Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 01 Jul 2010 16:44:44 +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/Jul/01/t1278002717rxc3ey4yhroyf7b.htm/, Retrieved Thu, 31 Oct 2024 23:19:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=77902, Retrieved Thu, 31 Oct 2024 23:19:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsSteffi Poppe
Estimated Impact210
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks1-Stap32] [2010-07-01 16:44:44] [b37bab310ab56201887748d7a7c0dc58] [Current]
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Dataseries X:
300
299
298
296
316
315
300
290
291
291
292
294
302
296
282
282
298
300
289
275
270
269
268
260
271
269
260
262
285
286
272
248
240
234
231
222
233
236
226
232
248
253
233
216
209
202
204
193
201
201
188
198
220
225
215
198
195
183
180
170
175
180
161
174
195
198
188
173
162
149
140
129
132
133
116
128
148
154
152
141
136
119
114
100
108
115
101
116
131
133
135
124
131
113
118
99
107
112
106
121
138
134
132
121
132
113
112
91
96
99
99
110
127
122
124
114
129
113
115
94




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77902&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77902&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77902&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'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.218782691587284
beta0.0803415209988776
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.218782691587284 \tabularnewline
beta & 0.0803415209988776 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77902&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]0.218782691587284[/C][/ROW]
[ROW][C]beta[/C][C]0.0803415209988776[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77902&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77902&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
alpha0.218782691587284
beta0.0803415209988776
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13302309.004540598291-7.0045405982907
14296301.106960022291-5.10696002229099
15282285.951437155768-3.95143715576808
16282285.270933627342-3.27093362734234
17298300.806818198952-2.8068181989525
18300302.894906811642-2.89490681164233
19289285.9128384160143.08716158398636
20275274.9188071161630.0811928838371045
21270275.018549047721-5.01854904772102
22269273.372676332563-4.37267633256295
23268272.874582728492-4.87458272849193
24260273.222665189107-13.2226651891068
25271271.748177474684-0.748177474684326
26269265.9442319360183.0557680639825
27260252.8631944376647.13680556233624
28262254.7210366621477.2789633378535
29285272.69387918959912.3061208104014
30286278.0514942035787.94850579642156
31272268.3375637384363.66243626156364
32248255.353681162444-7.35368116244422
33240249.944712765849-9.94471276584943
34234247.740976903980-13.7409769039805
35231244.651822838094-13.6518228380943
36222236.254309606184-14.2543096061836
37233243.977647140466-10.9776471404656
38236238.405817457709-2.40581745770933
39226226.720495262383-0.720495262382599
40232226.2346803297965.76531967020384
41248247.0413885817990.958611418200803
42253245.5503840413727.4496159586279
43233231.4084476211581.59155237884170
44216208.3586034862187.64139651378201
45209203.4628068948095.53719310519057
46202201.2093345378470.790665462152901
47204201.1533262554422.84667374455813
48193195.968950264157-2.96895026415689
49201208.993705898151-7.99370589815149
50201211.096213732631-10.0962137326314
51188199.234833252381-11.2348332523807
52198201.520544447966-3.52054444796642
53220216.3824123438753.61758765612541
54225220.4325982639534.56740173604695
55215200.92156833976314.0784316602368
56198185.38727200900212.6127279909977
57195180.08005112464014.9199488753598
58183176.4809921628696.51900783713114
59180179.6948226713340.305177328666275
60170169.7768597580790.223140241920760
61175179.996386554005-4.99638655400531
62180181.586648435665-1.58664843566476
63161171.321587716897-10.3215877168967
64174180.473773025011-6.4737730250111
65195200.854183947808-5.85418394780822
66198203.995858860635-5.99585886063471
67188189.840015066262-1.84001506626228
68173169.6342646986433.36573530135686
69162163.900124932070-1.90012493206956
70149149.556234523558-0.556234523558231
71140145.741478739935-5.74147873993545
72129133.703945470192-4.70394547019154
73132137.948743610793-5.9487436107934
74133141.158469882299-8.1584698822985
75116121.680284717314-5.68028471731375
76128133.984030051951-5.98403005195141
77148154.094374174646-6.09437417464602
78154156.207351028044-2.20735102804406
79152145.3281064449016.67189355509936
80141130.40217547636610.5978245236344
81136121.61437017680314.385629823197
82119111.6475113093167.35248869068398
83114105.4153788518558.58462114814515
8410097.47763597412692.52236402587312
85108102.6129357108985.3870642891025
86115107.05768542727.94231457279994
8710193.80230452701827.19769547298182
88116109.6768286395996.32317136040099
89131133.600491189554-2.60049118955439
90133140.782810590659-7.78281059065907
91135136.790701459255-1.79070145925476
92124124.101886486768-0.101886486767697
93131116.76577636452314.2342236354766
94113102.10222723183710.8977727681633
9511898.501467785715619.4985322142844
969989.3005600335689.69943996643195
9710799.45518753260347.5448124673966
98112107.6173027541574.38269724584303
9910694.187943083878611.8120569161214
100121111.6564376314969.34356236850446
101138130.5903016315087.40969836849243
102134137.410823895043-3.41082389504265
103132140.62988128064-8.62988128064012
104121129.217401209149-8.21740120914924
105132132.616022763925-0.616022763924605
106113113.146624311751-0.146624311750983
107112114.704093756428-2.70409375642821
1089193.4556419524094-2.45564195240935
1099699.5192883691687-3.51928836916871
11099102.847566041112-3.84756604111158
1119993.33394084653135.66605915346872
112110107.3337658033402.66623419666018
113127122.9830073239854.01699267601525
114122120.2354796837901.76452031621037
115124120.2279582552153.77204174478526
116114111.7873970138052.21260298619532
117129123.5259391969625.4740608030381
118113105.9823830772187.01761692278161
119115107.461988631277.53801136872994
1209489.18111943328294.81888056671713

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 302 & 309.004540598291 & -7.0045405982907 \tabularnewline
14 & 296 & 301.106960022291 & -5.10696002229099 \tabularnewline
15 & 282 & 285.951437155768 & -3.95143715576808 \tabularnewline
16 & 282 & 285.270933627342 & -3.27093362734234 \tabularnewline
17 & 298 & 300.806818198952 & -2.8068181989525 \tabularnewline
18 & 300 & 302.894906811642 & -2.89490681164233 \tabularnewline
19 & 289 & 285.912838416014 & 3.08716158398636 \tabularnewline
20 & 275 & 274.918807116163 & 0.0811928838371045 \tabularnewline
21 & 270 & 275.018549047721 & -5.01854904772102 \tabularnewline
22 & 269 & 273.372676332563 & -4.37267633256295 \tabularnewline
23 & 268 & 272.874582728492 & -4.87458272849193 \tabularnewline
24 & 260 & 273.222665189107 & -13.2226651891068 \tabularnewline
25 & 271 & 271.748177474684 & -0.748177474684326 \tabularnewline
26 & 269 & 265.944231936018 & 3.0557680639825 \tabularnewline
27 & 260 & 252.863194437664 & 7.13680556233624 \tabularnewline
28 & 262 & 254.721036662147 & 7.2789633378535 \tabularnewline
29 & 285 & 272.693879189599 & 12.3061208104014 \tabularnewline
30 & 286 & 278.051494203578 & 7.94850579642156 \tabularnewline
31 & 272 & 268.337563738436 & 3.66243626156364 \tabularnewline
32 & 248 & 255.353681162444 & -7.35368116244422 \tabularnewline
33 & 240 & 249.944712765849 & -9.94471276584943 \tabularnewline
34 & 234 & 247.740976903980 & -13.7409769039805 \tabularnewline
35 & 231 & 244.651822838094 & -13.6518228380943 \tabularnewline
36 & 222 & 236.254309606184 & -14.2543096061836 \tabularnewline
37 & 233 & 243.977647140466 & -10.9776471404656 \tabularnewline
38 & 236 & 238.405817457709 & -2.40581745770933 \tabularnewline
39 & 226 & 226.720495262383 & -0.720495262382599 \tabularnewline
40 & 232 & 226.234680329796 & 5.76531967020384 \tabularnewline
41 & 248 & 247.041388581799 & 0.958611418200803 \tabularnewline
42 & 253 & 245.550384041372 & 7.4496159586279 \tabularnewline
43 & 233 & 231.408447621158 & 1.59155237884170 \tabularnewline
44 & 216 & 208.358603486218 & 7.64139651378201 \tabularnewline
45 & 209 & 203.462806894809 & 5.53719310519057 \tabularnewline
46 & 202 & 201.209334537847 & 0.790665462152901 \tabularnewline
47 & 204 & 201.153326255442 & 2.84667374455813 \tabularnewline
48 & 193 & 195.968950264157 & -2.96895026415689 \tabularnewline
49 & 201 & 208.993705898151 & -7.99370589815149 \tabularnewline
50 & 201 & 211.096213732631 & -10.0962137326314 \tabularnewline
51 & 188 & 199.234833252381 & -11.2348332523807 \tabularnewline
52 & 198 & 201.520544447966 & -3.52054444796642 \tabularnewline
53 & 220 & 216.382412343875 & 3.61758765612541 \tabularnewline
54 & 225 & 220.432598263953 & 4.56740173604695 \tabularnewline
55 & 215 & 200.921568339763 & 14.0784316602368 \tabularnewline
56 & 198 & 185.387272009002 & 12.6127279909977 \tabularnewline
57 & 195 & 180.080051124640 & 14.9199488753598 \tabularnewline
58 & 183 & 176.480992162869 & 6.51900783713114 \tabularnewline
59 & 180 & 179.694822671334 & 0.305177328666275 \tabularnewline
60 & 170 & 169.776859758079 & 0.223140241920760 \tabularnewline
61 & 175 & 179.996386554005 & -4.99638655400531 \tabularnewline
62 & 180 & 181.586648435665 & -1.58664843566476 \tabularnewline
63 & 161 & 171.321587716897 & -10.3215877168967 \tabularnewline
64 & 174 & 180.473773025011 & -6.4737730250111 \tabularnewline
65 & 195 & 200.854183947808 & -5.85418394780822 \tabularnewline
66 & 198 & 203.995858860635 & -5.99585886063471 \tabularnewline
67 & 188 & 189.840015066262 & -1.84001506626228 \tabularnewline
68 & 173 & 169.634264698643 & 3.36573530135686 \tabularnewline
69 & 162 & 163.900124932070 & -1.90012493206956 \tabularnewline
70 & 149 & 149.556234523558 & -0.556234523558231 \tabularnewline
71 & 140 & 145.741478739935 & -5.74147873993545 \tabularnewline
72 & 129 & 133.703945470192 & -4.70394547019154 \tabularnewline
73 & 132 & 137.948743610793 & -5.9487436107934 \tabularnewline
74 & 133 & 141.158469882299 & -8.1584698822985 \tabularnewline
75 & 116 & 121.680284717314 & -5.68028471731375 \tabularnewline
76 & 128 & 133.984030051951 & -5.98403005195141 \tabularnewline
77 & 148 & 154.094374174646 & -6.09437417464602 \tabularnewline
78 & 154 & 156.207351028044 & -2.20735102804406 \tabularnewline
79 & 152 & 145.328106444901 & 6.67189355509936 \tabularnewline
80 & 141 & 130.402175476366 & 10.5978245236344 \tabularnewline
81 & 136 & 121.614370176803 & 14.385629823197 \tabularnewline
82 & 119 & 111.647511309316 & 7.35248869068398 \tabularnewline
83 & 114 & 105.415378851855 & 8.58462114814515 \tabularnewline
84 & 100 & 97.4776359741269 & 2.52236402587312 \tabularnewline
85 & 108 & 102.612935710898 & 5.3870642891025 \tabularnewline
86 & 115 & 107.0576854272 & 7.94231457279994 \tabularnewline
87 & 101 & 93.8023045270182 & 7.19769547298182 \tabularnewline
88 & 116 & 109.676828639599 & 6.32317136040099 \tabularnewline
89 & 131 & 133.600491189554 & -2.60049118955439 \tabularnewline
90 & 133 & 140.782810590659 & -7.78281059065907 \tabularnewline
91 & 135 & 136.790701459255 & -1.79070145925476 \tabularnewline
92 & 124 & 124.101886486768 & -0.101886486767697 \tabularnewline
93 & 131 & 116.765776364523 & 14.2342236354766 \tabularnewline
94 & 113 & 102.102227231837 & 10.8977727681633 \tabularnewline
95 & 118 & 98.5014677857156 & 19.4985322142844 \tabularnewline
96 & 99 & 89.300560033568 & 9.69943996643195 \tabularnewline
97 & 107 & 99.4551875326034 & 7.5448124673966 \tabularnewline
98 & 112 & 107.617302754157 & 4.38269724584303 \tabularnewline
99 & 106 & 94.1879430838786 & 11.8120569161214 \tabularnewline
100 & 121 & 111.656437631496 & 9.34356236850446 \tabularnewline
101 & 138 & 130.590301631508 & 7.40969836849243 \tabularnewline
102 & 134 & 137.410823895043 & -3.41082389504265 \tabularnewline
103 & 132 & 140.62988128064 & -8.62988128064012 \tabularnewline
104 & 121 & 129.217401209149 & -8.21740120914924 \tabularnewline
105 & 132 & 132.616022763925 & -0.616022763924605 \tabularnewline
106 & 113 & 113.146624311751 & -0.146624311750983 \tabularnewline
107 & 112 & 114.704093756428 & -2.70409375642821 \tabularnewline
108 & 91 & 93.4556419524094 & -2.45564195240935 \tabularnewline
109 & 96 & 99.5192883691687 & -3.51928836916871 \tabularnewline
110 & 99 & 102.847566041112 & -3.84756604111158 \tabularnewline
111 & 99 & 93.3339408465313 & 5.66605915346872 \tabularnewline
112 & 110 & 107.333765803340 & 2.66623419666018 \tabularnewline
113 & 127 & 122.983007323985 & 4.01699267601525 \tabularnewline
114 & 122 & 120.235479683790 & 1.76452031621037 \tabularnewline
115 & 124 & 120.227958255215 & 3.77204174478526 \tabularnewline
116 & 114 & 111.787397013805 & 2.21260298619532 \tabularnewline
117 & 129 & 123.525939196962 & 5.4740608030381 \tabularnewline
118 & 113 & 105.982383077218 & 7.01761692278161 \tabularnewline
119 & 115 & 107.46198863127 & 7.53801136872994 \tabularnewline
120 & 94 & 89.1811194332829 & 4.81888056671713 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77902&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]302[/C][C]309.004540598291[/C][C]-7.0045405982907[/C][/ROW]
[ROW][C]14[/C][C]296[/C][C]301.106960022291[/C][C]-5.10696002229099[/C][/ROW]
[ROW][C]15[/C][C]282[/C][C]285.951437155768[/C][C]-3.95143715576808[/C][/ROW]
[ROW][C]16[/C][C]282[/C][C]285.270933627342[/C][C]-3.27093362734234[/C][/ROW]
[ROW][C]17[/C][C]298[/C][C]300.806818198952[/C][C]-2.8068181989525[/C][/ROW]
[ROW][C]18[/C][C]300[/C][C]302.894906811642[/C][C]-2.89490681164233[/C][/ROW]
[ROW][C]19[/C][C]289[/C][C]285.912838416014[/C][C]3.08716158398636[/C][/ROW]
[ROW][C]20[/C][C]275[/C][C]274.918807116163[/C][C]0.0811928838371045[/C][/ROW]
[ROW][C]21[/C][C]270[/C][C]275.018549047721[/C][C]-5.01854904772102[/C][/ROW]
[ROW][C]22[/C][C]269[/C][C]273.372676332563[/C][C]-4.37267633256295[/C][/ROW]
[ROW][C]23[/C][C]268[/C][C]272.874582728492[/C][C]-4.87458272849193[/C][/ROW]
[ROW][C]24[/C][C]260[/C][C]273.222665189107[/C][C]-13.2226651891068[/C][/ROW]
[ROW][C]25[/C][C]271[/C][C]271.748177474684[/C][C]-0.748177474684326[/C][/ROW]
[ROW][C]26[/C][C]269[/C][C]265.944231936018[/C][C]3.0557680639825[/C][/ROW]
[ROW][C]27[/C][C]260[/C][C]252.863194437664[/C][C]7.13680556233624[/C][/ROW]
[ROW][C]28[/C][C]262[/C][C]254.721036662147[/C][C]7.2789633378535[/C][/ROW]
[ROW][C]29[/C][C]285[/C][C]272.693879189599[/C][C]12.3061208104014[/C][/ROW]
[ROW][C]30[/C][C]286[/C][C]278.051494203578[/C][C]7.94850579642156[/C][/ROW]
[ROW][C]31[/C][C]272[/C][C]268.337563738436[/C][C]3.66243626156364[/C][/ROW]
[ROW][C]32[/C][C]248[/C][C]255.353681162444[/C][C]-7.35368116244422[/C][/ROW]
[ROW][C]33[/C][C]240[/C][C]249.944712765849[/C][C]-9.94471276584943[/C][/ROW]
[ROW][C]34[/C][C]234[/C][C]247.740976903980[/C][C]-13.7409769039805[/C][/ROW]
[ROW][C]35[/C][C]231[/C][C]244.651822838094[/C][C]-13.6518228380943[/C][/ROW]
[ROW][C]36[/C][C]222[/C][C]236.254309606184[/C][C]-14.2543096061836[/C][/ROW]
[ROW][C]37[/C][C]233[/C][C]243.977647140466[/C][C]-10.9776471404656[/C][/ROW]
[ROW][C]38[/C][C]236[/C][C]238.405817457709[/C][C]-2.40581745770933[/C][/ROW]
[ROW][C]39[/C][C]226[/C][C]226.720495262383[/C][C]-0.720495262382599[/C][/ROW]
[ROW][C]40[/C][C]232[/C][C]226.234680329796[/C][C]5.76531967020384[/C][/ROW]
[ROW][C]41[/C][C]248[/C][C]247.041388581799[/C][C]0.958611418200803[/C][/ROW]
[ROW][C]42[/C][C]253[/C][C]245.550384041372[/C][C]7.4496159586279[/C][/ROW]
[ROW][C]43[/C][C]233[/C][C]231.408447621158[/C][C]1.59155237884170[/C][/ROW]
[ROW][C]44[/C][C]216[/C][C]208.358603486218[/C][C]7.64139651378201[/C][/ROW]
[ROW][C]45[/C][C]209[/C][C]203.462806894809[/C][C]5.53719310519057[/C][/ROW]
[ROW][C]46[/C][C]202[/C][C]201.209334537847[/C][C]0.790665462152901[/C][/ROW]
[ROW][C]47[/C][C]204[/C][C]201.153326255442[/C][C]2.84667374455813[/C][/ROW]
[ROW][C]48[/C][C]193[/C][C]195.968950264157[/C][C]-2.96895026415689[/C][/ROW]
[ROW][C]49[/C][C]201[/C][C]208.993705898151[/C][C]-7.99370589815149[/C][/ROW]
[ROW][C]50[/C][C]201[/C][C]211.096213732631[/C][C]-10.0962137326314[/C][/ROW]
[ROW][C]51[/C][C]188[/C][C]199.234833252381[/C][C]-11.2348332523807[/C][/ROW]
[ROW][C]52[/C][C]198[/C][C]201.520544447966[/C][C]-3.52054444796642[/C][/ROW]
[ROW][C]53[/C][C]220[/C][C]216.382412343875[/C][C]3.61758765612541[/C][/ROW]
[ROW][C]54[/C][C]225[/C][C]220.432598263953[/C][C]4.56740173604695[/C][/ROW]
[ROW][C]55[/C][C]215[/C][C]200.921568339763[/C][C]14.0784316602368[/C][/ROW]
[ROW][C]56[/C][C]198[/C][C]185.387272009002[/C][C]12.6127279909977[/C][/ROW]
[ROW][C]57[/C][C]195[/C][C]180.080051124640[/C][C]14.9199488753598[/C][/ROW]
[ROW][C]58[/C][C]183[/C][C]176.480992162869[/C][C]6.51900783713114[/C][/ROW]
[ROW][C]59[/C][C]180[/C][C]179.694822671334[/C][C]0.305177328666275[/C][/ROW]
[ROW][C]60[/C][C]170[/C][C]169.776859758079[/C][C]0.223140241920760[/C][/ROW]
[ROW][C]61[/C][C]175[/C][C]179.996386554005[/C][C]-4.99638655400531[/C][/ROW]
[ROW][C]62[/C][C]180[/C][C]181.586648435665[/C][C]-1.58664843566476[/C][/ROW]
[ROW][C]63[/C][C]161[/C][C]171.321587716897[/C][C]-10.3215877168967[/C][/ROW]
[ROW][C]64[/C][C]174[/C][C]180.473773025011[/C][C]-6.4737730250111[/C][/ROW]
[ROW][C]65[/C][C]195[/C][C]200.854183947808[/C][C]-5.85418394780822[/C][/ROW]
[ROW][C]66[/C][C]198[/C][C]203.995858860635[/C][C]-5.99585886063471[/C][/ROW]
[ROW][C]67[/C][C]188[/C][C]189.840015066262[/C][C]-1.84001506626228[/C][/ROW]
[ROW][C]68[/C][C]173[/C][C]169.634264698643[/C][C]3.36573530135686[/C][/ROW]
[ROW][C]69[/C][C]162[/C][C]163.900124932070[/C][C]-1.90012493206956[/C][/ROW]
[ROW][C]70[/C][C]149[/C][C]149.556234523558[/C][C]-0.556234523558231[/C][/ROW]
[ROW][C]71[/C][C]140[/C][C]145.741478739935[/C][C]-5.74147873993545[/C][/ROW]
[ROW][C]72[/C][C]129[/C][C]133.703945470192[/C][C]-4.70394547019154[/C][/ROW]
[ROW][C]73[/C][C]132[/C][C]137.948743610793[/C][C]-5.9487436107934[/C][/ROW]
[ROW][C]74[/C][C]133[/C][C]141.158469882299[/C][C]-8.1584698822985[/C][/ROW]
[ROW][C]75[/C][C]116[/C][C]121.680284717314[/C][C]-5.68028471731375[/C][/ROW]
[ROW][C]76[/C][C]128[/C][C]133.984030051951[/C][C]-5.98403005195141[/C][/ROW]
[ROW][C]77[/C][C]148[/C][C]154.094374174646[/C][C]-6.09437417464602[/C][/ROW]
[ROW][C]78[/C][C]154[/C][C]156.207351028044[/C][C]-2.20735102804406[/C][/ROW]
[ROW][C]79[/C][C]152[/C][C]145.328106444901[/C][C]6.67189355509936[/C][/ROW]
[ROW][C]80[/C][C]141[/C][C]130.402175476366[/C][C]10.5978245236344[/C][/ROW]
[ROW][C]81[/C][C]136[/C][C]121.614370176803[/C][C]14.385629823197[/C][/ROW]
[ROW][C]82[/C][C]119[/C][C]111.647511309316[/C][C]7.35248869068398[/C][/ROW]
[ROW][C]83[/C][C]114[/C][C]105.415378851855[/C][C]8.58462114814515[/C][/ROW]
[ROW][C]84[/C][C]100[/C][C]97.4776359741269[/C][C]2.52236402587312[/C][/ROW]
[ROW][C]85[/C][C]108[/C][C]102.612935710898[/C][C]5.3870642891025[/C][/ROW]
[ROW][C]86[/C][C]115[/C][C]107.0576854272[/C][C]7.94231457279994[/C][/ROW]
[ROW][C]87[/C][C]101[/C][C]93.8023045270182[/C][C]7.19769547298182[/C][/ROW]
[ROW][C]88[/C][C]116[/C][C]109.676828639599[/C][C]6.32317136040099[/C][/ROW]
[ROW][C]89[/C][C]131[/C][C]133.600491189554[/C][C]-2.60049118955439[/C][/ROW]
[ROW][C]90[/C][C]133[/C][C]140.782810590659[/C][C]-7.78281059065907[/C][/ROW]
[ROW][C]91[/C][C]135[/C][C]136.790701459255[/C][C]-1.79070145925476[/C][/ROW]
[ROW][C]92[/C][C]124[/C][C]124.101886486768[/C][C]-0.101886486767697[/C][/ROW]
[ROW][C]93[/C][C]131[/C][C]116.765776364523[/C][C]14.2342236354766[/C][/ROW]
[ROW][C]94[/C][C]113[/C][C]102.102227231837[/C][C]10.8977727681633[/C][/ROW]
[ROW][C]95[/C][C]118[/C][C]98.5014677857156[/C][C]19.4985322142844[/C][/ROW]
[ROW][C]96[/C][C]99[/C][C]89.300560033568[/C][C]9.69943996643195[/C][/ROW]
[ROW][C]97[/C][C]107[/C][C]99.4551875326034[/C][C]7.5448124673966[/C][/ROW]
[ROW][C]98[/C][C]112[/C][C]107.617302754157[/C][C]4.38269724584303[/C][/ROW]
[ROW][C]99[/C][C]106[/C][C]94.1879430838786[/C][C]11.8120569161214[/C][/ROW]
[ROW][C]100[/C][C]121[/C][C]111.656437631496[/C][C]9.34356236850446[/C][/ROW]
[ROW][C]101[/C][C]138[/C][C]130.590301631508[/C][C]7.40969836849243[/C][/ROW]
[ROW][C]102[/C][C]134[/C][C]137.410823895043[/C][C]-3.41082389504265[/C][/ROW]
[ROW][C]103[/C][C]132[/C][C]140.62988128064[/C][C]-8.62988128064012[/C][/ROW]
[ROW][C]104[/C][C]121[/C][C]129.217401209149[/C][C]-8.21740120914924[/C][/ROW]
[ROW][C]105[/C][C]132[/C][C]132.616022763925[/C][C]-0.616022763924605[/C][/ROW]
[ROW][C]106[/C][C]113[/C][C]113.146624311751[/C][C]-0.146624311750983[/C][/ROW]
[ROW][C]107[/C][C]112[/C][C]114.704093756428[/C][C]-2.70409375642821[/C][/ROW]
[ROW][C]108[/C][C]91[/C][C]93.4556419524094[/C][C]-2.45564195240935[/C][/ROW]
[ROW][C]109[/C][C]96[/C][C]99.5192883691687[/C][C]-3.51928836916871[/C][/ROW]
[ROW][C]110[/C][C]99[/C][C]102.847566041112[/C][C]-3.84756604111158[/C][/ROW]
[ROW][C]111[/C][C]99[/C][C]93.3339408465313[/C][C]5.66605915346872[/C][/ROW]
[ROW][C]112[/C][C]110[/C][C]107.333765803340[/C][C]2.66623419666018[/C][/ROW]
[ROW][C]113[/C][C]127[/C][C]122.983007323985[/C][C]4.01699267601525[/C][/ROW]
[ROW][C]114[/C][C]122[/C][C]120.235479683790[/C][C]1.76452031621037[/C][/ROW]
[ROW][C]115[/C][C]124[/C][C]120.227958255215[/C][C]3.77204174478526[/C][/ROW]
[ROW][C]116[/C][C]114[/C][C]111.787397013805[/C][C]2.21260298619532[/C][/ROW]
[ROW][C]117[/C][C]129[/C][C]123.525939196962[/C][C]5.4740608030381[/C][/ROW]
[ROW][C]118[/C][C]113[/C][C]105.982383077218[/C][C]7.01761692278161[/C][/ROW]
[ROW][C]119[/C][C]115[/C][C]107.46198863127[/C][C]7.53801136872994[/C][/ROW]
[ROW][C]120[/C][C]94[/C][C]89.1811194332829[/C][C]4.81888056671713[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77902&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77902&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
13302309.004540598291-7.0045405982907
14296301.106960022291-5.10696002229099
15282285.951437155768-3.95143715576808
16282285.270933627342-3.27093362734234
17298300.806818198952-2.8068181989525
18300302.894906811642-2.89490681164233
19289285.9128384160143.08716158398636
20275274.9188071161630.0811928838371045
21270275.018549047721-5.01854904772102
22269273.372676332563-4.37267633256295
23268272.874582728492-4.87458272849193
24260273.222665189107-13.2226651891068
25271271.748177474684-0.748177474684326
26269265.9442319360183.0557680639825
27260252.8631944376647.13680556233624
28262254.7210366621477.2789633378535
29285272.69387918959912.3061208104014
30286278.0514942035787.94850579642156
31272268.3375637384363.66243626156364
32248255.353681162444-7.35368116244422
33240249.944712765849-9.94471276584943
34234247.740976903980-13.7409769039805
35231244.651822838094-13.6518228380943
36222236.254309606184-14.2543096061836
37233243.977647140466-10.9776471404656
38236238.405817457709-2.40581745770933
39226226.720495262383-0.720495262382599
40232226.2346803297965.76531967020384
41248247.0413885817990.958611418200803
42253245.5503840413727.4496159586279
43233231.4084476211581.59155237884170
44216208.3586034862187.64139651378201
45209203.4628068948095.53719310519057
46202201.2093345378470.790665462152901
47204201.1533262554422.84667374455813
48193195.968950264157-2.96895026415689
49201208.993705898151-7.99370589815149
50201211.096213732631-10.0962137326314
51188199.234833252381-11.2348332523807
52198201.520544447966-3.52054444796642
53220216.3824123438753.61758765612541
54225220.4325982639534.56740173604695
55215200.92156833976314.0784316602368
56198185.38727200900212.6127279909977
57195180.08005112464014.9199488753598
58183176.4809921628696.51900783713114
59180179.6948226713340.305177328666275
60170169.7768597580790.223140241920760
61175179.996386554005-4.99638655400531
62180181.586648435665-1.58664843566476
63161171.321587716897-10.3215877168967
64174180.473773025011-6.4737730250111
65195200.854183947808-5.85418394780822
66198203.995858860635-5.99585886063471
67188189.840015066262-1.84001506626228
68173169.6342646986433.36573530135686
69162163.900124932070-1.90012493206956
70149149.556234523558-0.556234523558231
71140145.741478739935-5.74147873993545
72129133.703945470192-4.70394547019154
73132137.948743610793-5.9487436107934
74133141.158469882299-8.1584698822985
75116121.680284717314-5.68028471731375
76128133.984030051951-5.98403005195141
77148154.094374174646-6.09437417464602
78154156.207351028044-2.20735102804406
79152145.3281064449016.67189355509936
80141130.40217547636610.5978245236344
81136121.61437017680314.385629823197
82119111.6475113093167.35248869068398
83114105.4153788518558.58462114814515
8410097.47763597412692.52236402587312
85108102.6129357108985.3870642891025
86115107.05768542727.94231457279994
8710193.80230452701827.19769547298182
88116109.6768286395996.32317136040099
89131133.600491189554-2.60049118955439
90133140.782810590659-7.78281059065907
91135136.790701459255-1.79070145925476
92124124.101886486768-0.101886486767697
93131116.76577636452314.2342236354766
94113102.10222723183710.8977727681633
9511898.501467785715619.4985322142844
969989.3005600335689.69943996643195
9710799.45518753260347.5448124673966
98112107.6173027541574.38269724584303
9910694.187943083878611.8120569161214
100121111.6564376314969.34356236850446
101138130.5903016315087.40969836849243
102134137.410823895043-3.41082389504265
103132140.62988128064-8.62988128064012
104121129.217401209149-8.21740120914924
105132132.616022763925-0.616022763924605
106113113.146624311751-0.146624311750983
107112114.704093756428-2.70409375642821
1089193.4556419524094-2.45564195240935
1099699.5192883691687-3.51928836916871
11099102.847566041112-3.84756604111158
1119993.33394084653135.66605915346872
112110107.3337658033402.66623419666018
113127122.9830073239854.01699267601525
114122120.2354796837901.76452031621037
115124120.2279582552153.77204174478526
116114111.7873970138052.21260298619532
117129123.5259391969625.4740608030381
118113105.9823830772187.01761692278161
119115107.461988631277.53801136872994
1209489.18111943328294.81888056671713







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12196.665925619148682.533244564833110.798606673464
122101.23012532469386.7080403614705115.752210287916
123100.78053845761685.8215762634004115.739500651832
124111.88766715348596.4443874366208127.330946870348
125128.652407983997112.677822323689144.626993644306
126123.839342757327107.287259334772140.391426179883
127125.556051025776108.381344503599142.730757547952
128115.54763506479097.7064455756029133.388824553977
129129.786776921974111.236645377715148.336908466233
130112.59199602044293.2919447830204131.892047257864
131113.16001082332693.0705794066338133.249442240019
13291.190426236743370.2736714495036112.107181023983

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 96.6659256191486 & 82.533244564833 & 110.798606673464 \tabularnewline
122 & 101.230125324693 & 86.7080403614705 & 115.752210287916 \tabularnewline
123 & 100.780538457616 & 85.8215762634004 & 115.739500651832 \tabularnewline
124 & 111.887667153485 & 96.4443874366208 & 127.330946870348 \tabularnewline
125 & 128.652407983997 & 112.677822323689 & 144.626993644306 \tabularnewline
126 & 123.839342757327 & 107.287259334772 & 140.391426179883 \tabularnewline
127 & 125.556051025776 & 108.381344503599 & 142.730757547952 \tabularnewline
128 & 115.547635064790 & 97.7064455756029 & 133.388824553977 \tabularnewline
129 & 129.786776921974 & 111.236645377715 & 148.336908466233 \tabularnewline
130 & 112.591996020442 & 93.2919447830204 & 131.892047257864 \tabularnewline
131 & 113.160010823326 & 93.0705794066338 & 133.249442240019 \tabularnewline
132 & 91.1904262367433 & 70.2736714495036 & 112.107181023983 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77902&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]121[/C][C]96.6659256191486[/C][C]82.533244564833[/C][C]110.798606673464[/C][/ROW]
[ROW][C]122[/C][C]101.230125324693[/C][C]86.7080403614705[/C][C]115.752210287916[/C][/ROW]
[ROW][C]123[/C][C]100.780538457616[/C][C]85.8215762634004[/C][C]115.739500651832[/C][/ROW]
[ROW][C]124[/C][C]111.887667153485[/C][C]96.4443874366208[/C][C]127.330946870348[/C][/ROW]
[ROW][C]125[/C][C]128.652407983997[/C][C]112.677822323689[/C][C]144.626993644306[/C][/ROW]
[ROW][C]126[/C][C]123.839342757327[/C][C]107.287259334772[/C][C]140.391426179883[/C][/ROW]
[ROW][C]127[/C][C]125.556051025776[/C][C]108.381344503599[/C][C]142.730757547952[/C][/ROW]
[ROW][C]128[/C][C]115.547635064790[/C][C]97.7064455756029[/C][C]133.388824553977[/C][/ROW]
[ROW][C]129[/C][C]129.786776921974[/C][C]111.236645377715[/C][C]148.336908466233[/C][/ROW]
[ROW][C]130[/C][C]112.591996020442[/C][C]93.2919447830204[/C][C]131.892047257864[/C][/ROW]
[ROW][C]131[/C][C]113.160010823326[/C][C]93.0705794066338[/C][C]133.249442240019[/C][/ROW]
[ROW][C]132[/C][C]91.1904262367433[/C][C]70.2736714495036[/C][C]112.107181023983[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77902&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77902&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
12196.665925619148682.533244564833110.798606673464
122101.23012532469386.7080403614705115.752210287916
123100.78053845761685.8215762634004115.739500651832
124111.88766715348596.4443874366208127.330946870348
125128.652407983997112.677822323689144.626993644306
126123.839342757327107.287259334772140.391426179883
127125.556051025776108.381344503599142.730757547952
128115.54763506479097.7064455756029133.388824553977
129129.786776921974111.236645377715148.336908466233
130112.59199602044293.2919447830204131.892047257864
131113.16001082332693.0705794066338133.249442240019
13291.190426236743370.2736714495036112.107181023983



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')