Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 02 Apr 2015 18:00:26 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Apr/02/t14279941298fp5qxfnwla532n.htm/, Retrieved Thu, 09 May 2024 11:19:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278595, Retrieved Thu, 09 May 2024 11:19:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact72
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [opgave 10 eigen r...] [2015-04-02 17:00:26] [09743efd8c85782f9ae22fefb9801b71] [Current]
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Dataseries X:
551.91
551.46
550.12
549.95
548.01
548.92
548.92
549.06
547.07
546.5
544.95
544.23
544.23
541.6
541.37
540.43
540.47
540.52
540.52
539.7
540.89
540.51
537.43
538.14
538.14
537.74
540.33
540.02
539.21
539.84
539.84
537.3
536.27
536.75
536.21
536.99
536.99
536.57
536.91
536.97
540.45
542.42
542.42
542.98
540.19
537.16
537.35
537.03
537.03
536.27
534.71
537.12
537.07
537.33
537.33
538.79
539.24
537.17
536.46
532.3
532.3
532.89
533.47
532.54
533.8
534.15
534.15
534.15
534.28
535.63
534.21
533.78
533.78
534.55
536.93
536.09
533.91
533.99
533.99
533.76
532.5
529.5
528.62
528.7
521.27
521.19
519.43
516.81
516.78
515.45
516.22
517.01
518.19
516.79
516.87
514.1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278595&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 Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278595&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278595&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 Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278595&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]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278595&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278595&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
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3550.12551.01-0.8900000000001
4549.95549.670.279999999999973
5548.01549.5-1.49000000000012
6548.92547.561.3599999999999
7548.92548.470.449999999999932
8549.06548.470.589999999999918
9547.07548.61-1.53999999999996
10546.5546.62-0.120000000000118
11544.95546.05-1.10000000000002
12544.23544.5-0.270000000000095
13544.23543.780.449999999999932
14541.6543.78-2.18000000000006
15541.37541.150.219999999999914
16540.43540.92-0.490000000000123
17540.47539.980.490000000000009
18540.52540.020.499999999999886
19540.52540.070.449999999999932
20539.7540.07-0.370000000000005
21540.89539.251.63999999999987
22540.51540.440.0699999999999363
23537.43540.06-2.63000000000011
24538.14536.981.15999999999997
25538.14537.690.449999999999932
26537.74537.690.0499999999999545
27540.33537.293.03999999999996
28540.02539.880.139999999999873
29539.21539.57-0.360000000000014
30539.84538.761.07999999999993
31539.84539.390.449999999999932
32537.3539.39-2.09000000000015
33536.27536.85-0.580000000000041
34536.75535.820.92999999999995
35536.21536.3-0.0900000000000318
36536.99535.761.2299999999999
37536.99536.540.449999999999932
38536.57536.540.0299999999999727
39536.91536.120.78999999999985
40536.97536.460.509999999999991
41540.45536.523.92999999999995
42542.425402.41999999999985
43542.42541.970.449999999999932
44542.98541.971.00999999999999
45540.19542.53-2.34000000000003
46537.16539.74-2.58000000000015
47537.35536.710.639999999999986
48537.03536.90.129999999999882
49537.03536.580.449999999999932
50536.27536.58-0.310000000000059
51534.71535.82-1.11000000000001
52537.12534.262.8599999999999
53537.07536.670.399999999999977
54537.33536.620.709999999999923
55537.33536.880.449999999999932
56538.79536.881.90999999999985
57539.24538.340.899999999999977
58537.17538.79-1.62000000000012
59536.46536.72-0.259999999999991
60532.3536.01-3.71000000000015
61532.3531.850.449999999999932
62532.89531.851.03999999999996
63533.47532.441.02999999999997
64532.54533.02-0.480000000000132
65533.8532.091.70999999999992
66534.15533.350.799999999999955
67534.15533.70.449999999999932
68534.15533.70.449999999999932
69534.28533.70.579999999999927
70535.63533.831.79999999999995
71534.21535.18-0.970000000000027
72533.78533.760.0199999999998681
73533.78533.330.449999999999932
74534.55533.331.21999999999991
75536.93534.12.82999999999993
76536.09536.48-0.389999999999986
77533.91535.64-1.73000000000013
78533.99533.460.529999999999973
79533.99533.540.449999999999932
80533.76533.540.219999999999914
81532.5533.31-0.810000000000059
82529.5532.05-2.55000000000007
83528.62529.05-0.430000000000064
84528.7528.170.529999999999973
85521.27528.25-6.98000000000013
86521.19520.820.370000000000005
87519.43520.74-1.31000000000017
88516.81518.98-2.17000000000007
89516.78516.360.419999999999959
90515.45516.33-0.879999999999995
91516.225151.21999999999991
92517.01515.771.2399999999999
93518.19516.561.63
94516.79517.74-0.950000000000159
95516.87516.340.529999999999973
96514.1516.42-2.32000000000005

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 550.12 & 551.01 & -0.8900000000001 \tabularnewline
4 & 549.95 & 549.67 & 0.279999999999973 \tabularnewline
5 & 548.01 & 549.5 & -1.49000000000012 \tabularnewline
6 & 548.92 & 547.56 & 1.3599999999999 \tabularnewline
7 & 548.92 & 548.47 & 0.449999999999932 \tabularnewline
8 & 549.06 & 548.47 & 0.589999999999918 \tabularnewline
9 & 547.07 & 548.61 & -1.53999999999996 \tabularnewline
10 & 546.5 & 546.62 & -0.120000000000118 \tabularnewline
11 & 544.95 & 546.05 & -1.10000000000002 \tabularnewline
12 & 544.23 & 544.5 & -0.270000000000095 \tabularnewline
13 & 544.23 & 543.78 & 0.449999999999932 \tabularnewline
14 & 541.6 & 543.78 & -2.18000000000006 \tabularnewline
15 & 541.37 & 541.15 & 0.219999999999914 \tabularnewline
16 & 540.43 & 540.92 & -0.490000000000123 \tabularnewline
17 & 540.47 & 539.98 & 0.490000000000009 \tabularnewline
18 & 540.52 & 540.02 & 0.499999999999886 \tabularnewline
19 & 540.52 & 540.07 & 0.449999999999932 \tabularnewline
20 & 539.7 & 540.07 & -0.370000000000005 \tabularnewline
21 & 540.89 & 539.25 & 1.63999999999987 \tabularnewline
22 & 540.51 & 540.44 & 0.0699999999999363 \tabularnewline
23 & 537.43 & 540.06 & -2.63000000000011 \tabularnewline
24 & 538.14 & 536.98 & 1.15999999999997 \tabularnewline
25 & 538.14 & 537.69 & 0.449999999999932 \tabularnewline
26 & 537.74 & 537.69 & 0.0499999999999545 \tabularnewline
27 & 540.33 & 537.29 & 3.03999999999996 \tabularnewline
28 & 540.02 & 539.88 & 0.139999999999873 \tabularnewline
29 & 539.21 & 539.57 & -0.360000000000014 \tabularnewline
30 & 539.84 & 538.76 & 1.07999999999993 \tabularnewline
31 & 539.84 & 539.39 & 0.449999999999932 \tabularnewline
32 & 537.3 & 539.39 & -2.09000000000015 \tabularnewline
33 & 536.27 & 536.85 & -0.580000000000041 \tabularnewline
34 & 536.75 & 535.82 & 0.92999999999995 \tabularnewline
35 & 536.21 & 536.3 & -0.0900000000000318 \tabularnewline
36 & 536.99 & 535.76 & 1.2299999999999 \tabularnewline
37 & 536.99 & 536.54 & 0.449999999999932 \tabularnewline
38 & 536.57 & 536.54 & 0.0299999999999727 \tabularnewline
39 & 536.91 & 536.12 & 0.78999999999985 \tabularnewline
40 & 536.97 & 536.46 & 0.509999999999991 \tabularnewline
41 & 540.45 & 536.52 & 3.92999999999995 \tabularnewline
42 & 542.42 & 540 & 2.41999999999985 \tabularnewline
43 & 542.42 & 541.97 & 0.449999999999932 \tabularnewline
44 & 542.98 & 541.97 & 1.00999999999999 \tabularnewline
45 & 540.19 & 542.53 & -2.34000000000003 \tabularnewline
46 & 537.16 & 539.74 & -2.58000000000015 \tabularnewline
47 & 537.35 & 536.71 & 0.639999999999986 \tabularnewline
48 & 537.03 & 536.9 & 0.129999999999882 \tabularnewline
49 & 537.03 & 536.58 & 0.449999999999932 \tabularnewline
50 & 536.27 & 536.58 & -0.310000000000059 \tabularnewline
51 & 534.71 & 535.82 & -1.11000000000001 \tabularnewline
52 & 537.12 & 534.26 & 2.8599999999999 \tabularnewline
53 & 537.07 & 536.67 & 0.399999999999977 \tabularnewline
54 & 537.33 & 536.62 & 0.709999999999923 \tabularnewline
55 & 537.33 & 536.88 & 0.449999999999932 \tabularnewline
56 & 538.79 & 536.88 & 1.90999999999985 \tabularnewline
57 & 539.24 & 538.34 & 0.899999999999977 \tabularnewline
58 & 537.17 & 538.79 & -1.62000000000012 \tabularnewline
59 & 536.46 & 536.72 & -0.259999999999991 \tabularnewline
60 & 532.3 & 536.01 & -3.71000000000015 \tabularnewline
61 & 532.3 & 531.85 & 0.449999999999932 \tabularnewline
62 & 532.89 & 531.85 & 1.03999999999996 \tabularnewline
63 & 533.47 & 532.44 & 1.02999999999997 \tabularnewline
64 & 532.54 & 533.02 & -0.480000000000132 \tabularnewline
65 & 533.8 & 532.09 & 1.70999999999992 \tabularnewline
66 & 534.15 & 533.35 & 0.799999999999955 \tabularnewline
67 & 534.15 & 533.7 & 0.449999999999932 \tabularnewline
68 & 534.15 & 533.7 & 0.449999999999932 \tabularnewline
69 & 534.28 & 533.7 & 0.579999999999927 \tabularnewline
70 & 535.63 & 533.83 & 1.79999999999995 \tabularnewline
71 & 534.21 & 535.18 & -0.970000000000027 \tabularnewline
72 & 533.78 & 533.76 & 0.0199999999998681 \tabularnewline
73 & 533.78 & 533.33 & 0.449999999999932 \tabularnewline
74 & 534.55 & 533.33 & 1.21999999999991 \tabularnewline
75 & 536.93 & 534.1 & 2.82999999999993 \tabularnewline
76 & 536.09 & 536.48 & -0.389999999999986 \tabularnewline
77 & 533.91 & 535.64 & -1.73000000000013 \tabularnewline
78 & 533.99 & 533.46 & 0.529999999999973 \tabularnewline
79 & 533.99 & 533.54 & 0.449999999999932 \tabularnewline
80 & 533.76 & 533.54 & 0.219999999999914 \tabularnewline
81 & 532.5 & 533.31 & -0.810000000000059 \tabularnewline
82 & 529.5 & 532.05 & -2.55000000000007 \tabularnewline
83 & 528.62 & 529.05 & -0.430000000000064 \tabularnewline
84 & 528.7 & 528.17 & 0.529999999999973 \tabularnewline
85 & 521.27 & 528.25 & -6.98000000000013 \tabularnewline
86 & 521.19 & 520.82 & 0.370000000000005 \tabularnewline
87 & 519.43 & 520.74 & -1.31000000000017 \tabularnewline
88 & 516.81 & 518.98 & -2.17000000000007 \tabularnewline
89 & 516.78 & 516.36 & 0.419999999999959 \tabularnewline
90 & 515.45 & 516.33 & -0.879999999999995 \tabularnewline
91 & 516.22 & 515 & 1.21999999999991 \tabularnewline
92 & 517.01 & 515.77 & 1.2399999999999 \tabularnewline
93 & 518.19 & 516.56 & 1.63 \tabularnewline
94 & 516.79 & 517.74 & -0.950000000000159 \tabularnewline
95 & 516.87 & 516.34 & 0.529999999999973 \tabularnewline
96 & 514.1 & 516.42 & -2.32000000000005 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278595&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]550.12[/C][C]551.01[/C][C]-0.8900000000001[/C][/ROW]
[ROW][C]4[/C][C]549.95[/C][C]549.67[/C][C]0.279999999999973[/C][/ROW]
[ROW][C]5[/C][C]548.01[/C][C]549.5[/C][C]-1.49000000000012[/C][/ROW]
[ROW][C]6[/C][C]548.92[/C][C]547.56[/C][C]1.3599999999999[/C][/ROW]
[ROW][C]7[/C][C]548.92[/C][C]548.47[/C][C]0.449999999999932[/C][/ROW]
[ROW][C]8[/C][C]549.06[/C][C]548.47[/C][C]0.589999999999918[/C][/ROW]
[ROW][C]9[/C][C]547.07[/C][C]548.61[/C][C]-1.53999999999996[/C][/ROW]
[ROW][C]10[/C][C]546.5[/C][C]546.62[/C][C]-0.120000000000118[/C][/ROW]
[ROW][C]11[/C][C]544.95[/C][C]546.05[/C][C]-1.10000000000002[/C][/ROW]
[ROW][C]12[/C][C]544.23[/C][C]544.5[/C][C]-0.270000000000095[/C][/ROW]
[ROW][C]13[/C][C]544.23[/C][C]543.78[/C][C]0.449999999999932[/C][/ROW]
[ROW][C]14[/C][C]541.6[/C][C]543.78[/C][C]-2.18000000000006[/C][/ROW]
[ROW][C]15[/C][C]541.37[/C][C]541.15[/C][C]0.219999999999914[/C][/ROW]
[ROW][C]16[/C][C]540.43[/C][C]540.92[/C][C]-0.490000000000123[/C][/ROW]
[ROW][C]17[/C][C]540.47[/C][C]539.98[/C][C]0.490000000000009[/C][/ROW]
[ROW][C]18[/C][C]540.52[/C][C]540.02[/C][C]0.499999999999886[/C][/ROW]
[ROW][C]19[/C][C]540.52[/C][C]540.07[/C][C]0.449999999999932[/C][/ROW]
[ROW][C]20[/C][C]539.7[/C][C]540.07[/C][C]-0.370000000000005[/C][/ROW]
[ROW][C]21[/C][C]540.89[/C][C]539.25[/C][C]1.63999999999987[/C][/ROW]
[ROW][C]22[/C][C]540.51[/C][C]540.44[/C][C]0.0699999999999363[/C][/ROW]
[ROW][C]23[/C][C]537.43[/C][C]540.06[/C][C]-2.63000000000011[/C][/ROW]
[ROW][C]24[/C][C]538.14[/C][C]536.98[/C][C]1.15999999999997[/C][/ROW]
[ROW][C]25[/C][C]538.14[/C][C]537.69[/C][C]0.449999999999932[/C][/ROW]
[ROW][C]26[/C][C]537.74[/C][C]537.69[/C][C]0.0499999999999545[/C][/ROW]
[ROW][C]27[/C][C]540.33[/C][C]537.29[/C][C]3.03999999999996[/C][/ROW]
[ROW][C]28[/C][C]540.02[/C][C]539.88[/C][C]0.139999999999873[/C][/ROW]
[ROW][C]29[/C][C]539.21[/C][C]539.57[/C][C]-0.360000000000014[/C][/ROW]
[ROW][C]30[/C][C]539.84[/C][C]538.76[/C][C]1.07999999999993[/C][/ROW]
[ROW][C]31[/C][C]539.84[/C][C]539.39[/C][C]0.449999999999932[/C][/ROW]
[ROW][C]32[/C][C]537.3[/C][C]539.39[/C][C]-2.09000000000015[/C][/ROW]
[ROW][C]33[/C][C]536.27[/C][C]536.85[/C][C]-0.580000000000041[/C][/ROW]
[ROW][C]34[/C][C]536.75[/C][C]535.82[/C][C]0.92999999999995[/C][/ROW]
[ROW][C]35[/C][C]536.21[/C][C]536.3[/C][C]-0.0900000000000318[/C][/ROW]
[ROW][C]36[/C][C]536.99[/C][C]535.76[/C][C]1.2299999999999[/C][/ROW]
[ROW][C]37[/C][C]536.99[/C][C]536.54[/C][C]0.449999999999932[/C][/ROW]
[ROW][C]38[/C][C]536.57[/C][C]536.54[/C][C]0.0299999999999727[/C][/ROW]
[ROW][C]39[/C][C]536.91[/C][C]536.12[/C][C]0.78999999999985[/C][/ROW]
[ROW][C]40[/C][C]536.97[/C][C]536.46[/C][C]0.509999999999991[/C][/ROW]
[ROW][C]41[/C][C]540.45[/C][C]536.52[/C][C]3.92999999999995[/C][/ROW]
[ROW][C]42[/C][C]542.42[/C][C]540[/C][C]2.41999999999985[/C][/ROW]
[ROW][C]43[/C][C]542.42[/C][C]541.97[/C][C]0.449999999999932[/C][/ROW]
[ROW][C]44[/C][C]542.98[/C][C]541.97[/C][C]1.00999999999999[/C][/ROW]
[ROW][C]45[/C][C]540.19[/C][C]542.53[/C][C]-2.34000000000003[/C][/ROW]
[ROW][C]46[/C][C]537.16[/C][C]539.74[/C][C]-2.58000000000015[/C][/ROW]
[ROW][C]47[/C][C]537.35[/C][C]536.71[/C][C]0.639999999999986[/C][/ROW]
[ROW][C]48[/C][C]537.03[/C][C]536.9[/C][C]0.129999999999882[/C][/ROW]
[ROW][C]49[/C][C]537.03[/C][C]536.58[/C][C]0.449999999999932[/C][/ROW]
[ROW][C]50[/C][C]536.27[/C][C]536.58[/C][C]-0.310000000000059[/C][/ROW]
[ROW][C]51[/C][C]534.71[/C][C]535.82[/C][C]-1.11000000000001[/C][/ROW]
[ROW][C]52[/C][C]537.12[/C][C]534.26[/C][C]2.8599999999999[/C][/ROW]
[ROW][C]53[/C][C]537.07[/C][C]536.67[/C][C]0.399999999999977[/C][/ROW]
[ROW][C]54[/C][C]537.33[/C][C]536.62[/C][C]0.709999999999923[/C][/ROW]
[ROW][C]55[/C][C]537.33[/C][C]536.88[/C][C]0.449999999999932[/C][/ROW]
[ROW][C]56[/C][C]538.79[/C][C]536.88[/C][C]1.90999999999985[/C][/ROW]
[ROW][C]57[/C][C]539.24[/C][C]538.34[/C][C]0.899999999999977[/C][/ROW]
[ROW][C]58[/C][C]537.17[/C][C]538.79[/C][C]-1.62000000000012[/C][/ROW]
[ROW][C]59[/C][C]536.46[/C][C]536.72[/C][C]-0.259999999999991[/C][/ROW]
[ROW][C]60[/C][C]532.3[/C][C]536.01[/C][C]-3.71000000000015[/C][/ROW]
[ROW][C]61[/C][C]532.3[/C][C]531.85[/C][C]0.449999999999932[/C][/ROW]
[ROW][C]62[/C][C]532.89[/C][C]531.85[/C][C]1.03999999999996[/C][/ROW]
[ROW][C]63[/C][C]533.47[/C][C]532.44[/C][C]1.02999999999997[/C][/ROW]
[ROW][C]64[/C][C]532.54[/C][C]533.02[/C][C]-0.480000000000132[/C][/ROW]
[ROW][C]65[/C][C]533.8[/C][C]532.09[/C][C]1.70999999999992[/C][/ROW]
[ROW][C]66[/C][C]534.15[/C][C]533.35[/C][C]0.799999999999955[/C][/ROW]
[ROW][C]67[/C][C]534.15[/C][C]533.7[/C][C]0.449999999999932[/C][/ROW]
[ROW][C]68[/C][C]534.15[/C][C]533.7[/C][C]0.449999999999932[/C][/ROW]
[ROW][C]69[/C][C]534.28[/C][C]533.7[/C][C]0.579999999999927[/C][/ROW]
[ROW][C]70[/C][C]535.63[/C][C]533.83[/C][C]1.79999999999995[/C][/ROW]
[ROW][C]71[/C][C]534.21[/C][C]535.18[/C][C]-0.970000000000027[/C][/ROW]
[ROW][C]72[/C][C]533.78[/C][C]533.76[/C][C]0.0199999999998681[/C][/ROW]
[ROW][C]73[/C][C]533.78[/C][C]533.33[/C][C]0.449999999999932[/C][/ROW]
[ROW][C]74[/C][C]534.55[/C][C]533.33[/C][C]1.21999999999991[/C][/ROW]
[ROW][C]75[/C][C]536.93[/C][C]534.1[/C][C]2.82999999999993[/C][/ROW]
[ROW][C]76[/C][C]536.09[/C][C]536.48[/C][C]-0.389999999999986[/C][/ROW]
[ROW][C]77[/C][C]533.91[/C][C]535.64[/C][C]-1.73000000000013[/C][/ROW]
[ROW][C]78[/C][C]533.99[/C][C]533.46[/C][C]0.529999999999973[/C][/ROW]
[ROW][C]79[/C][C]533.99[/C][C]533.54[/C][C]0.449999999999932[/C][/ROW]
[ROW][C]80[/C][C]533.76[/C][C]533.54[/C][C]0.219999999999914[/C][/ROW]
[ROW][C]81[/C][C]532.5[/C][C]533.31[/C][C]-0.810000000000059[/C][/ROW]
[ROW][C]82[/C][C]529.5[/C][C]532.05[/C][C]-2.55000000000007[/C][/ROW]
[ROW][C]83[/C][C]528.62[/C][C]529.05[/C][C]-0.430000000000064[/C][/ROW]
[ROW][C]84[/C][C]528.7[/C][C]528.17[/C][C]0.529999999999973[/C][/ROW]
[ROW][C]85[/C][C]521.27[/C][C]528.25[/C][C]-6.98000000000013[/C][/ROW]
[ROW][C]86[/C][C]521.19[/C][C]520.82[/C][C]0.370000000000005[/C][/ROW]
[ROW][C]87[/C][C]519.43[/C][C]520.74[/C][C]-1.31000000000017[/C][/ROW]
[ROW][C]88[/C][C]516.81[/C][C]518.98[/C][C]-2.17000000000007[/C][/ROW]
[ROW][C]89[/C][C]516.78[/C][C]516.36[/C][C]0.419999999999959[/C][/ROW]
[ROW][C]90[/C][C]515.45[/C][C]516.33[/C][C]-0.879999999999995[/C][/ROW]
[ROW][C]91[/C][C]516.22[/C][C]515[/C][C]1.21999999999991[/C][/ROW]
[ROW][C]92[/C][C]517.01[/C][C]515.77[/C][C]1.2399999999999[/C][/ROW]
[ROW][C]93[/C][C]518.19[/C][C]516.56[/C][C]1.63[/C][/ROW]
[ROW][C]94[/C][C]516.79[/C][C]517.74[/C][C]-0.950000000000159[/C][/ROW]
[ROW][C]95[/C][C]516.87[/C][C]516.34[/C][C]0.529999999999973[/C][/ROW]
[ROW][C]96[/C][C]514.1[/C][C]516.42[/C][C]-2.32000000000005[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278595&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278595&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
3550.12551.01-0.8900000000001
4549.95549.670.279999999999973
5548.01549.5-1.49000000000012
6548.92547.561.3599999999999
7548.92548.470.449999999999932
8549.06548.470.589999999999918
9547.07548.61-1.53999999999996
10546.5546.62-0.120000000000118
11544.95546.05-1.10000000000002
12544.23544.5-0.270000000000095
13544.23543.780.449999999999932
14541.6543.78-2.18000000000006
15541.37541.150.219999999999914
16540.43540.92-0.490000000000123
17540.47539.980.490000000000009
18540.52540.020.499999999999886
19540.52540.070.449999999999932
20539.7540.07-0.370000000000005
21540.89539.251.63999999999987
22540.51540.440.0699999999999363
23537.43540.06-2.63000000000011
24538.14536.981.15999999999997
25538.14537.690.449999999999932
26537.74537.690.0499999999999545
27540.33537.293.03999999999996
28540.02539.880.139999999999873
29539.21539.57-0.360000000000014
30539.84538.761.07999999999993
31539.84539.390.449999999999932
32537.3539.39-2.09000000000015
33536.27536.85-0.580000000000041
34536.75535.820.92999999999995
35536.21536.3-0.0900000000000318
36536.99535.761.2299999999999
37536.99536.540.449999999999932
38536.57536.540.0299999999999727
39536.91536.120.78999999999985
40536.97536.460.509999999999991
41540.45536.523.92999999999995
42542.425402.41999999999985
43542.42541.970.449999999999932
44542.98541.971.00999999999999
45540.19542.53-2.34000000000003
46537.16539.74-2.58000000000015
47537.35536.710.639999999999986
48537.03536.90.129999999999882
49537.03536.580.449999999999932
50536.27536.58-0.310000000000059
51534.71535.82-1.11000000000001
52537.12534.262.8599999999999
53537.07536.670.399999999999977
54537.33536.620.709999999999923
55537.33536.880.449999999999932
56538.79536.881.90999999999985
57539.24538.340.899999999999977
58537.17538.79-1.62000000000012
59536.46536.72-0.259999999999991
60532.3536.01-3.71000000000015
61532.3531.850.449999999999932
62532.89531.851.03999999999996
63533.47532.441.02999999999997
64532.54533.02-0.480000000000132
65533.8532.091.70999999999992
66534.15533.350.799999999999955
67534.15533.70.449999999999932
68534.15533.70.449999999999932
69534.28533.70.579999999999927
70535.63533.831.79999999999995
71534.21535.18-0.970000000000027
72533.78533.760.0199999999998681
73533.78533.330.449999999999932
74534.55533.331.21999999999991
75536.93534.12.82999999999993
76536.09536.48-0.389999999999986
77533.91535.64-1.73000000000013
78533.99533.460.529999999999973
79533.99533.540.449999999999932
80533.76533.540.219999999999914
81532.5533.31-0.810000000000059
82529.5532.05-2.55000000000007
83528.62529.05-0.430000000000064
84528.7528.170.529999999999973
85521.27528.25-6.98000000000013
86521.19520.820.370000000000005
87519.43520.74-1.31000000000017
88516.81518.98-2.17000000000007
89516.78516.360.419999999999959
90515.45516.33-0.879999999999995
91516.225151.21999999999991
92517.01515.771.2399999999999
93518.19516.561.63
94516.79517.74-0.950000000000159
95516.87516.340.529999999999973
96514.1516.42-2.32000000000005







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
97513.65510.689464397714516.610535602287
98513.2509.013170399358517.386829600642
99512.75507.622201919223517.877798080777
100512.3506.378928795427518.221071204573
101511.85505.230041143479518.469958856521
102511.4504.148198409055518.651801590946
103510.950000000001503.117159048797518.782840951204
104510.500000000001502.126340798716518.873659201285
105510.050000000001501.168393193141518.93160680686
106509.600000000001500.237964402757518.962035597245
107509.150000000001499.331014228727518.968985771274
108508.700000000001498.444403838447518.955596161555

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 513.65 & 510.689464397714 & 516.610535602287 \tabularnewline
98 & 513.2 & 509.013170399358 & 517.386829600642 \tabularnewline
99 & 512.75 & 507.622201919223 & 517.877798080777 \tabularnewline
100 & 512.3 & 506.378928795427 & 518.221071204573 \tabularnewline
101 & 511.85 & 505.230041143479 & 518.469958856521 \tabularnewline
102 & 511.4 & 504.148198409055 & 518.651801590946 \tabularnewline
103 & 510.950000000001 & 503.117159048797 & 518.782840951204 \tabularnewline
104 & 510.500000000001 & 502.126340798716 & 518.873659201285 \tabularnewline
105 & 510.050000000001 & 501.168393193141 & 518.93160680686 \tabularnewline
106 & 509.600000000001 & 500.237964402757 & 518.962035597245 \tabularnewline
107 & 509.150000000001 & 499.331014228727 & 518.968985771274 \tabularnewline
108 & 508.700000000001 & 498.444403838447 & 518.955596161555 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278595&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]97[/C][C]513.65[/C][C]510.689464397714[/C][C]516.610535602287[/C][/ROW]
[ROW][C]98[/C][C]513.2[/C][C]509.013170399358[/C][C]517.386829600642[/C][/ROW]
[ROW][C]99[/C][C]512.75[/C][C]507.622201919223[/C][C]517.877798080777[/C][/ROW]
[ROW][C]100[/C][C]512.3[/C][C]506.378928795427[/C][C]518.221071204573[/C][/ROW]
[ROW][C]101[/C][C]511.85[/C][C]505.230041143479[/C][C]518.469958856521[/C][/ROW]
[ROW][C]102[/C][C]511.4[/C][C]504.148198409055[/C][C]518.651801590946[/C][/ROW]
[ROW][C]103[/C][C]510.950000000001[/C][C]503.117159048797[/C][C]518.782840951204[/C][/ROW]
[ROW][C]104[/C][C]510.500000000001[/C][C]502.126340798716[/C][C]518.873659201285[/C][/ROW]
[ROW][C]105[/C][C]510.050000000001[/C][C]501.168393193141[/C][C]518.93160680686[/C][/ROW]
[ROW][C]106[/C][C]509.600000000001[/C][C]500.237964402757[/C][C]518.962035597245[/C][/ROW]
[ROW][C]107[/C][C]509.150000000001[/C][C]499.331014228727[/C][C]518.968985771274[/C][/ROW]
[ROW][C]108[/C][C]508.700000000001[/C][C]498.444403838447[/C][C]518.955596161555[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278595&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278595&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
97513.65510.689464397714516.610535602287
98513.2509.013170399358517.386829600642
99512.75507.622201919223517.877798080777
100512.3506.378928795427518.221071204573
101511.85505.230041143479518.469958856521
102511.4504.148198409055518.651801590946
103510.950000000001503.117159048797518.782840951204
104510.500000000001502.126340798716518.873659201285
105510.050000000001501.168393193141518.93160680686
106509.600000000001500.237964402757518.962035597245
107509.150000000001499.331014228727518.968985771274
108508.700000000001498.444403838447518.955596161555



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
R code (references can be found in the software module):
par3 <- 'additive'
par2 <- 'Double'
par1 <- '12'
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')