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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Thu, 26 Nov 2015 15:23:46 +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/26/t1448551489wwtauhza5d1gpe0.htm/, Retrieved Mon, 13 May 2024 22:50:06 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284241, Retrieved Mon, 13 May 2024 22:50:06 +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] [] [2015-11-26 15:23:46] [db7ed3fbbcc36ff904ff15d7b0c6bd86] [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	'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284241&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284241&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284241&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	'George Udny Yule' @ yule.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.687703074785767
beta	0.00602379308448132
gamma	0.410620018388877

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.687703074785767 \tabularnewline
beta & 0.00602379308448132 \tabularnewline
gamma & 0.410620018388877 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284241&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]0.687703074785767[/C][/ROW]
[ROW][C]beta[/C][C]0.00602379308448132[/C][/ROW]
[ROW][C]gamma[/C][C]0.410620018388877[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284241&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284241&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	0.687703074785767
beta	0.00602379308448132
gamma	0.410620018388877

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	82.51	81.3530475427351	1.15695245726492
14	83.23	82.8670421372117	0.362957862788321
15	83.41	83.3235911233925	0.0864088766075213
16	83.88	83.8903144772205	-0.0103144772205326
17	83.96	83.9917281546599	-0.0317281546598593
18	84.32	84.3303674771635	-0.0103674771635269
19	85.82	85.6424036551467	0.177596344853271
20	85.72	85.8815221720612	-0.161522172061183
21	84.36	84.8438420568248	-0.483842056824827
22	84.36	84.3045805441811	0.0554194558189494
23	84.36	84.3255670781489	0.034432921851149
24	85.08	84.4039304160133	0.676069583986688
25	84.95	85.0455454911623	-0.0955454911623264
26	85.62	85.5988589528886	0.0211410471113709
27	86.22	85.7859438462133	0.434056153786713
28	86.4	86.5818498471627	-0.181849847162709
29	86.71	86.5643494339079	0.145650566092073
30	87.51	87.0302439496432	0.479756050356755
31	89.22	88.7080056782647	0.511994321735301
32	89.43	89.1395514782169	0.290448521783119
33	88.24	88.3791802690003	-0.139180269000306
34	88.9	88.1553439957074	0.74465600429258
35	88.78	88.6597324945799	0.120267505420117
36	89.25	88.8918637176453	0.358136282354707
37	88.8	89.2270283391131	-0.427028339113107
38	89.46	89.5771117732718	-0.117111773271773
39	89.66	89.7312657794464	-0.0712657794464064
40	90.29	90.1077817440768	0.182218255923217
41	90.08	90.3912597470906	-0.31125974709056
42	90.42	90.5924975136192	-0.172497513619192
43	92.14	91.8298522721004	0.310147727899633
44	92.09	92.0973571002353	-0.00735710023525371
45	91.35	91.0790363173993	0.270963682600694
46	91.22	91.2542413009996	-0.0342413009995539
47	90.99	91.143329322698	-0.153329322698042
48	91.48	91.2170952434901	0.262904756509911
49	90.98	91.3849733596593	-0.404973359659252
50	91.52	91.7889480837138	-0.268948083713838
51	91.62	91.8429156235353	-0.222915623535258
52	92.12	92.1453716744422	-0.0253716744422121
53	92.26	92.2196726835384	0.040327316461628
54	92.18	92.678813232247	-0.498813232246974
55	94.12	93.7506211203823	0.369378879617656
56	93.82	94.0153586766507	-0.195358676650699
57	93.2	92.8998750200461	0.300124979953878
58	93.34	93.0525528668532	0.287447133146756
59	93.11	93.1454849609122	-0.0354849609121715
60	93.63	93.3520461657796	0.277953834220426
61	93.29	93.4430677475153	-0.153067747515252
62	93.69	94.0372052918269	-0.347205291826853
63	94.19	94.0424172164562	0.147582783543768
64	94.82	94.6256922199525	0.194307780047481
65	94.52	94.8610963772592	-0.341096377259191
66	94.94	94.9888176906806	-0.0488176906806501
67	96.87	96.4833098743438	0.386690125656244
68	96.6	96.6894928539395	-0.0894928539395039
69	95.43	95.7127502917141	-0.282750291714052
70	95.56	95.4629409785334	0.0970590214666487
71	95.37	95.3827262732287	-0.0127262732287363
72	96	95.6444219236507	0.355578076349332
73	95.6	95.7331645748821	-0.133164574882144
74	96.17	96.3157875942132	-0.145787594213218
75	96.26	96.5234921111155	-0.263492111115497
76	97.2	96.8288862225043	0.371113777495665
77	97.23	97.116779871038	0.113220128961999
78	97.74	97.5958557638383	0.144144236161665
79	99.37	99.2811345797801	0.0888654202199177
80	99.37	99.2224439468097	0.147556053190328
81	98.22	98.3859250556108	-0.165925055610771
82	98.27	98.2676326096063	0.00236739039370093
83	97.98	98.1102983585109	-0.130298358510856
84	98.53	98.3399604545719	0.190039545428064
85	97.98	98.2530933839642	-0.273093383964209
86	98.63	98.7381942762476	-0.108194276247644
87	98.74	98.9571397474467	-0.217139747446737
88	99.37	99.3764632568015	-0.00646325680153836
89	99.51	99.3707346017361	0.139265398263873
90	99.66	99.8709050363436	-0.210905036343561
91	101.62	101.302673421855	0.317326578144943
92	101.71	101.407315608845	0.30268439115531
93	100.49	100.636615382844	-0.146615382843763
94	100.81	100.55259908991	0.257400910089771
95	100.48	100.554112018009	-0.0741120180086909
96	101.01	100.864197323847	0.145802676152684
97	100.62	100.688040186508	-0.0680401865084548
98	101.12	101.336673927082	-0.216673927082326
99	101.45	101.467968796339	-0.0179687963393036
100	101.34	102.053025890744	-0.713025890743609
101	101.39	101.578899446719	-0.188899446718665
102	101.93	101.805946163029	0.12405383697147
103	102.42	103.534652855601	-1.11465285560145
104	102.18	102.64555672975	-0.46555672975002
105	102.72	101.278652092277	1.44134790772347
106	102.43	102.334803973927	0.0951960260730687
107	102.35	102.177896233483	0.172103766516571
108	102.69	102.682165513893	0.00783448610691551

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 82.51 & 81.3530475427351 & 1.15695245726492 \tabularnewline
14 & 83.23 & 82.8670421372117 & 0.362957862788321 \tabularnewline
15 & 83.41 & 83.3235911233925 & 0.0864088766075213 \tabularnewline
16 & 83.88 & 83.8903144772205 & -0.0103144772205326 \tabularnewline
17 & 83.96 & 83.9917281546599 & -0.0317281546598593 \tabularnewline
18 & 84.32 & 84.3303674771635 & -0.0103674771635269 \tabularnewline
19 & 85.82 & 85.6424036551467 & 0.177596344853271 \tabularnewline
20 & 85.72 & 85.8815221720612 & -0.161522172061183 \tabularnewline
21 & 84.36 & 84.8438420568248 & -0.483842056824827 \tabularnewline
22 & 84.36 & 84.3045805441811 & 0.0554194558189494 \tabularnewline
23 & 84.36 & 84.3255670781489 & 0.034432921851149 \tabularnewline
24 & 85.08 & 84.4039304160133 & 0.676069583986688 \tabularnewline
25 & 84.95 & 85.0455454911623 & -0.0955454911623264 \tabularnewline
26 & 85.62 & 85.5988589528886 & 0.0211410471113709 \tabularnewline
27 & 86.22 & 85.7859438462133 & 0.434056153786713 \tabularnewline
28 & 86.4 & 86.5818498471627 & -0.181849847162709 \tabularnewline
29 & 86.71 & 86.5643494339079 & 0.145650566092073 \tabularnewline
30 & 87.51 & 87.0302439496432 & 0.479756050356755 \tabularnewline
31 & 89.22 & 88.7080056782647 & 0.511994321735301 \tabularnewline
32 & 89.43 & 89.1395514782169 & 0.290448521783119 \tabularnewline
33 & 88.24 & 88.3791802690003 & -0.139180269000306 \tabularnewline
34 & 88.9 & 88.1553439957074 & 0.74465600429258 \tabularnewline
35 & 88.78 & 88.6597324945799 & 0.120267505420117 \tabularnewline
36 & 89.25 & 88.8918637176453 & 0.358136282354707 \tabularnewline
37 & 88.8 & 89.2270283391131 & -0.427028339113107 \tabularnewline
38 & 89.46 & 89.5771117732718 & -0.117111773271773 \tabularnewline
39 & 89.66 & 89.7312657794464 & -0.0712657794464064 \tabularnewline
40 & 90.29 & 90.1077817440768 & 0.182218255923217 \tabularnewline
41 & 90.08 & 90.3912597470906 & -0.31125974709056 \tabularnewline
42 & 90.42 & 90.5924975136192 & -0.172497513619192 \tabularnewline
43 & 92.14 & 91.8298522721004 & 0.310147727899633 \tabularnewline
44 & 92.09 & 92.0973571002353 & -0.00735710023525371 \tabularnewline
45 & 91.35 & 91.0790363173993 & 0.270963682600694 \tabularnewline
46 & 91.22 & 91.2542413009996 & -0.0342413009995539 \tabularnewline
47 & 90.99 & 91.143329322698 & -0.153329322698042 \tabularnewline
48 & 91.48 & 91.2170952434901 & 0.262904756509911 \tabularnewline
49 & 90.98 & 91.3849733596593 & -0.404973359659252 \tabularnewline
50 & 91.52 & 91.7889480837138 & -0.268948083713838 \tabularnewline
51 & 91.62 & 91.8429156235353 & -0.222915623535258 \tabularnewline
52 & 92.12 & 92.1453716744422 & -0.0253716744422121 \tabularnewline
53 & 92.26 & 92.2196726835384 & 0.040327316461628 \tabularnewline
54 & 92.18 & 92.678813232247 & -0.498813232246974 \tabularnewline
55 & 94.12 & 93.7506211203823 & 0.369378879617656 \tabularnewline
56 & 93.82 & 94.0153586766507 & -0.195358676650699 \tabularnewline
57 & 93.2 & 92.8998750200461 & 0.300124979953878 \tabularnewline
58 & 93.34 & 93.0525528668532 & 0.287447133146756 \tabularnewline
59 & 93.11 & 93.1454849609122 & -0.0354849609121715 \tabularnewline
60 & 93.63 & 93.3520461657796 & 0.277953834220426 \tabularnewline
61 & 93.29 & 93.4430677475153 & -0.153067747515252 \tabularnewline
62 & 93.69 & 94.0372052918269 & -0.347205291826853 \tabularnewline
63 & 94.19 & 94.0424172164562 & 0.147582783543768 \tabularnewline
64 & 94.82 & 94.6256922199525 & 0.194307780047481 \tabularnewline
65 & 94.52 & 94.8610963772592 & -0.341096377259191 \tabularnewline
66 & 94.94 & 94.9888176906806 & -0.0488176906806501 \tabularnewline
67 & 96.87 & 96.4833098743438 & 0.386690125656244 \tabularnewline
68 & 96.6 & 96.6894928539395 & -0.0894928539395039 \tabularnewline
69 & 95.43 & 95.7127502917141 & -0.282750291714052 \tabularnewline
70 & 95.56 & 95.4629409785334 & 0.0970590214666487 \tabularnewline
71 & 95.37 & 95.3827262732287 & -0.0127262732287363 \tabularnewline
72 & 96 & 95.6444219236507 & 0.355578076349332 \tabularnewline
73 & 95.6 & 95.7331645748821 & -0.133164574882144 \tabularnewline
74 & 96.17 & 96.3157875942132 & -0.145787594213218 \tabularnewline
75 & 96.26 & 96.5234921111155 & -0.263492111115497 \tabularnewline
76 & 97.2 & 96.8288862225043 & 0.371113777495665 \tabularnewline
77 & 97.23 & 97.116779871038 & 0.113220128961999 \tabularnewline
78 & 97.74 & 97.5958557638383 & 0.144144236161665 \tabularnewline
79 & 99.37 & 99.2811345797801 & 0.0888654202199177 \tabularnewline
80 & 99.37 & 99.2224439468097 & 0.147556053190328 \tabularnewline
81 & 98.22 & 98.3859250556108 & -0.165925055610771 \tabularnewline
82 & 98.27 & 98.2676326096063 & 0.00236739039370093 \tabularnewline
83 & 97.98 & 98.1102983585109 & -0.130298358510856 \tabularnewline
84 & 98.53 & 98.3399604545719 & 0.190039545428064 \tabularnewline
85 & 97.98 & 98.2530933839642 & -0.273093383964209 \tabularnewline
86 & 98.63 & 98.7381942762476 & -0.108194276247644 \tabularnewline
87 & 98.74 & 98.9571397474467 & -0.217139747446737 \tabularnewline
88 & 99.37 & 99.3764632568015 & -0.00646325680153836 \tabularnewline
89 & 99.51 & 99.3707346017361 & 0.139265398263873 \tabularnewline
90 & 99.66 & 99.8709050363436 & -0.210905036343561 \tabularnewline
91 & 101.62 & 101.302673421855 & 0.317326578144943 \tabularnewline
92 & 101.71 & 101.407315608845 & 0.30268439115531 \tabularnewline
93 & 100.49 & 100.636615382844 & -0.146615382843763 \tabularnewline
94 & 100.81 & 100.55259908991 & 0.257400910089771 \tabularnewline
95 & 100.48 & 100.554112018009 & -0.0741120180086909 \tabularnewline
96 & 101.01 & 100.864197323847 & 0.145802676152684 \tabularnewline
97 & 100.62 & 100.688040186508 & -0.0680401865084548 \tabularnewline
98 & 101.12 & 101.336673927082 & -0.216673927082326 \tabularnewline
99 & 101.45 & 101.467968796339 & -0.0179687963393036 \tabularnewline
100 & 101.34 & 102.053025890744 & -0.713025890743609 \tabularnewline
101 & 101.39 & 101.578899446719 & -0.188899446718665 \tabularnewline
102 & 101.93 & 101.805946163029 & 0.12405383697147 \tabularnewline
103 & 102.42 & 103.534652855601 & -1.11465285560145 \tabularnewline
104 & 102.18 & 102.64555672975 & -0.46555672975002 \tabularnewline
105 & 102.72 & 101.278652092277 & 1.44134790772347 \tabularnewline
106 & 102.43 & 102.334803973927 & 0.0951960260730687 \tabularnewline
107 & 102.35 & 102.177896233483 & 0.172103766516571 \tabularnewline
108 & 102.69 & 102.682165513893 & 0.00783448610691551 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284241&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]82.51[/C][C]81.3530475427351[/C][C]1.15695245726492[/C][/ROW]
[ROW][C]14[/C][C]83.23[/C][C]82.8670421372117[/C][C]0.362957862788321[/C][/ROW]
[ROW][C]15[/C][C]83.41[/C][C]83.3235911233925[/C][C]0.0864088766075213[/C][/ROW]
[ROW][C]16[/C][C]83.88[/C][C]83.8903144772205[/C][C]-0.0103144772205326[/C][/ROW]
[ROW][C]17[/C][C]83.96[/C][C]83.9917281546599[/C][C]-0.0317281546598593[/C][/ROW]
[ROW][C]18[/C][C]84.32[/C][C]84.3303674771635[/C][C]-0.0103674771635269[/C][/ROW]
[ROW][C]19[/C][C]85.82[/C][C]85.6424036551467[/C][C]0.177596344853271[/C][/ROW]
[ROW][C]20[/C][C]85.72[/C][C]85.8815221720612[/C][C]-0.161522172061183[/C][/ROW]
[ROW][C]21[/C][C]84.36[/C][C]84.8438420568248[/C][C]-0.483842056824827[/C][/ROW]
[ROW][C]22[/C][C]84.36[/C][C]84.3045805441811[/C][C]0.0554194558189494[/C][/ROW]
[ROW][C]23[/C][C]84.36[/C][C]84.3255670781489[/C][C]0.034432921851149[/C][/ROW]
[ROW][C]24[/C][C]85.08[/C][C]84.4039304160133[/C][C]0.676069583986688[/C][/ROW]
[ROW][C]25[/C][C]84.95[/C][C]85.0455454911623[/C][C]-0.0955454911623264[/C][/ROW]
[ROW][C]26[/C][C]85.62[/C][C]85.5988589528886[/C][C]0.0211410471113709[/C][/ROW]
[ROW][C]27[/C][C]86.22[/C][C]85.7859438462133[/C][C]0.434056153786713[/C][/ROW]
[ROW][C]28[/C][C]86.4[/C][C]86.5818498471627[/C][C]-0.181849847162709[/C][/ROW]
[ROW][C]29[/C][C]86.71[/C][C]86.5643494339079[/C][C]0.145650566092073[/C][/ROW]
[ROW][C]30[/C][C]87.51[/C][C]87.0302439496432[/C][C]0.479756050356755[/C][/ROW]
[ROW][C]31[/C][C]89.22[/C][C]88.7080056782647[/C][C]0.511994321735301[/C][/ROW]
[ROW][C]32[/C][C]89.43[/C][C]89.1395514782169[/C][C]0.290448521783119[/C][/ROW]
[ROW][C]33[/C][C]88.24[/C][C]88.3791802690003[/C][C]-0.139180269000306[/C][/ROW]
[ROW][C]34[/C][C]88.9[/C][C]88.1553439957074[/C][C]0.74465600429258[/C][/ROW]
[ROW][C]35[/C][C]88.78[/C][C]88.6597324945799[/C][C]0.120267505420117[/C][/ROW]
[ROW][C]36[/C][C]89.25[/C][C]88.8918637176453[/C][C]0.358136282354707[/C][/ROW]
[ROW][C]37[/C][C]88.8[/C][C]89.2270283391131[/C][C]-0.427028339113107[/C][/ROW]
[ROW][C]38[/C][C]89.46[/C][C]89.5771117732718[/C][C]-0.117111773271773[/C][/ROW]
[ROW][C]39[/C][C]89.66[/C][C]89.7312657794464[/C][C]-0.0712657794464064[/C][/ROW]
[ROW][C]40[/C][C]90.29[/C][C]90.1077817440768[/C][C]0.182218255923217[/C][/ROW]
[ROW][C]41[/C][C]90.08[/C][C]90.3912597470906[/C][C]-0.31125974709056[/C][/ROW]
[ROW][C]42[/C][C]90.42[/C][C]90.5924975136192[/C][C]-0.172497513619192[/C][/ROW]
[ROW][C]43[/C][C]92.14[/C][C]91.8298522721004[/C][C]0.310147727899633[/C][/ROW]
[ROW][C]44[/C][C]92.09[/C][C]92.0973571002353[/C][C]-0.00735710023525371[/C][/ROW]
[ROW][C]45[/C][C]91.35[/C][C]91.0790363173993[/C][C]0.270963682600694[/C][/ROW]
[ROW][C]46[/C][C]91.22[/C][C]91.2542413009996[/C][C]-0.0342413009995539[/C][/ROW]
[ROW][C]47[/C][C]90.99[/C][C]91.143329322698[/C][C]-0.153329322698042[/C][/ROW]
[ROW][C]48[/C][C]91.48[/C][C]91.2170952434901[/C][C]0.262904756509911[/C][/ROW]
[ROW][C]49[/C][C]90.98[/C][C]91.3849733596593[/C][C]-0.404973359659252[/C][/ROW]
[ROW][C]50[/C][C]91.52[/C][C]91.7889480837138[/C][C]-0.268948083713838[/C][/ROW]
[ROW][C]51[/C][C]91.62[/C][C]91.8429156235353[/C][C]-0.222915623535258[/C][/ROW]
[ROW][C]52[/C][C]92.12[/C][C]92.1453716744422[/C][C]-0.0253716744422121[/C][/ROW]
[ROW][C]53[/C][C]92.26[/C][C]92.2196726835384[/C][C]0.040327316461628[/C][/ROW]
[ROW][C]54[/C][C]92.18[/C][C]92.678813232247[/C][C]-0.498813232246974[/C][/ROW]
[ROW][C]55[/C][C]94.12[/C][C]93.7506211203823[/C][C]0.369378879617656[/C][/ROW]
[ROW][C]56[/C][C]93.82[/C][C]94.0153586766507[/C][C]-0.195358676650699[/C][/ROW]
[ROW][C]57[/C][C]93.2[/C][C]92.8998750200461[/C][C]0.300124979953878[/C][/ROW]
[ROW][C]58[/C][C]93.34[/C][C]93.0525528668532[/C][C]0.287447133146756[/C][/ROW]
[ROW][C]59[/C][C]93.11[/C][C]93.1454849609122[/C][C]-0.0354849609121715[/C][/ROW]
[ROW][C]60[/C][C]93.63[/C][C]93.3520461657796[/C][C]0.277953834220426[/C][/ROW]
[ROW][C]61[/C][C]93.29[/C][C]93.4430677475153[/C][C]-0.153067747515252[/C][/ROW]
[ROW][C]62[/C][C]93.69[/C][C]94.0372052918269[/C][C]-0.347205291826853[/C][/ROW]
[ROW][C]63[/C][C]94.19[/C][C]94.0424172164562[/C][C]0.147582783543768[/C][/ROW]
[ROW][C]64[/C][C]94.82[/C][C]94.6256922199525[/C][C]0.194307780047481[/C][/ROW]
[ROW][C]65[/C][C]94.52[/C][C]94.8610963772592[/C][C]-0.341096377259191[/C][/ROW]
[ROW][C]66[/C][C]94.94[/C][C]94.9888176906806[/C][C]-0.0488176906806501[/C][/ROW]
[ROW][C]67[/C][C]96.87[/C][C]96.4833098743438[/C][C]0.386690125656244[/C][/ROW]
[ROW][C]68[/C][C]96.6[/C][C]96.6894928539395[/C][C]-0.0894928539395039[/C][/ROW]
[ROW][C]69[/C][C]95.43[/C][C]95.7127502917141[/C][C]-0.282750291714052[/C][/ROW]
[ROW][C]70[/C][C]95.56[/C][C]95.4629409785334[/C][C]0.0970590214666487[/C][/ROW]
[ROW][C]71[/C][C]95.37[/C][C]95.3827262732287[/C][C]-0.0127262732287363[/C][/ROW]
[ROW][C]72[/C][C]96[/C][C]95.6444219236507[/C][C]0.355578076349332[/C][/ROW]
[ROW][C]73[/C][C]95.6[/C][C]95.7331645748821[/C][C]-0.133164574882144[/C][/ROW]
[ROW][C]74[/C][C]96.17[/C][C]96.3157875942132[/C][C]-0.145787594213218[/C][/ROW]
[ROW][C]75[/C][C]96.26[/C][C]96.5234921111155[/C][C]-0.263492111115497[/C][/ROW]
[ROW][C]76[/C][C]97.2[/C][C]96.8288862225043[/C][C]0.371113777495665[/C][/ROW]
[ROW][C]77[/C][C]97.23[/C][C]97.116779871038[/C][C]0.113220128961999[/C][/ROW]
[ROW][C]78[/C][C]97.74[/C][C]97.5958557638383[/C][C]0.144144236161665[/C][/ROW]
[ROW][C]79[/C][C]99.37[/C][C]99.2811345797801[/C][C]0.0888654202199177[/C][/ROW]
[ROW][C]80[/C][C]99.37[/C][C]99.2224439468097[/C][C]0.147556053190328[/C][/ROW]
[ROW][C]81[/C][C]98.22[/C][C]98.3859250556108[/C][C]-0.165925055610771[/C][/ROW]
[ROW][C]82[/C][C]98.27[/C][C]98.2676326096063[/C][C]0.00236739039370093[/C][/ROW]
[ROW][C]83[/C][C]97.98[/C][C]98.1102983585109[/C][C]-0.130298358510856[/C][/ROW]
[ROW][C]84[/C][C]98.53[/C][C]98.3399604545719[/C][C]0.190039545428064[/C][/ROW]
[ROW][C]85[/C][C]97.98[/C][C]98.2530933839642[/C][C]-0.273093383964209[/C][/ROW]
[ROW][C]86[/C][C]98.63[/C][C]98.7381942762476[/C][C]-0.108194276247644[/C][/ROW]
[ROW][C]87[/C][C]98.74[/C][C]98.9571397474467[/C][C]-0.217139747446737[/C][/ROW]
[ROW][C]88[/C][C]99.37[/C][C]99.3764632568015[/C][C]-0.00646325680153836[/C][/ROW]
[ROW][C]89[/C][C]99.51[/C][C]99.3707346017361[/C][C]0.139265398263873[/C][/ROW]
[ROW][C]90[/C][C]99.66[/C][C]99.8709050363436[/C][C]-0.210905036343561[/C][/ROW]
[ROW][C]91[/C][C]101.62[/C][C]101.302673421855[/C][C]0.317326578144943[/C][/ROW]
[ROW][C]92[/C][C]101.71[/C][C]101.407315608845[/C][C]0.30268439115531[/C][/ROW]
[ROW][C]93[/C][C]100.49[/C][C]100.636615382844[/C][C]-0.146615382843763[/C][/ROW]
[ROW][C]94[/C][C]100.81[/C][C]100.55259908991[/C][C]0.257400910089771[/C][/ROW]
[ROW][C]95[/C][C]100.48[/C][C]100.554112018009[/C][C]-0.0741120180086909[/C][/ROW]
[ROW][C]96[/C][C]101.01[/C][C]100.864197323847[/C][C]0.145802676152684[/C][/ROW]
[ROW][C]97[/C][C]100.62[/C][C]100.688040186508[/C][C]-0.0680401865084548[/C][/ROW]
[ROW][C]98[/C][C]101.12[/C][C]101.336673927082[/C][C]-0.216673927082326[/C][/ROW]
[ROW][C]99[/C][C]101.45[/C][C]101.467968796339[/C][C]-0.0179687963393036[/C][/ROW]
[ROW][C]100[/C][C]101.34[/C][C]102.053025890744[/C][C]-0.713025890743609[/C][/ROW]
[ROW][C]101[/C][C]101.39[/C][C]101.578899446719[/C][C]-0.188899446718665[/C][/ROW]
[ROW][C]102[/C][C]101.93[/C][C]101.805946163029[/C][C]0.12405383697147[/C][/ROW]
[ROW][C]103[/C][C]102.42[/C][C]103.534652855601[/C][C]-1.11465285560145[/C][/ROW]
[ROW][C]104[/C][C]102.18[/C][C]102.64555672975[/C][C]-0.46555672975002[/C][/ROW]
[ROW][C]105[/C][C]102.72[/C][C]101.278652092277[/C][C]1.44134790772347[/C][/ROW]
[ROW][C]106[/C][C]102.43[/C][C]102.334803973927[/C][C]0.0951960260730687[/C][/ROW]
[ROW][C]107[/C][C]102.35[/C][C]102.177896233483[/C][C]0.172103766516571[/C][/ROW]
[ROW][C]108[/C][C]102.69[/C][C]102.682165513893[/C][C]0.00783448610691551[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284241&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284241&T=2

As an alternative you can also use a QR Code:

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

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	82.51	81.3530475427351	1.15695245726492
14	83.23	82.8670421372117	0.362957862788321
15	83.41	83.3235911233925	0.0864088766075213
16	83.88	83.8903144772205	-0.0103144772205326
17	83.96	83.9917281546599	-0.0317281546598593
18	84.32	84.3303674771635	-0.0103674771635269
19	85.82	85.6424036551467	0.177596344853271
20	85.72	85.8815221720612	-0.161522172061183
21	84.36	84.8438420568248	-0.483842056824827
22	84.36	84.3045805441811	0.0554194558189494
23	84.36	84.3255670781489	0.034432921851149
24	85.08	84.4039304160133	0.676069583986688
25	84.95	85.0455454911623	-0.0955454911623264
26	85.62	85.5988589528886	0.0211410471113709
27	86.22	85.7859438462133	0.434056153786713
28	86.4	86.5818498471627	-0.181849847162709
29	86.71	86.5643494339079	0.145650566092073
30	87.51	87.0302439496432	0.479756050356755
31	89.22	88.7080056782647	0.511994321735301
32	89.43	89.1395514782169	0.290448521783119
33	88.24	88.3791802690003	-0.139180269000306
34	88.9	88.1553439957074	0.74465600429258
35	88.78	88.6597324945799	0.120267505420117
36	89.25	88.8918637176453	0.358136282354707
37	88.8	89.2270283391131	-0.427028339113107
38	89.46	89.5771117732718	-0.117111773271773
39	89.66	89.7312657794464	-0.0712657794464064
40	90.29	90.1077817440768	0.182218255923217
41	90.08	90.3912597470906	-0.31125974709056
42	90.42	90.5924975136192	-0.172497513619192
43	92.14	91.8298522721004	0.310147727899633
44	92.09	92.0973571002353	-0.00735710023525371
45	91.35	91.0790363173993	0.270963682600694
46	91.22	91.2542413009996	-0.0342413009995539
47	90.99	91.143329322698	-0.153329322698042
48	91.48	91.2170952434901	0.262904756509911
49	90.98	91.3849733596593	-0.404973359659252
50	91.52	91.7889480837138	-0.268948083713838
51	91.62	91.8429156235353	-0.222915623535258
52	92.12	92.1453716744422	-0.0253716744422121
53	92.26	92.2196726835384	0.040327316461628
54	92.18	92.678813232247	-0.498813232246974
55	94.12	93.7506211203823	0.369378879617656
56	93.82	94.0153586766507	-0.195358676650699
57	93.2	92.8998750200461	0.300124979953878
58	93.34	93.0525528668532	0.287447133146756
59	93.11	93.1454849609122	-0.0354849609121715
60	93.63	93.3520461657796	0.277953834220426
61	93.29	93.4430677475153	-0.153067747515252
62	93.69	94.0372052918269	-0.347205291826853
63	94.19	94.0424172164562	0.147582783543768
64	94.82	94.6256922199525	0.194307780047481
65	94.52	94.8610963772592	-0.341096377259191
66	94.94	94.9888176906806	-0.0488176906806501
67	96.87	96.4833098743438	0.386690125656244
68	96.6	96.6894928539395	-0.0894928539395039
69	95.43	95.7127502917141	-0.282750291714052
70	95.56	95.4629409785334	0.0970590214666487
71	95.37	95.3827262732287	-0.0127262732287363
72	96	95.6444219236507	0.355578076349332
73	95.6	95.7331645748821	-0.133164574882144
74	96.17	96.3157875942132	-0.145787594213218
75	96.26	96.5234921111155	-0.263492111115497
76	97.2	96.8288862225043	0.371113777495665
77	97.23	97.116779871038	0.113220128961999
78	97.74	97.5958557638383	0.144144236161665
79	99.37	99.2811345797801	0.0888654202199177
80	99.37	99.2224439468097	0.147556053190328
81	98.22	98.3859250556108	-0.165925055610771
82	98.27	98.2676326096063	0.00236739039370093
83	97.98	98.1102983585109	-0.130298358510856
84	98.53	98.3399604545719	0.190039545428064
85	97.98	98.2530933839642	-0.273093383964209
86	98.63	98.7381942762476	-0.108194276247644
87	98.74	98.9571397474467	-0.217139747446737
88	99.37	99.3764632568015	-0.00646325680153836
89	99.51	99.3707346017361	0.139265398263873
90	99.66	99.8709050363436	-0.210905036343561
91	101.62	101.302673421855	0.317326578144943
92	101.71	101.407315608845	0.30268439115531
93	100.49	100.636615382844	-0.146615382843763
94	100.81	100.55259908991	0.257400910089771
95	100.48	100.554112018009	-0.0741120180086909
96	101.01	100.864197323847	0.145802676152684
97	100.62	100.688040186508	-0.0680401865084548
98	101.12	101.336673927082	-0.216673927082326
99	101.45	101.467968796339	-0.0179687963393036
100	101.34	102.053025890744	-0.713025890743609
101	101.39	101.578899446719	-0.188899446718665
102	101.93	101.805946163029	0.12405383697147
103	102.42	103.534652855601	-1.11465285560145
104	102.18	102.64555672975	-0.46555672975002
105	102.72	101.278652092277	1.44134790772347
106	102.43	102.334803973927	0.0951960260730687
107	102.35	102.177896233483	0.172103766516571
108	102.69	102.682165513893	0.00783448610691551

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
109	102.379793245692	101.71180503903	103.047781452353
110	103.052528427221	102.240256302904	103.864800551539
111	103.355579335534	102.41966849016	104.291490180908
112	103.861204847906	102.814948245244	104.907461450569
113	103.94493594149	102.797777441953	105.092094441028
114	104.343099491365	103.102170944443	105.584028038287
115	105.828212489084	104.499129609851	107.157295368317
116	105.794085700739	104.381407088416	107.206764313061
117	104.998989144505	103.506502072925	106.491476216085
118	104.892437120713	103.323345980604	106.461528260822
119	104.68067048171	103.037726715825	106.323614247596
120	105.045550795881	103.331145765193	106.759955826569

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 102.379793245692 & 101.71180503903 & 103.047781452353 \tabularnewline
110 & 103.052528427221 & 102.240256302904 & 103.864800551539 \tabularnewline
111 & 103.355579335534 & 102.41966849016 & 104.291490180908 \tabularnewline
112 & 103.861204847906 & 102.814948245244 & 104.907461450569 \tabularnewline
113 & 103.94493594149 & 102.797777441953 & 105.092094441028 \tabularnewline
114 & 104.343099491365 & 103.102170944443 & 105.584028038287 \tabularnewline
115 & 105.828212489084 & 104.499129609851 & 107.157295368317 \tabularnewline
116 & 105.794085700739 & 104.381407088416 & 107.206764313061 \tabularnewline
117 & 104.998989144505 & 103.506502072925 & 106.491476216085 \tabularnewline
118 & 104.892437120713 & 103.323345980604 & 106.461528260822 \tabularnewline
119 & 104.68067048171 & 103.037726715825 & 106.323614247596 \tabularnewline
120 & 105.045550795881 & 103.331145765193 & 106.759955826569 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284241&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]102.379793245692[/C][C]101.71180503903[/C][C]103.047781452353[/C][/ROW]
[ROW][C]110[/C][C]103.052528427221[/C][C]102.240256302904[/C][C]103.864800551539[/C][/ROW]
[ROW][C]111[/C][C]103.355579335534[/C][C]102.41966849016[/C][C]104.291490180908[/C][/ROW]
[ROW][C]112[/C][C]103.861204847906[/C][C]102.814948245244[/C][C]104.907461450569[/C][/ROW]
[ROW][C]113[/C][C]103.94493594149[/C][C]102.797777441953[/C][C]105.092094441028[/C][/ROW]
[ROW][C]114[/C][C]104.343099491365[/C][C]103.102170944443[/C][C]105.584028038287[/C][/ROW]
[ROW][C]115[/C][C]105.828212489084[/C][C]104.499129609851[/C][C]107.157295368317[/C][/ROW]
[ROW][C]116[/C][C]105.794085700739[/C][C]104.381407088416[/C][C]107.206764313061[/C][/ROW]
[ROW][C]117[/C][C]104.998989144505[/C][C]103.506502072925[/C][C]106.491476216085[/C][/ROW]
[ROW][C]118[/C][C]104.892437120713[/C][C]103.323345980604[/C][C]106.461528260822[/C][/ROW]
[ROW][C]119[/C][C]104.68067048171[/C][C]103.037726715825[/C][C]106.323614247596[/C][/ROW]
[ROW][C]120[/C][C]105.045550795881[/C][C]103.331145765193[/C][C]106.759955826569[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284241&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284241&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	102.379793245692	101.71180503903	103.047781452353
110	103.052528427221	102.240256302904	103.864800551539
111	103.355579335534	102.41966849016	104.291490180908
112	103.861204847906	102.814948245244	104.907461450569
113	103.94493594149	102.797777441953	105.092094441028
114	104.343099491365	103.102170944443	105.584028038287
115	105.828212489084	104.499129609851	107.157295368317
116	105.794085700739	104.381407088416	107.206764313061
117	104.998989144505	103.506502072925	106.491476216085
118	104.892437120713	103.323345980604	106.461528260822
119	104.68067048171	103.037726715825	106.323614247596
120	105.045550795881	103.331145765193	106.759955826569

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

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

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

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

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code