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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Fri, 23 Dec 2016 18:30:15 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/23/t1482517864v0p95rppkuoa56w.htm/, Retrieved Tue, 07 May 2024 16:13:25 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 07 May 2024 16:13:25 +0200

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Estimated Impact

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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	'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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

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

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

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

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	91.35	91.31	0.0400000000000063
4	91.52	91.56	-0.039999999999992
5	91.45	91.73	-0.279999999999987
6	91.88	91.66	0.219999999999999
7	91.9	92.09	-0.189999999999984
8	91.92	92.11	-0.189999999999998
9	92	92.13	-0.129999999999995
10	92	92.21	-0.209999999999994
11	92.2	92.21	-0.00999999999999091
12	92.34	92.41	-0.0699999999999932
13	92.29	92.55	-0.259999999999991
14	92.37	92.5	-0.129999999999995
15	92.58	92.58	0
16	92.73	92.79	-0.0599999999999881
17	92.78	92.94	-0.159999999999997
18	92.82	92.99	-0.170000000000002
19	92.82	93.03	-0.209999999999994
20	92.99	93.03	-0.039999999999992
21	93.18	93.2	-0.0199999999999818
22	93.88	93.39	0.489999999999995
23	94.29	94.09	0.200000000000017
24	94.04	94.5	-0.459999999999994
25	93.6	94.25	-0.650000000000006
26	95.99	93.81	2.18000000000001
27	98.1	96.2	1.90000000000001
28	98.7	98.31	0.390000000000015
29	99.31	98.91	0.400000000000006
30	99.58	99.52	0.0600000000000023
31	99.68	99.79	-0.109999999999985
32	102.38	99.89	2.48999999999999
33	102.69	102.59	0.100000000000009
34	103.01	102.9	0.110000000000014
35	103.35	103.22	0.129999999999995
36	103.61	103.56	0.0500000000000114
37	102.59	103.82	-1.22999999999999
38	102.75	102.8	-0.0499999999999972
39	102.88	102.96	-0.0799999999999983
40	102.85	103.09	-0.239999999999995
41	103.16	103.06	0.100000000000009
42	103.17	103.37	-0.199999999999989
43	103.04	103.38	-0.339999999999989
44	103.09	103.25	-0.159999999999997
45	103.12	103.3	-0.179999999999993
46	103.68	103.33	0.350000000000009
47	103.75	103.89	-0.140000000000001
48	103.81	103.96	-0.149999999999991
49	104.23	104.02	0.210000000000008
50	104.58	104.44	0.140000000000001
51	104.76	104.79	-0.0299999999999869
52	104.83	104.97	-0.140000000000001
53	104.88	105.04	-0.159999999999997
54	105.7	105.09	0.610000000000014
55	105.34	105.91	-0.569999999999993
56	105.57	105.55	0.019999999999996
57	105.66	105.78	-0.11999999999999
58	105.7	105.87	-0.169999999999987
59	105.76	105.91	-0.149999999999991
60	105.76	105.97	-0.209999999999994

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 91.35 & 91.31 & 0.0400000000000063 \tabularnewline
4 & 91.52 & 91.56 & -0.039999999999992 \tabularnewline
5 & 91.45 & 91.73 & -0.279999999999987 \tabularnewline
6 & 91.88 & 91.66 & 0.219999999999999 \tabularnewline
7 & 91.9 & 92.09 & -0.189999999999984 \tabularnewline
8 & 91.92 & 92.11 & -0.189999999999998 \tabularnewline
9 & 92 & 92.13 & -0.129999999999995 \tabularnewline
10 & 92 & 92.21 & -0.209999999999994 \tabularnewline
11 & 92.2 & 92.21 & -0.00999999999999091 \tabularnewline
12 & 92.34 & 92.41 & -0.0699999999999932 \tabularnewline
13 & 92.29 & 92.55 & -0.259999999999991 \tabularnewline
14 & 92.37 & 92.5 & -0.129999999999995 \tabularnewline
15 & 92.58 & 92.58 & 0 \tabularnewline
16 & 92.73 & 92.79 & -0.0599999999999881 \tabularnewline
17 & 92.78 & 92.94 & -0.159999999999997 \tabularnewline
18 & 92.82 & 92.99 & -0.170000000000002 \tabularnewline
19 & 92.82 & 93.03 & -0.209999999999994 \tabularnewline
20 & 92.99 & 93.03 & -0.039999999999992 \tabularnewline
21 & 93.18 & 93.2 & -0.0199999999999818 \tabularnewline
22 & 93.88 & 93.39 & 0.489999999999995 \tabularnewline
23 & 94.29 & 94.09 & 0.200000000000017 \tabularnewline
24 & 94.04 & 94.5 & -0.459999999999994 \tabularnewline
25 & 93.6 & 94.25 & -0.650000000000006 \tabularnewline
26 & 95.99 & 93.81 & 2.18000000000001 \tabularnewline
27 & 98.1 & 96.2 & 1.90000000000001 \tabularnewline
28 & 98.7 & 98.31 & 0.390000000000015 \tabularnewline
29 & 99.31 & 98.91 & 0.400000000000006 \tabularnewline
30 & 99.58 & 99.52 & 0.0600000000000023 \tabularnewline
31 & 99.68 & 99.79 & -0.109999999999985 \tabularnewline
32 & 102.38 & 99.89 & 2.48999999999999 \tabularnewline
33 & 102.69 & 102.59 & 0.100000000000009 \tabularnewline
34 & 103.01 & 102.9 & 0.110000000000014 \tabularnewline
35 & 103.35 & 103.22 & 0.129999999999995 \tabularnewline
36 & 103.61 & 103.56 & 0.0500000000000114 \tabularnewline
37 & 102.59 & 103.82 & -1.22999999999999 \tabularnewline
38 & 102.75 & 102.8 & -0.0499999999999972 \tabularnewline
39 & 102.88 & 102.96 & -0.0799999999999983 \tabularnewline
40 & 102.85 & 103.09 & -0.239999999999995 \tabularnewline
41 & 103.16 & 103.06 & 0.100000000000009 \tabularnewline
42 & 103.17 & 103.37 & -0.199999999999989 \tabularnewline
43 & 103.04 & 103.38 & -0.339999999999989 \tabularnewline
44 & 103.09 & 103.25 & -0.159999999999997 \tabularnewline
45 & 103.12 & 103.3 & -0.179999999999993 \tabularnewline
46 & 103.68 & 103.33 & 0.350000000000009 \tabularnewline
47 & 103.75 & 103.89 & -0.140000000000001 \tabularnewline
48 & 103.81 & 103.96 & -0.149999999999991 \tabularnewline
49 & 104.23 & 104.02 & 0.210000000000008 \tabularnewline
50 & 104.58 & 104.44 & 0.140000000000001 \tabularnewline
51 & 104.76 & 104.79 & -0.0299999999999869 \tabularnewline
52 & 104.83 & 104.97 & -0.140000000000001 \tabularnewline
53 & 104.88 & 105.04 & -0.159999999999997 \tabularnewline
54 & 105.7 & 105.09 & 0.610000000000014 \tabularnewline
55 & 105.34 & 105.91 & -0.569999999999993 \tabularnewline
56 & 105.57 & 105.55 & 0.019999999999996 \tabularnewline
57 & 105.66 & 105.78 & -0.11999999999999 \tabularnewline
58 & 105.7 & 105.87 & -0.169999999999987 \tabularnewline
59 & 105.76 & 105.91 & -0.149999999999991 \tabularnewline
60 & 105.76 & 105.97 & -0.209999999999994 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]91.35[/C][C]91.31[/C][C]0.0400000000000063[/C][/ROW]
[ROW][C]4[/C][C]91.52[/C][C]91.56[/C][C]-0.039999999999992[/C][/ROW]
[ROW][C]5[/C][C]91.45[/C][C]91.73[/C][C]-0.279999999999987[/C][/ROW]
[ROW][C]6[/C][C]91.88[/C][C]91.66[/C][C]0.219999999999999[/C][/ROW]
[ROW][C]7[/C][C]91.9[/C][C]92.09[/C][C]-0.189999999999984[/C][/ROW]
[ROW][C]8[/C][C]91.92[/C][C]92.11[/C][C]-0.189999999999998[/C][/ROW]
[ROW][C]9[/C][C]92[/C][C]92.13[/C][C]-0.129999999999995[/C][/ROW]
[ROW][C]10[/C][C]92[/C][C]92.21[/C][C]-0.209999999999994[/C][/ROW]
[ROW][C]11[/C][C]92.2[/C][C]92.21[/C][C]-0.00999999999999091[/C][/ROW]
[ROW][C]12[/C][C]92.34[/C][C]92.41[/C][C]-0.0699999999999932[/C][/ROW]
[ROW][C]13[/C][C]92.29[/C][C]92.55[/C][C]-0.259999999999991[/C][/ROW]
[ROW][C]14[/C][C]92.37[/C][C]92.5[/C][C]-0.129999999999995[/C][/ROW]
[ROW][C]15[/C][C]92.58[/C][C]92.58[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]92.73[/C][C]92.79[/C][C]-0.0599999999999881[/C][/ROW]
[ROW][C]17[/C][C]92.78[/C][C]92.94[/C][C]-0.159999999999997[/C][/ROW]
[ROW][C]18[/C][C]92.82[/C][C]92.99[/C][C]-0.170000000000002[/C][/ROW]
[ROW][C]19[/C][C]92.82[/C][C]93.03[/C][C]-0.209999999999994[/C][/ROW]
[ROW][C]20[/C][C]92.99[/C][C]93.03[/C][C]-0.039999999999992[/C][/ROW]
[ROW][C]21[/C][C]93.18[/C][C]93.2[/C][C]-0.0199999999999818[/C][/ROW]
[ROW][C]22[/C][C]93.88[/C][C]93.39[/C][C]0.489999999999995[/C][/ROW]
[ROW][C]23[/C][C]94.29[/C][C]94.09[/C][C]0.200000000000017[/C][/ROW]
[ROW][C]24[/C][C]94.04[/C][C]94.5[/C][C]-0.459999999999994[/C][/ROW]
[ROW][C]25[/C][C]93.6[/C][C]94.25[/C][C]-0.650000000000006[/C][/ROW]
[ROW][C]26[/C][C]95.99[/C][C]93.81[/C][C]2.18000000000001[/C][/ROW]
[ROW][C]27[/C][C]98.1[/C][C]96.2[/C][C]1.90000000000001[/C][/ROW]
[ROW][C]28[/C][C]98.7[/C][C]98.31[/C][C]0.390000000000015[/C][/ROW]
[ROW][C]29[/C][C]99.31[/C][C]98.91[/C][C]0.400000000000006[/C][/ROW]
[ROW][C]30[/C][C]99.58[/C][C]99.52[/C][C]0.0600000000000023[/C][/ROW]
[ROW][C]31[/C][C]99.68[/C][C]99.79[/C][C]-0.109999999999985[/C][/ROW]
[ROW][C]32[/C][C]102.38[/C][C]99.89[/C][C]2.48999999999999[/C][/ROW]
[ROW][C]33[/C][C]102.69[/C][C]102.59[/C][C]0.100000000000009[/C][/ROW]
[ROW][C]34[/C][C]103.01[/C][C]102.9[/C][C]0.110000000000014[/C][/ROW]
[ROW][C]35[/C][C]103.35[/C][C]103.22[/C][C]0.129999999999995[/C][/ROW]
[ROW][C]36[/C][C]103.61[/C][C]103.56[/C][C]0.0500000000000114[/C][/ROW]
[ROW][C]37[/C][C]102.59[/C][C]103.82[/C][C]-1.22999999999999[/C][/ROW]
[ROW][C]38[/C][C]102.75[/C][C]102.8[/C][C]-0.0499999999999972[/C][/ROW]
[ROW][C]39[/C][C]102.88[/C][C]102.96[/C][C]-0.0799999999999983[/C][/ROW]
[ROW][C]40[/C][C]102.85[/C][C]103.09[/C][C]-0.239999999999995[/C][/ROW]
[ROW][C]41[/C][C]103.16[/C][C]103.06[/C][C]0.100000000000009[/C][/ROW]
[ROW][C]42[/C][C]103.17[/C][C]103.37[/C][C]-0.199999999999989[/C][/ROW]
[ROW][C]43[/C][C]103.04[/C][C]103.38[/C][C]-0.339999999999989[/C][/ROW]
[ROW][C]44[/C][C]103.09[/C][C]103.25[/C][C]-0.159999999999997[/C][/ROW]
[ROW][C]45[/C][C]103.12[/C][C]103.3[/C][C]-0.179999999999993[/C][/ROW]
[ROW][C]46[/C][C]103.68[/C][C]103.33[/C][C]0.350000000000009[/C][/ROW]
[ROW][C]47[/C][C]103.75[/C][C]103.89[/C][C]-0.140000000000001[/C][/ROW]
[ROW][C]48[/C][C]103.81[/C][C]103.96[/C][C]-0.149999999999991[/C][/ROW]
[ROW][C]49[/C][C]104.23[/C][C]104.02[/C][C]0.210000000000008[/C][/ROW]
[ROW][C]50[/C][C]104.58[/C][C]104.44[/C][C]0.140000000000001[/C][/ROW]
[ROW][C]51[/C][C]104.76[/C][C]104.79[/C][C]-0.0299999999999869[/C][/ROW]
[ROW][C]52[/C][C]104.83[/C][C]104.97[/C][C]-0.140000000000001[/C][/ROW]
[ROW][C]53[/C][C]104.88[/C][C]105.04[/C][C]-0.159999999999997[/C][/ROW]
[ROW][C]54[/C][C]105.7[/C][C]105.09[/C][C]0.610000000000014[/C][/ROW]
[ROW][C]55[/C][C]105.34[/C][C]105.91[/C][C]-0.569999999999993[/C][/ROW]
[ROW][C]56[/C][C]105.57[/C][C]105.55[/C][C]0.019999999999996[/C][/ROW]
[ROW][C]57[/C][C]105.66[/C][C]105.78[/C][C]-0.11999999999999[/C][/ROW]
[ROW][C]58[/C][C]105.7[/C][C]105.87[/C][C]-0.169999999999987[/C][/ROW]
[ROW][C]59[/C][C]105.76[/C][C]105.91[/C][C]-0.149999999999991[/C][/ROW]
[ROW][C]60[/C][C]105.76[/C][C]105.97[/C][C]-0.209999999999994[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	91.35	91.31	0.0400000000000063
4	91.52	91.56	-0.039999999999992
5	91.45	91.73	-0.279999999999987
6	91.88	91.66	0.219999999999999
7	91.9	92.09	-0.189999999999984
8	91.92	92.11	-0.189999999999998
9	92	92.13	-0.129999999999995
10	92	92.21	-0.209999999999994
11	92.2	92.21	-0.00999999999999091
12	92.34	92.41	-0.0699999999999932
13	92.29	92.55	-0.259999999999991
14	92.37	92.5	-0.129999999999995
15	92.58	92.58	0
16	92.73	92.79	-0.0599999999999881
17	92.78	92.94	-0.159999999999997
18	92.82	92.99	-0.170000000000002
19	92.82	93.03	-0.209999999999994
20	92.99	93.03	-0.039999999999992
21	93.18	93.2	-0.0199999999999818
22	93.88	93.39	0.489999999999995
23	94.29	94.09	0.200000000000017
24	94.04	94.5	-0.459999999999994
25	93.6	94.25	-0.650000000000006
26	95.99	93.81	2.18000000000001
27	98.1	96.2	1.90000000000001
28	98.7	98.31	0.390000000000015
29	99.31	98.91	0.400000000000006
30	99.58	99.52	0.0600000000000023
31	99.68	99.79	-0.109999999999985
32	102.38	99.89	2.48999999999999
33	102.69	102.59	0.100000000000009
34	103.01	102.9	0.110000000000014
35	103.35	103.22	0.129999999999995
36	103.61	103.56	0.0500000000000114
37	102.59	103.82	-1.22999999999999
38	102.75	102.8	-0.0499999999999972
39	102.88	102.96	-0.0799999999999983
40	102.85	103.09	-0.239999999999995
41	103.16	103.06	0.100000000000009
42	103.17	103.37	-0.199999999999989
43	103.04	103.38	-0.339999999999989
44	103.09	103.25	-0.159999999999997
45	103.12	103.3	-0.179999999999993
46	103.68	103.33	0.350000000000009
47	103.75	103.89	-0.140000000000001
48	103.81	103.96	-0.149999999999991
49	104.23	104.02	0.210000000000008
50	104.58	104.44	0.140000000000001
51	104.76	104.79	-0.0299999999999869
52	104.83	104.97	-0.140000000000001
53	104.88	105.04	-0.159999999999997
54	105.7	105.09	0.610000000000014
55	105.34	105.91	-0.569999999999993
56	105.57	105.55	0.019999999999996
57	105.66	105.78	-0.11999999999999
58	105.7	105.87	-0.169999999999987
59	105.76	105.91	-0.149999999999991
60	105.76	105.97	-0.209999999999994

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	105.97	104.835988167424	107.104011832576
62	106.18	104.57626508648	107.78373491352
63	106.39	104.425833889595	108.354166110405
64	106.6	104.331976334849	108.868023665151
65	106.81	104.274272455072	109.345727544928
66	107.02	104.242249647911	109.797750352089
67	107.23	104.2296867072	110.2303132928
68	107.44	104.23253017296	110.64746982704
69	107.65	104.247964502273	111.052035497727
70	107.86	104.273939715479	111.446060284521
71	108.07	104.308908243523	111.831091756477
72	108.28	104.351667779189	112.208332220811

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 105.97 & 104.835988167424 & 107.104011832576 \tabularnewline
62 & 106.18 & 104.57626508648 & 107.78373491352 \tabularnewline
63 & 106.39 & 104.425833889595 & 108.354166110405 \tabularnewline
64 & 106.6 & 104.331976334849 & 108.868023665151 \tabularnewline
65 & 106.81 & 104.274272455072 & 109.345727544928 \tabularnewline
66 & 107.02 & 104.242249647911 & 109.797750352089 \tabularnewline
67 & 107.23 & 104.2296867072 & 110.2303132928 \tabularnewline
68 & 107.44 & 104.23253017296 & 110.64746982704 \tabularnewline
69 & 107.65 & 104.247964502273 & 111.052035497727 \tabularnewline
70 & 107.86 & 104.273939715479 & 111.446060284521 \tabularnewline
71 & 108.07 & 104.308908243523 & 111.831091756477 \tabularnewline
72 & 108.28 & 104.351667779189 & 112.208332220811 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]61[/C][C]105.97[/C][C]104.835988167424[/C][C]107.104011832576[/C][/ROW]
[ROW][C]62[/C][C]106.18[/C][C]104.57626508648[/C][C]107.78373491352[/C][/ROW]
[ROW][C]63[/C][C]106.39[/C][C]104.425833889595[/C][C]108.354166110405[/C][/ROW]
[ROW][C]64[/C][C]106.6[/C][C]104.331976334849[/C][C]108.868023665151[/C][/ROW]
[ROW][C]65[/C][C]106.81[/C][C]104.274272455072[/C][C]109.345727544928[/C][/ROW]
[ROW][C]66[/C][C]107.02[/C][C]104.242249647911[/C][C]109.797750352089[/C][/ROW]
[ROW][C]67[/C][C]107.23[/C][C]104.2296867072[/C][C]110.2303132928[/C][/ROW]
[ROW][C]68[/C][C]107.44[/C][C]104.23253017296[/C][C]110.64746982704[/C][/ROW]
[ROW][C]69[/C][C]107.65[/C][C]104.247964502273[/C][C]111.052035497727[/C][/ROW]
[ROW][C]70[/C][C]107.86[/C][C]104.273939715479[/C][C]111.446060284521[/C][/ROW]
[ROW][C]71[/C][C]108.07[/C][C]104.308908243523[/C][C]111.831091756477[/C][/ROW]
[ROW][C]72[/C][C]108.28[/C][C]104.351667779189[/C][C]112.208332220811[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
61	105.97	104.835988167424	107.104011832576
62	106.18	104.57626508648	107.78373491352
63	106.39	104.425833889595	108.354166110405
64	106.6	104.331976334849	108.868023665151
65	106.81	104.274272455072	109.345727544928
66	107.02	104.242249647911	109.797750352089
67	107.23	104.2296867072	110.2303132928
68	107.44	104.23253017296	110.64746982704
69	107.65	104.247964502273	111.052035497727
70	107.86	104.273939715479	111.446060284521
71	108.07	104.308908243523	111.831091756477
72	108.28	104.351667779189	112.208332220811

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