Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 25 Dec 2011 04:51:30 -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/2011/Dec/25/t132480674098hbx2h5aoaknae.htm/, Retrieved Sun, 05 May 2024 09:52:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160765, Retrieved Sun, 05 May 2024 09:52:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact165
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [oef 10 eigen reek...] [2011-12-25 09:51:30] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
63.6900
63.6900
63.6900
63.6900
63.6900
63.6900
63.6900
63.6900
65.0300
65.0300
65.0300
65.0300
65.0300
65.0300
65.0300
65.0300
65.0300
65.0300
65.0300
65.0300
65.0300
65.0300
65.0300
65.0300
101.16
101.16
101.16
101.16
101.16
101.16
101.16
101.16
101.16
101.21
101.21
101.21
103.16
103.16
103.16
103.16
101.13
101.13
100.53
100.53
100.53
100.53
100.53
100.53
100.53
100.53
100.53
99.42
99.42
99.42
99.42
100.31
100.31
102.25
102.25
102.25
101.81
101.81
101.81
101.81
101.81
101.81
101.81
101.81
101.81
101.81
101.81
101.81
101.81
101.81
101.81
101.81
101.81
101.81
101.81
101.94
101.94
101.94
101.94
101.94




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160765&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160765&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160765&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 time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999918963503717
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999918963503717 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160765&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]0.999918963503717[/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=160765&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160765&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
alpha0.999918963503717
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
263.6963.690
363.6963.690
463.6963.690
563.6963.690
663.6963.690
763.6963.690
863.6963.690
965.0363.691.34
1065.0365.0298914110950.000108588905021634
1165.0365.02999999120038.7996596676021e-09
1265.0365.02999999999937.105427357601e-13
1365.0365.030
1465.0365.030
1565.0365.030
1665.0365.030
1765.0365.030
1865.0365.030
1965.0365.030
2065.0365.030
2165.0365.030
2265.0365.030
2365.0365.030
2465.0365.030
25101.1665.0336.13
26101.16101.1570721513890.00292784861071027
27101.16101.1599997627372.37262597124754e-07
28101.16101.1599999999811.92272864296683e-11
29101.16101.160
30101.16101.160
31101.16101.160
32101.16101.160
33101.16101.160
34101.21101.160.0499999999999972
35101.21101.2099959481754.0518248169974e-06
36101.21101.2099999996723.28341798194742e-10
37103.16101.211.95000000000003
38103.16103.1598419788320.000158021167749212
39103.16103.1599999871951.28054864489968e-08
40103.16103.1599999999991.03739239420975e-12
41101.13103.16-2.03
42101.13101.130164504087-0.000164504087450723
43100.53101.130000013331-0.600000013330828
44100.53100.530048621899-4.8621898855572e-05
45100.53100.53000000394-3.94014421090105e-09
46100.53100.53-3.12638803734444e-13
47100.53100.530
48100.53100.530
49100.53100.530
50100.53100.530
51100.53100.530
5299.42100.53-1.11
5399.4299.4200899505109-8.99505108691301e-05
5499.4299.4200000072893-7.28927318505157e-09
5599.4299.4200000000006-5.96855898038484e-13
56100.3199.420.890000000000001
57100.31100.3099278775187.21224816970789e-05
58102.25100.3099999941551.94000000584455
59102.25102.2498427891970.000157210803266139
60102.25102.249999987261.27398180893579e-08
61101.81102.249999999999-0.43999999999896
62101.81101.810035656058-3.56560583583132e-05
63101.81101.810000002889-2.88943624582316e-09
64101.81101.81-2.27373675443232e-13
65101.81101.810
66101.81101.810
67101.81101.810
68101.81101.810
69101.81101.810
70101.81101.810
71101.81101.810
72101.81101.810
73101.81101.810
74101.81101.810
75101.81101.810
76101.81101.810
77101.81101.810
78101.81101.810
79101.81101.810
80101.94101.810.129999999999995
81101.94101.9399894652551.05347445185089e-05
82101.94101.9399999991468.53702886161045e-10
83101.94101.947.105427357601e-14
84101.94101.940

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 63.69 & 63.69 & 0 \tabularnewline
3 & 63.69 & 63.69 & 0 \tabularnewline
4 & 63.69 & 63.69 & 0 \tabularnewline
5 & 63.69 & 63.69 & 0 \tabularnewline
6 & 63.69 & 63.69 & 0 \tabularnewline
7 & 63.69 & 63.69 & 0 \tabularnewline
8 & 63.69 & 63.69 & 0 \tabularnewline
9 & 65.03 & 63.69 & 1.34 \tabularnewline
10 & 65.03 & 65.029891411095 & 0.000108588905021634 \tabularnewline
11 & 65.03 & 65.0299999912003 & 8.7996596676021e-09 \tabularnewline
12 & 65.03 & 65.0299999999993 & 7.105427357601e-13 \tabularnewline
13 & 65.03 & 65.03 & 0 \tabularnewline
14 & 65.03 & 65.03 & 0 \tabularnewline
15 & 65.03 & 65.03 & 0 \tabularnewline
16 & 65.03 & 65.03 & 0 \tabularnewline
17 & 65.03 & 65.03 & 0 \tabularnewline
18 & 65.03 & 65.03 & 0 \tabularnewline
19 & 65.03 & 65.03 & 0 \tabularnewline
20 & 65.03 & 65.03 & 0 \tabularnewline
21 & 65.03 & 65.03 & 0 \tabularnewline
22 & 65.03 & 65.03 & 0 \tabularnewline
23 & 65.03 & 65.03 & 0 \tabularnewline
24 & 65.03 & 65.03 & 0 \tabularnewline
25 & 101.16 & 65.03 & 36.13 \tabularnewline
26 & 101.16 & 101.157072151389 & 0.00292784861071027 \tabularnewline
27 & 101.16 & 101.159999762737 & 2.37262597124754e-07 \tabularnewline
28 & 101.16 & 101.159999999981 & 1.92272864296683e-11 \tabularnewline
29 & 101.16 & 101.16 & 0 \tabularnewline
30 & 101.16 & 101.16 & 0 \tabularnewline
31 & 101.16 & 101.16 & 0 \tabularnewline
32 & 101.16 & 101.16 & 0 \tabularnewline
33 & 101.16 & 101.16 & 0 \tabularnewline
34 & 101.21 & 101.16 & 0.0499999999999972 \tabularnewline
35 & 101.21 & 101.209995948175 & 4.0518248169974e-06 \tabularnewline
36 & 101.21 & 101.209999999672 & 3.28341798194742e-10 \tabularnewline
37 & 103.16 & 101.21 & 1.95000000000003 \tabularnewline
38 & 103.16 & 103.159841978832 & 0.000158021167749212 \tabularnewline
39 & 103.16 & 103.159999987195 & 1.28054864489968e-08 \tabularnewline
40 & 103.16 & 103.159999999999 & 1.03739239420975e-12 \tabularnewline
41 & 101.13 & 103.16 & -2.03 \tabularnewline
42 & 101.13 & 101.130164504087 & -0.000164504087450723 \tabularnewline
43 & 100.53 & 101.130000013331 & -0.600000013330828 \tabularnewline
44 & 100.53 & 100.530048621899 & -4.8621898855572e-05 \tabularnewline
45 & 100.53 & 100.53000000394 & -3.94014421090105e-09 \tabularnewline
46 & 100.53 & 100.53 & -3.12638803734444e-13 \tabularnewline
47 & 100.53 & 100.53 & 0 \tabularnewline
48 & 100.53 & 100.53 & 0 \tabularnewline
49 & 100.53 & 100.53 & 0 \tabularnewline
50 & 100.53 & 100.53 & 0 \tabularnewline
51 & 100.53 & 100.53 & 0 \tabularnewline
52 & 99.42 & 100.53 & -1.11 \tabularnewline
53 & 99.42 & 99.4200899505109 & -8.99505108691301e-05 \tabularnewline
54 & 99.42 & 99.4200000072893 & -7.28927318505157e-09 \tabularnewline
55 & 99.42 & 99.4200000000006 & -5.96855898038484e-13 \tabularnewline
56 & 100.31 & 99.42 & 0.890000000000001 \tabularnewline
57 & 100.31 & 100.309927877518 & 7.21224816970789e-05 \tabularnewline
58 & 102.25 & 100.309999994155 & 1.94000000584455 \tabularnewline
59 & 102.25 & 102.249842789197 & 0.000157210803266139 \tabularnewline
60 & 102.25 & 102.24999998726 & 1.27398180893579e-08 \tabularnewline
61 & 101.81 & 102.249999999999 & -0.43999999999896 \tabularnewline
62 & 101.81 & 101.810035656058 & -3.56560583583132e-05 \tabularnewline
63 & 101.81 & 101.810000002889 & -2.88943624582316e-09 \tabularnewline
64 & 101.81 & 101.81 & -2.27373675443232e-13 \tabularnewline
65 & 101.81 & 101.81 & 0 \tabularnewline
66 & 101.81 & 101.81 & 0 \tabularnewline
67 & 101.81 & 101.81 & 0 \tabularnewline
68 & 101.81 & 101.81 & 0 \tabularnewline
69 & 101.81 & 101.81 & 0 \tabularnewline
70 & 101.81 & 101.81 & 0 \tabularnewline
71 & 101.81 & 101.81 & 0 \tabularnewline
72 & 101.81 & 101.81 & 0 \tabularnewline
73 & 101.81 & 101.81 & 0 \tabularnewline
74 & 101.81 & 101.81 & 0 \tabularnewline
75 & 101.81 & 101.81 & 0 \tabularnewline
76 & 101.81 & 101.81 & 0 \tabularnewline
77 & 101.81 & 101.81 & 0 \tabularnewline
78 & 101.81 & 101.81 & 0 \tabularnewline
79 & 101.81 & 101.81 & 0 \tabularnewline
80 & 101.94 & 101.81 & 0.129999999999995 \tabularnewline
81 & 101.94 & 101.939989465255 & 1.05347445185089e-05 \tabularnewline
82 & 101.94 & 101.939999999146 & 8.53702886161045e-10 \tabularnewline
83 & 101.94 & 101.94 & 7.105427357601e-14 \tabularnewline
84 & 101.94 & 101.94 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160765&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]63.69[/C][C]63.69[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]63.69[/C][C]63.69[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]63.69[/C][C]63.69[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]63.69[/C][C]63.69[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]63.69[/C][C]63.69[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]63.69[/C][C]63.69[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]63.69[/C][C]63.69[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]65.03[/C][C]63.69[/C][C]1.34[/C][/ROW]
[ROW][C]10[/C][C]65.03[/C][C]65.029891411095[/C][C]0.000108588905021634[/C][/ROW]
[ROW][C]11[/C][C]65.03[/C][C]65.0299999912003[/C][C]8.7996596676021e-09[/C][/ROW]
[ROW][C]12[/C][C]65.03[/C][C]65.0299999999993[/C][C]7.105427357601e-13[/C][/ROW]
[ROW][C]13[/C][C]65.03[/C][C]65.03[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]65.03[/C][C]65.03[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]65.03[/C][C]65.03[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]65.03[/C][C]65.03[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]65.03[/C][C]65.03[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]65.03[/C][C]65.03[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]65.03[/C][C]65.03[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]65.03[/C][C]65.03[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]65.03[/C][C]65.03[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]65.03[/C][C]65.03[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]65.03[/C][C]65.03[/C][C]0[/C][/ROW]
[ROW][C]24[/C][C]65.03[/C][C]65.03[/C][C]0[/C][/ROW]
[ROW][C]25[/C][C]101.16[/C][C]65.03[/C][C]36.13[/C][/ROW]
[ROW][C]26[/C][C]101.16[/C][C]101.157072151389[/C][C]0.00292784861071027[/C][/ROW]
[ROW][C]27[/C][C]101.16[/C][C]101.159999762737[/C][C]2.37262597124754e-07[/C][/ROW]
[ROW][C]28[/C][C]101.16[/C][C]101.159999999981[/C][C]1.92272864296683e-11[/C][/ROW]
[ROW][C]29[/C][C]101.16[/C][C]101.16[/C][C]0[/C][/ROW]
[ROW][C]30[/C][C]101.16[/C][C]101.16[/C][C]0[/C][/ROW]
[ROW][C]31[/C][C]101.16[/C][C]101.16[/C][C]0[/C][/ROW]
[ROW][C]32[/C][C]101.16[/C][C]101.16[/C][C]0[/C][/ROW]
[ROW][C]33[/C][C]101.16[/C][C]101.16[/C][C]0[/C][/ROW]
[ROW][C]34[/C][C]101.21[/C][C]101.16[/C][C]0.0499999999999972[/C][/ROW]
[ROW][C]35[/C][C]101.21[/C][C]101.209995948175[/C][C]4.0518248169974e-06[/C][/ROW]
[ROW][C]36[/C][C]101.21[/C][C]101.209999999672[/C][C]3.28341798194742e-10[/C][/ROW]
[ROW][C]37[/C][C]103.16[/C][C]101.21[/C][C]1.95000000000003[/C][/ROW]
[ROW][C]38[/C][C]103.16[/C][C]103.159841978832[/C][C]0.000158021167749212[/C][/ROW]
[ROW][C]39[/C][C]103.16[/C][C]103.159999987195[/C][C]1.28054864489968e-08[/C][/ROW]
[ROW][C]40[/C][C]103.16[/C][C]103.159999999999[/C][C]1.03739239420975e-12[/C][/ROW]
[ROW][C]41[/C][C]101.13[/C][C]103.16[/C][C]-2.03[/C][/ROW]
[ROW][C]42[/C][C]101.13[/C][C]101.130164504087[/C][C]-0.000164504087450723[/C][/ROW]
[ROW][C]43[/C][C]100.53[/C][C]101.130000013331[/C][C]-0.600000013330828[/C][/ROW]
[ROW][C]44[/C][C]100.53[/C][C]100.530048621899[/C][C]-4.8621898855572e-05[/C][/ROW]
[ROW][C]45[/C][C]100.53[/C][C]100.53000000394[/C][C]-3.94014421090105e-09[/C][/ROW]
[ROW][C]46[/C][C]100.53[/C][C]100.53[/C][C]-3.12638803734444e-13[/C][/ROW]
[ROW][C]47[/C][C]100.53[/C][C]100.53[/C][C]0[/C][/ROW]
[ROW][C]48[/C][C]100.53[/C][C]100.53[/C][C]0[/C][/ROW]
[ROW][C]49[/C][C]100.53[/C][C]100.53[/C][C]0[/C][/ROW]
[ROW][C]50[/C][C]100.53[/C][C]100.53[/C][C]0[/C][/ROW]
[ROW][C]51[/C][C]100.53[/C][C]100.53[/C][C]0[/C][/ROW]
[ROW][C]52[/C][C]99.42[/C][C]100.53[/C][C]-1.11[/C][/ROW]
[ROW][C]53[/C][C]99.42[/C][C]99.4200899505109[/C][C]-8.99505108691301e-05[/C][/ROW]
[ROW][C]54[/C][C]99.42[/C][C]99.4200000072893[/C][C]-7.28927318505157e-09[/C][/ROW]
[ROW][C]55[/C][C]99.42[/C][C]99.4200000000006[/C][C]-5.96855898038484e-13[/C][/ROW]
[ROW][C]56[/C][C]100.31[/C][C]99.42[/C][C]0.890000000000001[/C][/ROW]
[ROW][C]57[/C][C]100.31[/C][C]100.309927877518[/C][C]7.21224816970789e-05[/C][/ROW]
[ROW][C]58[/C][C]102.25[/C][C]100.309999994155[/C][C]1.94000000584455[/C][/ROW]
[ROW][C]59[/C][C]102.25[/C][C]102.249842789197[/C][C]0.000157210803266139[/C][/ROW]
[ROW][C]60[/C][C]102.25[/C][C]102.24999998726[/C][C]1.27398180893579e-08[/C][/ROW]
[ROW][C]61[/C][C]101.81[/C][C]102.249999999999[/C][C]-0.43999999999896[/C][/ROW]
[ROW][C]62[/C][C]101.81[/C][C]101.810035656058[/C][C]-3.56560583583132e-05[/C][/ROW]
[ROW][C]63[/C][C]101.81[/C][C]101.810000002889[/C][C]-2.88943624582316e-09[/C][/ROW]
[ROW][C]64[/C][C]101.81[/C][C]101.81[/C][C]-2.27373675443232e-13[/C][/ROW]
[ROW][C]65[/C][C]101.81[/C][C]101.81[/C][C]0[/C][/ROW]
[ROW][C]66[/C][C]101.81[/C][C]101.81[/C][C]0[/C][/ROW]
[ROW][C]67[/C][C]101.81[/C][C]101.81[/C][C]0[/C][/ROW]
[ROW][C]68[/C][C]101.81[/C][C]101.81[/C][C]0[/C][/ROW]
[ROW][C]69[/C][C]101.81[/C][C]101.81[/C][C]0[/C][/ROW]
[ROW][C]70[/C][C]101.81[/C][C]101.81[/C][C]0[/C][/ROW]
[ROW][C]71[/C][C]101.81[/C][C]101.81[/C][C]0[/C][/ROW]
[ROW][C]72[/C][C]101.81[/C][C]101.81[/C][C]0[/C][/ROW]
[ROW][C]73[/C][C]101.81[/C][C]101.81[/C][C]0[/C][/ROW]
[ROW][C]74[/C][C]101.81[/C][C]101.81[/C][C]0[/C][/ROW]
[ROW][C]75[/C][C]101.81[/C][C]101.81[/C][C]0[/C][/ROW]
[ROW][C]76[/C][C]101.81[/C][C]101.81[/C][C]0[/C][/ROW]
[ROW][C]77[/C][C]101.81[/C][C]101.81[/C][C]0[/C][/ROW]
[ROW][C]78[/C][C]101.81[/C][C]101.81[/C][C]0[/C][/ROW]
[ROW][C]79[/C][C]101.81[/C][C]101.81[/C][C]0[/C][/ROW]
[ROW][C]80[/C][C]101.94[/C][C]101.81[/C][C]0.129999999999995[/C][/ROW]
[ROW][C]81[/C][C]101.94[/C][C]101.939989465255[/C][C]1.05347445185089e-05[/C][/ROW]
[ROW][C]82[/C][C]101.94[/C][C]101.939999999146[/C][C]8.53702886161045e-10[/C][/ROW]
[ROW][C]83[/C][C]101.94[/C][C]101.94[/C][C]7.105427357601e-14[/C][/ROW]
[ROW][C]84[/C][C]101.94[/C][C]101.94[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160765&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160765&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
263.6963.690
363.6963.690
463.6963.690
563.6963.690
663.6963.690
763.6963.690
863.6963.690
965.0363.691.34
1065.0365.0298914110950.000108588905021634
1165.0365.02999999120038.7996596676021e-09
1265.0365.02999999999937.105427357601e-13
1365.0365.030
1465.0365.030
1565.0365.030
1665.0365.030
1765.0365.030
1865.0365.030
1965.0365.030
2065.0365.030
2165.0365.030
2265.0365.030
2365.0365.030
2465.0365.030
25101.1665.0336.13
26101.16101.1570721513890.00292784861071027
27101.16101.1599997627372.37262597124754e-07
28101.16101.1599999999811.92272864296683e-11
29101.16101.160
30101.16101.160
31101.16101.160
32101.16101.160
33101.16101.160
34101.21101.160.0499999999999972
35101.21101.2099959481754.0518248169974e-06
36101.21101.2099999996723.28341798194742e-10
37103.16101.211.95000000000003
38103.16103.1598419788320.000158021167749212
39103.16103.1599999871951.28054864489968e-08
40103.16103.1599999999991.03739239420975e-12
41101.13103.16-2.03
42101.13101.130164504087-0.000164504087450723
43100.53101.130000013331-0.600000013330828
44100.53100.530048621899-4.8621898855572e-05
45100.53100.53000000394-3.94014421090105e-09
46100.53100.53-3.12638803734444e-13
47100.53100.530
48100.53100.530
49100.53100.530
50100.53100.530
51100.53100.530
5299.42100.53-1.11
5399.4299.4200899505109-8.99505108691301e-05
5499.4299.4200000072893-7.28927318505157e-09
5599.4299.4200000000006-5.96855898038484e-13
56100.3199.420.890000000000001
57100.31100.3099278775187.21224816970789e-05
58102.25100.3099999941551.94000000584455
59102.25102.2498427891970.000157210803266139
60102.25102.249999987261.27398180893579e-08
61101.81102.249999999999-0.43999999999896
62101.81101.810035656058-3.56560583583132e-05
63101.81101.810000002889-2.88943624582316e-09
64101.81101.81-2.27373675443232e-13
65101.81101.810
66101.81101.810
67101.81101.810
68101.81101.810
69101.81101.810
70101.81101.810
71101.81101.810
72101.81101.810
73101.81101.810
74101.81101.810
75101.81101.810
76101.81101.810
77101.81101.810
78101.81101.810
79101.81101.810
80101.94101.810.129999999999995
81101.94101.9399894652551.05347445185089e-05
82101.94101.9399999991468.53702886161045e-10
83101.94101.947.105427357601e-14
84101.94101.940







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85101.9494.124602311706109.755397688294
86101.9490.8878064184693112.992193581531
87101.9488.4040654219568115.475934578043
88101.9486.3101546124569117.569845387543
89101.9484.4653724281192119.414627571881
90101.9482.797556302463121.082443697537
91101.9481.2638375743754122.616162425625
92101.9479.8362845976463124.043715402354
93101.9478.495495814036125.384504185964
94101.9477.2273449734125126.652655026588
95101.9476.0211678426562127.858832157344
96101.9474.868679338865129.011320661135

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 101.94 & 94.124602311706 & 109.755397688294 \tabularnewline
86 & 101.94 & 90.8878064184693 & 112.992193581531 \tabularnewline
87 & 101.94 & 88.4040654219568 & 115.475934578043 \tabularnewline
88 & 101.94 & 86.3101546124569 & 117.569845387543 \tabularnewline
89 & 101.94 & 84.4653724281192 & 119.414627571881 \tabularnewline
90 & 101.94 & 82.797556302463 & 121.082443697537 \tabularnewline
91 & 101.94 & 81.2638375743754 & 122.616162425625 \tabularnewline
92 & 101.94 & 79.8362845976463 & 124.043715402354 \tabularnewline
93 & 101.94 & 78.495495814036 & 125.384504185964 \tabularnewline
94 & 101.94 & 77.2273449734125 & 126.652655026588 \tabularnewline
95 & 101.94 & 76.0211678426562 & 127.858832157344 \tabularnewline
96 & 101.94 & 74.868679338865 & 129.011320661135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160765&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]101.94[/C][C]94.124602311706[/C][C]109.755397688294[/C][/ROW]
[ROW][C]86[/C][C]101.94[/C][C]90.8878064184693[/C][C]112.992193581531[/C][/ROW]
[ROW][C]87[/C][C]101.94[/C][C]88.4040654219568[/C][C]115.475934578043[/C][/ROW]
[ROW][C]88[/C][C]101.94[/C][C]86.3101546124569[/C][C]117.569845387543[/C][/ROW]
[ROW][C]89[/C][C]101.94[/C][C]84.4653724281192[/C][C]119.414627571881[/C][/ROW]
[ROW][C]90[/C][C]101.94[/C][C]82.797556302463[/C][C]121.082443697537[/C][/ROW]
[ROW][C]91[/C][C]101.94[/C][C]81.2638375743754[/C][C]122.616162425625[/C][/ROW]
[ROW][C]92[/C][C]101.94[/C][C]79.8362845976463[/C][C]124.043715402354[/C][/ROW]
[ROW][C]93[/C][C]101.94[/C][C]78.495495814036[/C][C]125.384504185964[/C][/ROW]
[ROW][C]94[/C][C]101.94[/C][C]77.2273449734125[/C][C]126.652655026588[/C][/ROW]
[ROW][C]95[/C][C]101.94[/C][C]76.0211678426562[/C][C]127.858832157344[/C][/ROW]
[ROW][C]96[/C][C]101.94[/C][C]74.868679338865[/C][C]129.011320661135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160765&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160765&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
85101.9494.124602311706109.755397688294
86101.9490.8878064184693112.992193581531
87101.9488.4040654219568115.475934578043
88101.9486.3101546124569117.569845387543
89101.9484.4653724281192119.414627571881
90101.9482.797556302463121.082443697537
91101.9481.2638375743754122.616162425625
92101.9479.8362845976463124.043715402354
93101.9478.495495814036125.384504185964
94101.9477.2273449734125126.652655026588
95101.9476.0211678426562127.858832157344
96101.9474.868679338865129.011320661135



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')