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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 11 Aug 2010 21:53:03 +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/11/t1281563639kxh8szcxmek1y1o.htm/, Retrieved Sun, 05 May 2024 23:50:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78652, Retrieved Sun, 05 May 2024 23:50:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsMarianne Nykjaer
Estimated Impact158
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks 2 stap 27] [2010-08-11 21:53:03] [aec95ccba2c38285ca49e8d90cbfedc9] [Current]
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Dataseries X:
190
189
188
186
184
183
184
186
187
187
188
190
190
190
197
187
185
182
182
191
183
192
178
181
179
175
183
179
178
175
170
179
169
178
161
168
167
165
181
181
184
181
177
183
162
166
151
162
159
152
164
158
160
161
151
149
131
138
130
147
151
140
149
143
145
139
136
133
118
130
121
142
148
131
137
128
130
119
107
113
93
106
98
118




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=78652&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=78652&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78652&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
alpha0.568079894207184
beta0.000575352159398017
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.568079894207184 \tabularnewline
beta & 0.000575352159398017 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78652&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]0.568079894207184[/C][/ROW]
[ROW][C]beta[/C][C]0.000575352159398017[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78652&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78652&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
alpha0.568079894207184
beta0.000575352159398017
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
31881880
4186187-1
5184185.431593259799-1.43159325979897
6183183.617539155709-0.617539155709011
7184182.2657309807501.73426901924967
8186182.2505045838993.74949541610104
9187183.381313292933.61868670706988
10187184.4389949576272.56100504237335
11188184.8966659883763.10333401162416
12190185.6634375148924.33656248510823
13190187.1321987302332.86780126976689
14190187.7675235591042.23247644089611
15197188.0426628023848.95733719761637
16187192.140987902678-5.14098790267758
17185188.228657660198-3.22865766019768
18182185.401628505733-3.40162850573324
19182182.475226282986-0.47522628298637
20191181.2110989995389.78890100046155
21183185.781015520477-2.78101552047681
22192183.2093062302268.7906937697743
23178187.214125532419-9.2141255324185
24181180.9877573901850.0122426098149049
25179180.002707487556-1.00270748755614
26175178.440757110062-3.44075711006178
27183175.4926751632657.50732483673465
28179178.7664321896240.23356781037603
29178177.9081904346630.0918095653368596
30175176.969448678446-1.9694486784461
31170174.859103850756-4.8591038507565
32179171.1056158398587.89438416014173
33169174.599708196800-5.59970819680032
34178170.4262477529987.57375224700206
35161173.738840775034-12.7388407750336
36168165.5080944629642.49190553703585
37167165.9304433738931.06955662610659
38165165.545134046275-0.545134046274711
39181164.24237323743316.7576267625668
40181172.7744401215448.22555987845578
41184176.4622998440547.5377001559458
42181179.761863955271.23813604472991
43177179.483177032441-2.48317703244112
44183177.0896753539565.91032464604399
45162179.466284986945-17.4662849869454
46166168.557403907428-2.55740390742821
47151166.117122537089-15.1171225370889
48162156.5369765654005.46302343459979
49159158.6497833074010.350216692599275
50152157.858221803227-5.85822180322677
51164153.53785647882510.4621435211753
52158158.492182071028-0.492182071028481
53160157.2234146719642.77658532803605
54161157.8124758269393.18752417306109
55151158.636024907028-7.63602490702755
56149153.308437566603-4.30843756660343
57131149.869777494934-18.8697774949343
58138138.152945466085-0.152945466085100
59130137.068719406465-7.06871940646536
60147132.05347083581414.946529164186
61151139.54952755730211.4504724426977
62140145.063287287351-5.0632872873507
63149141.1942572218257.80574277817519
64143144.638415670228-1.63841567022797
65145142.7170020767882.28299792321172
66139143.024010891378-4.0240108913776
67136139.746819573972-3.7468195739722
68133136.625870437866-3.62587043786621
69118133.572444972977-15.5724449729770
70130123.727320918796.27267908120999
71121126.294022826277-5.29402282627674
72142122.28818360768019.7118163923197
73148132.49410161516515.5058983848348
74131140.315790206682-9.31579020668195
75137134.0337317403782.96626825962232
76128134.729833261155-6.7298332611553
77130129.9155748367470.0844251632531439
78119128.972387211203-9.97238721120311
79107122.312867241108-15.3128672411078
80113112.6145229912970.385477008703418
8193111.834218473762-18.8342184737621
82106100.1294354909995.87056450900097
8398102.460861781987-4.46086178198679
8411898.921754503778419.0782454962216

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 188 & 188 & 0 \tabularnewline
4 & 186 & 187 & -1 \tabularnewline
5 & 184 & 185.431593259799 & -1.43159325979897 \tabularnewline
6 & 183 & 183.617539155709 & -0.617539155709011 \tabularnewline
7 & 184 & 182.265730980750 & 1.73426901924967 \tabularnewline
8 & 186 & 182.250504583899 & 3.74949541610104 \tabularnewline
9 & 187 & 183.38131329293 & 3.61868670706988 \tabularnewline
10 & 187 & 184.438994957627 & 2.56100504237335 \tabularnewline
11 & 188 & 184.896665988376 & 3.10333401162416 \tabularnewline
12 & 190 & 185.663437514892 & 4.33656248510823 \tabularnewline
13 & 190 & 187.132198730233 & 2.86780126976689 \tabularnewline
14 & 190 & 187.767523559104 & 2.23247644089611 \tabularnewline
15 & 197 & 188.042662802384 & 8.95733719761637 \tabularnewline
16 & 187 & 192.140987902678 & -5.14098790267758 \tabularnewline
17 & 185 & 188.228657660198 & -3.22865766019768 \tabularnewline
18 & 182 & 185.401628505733 & -3.40162850573324 \tabularnewline
19 & 182 & 182.475226282986 & -0.47522628298637 \tabularnewline
20 & 191 & 181.211098999538 & 9.78890100046155 \tabularnewline
21 & 183 & 185.781015520477 & -2.78101552047681 \tabularnewline
22 & 192 & 183.209306230226 & 8.7906937697743 \tabularnewline
23 & 178 & 187.214125532419 & -9.2141255324185 \tabularnewline
24 & 181 & 180.987757390185 & 0.0122426098149049 \tabularnewline
25 & 179 & 180.002707487556 & -1.00270748755614 \tabularnewline
26 & 175 & 178.440757110062 & -3.44075711006178 \tabularnewline
27 & 183 & 175.492675163265 & 7.50732483673465 \tabularnewline
28 & 179 & 178.766432189624 & 0.23356781037603 \tabularnewline
29 & 178 & 177.908190434663 & 0.0918095653368596 \tabularnewline
30 & 175 & 176.969448678446 & -1.9694486784461 \tabularnewline
31 & 170 & 174.859103850756 & -4.8591038507565 \tabularnewline
32 & 179 & 171.105615839858 & 7.89438416014173 \tabularnewline
33 & 169 & 174.599708196800 & -5.59970819680032 \tabularnewline
34 & 178 & 170.426247752998 & 7.57375224700206 \tabularnewline
35 & 161 & 173.738840775034 & -12.7388407750336 \tabularnewline
36 & 168 & 165.508094462964 & 2.49190553703585 \tabularnewline
37 & 167 & 165.930443373893 & 1.06955662610659 \tabularnewline
38 & 165 & 165.545134046275 & -0.545134046274711 \tabularnewline
39 & 181 & 164.242373237433 & 16.7576267625668 \tabularnewline
40 & 181 & 172.774440121544 & 8.22555987845578 \tabularnewline
41 & 184 & 176.462299844054 & 7.5377001559458 \tabularnewline
42 & 181 & 179.76186395527 & 1.23813604472991 \tabularnewline
43 & 177 & 179.483177032441 & -2.48317703244112 \tabularnewline
44 & 183 & 177.089675353956 & 5.91032464604399 \tabularnewline
45 & 162 & 179.466284986945 & -17.4662849869454 \tabularnewline
46 & 166 & 168.557403907428 & -2.55740390742821 \tabularnewline
47 & 151 & 166.117122537089 & -15.1171225370889 \tabularnewline
48 & 162 & 156.536976565400 & 5.46302343459979 \tabularnewline
49 & 159 & 158.649783307401 & 0.350216692599275 \tabularnewline
50 & 152 & 157.858221803227 & -5.85822180322677 \tabularnewline
51 & 164 & 153.537856478825 & 10.4621435211753 \tabularnewline
52 & 158 & 158.492182071028 & -0.492182071028481 \tabularnewline
53 & 160 & 157.223414671964 & 2.77658532803605 \tabularnewline
54 & 161 & 157.812475826939 & 3.18752417306109 \tabularnewline
55 & 151 & 158.636024907028 & -7.63602490702755 \tabularnewline
56 & 149 & 153.308437566603 & -4.30843756660343 \tabularnewline
57 & 131 & 149.869777494934 & -18.8697774949343 \tabularnewline
58 & 138 & 138.152945466085 & -0.152945466085100 \tabularnewline
59 & 130 & 137.068719406465 & -7.06871940646536 \tabularnewline
60 & 147 & 132.053470835814 & 14.946529164186 \tabularnewline
61 & 151 & 139.549527557302 & 11.4504724426977 \tabularnewline
62 & 140 & 145.063287287351 & -5.0632872873507 \tabularnewline
63 & 149 & 141.194257221825 & 7.80574277817519 \tabularnewline
64 & 143 & 144.638415670228 & -1.63841567022797 \tabularnewline
65 & 145 & 142.717002076788 & 2.28299792321172 \tabularnewline
66 & 139 & 143.024010891378 & -4.0240108913776 \tabularnewline
67 & 136 & 139.746819573972 & -3.7468195739722 \tabularnewline
68 & 133 & 136.625870437866 & -3.62587043786621 \tabularnewline
69 & 118 & 133.572444972977 & -15.5724449729770 \tabularnewline
70 & 130 & 123.72732091879 & 6.27267908120999 \tabularnewline
71 & 121 & 126.294022826277 & -5.29402282627674 \tabularnewline
72 & 142 & 122.288183607680 & 19.7118163923197 \tabularnewline
73 & 148 & 132.494101615165 & 15.5058983848348 \tabularnewline
74 & 131 & 140.315790206682 & -9.31579020668195 \tabularnewline
75 & 137 & 134.033731740378 & 2.96626825962232 \tabularnewline
76 & 128 & 134.729833261155 & -6.7298332611553 \tabularnewline
77 & 130 & 129.915574836747 & 0.0844251632531439 \tabularnewline
78 & 119 & 128.972387211203 & -9.97238721120311 \tabularnewline
79 & 107 & 122.312867241108 & -15.3128672411078 \tabularnewline
80 & 113 & 112.614522991297 & 0.385477008703418 \tabularnewline
81 & 93 & 111.834218473762 & -18.8342184737621 \tabularnewline
82 & 106 & 100.129435490999 & 5.87056450900097 \tabularnewline
83 & 98 & 102.460861781987 & -4.46086178198679 \tabularnewline
84 & 118 & 98.9217545037784 & 19.0782454962216 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78652&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]188[/C][C]188[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]186[/C][C]187[/C][C]-1[/C][/ROW]
[ROW][C]5[/C][C]184[/C][C]185.431593259799[/C][C]-1.43159325979897[/C][/ROW]
[ROW][C]6[/C][C]183[/C][C]183.617539155709[/C][C]-0.617539155709011[/C][/ROW]
[ROW][C]7[/C][C]184[/C][C]182.265730980750[/C][C]1.73426901924967[/C][/ROW]
[ROW][C]8[/C][C]186[/C][C]182.250504583899[/C][C]3.74949541610104[/C][/ROW]
[ROW][C]9[/C][C]187[/C][C]183.38131329293[/C][C]3.61868670706988[/C][/ROW]
[ROW][C]10[/C][C]187[/C][C]184.438994957627[/C][C]2.56100504237335[/C][/ROW]
[ROW][C]11[/C][C]188[/C][C]184.896665988376[/C][C]3.10333401162416[/C][/ROW]
[ROW][C]12[/C][C]190[/C][C]185.663437514892[/C][C]4.33656248510823[/C][/ROW]
[ROW][C]13[/C][C]190[/C][C]187.132198730233[/C][C]2.86780126976689[/C][/ROW]
[ROW][C]14[/C][C]190[/C][C]187.767523559104[/C][C]2.23247644089611[/C][/ROW]
[ROW][C]15[/C][C]197[/C][C]188.042662802384[/C][C]8.95733719761637[/C][/ROW]
[ROW][C]16[/C][C]187[/C][C]192.140987902678[/C][C]-5.14098790267758[/C][/ROW]
[ROW][C]17[/C][C]185[/C][C]188.228657660198[/C][C]-3.22865766019768[/C][/ROW]
[ROW][C]18[/C][C]182[/C][C]185.401628505733[/C][C]-3.40162850573324[/C][/ROW]
[ROW][C]19[/C][C]182[/C][C]182.475226282986[/C][C]-0.47522628298637[/C][/ROW]
[ROW][C]20[/C][C]191[/C][C]181.211098999538[/C][C]9.78890100046155[/C][/ROW]
[ROW][C]21[/C][C]183[/C][C]185.781015520477[/C][C]-2.78101552047681[/C][/ROW]
[ROW][C]22[/C][C]192[/C][C]183.209306230226[/C][C]8.7906937697743[/C][/ROW]
[ROW][C]23[/C][C]178[/C][C]187.214125532419[/C][C]-9.2141255324185[/C][/ROW]
[ROW][C]24[/C][C]181[/C][C]180.987757390185[/C][C]0.0122426098149049[/C][/ROW]
[ROW][C]25[/C][C]179[/C][C]180.002707487556[/C][C]-1.00270748755614[/C][/ROW]
[ROW][C]26[/C][C]175[/C][C]178.440757110062[/C][C]-3.44075711006178[/C][/ROW]
[ROW][C]27[/C][C]183[/C][C]175.492675163265[/C][C]7.50732483673465[/C][/ROW]
[ROW][C]28[/C][C]179[/C][C]178.766432189624[/C][C]0.23356781037603[/C][/ROW]
[ROW][C]29[/C][C]178[/C][C]177.908190434663[/C][C]0.0918095653368596[/C][/ROW]
[ROW][C]30[/C][C]175[/C][C]176.969448678446[/C][C]-1.9694486784461[/C][/ROW]
[ROW][C]31[/C][C]170[/C][C]174.859103850756[/C][C]-4.8591038507565[/C][/ROW]
[ROW][C]32[/C][C]179[/C][C]171.105615839858[/C][C]7.89438416014173[/C][/ROW]
[ROW][C]33[/C][C]169[/C][C]174.599708196800[/C][C]-5.59970819680032[/C][/ROW]
[ROW][C]34[/C][C]178[/C][C]170.426247752998[/C][C]7.57375224700206[/C][/ROW]
[ROW][C]35[/C][C]161[/C][C]173.738840775034[/C][C]-12.7388407750336[/C][/ROW]
[ROW][C]36[/C][C]168[/C][C]165.508094462964[/C][C]2.49190553703585[/C][/ROW]
[ROW][C]37[/C][C]167[/C][C]165.930443373893[/C][C]1.06955662610659[/C][/ROW]
[ROW][C]38[/C][C]165[/C][C]165.545134046275[/C][C]-0.545134046274711[/C][/ROW]
[ROW][C]39[/C][C]181[/C][C]164.242373237433[/C][C]16.7576267625668[/C][/ROW]
[ROW][C]40[/C][C]181[/C][C]172.774440121544[/C][C]8.22555987845578[/C][/ROW]
[ROW][C]41[/C][C]184[/C][C]176.462299844054[/C][C]7.5377001559458[/C][/ROW]
[ROW][C]42[/C][C]181[/C][C]179.76186395527[/C][C]1.23813604472991[/C][/ROW]
[ROW][C]43[/C][C]177[/C][C]179.483177032441[/C][C]-2.48317703244112[/C][/ROW]
[ROW][C]44[/C][C]183[/C][C]177.089675353956[/C][C]5.91032464604399[/C][/ROW]
[ROW][C]45[/C][C]162[/C][C]179.466284986945[/C][C]-17.4662849869454[/C][/ROW]
[ROW][C]46[/C][C]166[/C][C]168.557403907428[/C][C]-2.55740390742821[/C][/ROW]
[ROW][C]47[/C][C]151[/C][C]166.117122537089[/C][C]-15.1171225370889[/C][/ROW]
[ROW][C]48[/C][C]162[/C][C]156.536976565400[/C][C]5.46302343459979[/C][/ROW]
[ROW][C]49[/C][C]159[/C][C]158.649783307401[/C][C]0.350216692599275[/C][/ROW]
[ROW][C]50[/C][C]152[/C][C]157.858221803227[/C][C]-5.85822180322677[/C][/ROW]
[ROW][C]51[/C][C]164[/C][C]153.537856478825[/C][C]10.4621435211753[/C][/ROW]
[ROW][C]52[/C][C]158[/C][C]158.492182071028[/C][C]-0.492182071028481[/C][/ROW]
[ROW][C]53[/C][C]160[/C][C]157.223414671964[/C][C]2.77658532803605[/C][/ROW]
[ROW][C]54[/C][C]161[/C][C]157.812475826939[/C][C]3.18752417306109[/C][/ROW]
[ROW][C]55[/C][C]151[/C][C]158.636024907028[/C][C]-7.63602490702755[/C][/ROW]
[ROW][C]56[/C][C]149[/C][C]153.308437566603[/C][C]-4.30843756660343[/C][/ROW]
[ROW][C]57[/C][C]131[/C][C]149.869777494934[/C][C]-18.8697774949343[/C][/ROW]
[ROW][C]58[/C][C]138[/C][C]138.152945466085[/C][C]-0.152945466085100[/C][/ROW]
[ROW][C]59[/C][C]130[/C][C]137.068719406465[/C][C]-7.06871940646536[/C][/ROW]
[ROW][C]60[/C][C]147[/C][C]132.053470835814[/C][C]14.946529164186[/C][/ROW]
[ROW][C]61[/C][C]151[/C][C]139.549527557302[/C][C]11.4504724426977[/C][/ROW]
[ROW][C]62[/C][C]140[/C][C]145.063287287351[/C][C]-5.0632872873507[/C][/ROW]
[ROW][C]63[/C][C]149[/C][C]141.194257221825[/C][C]7.80574277817519[/C][/ROW]
[ROW][C]64[/C][C]143[/C][C]144.638415670228[/C][C]-1.63841567022797[/C][/ROW]
[ROW][C]65[/C][C]145[/C][C]142.717002076788[/C][C]2.28299792321172[/C][/ROW]
[ROW][C]66[/C][C]139[/C][C]143.024010891378[/C][C]-4.0240108913776[/C][/ROW]
[ROW][C]67[/C][C]136[/C][C]139.746819573972[/C][C]-3.7468195739722[/C][/ROW]
[ROW][C]68[/C][C]133[/C][C]136.625870437866[/C][C]-3.62587043786621[/C][/ROW]
[ROW][C]69[/C][C]118[/C][C]133.572444972977[/C][C]-15.5724449729770[/C][/ROW]
[ROW][C]70[/C][C]130[/C][C]123.72732091879[/C][C]6.27267908120999[/C][/ROW]
[ROW][C]71[/C][C]121[/C][C]126.294022826277[/C][C]-5.29402282627674[/C][/ROW]
[ROW][C]72[/C][C]142[/C][C]122.288183607680[/C][C]19.7118163923197[/C][/ROW]
[ROW][C]73[/C][C]148[/C][C]132.494101615165[/C][C]15.5058983848348[/C][/ROW]
[ROW][C]74[/C][C]131[/C][C]140.315790206682[/C][C]-9.31579020668195[/C][/ROW]
[ROW][C]75[/C][C]137[/C][C]134.033731740378[/C][C]2.96626825962232[/C][/ROW]
[ROW][C]76[/C][C]128[/C][C]134.729833261155[/C][C]-6.7298332611553[/C][/ROW]
[ROW][C]77[/C][C]130[/C][C]129.915574836747[/C][C]0.0844251632531439[/C][/ROW]
[ROW][C]78[/C][C]119[/C][C]128.972387211203[/C][C]-9.97238721120311[/C][/ROW]
[ROW][C]79[/C][C]107[/C][C]122.312867241108[/C][C]-15.3128672411078[/C][/ROW]
[ROW][C]80[/C][C]113[/C][C]112.614522991297[/C][C]0.385477008703418[/C][/ROW]
[ROW][C]81[/C][C]93[/C][C]111.834218473762[/C][C]-18.8342184737621[/C][/ROW]
[ROW][C]82[/C][C]106[/C][C]100.129435490999[/C][C]5.87056450900097[/C][/ROW]
[ROW][C]83[/C][C]98[/C][C]102.460861781987[/C][C]-4.46086178198679[/C][/ROW]
[ROW][C]84[/C][C]118[/C][C]98.9217545037784[/C][C]19.0782454962216[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78652&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78652&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
31881880
4186187-1
5184185.431593259799-1.43159325979897
6183183.617539155709-0.617539155709011
7184182.2657309807501.73426901924967
8186182.2505045838993.74949541610104
9187183.381313292933.61868670706988
10187184.4389949576272.56100504237335
11188184.8966659883763.10333401162416
12190185.6634375148924.33656248510823
13190187.1321987302332.86780126976689
14190187.7675235591042.23247644089611
15197188.0426628023848.95733719761637
16187192.140987902678-5.14098790267758
17185188.228657660198-3.22865766019768
18182185.401628505733-3.40162850573324
19182182.475226282986-0.47522628298637
20191181.2110989995389.78890100046155
21183185.781015520477-2.78101552047681
22192183.2093062302268.7906937697743
23178187.214125532419-9.2141255324185
24181180.9877573901850.0122426098149049
25179180.002707487556-1.00270748755614
26175178.440757110062-3.44075711006178
27183175.4926751632657.50732483673465
28179178.7664321896240.23356781037603
29178177.9081904346630.0918095653368596
30175176.969448678446-1.9694486784461
31170174.859103850756-4.8591038507565
32179171.1056158398587.89438416014173
33169174.599708196800-5.59970819680032
34178170.4262477529987.57375224700206
35161173.738840775034-12.7388407750336
36168165.5080944629642.49190553703585
37167165.9304433738931.06955662610659
38165165.545134046275-0.545134046274711
39181164.24237323743316.7576267625668
40181172.7744401215448.22555987845578
41184176.4622998440547.5377001559458
42181179.761863955271.23813604472991
43177179.483177032441-2.48317703244112
44183177.0896753539565.91032464604399
45162179.466284986945-17.4662849869454
46166168.557403907428-2.55740390742821
47151166.117122537089-15.1171225370889
48162156.5369765654005.46302343459979
49159158.6497833074010.350216692599275
50152157.858221803227-5.85822180322677
51164153.53785647882510.4621435211753
52158158.492182071028-0.492182071028481
53160157.2234146719642.77658532803605
54161157.8124758269393.18752417306109
55151158.636024907028-7.63602490702755
56149153.308437566603-4.30843756660343
57131149.869777494934-18.8697774949343
58138138.152945466085-0.152945466085100
59130137.068719406465-7.06871940646536
60147132.05347083581414.946529164186
61151139.54952755730211.4504724426977
62140145.063287287351-5.0632872873507
63149141.1942572218257.80574277817519
64143144.638415670228-1.63841567022797
65145142.7170020767882.28299792321172
66139143.024010891378-4.0240108913776
67136139.746819573972-3.7468195739722
68133136.625870437866-3.62587043786621
69118133.572444972977-15.5724449729770
70130123.727320918796.27267908120999
71121126.294022826277-5.29402282627674
72142122.28818360768019.7118163923197
73148132.49410161516515.5058983848348
74131140.315790206682-9.31579020668195
75137134.0337317403782.96626825962232
76128134.729833261155-6.7298332611553
77130129.9155748367470.0844251632531439
78119128.972387211203-9.97238721120311
79107122.312867241108-15.3128672411078
80113112.6145229912970.385477008703418
8193111.834218473762-18.8342184737621
82106100.1294354909995.87056450900097
8398102.460861781987-4.46086178198679
8411898.921754503778419.0782454962216







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85108.76097644601693.0027355991867124.519217292846
86107.76223070510289.6362377274199125.888223682783
87106.76348496418786.5428672163812126.984102711993
88105.76473922327383.6448954247714127.884583021774
89104.76599348235880.8956353538283128.636351610888
90103.76724774144478.2644448033138129.270050679574
91102.76850200052975.7299291040873129.807074896971
92101.76975625961573.2764509061585130.263061613071
93100.77101051870070.8921703835138130.649850653887
9499.772264777785768.567867797423130.976661758148
9598.773519036871266.296197529809131.250840543933
9697.774773295956764.0711947771293131.478351814784

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 108.760976446016 & 93.0027355991867 & 124.519217292846 \tabularnewline
86 & 107.762230705102 & 89.6362377274199 & 125.888223682783 \tabularnewline
87 & 106.763484964187 & 86.5428672163812 & 126.984102711993 \tabularnewline
88 & 105.764739223273 & 83.6448954247714 & 127.884583021774 \tabularnewline
89 & 104.765993482358 & 80.8956353538283 & 128.636351610888 \tabularnewline
90 & 103.767247741444 & 78.2644448033138 & 129.270050679574 \tabularnewline
91 & 102.768502000529 & 75.7299291040873 & 129.807074896971 \tabularnewline
92 & 101.769756259615 & 73.2764509061585 & 130.263061613071 \tabularnewline
93 & 100.771010518700 & 70.8921703835138 & 130.649850653887 \tabularnewline
94 & 99.7722647777857 & 68.567867797423 & 130.976661758148 \tabularnewline
95 & 98.7735190368712 & 66.296197529809 & 131.250840543933 \tabularnewline
96 & 97.7747732959567 & 64.0711947771293 & 131.478351814784 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78652&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]108.760976446016[/C][C]93.0027355991867[/C][C]124.519217292846[/C][/ROW]
[ROW][C]86[/C][C]107.762230705102[/C][C]89.6362377274199[/C][C]125.888223682783[/C][/ROW]
[ROW][C]87[/C][C]106.763484964187[/C][C]86.5428672163812[/C][C]126.984102711993[/C][/ROW]
[ROW][C]88[/C][C]105.764739223273[/C][C]83.6448954247714[/C][C]127.884583021774[/C][/ROW]
[ROW][C]89[/C][C]104.765993482358[/C][C]80.8956353538283[/C][C]128.636351610888[/C][/ROW]
[ROW][C]90[/C][C]103.767247741444[/C][C]78.2644448033138[/C][C]129.270050679574[/C][/ROW]
[ROW][C]91[/C][C]102.768502000529[/C][C]75.7299291040873[/C][C]129.807074896971[/C][/ROW]
[ROW][C]92[/C][C]101.769756259615[/C][C]73.2764509061585[/C][C]130.263061613071[/C][/ROW]
[ROW][C]93[/C][C]100.771010518700[/C][C]70.8921703835138[/C][C]130.649850653887[/C][/ROW]
[ROW][C]94[/C][C]99.7722647777857[/C][C]68.567867797423[/C][C]130.976661758148[/C][/ROW]
[ROW][C]95[/C][C]98.7735190368712[/C][C]66.296197529809[/C][C]131.250840543933[/C][/ROW]
[ROW][C]96[/C][C]97.7747732959567[/C][C]64.0711947771293[/C][C]131.478351814784[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78652&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78652&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
85108.76097644601693.0027355991867124.519217292846
86107.76223070510289.6362377274199125.888223682783
87106.76348496418786.5428672163812126.984102711993
88105.76473922327383.6448954247714127.884583021774
89104.76599348235880.8956353538283128.636351610888
90103.76724774144478.2644448033138129.270050679574
91102.76850200052975.7299291040873129.807074896971
92101.76975625961573.2764509061585130.263061613071
93100.77101051870070.8921703835138130.649850653887
9499.772264777785768.567867797423130.976661758148
9598.773519036871266.296197529809131.250840543933
9697.774773295956764.0711947771293131.478351814784



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=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')