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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 02 Jun 2010 12:29:27 +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/Jun/02/t127548180920p72znewyigipt.htm/, Retrieved Thu, 25 Apr 2024 20:34:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=77284, Retrieved Thu, 25 Apr 2024 20:34:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact138
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2010-06-02 12:29:27] [850dbf9e683f79d78a1e8310559edb6e] [Current]
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Dataseries X:
306
303
344
254
309
310
379
294
356
318
405
545
268
243
273
273
236
222
302
285
309
322
362
471
198
253
173
186
185
105
228
214
189
270
277
378
185
182
258
179
197
168
250
211
260
234
305
347
203
217
227
242
185
175
252
319
202
254
336
431
150
280
187
279
193
227
225
205
259
254
275
394
159
230
188
195
189
220
274




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77284&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77284&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77284&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.215289717700249
beta0.032381255659449
gamma0.187381168803615

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.215289717700249 \tabularnewline
beta & 0.032381255659449 \tabularnewline
gamma & 0.187381168803615 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77284&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]0.215289717700249[/C][/ROW]
[ROW][C]beta[/C][C]0.032381255659449[/C][/ROW]
[ROW][C]gamma[/C][C]0.187381168803615[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77284&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77284&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
alpha0.215289717700249
beta0.032381255659449
gamma0.187381168803615







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13268293.967403205295-25.9674032052949
14243261.279066016922-18.2790660169215
15273287.52216433785-14.5221643378497
16273282.154029536538-9.15402953653762
17236240.052393908794-4.05239390879376
18222225.321974382947-3.32197438294742
19302331.62591223883-29.6259122388303
20285251.25291072260233.7470892773981
21309313.420014435399-4.42001443539868
22322276.64280803927445.3571919607256
23362362.153841458186-0.153841458186321
24471490.446318134576-19.4463181345757
25198237.556905757886-39.5569057578857
26253207.14475459958345.8552454004175
27173242.749178750529-69.749178750529
28186225.533027265585-39.5330272655852
29185185.187465645161-0.18746564516124
30105173.356597197516-68.356597197516
31228228.919913889412-0.919913889411617
32214180.48625537218633.5137446278141
33189220.432903705423-31.4329037054227
34270191.48028459707178.5197154029286
35277254.89582549068422.1041745093161
36378346.34201941393631.6579805860641
37185167.75060481695717.2493951830433
38182163.14461105354218.8553889464584
39258172.06550819789185.9344918021087
40179192.634343570042-13.6343435700416
41197166.78300833163630.2169916683642
42168152.74675228169415.2532477183061
43250242.9626707144087.03732928559191
44211200.51320122931310.486798770687
45260229.48416549191330.5158345080868
46234231.5340128017342.46598719826557
47305275.10336949746729.8966305025329
48347379.766922808021-32.7669228080214
49203178.91780500718424.0821949928156
50217177.13669908112739.8633009188732
51227202.58484713944524.4151528605552
52242196.24257084910845.7574291508921
53185189.642691850002-4.64269185000157
54175165.7313907429439.26860925705742
55252260.478030455908-8.47803045590757
56319214.338386057477104.661613942523
57202273.969829179295-71.9698291792946
58254250.9695357702263.03046422977351
59336304.6815724127831.3184275872205
60431411.22497025110119.775029748899
61150207.729195404114-57.7291954041145
62280191.14187644553388.8581235544666
63187227.712173791822-40.712173791822
64279210.73988492870468.2601150712957
65193201.106681466562-8.10668146656226
66227178.0466837277348.9533162722699
67225290.934832372585-65.9348323725854
68205246.610130541036-41.6101305410363
69259247.45853360637611.5414663936241
70254254.071138930979-0.0711389309789752
71275312.311437781-37.3114377809997
72394398.862204264107-4.86220426410745
73159188.910702268935-29.9107022689349
74230198.49577734957831.504222650422
75188203.293034542196-15.2930345421961
76195206.610537141597-11.6105371415968
77189172.66552783491716.3344721650835
78220163.92631391359956.0736860864014
79274251.89951483709422.1004851629063

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 268 & 293.967403205295 & -25.9674032052949 \tabularnewline
14 & 243 & 261.279066016922 & -18.2790660169215 \tabularnewline
15 & 273 & 287.52216433785 & -14.5221643378497 \tabularnewline
16 & 273 & 282.154029536538 & -9.15402953653762 \tabularnewline
17 & 236 & 240.052393908794 & -4.05239390879376 \tabularnewline
18 & 222 & 225.321974382947 & -3.32197438294742 \tabularnewline
19 & 302 & 331.62591223883 & -29.6259122388303 \tabularnewline
20 & 285 & 251.252910722602 & 33.7470892773981 \tabularnewline
21 & 309 & 313.420014435399 & -4.42001443539868 \tabularnewline
22 & 322 & 276.642808039274 & 45.3571919607256 \tabularnewline
23 & 362 & 362.153841458186 & -0.153841458186321 \tabularnewline
24 & 471 & 490.446318134576 & -19.4463181345757 \tabularnewline
25 & 198 & 237.556905757886 & -39.5569057578857 \tabularnewline
26 & 253 & 207.144754599583 & 45.8552454004175 \tabularnewline
27 & 173 & 242.749178750529 & -69.749178750529 \tabularnewline
28 & 186 & 225.533027265585 & -39.5330272655852 \tabularnewline
29 & 185 & 185.187465645161 & -0.18746564516124 \tabularnewline
30 & 105 & 173.356597197516 & -68.356597197516 \tabularnewline
31 & 228 & 228.919913889412 & -0.919913889411617 \tabularnewline
32 & 214 & 180.486255372186 & 33.5137446278141 \tabularnewline
33 & 189 & 220.432903705423 & -31.4329037054227 \tabularnewline
34 & 270 & 191.480284597071 & 78.5197154029286 \tabularnewline
35 & 277 & 254.895825490684 & 22.1041745093161 \tabularnewline
36 & 378 & 346.342019413936 & 31.6579805860641 \tabularnewline
37 & 185 & 167.750604816957 & 17.2493951830433 \tabularnewline
38 & 182 & 163.144611053542 & 18.8553889464584 \tabularnewline
39 & 258 & 172.065508197891 & 85.9344918021087 \tabularnewline
40 & 179 & 192.634343570042 & -13.6343435700416 \tabularnewline
41 & 197 & 166.783008331636 & 30.2169916683642 \tabularnewline
42 & 168 & 152.746752281694 & 15.2532477183061 \tabularnewline
43 & 250 & 242.962670714408 & 7.03732928559191 \tabularnewline
44 & 211 & 200.513201229313 & 10.486798770687 \tabularnewline
45 & 260 & 229.484165491913 & 30.5158345080868 \tabularnewline
46 & 234 & 231.534012801734 & 2.46598719826557 \tabularnewline
47 & 305 & 275.103369497467 & 29.8966305025329 \tabularnewline
48 & 347 & 379.766922808021 & -32.7669228080214 \tabularnewline
49 & 203 & 178.917805007184 & 24.0821949928156 \tabularnewline
50 & 217 & 177.136699081127 & 39.8633009188732 \tabularnewline
51 & 227 & 202.584847139445 & 24.4151528605552 \tabularnewline
52 & 242 & 196.242570849108 & 45.7574291508921 \tabularnewline
53 & 185 & 189.642691850002 & -4.64269185000157 \tabularnewline
54 & 175 & 165.731390742943 & 9.26860925705742 \tabularnewline
55 & 252 & 260.478030455908 & -8.47803045590757 \tabularnewline
56 & 319 & 214.338386057477 & 104.661613942523 \tabularnewline
57 & 202 & 273.969829179295 & -71.9698291792946 \tabularnewline
58 & 254 & 250.969535770226 & 3.03046422977351 \tabularnewline
59 & 336 & 304.68157241278 & 31.3184275872205 \tabularnewline
60 & 431 & 411.224970251101 & 19.775029748899 \tabularnewline
61 & 150 & 207.729195404114 & -57.7291954041145 \tabularnewline
62 & 280 & 191.141876445533 & 88.8581235544666 \tabularnewline
63 & 187 & 227.712173791822 & -40.712173791822 \tabularnewline
64 & 279 & 210.739884928704 & 68.2601150712957 \tabularnewline
65 & 193 & 201.106681466562 & -8.10668146656226 \tabularnewline
66 & 227 & 178.04668372773 & 48.9533162722699 \tabularnewline
67 & 225 & 290.934832372585 & -65.9348323725854 \tabularnewline
68 & 205 & 246.610130541036 & -41.6101305410363 \tabularnewline
69 & 259 & 247.458533606376 & 11.5414663936241 \tabularnewline
70 & 254 & 254.071138930979 & -0.0711389309789752 \tabularnewline
71 & 275 & 312.311437781 & -37.3114377809997 \tabularnewline
72 & 394 & 398.862204264107 & -4.86220426410745 \tabularnewline
73 & 159 & 188.910702268935 & -29.9107022689349 \tabularnewline
74 & 230 & 198.495777349578 & 31.504222650422 \tabularnewline
75 & 188 & 203.293034542196 & -15.2930345421961 \tabularnewline
76 & 195 & 206.610537141597 & -11.6105371415968 \tabularnewline
77 & 189 & 172.665527834917 & 16.3344721650835 \tabularnewline
78 & 220 & 163.926313913599 & 56.0736860864014 \tabularnewline
79 & 274 & 251.899514837094 & 22.1004851629063 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77284&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]268[/C][C]293.967403205295[/C][C]-25.9674032052949[/C][/ROW]
[ROW][C]14[/C][C]243[/C][C]261.279066016922[/C][C]-18.2790660169215[/C][/ROW]
[ROW][C]15[/C][C]273[/C][C]287.52216433785[/C][C]-14.5221643378497[/C][/ROW]
[ROW][C]16[/C][C]273[/C][C]282.154029536538[/C][C]-9.15402953653762[/C][/ROW]
[ROW][C]17[/C][C]236[/C][C]240.052393908794[/C][C]-4.05239390879376[/C][/ROW]
[ROW][C]18[/C][C]222[/C][C]225.321974382947[/C][C]-3.32197438294742[/C][/ROW]
[ROW][C]19[/C][C]302[/C][C]331.62591223883[/C][C]-29.6259122388303[/C][/ROW]
[ROW][C]20[/C][C]285[/C][C]251.252910722602[/C][C]33.7470892773981[/C][/ROW]
[ROW][C]21[/C][C]309[/C][C]313.420014435399[/C][C]-4.42001443539868[/C][/ROW]
[ROW][C]22[/C][C]322[/C][C]276.642808039274[/C][C]45.3571919607256[/C][/ROW]
[ROW][C]23[/C][C]362[/C][C]362.153841458186[/C][C]-0.153841458186321[/C][/ROW]
[ROW][C]24[/C][C]471[/C][C]490.446318134576[/C][C]-19.4463181345757[/C][/ROW]
[ROW][C]25[/C][C]198[/C][C]237.556905757886[/C][C]-39.5569057578857[/C][/ROW]
[ROW][C]26[/C][C]253[/C][C]207.144754599583[/C][C]45.8552454004175[/C][/ROW]
[ROW][C]27[/C][C]173[/C][C]242.749178750529[/C][C]-69.749178750529[/C][/ROW]
[ROW][C]28[/C][C]186[/C][C]225.533027265585[/C][C]-39.5330272655852[/C][/ROW]
[ROW][C]29[/C][C]185[/C][C]185.187465645161[/C][C]-0.18746564516124[/C][/ROW]
[ROW][C]30[/C][C]105[/C][C]173.356597197516[/C][C]-68.356597197516[/C][/ROW]
[ROW][C]31[/C][C]228[/C][C]228.919913889412[/C][C]-0.919913889411617[/C][/ROW]
[ROW][C]32[/C][C]214[/C][C]180.486255372186[/C][C]33.5137446278141[/C][/ROW]
[ROW][C]33[/C][C]189[/C][C]220.432903705423[/C][C]-31.4329037054227[/C][/ROW]
[ROW][C]34[/C][C]270[/C][C]191.480284597071[/C][C]78.5197154029286[/C][/ROW]
[ROW][C]35[/C][C]277[/C][C]254.895825490684[/C][C]22.1041745093161[/C][/ROW]
[ROW][C]36[/C][C]378[/C][C]346.342019413936[/C][C]31.6579805860641[/C][/ROW]
[ROW][C]37[/C][C]185[/C][C]167.750604816957[/C][C]17.2493951830433[/C][/ROW]
[ROW][C]38[/C][C]182[/C][C]163.144611053542[/C][C]18.8553889464584[/C][/ROW]
[ROW][C]39[/C][C]258[/C][C]172.065508197891[/C][C]85.9344918021087[/C][/ROW]
[ROW][C]40[/C][C]179[/C][C]192.634343570042[/C][C]-13.6343435700416[/C][/ROW]
[ROW][C]41[/C][C]197[/C][C]166.783008331636[/C][C]30.2169916683642[/C][/ROW]
[ROW][C]42[/C][C]168[/C][C]152.746752281694[/C][C]15.2532477183061[/C][/ROW]
[ROW][C]43[/C][C]250[/C][C]242.962670714408[/C][C]7.03732928559191[/C][/ROW]
[ROW][C]44[/C][C]211[/C][C]200.513201229313[/C][C]10.486798770687[/C][/ROW]
[ROW][C]45[/C][C]260[/C][C]229.484165491913[/C][C]30.5158345080868[/C][/ROW]
[ROW][C]46[/C][C]234[/C][C]231.534012801734[/C][C]2.46598719826557[/C][/ROW]
[ROW][C]47[/C][C]305[/C][C]275.103369497467[/C][C]29.8966305025329[/C][/ROW]
[ROW][C]48[/C][C]347[/C][C]379.766922808021[/C][C]-32.7669228080214[/C][/ROW]
[ROW][C]49[/C][C]203[/C][C]178.917805007184[/C][C]24.0821949928156[/C][/ROW]
[ROW][C]50[/C][C]217[/C][C]177.136699081127[/C][C]39.8633009188732[/C][/ROW]
[ROW][C]51[/C][C]227[/C][C]202.584847139445[/C][C]24.4151528605552[/C][/ROW]
[ROW][C]52[/C][C]242[/C][C]196.242570849108[/C][C]45.7574291508921[/C][/ROW]
[ROW][C]53[/C][C]185[/C][C]189.642691850002[/C][C]-4.64269185000157[/C][/ROW]
[ROW][C]54[/C][C]175[/C][C]165.731390742943[/C][C]9.26860925705742[/C][/ROW]
[ROW][C]55[/C][C]252[/C][C]260.478030455908[/C][C]-8.47803045590757[/C][/ROW]
[ROW][C]56[/C][C]319[/C][C]214.338386057477[/C][C]104.661613942523[/C][/ROW]
[ROW][C]57[/C][C]202[/C][C]273.969829179295[/C][C]-71.9698291792946[/C][/ROW]
[ROW][C]58[/C][C]254[/C][C]250.969535770226[/C][C]3.03046422977351[/C][/ROW]
[ROW][C]59[/C][C]336[/C][C]304.68157241278[/C][C]31.3184275872205[/C][/ROW]
[ROW][C]60[/C][C]431[/C][C]411.224970251101[/C][C]19.775029748899[/C][/ROW]
[ROW][C]61[/C][C]150[/C][C]207.729195404114[/C][C]-57.7291954041145[/C][/ROW]
[ROW][C]62[/C][C]280[/C][C]191.141876445533[/C][C]88.8581235544666[/C][/ROW]
[ROW][C]63[/C][C]187[/C][C]227.712173791822[/C][C]-40.712173791822[/C][/ROW]
[ROW][C]64[/C][C]279[/C][C]210.739884928704[/C][C]68.2601150712957[/C][/ROW]
[ROW][C]65[/C][C]193[/C][C]201.106681466562[/C][C]-8.10668146656226[/C][/ROW]
[ROW][C]66[/C][C]227[/C][C]178.04668372773[/C][C]48.9533162722699[/C][/ROW]
[ROW][C]67[/C][C]225[/C][C]290.934832372585[/C][C]-65.9348323725854[/C][/ROW]
[ROW][C]68[/C][C]205[/C][C]246.610130541036[/C][C]-41.6101305410363[/C][/ROW]
[ROW][C]69[/C][C]259[/C][C]247.458533606376[/C][C]11.5414663936241[/C][/ROW]
[ROW][C]70[/C][C]254[/C][C]254.071138930979[/C][C]-0.0711389309789752[/C][/ROW]
[ROW][C]71[/C][C]275[/C][C]312.311437781[/C][C]-37.3114377809997[/C][/ROW]
[ROW][C]72[/C][C]394[/C][C]398.862204264107[/C][C]-4.86220426410745[/C][/ROW]
[ROW][C]73[/C][C]159[/C][C]188.910702268935[/C][C]-29.9107022689349[/C][/ROW]
[ROW][C]74[/C][C]230[/C][C]198.495777349578[/C][C]31.504222650422[/C][/ROW]
[ROW][C]75[/C][C]188[/C][C]203.293034542196[/C][C]-15.2930345421961[/C][/ROW]
[ROW][C]76[/C][C]195[/C][C]206.610537141597[/C][C]-11.6105371415968[/C][/ROW]
[ROW][C]77[/C][C]189[/C][C]172.665527834917[/C][C]16.3344721650835[/C][/ROW]
[ROW][C]78[/C][C]220[/C][C]163.926313913599[/C][C]56.0736860864014[/C][/ROW]
[ROW][C]79[/C][C]274[/C][C]251.899514837094[/C][C]22.1004851629063[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77284&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77284&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
13268293.967403205295-25.9674032052949
14243261.279066016922-18.2790660169215
15273287.52216433785-14.5221643378497
16273282.154029536538-9.15402953653762
17236240.052393908794-4.05239390879376
18222225.321974382947-3.32197438294742
19302331.62591223883-29.6259122388303
20285251.25291072260233.7470892773981
21309313.420014435399-4.42001443539868
22322276.64280803927445.3571919607256
23362362.153841458186-0.153841458186321
24471490.446318134576-19.4463181345757
25198237.556905757886-39.5569057578857
26253207.14475459958345.8552454004175
27173242.749178750529-69.749178750529
28186225.533027265585-39.5330272655852
29185185.187465645161-0.18746564516124
30105173.356597197516-68.356597197516
31228228.919913889412-0.919913889411617
32214180.48625537218633.5137446278141
33189220.432903705423-31.4329037054227
34270191.48028459707178.5197154029286
35277254.89582549068422.1041745093161
36378346.34201941393631.6579805860641
37185167.75060481695717.2493951830433
38182163.14461105354218.8553889464584
39258172.06550819789185.9344918021087
40179192.634343570042-13.6343435700416
41197166.78300833163630.2169916683642
42168152.74675228169415.2532477183061
43250242.9626707144087.03732928559191
44211200.51320122931310.486798770687
45260229.48416549191330.5158345080868
46234231.5340128017342.46598719826557
47305275.10336949746729.8966305025329
48347379.766922808021-32.7669228080214
49203178.91780500718424.0821949928156
50217177.13669908112739.8633009188732
51227202.58484713944524.4151528605552
52242196.24257084910845.7574291508921
53185189.642691850002-4.64269185000157
54175165.7313907429439.26860925705742
55252260.478030455908-8.47803045590757
56319214.338386057477104.661613942523
57202273.969829179295-71.9698291792946
58254250.9695357702263.03046422977351
59336304.6815724127831.3184275872205
60431411.22497025110119.775029748899
61150207.729195404114-57.7291954041145
62280191.14187644553388.8581235544666
63187227.712173791822-40.712173791822
64279210.73988492870468.2601150712957
65193201.106681466562-8.10668146656226
66227178.0466837277348.9533162722699
67225290.934832372585-65.9348323725854
68205246.610130541036-41.6101305410363
69259247.45853360637611.5414663936241
70254254.071138930979-0.0711389309789752
71275312.311437781-37.3114377809997
72394398.862204264107-4.86220426410745
73159188.910702268935-29.9107022689349
74230198.49577734957831.504222650422
75188203.293034542196-15.2930345421961
76195206.610537141597-11.6105371415968
77189172.66552783491716.3344721650835
78220163.92631391359956.0736860864014
79274251.89951483709422.1004851629063







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
80231.040701285538203.79212270492258.289279866156
81249.081469270314216.3841820279281.778756512728
82251.865806467589214.621021325775289.110591609402
83304.523245620927258.040081787761351.006409454093
84406.817217799833343.993209779305469.641225820362
85189.373513740147150.07934087527228.667686605025
86216.730358229146169.517939860746263.942776597546
87208.114207807038158.498575390571257.729840223504
88216.359196790053161.365443341128271.352950238978
89187.825570647375135.064044334421240.587096960329
90181.062987484556126.105756282967236.020218686145
91250.825740951645167.49845593819334.153025965099

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
80 & 231.040701285538 & 203.79212270492 & 258.289279866156 \tabularnewline
81 & 249.081469270314 & 216.3841820279 & 281.778756512728 \tabularnewline
82 & 251.865806467589 & 214.621021325775 & 289.110591609402 \tabularnewline
83 & 304.523245620927 & 258.040081787761 & 351.006409454093 \tabularnewline
84 & 406.817217799833 & 343.993209779305 & 469.641225820362 \tabularnewline
85 & 189.373513740147 & 150.07934087527 & 228.667686605025 \tabularnewline
86 & 216.730358229146 & 169.517939860746 & 263.942776597546 \tabularnewline
87 & 208.114207807038 & 158.498575390571 & 257.729840223504 \tabularnewline
88 & 216.359196790053 & 161.365443341128 & 271.352950238978 \tabularnewline
89 & 187.825570647375 & 135.064044334421 & 240.587096960329 \tabularnewline
90 & 181.062987484556 & 126.105756282967 & 236.020218686145 \tabularnewline
91 & 250.825740951645 & 167.49845593819 & 334.153025965099 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77284&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]80[/C][C]231.040701285538[/C][C]203.79212270492[/C][C]258.289279866156[/C][/ROW]
[ROW][C]81[/C][C]249.081469270314[/C][C]216.3841820279[/C][C]281.778756512728[/C][/ROW]
[ROW][C]82[/C][C]251.865806467589[/C][C]214.621021325775[/C][C]289.110591609402[/C][/ROW]
[ROW][C]83[/C][C]304.523245620927[/C][C]258.040081787761[/C][C]351.006409454093[/C][/ROW]
[ROW][C]84[/C][C]406.817217799833[/C][C]343.993209779305[/C][C]469.641225820362[/C][/ROW]
[ROW][C]85[/C][C]189.373513740147[/C][C]150.07934087527[/C][C]228.667686605025[/C][/ROW]
[ROW][C]86[/C][C]216.730358229146[/C][C]169.517939860746[/C][C]263.942776597546[/C][/ROW]
[ROW][C]87[/C][C]208.114207807038[/C][C]158.498575390571[/C][C]257.729840223504[/C][/ROW]
[ROW][C]88[/C][C]216.359196790053[/C][C]161.365443341128[/C][C]271.352950238978[/C][/ROW]
[ROW][C]89[/C][C]187.825570647375[/C][C]135.064044334421[/C][C]240.587096960329[/C][/ROW]
[ROW][C]90[/C][C]181.062987484556[/C][C]126.105756282967[/C][C]236.020218686145[/C][/ROW]
[ROW][C]91[/C][C]250.825740951645[/C][C]167.49845593819[/C][C]334.153025965099[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77284&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77284&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
80231.040701285538203.79212270492258.289279866156
81249.081469270314216.3841820279281.778756512728
82251.865806467589214.621021325775289.110591609402
83304.523245620927258.040081787761351.006409454093
84406.817217799833343.993209779305469.641225820362
85189.373513740147150.07934087527228.667686605025
86216.730358229146169.517939860746263.942776597546
87208.114207807038158.498575390571257.729840223504
88216.359196790053161.365443341128271.352950238978
89187.825570647375135.064044334421240.587096960329
90181.062987484556126.105756282967236.020218686145
91250.825740951645167.49845593819334.153025965099



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')