FreeStatistics.org

Free Statistics

of Irreproducible Research!

Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 22 Apr 2015 18:48:53 +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/2015/Apr/22/t14297250833zsi5fmgbds1ke0.htm/, Retrieved Wed, 08 May 2024 18:02:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278802, Retrieved Wed, 08 May 2024 18:02:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact142

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [opgave10nr1] [2015-04-22 17:36:01] [6e96f11f3cecdcda3dd5ca25dc8c172c]
- R PD    [Exponential Smoothing] [Opgave10nr2-2] [2015-04-22 17:48:53] [70d22f55a70f3427b60459805adf1606] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
7,8
8
8,1
8,2
8,1
7,7
6,9
6,6
6,7
7
7,1
7
6,9
6,8
6,8
7
7
6,8
6,7
6,6
6,4
6,4
6,4
6,5
6,6
6,5
6,3
6,2
6,1
6,5
7,1
7,2
6,9
6,2
6
6,2
6,9
7,4
7,8
7,8
7,7
7,7
7,6
7,6
7,7
8
8,2
8,4
8,2
8,1
8,1
8,2
8,3
8,4
8,5
8,3
8,1
7,9
7,7
7,6
7,4
7,3
7
6,8
6,8
6,9
7,3
7,5
7,5
7,2
7
6,9
7
7,1
7,1
7,2
7,3
7,3
7,2
7,5
8
8,7
9
9
8,8
8,5
8,5
8,5
8,5
8,6
8,7
8,8
8,8
8,7
8,7
8,8

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278802&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278802&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278802&T=0

As an alternative you can also use a QR Code:  
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 time2 seconds
R Server'George Udny Yule' @ yule.wessa.net






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta1
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 1 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278802&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]1[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278802&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278802&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta1
gammaFALSE






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
38.18.2-0.0999999999999996
48.28.20
58.18.3-0.199999999999999
67.78-0.3
76.97.3-0.4
86.66.10.499999999999999
96.76.30.400000000000001
1076.80.199999999999999
117.17.3-0.2
1277.2-0.199999999999999
136.96.90
146.86.8-8.88178419700125e-16
156.86.70.100000000000001
1676.80.2
1777.2-0.2
186.87-0.2
196.76.60.100000000000001
206.66.6-8.88178419700125e-16
216.46.5-0.0999999999999988
226.46.20.199999999999999
236.46.40
246.56.40.0999999999999996
256.66.60
266.56.7-0.199999999999999
276.36.4-0.100000000000001
286.26.10.100000000000001
296.16.1-8.88178419700125e-16
306.560.500000000000001
317.16.90.199999999999999
327.27.7-0.499999999999999
336.97.3-0.4
346.26.6-0.4
3565.50.5
366.25.80.4
376.96.40.5
387.47.6-0.2
397.87.9-0.100000000000001
407.88.2-0.399999999999999
417.77.8-0.0999999999999996
427.77.60.0999999999999996
437.67.7-0.100000000000001
447.67.50.100000000000001
457.77.60.100000000000001
4687.80.199999999999999
478.28.3-0.100000000000001
488.48.41.77635683940025e-15
498.28.6-0.400000000000002
508.180.100000000000001
518.180.0999999999999996
528.28.10.0999999999999996
538.38.31.77635683940025e-15
548.48.4-1.77635683940025e-15
558.58.50
568.38.6-0.299999999999999
578.18.1-1.77635683940025e-15
587.97.91.77635683940025e-15
597.77.7-8.88178419700125e-16
607.67.50.0999999999999996
617.47.5-0.0999999999999988
627.37.20.0999999999999988
6377.2-0.199999999999999
646.86.70.0999999999999996
656.86.60.2
666.96.80.100000000000001
677.370.299999999999999
687.57.7-0.199999999999999
697.57.7-0.2
707.27.5-0.3
7176.90.0999999999999996
726.96.80.100000000000001
7376.80.199999999999999
747.17.10
757.17.2-0.0999999999999996
767.27.10.100000000000001
777.37.3-8.88178419700125e-16
787.37.4-0.0999999999999996
797.27.3-0.0999999999999996
807.57.10.399999999999999
8187.80.2
828.78.50.199999999999999
8399.4-0.399999999999999
8499.3-0.300000000000001
858.89-0.199999999999999
868.58.6-0.100000000000001
878.58.20.300000000000001
888.58.50
898.58.50
908.68.50.0999999999999996
918.78.70
928.88.81.77635683940025e-15
938.88.9-0.100000000000001
948.78.8-0.100000000000001
958.78.60.100000000000001
968.88.70.100000000000001

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 8.1 & 8.2 & -0.0999999999999996 \tabularnewline
4 & 8.2 & 8.2 & 0 \tabularnewline
5 & 8.1 & 8.3 & -0.199999999999999 \tabularnewline
6 & 7.7 & 8 & -0.3 \tabularnewline
7 & 6.9 & 7.3 & -0.4 \tabularnewline
8 & 6.6 & 6.1 & 0.499999999999999 \tabularnewline
9 & 6.7 & 6.3 & 0.400000000000001 \tabularnewline
10 & 7 & 6.8 & 0.199999999999999 \tabularnewline
11 & 7.1 & 7.3 & -0.2 \tabularnewline
12 & 7 & 7.2 & -0.199999999999999 \tabularnewline
13 & 6.9 & 6.9 & 0 \tabularnewline
14 & 6.8 & 6.8 & -8.88178419700125e-16 \tabularnewline
15 & 6.8 & 6.7 & 0.100000000000001 \tabularnewline
16 & 7 & 6.8 & 0.2 \tabularnewline
17 & 7 & 7.2 & -0.2 \tabularnewline
18 & 6.8 & 7 & -0.2 \tabularnewline
19 & 6.7 & 6.6 & 0.100000000000001 \tabularnewline
20 & 6.6 & 6.6 & -8.88178419700125e-16 \tabularnewline
21 & 6.4 & 6.5 & -0.0999999999999988 \tabularnewline
22 & 6.4 & 6.2 & 0.199999999999999 \tabularnewline
23 & 6.4 & 6.4 & 0 \tabularnewline
24 & 6.5 & 6.4 & 0.0999999999999996 \tabularnewline
25 & 6.6 & 6.6 & 0 \tabularnewline
26 & 6.5 & 6.7 & -0.199999999999999 \tabularnewline
27 & 6.3 & 6.4 & -0.100000000000001 \tabularnewline
28 & 6.2 & 6.1 & 0.100000000000001 \tabularnewline
29 & 6.1 & 6.1 & -8.88178419700125e-16 \tabularnewline
30 & 6.5 & 6 & 0.500000000000001 \tabularnewline
31 & 7.1 & 6.9 & 0.199999999999999 \tabularnewline
32 & 7.2 & 7.7 & -0.499999999999999 \tabularnewline
33 & 6.9 & 7.3 & -0.4 \tabularnewline
34 & 6.2 & 6.6 & -0.4 \tabularnewline
35 & 6 & 5.5 & 0.5 \tabularnewline
36 & 6.2 & 5.8 & 0.4 \tabularnewline
37 & 6.9 & 6.4 & 0.5 \tabularnewline
38 & 7.4 & 7.6 & -0.2 \tabularnewline
39 & 7.8 & 7.9 & -0.100000000000001 \tabularnewline
40 & 7.8 & 8.2 & -0.399999999999999 \tabularnewline
41 & 7.7 & 7.8 & -0.0999999999999996 \tabularnewline
42 & 7.7 & 7.6 & 0.0999999999999996 \tabularnewline
43 & 7.6 & 7.7 & -0.100000000000001 \tabularnewline
44 & 7.6 & 7.5 & 0.100000000000001 \tabularnewline
45 & 7.7 & 7.6 & 0.100000000000001 \tabularnewline
46 & 8 & 7.8 & 0.199999999999999 \tabularnewline
47 & 8.2 & 8.3 & -0.100000000000001 \tabularnewline
48 & 8.4 & 8.4 & 1.77635683940025e-15 \tabularnewline
49 & 8.2 & 8.6 & -0.400000000000002 \tabularnewline
50 & 8.1 & 8 & 0.100000000000001 \tabularnewline
51 & 8.1 & 8 & 0.0999999999999996 \tabularnewline
52 & 8.2 & 8.1 & 0.0999999999999996 \tabularnewline
53 & 8.3 & 8.3 & 1.77635683940025e-15 \tabularnewline
54 & 8.4 & 8.4 & -1.77635683940025e-15 \tabularnewline
55 & 8.5 & 8.5 & 0 \tabularnewline
56 & 8.3 & 8.6 & -0.299999999999999 \tabularnewline
57 & 8.1 & 8.1 & -1.77635683940025e-15 \tabularnewline
58 & 7.9 & 7.9 & 1.77635683940025e-15 \tabularnewline
59 & 7.7 & 7.7 & -8.88178419700125e-16 \tabularnewline
60 & 7.6 & 7.5 & 0.0999999999999996 \tabularnewline
61 & 7.4 & 7.5 & -0.0999999999999988 \tabularnewline
62 & 7.3 & 7.2 & 0.0999999999999988 \tabularnewline
63 & 7 & 7.2 & -0.199999999999999 \tabularnewline
64 & 6.8 & 6.7 & 0.0999999999999996 \tabularnewline
65 & 6.8 & 6.6 & 0.2 \tabularnewline
66 & 6.9 & 6.8 & 0.100000000000001 \tabularnewline
67 & 7.3 & 7 & 0.299999999999999 \tabularnewline
68 & 7.5 & 7.7 & -0.199999999999999 \tabularnewline
69 & 7.5 & 7.7 & -0.2 \tabularnewline
70 & 7.2 & 7.5 & -0.3 \tabularnewline
71 & 7 & 6.9 & 0.0999999999999996 \tabularnewline
72 & 6.9 & 6.8 & 0.100000000000001 \tabularnewline
73 & 7 & 6.8 & 0.199999999999999 \tabularnewline
74 & 7.1 & 7.1 & 0 \tabularnewline
75 & 7.1 & 7.2 & -0.0999999999999996 \tabularnewline
76 & 7.2 & 7.1 & 0.100000000000001 \tabularnewline
77 & 7.3 & 7.3 & -8.88178419700125e-16 \tabularnewline
78 & 7.3 & 7.4 & -0.0999999999999996 \tabularnewline
79 & 7.2 & 7.3 & -0.0999999999999996 \tabularnewline
80 & 7.5 & 7.1 & 0.399999999999999 \tabularnewline
81 & 8 & 7.8 & 0.2 \tabularnewline
82 & 8.7 & 8.5 & 0.199999999999999 \tabularnewline
83 & 9 & 9.4 & -0.399999999999999 \tabularnewline
84 & 9 & 9.3 & -0.300000000000001 \tabularnewline
85 & 8.8 & 9 & -0.199999999999999 \tabularnewline
86 & 8.5 & 8.6 & -0.100000000000001 \tabularnewline
87 & 8.5 & 8.2 & 0.300000000000001 \tabularnewline
88 & 8.5 & 8.5 & 0 \tabularnewline
89 & 8.5 & 8.5 & 0 \tabularnewline
90 & 8.6 & 8.5 & 0.0999999999999996 \tabularnewline
91 & 8.7 & 8.7 & 0 \tabularnewline
92 & 8.8 & 8.8 & 1.77635683940025e-15 \tabularnewline
93 & 8.8 & 8.9 & -0.100000000000001 \tabularnewline
94 & 8.7 & 8.8 & -0.100000000000001 \tabularnewline
95 & 8.7 & 8.6 & 0.100000000000001 \tabularnewline
96 & 8.8 & 8.7 & 0.100000000000001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278802&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]8.1[/C][C]8.2[/C][C]-0.0999999999999996[/C][/ROW]
[ROW][C]4[/C][C]8.2[/C][C]8.2[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]8.1[/C][C]8.3[/C][C]-0.199999999999999[/C][/ROW]
[ROW][C]6[/C][C]7.7[/C][C]8[/C][C]-0.3[/C][/ROW]
[ROW][C]7[/C][C]6.9[/C][C]7.3[/C][C]-0.4[/C][/ROW]
[ROW][C]8[/C][C]6.6[/C][C]6.1[/C][C]0.499999999999999[/C][/ROW]
[ROW][C]9[/C][C]6.7[/C][C]6.3[/C][C]0.400000000000001[/C][/ROW]
[ROW][C]10[/C][C]7[/C][C]6.8[/C][C]0.199999999999999[/C][/ROW]
[ROW][C]11[/C][C]7.1[/C][C]7.3[/C][C]-0.2[/C][/ROW]
[ROW][C]12[/C][C]7[/C][C]7.2[/C][C]-0.199999999999999[/C][/ROW]
[ROW][C]13[/C][C]6.9[/C][C]6.9[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]6.8[/C][C]6.8[/C][C]-8.88178419700125e-16[/C][/ROW]
[ROW][C]15[/C][C]6.8[/C][C]6.7[/C][C]0.100000000000001[/C][/ROW]
[ROW][C]16[/C][C]7[/C][C]6.8[/C][C]0.2[/C][/ROW]
[ROW][C]17[/C][C]7[/C][C]7.2[/C][C]-0.2[/C][/ROW]
[ROW][C]18[/C][C]6.8[/C][C]7[/C][C]-0.2[/C][/ROW]
[ROW][C]19[/C][C]6.7[/C][C]6.6[/C][C]0.100000000000001[/C][/ROW]
[ROW][C]20[/C][C]6.6[/C][C]6.6[/C][C]-8.88178419700125e-16[/C][/ROW]
[ROW][C]21[/C][C]6.4[/C][C]6.5[/C][C]-0.0999999999999988[/C][/ROW]
[ROW][C]22[/C][C]6.4[/C][C]6.2[/C][C]0.199999999999999[/C][/ROW]
[ROW][C]23[/C][C]6.4[/C][C]6.4[/C][C]0[/C][/ROW]
[ROW][C]24[/C][C]6.5[/C][C]6.4[/C][C]0.0999999999999996[/C][/ROW]
[ROW][C]25[/C][C]6.6[/C][C]6.6[/C][C]0[/C][/ROW]
[ROW][C]26[/C][C]6.5[/C][C]6.7[/C][C]-0.199999999999999[/C][/ROW]
[ROW][C]27[/C][C]6.3[/C][C]6.4[/C][C]-0.100000000000001[/C][/ROW]
[ROW][C]28[/C][C]6.2[/C][C]6.1[/C][C]0.100000000000001[/C][/ROW]
[ROW][C]29[/C][C]6.1[/C][C]6.1[/C][C]-8.88178419700125e-16[/C][/ROW]
[ROW][C]30[/C][C]6.5[/C][C]6[/C][C]0.500000000000001[/C][/ROW]
[ROW][C]31[/C][C]7.1[/C][C]6.9[/C][C]0.199999999999999[/C][/ROW]
[ROW][C]32[/C][C]7.2[/C][C]7.7[/C][C]-0.499999999999999[/C][/ROW]
[ROW][C]33[/C][C]6.9[/C][C]7.3[/C][C]-0.4[/C][/ROW]
[ROW][C]34[/C][C]6.2[/C][C]6.6[/C][C]-0.4[/C][/ROW]
[ROW][C]35[/C][C]6[/C][C]5.5[/C][C]0.5[/C][/ROW]
[ROW][C]36[/C][C]6.2[/C][C]5.8[/C][C]0.4[/C][/ROW]
[ROW][C]37[/C][C]6.9[/C][C]6.4[/C][C]0.5[/C][/ROW]
[ROW][C]38[/C][C]7.4[/C][C]7.6[/C][C]-0.2[/C][/ROW]
[ROW][C]39[/C][C]7.8[/C][C]7.9[/C][C]-0.100000000000001[/C][/ROW]
[ROW][C]40[/C][C]7.8[/C][C]8.2[/C][C]-0.399999999999999[/C][/ROW]
[ROW][C]41[/C][C]7.7[/C][C]7.8[/C][C]-0.0999999999999996[/C][/ROW]
[ROW][C]42[/C][C]7.7[/C][C]7.6[/C][C]0.0999999999999996[/C][/ROW]
[ROW][C]43[/C][C]7.6[/C][C]7.7[/C][C]-0.100000000000001[/C][/ROW]
[ROW][C]44[/C][C]7.6[/C][C]7.5[/C][C]0.100000000000001[/C][/ROW]
[ROW][C]45[/C][C]7.7[/C][C]7.6[/C][C]0.100000000000001[/C][/ROW]
[ROW][C]46[/C][C]8[/C][C]7.8[/C][C]0.199999999999999[/C][/ROW]
[ROW][C]47[/C][C]8.2[/C][C]8.3[/C][C]-0.100000000000001[/C][/ROW]
[ROW][C]48[/C][C]8.4[/C][C]8.4[/C][C]1.77635683940025e-15[/C][/ROW]
[ROW][C]49[/C][C]8.2[/C][C]8.6[/C][C]-0.400000000000002[/C][/ROW]
[ROW][C]50[/C][C]8.1[/C][C]8[/C][C]0.100000000000001[/C][/ROW]
[ROW][C]51[/C][C]8.1[/C][C]8[/C][C]0.0999999999999996[/C][/ROW]
[ROW][C]52[/C][C]8.2[/C][C]8.1[/C][C]0.0999999999999996[/C][/ROW]
[ROW][C]53[/C][C]8.3[/C][C]8.3[/C][C]1.77635683940025e-15[/C][/ROW]
[ROW][C]54[/C][C]8.4[/C][C]8.4[/C][C]-1.77635683940025e-15[/C][/ROW]
[ROW][C]55[/C][C]8.5[/C][C]8.5[/C][C]0[/C][/ROW]
[ROW][C]56[/C][C]8.3[/C][C]8.6[/C][C]-0.299999999999999[/C][/ROW]
[ROW][C]57[/C][C]8.1[/C][C]8.1[/C][C]-1.77635683940025e-15[/C][/ROW]
[ROW][C]58[/C][C]7.9[/C][C]7.9[/C][C]1.77635683940025e-15[/C][/ROW]
[ROW][C]59[/C][C]7.7[/C][C]7.7[/C][C]-8.88178419700125e-16[/C][/ROW]
[ROW][C]60[/C][C]7.6[/C][C]7.5[/C][C]0.0999999999999996[/C][/ROW]
[ROW][C]61[/C][C]7.4[/C][C]7.5[/C][C]-0.0999999999999988[/C][/ROW]
[ROW][C]62[/C][C]7.3[/C][C]7.2[/C][C]0.0999999999999988[/C][/ROW]
[ROW][C]63[/C][C]7[/C][C]7.2[/C][C]-0.199999999999999[/C][/ROW]
[ROW][C]64[/C][C]6.8[/C][C]6.7[/C][C]0.0999999999999996[/C][/ROW]
[ROW][C]65[/C][C]6.8[/C][C]6.6[/C][C]0.2[/C][/ROW]
[ROW][C]66[/C][C]6.9[/C][C]6.8[/C][C]0.100000000000001[/C][/ROW]
[ROW][C]67[/C][C]7.3[/C][C]7[/C][C]0.299999999999999[/C][/ROW]
[ROW][C]68[/C][C]7.5[/C][C]7.7[/C][C]-0.199999999999999[/C][/ROW]
[ROW][C]69[/C][C]7.5[/C][C]7.7[/C][C]-0.2[/C][/ROW]
[ROW][C]70[/C][C]7.2[/C][C]7.5[/C][C]-0.3[/C][/ROW]
[ROW][C]71[/C][C]7[/C][C]6.9[/C][C]0.0999999999999996[/C][/ROW]
[ROW][C]72[/C][C]6.9[/C][C]6.8[/C][C]0.100000000000001[/C][/ROW]
[ROW][C]73[/C][C]7[/C][C]6.8[/C][C]0.199999999999999[/C][/ROW]
[ROW][C]74[/C][C]7.1[/C][C]7.1[/C][C]0[/C][/ROW]
[ROW][C]75[/C][C]7.1[/C][C]7.2[/C][C]-0.0999999999999996[/C][/ROW]
[ROW][C]76[/C][C]7.2[/C][C]7.1[/C][C]0.100000000000001[/C][/ROW]
[ROW][C]77[/C][C]7.3[/C][C]7.3[/C][C]-8.88178419700125e-16[/C][/ROW]
[ROW][C]78[/C][C]7.3[/C][C]7.4[/C][C]-0.0999999999999996[/C][/ROW]
[ROW][C]79[/C][C]7.2[/C][C]7.3[/C][C]-0.0999999999999996[/C][/ROW]
[ROW][C]80[/C][C]7.5[/C][C]7.1[/C][C]0.399999999999999[/C][/ROW]
[ROW][C]81[/C][C]8[/C][C]7.8[/C][C]0.2[/C][/ROW]
[ROW][C]82[/C][C]8.7[/C][C]8.5[/C][C]0.199999999999999[/C][/ROW]
[ROW][C]83[/C][C]9[/C][C]9.4[/C][C]-0.399999999999999[/C][/ROW]
[ROW][C]84[/C][C]9[/C][C]9.3[/C][C]-0.300000000000001[/C][/ROW]
[ROW][C]85[/C][C]8.8[/C][C]9[/C][C]-0.199999999999999[/C][/ROW]
[ROW][C]86[/C][C]8.5[/C][C]8.6[/C][C]-0.100000000000001[/C][/ROW]
[ROW][C]87[/C][C]8.5[/C][C]8.2[/C][C]0.300000000000001[/C][/ROW]
[ROW][C]88[/C][C]8.5[/C][C]8.5[/C][C]0[/C][/ROW]
[ROW][C]89[/C][C]8.5[/C][C]8.5[/C][C]0[/C][/ROW]
[ROW][C]90[/C][C]8.6[/C][C]8.5[/C][C]0.0999999999999996[/C][/ROW]
[ROW][C]91[/C][C]8.7[/C][C]8.7[/C][C]0[/C][/ROW]
[ROW][C]92[/C][C]8.8[/C][C]8.8[/C][C]1.77635683940025e-15[/C][/ROW]
[ROW][C]93[/C][C]8.8[/C][C]8.9[/C][C]-0.100000000000001[/C][/ROW]
[ROW][C]94[/C][C]8.7[/C][C]8.8[/C][C]-0.100000000000001[/C][/ROW]
[ROW][C]95[/C][C]8.7[/C][C]8.6[/C][C]0.100000000000001[/C][/ROW]
[ROW][C]96[/C][C]8.8[/C][C]8.7[/C][C]0.100000000000001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278802&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278802&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
38.18.2-0.0999999999999996
48.28.20
58.18.3-0.199999999999999
67.78-0.3
76.97.3-0.4
86.66.10.499999999999999
96.76.30.400000000000001
1076.80.199999999999999
117.17.3-0.2
1277.2-0.199999999999999
136.96.90
146.86.8-8.88178419700125e-16
156.86.70.100000000000001
1676.80.2
1777.2-0.2
186.87-0.2
196.76.60.100000000000001
206.66.6-8.88178419700125e-16
216.46.5-0.0999999999999988
226.46.20.199999999999999
236.46.40
246.56.40.0999999999999996
256.66.60
266.56.7-0.199999999999999
276.36.4-0.100000000000001
286.26.10.100000000000001
296.16.1-8.88178419700125e-16
306.560.500000000000001
317.16.90.199999999999999
327.27.7-0.499999999999999
336.97.3-0.4
346.26.6-0.4
3565.50.5
366.25.80.4
376.96.40.5
387.47.6-0.2
397.87.9-0.100000000000001
407.88.2-0.399999999999999
417.77.8-0.0999999999999996
427.77.60.0999999999999996
437.67.7-0.100000000000001
447.67.50.100000000000001
457.77.60.100000000000001
4687.80.199999999999999
478.28.3-0.100000000000001
488.48.41.77635683940025e-15
498.28.6-0.400000000000002
508.180.100000000000001
518.180.0999999999999996
528.28.10.0999999999999996
538.38.31.77635683940025e-15
548.48.4-1.77635683940025e-15
558.58.50
568.38.6-0.299999999999999
578.18.1-1.77635683940025e-15
587.97.91.77635683940025e-15
597.77.7-8.88178419700125e-16
607.67.50.0999999999999996
617.47.5-0.0999999999999988
627.37.20.0999999999999988
6377.2-0.199999999999999
646.86.70.0999999999999996
656.86.60.2
666.96.80.100000000000001
677.370.299999999999999
687.57.7-0.199999999999999
697.57.7-0.2
707.27.5-0.3
7176.90.0999999999999996
726.96.80.100000000000001
7376.80.199999999999999
747.17.10
757.17.2-0.0999999999999996
767.27.10.100000000000001
777.37.3-8.88178419700125e-16
787.37.4-0.0999999999999996
797.27.3-0.0999999999999996
807.57.10.399999999999999
8187.80.2
828.78.50.199999999999999
8399.4-0.399999999999999
8499.3-0.300000000000001
858.89-0.199999999999999
868.58.6-0.100000000000001
878.58.20.300000000000001
888.58.50
898.58.50
908.68.50.0999999999999996
918.78.70
928.88.81.77635683940025e-15
938.88.9-0.100000000000001
948.78.8-0.100000000000001
958.78.60.100000000000001
968.88.70.100000000000001






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
978.98.475143713348229.32485628665178
9898.049992462378489.95000753762153
999.17.5103333367320210.689666663268
1009.200000000000016.8729662810293911.5270337189706
1019.300000000000016.1491814496999812.4508185503
1029.400000000000015.3471293319443113.4528706680557
1039.500000000000014.4730326236332414.5269673763668
1049.600000000000013.5318384729196415.6681615270804
1059.700000000000012.5276003786982816.8723996213017
1069.800000000000011.4637176896170918.1362823103829
1079.900000000000020.34309415450714419.4569058454929
10810-0.83175248055001420.8317524805501

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 8.9 & 8.47514371334822 & 9.32485628665178 \tabularnewline
98 & 9 & 8.04999246237848 & 9.95000753762153 \tabularnewline
99 & 9.1 & 7.51033333673202 & 10.689666663268 \tabularnewline
100 & 9.20000000000001 & 6.87296628102939 & 11.5270337189706 \tabularnewline
101 & 9.30000000000001 & 6.14918144969998 & 12.4508185503 \tabularnewline
102 & 9.40000000000001 & 5.34712933194431 & 13.4528706680557 \tabularnewline
103 & 9.50000000000001 & 4.47303262363324 & 14.5269673763668 \tabularnewline
104 & 9.60000000000001 & 3.53183847291964 & 15.6681615270804 \tabularnewline
105 & 9.70000000000001 & 2.52760037869828 & 16.8723996213017 \tabularnewline
106 & 9.80000000000001 & 1.46371768961709 & 18.1362823103829 \tabularnewline
107 & 9.90000000000002 & 0.343094154507144 & 19.4569058454929 \tabularnewline
108 & 10 & -0.831752480550014 & 20.8317524805501 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278802&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]97[/C][C]8.9[/C][C]8.47514371334822[/C][C]9.32485628665178[/C][/ROW]
[ROW][C]98[/C][C]9[/C][C]8.04999246237848[/C][C]9.95000753762153[/C][/ROW]
[ROW][C]99[/C][C]9.1[/C][C]7.51033333673202[/C][C]10.689666663268[/C][/ROW]
[ROW][C]100[/C][C]9.20000000000001[/C][C]6.87296628102939[/C][C]11.5270337189706[/C][/ROW]
[ROW][C]101[/C][C]9.30000000000001[/C][C]6.14918144969998[/C][C]12.4508185503[/C][/ROW]
[ROW][C]102[/C][C]9.40000000000001[/C][C]5.34712933194431[/C][C]13.4528706680557[/C][/ROW]
[ROW][C]103[/C][C]9.50000000000001[/C][C]4.47303262363324[/C][C]14.5269673763668[/C][/ROW]
[ROW][C]104[/C][C]9.60000000000001[/C][C]3.53183847291964[/C][C]15.6681615270804[/C][/ROW]
[ROW][C]105[/C][C]9.70000000000001[/C][C]2.52760037869828[/C][C]16.8723996213017[/C][/ROW]
[ROW][C]106[/C][C]9.80000000000001[/C][C]1.46371768961709[/C][C]18.1362823103829[/C][/ROW]
[ROW][C]107[/C][C]9.90000000000002[/C][C]0.343094154507144[/C][C]19.4569058454929[/C][/ROW]
[ROW][C]108[/C][C]10[/C][C]-0.831752480550014[/C][C]20.8317524805501[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278802&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278802&T=3

As an alternative you can also use a QR Code:  
QR Code


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

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
978.98.475143713348229.32485628665178
9898.049992462378489.95000753762153
999.17.5103333367320210.689666663268
1009.200000000000016.8729662810293911.5270337189706
1019.300000000000016.1491814496999812.4508185503
1029.400000000000015.3471293319443113.4528706680557
1039.500000000000014.4730326236332414.5269673763668
1049.600000000000013.5318384729196415.6681615270804
1059.700000000000012.5276003786982816.8723996213017
1069.800000000000011.4637176896170918.1362823103829
1079.900000000000020.34309415450714419.4569058454929
10810-0.83175248055001420.8317524805501


Figures (Output of Computation)

Input Parameters & R Code

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')