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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 computationThu, 19 Aug 2010 20:46:50 +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/t1282250779pa2mtv2cq1hsyh3.htm/, Retrieved Fri, 03 May 2024 13:22:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79383, Retrieved Fri, 03 May 2024 13:22:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsGregory Goris
Estimated Impact108
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks B - Sta...] [2010-08-19 20:46:50] [4069dbe0e58b4004934f5f5b0dc60f40] [Current]
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Dataseries X:
225
224
223
221
219
218
219
221
222
222
223
225
226
229
235
229
231
229
226
232
234
230
232
231
237
241
256
255
264
259
253
258
265
258
257
255
255
255
275
276
278
268
253
257
255
253
245
248
246
243
260
262
262
251
236
238
239
243
233
238
232
224
238
236
231
209
179
179
165
174
163
166
164
152
163
167
157
138
111
110
91
100
88
89




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=79383&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=79383&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79383&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
alpha0.999924474600477
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999924474600477 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79383&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]0.999924474600477[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79383&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79383&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
alpha0.999924474600477
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2224225-1
3223224.000075525400-1.00007552539952
4221223.000075531104-2.00007553110362
5219221.000151056504-2.00015105650357
6218219.000151062208-1.00015106220764
7219218.0000755368090.999924463191434
8221218.9999244803052.00007551969458
9222220.9998489434971.00015105650269
10222221.9999244631927.55368081399865e-05
11223221.9999999942951.00000000570495
12225222.99992447462.00007552539995
13226224.9998489434971.00015105650314
14229225.9999244631923.00007553680814
15235228.9997734180966.00022658190352
16229234.99954683049-5.99954683049017
17231229.0004531181711.99954688182868
18229230.999848983423-1.99984898342288
19226229.000151039393-3.00015103939347
20232226.0002265876065.99977341239412
21234231.9995468647162.00045313528403
22230233.999848914978-3.99984891497772
23232230.0003020901871.99969790981265
24231231.999848972016-0.999848972016423
25237231.0000755139935.99992448600693
26241236.9995468533064.00045314669393
27256240.99969786417815.0003021358222
28255255.998867096188-0.998867096188235
29264255.0000754398378.9999245601635
30259263.999320277102-4.9993202771019
31253259.000377575661-6.00037757566128
32258253.0004531809144.99954681908631
33265257.9996224072297.00037759277097
34258264.999471293685-6.99947129368547
35257258.000528637866-1.00052863786590
36255257.000075565325-2.00007556532512
37255255.000151056506-0.000151056506155101
38255255.000000011409-1.14086162739113e-08
39275255.00000000000119.9999999999991
40276274.9984894920101.00151050799047
41278275.9999243605192.00007563948122
42268277.999848943488-9.99984894348825
43253268.000755242587-15.0007552425866
44257253.0011329380333.99886706196716
45255256.999697983968-1.99969798396751
46253255.000151027989-2.00015102798918
47245253.000151062206-8.0001510622055
48248245.0006042146052.99939578539477
49246247.999773469435-1.99977346943498
50243246.00015103369-3.00015103369023
51260243.00022658760516.9997734123945
52262259.9987160853212.00128391467877
53262261.9998488522330.000151147767212478
54251261.999999988584-10.9999999885845
55236251.000830779394-15.0008307793939
56238236.0011329437381.99886705626221
57239237.9998490347671.00015096523302
58243238.9999244631994.00007553680123
59233242.999697892697-9.99969789269696
60238233.0007552311784.99924476882154
61232237.999622430042-5.99962243004151
62224232.000453123881-8.00045312388102
63238224.00060423741913.9993957625815
64236237.998942690042-1.99894269004196
65231236.000150970945-5.0001509709453
66209231.000377638400-22.0003776383998
67179209.001661587311-30.0016615873108
68179179.002265887478-0.00226588747773349
69165179.000000171132-14.0000001711321
70174165.0010573556068.99894264439376
71163173.999320351262-10.9993203512615
72166163.0008307280642.99916927193598
73164165.999773486542-1.99977348654249
74152164.000151033692-12.0001510336915
75163152.00090631620110.9990936837988
76167162.9991692890554.00083071094485
77157166.999697835662-9.99969783566212
78138157.000755231174-19.0007552311741
79111138.00143503963-27.0014350396301
80110111.002039294169-1.00203929416907
8191110.000075679418-19.0000756794180
8210091.00143498830678.99856501169334
838899.9993203797824-11.9993203797824
848988.00090625346570.999093746534314

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 224 & 225 & -1 \tabularnewline
3 & 223 & 224.000075525400 & -1.00007552539952 \tabularnewline
4 & 221 & 223.000075531104 & -2.00007553110362 \tabularnewline
5 & 219 & 221.000151056504 & -2.00015105650357 \tabularnewline
6 & 218 & 219.000151062208 & -1.00015106220764 \tabularnewline
7 & 219 & 218.000075536809 & 0.999924463191434 \tabularnewline
8 & 221 & 218.999924480305 & 2.00007551969458 \tabularnewline
9 & 222 & 220.999848943497 & 1.00015105650269 \tabularnewline
10 & 222 & 221.999924463192 & 7.55368081399865e-05 \tabularnewline
11 & 223 & 221.999999994295 & 1.00000000570495 \tabularnewline
12 & 225 & 222.9999244746 & 2.00007552539995 \tabularnewline
13 & 226 & 224.999848943497 & 1.00015105650314 \tabularnewline
14 & 229 & 225.999924463192 & 3.00007553680814 \tabularnewline
15 & 235 & 228.999773418096 & 6.00022658190352 \tabularnewline
16 & 229 & 234.99954683049 & -5.99954683049017 \tabularnewline
17 & 231 & 229.000453118171 & 1.99954688182868 \tabularnewline
18 & 229 & 230.999848983423 & -1.99984898342288 \tabularnewline
19 & 226 & 229.000151039393 & -3.00015103939347 \tabularnewline
20 & 232 & 226.000226587606 & 5.99977341239412 \tabularnewline
21 & 234 & 231.999546864716 & 2.00045313528403 \tabularnewline
22 & 230 & 233.999848914978 & -3.99984891497772 \tabularnewline
23 & 232 & 230.000302090187 & 1.99969790981265 \tabularnewline
24 & 231 & 231.999848972016 & -0.999848972016423 \tabularnewline
25 & 237 & 231.000075513993 & 5.99992448600693 \tabularnewline
26 & 241 & 236.999546853306 & 4.00045314669393 \tabularnewline
27 & 256 & 240.999697864178 & 15.0003021358222 \tabularnewline
28 & 255 & 255.998867096188 & -0.998867096188235 \tabularnewline
29 & 264 & 255.000075439837 & 8.9999245601635 \tabularnewline
30 & 259 & 263.999320277102 & -4.9993202771019 \tabularnewline
31 & 253 & 259.000377575661 & -6.00037757566128 \tabularnewline
32 & 258 & 253.000453180914 & 4.99954681908631 \tabularnewline
33 & 265 & 257.999622407229 & 7.00037759277097 \tabularnewline
34 & 258 & 264.999471293685 & -6.99947129368547 \tabularnewline
35 & 257 & 258.000528637866 & -1.00052863786590 \tabularnewline
36 & 255 & 257.000075565325 & -2.00007556532512 \tabularnewline
37 & 255 & 255.000151056506 & -0.000151056506155101 \tabularnewline
38 & 255 & 255.000000011409 & -1.14086162739113e-08 \tabularnewline
39 & 275 & 255.000000000001 & 19.9999999999991 \tabularnewline
40 & 276 & 274.998489492010 & 1.00151050799047 \tabularnewline
41 & 278 & 275.999924360519 & 2.00007563948122 \tabularnewline
42 & 268 & 277.999848943488 & -9.99984894348825 \tabularnewline
43 & 253 & 268.000755242587 & -15.0007552425866 \tabularnewline
44 & 257 & 253.001132938033 & 3.99886706196716 \tabularnewline
45 & 255 & 256.999697983968 & -1.99969798396751 \tabularnewline
46 & 253 & 255.000151027989 & -2.00015102798918 \tabularnewline
47 & 245 & 253.000151062206 & -8.0001510622055 \tabularnewline
48 & 248 & 245.000604214605 & 2.99939578539477 \tabularnewline
49 & 246 & 247.999773469435 & -1.99977346943498 \tabularnewline
50 & 243 & 246.00015103369 & -3.00015103369023 \tabularnewline
51 & 260 & 243.000226587605 & 16.9997734123945 \tabularnewline
52 & 262 & 259.998716085321 & 2.00128391467877 \tabularnewline
53 & 262 & 261.999848852233 & 0.000151147767212478 \tabularnewline
54 & 251 & 261.999999988584 & -10.9999999885845 \tabularnewline
55 & 236 & 251.000830779394 & -15.0008307793939 \tabularnewline
56 & 238 & 236.001132943738 & 1.99886705626221 \tabularnewline
57 & 239 & 237.999849034767 & 1.00015096523302 \tabularnewline
58 & 243 & 238.999924463199 & 4.00007553680123 \tabularnewline
59 & 233 & 242.999697892697 & -9.99969789269696 \tabularnewline
60 & 238 & 233.000755231178 & 4.99924476882154 \tabularnewline
61 & 232 & 237.999622430042 & -5.99962243004151 \tabularnewline
62 & 224 & 232.000453123881 & -8.00045312388102 \tabularnewline
63 & 238 & 224.000604237419 & 13.9993957625815 \tabularnewline
64 & 236 & 237.998942690042 & -1.99894269004196 \tabularnewline
65 & 231 & 236.000150970945 & -5.0001509709453 \tabularnewline
66 & 209 & 231.000377638400 & -22.0003776383998 \tabularnewline
67 & 179 & 209.001661587311 & -30.0016615873108 \tabularnewline
68 & 179 & 179.002265887478 & -0.00226588747773349 \tabularnewline
69 & 165 & 179.000000171132 & -14.0000001711321 \tabularnewline
70 & 174 & 165.001057355606 & 8.99894264439376 \tabularnewline
71 & 163 & 173.999320351262 & -10.9993203512615 \tabularnewline
72 & 166 & 163.000830728064 & 2.99916927193598 \tabularnewline
73 & 164 & 165.999773486542 & -1.99977348654249 \tabularnewline
74 & 152 & 164.000151033692 & -12.0001510336915 \tabularnewline
75 & 163 & 152.000906316201 & 10.9990936837988 \tabularnewline
76 & 167 & 162.999169289055 & 4.00083071094485 \tabularnewline
77 & 157 & 166.999697835662 & -9.99969783566212 \tabularnewline
78 & 138 & 157.000755231174 & -19.0007552311741 \tabularnewline
79 & 111 & 138.00143503963 & -27.0014350396301 \tabularnewline
80 & 110 & 111.002039294169 & -1.00203929416907 \tabularnewline
81 & 91 & 110.000075679418 & -19.0000756794180 \tabularnewline
82 & 100 & 91.0014349883067 & 8.99856501169334 \tabularnewline
83 & 88 & 99.9993203797824 & -11.9993203797824 \tabularnewline
84 & 89 & 88.0009062534657 & 0.999093746534314 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79383&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]2[/C][C]224[/C][C]225[/C][C]-1[/C][/ROW]
[ROW][C]3[/C][C]223[/C][C]224.000075525400[/C][C]-1.00007552539952[/C][/ROW]
[ROW][C]4[/C][C]221[/C][C]223.000075531104[/C][C]-2.00007553110362[/C][/ROW]
[ROW][C]5[/C][C]219[/C][C]221.000151056504[/C][C]-2.00015105650357[/C][/ROW]
[ROW][C]6[/C][C]218[/C][C]219.000151062208[/C][C]-1.00015106220764[/C][/ROW]
[ROW][C]7[/C][C]219[/C][C]218.000075536809[/C][C]0.999924463191434[/C][/ROW]
[ROW][C]8[/C][C]221[/C][C]218.999924480305[/C][C]2.00007551969458[/C][/ROW]
[ROW][C]9[/C][C]222[/C][C]220.999848943497[/C][C]1.00015105650269[/C][/ROW]
[ROW][C]10[/C][C]222[/C][C]221.999924463192[/C][C]7.55368081399865e-05[/C][/ROW]
[ROW][C]11[/C][C]223[/C][C]221.999999994295[/C][C]1.00000000570495[/C][/ROW]
[ROW][C]12[/C][C]225[/C][C]222.9999244746[/C][C]2.00007552539995[/C][/ROW]
[ROW][C]13[/C][C]226[/C][C]224.999848943497[/C][C]1.00015105650314[/C][/ROW]
[ROW][C]14[/C][C]229[/C][C]225.999924463192[/C][C]3.00007553680814[/C][/ROW]
[ROW][C]15[/C][C]235[/C][C]228.999773418096[/C][C]6.00022658190352[/C][/ROW]
[ROW][C]16[/C][C]229[/C][C]234.99954683049[/C][C]-5.99954683049017[/C][/ROW]
[ROW][C]17[/C][C]231[/C][C]229.000453118171[/C][C]1.99954688182868[/C][/ROW]
[ROW][C]18[/C][C]229[/C][C]230.999848983423[/C][C]-1.99984898342288[/C][/ROW]
[ROW][C]19[/C][C]226[/C][C]229.000151039393[/C][C]-3.00015103939347[/C][/ROW]
[ROW][C]20[/C][C]232[/C][C]226.000226587606[/C][C]5.99977341239412[/C][/ROW]
[ROW][C]21[/C][C]234[/C][C]231.999546864716[/C][C]2.00045313528403[/C][/ROW]
[ROW][C]22[/C][C]230[/C][C]233.999848914978[/C][C]-3.99984891497772[/C][/ROW]
[ROW][C]23[/C][C]232[/C][C]230.000302090187[/C][C]1.99969790981265[/C][/ROW]
[ROW][C]24[/C][C]231[/C][C]231.999848972016[/C][C]-0.999848972016423[/C][/ROW]
[ROW][C]25[/C][C]237[/C][C]231.000075513993[/C][C]5.99992448600693[/C][/ROW]
[ROW][C]26[/C][C]241[/C][C]236.999546853306[/C][C]4.00045314669393[/C][/ROW]
[ROW][C]27[/C][C]256[/C][C]240.999697864178[/C][C]15.0003021358222[/C][/ROW]
[ROW][C]28[/C][C]255[/C][C]255.998867096188[/C][C]-0.998867096188235[/C][/ROW]
[ROW][C]29[/C][C]264[/C][C]255.000075439837[/C][C]8.9999245601635[/C][/ROW]
[ROW][C]30[/C][C]259[/C][C]263.999320277102[/C][C]-4.9993202771019[/C][/ROW]
[ROW][C]31[/C][C]253[/C][C]259.000377575661[/C][C]-6.00037757566128[/C][/ROW]
[ROW][C]32[/C][C]258[/C][C]253.000453180914[/C][C]4.99954681908631[/C][/ROW]
[ROW][C]33[/C][C]265[/C][C]257.999622407229[/C][C]7.00037759277097[/C][/ROW]
[ROW][C]34[/C][C]258[/C][C]264.999471293685[/C][C]-6.99947129368547[/C][/ROW]
[ROW][C]35[/C][C]257[/C][C]258.000528637866[/C][C]-1.00052863786590[/C][/ROW]
[ROW][C]36[/C][C]255[/C][C]257.000075565325[/C][C]-2.00007556532512[/C][/ROW]
[ROW][C]37[/C][C]255[/C][C]255.000151056506[/C][C]-0.000151056506155101[/C][/ROW]
[ROW][C]38[/C][C]255[/C][C]255.000000011409[/C][C]-1.14086162739113e-08[/C][/ROW]
[ROW][C]39[/C][C]275[/C][C]255.000000000001[/C][C]19.9999999999991[/C][/ROW]
[ROW][C]40[/C][C]276[/C][C]274.998489492010[/C][C]1.00151050799047[/C][/ROW]
[ROW][C]41[/C][C]278[/C][C]275.999924360519[/C][C]2.00007563948122[/C][/ROW]
[ROW][C]42[/C][C]268[/C][C]277.999848943488[/C][C]-9.99984894348825[/C][/ROW]
[ROW][C]43[/C][C]253[/C][C]268.000755242587[/C][C]-15.0007552425866[/C][/ROW]
[ROW][C]44[/C][C]257[/C][C]253.001132938033[/C][C]3.99886706196716[/C][/ROW]
[ROW][C]45[/C][C]255[/C][C]256.999697983968[/C][C]-1.99969798396751[/C][/ROW]
[ROW][C]46[/C][C]253[/C][C]255.000151027989[/C][C]-2.00015102798918[/C][/ROW]
[ROW][C]47[/C][C]245[/C][C]253.000151062206[/C][C]-8.0001510622055[/C][/ROW]
[ROW][C]48[/C][C]248[/C][C]245.000604214605[/C][C]2.99939578539477[/C][/ROW]
[ROW][C]49[/C][C]246[/C][C]247.999773469435[/C][C]-1.99977346943498[/C][/ROW]
[ROW][C]50[/C][C]243[/C][C]246.00015103369[/C][C]-3.00015103369023[/C][/ROW]
[ROW][C]51[/C][C]260[/C][C]243.000226587605[/C][C]16.9997734123945[/C][/ROW]
[ROW][C]52[/C][C]262[/C][C]259.998716085321[/C][C]2.00128391467877[/C][/ROW]
[ROW][C]53[/C][C]262[/C][C]261.999848852233[/C][C]0.000151147767212478[/C][/ROW]
[ROW][C]54[/C][C]251[/C][C]261.999999988584[/C][C]-10.9999999885845[/C][/ROW]
[ROW][C]55[/C][C]236[/C][C]251.000830779394[/C][C]-15.0008307793939[/C][/ROW]
[ROW][C]56[/C][C]238[/C][C]236.001132943738[/C][C]1.99886705626221[/C][/ROW]
[ROW][C]57[/C][C]239[/C][C]237.999849034767[/C][C]1.00015096523302[/C][/ROW]
[ROW][C]58[/C][C]243[/C][C]238.999924463199[/C][C]4.00007553680123[/C][/ROW]
[ROW][C]59[/C][C]233[/C][C]242.999697892697[/C][C]-9.99969789269696[/C][/ROW]
[ROW][C]60[/C][C]238[/C][C]233.000755231178[/C][C]4.99924476882154[/C][/ROW]
[ROW][C]61[/C][C]232[/C][C]237.999622430042[/C][C]-5.99962243004151[/C][/ROW]
[ROW][C]62[/C][C]224[/C][C]232.000453123881[/C][C]-8.00045312388102[/C][/ROW]
[ROW][C]63[/C][C]238[/C][C]224.000604237419[/C][C]13.9993957625815[/C][/ROW]
[ROW][C]64[/C][C]236[/C][C]237.998942690042[/C][C]-1.99894269004196[/C][/ROW]
[ROW][C]65[/C][C]231[/C][C]236.000150970945[/C][C]-5.0001509709453[/C][/ROW]
[ROW][C]66[/C][C]209[/C][C]231.000377638400[/C][C]-22.0003776383998[/C][/ROW]
[ROW][C]67[/C][C]179[/C][C]209.001661587311[/C][C]-30.0016615873108[/C][/ROW]
[ROW][C]68[/C][C]179[/C][C]179.002265887478[/C][C]-0.00226588747773349[/C][/ROW]
[ROW][C]69[/C][C]165[/C][C]179.000000171132[/C][C]-14.0000001711321[/C][/ROW]
[ROW][C]70[/C][C]174[/C][C]165.001057355606[/C][C]8.99894264439376[/C][/ROW]
[ROW][C]71[/C][C]163[/C][C]173.999320351262[/C][C]-10.9993203512615[/C][/ROW]
[ROW][C]72[/C][C]166[/C][C]163.000830728064[/C][C]2.99916927193598[/C][/ROW]
[ROW][C]73[/C][C]164[/C][C]165.999773486542[/C][C]-1.99977348654249[/C][/ROW]
[ROW][C]74[/C][C]152[/C][C]164.000151033692[/C][C]-12.0001510336915[/C][/ROW]
[ROW][C]75[/C][C]163[/C][C]152.000906316201[/C][C]10.9990936837988[/C][/ROW]
[ROW][C]76[/C][C]167[/C][C]162.999169289055[/C][C]4.00083071094485[/C][/ROW]
[ROW][C]77[/C][C]157[/C][C]166.999697835662[/C][C]-9.99969783566212[/C][/ROW]
[ROW][C]78[/C][C]138[/C][C]157.000755231174[/C][C]-19.0007552311741[/C][/ROW]
[ROW][C]79[/C][C]111[/C][C]138.00143503963[/C][C]-27.0014350396301[/C][/ROW]
[ROW][C]80[/C][C]110[/C][C]111.002039294169[/C][C]-1.00203929416907[/C][/ROW]
[ROW][C]81[/C][C]91[/C][C]110.000075679418[/C][C]-19.0000756794180[/C][/ROW]
[ROW][C]82[/C][C]100[/C][C]91.0014349883067[/C][C]8.99856501169334[/C][/ROW]
[ROW][C]83[/C][C]88[/C][C]99.9993203797824[/C][C]-11.9993203797824[/C][/ROW]
[ROW][C]84[/C][C]89[/C][C]88.0009062534657[/C][C]0.999093746534314[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79383&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79383&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
2224225-1
3223224.000075525400-1.00007552539952
4221223.000075531104-2.00007553110362
5219221.000151056504-2.00015105650357
6218219.000151062208-1.00015106220764
7219218.0000755368090.999924463191434
8221218.9999244803052.00007551969458
9222220.9998489434971.00015105650269
10222221.9999244631927.55368081399865e-05
11223221.9999999942951.00000000570495
12225222.99992447462.00007552539995
13226224.9998489434971.00015105650314
14229225.9999244631923.00007553680814
15235228.9997734180966.00022658190352
16229234.99954683049-5.99954683049017
17231229.0004531181711.99954688182868
18229230.999848983423-1.99984898342288
19226229.000151039393-3.00015103939347
20232226.0002265876065.99977341239412
21234231.9995468647162.00045313528403
22230233.999848914978-3.99984891497772
23232230.0003020901871.99969790981265
24231231.999848972016-0.999848972016423
25237231.0000755139935.99992448600693
26241236.9995468533064.00045314669393
27256240.99969786417815.0003021358222
28255255.998867096188-0.998867096188235
29264255.0000754398378.9999245601635
30259263.999320277102-4.9993202771019
31253259.000377575661-6.00037757566128
32258253.0004531809144.99954681908631
33265257.9996224072297.00037759277097
34258264.999471293685-6.99947129368547
35257258.000528637866-1.00052863786590
36255257.000075565325-2.00007556532512
37255255.000151056506-0.000151056506155101
38255255.000000011409-1.14086162739113e-08
39275255.00000000000119.9999999999991
40276274.9984894920101.00151050799047
41278275.9999243605192.00007563948122
42268277.999848943488-9.99984894348825
43253268.000755242587-15.0007552425866
44257253.0011329380333.99886706196716
45255256.999697983968-1.99969798396751
46253255.000151027989-2.00015102798918
47245253.000151062206-8.0001510622055
48248245.0006042146052.99939578539477
49246247.999773469435-1.99977346943498
50243246.00015103369-3.00015103369023
51260243.00022658760516.9997734123945
52262259.9987160853212.00128391467877
53262261.9998488522330.000151147767212478
54251261.999999988584-10.9999999885845
55236251.000830779394-15.0008307793939
56238236.0011329437381.99886705626221
57239237.9998490347671.00015096523302
58243238.9999244631994.00007553680123
59233242.999697892697-9.99969789269696
60238233.0007552311784.99924476882154
61232237.999622430042-5.99962243004151
62224232.000453123881-8.00045312388102
63238224.00060423741913.9993957625815
64236237.998942690042-1.99894269004196
65231236.000150970945-5.0001509709453
66209231.000377638400-22.0003776383998
67179209.001661587311-30.0016615873108
68179179.002265887478-0.00226588747773349
69165179.000000171132-14.0000001711321
70174165.0010573556068.99894264439376
71163173.999320351262-10.9993203512615
72166163.0008307280642.99916927193598
73164165.999773486542-1.99977348654249
74152164.000151033692-12.0001510336915
75163152.00090631620110.9990936837988
76167162.9991692890554.00083071094485
77157166.999697835662-9.99969783566212
78138157.000755231174-19.0007552311741
79111138.00143503963-27.0014350396301
80110111.002039294169-1.00203929416907
8191110.000075679418-19.0000756794180
8210091.00143498830678.99856501169334
838899.9993203797824-11.9993203797824
848988.00090625346570.999093746534314







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8588.999924543045671.8050580448059106.194791041285
8688.999924543045664.68362940433113.316219681761
8788.999924543045659.2190416707404118.780807415351
8888.999924543045654.6121395019179123.387709584173
8988.999924543045650.5533572656456127.446491820446
9088.999924543045646.8839262668978131.115922819193
9188.999924543045643.5095290053354134.490320080756
9288.999924543045640.3687117105636137.631137375528
9388.999924543045637.4187880982270140.581060987864
9488.999924543045634.6286783524364143.371170733655
9588.999924543045631.9749196092389146.024929476852
9688.999924543045629.4392834863753148.560565599716

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 88.9999245430456 & 71.8050580448059 & 106.194791041285 \tabularnewline
86 & 88.9999245430456 & 64.68362940433 & 113.316219681761 \tabularnewline
87 & 88.9999245430456 & 59.2190416707404 & 118.780807415351 \tabularnewline
88 & 88.9999245430456 & 54.6121395019179 & 123.387709584173 \tabularnewline
89 & 88.9999245430456 & 50.5533572656456 & 127.446491820446 \tabularnewline
90 & 88.9999245430456 & 46.8839262668978 & 131.115922819193 \tabularnewline
91 & 88.9999245430456 & 43.5095290053354 & 134.490320080756 \tabularnewline
92 & 88.9999245430456 & 40.3687117105636 & 137.631137375528 \tabularnewline
93 & 88.9999245430456 & 37.4187880982270 & 140.581060987864 \tabularnewline
94 & 88.9999245430456 & 34.6286783524364 & 143.371170733655 \tabularnewline
95 & 88.9999245430456 & 31.9749196092389 & 146.024929476852 \tabularnewline
96 & 88.9999245430456 & 29.4392834863753 & 148.560565599716 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79383&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]88.9999245430456[/C][C]71.8050580448059[/C][C]106.194791041285[/C][/ROW]
[ROW][C]86[/C][C]88.9999245430456[/C][C]64.68362940433[/C][C]113.316219681761[/C][/ROW]
[ROW][C]87[/C][C]88.9999245430456[/C][C]59.2190416707404[/C][C]118.780807415351[/C][/ROW]
[ROW][C]88[/C][C]88.9999245430456[/C][C]54.6121395019179[/C][C]123.387709584173[/C][/ROW]
[ROW][C]89[/C][C]88.9999245430456[/C][C]50.5533572656456[/C][C]127.446491820446[/C][/ROW]
[ROW][C]90[/C][C]88.9999245430456[/C][C]46.8839262668978[/C][C]131.115922819193[/C][/ROW]
[ROW][C]91[/C][C]88.9999245430456[/C][C]43.5095290053354[/C][C]134.490320080756[/C][/ROW]
[ROW][C]92[/C][C]88.9999245430456[/C][C]40.3687117105636[/C][C]137.631137375528[/C][/ROW]
[ROW][C]93[/C][C]88.9999245430456[/C][C]37.4187880982270[/C][C]140.581060987864[/C][/ROW]
[ROW][C]94[/C][C]88.9999245430456[/C][C]34.6286783524364[/C][C]143.371170733655[/C][/ROW]
[ROW][C]95[/C][C]88.9999245430456[/C][C]31.9749196092389[/C][C]146.024929476852[/C][/ROW]
[ROW][C]96[/C][C]88.9999245430456[/C][C]29.4392834863753[/C][C]148.560565599716[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79383&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79383&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
8588.999924543045671.8050580448059106.194791041285
8688.999924543045664.68362940433113.316219681761
8788.999924543045659.2190416707404118.780807415351
8888.999924543045654.6121395019179123.387709584173
8988.999924543045650.5533572656456127.446491820446
9088.999924543045646.8839262668978131.115922819193
9188.999924543045643.5095290053354134.490320080756
9288.999924543045640.3687117105636137.631137375528
9388.999924543045637.4187880982270140.581060987864
9488.999924543045634.6286783524364143.371170733655
9588.999924543045631.9749196092389146.024929476852
9688.999924543045629.4392834863753148.560565599716



Parameters (Session):
par1 = 0.01 ; par2 = 0.99 ; par3 = 0.01 ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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')