Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 31 May 2010 18:05:52 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/May/31/t1275329183gjbby2pilkdp70l.htm/, Retrieved Thu, 31 Oct 2024 22:45:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=76777, Retrieved Thu, 31 Oct 2024 22:45:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact149
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2010-05-31 18:05:52] [2bab6b58187a1236dde7e79464907c61] [Current]
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Dataseries X:
132.8
132.5
131.4
131.4
130.7
131.5
131.2
130.1
130.5
129
128.2
128.4
127.3
127.7
127
123.9
125.4
124.6
124.5
124.8
124.1
124.2
122.8
122.3
121.1
121.7
122.2
122.2
122.7
121.7
121
119.8
120.2
116.6
116
118
117.1
116.2
113.3
114.3
113.6
113
112.9
112.7
112.5
113
111.9
110.9
109.8
108.3
109.2
109.2
108.7
109.8
110.8
110
109.6
109.5
110.8
111.6
113.1
114.3
114.1
113.8
112.6
112.7
111.5
110.7
110.4
109.7
110
111.3
109
108.2
107.2
108.7
110.3
110.3
109.5
109.5
109.4
109.6
111.3
110
109.5
110.693
109.195
108.095
108.199
106.87
105.278
108.711
111.192
109.641
109.42
109.935
111.126
110.733
110.34
111.766
111.294
111.54
112.008
111.007
114.963
112.045
110.703
108.894
107.51
111.35
112.964
115.203
115.182
115.191
112.346
110.774
113.07
111.138
109.092
107.971
107.051




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=76777&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=76777&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76777&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
alpha0.815582747009687
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.815582747009687 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76777&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]0.815582747009687[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76777&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76777&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.815582747009687
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13127.3130.810637626263-3.51063762626266
14127.7128.847422147280-1.14742214727978
15127127.699104440422-0.699104440421593
16123.9124.495593587123-0.595593587122551
17125.4125.934837733236-0.534837733235804
18124.6125.177799972226-0.577799972225591
19124.5126.031556283656-1.53155628365568
20124.8124.1116120692990.688387930701452
21124.1125.456382722162-1.35638272216170
22124.2123.3459737089580.85402629104209
23122.8123.775836150758-0.975836150757843
24122.3123.688294355625-1.38829435562475
25121.1121.375269950793-0.275269950793131
26121.7122.486582235014-0.786582235014251
27122.2121.7152368549980.484763145001978
28122.2119.4963571663352.70364283366544
29122.7123.637606043225-0.937606043225358
30121.7122.544154419449-0.8441544194486
31121123.004787520158-2.00478752015819
32119.8121.108280087767-1.30828008776702
33120.2120.447511766465-0.247511766465024
34116.6119.649116331588-3.04911633158767
35116116.558184786386-0.558184786385723
36118116.7352078291851.26479217081528
37117.1116.7912559248920.308744075108322
38116.2118.284585165773-2.08458516577342
39113.3116.689069012447-3.38906901244653
40114.3111.7199583482562.58004165174394
41113.6115.088891118331-1.48889111833141
42113113.563054990359-0.563054990358609
43112.9114.038907167466-1.13890716746577
44112.7112.977044799074-0.277044799074119
45112.5113.352958167211-0.85295816721127
46113111.5441068757811.45589312421889
47111.9112.586754070804-0.686754070803559
48110.9112.995106626148-2.09510662614763
49109.8110.134567467816-0.334567467816143
50108.3110.661851709232-2.36185170923171
51109.2108.5996324191640.600367580836476
52109.2107.9850444022291.21495559777104
53108.7109.490255134441-0.790255134440912
54109.8108.7049546168091.09504538319072
55110.8110.4269277747630.373072225236996
56110110.757152003328-0.757152003328429
57109.6110.635289857648-1.03528985764846
58109.5109.1035239979930.396476002006708
59110.8108.8869877564191.91301224358060
60111.6111.1559403545340.444059645466282
61113.1110.6909751944812.40902480551919
62114.3113.0820197680251.21798023197465
63114.1114.485733990629-0.385733990628566
64113.8113.1802391790120.619760820988191
65112.6113.830223865268-1.23022386526817
66112.7113.033774384073-0.333774384072896
67111.5113.457282484737-1.95728248473745
68110.7111.678476769940-0.978476769939817
69110.4111.324812544079-0.92481254407933
70109.7110.14719240207-0.447192402070058
71110109.5222502136650.477749786334726
72111.3110.3497273113020.950272688698092
73109110.659994252659-1.65999425265876
74108.2109.512767916658-1.31276791665766
75107.2108.556695040696-1.35669504069567
76108.7106.6447317396802.05526826031985
77110.3108.1243224327462.17567756725407
78110.3110.2709881486980.0290118513019877
79109.5110.690975539655-1.19097553965483
80109.5109.717665209314-0.217665209314490
81109.4109.994402375143-0.594402375142565
82109.6109.1743404609170.425659539083128
83111.3109.4318565539711.86814344602901
84110111.480456107635-1.48045610763479
85109.5109.3268843211460.173115678853534
86110.693109.7387453457100.95425465428987
87109.195110.623516046148-1.42851604614764
88108.095109.282201671490-1.18720167148965
89108.199108.1394953840930.0595046159068033
90106.87108.164364756814-1.29436475681351
91105.278107.280042295072-2.00204229507204
92108.711105.8247351297692.88626487023123
93111.192108.5635072831772.62849271682262
94109.641110.560100017482-0.919100017482208
95109.42109.986872336927-0.566872336926934
96109.935109.4319754982640.50302450173568
97111.126109.2010434422931.92495655770674
98110.733111.185731167210-0.452731167209521
99110.34110.483564479264-0.14356447926437
100111.766110.2347369673811.53126303261907
101111.294111.539077739818-0.245077739817759
102111.54111.0658581275410.474141872459242
103112.008111.4933912129980.514608787002174
104111.007112.992109429676-1.98510942967562
105114.963111.7103351174253.25266488257519
106112.045113.561754594492-1.51675459449223
107110.703112.566047013531-1.86304701353136
108108.894111.151319907488-2.25731990748849
109107.51108.931327379251-1.42132737925061
110111.35107.7483570198913.60164298010902
111112.964110.4098836077282.55411639227209
112115.203112.6701051605822.53289483941819
113115.182114.4637716678730.718228332127353
114115.191114.9088443731570.282155626843348
115112.346115.187259586243-2.84125958624323
116110.774113.487998289697-2.71399828969705
117113.07112.5776907491740.492309250826281
118111.138111.298248559056-0.160248559056427
119109.092111.345021600161-2.25302160016095
120107.971109.539527225459-1.56852722545864
121107.051108.035473570529-0.984473570528891

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 127.3 & 130.810637626263 & -3.51063762626266 \tabularnewline
14 & 127.7 & 128.847422147280 & -1.14742214727978 \tabularnewline
15 & 127 & 127.699104440422 & -0.699104440421593 \tabularnewline
16 & 123.9 & 124.495593587123 & -0.595593587122551 \tabularnewline
17 & 125.4 & 125.934837733236 & -0.534837733235804 \tabularnewline
18 & 124.6 & 125.177799972226 & -0.577799972225591 \tabularnewline
19 & 124.5 & 126.031556283656 & -1.53155628365568 \tabularnewline
20 & 124.8 & 124.111612069299 & 0.688387930701452 \tabularnewline
21 & 124.1 & 125.456382722162 & -1.35638272216170 \tabularnewline
22 & 124.2 & 123.345973708958 & 0.85402629104209 \tabularnewline
23 & 122.8 & 123.775836150758 & -0.975836150757843 \tabularnewline
24 & 122.3 & 123.688294355625 & -1.38829435562475 \tabularnewline
25 & 121.1 & 121.375269950793 & -0.275269950793131 \tabularnewline
26 & 121.7 & 122.486582235014 & -0.786582235014251 \tabularnewline
27 & 122.2 & 121.715236854998 & 0.484763145001978 \tabularnewline
28 & 122.2 & 119.496357166335 & 2.70364283366544 \tabularnewline
29 & 122.7 & 123.637606043225 & -0.937606043225358 \tabularnewline
30 & 121.7 & 122.544154419449 & -0.8441544194486 \tabularnewline
31 & 121 & 123.004787520158 & -2.00478752015819 \tabularnewline
32 & 119.8 & 121.108280087767 & -1.30828008776702 \tabularnewline
33 & 120.2 & 120.447511766465 & -0.247511766465024 \tabularnewline
34 & 116.6 & 119.649116331588 & -3.04911633158767 \tabularnewline
35 & 116 & 116.558184786386 & -0.558184786385723 \tabularnewline
36 & 118 & 116.735207829185 & 1.26479217081528 \tabularnewline
37 & 117.1 & 116.791255924892 & 0.308744075108322 \tabularnewline
38 & 116.2 & 118.284585165773 & -2.08458516577342 \tabularnewline
39 & 113.3 & 116.689069012447 & -3.38906901244653 \tabularnewline
40 & 114.3 & 111.719958348256 & 2.58004165174394 \tabularnewline
41 & 113.6 & 115.088891118331 & -1.48889111833141 \tabularnewline
42 & 113 & 113.563054990359 & -0.563054990358609 \tabularnewline
43 & 112.9 & 114.038907167466 & -1.13890716746577 \tabularnewline
44 & 112.7 & 112.977044799074 & -0.277044799074119 \tabularnewline
45 & 112.5 & 113.352958167211 & -0.85295816721127 \tabularnewline
46 & 113 & 111.544106875781 & 1.45589312421889 \tabularnewline
47 & 111.9 & 112.586754070804 & -0.686754070803559 \tabularnewline
48 & 110.9 & 112.995106626148 & -2.09510662614763 \tabularnewline
49 & 109.8 & 110.134567467816 & -0.334567467816143 \tabularnewline
50 & 108.3 & 110.661851709232 & -2.36185170923171 \tabularnewline
51 & 109.2 & 108.599632419164 & 0.600367580836476 \tabularnewline
52 & 109.2 & 107.985044402229 & 1.21495559777104 \tabularnewline
53 & 108.7 & 109.490255134441 & -0.790255134440912 \tabularnewline
54 & 109.8 & 108.704954616809 & 1.09504538319072 \tabularnewline
55 & 110.8 & 110.426927774763 & 0.373072225236996 \tabularnewline
56 & 110 & 110.757152003328 & -0.757152003328429 \tabularnewline
57 & 109.6 & 110.635289857648 & -1.03528985764846 \tabularnewline
58 & 109.5 & 109.103523997993 & 0.396476002006708 \tabularnewline
59 & 110.8 & 108.886987756419 & 1.91301224358060 \tabularnewline
60 & 111.6 & 111.155940354534 & 0.444059645466282 \tabularnewline
61 & 113.1 & 110.690975194481 & 2.40902480551919 \tabularnewline
62 & 114.3 & 113.082019768025 & 1.21798023197465 \tabularnewline
63 & 114.1 & 114.485733990629 & -0.385733990628566 \tabularnewline
64 & 113.8 & 113.180239179012 & 0.619760820988191 \tabularnewline
65 & 112.6 & 113.830223865268 & -1.23022386526817 \tabularnewline
66 & 112.7 & 113.033774384073 & -0.333774384072896 \tabularnewline
67 & 111.5 & 113.457282484737 & -1.95728248473745 \tabularnewline
68 & 110.7 & 111.678476769940 & -0.978476769939817 \tabularnewline
69 & 110.4 & 111.324812544079 & -0.92481254407933 \tabularnewline
70 & 109.7 & 110.14719240207 & -0.447192402070058 \tabularnewline
71 & 110 & 109.522250213665 & 0.477749786334726 \tabularnewline
72 & 111.3 & 110.349727311302 & 0.950272688698092 \tabularnewline
73 & 109 & 110.659994252659 & -1.65999425265876 \tabularnewline
74 & 108.2 & 109.512767916658 & -1.31276791665766 \tabularnewline
75 & 107.2 & 108.556695040696 & -1.35669504069567 \tabularnewline
76 & 108.7 & 106.644731739680 & 2.05526826031985 \tabularnewline
77 & 110.3 & 108.124322432746 & 2.17567756725407 \tabularnewline
78 & 110.3 & 110.270988148698 & 0.0290118513019877 \tabularnewline
79 & 109.5 & 110.690975539655 & -1.19097553965483 \tabularnewline
80 & 109.5 & 109.717665209314 & -0.217665209314490 \tabularnewline
81 & 109.4 & 109.994402375143 & -0.594402375142565 \tabularnewline
82 & 109.6 & 109.174340460917 & 0.425659539083128 \tabularnewline
83 & 111.3 & 109.431856553971 & 1.86814344602901 \tabularnewline
84 & 110 & 111.480456107635 & -1.48045610763479 \tabularnewline
85 & 109.5 & 109.326884321146 & 0.173115678853534 \tabularnewline
86 & 110.693 & 109.738745345710 & 0.95425465428987 \tabularnewline
87 & 109.195 & 110.623516046148 & -1.42851604614764 \tabularnewline
88 & 108.095 & 109.282201671490 & -1.18720167148965 \tabularnewline
89 & 108.199 & 108.139495384093 & 0.0595046159068033 \tabularnewline
90 & 106.87 & 108.164364756814 & -1.29436475681351 \tabularnewline
91 & 105.278 & 107.280042295072 & -2.00204229507204 \tabularnewline
92 & 108.711 & 105.824735129769 & 2.88626487023123 \tabularnewline
93 & 111.192 & 108.563507283177 & 2.62849271682262 \tabularnewline
94 & 109.641 & 110.560100017482 & -0.919100017482208 \tabularnewline
95 & 109.42 & 109.986872336927 & -0.566872336926934 \tabularnewline
96 & 109.935 & 109.431975498264 & 0.50302450173568 \tabularnewline
97 & 111.126 & 109.201043442293 & 1.92495655770674 \tabularnewline
98 & 110.733 & 111.185731167210 & -0.452731167209521 \tabularnewline
99 & 110.34 & 110.483564479264 & -0.14356447926437 \tabularnewline
100 & 111.766 & 110.234736967381 & 1.53126303261907 \tabularnewline
101 & 111.294 & 111.539077739818 & -0.245077739817759 \tabularnewline
102 & 111.54 & 111.065858127541 & 0.474141872459242 \tabularnewline
103 & 112.008 & 111.493391212998 & 0.514608787002174 \tabularnewline
104 & 111.007 & 112.992109429676 & -1.98510942967562 \tabularnewline
105 & 114.963 & 111.710335117425 & 3.25266488257519 \tabularnewline
106 & 112.045 & 113.561754594492 & -1.51675459449223 \tabularnewline
107 & 110.703 & 112.566047013531 & -1.86304701353136 \tabularnewline
108 & 108.894 & 111.151319907488 & -2.25731990748849 \tabularnewline
109 & 107.51 & 108.931327379251 & -1.42132737925061 \tabularnewline
110 & 111.35 & 107.748357019891 & 3.60164298010902 \tabularnewline
111 & 112.964 & 110.409883607728 & 2.55411639227209 \tabularnewline
112 & 115.203 & 112.670105160582 & 2.53289483941819 \tabularnewline
113 & 115.182 & 114.463771667873 & 0.718228332127353 \tabularnewline
114 & 115.191 & 114.908844373157 & 0.282155626843348 \tabularnewline
115 & 112.346 & 115.187259586243 & -2.84125958624323 \tabularnewline
116 & 110.774 & 113.487998289697 & -2.71399828969705 \tabularnewline
117 & 113.07 & 112.577690749174 & 0.492309250826281 \tabularnewline
118 & 111.138 & 111.298248559056 & -0.160248559056427 \tabularnewline
119 & 109.092 & 111.345021600161 & -2.25302160016095 \tabularnewline
120 & 107.971 & 109.539527225459 & -1.56852722545864 \tabularnewline
121 & 107.051 & 108.035473570529 & -0.984473570528891 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76777&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]13[/C][C]127.3[/C][C]130.810637626263[/C][C]-3.51063762626266[/C][/ROW]
[ROW][C]14[/C][C]127.7[/C][C]128.847422147280[/C][C]-1.14742214727978[/C][/ROW]
[ROW][C]15[/C][C]127[/C][C]127.699104440422[/C][C]-0.699104440421593[/C][/ROW]
[ROW][C]16[/C][C]123.9[/C][C]124.495593587123[/C][C]-0.595593587122551[/C][/ROW]
[ROW][C]17[/C][C]125.4[/C][C]125.934837733236[/C][C]-0.534837733235804[/C][/ROW]
[ROW][C]18[/C][C]124.6[/C][C]125.177799972226[/C][C]-0.577799972225591[/C][/ROW]
[ROW][C]19[/C][C]124.5[/C][C]126.031556283656[/C][C]-1.53155628365568[/C][/ROW]
[ROW][C]20[/C][C]124.8[/C][C]124.111612069299[/C][C]0.688387930701452[/C][/ROW]
[ROW][C]21[/C][C]124.1[/C][C]125.456382722162[/C][C]-1.35638272216170[/C][/ROW]
[ROW][C]22[/C][C]124.2[/C][C]123.345973708958[/C][C]0.85402629104209[/C][/ROW]
[ROW][C]23[/C][C]122.8[/C][C]123.775836150758[/C][C]-0.975836150757843[/C][/ROW]
[ROW][C]24[/C][C]122.3[/C][C]123.688294355625[/C][C]-1.38829435562475[/C][/ROW]
[ROW][C]25[/C][C]121.1[/C][C]121.375269950793[/C][C]-0.275269950793131[/C][/ROW]
[ROW][C]26[/C][C]121.7[/C][C]122.486582235014[/C][C]-0.786582235014251[/C][/ROW]
[ROW][C]27[/C][C]122.2[/C][C]121.715236854998[/C][C]0.484763145001978[/C][/ROW]
[ROW][C]28[/C][C]122.2[/C][C]119.496357166335[/C][C]2.70364283366544[/C][/ROW]
[ROW][C]29[/C][C]122.7[/C][C]123.637606043225[/C][C]-0.937606043225358[/C][/ROW]
[ROW][C]30[/C][C]121.7[/C][C]122.544154419449[/C][C]-0.8441544194486[/C][/ROW]
[ROW][C]31[/C][C]121[/C][C]123.004787520158[/C][C]-2.00478752015819[/C][/ROW]
[ROW][C]32[/C][C]119.8[/C][C]121.108280087767[/C][C]-1.30828008776702[/C][/ROW]
[ROW][C]33[/C][C]120.2[/C][C]120.447511766465[/C][C]-0.247511766465024[/C][/ROW]
[ROW][C]34[/C][C]116.6[/C][C]119.649116331588[/C][C]-3.04911633158767[/C][/ROW]
[ROW][C]35[/C][C]116[/C][C]116.558184786386[/C][C]-0.558184786385723[/C][/ROW]
[ROW][C]36[/C][C]118[/C][C]116.735207829185[/C][C]1.26479217081528[/C][/ROW]
[ROW][C]37[/C][C]117.1[/C][C]116.791255924892[/C][C]0.308744075108322[/C][/ROW]
[ROW][C]38[/C][C]116.2[/C][C]118.284585165773[/C][C]-2.08458516577342[/C][/ROW]
[ROW][C]39[/C][C]113.3[/C][C]116.689069012447[/C][C]-3.38906901244653[/C][/ROW]
[ROW][C]40[/C][C]114.3[/C][C]111.719958348256[/C][C]2.58004165174394[/C][/ROW]
[ROW][C]41[/C][C]113.6[/C][C]115.088891118331[/C][C]-1.48889111833141[/C][/ROW]
[ROW][C]42[/C][C]113[/C][C]113.563054990359[/C][C]-0.563054990358609[/C][/ROW]
[ROW][C]43[/C][C]112.9[/C][C]114.038907167466[/C][C]-1.13890716746577[/C][/ROW]
[ROW][C]44[/C][C]112.7[/C][C]112.977044799074[/C][C]-0.277044799074119[/C][/ROW]
[ROW][C]45[/C][C]112.5[/C][C]113.352958167211[/C][C]-0.85295816721127[/C][/ROW]
[ROW][C]46[/C][C]113[/C][C]111.544106875781[/C][C]1.45589312421889[/C][/ROW]
[ROW][C]47[/C][C]111.9[/C][C]112.586754070804[/C][C]-0.686754070803559[/C][/ROW]
[ROW][C]48[/C][C]110.9[/C][C]112.995106626148[/C][C]-2.09510662614763[/C][/ROW]
[ROW][C]49[/C][C]109.8[/C][C]110.134567467816[/C][C]-0.334567467816143[/C][/ROW]
[ROW][C]50[/C][C]108.3[/C][C]110.661851709232[/C][C]-2.36185170923171[/C][/ROW]
[ROW][C]51[/C][C]109.2[/C][C]108.599632419164[/C][C]0.600367580836476[/C][/ROW]
[ROW][C]52[/C][C]109.2[/C][C]107.985044402229[/C][C]1.21495559777104[/C][/ROW]
[ROW][C]53[/C][C]108.7[/C][C]109.490255134441[/C][C]-0.790255134440912[/C][/ROW]
[ROW][C]54[/C][C]109.8[/C][C]108.704954616809[/C][C]1.09504538319072[/C][/ROW]
[ROW][C]55[/C][C]110.8[/C][C]110.426927774763[/C][C]0.373072225236996[/C][/ROW]
[ROW][C]56[/C][C]110[/C][C]110.757152003328[/C][C]-0.757152003328429[/C][/ROW]
[ROW][C]57[/C][C]109.6[/C][C]110.635289857648[/C][C]-1.03528985764846[/C][/ROW]
[ROW][C]58[/C][C]109.5[/C][C]109.103523997993[/C][C]0.396476002006708[/C][/ROW]
[ROW][C]59[/C][C]110.8[/C][C]108.886987756419[/C][C]1.91301224358060[/C][/ROW]
[ROW][C]60[/C][C]111.6[/C][C]111.155940354534[/C][C]0.444059645466282[/C][/ROW]
[ROW][C]61[/C][C]113.1[/C][C]110.690975194481[/C][C]2.40902480551919[/C][/ROW]
[ROW][C]62[/C][C]114.3[/C][C]113.082019768025[/C][C]1.21798023197465[/C][/ROW]
[ROW][C]63[/C][C]114.1[/C][C]114.485733990629[/C][C]-0.385733990628566[/C][/ROW]
[ROW][C]64[/C][C]113.8[/C][C]113.180239179012[/C][C]0.619760820988191[/C][/ROW]
[ROW][C]65[/C][C]112.6[/C][C]113.830223865268[/C][C]-1.23022386526817[/C][/ROW]
[ROW][C]66[/C][C]112.7[/C][C]113.033774384073[/C][C]-0.333774384072896[/C][/ROW]
[ROW][C]67[/C][C]111.5[/C][C]113.457282484737[/C][C]-1.95728248473745[/C][/ROW]
[ROW][C]68[/C][C]110.7[/C][C]111.678476769940[/C][C]-0.978476769939817[/C][/ROW]
[ROW][C]69[/C][C]110.4[/C][C]111.324812544079[/C][C]-0.92481254407933[/C][/ROW]
[ROW][C]70[/C][C]109.7[/C][C]110.14719240207[/C][C]-0.447192402070058[/C][/ROW]
[ROW][C]71[/C][C]110[/C][C]109.522250213665[/C][C]0.477749786334726[/C][/ROW]
[ROW][C]72[/C][C]111.3[/C][C]110.349727311302[/C][C]0.950272688698092[/C][/ROW]
[ROW][C]73[/C][C]109[/C][C]110.659994252659[/C][C]-1.65999425265876[/C][/ROW]
[ROW][C]74[/C][C]108.2[/C][C]109.512767916658[/C][C]-1.31276791665766[/C][/ROW]
[ROW][C]75[/C][C]107.2[/C][C]108.556695040696[/C][C]-1.35669504069567[/C][/ROW]
[ROW][C]76[/C][C]108.7[/C][C]106.644731739680[/C][C]2.05526826031985[/C][/ROW]
[ROW][C]77[/C][C]110.3[/C][C]108.124322432746[/C][C]2.17567756725407[/C][/ROW]
[ROW][C]78[/C][C]110.3[/C][C]110.270988148698[/C][C]0.0290118513019877[/C][/ROW]
[ROW][C]79[/C][C]109.5[/C][C]110.690975539655[/C][C]-1.19097553965483[/C][/ROW]
[ROW][C]80[/C][C]109.5[/C][C]109.717665209314[/C][C]-0.217665209314490[/C][/ROW]
[ROW][C]81[/C][C]109.4[/C][C]109.994402375143[/C][C]-0.594402375142565[/C][/ROW]
[ROW][C]82[/C][C]109.6[/C][C]109.174340460917[/C][C]0.425659539083128[/C][/ROW]
[ROW][C]83[/C][C]111.3[/C][C]109.431856553971[/C][C]1.86814344602901[/C][/ROW]
[ROW][C]84[/C][C]110[/C][C]111.480456107635[/C][C]-1.48045610763479[/C][/ROW]
[ROW][C]85[/C][C]109.5[/C][C]109.326884321146[/C][C]0.173115678853534[/C][/ROW]
[ROW][C]86[/C][C]110.693[/C][C]109.738745345710[/C][C]0.95425465428987[/C][/ROW]
[ROW][C]87[/C][C]109.195[/C][C]110.623516046148[/C][C]-1.42851604614764[/C][/ROW]
[ROW][C]88[/C][C]108.095[/C][C]109.282201671490[/C][C]-1.18720167148965[/C][/ROW]
[ROW][C]89[/C][C]108.199[/C][C]108.139495384093[/C][C]0.0595046159068033[/C][/ROW]
[ROW][C]90[/C][C]106.87[/C][C]108.164364756814[/C][C]-1.29436475681351[/C][/ROW]
[ROW][C]91[/C][C]105.278[/C][C]107.280042295072[/C][C]-2.00204229507204[/C][/ROW]
[ROW][C]92[/C][C]108.711[/C][C]105.824735129769[/C][C]2.88626487023123[/C][/ROW]
[ROW][C]93[/C][C]111.192[/C][C]108.563507283177[/C][C]2.62849271682262[/C][/ROW]
[ROW][C]94[/C][C]109.641[/C][C]110.560100017482[/C][C]-0.919100017482208[/C][/ROW]
[ROW][C]95[/C][C]109.42[/C][C]109.986872336927[/C][C]-0.566872336926934[/C][/ROW]
[ROW][C]96[/C][C]109.935[/C][C]109.431975498264[/C][C]0.50302450173568[/C][/ROW]
[ROW][C]97[/C][C]111.126[/C][C]109.201043442293[/C][C]1.92495655770674[/C][/ROW]
[ROW][C]98[/C][C]110.733[/C][C]111.185731167210[/C][C]-0.452731167209521[/C][/ROW]
[ROW][C]99[/C][C]110.34[/C][C]110.483564479264[/C][C]-0.14356447926437[/C][/ROW]
[ROW][C]100[/C][C]111.766[/C][C]110.234736967381[/C][C]1.53126303261907[/C][/ROW]
[ROW][C]101[/C][C]111.294[/C][C]111.539077739818[/C][C]-0.245077739817759[/C][/ROW]
[ROW][C]102[/C][C]111.54[/C][C]111.065858127541[/C][C]0.474141872459242[/C][/ROW]
[ROW][C]103[/C][C]112.008[/C][C]111.493391212998[/C][C]0.514608787002174[/C][/ROW]
[ROW][C]104[/C][C]111.007[/C][C]112.992109429676[/C][C]-1.98510942967562[/C][/ROW]
[ROW][C]105[/C][C]114.963[/C][C]111.710335117425[/C][C]3.25266488257519[/C][/ROW]
[ROW][C]106[/C][C]112.045[/C][C]113.561754594492[/C][C]-1.51675459449223[/C][/ROW]
[ROW][C]107[/C][C]110.703[/C][C]112.566047013531[/C][C]-1.86304701353136[/C][/ROW]
[ROW][C]108[/C][C]108.894[/C][C]111.151319907488[/C][C]-2.25731990748849[/C][/ROW]
[ROW][C]109[/C][C]107.51[/C][C]108.931327379251[/C][C]-1.42132737925061[/C][/ROW]
[ROW][C]110[/C][C]111.35[/C][C]107.748357019891[/C][C]3.60164298010902[/C][/ROW]
[ROW][C]111[/C][C]112.964[/C][C]110.409883607728[/C][C]2.55411639227209[/C][/ROW]
[ROW][C]112[/C][C]115.203[/C][C]112.670105160582[/C][C]2.53289483941819[/C][/ROW]
[ROW][C]113[/C][C]115.182[/C][C]114.463771667873[/C][C]0.718228332127353[/C][/ROW]
[ROW][C]114[/C][C]115.191[/C][C]114.908844373157[/C][C]0.282155626843348[/C][/ROW]
[ROW][C]115[/C][C]112.346[/C][C]115.187259586243[/C][C]-2.84125958624323[/C][/ROW]
[ROW][C]116[/C][C]110.774[/C][C]113.487998289697[/C][C]-2.71399828969705[/C][/ROW]
[ROW][C]117[/C][C]113.07[/C][C]112.577690749174[/C][C]0.492309250826281[/C][/ROW]
[ROW][C]118[/C][C]111.138[/C][C]111.298248559056[/C][C]-0.160248559056427[/C][/ROW]
[ROW][C]119[/C][C]109.092[/C][C]111.345021600161[/C][C]-2.25302160016095[/C][/ROW]
[ROW][C]120[/C][C]107.971[/C][C]109.539527225459[/C][C]-1.56852722545864[/C][/ROW]
[ROW][C]121[/C][C]107.051[/C][C]108.035473570529[/C][C]-0.984473570528891[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76777&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76777&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
13127.3130.810637626263-3.51063762626266
14127.7128.847422147280-1.14742214727978
15127127.699104440422-0.699104440421593
16123.9124.495593587123-0.595593587122551
17125.4125.934837733236-0.534837733235804
18124.6125.177799972226-0.577799972225591
19124.5126.031556283656-1.53155628365568
20124.8124.1116120692990.688387930701452
21124.1125.456382722162-1.35638272216170
22124.2123.3459737089580.85402629104209
23122.8123.775836150758-0.975836150757843
24122.3123.688294355625-1.38829435562475
25121.1121.375269950793-0.275269950793131
26121.7122.486582235014-0.786582235014251
27122.2121.7152368549980.484763145001978
28122.2119.4963571663352.70364283366544
29122.7123.637606043225-0.937606043225358
30121.7122.544154419449-0.8441544194486
31121123.004787520158-2.00478752015819
32119.8121.108280087767-1.30828008776702
33120.2120.447511766465-0.247511766465024
34116.6119.649116331588-3.04911633158767
35116116.558184786386-0.558184786385723
36118116.7352078291851.26479217081528
37117.1116.7912559248920.308744075108322
38116.2118.284585165773-2.08458516577342
39113.3116.689069012447-3.38906901244653
40114.3111.7199583482562.58004165174394
41113.6115.088891118331-1.48889111833141
42113113.563054990359-0.563054990358609
43112.9114.038907167466-1.13890716746577
44112.7112.977044799074-0.277044799074119
45112.5113.352958167211-0.85295816721127
46113111.5441068757811.45589312421889
47111.9112.586754070804-0.686754070803559
48110.9112.995106626148-2.09510662614763
49109.8110.134567467816-0.334567467816143
50108.3110.661851709232-2.36185170923171
51109.2108.5996324191640.600367580836476
52109.2107.9850444022291.21495559777104
53108.7109.490255134441-0.790255134440912
54109.8108.7049546168091.09504538319072
55110.8110.4269277747630.373072225236996
56110110.757152003328-0.757152003328429
57109.6110.635289857648-1.03528985764846
58109.5109.1035239979930.396476002006708
59110.8108.8869877564191.91301224358060
60111.6111.1559403545340.444059645466282
61113.1110.6909751944812.40902480551919
62114.3113.0820197680251.21798023197465
63114.1114.485733990629-0.385733990628566
64113.8113.1802391790120.619760820988191
65112.6113.830223865268-1.23022386526817
66112.7113.033774384073-0.333774384072896
67111.5113.457282484737-1.95728248473745
68110.7111.678476769940-0.978476769939817
69110.4111.324812544079-0.92481254407933
70109.7110.14719240207-0.447192402070058
71110109.5222502136650.477749786334726
72111.3110.3497273113020.950272688698092
73109110.659994252659-1.65999425265876
74108.2109.512767916658-1.31276791665766
75107.2108.556695040696-1.35669504069567
76108.7106.6447317396802.05526826031985
77110.3108.1243224327462.17567756725407
78110.3110.2709881486980.0290118513019877
79109.5110.690975539655-1.19097553965483
80109.5109.717665209314-0.217665209314490
81109.4109.994402375143-0.594402375142565
82109.6109.1743404609170.425659539083128
83111.3109.4318565539711.86814344602901
84110111.480456107635-1.48045610763479
85109.5109.3268843211460.173115678853534
86110.693109.7387453457100.95425465428987
87109.195110.623516046148-1.42851604614764
88108.095109.282201671490-1.18720167148965
89108.199108.1394953840930.0595046159068033
90106.87108.164364756814-1.29436475681351
91105.278107.280042295072-2.00204229507204
92108.711105.8247351297692.88626487023123
93111.192108.5635072831772.62849271682262
94109.641110.560100017482-0.919100017482208
95109.42109.986872336927-0.566872336926934
96109.935109.4319754982640.50302450173568
97111.126109.2010434422931.92495655770674
98110.733111.185731167210-0.452731167209521
99110.34110.483564479264-0.14356447926437
100111.766110.2347369673811.53126303261907
101111.294111.539077739818-0.245077739817759
102111.54111.0658581275410.474141872459242
103112.008111.4933912129980.514608787002174
104111.007112.992109429676-1.98510942967562
105114.963111.7103351174253.25266488257519
106112.045113.561754594492-1.51675459449223
107110.703112.566047013531-1.86304701353136
108108.894111.151319907488-2.25731990748849
109107.51108.931327379251-1.42132737925061
110111.35107.7483570198913.60164298010902
111112.964110.4098836077282.55411639227209
112115.203112.6701051605822.53289483941819
113115.182114.4637716678730.718228332127353
114115.191114.9088443731570.282155626843348
115112.346115.187259586243-2.84125958624323
116110.774113.487998289697-2.71399828969705
117113.07112.5776907491740.492309250826281
118111.138111.298248559056-0.160248559056427
119109.092111.345021600161-2.25302160016095
120107.971109.539527225459-1.56852722545864
121107.051108.035473570529-0.984473570528891







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
122108.135116036053105.193744413258111.076487658848
123107.666022772661103.870427758045111.461617787277
124107.839237441642103.349090895417112.329383987867
125107.232462805545102.141658301524112.323267309567
126107.011341544320101.383627533306112.639055555334
127106.483623842636100.365941317255112.601306368017
128107.125114023127100.553895416738113.696332629516
129109.019595091960102.024183133787116.015007050132
130107.21829105195999.8229774713097114.613604632609
131107.00981659769199.235143778354114.784489417027
132107.16808034099099.0317167835196115.304443898460
133107.05198.5683538072768115.533646192723

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
122 & 108.135116036053 & 105.193744413258 & 111.076487658848 \tabularnewline
123 & 107.666022772661 & 103.870427758045 & 111.461617787277 \tabularnewline
124 & 107.839237441642 & 103.349090895417 & 112.329383987867 \tabularnewline
125 & 107.232462805545 & 102.141658301524 & 112.323267309567 \tabularnewline
126 & 107.011341544320 & 101.383627533306 & 112.639055555334 \tabularnewline
127 & 106.483623842636 & 100.365941317255 & 112.601306368017 \tabularnewline
128 & 107.125114023127 & 100.553895416738 & 113.696332629516 \tabularnewline
129 & 109.019595091960 & 102.024183133787 & 116.015007050132 \tabularnewline
130 & 107.218291051959 & 99.8229774713097 & 114.613604632609 \tabularnewline
131 & 107.009816597691 & 99.235143778354 & 114.784489417027 \tabularnewline
132 & 107.168080340990 & 99.0317167835196 & 115.304443898460 \tabularnewline
133 & 107.051 & 98.5683538072768 & 115.533646192723 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76777&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]122[/C][C]108.135116036053[/C][C]105.193744413258[/C][C]111.076487658848[/C][/ROW]
[ROW][C]123[/C][C]107.666022772661[/C][C]103.870427758045[/C][C]111.461617787277[/C][/ROW]
[ROW][C]124[/C][C]107.839237441642[/C][C]103.349090895417[/C][C]112.329383987867[/C][/ROW]
[ROW][C]125[/C][C]107.232462805545[/C][C]102.141658301524[/C][C]112.323267309567[/C][/ROW]
[ROW][C]126[/C][C]107.011341544320[/C][C]101.383627533306[/C][C]112.639055555334[/C][/ROW]
[ROW][C]127[/C][C]106.483623842636[/C][C]100.365941317255[/C][C]112.601306368017[/C][/ROW]
[ROW][C]128[/C][C]107.125114023127[/C][C]100.553895416738[/C][C]113.696332629516[/C][/ROW]
[ROW][C]129[/C][C]109.019595091960[/C][C]102.024183133787[/C][C]116.015007050132[/C][/ROW]
[ROW][C]130[/C][C]107.218291051959[/C][C]99.8229774713097[/C][C]114.613604632609[/C][/ROW]
[ROW][C]131[/C][C]107.009816597691[/C][C]99.235143778354[/C][C]114.784489417027[/C][/ROW]
[ROW][C]132[/C][C]107.168080340990[/C][C]99.0317167835196[/C][C]115.304443898460[/C][/ROW]
[ROW][C]133[/C][C]107.051[/C][C]98.5683538072768[/C][C]115.533646192723[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76777&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76777&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
122108.135116036053105.193744413258111.076487658848
123107.666022772661103.870427758045111.461617787277
124107.839237441642103.349090895417112.329383987867
125107.232462805545102.141658301524112.323267309567
126107.011341544320101.383627533306112.639055555334
127106.483623842636100.365941317255112.601306368017
128107.125114023127100.553895416738113.696332629516
129109.019595091960102.024183133787116.015007050132
130107.21829105195999.8229774713097114.613604632609
131107.00981659769199.235143778354114.784489417027
132107.16808034099099.0317167835196115.304443898460
133107.05198.5683538072768115.533646192723



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