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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 13 Jan 2014 03:24:33 -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/t13896014961jyu364dl23mna1.htm/, Retrieved Sun, 19 May 2024 09:09:35 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=233117, Retrieved Sun, 19 May 2024 09:09:35 +0000

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No (this computation is public)

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Estimated Impact

162

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

-       [Exponential Smoothing] [] [2014-01-13 08:24:33] [d41d8cd98f00b204e9800998ecf8427e] [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	3 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233117&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233117&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233117&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	3 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.999946231718186
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999946231718186 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233117&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]0.999946231718186[/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=233117&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233117&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	0.999946231718186
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	9.87	9.84	0.0299999999999994
3	9.9	9.86999838695155	0.0300016130484551
4	9.9	9.89999838686482	1.61313518454165e-06
5	9.87	9.89999999991326	-0.0299999999132652
6	9.87	9.87000161304845	-1.61304845036625e-06
7	9.88	9.87000000008673	0.00999999991327094
8	9.76	9.87999946231719	-0.119999462317187
9	9.76	9.76000645216491	-6.45216490724465e-06
10	9.76	9.76000000034692	-3.46922490734869e-10
11	9.77	9.76000000000002	0.00999999999998025
12	9.77	9.76999946231718	5.37682817380869e-07
13	9.77	9.76999999997109	2.89102075612391e-11
14	9.83	9.77	0.0600000000000023
15	9.85	9.82999677390309	0.0200032260969092
16	9.85	9.8499989244609	1.07553909778346e-06
17	9.89	9.84999999994217	0.0400000000578302
18	9.9	9.88999784926873	0.0100021507312746
19	9.92	9.89999946220154	0.0200005377984596
20	9.91	9.91999892460545	-0.00999892460544771
21	9.92	9.910000537625	0.0099994623750046
22	9.92	9.91999946234609	5.37653910726021e-07
23	9.96	9.91999999997109	0.0400000000289094
24	9.97	9.95999784926873	0.0100021507312746
25	9.98	9.96999946220154	0.0100005377984598
26	10.06	9.97999946228827	0.0800005377117348
27	10.07	10.0599956985085	0.0100043014914561
28	10.12	10.0699994620859	0.0500005379141015
29	10.1	10.119997311557	-0.0199973115569865
30	10.1	10.1000010752211	-1.07522108372393e-06
31	10.1	10.1000000000578	-5.78133096951206e-11
32	10.19	10.1	0.0899999999999963
33	10.21	10.1899951608546	0.0200048391453649
34	10.2	10.2099989243742	-0.00999892437417316
35	10.39	10.200000537625	0.189999462375019
36	10.39	10.3899897840554	1.02159446377925e-05
37	10.39	10.3899999994507	5.49293943663542e-10
38	10.45	10.39	0.0600000000000289
39	10.49	10.4499967739031	0.0400032260969105
40	10.48	10.4899978490953	-0.00999784909526547
41	10.49	10.4800005375672	0.00999946243283212
42	10.49	10.4899994623461	5.37653914278735e-07
43	10.5	10.4899999999711	0.0100000000289082
44	10.51	10.4999994623172	0.0100005376828189
45	10.51	10.5099994622883	5.3771172758843e-07
46	10.53	10.5099999999711	0.0200000000289116
47	10.54	10.5299989246344	0.0100010753656381
48	10.54	10.5399994622594	5.37740639572348e-07
49	10.55	10.5399999999711	0.0100000000289153
50	10.58	10.5499994623172	0.0300005376828185
51	10.59	10.5799983869226	0.0100016130773639
52	10.56	10.5899994622305	-0.0299994622304496
53	10.57	10.5600016130195	0.00999838698045963
54	10.59	10.5699994624039	0.0200005375960881
55	10.63	10.5899989246055	0.0400010753945423
56	10.63	10.6299978492109	2.15078909526767e-06
57	10.66	10.6299999998844	0.0300000001156437
58	10.69	10.6599983869515	0.0300016130484604
59	10.72	10.6899983868648	0.0300016131351857
60	10.72	10.7199983868648	1.61313518987072e-06
61	10.73	10.7199999999133	0.0100000000867357
62	10.75	10.7299994623172	0.0200005376828223
63	10.78	10.7499989246055	0.0300010753945461
64	10.79	10.7799983868937	0.0100016131062759
65	10.83	10.7899994622304	0.0400005377695525
66	10.83	10.8299978492398	2.15076018683646e-06
67	10.85	10.8299999998844	0.0200000001156422
68	10.88	10.8499989246344	0.030001075365643
69	10.97	10.8799983868937	0.0900016131062742
70	10.98	10.9699951607679	0.0100048392320975
71	11	10.979999462057	0.0200005379430142
72	11.04	10.9999989246054	0.0400010753945601
73	11.08	11.0399978492109	0.0400021507890962
74	11.16	11.0799978491531	0.0800021508469175
75	11.19	11.1599956984218	0.0300043015781917
76	11.2	11.1899983867203	0.0100016132797425
77	11.22	11.1999994622304	0.0200005377695636
78	11.26	11.2199989246054	0.0400010753945512
79	11.29	11.2599978492109	0.0300021507890946
80	11.31	11.2899983868359	0.0200016131640997
81	11.39	11.3099989245476	0.0800010754523726
82	11.37	11.3899956984796	-0.0199956984796312
83	11.39	11.3700010751344	0.01999892486565
84	11.39	11.3899989246922	1.07530782855747e-06

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 9.87 & 9.84 & 0.0299999999999994 \tabularnewline
3 & 9.9 & 9.86999838695155 & 0.0300016130484551 \tabularnewline
4 & 9.9 & 9.89999838686482 & 1.61313518454165e-06 \tabularnewline
5 & 9.87 & 9.89999999991326 & -0.0299999999132652 \tabularnewline
6 & 9.87 & 9.87000161304845 & -1.61304845036625e-06 \tabularnewline
7 & 9.88 & 9.87000000008673 & 0.00999999991327094 \tabularnewline
8 & 9.76 & 9.87999946231719 & -0.119999462317187 \tabularnewline
9 & 9.76 & 9.76000645216491 & -6.45216490724465e-06 \tabularnewline
10 & 9.76 & 9.76000000034692 & -3.46922490734869e-10 \tabularnewline
11 & 9.77 & 9.76000000000002 & 0.00999999999998025 \tabularnewline
12 & 9.77 & 9.76999946231718 & 5.37682817380869e-07 \tabularnewline
13 & 9.77 & 9.76999999997109 & 2.89102075612391e-11 \tabularnewline
14 & 9.83 & 9.77 & 0.0600000000000023 \tabularnewline
15 & 9.85 & 9.82999677390309 & 0.0200032260969092 \tabularnewline
16 & 9.85 & 9.8499989244609 & 1.07553909778346e-06 \tabularnewline
17 & 9.89 & 9.84999999994217 & 0.0400000000578302 \tabularnewline
18 & 9.9 & 9.88999784926873 & 0.0100021507312746 \tabularnewline
19 & 9.92 & 9.89999946220154 & 0.0200005377984596 \tabularnewline
20 & 9.91 & 9.91999892460545 & -0.00999892460544771 \tabularnewline
21 & 9.92 & 9.910000537625 & 0.0099994623750046 \tabularnewline
22 & 9.92 & 9.91999946234609 & 5.37653910726021e-07 \tabularnewline
23 & 9.96 & 9.91999999997109 & 0.0400000000289094 \tabularnewline
24 & 9.97 & 9.95999784926873 & 0.0100021507312746 \tabularnewline
25 & 9.98 & 9.96999946220154 & 0.0100005377984598 \tabularnewline
26 & 10.06 & 9.97999946228827 & 0.0800005377117348 \tabularnewline
27 & 10.07 & 10.0599956985085 & 0.0100043014914561 \tabularnewline
28 & 10.12 & 10.0699994620859 & 0.0500005379141015 \tabularnewline
29 & 10.1 & 10.119997311557 & -0.0199973115569865 \tabularnewline
30 & 10.1 & 10.1000010752211 & -1.07522108372393e-06 \tabularnewline
31 & 10.1 & 10.1000000000578 & -5.78133096951206e-11 \tabularnewline
32 & 10.19 & 10.1 & 0.0899999999999963 \tabularnewline
33 & 10.21 & 10.1899951608546 & 0.0200048391453649 \tabularnewline
34 & 10.2 & 10.2099989243742 & -0.00999892437417316 \tabularnewline
35 & 10.39 & 10.200000537625 & 0.189999462375019 \tabularnewline
36 & 10.39 & 10.3899897840554 & 1.02159446377925e-05 \tabularnewline
37 & 10.39 & 10.3899999994507 & 5.49293943663542e-10 \tabularnewline
38 & 10.45 & 10.39 & 0.0600000000000289 \tabularnewline
39 & 10.49 & 10.4499967739031 & 0.0400032260969105 \tabularnewline
40 & 10.48 & 10.4899978490953 & -0.00999784909526547 \tabularnewline
41 & 10.49 & 10.4800005375672 & 0.00999946243283212 \tabularnewline
42 & 10.49 & 10.4899994623461 & 5.37653914278735e-07 \tabularnewline
43 & 10.5 & 10.4899999999711 & 0.0100000000289082 \tabularnewline
44 & 10.51 & 10.4999994623172 & 0.0100005376828189 \tabularnewline
45 & 10.51 & 10.5099994622883 & 5.3771172758843e-07 \tabularnewline
46 & 10.53 & 10.5099999999711 & 0.0200000000289116 \tabularnewline
47 & 10.54 & 10.5299989246344 & 0.0100010753656381 \tabularnewline
48 & 10.54 & 10.5399994622594 & 5.37740639572348e-07 \tabularnewline
49 & 10.55 & 10.5399999999711 & 0.0100000000289153 \tabularnewline
50 & 10.58 & 10.5499994623172 & 0.0300005376828185 \tabularnewline
51 & 10.59 & 10.5799983869226 & 0.0100016130773639 \tabularnewline
52 & 10.56 & 10.5899994622305 & -0.0299994622304496 \tabularnewline
53 & 10.57 & 10.5600016130195 & 0.00999838698045963 \tabularnewline
54 & 10.59 & 10.5699994624039 & 0.0200005375960881 \tabularnewline
55 & 10.63 & 10.5899989246055 & 0.0400010753945423 \tabularnewline
56 & 10.63 & 10.6299978492109 & 2.15078909526767e-06 \tabularnewline
57 & 10.66 & 10.6299999998844 & 0.0300000001156437 \tabularnewline
58 & 10.69 & 10.6599983869515 & 0.0300016130484604 \tabularnewline
59 & 10.72 & 10.6899983868648 & 0.0300016131351857 \tabularnewline
60 & 10.72 & 10.7199983868648 & 1.61313518987072e-06 \tabularnewline
61 & 10.73 & 10.7199999999133 & 0.0100000000867357 \tabularnewline
62 & 10.75 & 10.7299994623172 & 0.0200005376828223 \tabularnewline
63 & 10.78 & 10.7499989246055 & 0.0300010753945461 \tabularnewline
64 & 10.79 & 10.7799983868937 & 0.0100016131062759 \tabularnewline
65 & 10.83 & 10.7899994622304 & 0.0400005377695525 \tabularnewline
66 & 10.83 & 10.8299978492398 & 2.15076018683646e-06 \tabularnewline
67 & 10.85 & 10.8299999998844 & 0.0200000001156422 \tabularnewline
68 & 10.88 & 10.8499989246344 & 0.030001075365643 \tabularnewline
69 & 10.97 & 10.8799983868937 & 0.0900016131062742 \tabularnewline
70 & 10.98 & 10.9699951607679 & 0.0100048392320975 \tabularnewline
71 & 11 & 10.979999462057 & 0.0200005379430142 \tabularnewline
72 & 11.04 & 10.9999989246054 & 0.0400010753945601 \tabularnewline
73 & 11.08 & 11.0399978492109 & 0.0400021507890962 \tabularnewline
74 & 11.16 & 11.0799978491531 & 0.0800021508469175 \tabularnewline
75 & 11.19 & 11.1599956984218 & 0.0300043015781917 \tabularnewline
76 & 11.2 & 11.1899983867203 & 0.0100016132797425 \tabularnewline
77 & 11.22 & 11.1999994622304 & 0.0200005377695636 \tabularnewline
78 & 11.26 & 11.2199989246054 & 0.0400010753945512 \tabularnewline
79 & 11.29 & 11.2599978492109 & 0.0300021507890946 \tabularnewline
80 & 11.31 & 11.2899983868359 & 0.0200016131640997 \tabularnewline
81 & 11.39 & 11.3099989245476 & 0.0800010754523726 \tabularnewline
82 & 11.37 & 11.3899956984796 & -0.0199956984796312 \tabularnewline
83 & 11.39 & 11.3700010751344 & 0.01999892486565 \tabularnewline
84 & 11.39 & 11.3899989246922 & 1.07530782855747e-06 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233117&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]9.87[/C][C]9.84[/C][C]0.0299999999999994[/C][/ROW]
[ROW][C]3[/C][C]9.9[/C][C]9.86999838695155[/C][C]0.0300016130484551[/C][/ROW]
[ROW][C]4[/C][C]9.9[/C][C]9.89999838686482[/C][C]1.61313518454165e-06[/C][/ROW]
[ROW][C]5[/C][C]9.87[/C][C]9.89999999991326[/C][C]-0.0299999999132652[/C][/ROW]
[ROW][C]6[/C][C]9.87[/C][C]9.87000161304845[/C][C]-1.61304845036625e-06[/C][/ROW]
[ROW][C]7[/C][C]9.88[/C][C]9.87000000008673[/C][C]0.00999999991327094[/C][/ROW]
[ROW][C]8[/C][C]9.76[/C][C]9.87999946231719[/C][C]-0.119999462317187[/C][/ROW]
[ROW][C]9[/C][C]9.76[/C][C]9.76000645216491[/C][C]-6.45216490724465e-06[/C][/ROW]
[ROW][C]10[/C][C]9.76[/C][C]9.76000000034692[/C][C]-3.46922490734869e-10[/C][/ROW]
[ROW][C]11[/C][C]9.77[/C][C]9.76000000000002[/C][C]0.00999999999998025[/C][/ROW]
[ROW][C]12[/C][C]9.77[/C][C]9.76999946231718[/C][C]5.37682817380869e-07[/C][/ROW]
[ROW][C]13[/C][C]9.77[/C][C]9.76999999997109[/C][C]2.89102075612391e-11[/C][/ROW]
[ROW][C]14[/C][C]9.83[/C][C]9.77[/C][C]0.0600000000000023[/C][/ROW]
[ROW][C]15[/C][C]9.85[/C][C]9.82999677390309[/C][C]0.0200032260969092[/C][/ROW]
[ROW][C]16[/C][C]9.85[/C][C]9.8499989244609[/C][C]1.07553909778346e-06[/C][/ROW]
[ROW][C]17[/C][C]9.89[/C][C]9.84999999994217[/C][C]0.0400000000578302[/C][/ROW]
[ROW][C]18[/C][C]9.9[/C][C]9.88999784926873[/C][C]0.0100021507312746[/C][/ROW]
[ROW][C]19[/C][C]9.92[/C][C]9.89999946220154[/C][C]0.0200005377984596[/C][/ROW]
[ROW][C]20[/C][C]9.91[/C][C]9.91999892460545[/C][C]-0.00999892460544771[/C][/ROW]
[ROW][C]21[/C][C]9.92[/C][C]9.910000537625[/C][C]0.0099994623750046[/C][/ROW]
[ROW][C]22[/C][C]9.92[/C][C]9.91999946234609[/C][C]5.37653910726021e-07[/C][/ROW]
[ROW][C]23[/C][C]9.96[/C][C]9.91999999997109[/C][C]0.0400000000289094[/C][/ROW]
[ROW][C]24[/C][C]9.97[/C][C]9.95999784926873[/C][C]0.0100021507312746[/C][/ROW]
[ROW][C]25[/C][C]9.98[/C][C]9.96999946220154[/C][C]0.0100005377984598[/C][/ROW]
[ROW][C]26[/C][C]10.06[/C][C]9.97999946228827[/C][C]0.0800005377117348[/C][/ROW]
[ROW][C]27[/C][C]10.07[/C][C]10.0599956985085[/C][C]0.0100043014914561[/C][/ROW]
[ROW][C]28[/C][C]10.12[/C][C]10.0699994620859[/C][C]0.0500005379141015[/C][/ROW]
[ROW][C]29[/C][C]10.1[/C][C]10.119997311557[/C][C]-0.0199973115569865[/C][/ROW]
[ROW][C]30[/C][C]10.1[/C][C]10.1000010752211[/C][C]-1.07522108372393e-06[/C][/ROW]
[ROW][C]31[/C][C]10.1[/C][C]10.1000000000578[/C][C]-5.78133096951206e-11[/C][/ROW]
[ROW][C]32[/C][C]10.19[/C][C]10.1[/C][C]0.0899999999999963[/C][/ROW]
[ROW][C]33[/C][C]10.21[/C][C]10.1899951608546[/C][C]0.0200048391453649[/C][/ROW]
[ROW][C]34[/C][C]10.2[/C][C]10.2099989243742[/C][C]-0.00999892437417316[/C][/ROW]
[ROW][C]35[/C][C]10.39[/C][C]10.200000537625[/C][C]0.189999462375019[/C][/ROW]
[ROW][C]36[/C][C]10.39[/C][C]10.3899897840554[/C][C]1.02159446377925e-05[/C][/ROW]
[ROW][C]37[/C][C]10.39[/C][C]10.3899999994507[/C][C]5.49293943663542e-10[/C][/ROW]
[ROW][C]38[/C][C]10.45[/C][C]10.39[/C][C]0.0600000000000289[/C][/ROW]
[ROW][C]39[/C][C]10.49[/C][C]10.4499967739031[/C][C]0.0400032260969105[/C][/ROW]
[ROW][C]40[/C][C]10.48[/C][C]10.4899978490953[/C][C]-0.00999784909526547[/C][/ROW]
[ROW][C]41[/C][C]10.49[/C][C]10.4800005375672[/C][C]0.00999946243283212[/C][/ROW]
[ROW][C]42[/C][C]10.49[/C][C]10.4899994623461[/C][C]5.37653914278735e-07[/C][/ROW]
[ROW][C]43[/C][C]10.5[/C][C]10.4899999999711[/C][C]0.0100000000289082[/C][/ROW]
[ROW][C]44[/C][C]10.51[/C][C]10.4999994623172[/C][C]0.0100005376828189[/C][/ROW]
[ROW][C]45[/C][C]10.51[/C][C]10.5099994622883[/C][C]5.3771172758843e-07[/C][/ROW]
[ROW][C]46[/C][C]10.53[/C][C]10.5099999999711[/C][C]0.0200000000289116[/C][/ROW]
[ROW][C]47[/C][C]10.54[/C][C]10.5299989246344[/C][C]0.0100010753656381[/C][/ROW]
[ROW][C]48[/C][C]10.54[/C][C]10.5399994622594[/C][C]5.37740639572348e-07[/C][/ROW]
[ROW][C]49[/C][C]10.55[/C][C]10.5399999999711[/C][C]0.0100000000289153[/C][/ROW]
[ROW][C]50[/C][C]10.58[/C][C]10.5499994623172[/C][C]0.0300005376828185[/C][/ROW]
[ROW][C]51[/C][C]10.59[/C][C]10.5799983869226[/C][C]0.0100016130773639[/C][/ROW]
[ROW][C]52[/C][C]10.56[/C][C]10.5899994622305[/C][C]-0.0299994622304496[/C][/ROW]
[ROW][C]53[/C][C]10.57[/C][C]10.5600016130195[/C][C]0.00999838698045963[/C][/ROW]
[ROW][C]54[/C][C]10.59[/C][C]10.5699994624039[/C][C]0.0200005375960881[/C][/ROW]
[ROW][C]55[/C][C]10.63[/C][C]10.5899989246055[/C][C]0.0400010753945423[/C][/ROW]
[ROW][C]56[/C][C]10.63[/C][C]10.6299978492109[/C][C]2.15078909526767e-06[/C][/ROW]
[ROW][C]57[/C][C]10.66[/C][C]10.6299999998844[/C][C]0.0300000001156437[/C][/ROW]
[ROW][C]58[/C][C]10.69[/C][C]10.6599983869515[/C][C]0.0300016130484604[/C][/ROW]
[ROW][C]59[/C][C]10.72[/C][C]10.6899983868648[/C][C]0.0300016131351857[/C][/ROW]
[ROW][C]60[/C][C]10.72[/C][C]10.7199983868648[/C][C]1.61313518987072e-06[/C][/ROW]
[ROW][C]61[/C][C]10.73[/C][C]10.7199999999133[/C][C]0.0100000000867357[/C][/ROW]
[ROW][C]62[/C][C]10.75[/C][C]10.7299994623172[/C][C]0.0200005376828223[/C][/ROW]
[ROW][C]63[/C][C]10.78[/C][C]10.7499989246055[/C][C]0.0300010753945461[/C][/ROW]
[ROW][C]64[/C][C]10.79[/C][C]10.7799983868937[/C][C]0.0100016131062759[/C][/ROW]
[ROW][C]65[/C][C]10.83[/C][C]10.7899994622304[/C][C]0.0400005377695525[/C][/ROW]
[ROW][C]66[/C][C]10.83[/C][C]10.8299978492398[/C][C]2.15076018683646e-06[/C][/ROW]
[ROW][C]67[/C][C]10.85[/C][C]10.8299999998844[/C][C]0.0200000001156422[/C][/ROW]
[ROW][C]68[/C][C]10.88[/C][C]10.8499989246344[/C][C]0.030001075365643[/C][/ROW]
[ROW][C]69[/C][C]10.97[/C][C]10.8799983868937[/C][C]0.0900016131062742[/C][/ROW]
[ROW][C]70[/C][C]10.98[/C][C]10.9699951607679[/C][C]0.0100048392320975[/C][/ROW]
[ROW][C]71[/C][C]11[/C][C]10.979999462057[/C][C]0.0200005379430142[/C][/ROW]
[ROW][C]72[/C][C]11.04[/C][C]10.9999989246054[/C][C]0.0400010753945601[/C][/ROW]
[ROW][C]73[/C][C]11.08[/C][C]11.0399978492109[/C][C]0.0400021507890962[/C][/ROW]
[ROW][C]74[/C][C]11.16[/C][C]11.0799978491531[/C][C]0.0800021508469175[/C][/ROW]
[ROW][C]75[/C][C]11.19[/C][C]11.1599956984218[/C][C]0.0300043015781917[/C][/ROW]
[ROW][C]76[/C][C]11.2[/C][C]11.1899983867203[/C][C]0.0100016132797425[/C][/ROW]
[ROW][C]77[/C][C]11.22[/C][C]11.1999994622304[/C][C]0.0200005377695636[/C][/ROW]
[ROW][C]78[/C][C]11.26[/C][C]11.2199989246054[/C][C]0.0400010753945512[/C][/ROW]
[ROW][C]79[/C][C]11.29[/C][C]11.2599978492109[/C][C]0.0300021507890946[/C][/ROW]
[ROW][C]80[/C][C]11.31[/C][C]11.2899983868359[/C][C]0.0200016131640997[/C][/ROW]
[ROW][C]81[/C][C]11.39[/C][C]11.3099989245476[/C][C]0.0800010754523726[/C][/ROW]
[ROW][C]82[/C][C]11.37[/C][C]11.3899956984796[/C][C]-0.0199956984796312[/C][/ROW]
[ROW][C]83[/C][C]11.39[/C][C]11.3700010751344[/C][C]0.01999892486565[/C][/ROW]
[ROW][C]84[/C][C]11.39[/C][C]11.3899989246922[/C][C]1.07530782855747e-06[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233117&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233117&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	9.87	9.84	0.0299999999999994
3	9.9	9.86999838695155	0.0300016130484551
4	9.9	9.89999838686482	1.61313518454165e-06
5	9.87	9.89999999991326	-0.0299999999132652
6	9.87	9.87000161304845	-1.61304845036625e-06
7	9.88	9.87000000008673	0.00999999991327094
8	9.76	9.87999946231719	-0.119999462317187
9	9.76	9.76000645216491	-6.45216490724465e-06
10	9.76	9.76000000034692	-3.46922490734869e-10
11	9.77	9.76000000000002	0.00999999999998025
12	9.77	9.76999946231718	5.37682817380869e-07
13	9.77	9.76999999997109	2.89102075612391e-11
14	9.83	9.77	0.0600000000000023
15	9.85	9.82999677390309	0.0200032260969092
16	9.85	9.8499989244609	1.07553909778346e-06
17	9.89	9.84999999994217	0.0400000000578302
18	9.9	9.88999784926873	0.0100021507312746
19	9.92	9.89999946220154	0.0200005377984596
20	9.91	9.91999892460545	-0.00999892460544771
21	9.92	9.910000537625	0.0099994623750046
22	9.92	9.91999946234609	5.37653910726021e-07
23	9.96	9.91999999997109	0.0400000000289094
24	9.97	9.95999784926873	0.0100021507312746
25	9.98	9.96999946220154	0.0100005377984598
26	10.06	9.97999946228827	0.0800005377117348
27	10.07	10.0599956985085	0.0100043014914561
28	10.12	10.0699994620859	0.0500005379141015
29	10.1	10.119997311557	-0.0199973115569865
30	10.1	10.1000010752211	-1.07522108372393e-06
31	10.1	10.1000000000578	-5.78133096951206e-11
32	10.19	10.1	0.0899999999999963
33	10.21	10.1899951608546	0.0200048391453649
34	10.2	10.2099989243742	-0.00999892437417316
35	10.39	10.200000537625	0.189999462375019
36	10.39	10.3899897840554	1.02159446377925e-05
37	10.39	10.3899999994507	5.49293943663542e-10
38	10.45	10.39	0.0600000000000289
39	10.49	10.4499967739031	0.0400032260969105
40	10.48	10.4899978490953	-0.00999784909526547
41	10.49	10.4800005375672	0.00999946243283212
42	10.49	10.4899994623461	5.37653914278735e-07
43	10.5	10.4899999999711	0.0100000000289082
44	10.51	10.4999994623172	0.0100005376828189
45	10.51	10.5099994622883	5.3771172758843e-07
46	10.53	10.5099999999711	0.0200000000289116
47	10.54	10.5299989246344	0.0100010753656381
48	10.54	10.5399994622594	5.37740639572348e-07
49	10.55	10.5399999999711	0.0100000000289153
50	10.58	10.5499994623172	0.0300005376828185
51	10.59	10.5799983869226	0.0100016130773639
52	10.56	10.5899994622305	-0.0299994622304496
53	10.57	10.5600016130195	0.00999838698045963
54	10.59	10.5699994624039	0.0200005375960881
55	10.63	10.5899989246055	0.0400010753945423
56	10.63	10.6299978492109	2.15078909526767e-06
57	10.66	10.6299999998844	0.0300000001156437
58	10.69	10.6599983869515	0.0300016130484604
59	10.72	10.6899983868648	0.0300016131351857
60	10.72	10.7199983868648	1.61313518987072e-06
61	10.73	10.7199999999133	0.0100000000867357
62	10.75	10.7299994623172	0.0200005376828223
63	10.78	10.7499989246055	0.0300010753945461
64	10.79	10.7799983868937	0.0100016131062759
65	10.83	10.7899994622304	0.0400005377695525
66	10.83	10.8299978492398	2.15076018683646e-06
67	10.85	10.8299999998844	0.0200000001156422
68	10.88	10.8499989246344	0.030001075365643
69	10.97	10.8799983868937	0.0900016131062742
70	10.98	10.9699951607679	0.0100048392320975
71	11	10.979999462057	0.0200005379430142
72	11.04	10.9999989246054	0.0400010753945601
73	11.08	11.0399978492109	0.0400021507890962
74	11.16	11.0799978491531	0.0800021508469175
75	11.19	11.1599956984218	0.0300043015781917
76	11.2	11.1899983867203	0.0100016132797425
77	11.22	11.1999994622304	0.0200005377695636
78	11.26	11.2199989246054	0.0400010753945512
79	11.29	11.2599978492109	0.0300021507890946
80	11.31	11.2899983868359	0.0200016131640997
81	11.39	11.3099989245476	0.0800010754523726
82	11.37	11.3899956984796	-0.0199956984796312
83	11.39	11.3700010751344	0.01999892486565
84	11.39	11.3899989246922	1.07530782855747e-06

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	11.3899999999422	11.3223974575774	11.457602542307
86	11.3899999999422	11.2943981378874	11.4856018619969
87	11.3899999999422	11.2729131589972	11.5070868408872
88	11.3899999999422	11.2548003674847	11.5251996323997
89	11.3899999999422	11.2388426219853	11.541157377899
90	11.3899999999422	11.2244156854527	11.5555843144316
91	11.3899999999422	11.2111487279336	11.5688512719508
92	11.3899999999422	11.1988001312361	11.5811998686483
93	11.3899999999422	11.1872020658122	11.5927979340722
94	11.3899999999422	11.1762323354521	11.6037676644322
95	11.3899999999422	11.1657986915703	11.6142013083141
96	11.3899999999422	11.1558294659935	11.6241705338909

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 11.3899999999422 & 11.3223974575774 & 11.457602542307 \tabularnewline
86 & 11.3899999999422 & 11.2943981378874 & 11.4856018619969 \tabularnewline
87 & 11.3899999999422 & 11.2729131589972 & 11.5070868408872 \tabularnewline
88 & 11.3899999999422 & 11.2548003674847 & 11.5251996323997 \tabularnewline
89 & 11.3899999999422 & 11.2388426219853 & 11.541157377899 \tabularnewline
90 & 11.3899999999422 & 11.2244156854527 & 11.5555843144316 \tabularnewline
91 & 11.3899999999422 & 11.2111487279336 & 11.5688512719508 \tabularnewline
92 & 11.3899999999422 & 11.1988001312361 & 11.5811998686483 \tabularnewline
93 & 11.3899999999422 & 11.1872020658122 & 11.5927979340722 \tabularnewline
94 & 11.3899999999422 & 11.1762323354521 & 11.6037676644322 \tabularnewline
95 & 11.3899999999422 & 11.1657986915703 & 11.6142013083141 \tabularnewline
96 & 11.3899999999422 & 11.1558294659935 & 11.6241705338909 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233117&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]11.3899999999422[/C][C]11.3223974575774[/C][C]11.457602542307[/C][/ROW]
[ROW][C]86[/C][C]11.3899999999422[/C][C]11.2943981378874[/C][C]11.4856018619969[/C][/ROW]
[ROW][C]87[/C][C]11.3899999999422[/C][C]11.2729131589972[/C][C]11.5070868408872[/C][/ROW]
[ROW][C]88[/C][C]11.3899999999422[/C][C]11.2548003674847[/C][C]11.5251996323997[/C][/ROW]
[ROW][C]89[/C][C]11.3899999999422[/C][C]11.2388426219853[/C][C]11.541157377899[/C][/ROW]
[ROW][C]90[/C][C]11.3899999999422[/C][C]11.2244156854527[/C][C]11.5555843144316[/C][/ROW]
[ROW][C]91[/C][C]11.3899999999422[/C][C]11.2111487279336[/C][C]11.5688512719508[/C][/ROW]
[ROW][C]92[/C][C]11.3899999999422[/C][C]11.1988001312361[/C][C]11.5811998686483[/C][/ROW]
[ROW][C]93[/C][C]11.3899999999422[/C][C]11.1872020658122[/C][C]11.5927979340722[/C][/ROW]
[ROW][C]94[/C][C]11.3899999999422[/C][C]11.1762323354521[/C][C]11.6037676644322[/C][/ROW]
[ROW][C]95[/C][C]11.3899999999422[/C][C]11.1657986915703[/C][C]11.6142013083141[/C][/ROW]
[ROW][C]96[/C][C]11.3899999999422[/C][C]11.1558294659935[/C][C]11.6241705338909[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233117&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233117&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	11.3899999999422	11.3223974575774	11.457602542307
86	11.3899999999422	11.2943981378874	11.4856018619969
87	11.3899999999422	11.2729131589972	11.5070868408872
88	11.3899999999422	11.2548003674847	11.5251996323997
89	11.3899999999422	11.2388426219853	11.541157377899
90	11.3899999999422	11.2244156854527	11.5555843144316
91	11.3899999999422	11.2111487279336	11.5688512719508
92	11.3899999999422	11.1988001312361	11.5811998686483
93	11.3899999999422	11.1872020658122	11.5927979340722
94	11.3899999999422	11.1762323354521	11.6037676644322
95	11.3899999999422	11.1657986915703	11.6142013083141
96	11.3899999999422	11.1558294659935	11.6241705338909

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 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Single ; par3 = multiplicative ;

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

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

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code