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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

Mon, 13 Jan 2014 04:07:58 -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/2014/Jan/13/t138960410003a61yj4t01con8.htm/, Retrieved Sun, 19 May 2024 09:39:10 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=233121, Retrieved Sun, 19 May 2024 09:39:10 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

142

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

-       [Exponential Smoothing] [] [2014-01-13 09:07:58] [e0c7fa3260b5bc60bc725c9d38409993] [Current]
-   PD    [Exponential Smoothing] [] [2014-01-13 09:10:05] [33591c51b6fd6c0de3aee2101c04ad72] 

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Dataseries X:

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Histogram

Boxplots

6,11
6,13
6,15
6,15
6,16
6,18
6,21
6,22
6,23
6,26
6,28
6,28
6,29
6,32
6,36
6,37
6,38
6,38
6,4
6,41
6,42
6,43
6,44
6,47
6,47
6,48
6,51
6,54
6,56
6,57
6,6
6,62
6,65
6,71
6,76
6,78
6,8
6,83
6,86
6,86
6,87
6,88
6,9
6,92
6,93
6,94
6,96
6,98
6,99
7,01
7,06
7,07
7,08
7,08
7,1
7,11
7,22
7,24
7,25
7,26
7,27
7,3
7,32
7,34
7,35
7,36
7,39
7,41
7,43
7,46
7,47
7,5
7,51
7,52
7,58
7,59
7,63
7,64
7,64
7,66
7,67
7,68
7,69
7,7

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233121&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]4 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=233121&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233121&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	4 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.999947955526374
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999947955526374 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233121&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]0.999947955526374[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233121&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233121&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	0.999947955526374
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	6.13	6.11	0.0199999999999996
3	6.15	6.12999895911053	0.0200010408894729
4	6.15	6.14999895905636	1.04094364505869e-06
5	6.16	6.14999999994583	0.0100000000541751
6	6.18	6.15999947955526	0.0200005204447384
7	6.21	6.17999895908344	0.0300010409165594
8	6.22	6.20999843861162	0.0100015613883828
9	6.23	6.219999479474	0.010000520525999
10	6.26	6.22999947952817	0.0300005204718259
11	6.28	6.2599984386387	0.0200015613612967
12	6.28	6.27999895902927	1.04097073272413e-06
13	6.29	6.27999999994582	0.0100000000541769
14	6.32	6.28999947955526	0.0300005204447391
15	6.36	6.3199984386387	0.0400015613612954
16	6.37	6.3599979181398	0.0100020818602049
17	6.38	6.36999947944691	0.0100005205530858
18	6.38	6.37999947952817	5.20471828302504e-07
19	6.4	6.37999999997291	0.0200000000270881
20	6.41	6.39999895911053	0.010001040889474
21	6.42	6.40999947950109	0.0100005204989086
22	6.43	6.41999947952817	0.0100005204718254
23	6.44	6.42999947952818	0.0100005204718245
24	6.47	6.43999947952818	0.0300005204718232
25	6.47	6.4699984386387	1.56136129625395e-06
26	6.48	6.46999999991874	0.010000000081261
27	6.51	6.47999947955526	0.03000052044474
28	6.54	6.5099984386387	0.0300015613612956
29	6.56	6.53999843858453	0.0200015614154685
30	6.57	6.55999895902926	0.0100010409707361
31	6.6	6.56999947950109	0.0300005204989127
32	6.62	6.5999984386387	0.0200015613612985
33	6.65	6.61999895902927	0.030001040970733
34	6.71	6.64999843861161	0.0600015613883853
35	6.76	6.70999687725032	0.0500031227496791
36	6.78	6.7599973976138	0.0200026023862039
37	6.8	6.77999895897509	0.0200010410249121
38	6.83	6.79999895905635	0.0300010409436524
39	6.86	6.82999843861162	0.0300015613883842
40	6.86	6.85999843858453	1.56141547069666e-06
41	6.87	6.85999999991874	0.0100000000812628
42	6.88	6.86999947955526	0.0100005204447404
43	6.9	6.87999947952818	0.0200005204718225
44	6.92	6.89999895908344	0.0200010409165596
45	6.93	6.91999895905635	0.0100010409436466
46	6.94	6.92999947950109	0.0100005204989122
47	6.96	6.93999947952817	0.0200005204718252
48	6.98	6.95999895908344	0.0200010409165605
49	6.99	6.97999895905635	0.0100010409436466
50	7.01	6.98999947950109	0.0200005204989111
51	7.06	7.00999895908344	0.0500010409165617
52	7.07	7.05999739772214	0.0100026022778561
53	7.08	7.06999947941983	0.0100005205801699
54	7.08	7.07999947952817	5.20471829190683e-07
55	7.1	7.07999999997291	0.0200000000270872
56	7.11	7.09999895911053	0.0100010408894748
57	7.22	7.10999947950109	0.110000520498908
58	7.24	7.21999427508081	0.0200057249191881
59	7.25	7.23999895881258	0.0100010411874223
60	7.26	7.24999947950108	0.0100005204989237
61	7.27	7.25999947952817	0.0100005204718254
62	7.3	7.26999947952818	0.0300005204718241
63	7.32	7.2999984386387	0.0200015613612967
64	7.34	7.31999895902927	0.0200010409707323
65	7.35	7.33999895905635	0.0100010409436493
66	7.36	7.34999947950109	0.0100005204989122
67	7.39	7.35999947952817	0.030000520471825
68	7.41	7.3899984386387	0.0200015613612967
69	7.43	7.40999895902927	0.0200010409707323
70	7.46	7.42999895905635	0.0300010409436497
71	7.47	7.45999843861162	0.0100015613883837
72	7.5	7.469999479474	0.0300005205259986
73	7.51	7.4999984386387	0.0100015613612987
74	7.52	7.509999479474	0.0100005205259963
75	7.58	7.51999947952817	0.060000520471827
76	7.59	7.5799968773045	0.0100031226955046
77	7.63	7.58999947939274	0.0400005206072551
78	7.64	7.62999791819396	0.0100020818060393
79	7.64	7.63999947944692	5.20553082417052e-07
80	7.66	7.63999999997291	0.0200000000270926
81	7.67	7.65999895911053	0.010001040889474
82	7.68	7.66999947950109	0.0100005204989086
83	7.69	7.67999947952817	0.0100005204718263
84	7.7	7.68999947952818	0.0100005204718236

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 6.13 & 6.11 & 0.0199999999999996 \tabularnewline
3 & 6.15 & 6.12999895911053 & 0.0200010408894729 \tabularnewline
4 & 6.15 & 6.14999895905636 & 1.04094364505869e-06 \tabularnewline
5 & 6.16 & 6.14999999994583 & 0.0100000000541751 \tabularnewline
6 & 6.18 & 6.15999947955526 & 0.0200005204447384 \tabularnewline
7 & 6.21 & 6.17999895908344 & 0.0300010409165594 \tabularnewline
8 & 6.22 & 6.20999843861162 & 0.0100015613883828 \tabularnewline
9 & 6.23 & 6.219999479474 & 0.010000520525999 \tabularnewline
10 & 6.26 & 6.22999947952817 & 0.0300005204718259 \tabularnewline
11 & 6.28 & 6.2599984386387 & 0.0200015613612967 \tabularnewline
12 & 6.28 & 6.27999895902927 & 1.04097073272413e-06 \tabularnewline
13 & 6.29 & 6.27999999994582 & 0.0100000000541769 \tabularnewline
14 & 6.32 & 6.28999947955526 & 0.0300005204447391 \tabularnewline
15 & 6.36 & 6.3199984386387 & 0.0400015613612954 \tabularnewline
16 & 6.37 & 6.3599979181398 & 0.0100020818602049 \tabularnewline
17 & 6.38 & 6.36999947944691 & 0.0100005205530858 \tabularnewline
18 & 6.38 & 6.37999947952817 & 5.20471828302504e-07 \tabularnewline
19 & 6.4 & 6.37999999997291 & 0.0200000000270881 \tabularnewline
20 & 6.41 & 6.39999895911053 & 0.010001040889474 \tabularnewline
21 & 6.42 & 6.40999947950109 & 0.0100005204989086 \tabularnewline
22 & 6.43 & 6.41999947952817 & 0.0100005204718254 \tabularnewline
23 & 6.44 & 6.42999947952818 & 0.0100005204718245 \tabularnewline
24 & 6.47 & 6.43999947952818 & 0.0300005204718232 \tabularnewline
25 & 6.47 & 6.4699984386387 & 1.56136129625395e-06 \tabularnewline
26 & 6.48 & 6.46999999991874 & 0.010000000081261 \tabularnewline
27 & 6.51 & 6.47999947955526 & 0.03000052044474 \tabularnewline
28 & 6.54 & 6.5099984386387 & 0.0300015613612956 \tabularnewline
29 & 6.56 & 6.53999843858453 & 0.0200015614154685 \tabularnewline
30 & 6.57 & 6.55999895902926 & 0.0100010409707361 \tabularnewline
31 & 6.6 & 6.56999947950109 & 0.0300005204989127 \tabularnewline
32 & 6.62 & 6.5999984386387 & 0.0200015613612985 \tabularnewline
33 & 6.65 & 6.61999895902927 & 0.030001040970733 \tabularnewline
34 & 6.71 & 6.64999843861161 & 0.0600015613883853 \tabularnewline
35 & 6.76 & 6.70999687725032 & 0.0500031227496791 \tabularnewline
36 & 6.78 & 6.7599973976138 & 0.0200026023862039 \tabularnewline
37 & 6.8 & 6.77999895897509 & 0.0200010410249121 \tabularnewline
38 & 6.83 & 6.79999895905635 & 0.0300010409436524 \tabularnewline
39 & 6.86 & 6.82999843861162 & 0.0300015613883842 \tabularnewline
40 & 6.86 & 6.85999843858453 & 1.56141547069666e-06 \tabularnewline
41 & 6.87 & 6.85999999991874 & 0.0100000000812628 \tabularnewline
42 & 6.88 & 6.86999947955526 & 0.0100005204447404 \tabularnewline
43 & 6.9 & 6.87999947952818 & 0.0200005204718225 \tabularnewline
44 & 6.92 & 6.89999895908344 & 0.0200010409165596 \tabularnewline
45 & 6.93 & 6.91999895905635 & 0.0100010409436466 \tabularnewline
46 & 6.94 & 6.92999947950109 & 0.0100005204989122 \tabularnewline
47 & 6.96 & 6.93999947952817 & 0.0200005204718252 \tabularnewline
48 & 6.98 & 6.95999895908344 & 0.0200010409165605 \tabularnewline
49 & 6.99 & 6.97999895905635 & 0.0100010409436466 \tabularnewline
50 & 7.01 & 6.98999947950109 & 0.0200005204989111 \tabularnewline
51 & 7.06 & 7.00999895908344 & 0.0500010409165617 \tabularnewline
52 & 7.07 & 7.05999739772214 & 0.0100026022778561 \tabularnewline
53 & 7.08 & 7.06999947941983 & 0.0100005205801699 \tabularnewline
54 & 7.08 & 7.07999947952817 & 5.20471829190683e-07 \tabularnewline
55 & 7.1 & 7.07999999997291 & 0.0200000000270872 \tabularnewline
56 & 7.11 & 7.09999895911053 & 0.0100010408894748 \tabularnewline
57 & 7.22 & 7.10999947950109 & 0.110000520498908 \tabularnewline
58 & 7.24 & 7.21999427508081 & 0.0200057249191881 \tabularnewline
59 & 7.25 & 7.23999895881258 & 0.0100010411874223 \tabularnewline
60 & 7.26 & 7.24999947950108 & 0.0100005204989237 \tabularnewline
61 & 7.27 & 7.25999947952817 & 0.0100005204718254 \tabularnewline
62 & 7.3 & 7.26999947952818 & 0.0300005204718241 \tabularnewline
63 & 7.32 & 7.2999984386387 & 0.0200015613612967 \tabularnewline
64 & 7.34 & 7.31999895902927 & 0.0200010409707323 \tabularnewline
65 & 7.35 & 7.33999895905635 & 0.0100010409436493 \tabularnewline
66 & 7.36 & 7.34999947950109 & 0.0100005204989122 \tabularnewline
67 & 7.39 & 7.35999947952817 & 0.030000520471825 \tabularnewline
68 & 7.41 & 7.3899984386387 & 0.0200015613612967 \tabularnewline
69 & 7.43 & 7.40999895902927 & 0.0200010409707323 \tabularnewline
70 & 7.46 & 7.42999895905635 & 0.0300010409436497 \tabularnewline
71 & 7.47 & 7.45999843861162 & 0.0100015613883837 \tabularnewline
72 & 7.5 & 7.469999479474 & 0.0300005205259986 \tabularnewline
73 & 7.51 & 7.4999984386387 & 0.0100015613612987 \tabularnewline
74 & 7.52 & 7.509999479474 & 0.0100005205259963 \tabularnewline
75 & 7.58 & 7.51999947952817 & 0.060000520471827 \tabularnewline
76 & 7.59 & 7.5799968773045 & 0.0100031226955046 \tabularnewline
77 & 7.63 & 7.58999947939274 & 0.0400005206072551 \tabularnewline
78 & 7.64 & 7.62999791819396 & 0.0100020818060393 \tabularnewline
79 & 7.64 & 7.63999947944692 & 5.20553082417052e-07 \tabularnewline
80 & 7.66 & 7.63999999997291 & 0.0200000000270926 \tabularnewline
81 & 7.67 & 7.65999895911053 & 0.010001040889474 \tabularnewline
82 & 7.68 & 7.66999947950109 & 0.0100005204989086 \tabularnewline
83 & 7.69 & 7.67999947952817 & 0.0100005204718263 \tabularnewline
84 & 7.7 & 7.68999947952818 & 0.0100005204718236 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233121&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]2[/C][C]6.13[/C][C]6.11[/C][C]0.0199999999999996[/C][/ROW]
[ROW][C]3[/C][C]6.15[/C][C]6.12999895911053[/C][C]0.0200010408894729[/C][/ROW]
[ROW][C]4[/C][C]6.15[/C][C]6.14999895905636[/C][C]1.04094364505869e-06[/C][/ROW]
[ROW][C]5[/C][C]6.16[/C][C]6.14999999994583[/C][C]0.0100000000541751[/C][/ROW]
[ROW][C]6[/C][C]6.18[/C][C]6.15999947955526[/C][C]0.0200005204447384[/C][/ROW]
[ROW][C]7[/C][C]6.21[/C][C]6.17999895908344[/C][C]0.0300010409165594[/C][/ROW]
[ROW][C]8[/C][C]6.22[/C][C]6.20999843861162[/C][C]0.0100015613883828[/C][/ROW]
[ROW][C]9[/C][C]6.23[/C][C]6.219999479474[/C][C]0.010000520525999[/C][/ROW]
[ROW][C]10[/C][C]6.26[/C][C]6.22999947952817[/C][C]0.0300005204718259[/C][/ROW]
[ROW][C]11[/C][C]6.28[/C][C]6.2599984386387[/C][C]0.0200015613612967[/C][/ROW]
[ROW][C]12[/C][C]6.28[/C][C]6.27999895902927[/C][C]1.04097073272413e-06[/C][/ROW]
[ROW][C]13[/C][C]6.29[/C][C]6.27999999994582[/C][C]0.0100000000541769[/C][/ROW]
[ROW][C]14[/C][C]6.32[/C][C]6.28999947955526[/C][C]0.0300005204447391[/C][/ROW]
[ROW][C]15[/C][C]6.36[/C][C]6.3199984386387[/C][C]0.0400015613612954[/C][/ROW]
[ROW][C]16[/C][C]6.37[/C][C]6.3599979181398[/C][C]0.0100020818602049[/C][/ROW]
[ROW][C]17[/C][C]6.38[/C][C]6.36999947944691[/C][C]0.0100005205530858[/C][/ROW]
[ROW][C]18[/C][C]6.38[/C][C]6.37999947952817[/C][C]5.20471828302504e-07[/C][/ROW]
[ROW][C]19[/C][C]6.4[/C][C]6.37999999997291[/C][C]0.0200000000270881[/C][/ROW]
[ROW][C]20[/C][C]6.41[/C][C]6.39999895911053[/C][C]0.010001040889474[/C][/ROW]
[ROW][C]21[/C][C]6.42[/C][C]6.40999947950109[/C][C]0.0100005204989086[/C][/ROW]
[ROW][C]22[/C][C]6.43[/C][C]6.41999947952817[/C][C]0.0100005204718254[/C][/ROW]
[ROW][C]23[/C][C]6.44[/C][C]6.42999947952818[/C][C]0.0100005204718245[/C][/ROW]
[ROW][C]24[/C][C]6.47[/C][C]6.43999947952818[/C][C]0.0300005204718232[/C][/ROW]
[ROW][C]25[/C][C]6.47[/C][C]6.4699984386387[/C][C]1.56136129625395e-06[/C][/ROW]
[ROW][C]26[/C][C]6.48[/C][C]6.46999999991874[/C][C]0.010000000081261[/C][/ROW]
[ROW][C]27[/C][C]6.51[/C][C]6.47999947955526[/C][C]0.03000052044474[/C][/ROW]
[ROW][C]28[/C][C]6.54[/C][C]6.5099984386387[/C][C]0.0300015613612956[/C][/ROW]
[ROW][C]29[/C][C]6.56[/C][C]6.53999843858453[/C][C]0.0200015614154685[/C][/ROW]
[ROW][C]30[/C][C]6.57[/C][C]6.55999895902926[/C][C]0.0100010409707361[/C][/ROW]
[ROW][C]31[/C][C]6.6[/C][C]6.56999947950109[/C][C]0.0300005204989127[/C][/ROW]
[ROW][C]32[/C][C]6.62[/C][C]6.5999984386387[/C][C]0.0200015613612985[/C][/ROW]
[ROW][C]33[/C][C]6.65[/C][C]6.61999895902927[/C][C]0.030001040970733[/C][/ROW]
[ROW][C]34[/C][C]6.71[/C][C]6.64999843861161[/C][C]0.0600015613883853[/C][/ROW]
[ROW][C]35[/C][C]6.76[/C][C]6.70999687725032[/C][C]0.0500031227496791[/C][/ROW]
[ROW][C]36[/C][C]6.78[/C][C]6.7599973976138[/C][C]0.0200026023862039[/C][/ROW]
[ROW][C]37[/C][C]6.8[/C][C]6.77999895897509[/C][C]0.0200010410249121[/C][/ROW]
[ROW][C]38[/C][C]6.83[/C][C]6.79999895905635[/C][C]0.0300010409436524[/C][/ROW]
[ROW][C]39[/C][C]6.86[/C][C]6.82999843861162[/C][C]0.0300015613883842[/C][/ROW]
[ROW][C]40[/C][C]6.86[/C][C]6.85999843858453[/C][C]1.56141547069666e-06[/C][/ROW]
[ROW][C]41[/C][C]6.87[/C][C]6.85999999991874[/C][C]0.0100000000812628[/C][/ROW]
[ROW][C]42[/C][C]6.88[/C][C]6.86999947955526[/C][C]0.0100005204447404[/C][/ROW]
[ROW][C]43[/C][C]6.9[/C][C]6.87999947952818[/C][C]0.0200005204718225[/C][/ROW]
[ROW][C]44[/C][C]6.92[/C][C]6.89999895908344[/C][C]0.0200010409165596[/C][/ROW]
[ROW][C]45[/C][C]6.93[/C][C]6.91999895905635[/C][C]0.0100010409436466[/C][/ROW]
[ROW][C]46[/C][C]6.94[/C][C]6.92999947950109[/C][C]0.0100005204989122[/C][/ROW]
[ROW][C]47[/C][C]6.96[/C][C]6.93999947952817[/C][C]0.0200005204718252[/C][/ROW]
[ROW][C]48[/C][C]6.98[/C][C]6.95999895908344[/C][C]0.0200010409165605[/C][/ROW]
[ROW][C]49[/C][C]6.99[/C][C]6.97999895905635[/C][C]0.0100010409436466[/C][/ROW]
[ROW][C]50[/C][C]7.01[/C][C]6.98999947950109[/C][C]0.0200005204989111[/C][/ROW]
[ROW][C]51[/C][C]7.06[/C][C]7.00999895908344[/C][C]0.0500010409165617[/C][/ROW]
[ROW][C]52[/C][C]7.07[/C][C]7.05999739772214[/C][C]0.0100026022778561[/C][/ROW]
[ROW][C]53[/C][C]7.08[/C][C]7.06999947941983[/C][C]0.0100005205801699[/C][/ROW]
[ROW][C]54[/C][C]7.08[/C][C]7.07999947952817[/C][C]5.20471829190683e-07[/C][/ROW]
[ROW][C]55[/C][C]7.1[/C][C]7.07999999997291[/C][C]0.0200000000270872[/C][/ROW]
[ROW][C]56[/C][C]7.11[/C][C]7.09999895911053[/C][C]0.0100010408894748[/C][/ROW]
[ROW][C]57[/C][C]7.22[/C][C]7.10999947950109[/C][C]0.110000520498908[/C][/ROW]
[ROW][C]58[/C][C]7.24[/C][C]7.21999427508081[/C][C]0.0200057249191881[/C][/ROW]
[ROW][C]59[/C][C]7.25[/C][C]7.23999895881258[/C][C]0.0100010411874223[/C][/ROW]
[ROW][C]60[/C][C]7.26[/C][C]7.24999947950108[/C][C]0.0100005204989237[/C][/ROW]
[ROW][C]61[/C][C]7.27[/C][C]7.25999947952817[/C][C]0.0100005204718254[/C][/ROW]
[ROW][C]62[/C][C]7.3[/C][C]7.26999947952818[/C][C]0.0300005204718241[/C][/ROW]
[ROW][C]63[/C][C]7.32[/C][C]7.2999984386387[/C][C]0.0200015613612967[/C][/ROW]
[ROW][C]64[/C][C]7.34[/C][C]7.31999895902927[/C][C]0.0200010409707323[/C][/ROW]
[ROW][C]65[/C][C]7.35[/C][C]7.33999895905635[/C][C]0.0100010409436493[/C][/ROW]
[ROW][C]66[/C][C]7.36[/C][C]7.34999947950109[/C][C]0.0100005204989122[/C][/ROW]
[ROW][C]67[/C][C]7.39[/C][C]7.35999947952817[/C][C]0.030000520471825[/C][/ROW]
[ROW][C]68[/C][C]7.41[/C][C]7.3899984386387[/C][C]0.0200015613612967[/C][/ROW]
[ROW][C]69[/C][C]7.43[/C][C]7.40999895902927[/C][C]0.0200010409707323[/C][/ROW]
[ROW][C]70[/C][C]7.46[/C][C]7.42999895905635[/C][C]0.0300010409436497[/C][/ROW]
[ROW][C]71[/C][C]7.47[/C][C]7.45999843861162[/C][C]0.0100015613883837[/C][/ROW]
[ROW][C]72[/C][C]7.5[/C][C]7.469999479474[/C][C]0.0300005205259986[/C][/ROW]
[ROW][C]73[/C][C]7.51[/C][C]7.4999984386387[/C][C]0.0100015613612987[/C][/ROW]
[ROW][C]74[/C][C]7.52[/C][C]7.509999479474[/C][C]0.0100005205259963[/C][/ROW]
[ROW][C]75[/C][C]7.58[/C][C]7.51999947952817[/C][C]0.060000520471827[/C][/ROW]
[ROW][C]76[/C][C]7.59[/C][C]7.5799968773045[/C][C]0.0100031226955046[/C][/ROW]
[ROW][C]77[/C][C]7.63[/C][C]7.58999947939274[/C][C]0.0400005206072551[/C][/ROW]
[ROW][C]78[/C][C]7.64[/C][C]7.62999791819396[/C][C]0.0100020818060393[/C][/ROW]
[ROW][C]79[/C][C]7.64[/C][C]7.63999947944692[/C][C]5.20553082417052e-07[/C][/ROW]
[ROW][C]80[/C][C]7.66[/C][C]7.63999999997291[/C][C]0.0200000000270926[/C][/ROW]
[ROW][C]81[/C][C]7.67[/C][C]7.65999895911053[/C][C]0.010001040889474[/C][/ROW]
[ROW][C]82[/C][C]7.68[/C][C]7.66999947950109[/C][C]0.0100005204989086[/C][/ROW]
[ROW][C]83[/C][C]7.69[/C][C]7.67999947952817[/C][C]0.0100005204718263[/C][/ROW]
[ROW][C]84[/C][C]7.7[/C][C]7.68999947952818[/C][C]0.0100005204718236[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233121&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233121&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
2	6.13	6.11	0.0199999999999996
3	6.15	6.12999895911053	0.0200010408894729
4	6.15	6.14999895905636	1.04094364505869e-06
5	6.16	6.14999999994583	0.0100000000541751
6	6.18	6.15999947955526	0.0200005204447384
7	6.21	6.17999895908344	0.0300010409165594
8	6.22	6.20999843861162	0.0100015613883828
9	6.23	6.219999479474	0.010000520525999
10	6.26	6.22999947952817	0.0300005204718259
11	6.28	6.2599984386387	0.0200015613612967
12	6.28	6.27999895902927	1.04097073272413e-06
13	6.29	6.27999999994582	0.0100000000541769
14	6.32	6.28999947955526	0.0300005204447391
15	6.36	6.3199984386387	0.0400015613612954
16	6.37	6.3599979181398	0.0100020818602049
17	6.38	6.36999947944691	0.0100005205530858
18	6.38	6.37999947952817	5.20471828302504e-07
19	6.4	6.37999999997291	0.0200000000270881
20	6.41	6.39999895911053	0.010001040889474
21	6.42	6.40999947950109	0.0100005204989086
22	6.43	6.41999947952817	0.0100005204718254
23	6.44	6.42999947952818	0.0100005204718245
24	6.47	6.43999947952818	0.0300005204718232
25	6.47	6.4699984386387	1.56136129625395e-06
26	6.48	6.46999999991874	0.010000000081261
27	6.51	6.47999947955526	0.03000052044474
28	6.54	6.5099984386387	0.0300015613612956
29	6.56	6.53999843858453	0.0200015614154685
30	6.57	6.55999895902926	0.0100010409707361
31	6.6	6.56999947950109	0.0300005204989127
32	6.62	6.5999984386387	0.0200015613612985
33	6.65	6.61999895902927	0.030001040970733
34	6.71	6.64999843861161	0.0600015613883853
35	6.76	6.70999687725032	0.0500031227496791
36	6.78	6.7599973976138	0.0200026023862039
37	6.8	6.77999895897509	0.0200010410249121
38	6.83	6.79999895905635	0.0300010409436524
39	6.86	6.82999843861162	0.0300015613883842
40	6.86	6.85999843858453	1.56141547069666e-06
41	6.87	6.85999999991874	0.0100000000812628
42	6.88	6.86999947955526	0.0100005204447404
43	6.9	6.87999947952818	0.0200005204718225
44	6.92	6.89999895908344	0.0200010409165596
45	6.93	6.91999895905635	0.0100010409436466
46	6.94	6.92999947950109	0.0100005204989122
47	6.96	6.93999947952817	0.0200005204718252
48	6.98	6.95999895908344	0.0200010409165605
49	6.99	6.97999895905635	0.0100010409436466
50	7.01	6.98999947950109	0.0200005204989111
51	7.06	7.00999895908344	0.0500010409165617
52	7.07	7.05999739772214	0.0100026022778561
53	7.08	7.06999947941983	0.0100005205801699
54	7.08	7.07999947952817	5.20471829190683e-07
55	7.1	7.07999999997291	0.0200000000270872
56	7.11	7.09999895911053	0.0100010408894748
57	7.22	7.10999947950109	0.110000520498908
58	7.24	7.21999427508081	0.0200057249191881
59	7.25	7.23999895881258	0.0100010411874223
60	7.26	7.24999947950108	0.0100005204989237
61	7.27	7.25999947952817	0.0100005204718254
62	7.3	7.26999947952818	0.0300005204718241
63	7.32	7.2999984386387	0.0200015613612967
64	7.34	7.31999895902927	0.0200010409707323
65	7.35	7.33999895905635	0.0100010409436493
66	7.36	7.34999947950109	0.0100005204989122
67	7.39	7.35999947952817	0.030000520471825
68	7.41	7.3899984386387	0.0200015613612967
69	7.43	7.40999895902927	0.0200010409707323
70	7.46	7.42999895905635	0.0300010409436497
71	7.47	7.45999843861162	0.0100015613883837
72	7.5	7.469999479474	0.0300005205259986
73	7.51	7.4999984386387	0.0100015613612987
74	7.52	7.509999479474	0.0100005205259963
75	7.58	7.51999947952817	0.060000520471827
76	7.59	7.5799968773045	0.0100031226955046
77	7.63	7.58999947939274	0.0400005206072551
78	7.64	7.62999791819396	0.0100020818060393
79	7.64	7.63999947944692	5.20553082417052e-07
80	7.66	7.63999999997291	0.0200000000270926
81	7.67	7.65999895911053	0.010001040889474
82	7.68	7.66999947950109	0.0100005204989086
83	7.69	7.67999947952817	0.0100005204718263
84	7.7	7.68999947952818	0.0100005204718236

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	7.69999947952818	7.66830642557834	7.73169253347802
86	7.69999947952818	7.6551798991202	7.74481905993615
87	7.69999947952818	7.64510740444236	7.75489155461399
88	7.69999947952818	7.63661584578487	7.76338311327149
89	7.69999947952818	7.62913460708925	7.77086435196711
90	7.69999947952818	7.62237103586823	7.77762792318812
91	7.69999947952818	7.61615128107201	7.78384767798434
92	7.69999947952818	7.61036206823343	7.78963689082293
93	7.69999947952818	7.60492471619477	7.79507424286159
94	7.69999947952818	7.59978193744006	7.80021702161629
95	7.69999947952818	7.59489048437808	7.80510847467827
96	7.69999947952818	7.59021675784237	7.80978220121398

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 7.69999947952818 & 7.66830642557834 & 7.73169253347802 \tabularnewline
86 & 7.69999947952818 & 7.6551798991202 & 7.74481905993615 \tabularnewline
87 & 7.69999947952818 & 7.64510740444236 & 7.75489155461399 \tabularnewline
88 & 7.69999947952818 & 7.63661584578487 & 7.76338311327149 \tabularnewline
89 & 7.69999947952818 & 7.62913460708925 & 7.77086435196711 \tabularnewline
90 & 7.69999947952818 & 7.62237103586823 & 7.77762792318812 \tabularnewline
91 & 7.69999947952818 & 7.61615128107201 & 7.78384767798434 \tabularnewline
92 & 7.69999947952818 & 7.61036206823343 & 7.78963689082293 \tabularnewline
93 & 7.69999947952818 & 7.60492471619477 & 7.79507424286159 \tabularnewline
94 & 7.69999947952818 & 7.59978193744006 & 7.80021702161629 \tabularnewline
95 & 7.69999947952818 & 7.59489048437808 & 7.80510847467827 \tabularnewline
96 & 7.69999947952818 & 7.59021675784237 & 7.80978220121398 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233121&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]85[/C][C]7.69999947952818[/C][C]7.66830642557834[/C][C]7.73169253347802[/C][/ROW]
[ROW][C]86[/C][C]7.69999947952818[/C][C]7.6551798991202[/C][C]7.74481905993615[/C][/ROW]
[ROW][C]87[/C][C]7.69999947952818[/C][C]7.64510740444236[/C][C]7.75489155461399[/C][/ROW]
[ROW][C]88[/C][C]7.69999947952818[/C][C]7.63661584578487[/C][C]7.76338311327149[/C][/ROW]
[ROW][C]89[/C][C]7.69999947952818[/C][C]7.62913460708925[/C][C]7.77086435196711[/C][/ROW]
[ROW][C]90[/C][C]7.69999947952818[/C][C]7.62237103586823[/C][C]7.77762792318812[/C][/ROW]
[ROW][C]91[/C][C]7.69999947952818[/C][C]7.61615128107201[/C][C]7.78384767798434[/C][/ROW]
[ROW][C]92[/C][C]7.69999947952818[/C][C]7.61036206823343[/C][C]7.78963689082293[/C][/ROW]
[ROW][C]93[/C][C]7.69999947952818[/C][C]7.60492471619477[/C][C]7.79507424286159[/C][/ROW]
[ROW][C]94[/C][C]7.69999947952818[/C][C]7.59978193744006[/C][C]7.80021702161629[/C][/ROW]
[ROW][C]95[/C][C]7.69999947952818[/C][C]7.59489048437808[/C][C]7.80510847467827[/C][/ROW]
[ROW][C]96[/C][C]7.69999947952818[/C][C]7.59021675784237[/C][C]7.80978220121398[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233121&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233121&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
85	7.69999947952818	7.66830642557834	7.73169253347802
86	7.69999947952818	7.6551798991202	7.74481905993615
87	7.69999947952818	7.64510740444236	7.75489155461399
88	7.69999947952818	7.63661584578487	7.76338311327149
89	7.69999947952818	7.62913460708925	7.77086435196711
90	7.69999947952818	7.62237103586823	7.77762792318812
91	7.69999947952818	7.61615128107201	7.78384767798434
92	7.69999947952818	7.61036206823343	7.78963689082293
93	7.69999947952818	7.60492471619477	7.79507424286159
94	7.69999947952818	7.59978193744006	7.80021702161629
95	7.69999947952818	7.59489048437808	7.80510847467827
96	7.69999947952818	7.59021675784237	7.80978220121398

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 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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