Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 18 Dec 2013 09:39:37 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Dec/18/t13873776016dpvydcp9421ux7.htm/, Retrieved Fri, 29 Mar 2024 05:36:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232439, Retrieved Fri, 29 Mar 2024 05:36:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact159
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Harrell-Davis Quantiles] [] [2013-10-03 12:28:46] [14940b3acdb362d975a3925771725f1c]
- R P   [Harrell-Davis Quantiles] [] [2013-10-07 06:42:43] [bc3b96987d5d985d411360ed2ed90621]
- RMPD      [Exponential Smoothing] [] [2013-12-18 14:39:37] [c1a61ab38fcc49939d713dd54579d7ce] [Current]
Feedback Forum

Post a new message
Dataseries X:
107.2
107.56
107.72
108.14
108.16
108.16
108.16
108.1
108.95
110.49
110.72
110.82
110.82
110.75
110.71
110.86
110.84
110.84
110.84
110.92
111.46
112.46
113.04
113.15
113.15
113.21
113.37
113.47
113.71
113.71
113.71
113.8
115.46
117
117.94
118.08
118.08
118.47
118.49
118.45
118.54
118.55
118.55
118.55
119.04
121.37
122
122.14
122.14
122.03
121.91
122.23
121.73
121.83
121.83
122.49
123.02
125.98
126.13
126.39
126.39
126.57
126.87
127.26
126.82
126.7
126.7
126.7
128.53
130.37
130.39
130.65
130.65
130.65
130.85
130.89
130.85
131.6
131.6
131.6
132.53
133.05
133.49
133.46




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time7 seconds
R Server'George Udny Yule' @ yule.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 & 7 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232439&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]7 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232439&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232439&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time7 seconds
R Server'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0
gammaFALSE

\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=232439&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=232439&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232439&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
ParameterValue
alpha1
beta0
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3107.72107.92-0.200000000000003
4108.14108.080.0600000000000023
5108.16108.5-0.340000000000003
6108.16108.52-0.359999999999999
7108.16108.52-0.359999999999999
8108.1108.52-0.420000000000002
9108.95108.460.490000000000009
10110.49109.311.17999999999999
11110.72110.85-0.129999999999995
12110.82111.08-0.260000000000005
13110.82111.18-0.359999999999999
14110.75111.18-0.429999999999993
15110.71111.11-0.400000000000006
16110.86111.07-0.209999999999994
17110.84111.22-0.379999999999995
18110.84111.2-0.359999999999999
19110.84111.2-0.359999999999999
20110.92111.2-0.280000000000001
21111.46111.280.179999999999993
22112.46111.820.640000000000001
23113.04112.820.220000000000013
24113.15113.4-0.25
25113.15113.51-0.359999999999999
26113.21113.51-0.300000000000011
27113.37113.57-0.199999999999989
28113.47113.73-0.260000000000005
29113.71113.83-0.120000000000005
30113.71114.07-0.359999999999999
31113.71114.07-0.359999999999999
32113.8114.07-0.269999999999996
33115.46114.161.3
34117115.821.18000000000001
35117.94117.360.579999999999998
36118.08118.3-0.219999999999999
37118.08118.44-0.359999999999999
38118.47118.440.0300000000000011
39118.49118.83-0.340000000000003
40118.45118.85-0.399999999999991
41118.54118.81-0.269999999999996
42118.55118.9-0.350000000000009
43118.55118.91-0.359999999999999
44118.55118.91-0.359999999999999
45119.04118.910.13000000000001
46121.37119.41.97
47122121.730.269999999999996
48122.14122.36-0.219999999999999
49122.14122.5-0.359999999999999
50122.03122.5-0.469999999999999
51121.91122.39-0.480000000000004
52122.23122.27-0.039999999999992
53121.73122.59-0.859999999999999
54121.83122.09-0.260000000000005
55121.83122.19-0.359999999999999
56122.49122.190.299999999999997
57123.02122.850.170000000000002
58125.98123.382.60000000000001
59126.13126.34-0.210000000000008
60126.39126.49-0.0999999999999943
61126.39126.75-0.359999999999999
62126.57126.75-0.180000000000007
63126.87126.93-0.0599999999999881
64127.26127.230.0300000000000011
65126.82127.62-0.800000000000011
66126.7127.18-0.47999999999999
67126.7127.06-0.359999999999999
68126.7127.06-0.359999999999999
69128.53127.061.47
70130.37128.891.48000000000002
71130.39130.73-0.340000000000032
72130.65130.75-0.0999999999999943
73130.65131.01-0.359999999999985
74130.65131.01-0.359999999999985
75130.85131.01-0.159999999999997
76130.89131.21-0.319999999999993
77130.85131.25-0.400000000000006
78131.6131.210.390000000000015
79131.6131.96-0.359999999999985
80131.6131.96-0.359999999999985
81132.53131.960.570000000000022
82133.05132.890.160000000000025
83133.49133.410.0799999999999841
84133.46133.85-0.390000000000015

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 107.72 & 107.92 & -0.200000000000003 \tabularnewline
4 & 108.14 & 108.08 & 0.0600000000000023 \tabularnewline
5 & 108.16 & 108.5 & -0.340000000000003 \tabularnewline
6 & 108.16 & 108.52 & -0.359999999999999 \tabularnewline
7 & 108.16 & 108.52 & -0.359999999999999 \tabularnewline
8 & 108.1 & 108.52 & -0.420000000000002 \tabularnewline
9 & 108.95 & 108.46 & 0.490000000000009 \tabularnewline
10 & 110.49 & 109.31 & 1.17999999999999 \tabularnewline
11 & 110.72 & 110.85 & -0.129999999999995 \tabularnewline
12 & 110.82 & 111.08 & -0.260000000000005 \tabularnewline
13 & 110.82 & 111.18 & -0.359999999999999 \tabularnewline
14 & 110.75 & 111.18 & -0.429999999999993 \tabularnewline
15 & 110.71 & 111.11 & -0.400000000000006 \tabularnewline
16 & 110.86 & 111.07 & -0.209999999999994 \tabularnewline
17 & 110.84 & 111.22 & -0.379999999999995 \tabularnewline
18 & 110.84 & 111.2 & -0.359999999999999 \tabularnewline
19 & 110.84 & 111.2 & -0.359999999999999 \tabularnewline
20 & 110.92 & 111.2 & -0.280000000000001 \tabularnewline
21 & 111.46 & 111.28 & 0.179999999999993 \tabularnewline
22 & 112.46 & 111.82 & 0.640000000000001 \tabularnewline
23 & 113.04 & 112.82 & 0.220000000000013 \tabularnewline
24 & 113.15 & 113.4 & -0.25 \tabularnewline
25 & 113.15 & 113.51 & -0.359999999999999 \tabularnewline
26 & 113.21 & 113.51 & -0.300000000000011 \tabularnewline
27 & 113.37 & 113.57 & -0.199999999999989 \tabularnewline
28 & 113.47 & 113.73 & -0.260000000000005 \tabularnewline
29 & 113.71 & 113.83 & -0.120000000000005 \tabularnewline
30 & 113.71 & 114.07 & -0.359999999999999 \tabularnewline
31 & 113.71 & 114.07 & -0.359999999999999 \tabularnewline
32 & 113.8 & 114.07 & -0.269999999999996 \tabularnewline
33 & 115.46 & 114.16 & 1.3 \tabularnewline
34 & 117 & 115.82 & 1.18000000000001 \tabularnewline
35 & 117.94 & 117.36 & 0.579999999999998 \tabularnewline
36 & 118.08 & 118.3 & -0.219999999999999 \tabularnewline
37 & 118.08 & 118.44 & -0.359999999999999 \tabularnewline
38 & 118.47 & 118.44 & 0.0300000000000011 \tabularnewline
39 & 118.49 & 118.83 & -0.340000000000003 \tabularnewline
40 & 118.45 & 118.85 & -0.399999999999991 \tabularnewline
41 & 118.54 & 118.81 & -0.269999999999996 \tabularnewline
42 & 118.55 & 118.9 & -0.350000000000009 \tabularnewline
43 & 118.55 & 118.91 & -0.359999999999999 \tabularnewline
44 & 118.55 & 118.91 & -0.359999999999999 \tabularnewline
45 & 119.04 & 118.91 & 0.13000000000001 \tabularnewline
46 & 121.37 & 119.4 & 1.97 \tabularnewline
47 & 122 & 121.73 & 0.269999999999996 \tabularnewline
48 & 122.14 & 122.36 & -0.219999999999999 \tabularnewline
49 & 122.14 & 122.5 & -0.359999999999999 \tabularnewline
50 & 122.03 & 122.5 & -0.469999999999999 \tabularnewline
51 & 121.91 & 122.39 & -0.480000000000004 \tabularnewline
52 & 122.23 & 122.27 & -0.039999999999992 \tabularnewline
53 & 121.73 & 122.59 & -0.859999999999999 \tabularnewline
54 & 121.83 & 122.09 & -0.260000000000005 \tabularnewline
55 & 121.83 & 122.19 & -0.359999999999999 \tabularnewline
56 & 122.49 & 122.19 & 0.299999999999997 \tabularnewline
57 & 123.02 & 122.85 & 0.170000000000002 \tabularnewline
58 & 125.98 & 123.38 & 2.60000000000001 \tabularnewline
59 & 126.13 & 126.34 & -0.210000000000008 \tabularnewline
60 & 126.39 & 126.49 & -0.0999999999999943 \tabularnewline
61 & 126.39 & 126.75 & -0.359999999999999 \tabularnewline
62 & 126.57 & 126.75 & -0.180000000000007 \tabularnewline
63 & 126.87 & 126.93 & -0.0599999999999881 \tabularnewline
64 & 127.26 & 127.23 & 0.0300000000000011 \tabularnewline
65 & 126.82 & 127.62 & -0.800000000000011 \tabularnewline
66 & 126.7 & 127.18 & -0.47999999999999 \tabularnewline
67 & 126.7 & 127.06 & -0.359999999999999 \tabularnewline
68 & 126.7 & 127.06 & -0.359999999999999 \tabularnewline
69 & 128.53 & 127.06 & 1.47 \tabularnewline
70 & 130.37 & 128.89 & 1.48000000000002 \tabularnewline
71 & 130.39 & 130.73 & -0.340000000000032 \tabularnewline
72 & 130.65 & 130.75 & -0.0999999999999943 \tabularnewline
73 & 130.65 & 131.01 & -0.359999999999985 \tabularnewline
74 & 130.65 & 131.01 & -0.359999999999985 \tabularnewline
75 & 130.85 & 131.01 & -0.159999999999997 \tabularnewline
76 & 130.89 & 131.21 & -0.319999999999993 \tabularnewline
77 & 130.85 & 131.25 & -0.400000000000006 \tabularnewline
78 & 131.6 & 131.21 & 0.390000000000015 \tabularnewline
79 & 131.6 & 131.96 & -0.359999999999985 \tabularnewline
80 & 131.6 & 131.96 & -0.359999999999985 \tabularnewline
81 & 132.53 & 131.96 & 0.570000000000022 \tabularnewline
82 & 133.05 & 132.89 & 0.160000000000025 \tabularnewline
83 & 133.49 & 133.41 & 0.0799999999999841 \tabularnewline
84 & 133.46 & 133.85 & -0.390000000000015 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232439&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]107.72[/C][C]107.92[/C][C]-0.200000000000003[/C][/ROW]
[ROW][C]4[/C][C]108.14[/C][C]108.08[/C][C]0.0600000000000023[/C][/ROW]
[ROW][C]5[/C][C]108.16[/C][C]108.5[/C][C]-0.340000000000003[/C][/ROW]
[ROW][C]6[/C][C]108.16[/C][C]108.52[/C][C]-0.359999999999999[/C][/ROW]
[ROW][C]7[/C][C]108.16[/C][C]108.52[/C][C]-0.359999999999999[/C][/ROW]
[ROW][C]8[/C][C]108.1[/C][C]108.52[/C][C]-0.420000000000002[/C][/ROW]
[ROW][C]9[/C][C]108.95[/C][C]108.46[/C][C]0.490000000000009[/C][/ROW]
[ROW][C]10[/C][C]110.49[/C][C]109.31[/C][C]1.17999999999999[/C][/ROW]
[ROW][C]11[/C][C]110.72[/C][C]110.85[/C][C]-0.129999999999995[/C][/ROW]
[ROW][C]12[/C][C]110.82[/C][C]111.08[/C][C]-0.260000000000005[/C][/ROW]
[ROW][C]13[/C][C]110.82[/C][C]111.18[/C][C]-0.359999999999999[/C][/ROW]
[ROW][C]14[/C][C]110.75[/C][C]111.18[/C][C]-0.429999999999993[/C][/ROW]
[ROW][C]15[/C][C]110.71[/C][C]111.11[/C][C]-0.400000000000006[/C][/ROW]
[ROW][C]16[/C][C]110.86[/C][C]111.07[/C][C]-0.209999999999994[/C][/ROW]
[ROW][C]17[/C][C]110.84[/C][C]111.22[/C][C]-0.379999999999995[/C][/ROW]
[ROW][C]18[/C][C]110.84[/C][C]111.2[/C][C]-0.359999999999999[/C][/ROW]
[ROW][C]19[/C][C]110.84[/C][C]111.2[/C][C]-0.359999999999999[/C][/ROW]
[ROW][C]20[/C][C]110.92[/C][C]111.2[/C][C]-0.280000000000001[/C][/ROW]
[ROW][C]21[/C][C]111.46[/C][C]111.28[/C][C]0.179999999999993[/C][/ROW]
[ROW][C]22[/C][C]112.46[/C][C]111.82[/C][C]0.640000000000001[/C][/ROW]
[ROW][C]23[/C][C]113.04[/C][C]112.82[/C][C]0.220000000000013[/C][/ROW]
[ROW][C]24[/C][C]113.15[/C][C]113.4[/C][C]-0.25[/C][/ROW]
[ROW][C]25[/C][C]113.15[/C][C]113.51[/C][C]-0.359999999999999[/C][/ROW]
[ROW][C]26[/C][C]113.21[/C][C]113.51[/C][C]-0.300000000000011[/C][/ROW]
[ROW][C]27[/C][C]113.37[/C][C]113.57[/C][C]-0.199999999999989[/C][/ROW]
[ROW][C]28[/C][C]113.47[/C][C]113.73[/C][C]-0.260000000000005[/C][/ROW]
[ROW][C]29[/C][C]113.71[/C][C]113.83[/C][C]-0.120000000000005[/C][/ROW]
[ROW][C]30[/C][C]113.71[/C][C]114.07[/C][C]-0.359999999999999[/C][/ROW]
[ROW][C]31[/C][C]113.71[/C][C]114.07[/C][C]-0.359999999999999[/C][/ROW]
[ROW][C]32[/C][C]113.8[/C][C]114.07[/C][C]-0.269999999999996[/C][/ROW]
[ROW][C]33[/C][C]115.46[/C][C]114.16[/C][C]1.3[/C][/ROW]
[ROW][C]34[/C][C]117[/C][C]115.82[/C][C]1.18000000000001[/C][/ROW]
[ROW][C]35[/C][C]117.94[/C][C]117.36[/C][C]0.579999999999998[/C][/ROW]
[ROW][C]36[/C][C]118.08[/C][C]118.3[/C][C]-0.219999999999999[/C][/ROW]
[ROW][C]37[/C][C]118.08[/C][C]118.44[/C][C]-0.359999999999999[/C][/ROW]
[ROW][C]38[/C][C]118.47[/C][C]118.44[/C][C]0.0300000000000011[/C][/ROW]
[ROW][C]39[/C][C]118.49[/C][C]118.83[/C][C]-0.340000000000003[/C][/ROW]
[ROW][C]40[/C][C]118.45[/C][C]118.85[/C][C]-0.399999999999991[/C][/ROW]
[ROW][C]41[/C][C]118.54[/C][C]118.81[/C][C]-0.269999999999996[/C][/ROW]
[ROW][C]42[/C][C]118.55[/C][C]118.9[/C][C]-0.350000000000009[/C][/ROW]
[ROW][C]43[/C][C]118.55[/C][C]118.91[/C][C]-0.359999999999999[/C][/ROW]
[ROW][C]44[/C][C]118.55[/C][C]118.91[/C][C]-0.359999999999999[/C][/ROW]
[ROW][C]45[/C][C]119.04[/C][C]118.91[/C][C]0.13000000000001[/C][/ROW]
[ROW][C]46[/C][C]121.37[/C][C]119.4[/C][C]1.97[/C][/ROW]
[ROW][C]47[/C][C]122[/C][C]121.73[/C][C]0.269999999999996[/C][/ROW]
[ROW][C]48[/C][C]122.14[/C][C]122.36[/C][C]-0.219999999999999[/C][/ROW]
[ROW][C]49[/C][C]122.14[/C][C]122.5[/C][C]-0.359999999999999[/C][/ROW]
[ROW][C]50[/C][C]122.03[/C][C]122.5[/C][C]-0.469999999999999[/C][/ROW]
[ROW][C]51[/C][C]121.91[/C][C]122.39[/C][C]-0.480000000000004[/C][/ROW]
[ROW][C]52[/C][C]122.23[/C][C]122.27[/C][C]-0.039999999999992[/C][/ROW]
[ROW][C]53[/C][C]121.73[/C][C]122.59[/C][C]-0.859999999999999[/C][/ROW]
[ROW][C]54[/C][C]121.83[/C][C]122.09[/C][C]-0.260000000000005[/C][/ROW]
[ROW][C]55[/C][C]121.83[/C][C]122.19[/C][C]-0.359999999999999[/C][/ROW]
[ROW][C]56[/C][C]122.49[/C][C]122.19[/C][C]0.299999999999997[/C][/ROW]
[ROW][C]57[/C][C]123.02[/C][C]122.85[/C][C]0.170000000000002[/C][/ROW]
[ROW][C]58[/C][C]125.98[/C][C]123.38[/C][C]2.60000000000001[/C][/ROW]
[ROW][C]59[/C][C]126.13[/C][C]126.34[/C][C]-0.210000000000008[/C][/ROW]
[ROW][C]60[/C][C]126.39[/C][C]126.49[/C][C]-0.0999999999999943[/C][/ROW]
[ROW][C]61[/C][C]126.39[/C][C]126.75[/C][C]-0.359999999999999[/C][/ROW]
[ROW][C]62[/C][C]126.57[/C][C]126.75[/C][C]-0.180000000000007[/C][/ROW]
[ROW][C]63[/C][C]126.87[/C][C]126.93[/C][C]-0.0599999999999881[/C][/ROW]
[ROW][C]64[/C][C]127.26[/C][C]127.23[/C][C]0.0300000000000011[/C][/ROW]
[ROW][C]65[/C][C]126.82[/C][C]127.62[/C][C]-0.800000000000011[/C][/ROW]
[ROW][C]66[/C][C]126.7[/C][C]127.18[/C][C]-0.47999999999999[/C][/ROW]
[ROW][C]67[/C][C]126.7[/C][C]127.06[/C][C]-0.359999999999999[/C][/ROW]
[ROW][C]68[/C][C]126.7[/C][C]127.06[/C][C]-0.359999999999999[/C][/ROW]
[ROW][C]69[/C][C]128.53[/C][C]127.06[/C][C]1.47[/C][/ROW]
[ROW][C]70[/C][C]130.37[/C][C]128.89[/C][C]1.48000000000002[/C][/ROW]
[ROW][C]71[/C][C]130.39[/C][C]130.73[/C][C]-0.340000000000032[/C][/ROW]
[ROW][C]72[/C][C]130.65[/C][C]130.75[/C][C]-0.0999999999999943[/C][/ROW]
[ROW][C]73[/C][C]130.65[/C][C]131.01[/C][C]-0.359999999999985[/C][/ROW]
[ROW][C]74[/C][C]130.65[/C][C]131.01[/C][C]-0.359999999999985[/C][/ROW]
[ROW][C]75[/C][C]130.85[/C][C]131.01[/C][C]-0.159999999999997[/C][/ROW]
[ROW][C]76[/C][C]130.89[/C][C]131.21[/C][C]-0.319999999999993[/C][/ROW]
[ROW][C]77[/C][C]130.85[/C][C]131.25[/C][C]-0.400000000000006[/C][/ROW]
[ROW][C]78[/C][C]131.6[/C][C]131.21[/C][C]0.390000000000015[/C][/ROW]
[ROW][C]79[/C][C]131.6[/C][C]131.96[/C][C]-0.359999999999985[/C][/ROW]
[ROW][C]80[/C][C]131.6[/C][C]131.96[/C][C]-0.359999999999985[/C][/ROW]
[ROW][C]81[/C][C]132.53[/C][C]131.96[/C][C]0.570000000000022[/C][/ROW]
[ROW][C]82[/C][C]133.05[/C][C]132.89[/C][C]0.160000000000025[/C][/ROW]
[ROW][C]83[/C][C]133.49[/C][C]133.41[/C][C]0.0799999999999841[/C][/ROW]
[ROW][C]84[/C][C]133.46[/C][C]133.85[/C][C]-0.390000000000015[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232439&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232439&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
tObservedFittedResiduals
3107.72107.92-0.200000000000003
4108.14108.080.0600000000000023
5108.16108.5-0.340000000000003
6108.16108.52-0.359999999999999
7108.16108.52-0.359999999999999
8108.1108.52-0.420000000000002
9108.95108.460.490000000000009
10110.49109.311.17999999999999
11110.72110.85-0.129999999999995
12110.82111.08-0.260000000000005
13110.82111.18-0.359999999999999
14110.75111.18-0.429999999999993
15110.71111.11-0.400000000000006
16110.86111.07-0.209999999999994
17110.84111.22-0.379999999999995
18110.84111.2-0.359999999999999
19110.84111.2-0.359999999999999
20110.92111.2-0.280000000000001
21111.46111.280.179999999999993
22112.46111.820.640000000000001
23113.04112.820.220000000000013
24113.15113.4-0.25
25113.15113.51-0.359999999999999
26113.21113.51-0.300000000000011
27113.37113.57-0.199999999999989
28113.47113.73-0.260000000000005
29113.71113.83-0.120000000000005
30113.71114.07-0.359999999999999
31113.71114.07-0.359999999999999
32113.8114.07-0.269999999999996
33115.46114.161.3
34117115.821.18000000000001
35117.94117.360.579999999999998
36118.08118.3-0.219999999999999
37118.08118.44-0.359999999999999
38118.47118.440.0300000000000011
39118.49118.83-0.340000000000003
40118.45118.85-0.399999999999991
41118.54118.81-0.269999999999996
42118.55118.9-0.350000000000009
43118.55118.91-0.359999999999999
44118.55118.91-0.359999999999999
45119.04118.910.13000000000001
46121.37119.41.97
47122121.730.269999999999996
48122.14122.36-0.219999999999999
49122.14122.5-0.359999999999999
50122.03122.5-0.469999999999999
51121.91122.39-0.480000000000004
52122.23122.27-0.039999999999992
53121.73122.59-0.859999999999999
54121.83122.09-0.260000000000005
55121.83122.19-0.359999999999999
56122.49122.190.299999999999997
57123.02122.850.170000000000002
58125.98123.382.60000000000001
59126.13126.34-0.210000000000008
60126.39126.49-0.0999999999999943
61126.39126.75-0.359999999999999
62126.57126.75-0.180000000000007
63126.87126.93-0.0599999999999881
64127.26127.230.0300000000000011
65126.82127.62-0.800000000000011
66126.7127.18-0.47999999999999
67126.7127.06-0.359999999999999
68126.7127.06-0.359999999999999
69128.53127.061.47
70130.37128.891.48000000000002
71130.39130.73-0.340000000000032
72130.65130.75-0.0999999999999943
73130.65131.01-0.359999999999985
74130.65131.01-0.359999999999985
75130.85131.01-0.159999999999997
76130.89131.21-0.319999999999993
77130.85131.25-0.400000000000006
78131.6131.210.390000000000015
79131.6131.96-0.359999999999985
80131.6131.96-0.359999999999985
81132.53131.960.570000000000022
82133.05132.890.160000000000025
83133.49133.410.0799999999999841
84133.46133.85-0.390000000000015







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85133.82132.659059657706134.980940342294
86134.18132.538182422821135.821817577179
87134.54132.52919234259136.55080765741
88134.9132.578119315412137.221880684588
89135.26132.664058476808137.855941523192
90135.62132.776288539567138.463711460433
91135.98132.908440567307139.051559432693
92136.34133.056364845643139.623635154357
93136.7133.217178973117140.182821026883
94137.06133.388784290775140.731215709225
95137.42133.569596480623141.270403519377
96137.78133.75838468518141.80161531482

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 133.82 & 132.659059657706 & 134.980940342294 \tabularnewline
86 & 134.18 & 132.538182422821 & 135.821817577179 \tabularnewline
87 & 134.54 & 132.52919234259 & 136.55080765741 \tabularnewline
88 & 134.9 & 132.578119315412 & 137.221880684588 \tabularnewline
89 & 135.26 & 132.664058476808 & 137.855941523192 \tabularnewline
90 & 135.62 & 132.776288539567 & 138.463711460433 \tabularnewline
91 & 135.98 & 132.908440567307 & 139.051559432693 \tabularnewline
92 & 136.34 & 133.056364845643 & 139.623635154357 \tabularnewline
93 & 136.7 & 133.217178973117 & 140.182821026883 \tabularnewline
94 & 137.06 & 133.388784290775 & 140.731215709225 \tabularnewline
95 & 137.42 & 133.569596480623 & 141.270403519377 \tabularnewline
96 & 137.78 & 133.75838468518 & 141.80161531482 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232439&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]133.82[/C][C]132.659059657706[/C][C]134.980940342294[/C][/ROW]
[ROW][C]86[/C][C]134.18[/C][C]132.538182422821[/C][C]135.821817577179[/C][/ROW]
[ROW][C]87[/C][C]134.54[/C][C]132.52919234259[/C][C]136.55080765741[/C][/ROW]
[ROW][C]88[/C][C]134.9[/C][C]132.578119315412[/C][C]137.221880684588[/C][/ROW]
[ROW][C]89[/C][C]135.26[/C][C]132.664058476808[/C][C]137.855941523192[/C][/ROW]
[ROW][C]90[/C][C]135.62[/C][C]132.776288539567[/C][C]138.463711460433[/C][/ROW]
[ROW][C]91[/C][C]135.98[/C][C]132.908440567307[/C][C]139.051559432693[/C][/ROW]
[ROW][C]92[/C][C]136.34[/C][C]133.056364845643[/C][C]139.623635154357[/C][/ROW]
[ROW][C]93[/C][C]136.7[/C][C]133.217178973117[/C][C]140.182821026883[/C][/ROW]
[ROW][C]94[/C][C]137.06[/C][C]133.388784290775[/C][C]140.731215709225[/C][/ROW]
[ROW][C]95[/C][C]137.42[/C][C]133.569596480623[/C][C]141.270403519377[/C][/ROW]
[ROW][C]96[/C][C]137.78[/C][C]133.75838468518[/C][C]141.80161531482[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232439&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232439&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
tForecast95% Lower Bound95% Upper Bound
85133.82132.659059657706134.980940342294
86134.18132.538182422821135.821817577179
87134.54132.52919234259136.55080765741
88134.9132.578119315412137.221880684588
89135.26132.664058476808137.855941523192
90135.62132.776288539567138.463711460433
91135.98132.908440567307139.051559432693
92136.34133.056364845643139.623635154357
93136.7133.217178973117140.182821026883
94137.06133.388784290775140.731215709225
95137.42133.569596480623141.270403519377
96137.78133.75838468518141.80161531482



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')