Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 26 Apr 2016 19:45:09 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Apr/26/t14616963536f3cugve4z7usmq.htm/, Retrieved Fri, 03 May 2024 22:51:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294962, Retrieved Fri, 03 May 2024 22:51:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact77
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-04-26 18:45:09] [d992272e6b10691b6ed213356daa79d7] [Current]
Feedback Forum

Post a new message
Dataseries X:
92.46
91.73
91.73
91.73
91.73
91.73
91.73
91.73
91.73
91.73
91.73
91.73
91.73
86.87
86.87
86.87
86.87
86.87
86.87
86.87
86.87
86.87
86.87
86.87
86.87
89.81
89.81
89.81
89.81
89.81
89.81
89.81
89.81
89.81
89.81
89.81
89.81
94.81
94.81
94.81
94.81
94.81
94.81
94.81
94.81
94.81
94.81
94.81
94.81
95.01
95.01
95.01
95.01
95.01
95.01
95.01
95.01
95.01
95.01
95.01
95.01
95.57
95.57
95.57
95.57
95.57
95.57
95.57
95.57
95.57
95.57
95.57
95.57
98.56
98.56
98.56
98.56
98.56
98.56
98.56
98.56
98.56
98.56
98.56
98.56
100.13
100.13
100.13
100.13
100.13
100.13
100.13
100.13
100.13
100.13
100.13
100.13
101.86
101.86
101.86
101.86
101.86
101.86
101.86
101.86
101.86
101.86
101.86
101.86
101.86
101.86
101.86
101.86
101.86
101.86
101.86
101.86
101.86
101.86
101.86





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=294962&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=294962&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294962&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 time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999959046879146
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999959046879146 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294962&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]0.999959046879146[/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=294962&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294962&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
alpha0.999959046879146
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
291.7392.46-0.72999999999999
391.7391.7300298957782-2.98957782121079e-05
491.7391.7300000012243-1.22432197713351e-09
591.7391.73-4.2632564145606e-14
691.7391.730
791.7391.730
891.7391.730
991.7391.730
1091.7391.730
1191.7391.730
1291.7391.730
1391.7391.730
1486.8791.73-4.86
1586.8786.8701990321674-0.000199032167358837
1686.8786.870000008151-8.15099099327199e-09
1786.8786.8700000000003-3.41060513164848e-13
1886.8786.870
1986.8786.870
2086.8786.870
2186.8786.870
2286.8786.870
2386.8786.870
2486.8786.870
2586.8786.870
2689.8186.872.94
2789.8189.80987959782470.000120402175312506
2889.8189.80999999506924.93083973651665e-09
2989.8189.80999999999981.98951966012828e-13
3089.8189.810
3189.8189.810
3289.8189.810
3389.8189.810
3489.8189.810
3589.8189.810
3689.8189.810
3789.8189.810
3894.8189.815
3994.8194.80979523439570.000204765604266299
4094.8194.80999999161428.38578273487656e-09
4194.8194.80999999999973.41060513164848e-13
4294.8194.810
4394.8194.810
4494.8194.810
4594.8194.810
4694.8194.810
4794.8194.810
4894.8194.810
4994.8194.810
5095.0194.810.200000000000003
5195.0195.00999180937588.19062417178884e-06
5295.0195.00999999966463.35433014697628e-10
5395.0195.011.4210854715202e-14
5495.0195.010
5595.0195.010
5695.0195.010
5795.0195.010
5895.0195.010
5995.0195.010
6095.0195.010
6195.0195.010
6295.5795.010.559999999999988
6395.5795.56997706625232.29337476866931e-05
6495.5795.56999999906089.39209598982416e-10
6595.5795.574.2632564145606e-14
6695.5795.570
6795.5795.570
6895.5795.570
6995.5795.570
7095.5795.570
7195.5795.570
7295.5795.570
7395.5795.570
7498.5695.572.99000000000001
7598.5698.55987755016870.000122449831351901
7698.5698.55999999498535.01471220104577e-09
7798.5698.55999999999982.1316282072803e-13
7898.5698.560
7998.5698.560
8098.5698.560
8198.5698.560
8298.5698.560
8398.5698.560
8498.5698.560
8598.5698.560
86100.1398.561.56999999999999
87100.13100.12993570366.42963997421475e-05
88100.13100.1299999973672.63314348103449e-09
89100.13100.131.13686837721616e-13
90100.13100.130
91100.13100.130
92100.13100.130
93100.13100.130
94100.13100.130
95100.13100.130
96100.13100.130
97100.13100.130
98101.86100.131.73
99101.86101.8599291511017.08488990710521e-05
100101.86101.8599999970992.90148705062165e-09
101101.86101.861.13686837721616e-13
102101.86101.860
103101.86101.860
104101.86101.860
105101.86101.860
106101.86101.860
107101.86101.860
108101.86101.860
109101.86101.860
110101.86101.860
111101.86101.860
112101.86101.860
113101.86101.860
114101.86101.860
115101.86101.860
116101.86101.860
117101.86101.860
118101.86101.860
119101.86101.860
120101.86101.860

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 91.73 & 92.46 & -0.72999999999999 \tabularnewline
3 & 91.73 & 91.7300298957782 & -2.98957782121079e-05 \tabularnewline
4 & 91.73 & 91.7300000012243 & -1.22432197713351e-09 \tabularnewline
5 & 91.73 & 91.73 & -4.2632564145606e-14 \tabularnewline
6 & 91.73 & 91.73 & 0 \tabularnewline
7 & 91.73 & 91.73 & 0 \tabularnewline
8 & 91.73 & 91.73 & 0 \tabularnewline
9 & 91.73 & 91.73 & 0 \tabularnewline
10 & 91.73 & 91.73 & 0 \tabularnewline
11 & 91.73 & 91.73 & 0 \tabularnewline
12 & 91.73 & 91.73 & 0 \tabularnewline
13 & 91.73 & 91.73 & 0 \tabularnewline
14 & 86.87 & 91.73 & -4.86 \tabularnewline
15 & 86.87 & 86.8701990321674 & -0.000199032167358837 \tabularnewline
16 & 86.87 & 86.870000008151 & -8.15099099327199e-09 \tabularnewline
17 & 86.87 & 86.8700000000003 & -3.41060513164848e-13 \tabularnewline
18 & 86.87 & 86.87 & 0 \tabularnewline
19 & 86.87 & 86.87 & 0 \tabularnewline
20 & 86.87 & 86.87 & 0 \tabularnewline
21 & 86.87 & 86.87 & 0 \tabularnewline
22 & 86.87 & 86.87 & 0 \tabularnewline
23 & 86.87 & 86.87 & 0 \tabularnewline
24 & 86.87 & 86.87 & 0 \tabularnewline
25 & 86.87 & 86.87 & 0 \tabularnewline
26 & 89.81 & 86.87 & 2.94 \tabularnewline
27 & 89.81 & 89.8098795978247 & 0.000120402175312506 \tabularnewline
28 & 89.81 & 89.8099999950692 & 4.93083973651665e-09 \tabularnewline
29 & 89.81 & 89.8099999999998 & 1.98951966012828e-13 \tabularnewline
30 & 89.81 & 89.81 & 0 \tabularnewline
31 & 89.81 & 89.81 & 0 \tabularnewline
32 & 89.81 & 89.81 & 0 \tabularnewline
33 & 89.81 & 89.81 & 0 \tabularnewline
34 & 89.81 & 89.81 & 0 \tabularnewline
35 & 89.81 & 89.81 & 0 \tabularnewline
36 & 89.81 & 89.81 & 0 \tabularnewline
37 & 89.81 & 89.81 & 0 \tabularnewline
38 & 94.81 & 89.81 & 5 \tabularnewline
39 & 94.81 & 94.8097952343957 & 0.000204765604266299 \tabularnewline
40 & 94.81 & 94.8099999916142 & 8.38578273487656e-09 \tabularnewline
41 & 94.81 & 94.8099999999997 & 3.41060513164848e-13 \tabularnewline
42 & 94.81 & 94.81 & 0 \tabularnewline
43 & 94.81 & 94.81 & 0 \tabularnewline
44 & 94.81 & 94.81 & 0 \tabularnewline
45 & 94.81 & 94.81 & 0 \tabularnewline
46 & 94.81 & 94.81 & 0 \tabularnewline
47 & 94.81 & 94.81 & 0 \tabularnewline
48 & 94.81 & 94.81 & 0 \tabularnewline
49 & 94.81 & 94.81 & 0 \tabularnewline
50 & 95.01 & 94.81 & 0.200000000000003 \tabularnewline
51 & 95.01 & 95.0099918093758 & 8.19062417178884e-06 \tabularnewline
52 & 95.01 & 95.0099999996646 & 3.35433014697628e-10 \tabularnewline
53 & 95.01 & 95.01 & 1.4210854715202e-14 \tabularnewline
54 & 95.01 & 95.01 & 0 \tabularnewline
55 & 95.01 & 95.01 & 0 \tabularnewline
56 & 95.01 & 95.01 & 0 \tabularnewline
57 & 95.01 & 95.01 & 0 \tabularnewline
58 & 95.01 & 95.01 & 0 \tabularnewline
59 & 95.01 & 95.01 & 0 \tabularnewline
60 & 95.01 & 95.01 & 0 \tabularnewline
61 & 95.01 & 95.01 & 0 \tabularnewline
62 & 95.57 & 95.01 & 0.559999999999988 \tabularnewline
63 & 95.57 & 95.5699770662523 & 2.29337476866931e-05 \tabularnewline
64 & 95.57 & 95.5699999990608 & 9.39209598982416e-10 \tabularnewline
65 & 95.57 & 95.57 & 4.2632564145606e-14 \tabularnewline
66 & 95.57 & 95.57 & 0 \tabularnewline
67 & 95.57 & 95.57 & 0 \tabularnewline
68 & 95.57 & 95.57 & 0 \tabularnewline
69 & 95.57 & 95.57 & 0 \tabularnewline
70 & 95.57 & 95.57 & 0 \tabularnewline
71 & 95.57 & 95.57 & 0 \tabularnewline
72 & 95.57 & 95.57 & 0 \tabularnewline
73 & 95.57 & 95.57 & 0 \tabularnewline
74 & 98.56 & 95.57 & 2.99000000000001 \tabularnewline
75 & 98.56 & 98.5598775501687 & 0.000122449831351901 \tabularnewline
76 & 98.56 & 98.5599999949853 & 5.01471220104577e-09 \tabularnewline
77 & 98.56 & 98.5599999999998 & 2.1316282072803e-13 \tabularnewline
78 & 98.56 & 98.56 & 0 \tabularnewline
79 & 98.56 & 98.56 & 0 \tabularnewline
80 & 98.56 & 98.56 & 0 \tabularnewline
81 & 98.56 & 98.56 & 0 \tabularnewline
82 & 98.56 & 98.56 & 0 \tabularnewline
83 & 98.56 & 98.56 & 0 \tabularnewline
84 & 98.56 & 98.56 & 0 \tabularnewline
85 & 98.56 & 98.56 & 0 \tabularnewline
86 & 100.13 & 98.56 & 1.56999999999999 \tabularnewline
87 & 100.13 & 100.1299357036 & 6.42963997421475e-05 \tabularnewline
88 & 100.13 & 100.129999997367 & 2.63314348103449e-09 \tabularnewline
89 & 100.13 & 100.13 & 1.13686837721616e-13 \tabularnewline
90 & 100.13 & 100.13 & 0 \tabularnewline
91 & 100.13 & 100.13 & 0 \tabularnewline
92 & 100.13 & 100.13 & 0 \tabularnewline
93 & 100.13 & 100.13 & 0 \tabularnewline
94 & 100.13 & 100.13 & 0 \tabularnewline
95 & 100.13 & 100.13 & 0 \tabularnewline
96 & 100.13 & 100.13 & 0 \tabularnewline
97 & 100.13 & 100.13 & 0 \tabularnewline
98 & 101.86 & 100.13 & 1.73 \tabularnewline
99 & 101.86 & 101.859929151101 & 7.08488990710521e-05 \tabularnewline
100 & 101.86 & 101.859999997099 & 2.90148705062165e-09 \tabularnewline
101 & 101.86 & 101.86 & 1.13686837721616e-13 \tabularnewline
102 & 101.86 & 101.86 & 0 \tabularnewline
103 & 101.86 & 101.86 & 0 \tabularnewline
104 & 101.86 & 101.86 & 0 \tabularnewline
105 & 101.86 & 101.86 & 0 \tabularnewline
106 & 101.86 & 101.86 & 0 \tabularnewline
107 & 101.86 & 101.86 & 0 \tabularnewline
108 & 101.86 & 101.86 & 0 \tabularnewline
109 & 101.86 & 101.86 & 0 \tabularnewline
110 & 101.86 & 101.86 & 0 \tabularnewline
111 & 101.86 & 101.86 & 0 \tabularnewline
112 & 101.86 & 101.86 & 0 \tabularnewline
113 & 101.86 & 101.86 & 0 \tabularnewline
114 & 101.86 & 101.86 & 0 \tabularnewline
115 & 101.86 & 101.86 & 0 \tabularnewline
116 & 101.86 & 101.86 & 0 \tabularnewline
117 & 101.86 & 101.86 & 0 \tabularnewline
118 & 101.86 & 101.86 & 0 \tabularnewline
119 & 101.86 & 101.86 & 0 \tabularnewline
120 & 101.86 & 101.86 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294962&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]91.73[/C][C]92.46[/C][C]-0.72999999999999[/C][/ROW]
[ROW][C]3[/C][C]91.73[/C][C]91.7300298957782[/C][C]-2.98957782121079e-05[/C][/ROW]
[ROW][C]4[/C][C]91.73[/C][C]91.7300000012243[/C][C]-1.22432197713351e-09[/C][/ROW]
[ROW][C]5[/C][C]91.73[/C][C]91.73[/C][C]-4.2632564145606e-14[/C][/ROW]
[ROW][C]6[/C][C]91.73[/C][C]91.73[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]91.73[/C][C]91.73[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]91.73[/C][C]91.73[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]91.73[/C][C]91.73[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]91.73[/C][C]91.73[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]91.73[/C][C]91.73[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]91.73[/C][C]91.73[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]91.73[/C][C]91.73[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]86.87[/C][C]91.73[/C][C]-4.86[/C][/ROW]
[ROW][C]15[/C][C]86.87[/C][C]86.8701990321674[/C][C]-0.000199032167358837[/C][/ROW]
[ROW][C]16[/C][C]86.87[/C][C]86.870000008151[/C][C]-8.15099099327199e-09[/C][/ROW]
[ROW][C]17[/C][C]86.87[/C][C]86.8700000000003[/C][C]-3.41060513164848e-13[/C][/ROW]
[ROW][C]18[/C][C]86.87[/C][C]86.87[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]86.87[/C][C]86.87[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]86.87[/C][C]86.87[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]86.87[/C][C]86.87[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]86.87[/C][C]86.87[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]86.87[/C][C]86.87[/C][C]0[/C][/ROW]
[ROW][C]24[/C][C]86.87[/C][C]86.87[/C][C]0[/C][/ROW]
[ROW][C]25[/C][C]86.87[/C][C]86.87[/C][C]0[/C][/ROW]
[ROW][C]26[/C][C]89.81[/C][C]86.87[/C][C]2.94[/C][/ROW]
[ROW][C]27[/C][C]89.81[/C][C]89.8098795978247[/C][C]0.000120402175312506[/C][/ROW]
[ROW][C]28[/C][C]89.81[/C][C]89.8099999950692[/C][C]4.93083973651665e-09[/C][/ROW]
[ROW][C]29[/C][C]89.81[/C][C]89.8099999999998[/C][C]1.98951966012828e-13[/C][/ROW]
[ROW][C]30[/C][C]89.81[/C][C]89.81[/C][C]0[/C][/ROW]
[ROW][C]31[/C][C]89.81[/C][C]89.81[/C][C]0[/C][/ROW]
[ROW][C]32[/C][C]89.81[/C][C]89.81[/C][C]0[/C][/ROW]
[ROW][C]33[/C][C]89.81[/C][C]89.81[/C][C]0[/C][/ROW]
[ROW][C]34[/C][C]89.81[/C][C]89.81[/C][C]0[/C][/ROW]
[ROW][C]35[/C][C]89.81[/C][C]89.81[/C][C]0[/C][/ROW]
[ROW][C]36[/C][C]89.81[/C][C]89.81[/C][C]0[/C][/ROW]
[ROW][C]37[/C][C]89.81[/C][C]89.81[/C][C]0[/C][/ROW]
[ROW][C]38[/C][C]94.81[/C][C]89.81[/C][C]5[/C][/ROW]
[ROW][C]39[/C][C]94.81[/C][C]94.8097952343957[/C][C]0.000204765604266299[/C][/ROW]
[ROW][C]40[/C][C]94.81[/C][C]94.8099999916142[/C][C]8.38578273487656e-09[/C][/ROW]
[ROW][C]41[/C][C]94.81[/C][C]94.8099999999997[/C][C]3.41060513164848e-13[/C][/ROW]
[ROW][C]42[/C][C]94.81[/C][C]94.81[/C][C]0[/C][/ROW]
[ROW][C]43[/C][C]94.81[/C][C]94.81[/C][C]0[/C][/ROW]
[ROW][C]44[/C][C]94.81[/C][C]94.81[/C][C]0[/C][/ROW]
[ROW][C]45[/C][C]94.81[/C][C]94.81[/C][C]0[/C][/ROW]
[ROW][C]46[/C][C]94.81[/C][C]94.81[/C][C]0[/C][/ROW]
[ROW][C]47[/C][C]94.81[/C][C]94.81[/C][C]0[/C][/ROW]
[ROW][C]48[/C][C]94.81[/C][C]94.81[/C][C]0[/C][/ROW]
[ROW][C]49[/C][C]94.81[/C][C]94.81[/C][C]0[/C][/ROW]
[ROW][C]50[/C][C]95.01[/C][C]94.81[/C][C]0.200000000000003[/C][/ROW]
[ROW][C]51[/C][C]95.01[/C][C]95.0099918093758[/C][C]8.19062417178884e-06[/C][/ROW]
[ROW][C]52[/C][C]95.01[/C][C]95.0099999996646[/C][C]3.35433014697628e-10[/C][/ROW]
[ROW][C]53[/C][C]95.01[/C][C]95.01[/C][C]1.4210854715202e-14[/C][/ROW]
[ROW][C]54[/C][C]95.01[/C][C]95.01[/C][C]0[/C][/ROW]
[ROW][C]55[/C][C]95.01[/C][C]95.01[/C][C]0[/C][/ROW]
[ROW][C]56[/C][C]95.01[/C][C]95.01[/C][C]0[/C][/ROW]
[ROW][C]57[/C][C]95.01[/C][C]95.01[/C][C]0[/C][/ROW]
[ROW][C]58[/C][C]95.01[/C][C]95.01[/C][C]0[/C][/ROW]
[ROW][C]59[/C][C]95.01[/C][C]95.01[/C][C]0[/C][/ROW]
[ROW][C]60[/C][C]95.01[/C][C]95.01[/C][C]0[/C][/ROW]
[ROW][C]61[/C][C]95.01[/C][C]95.01[/C][C]0[/C][/ROW]
[ROW][C]62[/C][C]95.57[/C][C]95.01[/C][C]0.559999999999988[/C][/ROW]
[ROW][C]63[/C][C]95.57[/C][C]95.5699770662523[/C][C]2.29337476866931e-05[/C][/ROW]
[ROW][C]64[/C][C]95.57[/C][C]95.5699999990608[/C][C]9.39209598982416e-10[/C][/ROW]
[ROW][C]65[/C][C]95.57[/C][C]95.57[/C][C]4.2632564145606e-14[/C][/ROW]
[ROW][C]66[/C][C]95.57[/C][C]95.57[/C][C]0[/C][/ROW]
[ROW][C]67[/C][C]95.57[/C][C]95.57[/C][C]0[/C][/ROW]
[ROW][C]68[/C][C]95.57[/C][C]95.57[/C][C]0[/C][/ROW]
[ROW][C]69[/C][C]95.57[/C][C]95.57[/C][C]0[/C][/ROW]
[ROW][C]70[/C][C]95.57[/C][C]95.57[/C][C]0[/C][/ROW]
[ROW][C]71[/C][C]95.57[/C][C]95.57[/C][C]0[/C][/ROW]
[ROW][C]72[/C][C]95.57[/C][C]95.57[/C][C]0[/C][/ROW]
[ROW][C]73[/C][C]95.57[/C][C]95.57[/C][C]0[/C][/ROW]
[ROW][C]74[/C][C]98.56[/C][C]95.57[/C][C]2.99000000000001[/C][/ROW]
[ROW][C]75[/C][C]98.56[/C][C]98.5598775501687[/C][C]0.000122449831351901[/C][/ROW]
[ROW][C]76[/C][C]98.56[/C][C]98.5599999949853[/C][C]5.01471220104577e-09[/C][/ROW]
[ROW][C]77[/C][C]98.56[/C][C]98.5599999999998[/C][C]2.1316282072803e-13[/C][/ROW]
[ROW][C]78[/C][C]98.56[/C][C]98.56[/C][C]0[/C][/ROW]
[ROW][C]79[/C][C]98.56[/C][C]98.56[/C][C]0[/C][/ROW]
[ROW][C]80[/C][C]98.56[/C][C]98.56[/C][C]0[/C][/ROW]
[ROW][C]81[/C][C]98.56[/C][C]98.56[/C][C]0[/C][/ROW]
[ROW][C]82[/C][C]98.56[/C][C]98.56[/C][C]0[/C][/ROW]
[ROW][C]83[/C][C]98.56[/C][C]98.56[/C][C]0[/C][/ROW]
[ROW][C]84[/C][C]98.56[/C][C]98.56[/C][C]0[/C][/ROW]
[ROW][C]85[/C][C]98.56[/C][C]98.56[/C][C]0[/C][/ROW]
[ROW][C]86[/C][C]100.13[/C][C]98.56[/C][C]1.56999999999999[/C][/ROW]
[ROW][C]87[/C][C]100.13[/C][C]100.1299357036[/C][C]6.42963997421475e-05[/C][/ROW]
[ROW][C]88[/C][C]100.13[/C][C]100.129999997367[/C][C]2.63314348103449e-09[/C][/ROW]
[ROW][C]89[/C][C]100.13[/C][C]100.13[/C][C]1.13686837721616e-13[/C][/ROW]
[ROW][C]90[/C][C]100.13[/C][C]100.13[/C][C]0[/C][/ROW]
[ROW][C]91[/C][C]100.13[/C][C]100.13[/C][C]0[/C][/ROW]
[ROW][C]92[/C][C]100.13[/C][C]100.13[/C][C]0[/C][/ROW]
[ROW][C]93[/C][C]100.13[/C][C]100.13[/C][C]0[/C][/ROW]
[ROW][C]94[/C][C]100.13[/C][C]100.13[/C][C]0[/C][/ROW]
[ROW][C]95[/C][C]100.13[/C][C]100.13[/C][C]0[/C][/ROW]
[ROW][C]96[/C][C]100.13[/C][C]100.13[/C][C]0[/C][/ROW]
[ROW][C]97[/C][C]100.13[/C][C]100.13[/C][C]0[/C][/ROW]
[ROW][C]98[/C][C]101.86[/C][C]100.13[/C][C]1.73[/C][/ROW]
[ROW][C]99[/C][C]101.86[/C][C]101.859929151101[/C][C]7.08488990710521e-05[/C][/ROW]
[ROW][C]100[/C][C]101.86[/C][C]101.859999997099[/C][C]2.90148705062165e-09[/C][/ROW]
[ROW][C]101[/C][C]101.86[/C][C]101.86[/C][C]1.13686837721616e-13[/C][/ROW]
[ROW][C]102[/C][C]101.86[/C][C]101.86[/C][C]0[/C][/ROW]
[ROW][C]103[/C][C]101.86[/C][C]101.86[/C][C]0[/C][/ROW]
[ROW][C]104[/C][C]101.86[/C][C]101.86[/C][C]0[/C][/ROW]
[ROW][C]105[/C][C]101.86[/C][C]101.86[/C][C]0[/C][/ROW]
[ROW][C]106[/C][C]101.86[/C][C]101.86[/C][C]0[/C][/ROW]
[ROW][C]107[/C][C]101.86[/C][C]101.86[/C][C]0[/C][/ROW]
[ROW][C]108[/C][C]101.86[/C][C]101.86[/C][C]0[/C][/ROW]
[ROW][C]109[/C][C]101.86[/C][C]101.86[/C][C]0[/C][/ROW]
[ROW][C]110[/C][C]101.86[/C][C]101.86[/C][C]0[/C][/ROW]
[ROW][C]111[/C][C]101.86[/C][C]101.86[/C][C]0[/C][/ROW]
[ROW][C]112[/C][C]101.86[/C][C]101.86[/C][C]0[/C][/ROW]
[ROW][C]113[/C][C]101.86[/C][C]101.86[/C][C]0[/C][/ROW]
[ROW][C]114[/C][C]101.86[/C][C]101.86[/C][C]0[/C][/ROW]
[ROW][C]115[/C][C]101.86[/C][C]101.86[/C][C]0[/C][/ROW]
[ROW][C]116[/C][C]101.86[/C][C]101.86[/C][C]0[/C][/ROW]
[ROW][C]117[/C][C]101.86[/C][C]101.86[/C][C]0[/C][/ROW]
[ROW][C]118[/C][C]101.86[/C][C]101.86[/C][C]0[/C][/ROW]
[ROW][C]119[/C][C]101.86[/C][C]101.86[/C][C]0[/C][/ROW]
[ROW][C]120[/C][C]101.86[/C][C]101.86[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294962&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294962&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
291.7392.46-0.72999999999999
391.7391.7300298957782-2.98957782121079e-05
491.7391.7300000012243-1.22432197713351e-09
591.7391.73-4.2632564145606e-14
691.7391.730
791.7391.730
891.7391.730
991.7391.730
1091.7391.730
1191.7391.730
1291.7391.730
1391.7391.730
1486.8791.73-4.86
1586.8786.8701990321674-0.000199032167358837
1686.8786.870000008151-8.15099099327199e-09
1786.8786.8700000000003-3.41060513164848e-13
1886.8786.870
1986.8786.870
2086.8786.870
2186.8786.870
2286.8786.870
2386.8786.870
2486.8786.870
2586.8786.870
2689.8186.872.94
2789.8189.80987959782470.000120402175312506
2889.8189.80999999506924.93083973651665e-09
2989.8189.80999999999981.98951966012828e-13
3089.8189.810
3189.8189.810
3289.8189.810
3389.8189.810
3489.8189.810
3589.8189.810
3689.8189.810
3789.8189.810
3894.8189.815
3994.8194.80979523439570.000204765604266299
4094.8194.80999999161428.38578273487656e-09
4194.8194.80999999999973.41060513164848e-13
4294.8194.810
4394.8194.810
4494.8194.810
4594.8194.810
4694.8194.810
4794.8194.810
4894.8194.810
4994.8194.810
5095.0194.810.200000000000003
5195.0195.00999180937588.19062417178884e-06
5295.0195.00999999966463.35433014697628e-10
5395.0195.011.4210854715202e-14
5495.0195.010
5595.0195.010
5695.0195.010
5795.0195.010
5895.0195.010
5995.0195.010
6095.0195.010
6195.0195.010
6295.5795.010.559999999999988
6395.5795.56997706625232.29337476866931e-05
6495.5795.56999999906089.39209598982416e-10
6595.5795.574.2632564145606e-14
6695.5795.570
6795.5795.570
6895.5795.570
6995.5795.570
7095.5795.570
7195.5795.570
7295.5795.570
7395.5795.570
7498.5695.572.99000000000001
7598.5698.55987755016870.000122449831351901
7698.5698.55999999498535.01471220104577e-09
7798.5698.55999999999982.1316282072803e-13
7898.5698.560
7998.5698.560
8098.5698.560
8198.5698.560
8298.5698.560
8398.5698.560
8498.5698.560
8598.5698.560
86100.1398.561.56999999999999
87100.13100.12993570366.42963997421475e-05
88100.13100.1299999973672.63314348103449e-09
89100.13100.131.13686837721616e-13
90100.13100.130
91100.13100.130
92100.13100.130
93100.13100.130
94100.13100.130
95100.13100.130
96100.13100.130
97100.13100.130
98101.86100.131.73
99101.86101.8599291511017.08488990710521e-05
100101.86101.8599999970992.90148705062165e-09
101101.86101.861.13686837721616e-13
102101.86101.860
103101.86101.860
104101.86101.860
105101.86101.860
106101.86101.860
107101.86101.860
108101.86101.860
109101.86101.860
110101.86101.860
111101.86101.860
112101.86101.860
113101.86101.860
114101.86101.860
115101.86101.860
116101.86101.860
117101.86101.860
118101.86101.860
119101.86101.860
120101.86101.860







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121101.86100.331080970957103.388919029043
122101.8699.6978262476922104.022173752308
123101.8699.2119068609717104.508093139028
124101.8698.8022558624423104.917744137558
125101.8698.4413451258472105.278654874153
126101.8698.1150563306816105.604943669318
127101.8697.8150024692013105.904997530799
128101.8697.5357189080764106.184281091924
129101.8697.2734098831738106.446590116826
130101.8697.0253117124713106.694688287529
131101.8696.7893380338099106.93066196619
132101.8696.5638679479108107.156132052089

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 101.86 & 100.331080970957 & 103.388919029043 \tabularnewline
122 & 101.86 & 99.6978262476922 & 104.022173752308 \tabularnewline
123 & 101.86 & 99.2119068609717 & 104.508093139028 \tabularnewline
124 & 101.86 & 98.8022558624423 & 104.917744137558 \tabularnewline
125 & 101.86 & 98.4413451258472 & 105.278654874153 \tabularnewline
126 & 101.86 & 98.1150563306816 & 105.604943669318 \tabularnewline
127 & 101.86 & 97.8150024692013 & 105.904997530799 \tabularnewline
128 & 101.86 & 97.5357189080764 & 106.184281091924 \tabularnewline
129 & 101.86 & 97.2734098831738 & 106.446590116826 \tabularnewline
130 & 101.86 & 97.0253117124713 & 106.694688287529 \tabularnewline
131 & 101.86 & 96.7893380338099 & 106.93066196619 \tabularnewline
132 & 101.86 & 96.5638679479108 & 107.156132052089 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294962&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]121[/C][C]101.86[/C][C]100.331080970957[/C][C]103.388919029043[/C][/ROW]
[ROW][C]122[/C][C]101.86[/C][C]99.6978262476922[/C][C]104.022173752308[/C][/ROW]
[ROW][C]123[/C][C]101.86[/C][C]99.2119068609717[/C][C]104.508093139028[/C][/ROW]
[ROW][C]124[/C][C]101.86[/C][C]98.8022558624423[/C][C]104.917744137558[/C][/ROW]
[ROW][C]125[/C][C]101.86[/C][C]98.4413451258472[/C][C]105.278654874153[/C][/ROW]
[ROW][C]126[/C][C]101.86[/C][C]98.1150563306816[/C][C]105.604943669318[/C][/ROW]
[ROW][C]127[/C][C]101.86[/C][C]97.8150024692013[/C][C]105.904997530799[/C][/ROW]
[ROW][C]128[/C][C]101.86[/C][C]97.5357189080764[/C][C]106.184281091924[/C][/ROW]
[ROW][C]129[/C][C]101.86[/C][C]97.2734098831738[/C][C]106.446590116826[/C][/ROW]
[ROW][C]130[/C][C]101.86[/C][C]97.0253117124713[/C][C]106.694688287529[/C][/ROW]
[ROW][C]131[/C][C]101.86[/C][C]96.7893380338099[/C][C]106.93066196619[/C][/ROW]
[ROW][C]132[/C][C]101.86[/C][C]96.5638679479108[/C][C]107.156132052089[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294962&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294962&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
121101.86100.331080970957103.388919029043
122101.8699.6978262476922104.022173752308
123101.8699.2119068609717104.508093139028
124101.8698.8022558624423104.917744137558
125101.8698.4413451258472105.278654874153
126101.8698.1150563306816105.604943669318
127101.8697.8150024692013105.904997530799
128101.8697.5357189080764106.184281091924
129101.8697.2734098831738106.446590116826
130101.8697.0253117124713106.694688287529
131101.8696.7893380338099106.93066196619
132101.8696.5638679479108107.156132052089



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')