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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 28 Dec 2013 07:24:46 -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/28/t1388233504rwijg3dqn98xm5y.htm/, Retrieved Thu, 28 Mar 2024 23:03:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232643, Retrieved Thu, 28 Mar 2024 23:03:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact127
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-12-28 12:24:46] [8131d2127c476fae44a4d982df34064a] [Current]
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Dataseries X:
99,42
99,42
99,42
99,42
99,42
109,26
110
110
109,26
100,07
100,07
100,05
100,05
100,05
100,05
100,05
100,05
108,77
111,32
111,6
108,52
103,13
102,87
102,75
102,75
102,75
102,75
102,75
102,75
115,22
115,53
115,4
111,99
107,93
107,43
106,98
106,98
106,98
106,98
106,98
106,98
113,71
118,77
118,54
116,16
110,52
110,06
109,9
109,9
110,72
110,09
110,07
112,45
113,06
119,83
119,84
113,73
110,5
110,12
109,86
110,36
110,36
110,59
112,52
112,1
115,9
122,96
121,26
114,55
111,57
110,65
109,77
112,38
112,35
112,2
114,46
116,26
119,57
127,77
126,59
120,45
116,38
116,3
115,05




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232643&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]4 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=232643&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232643&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 time4 seconds
R Server'Gwilym Jenkins' @ jenkins.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=232643&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=232643&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232643&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
399.4299.420
499.4299.420
599.4299.420
6109.2699.429.84
7110109.260.739999999999995
81101100
9109.26110-0.739999999999995
10100.07109.26-9.19000000000001
11100.07100.070
12100.05100.07-0.019999999999996
13100.05100.050
14100.05100.050
15100.05100.050
16100.05100.050
17100.05100.050
18108.77100.058.72
19111.32108.772.55
20111.6111.320.280000000000001
21108.52111.6-3.08
22103.13108.52-5.39
23102.87103.13-0.259999999999991
24102.75102.87-0.120000000000005
25102.75102.750
26102.75102.750
27102.75102.750
28102.75102.750
29102.75102.750
30115.22102.7512.47
31115.53115.220.310000000000002
32115.4115.53-0.129999999999995
33111.99115.4-3.41000000000001
34107.93111.99-4.05999999999999
35107.43107.93-0.5
36106.98107.43-0.450000000000003
37106.98106.980
38106.98106.980
39106.98106.980
40106.98106.980
41106.98106.980
42113.71106.986.72999999999999
43118.77113.715.06
44118.54118.77-0.22999999999999
45116.16118.54-2.38000000000001
46110.52116.16-5.64
47110.06110.52-0.459999999999994
48109.9110.06-0.159999999999997
49109.9109.90
50110.72109.90.819999999999993
51110.09110.72-0.629999999999995
52110.07110.09-0.0200000000000102
53112.45110.072.38000000000001
54113.06112.450.609999999999999
55119.83113.066.77
56119.84119.830.0100000000000051
57113.73119.84-6.11
58110.5113.73-3.23
59110.12110.5-0.379999999999995
60109.86110.12-0.260000000000005
61110.36109.860.5
62110.36110.360
63110.59110.360.230000000000004
64112.52110.591.92999999999999
65112.1112.52-0.420000000000002
66115.9112.13.80000000000001
67122.96115.97.05999999999999
68121.26122.96-1.69999999999999
69114.55121.26-6.71000000000001
70111.57114.55-2.98
71110.65111.57-0.919999999999987
72109.77110.65-0.88000000000001
73112.38109.772.61
74112.35112.38-0.0300000000000011
75112.2112.35-0.149999999999991
76114.46112.22.25999999999999
77116.26114.461.80000000000001
78119.57116.263.30999999999999
79127.77119.578.2
80126.59127.77-1.17999999999999
81120.45126.59-6.14
82116.38120.45-4.07000000000001
83116.3116.38-0.0799999999999983
84115.05116.3-1.25

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 99.42 & 99.42 & 0 \tabularnewline
4 & 99.42 & 99.42 & 0 \tabularnewline
5 & 99.42 & 99.42 & 0 \tabularnewline
6 & 109.26 & 99.42 & 9.84 \tabularnewline
7 & 110 & 109.26 & 0.739999999999995 \tabularnewline
8 & 110 & 110 & 0 \tabularnewline
9 & 109.26 & 110 & -0.739999999999995 \tabularnewline
10 & 100.07 & 109.26 & -9.19000000000001 \tabularnewline
11 & 100.07 & 100.07 & 0 \tabularnewline
12 & 100.05 & 100.07 & -0.019999999999996 \tabularnewline
13 & 100.05 & 100.05 & 0 \tabularnewline
14 & 100.05 & 100.05 & 0 \tabularnewline
15 & 100.05 & 100.05 & 0 \tabularnewline
16 & 100.05 & 100.05 & 0 \tabularnewline
17 & 100.05 & 100.05 & 0 \tabularnewline
18 & 108.77 & 100.05 & 8.72 \tabularnewline
19 & 111.32 & 108.77 & 2.55 \tabularnewline
20 & 111.6 & 111.32 & 0.280000000000001 \tabularnewline
21 & 108.52 & 111.6 & -3.08 \tabularnewline
22 & 103.13 & 108.52 & -5.39 \tabularnewline
23 & 102.87 & 103.13 & -0.259999999999991 \tabularnewline
24 & 102.75 & 102.87 & -0.120000000000005 \tabularnewline
25 & 102.75 & 102.75 & 0 \tabularnewline
26 & 102.75 & 102.75 & 0 \tabularnewline
27 & 102.75 & 102.75 & 0 \tabularnewline
28 & 102.75 & 102.75 & 0 \tabularnewline
29 & 102.75 & 102.75 & 0 \tabularnewline
30 & 115.22 & 102.75 & 12.47 \tabularnewline
31 & 115.53 & 115.22 & 0.310000000000002 \tabularnewline
32 & 115.4 & 115.53 & -0.129999999999995 \tabularnewline
33 & 111.99 & 115.4 & -3.41000000000001 \tabularnewline
34 & 107.93 & 111.99 & -4.05999999999999 \tabularnewline
35 & 107.43 & 107.93 & -0.5 \tabularnewline
36 & 106.98 & 107.43 & -0.450000000000003 \tabularnewline
37 & 106.98 & 106.98 & 0 \tabularnewline
38 & 106.98 & 106.98 & 0 \tabularnewline
39 & 106.98 & 106.98 & 0 \tabularnewline
40 & 106.98 & 106.98 & 0 \tabularnewline
41 & 106.98 & 106.98 & 0 \tabularnewline
42 & 113.71 & 106.98 & 6.72999999999999 \tabularnewline
43 & 118.77 & 113.71 & 5.06 \tabularnewline
44 & 118.54 & 118.77 & -0.22999999999999 \tabularnewline
45 & 116.16 & 118.54 & -2.38000000000001 \tabularnewline
46 & 110.52 & 116.16 & -5.64 \tabularnewline
47 & 110.06 & 110.52 & -0.459999999999994 \tabularnewline
48 & 109.9 & 110.06 & -0.159999999999997 \tabularnewline
49 & 109.9 & 109.9 & 0 \tabularnewline
50 & 110.72 & 109.9 & 0.819999999999993 \tabularnewline
51 & 110.09 & 110.72 & -0.629999999999995 \tabularnewline
52 & 110.07 & 110.09 & -0.0200000000000102 \tabularnewline
53 & 112.45 & 110.07 & 2.38000000000001 \tabularnewline
54 & 113.06 & 112.45 & 0.609999999999999 \tabularnewline
55 & 119.83 & 113.06 & 6.77 \tabularnewline
56 & 119.84 & 119.83 & 0.0100000000000051 \tabularnewline
57 & 113.73 & 119.84 & -6.11 \tabularnewline
58 & 110.5 & 113.73 & -3.23 \tabularnewline
59 & 110.12 & 110.5 & -0.379999999999995 \tabularnewline
60 & 109.86 & 110.12 & -0.260000000000005 \tabularnewline
61 & 110.36 & 109.86 & 0.5 \tabularnewline
62 & 110.36 & 110.36 & 0 \tabularnewline
63 & 110.59 & 110.36 & 0.230000000000004 \tabularnewline
64 & 112.52 & 110.59 & 1.92999999999999 \tabularnewline
65 & 112.1 & 112.52 & -0.420000000000002 \tabularnewline
66 & 115.9 & 112.1 & 3.80000000000001 \tabularnewline
67 & 122.96 & 115.9 & 7.05999999999999 \tabularnewline
68 & 121.26 & 122.96 & -1.69999999999999 \tabularnewline
69 & 114.55 & 121.26 & -6.71000000000001 \tabularnewline
70 & 111.57 & 114.55 & -2.98 \tabularnewline
71 & 110.65 & 111.57 & -0.919999999999987 \tabularnewline
72 & 109.77 & 110.65 & -0.88000000000001 \tabularnewline
73 & 112.38 & 109.77 & 2.61 \tabularnewline
74 & 112.35 & 112.38 & -0.0300000000000011 \tabularnewline
75 & 112.2 & 112.35 & -0.149999999999991 \tabularnewline
76 & 114.46 & 112.2 & 2.25999999999999 \tabularnewline
77 & 116.26 & 114.46 & 1.80000000000001 \tabularnewline
78 & 119.57 & 116.26 & 3.30999999999999 \tabularnewline
79 & 127.77 & 119.57 & 8.2 \tabularnewline
80 & 126.59 & 127.77 & -1.17999999999999 \tabularnewline
81 & 120.45 & 126.59 & -6.14 \tabularnewline
82 & 116.38 & 120.45 & -4.07000000000001 \tabularnewline
83 & 116.3 & 116.38 & -0.0799999999999983 \tabularnewline
84 & 115.05 & 116.3 & -1.25 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232643&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]99.42[/C][C]99.42[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]99.42[/C][C]99.42[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]99.42[/C][C]99.42[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]109.26[/C][C]99.42[/C][C]9.84[/C][/ROW]
[ROW][C]7[/C][C]110[/C][C]109.26[/C][C]0.739999999999995[/C][/ROW]
[ROW][C]8[/C][C]110[/C][C]110[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]109.26[/C][C]110[/C][C]-0.739999999999995[/C][/ROW]
[ROW][C]10[/C][C]100.07[/C][C]109.26[/C][C]-9.19000000000001[/C][/ROW]
[ROW][C]11[/C][C]100.07[/C][C]100.07[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]100.05[/C][C]100.07[/C][C]-0.019999999999996[/C][/ROW]
[ROW][C]13[/C][C]100.05[/C][C]100.05[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]100.05[/C][C]100.05[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]100.05[/C][C]100.05[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]100.05[/C][C]100.05[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]100.05[/C][C]100.05[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]108.77[/C][C]100.05[/C][C]8.72[/C][/ROW]
[ROW][C]19[/C][C]111.32[/C][C]108.77[/C][C]2.55[/C][/ROW]
[ROW][C]20[/C][C]111.6[/C][C]111.32[/C][C]0.280000000000001[/C][/ROW]
[ROW][C]21[/C][C]108.52[/C][C]111.6[/C][C]-3.08[/C][/ROW]
[ROW][C]22[/C][C]103.13[/C][C]108.52[/C][C]-5.39[/C][/ROW]
[ROW][C]23[/C][C]102.87[/C][C]103.13[/C][C]-0.259999999999991[/C][/ROW]
[ROW][C]24[/C][C]102.75[/C][C]102.87[/C][C]-0.120000000000005[/C][/ROW]
[ROW][C]25[/C][C]102.75[/C][C]102.75[/C][C]0[/C][/ROW]
[ROW][C]26[/C][C]102.75[/C][C]102.75[/C][C]0[/C][/ROW]
[ROW][C]27[/C][C]102.75[/C][C]102.75[/C][C]0[/C][/ROW]
[ROW][C]28[/C][C]102.75[/C][C]102.75[/C][C]0[/C][/ROW]
[ROW][C]29[/C][C]102.75[/C][C]102.75[/C][C]0[/C][/ROW]
[ROW][C]30[/C][C]115.22[/C][C]102.75[/C][C]12.47[/C][/ROW]
[ROW][C]31[/C][C]115.53[/C][C]115.22[/C][C]0.310000000000002[/C][/ROW]
[ROW][C]32[/C][C]115.4[/C][C]115.53[/C][C]-0.129999999999995[/C][/ROW]
[ROW][C]33[/C][C]111.99[/C][C]115.4[/C][C]-3.41000000000001[/C][/ROW]
[ROW][C]34[/C][C]107.93[/C][C]111.99[/C][C]-4.05999999999999[/C][/ROW]
[ROW][C]35[/C][C]107.43[/C][C]107.93[/C][C]-0.5[/C][/ROW]
[ROW][C]36[/C][C]106.98[/C][C]107.43[/C][C]-0.450000000000003[/C][/ROW]
[ROW][C]37[/C][C]106.98[/C][C]106.98[/C][C]0[/C][/ROW]
[ROW][C]38[/C][C]106.98[/C][C]106.98[/C][C]0[/C][/ROW]
[ROW][C]39[/C][C]106.98[/C][C]106.98[/C][C]0[/C][/ROW]
[ROW][C]40[/C][C]106.98[/C][C]106.98[/C][C]0[/C][/ROW]
[ROW][C]41[/C][C]106.98[/C][C]106.98[/C][C]0[/C][/ROW]
[ROW][C]42[/C][C]113.71[/C][C]106.98[/C][C]6.72999999999999[/C][/ROW]
[ROW][C]43[/C][C]118.77[/C][C]113.71[/C][C]5.06[/C][/ROW]
[ROW][C]44[/C][C]118.54[/C][C]118.77[/C][C]-0.22999999999999[/C][/ROW]
[ROW][C]45[/C][C]116.16[/C][C]118.54[/C][C]-2.38000000000001[/C][/ROW]
[ROW][C]46[/C][C]110.52[/C][C]116.16[/C][C]-5.64[/C][/ROW]
[ROW][C]47[/C][C]110.06[/C][C]110.52[/C][C]-0.459999999999994[/C][/ROW]
[ROW][C]48[/C][C]109.9[/C][C]110.06[/C][C]-0.159999999999997[/C][/ROW]
[ROW][C]49[/C][C]109.9[/C][C]109.9[/C][C]0[/C][/ROW]
[ROW][C]50[/C][C]110.72[/C][C]109.9[/C][C]0.819999999999993[/C][/ROW]
[ROW][C]51[/C][C]110.09[/C][C]110.72[/C][C]-0.629999999999995[/C][/ROW]
[ROW][C]52[/C][C]110.07[/C][C]110.09[/C][C]-0.0200000000000102[/C][/ROW]
[ROW][C]53[/C][C]112.45[/C][C]110.07[/C][C]2.38000000000001[/C][/ROW]
[ROW][C]54[/C][C]113.06[/C][C]112.45[/C][C]0.609999999999999[/C][/ROW]
[ROW][C]55[/C][C]119.83[/C][C]113.06[/C][C]6.77[/C][/ROW]
[ROW][C]56[/C][C]119.84[/C][C]119.83[/C][C]0.0100000000000051[/C][/ROW]
[ROW][C]57[/C][C]113.73[/C][C]119.84[/C][C]-6.11[/C][/ROW]
[ROW][C]58[/C][C]110.5[/C][C]113.73[/C][C]-3.23[/C][/ROW]
[ROW][C]59[/C][C]110.12[/C][C]110.5[/C][C]-0.379999999999995[/C][/ROW]
[ROW][C]60[/C][C]109.86[/C][C]110.12[/C][C]-0.260000000000005[/C][/ROW]
[ROW][C]61[/C][C]110.36[/C][C]109.86[/C][C]0.5[/C][/ROW]
[ROW][C]62[/C][C]110.36[/C][C]110.36[/C][C]0[/C][/ROW]
[ROW][C]63[/C][C]110.59[/C][C]110.36[/C][C]0.230000000000004[/C][/ROW]
[ROW][C]64[/C][C]112.52[/C][C]110.59[/C][C]1.92999999999999[/C][/ROW]
[ROW][C]65[/C][C]112.1[/C][C]112.52[/C][C]-0.420000000000002[/C][/ROW]
[ROW][C]66[/C][C]115.9[/C][C]112.1[/C][C]3.80000000000001[/C][/ROW]
[ROW][C]67[/C][C]122.96[/C][C]115.9[/C][C]7.05999999999999[/C][/ROW]
[ROW][C]68[/C][C]121.26[/C][C]122.96[/C][C]-1.69999999999999[/C][/ROW]
[ROW][C]69[/C][C]114.55[/C][C]121.26[/C][C]-6.71000000000001[/C][/ROW]
[ROW][C]70[/C][C]111.57[/C][C]114.55[/C][C]-2.98[/C][/ROW]
[ROW][C]71[/C][C]110.65[/C][C]111.57[/C][C]-0.919999999999987[/C][/ROW]
[ROW][C]72[/C][C]109.77[/C][C]110.65[/C][C]-0.88000000000001[/C][/ROW]
[ROW][C]73[/C][C]112.38[/C][C]109.77[/C][C]2.61[/C][/ROW]
[ROW][C]74[/C][C]112.35[/C][C]112.38[/C][C]-0.0300000000000011[/C][/ROW]
[ROW][C]75[/C][C]112.2[/C][C]112.35[/C][C]-0.149999999999991[/C][/ROW]
[ROW][C]76[/C][C]114.46[/C][C]112.2[/C][C]2.25999999999999[/C][/ROW]
[ROW][C]77[/C][C]116.26[/C][C]114.46[/C][C]1.80000000000001[/C][/ROW]
[ROW][C]78[/C][C]119.57[/C][C]116.26[/C][C]3.30999999999999[/C][/ROW]
[ROW][C]79[/C][C]127.77[/C][C]119.57[/C][C]8.2[/C][/ROW]
[ROW][C]80[/C][C]126.59[/C][C]127.77[/C][C]-1.17999999999999[/C][/ROW]
[ROW][C]81[/C][C]120.45[/C][C]126.59[/C][C]-6.14[/C][/ROW]
[ROW][C]82[/C][C]116.38[/C][C]120.45[/C][C]-4.07000000000001[/C][/ROW]
[ROW][C]83[/C][C]116.3[/C][C]116.38[/C][C]-0.0799999999999983[/C][/ROW]
[ROW][C]84[/C][C]115.05[/C][C]116.3[/C][C]-1.25[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232643&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232643&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
399.4299.420
499.4299.420
599.4299.420
6109.2699.429.84
7110109.260.739999999999995
81101100
9109.26110-0.739999999999995
10100.07109.26-9.19000000000001
11100.07100.070
12100.05100.07-0.019999999999996
13100.05100.050
14100.05100.050
15100.05100.050
16100.05100.050
17100.05100.050
18108.77100.058.72
19111.32108.772.55
20111.6111.320.280000000000001
21108.52111.6-3.08
22103.13108.52-5.39
23102.87103.13-0.259999999999991
24102.75102.87-0.120000000000005
25102.75102.750
26102.75102.750
27102.75102.750
28102.75102.750
29102.75102.750
30115.22102.7512.47
31115.53115.220.310000000000002
32115.4115.53-0.129999999999995
33111.99115.4-3.41000000000001
34107.93111.99-4.05999999999999
35107.43107.93-0.5
36106.98107.43-0.450000000000003
37106.98106.980
38106.98106.980
39106.98106.980
40106.98106.980
41106.98106.980
42113.71106.986.72999999999999
43118.77113.715.06
44118.54118.77-0.22999999999999
45116.16118.54-2.38000000000001
46110.52116.16-5.64
47110.06110.52-0.459999999999994
48109.9110.06-0.159999999999997
49109.9109.90
50110.72109.90.819999999999993
51110.09110.72-0.629999999999995
52110.07110.09-0.0200000000000102
53112.45110.072.38000000000001
54113.06112.450.609999999999999
55119.83113.066.77
56119.84119.830.0100000000000051
57113.73119.84-6.11
58110.5113.73-3.23
59110.12110.5-0.379999999999995
60109.86110.12-0.260000000000005
61110.36109.860.5
62110.36110.360
63110.59110.360.230000000000004
64112.52110.591.92999999999999
65112.1112.52-0.420000000000002
66115.9112.13.80000000000001
67122.96115.97.05999999999999
68121.26122.96-1.69999999999999
69114.55121.26-6.71000000000001
70111.57114.55-2.98
71110.65111.57-0.919999999999987
72109.77110.65-0.88000000000001
73112.38109.772.61
74112.35112.38-0.0300000000000011
75112.2112.35-0.149999999999991
76114.46112.22.25999999999999
77116.26114.461.80000000000001
78119.57116.263.30999999999999
79127.77119.578.2
80126.59127.77-1.17999999999999
81120.45126.59-6.14
82116.38120.45-4.07000000000001
83116.3116.38-0.0799999999999983
84115.05116.3-1.25







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85115.05108.260831822413121.839168177587
86115.05105.448666286025124.651333713975
87115.05103.29081577529126.80918422471
88115.05101.471663644827128.628336355173
89115.0599.868958444238130.231041555762
90115.0598.4200021869717131.679997813028
91115.0597.0875493931123133.012450606888
92115.0595.8473325720504134.25266742795
93115.0594.6824954672402135.41750453276
94115.0593.5807651408919136.519234859108
95115.0592.5328765163243137.567123483676
96115.0591.5316315505804138.56836844942

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 115.05 & 108.260831822413 & 121.839168177587 \tabularnewline
86 & 115.05 & 105.448666286025 & 124.651333713975 \tabularnewline
87 & 115.05 & 103.29081577529 & 126.80918422471 \tabularnewline
88 & 115.05 & 101.471663644827 & 128.628336355173 \tabularnewline
89 & 115.05 & 99.868958444238 & 130.231041555762 \tabularnewline
90 & 115.05 & 98.4200021869717 & 131.679997813028 \tabularnewline
91 & 115.05 & 97.0875493931123 & 133.012450606888 \tabularnewline
92 & 115.05 & 95.8473325720504 & 134.25266742795 \tabularnewline
93 & 115.05 & 94.6824954672402 & 135.41750453276 \tabularnewline
94 & 115.05 & 93.5807651408919 & 136.519234859108 \tabularnewline
95 & 115.05 & 92.5328765163243 & 137.567123483676 \tabularnewline
96 & 115.05 & 91.5316315505804 & 138.56836844942 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232643&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]115.05[/C][C]108.260831822413[/C][C]121.839168177587[/C][/ROW]
[ROW][C]86[/C][C]115.05[/C][C]105.448666286025[/C][C]124.651333713975[/C][/ROW]
[ROW][C]87[/C][C]115.05[/C][C]103.29081577529[/C][C]126.80918422471[/C][/ROW]
[ROW][C]88[/C][C]115.05[/C][C]101.471663644827[/C][C]128.628336355173[/C][/ROW]
[ROW][C]89[/C][C]115.05[/C][C]99.868958444238[/C][C]130.231041555762[/C][/ROW]
[ROW][C]90[/C][C]115.05[/C][C]98.4200021869717[/C][C]131.679997813028[/C][/ROW]
[ROW][C]91[/C][C]115.05[/C][C]97.0875493931123[/C][C]133.012450606888[/C][/ROW]
[ROW][C]92[/C][C]115.05[/C][C]95.8473325720504[/C][C]134.25266742795[/C][/ROW]
[ROW][C]93[/C][C]115.05[/C][C]94.6824954672402[/C][C]135.41750453276[/C][/ROW]
[ROW][C]94[/C][C]115.05[/C][C]93.5807651408919[/C][C]136.519234859108[/C][/ROW]
[ROW][C]95[/C][C]115.05[/C][C]92.5328765163243[/C][C]137.567123483676[/C][/ROW]
[ROW][C]96[/C][C]115.05[/C][C]91.5316315505804[/C][C]138.56836844942[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232643&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232643&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
85115.05108.260831822413121.839168177587
86115.05105.448666286025124.651333713975
87115.05103.29081577529126.80918422471
88115.05101.471663644827128.628336355173
89115.0599.868958444238130.231041555762
90115.0598.4200021869717131.679997813028
91115.0597.0875493931123133.012450606888
92115.0595.8473325720504134.25266742795
93115.0594.6824954672402135.41750453276
94115.0593.5807651408919136.519234859108
95115.0592.5328765163243137.567123483676
96115.0591.5316315505804138.56836844942



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')