Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 24 Dec 2014 11:44:57 +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/Dec/24/t1419421528gtbl3zqg3czantj.htm/, Retrieved Thu, 31 Oct 2024 23:12:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=271435, Retrieved Thu, 31 Oct 2024 23:12:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact181
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [-] [2014-12-24 11:44:57] [76c30f62b7052b57088120e90a652e05] [Current]
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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 time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271435&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271435&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271435&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 time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.312319947818984
beta0
gamma0.335705474445768

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.312319947818984 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.335705474445768 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271435&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]0.312319947818984[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.335705474445768[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271435&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271435&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
alpha0.312319947818984
beta0
gamma0.335705474445768







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13232209.73211456266322.2678854373373
14143135.4944437068357.50555629316509
15161155.2493363404165.75066365958352
16159152.4180601498666.58193985013401
17243237.4029745813465.59702541865357
18192192.755342615731-0.755342615730569
19157160.776428609988-3.77642860998813
20143183.103304403763-40.1033044037634
21221169.03652016861251.9634798313885
22227207.23167600469819.7683239953018
23132193.268207677378-61.2682076773777
244150.0469734306507-9.04697343065067
25273237.93154494767935.0684550523211
26182153.71818353628.2818164639999
27188182.0194594621225.98054053787834
28162178.413648366911-16.4136483669114
29140264.835051601105-124.835051601105
30186181.0251642974914.9748357025087
31178151.87254720161526.1274527983846
32236174.57552037698361.4244796230168
33202215.735873300075-13.735873300075
34184226.716513456115-42.7165134561153
35119173.866345174049-54.8663451740491
361646.8705239997778-30.8705239997778
37340203.167195430449136.832804569551
38151153.078848320143-2.07884832014298
39240165.51918812680374.480811873197
40235177.78689495627357.2131050437265
41174266.316487975641-92.3164879756412
42309219.10775753027589.8922424697253
43174211.370308402346-37.3703084023462
44207224.868087171367-17.8680871713667
45209223.979839056125-14.9798390561247
46171227.569810263822-56.5698102638217
47117164.777805972124-47.7778059721241
481039.4038408186841-29.4038408186841
49339230.152614541864108.847385458136
50139145.346213872446-6.34621387244633
51186170.51147553804415.4885244619559
52155161.858195928297-6.85819592829728
53153185.900616418039-32.9006164180385
54222193.41129053566228.5887094643376
55102153.172878214188-51.1728782141876
56107159.006557706602-52.006557706602
57188146.98155828895241.0184417110476
58162158.5289904515743.47100954842617
59185124.07882648065260.921173519348
602431.4842020301466-7.48420203014656
61394312.62047714103581.3795228589652
62209167.80721702043441.1927829795659
63248220.93539061502527.0646093849747
64254204.90817948976749.0918205102332
65202246.87588464089-44.8758846408895
66258275.808131483415-17.8081314834151
67215180.56810978213934.4318902178611
68309221.23152332815487.7684766718459
69240294.039594395892-54.0395943958922
70258259.565194486389-1.56519448638937
71276219.01480899169556.9851910083051
724844.46143728548333.53856271451669
73455545.8493838124-90.8493838124004
74345255.31532502790589.6846749720945
75311337.010306589511-26.0103065895114
76346299.91379257105546.0862074289448
77310319.438166127972-9.43816612797241
78297385.303629750913-88.3036297509128
79300252.1977377855847.80226221442
80274320.031429516032-46.0314295160325
81292318.888034812655-26.8880348126552
82304303.6989488689790.301051131021381
83186271.141559152898-85.1415591528983
841444.2847738030314-30.2847738030314
85321394.154380970069-73.1543809700686
86206205.4014889268760.598511073124257
87160224.440167180788-64.4401671807877
88217196.9733724402620.0266275597399
89204199.1683784289694.83162157103135
90246232.8280062275713.1719937724299
91234184.99475001800349.0052499819972
92175222.993964373499-47.9939643734995
93364220.94945776572143.05054223428
94328265.44152938442262.5584706155778
95158233.958764015873-75.958764015873
964033.1045866010136.895413398987
97556475.6210738598680.3789261401399
98193289.548752016511-96.5487520165114
99221261.853949435682-40.8539494356825
100278264.22090951099913.7790904890011
101230258.14067887283-28.1406788728302
102253290.836776945701-37.8367769457006
103240226.92540439958213.0745956004184
104252230.29295763759421.7070423624063
105228298.585389472139-70.5853894721391
106306258.40663266197447.5933673380265
107206195.85064120438210.1493587956181
1084835.725061985671612.2749380143284
109557529.23432760711827.765672392882
110279274.0948449367764.90515506322447
111399292.552360366631106.447639633369
112364362.658247221271.34175277872981
113306335.294669833338-29.2946698333378
114471377.57009589431493.4299041056858
115293344.986214958912-51.9862149589121
116333329.5635900861743.4364099138258
117316382.965907087671-66.9659070876712
118329373.059946972112-44.0599469721117
119265250.05303981775414.9469601822465
1206148.350377092731112.6496229072689
121679659.84678440542319.1532155945771
122428336.24464310330991.7553568966906
123394414.148233720329-20.1482337203292
124352422.161388036839-70.1613880368391
125387361.4510303548625.5489696451401
126590459.517675794314130.482324205686
127177387.916111041505-210.916111041505
128199335.843867529782-136.843867529782
129203324.46470148262-121.46470148262
130255300.061606221413-45.0616062214125
131261207.89348526928153.1065147307194
13211544.428665846897670.5713341531024

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 232 & 209.732114562663 & 22.2678854373373 \tabularnewline
14 & 143 & 135.494443706835 & 7.50555629316509 \tabularnewline
15 & 161 & 155.249336340416 & 5.75066365958352 \tabularnewline
16 & 159 & 152.418060149866 & 6.58193985013401 \tabularnewline
17 & 243 & 237.402974581346 & 5.59702541865357 \tabularnewline
18 & 192 & 192.755342615731 & -0.755342615730569 \tabularnewline
19 & 157 & 160.776428609988 & -3.77642860998813 \tabularnewline
20 & 143 & 183.103304403763 & -40.1033044037634 \tabularnewline
21 & 221 & 169.036520168612 & 51.9634798313885 \tabularnewline
22 & 227 & 207.231676004698 & 19.7683239953018 \tabularnewline
23 & 132 & 193.268207677378 & -61.2682076773777 \tabularnewline
24 & 41 & 50.0469734306507 & -9.04697343065067 \tabularnewline
25 & 273 & 237.931544947679 & 35.0684550523211 \tabularnewline
26 & 182 & 153.718183536 & 28.2818164639999 \tabularnewline
27 & 188 & 182.019459462122 & 5.98054053787834 \tabularnewline
28 & 162 & 178.413648366911 & -16.4136483669114 \tabularnewline
29 & 140 & 264.835051601105 & -124.835051601105 \tabularnewline
30 & 186 & 181.025164297491 & 4.9748357025087 \tabularnewline
31 & 178 & 151.872547201615 & 26.1274527983846 \tabularnewline
32 & 236 & 174.575520376983 & 61.4244796230168 \tabularnewline
33 & 202 & 215.735873300075 & -13.735873300075 \tabularnewline
34 & 184 & 226.716513456115 & -42.7165134561153 \tabularnewline
35 & 119 & 173.866345174049 & -54.8663451740491 \tabularnewline
36 & 16 & 46.8705239997778 & -30.8705239997778 \tabularnewline
37 & 340 & 203.167195430449 & 136.832804569551 \tabularnewline
38 & 151 & 153.078848320143 & -2.07884832014298 \tabularnewline
39 & 240 & 165.519188126803 & 74.480811873197 \tabularnewline
40 & 235 & 177.786894956273 & 57.2131050437265 \tabularnewline
41 & 174 & 266.316487975641 & -92.3164879756412 \tabularnewline
42 & 309 & 219.107757530275 & 89.8922424697253 \tabularnewline
43 & 174 & 211.370308402346 & -37.3703084023462 \tabularnewline
44 & 207 & 224.868087171367 & -17.8680871713667 \tabularnewline
45 & 209 & 223.979839056125 & -14.9798390561247 \tabularnewline
46 & 171 & 227.569810263822 & -56.5698102638217 \tabularnewline
47 & 117 & 164.777805972124 & -47.7778059721241 \tabularnewline
48 & 10 & 39.4038408186841 & -29.4038408186841 \tabularnewline
49 & 339 & 230.152614541864 & 108.847385458136 \tabularnewline
50 & 139 & 145.346213872446 & -6.34621387244633 \tabularnewline
51 & 186 & 170.511475538044 & 15.4885244619559 \tabularnewline
52 & 155 & 161.858195928297 & -6.85819592829728 \tabularnewline
53 & 153 & 185.900616418039 & -32.9006164180385 \tabularnewline
54 & 222 & 193.411290535662 & 28.5887094643376 \tabularnewline
55 & 102 & 153.172878214188 & -51.1728782141876 \tabularnewline
56 & 107 & 159.006557706602 & -52.006557706602 \tabularnewline
57 & 188 & 146.981558288952 & 41.0184417110476 \tabularnewline
58 & 162 & 158.528990451574 & 3.47100954842617 \tabularnewline
59 & 185 & 124.078826480652 & 60.921173519348 \tabularnewline
60 & 24 & 31.4842020301466 & -7.48420203014656 \tabularnewline
61 & 394 & 312.620477141035 & 81.3795228589652 \tabularnewline
62 & 209 & 167.807217020434 & 41.1927829795659 \tabularnewline
63 & 248 & 220.935390615025 & 27.0646093849747 \tabularnewline
64 & 254 & 204.908179489767 & 49.0918205102332 \tabularnewline
65 & 202 & 246.87588464089 & -44.8758846408895 \tabularnewline
66 & 258 & 275.808131483415 & -17.8081314834151 \tabularnewline
67 & 215 & 180.568109782139 & 34.4318902178611 \tabularnewline
68 & 309 & 221.231523328154 & 87.7684766718459 \tabularnewline
69 & 240 & 294.039594395892 & -54.0395943958922 \tabularnewline
70 & 258 & 259.565194486389 & -1.56519448638937 \tabularnewline
71 & 276 & 219.014808991695 & 56.9851910083051 \tabularnewline
72 & 48 & 44.4614372854833 & 3.53856271451669 \tabularnewline
73 & 455 & 545.8493838124 & -90.8493838124004 \tabularnewline
74 & 345 & 255.315325027905 & 89.6846749720945 \tabularnewline
75 & 311 & 337.010306589511 & -26.0103065895114 \tabularnewline
76 & 346 & 299.913792571055 & 46.0862074289448 \tabularnewline
77 & 310 & 319.438166127972 & -9.43816612797241 \tabularnewline
78 & 297 & 385.303629750913 & -88.3036297509128 \tabularnewline
79 & 300 & 252.19773778558 & 47.80226221442 \tabularnewline
80 & 274 & 320.031429516032 & -46.0314295160325 \tabularnewline
81 & 292 & 318.888034812655 & -26.8880348126552 \tabularnewline
82 & 304 & 303.698948868979 & 0.301051131021381 \tabularnewline
83 & 186 & 271.141559152898 & -85.1415591528983 \tabularnewline
84 & 14 & 44.2847738030314 & -30.2847738030314 \tabularnewline
85 & 321 & 394.154380970069 & -73.1543809700686 \tabularnewline
86 & 206 & 205.401488926876 & 0.598511073124257 \tabularnewline
87 & 160 & 224.440167180788 & -64.4401671807877 \tabularnewline
88 & 217 & 196.97337244026 & 20.0266275597399 \tabularnewline
89 & 204 & 199.168378428969 & 4.83162157103135 \tabularnewline
90 & 246 & 232.82800622757 & 13.1719937724299 \tabularnewline
91 & 234 & 184.994750018003 & 49.0052499819972 \tabularnewline
92 & 175 & 222.993964373499 & -47.9939643734995 \tabularnewline
93 & 364 & 220.94945776572 & 143.05054223428 \tabularnewline
94 & 328 & 265.441529384422 & 62.5584706155778 \tabularnewline
95 & 158 & 233.958764015873 & -75.958764015873 \tabularnewline
96 & 40 & 33.104586601013 & 6.895413398987 \tabularnewline
97 & 556 & 475.62107385986 & 80.3789261401399 \tabularnewline
98 & 193 & 289.548752016511 & -96.5487520165114 \tabularnewline
99 & 221 & 261.853949435682 & -40.8539494356825 \tabularnewline
100 & 278 & 264.220909510999 & 13.7790904890011 \tabularnewline
101 & 230 & 258.14067887283 & -28.1406788728302 \tabularnewline
102 & 253 & 290.836776945701 & -37.8367769457006 \tabularnewline
103 & 240 & 226.925404399582 & 13.0745956004184 \tabularnewline
104 & 252 & 230.292957637594 & 21.7070423624063 \tabularnewline
105 & 228 & 298.585389472139 & -70.5853894721391 \tabularnewline
106 & 306 & 258.406632661974 & 47.5933673380265 \tabularnewline
107 & 206 & 195.850641204382 & 10.1493587956181 \tabularnewline
108 & 48 & 35.7250619856716 & 12.2749380143284 \tabularnewline
109 & 557 & 529.234327607118 & 27.765672392882 \tabularnewline
110 & 279 & 274.094844936776 & 4.90515506322447 \tabularnewline
111 & 399 & 292.552360366631 & 106.447639633369 \tabularnewline
112 & 364 & 362.65824722127 & 1.34175277872981 \tabularnewline
113 & 306 & 335.294669833338 & -29.2946698333378 \tabularnewline
114 & 471 & 377.570095894314 & 93.4299041056858 \tabularnewline
115 & 293 & 344.986214958912 & -51.9862149589121 \tabularnewline
116 & 333 & 329.563590086174 & 3.4364099138258 \tabularnewline
117 & 316 & 382.965907087671 & -66.9659070876712 \tabularnewline
118 & 329 & 373.059946972112 & -44.0599469721117 \tabularnewline
119 & 265 & 250.053039817754 & 14.9469601822465 \tabularnewline
120 & 61 & 48.3503770927311 & 12.6496229072689 \tabularnewline
121 & 679 & 659.846784405423 & 19.1532155945771 \tabularnewline
122 & 428 & 336.244643103309 & 91.7553568966906 \tabularnewline
123 & 394 & 414.148233720329 & -20.1482337203292 \tabularnewline
124 & 352 & 422.161388036839 & -70.1613880368391 \tabularnewline
125 & 387 & 361.45103035486 & 25.5489696451401 \tabularnewline
126 & 590 & 459.517675794314 & 130.482324205686 \tabularnewline
127 & 177 & 387.916111041505 & -210.916111041505 \tabularnewline
128 & 199 & 335.843867529782 & -136.843867529782 \tabularnewline
129 & 203 & 324.46470148262 & -121.46470148262 \tabularnewline
130 & 255 & 300.061606221413 & -45.0616062214125 \tabularnewline
131 & 261 & 207.893485269281 & 53.1065147307194 \tabularnewline
132 & 115 & 44.4286658468976 & 70.5713341531024 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271435&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]209.732114562663[/C][C]22.2678854373373[/C][/ROW]
[ROW][C]14[/C][C]143[/C][C]135.494443706835[/C][C]7.50555629316509[/C][/ROW]
[ROW][C]15[/C][C]161[/C][C]155.249336340416[/C][C]5.75066365958352[/C][/ROW]
[ROW][C]16[/C][C]159[/C][C]152.418060149866[/C][C]6.58193985013401[/C][/ROW]
[ROW][C]17[/C][C]243[/C][C]237.402974581346[/C][C]5.59702541865357[/C][/ROW]
[ROW][C]18[/C][C]192[/C][C]192.755342615731[/C][C]-0.755342615730569[/C][/ROW]
[ROW][C]19[/C][C]157[/C][C]160.776428609988[/C][C]-3.77642860998813[/C][/ROW]
[ROW][C]20[/C][C]143[/C][C]183.103304403763[/C][C]-40.1033044037634[/C][/ROW]
[ROW][C]21[/C][C]221[/C][C]169.036520168612[/C][C]51.9634798313885[/C][/ROW]
[ROW][C]22[/C][C]227[/C][C]207.231676004698[/C][C]19.7683239953018[/C][/ROW]
[ROW][C]23[/C][C]132[/C][C]193.268207677378[/C][C]-61.2682076773777[/C][/ROW]
[ROW][C]24[/C][C]41[/C][C]50.0469734306507[/C][C]-9.04697343065067[/C][/ROW]
[ROW][C]25[/C][C]273[/C][C]237.931544947679[/C][C]35.0684550523211[/C][/ROW]
[ROW][C]26[/C][C]182[/C][C]153.718183536[/C][C]28.2818164639999[/C][/ROW]
[ROW][C]27[/C][C]188[/C][C]182.019459462122[/C][C]5.98054053787834[/C][/ROW]
[ROW][C]28[/C][C]162[/C][C]178.413648366911[/C][C]-16.4136483669114[/C][/ROW]
[ROW][C]29[/C][C]140[/C][C]264.835051601105[/C][C]-124.835051601105[/C][/ROW]
[ROW][C]30[/C][C]186[/C][C]181.025164297491[/C][C]4.9748357025087[/C][/ROW]
[ROW][C]31[/C][C]178[/C][C]151.872547201615[/C][C]26.1274527983846[/C][/ROW]
[ROW][C]32[/C][C]236[/C][C]174.575520376983[/C][C]61.4244796230168[/C][/ROW]
[ROW][C]33[/C][C]202[/C][C]215.735873300075[/C][C]-13.735873300075[/C][/ROW]
[ROW][C]34[/C][C]184[/C][C]226.716513456115[/C][C]-42.7165134561153[/C][/ROW]
[ROW][C]35[/C][C]119[/C][C]173.866345174049[/C][C]-54.8663451740491[/C][/ROW]
[ROW][C]36[/C][C]16[/C][C]46.8705239997778[/C][C]-30.8705239997778[/C][/ROW]
[ROW][C]37[/C][C]340[/C][C]203.167195430449[/C][C]136.832804569551[/C][/ROW]
[ROW][C]38[/C][C]151[/C][C]153.078848320143[/C][C]-2.07884832014298[/C][/ROW]
[ROW][C]39[/C][C]240[/C][C]165.519188126803[/C][C]74.480811873197[/C][/ROW]
[ROW][C]40[/C][C]235[/C][C]177.786894956273[/C][C]57.2131050437265[/C][/ROW]
[ROW][C]41[/C][C]174[/C][C]266.316487975641[/C][C]-92.3164879756412[/C][/ROW]
[ROW][C]42[/C][C]309[/C][C]219.107757530275[/C][C]89.8922424697253[/C][/ROW]
[ROW][C]43[/C][C]174[/C][C]211.370308402346[/C][C]-37.3703084023462[/C][/ROW]
[ROW][C]44[/C][C]207[/C][C]224.868087171367[/C][C]-17.8680871713667[/C][/ROW]
[ROW][C]45[/C][C]209[/C][C]223.979839056125[/C][C]-14.9798390561247[/C][/ROW]
[ROW][C]46[/C][C]171[/C][C]227.569810263822[/C][C]-56.5698102638217[/C][/ROW]
[ROW][C]47[/C][C]117[/C][C]164.777805972124[/C][C]-47.7778059721241[/C][/ROW]
[ROW][C]48[/C][C]10[/C][C]39.4038408186841[/C][C]-29.4038408186841[/C][/ROW]
[ROW][C]49[/C][C]339[/C][C]230.152614541864[/C][C]108.847385458136[/C][/ROW]
[ROW][C]50[/C][C]139[/C][C]145.346213872446[/C][C]-6.34621387244633[/C][/ROW]
[ROW][C]51[/C][C]186[/C][C]170.511475538044[/C][C]15.4885244619559[/C][/ROW]
[ROW][C]52[/C][C]155[/C][C]161.858195928297[/C][C]-6.85819592829728[/C][/ROW]
[ROW][C]53[/C][C]153[/C][C]185.900616418039[/C][C]-32.9006164180385[/C][/ROW]
[ROW][C]54[/C][C]222[/C][C]193.411290535662[/C][C]28.5887094643376[/C][/ROW]
[ROW][C]55[/C][C]102[/C][C]153.172878214188[/C][C]-51.1728782141876[/C][/ROW]
[ROW][C]56[/C][C]107[/C][C]159.006557706602[/C][C]-52.006557706602[/C][/ROW]
[ROW][C]57[/C][C]188[/C][C]146.981558288952[/C][C]41.0184417110476[/C][/ROW]
[ROW][C]58[/C][C]162[/C][C]158.528990451574[/C][C]3.47100954842617[/C][/ROW]
[ROW][C]59[/C][C]185[/C][C]124.078826480652[/C][C]60.921173519348[/C][/ROW]
[ROW][C]60[/C][C]24[/C][C]31.4842020301466[/C][C]-7.48420203014656[/C][/ROW]
[ROW][C]61[/C][C]394[/C][C]312.620477141035[/C][C]81.3795228589652[/C][/ROW]
[ROW][C]62[/C][C]209[/C][C]167.807217020434[/C][C]41.1927829795659[/C][/ROW]
[ROW][C]63[/C][C]248[/C][C]220.935390615025[/C][C]27.0646093849747[/C][/ROW]
[ROW][C]64[/C][C]254[/C][C]204.908179489767[/C][C]49.0918205102332[/C][/ROW]
[ROW][C]65[/C][C]202[/C][C]246.87588464089[/C][C]-44.8758846408895[/C][/ROW]
[ROW][C]66[/C][C]258[/C][C]275.808131483415[/C][C]-17.8081314834151[/C][/ROW]
[ROW][C]67[/C][C]215[/C][C]180.568109782139[/C][C]34.4318902178611[/C][/ROW]
[ROW][C]68[/C][C]309[/C][C]221.231523328154[/C][C]87.7684766718459[/C][/ROW]
[ROW][C]69[/C][C]240[/C][C]294.039594395892[/C][C]-54.0395943958922[/C][/ROW]
[ROW][C]70[/C][C]258[/C][C]259.565194486389[/C][C]-1.56519448638937[/C][/ROW]
[ROW][C]71[/C][C]276[/C][C]219.014808991695[/C][C]56.9851910083051[/C][/ROW]
[ROW][C]72[/C][C]48[/C][C]44.4614372854833[/C][C]3.53856271451669[/C][/ROW]
[ROW][C]73[/C][C]455[/C][C]545.8493838124[/C][C]-90.8493838124004[/C][/ROW]
[ROW][C]74[/C][C]345[/C][C]255.315325027905[/C][C]89.6846749720945[/C][/ROW]
[ROW][C]75[/C][C]311[/C][C]337.010306589511[/C][C]-26.0103065895114[/C][/ROW]
[ROW][C]76[/C][C]346[/C][C]299.913792571055[/C][C]46.0862074289448[/C][/ROW]
[ROW][C]77[/C][C]310[/C][C]319.438166127972[/C][C]-9.43816612797241[/C][/ROW]
[ROW][C]78[/C][C]297[/C][C]385.303629750913[/C][C]-88.3036297509128[/C][/ROW]
[ROW][C]79[/C][C]300[/C][C]252.19773778558[/C][C]47.80226221442[/C][/ROW]
[ROW][C]80[/C][C]274[/C][C]320.031429516032[/C][C]-46.0314295160325[/C][/ROW]
[ROW][C]81[/C][C]292[/C][C]318.888034812655[/C][C]-26.8880348126552[/C][/ROW]
[ROW][C]82[/C][C]304[/C][C]303.698948868979[/C][C]0.301051131021381[/C][/ROW]
[ROW][C]83[/C][C]186[/C][C]271.141559152898[/C][C]-85.1415591528983[/C][/ROW]
[ROW][C]84[/C][C]14[/C][C]44.2847738030314[/C][C]-30.2847738030314[/C][/ROW]
[ROW][C]85[/C][C]321[/C][C]394.154380970069[/C][C]-73.1543809700686[/C][/ROW]
[ROW][C]86[/C][C]206[/C][C]205.401488926876[/C][C]0.598511073124257[/C][/ROW]
[ROW][C]87[/C][C]160[/C][C]224.440167180788[/C][C]-64.4401671807877[/C][/ROW]
[ROW][C]88[/C][C]217[/C][C]196.97337244026[/C][C]20.0266275597399[/C][/ROW]
[ROW][C]89[/C][C]204[/C][C]199.168378428969[/C][C]4.83162157103135[/C][/ROW]
[ROW][C]90[/C][C]246[/C][C]232.82800622757[/C][C]13.1719937724299[/C][/ROW]
[ROW][C]91[/C][C]234[/C][C]184.994750018003[/C][C]49.0052499819972[/C][/ROW]
[ROW][C]92[/C][C]175[/C][C]222.993964373499[/C][C]-47.9939643734995[/C][/ROW]
[ROW][C]93[/C][C]364[/C][C]220.94945776572[/C][C]143.05054223428[/C][/ROW]
[ROW][C]94[/C][C]328[/C][C]265.441529384422[/C][C]62.5584706155778[/C][/ROW]
[ROW][C]95[/C][C]158[/C][C]233.958764015873[/C][C]-75.958764015873[/C][/ROW]
[ROW][C]96[/C][C]40[/C][C]33.104586601013[/C][C]6.895413398987[/C][/ROW]
[ROW][C]97[/C][C]556[/C][C]475.62107385986[/C][C]80.3789261401399[/C][/ROW]
[ROW][C]98[/C][C]193[/C][C]289.548752016511[/C][C]-96.5487520165114[/C][/ROW]
[ROW][C]99[/C][C]221[/C][C]261.853949435682[/C][C]-40.8539494356825[/C][/ROW]
[ROW][C]100[/C][C]278[/C][C]264.220909510999[/C][C]13.7790904890011[/C][/ROW]
[ROW][C]101[/C][C]230[/C][C]258.14067887283[/C][C]-28.1406788728302[/C][/ROW]
[ROW][C]102[/C][C]253[/C][C]290.836776945701[/C][C]-37.8367769457006[/C][/ROW]
[ROW][C]103[/C][C]240[/C][C]226.925404399582[/C][C]13.0745956004184[/C][/ROW]
[ROW][C]104[/C][C]252[/C][C]230.292957637594[/C][C]21.7070423624063[/C][/ROW]
[ROW][C]105[/C][C]228[/C][C]298.585389472139[/C][C]-70.5853894721391[/C][/ROW]
[ROW][C]106[/C][C]306[/C][C]258.406632661974[/C][C]47.5933673380265[/C][/ROW]
[ROW][C]107[/C][C]206[/C][C]195.850641204382[/C][C]10.1493587956181[/C][/ROW]
[ROW][C]108[/C][C]48[/C][C]35.7250619856716[/C][C]12.2749380143284[/C][/ROW]
[ROW][C]109[/C][C]557[/C][C]529.234327607118[/C][C]27.765672392882[/C][/ROW]
[ROW][C]110[/C][C]279[/C][C]274.094844936776[/C][C]4.90515506322447[/C][/ROW]
[ROW][C]111[/C][C]399[/C][C]292.552360366631[/C][C]106.447639633369[/C][/ROW]
[ROW][C]112[/C][C]364[/C][C]362.65824722127[/C][C]1.34175277872981[/C][/ROW]
[ROW][C]113[/C][C]306[/C][C]335.294669833338[/C][C]-29.2946698333378[/C][/ROW]
[ROW][C]114[/C][C]471[/C][C]377.570095894314[/C][C]93.4299041056858[/C][/ROW]
[ROW][C]115[/C][C]293[/C][C]344.986214958912[/C][C]-51.9862149589121[/C][/ROW]
[ROW][C]116[/C][C]333[/C][C]329.563590086174[/C][C]3.4364099138258[/C][/ROW]
[ROW][C]117[/C][C]316[/C][C]382.965907087671[/C][C]-66.9659070876712[/C][/ROW]
[ROW][C]118[/C][C]329[/C][C]373.059946972112[/C][C]-44.0599469721117[/C][/ROW]
[ROW][C]119[/C][C]265[/C][C]250.053039817754[/C][C]14.9469601822465[/C][/ROW]
[ROW][C]120[/C][C]61[/C][C]48.3503770927311[/C][C]12.6496229072689[/C][/ROW]
[ROW][C]121[/C][C]679[/C][C]659.846784405423[/C][C]19.1532155945771[/C][/ROW]
[ROW][C]122[/C][C]428[/C][C]336.244643103309[/C][C]91.7553568966906[/C][/ROW]
[ROW][C]123[/C][C]394[/C][C]414.148233720329[/C][C]-20.1482337203292[/C][/ROW]
[ROW][C]124[/C][C]352[/C][C]422.161388036839[/C][C]-70.1613880368391[/C][/ROW]
[ROW][C]125[/C][C]387[/C][C]361.45103035486[/C][C]25.5489696451401[/C][/ROW]
[ROW][C]126[/C][C]590[/C][C]459.517675794314[/C][C]130.482324205686[/C][/ROW]
[ROW][C]127[/C][C]177[/C][C]387.916111041505[/C][C]-210.916111041505[/C][/ROW]
[ROW][C]128[/C][C]199[/C][C]335.843867529782[/C][C]-136.843867529782[/C][/ROW]
[ROW][C]129[/C][C]203[/C][C]324.46470148262[/C][C]-121.46470148262[/C][/ROW]
[ROW][C]130[/C][C]255[/C][C]300.061606221413[/C][C]-45.0616062214125[/C][/ROW]
[ROW][C]131[/C][C]261[/C][C]207.893485269281[/C][C]53.1065147307194[/C][/ROW]
[ROW][C]132[/C][C]115[/C][C]44.4286658468976[/C][C]70.5713341531024[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271435&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271435&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
13232209.73211456266322.2678854373373
14143135.4944437068357.50555629316509
15161155.2493363404165.75066365958352
16159152.4180601498666.58193985013401
17243237.4029745813465.59702541865357
18192192.755342615731-0.755342615730569
19157160.776428609988-3.77642860998813
20143183.103304403763-40.1033044037634
21221169.03652016861251.9634798313885
22227207.23167600469819.7683239953018
23132193.268207677378-61.2682076773777
244150.0469734306507-9.04697343065067
25273237.93154494767935.0684550523211
26182153.71818353628.2818164639999
27188182.0194594621225.98054053787834
28162178.413648366911-16.4136483669114
29140264.835051601105-124.835051601105
30186181.0251642974914.9748357025087
31178151.87254720161526.1274527983846
32236174.57552037698361.4244796230168
33202215.735873300075-13.735873300075
34184226.716513456115-42.7165134561153
35119173.866345174049-54.8663451740491
361646.8705239997778-30.8705239997778
37340203.167195430449136.832804569551
38151153.078848320143-2.07884832014298
39240165.51918812680374.480811873197
40235177.78689495627357.2131050437265
41174266.316487975641-92.3164879756412
42309219.10775753027589.8922424697253
43174211.370308402346-37.3703084023462
44207224.868087171367-17.8680871713667
45209223.979839056125-14.9798390561247
46171227.569810263822-56.5698102638217
47117164.777805972124-47.7778059721241
481039.4038408186841-29.4038408186841
49339230.152614541864108.847385458136
50139145.346213872446-6.34621387244633
51186170.51147553804415.4885244619559
52155161.858195928297-6.85819592829728
53153185.900616418039-32.9006164180385
54222193.41129053566228.5887094643376
55102153.172878214188-51.1728782141876
56107159.006557706602-52.006557706602
57188146.98155828895241.0184417110476
58162158.5289904515743.47100954842617
59185124.07882648065260.921173519348
602431.4842020301466-7.48420203014656
61394312.62047714103581.3795228589652
62209167.80721702043441.1927829795659
63248220.93539061502527.0646093849747
64254204.90817948976749.0918205102332
65202246.87588464089-44.8758846408895
66258275.808131483415-17.8081314834151
67215180.56810978213934.4318902178611
68309221.23152332815487.7684766718459
69240294.039594395892-54.0395943958922
70258259.565194486389-1.56519448638937
71276219.01480899169556.9851910083051
724844.46143728548333.53856271451669
73455545.8493838124-90.8493838124004
74345255.31532502790589.6846749720945
75311337.010306589511-26.0103065895114
76346299.91379257105546.0862074289448
77310319.438166127972-9.43816612797241
78297385.303629750913-88.3036297509128
79300252.1977377855847.80226221442
80274320.031429516032-46.0314295160325
81292318.888034812655-26.8880348126552
82304303.6989488689790.301051131021381
83186271.141559152898-85.1415591528983
841444.2847738030314-30.2847738030314
85321394.154380970069-73.1543809700686
86206205.4014889268760.598511073124257
87160224.440167180788-64.4401671807877
88217196.9733724402620.0266275597399
89204199.1683784289694.83162157103135
90246232.8280062275713.1719937724299
91234184.99475001800349.0052499819972
92175222.993964373499-47.9939643734995
93364220.94945776572143.05054223428
94328265.44152938442262.5584706155778
95158233.958764015873-75.958764015873
964033.1045866010136.895413398987
97556475.6210738598680.3789261401399
98193289.548752016511-96.5487520165114
99221261.853949435682-40.8539494356825
100278264.22090951099913.7790904890011
101230258.14067887283-28.1406788728302
102253290.836776945701-37.8367769457006
103240226.92540439958213.0745956004184
104252230.29295763759421.7070423624063
105228298.585389472139-70.5853894721391
106306258.40663266197447.5933673380265
107206195.85064120438210.1493587956181
1084835.725061985671612.2749380143284
109557529.23432760711827.765672392882
110279274.0948449367764.90515506322447
111399292.552360366631106.447639633369
112364362.658247221271.34175277872981
113306335.294669833338-29.2946698333378
114471377.57009589431493.4299041056858
115293344.986214958912-51.9862149589121
116333329.5635900861743.4364099138258
117316382.965907087671-66.9659070876712
118329373.059946972112-44.0599469721117
119265250.05303981775414.9469601822465
1206148.350377092731112.6496229072689
121679659.84678440542319.1532155945771
122428336.24464310330991.7553568966906
123394414.148233720329-20.1482337203292
124352422.161388036839-70.1613880368391
125387361.4510303548625.5489696451401
126590459.517675794314130.482324205686
127177387.916111041505-210.916111041505
128199335.843867529782-136.843867529782
129203324.46470148262-121.46470148262
130255300.061606221413-45.0616062214125
131261207.89348526928153.1065147307194
13211544.428665846897670.5713341531024







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
133798.764934198327736.443269931044861.08659846561
134423.599640328342358.470806351535488.728474305149
135449.006294923899373.430930102744524.581659745054
136450.855805794086367.234582298382534.477029289789
137430.754629999749342.115602716871519.393657282628
138558.753726182992446.287551520301671.219900845684
139346.786520585856258.92543247389434.647608697822
140379.6829648682279.85546426996479.510465466439
141424.113269898511310.132690828434538.093848968587
142473.055628745389343.840526408348602.270731082429
143375.1475556788262.58548069461487.709630662991
14487.432122371755163.3950033484696111.469241395041

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
133 & 798.764934198327 & 736.443269931044 & 861.08659846561 \tabularnewline
134 & 423.599640328342 & 358.470806351535 & 488.728474305149 \tabularnewline
135 & 449.006294923899 & 373.430930102744 & 524.581659745054 \tabularnewline
136 & 450.855805794086 & 367.234582298382 & 534.477029289789 \tabularnewline
137 & 430.754629999749 & 342.115602716871 & 519.393657282628 \tabularnewline
138 & 558.753726182992 & 446.287551520301 & 671.219900845684 \tabularnewline
139 & 346.786520585856 & 258.92543247389 & 434.647608697822 \tabularnewline
140 & 379.6829648682 & 279.85546426996 & 479.510465466439 \tabularnewline
141 & 424.113269898511 & 310.132690828434 & 538.093848968587 \tabularnewline
142 & 473.055628745389 & 343.840526408348 & 602.270731082429 \tabularnewline
143 & 375.1475556788 & 262.58548069461 & 487.709630662991 \tabularnewline
144 & 87.4321223717551 & 63.3950033484696 & 111.469241395041 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271435&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]798.764934198327[/C][C]736.443269931044[/C][C]861.08659846561[/C][/ROW]
[ROW][C]134[/C][C]423.599640328342[/C][C]358.470806351535[/C][C]488.728474305149[/C][/ROW]
[ROW][C]135[/C][C]449.006294923899[/C][C]373.430930102744[/C][C]524.581659745054[/C][/ROW]
[ROW][C]136[/C][C]450.855805794086[/C][C]367.234582298382[/C][C]534.477029289789[/C][/ROW]
[ROW][C]137[/C][C]430.754629999749[/C][C]342.115602716871[/C][C]519.393657282628[/C][/ROW]
[ROW][C]138[/C][C]558.753726182992[/C][C]446.287551520301[/C][C]671.219900845684[/C][/ROW]
[ROW][C]139[/C][C]346.786520585856[/C][C]258.92543247389[/C][C]434.647608697822[/C][/ROW]
[ROW][C]140[/C][C]379.6829648682[/C][C]279.85546426996[/C][C]479.510465466439[/C][/ROW]
[ROW][C]141[/C][C]424.113269898511[/C][C]310.132690828434[/C][C]538.093848968587[/C][/ROW]
[ROW][C]142[/C][C]473.055628745389[/C][C]343.840526408348[/C][C]602.270731082429[/C][/ROW]
[ROW][C]143[/C][C]375.1475556788[/C][C]262.58548069461[/C][C]487.709630662991[/C][/ROW]
[ROW][C]144[/C][C]87.4321223717551[/C][C]63.3950033484696[/C][C]111.469241395041[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271435&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271435&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
133798.764934198327736.443269931044861.08659846561
134423.599640328342358.470806351535488.728474305149
135449.006294923899373.430930102744524.581659745054
136450.855805794086367.234582298382534.477029289789
137430.754629999749342.115602716871519.393657282628
138558.753726182992446.287551520301671.219900845684
139346.786520585856258.92543247389434.647608697822
140379.6829648682279.85546426996479.510465466439
141424.113269898511310.132690828434538.093848968587
142473.055628745389343.840526408348602.270731082429
143375.1475556788262.58548069461487.709630662991
14487.432122371755163.3950033484696111.469241395041



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')