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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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999933893038648
betaFALSE
gammaFALSE

\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
ParameterValue
alpha0.999933893038648
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
219.419.40
319.419.40
419.519.40.100000000000001
519.519.49999338930396.61069613627774e-06
619.519.4999999995634.37012204201892e-10
728.719.59.20000000000003
828.728.69939181595560.000608184044438076
928.728.69999995979484.02051973935613e-08
1021.828.6999999999973-6.89999999999734
1121.821.8004561380333-0.000456138033328557
1221.821.8000000301539-3.01538989333494e-08
132021.800000000002-1.80000000000199
142020.0001189925304-0.000118992530435236
152020.0000000078662-7.86623388648877e-09
1622.620.00000000000052.59999999999948
1722.622.59982812190050.000171878099514799
1822.622.59999998863771.13623386255313e-08
1922.422.5999999999993-0.199999999999253
2022.422.4000132213923-1.32213922690028e-05
2122.422.400000000874-8.74024408403784e-10
2218.622.4000000000001-3.80000000000005
2318.618.6002512064531-0.000251206453135921
2418.618.6000000166065-1.6606495734095e-08
2516.218.6000000000011-2.4000000000011
2616.216.2001586567072-0.000158656707245797
2716.216.2000000104883-1.04883142171275e-08
2813.816.2000000000007-2.40000000000069
2913.813.8001586567072-0.00015865670724402
3013.813.8000000104883-1.04883124407706e-08
3124.113.800000000000710.2999999999993
3224.124.09931909829810.00068090170192292
3324.124.09999995498774.50123422979232e-08
3419.924.099999999997-4.19999999999703
3519.919.9002776492377-0.00027764923767748
3619.919.9000000183545-1.83545481036163e-08
3722.319.90000000000122.39999999999879
3822.322.29984134329280.000158656707245797
3922.322.29999998951171.04883142171275e-08
4020.922.2999999999993-1.39999999999931
4120.920.9000925497459-9.25497458936775e-05
4220.920.9000000061182-6.11818151696752e-09
4323.520.90000000000042.5999999999996
4423.523.49982812190050.000171878099514799
4523.523.49999998863771.13623386255313e-08
4623.123.4999999999993-0.399999999999249
4723.123.1000264427845-2.64427845415582e-05
4823.123.1000000017481-1.74805236952125e-09
4925.723.10000000000012.59999999999988
5025.725.69982812190050.000171878099514799
5125.725.69999998863771.13623386255313e-08
5219.725.6999999999992-5.99999999999925
5319.719.7003966417681-0.000396641768112715
5419.719.7000000262208-2.6220781990105e-08
5523.119.70000000000173.39999999999827
5623.123.09977523633140.000224763668597916
5723.123.09999998514161.48584433645738e-08
5820.723.099999999999-2.39999999999902
5920.720.7001586567072-0.000158656707245797
6020.720.7000000104883-1.04883142171275e-08
611820.7000000000007-2.70000000000069
621818.0001784887957-0.000178488795651077
631818.0000000117994-1.17993508297332e-08
6416.918.0000000000008-1.10000000000078
6516.916.9000727176575-7.2717657488397e-05
6616.916.9000000048071-4.80714490436185e-09
6724.416.90000000000037.49999999999968
6824.424.39950419778990.000495802210139118
6924.424.3999999672243.27759792639881e-08
7015.524.3999999999978-8.89999999999783
7115.515.500588351956-0.000588351956031019
7215.515.5000000388942-3.88941607809556e-08
7318.415.50000000000262.89999999999743
7418.418.39980828981210.00019171018792008
7518.418.39999998732661.26733787908506e-08
7616.218.3999999999992-2.19999999999916
7716.216.200145435315-0.000145435314973241
7816.216.2000000096143-9.61428625601002e-09
7920.616.20000000000064.39999999999937
8020.620.59970912937010.000290870629950035
8120.620.59999998077141.922857251202e-08
8219.820.5999999999987-0.799999999998729
8319.819.8000528855691-5.28855690831165e-05
8419.819.8000000034961-3.49610473904249e-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
tObservedFittedResiduals
219.419.40
319.419.40
419.519.40.100000000000001
519.519.49999338930396.61069613627774e-06
619.519.4999999995634.37012204201892e-10
728.719.59.20000000000003
828.728.69939181595560.000608184044438076
928.728.69999995979484.02051973935613e-08
1021.828.6999999999973-6.89999999999734
1121.821.8004561380333-0.000456138033328557
1221.821.8000000301539-3.01538989333494e-08
132021.800000000002-1.80000000000199
142020.0001189925304-0.000118992530435236
152020.0000000078662-7.86623388648877e-09
1622.620.00000000000052.59999999999948
1722.622.59982812190050.000171878099514799
1822.622.59999998863771.13623386255313e-08
1922.422.5999999999993-0.199999999999253
2022.422.4000132213923-1.32213922690028e-05
2122.422.400000000874-8.74024408403784e-10
2218.622.4000000000001-3.80000000000005
2318.618.6002512064531-0.000251206453135921
2418.618.6000000166065-1.6606495734095e-08
2516.218.6000000000011-2.4000000000011
2616.216.2001586567072-0.000158656707245797
2716.216.2000000104883-1.04883142171275e-08
2813.816.2000000000007-2.40000000000069
2913.813.8001586567072-0.00015865670724402
3013.813.8000000104883-1.04883124407706e-08
3124.113.800000000000710.2999999999993
3224.124.09931909829810.00068090170192292
3324.124.09999995498774.50123422979232e-08
3419.924.099999999997-4.19999999999703
3519.919.9002776492377-0.00027764923767748
3619.919.9000000183545-1.83545481036163e-08
3722.319.90000000000122.39999999999879
3822.322.29984134329280.000158656707245797
3922.322.29999998951171.04883142171275e-08
4020.922.2999999999993-1.39999999999931
4120.920.9000925497459-9.25497458936775e-05
4220.920.9000000061182-6.11818151696752e-09
4323.520.90000000000042.5999999999996
4423.523.49982812190050.000171878099514799
4523.523.49999998863771.13623386255313e-08
4623.123.4999999999993-0.399999999999249
4723.123.1000264427845-2.64427845415582e-05
4823.123.1000000017481-1.74805236952125e-09
4925.723.10000000000012.59999999999988
5025.725.69982812190050.000171878099514799
5125.725.69999998863771.13623386255313e-08
5219.725.6999999999992-5.99999999999925
5319.719.7003966417681-0.000396641768112715
5419.719.7000000262208-2.6220781990105e-08
5523.119.70000000000173.39999999999827
5623.123.09977523633140.000224763668597916
5723.123.09999998514161.48584433645738e-08
5820.723.099999999999-2.39999999999902
5920.720.7001586567072-0.000158656707245797
6020.720.7000000104883-1.04883142171275e-08
611820.7000000000007-2.70000000000069
621818.0001784887957-0.000178488795651077
631818.0000000117994-1.17993508297332e-08
6416.918.0000000000008-1.10000000000078
6516.916.9000727176575-7.2717657488397e-05
6616.916.9000000048071-4.80714490436185e-09
6724.416.90000000000037.49999999999968
6824.424.39950419778990.000495802210139118
6924.424.3999999672243.27759792639881e-08
7015.524.3999999999978-8.89999999999783
7115.515.500588351956-0.000588351956031019
7215.515.5000000388942-3.88941607809556e-08
7318.415.50000000000262.89999999999743
7418.418.39980828981210.00019171018792008
7518.418.39999998732661.26733787908506e-08
7616.218.3999999999992-2.19999999999916
7716.216.200145435315-0.000145435314973241
7816.216.2000000096143-9.61428625601002e-09
7920.616.20000000000064.39999999999937
8020.620.59970912937010.000290870629950035
8120.620.59999998077141.922857251202e-08
8219.820.5999999999987-0.799999999998729
8319.819.8000528855691-5.28855690831165e-05
8419.819.8000000034961-3.49610473904249e-09







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8519.800000000000214.752132924857424.847867075143
8619.800000000000212.661473878311326.9385261216892
8719.800000000000211.057223074345628.5427769256549
8819.80000000000029.7047663943086729.8952336056918
8919.80000000000028.5132230138447731.0867769861557
9019.80000000000027.4359825332973832.1640174667031
9119.80000000000026.4453558228363333.1546441771641
9219.80000000000025.5233017024111834.0766982975893
9319.80000000000024.6572886357132334.9427113642872
9419.80000000000023.8381924380782135.7618075619223
9519.80000000000023.0591250579443236.5408749420561
9619.80000000000022.3147351462074837.285264853793

\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
tForecast95% Lower Bound95% Upper Bound
8519.800000000000214.752132924857424.847867075143
8619.800000000000212.661473878311326.9385261216892
8719.800000000000211.057223074345628.5427769256549
8819.80000000000029.7047663943086729.8952336056918
8919.80000000000028.5132230138447731.0867769861557
9019.80000000000027.4359825332973832.1640174667031
9119.80000000000026.4453558228363333.1546441771641
9219.80000000000025.5233017024111834.0766982975893
9319.80000000000024.6572886357132334.9427113642872
9419.80000000000023.8381924380782135.7618075619223
9519.80000000000023.0591250579443236.5408749420561
9619.80000000000022.3147351462074837.285264853793



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')