Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 21 Dec 2012 10:58:17 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/21/t1356106664medskfxmvmd3j3c.htm/, Retrieved Wed, 24 Apr 2024 15:10:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=203882, Retrieved Wed, 24 Apr 2024 15:10:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact83
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential smoot...] [2012-12-21 15:58:17] [70625068b3924f89f7a6efd1a4acaa7e] [Current]
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Dataseries X:
41
39
50
40
43
38
44
35
39
35
29
49
50
59
63
32
39
47
53
60
57
52
70
90
74
62
55
84
94
70
108
139
120
97
126
149
158
124
140
109
114
77
120
133
110
92
97
78
99
107
112
90
98
125
155
190
236
189
174
178
136
161
171
149
184
155
276
224
213
279
268
287
238
213
257
293
212
246
353
339
308
247
257
322
298
273
312
249
286
279
309
401
309
328
353
354
327
324
285
243
241
287
355
460
364
487
452
391
500
451
375
372
302
316
398
394
431
431




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203882&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203882&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203882&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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.644861384977089
beta0.0138899171733415
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.644861384977089 \tabularnewline
beta & 0.0138899171733415 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203882&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]0.644861384977089[/C][/ROW]
[ROW][C]beta[/C][C]0.0138899171733415[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203882&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203882&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
alpha0.644861384977089
beta0.0138899171733415
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3503713
44043.4996399306352-3.49963993063519
54339.3279526798553.67204732014502
63839.8139003916258-1.81390039162581
74436.74592502906827.25407497093177
83539.5905120839383-4.59051208393826
93934.75586478242524.24413521757479
103535.6563553969849-0.656355396984942
112933.3908298247323-4.39082982473234
124928.677756925361320.3222430746387
135040.08321822160249.91678177839765
145944.867424655741914.1325753442581
156352.496820051499710.5031799485003
163257.8798362366138-25.8798362366138
173939.5690426784727-0.569042678472705
184737.57510555330229.42489444669783
195342.110292014896110.8897079851039
206047.687620053648512.3123799463515
215754.29265716783542.70734283216461
225254.7280266083913-2.72802660839127
237051.633901055011418.3660989449886
249062.307068977251727.6929310227483
257479.2427983062217-5.24279830622173
266274.8925874870312-12.8925874870312
275565.4938431975173-10.4938431975173
288457.547962371794626.4520376282054
299473.663986209644520.3360137903555
307086.018173568831-16.018173568831
3110874.785473396295533.2145266037045
3213995.598545323697643.4014546763024
33120123.369523717488-3.36952371748829
3497120.949523143592-23.9495231435916
35126105.04375805233420.9562419476665
36149118.28369338302730.7163066169735
37158138.09264567999119.9073543200091
38124151.109633619142-27.1096336191415
39140133.5643586791736.4356413208267
40109137.708780694123-28.7087806941234
41114118.932775460816-4.93277546081553
4277115.444814670339-38.4448146703386
4312090.001880918544229.9981190814558
44133108.96384750707424.0361524929257
45110124.296465594007-14.2964655940067
4692114.781804031002-22.7818040310019
479799.5912171301633-2.5912171301633
487897.3975503453038-19.3975503453038
499984.19238300689714.807616993103
5010793.177440131797213.8225598682028
51112101.65108160811310.3489183918875
5290107.977401830242-17.9774018302416
539895.87614709397892.12385290602109
5412596.756438828471828.2435611715282
55155114.73330139933640.2666986006643
56190140.82409271190949.1759072880912
57236173.1005607818762.8994392181303
58189214.790199416141-25.7901994161412
59174199.056310194506-25.0563101945055
60178183.57124663769-5.57124663769022
61136180.60144609954-44.6014460995402
62161152.063078751018.93692124898965
63171158.12958576043112.8704142395694
64149166.847931724601-17.8479317246008
65184155.59733737042428.4026626295764
66155174.426370019665-19.426370019665
67276162.238303052681113.761696947319
68224236.957049034752-12.9570490347517
69213229.843711769186-16.8437117691863
70279220.07314546373458.9268545362659
71268259.6919035196978.30809648030282
72287266.74299536179520.2570046382049
73238281.680920100924-43.6809201009239
74213254.996493027673-41.9964930276727
75257229.02212235049627.9778776495039
76293248.42212110395244.5778788960479
77212278.926106888235-66.9261068882347
78246236.9260160629489.07398393705208
79353244.016725386064108.983274613936
80339316.51124922027322.4887507797273
81308333.430227964329-25.4302279643288
82247319.220327345645-72.220327345645
83257274.190415820738-17.1904158207376
84322264.49319347804457.5068065219557
85298303.480417951177-5.48041795117678
86273301.800525120767-28.8005251207674
87312284.8244273283227.1755726716802
88249304.18856702394-55.1885670239401
89286269.94492559732316.055074402677
90279281.787363896843-2.78736389684269
91309281.45407472123327.545925278767
92401300.928283229015100.071716770985
93309368.067923579816-59.067923579816
94328332.05547945059-4.0554794505897
95353331.48211101521821.5178889847819
96354347.5927576318716.40724236812872
97327354.016521869661-27.0165218696612
98324338.644602299267-14.6446022992671
99285331.119683171997-46.1196831719972
100243302.884602513798-59.8846025137981
101241265.236666254713-24.2366662547135
102287250.35961799732236.6403820026778
103355275.06801790384179.9319820961588
104460328.409455461357131.590544538643
105364416.242171021509-52.2421710215087
106487385.060330174621101.939669825379
107452454.217485637917-2.2174856379167
108391456.187851397077-65.1878513970768
109500416.96716765226283.0328323477376
110451474.072010302784-23.0720103027837
111375462.547279529313-87.5472795293135
112372408.660770127299-36.6607701272994
113302387.260632525702-85.2606325257016
114316333.7566347899-17.7566347899002
115398323.62431108295874.3756889170425
116394373.57075358591620.4292464140842
117431388.91220467704642.0877953229539
118431418.59740099458112.4025990054188

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 50 & 37 & 13 \tabularnewline
4 & 40 & 43.4996399306352 & -3.49963993063519 \tabularnewline
5 & 43 & 39.327952679855 & 3.67204732014502 \tabularnewline
6 & 38 & 39.8139003916258 & -1.81390039162581 \tabularnewline
7 & 44 & 36.7459250290682 & 7.25407497093177 \tabularnewline
8 & 35 & 39.5905120839383 & -4.59051208393826 \tabularnewline
9 & 39 & 34.7558647824252 & 4.24413521757479 \tabularnewline
10 & 35 & 35.6563553969849 & -0.656355396984942 \tabularnewline
11 & 29 & 33.3908298247323 & -4.39082982473234 \tabularnewline
12 & 49 & 28.6777569253613 & 20.3222430746387 \tabularnewline
13 & 50 & 40.0832182216024 & 9.91678177839765 \tabularnewline
14 & 59 & 44.8674246557419 & 14.1325753442581 \tabularnewline
15 & 63 & 52.4968200514997 & 10.5031799485003 \tabularnewline
16 & 32 & 57.8798362366138 & -25.8798362366138 \tabularnewline
17 & 39 & 39.5690426784727 & -0.569042678472705 \tabularnewline
18 & 47 & 37.5751055533022 & 9.42489444669783 \tabularnewline
19 & 53 & 42.1102920148961 & 10.8897079851039 \tabularnewline
20 & 60 & 47.6876200536485 & 12.3123799463515 \tabularnewline
21 & 57 & 54.2926571678354 & 2.70734283216461 \tabularnewline
22 & 52 & 54.7280266083913 & -2.72802660839127 \tabularnewline
23 & 70 & 51.6339010550114 & 18.3660989449886 \tabularnewline
24 & 90 & 62.3070689772517 & 27.6929310227483 \tabularnewline
25 & 74 & 79.2427983062217 & -5.24279830622173 \tabularnewline
26 & 62 & 74.8925874870312 & -12.8925874870312 \tabularnewline
27 & 55 & 65.4938431975173 & -10.4938431975173 \tabularnewline
28 & 84 & 57.5479623717946 & 26.4520376282054 \tabularnewline
29 & 94 & 73.6639862096445 & 20.3360137903555 \tabularnewline
30 & 70 & 86.018173568831 & -16.018173568831 \tabularnewline
31 & 108 & 74.7854733962955 & 33.2145266037045 \tabularnewline
32 & 139 & 95.5985453236976 & 43.4014546763024 \tabularnewline
33 & 120 & 123.369523717488 & -3.36952371748829 \tabularnewline
34 & 97 & 120.949523143592 & -23.9495231435916 \tabularnewline
35 & 126 & 105.043758052334 & 20.9562419476665 \tabularnewline
36 & 149 & 118.283693383027 & 30.7163066169735 \tabularnewline
37 & 158 & 138.092645679991 & 19.9073543200091 \tabularnewline
38 & 124 & 151.109633619142 & -27.1096336191415 \tabularnewline
39 & 140 & 133.564358679173 & 6.4356413208267 \tabularnewline
40 & 109 & 137.708780694123 & -28.7087806941234 \tabularnewline
41 & 114 & 118.932775460816 & -4.93277546081553 \tabularnewline
42 & 77 & 115.444814670339 & -38.4448146703386 \tabularnewline
43 & 120 & 90.0018809185442 & 29.9981190814558 \tabularnewline
44 & 133 & 108.963847507074 & 24.0361524929257 \tabularnewline
45 & 110 & 124.296465594007 & -14.2964655940067 \tabularnewline
46 & 92 & 114.781804031002 & -22.7818040310019 \tabularnewline
47 & 97 & 99.5912171301633 & -2.5912171301633 \tabularnewline
48 & 78 & 97.3975503453038 & -19.3975503453038 \tabularnewline
49 & 99 & 84.192383006897 & 14.807616993103 \tabularnewline
50 & 107 & 93.1774401317972 & 13.8225598682028 \tabularnewline
51 & 112 & 101.651081608113 & 10.3489183918875 \tabularnewline
52 & 90 & 107.977401830242 & -17.9774018302416 \tabularnewline
53 & 98 & 95.8761470939789 & 2.12385290602109 \tabularnewline
54 & 125 & 96.7564388284718 & 28.2435611715282 \tabularnewline
55 & 155 & 114.733301399336 & 40.2666986006643 \tabularnewline
56 & 190 & 140.824092711909 & 49.1759072880912 \tabularnewline
57 & 236 & 173.10056078187 & 62.8994392181303 \tabularnewline
58 & 189 & 214.790199416141 & -25.7901994161412 \tabularnewline
59 & 174 & 199.056310194506 & -25.0563101945055 \tabularnewline
60 & 178 & 183.57124663769 & -5.57124663769022 \tabularnewline
61 & 136 & 180.60144609954 & -44.6014460995402 \tabularnewline
62 & 161 & 152.06307875101 & 8.93692124898965 \tabularnewline
63 & 171 & 158.129585760431 & 12.8704142395694 \tabularnewline
64 & 149 & 166.847931724601 & -17.8479317246008 \tabularnewline
65 & 184 & 155.597337370424 & 28.4026626295764 \tabularnewline
66 & 155 & 174.426370019665 & -19.426370019665 \tabularnewline
67 & 276 & 162.238303052681 & 113.761696947319 \tabularnewline
68 & 224 & 236.957049034752 & -12.9570490347517 \tabularnewline
69 & 213 & 229.843711769186 & -16.8437117691863 \tabularnewline
70 & 279 & 220.073145463734 & 58.9268545362659 \tabularnewline
71 & 268 & 259.691903519697 & 8.30809648030282 \tabularnewline
72 & 287 & 266.742995361795 & 20.2570046382049 \tabularnewline
73 & 238 & 281.680920100924 & -43.6809201009239 \tabularnewline
74 & 213 & 254.996493027673 & -41.9964930276727 \tabularnewline
75 & 257 & 229.022122350496 & 27.9778776495039 \tabularnewline
76 & 293 & 248.422121103952 & 44.5778788960479 \tabularnewline
77 & 212 & 278.926106888235 & -66.9261068882347 \tabularnewline
78 & 246 & 236.926016062948 & 9.07398393705208 \tabularnewline
79 & 353 & 244.016725386064 & 108.983274613936 \tabularnewline
80 & 339 & 316.511249220273 & 22.4887507797273 \tabularnewline
81 & 308 & 333.430227964329 & -25.4302279643288 \tabularnewline
82 & 247 & 319.220327345645 & -72.220327345645 \tabularnewline
83 & 257 & 274.190415820738 & -17.1904158207376 \tabularnewline
84 & 322 & 264.493193478044 & 57.5068065219557 \tabularnewline
85 & 298 & 303.480417951177 & -5.48041795117678 \tabularnewline
86 & 273 & 301.800525120767 & -28.8005251207674 \tabularnewline
87 & 312 & 284.82442732832 & 27.1755726716802 \tabularnewline
88 & 249 & 304.18856702394 & -55.1885670239401 \tabularnewline
89 & 286 & 269.944925597323 & 16.055074402677 \tabularnewline
90 & 279 & 281.787363896843 & -2.78736389684269 \tabularnewline
91 & 309 & 281.454074721233 & 27.545925278767 \tabularnewline
92 & 401 & 300.928283229015 & 100.071716770985 \tabularnewline
93 & 309 & 368.067923579816 & -59.067923579816 \tabularnewline
94 & 328 & 332.05547945059 & -4.0554794505897 \tabularnewline
95 & 353 & 331.482111015218 & 21.5178889847819 \tabularnewline
96 & 354 & 347.592757631871 & 6.40724236812872 \tabularnewline
97 & 327 & 354.016521869661 & -27.0165218696612 \tabularnewline
98 & 324 & 338.644602299267 & -14.6446022992671 \tabularnewline
99 & 285 & 331.119683171997 & -46.1196831719972 \tabularnewline
100 & 243 & 302.884602513798 & -59.8846025137981 \tabularnewline
101 & 241 & 265.236666254713 & -24.2366662547135 \tabularnewline
102 & 287 & 250.359617997322 & 36.6403820026778 \tabularnewline
103 & 355 & 275.068017903841 & 79.9319820961588 \tabularnewline
104 & 460 & 328.409455461357 & 131.590544538643 \tabularnewline
105 & 364 & 416.242171021509 & -52.2421710215087 \tabularnewline
106 & 487 & 385.060330174621 & 101.939669825379 \tabularnewline
107 & 452 & 454.217485637917 & -2.2174856379167 \tabularnewline
108 & 391 & 456.187851397077 & -65.1878513970768 \tabularnewline
109 & 500 & 416.967167652262 & 83.0328323477376 \tabularnewline
110 & 451 & 474.072010302784 & -23.0720103027837 \tabularnewline
111 & 375 & 462.547279529313 & -87.5472795293135 \tabularnewline
112 & 372 & 408.660770127299 & -36.6607701272994 \tabularnewline
113 & 302 & 387.260632525702 & -85.2606325257016 \tabularnewline
114 & 316 & 333.7566347899 & -17.7566347899002 \tabularnewline
115 & 398 & 323.624311082958 & 74.3756889170425 \tabularnewline
116 & 394 & 373.570753585916 & 20.4292464140842 \tabularnewline
117 & 431 & 388.912204677046 & 42.0877953229539 \tabularnewline
118 & 431 & 418.597400994581 & 12.4025990054188 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203882&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]3[/C][C]50[/C][C]37[/C][C]13[/C][/ROW]
[ROW][C]4[/C][C]40[/C][C]43.4996399306352[/C][C]-3.49963993063519[/C][/ROW]
[ROW][C]5[/C][C]43[/C][C]39.327952679855[/C][C]3.67204732014502[/C][/ROW]
[ROW][C]6[/C][C]38[/C][C]39.8139003916258[/C][C]-1.81390039162581[/C][/ROW]
[ROW][C]7[/C][C]44[/C][C]36.7459250290682[/C][C]7.25407497093177[/C][/ROW]
[ROW][C]8[/C][C]35[/C][C]39.5905120839383[/C][C]-4.59051208393826[/C][/ROW]
[ROW][C]9[/C][C]39[/C][C]34.7558647824252[/C][C]4.24413521757479[/C][/ROW]
[ROW][C]10[/C][C]35[/C][C]35.6563553969849[/C][C]-0.656355396984942[/C][/ROW]
[ROW][C]11[/C][C]29[/C][C]33.3908298247323[/C][C]-4.39082982473234[/C][/ROW]
[ROW][C]12[/C][C]49[/C][C]28.6777569253613[/C][C]20.3222430746387[/C][/ROW]
[ROW][C]13[/C][C]50[/C][C]40.0832182216024[/C][C]9.91678177839765[/C][/ROW]
[ROW][C]14[/C][C]59[/C][C]44.8674246557419[/C][C]14.1325753442581[/C][/ROW]
[ROW][C]15[/C][C]63[/C][C]52.4968200514997[/C][C]10.5031799485003[/C][/ROW]
[ROW][C]16[/C][C]32[/C][C]57.8798362366138[/C][C]-25.8798362366138[/C][/ROW]
[ROW][C]17[/C][C]39[/C][C]39.5690426784727[/C][C]-0.569042678472705[/C][/ROW]
[ROW][C]18[/C][C]47[/C][C]37.5751055533022[/C][C]9.42489444669783[/C][/ROW]
[ROW][C]19[/C][C]53[/C][C]42.1102920148961[/C][C]10.8897079851039[/C][/ROW]
[ROW][C]20[/C][C]60[/C][C]47.6876200536485[/C][C]12.3123799463515[/C][/ROW]
[ROW][C]21[/C][C]57[/C][C]54.2926571678354[/C][C]2.70734283216461[/C][/ROW]
[ROW][C]22[/C][C]52[/C][C]54.7280266083913[/C][C]-2.72802660839127[/C][/ROW]
[ROW][C]23[/C][C]70[/C][C]51.6339010550114[/C][C]18.3660989449886[/C][/ROW]
[ROW][C]24[/C][C]90[/C][C]62.3070689772517[/C][C]27.6929310227483[/C][/ROW]
[ROW][C]25[/C][C]74[/C][C]79.2427983062217[/C][C]-5.24279830622173[/C][/ROW]
[ROW][C]26[/C][C]62[/C][C]74.8925874870312[/C][C]-12.8925874870312[/C][/ROW]
[ROW][C]27[/C][C]55[/C][C]65.4938431975173[/C][C]-10.4938431975173[/C][/ROW]
[ROW][C]28[/C][C]84[/C][C]57.5479623717946[/C][C]26.4520376282054[/C][/ROW]
[ROW][C]29[/C][C]94[/C][C]73.6639862096445[/C][C]20.3360137903555[/C][/ROW]
[ROW][C]30[/C][C]70[/C][C]86.018173568831[/C][C]-16.018173568831[/C][/ROW]
[ROW][C]31[/C][C]108[/C][C]74.7854733962955[/C][C]33.2145266037045[/C][/ROW]
[ROW][C]32[/C][C]139[/C][C]95.5985453236976[/C][C]43.4014546763024[/C][/ROW]
[ROW][C]33[/C][C]120[/C][C]123.369523717488[/C][C]-3.36952371748829[/C][/ROW]
[ROW][C]34[/C][C]97[/C][C]120.949523143592[/C][C]-23.9495231435916[/C][/ROW]
[ROW][C]35[/C][C]126[/C][C]105.043758052334[/C][C]20.9562419476665[/C][/ROW]
[ROW][C]36[/C][C]149[/C][C]118.283693383027[/C][C]30.7163066169735[/C][/ROW]
[ROW][C]37[/C][C]158[/C][C]138.092645679991[/C][C]19.9073543200091[/C][/ROW]
[ROW][C]38[/C][C]124[/C][C]151.109633619142[/C][C]-27.1096336191415[/C][/ROW]
[ROW][C]39[/C][C]140[/C][C]133.564358679173[/C][C]6.4356413208267[/C][/ROW]
[ROW][C]40[/C][C]109[/C][C]137.708780694123[/C][C]-28.7087806941234[/C][/ROW]
[ROW][C]41[/C][C]114[/C][C]118.932775460816[/C][C]-4.93277546081553[/C][/ROW]
[ROW][C]42[/C][C]77[/C][C]115.444814670339[/C][C]-38.4448146703386[/C][/ROW]
[ROW][C]43[/C][C]120[/C][C]90.0018809185442[/C][C]29.9981190814558[/C][/ROW]
[ROW][C]44[/C][C]133[/C][C]108.963847507074[/C][C]24.0361524929257[/C][/ROW]
[ROW][C]45[/C][C]110[/C][C]124.296465594007[/C][C]-14.2964655940067[/C][/ROW]
[ROW][C]46[/C][C]92[/C][C]114.781804031002[/C][C]-22.7818040310019[/C][/ROW]
[ROW][C]47[/C][C]97[/C][C]99.5912171301633[/C][C]-2.5912171301633[/C][/ROW]
[ROW][C]48[/C][C]78[/C][C]97.3975503453038[/C][C]-19.3975503453038[/C][/ROW]
[ROW][C]49[/C][C]99[/C][C]84.192383006897[/C][C]14.807616993103[/C][/ROW]
[ROW][C]50[/C][C]107[/C][C]93.1774401317972[/C][C]13.8225598682028[/C][/ROW]
[ROW][C]51[/C][C]112[/C][C]101.651081608113[/C][C]10.3489183918875[/C][/ROW]
[ROW][C]52[/C][C]90[/C][C]107.977401830242[/C][C]-17.9774018302416[/C][/ROW]
[ROW][C]53[/C][C]98[/C][C]95.8761470939789[/C][C]2.12385290602109[/C][/ROW]
[ROW][C]54[/C][C]125[/C][C]96.7564388284718[/C][C]28.2435611715282[/C][/ROW]
[ROW][C]55[/C][C]155[/C][C]114.733301399336[/C][C]40.2666986006643[/C][/ROW]
[ROW][C]56[/C][C]190[/C][C]140.824092711909[/C][C]49.1759072880912[/C][/ROW]
[ROW][C]57[/C][C]236[/C][C]173.10056078187[/C][C]62.8994392181303[/C][/ROW]
[ROW][C]58[/C][C]189[/C][C]214.790199416141[/C][C]-25.7901994161412[/C][/ROW]
[ROW][C]59[/C][C]174[/C][C]199.056310194506[/C][C]-25.0563101945055[/C][/ROW]
[ROW][C]60[/C][C]178[/C][C]183.57124663769[/C][C]-5.57124663769022[/C][/ROW]
[ROW][C]61[/C][C]136[/C][C]180.60144609954[/C][C]-44.6014460995402[/C][/ROW]
[ROW][C]62[/C][C]161[/C][C]152.06307875101[/C][C]8.93692124898965[/C][/ROW]
[ROW][C]63[/C][C]171[/C][C]158.129585760431[/C][C]12.8704142395694[/C][/ROW]
[ROW][C]64[/C][C]149[/C][C]166.847931724601[/C][C]-17.8479317246008[/C][/ROW]
[ROW][C]65[/C][C]184[/C][C]155.597337370424[/C][C]28.4026626295764[/C][/ROW]
[ROW][C]66[/C][C]155[/C][C]174.426370019665[/C][C]-19.426370019665[/C][/ROW]
[ROW][C]67[/C][C]276[/C][C]162.238303052681[/C][C]113.761696947319[/C][/ROW]
[ROW][C]68[/C][C]224[/C][C]236.957049034752[/C][C]-12.9570490347517[/C][/ROW]
[ROW][C]69[/C][C]213[/C][C]229.843711769186[/C][C]-16.8437117691863[/C][/ROW]
[ROW][C]70[/C][C]279[/C][C]220.073145463734[/C][C]58.9268545362659[/C][/ROW]
[ROW][C]71[/C][C]268[/C][C]259.691903519697[/C][C]8.30809648030282[/C][/ROW]
[ROW][C]72[/C][C]287[/C][C]266.742995361795[/C][C]20.2570046382049[/C][/ROW]
[ROW][C]73[/C][C]238[/C][C]281.680920100924[/C][C]-43.6809201009239[/C][/ROW]
[ROW][C]74[/C][C]213[/C][C]254.996493027673[/C][C]-41.9964930276727[/C][/ROW]
[ROW][C]75[/C][C]257[/C][C]229.022122350496[/C][C]27.9778776495039[/C][/ROW]
[ROW][C]76[/C][C]293[/C][C]248.422121103952[/C][C]44.5778788960479[/C][/ROW]
[ROW][C]77[/C][C]212[/C][C]278.926106888235[/C][C]-66.9261068882347[/C][/ROW]
[ROW][C]78[/C][C]246[/C][C]236.926016062948[/C][C]9.07398393705208[/C][/ROW]
[ROW][C]79[/C][C]353[/C][C]244.016725386064[/C][C]108.983274613936[/C][/ROW]
[ROW][C]80[/C][C]339[/C][C]316.511249220273[/C][C]22.4887507797273[/C][/ROW]
[ROW][C]81[/C][C]308[/C][C]333.430227964329[/C][C]-25.4302279643288[/C][/ROW]
[ROW][C]82[/C][C]247[/C][C]319.220327345645[/C][C]-72.220327345645[/C][/ROW]
[ROW][C]83[/C][C]257[/C][C]274.190415820738[/C][C]-17.1904158207376[/C][/ROW]
[ROW][C]84[/C][C]322[/C][C]264.493193478044[/C][C]57.5068065219557[/C][/ROW]
[ROW][C]85[/C][C]298[/C][C]303.480417951177[/C][C]-5.48041795117678[/C][/ROW]
[ROW][C]86[/C][C]273[/C][C]301.800525120767[/C][C]-28.8005251207674[/C][/ROW]
[ROW][C]87[/C][C]312[/C][C]284.82442732832[/C][C]27.1755726716802[/C][/ROW]
[ROW][C]88[/C][C]249[/C][C]304.18856702394[/C][C]-55.1885670239401[/C][/ROW]
[ROW][C]89[/C][C]286[/C][C]269.944925597323[/C][C]16.055074402677[/C][/ROW]
[ROW][C]90[/C][C]279[/C][C]281.787363896843[/C][C]-2.78736389684269[/C][/ROW]
[ROW][C]91[/C][C]309[/C][C]281.454074721233[/C][C]27.545925278767[/C][/ROW]
[ROW][C]92[/C][C]401[/C][C]300.928283229015[/C][C]100.071716770985[/C][/ROW]
[ROW][C]93[/C][C]309[/C][C]368.067923579816[/C][C]-59.067923579816[/C][/ROW]
[ROW][C]94[/C][C]328[/C][C]332.05547945059[/C][C]-4.0554794505897[/C][/ROW]
[ROW][C]95[/C][C]353[/C][C]331.482111015218[/C][C]21.5178889847819[/C][/ROW]
[ROW][C]96[/C][C]354[/C][C]347.592757631871[/C][C]6.40724236812872[/C][/ROW]
[ROW][C]97[/C][C]327[/C][C]354.016521869661[/C][C]-27.0165218696612[/C][/ROW]
[ROW][C]98[/C][C]324[/C][C]338.644602299267[/C][C]-14.6446022992671[/C][/ROW]
[ROW][C]99[/C][C]285[/C][C]331.119683171997[/C][C]-46.1196831719972[/C][/ROW]
[ROW][C]100[/C][C]243[/C][C]302.884602513798[/C][C]-59.8846025137981[/C][/ROW]
[ROW][C]101[/C][C]241[/C][C]265.236666254713[/C][C]-24.2366662547135[/C][/ROW]
[ROW][C]102[/C][C]287[/C][C]250.359617997322[/C][C]36.6403820026778[/C][/ROW]
[ROW][C]103[/C][C]355[/C][C]275.068017903841[/C][C]79.9319820961588[/C][/ROW]
[ROW][C]104[/C][C]460[/C][C]328.409455461357[/C][C]131.590544538643[/C][/ROW]
[ROW][C]105[/C][C]364[/C][C]416.242171021509[/C][C]-52.2421710215087[/C][/ROW]
[ROW][C]106[/C][C]487[/C][C]385.060330174621[/C][C]101.939669825379[/C][/ROW]
[ROW][C]107[/C][C]452[/C][C]454.217485637917[/C][C]-2.2174856379167[/C][/ROW]
[ROW][C]108[/C][C]391[/C][C]456.187851397077[/C][C]-65.1878513970768[/C][/ROW]
[ROW][C]109[/C][C]500[/C][C]416.967167652262[/C][C]83.0328323477376[/C][/ROW]
[ROW][C]110[/C][C]451[/C][C]474.072010302784[/C][C]-23.0720103027837[/C][/ROW]
[ROW][C]111[/C][C]375[/C][C]462.547279529313[/C][C]-87.5472795293135[/C][/ROW]
[ROW][C]112[/C][C]372[/C][C]408.660770127299[/C][C]-36.6607701272994[/C][/ROW]
[ROW][C]113[/C][C]302[/C][C]387.260632525702[/C][C]-85.2606325257016[/C][/ROW]
[ROW][C]114[/C][C]316[/C][C]333.7566347899[/C][C]-17.7566347899002[/C][/ROW]
[ROW][C]115[/C][C]398[/C][C]323.624311082958[/C][C]74.3756889170425[/C][/ROW]
[ROW][C]116[/C][C]394[/C][C]373.570753585916[/C][C]20.4292464140842[/C][/ROW]
[ROW][C]117[/C][C]431[/C][C]388.912204677046[/C][C]42.0877953229539[/C][/ROW]
[ROW][C]118[/C][C]431[/C][C]418.597400994581[/C][C]12.4025990054188[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203882&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203882&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
3503713
44043.4996399306352-3.49963993063519
54339.3279526798553.67204732014502
63839.8139003916258-1.81390039162581
74436.74592502906827.25407497093177
83539.5905120839383-4.59051208393826
93934.75586478242524.24413521757479
103535.6563553969849-0.656355396984942
112933.3908298247323-4.39082982473234
124928.677756925361320.3222430746387
135040.08321822160249.91678177839765
145944.867424655741914.1325753442581
156352.496820051499710.5031799485003
163257.8798362366138-25.8798362366138
173939.5690426784727-0.569042678472705
184737.57510555330229.42489444669783
195342.110292014896110.8897079851039
206047.687620053648512.3123799463515
215754.29265716783542.70734283216461
225254.7280266083913-2.72802660839127
237051.633901055011418.3660989449886
249062.307068977251727.6929310227483
257479.2427983062217-5.24279830622173
266274.8925874870312-12.8925874870312
275565.4938431975173-10.4938431975173
288457.547962371794626.4520376282054
299473.663986209644520.3360137903555
307086.018173568831-16.018173568831
3110874.785473396295533.2145266037045
3213995.598545323697643.4014546763024
33120123.369523717488-3.36952371748829
3497120.949523143592-23.9495231435916
35126105.04375805233420.9562419476665
36149118.28369338302730.7163066169735
37158138.09264567999119.9073543200091
38124151.109633619142-27.1096336191415
39140133.5643586791736.4356413208267
40109137.708780694123-28.7087806941234
41114118.932775460816-4.93277546081553
4277115.444814670339-38.4448146703386
4312090.001880918544229.9981190814558
44133108.96384750707424.0361524929257
45110124.296465594007-14.2964655940067
4692114.781804031002-22.7818040310019
479799.5912171301633-2.5912171301633
487897.3975503453038-19.3975503453038
499984.19238300689714.807616993103
5010793.177440131797213.8225598682028
51112101.65108160811310.3489183918875
5290107.977401830242-17.9774018302416
539895.87614709397892.12385290602109
5412596.756438828471828.2435611715282
55155114.73330139933640.2666986006643
56190140.82409271190949.1759072880912
57236173.1005607818762.8994392181303
58189214.790199416141-25.7901994161412
59174199.056310194506-25.0563101945055
60178183.57124663769-5.57124663769022
61136180.60144609954-44.6014460995402
62161152.063078751018.93692124898965
63171158.12958576043112.8704142395694
64149166.847931724601-17.8479317246008
65184155.59733737042428.4026626295764
66155174.426370019665-19.426370019665
67276162.238303052681113.761696947319
68224236.957049034752-12.9570490347517
69213229.843711769186-16.8437117691863
70279220.07314546373458.9268545362659
71268259.6919035196978.30809648030282
72287266.74299536179520.2570046382049
73238281.680920100924-43.6809201009239
74213254.996493027673-41.9964930276727
75257229.02212235049627.9778776495039
76293248.42212110395244.5778788960479
77212278.926106888235-66.9261068882347
78246236.9260160629489.07398393705208
79353244.016725386064108.983274613936
80339316.51124922027322.4887507797273
81308333.430227964329-25.4302279643288
82247319.220327345645-72.220327345645
83257274.190415820738-17.1904158207376
84322264.49319347804457.5068065219557
85298303.480417951177-5.48041795117678
86273301.800525120767-28.8005251207674
87312284.8244273283227.1755726716802
88249304.18856702394-55.1885670239401
89286269.94492559732316.055074402677
90279281.787363896843-2.78736389684269
91309281.45407472123327.545925278767
92401300.928283229015100.071716770985
93309368.067923579816-59.067923579816
94328332.05547945059-4.0554794505897
95353331.48211101521821.5178889847819
96354347.5927576318716.40724236812872
97327354.016521869661-27.0165218696612
98324338.644602299267-14.6446022992671
99285331.119683171997-46.1196831719972
100243302.884602513798-59.8846025137981
101241265.236666254713-24.2366662547135
102287250.35961799732236.6403820026778
103355275.06801790384179.9319820961588
104460328.409455461357131.590544538643
105364416.242171021509-52.2421710215087
106487385.060330174621101.939669825379
107452454.217485637917-2.2174856379167
108391456.187851397077-65.1878513970768
109500416.96716765226283.0328323477376
110451474.072010302784-23.0720103027837
111375462.547279529313-87.5472795293135
112372408.660770127299-36.6607701272994
113302387.260632525702-85.2606325257016
114316333.7566347899-17.7566347899002
115398323.62431108295874.3756889170425
116394373.57075358591620.4292464140842
117431388.91220467704642.0877953229539
118431418.59740099458112.4025990054188







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
119429.250851464148351.749585805903506.752117122393
120431.906344761765339.310053130275524.502636393255
121434.561838059382328.672588159493540.451087959271
122437.217331356999319.222458485999555.212204227999
123439.872824654616310.621877477458569.123771831774
124442.528317952233302.662135494678582.394500409788
125445.18381124985295.203883409962595.163739089738
126447.839304547467288.148790086344607.529819008591
127450.494797845084281.424523281243619.565072408926
128453.150291142701274.976122040098631.324460245305
129455.805784440318268.760724159029642.850844721608
130458.461277737935262.744181791723654.178373684148

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
119 & 429.250851464148 & 351.749585805903 & 506.752117122393 \tabularnewline
120 & 431.906344761765 & 339.310053130275 & 524.502636393255 \tabularnewline
121 & 434.561838059382 & 328.672588159493 & 540.451087959271 \tabularnewline
122 & 437.217331356999 & 319.222458485999 & 555.212204227999 \tabularnewline
123 & 439.872824654616 & 310.621877477458 & 569.123771831774 \tabularnewline
124 & 442.528317952233 & 302.662135494678 & 582.394500409788 \tabularnewline
125 & 445.18381124985 & 295.203883409962 & 595.163739089738 \tabularnewline
126 & 447.839304547467 & 288.148790086344 & 607.529819008591 \tabularnewline
127 & 450.494797845084 & 281.424523281243 & 619.565072408926 \tabularnewline
128 & 453.150291142701 & 274.976122040098 & 631.324460245305 \tabularnewline
129 & 455.805784440318 & 268.760724159029 & 642.850844721608 \tabularnewline
130 & 458.461277737935 & 262.744181791723 & 654.178373684148 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203882&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]119[/C][C]429.250851464148[/C][C]351.749585805903[/C][C]506.752117122393[/C][/ROW]
[ROW][C]120[/C][C]431.906344761765[/C][C]339.310053130275[/C][C]524.502636393255[/C][/ROW]
[ROW][C]121[/C][C]434.561838059382[/C][C]328.672588159493[/C][C]540.451087959271[/C][/ROW]
[ROW][C]122[/C][C]437.217331356999[/C][C]319.222458485999[/C][C]555.212204227999[/C][/ROW]
[ROW][C]123[/C][C]439.872824654616[/C][C]310.621877477458[/C][C]569.123771831774[/C][/ROW]
[ROW][C]124[/C][C]442.528317952233[/C][C]302.662135494678[/C][C]582.394500409788[/C][/ROW]
[ROW][C]125[/C][C]445.18381124985[/C][C]295.203883409962[/C][C]595.163739089738[/C][/ROW]
[ROW][C]126[/C][C]447.839304547467[/C][C]288.148790086344[/C][C]607.529819008591[/C][/ROW]
[ROW][C]127[/C][C]450.494797845084[/C][C]281.424523281243[/C][C]619.565072408926[/C][/ROW]
[ROW][C]128[/C][C]453.150291142701[/C][C]274.976122040098[/C][C]631.324460245305[/C][/ROW]
[ROW][C]129[/C][C]455.805784440318[/C][C]268.760724159029[/C][C]642.850844721608[/C][/ROW]
[ROW][C]130[/C][C]458.461277737935[/C][C]262.744181791723[/C][C]654.178373684148[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203882&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203882&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
119429.250851464148351.749585805903506.752117122393
120431.906344761765339.310053130275524.502636393255
121434.561838059382328.672588159493540.451087959271
122437.217331356999319.222458485999555.212204227999
123439.872824654616310.621877477458569.123771831774
124442.528317952233302.662135494678582.394500409788
125445.18381124985295.203883409962595.163739089738
126447.839304547467288.148790086344607.529819008591
127450.494797845084281.424523281243619.565072408926
128453.150291142701274.976122040098631.324460245305
129455.805784440318268.760724159029642.850844721608
130458.461277737935262.744181791723654.178373684148



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')