Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 19 Aug 2010 10:19:50 +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/19/t1282213237myxuen5b94f700a.htm/, Retrieved Fri, 03 May 2024 06:59:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79265, Retrieved Fri, 03 May 2024 06:59:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsQuaglia Laura
Estimated Impact168
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [] [Tijdreeks A - Sta...] [1970-01-01 00:00:00] [af95ebf906227b9d031fe2c98e4f0d3b]
- RMPD    [Exponential Smoothing] [Tijdreeks A - Sta...] [2010-08-19 10:19:50] [f9e29edf9cfe01f572cce0cb5a360ea2] [Current]
Feedback Forum

Post a new message
Dataseries X:
239
238
237
235
255
254
239
229
230
230
231
233
239
236
231
235
253
257
236
226
226
221
217
219
225
226
225
229
242
252
233
232
225
218
209
211
220
225
215
222
238
246
226
230
222
214
208
203
208
212
199
200
223
225
203
207
195
198
193
189
184
188
180
186
215
212
191
190
180
190
189
181
174
179
165
185
211
209
183
178
170
182
195
188
175
176
162
193
211
207
179
176
167
175
190
173
159
159
147
181
196
199
171
170
156
164
178
155
138
142
113
148
156
158
141
139
119
120
125
102




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=79265&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=79265&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79265&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
alpha0.318694192704481
beta0.0303866885745872
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.318694192704481 \tabularnewline
beta & 0.0303866885745872 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79265&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]0.318694192704481[/C][/ROW]
[ROW][C]beta[/C][C]0.0303866885745872[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79265&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79265&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
alpha0.318694192704481
beta0.0303866885745872
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13239239.501602564103-0.501602564102598
14236236.306292784362-0.306292784362086
15231231.211927605806-0.211927605805784
16235235.395583741748-0.395583741747743
17253253.933545543219-0.933545543218514
18257258.499354863838-1.49935486383822
19236235.7869908622270.213009137773327
20226225.6224101172480.377589882751977
21226226.763936903452-0.763936903452105
22221226.450934387029-5.45093438702912
23217225.424759142588-8.42475914258767
24219224.244257335430-5.24425733542958
25225227.726499201986-2.72649920198592
26226223.7095428062512.29045719374929
27225219.2865347301575.71346526984334
28229225.0703314606223.92966853937796
29242244.498973841876-2.49897384187616
30252248.0440056704873.95599432951349
31233228.1533078416714.84669215832898
32232219.53889218057712.4611078194228
33225223.8319620561121.16803794388841
34218221.038424386372-3.03842438637179
35209218.875415174319-9.87541517431916
36211219.505841004978-8.5058410049777
37220223.738761898307-3.73876189830708
38225222.8822455368372.11775446316290
39215220.799601670005-5.79960167000496
40222221.6507347962600.349265203740174
41238235.4755742358032.52442576419671
42246244.9851107529881.01488924701195
43226224.7012246814041.29877531859557
44230220.0467831564439.95321684355702
45222215.7252111040726.27478889592774
46214211.6213746316672.37862536833345
47208206.5072217701451.49277822985491
48203211.784369516200-8.78436951619969
49208219.264312243418-11.2643122434177
50212220.014595981365-8.01459598136529
51199209.225638539535-10.2256385395351
52200212.72956449837-12.7295644983699
53223223.615636569291-0.615636569291297
54225230.813019087993-5.81301908799298
55203208.197431256241-5.19743125624066
56207206.9569977745250.0430022254745381
57195196.462982511168-1.46298251116784
58198186.65577029627611.3442297037240
59193183.2992800385999.70071996140123
60189183.7737662845495.22623371545146
61184193.748282632906-9.74828263290559
62188196.929523205335-8.92952320533482
63180184.067483864448-4.06748386444804
64186187.612570834901-1.61257083490079
65215210.1870434964494.8129565035513
66212215.518240859261-3.51824085926091
67191194.020372509962-3.02037250996233
68190197.032158964540-7.03215896454046
69180183.176844669691-3.17684466969106
70190181.4520153480368.5479846519637
71189175.96051904400813.0394809559917
72181174.3587620762996.64123792370097
73174174.503916596795-0.503916596795193
74179181.200540997147-2.20054099714739
75165173.872121226677-8.87212122667705
76185177.5886126525987.41138734740161
77211207.5341740132653.46582598673487
78209206.8643664047832.13563359521675
79183187.666718920437-4.66671892043723
80178187.563790918699-9.56379091869866
81170175.647011754299-5.64701175429934
82182181.2179310992550.782068900745287
83195176.33114172146818.6688582785322
84188172.23836637683315.7616336231667
85175170.5845171392834.41548286071702
86176177.903059653120-1.90305965311964
87162166.33699406429-4.33699406429005
88193182.84970654270310.1502934572968
89211211.263384649236-0.263384649236059
90207208.746094704912-1.74609470491191
91179183.886553025488-4.8865530254879
92176180.584705037044-4.58470503704382
93167173.179017248116-6.17901724811594
94175183.211168773218-8.21116877321765
95190187.8081784438662.1918215561341
96173176.487511702037-3.48751170203701
97159160.786416888864-1.78641688886418
98159161.581074342772-2.58107434277193
99147147.891593907455-0.891593907455132
100181175.1568921403155.84310785968518
101196194.8455684043451.15443159565464
102199191.526252075037.47374792496998
103171167.3109965110653.68900348893504
104170166.8764138874433.12358611255709
105156160.844381635660-4.84438163566017
106164169.933563917539-5.93356391753915
107178182.382313991437-4.38231399143731
108155165.071744605154-10.0717446051538
109138148.342095570001-10.3420955700008
110142145.696686252288-3.69668625228783
111113132.619899034861-19.6198990348613
112148158.140799978916-10.1407999789158
113156169.022099499516-13.0220994995162
114158164.833929784938-6.83392978493771
115141132.6855134681538.31448653184705
116139132.5897981552976.41020184470264
117119121.458371208245-2.45837120824541
118120129.870803870640-9.8708038706402
119125141.388434474232-16.388434474232
120102115.525854545312-13.5258545453119

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 239 & 239.501602564103 & -0.501602564102598 \tabularnewline
14 & 236 & 236.306292784362 & -0.306292784362086 \tabularnewline
15 & 231 & 231.211927605806 & -0.211927605805784 \tabularnewline
16 & 235 & 235.395583741748 & -0.395583741747743 \tabularnewline
17 & 253 & 253.933545543219 & -0.933545543218514 \tabularnewline
18 & 257 & 258.499354863838 & -1.49935486383822 \tabularnewline
19 & 236 & 235.786990862227 & 0.213009137773327 \tabularnewline
20 & 226 & 225.622410117248 & 0.377589882751977 \tabularnewline
21 & 226 & 226.763936903452 & -0.763936903452105 \tabularnewline
22 & 221 & 226.450934387029 & -5.45093438702912 \tabularnewline
23 & 217 & 225.424759142588 & -8.42475914258767 \tabularnewline
24 & 219 & 224.244257335430 & -5.24425733542958 \tabularnewline
25 & 225 & 227.726499201986 & -2.72649920198592 \tabularnewline
26 & 226 & 223.709542806251 & 2.29045719374929 \tabularnewline
27 & 225 & 219.286534730157 & 5.71346526984334 \tabularnewline
28 & 229 & 225.070331460622 & 3.92966853937796 \tabularnewline
29 & 242 & 244.498973841876 & -2.49897384187616 \tabularnewline
30 & 252 & 248.044005670487 & 3.95599432951349 \tabularnewline
31 & 233 & 228.153307841671 & 4.84669215832898 \tabularnewline
32 & 232 & 219.538892180577 & 12.4611078194228 \tabularnewline
33 & 225 & 223.831962056112 & 1.16803794388841 \tabularnewline
34 & 218 & 221.038424386372 & -3.03842438637179 \tabularnewline
35 & 209 & 218.875415174319 & -9.87541517431916 \tabularnewline
36 & 211 & 219.505841004978 & -8.5058410049777 \tabularnewline
37 & 220 & 223.738761898307 & -3.73876189830708 \tabularnewline
38 & 225 & 222.882245536837 & 2.11775446316290 \tabularnewline
39 & 215 & 220.799601670005 & -5.79960167000496 \tabularnewline
40 & 222 & 221.650734796260 & 0.349265203740174 \tabularnewline
41 & 238 & 235.475574235803 & 2.52442576419671 \tabularnewline
42 & 246 & 244.985110752988 & 1.01488924701195 \tabularnewline
43 & 226 & 224.701224681404 & 1.29877531859557 \tabularnewline
44 & 230 & 220.046783156443 & 9.95321684355702 \tabularnewline
45 & 222 & 215.725211104072 & 6.27478889592774 \tabularnewline
46 & 214 & 211.621374631667 & 2.37862536833345 \tabularnewline
47 & 208 & 206.507221770145 & 1.49277822985491 \tabularnewline
48 & 203 & 211.784369516200 & -8.78436951619969 \tabularnewline
49 & 208 & 219.264312243418 & -11.2643122434177 \tabularnewline
50 & 212 & 220.014595981365 & -8.01459598136529 \tabularnewline
51 & 199 & 209.225638539535 & -10.2256385395351 \tabularnewline
52 & 200 & 212.72956449837 & -12.7295644983699 \tabularnewline
53 & 223 & 223.615636569291 & -0.615636569291297 \tabularnewline
54 & 225 & 230.813019087993 & -5.81301908799298 \tabularnewline
55 & 203 & 208.197431256241 & -5.19743125624066 \tabularnewline
56 & 207 & 206.956997774525 & 0.0430022254745381 \tabularnewline
57 & 195 & 196.462982511168 & -1.46298251116784 \tabularnewline
58 & 198 & 186.655770296276 & 11.3442297037240 \tabularnewline
59 & 193 & 183.299280038599 & 9.70071996140123 \tabularnewline
60 & 189 & 183.773766284549 & 5.22623371545146 \tabularnewline
61 & 184 & 193.748282632906 & -9.74828263290559 \tabularnewline
62 & 188 & 196.929523205335 & -8.92952320533482 \tabularnewline
63 & 180 & 184.067483864448 & -4.06748386444804 \tabularnewline
64 & 186 & 187.612570834901 & -1.61257083490079 \tabularnewline
65 & 215 & 210.187043496449 & 4.8129565035513 \tabularnewline
66 & 212 & 215.518240859261 & -3.51824085926091 \tabularnewline
67 & 191 & 194.020372509962 & -3.02037250996233 \tabularnewline
68 & 190 & 197.032158964540 & -7.03215896454046 \tabularnewline
69 & 180 & 183.176844669691 & -3.17684466969106 \tabularnewline
70 & 190 & 181.452015348036 & 8.5479846519637 \tabularnewline
71 & 189 & 175.960519044008 & 13.0394809559917 \tabularnewline
72 & 181 & 174.358762076299 & 6.64123792370097 \tabularnewline
73 & 174 & 174.503916596795 & -0.503916596795193 \tabularnewline
74 & 179 & 181.200540997147 & -2.20054099714739 \tabularnewline
75 & 165 & 173.872121226677 & -8.87212122667705 \tabularnewline
76 & 185 & 177.588612652598 & 7.41138734740161 \tabularnewline
77 & 211 & 207.534174013265 & 3.46582598673487 \tabularnewline
78 & 209 & 206.864366404783 & 2.13563359521675 \tabularnewline
79 & 183 & 187.666718920437 & -4.66671892043723 \tabularnewline
80 & 178 & 187.563790918699 & -9.56379091869866 \tabularnewline
81 & 170 & 175.647011754299 & -5.64701175429934 \tabularnewline
82 & 182 & 181.217931099255 & 0.782068900745287 \tabularnewline
83 & 195 & 176.331141721468 & 18.6688582785322 \tabularnewline
84 & 188 & 172.238366376833 & 15.7616336231667 \tabularnewline
85 & 175 & 170.584517139283 & 4.41548286071702 \tabularnewline
86 & 176 & 177.903059653120 & -1.90305965311964 \tabularnewline
87 & 162 & 166.33699406429 & -4.33699406429005 \tabularnewline
88 & 193 & 182.849706542703 & 10.1502934572968 \tabularnewline
89 & 211 & 211.263384649236 & -0.263384649236059 \tabularnewline
90 & 207 & 208.746094704912 & -1.74609470491191 \tabularnewline
91 & 179 & 183.886553025488 & -4.8865530254879 \tabularnewline
92 & 176 & 180.584705037044 & -4.58470503704382 \tabularnewline
93 & 167 & 173.179017248116 & -6.17901724811594 \tabularnewline
94 & 175 & 183.211168773218 & -8.21116877321765 \tabularnewline
95 & 190 & 187.808178443866 & 2.1918215561341 \tabularnewline
96 & 173 & 176.487511702037 & -3.48751170203701 \tabularnewline
97 & 159 & 160.786416888864 & -1.78641688886418 \tabularnewline
98 & 159 & 161.581074342772 & -2.58107434277193 \tabularnewline
99 & 147 & 147.891593907455 & -0.891593907455132 \tabularnewline
100 & 181 & 175.156892140315 & 5.84310785968518 \tabularnewline
101 & 196 & 194.845568404345 & 1.15443159565464 \tabularnewline
102 & 199 & 191.52625207503 & 7.47374792496998 \tabularnewline
103 & 171 & 167.310996511065 & 3.68900348893504 \tabularnewline
104 & 170 & 166.876413887443 & 3.12358611255709 \tabularnewline
105 & 156 & 160.844381635660 & -4.84438163566017 \tabularnewline
106 & 164 & 169.933563917539 & -5.93356391753915 \tabularnewline
107 & 178 & 182.382313991437 & -4.38231399143731 \tabularnewline
108 & 155 & 165.071744605154 & -10.0717446051538 \tabularnewline
109 & 138 & 148.342095570001 & -10.3420955700008 \tabularnewline
110 & 142 & 145.696686252288 & -3.69668625228783 \tabularnewline
111 & 113 & 132.619899034861 & -19.6198990348613 \tabularnewline
112 & 148 & 158.140799978916 & -10.1407999789158 \tabularnewline
113 & 156 & 169.022099499516 & -13.0220994995162 \tabularnewline
114 & 158 & 164.833929784938 & -6.83392978493771 \tabularnewline
115 & 141 & 132.685513468153 & 8.31448653184705 \tabularnewline
116 & 139 & 132.589798155297 & 6.41020184470264 \tabularnewline
117 & 119 & 121.458371208245 & -2.45837120824541 \tabularnewline
118 & 120 & 129.870803870640 & -9.8708038706402 \tabularnewline
119 & 125 & 141.388434474232 & -16.388434474232 \tabularnewline
120 & 102 & 115.525854545312 & -13.5258545453119 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79265&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]239[/C][C]239.501602564103[/C][C]-0.501602564102598[/C][/ROW]
[ROW][C]14[/C][C]236[/C][C]236.306292784362[/C][C]-0.306292784362086[/C][/ROW]
[ROW][C]15[/C][C]231[/C][C]231.211927605806[/C][C]-0.211927605805784[/C][/ROW]
[ROW][C]16[/C][C]235[/C][C]235.395583741748[/C][C]-0.395583741747743[/C][/ROW]
[ROW][C]17[/C][C]253[/C][C]253.933545543219[/C][C]-0.933545543218514[/C][/ROW]
[ROW][C]18[/C][C]257[/C][C]258.499354863838[/C][C]-1.49935486383822[/C][/ROW]
[ROW][C]19[/C][C]236[/C][C]235.786990862227[/C][C]0.213009137773327[/C][/ROW]
[ROW][C]20[/C][C]226[/C][C]225.622410117248[/C][C]0.377589882751977[/C][/ROW]
[ROW][C]21[/C][C]226[/C][C]226.763936903452[/C][C]-0.763936903452105[/C][/ROW]
[ROW][C]22[/C][C]221[/C][C]226.450934387029[/C][C]-5.45093438702912[/C][/ROW]
[ROW][C]23[/C][C]217[/C][C]225.424759142588[/C][C]-8.42475914258767[/C][/ROW]
[ROW][C]24[/C][C]219[/C][C]224.244257335430[/C][C]-5.24425733542958[/C][/ROW]
[ROW][C]25[/C][C]225[/C][C]227.726499201986[/C][C]-2.72649920198592[/C][/ROW]
[ROW][C]26[/C][C]226[/C][C]223.709542806251[/C][C]2.29045719374929[/C][/ROW]
[ROW][C]27[/C][C]225[/C][C]219.286534730157[/C][C]5.71346526984334[/C][/ROW]
[ROW][C]28[/C][C]229[/C][C]225.070331460622[/C][C]3.92966853937796[/C][/ROW]
[ROW][C]29[/C][C]242[/C][C]244.498973841876[/C][C]-2.49897384187616[/C][/ROW]
[ROW][C]30[/C][C]252[/C][C]248.044005670487[/C][C]3.95599432951349[/C][/ROW]
[ROW][C]31[/C][C]233[/C][C]228.153307841671[/C][C]4.84669215832898[/C][/ROW]
[ROW][C]32[/C][C]232[/C][C]219.538892180577[/C][C]12.4611078194228[/C][/ROW]
[ROW][C]33[/C][C]225[/C][C]223.831962056112[/C][C]1.16803794388841[/C][/ROW]
[ROW][C]34[/C][C]218[/C][C]221.038424386372[/C][C]-3.03842438637179[/C][/ROW]
[ROW][C]35[/C][C]209[/C][C]218.875415174319[/C][C]-9.87541517431916[/C][/ROW]
[ROW][C]36[/C][C]211[/C][C]219.505841004978[/C][C]-8.5058410049777[/C][/ROW]
[ROW][C]37[/C][C]220[/C][C]223.738761898307[/C][C]-3.73876189830708[/C][/ROW]
[ROW][C]38[/C][C]225[/C][C]222.882245536837[/C][C]2.11775446316290[/C][/ROW]
[ROW][C]39[/C][C]215[/C][C]220.799601670005[/C][C]-5.79960167000496[/C][/ROW]
[ROW][C]40[/C][C]222[/C][C]221.650734796260[/C][C]0.349265203740174[/C][/ROW]
[ROW][C]41[/C][C]238[/C][C]235.475574235803[/C][C]2.52442576419671[/C][/ROW]
[ROW][C]42[/C][C]246[/C][C]244.985110752988[/C][C]1.01488924701195[/C][/ROW]
[ROW][C]43[/C][C]226[/C][C]224.701224681404[/C][C]1.29877531859557[/C][/ROW]
[ROW][C]44[/C][C]230[/C][C]220.046783156443[/C][C]9.95321684355702[/C][/ROW]
[ROW][C]45[/C][C]222[/C][C]215.725211104072[/C][C]6.27478889592774[/C][/ROW]
[ROW][C]46[/C][C]214[/C][C]211.621374631667[/C][C]2.37862536833345[/C][/ROW]
[ROW][C]47[/C][C]208[/C][C]206.507221770145[/C][C]1.49277822985491[/C][/ROW]
[ROW][C]48[/C][C]203[/C][C]211.784369516200[/C][C]-8.78436951619969[/C][/ROW]
[ROW][C]49[/C][C]208[/C][C]219.264312243418[/C][C]-11.2643122434177[/C][/ROW]
[ROW][C]50[/C][C]212[/C][C]220.014595981365[/C][C]-8.01459598136529[/C][/ROW]
[ROW][C]51[/C][C]199[/C][C]209.225638539535[/C][C]-10.2256385395351[/C][/ROW]
[ROW][C]52[/C][C]200[/C][C]212.72956449837[/C][C]-12.7295644983699[/C][/ROW]
[ROW][C]53[/C][C]223[/C][C]223.615636569291[/C][C]-0.615636569291297[/C][/ROW]
[ROW][C]54[/C][C]225[/C][C]230.813019087993[/C][C]-5.81301908799298[/C][/ROW]
[ROW][C]55[/C][C]203[/C][C]208.197431256241[/C][C]-5.19743125624066[/C][/ROW]
[ROW][C]56[/C][C]207[/C][C]206.956997774525[/C][C]0.0430022254745381[/C][/ROW]
[ROW][C]57[/C][C]195[/C][C]196.462982511168[/C][C]-1.46298251116784[/C][/ROW]
[ROW][C]58[/C][C]198[/C][C]186.655770296276[/C][C]11.3442297037240[/C][/ROW]
[ROW][C]59[/C][C]193[/C][C]183.299280038599[/C][C]9.70071996140123[/C][/ROW]
[ROW][C]60[/C][C]189[/C][C]183.773766284549[/C][C]5.22623371545146[/C][/ROW]
[ROW][C]61[/C][C]184[/C][C]193.748282632906[/C][C]-9.74828263290559[/C][/ROW]
[ROW][C]62[/C][C]188[/C][C]196.929523205335[/C][C]-8.92952320533482[/C][/ROW]
[ROW][C]63[/C][C]180[/C][C]184.067483864448[/C][C]-4.06748386444804[/C][/ROW]
[ROW][C]64[/C][C]186[/C][C]187.612570834901[/C][C]-1.61257083490079[/C][/ROW]
[ROW][C]65[/C][C]215[/C][C]210.187043496449[/C][C]4.8129565035513[/C][/ROW]
[ROW][C]66[/C][C]212[/C][C]215.518240859261[/C][C]-3.51824085926091[/C][/ROW]
[ROW][C]67[/C][C]191[/C][C]194.020372509962[/C][C]-3.02037250996233[/C][/ROW]
[ROW][C]68[/C][C]190[/C][C]197.032158964540[/C][C]-7.03215896454046[/C][/ROW]
[ROW][C]69[/C][C]180[/C][C]183.176844669691[/C][C]-3.17684466969106[/C][/ROW]
[ROW][C]70[/C][C]190[/C][C]181.452015348036[/C][C]8.5479846519637[/C][/ROW]
[ROW][C]71[/C][C]189[/C][C]175.960519044008[/C][C]13.0394809559917[/C][/ROW]
[ROW][C]72[/C][C]181[/C][C]174.358762076299[/C][C]6.64123792370097[/C][/ROW]
[ROW][C]73[/C][C]174[/C][C]174.503916596795[/C][C]-0.503916596795193[/C][/ROW]
[ROW][C]74[/C][C]179[/C][C]181.200540997147[/C][C]-2.20054099714739[/C][/ROW]
[ROW][C]75[/C][C]165[/C][C]173.872121226677[/C][C]-8.87212122667705[/C][/ROW]
[ROW][C]76[/C][C]185[/C][C]177.588612652598[/C][C]7.41138734740161[/C][/ROW]
[ROW][C]77[/C][C]211[/C][C]207.534174013265[/C][C]3.46582598673487[/C][/ROW]
[ROW][C]78[/C][C]209[/C][C]206.864366404783[/C][C]2.13563359521675[/C][/ROW]
[ROW][C]79[/C][C]183[/C][C]187.666718920437[/C][C]-4.66671892043723[/C][/ROW]
[ROW][C]80[/C][C]178[/C][C]187.563790918699[/C][C]-9.56379091869866[/C][/ROW]
[ROW][C]81[/C][C]170[/C][C]175.647011754299[/C][C]-5.64701175429934[/C][/ROW]
[ROW][C]82[/C][C]182[/C][C]181.217931099255[/C][C]0.782068900745287[/C][/ROW]
[ROW][C]83[/C][C]195[/C][C]176.331141721468[/C][C]18.6688582785322[/C][/ROW]
[ROW][C]84[/C][C]188[/C][C]172.238366376833[/C][C]15.7616336231667[/C][/ROW]
[ROW][C]85[/C][C]175[/C][C]170.584517139283[/C][C]4.41548286071702[/C][/ROW]
[ROW][C]86[/C][C]176[/C][C]177.903059653120[/C][C]-1.90305965311964[/C][/ROW]
[ROW][C]87[/C][C]162[/C][C]166.33699406429[/C][C]-4.33699406429005[/C][/ROW]
[ROW][C]88[/C][C]193[/C][C]182.849706542703[/C][C]10.1502934572968[/C][/ROW]
[ROW][C]89[/C][C]211[/C][C]211.263384649236[/C][C]-0.263384649236059[/C][/ROW]
[ROW][C]90[/C][C]207[/C][C]208.746094704912[/C][C]-1.74609470491191[/C][/ROW]
[ROW][C]91[/C][C]179[/C][C]183.886553025488[/C][C]-4.8865530254879[/C][/ROW]
[ROW][C]92[/C][C]176[/C][C]180.584705037044[/C][C]-4.58470503704382[/C][/ROW]
[ROW][C]93[/C][C]167[/C][C]173.179017248116[/C][C]-6.17901724811594[/C][/ROW]
[ROW][C]94[/C][C]175[/C][C]183.211168773218[/C][C]-8.21116877321765[/C][/ROW]
[ROW][C]95[/C][C]190[/C][C]187.808178443866[/C][C]2.1918215561341[/C][/ROW]
[ROW][C]96[/C][C]173[/C][C]176.487511702037[/C][C]-3.48751170203701[/C][/ROW]
[ROW][C]97[/C][C]159[/C][C]160.786416888864[/C][C]-1.78641688886418[/C][/ROW]
[ROW][C]98[/C][C]159[/C][C]161.581074342772[/C][C]-2.58107434277193[/C][/ROW]
[ROW][C]99[/C][C]147[/C][C]147.891593907455[/C][C]-0.891593907455132[/C][/ROW]
[ROW][C]100[/C][C]181[/C][C]175.156892140315[/C][C]5.84310785968518[/C][/ROW]
[ROW][C]101[/C][C]196[/C][C]194.845568404345[/C][C]1.15443159565464[/C][/ROW]
[ROW][C]102[/C][C]199[/C][C]191.52625207503[/C][C]7.47374792496998[/C][/ROW]
[ROW][C]103[/C][C]171[/C][C]167.310996511065[/C][C]3.68900348893504[/C][/ROW]
[ROW][C]104[/C][C]170[/C][C]166.876413887443[/C][C]3.12358611255709[/C][/ROW]
[ROW][C]105[/C][C]156[/C][C]160.844381635660[/C][C]-4.84438163566017[/C][/ROW]
[ROW][C]106[/C][C]164[/C][C]169.933563917539[/C][C]-5.93356391753915[/C][/ROW]
[ROW][C]107[/C][C]178[/C][C]182.382313991437[/C][C]-4.38231399143731[/C][/ROW]
[ROW][C]108[/C][C]155[/C][C]165.071744605154[/C][C]-10.0717446051538[/C][/ROW]
[ROW][C]109[/C][C]138[/C][C]148.342095570001[/C][C]-10.3420955700008[/C][/ROW]
[ROW][C]110[/C][C]142[/C][C]145.696686252288[/C][C]-3.69668625228783[/C][/ROW]
[ROW][C]111[/C][C]113[/C][C]132.619899034861[/C][C]-19.6198990348613[/C][/ROW]
[ROW][C]112[/C][C]148[/C][C]158.140799978916[/C][C]-10.1407999789158[/C][/ROW]
[ROW][C]113[/C][C]156[/C][C]169.022099499516[/C][C]-13.0220994995162[/C][/ROW]
[ROW][C]114[/C][C]158[/C][C]164.833929784938[/C][C]-6.83392978493771[/C][/ROW]
[ROW][C]115[/C][C]141[/C][C]132.685513468153[/C][C]8.31448653184705[/C][/ROW]
[ROW][C]116[/C][C]139[/C][C]132.589798155297[/C][C]6.41020184470264[/C][/ROW]
[ROW][C]117[/C][C]119[/C][C]121.458371208245[/C][C]-2.45837120824541[/C][/ROW]
[ROW][C]118[/C][C]120[/C][C]129.870803870640[/C][C]-9.8708038706402[/C][/ROW]
[ROW][C]119[/C][C]125[/C][C]141.388434474232[/C][C]-16.388434474232[/C][/ROW]
[ROW][C]120[/C][C]102[/C][C]115.525854545312[/C][C]-13.5258545453119[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79265&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79265&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
13239239.501602564103-0.501602564102598
14236236.306292784362-0.306292784362086
15231231.211927605806-0.211927605805784
16235235.395583741748-0.395583741747743
17253253.933545543219-0.933545543218514
18257258.499354863838-1.49935486383822
19236235.7869908622270.213009137773327
20226225.6224101172480.377589882751977
21226226.763936903452-0.763936903452105
22221226.450934387029-5.45093438702912
23217225.424759142588-8.42475914258767
24219224.244257335430-5.24425733542958
25225227.726499201986-2.72649920198592
26226223.7095428062512.29045719374929
27225219.2865347301575.71346526984334
28229225.0703314606223.92966853937796
29242244.498973841876-2.49897384187616
30252248.0440056704873.95599432951349
31233228.1533078416714.84669215832898
32232219.53889218057712.4611078194228
33225223.8319620561121.16803794388841
34218221.038424386372-3.03842438637179
35209218.875415174319-9.87541517431916
36211219.505841004978-8.5058410049777
37220223.738761898307-3.73876189830708
38225222.8822455368372.11775446316290
39215220.799601670005-5.79960167000496
40222221.6507347962600.349265203740174
41238235.4755742358032.52442576419671
42246244.9851107529881.01488924701195
43226224.7012246814041.29877531859557
44230220.0467831564439.95321684355702
45222215.7252111040726.27478889592774
46214211.6213746316672.37862536833345
47208206.5072217701451.49277822985491
48203211.784369516200-8.78436951619969
49208219.264312243418-11.2643122434177
50212220.014595981365-8.01459598136529
51199209.225638539535-10.2256385395351
52200212.72956449837-12.7295644983699
53223223.615636569291-0.615636569291297
54225230.813019087993-5.81301908799298
55203208.197431256241-5.19743125624066
56207206.9569977745250.0430022254745381
57195196.462982511168-1.46298251116784
58198186.65577029627611.3442297037240
59193183.2992800385999.70071996140123
60189183.7737662845495.22623371545146
61184193.748282632906-9.74828263290559
62188196.929523205335-8.92952320533482
63180184.067483864448-4.06748386444804
64186187.612570834901-1.61257083490079
65215210.1870434964494.8129565035513
66212215.518240859261-3.51824085926091
67191194.020372509962-3.02037250996233
68190197.032158964540-7.03215896454046
69180183.176844669691-3.17684466969106
70190181.4520153480368.5479846519637
71189175.96051904400813.0394809559917
72181174.3587620762996.64123792370097
73174174.503916596795-0.503916596795193
74179181.200540997147-2.20054099714739
75165173.872121226677-8.87212122667705
76185177.5886126525987.41138734740161
77211207.5341740132653.46582598673487
78209206.8643664047832.13563359521675
79183187.666718920437-4.66671892043723
80178187.563790918699-9.56379091869866
81170175.647011754299-5.64701175429934
82182181.2179310992550.782068900745287
83195176.33114172146818.6688582785322
84188172.23836637683315.7616336231667
85175170.5845171392834.41548286071702
86176177.903059653120-1.90305965311964
87162166.33699406429-4.33699406429005
88193182.84970654270310.1502934572968
89211211.263384649236-0.263384649236059
90207208.746094704912-1.74609470491191
91179183.886553025488-4.8865530254879
92176180.584705037044-4.58470503704382
93167173.179017248116-6.17901724811594
94175183.211168773218-8.21116877321765
95190187.8081784438662.1918215561341
96173176.487511702037-3.48751170203701
97159160.786416888864-1.78641688886418
98159161.581074342772-2.58107434277193
99147147.891593907455-0.891593907455132
100181175.1568921403155.84310785968518
101196194.8455684043451.15443159565464
102199191.526252075037.47374792496998
103171167.3109965110653.68900348893504
104170166.8764138874433.12358611255709
105156160.844381635660-4.84438163566017
106164169.933563917539-5.93356391753915
107178182.382313991437-4.38231399143731
108155165.071744605154-10.0717446051538
109138148.342095570001-10.3420955700008
110142145.696686252288-3.69668625228783
111113132.619899034861-19.6198990348613
112148158.140799978916-10.1407999789158
113156169.022099499516-13.0220994995162
114158164.833929784938-6.83392978493771
115141132.6855134681538.31448653184705
116139132.5897981552976.41020184470264
117119121.458371208245-2.45837120824541
118120129.870803870640-9.8708038706402
119125141.388434474232-16.388434474232
120102115.525854545312-13.5258545453119







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12196.628271686382283.194194931532110.062348441232
122101.02360025098386.883749267713115.163451234253
12377.529363194433462.678063303448292.3806630854186
124115.20419261936699.635459970831130.772925267901
125126.895479596409110.603081998895143.187877193922
126130.740739630246113.718245447803147.763233812690
127110.82446754942193.0652853445223128.583649754320
128106.43456194335587.9319728591344124.937151027575
12986.80894227997167.556126666479106.061757893463
13090.569428877099770.559488311789110.579369442410
131100.50263596640779.7286115580843121.27666037473
13281.682262058377660.1371497292265103.227374387529

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 96.6282716863822 & 83.194194931532 & 110.062348441232 \tabularnewline
122 & 101.023600250983 & 86.883749267713 & 115.163451234253 \tabularnewline
123 & 77.5293631944334 & 62.6780633034482 & 92.3806630854186 \tabularnewline
124 & 115.204192619366 & 99.635459970831 & 130.772925267901 \tabularnewline
125 & 126.895479596409 & 110.603081998895 & 143.187877193922 \tabularnewline
126 & 130.740739630246 & 113.718245447803 & 147.763233812690 \tabularnewline
127 & 110.824467549421 & 93.0652853445223 & 128.583649754320 \tabularnewline
128 & 106.434561943355 & 87.9319728591344 & 124.937151027575 \tabularnewline
129 & 86.808942279971 & 67.556126666479 & 106.061757893463 \tabularnewline
130 & 90.5694288770997 & 70.559488311789 & 110.579369442410 \tabularnewline
131 & 100.502635966407 & 79.7286115580843 & 121.27666037473 \tabularnewline
132 & 81.6822620583776 & 60.1371497292265 & 103.227374387529 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79265&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]96.6282716863822[/C][C]83.194194931532[/C][C]110.062348441232[/C][/ROW]
[ROW][C]122[/C][C]101.023600250983[/C][C]86.883749267713[/C][C]115.163451234253[/C][/ROW]
[ROW][C]123[/C][C]77.5293631944334[/C][C]62.6780633034482[/C][C]92.3806630854186[/C][/ROW]
[ROW][C]124[/C][C]115.204192619366[/C][C]99.635459970831[/C][C]130.772925267901[/C][/ROW]
[ROW][C]125[/C][C]126.895479596409[/C][C]110.603081998895[/C][C]143.187877193922[/C][/ROW]
[ROW][C]126[/C][C]130.740739630246[/C][C]113.718245447803[/C][C]147.763233812690[/C][/ROW]
[ROW][C]127[/C][C]110.824467549421[/C][C]93.0652853445223[/C][C]128.583649754320[/C][/ROW]
[ROW][C]128[/C][C]106.434561943355[/C][C]87.9319728591344[/C][C]124.937151027575[/C][/ROW]
[ROW][C]129[/C][C]86.808942279971[/C][C]67.556126666479[/C][C]106.061757893463[/C][/ROW]
[ROW][C]130[/C][C]90.5694288770997[/C][C]70.559488311789[/C][C]110.579369442410[/C][/ROW]
[ROW][C]131[/C][C]100.502635966407[/C][C]79.7286115580843[/C][C]121.27666037473[/C][/ROW]
[ROW][C]132[/C][C]81.6822620583776[/C][C]60.1371497292265[/C][C]103.227374387529[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79265&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79265&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
12196.628271686382283.194194931532110.062348441232
122101.02360025098386.883749267713115.163451234253
12377.529363194433462.678063303448292.3806630854186
124115.20419261936699.635459970831130.772925267901
125126.895479596409110.603081998895143.187877193922
126130.740739630246113.718245447803147.763233812690
127110.82446754942193.0652853445223128.583649754320
128106.43456194335587.9319728591344124.937151027575
12986.80894227997167.556126666479106.061757893463
13090.569428877099770.559488311789110.579369442410
131100.50263596640779.7286115580843121.27666037473
13281.682262058377660.1371497292265103.227374387529



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')