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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 20:45:08 +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/t12822507739u2q9k5tijgkv51.htm/, Retrieved Fri, 03 May 2024 04:17:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79382, Retrieved Fri, 03 May 2024 04:17:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsMertens Jeroen
Estimated Impact104
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [TIJDREEKS - STAP32] [2010-08-19 20:45:08] [2c551c5731a2f7145d4349f791500f25] [Current]
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Dataseries X:
349
348
347
345
365
364
349
339
340
340
341
343
341
343
341
335
355
357
337
325
336
338
337
328
326
327
319
310
320
322
303
292
303
315
311
307
308
312
309
310
309
304
287
275
290
298
294
286
294
292
287
281
280
271
264
259
271
279
279
273
286
286
280
277
269
255
252
245
257
267
261
258
271
262
258
253
236
228
235
226
231
235
227
222
233
221
218
220
204
196
208
190
191
194
179
162
179
176
168
170
153
142
155
136
136
144
135
114
135
132
123
123
103
97
113
108
111
121
111
97




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79382&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]3 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=79382&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79382&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.531154412223295
beta0.0234130278133079
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.531154412223295 \tabularnewline
beta & 0.0234130278133079 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79382&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]0.531154412223295[/C][/ROW]
[ROW][C]beta[/C][C]0.0234130278133079[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79382&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79382&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
alpha0.531154412223295
beta0.0234130278133079
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13341344.971005098799-3.97100509879908
14343345.230084535257-2.23008453525716
15341342.031277410535-1.03127741053476
16335334.9613611972320.0386388027675366
17355354.436223561250.563776438749869
18357356.7604070728310.239592927169099
19337340.962517825021-3.96251782502145
20325328.868357744425-3.86835774442505
21336327.3655750327928.6344249672075
22338331.8521386191246.14786138087607
23337336.2485901064860.75140989351371
24328338.656364206358-10.6563642063585
25326329.227864980564-3.22786498056416
26327330.433855824206-3.43385582420603
27319327.065605231230-8.06560523123034
28310316.837320985567-6.8373209855668
29320331.263876005043-11.2638760050435
30322326.471034633389-4.47103463338897
31303307.277186128511-4.27718612851055
32292295.435934275592-3.4359342755921
33303298.7835312528874.21646874711342
34315299.24267660013715.7573233998633
35311305.8544081887815.14559181121939
36307305.0300281997621.96997180023806
37308305.5384202234752.46157977652547
38312309.3037699134282.6962300865722
39309307.0477941624931.95220583750677
40310302.8880431177397.11195688226121
41309322.610335665247-13.6103356652467
42304319.873465336919-15.8734653369193
43287295.275493038155-8.27549303815533
44275282.029435349058-7.0294353490579
45290286.5393074430893.46069255691071
46298291.5391678939546.46083210604621
47294288.4199756836055.58002431639483
48286286.439241295129-0.439241295128795
49294285.6674438309818.33255616901937
50292292.341572900368-0.341572900368249
51287288.173121250955-1.17312125095521
52281284.681943920705-3.68194392070501
53280287.876034282732-7.87603428273155
54271286.31467221216-15.3146722121599
55264266.245851842678-2.24585184267846
56259257.1135237064971.88647629350316
57271270.3107698971460.689230102854026
58279274.7161653905924.28383460940785
59279270.2789075638548.7210924361458
60273267.4873406507985.51265934920156
61286273.66188310441912.3381168955813
62286278.4678562630207.53214373698034
63280278.3314950937031.66850490629741
64277275.4089835343371.59101646566251
65269279.546521296137-10.5465212961367
66255273.066915316-18.066915316
67252257.940750965684-5.9407509656844
68245249.051848488310-4.05184848830973
69257257.961202050557-0.961202050557006
70267262.8186396356734.18136036432747
71261260.5205285799270.479471420072628
72258252.2372218254925.7627781745079
73271261.0363796786139.96362032138666
74262262.367878948694-0.367878948693885
75258255.5682526485992.43174735140101
76253253.055750819112-0.0557508191115801
77236250.447748694841-14.4477486948412
78228238.157417061136-10.1574170611362
79235232.5901676070752.4098323929249
80226229.192164888464-3.19216488846354
81231238.947510546337-7.94751054633679
82235241.53163023721-6.53163023720987
83227232.049073345839-5.0490733458391
84222223.499654305332-1.49965430533229
85233228.6396465223684.36035347763192
86221222.767286701235-1.76728670123529
87218216.6452846902561.35471530974414
88220212.476162143527.52383785647987
89204207.737225301989-3.73722530198881
90196202.938562717491-6.93856271749127
91208203.8113786313084.18862136869248
92190199.227057633402-9.22705763340161
93191201.675223548629-10.6752235486290
94194201.692966021135-7.69296602113548
95179192.469333396527-13.4693333965270
96162181.090369306887-19.090369306887
97179176.4768739790832.52312602091683
98176168.2521410719717.74785892802885
99168168.494785808252-0.494785808251777
100170165.6398719265194.36012807348078
101153156.268837803188-3.26883780318838
102142150.243512661275-8.24351266127513
103155152.0289651465922.9710348534083
104136142.808469363308-6.80846936330826
105136142.870668125711-6.87066812571109
106144143.1811185372950.81888146270461
107135136.611460286680-1.61146028667986
108114129.298602276119-15.2986022761191
109135131.8835361844933.11646381550671
110132127.2065710261944.79342897380643
111123123.085158709136-0.0851587091361665
112123121.8057824601921.19421753980778
113103110.479564649033-7.47956464903281
11497100.779417214822-3.77941721482249
115113105.5922837992367.40771620076369
11610897.66323098073610.3367690192641
117111105.1975890851385.80241091486204
118121113.8351017938627.16489820613818
119111110.6643263444680.335673655531906
1209799.6124134355594-2.61241343555938

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 341 & 344.971005098799 & -3.97100509879908 \tabularnewline
14 & 343 & 345.230084535257 & -2.23008453525716 \tabularnewline
15 & 341 & 342.031277410535 & -1.03127741053476 \tabularnewline
16 & 335 & 334.961361197232 & 0.0386388027675366 \tabularnewline
17 & 355 & 354.43622356125 & 0.563776438749869 \tabularnewline
18 & 357 & 356.760407072831 & 0.239592927169099 \tabularnewline
19 & 337 & 340.962517825021 & -3.96251782502145 \tabularnewline
20 & 325 & 328.868357744425 & -3.86835774442505 \tabularnewline
21 & 336 & 327.365575032792 & 8.6344249672075 \tabularnewline
22 & 338 & 331.852138619124 & 6.14786138087607 \tabularnewline
23 & 337 & 336.248590106486 & 0.75140989351371 \tabularnewline
24 & 328 & 338.656364206358 & -10.6563642063585 \tabularnewline
25 & 326 & 329.227864980564 & -3.22786498056416 \tabularnewline
26 & 327 & 330.433855824206 & -3.43385582420603 \tabularnewline
27 & 319 & 327.065605231230 & -8.06560523123034 \tabularnewline
28 & 310 & 316.837320985567 & -6.8373209855668 \tabularnewline
29 & 320 & 331.263876005043 & -11.2638760050435 \tabularnewline
30 & 322 & 326.471034633389 & -4.47103463338897 \tabularnewline
31 & 303 & 307.277186128511 & -4.27718612851055 \tabularnewline
32 & 292 & 295.435934275592 & -3.4359342755921 \tabularnewline
33 & 303 & 298.783531252887 & 4.21646874711342 \tabularnewline
34 & 315 & 299.242676600137 & 15.7573233998633 \tabularnewline
35 & 311 & 305.854408188781 & 5.14559181121939 \tabularnewline
36 & 307 & 305.030028199762 & 1.96997180023806 \tabularnewline
37 & 308 & 305.538420223475 & 2.46157977652547 \tabularnewline
38 & 312 & 309.303769913428 & 2.6962300865722 \tabularnewline
39 & 309 & 307.047794162493 & 1.95220583750677 \tabularnewline
40 & 310 & 302.888043117739 & 7.11195688226121 \tabularnewline
41 & 309 & 322.610335665247 & -13.6103356652467 \tabularnewline
42 & 304 & 319.873465336919 & -15.8734653369193 \tabularnewline
43 & 287 & 295.275493038155 & -8.27549303815533 \tabularnewline
44 & 275 & 282.029435349058 & -7.0294353490579 \tabularnewline
45 & 290 & 286.539307443089 & 3.46069255691071 \tabularnewline
46 & 298 & 291.539167893954 & 6.46083210604621 \tabularnewline
47 & 294 & 288.419975683605 & 5.58002431639483 \tabularnewline
48 & 286 & 286.439241295129 & -0.439241295128795 \tabularnewline
49 & 294 & 285.667443830981 & 8.33255616901937 \tabularnewline
50 & 292 & 292.341572900368 & -0.341572900368249 \tabularnewline
51 & 287 & 288.173121250955 & -1.17312125095521 \tabularnewline
52 & 281 & 284.681943920705 & -3.68194392070501 \tabularnewline
53 & 280 & 287.876034282732 & -7.87603428273155 \tabularnewline
54 & 271 & 286.31467221216 & -15.3146722121599 \tabularnewline
55 & 264 & 266.245851842678 & -2.24585184267846 \tabularnewline
56 & 259 & 257.113523706497 & 1.88647629350316 \tabularnewline
57 & 271 & 270.310769897146 & 0.689230102854026 \tabularnewline
58 & 279 & 274.716165390592 & 4.28383460940785 \tabularnewline
59 & 279 & 270.278907563854 & 8.7210924361458 \tabularnewline
60 & 273 & 267.487340650798 & 5.51265934920156 \tabularnewline
61 & 286 & 273.661883104419 & 12.3381168955813 \tabularnewline
62 & 286 & 278.467856263020 & 7.53214373698034 \tabularnewline
63 & 280 & 278.331495093703 & 1.66850490629741 \tabularnewline
64 & 277 & 275.408983534337 & 1.59101646566251 \tabularnewline
65 & 269 & 279.546521296137 & -10.5465212961367 \tabularnewline
66 & 255 & 273.066915316 & -18.066915316 \tabularnewline
67 & 252 & 257.940750965684 & -5.9407509656844 \tabularnewline
68 & 245 & 249.051848488310 & -4.05184848830973 \tabularnewline
69 & 257 & 257.961202050557 & -0.961202050557006 \tabularnewline
70 & 267 & 262.818639635673 & 4.18136036432747 \tabularnewline
71 & 261 & 260.520528579927 & 0.479471420072628 \tabularnewline
72 & 258 & 252.237221825492 & 5.7627781745079 \tabularnewline
73 & 271 & 261.036379678613 & 9.96362032138666 \tabularnewline
74 & 262 & 262.367878948694 & -0.367878948693885 \tabularnewline
75 & 258 & 255.568252648599 & 2.43174735140101 \tabularnewline
76 & 253 & 253.055750819112 & -0.0557508191115801 \tabularnewline
77 & 236 & 250.447748694841 & -14.4477486948412 \tabularnewline
78 & 228 & 238.157417061136 & -10.1574170611362 \tabularnewline
79 & 235 & 232.590167607075 & 2.4098323929249 \tabularnewline
80 & 226 & 229.192164888464 & -3.19216488846354 \tabularnewline
81 & 231 & 238.947510546337 & -7.94751054633679 \tabularnewline
82 & 235 & 241.53163023721 & -6.53163023720987 \tabularnewline
83 & 227 & 232.049073345839 & -5.0490733458391 \tabularnewline
84 & 222 & 223.499654305332 & -1.49965430533229 \tabularnewline
85 & 233 & 228.639646522368 & 4.36035347763192 \tabularnewline
86 & 221 & 222.767286701235 & -1.76728670123529 \tabularnewline
87 & 218 & 216.645284690256 & 1.35471530974414 \tabularnewline
88 & 220 & 212.47616214352 & 7.52383785647987 \tabularnewline
89 & 204 & 207.737225301989 & -3.73722530198881 \tabularnewline
90 & 196 & 202.938562717491 & -6.93856271749127 \tabularnewline
91 & 208 & 203.811378631308 & 4.18862136869248 \tabularnewline
92 & 190 & 199.227057633402 & -9.22705763340161 \tabularnewline
93 & 191 & 201.675223548629 & -10.6752235486290 \tabularnewline
94 & 194 & 201.692966021135 & -7.69296602113548 \tabularnewline
95 & 179 & 192.469333396527 & -13.4693333965270 \tabularnewline
96 & 162 & 181.090369306887 & -19.090369306887 \tabularnewline
97 & 179 & 176.476873979083 & 2.52312602091683 \tabularnewline
98 & 176 & 168.252141071971 & 7.74785892802885 \tabularnewline
99 & 168 & 168.494785808252 & -0.494785808251777 \tabularnewline
100 & 170 & 165.639871926519 & 4.36012807348078 \tabularnewline
101 & 153 & 156.268837803188 & -3.26883780318838 \tabularnewline
102 & 142 & 150.243512661275 & -8.24351266127513 \tabularnewline
103 & 155 & 152.028965146592 & 2.9710348534083 \tabularnewline
104 & 136 & 142.808469363308 & -6.80846936330826 \tabularnewline
105 & 136 & 142.870668125711 & -6.87066812571109 \tabularnewline
106 & 144 & 143.181118537295 & 0.81888146270461 \tabularnewline
107 & 135 & 136.611460286680 & -1.61146028667986 \tabularnewline
108 & 114 & 129.298602276119 & -15.2986022761191 \tabularnewline
109 & 135 & 131.883536184493 & 3.11646381550671 \tabularnewline
110 & 132 & 127.206571026194 & 4.79342897380643 \tabularnewline
111 & 123 & 123.085158709136 & -0.0851587091361665 \tabularnewline
112 & 123 & 121.805782460192 & 1.19421753980778 \tabularnewline
113 & 103 & 110.479564649033 & -7.47956464903281 \tabularnewline
114 & 97 & 100.779417214822 & -3.77941721482249 \tabularnewline
115 & 113 & 105.592283799236 & 7.40771620076369 \tabularnewline
116 & 108 & 97.663230980736 & 10.3367690192641 \tabularnewline
117 & 111 & 105.197589085138 & 5.80241091486204 \tabularnewline
118 & 121 & 113.835101793862 & 7.16489820613818 \tabularnewline
119 & 111 & 110.664326344468 & 0.335673655531906 \tabularnewline
120 & 97 & 99.6124134355594 & -2.61241343555938 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79382&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]341[/C][C]344.971005098799[/C][C]-3.97100509879908[/C][/ROW]
[ROW][C]14[/C][C]343[/C][C]345.230084535257[/C][C]-2.23008453525716[/C][/ROW]
[ROW][C]15[/C][C]341[/C][C]342.031277410535[/C][C]-1.03127741053476[/C][/ROW]
[ROW][C]16[/C][C]335[/C][C]334.961361197232[/C][C]0.0386388027675366[/C][/ROW]
[ROW][C]17[/C][C]355[/C][C]354.43622356125[/C][C]0.563776438749869[/C][/ROW]
[ROW][C]18[/C][C]357[/C][C]356.760407072831[/C][C]0.239592927169099[/C][/ROW]
[ROW][C]19[/C][C]337[/C][C]340.962517825021[/C][C]-3.96251782502145[/C][/ROW]
[ROW][C]20[/C][C]325[/C][C]328.868357744425[/C][C]-3.86835774442505[/C][/ROW]
[ROW][C]21[/C][C]336[/C][C]327.365575032792[/C][C]8.6344249672075[/C][/ROW]
[ROW][C]22[/C][C]338[/C][C]331.852138619124[/C][C]6.14786138087607[/C][/ROW]
[ROW][C]23[/C][C]337[/C][C]336.248590106486[/C][C]0.75140989351371[/C][/ROW]
[ROW][C]24[/C][C]328[/C][C]338.656364206358[/C][C]-10.6563642063585[/C][/ROW]
[ROW][C]25[/C][C]326[/C][C]329.227864980564[/C][C]-3.22786498056416[/C][/ROW]
[ROW][C]26[/C][C]327[/C][C]330.433855824206[/C][C]-3.43385582420603[/C][/ROW]
[ROW][C]27[/C][C]319[/C][C]327.065605231230[/C][C]-8.06560523123034[/C][/ROW]
[ROW][C]28[/C][C]310[/C][C]316.837320985567[/C][C]-6.8373209855668[/C][/ROW]
[ROW][C]29[/C][C]320[/C][C]331.263876005043[/C][C]-11.2638760050435[/C][/ROW]
[ROW][C]30[/C][C]322[/C][C]326.471034633389[/C][C]-4.47103463338897[/C][/ROW]
[ROW][C]31[/C][C]303[/C][C]307.277186128511[/C][C]-4.27718612851055[/C][/ROW]
[ROW][C]32[/C][C]292[/C][C]295.435934275592[/C][C]-3.4359342755921[/C][/ROW]
[ROW][C]33[/C][C]303[/C][C]298.783531252887[/C][C]4.21646874711342[/C][/ROW]
[ROW][C]34[/C][C]315[/C][C]299.242676600137[/C][C]15.7573233998633[/C][/ROW]
[ROW][C]35[/C][C]311[/C][C]305.854408188781[/C][C]5.14559181121939[/C][/ROW]
[ROW][C]36[/C][C]307[/C][C]305.030028199762[/C][C]1.96997180023806[/C][/ROW]
[ROW][C]37[/C][C]308[/C][C]305.538420223475[/C][C]2.46157977652547[/C][/ROW]
[ROW][C]38[/C][C]312[/C][C]309.303769913428[/C][C]2.6962300865722[/C][/ROW]
[ROW][C]39[/C][C]309[/C][C]307.047794162493[/C][C]1.95220583750677[/C][/ROW]
[ROW][C]40[/C][C]310[/C][C]302.888043117739[/C][C]7.11195688226121[/C][/ROW]
[ROW][C]41[/C][C]309[/C][C]322.610335665247[/C][C]-13.6103356652467[/C][/ROW]
[ROW][C]42[/C][C]304[/C][C]319.873465336919[/C][C]-15.8734653369193[/C][/ROW]
[ROW][C]43[/C][C]287[/C][C]295.275493038155[/C][C]-8.27549303815533[/C][/ROW]
[ROW][C]44[/C][C]275[/C][C]282.029435349058[/C][C]-7.0294353490579[/C][/ROW]
[ROW][C]45[/C][C]290[/C][C]286.539307443089[/C][C]3.46069255691071[/C][/ROW]
[ROW][C]46[/C][C]298[/C][C]291.539167893954[/C][C]6.46083210604621[/C][/ROW]
[ROW][C]47[/C][C]294[/C][C]288.419975683605[/C][C]5.58002431639483[/C][/ROW]
[ROW][C]48[/C][C]286[/C][C]286.439241295129[/C][C]-0.439241295128795[/C][/ROW]
[ROW][C]49[/C][C]294[/C][C]285.667443830981[/C][C]8.33255616901937[/C][/ROW]
[ROW][C]50[/C][C]292[/C][C]292.341572900368[/C][C]-0.341572900368249[/C][/ROW]
[ROW][C]51[/C][C]287[/C][C]288.173121250955[/C][C]-1.17312125095521[/C][/ROW]
[ROW][C]52[/C][C]281[/C][C]284.681943920705[/C][C]-3.68194392070501[/C][/ROW]
[ROW][C]53[/C][C]280[/C][C]287.876034282732[/C][C]-7.87603428273155[/C][/ROW]
[ROW][C]54[/C][C]271[/C][C]286.31467221216[/C][C]-15.3146722121599[/C][/ROW]
[ROW][C]55[/C][C]264[/C][C]266.245851842678[/C][C]-2.24585184267846[/C][/ROW]
[ROW][C]56[/C][C]259[/C][C]257.113523706497[/C][C]1.88647629350316[/C][/ROW]
[ROW][C]57[/C][C]271[/C][C]270.310769897146[/C][C]0.689230102854026[/C][/ROW]
[ROW][C]58[/C][C]279[/C][C]274.716165390592[/C][C]4.28383460940785[/C][/ROW]
[ROW][C]59[/C][C]279[/C][C]270.278907563854[/C][C]8.7210924361458[/C][/ROW]
[ROW][C]60[/C][C]273[/C][C]267.487340650798[/C][C]5.51265934920156[/C][/ROW]
[ROW][C]61[/C][C]286[/C][C]273.661883104419[/C][C]12.3381168955813[/C][/ROW]
[ROW][C]62[/C][C]286[/C][C]278.467856263020[/C][C]7.53214373698034[/C][/ROW]
[ROW][C]63[/C][C]280[/C][C]278.331495093703[/C][C]1.66850490629741[/C][/ROW]
[ROW][C]64[/C][C]277[/C][C]275.408983534337[/C][C]1.59101646566251[/C][/ROW]
[ROW][C]65[/C][C]269[/C][C]279.546521296137[/C][C]-10.5465212961367[/C][/ROW]
[ROW][C]66[/C][C]255[/C][C]273.066915316[/C][C]-18.066915316[/C][/ROW]
[ROW][C]67[/C][C]252[/C][C]257.940750965684[/C][C]-5.9407509656844[/C][/ROW]
[ROW][C]68[/C][C]245[/C][C]249.051848488310[/C][C]-4.05184848830973[/C][/ROW]
[ROW][C]69[/C][C]257[/C][C]257.961202050557[/C][C]-0.961202050557006[/C][/ROW]
[ROW][C]70[/C][C]267[/C][C]262.818639635673[/C][C]4.18136036432747[/C][/ROW]
[ROW][C]71[/C][C]261[/C][C]260.520528579927[/C][C]0.479471420072628[/C][/ROW]
[ROW][C]72[/C][C]258[/C][C]252.237221825492[/C][C]5.7627781745079[/C][/ROW]
[ROW][C]73[/C][C]271[/C][C]261.036379678613[/C][C]9.96362032138666[/C][/ROW]
[ROW][C]74[/C][C]262[/C][C]262.367878948694[/C][C]-0.367878948693885[/C][/ROW]
[ROW][C]75[/C][C]258[/C][C]255.568252648599[/C][C]2.43174735140101[/C][/ROW]
[ROW][C]76[/C][C]253[/C][C]253.055750819112[/C][C]-0.0557508191115801[/C][/ROW]
[ROW][C]77[/C][C]236[/C][C]250.447748694841[/C][C]-14.4477486948412[/C][/ROW]
[ROW][C]78[/C][C]228[/C][C]238.157417061136[/C][C]-10.1574170611362[/C][/ROW]
[ROW][C]79[/C][C]235[/C][C]232.590167607075[/C][C]2.4098323929249[/C][/ROW]
[ROW][C]80[/C][C]226[/C][C]229.192164888464[/C][C]-3.19216488846354[/C][/ROW]
[ROW][C]81[/C][C]231[/C][C]238.947510546337[/C][C]-7.94751054633679[/C][/ROW]
[ROW][C]82[/C][C]235[/C][C]241.53163023721[/C][C]-6.53163023720987[/C][/ROW]
[ROW][C]83[/C][C]227[/C][C]232.049073345839[/C][C]-5.0490733458391[/C][/ROW]
[ROW][C]84[/C][C]222[/C][C]223.499654305332[/C][C]-1.49965430533229[/C][/ROW]
[ROW][C]85[/C][C]233[/C][C]228.639646522368[/C][C]4.36035347763192[/C][/ROW]
[ROW][C]86[/C][C]221[/C][C]222.767286701235[/C][C]-1.76728670123529[/C][/ROW]
[ROW][C]87[/C][C]218[/C][C]216.645284690256[/C][C]1.35471530974414[/C][/ROW]
[ROW][C]88[/C][C]220[/C][C]212.47616214352[/C][C]7.52383785647987[/C][/ROW]
[ROW][C]89[/C][C]204[/C][C]207.737225301989[/C][C]-3.73722530198881[/C][/ROW]
[ROW][C]90[/C][C]196[/C][C]202.938562717491[/C][C]-6.93856271749127[/C][/ROW]
[ROW][C]91[/C][C]208[/C][C]203.811378631308[/C][C]4.18862136869248[/C][/ROW]
[ROW][C]92[/C][C]190[/C][C]199.227057633402[/C][C]-9.22705763340161[/C][/ROW]
[ROW][C]93[/C][C]191[/C][C]201.675223548629[/C][C]-10.6752235486290[/C][/ROW]
[ROW][C]94[/C][C]194[/C][C]201.692966021135[/C][C]-7.69296602113548[/C][/ROW]
[ROW][C]95[/C][C]179[/C][C]192.469333396527[/C][C]-13.4693333965270[/C][/ROW]
[ROW][C]96[/C][C]162[/C][C]181.090369306887[/C][C]-19.090369306887[/C][/ROW]
[ROW][C]97[/C][C]179[/C][C]176.476873979083[/C][C]2.52312602091683[/C][/ROW]
[ROW][C]98[/C][C]176[/C][C]168.252141071971[/C][C]7.74785892802885[/C][/ROW]
[ROW][C]99[/C][C]168[/C][C]168.494785808252[/C][C]-0.494785808251777[/C][/ROW]
[ROW][C]100[/C][C]170[/C][C]165.639871926519[/C][C]4.36012807348078[/C][/ROW]
[ROW][C]101[/C][C]153[/C][C]156.268837803188[/C][C]-3.26883780318838[/C][/ROW]
[ROW][C]102[/C][C]142[/C][C]150.243512661275[/C][C]-8.24351266127513[/C][/ROW]
[ROW][C]103[/C][C]155[/C][C]152.028965146592[/C][C]2.9710348534083[/C][/ROW]
[ROW][C]104[/C][C]136[/C][C]142.808469363308[/C][C]-6.80846936330826[/C][/ROW]
[ROW][C]105[/C][C]136[/C][C]142.870668125711[/C][C]-6.87066812571109[/C][/ROW]
[ROW][C]106[/C][C]144[/C][C]143.181118537295[/C][C]0.81888146270461[/C][/ROW]
[ROW][C]107[/C][C]135[/C][C]136.611460286680[/C][C]-1.61146028667986[/C][/ROW]
[ROW][C]108[/C][C]114[/C][C]129.298602276119[/C][C]-15.2986022761191[/C][/ROW]
[ROW][C]109[/C][C]135[/C][C]131.883536184493[/C][C]3.11646381550671[/C][/ROW]
[ROW][C]110[/C][C]132[/C][C]127.206571026194[/C][C]4.79342897380643[/C][/ROW]
[ROW][C]111[/C][C]123[/C][C]123.085158709136[/C][C]-0.0851587091361665[/C][/ROW]
[ROW][C]112[/C][C]123[/C][C]121.805782460192[/C][C]1.19421753980778[/C][/ROW]
[ROW][C]113[/C][C]103[/C][C]110.479564649033[/C][C]-7.47956464903281[/C][/ROW]
[ROW][C]114[/C][C]97[/C][C]100.779417214822[/C][C]-3.77941721482249[/C][/ROW]
[ROW][C]115[/C][C]113[/C][C]105.592283799236[/C][C]7.40771620076369[/C][/ROW]
[ROW][C]116[/C][C]108[/C][C]97.663230980736[/C][C]10.3367690192641[/C][/ROW]
[ROW][C]117[/C][C]111[/C][C]105.197589085138[/C][C]5.80241091486204[/C][/ROW]
[ROW][C]118[/C][C]121[/C][C]113.835101793862[/C][C]7.16489820613818[/C][/ROW]
[ROW][C]119[/C][C]111[/C][C]110.664326344468[/C][C]0.335673655531906[/C][/ROW]
[ROW][C]120[/C][C]97[/C][C]99.6124134355594[/C][C]-2.61241343555938[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79382&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79382&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
13341344.971005098799-3.97100509879908
14343345.230084535257-2.23008453525716
15341342.031277410535-1.03127741053476
16335334.9613611972320.0386388027675366
17355354.436223561250.563776438749869
18357356.7604070728310.239592927169099
19337340.962517825021-3.96251782502145
20325328.868357744425-3.86835774442505
21336327.3655750327928.6344249672075
22338331.8521386191246.14786138087607
23337336.2485901064860.75140989351371
24328338.656364206358-10.6563642063585
25326329.227864980564-3.22786498056416
26327330.433855824206-3.43385582420603
27319327.065605231230-8.06560523123034
28310316.837320985567-6.8373209855668
29320331.263876005043-11.2638760050435
30322326.471034633389-4.47103463338897
31303307.277186128511-4.27718612851055
32292295.435934275592-3.4359342755921
33303298.7835312528874.21646874711342
34315299.24267660013715.7573233998633
35311305.8544081887815.14559181121939
36307305.0300281997621.96997180023806
37308305.5384202234752.46157977652547
38312309.3037699134282.6962300865722
39309307.0477941624931.95220583750677
40310302.8880431177397.11195688226121
41309322.610335665247-13.6103356652467
42304319.873465336919-15.8734653369193
43287295.275493038155-8.27549303815533
44275282.029435349058-7.0294353490579
45290286.5393074430893.46069255691071
46298291.5391678939546.46083210604621
47294288.4199756836055.58002431639483
48286286.439241295129-0.439241295128795
49294285.6674438309818.33255616901937
50292292.341572900368-0.341572900368249
51287288.173121250955-1.17312125095521
52281284.681943920705-3.68194392070501
53280287.876034282732-7.87603428273155
54271286.31467221216-15.3146722121599
55264266.245851842678-2.24585184267846
56259257.1135237064971.88647629350316
57271270.3107698971460.689230102854026
58279274.7161653905924.28383460940785
59279270.2789075638548.7210924361458
60273267.4873406507985.51265934920156
61286273.66188310441912.3381168955813
62286278.4678562630207.53214373698034
63280278.3314950937031.66850490629741
64277275.4089835343371.59101646566251
65269279.546521296137-10.5465212961367
66255273.066915316-18.066915316
67252257.940750965684-5.9407509656844
68245249.051848488310-4.05184848830973
69257257.961202050557-0.961202050557006
70267262.8186396356734.18136036432747
71261260.5205285799270.479471420072628
72258252.2372218254925.7627781745079
73271261.0363796786139.96362032138666
74262262.367878948694-0.367878948693885
75258255.5682526485992.43174735140101
76253253.055750819112-0.0557508191115801
77236250.447748694841-14.4477486948412
78228238.157417061136-10.1574170611362
79235232.5901676070752.4098323929249
80226229.192164888464-3.19216488846354
81231238.947510546337-7.94751054633679
82235241.53163023721-6.53163023720987
83227232.049073345839-5.0490733458391
84222223.499654305332-1.49965430533229
85233228.6396465223684.36035347763192
86221222.767286701235-1.76728670123529
87218216.6452846902561.35471530974414
88220212.476162143527.52383785647987
89204207.737225301989-3.73722530198881
90196202.938562717491-6.93856271749127
91208203.8113786313084.18862136869248
92190199.227057633402-9.22705763340161
93191201.675223548629-10.6752235486290
94194201.692966021135-7.69296602113548
95179192.469333396527-13.4693333965270
96162181.090369306887-19.090369306887
97179176.4768739790832.52312602091683
98176168.2521410719717.74785892802885
99168168.494785808252-0.494785808251777
100170165.6398719265194.36012807348078
101153156.268837803188-3.26883780318838
102142150.243512661275-8.24351266127513
103155152.0289651465922.9710348534083
104136142.808469363308-6.80846936330826
105136142.870668125711-6.87066812571109
106144143.1811185372950.81888146270461
107135136.611460286680-1.61146028667986
108114129.298602276119-15.2986022761191
109135131.8835361844933.11646381550671
110132127.2065710261944.79342897380643
111123123.085158709136-0.0851587091361665
112123121.8057824601921.19421753980778
113103110.479564649033-7.47956464903281
11497100.779417214822-3.77941721482249
115113105.5922837992367.40771620076369
11610897.66323098073610.3367690192641
117111105.1975890851385.80241091486204
118121113.8351017938627.16489820613818
119111110.6643263444680.335673655531906
1209799.6124134355594-2.61241343555938







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121114.816336493040101.307662274083128.325010711998
122109.93786119009694.633224997304125.242497382889
123102.26582499524285.5186842746664119.012965715817
124101.51555888428582.9645523451852120.066565423386
12587.958601887472669.0316348189462106.885568955999
12684.443135279758664.1282615071186104.758009052399
12794.8440273693270.8973535825154118.790701156125
12885.671648100242361.5890113991952109.754284801289
12985.161603525366459.2495411975863111.073665853146
13089.286448168071460.3402311909033118.232665145240
13181.132528108068452.3728565984233109.892199617713
13271.301487241887846.431434729919596.171539753856

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 114.816336493040 & 101.307662274083 & 128.325010711998 \tabularnewline
122 & 109.937861190096 & 94.633224997304 & 125.242497382889 \tabularnewline
123 & 102.265824995242 & 85.5186842746664 & 119.012965715817 \tabularnewline
124 & 101.515558884285 & 82.9645523451852 & 120.066565423386 \tabularnewline
125 & 87.9586018874726 & 69.0316348189462 & 106.885568955999 \tabularnewline
126 & 84.4431352797586 & 64.1282615071186 & 104.758009052399 \tabularnewline
127 & 94.84402736932 & 70.8973535825154 & 118.790701156125 \tabularnewline
128 & 85.6716481002423 & 61.5890113991952 & 109.754284801289 \tabularnewline
129 & 85.1616035253664 & 59.2495411975863 & 111.073665853146 \tabularnewline
130 & 89.2864481680714 & 60.3402311909033 & 118.232665145240 \tabularnewline
131 & 81.1325281080684 & 52.3728565984233 & 109.892199617713 \tabularnewline
132 & 71.3014872418878 & 46.4314347299195 & 96.171539753856 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79382&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]114.816336493040[/C][C]101.307662274083[/C][C]128.325010711998[/C][/ROW]
[ROW][C]122[/C][C]109.937861190096[/C][C]94.633224997304[/C][C]125.242497382889[/C][/ROW]
[ROW][C]123[/C][C]102.265824995242[/C][C]85.5186842746664[/C][C]119.012965715817[/C][/ROW]
[ROW][C]124[/C][C]101.515558884285[/C][C]82.9645523451852[/C][C]120.066565423386[/C][/ROW]
[ROW][C]125[/C][C]87.9586018874726[/C][C]69.0316348189462[/C][C]106.885568955999[/C][/ROW]
[ROW][C]126[/C][C]84.4431352797586[/C][C]64.1282615071186[/C][C]104.758009052399[/C][/ROW]
[ROW][C]127[/C][C]94.84402736932[/C][C]70.8973535825154[/C][C]118.790701156125[/C][/ROW]
[ROW][C]128[/C][C]85.6716481002423[/C][C]61.5890113991952[/C][C]109.754284801289[/C][/ROW]
[ROW][C]129[/C][C]85.1616035253664[/C][C]59.2495411975863[/C][C]111.073665853146[/C][/ROW]
[ROW][C]130[/C][C]89.2864481680714[/C][C]60.3402311909033[/C][C]118.232665145240[/C][/ROW]
[ROW][C]131[/C][C]81.1325281080684[/C][C]52.3728565984233[/C][C]109.892199617713[/C][/ROW]
[ROW][C]132[/C][C]71.3014872418878[/C][C]46.4314347299195[/C][C]96.171539753856[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79382&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79382&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
121114.816336493040101.307662274083128.325010711998
122109.93786119009694.633224997304125.242497382889
123102.26582499524285.5186842746664119.012965715817
124101.51555888428582.9645523451852120.066565423386
12587.958601887472669.0316348189462106.885568955999
12684.443135279758664.1282615071186104.758009052399
12794.8440273693270.8973535825154118.790701156125
12885.671648100242361.5890113991952109.754284801289
12985.161603525366459.2495411975863111.073665853146
13089.286448168071460.3402311909033118.232665145240
13181.132528108068452.3728565984233109.892199617713
13271.301487241887846.431434729919596.171539753856



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')