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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Tue, 15 Jan 2013 14:26:14 -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/2013/Jan/15/t1358277994uofdnjk8rv3wpdz.htm/, Retrieved Sun, 28 Apr 2024 17:07:02 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=205513, Retrieved Sun, 28 Apr 2024 17:07:02 +0000

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Estimated Impact

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

-       [Exponential Smoothing] [smoothing model] [2013-01-15 19:26:14] [76c30f62b7052b57088120e90a652e05] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205513&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205513&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205513&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.880391676888377
beta	0.129542012995612
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.880391676888377 \tabularnewline
beta & 0.129542012995612 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205513&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]0.880391676888377[/C][/ROW]
[ROW][C]beta[/C][C]0.129542012995612[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205513&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205513&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	0.880391676888377
beta	0.129542012995612
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	95.91	95.79	0.11999999999999
4	95.86	95.0493327264325	0.810667273567546
5	95.7	95.0091779181748	0.690822081825232
6	95.57	94.9422990770753	0.627700922924689
7	95.57	94.8914367458993	0.678563254100723
8	95.57	94.9627417730111	0.607258226988861
9	94.87	95.0405268579297	-0.17052685792973
10	95.07	94.4141082300294	0.655891769970594
11	95.13	94.590064638163	0.539935361837038
12	95.48	94.7255123812857	0.754487618714307
13	95.38	95.1358977307953	0.244102269204731
14	95.38	95.1247833714113	0.25521662858867
15	95.48	95.1525608735798	0.32743912642016
16	95.77	95.2812661442719	0.488733855728142
17	94.78	95.6077129292416	-0.827712929241642
18	92.51	94.6807721574999	-2.17077215749985
19	92.17	92.3238416260311	-0.153841626031081
20	91.75	91.7250546621705	0.0249453378295499
21	90.43	91.2865152118847	-0.856515211884698
22	90.55	89.9742616315878	0.575738368412246
23	90.37	89.9886138250824	0.381386174917594
24	90.4	89.875356184933	0.524643815067051
25	90.41	89.9480558045214	0.461944195478623
26	90.41	90.0182388785447	0.391761121455303
27	90.41	90.0713128171275	0.338687182872462
28	89.77	90.1162873995518	-0.346287399551812
29	89.77	89.5187227757921	0.251277224207939
30	89.77	89.4759066652016	0.294093334798362
31	89.37	89.5043261733861	-0.134326173386086
32	89.81	89.1402491198741	0.669750880125946
33	89.07	89.5604583660324	-0.490458366032428
34	89.84	88.9032933949038	0.936706605096219
35	89.73	89.6094218292022	0.120578170797828
36	90.02	89.6107892469337	0.409210753066333
37	88.39	89.9129359370877	-1.52293593708765
38	90.13	88.3403494065269	1.78965059347306
39	90.13	89.8882420384173	0.241757961582678
40	90.37	90.1009548223791	0.269045177620882
41	89.73	90.3683750306337	-0.638375030633696
42	89.73	89.7641048297046	-0.0341048297045887
43	89.73	89.6879395065357	0.0420604934642768
44	89.73	89.6836264029154	0.0463735970846386
45	89.6	89.6883993223781	-0.0883993223781516
46	89.63	89.5644375449889	0.0655624550111327
47	86.42	89.5834996828312	-3.16349968283123
48	86.8	86.3989324957951	0.401067504204889
49	86.51	86.3983214223645	0.111678577635502
50	86.41	86.1556714326394	0.254328567360616
51	86.39	86.0676148972839	0.322385102716083
52	86.62	86.0762420519318	0.543757948068162
53	85.85	86.3417783659148	-0.491778365914783
54	87.36	85.6395509314674	1.7204490685326
55	87.28	87.0811633942132	0.198836605786809
56	87.35	87.2058377688718	0.144162231128192
57	87.35	87.2988186514776	0.0511813485224195
58	87.35	87.3157770545237	0.0342229454763299
59	87.38	87.3217084692374	0.0582915307626308
60	88.17	87.3554776817103	0.81452231828969
61	88.37	88.1479205905133	0.222079409486682
62	87.44	88.4441093414756	-1.00410934147556
63	87.44	87.5462553507627	-0.10625535076268
64	87.47	87.4267463610995	0.043253638900481
65	87.47	87.4437968200237	0.0262031799763207
66	87.48	87.4488246094962	0.031175390503833
67	87.11	87.4617853736297	-0.351785373629667
68	87.11	87.0974703521541	0.0125296478458807
69	86.26	87.0553242209956	-0.795324220995582
70	86.28	86.2112453614161	0.0687546385838544
71	86.28	86.1357356470714	0.144264352928644
72	86.28	86.1431570758531	0.136842924146876

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 95.91 & 95.79 & 0.11999999999999 \tabularnewline
4 & 95.86 & 95.0493327264325 & 0.810667273567546 \tabularnewline
5 & 95.7 & 95.0091779181748 & 0.690822081825232 \tabularnewline
6 & 95.57 & 94.9422990770753 & 0.627700922924689 \tabularnewline
7 & 95.57 & 94.8914367458993 & 0.678563254100723 \tabularnewline
8 & 95.57 & 94.9627417730111 & 0.607258226988861 \tabularnewline
9 & 94.87 & 95.0405268579297 & -0.17052685792973 \tabularnewline
10 & 95.07 & 94.4141082300294 & 0.655891769970594 \tabularnewline
11 & 95.13 & 94.590064638163 & 0.539935361837038 \tabularnewline
12 & 95.48 & 94.7255123812857 & 0.754487618714307 \tabularnewline
13 & 95.38 & 95.1358977307953 & 0.244102269204731 \tabularnewline
14 & 95.38 & 95.1247833714113 & 0.25521662858867 \tabularnewline
15 & 95.48 & 95.1525608735798 & 0.32743912642016 \tabularnewline
16 & 95.77 & 95.2812661442719 & 0.488733855728142 \tabularnewline
17 & 94.78 & 95.6077129292416 & -0.827712929241642 \tabularnewline
18 & 92.51 & 94.6807721574999 & -2.17077215749985 \tabularnewline
19 & 92.17 & 92.3238416260311 & -0.153841626031081 \tabularnewline
20 & 91.75 & 91.7250546621705 & 0.0249453378295499 \tabularnewline
21 & 90.43 & 91.2865152118847 & -0.856515211884698 \tabularnewline
22 & 90.55 & 89.9742616315878 & 0.575738368412246 \tabularnewline
23 & 90.37 & 89.9886138250824 & 0.381386174917594 \tabularnewline
24 & 90.4 & 89.875356184933 & 0.524643815067051 \tabularnewline
25 & 90.41 & 89.9480558045214 & 0.461944195478623 \tabularnewline
26 & 90.41 & 90.0182388785447 & 0.391761121455303 \tabularnewline
27 & 90.41 & 90.0713128171275 & 0.338687182872462 \tabularnewline
28 & 89.77 & 90.1162873995518 & -0.346287399551812 \tabularnewline
29 & 89.77 & 89.5187227757921 & 0.251277224207939 \tabularnewline
30 & 89.77 & 89.4759066652016 & 0.294093334798362 \tabularnewline
31 & 89.37 & 89.5043261733861 & -0.134326173386086 \tabularnewline
32 & 89.81 & 89.1402491198741 & 0.669750880125946 \tabularnewline
33 & 89.07 & 89.5604583660324 & -0.490458366032428 \tabularnewline
34 & 89.84 & 88.9032933949038 & 0.936706605096219 \tabularnewline
35 & 89.73 & 89.6094218292022 & 0.120578170797828 \tabularnewline
36 & 90.02 & 89.6107892469337 & 0.409210753066333 \tabularnewline
37 & 88.39 & 89.9129359370877 & -1.52293593708765 \tabularnewline
38 & 90.13 & 88.3403494065269 & 1.78965059347306 \tabularnewline
39 & 90.13 & 89.8882420384173 & 0.241757961582678 \tabularnewline
40 & 90.37 & 90.1009548223791 & 0.269045177620882 \tabularnewline
41 & 89.73 & 90.3683750306337 & -0.638375030633696 \tabularnewline
42 & 89.73 & 89.7641048297046 & -0.0341048297045887 \tabularnewline
43 & 89.73 & 89.6879395065357 & 0.0420604934642768 \tabularnewline
44 & 89.73 & 89.6836264029154 & 0.0463735970846386 \tabularnewline
45 & 89.6 & 89.6883993223781 & -0.0883993223781516 \tabularnewline
46 & 89.63 & 89.5644375449889 & 0.0655624550111327 \tabularnewline
47 & 86.42 & 89.5834996828312 & -3.16349968283123 \tabularnewline
48 & 86.8 & 86.3989324957951 & 0.401067504204889 \tabularnewline
49 & 86.51 & 86.3983214223645 & 0.111678577635502 \tabularnewline
50 & 86.41 & 86.1556714326394 & 0.254328567360616 \tabularnewline
51 & 86.39 & 86.0676148972839 & 0.322385102716083 \tabularnewline
52 & 86.62 & 86.0762420519318 & 0.543757948068162 \tabularnewline
53 & 85.85 & 86.3417783659148 & -0.491778365914783 \tabularnewline
54 & 87.36 & 85.6395509314674 & 1.7204490685326 \tabularnewline
55 & 87.28 & 87.0811633942132 & 0.198836605786809 \tabularnewline
56 & 87.35 & 87.2058377688718 & 0.144162231128192 \tabularnewline
57 & 87.35 & 87.2988186514776 & 0.0511813485224195 \tabularnewline
58 & 87.35 & 87.3157770545237 & 0.0342229454763299 \tabularnewline
59 & 87.38 & 87.3217084692374 & 0.0582915307626308 \tabularnewline
60 & 88.17 & 87.3554776817103 & 0.81452231828969 \tabularnewline
61 & 88.37 & 88.1479205905133 & 0.222079409486682 \tabularnewline
62 & 87.44 & 88.4441093414756 & -1.00410934147556 \tabularnewline
63 & 87.44 & 87.5462553507627 & -0.10625535076268 \tabularnewline
64 & 87.47 & 87.4267463610995 & 0.043253638900481 \tabularnewline
65 & 87.47 & 87.4437968200237 & 0.0262031799763207 \tabularnewline
66 & 87.48 & 87.4488246094962 & 0.031175390503833 \tabularnewline
67 & 87.11 & 87.4617853736297 & -0.351785373629667 \tabularnewline
68 & 87.11 & 87.0974703521541 & 0.0125296478458807 \tabularnewline
69 & 86.26 & 87.0553242209956 & -0.795324220995582 \tabularnewline
70 & 86.28 & 86.2112453614161 & 0.0687546385838544 \tabularnewline
71 & 86.28 & 86.1357356470714 & 0.144264352928644 \tabularnewline
72 & 86.28 & 86.1431570758531 & 0.136842924146876 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205513&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]95.91[/C][C]95.79[/C][C]0.11999999999999[/C][/ROW]
[ROW][C]4[/C][C]95.86[/C][C]95.0493327264325[/C][C]0.810667273567546[/C][/ROW]
[ROW][C]5[/C][C]95.7[/C][C]95.0091779181748[/C][C]0.690822081825232[/C][/ROW]
[ROW][C]6[/C][C]95.57[/C][C]94.9422990770753[/C][C]0.627700922924689[/C][/ROW]
[ROW][C]7[/C][C]95.57[/C][C]94.8914367458993[/C][C]0.678563254100723[/C][/ROW]
[ROW][C]8[/C][C]95.57[/C][C]94.9627417730111[/C][C]0.607258226988861[/C][/ROW]
[ROW][C]9[/C][C]94.87[/C][C]95.0405268579297[/C][C]-0.17052685792973[/C][/ROW]
[ROW][C]10[/C][C]95.07[/C][C]94.4141082300294[/C][C]0.655891769970594[/C][/ROW]
[ROW][C]11[/C][C]95.13[/C][C]94.590064638163[/C][C]0.539935361837038[/C][/ROW]
[ROW][C]12[/C][C]95.48[/C][C]94.7255123812857[/C][C]0.754487618714307[/C][/ROW]
[ROW][C]13[/C][C]95.38[/C][C]95.1358977307953[/C][C]0.244102269204731[/C][/ROW]
[ROW][C]14[/C][C]95.38[/C][C]95.1247833714113[/C][C]0.25521662858867[/C][/ROW]
[ROW][C]15[/C][C]95.48[/C][C]95.1525608735798[/C][C]0.32743912642016[/C][/ROW]
[ROW][C]16[/C][C]95.77[/C][C]95.2812661442719[/C][C]0.488733855728142[/C][/ROW]
[ROW][C]17[/C][C]94.78[/C][C]95.6077129292416[/C][C]-0.827712929241642[/C][/ROW]
[ROW][C]18[/C][C]92.51[/C][C]94.6807721574999[/C][C]-2.17077215749985[/C][/ROW]
[ROW][C]19[/C][C]92.17[/C][C]92.3238416260311[/C][C]-0.153841626031081[/C][/ROW]
[ROW][C]20[/C][C]91.75[/C][C]91.7250546621705[/C][C]0.0249453378295499[/C][/ROW]
[ROW][C]21[/C][C]90.43[/C][C]91.2865152118847[/C][C]-0.856515211884698[/C][/ROW]
[ROW][C]22[/C][C]90.55[/C][C]89.9742616315878[/C][C]0.575738368412246[/C][/ROW]
[ROW][C]23[/C][C]90.37[/C][C]89.9886138250824[/C][C]0.381386174917594[/C][/ROW]
[ROW][C]24[/C][C]90.4[/C][C]89.875356184933[/C][C]0.524643815067051[/C][/ROW]
[ROW][C]25[/C][C]90.41[/C][C]89.9480558045214[/C][C]0.461944195478623[/C][/ROW]
[ROW][C]26[/C][C]90.41[/C][C]90.0182388785447[/C][C]0.391761121455303[/C][/ROW]
[ROW][C]27[/C][C]90.41[/C][C]90.0713128171275[/C][C]0.338687182872462[/C][/ROW]
[ROW][C]28[/C][C]89.77[/C][C]90.1162873995518[/C][C]-0.346287399551812[/C][/ROW]
[ROW][C]29[/C][C]89.77[/C][C]89.5187227757921[/C][C]0.251277224207939[/C][/ROW]
[ROW][C]30[/C][C]89.77[/C][C]89.4759066652016[/C][C]0.294093334798362[/C][/ROW]
[ROW][C]31[/C][C]89.37[/C][C]89.5043261733861[/C][C]-0.134326173386086[/C][/ROW]
[ROW][C]32[/C][C]89.81[/C][C]89.1402491198741[/C][C]0.669750880125946[/C][/ROW]
[ROW][C]33[/C][C]89.07[/C][C]89.5604583660324[/C][C]-0.490458366032428[/C][/ROW]
[ROW][C]34[/C][C]89.84[/C][C]88.9032933949038[/C][C]0.936706605096219[/C][/ROW]
[ROW][C]35[/C][C]89.73[/C][C]89.6094218292022[/C][C]0.120578170797828[/C][/ROW]
[ROW][C]36[/C][C]90.02[/C][C]89.6107892469337[/C][C]0.409210753066333[/C][/ROW]
[ROW][C]37[/C][C]88.39[/C][C]89.9129359370877[/C][C]-1.52293593708765[/C][/ROW]
[ROW][C]38[/C][C]90.13[/C][C]88.3403494065269[/C][C]1.78965059347306[/C][/ROW]
[ROW][C]39[/C][C]90.13[/C][C]89.8882420384173[/C][C]0.241757961582678[/C][/ROW]
[ROW][C]40[/C][C]90.37[/C][C]90.1009548223791[/C][C]0.269045177620882[/C][/ROW]
[ROW][C]41[/C][C]89.73[/C][C]90.3683750306337[/C][C]-0.638375030633696[/C][/ROW]
[ROW][C]42[/C][C]89.73[/C][C]89.7641048297046[/C][C]-0.0341048297045887[/C][/ROW]
[ROW][C]43[/C][C]89.73[/C][C]89.6879395065357[/C][C]0.0420604934642768[/C][/ROW]
[ROW][C]44[/C][C]89.73[/C][C]89.6836264029154[/C][C]0.0463735970846386[/C][/ROW]
[ROW][C]45[/C][C]89.6[/C][C]89.6883993223781[/C][C]-0.0883993223781516[/C][/ROW]
[ROW][C]46[/C][C]89.63[/C][C]89.5644375449889[/C][C]0.0655624550111327[/C][/ROW]
[ROW][C]47[/C][C]86.42[/C][C]89.5834996828312[/C][C]-3.16349968283123[/C][/ROW]
[ROW][C]48[/C][C]86.8[/C][C]86.3989324957951[/C][C]0.401067504204889[/C][/ROW]
[ROW][C]49[/C][C]86.51[/C][C]86.3983214223645[/C][C]0.111678577635502[/C][/ROW]
[ROW][C]50[/C][C]86.41[/C][C]86.1556714326394[/C][C]0.254328567360616[/C][/ROW]
[ROW][C]51[/C][C]86.39[/C][C]86.0676148972839[/C][C]0.322385102716083[/C][/ROW]
[ROW][C]52[/C][C]86.62[/C][C]86.0762420519318[/C][C]0.543757948068162[/C][/ROW]
[ROW][C]53[/C][C]85.85[/C][C]86.3417783659148[/C][C]-0.491778365914783[/C][/ROW]
[ROW][C]54[/C][C]87.36[/C][C]85.6395509314674[/C][C]1.7204490685326[/C][/ROW]
[ROW][C]55[/C][C]87.28[/C][C]87.0811633942132[/C][C]0.198836605786809[/C][/ROW]
[ROW][C]56[/C][C]87.35[/C][C]87.2058377688718[/C][C]0.144162231128192[/C][/ROW]
[ROW][C]57[/C][C]87.35[/C][C]87.2988186514776[/C][C]0.0511813485224195[/C][/ROW]
[ROW][C]58[/C][C]87.35[/C][C]87.3157770545237[/C][C]0.0342229454763299[/C][/ROW]
[ROW][C]59[/C][C]87.38[/C][C]87.3217084692374[/C][C]0.0582915307626308[/C][/ROW]
[ROW][C]60[/C][C]88.17[/C][C]87.3554776817103[/C][C]0.81452231828969[/C][/ROW]
[ROW][C]61[/C][C]88.37[/C][C]88.1479205905133[/C][C]0.222079409486682[/C][/ROW]
[ROW][C]62[/C][C]87.44[/C][C]88.4441093414756[/C][C]-1.00410934147556[/C][/ROW]
[ROW][C]63[/C][C]87.44[/C][C]87.5462553507627[/C][C]-0.10625535076268[/C][/ROW]
[ROW][C]64[/C][C]87.47[/C][C]87.4267463610995[/C][C]0.043253638900481[/C][/ROW]
[ROW][C]65[/C][C]87.47[/C][C]87.4437968200237[/C][C]0.0262031799763207[/C][/ROW]
[ROW][C]66[/C][C]87.48[/C][C]87.4488246094962[/C][C]0.031175390503833[/C][/ROW]
[ROW][C]67[/C][C]87.11[/C][C]87.4617853736297[/C][C]-0.351785373629667[/C][/ROW]
[ROW][C]68[/C][C]87.11[/C][C]87.0974703521541[/C][C]0.0125296478458807[/C][/ROW]
[ROW][C]69[/C][C]86.26[/C][C]87.0553242209956[/C][C]-0.795324220995582[/C][/ROW]
[ROW][C]70[/C][C]86.28[/C][C]86.2112453614161[/C][C]0.0687546385838544[/C][/ROW]
[ROW][C]71[/C][C]86.28[/C][C]86.1357356470714[/C][C]0.144264352928644[/C][/ROW]
[ROW][C]72[/C][C]86.28[/C][C]86.1431570758531[/C][C]0.136842924146876[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205513&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205513&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	95.91	95.79	0.11999999999999
4	95.86	95.0493327264325	0.810667273567546
5	95.7	95.0091779181748	0.690822081825232
6	95.57	94.9422990770753	0.627700922924689
7	95.57	94.8914367458993	0.678563254100723
8	95.57	94.9627417730111	0.607258226988861
9	94.87	95.0405268579297	-0.17052685792973
10	95.07	94.4141082300294	0.655891769970594
11	95.13	94.590064638163	0.539935361837038
12	95.48	94.7255123812857	0.754487618714307
13	95.38	95.1358977307953	0.244102269204731
14	95.38	95.1247833714113	0.25521662858867
15	95.48	95.1525608735798	0.32743912642016
16	95.77	95.2812661442719	0.488733855728142
17	94.78	95.6077129292416	-0.827712929241642
18	92.51	94.6807721574999	-2.17077215749985
19	92.17	92.3238416260311	-0.153841626031081
20	91.75	91.7250546621705	0.0249453378295499
21	90.43	91.2865152118847	-0.856515211884698
22	90.55	89.9742616315878	0.575738368412246
23	90.37	89.9886138250824	0.381386174917594
24	90.4	89.875356184933	0.524643815067051
25	90.41	89.9480558045214	0.461944195478623
26	90.41	90.0182388785447	0.391761121455303
27	90.41	90.0713128171275	0.338687182872462
28	89.77	90.1162873995518	-0.346287399551812
29	89.77	89.5187227757921	0.251277224207939
30	89.77	89.4759066652016	0.294093334798362
31	89.37	89.5043261733861	-0.134326173386086
32	89.81	89.1402491198741	0.669750880125946
33	89.07	89.5604583660324	-0.490458366032428
34	89.84	88.9032933949038	0.936706605096219
35	89.73	89.6094218292022	0.120578170797828
36	90.02	89.6107892469337	0.409210753066333
37	88.39	89.9129359370877	-1.52293593708765
38	90.13	88.3403494065269	1.78965059347306
39	90.13	89.8882420384173	0.241757961582678
40	90.37	90.1009548223791	0.269045177620882
41	89.73	90.3683750306337	-0.638375030633696
42	89.73	89.7641048297046	-0.0341048297045887
43	89.73	89.6879395065357	0.0420604934642768
44	89.73	89.6836264029154	0.0463735970846386
45	89.6	89.6883993223781	-0.0883993223781516
46	89.63	89.5644375449889	0.0655624550111327
47	86.42	89.5834996828312	-3.16349968283123
48	86.8	86.3989324957951	0.401067504204889
49	86.51	86.3983214223645	0.111678577635502
50	86.41	86.1556714326394	0.254328567360616
51	86.39	86.0676148972839	0.322385102716083
52	86.62	86.0762420519318	0.543757948068162
53	85.85	86.3417783659148	-0.491778365914783
54	87.36	85.6395509314674	1.7204490685326
55	87.28	87.0811633942132	0.198836605786809
56	87.35	87.2058377688718	0.144162231128192
57	87.35	87.2988186514776	0.0511813485224195
58	87.35	87.3157770545237	0.0342229454763299
59	87.38	87.3217084692374	0.0582915307626308
60	88.17	87.3554776817103	0.81452231828969
61	88.37	88.1479205905133	0.222079409486682
62	87.44	88.4441093414756	-1.00410934147556
63	87.44	87.5462553507627	-0.10625535076268
64	87.47	87.4267463610995	0.043253638900481
65	87.47	87.4437968200237	0.0262031799763207
66	87.48	87.4488246094962	0.031175390503833
67	87.11	87.4617853736297	-0.351785373629667
68	87.11	87.0974703521541	0.0125296478458807
69	86.26	87.0553242209956	-0.795324220995582
70	86.28	86.2112453614161	0.0687546385838544
71	86.28	86.1357356470714	0.144264352928644
72	86.28	86.1431570758531	0.136842924146876

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	86.1596513626401	84.7540195553497	87.5652831699305
74	86.0556702779671	84.0733258778464	88.0380146780879
75	85.9516891932941	83.4302923644666	88.4730860221216
76	85.8477081086211	82.7964040056579	88.8990122115843
77	85.7437270239482	82.1604140862319	89.3270399616644
78	85.6397459392752	81.5168992747901	89.7625926037602
79	85.5357648546022	80.8629655047037	90.2085642045006
80	85.4317837699292	80.1969870160741	90.6665805237843
81	85.3278026852562	79.518035693712	91.1375696768003
82	85.2238216005832	78.8255923066376	91.6220508945288
83	85.1198405159102	78.1193882542579	92.1202927775625
84	85.0158594312372	77.3993135071818	92.6324053552926

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 86.1596513626401 & 84.7540195553497 & 87.5652831699305 \tabularnewline
74 & 86.0556702779671 & 84.0733258778464 & 88.0380146780879 \tabularnewline
75 & 85.9516891932941 & 83.4302923644666 & 88.4730860221216 \tabularnewline
76 & 85.8477081086211 & 82.7964040056579 & 88.8990122115843 \tabularnewline
77 & 85.7437270239482 & 82.1604140862319 & 89.3270399616644 \tabularnewline
78 & 85.6397459392752 & 81.5168992747901 & 89.7625926037602 \tabularnewline
79 & 85.5357648546022 & 80.8629655047037 & 90.2085642045006 \tabularnewline
80 & 85.4317837699292 & 80.1969870160741 & 90.6665805237843 \tabularnewline
81 & 85.3278026852562 & 79.518035693712 & 91.1375696768003 \tabularnewline
82 & 85.2238216005832 & 78.8255923066376 & 91.6220508945288 \tabularnewline
83 & 85.1198405159102 & 78.1193882542579 & 92.1202927775625 \tabularnewline
84 & 85.0158594312372 & 77.3993135071818 & 92.6324053552926 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205513&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]73[/C][C]86.1596513626401[/C][C]84.7540195553497[/C][C]87.5652831699305[/C][/ROW]
[ROW][C]74[/C][C]86.0556702779671[/C][C]84.0733258778464[/C][C]88.0380146780879[/C][/ROW]
[ROW][C]75[/C][C]85.9516891932941[/C][C]83.4302923644666[/C][C]88.4730860221216[/C][/ROW]
[ROW][C]76[/C][C]85.8477081086211[/C][C]82.7964040056579[/C][C]88.8990122115843[/C][/ROW]
[ROW][C]77[/C][C]85.7437270239482[/C][C]82.1604140862319[/C][C]89.3270399616644[/C][/ROW]
[ROW][C]78[/C][C]85.6397459392752[/C][C]81.5168992747901[/C][C]89.7625926037602[/C][/ROW]
[ROW][C]79[/C][C]85.5357648546022[/C][C]80.8629655047037[/C][C]90.2085642045006[/C][/ROW]
[ROW][C]80[/C][C]85.4317837699292[/C][C]80.1969870160741[/C][C]90.6665805237843[/C][/ROW]
[ROW][C]81[/C][C]85.3278026852562[/C][C]79.518035693712[/C][C]91.1375696768003[/C][/ROW]
[ROW][C]82[/C][C]85.2238216005832[/C][C]78.8255923066376[/C][C]91.6220508945288[/C][/ROW]
[ROW][C]83[/C][C]85.1198405159102[/C][C]78.1193882542579[/C][C]92.1202927775625[/C][/ROW]
[ROW][C]84[/C][C]85.0158594312372[/C][C]77.3993135071818[/C][C]92.6324053552926[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205513&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205513&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
73	86.1596513626401	84.7540195553497	87.5652831699305
74	86.0556702779671	84.0733258778464	88.0380146780879
75	85.9516891932941	83.4302923644666	88.4730860221216
76	85.8477081086211	82.7964040056579	88.8990122115843
77	85.7437270239482	82.1604140862319	89.3270399616644
78	85.6397459392752	81.5168992747901	89.7625926037602
79	85.5357648546022	80.8629655047037	90.2085642045006
80	85.4317837699292	80.1969870160741	90.6665805237843
81	85.3278026852562	79.518035693712	91.1375696768003
82	85.2238216005832	78.8255923066376	91.6220508945288
83	85.1198405159102	78.1193882542579	92.1202927775625
84	85.0158594312372	77.3993135071818	92.6324053552926

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