Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 29 Nov 2014 15:37:27 +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/2014/Nov/29/t14172760592k55jseu93m7l2c.htm/, Retrieved Fri, 01 Nov 2024 01:01:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=261188, Retrieved Fri, 01 Nov 2024 01:01:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact135
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-11-29 15:37:27] [c53b0bb515ebe5f6f1384250cc1174dd] [Current]
- R P     [Exponential Smoothing] [] [2014-12-04 10:03:21] [52bcad4f2450da6a1432dda11dba2117]
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Dataseries X:
254
200
165
123
162
145
145
161
155
173
160
47
232
143
161
159
243
192
157
143
221
227
132
41
273
182
188
162
140
186
178
236
202
184
119
16
340
151
240
235
174
309
174
207
209
171
117
10
339
139
186
155
153
222
102
107
188
162
185
24
394
209
248
254
202
258
215
309
240
258
276
48
455
345
311
346
310
297
300
274
292
304
186
14
321
206
160
217
204
246
234
175
364
328
158
40
556
193
221
278
230
253
240
252
228
306
206
48
557
279
399
364
306
471
293
333
316
329
265
61
679
428
394
352
387
590
177
199
203
255
261
115




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261188&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261188&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261188&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.362348627852194
beta0
gamma0.765301978637238

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.362348627852194 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.765301978637238 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261188&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]0.362348627852194[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.765301978637238[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261188&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261188&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
alpha0.362348627852194
beta0
gamma0.765301978637238







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13232215.74065170940216.2593482905981
14143134.897792830368.10220716964039
15161155.8492050589425.15079494105842
16159152.7311771162716.26882288372934
17243239.9349317311943.06506826880627
18192193.477810257424-1.47781025742418
19157162.541249649843-5.54124964984257
20143181.840640687391-38.8406406873909
21221166.3240430741754.6759569258301
22227204.81805628750522.1819437124946
23132196.996241732911-64.996241732911
244157.1271979701965-16.1271979701965
25273243.77527975919429.224720240806
26182163.64975454566118.3502454543388
27188186.8742524456661.12574755433357
28162182.843347109169-20.8433471091695
29140258.65962515083-118.65962515083
30186165.87882214204620.1211778579536
31178140.78568365326937.2143163467313
32236159.32753050291776.6724694970831
33202231.302662039905-29.3026620399047
34184223.510194083644-39.5101940836441
35119150.791724749917-31.7917247499174
361646.8021830357578-30.8021830357578
37340250.2643523067489.7356476932598
38151186.758179985154-35.7581799851537
39240181.97108056150458.0289194384964
40235187.83813430455347.1618656954466
41174240.562069482258-66.5620694822578
42309234.38320115408174.6167988459191
43174237.377856916229-63.3778569162294
44207238.725683065152-31.7256830651517
45209219.707467647156-10.7074676471561
46171213.671709518403-42.671709518403
47117143.574250460542-26.5742504605423
481041.9581456526181-31.9581456526181
49339303.82341543720135.1765845627989
50139159.307373494176-20.3073734941759
51186205.886568540409-19.8865685404091
52155178.217974923795-23.2179749237951
53153149.9430622406033.05693775939744
54222237.885248468683-15.8852484686825
55102140.745791298106-38.7457912981057
56107166.4651423225-59.4651423224995
57188147.65237394624840.3476260537516
58162144.51794136642717.4820586335726
59185104.07261098358480.9273890164163
602438.7822591848966-14.7822591848966
61394339.63265805473754.367341945263
62209174.9944190668334.0055809331702
63248241.4591896983646.54081030163633
64254221.74080803053432.2591919694661
65202226.39001917504-24.3900191750395
66258295.143129821446-37.1431298214463
67215179.14505832702635.8549416729744
68309221.7849251250787.2150748749296
69240304.829749605267-64.8297496052674
70258252.426137110215.57386288978998
71276238.62694669862437.3730533013759
7248110.848829339943-62.8488293399431
73455428.02709131842726.9729086815734
74345243.526062015876101.473937984124
75311321.035204972513-10.0352049725132
76346307.86099061196738.1390093880335
77310286.99616520142823.0038347985723
78297366.698908647227-69.6989086472269
79300274.52705180923225.4729481907684
80274338.468549721132-64.4685497211324
81292292.35377656929-0.353776569289607
82304297.6696156335716.33038436642869
83186299.662422910972-113.662422910972
841468.2489445015412-54.2489445015412
85321432.375998954676-111.375998954676
86206234.100626431178-28.1006264311778
87160210.242604010848-50.2426040108475
88217206.00811079109610.9918892089036
89204167.9206611421336.0793388578705
90246207.12274082809538.8772591719048
91234200.73678123633333.263218763667
92175223.609994666835-48.6099946668347
93364214.529290835474149.470709164526
94328277.39566956678250.6043304332175
95158236.875087655658-78.8750876556579
964047.0602837436393-7.06028374363933
97556400.408318789095155.591681210905
98193339.506355618212-146.506355618212
99221261.938986377206-40.9389863772058
100278290.957825224662-12.9578252246625
101230256.434800899251-26.4348008992508
102253274.350341343728-21.3503413437279
103240243.40136488725-3.40136488724988
104252213.03542780527338.9645721947271
105228332.349810889803-104.349810889803
106306254.99828926243351.0017107375666
107206151.43627799296154.5637220070391
1084845.01817042937652.98182957062355
109557481.37843645082475.621563549176
110279244.07682056040334.9231794395972
111399283.766633200808115.233366799192
112364383.029000640668-19.0290006406682
113306339.729385942619-33.7293859426193
114471357.482938702969113.517061297031
115293384.162006679661-91.1620066796606
116333342.670523229614-9.67052322961422
117316374.425221058658-58.4252210586578
118329389.525310440753-60.5253104407526
119265247.28988282019917.7101171798008
12061102.346172321934-41.3461723219336
121679558.092136901716120.907863098284
122428317.339306690079110.660693309921
123394423.663542247479-29.6635422474794
124352404.903234481394-52.9032344813945
125387342.15561051111244.8443894888881
126590460.235919163564129.764080836436
127177392.91953523371-215.91953523371
128199345.989838784797-146.989838784797
129203304.194980505417-101.194980505417
130255302.772671321069-47.7726713210689
131261203.33670951969657.6632904803037
13211544.050751951239470.9492480487606

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 232 & 215.740651709402 & 16.2593482905981 \tabularnewline
14 & 143 & 134.89779283036 & 8.10220716964039 \tabularnewline
15 & 161 & 155.849205058942 & 5.15079494105842 \tabularnewline
16 & 159 & 152.731177116271 & 6.26882288372934 \tabularnewline
17 & 243 & 239.934931731194 & 3.06506826880627 \tabularnewline
18 & 192 & 193.477810257424 & -1.47781025742418 \tabularnewline
19 & 157 & 162.541249649843 & -5.54124964984257 \tabularnewline
20 & 143 & 181.840640687391 & -38.8406406873909 \tabularnewline
21 & 221 & 166.32404307417 & 54.6759569258301 \tabularnewline
22 & 227 & 204.818056287505 & 22.1819437124946 \tabularnewline
23 & 132 & 196.996241732911 & -64.996241732911 \tabularnewline
24 & 41 & 57.1271979701965 & -16.1271979701965 \tabularnewline
25 & 273 & 243.775279759194 & 29.224720240806 \tabularnewline
26 & 182 & 163.649754545661 & 18.3502454543388 \tabularnewline
27 & 188 & 186.874252445666 & 1.12574755433357 \tabularnewline
28 & 162 & 182.843347109169 & -20.8433471091695 \tabularnewline
29 & 140 & 258.65962515083 & -118.65962515083 \tabularnewline
30 & 186 & 165.878822142046 & 20.1211778579536 \tabularnewline
31 & 178 & 140.785683653269 & 37.2143163467313 \tabularnewline
32 & 236 & 159.327530502917 & 76.6724694970831 \tabularnewline
33 & 202 & 231.302662039905 & -29.3026620399047 \tabularnewline
34 & 184 & 223.510194083644 & -39.5101940836441 \tabularnewline
35 & 119 & 150.791724749917 & -31.7917247499174 \tabularnewline
36 & 16 & 46.8021830357578 & -30.8021830357578 \tabularnewline
37 & 340 & 250.26435230674 & 89.7356476932598 \tabularnewline
38 & 151 & 186.758179985154 & -35.7581799851537 \tabularnewline
39 & 240 & 181.971080561504 & 58.0289194384964 \tabularnewline
40 & 235 & 187.838134304553 & 47.1618656954466 \tabularnewline
41 & 174 & 240.562069482258 & -66.5620694822578 \tabularnewline
42 & 309 & 234.383201154081 & 74.6167988459191 \tabularnewline
43 & 174 & 237.377856916229 & -63.3778569162294 \tabularnewline
44 & 207 & 238.725683065152 & -31.7256830651517 \tabularnewline
45 & 209 & 219.707467647156 & -10.7074676471561 \tabularnewline
46 & 171 & 213.671709518403 & -42.671709518403 \tabularnewline
47 & 117 & 143.574250460542 & -26.5742504605423 \tabularnewline
48 & 10 & 41.9581456526181 & -31.9581456526181 \tabularnewline
49 & 339 & 303.823415437201 & 35.1765845627989 \tabularnewline
50 & 139 & 159.307373494176 & -20.3073734941759 \tabularnewline
51 & 186 & 205.886568540409 & -19.8865685404091 \tabularnewline
52 & 155 & 178.217974923795 & -23.2179749237951 \tabularnewline
53 & 153 & 149.943062240603 & 3.05693775939744 \tabularnewline
54 & 222 & 237.885248468683 & -15.8852484686825 \tabularnewline
55 & 102 & 140.745791298106 & -38.7457912981057 \tabularnewline
56 & 107 & 166.4651423225 & -59.4651423224995 \tabularnewline
57 & 188 & 147.652373946248 & 40.3476260537516 \tabularnewline
58 & 162 & 144.517941366427 & 17.4820586335726 \tabularnewline
59 & 185 & 104.072610983584 & 80.9273890164163 \tabularnewline
60 & 24 & 38.7822591848966 & -14.7822591848966 \tabularnewline
61 & 394 & 339.632658054737 & 54.367341945263 \tabularnewline
62 & 209 & 174.99441906683 & 34.0055809331702 \tabularnewline
63 & 248 & 241.459189698364 & 6.54081030163633 \tabularnewline
64 & 254 & 221.740808030534 & 32.2591919694661 \tabularnewline
65 & 202 & 226.39001917504 & -24.3900191750395 \tabularnewline
66 & 258 & 295.143129821446 & -37.1431298214463 \tabularnewline
67 & 215 & 179.145058327026 & 35.8549416729744 \tabularnewline
68 & 309 & 221.78492512507 & 87.2150748749296 \tabularnewline
69 & 240 & 304.829749605267 & -64.8297496052674 \tabularnewline
70 & 258 & 252.42613711021 & 5.57386288978998 \tabularnewline
71 & 276 & 238.626946698624 & 37.3730533013759 \tabularnewline
72 & 48 & 110.848829339943 & -62.8488293399431 \tabularnewline
73 & 455 & 428.027091318427 & 26.9729086815734 \tabularnewline
74 & 345 & 243.526062015876 & 101.473937984124 \tabularnewline
75 & 311 & 321.035204972513 & -10.0352049725132 \tabularnewline
76 & 346 & 307.860990611967 & 38.1390093880335 \tabularnewline
77 & 310 & 286.996165201428 & 23.0038347985723 \tabularnewline
78 & 297 & 366.698908647227 & -69.6989086472269 \tabularnewline
79 & 300 & 274.527051809232 & 25.4729481907684 \tabularnewline
80 & 274 & 338.468549721132 & -64.4685497211324 \tabularnewline
81 & 292 & 292.35377656929 & -0.353776569289607 \tabularnewline
82 & 304 & 297.669615633571 & 6.33038436642869 \tabularnewline
83 & 186 & 299.662422910972 & -113.662422910972 \tabularnewline
84 & 14 & 68.2489445015412 & -54.2489445015412 \tabularnewline
85 & 321 & 432.375998954676 & -111.375998954676 \tabularnewline
86 & 206 & 234.100626431178 & -28.1006264311778 \tabularnewline
87 & 160 & 210.242604010848 & -50.2426040108475 \tabularnewline
88 & 217 & 206.008110791096 & 10.9918892089036 \tabularnewline
89 & 204 & 167.92066114213 & 36.0793388578705 \tabularnewline
90 & 246 & 207.122740828095 & 38.8772591719048 \tabularnewline
91 & 234 & 200.736781236333 & 33.263218763667 \tabularnewline
92 & 175 & 223.609994666835 & -48.6099946668347 \tabularnewline
93 & 364 & 214.529290835474 & 149.470709164526 \tabularnewline
94 & 328 & 277.395669566782 & 50.6043304332175 \tabularnewline
95 & 158 & 236.875087655658 & -78.8750876556579 \tabularnewline
96 & 40 & 47.0602837436393 & -7.06028374363933 \tabularnewline
97 & 556 & 400.408318789095 & 155.591681210905 \tabularnewline
98 & 193 & 339.506355618212 & -146.506355618212 \tabularnewline
99 & 221 & 261.938986377206 & -40.9389863772058 \tabularnewline
100 & 278 & 290.957825224662 & -12.9578252246625 \tabularnewline
101 & 230 & 256.434800899251 & -26.4348008992508 \tabularnewline
102 & 253 & 274.350341343728 & -21.3503413437279 \tabularnewline
103 & 240 & 243.40136488725 & -3.40136488724988 \tabularnewline
104 & 252 & 213.035427805273 & 38.9645721947271 \tabularnewline
105 & 228 & 332.349810889803 & -104.349810889803 \tabularnewline
106 & 306 & 254.998289262433 & 51.0017107375666 \tabularnewline
107 & 206 & 151.436277992961 & 54.5637220070391 \tabularnewline
108 & 48 & 45.0181704293765 & 2.98182957062355 \tabularnewline
109 & 557 & 481.378436450824 & 75.621563549176 \tabularnewline
110 & 279 & 244.076820560403 & 34.9231794395972 \tabularnewline
111 & 399 & 283.766633200808 & 115.233366799192 \tabularnewline
112 & 364 & 383.029000640668 & -19.0290006406682 \tabularnewline
113 & 306 & 339.729385942619 & -33.7293859426193 \tabularnewline
114 & 471 & 357.482938702969 & 113.517061297031 \tabularnewline
115 & 293 & 384.162006679661 & -91.1620066796606 \tabularnewline
116 & 333 & 342.670523229614 & -9.67052322961422 \tabularnewline
117 & 316 & 374.425221058658 & -58.4252210586578 \tabularnewline
118 & 329 & 389.525310440753 & -60.5253104407526 \tabularnewline
119 & 265 & 247.289882820199 & 17.7101171798008 \tabularnewline
120 & 61 & 102.346172321934 & -41.3461723219336 \tabularnewline
121 & 679 & 558.092136901716 & 120.907863098284 \tabularnewline
122 & 428 & 317.339306690079 & 110.660693309921 \tabularnewline
123 & 394 & 423.663542247479 & -29.6635422474794 \tabularnewline
124 & 352 & 404.903234481394 & -52.9032344813945 \tabularnewline
125 & 387 & 342.155610511112 & 44.8443894888881 \tabularnewline
126 & 590 & 460.235919163564 & 129.764080836436 \tabularnewline
127 & 177 & 392.91953523371 & -215.91953523371 \tabularnewline
128 & 199 & 345.989838784797 & -146.989838784797 \tabularnewline
129 & 203 & 304.194980505417 & -101.194980505417 \tabularnewline
130 & 255 & 302.772671321069 & -47.7726713210689 \tabularnewline
131 & 261 & 203.336709519696 & 57.6632904803037 \tabularnewline
132 & 115 & 44.0507519512394 & 70.9492480487606 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261188&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]232[/C][C]215.740651709402[/C][C]16.2593482905981[/C][/ROW]
[ROW][C]14[/C][C]143[/C][C]134.89779283036[/C][C]8.10220716964039[/C][/ROW]
[ROW][C]15[/C][C]161[/C][C]155.849205058942[/C][C]5.15079494105842[/C][/ROW]
[ROW][C]16[/C][C]159[/C][C]152.731177116271[/C][C]6.26882288372934[/C][/ROW]
[ROW][C]17[/C][C]243[/C][C]239.934931731194[/C][C]3.06506826880627[/C][/ROW]
[ROW][C]18[/C][C]192[/C][C]193.477810257424[/C][C]-1.47781025742418[/C][/ROW]
[ROW][C]19[/C][C]157[/C][C]162.541249649843[/C][C]-5.54124964984257[/C][/ROW]
[ROW][C]20[/C][C]143[/C][C]181.840640687391[/C][C]-38.8406406873909[/C][/ROW]
[ROW][C]21[/C][C]221[/C][C]166.32404307417[/C][C]54.6759569258301[/C][/ROW]
[ROW][C]22[/C][C]227[/C][C]204.818056287505[/C][C]22.1819437124946[/C][/ROW]
[ROW][C]23[/C][C]132[/C][C]196.996241732911[/C][C]-64.996241732911[/C][/ROW]
[ROW][C]24[/C][C]41[/C][C]57.1271979701965[/C][C]-16.1271979701965[/C][/ROW]
[ROW][C]25[/C][C]273[/C][C]243.775279759194[/C][C]29.224720240806[/C][/ROW]
[ROW][C]26[/C][C]182[/C][C]163.649754545661[/C][C]18.3502454543388[/C][/ROW]
[ROW][C]27[/C][C]188[/C][C]186.874252445666[/C][C]1.12574755433357[/C][/ROW]
[ROW][C]28[/C][C]162[/C][C]182.843347109169[/C][C]-20.8433471091695[/C][/ROW]
[ROW][C]29[/C][C]140[/C][C]258.65962515083[/C][C]-118.65962515083[/C][/ROW]
[ROW][C]30[/C][C]186[/C][C]165.878822142046[/C][C]20.1211778579536[/C][/ROW]
[ROW][C]31[/C][C]178[/C][C]140.785683653269[/C][C]37.2143163467313[/C][/ROW]
[ROW][C]32[/C][C]236[/C][C]159.327530502917[/C][C]76.6724694970831[/C][/ROW]
[ROW][C]33[/C][C]202[/C][C]231.302662039905[/C][C]-29.3026620399047[/C][/ROW]
[ROW][C]34[/C][C]184[/C][C]223.510194083644[/C][C]-39.5101940836441[/C][/ROW]
[ROW][C]35[/C][C]119[/C][C]150.791724749917[/C][C]-31.7917247499174[/C][/ROW]
[ROW][C]36[/C][C]16[/C][C]46.8021830357578[/C][C]-30.8021830357578[/C][/ROW]
[ROW][C]37[/C][C]340[/C][C]250.26435230674[/C][C]89.7356476932598[/C][/ROW]
[ROW][C]38[/C][C]151[/C][C]186.758179985154[/C][C]-35.7581799851537[/C][/ROW]
[ROW][C]39[/C][C]240[/C][C]181.971080561504[/C][C]58.0289194384964[/C][/ROW]
[ROW][C]40[/C][C]235[/C][C]187.838134304553[/C][C]47.1618656954466[/C][/ROW]
[ROW][C]41[/C][C]174[/C][C]240.562069482258[/C][C]-66.5620694822578[/C][/ROW]
[ROW][C]42[/C][C]309[/C][C]234.383201154081[/C][C]74.6167988459191[/C][/ROW]
[ROW][C]43[/C][C]174[/C][C]237.377856916229[/C][C]-63.3778569162294[/C][/ROW]
[ROW][C]44[/C][C]207[/C][C]238.725683065152[/C][C]-31.7256830651517[/C][/ROW]
[ROW][C]45[/C][C]209[/C][C]219.707467647156[/C][C]-10.7074676471561[/C][/ROW]
[ROW][C]46[/C][C]171[/C][C]213.671709518403[/C][C]-42.671709518403[/C][/ROW]
[ROW][C]47[/C][C]117[/C][C]143.574250460542[/C][C]-26.5742504605423[/C][/ROW]
[ROW][C]48[/C][C]10[/C][C]41.9581456526181[/C][C]-31.9581456526181[/C][/ROW]
[ROW][C]49[/C][C]339[/C][C]303.823415437201[/C][C]35.1765845627989[/C][/ROW]
[ROW][C]50[/C][C]139[/C][C]159.307373494176[/C][C]-20.3073734941759[/C][/ROW]
[ROW][C]51[/C][C]186[/C][C]205.886568540409[/C][C]-19.8865685404091[/C][/ROW]
[ROW][C]52[/C][C]155[/C][C]178.217974923795[/C][C]-23.2179749237951[/C][/ROW]
[ROW][C]53[/C][C]153[/C][C]149.943062240603[/C][C]3.05693775939744[/C][/ROW]
[ROW][C]54[/C][C]222[/C][C]237.885248468683[/C][C]-15.8852484686825[/C][/ROW]
[ROW][C]55[/C][C]102[/C][C]140.745791298106[/C][C]-38.7457912981057[/C][/ROW]
[ROW][C]56[/C][C]107[/C][C]166.4651423225[/C][C]-59.4651423224995[/C][/ROW]
[ROW][C]57[/C][C]188[/C][C]147.652373946248[/C][C]40.3476260537516[/C][/ROW]
[ROW][C]58[/C][C]162[/C][C]144.517941366427[/C][C]17.4820586335726[/C][/ROW]
[ROW][C]59[/C][C]185[/C][C]104.072610983584[/C][C]80.9273890164163[/C][/ROW]
[ROW][C]60[/C][C]24[/C][C]38.7822591848966[/C][C]-14.7822591848966[/C][/ROW]
[ROW][C]61[/C][C]394[/C][C]339.632658054737[/C][C]54.367341945263[/C][/ROW]
[ROW][C]62[/C][C]209[/C][C]174.99441906683[/C][C]34.0055809331702[/C][/ROW]
[ROW][C]63[/C][C]248[/C][C]241.459189698364[/C][C]6.54081030163633[/C][/ROW]
[ROW][C]64[/C][C]254[/C][C]221.740808030534[/C][C]32.2591919694661[/C][/ROW]
[ROW][C]65[/C][C]202[/C][C]226.39001917504[/C][C]-24.3900191750395[/C][/ROW]
[ROW][C]66[/C][C]258[/C][C]295.143129821446[/C][C]-37.1431298214463[/C][/ROW]
[ROW][C]67[/C][C]215[/C][C]179.145058327026[/C][C]35.8549416729744[/C][/ROW]
[ROW][C]68[/C][C]309[/C][C]221.78492512507[/C][C]87.2150748749296[/C][/ROW]
[ROW][C]69[/C][C]240[/C][C]304.829749605267[/C][C]-64.8297496052674[/C][/ROW]
[ROW][C]70[/C][C]258[/C][C]252.42613711021[/C][C]5.57386288978998[/C][/ROW]
[ROW][C]71[/C][C]276[/C][C]238.626946698624[/C][C]37.3730533013759[/C][/ROW]
[ROW][C]72[/C][C]48[/C][C]110.848829339943[/C][C]-62.8488293399431[/C][/ROW]
[ROW][C]73[/C][C]455[/C][C]428.027091318427[/C][C]26.9729086815734[/C][/ROW]
[ROW][C]74[/C][C]345[/C][C]243.526062015876[/C][C]101.473937984124[/C][/ROW]
[ROW][C]75[/C][C]311[/C][C]321.035204972513[/C][C]-10.0352049725132[/C][/ROW]
[ROW][C]76[/C][C]346[/C][C]307.860990611967[/C][C]38.1390093880335[/C][/ROW]
[ROW][C]77[/C][C]310[/C][C]286.996165201428[/C][C]23.0038347985723[/C][/ROW]
[ROW][C]78[/C][C]297[/C][C]366.698908647227[/C][C]-69.6989086472269[/C][/ROW]
[ROW][C]79[/C][C]300[/C][C]274.527051809232[/C][C]25.4729481907684[/C][/ROW]
[ROW][C]80[/C][C]274[/C][C]338.468549721132[/C][C]-64.4685497211324[/C][/ROW]
[ROW][C]81[/C][C]292[/C][C]292.35377656929[/C][C]-0.353776569289607[/C][/ROW]
[ROW][C]82[/C][C]304[/C][C]297.669615633571[/C][C]6.33038436642869[/C][/ROW]
[ROW][C]83[/C][C]186[/C][C]299.662422910972[/C][C]-113.662422910972[/C][/ROW]
[ROW][C]84[/C][C]14[/C][C]68.2489445015412[/C][C]-54.2489445015412[/C][/ROW]
[ROW][C]85[/C][C]321[/C][C]432.375998954676[/C][C]-111.375998954676[/C][/ROW]
[ROW][C]86[/C][C]206[/C][C]234.100626431178[/C][C]-28.1006264311778[/C][/ROW]
[ROW][C]87[/C][C]160[/C][C]210.242604010848[/C][C]-50.2426040108475[/C][/ROW]
[ROW][C]88[/C][C]217[/C][C]206.008110791096[/C][C]10.9918892089036[/C][/ROW]
[ROW][C]89[/C][C]204[/C][C]167.92066114213[/C][C]36.0793388578705[/C][/ROW]
[ROW][C]90[/C][C]246[/C][C]207.122740828095[/C][C]38.8772591719048[/C][/ROW]
[ROW][C]91[/C][C]234[/C][C]200.736781236333[/C][C]33.263218763667[/C][/ROW]
[ROW][C]92[/C][C]175[/C][C]223.609994666835[/C][C]-48.6099946668347[/C][/ROW]
[ROW][C]93[/C][C]364[/C][C]214.529290835474[/C][C]149.470709164526[/C][/ROW]
[ROW][C]94[/C][C]328[/C][C]277.395669566782[/C][C]50.6043304332175[/C][/ROW]
[ROW][C]95[/C][C]158[/C][C]236.875087655658[/C][C]-78.8750876556579[/C][/ROW]
[ROW][C]96[/C][C]40[/C][C]47.0602837436393[/C][C]-7.06028374363933[/C][/ROW]
[ROW][C]97[/C][C]556[/C][C]400.408318789095[/C][C]155.591681210905[/C][/ROW]
[ROW][C]98[/C][C]193[/C][C]339.506355618212[/C][C]-146.506355618212[/C][/ROW]
[ROW][C]99[/C][C]221[/C][C]261.938986377206[/C][C]-40.9389863772058[/C][/ROW]
[ROW][C]100[/C][C]278[/C][C]290.957825224662[/C][C]-12.9578252246625[/C][/ROW]
[ROW][C]101[/C][C]230[/C][C]256.434800899251[/C][C]-26.4348008992508[/C][/ROW]
[ROW][C]102[/C][C]253[/C][C]274.350341343728[/C][C]-21.3503413437279[/C][/ROW]
[ROW][C]103[/C][C]240[/C][C]243.40136488725[/C][C]-3.40136488724988[/C][/ROW]
[ROW][C]104[/C][C]252[/C][C]213.035427805273[/C][C]38.9645721947271[/C][/ROW]
[ROW][C]105[/C][C]228[/C][C]332.349810889803[/C][C]-104.349810889803[/C][/ROW]
[ROW][C]106[/C][C]306[/C][C]254.998289262433[/C][C]51.0017107375666[/C][/ROW]
[ROW][C]107[/C][C]206[/C][C]151.436277992961[/C][C]54.5637220070391[/C][/ROW]
[ROW][C]108[/C][C]48[/C][C]45.0181704293765[/C][C]2.98182957062355[/C][/ROW]
[ROW][C]109[/C][C]557[/C][C]481.378436450824[/C][C]75.621563549176[/C][/ROW]
[ROW][C]110[/C][C]279[/C][C]244.076820560403[/C][C]34.9231794395972[/C][/ROW]
[ROW][C]111[/C][C]399[/C][C]283.766633200808[/C][C]115.233366799192[/C][/ROW]
[ROW][C]112[/C][C]364[/C][C]383.029000640668[/C][C]-19.0290006406682[/C][/ROW]
[ROW][C]113[/C][C]306[/C][C]339.729385942619[/C][C]-33.7293859426193[/C][/ROW]
[ROW][C]114[/C][C]471[/C][C]357.482938702969[/C][C]113.517061297031[/C][/ROW]
[ROW][C]115[/C][C]293[/C][C]384.162006679661[/C][C]-91.1620066796606[/C][/ROW]
[ROW][C]116[/C][C]333[/C][C]342.670523229614[/C][C]-9.67052322961422[/C][/ROW]
[ROW][C]117[/C][C]316[/C][C]374.425221058658[/C][C]-58.4252210586578[/C][/ROW]
[ROW][C]118[/C][C]329[/C][C]389.525310440753[/C][C]-60.5253104407526[/C][/ROW]
[ROW][C]119[/C][C]265[/C][C]247.289882820199[/C][C]17.7101171798008[/C][/ROW]
[ROW][C]120[/C][C]61[/C][C]102.346172321934[/C][C]-41.3461723219336[/C][/ROW]
[ROW][C]121[/C][C]679[/C][C]558.092136901716[/C][C]120.907863098284[/C][/ROW]
[ROW][C]122[/C][C]428[/C][C]317.339306690079[/C][C]110.660693309921[/C][/ROW]
[ROW][C]123[/C][C]394[/C][C]423.663542247479[/C][C]-29.6635422474794[/C][/ROW]
[ROW][C]124[/C][C]352[/C][C]404.903234481394[/C][C]-52.9032344813945[/C][/ROW]
[ROW][C]125[/C][C]387[/C][C]342.155610511112[/C][C]44.8443894888881[/C][/ROW]
[ROW][C]126[/C][C]590[/C][C]460.235919163564[/C][C]129.764080836436[/C][/ROW]
[ROW][C]127[/C][C]177[/C][C]392.91953523371[/C][C]-215.91953523371[/C][/ROW]
[ROW][C]128[/C][C]199[/C][C]345.989838784797[/C][C]-146.989838784797[/C][/ROW]
[ROW][C]129[/C][C]203[/C][C]304.194980505417[/C][C]-101.194980505417[/C][/ROW]
[ROW][C]130[/C][C]255[/C][C]302.772671321069[/C][C]-47.7726713210689[/C][/ROW]
[ROW][C]131[/C][C]261[/C][C]203.336709519696[/C][C]57.6632904803037[/C][/ROW]
[ROW][C]132[/C][C]115[/C][C]44.0507519512394[/C][C]70.9492480487606[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261188&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261188&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
13232215.74065170940216.2593482905981
14143134.897792830368.10220716964039
15161155.8492050589425.15079494105842
16159152.7311771162716.26882288372934
17243239.9349317311943.06506826880627
18192193.477810257424-1.47781025742418
19157162.541249649843-5.54124964984257
20143181.840640687391-38.8406406873909
21221166.3240430741754.6759569258301
22227204.81805628750522.1819437124946
23132196.996241732911-64.996241732911
244157.1271979701965-16.1271979701965
25273243.77527975919429.224720240806
26182163.64975454566118.3502454543388
27188186.8742524456661.12574755433357
28162182.843347109169-20.8433471091695
29140258.65962515083-118.65962515083
30186165.87882214204620.1211778579536
31178140.78568365326937.2143163467313
32236159.32753050291776.6724694970831
33202231.302662039905-29.3026620399047
34184223.510194083644-39.5101940836441
35119150.791724749917-31.7917247499174
361646.8021830357578-30.8021830357578
37340250.2643523067489.7356476932598
38151186.758179985154-35.7581799851537
39240181.97108056150458.0289194384964
40235187.83813430455347.1618656954466
41174240.562069482258-66.5620694822578
42309234.38320115408174.6167988459191
43174237.377856916229-63.3778569162294
44207238.725683065152-31.7256830651517
45209219.707467647156-10.7074676471561
46171213.671709518403-42.671709518403
47117143.574250460542-26.5742504605423
481041.9581456526181-31.9581456526181
49339303.82341543720135.1765845627989
50139159.307373494176-20.3073734941759
51186205.886568540409-19.8865685404091
52155178.217974923795-23.2179749237951
53153149.9430622406033.05693775939744
54222237.885248468683-15.8852484686825
55102140.745791298106-38.7457912981057
56107166.4651423225-59.4651423224995
57188147.65237394624840.3476260537516
58162144.51794136642717.4820586335726
59185104.07261098358480.9273890164163
602438.7822591848966-14.7822591848966
61394339.63265805473754.367341945263
62209174.9944190668334.0055809331702
63248241.4591896983646.54081030163633
64254221.74080803053432.2591919694661
65202226.39001917504-24.3900191750395
66258295.143129821446-37.1431298214463
67215179.14505832702635.8549416729744
68309221.7849251250787.2150748749296
69240304.829749605267-64.8297496052674
70258252.426137110215.57386288978998
71276238.62694669862437.3730533013759
7248110.848829339943-62.8488293399431
73455428.02709131842726.9729086815734
74345243.526062015876101.473937984124
75311321.035204972513-10.0352049725132
76346307.86099061196738.1390093880335
77310286.99616520142823.0038347985723
78297366.698908647227-69.6989086472269
79300274.52705180923225.4729481907684
80274338.468549721132-64.4685497211324
81292292.35377656929-0.353776569289607
82304297.6696156335716.33038436642869
83186299.662422910972-113.662422910972
841468.2489445015412-54.2489445015412
85321432.375998954676-111.375998954676
86206234.100626431178-28.1006264311778
87160210.242604010848-50.2426040108475
88217206.00811079109610.9918892089036
89204167.9206611421336.0793388578705
90246207.12274082809538.8772591719048
91234200.73678123633333.263218763667
92175223.609994666835-48.6099946668347
93364214.529290835474149.470709164526
94328277.39566956678250.6043304332175
95158236.875087655658-78.8750876556579
964047.0602837436393-7.06028374363933
97556400.408318789095155.591681210905
98193339.506355618212-146.506355618212
99221261.938986377206-40.9389863772058
100278290.957825224662-12.9578252246625
101230256.434800899251-26.4348008992508
102253274.350341343728-21.3503413437279
103240243.40136488725-3.40136488724988
104252213.03542780527338.9645721947271
105228332.349810889803-104.349810889803
106306254.99828926243351.0017107375666
107206151.43627799296154.5637220070391
1084845.01817042937652.98182957062355
109557481.37843645082475.621563549176
110279244.07682056040334.9231794395972
111399283.766633200808115.233366799192
112364383.029000640668-19.0290006406682
113306339.729385942619-33.7293859426193
114471357.482938702969113.517061297031
115293384.162006679661-91.1620066796606
116333342.670523229614-9.67052322961422
117316374.425221058658-58.4252210586578
118329389.525310440753-60.5253104407526
119265247.28988282019917.7101171798008
12061102.346172321934-41.3461723219336
121679558.092136901716120.907863098284
122428317.339306690079110.660693309921
123394423.663542247479-29.6635422474794
124352404.903234481394-52.9032344813945
125387342.15561051111244.8443894888881
126590460.235919163564129.764080836436
127177392.91953523371-215.91953523371
128199345.989838784797-146.989838784797
129203304.194980505417-101.194980505417
130255302.772671321069-47.7726713210689
131261203.33670951969657.6632904803037
13211544.050751951239470.9492480487606







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
133619.666105048216497.494938417446741.837271678987
134330.101900145877200.157685647627460.046114644128
135327.850739766656190.572905404327465.128574128985
136308.498102308061164.259034324193452.737170291929
137312.620328269176161.740860950065463.499795588287
138455.891791460564298.652106316697613.131476604431
139172.8633984942789.51094669208959336.215850296466
140237.80925564033268.5646739384948407.05383734217
141271.62366485525496.6852946757139446.562035034794
142332.939083544447152.48649063784513.391676451054
143302.265796160358116.462558265102488.069034055614
144128.569116655755-62.4349360185404319.573169330051

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
133 & 619.666105048216 & 497.494938417446 & 741.837271678987 \tabularnewline
134 & 330.101900145877 & 200.157685647627 & 460.046114644128 \tabularnewline
135 & 327.850739766656 & 190.572905404327 & 465.128574128985 \tabularnewline
136 & 308.498102308061 & 164.259034324193 & 452.737170291929 \tabularnewline
137 & 312.620328269176 & 161.740860950065 & 463.499795588287 \tabularnewline
138 & 455.891791460564 & 298.652106316697 & 613.131476604431 \tabularnewline
139 & 172.863398494278 & 9.51094669208959 & 336.215850296466 \tabularnewline
140 & 237.809255640332 & 68.5646739384948 & 407.05383734217 \tabularnewline
141 & 271.623664855254 & 96.6852946757139 & 446.562035034794 \tabularnewline
142 & 332.939083544447 & 152.48649063784 & 513.391676451054 \tabularnewline
143 & 302.265796160358 & 116.462558265102 & 488.069034055614 \tabularnewline
144 & 128.569116655755 & -62.4349360185404 & 319.573169330051 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261188&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]133[/C][C]619.666105048216[/C][C]497.494938417446[/C][C]741.837271678987[/C][/ROW]
[ROW][C]134[/C][C]330.101900145877[/C][C]200.157685647627[/C][C]460.046114644128[/C][/ROW]
[ROW][C]135[/C][C]327.850739766656[/C][C]190.572905404327[/C][C]465.128574128985[/C][/ROW]
[ROW][C]136[/C][C]308.498102308061[/C][C]164.259034324193[/C][C]452.737170291929[/C][/ROW]
[ROW][C]137[/C][C]312.620328269176[/C][C]161.740860950065[/C][C]463.499795588287[/C][/ROW]
[ROW][C]138[/C][C]455.891791460564[/C][C]298.652106316697[/C][C]613.131476604431[/C][/ROW]
[ROW][C]139[/C][C]172.863398494278[/C][C]9.51094669208959[/C][C]336.215850296466[/C][/ROW]
[ROW][C]140[/C][C]237.809255640332[/C][C]68.5646739384948[/C][C]407.05383734217[/C][/ROW]
[ROW][C]141[/C][C]271.623664855254[/C][C]96.6852946757139[/C][C]446.562035034794[/C][/ROW]
[ROW][C]142[/C][C]332.939083544447[/C][C]152.48649063784[/C][C]513.391676451054[/C][/ROW]
[ROW][C]143[/C][C]302.265796160358[/C][C]116.462558265102[/C][C]488.069034055614[/C][/ROW]
[ROW][C]144[/C][C]128.569116655755[/C][C]-62.4349360185404[/C][C]319.573169330051[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261188&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261188&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
133619.666105048216497.494938417446741.837271678987
134330.101900145877200.157685647627460.046114644128
135327.850739766656190.572905404327465.128574128985
136308.498102308061164.259034324193452.737170291929
137312.620328269176161.740860950065463.499795588287
138455.891791460564298.652106316697613.131476604431
139172.8633984942789.51094669208959336.215850296466
140237.80925564033268.5646739384948407.05383734217
141271.62366485525496.6852946757139446.562035034794
142332.939083544447152.48649063784513.391676451054
143302.265796160358116.462558265102488.069034055614
144128.569116655755-62.4349360185404319.573169330051



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