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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 30 Nov 2015 16:31:39 +0000

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/2015/Nov/30/t1448901141yl7tayicocldobq.htm/, Retrieved Tue, 14 May 2024 06:41:49 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284624, Retrieved Tue, 14 May 2024 06:41:49 +0000

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Estimated Impact

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

-       [Exponential Smoothing] [] [2015-11-30 16:31:39] [bdd544630eb102d4e9b9d691f462dd0a] [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	'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284624&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' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284624&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284624&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' @ fisher.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.00732323572540669
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.00732323572540669 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284624&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]0.00732323572540669[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284624&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284624&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	0.00732323572540669
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	86.7	86.48	0.219999999999999
4	87.86	86.7016111118596	1.15838888814041
5	88.24	87.8700942667491	0.36990573325086
6	88.23	88.2528031736299	-0.0228031736298959
7	88.73	88.2426361806141	0.487363819385877
8	88.82	88.7462052607475	0.0737947392524632
9	87.16	88.8367456770184	-1.67674567701836
10	86.29	87.164466473174	-0.874466473173996
11	86.37	86.288062549057	0.0819374509430162
12	86.59	86.368662596325	0.221337403675022
13	85.46	86.5902835023069	-1.13028350230695
14	85.85	85.452006169783	0.39799383021699
15	86.93	85.8449207724189	1.08507922758106
16	87.66	86.9328670633833	0.727132936616727
17	87.84	87.6681920292818	0.171807970718191
18	88.09	87.8494502195509	0.240549780449115
19	88.58	88.1012118222968	0.47878817770318
20	88.06	88.5947181009847	-0.534718100984662
21	88.26	88.0708022342845	0.189197765715477
22	89	88.2721877741216	0.727812225878424
23	90.78	89.0175177146155	1.76248228538448
24	90	90.8104247878532	-0.810424787853236
25	89.84	90.0244898560941	-0.184489856094075
26	89.82	89.863138793389	-0.0431387933889624
27	91.12	89.8428228778361	1.27717712216395
28	91.5	91.1521759469648	0.347824053035239
29	93.03	91.5347231444961	1.4952768555039
30	94.23	93.0756734093837	1.15432659061629
31	94.76	94.2841268151109	0.47587318488911
32	92.83	94.8176117466192	-1.98761174661924
33	92.49	92.8730559972682	-0.383055997268158
34	90.85	92.5302507879041	-1.68025078790413
35	88.19	90.8779459153065	-2.6879459153065
36	86.31	88.1982614537516	-1.88826145375157
37	85.74	86.3044332700146	-0.564433270014561
38	86.62	85.730299792127	0.889700207873034
39	86.66	86.6168152764742	0.043184723525826
40	87.39	86.6571315283843	0.732868471615717
41	87.59	87.3924984969576	0.197501503042361
42	88.8	87.5939448470206	1.20605515297945
43	88.64	88.8127770732037	-0.172777073203662
44	89.55	88.6515117859686	0.89848821403136
45	89.04	89.5680916269565	-0.528091626956481
46	88.49	89.0542242874877	-0.56422428748769
47	89.5	88.5000923400284	0.999907659971598
48	89.46	89.517414899526	-0.0574148995260231
49	90.33	89.4769944366826	0.853005563317367
50	90.27	90.3532411974979	-0.0832411974978982
51	91.5	90.2926316025866	1.20736839741345
52	92.53	91.5314734459682	0.998526554031784
53	93.14	92.5687858913015	0.571214108698527
54	93.01	93.1829690268691	-0.17296902686914
55	92.84	93.0517023339122	-0.211702333912186
56	92.88	92.8801519878173	-0.000151987817346821
57	93.05	92.9201508747747	0.129849125225277
58	93.17	93.0911017905275	0.078898209472527
59	93.67	93.2116795807138	0.458320419286238
60	94.9	93.715035969182	1.18496403081804
61	95.72	94.9537137401058	0.76628625989423
62	96.08	95.7793254350201	0.300674564979886
63	97.52	96.1415273457361	1.3784726542639
64	98.26	97.5916222259243	0.668377774075708
65	98.48	98.3365169139175	0.143483086082526
66	98.09	98.5575676743795	-0.467567674379467
67	98.03	98.1641435660824	-0.134143566082415
68	98.14	98.1031612011269	0.0368387988730632
69	98.71	98.2134309803349	0.49656901966506
70	98.69	98.7870674723199	-0.0970674723198641
71	98.72	98.7663566243388	-0.0463566243387987
72	98.47	98.7960171438513	-0.326017143851331
73	99.49	98.5436296434564	0.946370356543611
74	99.84	99.5705601366609	0.269439863339116
75	100.9	99.9225333082939	0.977466691706056
76	101.31	100.989691527291	0.320308472708959
77	100.09	101.402037221742	-1.31203722174153
78	99.28	100.172428863886	-0.892428863886224
79	99.57	99.3558933969478	0.214106603052173
80	101.04	99.6474613500723	1.39253864992767
81	101.87	101.127659238863	0.742340761137498
82	101.39	101.963095575245	-0.573095575244892
83	100.3	101.478898661254	-1.17889866125418
84	99.95	100.380265308461	-0.430265308461443
85	99.87	100.027114374183	-0.157114374183124
86	100.51	99.9459637885851	0.564036211414873
87	100.27	100.590094358719	-0.32009435871899
88	100.04	100.347750232276	-0.307750232275708
89	99.23	100.11549650478	-0.885496504780207
90	99.32	99.2990118051417	0.0209881948583046
91	99.95	99.3891655066401	0.560834493359934
92	100.23	100.023272629838	0.206727370162113
93	101.02	100.3047865431	0.715213456899505
94	99.83	101.100024219839	-1.27002421983934
95	99.61	99.9007235331005	-0.290723533100476
96	100.12	99.6785944961367	0.441405503863336
97	99.83	100.191827012692	-0.361827012691947
98	100.03	99.8991772681862	0.130822731813822
99	100.07	100.100135313889	-0.0301353138895024
100	100.46	100.139914625882	0.320085374117781
101	100.43	100.532258686529	-0.102258686529126
102	100.68	100.501509822063	0.178490177937277
103	101.8	100.75281694771	1.04718305228957
104	101.21	101.88048571605	-0.670485716049996
105	100.63	101.285575591101	-0.655575591100842
106	100.55	100.700774656511	-0.150774656511388
107	99.76	100.61967049816	-0.859670498160327
108	98.8	99.8233749284561	-1.02337492845614

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 86.7 & 86.48 & 0.219999999999999 \tabularnewline
4 & 87.86 & 86.7016111118596 & 1.15838888814041 \tabularnewline
5 & 88.24 & 87.8700942667491 & 0.36990573325086 \tabularnewline
6 & 88.23 & 88.2528031736299 & -0.0228031736298959 \tabularnewline
7 & 88.73 & 88.2426361806141 & 0.487363819385877 \tabularnewline
8 & 88.82 & 88.7462052607475 & 0.0737947392524632 \tabularnewline
9 & 87.16 & 88.8367456770184 & -1.67674567701836 \tabularnewline
10 & 86.29 & 87.164466473174 & -0.874466473173996 \tabularnewline
11 & 86.37 & 86.288062549057 & 0.0819374509430162 \tabularnewline
12 & 86.59 & 86.368662596325 & 0.221337403675022 \tabularnewline
13 & 85.46 & 86.5902835023069 & -1.13028350230695 \tabularnewline
14 & 85.85 & 85.452006169783 & 0.39799383021699 \tabularnewline
15 & 86.93 & 85.8449207724189 & 1.08507922758106 \tabularnewline
16 & 87.66 & 86.9328670633833 & 0.727132936616727 \tabularnewline
17 & 87.84 & 87.6681920292818 & 0.171807970718191 \tabularnewline
18 & 88.09 & 87.8494502195509 & 0.240549780449115 \tabularnewline
19 & 88.58 & 88.1012118222968 & 0.47878817770318 \tabularnewline
20 & 88.06 & 88.5947181009847 & -0.534718100984662 \tabularnewline
21 & 88.26 & 88.0708022342845 & 0.189197765715477 \tabularnewline
22 & 89 & 88.2721877741216 & 0.727812225878424 \tabularnewline
23 & 90.78 & 89.0175177146155 & 1.76248228538448 \tabularnewline
24 & 90 & 90.8104247878532 & -0.810424787853236 \tabularnewline
25 & 89.84 & 90.0244898560941 & -0.184489856094075 \tabularnewline
26 & 89.82 & 89.863138793389 & -0.0431387933889624 \tabularnewline
27 & 91.12 & 89.8428228778361 & 1.27717712216395 \tabularnewline
28 & 91.5 & 91.1521759469648 & 0.347824053035239 \tabularnewline
29 & 93.03 & 91.5347231444961 & 1.4952768555039 \tabularnewline
30 & 94.23 & 93.0756734093837 & 1.15432659061629 \tabularnewline
31 & 94.76 & 94.2841268151109 & 0.47587318488911 \tabularnewline
32 & 92.83 & 94.8176117466192 & -1.98761174661924 \tabularnewline
33 & 92.49 & 92.8730559972682 & -0.383055997268158 \tabularnewline
34 & 90.85 & 92.5302507879041 & -1.68025078790413 \tabularnewline
35 & 88.19 & 90.8779459153065 & -2.6879459153065 \tabularnewline
36 & 86.31 & 88.1982614537516 & -1.88826145375157 \tabularnewline
37 & 85.74 & 86.3044332700146 & -0.564433270014561 \tabularnewline
38 & 86.62 & 85.730299792127 & 0.889700207873034 \tabularnewline
39 & 86.66 & 86.6168152764742 & 0.043184723525826 \tabularnewline
40 & 87.39 & 86.6571315283843 & 0.732868471615717 \tabularnewline
41 & 87.59 & 87.3924984969576 & 0.197501503042361 \tabularnewline
42 & 88.8 & 87.5939448470206 & 1.20605515297945 \tabularnewline
43 & 88.64 & 88.8127770732037 & -0.172777073203662 \tabularnewline
44 & 89.55 & 88.6515117859686 & 0.89848821403136 \tabularnewline
45 & 89.04 & 89.5680916269565 & -0.528091626956481 \tabularnewline
46 & 88.49 & 89.0542242874877 & -0.56422428748769 \tabularnewline
47 & 89.5 & 88.5000923400284 & 0.999907659971598 \tabularnewline
48 & 89.46 & 89.517414899526 & -0.0574148995260231 \tabularnewline
49 & 90.33 & 89.4769944366826 & 0.853005563317367 \tabularnewline
50 & 90.27 & 90.3532411974979 & -0.0832411974978982 \tabularnewline
51 & 91.5 & 90.2926316025866 & 1.20736839741345 \tabularnewline
52 & 92.53 & 91.5314734459682 & 0.998526554031784 \tabularnewline
53 & 93.14 & 92.5687858913015 & 0.571214108698527 \tabularnewline
54 & 93.01 & 93.1829690268691 & -0.17296902686914 \tabularnewline
55 & 92.84 & 93.0517023339122 & -0.211702333912186 \tabularnewline
56 & 92.88 & 92.8801519878173 & -0.000151987817346821 \tabularnewline
57 & 93.05 & 92.9201508747747 & 0.129849125225277 \tabularnewline
58 & 93.17 & 93.0911017905275 & 0.078898209472527 \tabularnewline
59 & 93.67 & 93.2116795807138 & 0.458320419286238 \tabularnewline
60 & 94.9 & 93.715035969182 & 1.18496403081804 \tabularnewline
61 & 95.72 & 94.9537137401058 & 0.76628625989423 \tabularnewline
62 & 96.08 & 95.7793254350201 & 0.300674564979886 \tabularnewline
63 & 97.52 & 96.1415273457361 & 1.3784726542639 \tabularnewline
64 & 98.26 & 97.5916222259243 & 0.668377774075708 \tabularnewline
65 & 98.48 & 98.3365169139175 & 0.143483086082526 \tabularnewline
66 & 98.09 & 98.5575676743795 & -0.467567674379467 \tabularnewline
67 & 98.03 & 98.1641435660824 & -0.134143566082415 \tabularnewline
68 & 98.14 & 98.1031612011269 & 0.0368387988730632 \tabularnewline
69 & 98.71 & 98.2134309803349 & 0.49656901966506 \tabularnewline
70 & 98.69 & 98.7870674723199 & -0.0970674723198641 \tabularnewline
71 & 98.72 & 98.7663566243388 & -0.0463566243387987 \tabularnewline
72 & 98.47 & 98.7960171438513 & -0.326017143851331 \tabularnewline
73 & 99.49 & 98.5436296434564 & 0.946370356543611 \tabularnewline
74 & 99.84 & 99.5705601366609 & 0.269439863339116 \tabularnewline
75 & 100.9 & 99.9225333082939 & 0.977466691706056 \tabularnewline
76 & 101.31 & 100.989691527291 & 0.320308472708959 \tabularnewline
77 & 100.09 & 101.402037221742 & -1.31203722174153 \tabularnewline
78 & 99.28 & 100.172428863886 & -0.892428863886224 \tabularnewline
79 & 99.57 & 99.3558933969478 & 0.214106603052173 \tabularnewline
80 & 101.04 & 99.6474613500723 & 1.39253864992767 \tabularnewline
81 & 101.87 & 101.127659238863 & 0.742340761137498 \tabularnewline
82 & 101.39 & 101.963095575245 & -0.573095575244892 \tabularnewline
83 & 100.3 & 101.478898661254 & -1.17889866125418 \tabularnewline
84 & 99.95 & 100.380265308461 & -0.430265308461443 \tabularnewline
85 & 99.87 & 100.027114374183 & -0.157114374183124 \tabularnewline
86 & 100.51 & 99.9459637885851 & 0.564036211414873 \tabularnewline
87 & 100.27 & 100.590094358719 & -0.32009435871899 \tabularnewline
88 & 100.04 & 100.347750232276 & -0.307750232275708 \tabularnewline
89 & 99.23 & 100.11549650478 & -0.885496504780207 \tabularnewline
90 & 99.32 & 99.2990118051417 & 0.0209881948583046 \tabularnewline
91 & 99.95 & 99.3891655066401 & 0.560834493359934 \tabularnewline
92 & 100.23 & 100.023272629838 & 0.206727370162113 \tabularnewline
93 & 101.02 & 100.3047865431 & 0.715213456899505 \tabularnewline
94 & 99.83 & 101.100024219839 & -1.27002421983934 \tabularnewline
95 & 99.61 & 99.9007235331005 & -0.290723533100476 \tabularnewline
96 & 100.12 & 99.6785944961367 & 0.441405503863336 \tabularnewline
97 & 99.83 & 100.191827012692 & -0.361827012691947 \tabularnewline
98 & 100.03 & 99.8991772681862 & 0.130822731813822 \tabularnewline
99 & 100.07 & 100.100135313889 & -0.0301353138895024 \tabularnewline
100 & 100.46 & 100.139914625882 & 0.320085374117781 \tabularnewline
101 & 100.43 & 100.532258686529 & -0.102258686529126 \tabularnewline
102 & 100.68 & 100.501509822063 & 0.178490177937277 \tabularnewline
103 & 101.8 & 100.75281694771 & 1.04718305228957 \tabularnewline
104 & 101.21 & 101.88048571605 & -0.670485716049996 \tabularnewline
105 & 100.63 & 101.285575591101 & -0.655575591100842 \tabularnewline
106 & 100.55 & 100.700774656511 & -0.150774656511388 \tabularnewline
107 & 99.76 & 100.61967049816 & -0.859670498160327 \tabularnewline
108 & 98.8 & 99.8233749284561 & -1.02337492845614 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284624&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]86.7[/C][C]86.48[/C][C]0.219999999999999[/C][/ROW]
[ROW][C]4[/C][C]87.86[/C][C]86.7016111118596[/C][C]1.15838888814041[/C][/ROW]
[ROW][C]5[/C][C]88.24[/C][C]87.8700942667491[/C][C]0.36990573325086[/C][/ROW]
[ROW][C]6[/C][C]88.23[/C][C]88.2528031736299[/C][C]-0.0228031736298959[/C][/ROW]
[ROW][C]7[/C][C]88.73[/C][C]88.2426361806141[/C][C]0.487363819385877[/C][/ROW]
[ROW][C]8[/C][C]88.82[/C][C]88.7462052607475[/C][C]0.0737947392524632[/C][/ROW]
[ROW][C]9[/C][C]87.16[/C][C]88.8367456770184[/C][C]-1.67674567701836[/C][/ROW]
[ROW][C]10[/C][C]86.29[/C][C]87.164466473174[/C][C]-0.874466473173996[/C][/ROW]
[ROW][C]11[/C][C]86.37[/C][C]86.288062549057[/C][C]0.0819374509430162[/C][/ROW]
[ROW][C]12[/C][C]86.59[/C][C]86.368662596325[/C][C]0.221337403675022[/C][/ROW]
[ROW][C]13[/C][C]85.46[/C][C]86.5902835023069[/C][C]-1.13028350230695[/C][/ROW]
[ROW][C]14[/C][C]85.85[/C][C]85.452006169783[/C][C]0.39799383021699[/C][/ROW]
[ROW][C]15[/C][C]86.93[/C][C]85.8449207724189[/C][C]1.08507922758106[/C][/ROW]
[ROW][C]16[/C][C]87.66[/C][C]86.9328670633833[/C][C]0.727132936616727[/C][/ROW]
[ROW][C]17[/C][C]87.84[/C][C]87.6681920292818[/C][C]0.171807970718191[/C][/ROW]
[ROW][C]18[/C][C]88.09[/C][C]87.8494502195509[/C][C]0.240549780449115[/C][/ROW]
[ROW][C]19[/C][C]88.58[/C][C]88.1012118222968[/C][C]0.47878817770318[/C][/ROW]
[ROW][C]20[/C][C]88.06[/C][C]88.5947181009847[/C][C]-0.534718100984662[/C][/ROW]
[ROW][C]21[/C][C]88.26[/C][C]88.0708022342845[/C][C]0.189197765715477[/C][/ROW]
[ROW][C]22[/C][C]89[/C][C]88.2721877741216[/C][C]0.727812225878424[/C][/ROW]
[ROW][C]23[/C][C]90.78[/C][C]89.0175177146155[/C][C]1.76248228538448[/C][/ROW]
[ROW][C]24[/C][C]90[/C][C]90.8104247878532[/C][C]-0.810424787853236[/C][/ROW]
[ROW][C]25[/C][C]89.84[/C][C]90.0244898560941[/C][C]-0.184489856094075[/C][/ROW]
[ROW][C]26[/C][C]89.82[/C][C]89.863138793389[/C][C]-0.0431387933889624[/C][/ROW]
[ROW][C]27[/C][C]91.12[/C][C]89.8428228778361[/C][C]1.27717712216395[/C][/ROW]
[ROW][C]28[/C][C]91.5[/C][C]91.1521759469648[/C][C]0.347824053035239[/C][/ROW]
[ROW][C]29[/C][C]93.03[/C][C]91.5347231444961[/C][C]1.4952768555039[/C][/ROW]
[ROW][C]30[/C][C]94.23[/C][C]93.0756734093837[/C][C]1.15432659061629[/C][/ROW]
[ROW][C]31[/C][C]94.76[/C][C]94.2841268151109[/C][C]0.47587318488911[/C][/ROW]
[ROW][C]32[/C][C]92.83[/C][C]94.8176117466192[/C][C]-1.98761174661924[/C][/ROW]
[ROW][C]33[/C][C]92.49[/C][C]92.8730559972682[/C][C]-0.383055997268158[/C][/ROW]
[ROW][C]34[/C][C]90.85[/C][C]92.5302507879041[/C][C]-1.68025078790413[/C][/ROW]
[ROW][C]35[/C][C]88.19[/C][C]90.8779459153065[/C][C]-2.6879459153065[/C][/ROW]
[ROW][C]36[/C][C]86.31[/C][C]88.1982614537516[/C][C]-1.88826145375157[/C][/ROW]
[ROW][C]37[/C][C]85.74[/C][C]86.3044332700146[/C][C]-0.564433270014561[/C][/ROW]
[ROW][C]38[/C][C]86.62[/C][C]85.730299792127[/C][C]0.889700207873034[/C][/ROW]
[ROW][C]39[/C][C]86.66[/C][C]86.6168152764742[/C][C]0.043184723525826[/C][/ROW]
[ROW][C]40[/C][C]87.39[/C][C]86.6571315283843[/C][C]0.732868471615717[/C][/ROW]
[ROW][C]41[/C][C]87.59[/C][C]87.3924984969576[/C][C]0.197501503042361[/C][/ROW]
[ROW][C]42[/C][C]88.8[/C][C]87.5939448470206[/C][C]1.20605515297945[/C][/ROW]
[ROW][C]43[/C][C]88.64[/C][C]88.8127770732037[/C][C]-0.172777073203662[/C][/ROW]
[ROW][C]44[/C][C]89.55[/C][C]88.6515117859686[/C][C]0.89848821403136[/C][/ROW]
[ROW][C]45[/C][C]89.04[/C][C]89.5680916269565[/C][C]-0.528091626956481[/C][/ROW]
[ROW][C]46[/C][C]88.49[/C][C]89.0542242874877[/C][C]-0.56422428748769[/C][/ROW]
[ROW][C]47[/C][C]89.5[/C][C]88.5000923400284[/C][C]0.999907659971598[/C][/ROW]
[ROW][C]48[/C][C]89.46[/C][C]89.517414899526[/C][C]-0.0574148995260231[/C][/ROW]
[ROW][C]49[/C][C]90.33[/C][C]89.4769944366826[/C][C]0.853005563317367[/C][/ROW]
[ROW][C]50[/C][C]90.27[/C][C]90.3532411974979[/C][C]-0.0832411974978982[/C][/ROW]
[ROW][C]51[/C][C]91.5[/C][C]90.2926316025866[/C][C]1.20736839741345[/C][/ROW]
[ROW][C]52[/C][C]92.53[/C][C]91.5314734459682[/C][C]0.998526554031784[/C][/ROW]
[ROW][C]53[/C][C]93.14[/C][C]92.5687858913015[/C][C]0.571214108698527[/C][/ROW]
[ROW][C]54[/C][C]93.01[/C][C]93.1829690268691[/C][C]-0.17296902686914[/C][/ROW]
[ROW][C]55[/C][C]92.84[/C][C]93.0517023339122[/C][C]-0.211702333912186[/C][/ROW]
[ROW][C]56[/C][C]92.88[/C][C]92.8801519878173[/C][C]-0.000151987817346821[/C][/ROW]
[ROW][C]57[/C][C]93.05[/C][C]92.9201508747747[/C][C]0.129849125225277[/C][/ROW]
[ROW][C]58[/C][C]93.17[/C][C]93.0911017905275[/C][C]0.078898209472527[/C][/ROW]
[ROW][C]59[/C][C]93.67[/C][C]93.2116795807138[/C][C]0.458320419286238[/C][/ROW]
[ROW][C]60[/C][C]94.9[/C][C]93.715035969182[/C][C]1.18496403081804[/C][/ROW]
[ROW][C]61[/C][C]95.72[/C][C]94.9537137401058[/C][C]0.76628625989423[/C][/ROW]
[ROW][C]62[/C][C]96.08[/C][C]95.7793254350201[/C][C]0.300674564979886[/C][/ROW]
[ROW][C]63[/C][C]97.52[/C][C]96.1415273457361[/C][C]1.3784726542639[/C][/ROW]
[ROW][C]64[/C][C]98.26[/C][C]97.5916222259243[/C][C]0.668377774075708[/C][/ROW]
[ROW][C]65[/C][C]98.48[/C][C]98.3365169139175[/C][C]0.143483086082526[/C][/ROW]
[ROW][C]66[/C][C]98.09[/C][C]98.5575676743795[/C][C]-0.467567674379467[/C][/ROW]
[ROW][C]67[/C][C]98.03[/C][C]98.1641435660824[/C][C]-0.134143566082415[/C][/ROW]
[ROW][C]68[/C][C]98.14[/C][C]98.1031612011269[/C][C]0.0368387988730632[/C][/ROW]
[ROW][C]69[/C][C]98.71[/C][C]98.2134309803349[/C][C]0.49656901966506[/C][/ROW]
[ROW][C]70[/C][C]98.69[/C][C]98.7870674723199[/C][C]-0.0970674723198641[/C][/ROW]
[ROW][C]71[/C][C]98.72[/C][C]98.7663566243388[/C][C]-0.0463566243387987[/C][/ROW]
[ROW][C]72[/C][C]98.47[/C][C]98.7960171438513[/C][C]-0.326017143851331[/C][/ROW]
[ROW][C]73[/C][C]99.49[/C][C]98.5436296434564[/C][C]0.946370356543611[/C][/ROW]
[ROW][C]74[/C][C]99.84[/C][C]99.5705601366609[/C][C]0.269439863339116[/C][/ROW]
[ROW][C]75[/C][C]100.9[/C][C]99.9225333082939[/C][C]0.977466691706056[/C][/ROW]
[ROW][C]76[/C][C]101.31[/C][C]100.989691527291[/C][C]0.320308472708959[/C][/ROW]
[ROW][C]77[/C][C]100.09[/C][C]101.402037221742[/C][C]-1.31203722174153[/C][/ROW]
[ROW][C]78[/C][C]99.28[/C][C]100.172428863886[/C][C]-0.892428863886224[/C][/ROW]
[ROW][C]79[/C][C]99.57[/C][C]99.3558933969478[/C][C]0.214106603052173[/C][/ROW]
[ROW][C]80[/C][C]101.04[/C][C]99.6474613500723[/C][C]1.39253864992767[/C][/ROW]
[ROW][C]81[/C][C]101.87[/C][C]101.127659238863[/C][C]0.742340761137498[/C][/ROW]
[ROW][C]82[/C][C]101.39[/C][C]101.963095575245[/C][C]-0.573095575244892[/C][/ROW]
[ROW][C]83[/C][C]100.3[/C][C]101.478898661254[/C][C]-1.17889866125418[/C][/ROW]
[ROW][C]84[/C][C]99.95[/C][C]100.380265308461[/C][C]-0.430265308461443[/C][/ROW]
[ROW][C]85[/C][C]99.87[/C][C]100.027114374183[/C][C]-0.157114374183124[/C][/ROW]
[ROW][C]86[/C][C]100.51[/C][C]99.9459637885851[/C][C]0.564036211414873[/C][/ROW]
[ROW][C]87[/C][C]100.27[/C][C]100.590094358719[/C][C]-0.32009435871899[/C][/ROW]
[ROW][C]88[/C][C]100.04[/C][C]100.347750232276[/C][C]-0.307750232275708[/C][/ROW]
[ROW][C]89[/C][C]99.23[/C][C]100.11549650478[/C][C]-0.885496504780207[/C][/ROW]
[ROW][C]90[/C][C]99.32[/C][C]99.2990118051417[/C][C]0.0209881948583046[/C][/ROW]
[ROW][C]91[/C][C]99.95[/C][C]99.3891655066401[/C][C]0.560834493359934[/C][/ROW]
[ROW][C]92[/C][C]100.23[/C][C]100.023272629838[/C][C]0.206727370162113[/C][/ROW]
[ROW][C]93[/C][C]101.02[/C][C]100.3047865431[/C][C]0.715213456899505[/C][/ROW]
[ROW][C]94[/C][C]99.83[/C][C]101.100024219839[/C][C]-1.27002421983934[/C][/ROW]
[ROW][C]95[/C][C]99.61[/C][C]99.9007235331005[/C][C]-0.290723533100476[/C][/ROW]
[ROW][C]96[/C][C]100.12[/C][C]99.6785944961367[/C][C]0.441405503863336[/C][/ROW]
[ROW][C]97[/C][C]99.83[/C][C]100.191827012692[/C][C]-0.361827012691947[/C][/ROW]
[ROW][C]98[/C][C]100.03[/C][C]99.8991772681862[/C][C]0.130822731813822[/C][/ROW]
[ROW][C]99[/C][C]100.07[/C][C]100.100135313889[/C][C]-0.0301353138895024[/C][/ROW]
[ROW][C]100[/C][C]100.46[/C][C]100.139914625882[/C][C]0.320085374117781[/C][/ROW]
[ROW][C]101[/C][C]100.43[/C][C]100.532258686529[/C][C]-0.102258686529126[/C][/ROW]
[ROW][C]102[/C][C]100.68[/C][C]100.501509822063[/C][C]0.178490177937277[/C][/ROW]
[ROW][C]103[/C][C]101.8[/C][C]100.75281694771[/C][C]1.04718305228957[/C][/ROW]
[ROW][C]104[/C][C]101.21[/C][C]101.88048571605[/C][C]-0.670485716049996[/C][/ROW]
[ROW][C]105[/C][C]100.63[/C][C]101.285575591101[/C][C]-0.655575591100842[/C][/ROW]
[ROW][C]106[/C][C]100.55[/C][C]100.700774656511[/C][C]-0.150774656511388[/C][/ROW]
[ROW][C]107[/C][C]99.76[/C][C]100.61967049816[/C][C]-0.859670498160327[/C][/ROW]
[ROW][C]108[/C][C]98.8[/C][C]99.8233749284561[/C][C]-1.02337492845614[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284624&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284624&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	86.7	86.48	0.219999999999999
4	87.86	86.7016111118596	1.15838888814041
5	88.24	87.8700942667491	0.36990573325086
6	88.23	88.2528031736299	-0.0228031736298959
7	88.73	88.2426361806141	0.487363819385877
8	88.82	88.7462052607475	0.0737947392524632
9	87.16	88.8367456770184	-1.67674567701836
10	86.29	87.164466473174	-0.874466473173996
11	86.37	86.288062549057	0.0819374509430162
12	86.59	86.368662596325	0.221337403675022
13	85.46	86.5902835023069	-1.13028350230695
14	85.85	85.452006169783	0.39799383021699
15	86.93	85.8449207724189	1.08507922758106
16	87.66	86.9328670633833	0.727132936616727
17	87.84	87.6681920292818	0.171807970718191
18	88.09	87.8494502195509	0.240549780449115
19	88.58	88.1012118222968	0.47878817770318
20	88.06	88.5947181009847	-0.534718100984662
21	88.26	88.0708022342845	0.189197765715477
22	89	88.2721877741216	0.727812225878424
23	90.78	89.0175177146155	1.76248228538448
24	90	90.8104247878532	-0.810424787853236
25	89.84	90.0244898560941	-0.184489856094075
26	89.82	89.863138793389	-0.0431387933889624
27	91.12	89.8428228778361	1.27717712216395
28	91.5	91.1521759469648	0.347824053035239
29	93.03	91.5347231444961	1.4952768555039
30	94.23	93.0756734093837	1.15432659061629
31	94.76	94.2841268151109	0.47587318488911
32	92.83	94.8176117466192	-1.98761174661924
33	92.49	92.8730559972682	-0.383055997268158
34	90.85	92.5302507879041	-1.68025078790413
35	88.19	90.8779459153065	-2.6879459153065
36	86.31	88.1982614537516	-1.88826145375157
37	85.74	86.3044332700146	-0.564433270014561
38	86.62	85.730299792127	0.889700207873034
39	86.66	86.6168152764742	0.043184723525826
40	87.39	86.6571315283843	0.732868471615717
41	87.59	87.3924984969576	0.197501503042361
42	88.8	87.5939448470206	1.20605515297945
43	88.64	88.8127770732037	-0.172777073203662
44	89.55	88.6515117859686	0.89848821403136
45	89.04	89.5680916269565	-0.528091626956481
46	88.49	89.0542242874877	-0.56422428748769
47	89.5	88.5000923400284	0.999907659971598
48	89.46	89.517414899526	-0.0574148995260231
49	90.33	89.4769944366826	0.853005563317367
50	90.27	90.3532411974979	-0.0832411974978982
51	91.5	90.2926316025866	1.20736839741345
52	92.53	91.5314734459682	0.998526554031784
53	93.14	92.5687858913015	0.571214108698527
54	93.01	93.1829690268691	-0.17296902686914
55	92.84	93.0517023339122	-0.211702333912186
56	92.88	92.8801519878173	-0.000151987817346821
57	93.05	92.9201508747747	0.129849125225277
58	93.17	93.0911017905275	0.078898209472527
59	93.67	93.2116795807138	0.458320419286238
60	94.9	93.715035969182	1.18496403081804
61	95.72	94.9537137401058	0.76628625989423
62	96.08	95.7793254350201	0.300674564979886
63	97.52	96.1415273457361	1.3784726542639
64	98.26	97.5916222259243	0.668377774075708
65	98.48	98.3365169139175	0.143483086082526
66	98.09	98.5575676743795	-0.467567674379467
67	98.03	98.1641435660824	-0.134143566082415
68	98.14	98.1031612011269	0.0368387988730632
69	98.71	98.2134309803349	0.49656901966506
70	98.69	98.7870674723199	-0.0970674723198641
71	98.72	98.7663566243388	-0.0463566243387987
72	98.47	98.7960171438513	-0.326017143851331
73	99.49	98.5436296434564	0.946370356543611
74	99.84	99.5705601366609	0.269439863339116
75	100.9	99.9225333082939	0.977466691706056
76	101.31	100.989691527291	0.320308472708959
77	100.09	101.402037221742	-1.31203722174153
78	99.28	100.172428863886	-0.892428863886224
79	99.57	99.3558933969478	0.214106603052173
80	101.04	99.6474613500723	1.39253864992767
81	101.87	101.127659238863	0.742340761137498
82	101.39	101.963095575245	-0.573095575244892
83	100.3	101.478898661254	-1.17889866125418
84	99.95	100.380265308461	-0.430265308461443
85	99.87	100.027114374183	-0.157114374183124
86	100.51	99.9459637885851	0.564036211414873
87	100.27	100.590094358719	-0.32009435871899
88	100.04	100.347750232276	-0.307750232275708
89	99.23	100.11549650478	-0.885496504780207
90	99.32	99.2990118051417	0.0209881948583046
91	99.95	99.3891655066401	0.560834493359934
92	100.23	100.023272629838	0.206727370162113
93	101.02	100.3047865431	0.715213456899505
94	99.83	101.100024219839	-1.27002421983934
95	99.61	99.9007235331005	-0.290723533100476
96	100.12	99.6785944961367	0.441405503863336
97	99.83	100.191827012692	-0.361827012691947
98	100.03	99.8991772681862	0.130822731813822
99	100.07	100.100135313889	-0.0301353138895024
100	100.46	100.139914625882	0.320085374117781
101	100.43	100.532258686529	-0.102258686529126
102	100.68	100.501509822063	0.178490177937277
103	101.8	100.75281694771	1.04718305228957
104	101.21	101.88048571605	-0.670485716049996
105	100.63	101.285575591101	-0.655575591100842
106	100.55	100.700774656511	-0.150774656511388
107	99.76	100.61967049816	-0.859670498160327
108	98.8	99.8233749284561	-1.02337492845614

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
109	98.8558805126196	97.2806504217981	100.431110603441
110	98.9117610252391	96.6758773583447	101.147644692134
111	98.9676415378587	96.2192340085671	101.71604906715
112	99.0235220504783	95.8383500750468	102.20869402591
113	99.0794025630979	95.5053052479139	102.653499878282
114	99.1352830757175	95.2058348432603	103.064731308175
115	99.191163588337	94.9314966951353	103.450830481539
116	99.2470441009566	94.6768106654153	103.817277536498
117	99.3029246135762	94.4379842847579	104.167864942394
118	99.3588051261957	94.2122664415644	104.505343810827
119	99.4146856388153	93.997587901819	104.831783375812
120	99.4705661514349	93.792346982474	105.148785320396

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 98.8558805126196 & 97.2806504217981 & 100.431110603441 \tabularnewline
110 & 98.9117610252391 & 96.6758773583447 & 101.147644692134 \tabularnewline
111 & 98.9676415378587 & 96.2192340085671 & 101.71604906715 \tabularnewline
112 & 99.0235220504783 & 95.8383500750468 & 102.20869402591 \tabularnewline
113 & 99.0794025630979 & 95.5053052479139 & 102.653499878282 \tabularnewline
114 & 99.1352830757175 & 95.2058348432603 & 103.064731308175 \tabularnewline
115 & 99.191163588337 & 94.9314966951353 & 103.450830481539 \tabularnewline
116 & 99.2470441009566 & 94.6768106654153 & 103.817277536498 \tabularnewline
117 & 99.3029246135762 & 94.4379842847579 & 104.167864942394 \tabularnewline
118 & 99.3588051261957 & 94.2122664415644 & 104.505343810827 \tabularnewline
119 & 99.4146856388153 & 93.997587901819 & 104.831783375812 \tabularnewline
120 & 99.4705661514349 & 93.792346982474 & 105.148785320396 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284624&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]109[/C][C]98.8558805126196[/C][C]97.2806504217981[/C][C]100.431110603441[/C][/ROW]
[ROW][C]110[/C][C]98.9117610252391[/C][C]96.6758773583447[/C][C]101.147644692134[/C][/ROW]
[ROW][C]111[/C][C]98.9676415378587[/C][C]96.2192340085671[/C][C]101.71604906715[/C][/ROW]
[ROW][C]112[/C][C]99.0235220504783[/C][C]95.8383500750468[/C][C]102.20869402591[/C][/ROW]
[ROW][C]113[/C][C]99.0794025630979[/C][C]95.5053052479139[/C][C]102.653499878282[/C][/ROW]
[ROW][C]114[/C][C]99.1352830757175[/C][C]95.2058348432603[/C][C]103.064731308175[/C][/ROW]
[ROW][C]115[/C][C]99.191163588337[/C][C]94.9314966951353[/C][C]103.450830481539[/C][/ROW]
[ROW][C]116[/C][C]99.2470441009566[/C][C]94.6768106654153[/C][C]103.817277536498[/C][/ROW]
[ROW][C]117[/C][C]99.3029246135762[/C][C]94.4379842847579[/C][C]104.167864942394[/C][/ROW]
[ROW][C]118[/C][C]99.3588051261957[/C][C]94.2122664415644[/C][C]104.505343810827[/C][/ROW]
[ROW][C]119[/C][C]99.4146856388153[/C][C]93.997587901819[/C][C]104.831783375812[/C][/ROW]
[ROW][C]120[/C][C]99.4705661514349[/C][C]93.792346982474[/C][C]105.148785320396[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284624&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284624&T=3

As an alternative you can also use a QR Code:

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

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
109	98.8558805126196	97.2806504217981	100.431110603441
110	98.9117610252391	96.6758773583447	101.147644692134
111	98.9676415378587	96.2192340085671	101.71604906715
112	99.0235220504783	95.8383500750468	102.20869402591
113	99.0794025630979	95.5053052479139	102.653499878282
114	99.1352830757175	95.2058348432603	103.064731308175
115	99.191163588337	94.9314966951353	103.450830481539
116	99.2470441009566	94.6768106654153	103.817277536498
117	99.3029246135762	94.4379842847579	104.167864942394
118	99.3588051261957	94.2122664415644	104.505343810827
119	99.4146856388153	93.997587901819	104.831783375812
120	99.4705661514349	93.792346982474	105.148785320396

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 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

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