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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 23 Dec 2013 08:27:44 -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/23/t13878053204cfr07eqya3tez8.htm/, Retrieved Thu, 28 Mar 2024 19:39:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232598, Retrieved Thu, 28 Mar 2024 19:39:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact161
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [] [2013-12-13 15:40:46] [6a1a05b03d1c87a66b915fc3d5866cc8]
- R  D    [Exponential Smoothing] [] [2013-12-23 13:27:44] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
125
123
117
114
111
112
144
150
149
134
123
116
117
111
105
102
95
93
124
130
124
115
106
105
105
101
95
93
84
87
116
120
117
109
105
107
109
109
108
107
99
103
131
137
135
124
118
121
121
118
113
107
100
102
130
136
133
120
112
109
110
106
102
98
92
92
120
127
124
114
108
106
111
110
104
100
96
98
122
134
133
125
118
116




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 5 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232598&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232598&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232598&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 time5 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.818907146662061
beta0.059781083692388
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.818907146662061 \tabularnewline
beta & 0.059781083692388 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232598&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]0.818907146662061[/C][/ROW]
[ROW][C]beta[/C][C]0.059781083692388[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232598&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232598&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
alpha0.818907146662061
beta0.059781083692388
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13117124.89373511357-7.8937351135703
14111112.212706699933-1.21270669993295
15105105.186931229607-0.186931229607083
16102101.9631360805960.0368639194041265
179594.64685859446310.353141405536945
189392.33155854320440.668441456795648
19124124.460464104576-0.460464104575792
20130127.8749826174222.12501738257809
21124127.649869308913-3.64986930891277
22115110.9210098296164.0789901703839
23106104.1230250813571.87697491864319
2410599.2583866593755.74161334062504
25105103.6798678561941.32013214380561
26101100.6048192160230.395180783977295
279596.0222531678387-1.02225316783874
289392.7974015956510.202598404348961
298486.6746941070883-2.6746941070883
308782.38945258823214.61054741176794
31116115.8144870920120.185512907987729
32120120.605400824058-0.605400824058236
33117117.818066116579-0.818066116579075
34109106.0905505868312.9094494131686
3510599.05678104084465.9432189591554
3610799.05002548495787.94997451504217
37109105.3795463498033.62045365019704
38109104.9058364181934.09416358180739
39108103.925027500024.07497249998045
40107106.3251942008460.674805799153631
4199100.496523459823-1.49652345982302
4210399.89521977043.10478022960002
43131138.375031600907-7.37503160090696
44137139.091588092792-2.09158809279208
45135136.263788430721-1.26378843072092
46124124.649464725069-0.649464725068782
47118115.09261972132.9073802787004
48121113.2147047539437.78529524605675
49121119.3133879739411.68661202605894
50118117.6388229293370.361177070663217
51113113.673705258106-0.673705258106438
52107111.703482878895-4.70348287889504
53100100.974206229768-0.974206229768313
54102101.6165809030180.383419096982308
55130135.356524517523-5.35652451752293
56136138.56180487774-2.56180487774003
57133135.363440608322-2.36344060832218
58120122.903003425041-2.90300342504104
59112112.096480625939-0.0964806259386108
60109108.3365323105040.66346768949613
61110106.9225354783693.07746452163069
62106105.8439505941890.156049405810577
63102101.3788059545690.621194045431395
649899.3963153462099-1.39631534620993
659292.188074684128-0.188074684128011
669293.2462560465526-1.24625604655257
67120120.932102787842-0.932102787841515
68127127.270142757204-0.270142757204326
69124125.77750774067-1.77750774066951
70114114.15179164018-0.151791640180349
71108106.4082822089821.59171779101763
72106104.2988375851331.70116241486741
73111104.2555105241076.74448947589272
74110105.891171036544.10882896345954
75104105.02396905113-1.02396905113011
76100101.588464553784-1.58846455378438
779694.6032440421011.39675595789896
789897.19216679197510.807833208024874
79122129.098994836771-7.09899483677066
80134131.0631847471342.93681525286635
81133132.3648863291040.635113670896061
82125122.9103693711582.08963062884197
83118117.3212165940310.678783405968659
84116114.7862605846171.21373941538265

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 117 & 124.89373511357 & -7.8937351135703 \tabularnewline
14 & 111 & 112.212706699933 & -1.21270669993295 \tabularnewline
15 & 105 & 105.186931229607 & -0.186931229607083 \tabularnewline
16 & 102 & 101.963136080596 & 0.0368639194041265 \tabularnewline
17 & 95 & 94.6468585944631 & 0.353141405536945 \tabularnewline
18 & 93 & 92.3315585432044 & 0.668441456795648 \tabularnewline
19 & 124 & 124.460464104576 & -0.460464104575792 \tabularnewline
20 & 130 & 127.874982617422 & 2.12501738257809 \tabularnewline
21 & 124 & 127.649869308913 & -3.64986930891277 \tabularnewline
22 & 115 & 110.921009829616 & 4.0789901703839 \tabularnewline
23 & 106 & 104.123025081357 & 1.87697491864319 \tabularnewline
24 & 105 & 99.258386659375 & 5.74161334062504 \tabularnewline
25 & 105 & 103.679867856194 & 1.32013214380561 \tabularnewline
26 & 101 & 100.604819216023 & 0.395180783977295 \tabularnewline
27 & 95 & 96.0222531678387 & -1.02225316783874 \tabularnewline
28 & 93 & 92.797401595651 & 0.202598404348961 \tabularnewline
29 & 84 & 86.6746941070883 & -2.6746941070883 \tabularnewline
30 & 87 & 82.3894525882321 & 4.61054741176794 \tabularnewline
31 & 116 & 115.814487092012 & 0.185512907987729 \tabularnewline
32 & 120 & 120.605400824058 & -0.605400824058236 \tabularnewline
33 & 117 & 117.818066116579 & -0.818066116579075 \tabularnewline
34 & 109 & 106.090550586831 & 2.9094494131686 \tabularnewline
35 & 105 & 99.0567810408446 & 5.9432189591554 \tabularnewline
36 & 107 & 99.0500254849578 & 7.94997451504217 \tabularnewline
37 & 109 & 105.379546349803 & 3.62045365019704 \tabularnewline
38 & 109 & 104.905836418193 & 4.09416358180739 \tabularnewline
39 & 108 & 103.92502750002 & 4.07497249998045 \tabularnewline
40 & 107 & 106.325194200846 & 0.674805799153631 \tabularnewline
41 & 99 & 100.496523459823 & -1.49652345982302 \tabularnewline
42 & 103 & 99.8952197704 & 3.10478022960002 \tabularnewline
43 & 131 & 138.375031600907 & -7.37503160090696 \tabularnewline
44 & 137 & 139.091588092792 & -2.09158809279208 \tabularnewline
45 & 135 & 136.263788430721 & -1.26378843072092 \tabularnewline
46 & 124 & 124.649464725069 & -0.649464725068782 \tabularnewline
47 & 118 & 115.0926197213 & 2.9073802787004 \tabularnewline
48 & 121 & 113.214704753943 & 7.78529524605675 \tabularnewline
49 & 121 & 119.313387973941 & 1.68661202605894 \tabularnewline
50 & 118 & 117.638822929337 & 0.361177070663217 \tabularnewline
51 & 113 & 113.673705258106 & -0.673705258106438 \tabularnewline
52 & 107 & 111.703482878895 & -4.70348287889504 \tabularnewline
53 & 100 & 100.974206229768 & -0.974206229768313 \tabularnewline
54 & 102 & 101.616580903018 & 0.383419096982308 \tabularnewline
55 & 130 & 135.356524517523 & -5.35652451752293 \tabularnewline
56 & 136 & 138.56180487774 & -2.56180487774003 \tabularnewline
57 & 133 & 135.363440608322 & -2.36344060832218 \tabularnewline
58 & 120 & 122.903003425041 & -2.90300342504104 \tabularnewline
59 & 112 & 112.096480625939 & -0.0964806259386108 \tabularnewline
60 & 109 & 108.336532310504 & 0.66346768949613 \tabularnewline
61 & 110 & 106.922535478369 & 3.07746452163069 \tabularnewline
62 & 106 & 105.843950594189 & 0.156049405810577 \tabularnewline
63 & 102 & 101.378805954569 & 0.621194045431395 \tabularnewline
64 & 98 & 99.3963153462099 & -1.39631534620993 \tabularnewline
65 & 92 & 92.188074684128 & -0.188074684128011 \tabularnewline
66 & 92 & 93.2462560465526 & -1.24625604655257 \tabularnewline
67 & 120 & 120.932102787842 & -0.932102787841515 \tabularnewline
68 & 127 & 127.270142757204 & -0.270142757204326 \tabularnewline
69 & 124 & 125.77750774067 & -1.77750774066951 \tabularnewline
70 & 114 & 114.15179164018 & -0.151791640180349 \tabularnewline
71 & 108 & 106.408282208982 & 1.59171779101763 \tabularnewline
72 & 106 & 104.298837585133 & 1.70116241486741 \tabularnewline
73 & 111 & 104.255510524107 & 6.74448947589272 \tabularnewline
74 & 110 & 105.89117103654 & 4.10882896345954 \tabularnewline
75 & 104 & 105.02396905113 & -1.02396905113011 \tabularnewline
76 & 100 & 101.588464553784 & -1.58846455378438 \tabularnewline
77 & 96 & 94.603244042101 & 1.39675595789896 \tabularnewline
78 & 98 & 97.1921667919751 & 0.807833208024874 \tabularnewline
79 & 122 & 129.098994836771 & -7.09899483677066 \tabularnewline
80 & 134 & 131.063184747134 & 2.93681525286635 \tabularnewline
81 & 133 & 132.364886329104 & 0.635113670896061 \tabularnewline
82 & 125 & 122.910369371158 & 2.08963062884197 \tabularnewline
83 & 118 & 117.321216594031 & 0.678783405968659 \tabularnewline
84 & 116 & 114.786260584617 & 1.21373941538265 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232598&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]117[/C][C]124.89373511357[/C][C]-7.8937351135703[/C][/ROW]
[ROW][C]14[/C][C]111[/C][C]112.212706699933[/C][C]-1.21270669993295[/C][/ROW]
[ROW][C]15[/C][C]105[/C][C]105.186931229607[/C][C]-0.186931229607083[/C][/ROW]
[ROW][C]16[/C][C]102[/C][C]101.963136080596[/C][C]0.0368639194041265[/C][/ROW]
[ROW][C]17[/C][C]95[/C][C]94.6468585944631[/C][C]0.353141405536945[/C][/ROW]
[ROW][C]18[/C][C]93[/C][C]92.3315585432044[/C][C]0.668441456795648[/C][/ROW]
[ROW][C]19[/C][C]124[/C][C]124.460464104576[/C][C]-0.460464104575792[/C][/ROW]
[ROW][C]20[/C][C]130[/C][C]127.874982617422[/C][C]2.12501738257809[/C][/ROW]
[ROW][C]21[/C][C]124[/C][C]127.649869308913[/C][C]-3.64986930891277[/C][/ROW]
[ROW][C]22[/C][C]115[/C][C]110.921009829616[/C][C]4.0789901703839[/C][/ROW]
[ROW][C]23[/C][C]106[/C][C]104.123025081357[/C][C]1.87697491864319[/C][/ROW]
[ROW][C]24[/C][C]105[/C][C]99.258386659375[/C][C]5.74161334062504[/C][/ROW]
[ROW][C]25[/C][C]105[/C][C]103.679867856194[/C][C]1.32013214380561[/C][/ROW]
[ROW][C]26[/C][C]101[/C][C]100.604819216023[/C][C]0.395180783977295[/C][/ROW]
[ROW][C]27[/C][C]95[/C][C]96.0222531678387[/C][C]-1.02225316783874[/C][/ROW]
[ROW][C]28[/C][C]93[/C][C]92.797401595651[/C][C]0.202598404348961[/C][/ROW]
[ROW][C]29[/C][C]84[/C][C]86.6746941070883[/C][C]-2.6746941070883[/C][/ROW]
[ROW][C]30[/C][C]87[/C][C]82.3894525882321[/C][C]4.61054741176794[/C][/ROW]
[ROW][C]31[/C][C]116[/C][C]115.814487092012[/C][C]0.185512907987729[/C][/ROW]
[ROW][C]32[/C][C]120[/C][C]120.605400824058[/C][C]-0.605400824058236[/C][/ROW]
[ROW][C]33[/C][C]117[/C][C]117.818066116579[/C][C]-0.818066116579075[/C][/ROW]
[ROW][C]34[/C][C]109[/C][C]106.090550586831[/C][C]2.9094494131686[/C][/ROW]
[ROW][C]35[/C][C]105[/C][C]99.0567810408446[/C][C]5.9432189591554[/C][/ROW]
[ROW][C]36[/C][C]107[/C][C]99.0500254849578[/C][C]7.94997451504217[/C][/ROW]
[ROW][C]37[/C][C]109[/C][C]105.379546349803[/C][C]3.62045365019704[/C][/ROW]
[ROW][C]38[/C][C]109[/C][C]104.905836418193[/C][C]4.09416358180739[/C][/ROW]
[ROW][C]39[/C][C]108[/C][C]103.92502750002[/C][C]4.07497249998045[/C][/ROW]
[ROW][C]40[/C][C]107[/C][C]106.325194200846[/C][C]0.674805799153631[/C][/ROW]
[ROW][C]41[/C][C]99[/C][C]100.496523459823[/C][C]-1.49652345982302[/C][/ROW]
[ROW][C]42[/C][C]103[/C][C]99.8952197704[/C][C]3.10478022960002[/C][/ROW]
[ROW][C]43[/C][C]131[/C][C]138.375031600907[/C][C]-7.37503160090696[/C][/ROW]
[ROW][C]44[/C][C]137[/C][C]139.091588092792[/C][C]-2.09158809279208[/C][/ROW]
[ROW][C]45[/C][C]135[/C][C]136.263788430721[/C][C]-1.26378843072092[/C][/ROW]
[ROW][C]46[/C][C]124[/C][C]124.649464725069[/C][C]-0.649464725068782[/C][/ROW]
[ROW][C]47[/C][C]118[/C][C]115.0926197213[/C][C]2.9073802787004[/C][/ROW]
[ROW][C]48[/C][C]121[/C][C]113.214704753943[/C][C]7.78529524605675[/C][/ROW]
[ROW][C]49[/C][C]121[/C][C]119.313387973941[/C][C]1.68661202605894[/C][/ROW]
[ROW][C]50[/C][C]118[/C][C]117.638822929337[/C][C]0.361177070663217[/C][/ROW]
[ROW][C]51[/C][C]113[/C][C]113.673705258106[/C][C]-0.673705258106438[/C][/ROW]
[ROW][C]52[/C][C]107[/C][C]111.703482878895[/C][C]-4.70348287889504[/C][/ROW]
[ROW][C]53[/C][C]100[/C][C]100.974206229768[/C][C]-0.974206229768313[/C][/ROW]
[ROW][C]54[/C][C]102[/C][C]101.616580903018[/C][C]0.383419096982308[/C][/ROW]
[ROW][C]55[/C][C]130[/C][C]135.356524517523[/C][C]-5.35652451752293[/C][/ROW]
[ROW][C]56[/C][C]136[/C][C]138.56180487774[/C][C]-2.56180487774003[/C][/ROW]
[ROW][C]57[/C][C]133[/C][C]135.363440608322[/C][C]-2.36344060832218[/C][/ROW]
[ROW][C]58[/C][C]120[/C][C]122.903003425041[/C][C]-2.90300342504104[/C][/ROW]
[ROW][C]59[/C][C]112[/C][C]112.096480625939[/C][C]-0.0964806259386108[/C][/ROW]
[ROW][C]60[/C][C]109[/C][C]108.336532310504[/C][C]0.66346768949613[/C][/ROW]
[ROW][C]61[/C][C]110[/C][C]106.922535478369[/C][C]3.07746452163069[/C][/ROW]
[ROW][C]62[/C][C]106[/C][C]105.843950594189[/C][C]0.156049405810577[/C][/ROW]
[ROW][C]63[/C][C]102[/C][C]101.378805954569[/C][C]0.621194045431395[/C][/ROW]
[ROW][C]64[/C][C]98[/C][C]99.3963153462099[/C][C]-1.39631534620993[/C][/ROW]
[ROW][C]65[/C][C]92[/C][C]92.188074684128[/C][C]-0.188074684128011[/C][/ROW]
[ROW][C]66[/C][C]92[/C][C]93.2462560465526[/C][C]-1.24625604655257[/C][/ROW]
[ROW][C]67[/C][C]120[/C][C]120.932102787842[/C][C]-0.932102787841515[/C][/ROW]
[ROW][C]68[/C][C]127[/C][C]127.270142757204[/C][C]-0.270142757204326[/C][/ROW]
[ROW][C]69[/C][C]124[/C][C]125.77750774067[/C][C]-1.77750774066951[/C][/ROW]
[ROW][C]70[/C][C]114[/C][C]114.15179164018[/C][C]-0.151791640180349[/C][/ROW]
[ROW][C]71[/C][C]108[/C][C]106.408282208982[/C][C]1.59171779101763[/C][/ROW]
[ROW][C]72[/C][C]106[/C][C]104.298837585133[/C][C]1.70116241486741[/C][/ROW]
[ROW][C]73[/C][C]111[/C][C]104.255510524107[/C][C]6.74448947589272[/C][/ROW]
[ROW][C]74[/C][C]110[/C][C]105.89117103654[/C][C]4.10882896345954[/C][/ROW]
[ROW][C]75[/C][C]104[/C][C]105.02396905113[/C][C]-1.02396905113011[/C][/ROW]
[ROW][C]76[/C][C]100[/C][C]101.588464553784[/C][C]-1.58846455378438[/C][/ROW]
[ROW][C]77[/C][C]96[/C][C]94.603244042101[/C][C]1.39675595789896[/C][/ROW]
[ROW][C]78[/C][C]98[/C][C]97.1921667919751[/C][C]0.807833208024874[/C][/ROW]
[ROW][C]79[/C][C]122[/C][C]129.098994836771[/C][C]-7.09899483677066[/C][/ROW]
[ROW][C]80[/C][C]134[/C][C]131.063184747134[/C][C]2.93681525286635[/C][/ROW]
[ROW][C]81[/C][C]133[/C][C]132.364886329104[/C][C]0.635113670896061[/C][/ROW]
[ROW][C]82[/C][C]125[/C][C]122.910369371158[/C][C]2.08963062884197[/C][/ROW]
[ROW][C]83[/C][C]118[/C][C]117.321216594031[/C][C]0.678783405968659[/C][/ROW]
[ROW][C]84[/C][C]116[/C][C]114.786260584617[/C][C]1.21373941538265[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232598&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232598&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
13117124.89373511357-7.8937351135703
14111112.212706699933-1.21270669993295
15105105.186931229607-0.186931229607083
16102101.9631360805960.0368639194041265
179594.64685859446310.353141405536945
189392.33155854320440.668441456795648
19124124.460464104576-0.460464104575792
20130127.8749826174222.12501738257809
21124127.649869308913-3.64986930891277
22115110.9210098296164.0789901703839
23106104.1230250813571.87697491864319
2410599.2583866593755.74161334062504
25105103.6798678561941.32013214380561
26101100.6048192160230.395180783977295
279596.0222531678387-1.02225316783874
289392.7974015956510.202598404348961
298486.6746941070883-2.6746941070883
308782.38945258823214.61054741176794
31116115.8144870920120.185512907987729
32120120.605400824058-0.605400824058236
33117117.818066116579-0.818066116579075
34109106.0905505868312.9094494131686
3510599.05678104084465.9432189591554
3610799.05002548495787.94997451504217
37109105.3795463498033.62045365019704
38109104.9058364181934.09416358180739
39108103.925027500024.07497249998045
40107106.3251942008460.674805799153631
4199100.496523459823-1.49652345982302
4210399.89521977043.10478022960002
43131138.375031600907-7.37503160090696
44137139.091588092792-2.09158809279208
45135136.263788430721-1.26378843072092
46124124.649464725069-0.649464725068782
47118115.09261972132.9073802787004
48121113.2147047539437.78529524605675
49121119.3133879739411.68661202605894
50118117.6388229293370.361177070663217
51113113.673705258106-0.673705258106438
52107111.703482878895-4.70348287889504
53100100.974206229768-0.974206229768313
54102101.6165809030180.383419096982308
55130135.356524517523-5.35652451752293
56136138.56180487774-2.56180487774003
57133135.363440608322-2.36344060832218
58120122.903003425041-2.90300342504104
59112112.096480625939-0.0964806259386108
60109108.3365323105040.66346768949613
61110106.9225354783693.07746452163069
62106105.8439505941890.156049405810577
63102101.3788059545690.621194045431395
649899.3963153462099-1.39631534620993
659292.188074684128-0.188074684128011
669293.2462560465526-1.24625604655257
67120120.932102787842-0.932102787841515
68127127.270142757204-0.270142757204326
69124125.77750774067-1.77750774066951
70114114.15179164018-0.151791640180349
71108106.4082822089821.59171779101763
72106104.2988375851331.70116241486741
73111104.2555105241076.74448947589272
74110105.891171036544.10882896345954
75104105.02396905113-1.02396905113011
76100101.588464553784-1.58846455378438
779694.6032440421011.39675595789896
789897.19216679197510.807833208024874
79122129.098994836771-7.09899483677066
80134131.0631847471342.93681525286635
81133132.3648863291040.635113670896061
82125122.9103693711582.08963062884197
83118117.3212165940310.678783405968659
84116114.7862605846171.21373941538265







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85115.725947845115109.634712431382121.817183258848
86111.361831809256103.431596666761119.292066951751
87106.1396988587696.7350638794539115.544333838066
88103.43400660702492.5890022298449114.279010984203
8998.234892815508886.2963189902723110.173466640745
9099.659035500608186.0411498165643113.276921184652
91129.936350028402110.911704311083148.960995745721
92140.552688792264118.486383069698162.618994514831
93139.208440936051115.814477701217162.602404170885
94129.240572264055105.984929324738152.496215203372
95121.51818524682798.1472637248048144.889106768848
96118.48816196133280.8457422121104156.130581710554

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 115.725947845115 & 109.634712431382 & 121.817183258848 \tabularnewline
86 & 111.361831809256 & 103.431596666761 & 119.292066951751 \tabularnewline
87 & 106.13969885876 & 96.7350638794539 & 115.544333838066 \tabularnewline
88 & 103.434006607024 & 92.5890022298449 & 114.279010984203 \tabularnewline
89 & 98.2348928155088 & 86.2963189902723 & 110.173466640745 \tabularnewline
90 & 99.6590355006081 & 86.0411498165643 & 113.276921184652 \tabularnewline
91 & 129.936350028402 & 110.911704311083 & 148.960995745721 \tabularnewline
92 & 140.552688792264 & 118.486383069698 & 162.618994514831 \tabularnewline
93 & 139.208440936051 & 115.814477701217 & 162.602404170885 \tabularnewline
94 & 129.240572264055 & 105.984929324738 & 152.496215203372 \tabularnewline
95 & 121.518185246827 & 98.1472637248048 & 144.889106768848 \tabularnewline
96 & 118.488161961332 & 80.8457422121104 & 156.130581710554 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232598&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]115.725947845115[/C][C]109.634712431382[/C][C]121.817183258848[/C][/ROW]
[ROW][C]86[/C][C]111.361831809256[/C][C]103.431596666761[/C][C]119.292066951751[/C][/ROW]
[ROW][C]87[/C][C]106.13969885876[/C][C]96.7350638794539[/C][C]115.544333838066[/C][/ROW]
[ROW][C]88[/C][C]103.434006607024[/C][C]92.5890022298449[/C][C]114.279010984203[/C][/ROW]
[ROW][C]89[/C][C]98.2348928155088[/C][C]86.2963189902723[/C][C]110.173466640745[/C][/ROW]
[ROW][C]90[/C][C]99.6590355006081[/C][C]86.0411498165643[/C][C]113.276921184652[/C][/ROW]
[ROW][C]91[/C][C]129.936350028402[/C][C]110.911704311083[/C][C]148.960995745721[/C][/ROW]
[ROW][C]92[/C][C]140.552688792264[/C][C]118.486383069698[/C][C]162.618994514831[/C][/ROW]
[ROW][C]93[/C][C]139.208440936051[/C][C]115.814477701217[/C][C]162.602404170885[/C][/ROW]
[ROW][C]94[/C][C]129.240572264055[/C][C]105.984929324738[/C][C]152.496215203372[/C][/ROW]
[ROW][C]95[/C][C]121.518185246827[/C][C]98.1472637248048[/C][C]144.889106768848[/C][/ROW]
[ROW][C]96[/C][C]118.488161961332[/C][C]80.8457422121104[/C][C]156.130581710554[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232598&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232598&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
85115.725947845115109.634712431382121.817183258848
86111.361831809256103.431596666761119.292066951751
87106.1396988587696.7350638794539115.544333838066
88103.43400660702492.5890022298449114.279010984203
8998.234892815508886.2963189902723110.173466640745
9099.659035500608186.0411498165643113.276921184652
91129.936350028402110.911704311083148.960995745721
92140.552688792264118.486383069698162.618994514831
93139.208440936051115.814477701217162.602404170885
94129.240572264055105.984929324738152.496215203372
95121.51818524682798.1472637248048144.889106768848
96118.48816196133280.8457422121104156.130581710554



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