## Free Statistics

of Irreproducible Research!

Author's title
Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 12 Dec 2013 02:35:50 -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/12/t1386833978pejo9lrb4cwikey.htm/, Retrieved Tue, 07 Dec 2021 12:18:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232209, Retrieved Tue, 07 Dec 2021 12:18:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact62
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-12-12 07:35:50] [20efb5145ec2a2ddd8dcd418764211fa] [Current]
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Dataseries X:
19,4
19,4
19,4
19,5
19,5
19,5
28,7
28,7
28,7
21,8
21,8
21,8
20
20
20
22,6
22,6
22,6
22,4
22,4
22,4
18,6
18,6
18,6
16,2
16,2
16,2
13,8
13,8
13,8
24,1
24,1
24,1
19,9
19,9
19,9
22,3
22,3
22,3
20,9
20,9
20,9
23,5
23,5
23,5
23,1
23,1
23,1
25,7
25,7
25,7
19,7
19,7
19,7
23,1
23,1
23,1
20,7
20,7
20,7
18
18
18
16,9
16,9
16,9
24,4
24,4
24,4
15,5
15,5
15,5
18,4
18,4
18,4
16,2
16,2
16,2
20,6
20,6
20,6
19,8
19,8
19,8


 Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 5 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 & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232209&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]5 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=232209&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232209&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 5 seconds R Server 'Gwilym Jenkins' @ jenkins.wessa.net

 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.999933893038648 beta FALSE gamma FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999933893038648 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232209&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]0.999933893038648[/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=232209&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232209&T=1

As an alternative you can also use a QR Code:

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

 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.999933893038648 beta FALSE gamma FALSE

 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 2 19.4 19.4 0 3 19.4 19.4 0 4 19.5 19.4 0.100000000000001 5 19.5 19.4999933893039 6.61069613627774e-06 6 19.5 19.499999999563 4.37012204201892e-10 7 28.7 19.5 9.20000000000003 8 28.7 28.6993918159556 0.000608184044438076 9 28.7 28.6999999597948 4.02051973935613e-08 10 21.8 28.6999999999973 -6.89999999999734 11 21.8 21.8004561380333 -0.000456138033328557 12 21.8 21.8000000301539 -3.01538989333494e-08 13 20 21.800000000002 -1.80000000000199 14 20 20.0001189925304 -0.000118992530435236 15 20 20.0000000078662 -7.86623388648877e-09 16 22.6 20.0000000000005 2.59999999999948 17 22.6 22.5998281219005 0.000171878099514799 18 22.6 22.5999999886377 1.13623386255313e-08 19 22.4 22.5999999999993 -0.199999999999253 20 22.4 22.4000132213923 -1.32213922690028e-05 21 22.4 22.400000000874 -8.74024408403784e-10 22 18.6 22.4000000000001 -3.80000000000005 23 18.6 18.6002512064531 -0.000251206453135921 24 18.6 18.6000000166065 -1.6606495734095e-08 25 16.2 18.6000000000011 -2.4000000000011 26 16.2 16.2001586567072 -0.000158656707245797 27 16.2 16.2000000104883 -1.04883142171275e-08 28 13.8 16.2000000000007 -2.40000000000069 29 13.8 13.8001586567072 -0.00015865670724402 30 13.8 13.8000000104883 -1.04883124407706e-08 31 24.1 13.8000000000007 10.2999999999993 32 24.1 24.0993190982981 0.00068090170192292 33 24.1 24.0999999549877 4.50123422979232e-08 34 19.9 24.099999999997 -4.19999999999703 35 19.9 19.9002776492377 -0.00027764923767748 36 19.9 19.9000000183545 -1.83545481036163e-08 37 22.3 19.9000000000012 2.39999999999879 38 22.3 22.2998413432928 0.000158656707245797 39 22.3 22.2999999895117 1.04883142171275e-08 40 20.9 22.2999999999993 -1.39999999999931 41 20.9 20.9000925497459 -9.25497458936775e-05 42 20.9 20.9000000061182 -6.11818151696752e-09 43 23.5 20.9000000000004 2.5999999999996 44 23.5 23.4998281219005 0.000171878099514799 45 23.5 23.4999999886377 1.13623386255313e-08 46 23.1 23.4999999999993 -0.399999999999249 47 23.1 23.1000264427845 -2.64427845415582e-05 48 23.1 23.1000000017481 -1.74805236952125e-09 49 25.7 23.1000000000001 2.59999999999988 50 25.7 25.6998281219005 0.000171878099514799 51 25.7 25.6999999886377 1.13623386255313e-08 52 19.7 25.6999999999992 -5.99999999999925 53 19.7 19.7003966417681 -0.000396641768112715 54 19.7 19.7000000262208 -2.6220781990105e-08 55 23.1 19.7000000000017 3.39999999999827 56 23.1 23.0997752363314 0.000224763668597916 57 23.1 23.0999999851416 1.48584433645738e-08 58 20.7 23.099999999999 -2.39999999999902 59 20.7 20.7001586567072 -0.000158656707245797 60 20.7 20.7000000104883 -1.04883142171275e-08 61 18 20.7000000000007 -2.70000000000069 62 18 18.0001784887957 -0.000178488795651077 63 18 18.0000000117994 -1.17993508297332e-08 64 16.9 18.0000000000008 -1.10000000000078 65 16.9 16.9000727176575 -7.2717657488397e-05 66 16.9 16.9000000048071 -4.80714490436185e-09 67 24.4 16.9000000000003 7.49999999999968 68 24.4 24.3995041977899 0.000495802210139118 69 24.4 24.399999967224 3.27759792639881e-08 70 15.5 24.3999999999978 -8.89999999999783 71 15.5 15.500588351956 -0.000588351956031019 72 15.5 15.5000000388942 -3.88941607809556e-08 73 18.4 15.5000000000026 2.89999999999743 74 18.4 18.3998082898121 0.00019171018792008 75 18.4 18.3999999873266 1.26733787908506e-08 76 16.2 18.3999999999992 -2.19999999999916 77 16.2 16.200145435315 -0.000145435314973241 78 16.2 16.2000000096143 -9.61428625601002e-09 79 20.6 16.2000000000006 4.39999999999937 80 20.6 20.5997091293701 0.000290870629950035 81 20.6 20.5999999807714 1.922857251202e-08 82 19.8 20.5999999999987 -0.799999999998729 83 19.8 19.8000528855691 -5.28855690831165e-05 84 19.8 19.8000000034961 -3.49610473904249e-09

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 19.4 & 19.4 & 0 \tabularnewline
3 & 19.4 & 19.4 & 0 \tabularnewline
4 & 19.5 & 19.4 & 0.100000000000001 \tabularnewline
5 & 19.5 & 19.4999933893039 & 6.61069613627774e-06 \tabularnewline
6 & 19.5 & 19.499999999563 & 4.37012204201892e-10 \tabularnewline
7 & 28.7 & 19.5 & 9.20000000000003 \tabularnewline
8 & 28.7 & 28.6993918159556 & 0.000608184044438076 \tabularnewline
9 & 28.7 & 28.6999999597948 & 4.02051973935613e-08 \tabularnewline
10 & 21.8 & 28.6999999999973 & -6.89999999999734 \tabularnewline
11 & 21.8 & 21.8004561380333 & -0.000456138033328557 \tabularnewline
12 & 21.8 & 21.8000000301539 & -3.01538989333494e-08 \tabularnewline
13 & 20 & 21.800000000002 & -1.80000000000199 \tabularnewline
14 & 20 & 20.0001189925304 & -0.000118992530435236 \tabularnewline
15 & 20 & 20.0000000078662 & -7.86623388648877e-09 \tabularnewline
16 & 22.6 & 20.0000000000005 & 2.59999999999948 \tabularnewline
17 & 22.6 & 22.5998281219005 & 0.000171878099514799 \tabularnewline
18 & 22.6 & 22.5999999886377 & 1.13623386255313e-08 \tabularnewline
19 & 22.4 & 22.5999999999993 & -0.199999999999253 \tabularnewline
20 & 22.4 & 22.4000132213923 & -1.32213922690028e-05 \tabularnewline
21 & 22.4 & 22.400000000874 & -8.74024408403784e-10 \tabularnewline
22 & 18.6 & 22.4000000000001 & -3.80000000000005 \tabularnewline
23 & 18.6 & 18.6002512064531 & -0.000251206453135921 \tabularnewline
24 & 18.6 & 18.6000000166065 & -1.6606495734095e-08 \tabularnewline
25 & 16.2 & 18.6000000000011 & -2.4000000000011 \tabularnewline
26 & 16.2 & 16.2001586567072 & -0.000158656707245797 \tabularnewline
27 & 16.2 & 16.2000000104883 & -1.04883142171275e-08 \tabularnewline
28 & 13.8 & 16.2000000000007 & -2.40000000000069 \tabularnewline
29 & 13.8 & 13.8001586567072 & -0.00015865670724402 \tabularnewline
30 & 13.8 & 13.8000000104883 & -1.04883124407706e-08 \tabularnewline
31 & 24.1 & 13.8000000000007 & 10.2999999999993 \tabularnewline
32 & 24.1 & 24.0993190982981 & 0.00068090170192292 \tabularnewline
33 & 24.1 & 24.0999999549877 & 4.50123422979232e-08 \tabularnewline
34 & 19.9 & 24.099999999997 & -4.19999999999703 \tabularnewline
35 & 19.9 & 19.9002776492377 & -0.00027764923767748 \tabularnewline
36 & 19.9 & 19.9000000183545 & -1.83545481036163e-08 \tabularnewline
37 & 22.3 & 19.9000000000012 & 2.39999999999879 \tabularnewline
38 & 22.3 & 22.2998413432928 & 0.000158656707245797 \tabularnewline
39 & 22.3 & 22.2999999895117 & 1.04883142171275e-08 \tabularnewline
40 & 20.9 & 22.2999999999993 & -1.39999999999931 \tabularnewline
41 & 20.9 & 20.9000925497459 & -9.25497458936775e-05 \tabularnewline
42 & 20.9 & 20.9000000061182 & -6.11818151696752e-09 \tabularnewline
43 & 23.5 & 20.9000000000004 & 2.5999999999996 \tabularnewline
44 & 23.5 & 23.4998281219005 & 0.000171878099514799 \tabularnewline
45 & 23.5 & 23.4999999886377 & 1.13623386255313e-08 \tabularnewline
46 & 23.1 & 23.4999999999993 & -0.399999999999249 \tabularnewline
47 & 23.1 & 23.1000264427845 & -2.64427845415582e-05 \tabularnewline
48 & 23.1 & 23.1000000017481 & -1.74805236952125e-09 \tabularnewline
49 & 25.7 & 23.1000000000001 & 2.59999999999988 \tabularnewline
50 & 25.7 & 25.6998281219005 & 0.000171878099514799 \tabularnewline
51 & 25.7 & 25.6999999886377 & 1.13623386255313e-08 \tabularnewline
52 & 19.7 & 25.6999999999992 & -5.99999999999925 \tabularnewline
53 & 19.7 & 19.7003966417681 & -0.000396641768112715 \tabularnewline
54 & 19.7 & 19.7000000262208 & -2.6220781990105e-08 \tabularnewline
55 & 23.1 & 19.7000000000017 & 3.39999999999827 \tabularnewline
56 & 23.1 & 23.0997752363314 & 0.000224763668597916 \tabularnewline
57 & 23.1 & 23.0999999851416 & 1.48584433645738e-08 \tabularnewline
58 & 20.7 & 23.099999999999 & -2.39999999999902 \tabularnewline
59 & 20.7 & 20.7001586567072 & -0.000158656707245797 \tabularnewline
60 & 20.7 & 20.7000000104883 & -1.04883142171275e-08 \tabularnewline
61 & 18 & 20.7000000000007 & -2.70000000000069 \tabularnewline
62 & 18 & 18.0001784887957 & -0.000178488795651077 \tabularnewline
63 & 18 & 18.0000000117994 & -1.17993508297332e-08 \tabularnewline
64 & 16.9 & 18.0000000000008 & -1.10000000000078 \tabularnewline
65 & 16.9 & 16.9000727176575 & -7.2717657488397e-05 \tabularnewline
66 & 16.9 & 16.9000000048071 & -4.80714490436185e-09 \tabularnewline
67 & 24.4 & 16.9000000000003 & 7.49999999999968 \tabularnewline
68 & 24.4 & 24.3995041977899 & 0.000495802210139118 \tabularnewline
69 & 24.4 & 24.399999967224 & 3.27759792639881e-08 \tabularnewline
70 & 15.5 & 24.3999999999978 & -8.89999999999783 \tabularnewline
71 & 15.5 & 15.500588351956 & -0.000588351956031019 \tabularnewline
72 & 15.5 & 15.5000000388942 & -3.88941607809556e-08 \tabularnewline
73 & 18.4 & 15.5000000000026 & 2.89999999999743 \tabularnewline
74 & 18.4 & 18.3998082898121 & 0.00019171018792008 \tabularnewline
75 & 18.4 & 18.3999999873266 & 1.26733787908506e-08 \tabularnewline
76 & 16.2 & 18.3999999999992 & -2.19999999999916 \tabularnewline
77 & 16.2 & 16.200145435315 & -0.000145435314973241 \tabularnewline
78 & 16.2 & 16.2000000096143 & -9.61428625601002e-09 \tabularnewline
79 & 20.6 & 16.2000000000006 & 4.39999999999937 \tabularnewline
80 & 20.6 & 20.5997091293701 & 0.000290870629950035 \tabularnewline
81 & 20.6 & 20.5999999807714 & 1.922857251202e-08 \tabularnewline
82 & 19.8 & 20.5999999999987 & -0.799999999998729 \tabularnewline
83 & 19.8 & 19.8000528855691 & -5.28855690831165e-05 \tabularnewline
84 & 19.8 & 19.8000000034961 & -3.49610473904249e-09 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232209&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]19.4[/C][C]19.4[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]19.4[/C][C]19.4[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]19.5[/C][C]19.4[/C][C]0.100000000000001[/C][/ROW]
[ROW][C]5[/C][C]19.5[/C][C]19.4999933893039[/C][C]6.61069613627774e-06[/C][/ROW]
[ROW][C]6[/C][C]19.5[/C][C]19.499999999563[/C][C]4.37012204201892e-10[/C][/ROW]
[ROW][C]7[/C][C]28.7[/C][C]19.5[/C][C]9.20000000000003[/C][/ROW]
[ROW][C]8[/C][C]28.7[/C][C]28.6993918159556[/C][C]0.000608184044438076[/C][/ROW]
[ROW][C]9[/C][C]28.7[/C][C]28.6999999597948[/C][C]4.02051973935613e-08[/C][/ROW]
[ROW][C]10[/C][C]21.8[/C][C]28.6999999999973[/C][C]-6.89999999999734[/C][/ROW]
[ROW][C]11[/C][C]21.8[/C][C]21.8004561380333[/C][C]-0.000456138033328557[/C][/ROW]
[ROW][C]12[/C][C]21.8[/C][C]21.8000000301539[/C][C]-3.01538989333494e-08[/C][/ROW]
[ROW][C]13[/C][C]20[/C][C]21.800000000002[/C][C]-1.80000000000199[/C][/ROW]
[ROW][C]14[/C][C]20[/C][C]20.0001189925304[/C][C]-0.000118992530435236[/C][/ROW]
[ROW][C]15[/C][C]20[/C][C]20.0000000078662[/C][C]-7.86623388648877e-09[/C][/ROW]
[ROW][C]16[/C][C]22.6[/C][C]20.0000000000005[/C][C]2.59999999999948[/C][/ROW]
[ROW][C]17[/C][C]22.6[/C][C]22.5998281219005[/C][C]0.000171878099514799[/C][/ROW]
[ROW][C]18[/C][C]22.6[/C][C]22.5999999886377[/C][C]1.13623386255313e-08[/C][/ROW]
[ROW][C]19[/C][C]22.4[/C][C]22.5999999999993[/C][C]-0.199999999999253[/C][/ROW]
[ROW][C]20[/C][C]22.4[/C][C]22.4000132213923[/C][C]-1.32213922690028e-05[/C][/ROW]
[ROW][C]21[/C][C]22.4[/C][C]22.400000000874[/C][C]-8.74024408403784e-10[/C][/ROW]
[ROW][C]22[/C][C]18.6[/C][C]22.4000000000001[/C][C]-3.80000000000005[/C][/ROW]
[ROW][C]23[/C][C]18.6[/C][C]18.6002512064531[/C][C]-0.000251206453135921[/C][/ROW]
[ROW][C]24[/C][C]18.6[/C][C]18.6000000166065[/C][C]-1.6606495734095e-08[/C][/ROW]
[ROW][C]25[/C][C]16.2[/C][C]18.6000000000011[/C][C]-2.4000000000011[/C][/ROW]
[ROW][C]26[/C][C]16.2[/C][C]16.2001586567072[/C][C]-0.000158656707245797[/C][/ROW]
[ROW][C]27[/C][C]16.2[/C][C]16.2000000104883[/C][C]-1.04883142171275e-08[/C][/ROW]
[ROW][C]28[/C][C]13.8[/C][C]16.2000000000007[/C][C]-2.40000000000069[/C][/ROW]
[ROW][C]29[/C][C]13.8[/C][C]13.8001586567072[/C][C]-0.00015865670724402[/C][/ROW]
[ROW][C]30[/C][C]13.8[/C][C]13.8000000104883[/C][C]-1.04883124407706e-08[/C][/ROW]
[ROW][C]31[/C][C]24.1[/C][C]13.8000000000007[/C][C]10.2999999999993[/C][/ROW]
[ROW][C]32[/C][C]24.1[/C][C]24.0993190982981[/C][C]0.00068090170192292[/C][/ROW]
[ROW][C]33[/C][C]24.1[/C][C]24.0999999549877[/C][C]4.50123422979232e-08[/C][/ROW]
[ROW][C]34[/C][C]19.9[/C][C]24.099999999997[/C][C]-4.19999999999703[/C][/ROW]
[ROW][C]35[/C][C]19.9[/C][C]19.9002776492377[/C][C]-0.00027764923767748[/C][/ROW]
[ROW][C]36[/C][C]19.9[/C][C]19.9000000183545[/C][C]-1.83545481036163e-08[/C][/ROW]
[ROW][C]37[/C][C]22.3[/C][C]19.9000000000012[/C][C]2.39999999999879[/C][/ROW]
[ROW][C]38[/C][C]22.3[/C][C]22.2998413432928[/C][C]0.000158656707245797[/C][/ROW]
[ROW][C]39[/C][C]22.3[/C][C]22.2999999895117[/C][C]1.04883142171275e-08[/C][/ROW]
[ROW][C]40[/C][C]20.9[/C][C]22.2999999999993[/C][C]-1.39999999999931[/C][/ROW]
[ROW][C]41[/C][C]20.9[/C][C]20.9000925497459[/C][C]-9.25497458936775e-05[/C][/ROW]
[ROW][C]42[/C][C]20.9[/C][C]20.9000000061182[/C][C]-6.11818151696752e-09[/C][/ROW]
[ROW][C]43[/C][C]23.5[/C][C]20.9000000000004[/C][C]2.5999999999996[/C][/ROW]
[ROW][C]44[/C][C]23.5[/C][C]23.4998281219005[/C][C]0.000171878099514799[/C][/ROW]
[ROW][C]45[/C][C]23.5[/C][C]23.4999999886377[/C][C]1.13623386255313e-08[/C][/ROW]
[ROW][C]46[/C][C]23.1[/C][C]23.4999999999993[/C][C]-0.399999999999249[/C][/ROW]
[ROW][C]47[/C][C]23.1[/C][C]23.1000264427845[/C][C]-2.64427845415582e-05[/C][/ROW]
[ROW][C]48[/C][C]23.1[/C][C]23.1000000017481[/C][C]-1.74805236952125e-09[/C][/ROW]
[ROW][C]49[/C][C]25.7[/C][C]23.1000000000001[/C][C]2.59999999999988[/C][/ROW]
[ROW][C]50[/C][C]25.7[/C][C]25.6998281219005[/C][C]0.000171878099514799[/C][/ROW]
[ROW][C]51[/C][C]25.7[/C][C]25.6999999886377[/C][C]1.13623386255313e-08[/C][/ROW]
[ROW][C]52[/C][C]19.7[/C][C]25.6999999999992[/C][C]-5.99999999999925[/C][/ROW]
[ROW][C]53[/C][C]19.7[/C][C]19.7003966417681[/C][C]-0.000396641768112715[/C][/ROW]
[ROW][C]54[/C][C]19.7[/C][C]19.7000000262208[/C][C]-2.6220781990105e-08[/C][/ROW]
[ROW][C]55[/C][C]23.1[/C][C]19.7000000000017[/C][C]3.39999999999827[/C][/ROW]
[ROW][C]56[/C][C]23.1[/C][C]23.0997752363314[/C][C]0.000224763668597916[/C][/ROW]
[ROW][C]57[/C][C]23.1[/C][C]23.0999999851416[/C][C]1.48584433645738e-08[/C][/ROW]
[ROW][C]58[/C][C]20.7[/C][C]23.099999999999[/C][C]-2.39999999999902[/C][/ROW]
[ROW][C]59[/C][C]20.7[/C][C]20.7001586567072[/C][C]-0.000158656707245797[/C][/ROW]
[ROW][C]60[/C][C]20.7[/C][C]20.7000000104883[/C][C]-1.04883142171275e-08[/C][/ROW]
[ROW][C]61[/C][C]18[/C][C]20.7000000000007[/C][C]-2.70000000000069[/C][/ROW]
[ROW][C]62[/C][C]18[/C][C]18.0001784887957[/C][C]-0.000178488795651077[/C][/ROW]
[ROW][C]63[/C][C]18[/C][C]18.0000000117994[/C][C]-1.17993508297332e-08[/C][/ROW]
[ROW][C]64[/C][C]16.9[/C][C]18.0000000000008[/C][C]-1.10000000000078[/C][/ROW]
[ROW][C]65[/C][C]16.9[/C][C]16.9000727176575[/C][C]-7.2717657488397e-05[/C][/ROW]
[ROW][C]66[/C][C]16.9[/C][C]16.9000000048071[/C][C]-4.80714490436185e-09[/C][/ROW]
[ROW][C]67[/C][C]24.4[/C][C]16.9000000000003[/C][C]7.49999999999968[/C][/ROW]
[ROW][C]68[/C][C]24.4[/C][C]24.3995041977899[/C][C]0.000495802210139118[/C][/ROW]
[ROW][C]69[/C][C]24.4[/C][C]24.399999967224[/C][C]3.27759792639881e-08[/C][/ROW]
[ROW][C]70[/C][C]15.5[/C][C]24.3999999999978[/C][C]-8.89999999999783[/C][/ROW]
[ROW][C]71[/C][C]15.5[/C][C]15.500588351956[/C][C]-0.000588351956031019[/C][/ROW]
[ROW][C]72[/C][C]15.5[/C][C]15.5000000388942[/C][C]-3.88941607809556e-08[/C][/ROW]
[ROW][C]73[/C][C]18.4[/C][C]15.5000000000026[/C][C]2.89999999999743[/C][/ROW]
[ROW][C]74[/C][C]18.4[/C][C]18.3998082898121[/C][C]0.00019171018792008[/C][/ROW]
[ROW][C]75[/C][C]18.4[/C][C]18.3999999873266[/C][C]1.26733787908506e-08[/C][/ROW]
[ROW][C]76[/C][C]16.2[/C][C]18.3999999999992[/C][C]-2.19999999999916[/C][/ROW]
[ROW][C]77[/C][C]16.2[/C][C]16.200145435315[/C][C]-0.000145435314973241[/C][/ROW]
[ROW][C]78[/C][C]16.2[/C][C]16.2000000096143[/C][C]-9.61428625601002e-09[/C][/ROW]
[ROW][C]79[/C][C]20.6[/C][C]16.2000000000006[/C][C]4.39999999999937[/C][/ROW]
[ROW][C]80[/C][C]20.6[/C][C]20.5997091293701[/C][C]0.000290870629950035[/C][/ROW]
[ROW][C]81[/C][C]20.6[/C][C]20.5999999807714[/C][C]1.922857251202e-08[/C][/ROW]
[ROW][C]82[/C][C]19.8[/C][C]20.5999999999987[/C][C]-0.799999999998729[/C][/ROW]
[ROW][C]83[/C][C]19.8[/C][C]19.8000528855691[/C][C]-5.28855690831165e-05[/C][/ROW]
[ROW][C]84[/C][C]19.8[/C][C]19.8000000034961[/C][C]-3.49610473904249e-09[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232209&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232209&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 2 19.4 19.4 0 3 19.4 19.4 0 4 19.5 19.4 0.100000000000001 5 19.5 19.4999933893039 6.61069613627774e-06 6 19.5 19.499999999563 4.37012204201892e-10 7 28.7 19.5 9.20000000000003 8 28.7 28.6993918159556 0.000608184044438076 9 28.7 28.6999999597948 4.02051973935613e-08 10 21.8 28.6999999999973 -6.89999999999734 11 21.8 21.8004561380333 -0.000456138033328557 12 21.8 21.8000000301539 -3.01538989333494e-08 13 20 21.800000000002 -1.80000000000199 14 20 20.0001189925304 -0.000118992530435236 15 20 20.0000000078662 -7.86623388648877e-09 16 22.6 20.0000000000005 2.59999999999948 17 22.6 22.5998281219005 0.000171878099514799 18 22.6 22.5999999886377 1.13623386255313e-08 19 22.4 22.5999999999993 -0.199999999999253 20 22.4 22.4000132213923 -1.32213922690028e-05 21 22.4 22.400000000874 -8.74024408403784e-10 22 18.6 22.4000000000001 -3.80000000000005 23 18.6 18.6002512064531 -0.000251206453135921 24 18.6 18.6000000166065 -1.6606495734095e-08 25 16.2 18.6000000000011 -2.4000000000011 26 16.2 16.2001586567072 -0.000158656707245797 27 16.2 16.2000000104883 -1.04883142171275e-08 28 13.8 16.2000000000007 -2.40000000000069 29 13.8 13.8001586567072 -0.00015865670724402 30 13.8 13.8000000104883 -1.04883124407706e-08 31 24.1 13.8000000000007 10.2999999999993 32 24.1 24.0993190982981 0.00068090170192292 33 24.1 24.0999999549877 4.50123422979232e-08 34 19.9 24.099999999997 -4.19999999999703 35 19.9 19.9002776492377 -0.00027764923767748 36 19.9 19.9000000183545 -1.83545481036163e-08 37 22.3 19.9000000000012 2.39999999999879 38 22.3 22.2998413432928 0.000158656707245797 39 22.3 22.2999999895117 1.04883142171275e-08 40 20.9 22.2999999999993 -1.39999999999931 41 20.9 20.9000925497459 -9.25497458936775e-05 42 20.9 20.9000000061182 -6.11818151696752e-09 43 23.5 20.9000000000004 2.5999999999996 44 23.5 23.4998281219005 0.000171878099514799 45 23.5 23.4999999886377 1.13623386255313e-08 46 23.1 23.4999999999993 -0.399999999999249 47 23.1 23.1000264427845 -2.64427845415582e-05 48 23.1 23.1000000017481 -1.74805236952125e-09 49 25.7 23.1000000000001 2.59999999999988 50 25.7 25.6998281219005 0.000171878099514799 51 25.7 25.6999999886377 1.13623386255313e-08 52 19.7 25.6999999999992 -5.99999999999925 53 19.7 19.7003966417681 -0.000396641768112715 54 19.7 19.7000000262208 -2.6220781990105e-08 55 23.1 19.7000000000017 3.39999999999827 56 23.1 23.0997752363314 0.000224763668597916 57 23.1 23.0999999851416 1.48584433645738e-08 58 20.7 23.099999999999 -2.39999999999902 59 20.7 20.7001586567072 -0.000158656707245797 60 20.7 20.7000000104883 -1.04883142171275e-08 61 18 20.7000000000007 -2.70000000000069 62 18 18.0001784887957 -0.000178488795651077 63 18 18.0000000117994 -1.17993508297332e-08 64 16.9 18.0000000000008 -1.10000000000078 65 16.9 16.9000727176575 -7.2717657488397e-05 66 16.9 16.9000000048071 -4.80714490436185e-09 67 24.4 16.9000000000003 7.49999999999968 68 24.4 24.3995041977899 0.000495802210139118 69 24.4 24.399999967224 3.27759792639881e-08 70 15.5 24.3999999999978 -8.89999999999783 71 15.5 15.500588351956 -0.000588351956031019 72 15.5 15.5000000388942 -3.88941607809556e-08 73 18.4 15.5000000000026 2.89999999999743 74 18.4 18.3998082898121 0.00019171018792008 75 18.4 18.3999999873266 1.26733787908506e-08 76 16.2 18.3999999999992 -2.19999999999916 77 16.2 16.200145435315 -0.000145435314973241 78 16.2 16.2000000096143 -9.61428625601002e-09 79 20.6 16.2000000000006 4.39999999999937 80 20.6 20.5997091293701 0.000290870629950035 81 20.6 20.5999999807714 1.922857251202e-08 82 19.8 20.5999999999987 -0.799999999998729 83 19.8 19.8000528855691 -5.28855690831165e-05 84 19.8 19.8000000034961 -3.49610473904249e-09

 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 85 19.8000000000002 14.7521329248574 24.847867075143 86 19.8000000000002 12.6614738783113 26.9385261216892 87 19.8000000000002 11.0572230743456 28.5427769256549 88 19.8000000000002 9.70476639430867 29.8952336056918 89 19.8000000000002 8.51322301384477 31.0867769861557 90 19.8000000000002 7.43598253329738 32.1640174667031 91 19.8000000000002 6.44535582283633 33.1546441771641 92 19.8000000000002 5.52330170241118 34.0766982975893 93 19.8000000000002 4.65728863571323 34.9427113642872 94 19.8000000000002 3.83819243807821 35.7618075619223 95 19.8000000000002 3.05912505794432 36.5408749420561 96 19.8000000000002 2.31473514620748 37.285264853793

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 19.8000000000002 & 14.7521329248574 & 24.847867075143 \tabularnewline
86 & 19.8000000000002 & 12.6614738783113 & 26.9385261216892 \tabularnewline
87 & 19.8000000000002 & 11.0572230743456 & 28.5427769256549 \tabularnewline
88 & 19.8000000000002 & 9.70476639430867 & 29.8952336056918 \tabularnewline
89 & 19.8000000000002 & 8.51322301384477 & 31.0867769861557 \tabularnewline
90 & 19.8000000000002 & 7.43598253329738 & 32.1640174667031 \tabularnewline
91 & 19.8000000000002 & 6.44535582283633 & 33.1546441771641 \tabularnewline
92 & 19.8000000000002 & 5.52330170241118 & 34.0766982975893 \tabularnewline
93 & 19.8000000000002 & 4.65728863571323 & 34.9427113642872 \tabularnewline
94 & 19.8000000000002 & 3.83819243807821 & 35.7618075619223 \tabularnewline
95 & 19.8000000000002 & 3.05912505794432 & 36.5408749420561 \tabularnewline
96 & 19.8000000000002 & 2.31473514620748 & 37.285264853793 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232209&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]19.8000000000002[/C][C]14.7521329248574[/C][C]24.847867075143[/C][/ROW]
[ROW][C]86[/C][C]19.8000000000002[/C][C]12.6614738783113[/C][C]26.9385261216892[/C][/ROW]
[ROW][C]87[/C][C]19.8000000000002[/C][C]11.0572230743456[/C][C]28.5427769256549[/C][/ROW]
[ROW][C]88[/C][C]19.8000000000002[/C][C]9.70476639430867[/C][C]29.8952336056918[/C][/ROW]
[ROW][C]89[/C][C]19.8000000000002[/C][C]8.51322301384477[/C][C]31.0867769861557[/C][/ROW]
[ROW][C]90[/C][C]19.8000000000002[/C][C]7.43598253329738[/C][C]32.1640174667031[/C][/ROW]
[ROW][C]91[/C][C]19.8000000000002[/C][C]6.44535582283633[/C][C]33.1546441771641[/C][/ROW]
[ROW][C]92[/C][C]19.8000000000002[/C][C]5.52330170241118[/C][C]34.0766982975893[/C][/ROW]
[ROW][C]93[/C][C]19.8000000000002[/C][C]4.65728863571323[/C][C]34.9427113642872[/C][/ROW]
[ROW][C]94[/C][C]19.8000000000002[/C][C]3.83819243807821[/C][C]35.7618075619223[/C][/ROW]
[ROW][C]95[/C][C]19.8000000000002[/C][C]3.05912505794432[/C][C]36.5408749420561[/C][/ROW]
[ROW][C]96[/C][C]19.8000000000002[/C][C]2.31473514620748[/C][C]37.285264853793[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232209&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232209&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 85 19.8000000000002 14.7521329248574 24.847867075143 86 19.8000000000002 12.6614738783113 26.9385261216892 87 19.8000000000002 11.0572230743456 28.5427769256549 88 19.8000000000002 9.70476639430867 29.8952336056918 89 19.8000000000002 8.51322301384477 31.0867769861557 90 19.8000000000002 7.43598253329738 32.1640174667031 91 19.8000000000002 6.44535582283633 33.1546441771641 92 19.8000000000002 5.52330170241118 34.0766982975893 93 19.8000000000002 4.65728863571323 34.9427113642872 94 19.8000000000002 3.83819243807821 35.7618075619223 95 19.8000000000002 3.05912505794432 36.5408749420561 96 19.8000000000002 2.31473514620748 37.285264853793

par1 <- as.numeric(par1)if (par2 == 'Single') K <- 1if (par2 == 'Double') K <- 2if (par2 == 'Triple') K <- par1nx <- length(x)nxmK <- nx - Kx <- 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)fitmyresid <- 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')