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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 28 May 2008 16:25:16 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/May/29/t1212013627hlndt3imyb7djxs.htm/, Retrieved Thu, 31 Oct 2024 23:22:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13485, Retrieved Thu, 31 Oct 2024 23:22:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact265
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Standard Deviation-Mean Plot] [Sophie Volckaerts...] [2008-05-24 14:41:00] [4b92e24c7e9c2a828d526c4c975b3e2c]
- RMPD    [Exponential Smoothing] [Robin Van Wijnsbe...] [2008-05-28 22:25:16] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
1,61
1,6
1,59
1,6
1,6
1,59
1,59
1,58
1,59
1,59
1,58
1,58
1,58
1,57
1,57
1,57
1,57
1,58
1,58
1,57
1,58
1,57
1,57
1,57
1,57
1,57
1,57
1,59
1,6
1,6
1,6
1,6
1,61
1,61
1,62
1,62
1,62
1,62
1,62
1,62
1,61
1,59
1,58
1,56
1,56
1,54
1,55
1,56
1,57
1,58
1,59
1,6
1,6
1,61
1,61
1,62
1,61
1,6
1,6
1,6
1,61
1,62
1,63
1,63
1,66
1,66
1,66
1,65
1,65
1,64
1,64
1,65
1,64




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13485&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13485&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13485&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13485&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]0[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13485&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13485&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
alpha1
beta0
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
21.61.61-0.01
31.591.6-0.01
41.61.590.01
51.61.60
61.591.6-0.01
71.591.590
81.581.59-0.01
91.591.580.01
101.591.590
111.581.59-0.01
121.581.580
131.581.580
141.571.58-0.01
151.571.570
161.571.570
171.571.570
181.581.570.01
191.581.580
201.571.58-0.01
211.581.570.01
221.571.58-0.01
231.571.570
241.571.570
251.571.570
261.571.570
271.571.570
281.591.570.02
291.61.590.01
301.61.60
311.61.60
321.61.60
331.611.60.01
341.611.610
351.621.610.01
361.621.620
371.621.620
381.621.620
391.621.620
401.621.620
411.611.62-0.01
421.591.61-0.02
431.581.59-0.01
441.561.58-0.02
451.561.560
461.541.56-0.02
471.551.540.01
481.561.550.01
491.571.560.01
501.581.570.01
511.591.580.01
521.61.590.01
531.61.60
541.611.60.01
551.611.610
561.621.610.01
571.611.62-0.01
581.61.61-0.01
591.61.60
601.61.60
611.611.60.01
621.621.610.01
631.631.620.00999999999999979
641.631.630
651.661.630.03
661.661.660
671.661.660
681.651.66-0.01
691.651.650
701.641.65-0.01
711.641.640
721.651.640.01
731.641.65-0.01

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 1.6 & 1.61 & -0.01 \tabularnewline
3 & 1.59 & 1.6 & -0.01 \tabularnewline
4 & 1.6 & 1.59 & 0.01 \tabularnewline
5 & 1.6 & 1.6 & 0 \tabularnewline
6 & 1.59 & 1.6 & -0.01 \tabularnewline
7 & 1.59 & 1.59 & 0 \tabularnewline
8 & 1.58 & 1.59 & -0.01 \tabularnewline
9 & 1.59 & 1.58 & 0.01 \tabularnewline
10 & 1.59 & 1.59 & 0 \tabularnewline
11 & 1.58 & 1.59 & -0.01 \tabularnewline
12 & 1.58 & 1.58 & 0 \tabularnewline
13 & 1.58 & 1.58 & 0 \tabularnewline
14 & 1.57 & 1.58 & -0.01 \tabularnewline
15 & 1.57 & 1.57 & 0 \tabularnewline
16 & 1.57 & 1.57 & 0 \tabularnewline
17 & 1.57 & 1.57 & 0 \tabularnewline
18 & 1.58 & 1.57 & 0.01 \tabularnewline
19 & 1.58 & 1.58 & 0 \tabularnewline
20 & 1.57 & 1.58 & -0.01 \tabularnewline
21 & 1.58 & 1.57 & 0.01 \tabularnewline
22 & 1.57 & 1.58 & -0.01 \tabularnewline
23 & 1.57 & 1.57 & 0 \tabularnewline
24 & 1.57 & 1.57 & 0 \tabularnewline
25 & 1.57 & 1.57 & 0 \tabularnewline
26 & 1.57 & 1.57 & 0 \tabularnewline
27 & 1.57 & 1.57 & 0 \tabularnewline
28 & 1.59 & 1.57 & 0.02 \tabularnewline
29 & 1.6 & 1.59 & 0.01 \tabularnewline
30 & 1.6 & 1.6 & 0 \tabularnewline
31 & 1.6 & 1.6 & 0 \tabularnewline
32 & 1.6 & 1.6 & 0 \tabularnewline
33 & 1.61 & 1.6 & 0.01 \tabularnewline
34 & 1.61 & 1.61 & 0 \tabularnewline
35 & 1.62 & 1.61 & 0.01 \tabularnewline
36 & 1.62 & 1.62 & 0 \tabularnewline
37 & 1.62 & 1.62 & 0 \tabularnewline
38 & 1.62 & 1.62 & 0 \tabularnewline
39 & 1.62 & 1.62 & 0 \tabularnewline
40 & 1.62 & 1.62 & 0 \tabularnewline
41 & 1.61 & 1.62 & -0.01 \tabularnewline
42 & 1.59 & 1.61 & -0.02 \tabularnewline
43 & 1.58 & 1.59 & -0.01 \tabularnewline
44 & 1.56 & 1.58 & -0.02 \tabularnewline
45 & 1.56 & 1.56 & 0 \tabularnewline
46 & 1.54 & 1.56 & -0.02 \tabularnewline
47 & 1.55 & 1.54 & 0.01 \tabularnewline
48 & 1.56 & 1.55 & 0.01 \tabularnewline
49 & 1.57 & 1.56 & 0.01 \tabularnewline
50 & 1.58 & 1.57 & 0.01 \tabularnewline
51 & 1.59 & 1.58 & 0.01 \tabularnewline
52 & 1.6 & 1.59 & 0.01 \tabularnewline
53 & 1.6 & 1.6 & 0 \tabularnewline
54 & 1.61 & 1.6 & 0.01 \tabularnewline
55 & 1.61 & 1.61 & 0 \tabularnewline
56 & 1.62 & 1.61 & 0.01 \tabularnewline
57 & 1.61 & 1.62 & -0.01 \tabularnewline
58 & 1.6 & 1.61 & -0.01 \tabularnewline
59 & 1.6 & 1.6 & 0 \tabularnewline
60 & 1.6 & 1.6 & 0 \tabularnewline
61 & 1.61 & 1.6 & 0.01 \tabularnewline
62 & 1.62 & 1.61 & 0.01 \tabularnewline
63 & 1.63 & 1.62 & 0.00999999999999979 \tabularnewline
64 & 1.63 & 1.63 & 0 \tabularnewline
65 & 1.66 & 1.63 & 0.03 \tabularnewline
66 & 1.66 & 1.66 & 0 \tabularnewline
67 & 1.66 & 1.66 & 0 \tabularnewline
68 & 1.65 & 1.66 & -0.01 \tabularnewline
69 & 1.65 & 1.65 & 0 \tabularnewline
70 & 1.64 & 1.65 & -0.01 \tabularnewline
71 & 1.64 & 1.64 & 0 \tabularnewline
72 & 1.65 & 1.64 & 0.01 \tabularnewline
73 & 1.64 & 1.65 & -0.01 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13485&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]1.6[/C][C]1.61[/C][C]-0.01[/C][/ROW]
[ROW][C]3[/C][C]1.59[/C][C]1.6[/C][C]-0.01[/C][/ROW]
[ROW][C]4[/C][C]1.6[/C][C]1.59[/C][C]0.01[/C][/ROW]
[ROW][C]5[/C][C]1.6[/C][C]1.6[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]1.59[/C][C]1.6[/C][C]-0.01[/C][/ROW]
[ROW][C]7[/C][C]1.59[/C][C]1.59[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]1.58[/C][C]1.59[/C][C]-0.01[/C][/ROW]
[ROW][C]9[/C][C]1.59[/C][C]1.58[/C][C]0.01[/C][/ROW]
[ROW][C]10[/C][C]1.59[/C][C]1.59[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]1.58[/C][C]1.59[/C][C]-0.01[/C][/ROW]
[ROW][C]12[/C][C]1.58[/C][C]1.58[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]1.58[/C][C]1.58[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]1.57[/C][C]1.58[/C][C]-0.01[/C][/ROW]
[ROW][C]15[/C][C]1.57[/C][C]1.57[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]1.57[/C][C]1.57[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]1.57[/C][C]1.57[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]1.58[/C][C]1.57[/C][C]0.01[/C][/ROW]
[ROW][C]19[/C][C]1.58[/C][C]1.58[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]1.57[/C][C]1.58[/C][C]-0.01[/C][/ROW]
[ROW][C]21[/C][C]1.58[/C][C]1.57[/C][C]0.01[/C][/ROW]
[ROW][C]22[/C][C]1.57[/C][C]1.58[/C][C]-0.01[/C][/ROW]
[ROW][C]23[/C][C]1.57[/C][C]1.57[/C][C]0[/C][/ROW]
[ROW][C]24[/C][C]1.57[/C][C]1.57[/C][C]0[/C][/ROW]
[ROW][C]25[/C][C]1.57[/C][C]1.57[/C][C]0[/C][/ROW]
[ROW][C]26[/C][C]1.57[/C][C]1.57[/C][C]0[/C][/ROW]
[ROW][C]27[/C][C]1.57[/C][C]1.57[/C][C]0[/C][/ROW]
[ROW][C]28[/C][C]1.59[/C][C]1.57[/C][C]0.02[/C][/ROW]
[ROW][C]29[/C][C]1.6[/C][C]1.59[/C][C]0.01[/C][/ROW]
[ROW][C]30[/C][C]1.6[/C][C]1.6[/C][C]0[/C][/ROW]
[ROW][C]31[/C][C]1.6[/C][C]1.6[/C][C]0[/C][/ROW]
[ROW][C]32[/C][C]1.6[/C][C]1.6[/C][C]0[/C][/ROW]
[ROW][C]33[/C][C]1.61[/C][C]1.6[/C][C]0.01[/C][/ROW]
[ROW][C]34[/C][C]1.61[/C][C]1.61[/C][C]0[/C][/ROW]
[ROW][C]35[/C][C]1.62[/C][C]1.61[/C][C]0.01[/C][/ROW]
[ROW][C]36[/C][C]1.62[/C][C]1.62[/C][C]0[/C][/ROW]
[ROW][C]37[/C][C]1.62[/C][C]1.62[/C][C]0[/C][/ROW]
[ROW][C]38[/C][C]1.62[/C][C]1.62[/C][C]0[/C][/ROW]
[ROW][C]39[/C][C]1.62[/C][C]1.62[/C][C]0[/C][/ROW]
[ROW][C]40[/C][C]1.62[/C][C]1.62[/C][C]0[/C][/ROW]
[ROW][C]41[/C][C]1.61[/C][C]1.62[/C][C]-0.01[/C][/ROW]
[ROW][C]42[/C][C]1.59[/C][C]1.61[/C][C]-0.02[/C][/ROW]
[ROW][C]43[/C][C]1.58[/C][C]1.59[/C][C]-0.01[/C][/ROW]
[ROW][C]44[/C][C]1.56[/C][C]1.58[/C][C]-0.02[/C][/ROW]
[ROW][C]45[/C][C]1.56[/C][C]1.56[/C][C]0[/C][/ROW]
[ROW][C]46[/C][C]1.54[/C][C]1.56[/C][C]-0.02[/C][/ROW]
[ROW][C]47[/C][C]1.55[/C][C]1.54[/C][C]0.01[/C][/ROW]
[ROW][C]48[/C][C]1.56[/C][C]1.55[/C][C]0.01[/C][/ROW]
[ROW][C]49[/C][C]1.57[/C][C]1.56[/C][C]0.01[/C][/ROW]
[ROW][C]50[/C][C]1.58[/C][C]1.57[/C][C]0.01[/C][/ROW]
[ROW][C]51[/C][C]1.59[/C][C]1.58[/C][C]0.01[/C][/ROW]
[ROW][C]52[/C][C]1.6[/C][C]1.59[/C][C]0.01[/C][/ROW]
[ROW][C]53[/C][C]1.6[/C][C]1.6[/C][C]0[/C][/ROW]
[ROW][C]54[/C][C]1.61[/C][C]1.6[/C][C]0.01[/C][/ROW]
[ROW][C]55[/C][C]1.61[/C][C]1.61[/C][C]0[/C][/ROW]
[ROW][C]56[/C][C]1.62[/C][C]1.61[/C][C]0.01[/C][/ROW]
[ROW][C]57[/C][C]1.61[/C][C]1.62[/C][C]-0.01[/C][/ROW]
[ROW][C]58[/C][C]1.6[/C][C]1.61[/C][C]-0.01[/C][/ROW]
[ROW][C]59[/C][C]1.6[/C][C]1.6[/C][C]0[/C][/ROW]
[ROW][C]60[/C][C]1.6[/C][C]1.6[/C][C]0[/C][/ROW]
[ROW][C]61[/C][C]1.61[/C][C]1.6[/C][C]0.01[/C][/ROW]
[ROW][C]62[/C][C]1.62[/C][C]1.61[/C][C]0.01[/C][/ROW]
[ROW][C]63[/C][C]1.63[/C][C]1.62[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]64[/C][C]1.63[/C][C]1.63[/C][C]0[/C][/ROW]
[ROW][C]65[/C][C]1.66[/C][C]1.63[/C][C]0.03[/C][/ROW]
[ROW][C]66[/C][C]1.66[/C][C]1.66[/C][C]0[/C][/ROW]
[ROW][C]67[/C][C]1.66[/C][C]1.66[/C][C]0[/C][/ROW]
[ROW][C]68[/C][C]1.65[/C][C]1.66[/C][C]-0.01[/C][/ROW]
[ROW][C]69[/C][C]1.65[/C][C]1.65[/C][C]0[/C][/ROW]
[ROW][C]70[/C][C]1.64[/C][C]1.65[/C][C]-0.01[/C][/ROW]
[ROW][C]71[/C][C]1.64[/C][C]1.64[/C][C]0[/C][/ROW]
[ROW][C]72[/C][C]1.65[/C][C]1.64[/C][C]0.01[/C][/ROW]
[ROW][C]73[/C][C]1.64[/C][C]1.65[/C][C]-0.01[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13485&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13485&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
21.61.61-0.01
31.591.6-0.01
41.61.590.01
51.61.60
61.591.6-0.01
71.591.590
81.581.59-0.01
91.591.580.01
101.591.590
111.581.59-0.01
121.581.580
131.581.580
141.571.58-0.01
151.571.570
161.571.570
171.571.570
181.581.570.01
191.581.580
201.571.58-0.01
211.581.570.01
221.571.58-0.01
231.571.570
241.571.570
251.571.570
261.571.570
271.571.570
281.591.570.02
291.61.590.01
301.61.60
311.61.60
321.61.60
331.611.60.01
341.611.610
351.621.610.01
361.621.620
371.621.620
381.621.620
391.621.620
401.621.620
411.611.62-0.01
421.591.61-0.02
431.581.59-0.01
441.561.58-0.02
451.561.560
461.541.56-0.02
471.551.540.01
481.561.550.01
491.571.560.01
501.581.570.01
511.591.580.01
521.61.590.01
531.61.60
541.611.60.01
551.611.610
561.621.610.01
571.611.62-0.01
581.61.61-0.01
591.61.60
601.61.60
611.611.60.01
621.621.610.01
631.631.620.00999999999999979
641.631.630
651.661.630.03
661.661.660
671.661.660
681.651.66-0.01
691.651.650
701.641.65-0.01
711.641.640
721.651.640.01
731.641.65-0.01







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
741.641.622152212901271.65784778709873
751.641.614759417426631.66524058257337
761.641.609086725942321.67091327405768
771.641.604304425802541.67569557419746
781.641.600091134799291.67990886520071
791.641.596282028570281.68371797142972
801.641.592779193883931.68722080611607
811.641.589518834853251.69048116514675
821.641.586456638703811.69354336129619
831.641.583560341574241.69643965842576
841.641.580805586855361.69919441314464
851.641.578173451884651.70182654811535

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
74 & 1.64 & 1.62215221290127 & 1.65784778709873 \tabularnewline
75 & 1.64 & 1.61475941742663 & 1.66524058257337 \tabularnewline
76 & 1.64 & 1.60908672594232 & 1.67091327405768 \tabularnewline
77 & 1.64 & 1.60430442580254 & 1.67569557419746 \tabularnewline
78 & 1.64 & 1.60009113479929 & 1.67990886520071 \tabularnewline
79 & 1.64 & 1.59628202857028 & 1.68371797142972 \tabularnewline
80 & 1.64 & 1.59277919388393 & 1.68722080611607 \tabularnewline
81 & 1.64 & 1.58951883485325 & 1.69048116514675 \tabularnewline
82 & 1.64 & 1.58645663870381 & 1.69354336129619 \tabularnewline
83 & 1.64 & 1.58356034157424 & 1.69643965842576 \tabularnewline
84 & 1.64 & 1.58080558685536 & 1.69919441314464 \tabularnewline
85 & 1.64 & 1.57817345188465 & 1.70182654811535 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13485&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]74[/C][C]1.64[/C][C]1.62215221290127[/C][C]1.65784778709873[/C][/ROW]
[ROW][C]75[/C][C]1.64[/C][C]1.61475941742663[/C][C]1.66524058257337[/C][/ROW]
[ROW][C]76[/C][C]1.64[/C][C]1.60908672594232[/C][C]1.67091327405768[/C][/ROW]
[ROW][C]77[/C][C]1.64[/C][C]1.60430442580254[/C][C]1.67569557419746[/C][/ROW]
[ROW][C]78[/C][C]1.64[/C][C]1.60009113479929[/C][C]1.67990886520071[/C][/ROW]
[ROW][C]79[/C][C]1.64[/C][C]1.59628202857028[/C][C]1.68371797142972[/C][/ROW]
[ROW][C]80[/C][C]1.64[/C][C]1.59277919388393[/C][C]1.68722080611607[/C][/ROW]
[ROW][C]81[/C][C]1.64[/C][C]1.58951883485325[/C][C]1.69048116514675[/C][/ROW]
[ROW][C]82[/C][C]1.64[/C][C]1.58645663870381[/C][C]1.69354336129619[/C][/ROW]
[ROW][C]83[/C][C]1.64[/C][C]1.58356034157424[/C][C]1.69643965842576[/C][/ROW]
[ROW][C]84[/C][C]1.64[/C][C]1.58080558685536[/C][C]1.69919441314464[/C][/ROW]
[ROW][C]85[/C][C]1.64[/C][C]1.57817345188465[/C][C]1.70182654811535[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13485&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13485&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
741.641.622152212901271.65784778709873
751.641.614759417426631.66524058257337
761.641.609086725942321.67091327405768
771.641.604304425802541.67569557419746
781.641.600091134799291.67990886520071
791.641.596282028570281.68371797142972
801.641.592779193883931.68722080611607
811.641.589518834853251.69048116514675
821.641.586456638703811.69354336129619
831.641.583560341574241.69643965842576
841.641.580805586855361.69919441314464
851.641.578173451884651.70182654811535



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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')