	97.29	97.490899984879	-0.20089998487903
12	97.36	97.2968136981955	0.0631863018045351
13	97.47	97.3691113914425	0.100888608557497
14	97.48	97.487072219655	-0.00707221965501503
15	97.84	97.4976914776992	0.342308522300783
16	97.9	97.8822264494716	0.0177735505284176
17	97.53	97.9473310024303	-0.417331002430302
18	97.61	97.5475210916592	0.0624789083408217
19	97.73	97.6273485243456	0.102651475654383
20	97.76	97.7554282055766	0.00457179442344113
21	97.87	97.7869044442247	0.0830955557752588
22	97.85	97.9029306177132	-0.0529306177131588
23	98.13	97.8800534814364	0.249946518563632
24	98.21	98.1774344404816	0.0325655595184315
25	98.3	98.2625701498662	0.0374298501338046
26	98.34	98.3556256170745	-0.0156256170745337
27	98.38	98.3949204549331	-0.0149204549330904
28	98.42	98.4336729125725	-0.0136729125725026
29	98.16	98.4725229586883	-0.312522958688305
30	98.18	98.1898978455771	-0.00989784557712881
31	98.22	98.205692563649	0.0143074363510038
32	98.29	98.2466107098506	0.0433892901494346
33	98.45	98.3198905962561	0.130109403743916
34	98.54	98.4897312715596	0.0502687284404004
35	98.54	98.5848003340279	-0.0448003340279257
36	98.78	98.5821408559396	0.197859144060374
37	98.84	98.8358673065028	0.00413269349716927
38	99.14	98.8983762591576	0.241623740842428
39	99.2	99.2157966483854	-0.0157966483854182
40	99.33	99.2773617889238	0.0526382110762285
41	98.56	99.4109702066606	-0.850970206660605
42	98.65	98.580368782511	0.0696312174890039
43	98.77	98.6658630318436	0.104136968156411
44	98.82	98.7941294816354	0.0258705183645702
45	98.9	98.8471538315893	0.0528461684106816
46	98.89	98.9312429830935	-0.0412429830934684
47	98.9	98.9188681119632	-0.018868111963215
48	99.07	98.9270503432953	0.142949656704658
49	99.09	99.1071183592539	-0.0171183592539279
50	99.12	99.1274854232323	-0.00748542323226786
51	99.03	99.1567558173409	-0.126755817340893
52	99	99.0575576397449	-0.0575576397448714
53	99.21	99.0220019493618	0.187998050638214
54	99.35	99.2448767195963	0.105123280403731
55	99.37	99.3945372660523	-0.0245372660523202
56	99.39	99.4139480205279	-0.0239480205278824
57	99.41	99.4319517225127	-0.021951722512739
58	99.43	99.450105557197	-0.0201055571969988
59	99.6	99.4684144580123	0.131585541987675
60	99.73	99.6476514932827	0.0823485067172669
61	99.78	99.7850437847509	-0.00504378475085332
62	99.8	99.8356016470976	-0.0356016470976357
63	99.88	99.8529852933978	0.0270147066021877
64	99.74	99.934529835908	-0.194529835908028
65	100.15	99.7808439641753	0.369156035824687
66	100.27	100.215213919863	0.0547860801371058
67	100.26	100.343280012467	-0.0832800124674691
68	100.36	100.327904113094	0.0320958869061769
69	100.37	100.429281045698	-0.0592810456979151
70	100.54	100.435377171027	0.104622828972524
71	99.8	100.612237499106	-0.812237499105819
72	99.82	99.8150023031957	0.00499769680429551
73	99.82	99.8262819932381	-0.006281993238062
74	99.82	99.8258861475969	-0.00588614759688255
75	99.67	99.8253926745345	-0.155392674534511
76	99.78	99.6641532133551	0.115846786644923
77	99.44	99.7807462180967	-0.340746218096683
78	99.61	99.417539532193	0.192460467806953
79	99.71	99.5975695264082	0.112430473591772
80	99.71	99.707805387296	0.00219461270394561
81	99.77	99.7092200078263	0.0607799921736927
82	99.77	99.7736149853254	-0.00361498532538462
83	99.89	99.7740344811991	0.11596551880092
84	99.96	99.9023326848458	0.0576673151541769
85	100.02	99.9777756411667	0.0422243588333373
86	100	100.041456464581	-0.04145646458052
87	100.04	100.018947505945	0.0210524940548709
88	99.99	100.059997881093	-0.0699978810931441
89	99.97	100.005199952268	-0.0351999522682007
90	99.77	99.9818863872763	-0.211886387276337
91	99.93	99.7662570032445	0.16374299675546
92	99.9	99.9356625114937	-0.0356625114937259
93	100.01	99.9049285803913	0.105071419608677
94	100.08	100.022085186852	0.0579148131477893
95	100.21	100.097424159033	0.112575840966826
96	100.28	100.23616644129	0.0438335587096361
97	100.48	100.310576775981	0.16942322401907
98	100.72	100.523249316299	0.196750683700699
99	100.74	100.779290780381	-0.0392907803807816
100	100.88	100.798664934626	0.0813350653743043
101	101.03	100.944074196359	0.085925803640535
102	101.47	101.101161987125	0.368838012875059
103	101.46	101.568644175137	-0.108644175136831
104	101.46	101.554955100266	-0.0949551002656221
105	101.45	101.546912771607	-0.0969127716066964
106	101.74	101.528882699301	0.211117300698518
107	102.41	101.832979946745	0.577020053255168
108	102.54	102.546831133154	-0.00683113315386663
109	102.67	102.682790207458	-0.0127902074575132
110	102.87	102.811794152602	0.0582058473977725
111	102.9	103.015836524463	-0.115836524463063
112	102.88	103.038157845431	-0.158157845431035
113	102.82	103.005490461174	-0.185490461173657
114	102.94	102.930384605519	0.00961539448123006
115	102.97	103.049002487083	-0.0790024870825334
116	103.01	103.073429222546	-0.0634292225459205
117	103.11	103.107985145406	0.00201485459388095
118	103.21	103.207420975892	0.0025790241076038
119	104.66	103.307628946388	1.35237105361156
120	104.79	104.854901340193	-0.0649013401931313

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
121	104.995352154434	104.571122863828	105.41958144504
122	105.199978803056	104.578083777736	105.821873828376
123	105.404605451678	104.612876565578	106.196334337778
124	105.6092321003	104.659127474479	106.559336726121
125	105.813858748922	104.710758289044	106.9169592088
126	106.018485397544	104.764804899126	107.272165895961
127	106.223112046166	104.819603588089	107.626620504242
128	106.427738694787	104.874136778843	107.981340610732
129	106.632365343409	104.927745665766	108.336985021052
130	106.836991992031	104.979986693778	108.693997290284
131	107.041618640653	105.030553027721	109.052684253585
132	107.246245289275	105.079228538061	109.413262040489

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 104.995352154434 & 104.571122863828 & 105.41958144504 \tabularnewline
122 & 105.199978803056 & 104.578083777736 & 105.821873828376 \tabularnewline
123 & 105.404605451678 & 104.612876565578 & 106.196334337778 \tabularnewline
124 & 105.6092321003 & 104.659127474479 & 106.559336726121 \tabularnewline
125 & 105.813858748922 & 104.710758289044 & 106.9169592088 \tabularnewline
126 & 106.018485397544 & 104.764804899126 & 107.272165895961 \tabularnewline
127 & 106.223112046166 & 104.819603588089 & 107.626620504242 \tabularnewline
128 & 106.427738694787 & 104.874136778843 & 107.981340610732 \tabularnewline
129 & 106.632365343409 & 104.927745665766 & 108.336985021052 \tabularnewline
130 & 106.836991992031 & 104.979986693778 & 108.693997290284 \tabularnewline
131 & 107.041618640653 & 105.030553027721 & 109.052684253585 \tabularnewline
132 & 107.246245289275 & 105.079228538061 & 109.413262040489 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294628&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]104.995352154434[/C][C]104.571122863828[/C][C]105.41958144504[/C][/ROW]
[ROW][C]122[/C][C]105.199978803056[/C][C]104.578083777736[/C][C]105.821873828376[/C][/ROW]
[ROW][C]123[/C][C]105.404605451678[/C][C]104.612876565578[/C][C]106.196334337778[/C][/ROW]
[ROW][C]124[/C][C]105.6092321003[/C][C]104.659127474479[/C][C]106.559336726121[/C][/ROW]
[ROW][C]125[/C][C]105.813858748922[/C][C]104.710758289044[/C][C]106.9169592088[/C][/ROW]
[ROW][C]126[/C][C]106.018485397544[/C][C]104.764804899126[/C][C]107.272165895961[/C][/ROW]
[ROW][C]127[/C][C]106.223112046166[/C][C]104.819603588089[/C][C]107.626620504242[/C][/ROW]
[ROW][C]128[/C][C]106.427738694787[/C][C]104.874136778843[/C][C]107.981340610732[/C][/ROW]
[ROW][C]129[/C][C]106.632365343409[/C][C]104.927745665766[/C][C]108.336985021052[/C][/ROW]
[ROW][C]130[/C][C]106.836991992031[/C][C]104.979986693778[/C][C]108.693997290284[/C][/ROW]
[ROW][C]131[/C][C]107.041618640653[/C][C]105.030553027721[/C][C]109.052684253585[/C][/ROW]
[ROW][C]132[/C][C]107.246245289275[/C][C]105.079228538061[/C][C]109.413262040489[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294628&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294628&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	104.995352154434	104.571122863828	105.41958144504
122	105.199978803056	104.578083777736	105.821873828376
123	105.404605451678	104.612876565578	106.196334337778
124	105.6092321003	104.659127474479	106.559336726121
125	105.813858748922	104.710758289044	106.9169592088
126	106.018485397544	104.764804899126	107.272165895961
127	106.223112046166	104.819603588089	107.626620504242
128	106.427738694787	104.874136778843	107.981340610732
129	106.632365343409	104.927745665766	108.336985021052
130	106.836991992031	104.979986693778	108.693997290284
131	107.041618640653	105.030553027721	109.052684253585
132	107.246245289275	105.079228538061	109.413262040489

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