Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 15 Aug 2010 16:29:17 +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/Aug/15/t128188985236qr8mcu57dcq00.htm/, Retrieved Sat, 27 Apr 2024 14:04:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78902, Retrieved Sat, 27 Apr 2024 14:04:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact134
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Mean Plot] [Mean vs Median pl...] [2010-08-15 15:07:22] [f5ecd041e4b32af12787a4e421b18aaf]
-   P   [Mean Plot] [Mean&Median Plot ...] [2010-08-15 15:22:42] [f5ecd041e4b32af12787a4e421b18aaf]
- RM      [Classical Decomposition] [Classical Decompo...] [2010-08-15 16:13:21] [f5ecd041e4b32af12787a4e421b18aaf]
-           [Classical Decomposition] [Classical Decompo...] [2010-08-15 16:22:14] [f5ecd041e4b32af12787a4e421b18aaf]
- RM            [Exponential Smoothing] [Exponential smoot...] [2010-08-15 16:29:17] [05b8da000f2ebbd12b039a4b088dd3f2] [Current]
Feedback Forum

Post a new message
Dataseries X:
118
117
116
114
112
111
112
114
115
115
116
118
126
131
122
124
119
112
109
108
117
122
127
124
129
141
127
133
114
98
93
101
111
128
126
134
140
158
144
146
138
119
113
120
127
141
144
150
156
174
163
167
160
141
132
144
155
164
162
181
187
209
189
201
193
177
159
158
155
164
163
185
191
217
193
192
184
166
145
146
138
149
145
166




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78902&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78902&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78902&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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.84931647663477
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.84931647663477 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78902&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]0.84931647663477[/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=78902&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78902&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
alpha0.84931647663477
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13126122.8352029914533.16479700854697
14131131.214696490096-0.214696490095662
15122122.515597144328-0.515597144327671
16124124.019271248424-0.0192712484235642
17119118.5694831136910.43051688630861
18112111.5433741194490.4566258805513
19109116.914439924205-7.91443992420471
20108111.592488280654-3.59248828065422
21117109.0245747125237.9754252874768
22122115.4481474047596.55185259524059
23127121.6209896871255.37901031287457
24124128.172717694584-4.17271769458407
25129133.505555155625-4.50555515562456
26141134.8612581920806.13874180792021
27127131.512897905336-4.51289790533644
28133129.6963867457753.30361325422487
29114127.136554830006-13.1365548300059
3098108.591642482656-10.5916424826558
3193103.317850238475-10.3178502384745
3210196.60588951636514.39411048363492
33111102.5642198454468.43578015455383
34128109.16427056235718.8357294376428
35126125.5932838364690.406716163530916
36134126.4826724658257.51732753417475
37140141.693904830919-1.69390483091871
38158147.04150898489510.9584910151051
39144146.181614511451-2.18161451145050
40146147.522920191968-1.52292019196787
41138138.386571443670-0.386571443669823
42119131.053906422309-12.0539064223089
43113124.579445301015-11.5794453010146
44120119.0128411826670.987158817332855
45127122.6866043527524.31339564724793
46141127.3525469853813.6474530146201
47144136.5981229557957.40187704420492
48150144.5000689524285.49993104757183
49156156.609912294237-0.609912294236551
50174164.7846767552569.21532324474353
51163160.4642837747732.53571622522702
52167165.9113505565671.08864944343350
53160159.1642799626590.835720037340877
54141151.111652092507-10.1116520925071
55132146.358273048785-14.3582730487852
56144140.3251449238153.67485507618511
57155146.7828218958118.21717810418858
58164156.1707999417267.8292000582745
59162159.533732418422.46626758157998
60181162.95719205218818.0428079478118
61187184.7992546878192.20074531218125
62209196.84165807305512.1583419269451
63189194.014312630013-5.01431263001331
64201192.8309663847588.16903361524214
65193192.0592704347990.94072956520111
66177182.446240282746-5.44624028274643
67159181.015376551252-22.0153765512520
68158171.196239541506-13.1962395415060
69155164.009471113956-9.00947111395593
70164158.7081102427465.29188975725427
71163159.1079577132913.89204228670948
72185166.08947928031918.9105207196812
73191186.2813668547754.71863314522503
74217201.96269960509615.0373003949043
75193198.992864930263-5.99286493026256
76192198.964931155135-6.96493115513545
77184184.250523246669-0.250523246669303
78166172.663331333342-6.66333133334157
79145167.702076286955-22.7020762869549
80146158.628612514845-12.6286125148450
81138152.554816091799-14.5548160917989
82149144.6986818072744.30131819272563
83145144.0462865777440.953713422256499
84166150.79527427228515.2047257277148

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 126 & 122.835202991453 & 3.16479700854697 \tabularnewline
14 & 131 & 131.214696490096 & -0.214696490095662 \tabularnewline
15 & 122 & 122.515597144328 & -0.515597144327671 \tabularnewline
16 & 124 & 124.019271248424 & -0.0192712484235642 \tabularnewline
17 & 119 & 118.569483113691 & 0.43051688630861 \tabularnewline
18 & 112 & 111.543374119449 & 0.4566258805513 \tabularnewline
19 & 109 & 116.914439924205 & -7.91443992420471 \tabularnewline
20 & 108 & 111.592488280654 & -3.59248828065422 \tabularnewline
21 & 117 & 109.024574712523 & 7.9754252874768 \tabularnewline
22 & 122 & 115.448147404759 & 6.55185259524059 \tabularnewline
23 & 127 & 121.620989687125 & 5.37901031287457 \tabularnewline
24 & 124 & 128.172717694584 & -4.17271769458407 \tabularnewline
25 & 129 & 133.505555155625 & -4.50555515562456 \tabularnewline
26 & 141 & 134.861258192080 & 6.13874180792021 \tabularnewline
27 & 127 & 131.512897905336 & -4.51289790533644 \tabularnewline
28 & 133 & 129.696386745775 & 3.30361325422487 \tabularnewline
29 & 114 & 127.136554830006 & -13.1365548300059 \tabularnewline
30 & 98 & 108.591642482656 & -10.5916424826558 \tabularnewline
31 & 93 & 103.317850238475 & -10.3178502384745 \tabularnewline
32 & 101 & 96.6058895163651 & 4.39411048363492 \tabularnewline
33 & 111 & 102.564219845446 & 8.43578015455383 \tabularnewline
34 & 128 & 109.164270562357 & 18.8357294376428 \tabularnewline
35 & 126 & 125.593283836469 & 0.406716163530916 \tabularnewline
36 & 134 & 126.482672465825 & 7.51732753417475 \tabularnewline
37 & 140 & 141.693904830919 & -1.69390483091871 \tabularnewline
38 & 158 & 147.041508984895 & 10.9584910151051 \tabularnewline
39 & 144 & 146.181614511451 & -2.18161451145050 \tabularnewline
40 & 146 & 147.522920191968 & -1.52292019196787 \tabularnewline
41 & 138 & 138.386571443670 & -0.386571443669823 \tabularnewline
42 & 119 & 131.053906422309 & -12.0539064223089 \tabularnewline
43 & 113 & 124.579445301015 & -11.5794453010146 \tabularnewline
44 & 120 & 119.012841182667 & 0.987158817332855 \tabularnewline
45 & 127 & 122.686604352752 & 4.31339564724793 \tabularnewline
46 & 141 & 127.35254698538 & 13.6474530146201 \tabularnewline
47 & 144 & 136.598122955795 & 7.40187704420492 \tabularnewline
48 & 150 & 144.500068952428 & 5.49993104757183 \tabularnewline
49 & 156 & 156.609912294237 & -0.609912294236551 \tabularnewline
50 & 174 & 164.784676755256 & 9.21532324474353 \tabularnewline
51 & 163 & 160.464283774773 & 2.53571622522702 \tabularnewline
52 & 167 & 165.911350556567 & 1.08864944343350 \tabularnewline
53 & 160 & 159.164279962659 & 0.835720037340877 \tabularnewline
54 & 141 & 151.111652092507 & -10.1116520925071 \tabularnewline
55 & 132 & 146.358273048785 & -14.3582730487852 \tabularnewline
56 & 144 & 140.325144923815 & 3.67485507618511 \tabularnewline
57 & 155 & 146.782821895811 & 8.21717810418858 \tabularnewline
58 & 164 & 156.170799941726 & 7.8292000582745 \tabularnewline
59 & 162 & 159.53373241842 & 2.46626758157998 \tabularnewline
60 & 181 & 162.957192052188 & 18.0428079478118 \tabularnewline
61 & 187 & 184.799254687819 & 2.20074531218125 \tabularnewline
62 & 209 & 196.841658073055 & 12.1583419269451 \tabularnewline
63 & 189 & 194.014312630013 & -5.01431263001331 \tabularnewline
64 & 201 & 192.830966384758 & 8.16903361524214 \tabularnewline
65 & 193 & 192.059270434799 & 0.94072956520111 \tabularnewline
66 & 177 & 182.446240282746 & -5.44624028274643 \tabularnewline
67 & 159 & 181.015376551252 & -22.0153765512520 \tabularnewline
68 & 158 & 171.196239541506 & -13.1962395415060 \tabularnewline
69 & 155 & 164.009471113956 & -9.00947111395593 \tabularnewline
70 & 164 & 158.708110242746 & 5.29188975725427 \tabularnewline
71 & 163 & 159.107957713291 & 3.89204228670948 \tabularnewline
72 & 185 & 166.089479280319 & 18.9105207196812 \tabularnewline
73 & 191 & 186.281366854775 & 4.71863314522503 \tabularnewline
74 & 217 & 201.962699605096 & 15.0373003949043 \tabularnewline
75 & 193 & 198.992864930263 & -5.99286493026256 \tabularnewline
76 & 192 & 198.964931155135 & -6.96493115513545 \tabularnewline
77 & 184 & 184.250523246669 & -0.250523246669303 \tabularnewline
78 & 166 & 172.663331333342 & -6.66333133334157 \tabularnewline
79 & 145 & 167.702076286955 & -22.7020762869549 \tabularnewline
80 & 146 & 158.628612514845 & -12.6286125148450 \tabularnewline
81 & 138 & 152.554816091799 & -14.5548160917989 \tabularnewline
82 & 149 & 144.698681807274 & 4.30131819272563 \tabularnewline
83 & 145 & 144.046286577744 & 0.953713422256499 \tabularnewline
84 & 166 & 150.795274272285 & 15.2047257277148 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78902&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]126[/C][C]122.835202991453[/C][C]3.16479700854697[/C][/ROW]
[ROW][C]14[/C][C]131[/C][C]131.214696490096[/C][C]-0.214696490095662[/C][/ROW]
[ROW][C]15[/C][C]122[/C][C]122.515597144328[/C][C]-0.515597144327671[/C][/ROW]
[ROW][C]16[/C][C]124[/C][C]124.019271248424[/C][C]-0.0192712484235642[/C][/ROW]
[ROW][C]17[/C][C]119[/C][C]118.569483113691[/C][C]0.43051688630861[/C][/ROW]
[ROW][C]18[/C][C]112[/C][C]111.543374119449[/C][C]0.4566258805513[/C][/ROW]
[ROW][C]19[/C][C]109[/C][C]116.914439924205[/C][C]-7.91443992420471[/C][/ROW]
[ROW][C]20[/C][C]108[/C][C]111.592488280654[/C][C]-3.59248828065422[/C][/ROW]
[ROW][C]21[/C][C]117[/C][C]109.024574712523[/C][C]7.9754252874768[/C][/ROW]
[ROW][C]22[/C][C]122[/C][C]115.448147404759[/C][C]6.55185259524059[/C][/ROW]
[ROW][C]23[/C][C]127[/C][C]121.620989687125[/C][C]5.37901031287457[/C][/ROW]
[ROW][C]24[/C][C]124[/C][C]128.172717694584[/C][C]-4.17271769458407[/C][/ROW]
[ROW][C]25[/C][C]129[/C][C]133.505555155625[/C][C]-4.50555515562456[/C][/ROW]
[ROW][C]26[/C][C]141[/C][C]134.861258192080[/C][C]6.13874180792021[/C][/ROW]
[ROW][C]27[/C][C]127[/C][C]131.512897905336[/C][C]-4.51289790533644[/C][/ROW]
[ROW][C]28[/C][C]133[/C][C]129.696386745775[/C][C]3.30361325422487[/C][/ROW]
[ROW][C]29[/C][C]114[/C][C]127.136554830006[/C][C]-13.1365548300059[/C][/ROW]
[ROW][C]30[/C][C]98[/C][C]108.591642482656[/C][C]-10.5916424826558[/C][/ROW]
[ROW][C]31[/C][C]93[/C][C]103.317850238475[/C][C]-10.3178502384745[/C][/ROW]
[ROW][C]32[/C][C]101[/C][C]96.6058895163651[/C][C]4.39411048363492[/C][/ROW]
[ROW][C]33[/C][C]111[/C][C]102.564219845446[/C][C]8.43578015455383[/C][/ROW]
[ROW][C]34[/C][C]128[/C][C]109.164270562357[/C][C]18.8357294376428[/C][/ROW]
[ROW][C]35[/C][C]126[/C][C]125.593283836469[/C][C]0.406716163530916[/C][/ROW]
[ROW][C]36[/C][C]134[/C][C]126.482672465825[/C][C]7.51732753417475[/C][/ROW]
[ROW][C]37[/C][C]140[/C][C]141.693904830919[/C][C]-1.69390483091871[/C][/ROW]
[ROW][C]38[/C][C]158[/C][C]147.041508984895[/C][C]10.9584910151051[/C][/ROW]
[ROW][C]39[/C][C]144[/C][C]146.181614511451[/C][C]-2.18161451145050[/C][/ROW]
[ROW][C]40[/C][C]146[/C][C]147.522920191968[/C][C]-1.52292019196787[/C][/ROW]
[ROW][C]41[/C][C]138[/C][C]138.386571443670[/C][C]-0.386571443669823[/C][/ROW]
[ROW][C]42[/C][C]119[/C][C]131.053906422309[/C][C]-12.0539064223089[/C][/ROW]
[ROW][C]43[/C][C]113[/C][C]124.579445301015[/C][C]-11.5794453010146[/C][/ROW]
[ROW][C]44[/C][C]120[/C][C]119.012841182667[/C][C]0.987158817332855[/C][/ROW]
[ROW][C]45[/C][C]127[/C][C]122.686604352752[/C][C]4.31339564724793[/C][/ROW]
[ROW][C]46[/C][C]141[/C][C]127.35254698538[/C][C]13.6474530146201[/C][/ROW]
[ROW][C]47[/C][C]144[/C][C]136.598122955795[/C][C]7.40187704420492[/C][/ROW]
[ROW][C]48[/C][C]150[/C][C]144.500068952428[/C][C]5.49993104757183[/C][/ROW]
[ROW][C]49[/C][C]156[/C][C]156.609912294237[/C][C]-0.609912294236551[/C][/ROW]
[ROW][C]50[/C][C]174[/C][C]164.784676755256[/C][C]9.21532324474353[/C][/ROW]
[ROW][C]51[/C][C]163[/C][C]160.464283774773[/C][C]2.53571622522702[/C][/ROW]
[ROW][C]52[/C][C]167[/C][C]165.911350556567[/C][C]1.08864944343350[/C][/ROW]
[ROW][C]53[/C][C]160[/C][C]159.164279962659[/C][C]0.835720037340877[/C][/ROW]
[ROW][C]54[/C][C]141[/C][C]151.111652092507[/C][C]-10.1116520925071[/C][/ROW]
[ROW][C]55[/C][C]132[/C][C]146.358273048785[/C][C]-14.3582730487852[/C][/ROW]
[ROW][C]56[/C][C]144[/C][C]140.325144923815[/C][C]3.67485507618511[/C][/ROW]
[ROW][C]57[/C][C]155[/C][C]146.782821895811[/C][C]8.21717810418858[/C][/ROW]
[ROW][C]58[/C][C]164[/C][C]156.170799941726[/C][C]7.8292000582745[/C][/ROW]
[ROW][C]59[/C][C]162[/C][C]159.53373241842[/C][C]2.46626758157998[/C][/ROW]
[ROW][C]60[/C][C]181[/C][C]162.957192052188[/C][C]18.0428079478118[/C][/ROW]
[ROW][C]61[/C][C]187[/C][C]184.799254687819[/C][C]2.20074531218125[/C][/ROW]
[ROW][C]62[/C][C]209[/C][C]196.841658073055[/C][C]12.1583419269451[/C][/ROW]
[ROW][C]63[/C][C]189[/C][C]194.014312630013[/C][C]-5.01431263001331[/C][/ROW]
[ROW][C]64[/C][C]201[/C][C]192.830966384758[/C][C]8.16903361524214[/C][/ROW]
[ROW][C]65[/C][C]193[/C][C]192.059270434799[/C][C]0.94072956520111[/C][/ROW]
[ROW][C]66[/C][C]177[/C][C]182.446240282746[/C][C]-5.44624028274643[/C][/ROW]
[ROW][C]67[/C][C]159[/C][C]181.015376551252[/C][C]-22.0153765512520[/C][/ROW]
[ROW][C]68[/C][C]158[/C][C]171.196239541506[/C][C]-13.1962395415060[/C][/ROW]
[ROW][C]69[/C][C]155[/C][C]164.009471113956[/C][C]-9.00947111395593[/C][/ROW]
[ROW][C]70[/C][C]164[/C][C]158.708110242746[/C][C]5.29188975725427[/C][/ROW]
[ROW][C]71[/C][C]163[/C][C]159.107957713291[/C][C]3.89204228670948[/C][/ROW]
[ROW][C]72[/C][C]185[/C][C]166.089479280319[/C][C]18.9105207196812[/C][/ROW]
[ROW][C]73[/C][C]191[/C][C]186.281366854775[/C][C]4.71863314522503[/C][/ROW]
[ROW][C]74[/C][C]217[/C][C]201.962699605096[/C][C]15.0373003949043[/C][/ROW]
[ROW][C]75[/C][C]193[/C][C]198.992864930263[/C][C]-5.99286493026256[/C][/ROW]
[ROW][C]76[/C][C]192[/C][C]198.964931155135[/C][C]-6.96493115513545[/C][/ROW]
[ROW][C]77[/C][C]184[/C][C]184.250523246669[/C][C]-0.250523246669303[/C][/ROW]
[ROW][C]78[/C][C]166[/C][C]172.663331333342[/C][C]-6.66333133334157[/C][/ROW]
[ROW][C]79[/C][C]145[/C][C]167.702076286955[/C][C]-22.7020762869549[/C][/ROW]
[ROW][C]80[/C][C]146[/C][C]158.628612514845[/C][C]-12.6286125148450[/C][/ROW]
[ROW][C]81[/C][C]138[/C][C]152.554816091799[/C][C]-14.5548160917989[/C][/ROW]
[ROW][C]82[/C][C]149[/C][C]144.698681807274[/C][C]4.30131819272563[/C][/ROW]
[ROW][C]83[/C][C]145[/C][C]144.046286577744[/C][C]0.953713422256499[/C][/ROW]
[ROW][C]84[/C][C]166[/C][C]150.795274272285[/C][C]15.2047257277148[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78902&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78902&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
13126122.8352029914533.16479700854697
14131131.214696490096-0.214696490095662
15122122.515597144328-0.515597144327671
16124124.019271248424-0.0192712484235642
17119118.5694831136910.43051688630861
18112111.5433741194490.4566258805513
19109116.914439924205-7.91443992420471
20108111.592488280654-3.59248828065422
21117109.0245747125237.9754252874768
22122115.4481474047596.55185259524059
23127121.6209896871255.37901031287457
24124128.172717694584-4.17271769458407
25129133.505555155625-4.50555515562456
26141134.8612581920806.13874180792021
27127131.512897905336-4.51289790533644
28133129.6963867457753.30361325422487
29114127.136554830006-13.1365548300059
3098108.591642482656-10.5916424826558
3193103.317850238475-10.3178502384745
3210196.60588951636514.39411048363492
33111102.5642198454468.43578015455383
34128109.16427056235718.8357294376428
35126125.5932838364690.406716163530916
36134126.4826724658257.51732753417475
37140141.693904830919-1.69390483091871
38158147.04150898489510.9584910151051
39144146.181614511451-2.18161451145050
40146147.522920191968-1.52292019196787
41138138.386571443670-0.386571443669823
42119131.053906422309-12.0539064223089
43113124.579445301015-11.5794453010146
44120119.0128411826670.987158817332855
45127122.6866043527524.31339564724793
46141127.3525469853813.6474530146201
47144136.5981229557957.40187704420492
48150144.5000689524285.49993104757183
49156156.609912294237-0.609912294236551
50174164.7846767552569.21532324474353
51163160.4642837747732.53571622522702
52167165.9113505565671.08864944343350
53160159.1642799626590.835720037340877
54141151.111652092507-10.1116520925071
55132146.358273048785-14.3582730487852
56144140.3251449238153.67485507618511
57155146.7828218958118.21717810418858
58164156.1707999417267.8292000582745
59162159.533732418422.46626758157998
60181162.95719205218818.0428079478118
61187184.7992546878192.20074531218125
62209196.84165807305512.1583419269451
63189194.014312630013-5.01431263001331
64201192.8309663847588.16903361524214
65193192.0592704347990.94072956520111
66177182.446240282746-5.44624028274643
67159181.015376551252-22.0153765512520
68158171.196239541506-13.1962395415060
69155164.009471113956-9.00947111395593
70164158.7081102427465.29188975725427
71163159.1079577132913.89204228670948
72185166.08947928031918.9105207196812
73191186.2813668547754.71863314522503
74217201.96269960509615.0373003949043
75193198.992864930263-5.99286493026256
76192198.964931155135-6.96493115513545
77184184.250523246669-0.250523246669303
78166172.663331333342-6.66333133334157
79145167.702076286955-22.7020762869549
80146158.628612514845-12.6286125148450
81138152.554816091799-14.5548160917989
82149144.6986818072744.30131819272563
83145144.0462865777440.953713422256499
84166150.79527427228515.2047257277148







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85165.701285478111148.107702774827183.294868181396
86178.929858488613155.847115009698202.012601967528
87160.019697416131132.522571371952187.516823460311
88164.935128204815133.640227104706196.230029304923
89157.147901725991122.468661119518191.827142332464
90144.807178816675107.045708728532182.568648904818
91143.088426261005102.477990195951183.698862326059
92154.814114946899111.541878910730198.086350983068
93159.175760068053113.396230737292204.955289398813
94166.522579655722118.366124222187214.679035089257
95161.712575132212111.291120431875212.134029832549
96169.798951048951117.209959917021222.387942180881

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 165.701285478111 & 148.107702774827 & 183.294868181396 \tabularnewline
86 & 178.929858488613 & 155.847115009698 & 202.012601967528 \tabularnewline
87 & 160.019697416131 & 132.522571371952 & 187.516823460311 \tabularnewline
88 & 164.935128204815 & 133.640227104706 & 196.230029304923 \tabularnewline
89 & 157.147901725991 & 122.468661119518 & 191.827142332464 \tabularnewline
90 & 144.807178816675 & 107.045708728532 & 182.568648904818 \tabularnewline
91 & 143.088426261005 & 102.477990195951 & 183.698862326059 \tabularnewline
92 & 154.814114946899 & 111.541878910730 & 198.086350983068 \tabularnewline
93 & 159.175760068053 & 113.396230737292 & 204.955289398813 \tabularnewline
94 & 166.522579655722 & 118.366124222187 & 214.679035089257 \tabularnewline
95 & 161.712575132212 & 111.291120431875 & 212.134029832549 \tabularnewline
96 & 169.798951048951 & 117.209959917021 & 222.387942180881 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78902&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]165.701285478111[/C][C]148.107702774827[/C][C]183.294868181396[/C][/ROW]
[ROW][C]86[/C][C]178.929858488613[/C][C]155.847115009698[/C][C]202.012601967528[/C][/ROW]
[ROW][C]87[/C][C]160.019697416131[/C][C]132.522571371952[/C][C]187.516823460311[/C][/ROW]
[ROW][C]88[/C][C]164.935128204815[/C][C]133.640227104706[/C][C]196.230029304923[/C][/ROW]
[ROW][C]89[/C][C]157.147901725991[/C][C]122.468661119518[/C][C]191.827142332464[/C][/ROW]
[ROW][C]90[/C][C]144.807178816675[/C][C]107.045708728532[/C][C]182.568648904818[/C][/ROW]
[ROW][C]91[/C][C]143.088426261005[/C][C]102.477990195951[/C][C]183.698862326059[/C][/ROW]
[ROW][C]92[/C][C]154.814114946899[/C][C]111.541878910730[/C][C]198.086350983068[/C][/ROW]
[ROW][C]93[/C][C]159.175760068053[/C][C]113.396230737292[/C][C]204.955289398813[/C][/ROW]
[ROW][C]94[/C][C]166.522579655722[/C][C]118.366124222187[/C][C]214.679035089257[/C][/ROW]
[ROW][C]95[/C][C]161.712575132212[/C][C]111.291120431875[/C][C]212.134029832549[/C][/ROW]
[ROW][C]96[/C][C]169.798951048951[/C][C]117.209959917021[/C][C]222.387942180881[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78902&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78902&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
85165.701285478111148.107702774827183.294868181396
86178.929858488613155.847115009698202.012601967528
87160.019697416131132.522571371952187.516823460311
88164.935128204815133.640227104706196.230029304923
89157.147901725991122.468661119518191.827142332464
90144.807178816675107.045708728532182.568648904818
91143.088426261005102.477990195951183.698862326059
92154.814114946899111.541878910730198.086350983068
93159.175760068053113.396230737292204.955289398813
94166.522579655722118.366124222187214.679035089257
95161.712575132212111.291120431875212.134029832549
96169.798951048951117.209959917021222.387942180881



Parameters (Session):
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')