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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 18 Aug 2009 16:05:12 -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/2009/Aug/19/t12506331903ny7hrp8w44el6s.htm/, Retrieved Tue, 07 May 2024 09:28:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=42902, Retrieved Tue, 07 May 2024 09:28:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact171
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential smoot...] [2009-08-18 22:05:12] [1596366c2ece8f787477cc7d1246d4c7] [Current]
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Dataseries X:
105.46
104.66
103.52
103.71
103.78
103.67
103.66
102.76
102
101.5
101.5
99.22
98.97
98.9
99.78
104.4
106.21
105.46
108.33
111.72
111.88
112.86
113.09
116.9
114.62
118.86
124.71
122.53
127.89
136.16
134.12
130.26
135.35
131.43
129.61
123.96
121.1
125.38
123.1
129.92
136.68
131.17
124.82
122.47
126.15
118.74
116.8
116.64
116.53
117.68
119.46
126.19
124.39
121.9
122.53
122.93
124.66
124.41
120.93
120.18
123.44
126.1
125.82
122.18
117.27
117.86
119.09
123.08
125.42
121.81
121.66
121.27
120.92
122.16
124.17
127.26
134.16
134.09
135.57
136.13
136.23
140.6
136.5
130.59
129.5
135.25
138.06
146.28
145.04
147.96
156.71
160.97
168.17
163.91
153.05
151.76
119.55
119.44
120.25
124.92
126.34
125.88
127.34
127.48
119.41
114.82
115.28
116.37
111.99
113.57
117.69
120.74
122.37
123.57
124.86
122.08
123.56
126.92
134.88
130.64
131.65
130.97
136.77
138.17
146.4
152.07
153.05
142.89
141.11
131.9
118.42
108.27




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42902&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]3 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=42902&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42902&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 time3 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=42902&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=42902&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42902&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
3103.52104.66-1.14
4103.71103.520.189999999999998
5103.78103.710.0700000000000074
6103.67103.78-0.109999999999999
7103.66103.67-0.0100000000000051
8102.76103.66-0.899999999999991
9102102.76-0.760000000000005
10101.5102-0.5
11101.5101.50
1299.22101.5-2.28
1398.9799.22-0.25
1498.998.97-0.0699999999999932
1599.7898.90.879999999999995
16104.499.784.62
17106.21104.41.80999999999999
18105.46106.21-0.75
19108.33105.462.87000000000000
20111.72108.333.39
21111.88111.720.159999999999997
22112.86111.880.980000000000004
23113.09112.860.230000000000004
24116.9113.093.81
25114.62116.9-2.28
26118.86114.624.23999999999999
27124.71118.865.85
28122.53124.71-2.17999999999999
29127.89122.535.36
30136.16127.898.27
31134.12136.16-2.03999999999999
32130.26134.12-3.86000000000001
33135.35130.265.09
34131.43135.35-3.91999999999999
35129.61131.43-1.81999999999999
36123.96129.61-5.65000000000002
37121.1123.96-2.86
38125.38121.14.28
39123.1125.38-2.28
40129.92123.16.81999999999999
41136.68129.926.76000000000002
42131.17136.68-5.51000000000002
43124.82131.17-6.35
44122.47124.82-2.34999999999999
45126.15122.473.68000000000001
46118.74126.15-7.41000000000001
47116.8118.74-1.94000000000000
48116.64116.8-0.159999999999997
49116.53116.64-0.109999999999999
50117.68116.531.15000000000001
51119.46117.681.77999999999999
52126.19119.466.73
53124.39126.19-1.80000000000000
54121.9124.39-2.48999999999999
55122.53121.90.629999999999995
56122.93122.530.400000000000006
57124.66122.931.72999999999999
58124.41124.66-0.25
59120.93124.41-3.47999999999999
60120.18120.93-0.75
61123.44120.183.25999999999999
62126.1123.442.66000000000000
63125.82126.1-0.280000000000001
64122.18125.82-3.63999999999999
65117.27122.18-4.91000000000001
66117.86117.270.590000000000003
67119.09117.861.23000000000000
68123.08119.093.98999999999999
69125.42123.082.34000000000000
70121.81125.42-3.61
71121.66121.81-0.150000000000006
72121.27121.66-0.390000000000001
73120.92121.27-0.349999999999994
74122.16120.921.23999999999999
75124.17122.162.01000000000001
76127.26124.173.09000000000000
77134.16127.266.89999999999999
78134.09134.16-0.0699999999999932
79135.57134.091.47999999999999
80136.13135.570.560000000000002
81136.23136.130.0999999999999943
82140.6136.234.37000000000000
83136.5140.6-4.09999999999999
84130.59136.5-5.91
85129.5130.59-1.09000000000000
86135.25129.55.75
87138.06135.252.81
88146.28138.068.22
89145.04146.28-1.24000000000001
90147.96145.042.92000000000002
91156.71147.968.75
92160.97156.714.25999999999999
93168.17160.977.19999999999999
94163.91168.17-4.25999999999999
95153.05163.91-10.8600000000000
96151.76153.05-1.29000000000002
97119.55151.76-32.21
98119.44119.55-0.109999999999999
99120.25119.440.810000000000002
100124.92120.254.67
101126.34124.921.42000000000000
102125.88126.34-0.460000000000008
103127.34125.881.46000000000001
104127.48127.340.140000000000001
105119.41127.48-8.07
106114.82119.41-4.59
107115.28114.820.460000000000008
108116.37115.281.09000000000000
109111.99116.37-4.38000000000001
110113.57111.991.58000000000000
111117.69113.574.12000000000000
112120.74117.693.05
113122.37120.741.63000000000001
114123.57122.371.19999999999999
115124.86123.571.29000000000001
116122.08124.86-2.78
117123.56122.081.48000000000000
118126.92123.563.36
119134.88126.927.96
120130.64134.88-4.24000000000001
121131.65130.641.01000000000002
122130.97131.65-0.680000000000007
123136.77130.975.80000000000001
124138.17136.771.39999999999998
125146.4138.178.23000000000002
126152.07146.45.66999999999999
127153.05152.070.980000000000018
128142.89153.05-10.1600000000000
129141.11142.89-1.77999999999997
130131.9141.11-9.21
131118.42131.9-13.48
132108.27118.42-10.15

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 103.52 & 104.66 & -1.14 \tabularnewline
4 & 103.71 & 103.52 & 0.189999999999998 \tabularnewline
5 & 103.78 & 103.71 & 0.0700000000000074 \tabularnewline
6 & 103.67 & 103.78 & -0.109999999999999 \tabularnewline
7 & 103.66 & 103.67 & -0.0100000000000051 \tabularnewline
8 & 102.76 & 103.66 & -0.899999999999991 \tabularnewline
9 & 102 & 102.76 & -0.760000000000005 \tabularnewline
10 & 101.5 & 102 & -0.5 \tabularnewline
11 & 101.5 & 101.5 & 0 \tabularnewline
12 & 99.22 & 101.5 & -2.28 \tabularnewline
13 & 98.97 & 99.22 & -0.25 \tabularnewline
14 & 98.9 & 98.97 & -0.0699999999999932 \tabularnewline
15 & 99.78 & 98.9 & 0.879999999999995 \tabularnewline
16 & 104.4 & 99.78 & 4.62 \tabularnewline
17 & 106.21 & 104.4 & 1.80999999999999 \tabularnewline
18 & 105.46 & 106.21 & -0.75 \tabularnewline
19 & 108.33 & 105.46 & 2.87000000000000 \tabularnewline
20 & 111.72 & 108.33 & 3.39 \tabularnewline
21 & 111.88 & 111.72 & 0.159999999999997 \tabularnewline
22 & 112.86 & 111.88 & 0.980000000000004 \tabularnewline
23 & 113.09 & 112.86 & 0.230000000000004 \tabularnewline
24 & 116.9 & 113.09 & 3.81 \tabularnewline
25 & 114.62 & 116.9 & -2.28 \tabularnewline
26 & 118.86 & 114.62 & 4.23999999999999 \tabularnewline
27 & 124.71 & 118.86 & 5.85 \tabularnewline
28 & 122.53 & 124.71 & -2.17999999999999 \tabularnewline
29 & 127.89 & 122.53 & 5.36 \tabularnewline
30 & 136.16 & 127.89 & 8.27 \tabularnewline
31 & 134.12 & 136.16 & -2.03999999999999 \tabularnewline
32 & 130.26 & 134.12 & -3.86000000000001 \tabularnewline
33 & 135.35 & 130.26 & 5.09 \tabularnewline
34 & 131.43 & 135.35 & -3.91999999999999 \tabularnewline
35 & 129.61 & 131.43 & -1.81999999999999 \tabularnewline
36 & 123.96 & 129.61 & -5.65000000000002 \tabularnewline
37 & 121.1 & 123.96 & -2.86 \tabularnewline
38 & 125.38 & 121.1 & 4.28 \tabularnewline
39 & 123.1 & 125.38 & -2.28 \tabularnewline
40 & 129.92 & 123.1 & 6.81999999999999 \tabularnewline
41 & 136.68 & 129.92 & 6.76000000000002 \tabularnewline
42 & 131.17 & 136.68 & -5.51000000000002 \tabularnewline
43 & 124.82 & 131.17 & -6.35 \tabularnewline
44 & 122.47 & 124.82 & -2.34999999999999 \tabularnewline
45 & 126.15 & 122.47 & 3.68000000000001 \tabularnewline
46 & 118.74 & 126.15 & -7.41000000000001 \tabularnewline
47 & 116.8 & 118.74 & -1.94000000000000 \tabularnewline
48 & 116.64 & 116.8 & -0.159999999999997 \tabularnewline
49 & 116.53 & 116.64 & -0.109999999999999 \tabularnewline
50 & 117.68 & 116.53 & 1.15000000000001 \tabularnewline
51 & 119.46 & 117.68 & 1.77999999999999 \tabularnewline
52 & 126.19 & 119.46 & 6.73 \tabularnewline
53 & 124.39 & 126.19 & -1.80000000000000 \tabularnewline
54 & 121.9 & 124.39 & -2.48999999999999 \tabularnewline
55 & 122.53 & 121.9 & 0.629999999999995 \tabularnewline
56 & 122.93 & 122.53 & 0.400000000000006 \tabularnewline
57 & 124.66 & 122.93 & 1.72999999999999 \tabularnewline
58 & 124.41 & 124.66 & -0.25 \tabularnewline
59 & 120.93 & 124.41 & -3.47999999999999 \tabularnewline
60 & 120.18 & 120.93 & -0.75 \tabularnewline
61 & 123.44 & 120.18 & 3.25999999999999 \tabularnewline
62 & 126.1 & 123.44 & 2.66000000000000 \tabularnewline
63 & 125.82 & 126.1 & -0.280000000000001 \tabularnewline
64 & 122.18 & 125.82 & -3.63999999999999 \tabularnewline
65 & 117.27 & 122.18 & -4.91000000000001 \tabularnewline
66 & 117.86 & 117.27 & 0.590000000000003 \tabularnewline
67 & 119.09 & 117.86 & 1.23000000000000 \tabularnewline
68 & 123.08 & 119.09 & 3.98999999999999 \tabularnewline
69 & 125.42 & 123.08 & 2.34000000000000 \tabularnewline
70 & 121.81 & 125.42 & -3.61 \tabularnewline
71 & 121.66 & 121.81 & -0.150000000000006 \tabularnewline
72 & 121.27 & 121.66 & -0.390000000000001 \tabularnewline
73 & 120.92 & 121.27 & -0.349999999999994 \tabularnewline
74 & 122.16 & 120.92 & 1.23999999999999 \tabularnewline
75 & 124.17 & 122.16 & 2.01000000000001 \tabularnewline
76 & 127.26 & 124.17 & 3.09000000000000 \tabularnewline
77 & 134.16 & 127.26 & 6.89999999999999 \tabularnewline
78 & 134.09 & 134.16 & -0.0699999999999932 \tabularnewline
79 & 135.57 & 134.09 & 1.47999999999999 \tabularnewline
80 & 136.13 & 135.57 & 0.560000000000002 \tabularnewline
81 & 136.23 & 136.13 & 0.0999999999999943 \tabularnewline
82 & 140.6 & 136.23 & 4.37000000000000 \tabularnewline
83 & 136.5 & 140.6 & -4.09999999999999 \tabularnewline
84 & 130.59 & 136.5 & -5.91 \tabularnewline
85 & 129.5 & 130.59 & -1.09000000000000 \tabularnewline
86 & 135.25 & 129.5 & 5.75 \tabularnewline
87 & 138.06 & 135.25 & 2.81 \tabularnewline
88 & 146.28 & 138.06 & 8.22 \tabularnewline
89 & 145.04 & 146.28 & -1.24000000000001 \tabularnewline
90 & 147.96 & 145.04 & 2.92000000000002 \tabularnewline
91 & 156.71 & 147.96 & 8.75 \tabularnewline
92 & 160.97 & 156.71 & 4.25999999999999 \tabularnewline
93 & 168.17 & 160.97 & 7.19999999999999 \tabularnewline
94 & 163.91 & 168.17 & -4.25999999999999 \tabularnewline
95 & 153.05 & 163.91 & -10.8600000000000 \tabularnewline
96 & 151.76 & 153.05 & -1.29000000000002 \tabularnewline
97 & 119.55 & 151.76 & -32.21 \tabularnewline
98 & 119.44 & 119.55 & -0.109999999999999 \tabularnewline
99 & 120.25 & 119.44 & 0.810000000000002 \tabularnewline
100 & 124.92 & 120.25 & 4.67 \tabularnewline
101 & 126.34 & 124.92 & 1.42000000000000 \tabularnewline
102 & 125.88 & 126.34 & -0.460000000000008 \tabularnewline
103 & 127.34 & 125.88 & 1.46000000000001 \tabularnewline
104 & 127.48 & 127.34 & 0.140000000000001 \tabularnewline
105 & 119.41 & 127.48 & -8.07 \tabularnewline
106 & 114.82 & 119.41 & -4.59 \tabularnewline
107 & 115.28 & 114.82 & 0.460000000000008 \tabularnewline
108 & 116.37 & 115.28 & 1.09000000000000 \tabularnewline
109 & 111.99 & 116.37 & -4.38000000000001 \tabularnewline
110 & 113.57 & 111.99 & 1.58000000000000 \tabularnewline
111 & 117.69 & 113.57 & 4.12000000000000 \tabularnewline
112 & 120.74 & 117.69 & 3.05 \tabularnewline
113 & 122.37 & 120.74 & 1.63000000000001 \tabularnewline
114 & 123.57 & 122.37 & 1.19999999999999 \tabularnewline
115 & 124.86 & 123.57 & 1.29000000000001 \tabularnewline
116 & 122.08 & 124.86 & -2.78 \tabularnewline
117 & 123.56 & 122.08 & 1.48000000000000 \tabularnewline
118 & 126.92 & 123.56 & 3.36 \tabularnewline
119 & 134.88 & 126.92 & 7.96 \tabularnewline
120 & 130.64 & 134.88 & -4.24000000000001 \tabularnewline
121 & 131.65 & 130.64 & 1.01000000000002 \tabularnewline
122 & 130.97 & 131.65 & -0.680000000000007 \tabularnewline
123 & 136.77 & 130.97 & 5.80000000000001 \tabularnewline
124 & 138.17 & 136.77 & 1.39999999999998 \tabularnewline
125 & 146.4 & 138.17 & 8.23000000000002 \tabularnewline
126 & 152.07 & 146.4 & 5.66999999999999 \tabularnewline
127 & 153.05 & 152.07 & 0.980000000000018 \tabularnewline
128 & 142.89 & 153.05 & -10.1600000000000 \tabularnewline
129 & 141.11 & 142.89 & -1.77999999999997 \tabularnewline
130 & 131.9 & 141.11 & -9.21 \tabularnewline
131 & 118.42 & 131.9 & -13.48 \tabularnewline
132 & 108.27 & 118.42 & -10.15 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42902&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]103.52[/C][C]104.66[/C][C]-1.14[/C][/ROW]
[ROW][C]4[/C][C]103.71[/C][C]103.52[/C][C]0.189999999999998[/C][/ROW]
[ROW][C]5[/C][C]103.78[/C][C]103.71[/C][C]0.0700000000000074[/C][/ROW]
[ROW][C]6[/C][C]103.67[/C][C]103.78[/C][C]-0.109999999999999[/C][/ROW]
[ROW][C]7[/C][C]103.66[/C][C]103.67[/C][C]-0.0100000000000051[/C][/ROW]
[ROW][C]8[/C][C]102.76[/C][C]103.66[/C][C]-0.899999999999991[/C][/ROW]
[ROW][C]9[/C][C]102[/C][C]102.76[/C][C]-0.760000000000005[/C][/ROW]
[ROW][C]10[/C][C]101.5[/C][C]102[/C][C]-0.5[/C][/ROW]
[ROW][C]11[/C][C]101.5[/C][C]101.5[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]99.22[/C][C]101.5[/C][C]-2.28[/C][/ROW]
[ROW][C]13[/C][C]98.97[/C][C]99.22[/C][C]-0.25[/C][/ROW]
[ROW][C]14[/C][C]98.9[/C][C]98.97[/C][C]-0.0699999999999932[/C][/ROW]
[ROW][C]15[/C][C]99.78[/C][C]98.9[/C][C]0.879999999999995[/C][/ROW]
[ROW][C]16[/C][C]104.4[/C][C]99.78[/C][C]4.62[/C][/ROW]
[ROW][C]17[/C][C]106.21[/C][C]104.4[/C][C]1.80999999999999[/C][/ROW]
[ROW][C]18[/C][C]105.46[/C][C]106.21[/C][C]-0.75[/C][/ROW]
[ROW][C]19[/C][C]108.33[/C][C]105.46[/C][C]2.87000000000000[/C][/ROW]
[ROW][C]20[/C][C]111.72[/C][C]108.33[/C][C]3.39[/C][/ROW]
[ROW][C]21[/C][C]111.88[/C][C]111.72[/C][C]0.159999999999997[/C][/ROW]
[ROW][C]22[/C][C]112.86[/C][C]111.88[/C][C]0.980000000000004[/C][/ROW]
[ROW][C]23[/C][C]113.09[/C][C]112.86[/C][C]0.230000000000004[/C][/ROW]
[ROW][C]24[/C][C]116.9[/C][C]113.09[/C][C]3.81[/C][/ROW]
[ROW][C]25[/C][C]114.62[/C][C]116.9[/C][C]-2.28[/C][/ROW]
[ROW][C]26[/C][C]118.86[/C][C]114.62[/C][C]4.23999999999999[/C][/ROW]
[ROW][C]27[/C][C]124.71[/C][C]118.86[/C][C]5.85[/C][/ROW]
[ROW][C]28[/C][C]122.53[/C][C]124.71[/C][C]-2.17999999999999[/C][/ROW]
[ROW][C]29[/C][C]127.89[/C][C]122.53[/C][C]5.36[/C][/ROW]
[ROW][C]30[/C][C]136.16[/C][C]127.89[/C][C]8.27[/C][/ROW]
[ROW][C]31[/C][C]134.12[/C][C]136.16[/C][C]-2.03999999999999[/C][/ROW]
[ROW][C]32[/C][C]130.26[/C][C]134.12[/C][C]-3.86000000000001[/C][/ROW]
[ROW][C]33[/C][C]135.35[/C][C]130.26[/C][C]5.09[/C][/ROW]
[ROW][C]34[/C][C]131.43[/C][C]135.35[/C][C]-3.91999999999999[/C][/ROW]
[ROW][C]35[/C][C]129.61[/C][C]131.43[/C][C]-1.81999999999999[/C][/ROW]
[ROW][C]36[/C][C]123.96[/C][C]129.61[/C][C]-5.65000000000002[/C][/ROW]
[ROW][C]37[/C][C]121.1[/C][C]123.96[/C][C]-2.86[/C][/ROW]
[ROW][C]38[/C][C]125.38[/C][C]121.1[/C][C]4.28[/C][/ROW]
[ROW][C]39[/C][C]123.1[/C][C]125.38[/C][C]-2.28[/C][/ROW]
[ROW][C]40[/C][C]129.92[/C][C]123.1[/C][C]6.81999999999999[/C][/ROW]
[ROW][C]41[/C][C]136.68[/C][C]129.92[/C][C]6.76000000000002[/C][/ROW]
[ROW][C]42[/C][C]131.17[/C][C]136.68[/C][C]-5.51000000000002[/C][/ROW]
[ROW][C]43[/C][C]124.82[/C][C]131.17[/C][C]-6.35[/C][/ROW]
[ROW][C]44[/C][C]122.47[/C][C]124.82[/C][C]-2.34999999999999[/C][/ROW]
[ROW][C]45[/C][C]126.15[/C][C]122.47[/C][C]3.68000000000001[/C][/ROW]
[ROW][C]46[/C][C]118.74[/C][C]126.15[/C][C]-7.41000000000001[/C][/ROW]
[ROW][C]47[/C][C]116.8[/C][C]118.74[/C][C]-1.94000000000000[/C][/ROW]
[ROW][C]48[/C][C]116.64[/C][C]116.8[/C][C]-0.159999999999997[/C][/ROW]
[ROW][C]49[/C][C]116.53[/C][C]116.64[/C][C]-0.109999999999999[/C][/ROW]
[ROW][C]50[/C][C]117.68[/C][C]116.53[/C][C]1.15000000000001[/C][/ROW]
[ROW][C]51[/C][C]119.46[/C][C]117.68[/C][C]1.77999999999999[/C][/ROW]
[ROW][C]52[/C][C]126.19[/C][C]119.46[/C][C]6.73[/C][/ROW]
[ROW][C]53[/C][C]124.39[/C][C]126.19[/C][C]-1.80000000000000[/C][/ROW]
[ROW][C]54[/C][C]121.9[/C][C]124.39[/C][C]-2.48999999999999[/C][/ROW]
[ROW][C]55[/C][C]122.53[/C][C]121.9[/C][C]0.629999999999995[/C][/ROW]
[ROW][C]56[/C][C]122.93[/C][C]122.53[/C][C]0.400000000000006[/C][/ROW]
[ROW][C]57[/C][C]124.66[/C][C]122.93[/C][C]1.72999999999999[/C][/ROW]
[ROW][C]58[/C][C]124.41[/C][C]124.66[/C][C]-0.25[/C][/ROW]
[ROW][C]59[/C][C]120.93[/C][C]124.41[/C][C]-3.47999999999999[/C][/ROW]
[ROW][C]60[/C][C]120.18[/C][C]120.93[/C][C]-0.75[/C][/ROW]
[ROW][C]61[/C][C]123.44[/C][C]120.18[/C][C]3.25999999999999[/C][/ROW]
[ROW][C]62[/C][C]126.1[/C][C]123.44[/C][C]2.66000000000000[/C][/ROW]
[ROW][C]63[/C][C]125.82[/C][C]126.1[/C][C]-0.280000000000001[/C][/ROW]
[ROW][C]64[/C][C]122.18[/C][C]125.82[/C][C]-3.63999999999999[/C][/ROW]
[ROW][C]65[/C][C]117.27[/C][C]122.18[/C][C]-4.91000000000001[/C][/ROW]
[ROW][C]66[/C][C]117.86[/C][C]117.27[/C][C]0.590000000000003[/C][/ROW]
[ROW][C]67[/C][C]119.09[/C][C]117.86[/C][C]1.23000000000000[/C][/ROW]
[ROW][C]68[/C][C]123.08[/C][C]119.09[/C][C]3.98999999999999[/C][/ROW]
[ROW][C]69[/C][C]125.42[/C][C]123.08[/C][C]2.34000000000000[/C][/ROW]
[ROW][C]70[/C][C]121.81[/C][C]125.42[/C][C]-3.61[/C][/ROW]
[ROW][C]71[/C][C]121.66[/C][C]121.81[/C][C]-0.150000000000006[/C][/ROW]
[ROW][C]72[/C][C]121.27[/C][C]121.66[/C][C]-0.390000000000001[/C][/ROW]
[ROW][C]73[/C][C]120.92[/C][C]121.27[/C][C]-0.349999999999994[/C][/ROW]
[ROW][C]74[/C][C]122.16[/C][C]120.92[/C][C]1.23999999999999[/C][/ROW]
[ROW][C]75[/C][C]124.17[/C][C]122.16[/C][C]2.01000000000001[/C][/ROW]
[ROW][C]76[/C][C]127.26[/C][C]124.17[/C][C]3.09000000000000[/C][/ROW]
[ROW][C]77[/C][C]134.16[/C][C]127.26[/C][C]6.89999999999999[/C][/ROW]
[ROW][C]78[/C][C]134.09[/C][C]134.16[/C][C]-0.0699999999999932[/C][/ROW]
[ROW][C]79[/C][C]135.57[/C][C]134.09[/C][C]1.47999999999999[/C][/ROW]
[ROW][C]80[/C][C]136.13[/C][C]135.57[/C][C]0.560000000000002[/C][/ROW]
[ROW][C]81[/C][C]136.23[/C][C]136.13[/C][C]0.0999999999999943[/C][/ROW]
[ROW][C]82[/C][C]140.6[/C][C]136.23[/C][C]4.37000000000000[/C][/ROW]
[ROW][C]83[/C][C]136.5[/C][C]140.6[/C][C]-4.09999999999999[/C][/ROW]
[ROW][C]84[/C][C]130.59[/C][C]136.5[/C][C]-5.91[/C][/ROW]
[ROW][C]85[/C][C]129.5[/C][C]130.59[/C][C]-1.09000000000000[/C][/ROW]
[ROW][C]86[/C][C]135.25[/C][C]129.5[/C][C]5.75[/C][/ROW]
[ROW][C]87[/C][C]138.06[/C][C]135.25[/C][C]2.81[/C][/ROW]
[ROW][C]88[/C][C]146.28[/C][C]138.06[/C][C]8.22[/C][/ROW]
[ROW][C]89[/C][C]145.04[/C][C]146.28[/C][C]-1.24000000000001[/C][/ROW]
[ROW][C]90[/C][C]147.96[/C][C]145.04[/C][C]2.92000000000002[/C][/ROW]
[ROW][C]91[/C][C]156.71[/C][C]147.96[/C][C]8.75[/C][/ROW]
[ROW][C]92[/C][C]160.97[/C][C]156.71[/C][C]4.25999999999999[/C][/ROW]
[ROW][C]93[/C][C]168.17[/C][C]160.97[/C][C]7.19999999999999[/C][/ROW]
[ROW][C]94[/C][C]163.91[/C][C]168.17[/C][C]-4.25999999999999[/C][/ROW]
[ROW][C]95[/C][C]153.05[/C][C]163.91[/C][C]-10.8600000000000[/C][/ROW]
[ROW][C]96[/C][C]151.76[/C][C]153.05[/C][C]-1.29000000000002[/C][/ROW]
[ROW][C]97[/C][C]119.55[/C][C]151.76[/C][C]-32.21[/C][/ROW]
[ROW][C]98[/C][C]119.44[/C][C]119.55[/C][C]-0.109999999999999[/C][/ROW]
[ROW][C]99[/C][C]120.25[/C][C]119.44[/C][C]0.810000000000002[/C][/ROW]
[ROW][C]100[/C][C]124.92[/C][C]120.25[/C][C]4.67[/C][/ROW]
[ROW][C]101[/C][C]126.34[/C][C]124.92[/C][C]1.42000000000000[/C][/ROW]
[ROW][C]102[/C][C]125.88[/C][C]126.34[/C][C]-0.460000000000008[/C][/ROW]
[ROW][C]103[/C][C]127.34[/C][C]125.88[/C][C]1.46000000000001[/C][/ROW]
[ROW][C]104[/C][C]127.48[/C][C]127.34[/C][C]0.140000000000001[/C][/ROW]
[ROW][C]105[/C][C]119.41[/C][C]127.48[/C][C]-8.07[/C][/ROW]
[ROW][C]106[/C][C]114.82[/C][C]119.41[/C][C]-4.59[/C][/ROW]
[ROW][C]107[/C][C]115.28[/C][C]114.82[/C][C]0.460000000000008[/C][/ROW]
[ROW][C]108[/C][C]116.37[/C][C]115.28[/C][C]1.09000000000000[/C][/ROW]
[ROW][C]109[/C][C]111.99[/C][C]116.37[/C][C]-4.38000000000001[/C][/ROW]
[ROW][C]110[/C][C]113.57[/C][C]111.99[/C][C]1.58000000000000[/C][/ROW]
[ROW][C]111[/C][C]117.69[/C][C]113.57[/C][C]4.12000000000000[/C][/ROW]
[ROW][C]112[/C][C]120.74[/C][C]117.69[/C][C]3.05[/C][/ROW]
[ROW][C]113[/C][C]122.37[/C][C]120.74[/C][C]1.63000000000001[/C][/ROW]
[ROW][C]114[/C][C]123.57[/C][C]122.37[/C][C]1.19999999999999[/C][/ROW]
[ROW][C]115[/C][C]124.86[/C][C]123.57[/C][C]1.29000000000001[/C][/ROW]
[ROW][C]116[/C][C]122.08[/C][C]124.86[/C][C]-2.78[/C][/ROW]
[ROW][C]117[/C][C]123.56[/C][C]122.08[/C][C]1.48000000000000[/C][/ROW]
[ROW][C]118[/C][C]126.92[/C][C]123.56[/C][C]3.36[/C][/ROW]
[ROW][C]119[/C][C]134.88[/C][C]126.92[/C][C]7.96[/C][/ROW]
[ROW][C]120[/C][C]130.64[/C][C]134.88[/C][C]-4.24000000000001[/C][/ROW]
[ROW][C]121[/C][C]131.65[/C][C]130.64[/C][C]1.01000000000002[/C][/ROW]
[ROW][C]122[/C][C]130.97[/C][C]131.65[/C][C]-0.680000000000007[/C][/ROW]
[ROW][C]123[/C][C]136.77[/C][C]130.97[/C][C]5.80000000000001[/C][/ROW]
[ROW][C]124[/C][C]138.17[/C][C]136.77[/C][C]1.39999999999998[/C][/ROW]
[ROW][C]125[/C][C]146.4[/C][C]138.17[/C][C]8.23000000000002[/C][/ROW]
[ROW][C]126[/C][C]152.07[/C][C]146.4[/C][C]5.66999999999999[/C][/ROW]
[ROW][C]127[/C][C]153.05[/C][C]152.07[/C][C]0.980000000000018[/C][/ROW]
[ROW][C]128[/C][C]142.89[/C][C]153.05[/C][C]-10.1600000000000[/C][/ROW]
[ROW][C]129[/C][C]141.11[/C][C]142.89[/C][C]-1.77999999999997[/C][/ROW]
[ROW][C]130[/C][C]131.9[/C][C]141.11[/C][C]-9.21[/C][/ROW]
[ROW][C]131[/C][C]118.42[/C][C]131.9[/C][C]-13.48[/C][/ROW]
[ROW][C]132[/C][C]108.27[/C][C]118.42[/C][C]-10.15[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42902&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42902&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
3103.52104.66-1.14
4103.71103.520.189999999999998
5103.78103.710.0700000000000074
6103.67103.78-0.109999999999999
7103.66103.67-0.0100000000000051
8102.76103.66-0.899999999999991
9102102.76-0.760000000000005
10101.5102-0.5
11101.5101.50
1299.22101.5-2.28
1398.9799.22-0.25
1498.998.97-0.0699999999999932
1599.7898.90.879999999999995
16104.499.784.62
17106.21104.41.80999999999999
18105.46106.21-0.75
19108.33105.462.87000000000000
20111.72108.333.39
21111.88111.720.159999999999997
22112.86111.880.980000000000004
23113.09112.860.230000000000004
24116.9113.093.81
25114.62116.9-2.28
26118.86114.624.23999999999999
27124.71118.865.85
28122.53124.71-2.17999999999999
29127.89122.535.36
30136.16127.898.27
31134.12136.16-2.03999999999999
32130.26134.12-3.86000000000001
33135.35130.265.09
34131.43135.35-3.91999999999999
35129.61131.43-1.81999999999999
36123.96129.61-5.65000000000002
37121.1123.96-2.86
38125.38121.14.28
39123.1125.38-2.28
40129.92123.16.81999999999999
41136.68129.926.76000000000002
42131.17136.68-5.51000000000002
43124.82131.17-6.35
44122.47124.82-2.34999999999999
45126.15122.473.68000000000001
46118.74126.15-7.41000000000001
47116.8118.74-1.94000000000000
48116.64116.8-0.159999999999997
49116.53116.64-0.109999999999999
50117.68116.531.15000000000001
51119.46117.681.77999999999999
52126.19119.466.73
53124.39126.19-1.80000000000000
54121.9124.39-2.48999999999999
55122.53121.90.629999999999995
56122.93122.530.400000000000006
57124.66122.931.72999999999999
58124.41124.66-0.25
59120.93124.41-3.47999999999999
60120.18120.93-0.75
61123.44120.183.25999999999999
62126.1123.442.66000000000000
63125.82126.1-0.280000000000001
64122.18125.82-3.63999999999999
65117.27122.18-4.91000000000001
66117.86117.270.590000000000003
67119.09117.861.23000000000000
68123.08119.093.98999999999999
69125.42123.082.34000000000000
70121.81125.42-3.61
71121.66121.81-0.150000000000006
72121.27121.66-0.390000000000001
73120.92121.27-0.349999999999994
74122.16120.921.23999999999999
75124.17122.162.01000000000001
76127.26124.173.09000000000000
77134.16127.266.89999999999999
78134.09134.16-0.0699999999999932
79135.57134.091.47999999999999
80136.13135.570.560000000000002
81136.23136.130.0999999999999943
82140.6136.234.37000000000000
83136.5140.6-4.09999999999999
84130.59136.5-5.91
85129.5130.59-1.09000000000000
86135.25129.55.75
87138.06135.252.81
88146.28138.068.22
89145.04146.28-1.24000000000001
90147.96145.042.92000000000002
91156.71147.968.75
92160.97156.714.25999999999999
93168.17160.977.19999999999999
94163.91168.17-4.25999999999999
95153.05163.91-10.8600000000000
96151.76153.05-1.29000000000002
97119.55151.76-32.21
98119.44119.55-0.109999999999999
99120.25119.440.810000000000002
100124.92120.254.67
101126.34124.921.42000000000000
102125.88126.34-0.460000000000008
103127.34125.881.46000000000001
104127.48127.340.140000000000001
105119.41127.48-8.07
106114.82119.41-4.59
107115.28114.820.460000000000008
108116.37115.281.09000000000000
109111.99116.37-4.38000000000001
110113.57111.991.58000000000000
111117.69113.574.12000000000000
112120.74117.693.05
113122.37120.741.63000000000001
114123.57122.371.19999999999999
115124.86123.571.29000000000001
116122.08124.86-2.78
117123.56122.081.48000000000000
118126.92123.563.36
119134.88126.927.96
120130.64134.88-4.24000000000001
121131.65130.641.01000000000002
122130.97131.65-0.680000000000007
123136.77130.975.80000000000001
124138.17136.771.39999999999998
125146.4138.178.23000000000002
126152.07146.45.66999999999999
127153.05152.070.980000000000018
128142.89153.05-10.1600000000000
129141.11142.89-1.77999999999997
130131.9141.11-9.21
131118.42131.9-13.48
132108.27118.42-10.15







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
133108.2798.4685328537376118.071467146262
134108.2794.4086322306014122.131367769399
135108.2791.2933609139563125.246639086044
136108.2788.6670657074751127.872934292525
137108.2786.3532531817263130.186746818274
138108.2784.2614067610039132.278593238996
139108.2782.3377554474197134.202244552580
140108.2780.5472644612027135.992735538797
141108.2778.8655985612127137.674401438787
142108.2777.2750394065139.2649605935
143108.2775.762211080852140.777788919148
144108.2774.3167218279127142.223278172087

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
133 & 108.27 & 98.4685328537376 & 118.071467146262 \tabularnewline
134 & 108.27 & 94.4086322306014 & 122.131367769399 \tabularnewline
135 & 108.27 & 91.2933609139563 & 125.246639086044 \tabularnewline
136 & 108.27 & 88.6670657074751 & 127.872934292525 \tabularnewline
137 & 108.27 & 86.3532531817263 & 130.186746818274 \tabularnewline
138 & 108.27 & 84.2614067610039 & 132.278593238996 \tabularnewline
139 & 108.27 & 82.3377554474197 & 134.202244552580 \tabularnewline
140 & 108.27 & 80.5472644612027 & 135.992735538797 \tabularnewline
141 & 108.27 & 78.8655985612127 & 137.674401438787 \tabularnewline
142 & 108.27 & 77.2750394065 & 139.2649605935 \tabularnewline
143 & 108.27 & 75.762211080852 & 140.777788919148 \tabularnewline
144 & 108.27 & 74.3167218279127 & 142.223278172087 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42902&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]133[/C][C]108.27[/C][C]98.4685328537376[/C][C]118.071467146262[/C][/ROW]
[ROW][C]134[/C][C]108.27[/C][C]94.4086322306014[/C][C]122.131367769399[/C][/ROW]
[ROW][C]135[/C][C]108.27[/C][C]91.2933609139563[/C][C]125.246639086044[/C][/ROW]
[ROW][C]136[/C][C]108.27[/C][C]88.6670657074751[/C][C]127.872934292525[/C][/ROW]
[ROW][C]137[/C][C]108.27[/C][C]86.3532531817263[/C][C]130.186746818274[/C][/ROW]
[ROW][C]138[/C][C]108.27[/C][C]84.2614067610039[/C][C]132.278593238996[/C][/ROW]
[ROW][C]139[/C][C]108.27[/C][C]82.3377554474197[/C][C]134.202244552580[/C][/ROW]
[ROW][C]140[/C][C]108.27[/C][C]80.5472644612027[/C][C]135.992735538797[/C][/ROW]
[ROW][C]141[/C][C]108.27[/C][C]78.8655985612127[/C][C]137.674401438787[/C][/ROW]
[ROW][C]142[/C][C]108.27[/C][C]77.2750394065[/C][C]139.2649605935[/C][/ROW]
[ROW][C]143[/C][C]108.27[/C][C]75.762211080852[/C][C]140.777788919148[/C][/ROW]
[ROW][C]144[/C][C]108.27[/C][C]74.3167218279127[/C][C]142.223278172087[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42902&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42902&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
133108.2798.4685328537376118.071467146262
134108.2794.4086322306014122.131367769399
135108.2791.2933609139563125.246639086044
136108.2788.6670657074751127.872934292525
137108.2786.3532531817263130.186746818274
138108.2784.2614067610039132.278593238996
139108.2782.3377554474197134.202244552580
140108.2780.5472644612027135.992735538797
141108.2778.8655985612127137.674401438787
142108.2777.2750394065139.2649605935
143108.2775.762211080852140.777788919148
144108.2774.3167218279127142.223278172087



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):
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')