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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

Fri, 23 Dec 2011 09:45:47 -0500

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/23/t1324651594kdcue3y2mb14a56.htm/, Retrieved Mon, 29 Apr 2024 17:55:59 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160465, Retrieved Mon, 29 Apr 2024 17:55:59 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KEYWORD: KDGP2W102

Estimated Impact

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

-       [Exponential Smoothing] [opdracht 10 oef2] [2011-12-23 14:45:47] [76c30f62b7052b57088120e90a652e05] [Current]

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Dataseries X:

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7,08
7,08
7,09
7,07
7,06
6,99
6,99
6,99
6,98
6,96
6,95
6,91
6,91
6,87
6,91
6,89
6,88
6,9
6,91
6,85
6,86
6,82
6,8
6,83
6,84
6,89
7,14
7,21
7,25
7,31
7,3
7,48
7,49
7,4
7,44
7,42
7,14
7,24
7,33
7,61
7,66
7,69
7,7
7,68
7,71
7,71
7,72
7,68
7,72
7,74
7,76
7,9
7,97
7,96
7,95
7,97
7,93
7,99
7,96
7,92
7,97
7,98
8
8,04
8,17
8,29
8,26
8,3
8,32
8,28
8,27
8,32
8,31
8,34
8,32
8,36
8,33
8,35
8,34
8,37
8,31
8,33
8,34
8,25
8,27
8,31
8,25
8,3
8,3
8,35
8,78
8,9
8,9
8,9
9
9,05

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ jenkins.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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160465&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160465&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160465&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	1 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.0321252473275465
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0321252473275465 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160465&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]0.0321252473275465[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160465&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160465&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	0.0321252473275465
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	7.09	7.08	0.00999999999999979
4	7.07	7.09032125247328	-0.0203212524732752
5	7.06	7.06966842721157	-0.00966842721156702
6	6.99	7.05935782659613	-0.069357826596125
7	6.99	6.98712968926262	0.00287031073737598
8	6.99	6.98722189870497	0.00277810129503031
9	6.98	6.98731114589617	-0.00731114589617299
10	6.96	6.97707627352601	-0.017076273526011
11	6.95	6.95652769401555	-0.00652769401555453
12	6.91	6.94631799023083	-0.0363179902308266
13	6.91	6.90515126581222	0.00484873418777809
14	6.87	6.90530703259723	-0.0353070325972302
15	6.91	6.86417278544264	0.0458272145573577
16	6.89	6.90564499604463	-0.0156449960446308
17	6.88	6.88514239667726	-0.00514239667725747
18	6.9	6.87497719591214	0.0250228040878557
19	6.91	6.8957810596823	0.0142189403177042
20	6.85	6.90623784665674	-0.0562378466567379
21	6.86	6.84443119192372	0.0155688080762797
22	6.82	6.85493134373377	-0.0349313437337671
23	6.8	6.81380916567684	-0.013809165676836
24	6.83	6.79336554281408	0.0366344571859196
25	6.84	6.82454243381189	0.0154575661881111
26	6.89	6.83503901194876	0.0549609880512367
27	7.14	6.88680464728328	0.253195352716724
28	7.21	7.14493861061149	0.0650613893885144
29	7.25	7.21702872383707	0.0329712761629342
30	7.31	7.2580879342385	0.0519120657614947
31	7.3	7.31975562219038	-0.0197556221903765
32	7.48	7.3091209679414	0.1708790320586
33	7.49	7.49461049910938	-0.00461049910937561
34	7.4	7.50446238568518	-0.104462385685183
35	7.44	7.41110650570862	0.0288934942913786
36	7.42	7.45203471635889	-0.032034716358889
37	7.14	7.43100559317279	-0.291005593172792
38	7.24	7.14165696651842	0.0983430334815836
39	7.33	7.24481626079195	0.0851837392080466
40	7.61	7.3375528094823	0.272447190517703
41	7.66	7.62630524286137	0.0336947571386261
42	7.69	7.67738769526809	0.0126123047319062
43	7.7	7.70779286867698	-0.00779286867697682
44	7.68	7.71754252084334	-0.0375425208433384
45	7.71	7.69633645807595	0.0136635419240543
46	7.71	7.72677540273963	-0.0167754027396265
47	7.72	7.7262364887776	-0.00623648877759653
48	7.68	7.73603614003316	-0.0560361400331608
49	7.72	7.69423596517531	0.0257640348246859
50	7.74	7.73506364116621	0.0049363588337874
51	7.76	7.75522222291465	0.00477777708535321
52	7.9	7.77537571018519	0.124624289814812
53	7.97	7.91937929631851	0.0506207036814894
54	7.96	7.99100549894417	-0.0310054989441717
55	7.95	7.98000943962208	-0.0300094396220763
56	7.97	7.96904537895206	0.00095462104794386
57	7.93	7.98907604638933	-0.0590760463893254
58	7.99	7.94717821378793	0.0428217862120661
59	7.96	8.008553874261	-0.0485538742610041
60	7.92	7.97699406904166	-0.056994069041659
61	7.97	7.93516312047749	0.0348368795225076
62	7.98	7.98628226384827	-0.00628226384827268
63	8	7.99608044456837	0.00391955543162936
64	8.04	8.01620636125603	0.0237936387439728
65	8.17	8.0569707377855	0.113029262214503
66	8.29	8.19060183078939	0.0993981692106107
67	8.26	8.31379502155918	-0.0537950215591838
68	8.3	8.28206684318661	0.0179331568133954
69	8.32	8.3226429502846	-0.00264295028459927
70	8.28	8.34255804485303	-0.0625580448530343
71	8.27	8.3005483521898	-0.0305483521898005
72	8.32	8.28956697882025	0.0304330211797463
73	8.31	8.34054464715258	-0.0305446471525777
74	8.34	8.32956339280827	0.0104366071917301
75	8.32	8.35989867139556	-0.039898671395564
76	8.36	8.33861691670894	0.0213830832910578
77	8.33	8.37930385354829	-0.0493038535482917
78	8.35	8.34771995505885	0.00228004494114842
79	8.34	8.3677932020665	-0.0277932020665048
80	8.37	8.35690033857609	0.0130996614239063
81	8.31	8.38732116843924	-0.0773211684392425
82	8.33	8.32483720677948	0.00516279322052249
83	8.34	8.34500306278859	-0.00500306278858886
84	8.25	8.35484233815911	-0.104842338159109
85	8.27	8.26147425211535	0.00852574788464899
86	8.31	8.2817481438748	0.0282518561252036
87	8.25	8.32265574174028	-0.0726557417402809
88	8.3	8.26032165806711	0.039678341932893
89	8.3	8.31159633461525	-0.0115963346152483
90	8.35	8.31122379949764	0.0387762005023582
91	8.78	8.3624694945292	0.417530505470797
92	8.9	8.80588276528425	0.0941172347157533
93	8.9	8.92890630472728	-0.0289063047272755
94	8.9	8.92797768253859	-0.0279776825385856
95	9	8.92707889256738	0.0729211074326166
96	9.05	9.02942150117905	0.0205784988209476

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 7.09 & 7.08 & 0.00999999999999979 \tabularnewline
4 & 7.07 & 7.09032125247328 & -0.0203212524732752 \tabularnewline
5 & 7.06 & 7.06966842721157 & -0.00966842721156702 \tabularnewline
6 & 6.99 & 7.05935782659613 & -0.069357826596125 \tabularnewline
7 & 6.99 & 6.98712968926262 & 0.00287031073737598 \tabularnewline
8 & 6.99 & 6.98722189870497 & 0.00277810129503031 \tabularnewline
9 & 6.98 & 6.98731114589617 & -0.00731114589617299 \tabularnewline
10 & 6.96 & 6.97707627352601 & -0.017076273526011 \tabularnewline
11 & 6.95 & 6.95652769401555 & -0.00652769401555453 \tabularnewline
12 & 6.91 & 6.94631799023083 & -0.0363179902308266 \tabularnewline
13 & 6.91 & 6.90515126581222 & 0.00484873418777809 \tabularnewline
14 & 6.87 & 6.90530703259723 & -0.0353070325972302 \tabularnewline
15 & 6.91 & 6.86417278544264 & 0.0458272145573577 \tabularnewline
16 & 6.89 & 6.90564499604463 & -0.0156449960446308 \tabularnewline
17 & 6.88 & 6.88514239667726 & -0.00514239667725747 \tabularnewline
18 & 6.9 & 6.87497719591214 & 0.0250228040878557 \tabularnewline
19 & 6.91 & 6.8957810596823 & 0.0142189403177042 \tabularnewline
20 & 6.85 & 6.90623784665674 & -0.0562378466567379 \tabularnewline
21 & 6.86 & 6.84443119192372 & 0.0155688080762797 \tabularnewline
22 & 6.82 & 6.85493134373377 & -0.0349313437337671 \tabularnewline
23 & 6.8 & 6.81380916567684 & -0.013809165676836 \tabularnewline
24 & 6.83 & 6.79336554281408 & 0.0366344571859196 \tabularnewline
25 & 6.84 & 6.82454243381189 & 0.0154575661881111 \tabularnewline
26 & 6.89 & 6.83503901194876 & 0.0549609880512367 \tabularnewline
27 & 7.14 & 6.88680464728328 & 0.253195352716724 \tabularnewline
28 & 7.21 & 7.14493861061149 & 0.0650613893885144 \tabularnewline
29 & 7.25 & 7.21702872383707 & 0.0329712761629342 \tabularnewline
30 & 7.31 & 7.2580879342385 & 0.0519120657614947 \tabularnewline
31 & 7.3 & 7.31975562219038 & -0.0197556221903765 \tabularnewline
32 & 7.48 & 7.3091209679414 & 0.1708790320586 \tabularnewline
33 & 7.49 & 7.49461049910938 & -0.00461049910937561 \tabularnewline
34 & 7.4 & 7.50446238568518 & -0.104462385685183 \tabularnewline
35 & 7.44 & 7.41110650570862 & 0.0288934942913786 \tabularnewline
36 & 7.42 & 7.45203471635889 & -0.032034716358889 \tabularnewline
37 & 7.14 & 7.43100559317279 & -0.291005593172792 \tabularnewline
38 & 7.24 & 7.14165696651842 & 0.0983430334815836 \tabularnewline
39 & 7.33 & 7.24481626079195 & 0.0851837392080466 \tabularnewline
40 & 7.61 & 7.3375528094823 & 0.272447190517703 \tabularnewline
41 & 7.66 & 7.62630524286137 & 0.0336947571386261 \tabularnewline
42 & 7.69 & 7.67738769526809 & 0.0126123047319062 \tabularnewline
43 & 7.7 & 7.70779286867698 & -0.00779286867697682 \tabularnewline
44 & 7.68 & 7.71754252084334 & -0.0375425208433384 \tabularnewline
45 & 7.71 & 7.69633645807595 & 0.0136635419240543 \tabularnewline
46 & 7.71 & 7.72677540273963 & -0.0167754027396265 \tabularnewline
47 & 7.72 & 7.7262364887776 & -0.00623648877759653 \tabularnewline
48 & 7.68 & 7.73603614003316 & -0.0560361400331608 \tabularnewline
49 & 7.72 & 7.69423596517531 & 0.0257640348246859 \tabularnewline
50 & 7.74 & 7.73506364116621 & 0.0049363588337874 \tabularnewline
51 & 7.76 & 7.75522222291465 & 0.00477777708535321 \tabularnewline
52 & 7.9 & 7.77537571018519 & 0.124624289814812 \tabularnewline
53 & 7.97 & 7.91937929631851 & 0.0506207036814894 \tabularnewline
54 & 7.96 & 7.99100549894417 & -0.0310054989441717 \tabularnewline
55 & 7.95 & 7.98000943962208 & -0.0300094396220763 \tabularnewline
56 & 7.97 & 7.96904537895206 & 0.00095462104794386 \tabularnewline
57 & 7.93 & 7.98907604638933 & -0.0590760463893254 \tabularnewline
58 & 7.99 & 7.94717821378793 & 0.0428217862120661 \tabularnewline
59 & 7.96 & 8.008553874261 & -0.0485538742610041 \tabularnewline
60 & 7.92 & 7.97699406904166 & -0.056994069041659 \tabularnewline
61 & 7.97 & 7.93516312047749 & 0.0348368795225076 \tabularnewline
62 & 7.98 & 7.98628226384827 & -0.00628226384827268 \tabularnewline
63 & 8 & 7.99608044456837 & 0.00391955543162936 \tabularnewline
64 & 8.04 & 8.01620636125603 & 0.0237936387439728 \tabularnewline
65 & 8.17 & 8.0569707377855 & 0.113029262214503 \tabularnewline
66 & 8.29 & 8.19060183078939 & 0.0993981692106107 \tabularnewline
67 & 8.26 & 8.31379502155918 & -0.0537950215591838 \tabularnewline
68 & 8.3 & 8.28206684318661 & 0.0179331568133954 \tabularnewline
69 & 8.32 & 8.3226429502846 & -0.00264295028459927 \tabularnewline
70 & 8.28 & 8.34255804485303 & -0.0625580448530343 \tabularnewline
71 & 8.27 & 8.3005483521898 & -0.0305483521898005 \tabularnewline
72 & 8.32 & 8.28956697882025 & 0.0304330211797463 \tabularnewline
73 & 8.31 & 8.34054464715258 & -0.0305446471525777 \tabularnewline
74 & 8.34 & 8.32956339280827 & 0.0104366071917301 \tabularnewline
75 & 8.32 & 8.35989867139556 & -0.039898671395564 \tabularnewline
76 & 8.36 & 8.33861691670894 & 0.0213830832910578 \tabularnewline
77 & 8.33 & 8.37930385354829 & -0.0493038535482917 \tabularnewline
78 & 8.35 & 8.34771995505885 & 0.00228004494114842 \tabularnewline
79 & 8.34 & 8.3677932020665 & -0.0277932020665048 \tabularnewline
80 & 8.37 & 8.35690033857609 & 0.0130996614239063 \tabularnewline
81 & 8.31 & 8.38732116843924 & -0.0773211684392425 \tabularnewline
82 & 8.33 & 8.32483720677948 & 0.00516279322052249 \tabularnewline
83 & 8.34 & 8.34500306278859 & -0.00500306278858886 \tabularnewline
84 & 8.25 & 8.35484233815911 & -0.104842338159109 \tabularnewline
85 & 8.27 & 8.26147425211535 & 0.00852574788464899 \tabularnewline
86 & 8.31 & 8.2817481438748 & 0.0282518561252036 \tabularnewline
87 & 8.25 & 8.32265574174028 & -0.0726557417402809 \tabularnewline
88 & 8.3 & 8.26032165806711 & 0.039678341932893 \tabularnewline
89 & 8.3 & 8.31159633461525 & -0.0115963346152483 \tabularnewline
90 & 8.35 & 8.31122379949764 & 0.0387762005023582 \tabularnewline
91 & 8.78 & 8.3624694945292 & 0.417530505470797 \tabularnewline
92 & 8.9 & 8.80588276528425 & 0.0941172347157533 \tabularnewline
93 & 8.9 & 8.92890630472728 & -0.0289063047272755 \tabularnewline
94 & 8.9 & 8.92797768253859 & -0.0279776825385856 \tabularnewline
95 & 9 & 8.92707889256738 & 0.0729211074326166 \tabularnewline
96 & 9.05 & 9.02942150117905 & 0.0205784988209476 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160465&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]7.09[/C][C]7.08[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]4[/C][C]7.07[/C][C]7.09032125247328[/C][C]-0.0203212524732752[/C][/ROW]
[ROW][C]5[/C][C]7.06[/C][C]7.06966842721157[/C][C]-0.00966842721156702[/C][/ROW]
[ROW][C]6[/C][C]6.99[/C][C]7.05935782659613[/C][C]-0.069357826596125[/C][/ROW]
[ROW][C]7[/C][C]6.99[/C][C]6.98712968926262[/C][C]0.00287031073737598[/C][/ROW]
[ROW][C]8[/C][C]6.99[/C][C]6.98722189870497[/C][C]0.00277810129503031[/C][/ROW]
[ROW][C]9[/C][C]6.98[/C][C]6.98731114589617[/C][C]-0.00731114589617299[/C][/ROW]
[ROW][C]10[/C][C]6.96[/C][C]6.97707627352601[/C][C]-0.017076273526011[/C][/ROW]
[ROW][C]11[/C][C]6.95[/C][C]6.95652769401555[/C][C]-0.00652769401555453[/C][/ROW]
[ROW][C]12[/C][C]6.91[/C][C]6.94631799023083[/C][C]-0.0363179902308266[/C][/ROW]
[ROW][C]13[/C][C]6.91[/C][C]6.90515126581222[/C][C]0.00484873418777809[/C][/ROW]
[ROW][C]14[/C][C]6.87[/C][C]6.90530703259723[/C][C]-0.0353070325972302[/C][/ROW]
[ROW][C]15[/C][C]6.91[/C][C]6.86417278544264[/C][C]0.0458272145573577[/C][/ROW]
[ROW][C]16[/C][C]6.89[/C][C]6.90564499604463[/C][C]-0.0156449960446308[/C][/ROW]
[ROW][C]17[/C][C]6.88[/C][C]6.88514239667726[/C][C]-0.00514239667725747[/C][/ROW]
[ROW][C]18[/C][C]6.9[/C][C]6.87497719591214[/C][C]0.0250228040878557[/C][/ROW]
[ROW][C]19[/C][C]6.91[/C][C]6.8957810596823[/C][C]0.0142189403177042[/C][/ROW]
[ROW][C]20[/C][C]6.85[/C][C]6.90623784665674[/C][C]-0.0562378466567379[/C][/ROW]
[ROW][C]21[/C][C]6.86[/C][C]6.84443119192372[/C][C]0.0155688080762797[/C][/ROW]
[ROW][C]22[/C][C]6.82[/C][C]6.85493134373377[/C][C]-0.0349313437337671[/C][/ROW]
[ROW][C]23[/C][C]6.8[/C][C]6.81380916567684[/C][C]-0.013809165676836[/C][/ROW]
[ROW][C]24[/C][C]6.83[/C][C]6.79336554281408[/C][C]0.0366344571859196[/C][/ROW]
[ROW][C]25[/C][C]6.84[/C][C]6.82454243381189[/C][C]0.0154575661881111[/C][/ROW]
[ROW][C]26[/C][C]6.89[/C][C]6.83503901194876[/C][C]0.0549609880512367[/C][/ROW]
[ROW][C]27[/C][C]7.14[/C][C]6.88680464728328[/C][C]0.253195352716724[/C][/ROW]
[ROW][C]28[/C][C]7.21[/C][C]7.14493861061149[/C][C]0.0650613893885144[/C][/ROW]
[ROW][C]29[/C][C]7.25[/C][C]7.21702872383707[/C][C]0.0329712761629342[/C][/ROW]
[ROW][C]30[/C][C]7.31[/C][C]7.2580879342385[/C][C]0.0519120657614947[/C][/ROW]
[ROW][C]31[/C][C]7.3[/C][C]7.31975562219038[/C][C]-0.0197556221903765[/C][/ROW]
[ROW][C]32[/C][C]7.48[/C][C]7.3091209679414[/C][C]0.1708790320586[/C][/ROW]
[ROW][C]33[/C][C]7.49[/C][C]7.49461049910938[/C][C]-0.00461049910937561[/C][/ROW]
[ROW][C]34[/C][C]7.4[/C][C]7.50446238568518[/C][C]-0.104462385685183[/C][/ROW]
[ROW][C]35[/C][C]7.44[/C][C]7.41110650570862[/C][C]0.0288934942913786[/C][/ROW]
[ROW][C]36[/C][C]7.42[/C][C]7.45203471635889[/C][C]-0.032034716358889[/C][/ROW]
[ROW][C]37[/C][C]7.14[/C][C]7.43100559317279[/C][C]-0.291005593172792[/C][/ROW]
[ROW][C]38[/C][C]7.24[/C][C]7.14165696651842[/C][C]0.0983430334815836[/C][/ROW]
[ROW][C]39[/C][C]7.33[/C][C]7.24481626079195[/C][C]0.0851837392080466[/C][/ROW]
[ROW][C]40[/C][C]7.61[/C][C]7.3375528094823[/C][C]0.272447190517703[/C][/ROW]
[ROW][C]41[/C][C]7.66[/C][C]7.62630524286137[/C][C]0.0336947571386261[/C][/ROW]
[ROW][C]42[/C][C]7.69[/C][C]7.67738769526809[/C][C]0.0126123047319062[/C][/ROW]
[ROW][C]43[/C][C]7.7[/C][C]7.70779286867698[/C][C]-0.00779286867697682[/C][/ROW]
[ROW][C]44[/C][C]7.68[/C][C]7.71754252084334[/C][C]-0.0375425208433384[/C][/ROW]
[ROW][C]45[/C][C]7.71[/C][C]7.69633645807595[/C][C]0.0136635419240543[/C][/ROW]
[ROW][C]46[/C][C]7.71[/C][C]7.72677540273963[/C][C]-0.0167754027396265[/C][/ROW]
[ROW][C]47[/C][C]7.72[/C][C]7.7262364887776[/C][C]-0.00623648877759653[/C][/ROW]
[ROW][C]48[/C][C]7.68[/C][C]7.73603614003316[/C][C]-0.0560361400331608[/C][/ROW]
[ROW][C]49[/C][C]7.72[/C][C]7.69423596517531[/C][C]0.0257640348246859[/C][/ROW]
[ROW][C]50[/C][C]7.74[/C][C]7.73506364116621[/C][C]0.0049363588337874[/C][/ROW]
[ROW][C]51[/C][C]7.76[/C][C]7.75522222291465[/C][C]0.00477777708535321[/C][/ROW]
[ROW][C]52[/C][C]7.9[/C][C]7.77537571018519[/C][C]0.124624289814812[/C][/ROW]
[ROW][C]53[/C][C]7.97[/C][C]7.91937929631851[/C][C]0.0506207036814894[/C][/ROW]
[ROW][C]54[/C][C]7.96[/C][C]7.99100549894417[/C][C]-0.0310054989441717[/C][/ROW]
[ROW][C]55[/C][C]7.95[/C][C]7.98000943962208[/C][C]-0.0300094396220763[/C][/ROW]
[ROW][C]56[/C][C]7.97[/C][C]7.96904537895206[/C][C]0.00095462104794386[/C][/ROW]
[ROW][C]57[/C][C]7.93[/C][C]7.98907604638933[/C][C]-0.0590760463893254[/C][/ROW]
[ROW][C]58[/C][C]7.99[/C][C]7.94717821378793[/C][C]0.0428217862120661[/C][/ROW]
[ROW][C]59[/C][C]7.96[/C][C]8.008553874261[/C][C]-0.0485538742610041[/C][/ROW]
[ROW][C]60[/C][C]7.92[/C][C]7.97699406904166[/C][C]-0.056994069041659[/C][/ROW]
[ROW][C]61[/C][C]7.97[/C][C]7.93516312047749[/C][C]0.0348368795225076[/C][/ROW]
[ROW][C]62[/C][C]7.98[/C][C]7.98628226384827[/C][C]-0.00628226384827268[/C][/ROW]
[ROW][C]63[/C][C]8[/C][C]7.99608044456837[/C][C]0.00391955543162936[/C][/ROW]
[ROW][C]64[/C][C]8.04[/C][C]8.01620636125603[/C][C]0.0237936387439728[/C][/ROW]
[ROW][C]65[/C][C]8.17[/C][C]8.0569707377855[/C][C]0.113029262214503[/C][/ROW]
[ROW][C]66[/C][C]8.29[/C][C]8.19060183078939[/C][C]0.0993981692106107[/C][/ROW]
[ROW][C]67[/C][C]8.26[/C][C]8.31379502155918[/C][C]-0.0537950215591838[/C][/ROW]
[ROW][C]68[/C][C]8.3[/C][C]8.28206684318661[/C][C]0.0179331568133954[/C][/ROW]
[ROW][C]69[/C][C]8.32[/C][C]8.3226429502846[/C][C]-0.00264295028459927[/C][/ROW]
[ROW][C]70[/C][C]8.28[/C][C]8.34255804485303[/C][C]-0.0625580448530343[/C][/ROW]
[ROW][C]71[/C][C]8.27[/C][C]8.3005483521898[/C][C]-0.0305483521898005[/C][/ROW]
[ROW][C]72[/C][C]8.32[/C][C]8.28956697882025[/C][C]0.0304330211797463[/C][/ROW]
[ROW][C]73[/C][C]8.31[/C][C]8.34054464715258[/C][C]-0.0305446471525777[/C][/ROW]
[ROW][C]74[/C][C]8.34[/C][C]8.32956339280827[/C][C]0.0104366071917301[/C][/ROW]
[ROW][C]75[/C][C]8.32[/C][C]8.35989867139556[/C][C]-0.039898671395564[/C][/ROW]
[ROW][C]76[/C][C]8.36[/C][C]8.33861691670894[/C][C]0.0213830832910578[/C][/ROW]
[ROW][C]77[/C][C]8.33[/C][C]8.37930385354829[/C][C]-0.0493038535482917[/C][/ROW]
[ROW][C]78[/C][C]8.35[/C][C]8.34771995505885[/C][C]0.00228004494114842[/C][/ROW]
[ROW][C]79[/C][C]8.34[/C][C]8.3677932020665[/C][C]-0.0277932020665048[/C][/ROW]
[ROW][C]80[/C][C]8.37[/C][C]8.35690033857609[/C][C]0.0130996614239063[/C][/ROW]
[ROW][C]81[/C][C]8.31[/C][C]8.38732116843924[/C][C]-0.0773211684392425[/C][/ROW]
[ROW][C]82[/C][C]8.33[/C][C]8.32483720677948[/C][C]0.00516279322052249[/C][/ROW]
[ROW][C]83[/C][C]8.34[/C][C]8.34500306278859[/C][C]-0.00500306278858886[/C][/ROW]
[ROW][C]84[/C][C]8.25[/C][C]8.35484233815911[/C][C]-0.104842338159109[/C][/ROW]
[ROW][C]85[/C][C]8.27[/C][C]8.26147425211535[/C][C]0.00852574788464899[/C][/ROW]
[ROW][C]86[/C][C]8.31[/C][C]8.2817481438748[/C][C]0.0282518561252036[/C][/ROW]
[ROW][C]87[/C][C]8.25[/C][C]8.32265574174028[/C][C]-0.0726557417402809[/C][/ROW]
[ROW][C]88[/C][C]8.3[/C][C]8.26032165806711[/C][C]0.039678341932893[/C][/ROW]
[ROW][C]89[/C][C]8.3[/C][C]8.31159633461525[/C][C]-0.0115963346152483[/C][/ROW]
[ROW][C]90[/C][C]8.35[/C][C]8.31122379949764[/C][C]0.0387762005023582[/C][/ROW]
[ROW][C]91[/C][C]8.78[/C][C]8.3624694945292[/C][C]0.417530505470797[/C][/ROW]
[ROW][C]92[/C][C]8.9[/C][C]8.80588276528425[/C][C]0.0941172347157533[/C][/ROW]
[ROW][C]93[/C][C]8.9[/C][C]8.92890630472728[/C][C]-0.0289063047272755[/C][/ROW]
[ROW][C]94[/C][C]8.9[/C][C]8.92797768253859[/C][C]-0.0279776825385856[/C][/ROW]
[ROW][C]95[/C][C]9[/C][C]8.92707889256738[/C][C]0.0729211074326166[/C][/ROW]
[ROW][C]96[/C][C]9.05[/C][C]9.02942150117905[/C][C]0.0205784988209476[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160465&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160465&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	7.09	7.08	0.00999999999999979
4	7.07	7.09032125247328	-0.0203212524732752
5	7.06	7.06966842721157	-0.00966842721156702
6	6.99	7.05935782659613	-0.069357826596125
7	6.99	6.98712968926262	0.00287031073737598
8	6.99	6.98722189870497	0.00277810129503031
9	6.98	6.98731114589617	-0.00731114589617299
10	6.96	6.97707627352601	-0.017076273526011
11	6.95	6.95652769401555	-0.00652769401555453
12	6.91	6.94631799023083	-0.0363179902308266
13	6.91	6.90515126581222	0.00484873418777809
14	6.87	6.90530703259723	-0.0353070325972302
15	6.91	6.86417278544264	0.0458272145573577
16	6.89	6.90564499604463	-0.0156449960446308
17	6.88	6.88514239667726	-0.00514239667725747
18	6.9	6.87497719591214	0.0250228040878557
19	6.91	6.8957810596823	0.0142189403177042
20	6.85	6.90623784665674	-0.0562378466567379
21	6.86	6.84443119192372	0.0155688080762797
22	6.82	6.85493134373377	-0.0349313437337671
23	6.8	6.81380916567684	-0.013809165676836
24	6.83	6.79336554281408	0.0366344571859196
25	6.84	6.82454243381189	0.0154575661881111
26	6.89	6.83503901194876	0.0549609880512367
27	7.14	6.88680464728328	0.253195352716724
28	7.21	7.14493861061149	0.0650613893885144
29	7.25	7.21702872383707	0.0329712761629342
30	7.31	7.2580879342385	0.0519120657614947
31	7.3	7.31975562219038	-0.0197556221903765
32	7.48	7.3091209679414	0.1708790320586
33	7.49	7.49461049910938	-0.00461049910937561
34	7.4	7.50446238568518	-0.104462385685183
35	7.44	7.41110650570862	0.0288934942913786
36	7.42	7.45203471635889	-0.032034716358889
37	7.14	7.43100559317279	-0.291005593172792
38	7.24	7.14165696651842	0.0983430334815836
39	7.33	7.24481626079195	0.0851837392080466
40	7.61	7.3375528094823	0.272447190517703
41	7.66	7.62630524286137	0.0336947571386261
42	7.69	7.67738769526809	0.0126123047319062
43	7.7	7.70779286867698	-0.00779286867697682
44	7.68	7.71754252084334	-0.0375425208433384
45	7.71	7.69633645807595	0.0136635419240543
46	7.71	7.72677540273963	-0.0167754027396265
47	7.72	7.7262364887776	-0.00623648877759653
48	7.68	7.73603614003316	-0.0560361400331608
49	7.72	7.69423596517531	0.0257640348246859
50	7.74	7.73506364116621	0.0049363588337874
51	7.76	7.75522222291465	0.00477777708535321
52	7.9	7.77537571018519	0.124624289814812
53	7.97	7.91937929631851	0.0506207036814894
54	7.96	7.99100549894417	-0.0310054989441717
55	7.95	7.98000943962208	-0.0300094396220763
56	7.97	7.96904537895206	0.00095462104794386
57	7.93	7.98907604638933	-0.0590760463893254
58	7.99	7.94717821378793	0.0428217862120661
59	7.96	8.008553874261	-0.0485538742610041
60	7.92	7.97699406904166	-0.056994069041659
61	7.97	7.93516312047749	0.0348368795225076
62	7.98	7.98628226384827	-0.00628226384827268
63	8	7.99608044456837	0.00391955543162936
64	8.04	8.01620636125603	0.0237936387439728
65	8.17	8.0569707377855	0.113029262214503
66	8.29	8.19060183078939	0.0993981692106107
67	8.26	8.31379502155918	-0.0537950215591838
68	8.3	8.28206684318661	0.0179331568133954
69	8.32	8.3226429502846	-0.00264295028459927
70	8.28	8.34255804485303	-0.0625580448530343
71	8.27	8.3005483521898	-0.0305483521898005
72	8.32	8.28956697882025	0.0304330211797463
73	8.31	8.34054464715258	-0.0305446471525777
74	8.34	8.32956339280827	0.0104366071917301
75	8.32	8.35989867139556	-0.039898671395564
76	8.36	8.33861691670894	0.0213830832910578
77	8.33	8.37930385354829	-0.0493038535482917
78	8.35	8.34771995505885	0.00228004494114842
79	8.34	8.3677932020665	-0.0277932020665048
80	8.37	8.35690033857609	0.0130996614239063
81	8.31	8.38732116843924	-0.0773211684392425
82	8.33	8.32483720677948	0.00516279322052249
83	8.34	8.34500306278859	-0.00500306278858886
84	8.25	8.35484233815911	-0.104842338159109
85	8.27	8.26147425211535	0.00852574788464899
86	8.31	8.2817481438748	0.0282518561252036
87	8.25	8.32265574174028	-0.0726557417402809
88	8.3	8.26032165806711	0.039678341932893
89	8.3	8.31159633461525	-0.0115963346152483
90	8.35	8.31122379949764	0.0387762005023582
91	8.78	8.3624694945292	0.417530505470797
92	8.9	8.80588276528425	0.0941172347157533
93	8.9	8.92890630472728	-0.0289063047272755
94	8.9	8.92797768253859	-0.0279776825385856
95	9	8.92707889256738	0.0729211074326166
96	9.05	9.02942150117905	0.0205784988209476

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
97	9.08008259054331	8.9230559143047	9.23710926678191
98	9.11016518108661	8.88450071785925	9.33582964431398
99	9.14024777162992	8.85944158736774	9.4210539558921
100	9.17033036217323	8.84095024604667	9.49971047829978
101	9.20041295271653	8.82639050996329	9.57443539546977
102	9.23049554325984	8.81443354325145	9.64655754326823
103	9.26057813380315	8.80430348429519	9.7168527833111
104	9.29066072434645	8.79550359185069	9.78581785684222
105	9.32074331488976	8.78769493766227	9.85379169211724
106	9.35082590543307	8.78063522682254	9.92101658404359
107	9.38090849597637	8.77414495655573	9.98767203539701
108	9.41099108651968	8.76808734937616	10.0538948236632

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 9.08008259054331 & 8.9230559143047 & 9.23710926678191 \tabularnewline
98 & 9.11016518108661 & 8.88450071785925 & 9.33582964431398 \tabularnewline
99 & 9.14024777162992 & 8.85944158736774 & 9.4210539558921 \tabularnewline
100 & 9.17033036217323 & 8.84095024604667 & 9.49971047829978 \tabularnewline
101 & 9.20041295271653 & 8.82639050996329 & 9.57443539546977 \tabularnewline
102 & 9.23049554325984 & 8.81443354325145 & 9.64655754326823 \tabularnewline
103 & 9.26057813380315 & 8.80430348429519 & 9.7168527833111 \tabularnewline
104 & 9.29066072434645 & 8.79550359185069 & 9.78581785684222 \tabularnewline
105 & 9.32074331488976 & 8.78769493766227 & 9.85379169211724 \tabularnewline
106 & 9.35082590543307 & 8.78063522682254 & 9.92101658404359 \tabularnewline
107 & 9.38090849597637 & 8.77414495655573 & 9.98767203539701 \tabularnewline
108 & 9.41099108651968 & 8.76808734937616 & 10.0538948236632 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160465&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]97[/C][C]9.08008259054331[/C][C]8.9230559143047[/C][C]9.23710926678191[/C][/ROW]
[ROW][C]98[/C][C]9.11016518108661[/C][C]8.88450071785925[/C][C]9.33582964431398[/C][/ROW]
[ROW][C]99[/C][C]9.14024777162992[/C][C]8.85944158736774[/C][C]9.4210539558921[/C][/ROW]
[ROW][C]100[/C][C]9.17033036217323[/C][C]8.84095024604667[/C][C]9.49971047829978[/C][/ROW]
[ROW][C]101[/C][C]9.20041295271653[/C][C]8.82639050996329[/C][C]9.57443539546977[/C][/ROW]
[ROW][C]102[/C][C]9.23049554325984[/C][C]8.81443354325145[/C][C]9.64655754326823[/C][/ROW]
[ROW][C]103[/C][C]9.26057813380315[/C][C]8.80430348429519[/C][C]9.7168527833111[/C][/ROW]
[ROW][C]104[/C][C]9.29066072434645[/C][C]8.79550359185069[/C][C]9.78581785684222[/C][/ROW]
[ROW][C]105[/C][C]9.32074331488976[/C][C]8.78769493766227[/C][C]9.85379169211724[/C][/ROW]
[ROW][C]106[/C][C]9.35082590543307[/C][C]8.78063522682254[/C][C]9.92101658404359[/C][/ROW]
[ROW][C]107[/C][C]9.38090849597637[/C][C]8.77414495655573[/C][C]9.98767203539701[/C][/ROW]
[ROW][C]108[/C][C]9.41099108651968[/C][C]8.76808734937616[/C][C]10.0538948236632[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160465&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160465&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
97	9.08008259054331	8.9230559143047	9.23710926678191
98	9.11016518108661	8.88450071785925	9.33582964431398
99	9.14024777162992	8.85944158736774	9.4210539558921
100	9.17033036217323	8.84095024604667	9.49971047829978
101	9.20041295271653	8.82639050996329	9.57443539546977
102	9.23049554325984	8.81443354325145	9.64655754326823
103	9.26057813380315	8.80430348429519	9.7168527833111
104	9.29066072434645	8.79550359185069	9.78581785684222
105	9.32074331488976	8.78769493766227	9.85379169211724
106	9.35082590543307	8.78063522682254	9.92101658404359
107	9.38090849597637	8.77414495655573	9.98767203539701
108	9.41099108651968	8.76808734937616	10.0538948236632

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