Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 21 May 2014 19:50:58 -0400
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/May/21/t1400716331ep0uwzdb3cr5nft.htm/, Retrieved Tue, 14 May 2024 14:50:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235072, Retrieved Tue, 14 May 2024 14:50:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact101
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bootstrap Plot - Central Tendency] [] [2014-04-24 06:43:24] [967af62594a7ddaeafac2725d7422db7]
- R P   [Bootstrap Plot - Central Tendency] [] [2014-05-21 15:16:46] [967af62594a7ddaeafac2725d7422db7]
- RMPD    [Classical Decomposition] [] [2014-05-21 16:26:08] [967af62594a7ddaeafac2725d7422db7]
- RMP         [Exponential Smoothing] [] [2014-05-21 23:50:58] [62c8c0f0c987c854521aa0b45bb2685a] [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 time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235072&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235072&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235072&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.312319947819092
beta0
gamma0.335705474445854

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.312319947819092 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.335705474445854 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235072&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]0.312319947819092[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.335705474445854[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235072&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235072&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
alpha0.312319947819092
beta0
gamma0.335705474445854







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13232209.73211456266222.2678854373376
14143135.4944437068367.50555629316372
15161155.2493363404185.75066365958156
16159152.4180601498686.5819398501321
17243237.4029745813495.5970254186505
18192192.755342615733-0.755342615732729
19157160.776428609989-3.7764286099893
20143183.103304403764-40.1033044037639
21221169.03652016860851.9634798313924
22227207.23167600470119.7683239952986
23132193.268207677382-61.2682076773816
244150.0469734306496-9.04697343064956
25273237.93154494767135.0684550523292
26182153.71818353599828.2818164640016
27188182.0194594621245.98054053787632
28162178.413648366913-16.4136483669134
29140264.835051601104-124.835051601104
30186181.025164297484.97483570251987
31178151.8725472016126.1274527983904
32236174.57552037698161.424479623019
33202215.735873300084-13.7358733000843
34184226.716513456118-42.716513456118
35119173.866345174044-54.8663451740444
361646.8705239997758-30.8705239997758
37340203.167195430427136.832804569573
38151153.078848320141-2.07884832014122
39240165.519188126874.4808118731999
40235177.78689495627957.2131050437214
41174266.316487975649-92.3164879756494
42309219.10775753027989.8922424697211
43174211.370308402356-37.3703084023564
44207224.868087171368-17.8680871713677
45209223.979839056123-14.9798390561232
46171227.569810263817-56.5698102638171
47117164.777805972115-47.7778059721149
481039.4038408186805-29.4038408186805
49339230.15261454184108.84738545816
50139145.346213872439-6.34621387243851
51186170.51147553803715.4885244619634
52155161.858195928292-6.85819592829188
53153185.900616418027-32.9006164180267
54222193.41129053566128.5887094643393
55102153.172878214186-51.1728782141862
56107159.006557706595-52.0065577065951
57188146.98155828894241.0184417110579
58162158.5289904515693.47100954843077
59185124.07882648064960.921173519351
602431.4842020301455-7.48420203014551
61394312.62047714106881.3795228589324
62209167.8072170204441.1927829795595
63248220.93539061503627.0646093849643
64254204.90817948977249.0918205102282
65202246.875884640891-44.8758846408909
66258275.808131483425-17.8081314834252
67215180.56810978213634.431890217864
68309221.23152332815887.7684766718416
69240294.039594395914-54.0395943959143
70258259.565194486391-1.56519448639136
71276219.01480899169556.9851910083048
724844.46143728548113.53856271451887
73455545.849383812462-90.849383812462
74345255.31532502791289.6846749720884
75311337.010306589526-26.0103065895262
76346299.91379257105846.0862074289419
77310319.438166127967-9.43816612796718
78297385.303629750926-88.3036297509265
79300252.19773778557547.8022622144246
80274320.031429516036-46.031429516036
81292318.888034812654-26.8880348126536
82304303.6989488689730.301051131026895
83186271.141559152895-85.1415591528954
841444.2847738030264-30.2847738030264
85321394.154380970031-73.1543809700309
86206205.4014889268550.598511073144863
87160224.440167180769-64.4401671807691
88217196.97337244024120.0266275597589
89204199.1683784289514.83162157104906
90246232.82800622756413.171993772436
91234184.99475001800249.0052499819984
92175222.993964373502-47.9939643735022
93364220.949457765718143.050542234282
94328265.44152938443662.5584706155636
95158233.958764015884-75.9587640158837
964033.10458660100996.89541339899006
97556475.62107385990980.378926140091
98193289.548752016535-96.548752016535
99221261.85394943568-40.8539494356801
100278264.22090951099713.7790904890031
101230258.14067887282-28.1406788728203
102253290.836776945694-37.8367769456945
103240226.92540439957613.0745956004245
104252230.29295763758521.7070423624148
105228298.585389472142-70.5853894721419
106306258.40663266196447.5933673380357
107206195.85064120437610.1493587956239
1084835.725061985669612.2749380143304
109557529.23432760716827.7656723928322
110279274.0948449367914.90515506320867
111399292.552360366641106.447639633359
112364362.6582472212991.34175277870077
113306335.294669833344-29.2946698333441
114471377.57009589432193.4299041056794
115293344.986214958927-51.9862149589275
116333329.5635900861723.43640991382802
117316382.965907087671-66.9659070876714
118329373.059946972107-44.0599469721066
119265250.05303981774114.9469601822593
1206148.350377092728212.6496229072718
121679659.84678440545319.1532155945474
122428336.2446431033291.7553568966803
123394414.14823372035-20.1482337203503
124352422.161388036855-70.1613880368554
125387361.45103035485425.5489696451457
126590459.517675794322130.482324205678
127177387.916111041518-210.916111041518
128199335.843867529765-136.843867529765
129203324.46470148259-121.46470148259
130255300.061606221381-45.061606221381
131261207.89348526925853.1065147307417
13211544.428665846894570.5713341531055

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 232 & 209.732114562662 & 22.2678854373376 \tabularnewline
14 & 143 & 135.494443706836 & 7.50555629316372 \tabularnewline
15 & 161 & 155.249336340418 & 5.75066365958156 \tabularnewline
16 & 159 & 152.418060149868 & 6.5819398501321 \tabularnewline
17 & 243 & 237.402974581349 & 5.5970254186505 \tabularnewline
18 & 192 & 192.755342615733 & -0.755342615732729 \tabularnewline
19 & 157 & 160.776428609989 & -3.7764286099893 \tabularnewline
20 & 143 & 183.103304403764 & -40.1033044037639 \tabularnewline
21 & 221 & 169.036520168608 & 51.9634798313924 \tabularnewline
22 & 227 & 207.231676004701 & 19.7683239952986 \tabularnewline
23 & 132 & 193.268207677382 & -61.2682076773816 \tabularnewline
24 & 41 & 50.0469734306496 & -9.04697343064956 \tabularnewline
25 & 273 & 237.931544947671 & 35.0684550523292 \tabularnewline
26 & 182 & 153.718183535998 & 28.2818164640016 \tabularnewline
27 & 188 & 182.019459462124 & 5.98054053787632 \tabularnewline
28 & 162 & 178.413648366913 & -16.4136483669134 \tabularnewline
29 & 140 & 264.835051601104 & -124.835051601104 \tabularnewline
30 & 186 & 181.02516429748 & 4.97483570251987 \tabularnewline
31 & 178 & 151.87254720161 & 26.1274527983904 \tabularnewline
32 & 236 & 174.575520376981 & 61.424479623019 \tabularnewline
33 & 202 & 215.735873300084 & -13.7358733000843 \tabularnewline
34 & 184 & 226.716513456118 & -42.716513456118 \tabularnewline
35 & 119 & 173.866345174044 & -54.8663451740444 \tabularnewline
36 & 16 & 46.8705239997758 & -30.8705239997758 \tabularnewline
37 & 340 & 203.167195430427 & 136.832804569573 \tabularnewline
38 & 151 & 153.078848320141 & -2.07884832014122 \tabularnewline
39 & 240 & 165.5191881268 & 74.4808118731999 \tabularnewline
40 & 235 & 177.786894956279 & 57.2131050437214 \tabularnewline
41 & 174 & 266.316487975649 & -92.3164879756494 \tabularnewline
42 & 309 & 219.107757530279 & 89.8922424697211 \tabularnewline
43 & 174 & 211.370308402356 & -37.3703084023564 \tabularnewline
44 & 207 & 224.868087171368 & -17.8680871713677 \tabularnewline
45 & 209 & 223.979839056123 & -14.9798390561232 \tabularnewline
46 & 171 & 227.569810263817 & -56.5698102638171 \tabularnewline
47 & 117 & 164.777805972115 & -47.7778059721149 \tabularnewline
48 & 10 & 39.4038408186805 & -29.4038408186805 \tabularnewline
49 & 339 & 230.15261454184 & 108.84738545816 \tabularnewline
50 & 139 & 145.346213872439 & -6.34621387243851 \tabularnewline
51 & 186 & 170.511475538037 & 15.4885244619634 \tabularnewline
52 & 155 & 161.858195928292 & -6.85819592829188 \tabularnewline
53 & 153 & 185.900616418027 & -32.9006164180267 \tabularnewline
54 & 222 & 193.411290535661 & 28.5887094643393 \tabularnewline
55 & 102 & 153.172878214186 & -51.1728782141862 \tabularnewline
56 & 107 & 159.006557706595 & -52.0065577065951 \tabularnewline
57 & 188 & 146.981558288942 & 41.0184417110579 \tabularnewline
58 & 162 & 158.528990451569 & 3.47100954843077 \tabularnewline
59 & 185 & 124.078826480649 & 60.921173519351 \tabularnewline
60 & 24 & 31.4842020301455 & -7.48420203014551 \tabularnewline
61 & 394 & 312.620477141068 & 81.3795228589324 \tabularnewline
62 & 209 & 167.80721702044 & 41.1927829795595 \tabularnewline
63 & 248 & 220.935390615036 & 27.0646093849643 \tabularnewline
64 & 254 & 204.908179489772 & 49.0918205102282 \tabularnewline
65 & 202 & 246.875884640891 & -44.8758846408909 \tabularnewline
66 & 258 & 275.808131483425 & -17.8081314834252 \tabularnewline
67 & 215 & 180.568109782136 & 34.431890217864 \tabularnewline
68 & 309 & 221.231523328158 & 87.7684766718416 \tabularnewline
69 & 240 & 294.039594395914 & -54.0395943959143 \tabularnewline
70 & 258 & 259.565194486391 & -1.56519448639136 \tabularnewline
71 & 276 & 219.014808991695 & 56.9851910083048 \tabularnewline
72 & 48 & 44.4614372854811 & 3.53856271451887 \tabularnewline
73 & 455 & 545.849383812462 & -90.849383812462 \tabularnewline
74 & 345 & 255.315325027912 & 89.6846749720884 \tabularnewline
75 & 311 & 337.010306589526 & -26.0103065895262 \tabularnewline
76 & 346 & 299.913792571058 & 46.0862074289419 \tabularnewline
77 & 310 & 319.438166127967 & -9.43816612796718 \tabularnewline
78 & 297 & 385.303629750926 & -88.3036297509265 \tabularnewline
79 & 300 & 252.197737785575 & 47.8022622144246 \tabularnewline
80 & 274 & 320.031429516036 & -46.031429516036 \tabularnewline
81 & 292 & 318.888034812654 & -26.8880348126536 \tabularnewline
82 & 304 & 303.698948868973 & 0.301051131026895 \tabularnewline
83 & 186 & 271.141559152895 & -85.1415591528954 \tabularnewline
84 & 14 & 44.2847738030264 & -30.2847738030264 \tabularnewline
85 & 321 & 394.154380970031 & -73.1543809700309 \tabularnewline
86 & 206 & 205.401488926855 & 0.598511073144863 \tabularnewline
87 & 160 & 224.440167180769 & -64.4401671807691 \tabularnewline
88 & 217 & 196.973372440241 & 20.0266275597589 \tabularnewline
89 & 204 & 199.168378428951 & 4.83162157104906 \tabularnewline
90 & 246 & 232.828006227564 & 13.171993772436 \tabularnewline
91 & 234 & 184.994750018002 & 49.0052499819984 \tabularnewline
92 & 175 & 222.993964373502 & -47.9939643735022 \tabularnewline
93 & 364 & 220.949457765718 & 143.050542234282 \tabularnewline
94 & 328 & 265.441529384436 & 62.5584706155636 \tabularnewline
95 & 158 & 233.958764015884 & -75.9587640158837 \tabularnewline
96 & 40 & 33.1045866010099 & 6.89541339899006 \tabularnewline
97 & 556 & 475.621073859909 & 80.378926140091 \tabularnewline
98 & 193 & 289.548752016535 & -96.548752016535 \tabularnewline
99 & 221 & 261.85394943568 & -40.8539494356801 \tabularnewline
100 & 278 & 264.220909510997 & 13.7790904890031 \tabularnewline
101 & 230 & 258.14067887282 & -28.1406788728203 \tabularnewline
102 & 253 & 290.836776945694 & -37.8367769456945 \tabularnewline
103 & 240 & 226.925404399576 & 13.0745956004245 \tabularnewline
104 & 252 & 230.292957637585 & 21.7070423624148 \tabularnewline
105 & 228 & 298.585389472142 & -70.5853894721419 \tabularnewline
106 & 306 & 258.406632661964 & 47.5933673380357 \tabularnewline
107 & 206 & 195.850641204376 & 10.1493587956239 \tabularnewline
108 & 48 & 35.7250619856696 & 12.2749380143304 \tabularnewline
109 & 557 & 529.234327607168 & 27.7656723928322 \tabularnewline
110 & 279 & 274.094844936791 & 4.90515506320867 \tabularnewline
111 & 399 & 292.552360366641 & 106.447639633359 \tabularnewline
112 & 364 & 362.658247221299 & 1.34175277870077 \tabularnewline
113 & 306 & 335.294669833344 & -29.2946698333441 \tabularnewline
114 & 471 & 377.570095894321 & 93.4299041056794 \tabularnewline
115 & 293 & 344.986214958927 & -51.9862149589275 \tabularnewline
116 & 333 & 329.563590086172 & 3.43640991382802 \tabularnewline
117 & 316 & 382.965907087671 & -66.9659070876714 \tabularnewline
118 & 329 & 373.059946972107 & -44.0599469721066 \tabularnewline
119 & 265 & 250.053039817741 & 14.9469601822593 \tabularnewline
120 & 61 & 48.3503770927282 & 12.6496229072718 \tabularnewline
121 & 679 & 659.846784405453 & 19.1532155945474 \tabularnewline
122 & 428 & 336.24464310332 & 91.7553568966803 \tabularnewline
123 & 394 & 414.14823372035 & -20.1482337203503 \tabularnewline
124 & 352 & 422.161388036855 & -70.1613880368554 \tabularnewline
125 & 387 & 361.451030354854 & 25.5489696451457 \tabularnewline
126 & 590 & 459.517675794322 & 130.482324205678 \tabularnewline
127 & 177 & 387.916111041518 & -210.916111041518 \tabularnewline
128 & 199 & 335.843867529765 & -136.843867529765 \tabularnewline
129 & 203 & 324.46470148259 & -121.46470148259 \tabularnewline
130 & 255 & 300.061606221381 & -45.061606221381 \tabularnewline
131 & 261 & 207.893485269258 & 53.1065147307417 \tabularnewline
132 & 115 & 44.4286658468945 & 70.5713341531055 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235072&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]209.732114562662[/C][C]22.2678854373376[/C][/ROW]
[ROW][C]14[/C][C]143[/C][C]135.494443706836[/C][C]7.50555629316372[/C][/ROW]
[ROW][C]15[/C][C]161[/C][C]155.249336340418[/C][C]5.75066365958156[/C][/ROW]
[ROW][C]16[/C][C]159[/C][C]152.418060149868[/C][C]6.5819398501321[/C][/ROW]
[ROW][C]17[/C][C]243[/C][C]237.402974581349[/C][C]5.5970254186505[/C][/ROW]
[ROW][C]18[/C][C]192[/C][C]192.755342615733[/C][C]-0.755342615732729[/C][/ROW]
[ROW][C]19[/C][C]157[/C][C]160.776428609989[/C][C]-3.7764286099893[/C][/ROW]
[ROW][C]20[/C][C]143[/C][C]183.103304403764[/C][C]-40.1033044037639[/C][/ROW]
[ROW][C]21[/C][C]221[/C][C]169.036520168608[/C][C]51.9634798313924[/C][/ROW]
[ROW][C]22[/C][C]227[/C][C]207.231676004701[/C][C]19.7683239952986[/C][/ROW]
[ROW][C]23[/C][C]132[/C][C]193.268207677382[/C][C]-61.2682076773816[/C][/ROW]
[ROW][C]24[/C][C]41[/C][C]50.0469734306496[/C][C]-9.04697343064956[/C][/ROW]
[ROW][C]25[/C][C]273[/C][C]237.931544947671[/C][C]35.0684550523292[/C][/ROW]
[ROW][C]26[/C][C]182[/C][C]153.718183535998[/C][C]28.2818164640016[/C][/ROW]
[ROW][C]27[/C][C]188[/C][C]182.019459462124[/C][C]5.98054053787632[/C][/ROW]
[ROW][C]28[/C][C]162[/C][C]178.413648366913[/C][C]-16.4136483669134[/C][/ROW]
[ROW][C]29[/C][C]140[/C][C]264.835051601104[/C][C]-124.835051601104[/C][/ROW]
[ROW][C]30[/C][C]186[/C][C]181.02516429748[/C][C]4.97483570251987[/C][/ROW]
[ROW][C]31[/C][C]178[/C][C]151.87254720161[/C][C]26.1274527983904[/C][/ROW]
[ROW][C]32[/C][C]236[/C][C]174.575520376981[/C][C]61.424479623019[/C][/ROW]
[ROW][C]33[/C][C]202[/C][C]215.735873300084[/C][C]-13.7358733000843[/C][/ROW]
[ROW][C]34[/C][C]184[/C][C]226.716513456118[/C][C]-42.716513456118[/C][/ROW]
[ROW][C]35[/C][C]119[/C][C]173.866345174044[/C][C]-54.8663451740444[/C][/ROW]
[ROW][C]36[/C][C]16[/C][C]46.8705239997758[/C][C]-30.8705239997758[/C][/ROW]
[ROW][C]37[/C][C]340[/C][C]203.167195430427[/C][C]136.832804569573[/C][/ROW]
[ROW][C]38[/C][C]151[/C][C]153.078848320141[/C][C]-2.07884832014122[/C][/ROW]
[ROW][C]39[/C][C]240[/C][C]165.5191881268[/C][C]74.4808118731999[/C][/ROW]
[ROW][C]40[/C][C]235[/C][C]177.786894956279[/C][C]57.2131050437214[/C][/ROW]
[ROW][C]41[/C][C]174[/C][C]266.316487975649[/C][C]-92.3164879756494[/C][/ROW]
[ROW][C]42[/C][C]309[/C][C]219.107757530279[/C][C]89.8922424697211[/C][/ROW]
[ROW][C]43[/C][C]174[/C][C]211.370308402356[/C][C]-37.3703084023564[/C][/ROW]
[ROW][C]44[/C][C]207[/C][C]224.868087171368[/C][C]-17.8680871713677[/C][/ROW]
[ROW][C]45[/C][C]209[/C][C]223.979839056123[/C][C]-14.9798390561232[/C][/ROW]
[ROW][C]46[/C][C]171[/C][C]227.569810263817[/C][C]-56.5698102638171[/C][/ROW]
[ROW][C]47[/C][C]117[/C][C]164.777805972115[/C][C]-47.7778059721149[/C][/ROW]
[ROW][C]48[/C][C]10[/C][C]39.4038408186805[/C][C]-29.4038408186805[/C][/ROW]
[ROW][C]49[/C][C]339[/C][C]230.15261454184[/C][C]108.84738545816[/C][/ROW]
[ROW][C]50[/C][C]139[/C][C]145.346213872439[/C][C]-6.34621387243851[/C][/ROW]
[ROW][C]51[/C][C]186[/C][C]170.511475538037[/C][C]15.4885244619634[/C][/ROW]
[ROW][C]52[/C][C]155[/C][C]161.858195928292[/C][C]-6.85819592829188[/C][/ROW]
[ROW][C]53[/C][C]153[/C][C]185.900616418027[/C][C]-32.9006164180267[/C][/ROW]
[ROW][C]54[/C][C]222[/C][C]193.411290535661[/C][C]28.5887094643393[/C][/ROW]
[ROW][C]55[/C][C]102[/C][C]153.172878214186[/C][C]-51.1728782141862[/C][/ROW]
[ROW][C]56[/C][C]107[/C][C]159.006557706595[/C][C]-52.0065577065951[/C][/ROW]
[ROW][C]57[/C][C]188[/C][C]146.981558288942[/C][C]41.0184417110579[/C][/ROW]
[ROW][C]58[/C][C]162[/C][C]158.528990451569[/C][C]3.47100954843077[/C][/ROW]
[ROW][C]59[/C][C]185[/C][C]124.078826480649[/C][C]60.921173519351[/C][/ROW]
[ROW][C]60[/C][C]24[/C][C]31.4842020301455[/C][C]-7.48420203014551[/C][/ROW]
[ROW][C]61[/C][C]394[/C][C]312.620477141068[/C][C]81.3795228589324[/C][/ROW]
[ROW][C]62[/C][C]209[/C][C]167.80721702044[/C][C]41.1927829795595[/C][/ROW]
[ROW][C]63[/C][C]248[/C][C]220.935390615036[/C][C]27.0646093849643[/C][/ROW]
[ROW][C]64[/C][C]254[/C][C]204.908179489772[/C][C]49.0918205102282[/C][/ROW]
[ROW][C]65[/C][C]202[/C][C]246.875884640891[/C][C]-44.8758846408909[/C][/ROW]
[ROW][C]66[/C][C]258[/C][C]275.808131483425[/C][C]-17.8081314834252[/C][/ROW]
[ROW][C]67[/C][C]215[/C][C]180.568109782136[/C][C]34.431890217864[/C][/ROW]
[ROW][C]68[/C][C]309[/C][C]221.231523328158[/C][C]87.7684766718416[/C][/ROW]
[ROW][C]69[/C][C]240[/C][C]294.039594395914[/C][C]-54.0395943959143[/C][/ROW]
[ROW][C]70[/C][C]258[/C][C]259.565194486391[/C][C]-1.56519448639136[/C][/ROW]
[ROW][C]71[/C][C]276[/C][C]219.014808991695[/C][C]56.9851910083048[/C][/ROW]
[ROW][C]72[/C][C]48[/C][C]44.4614372854811[/C][C]3.53856271451887[/C][/ROW]
[ROW][C]73[/C][C]455[/C][C]545.849383812462[/C][C]-90.849383812462[/C][/ROW]
[ROW][C]74[/C][C]345[/C][C]255.315325027912[/C][C]89.6846749720884[/C][/ROW]
[ROW][C]75[/C][C]311[/C][C]337.010306589526[/C][C]-26.0103065895262[/C][/ROW]
[ROW][C]76[/C][C]346[/C][C]299.913792571058[/C][C]46.0862074289419[/C][/ROW]
[ROW][C]77[/C][C]310[/C][C]319.438166127967[/C][C]-9.43816612796718[/C][/ROW]
[ROW][C]78[/C][C]297[/C][C]385.303629750926[/C][C]-88.3036297509265[/C][/ROW]
[ROW][C]79[/C][C]300[/C][C]252.197737785575[/C][C]47.8022622144246[/C][/ROW]
[ROW][C]80[/C][C]274[/C][C]320.031429516036[/C][C]-46.031429516036[/C][/ROW]
[ROW][C]81[/C][C]292[/C][C]318.888034812654[/C][C]-26.8880348126536[/C][/ROW]
[ROW][C]82[/C][C]304[/C][C]303.698948868973[/C][C]0.301051131026895[/C][/ROW]
[ROW][C]83[/C][C]186[/C][C]271.141559152895[/C][C]-85.1415591528954[/C][/ROW]
[ROW][C]84[/C][C]14[/C][C]44.2847738030264[/C][C]-30.2847738030264[/C][/ROW]
[ROW][C]85[/C][C]321[/C][C]394.154380970031[/C][C]-73.1543809700309[/C][/ROW]
[ROW][C]86[/C][C]206[/C][C]205.401488926855[/C][C]0.598511073144863[/C][/ROW]
[ROW][C]87[/C][C]160[/C][C]224.440167180769[/C][C]-64.4401671807691[/C][/ROW]
[ROW][C]88[/C][C]217[/C][C]196.973372440241[/C][C]20.0266275597589[/C][/ROW]
[ROW][C]89[/C][C]204[/C][C]199.168378428951[/C][C]4.83162157104906[/C][/ROW]
[ROW][C]90[/C][C]246[/C][C]232.828006227564[/C][C]13.171993772436[/C][/ROW]
[ROW][C]91[/C][C]234[/C][C]184.994750018002[/C][C]49.0052499819984[/C][/ROW]
[ROW][C]92[/C][C]175[/C][C]222.993964373502[/C][C]-47.9939643735022[/C][/ROW]
[ROW][C]93[/C][C]364[/C][C]220.949457765718[/C][C]143.050542234282[/C][/ROW]
[ROW][C]94[/C][C]328[/C][C]265.441529384436[/C][C]62.5584706155636[/C][/ROW]
[ROW][C]95[/C][C]158[/C][C]233.958764015884[/C][C]-75.9587640158837[/C][/ROW]
[ROW][C]96[/C][C]40[/C][C]33.1045866010099[/C][C]6.89541339899006[/C][/ROW]
[ROW][C]97[/C][C]556[/C][C]475.621073859909[/C][C]80.378926140091[/C][/ROW]
[ROW][C]98[/C][C]193[/C][C]289.548752016535[/C][C]-96.548752016535[/C][/ROW]
[ROW][C]99[/C][C]221[/C][C]261.85394943568[/C][C]-40.8539494356801[/C][/ROW]
[ROW][C]100[/C][C]278[/C][C]264.220909510997[/C][C]13.7790904890031[/C][/ROW]
[ROW][C]101[/C][C]230[/C][C]258.14067887282[/C][C]-28.1406788728203[/C][/ROW]
[ROW][C]102[/C][C]253[/C][C]290.836776945694[/C][C]-37.8367769456945[/C][/ROW]
[ROW][C]103[/C][C]240[/C][C]226.925404399576[/C][C]13.0745956004245[/C][/ROW]
[ROW][C]104[/C][C]252[/C][C]230.292957637585[/C][C]21.7070423624148[/C][/ROW]
[ROW][C]105[/C][C]228[/C][C]298.585389472142[/C][C]-70.5853894721419[/C][/ROW]
[ROW][C]106[/C][C]306[/C][C]258.406632661964[/C][C]47.5933673380357[/C][/ROW]
[ROW][C]107[/C][C]206[/C][C]195.850641204376[/C][C]10.1493587956239[/C][/ROW]
[ROW][C]108[/C][C]48[/C][C]35.7250619856696[/C][C]12.2749380143304[/C][/ROW]
[ROW][C]109[/C][C]557[/C][C]529.234327607168[/C][C]27.7656723928322[/C][/ROW]
[ROW][C]110[/C][C]279[/C][C]274.094844936791[/C][C]4.90515506320867[/C][/ROW]
[ROW][C]111[/C][C]399[/C][C]292.552360366641[/C][C]106.447639633359[/C][/ROW]
[ROW][C]112[/C][C]364[/C][C]362.658247221299[/C][C]1.34175277870077[/C][/ROW]
[ROW][C]113[/C][C]306[/C][C]335.294669833344[/C][C]-29.2946698333441[/C][/ROW]
[ROW][C]114[/C][C]471[/C][C]377.570095894321[/C][C]93.4299041056794[/C][/ROW]
[ROW][C]115[/C][C]293[/C][C]344.986214958927[/C][C]-51.9862149589275[/C][/ROW]
[ROW][C]116[/C][C]333[/C][C]329.563590086172[/C][C]3.43640991382802[/C][/ROW]
[ROW][C]117[/C][C]316[/C][C]382.965907087671[/C][C]-66.9659070876714[/C][/ROW]
[ROW][C]118[/C][C]329[/C][C]373.059946972107[/C][C]-44.0599469721066[/C][/ROW]
[ROW][C]119[/C][C]265[/C][C]250.053039817741[/C][C]14.9469601822593[/C][/ROW]
[ROW][C]120[/C][C]61[/C][C]48.3503770927282[/C][C]12.6496229072718[/C][/ROW]
[ROW][C]121[/C][C]679[/C][C]659.846784405453[/C][C]19.1532155945474[/C][/ROW]
[ROW][C]122[/C][C]428[/C][C]336.24464310332[/C][C]91.7553568966803[/C][/ROW]
[ROW][C]123[/C][C]394[/C][C]414.14823372035[/C][C]-20.1482337203503[/C][/ROW]
[ROW][C]124[/C][C]352[/C][C]422.161388036855[/C][C]-70.1613880368554[/C][/ROW]
[ROW][C]125[/C][C]387[/C][C]361.451030354854[/C][C]25.5489696451457[/C][/ROW]
[ROW][C]126[/C][C]590[/C][C]459.517675794322[/C][C]130.482324205678[/C][/ROW]
[ROW][C]127[/C][C]177[/C][C]387.916111041518[/C][C]-210.916111041518[/C][/ROW]
[ROW][C]128[/C][C]199[/C][C]335.843867529765[/C][C]-136.843867529765[/C][/ROW]
[ROW][C]129[/C][C]203[/C][C]324.46470148259[/C][C]-121.46470148259[/C][/ROW]
[ROW][C]130[/C][C]255[/C][C]300.061606221381[/C][C]-45.061606221381[/C][/ROW]
[ROW][C]131[/C][C]261[/C][C]207.893485269258[/C][C]53.1065147307417[/C][/ROW]
[ROW][C]132[/C][C]115[/C][C]44.4286658468945[/C][C]70.5713341531055[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235072&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235072&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
13232209.73211456266222.2678854373376
14143135.4944437068367.50555629316372
15161155.2493363404185.75066365958156
16159152.4180601498686.5819398501321
17243237.4029745813495.5970254186505
18192192.755342615733-0.755342615732729
19157160.776428609989-3.7764286099893
20143183.103304403764-40.1033044037639
21221169.03652016860851.9634798313924
22227207.23167600470119.7683239952986
23132193.268207677382-61.2682076773816
244150.0469734306496-9.04697343064956
25273237.93154494767135.0684550523292
26182153.71818353599828.2818164640016
27188182.0194594621245.98054053787632
28162178.413648366913-16.4136483669134
29140264.835051601104-124.835051601104
30186181.025164297484.97483570251987
31178151.8725472016126.1274527983904
32236174.57552037698161.424479623019
33202215.735873300084-13.7358733000843
34184226.716513456118-42.716513456118
35119173.866345174044-54.8663451740444
361646.8705239997758-30.8705239997758
37340203.167195430427136.832804569573
38151153.078848320141-2.07884832014122
39240165.519188126874.4808118731999
40235177.78689495627957.2131050437214
41174266.316487975649-92.3164879756494
42309219.10775753027989.8922424697211
43174211.370308402356-37.3703084023564
44207224.868087171368-17.8680871713677
45209223.979839056123-14.9798390561232
46171227.569810263817-56.5698102638171
47117164.777805972115-47.7778059721149
481039.4038408186805-29.4038408186805
49339230.15261454184108.84738545816
50139145.346213872439-6.34621387243851
51186170.51147553803715.4885244619634
52155161.858195928292-6.85819592829188
53153185.900616418027-32.9006164180267
54222193.41129053566128.5887094643393
55102153.172878214186-51.1728782141862
56107159.006557706595-52.0065577065951
57188146.98155828894241.0184417110579
58162158.5289904515693.47100954843077
59185124.07882648064960.921173519351
602431.4842020301455-7.48420203014551
61394312.62047714106881.3795228589324
62209167.8072170204441.1927829795595
63248220.93539061503627.0646093849643
64254204.90817948977249.0918205102282
65202246.875884640891-44.8758846408909
66258275.808131483425-17.8081314834252
67215180.56810978213634.431890217864
68309221.23152332815887.7684766718416
69240294.039594395914-54.0395943959143
70258259.565194486391-1.56519448639136
71276219.01480899169556.9851910083048
724844.46143728548113.53856271451887
73455545.849383812462-90.849383812462
74345255.31532502791289.6846749720884
75311337.010306589526-26.0103065895262
76346299.91379257105846.0862074289419
77310319.438166127967-9.43816612796718
78297385.303629750926-88.3036297509265
79300252.19773778557547.8022622144246
80274320.031429516036-46.031429516036
81292318.888034812654-26.8880348126536
82304303.6989488689730.301051131026895
83186271.141559152895-85.1415591528954
841444.2847738030264-30.2847738030264
85321394.154380970031-73.1543809700309
86206205.4014889268550.598511073144863
87160224.440167180769-64.4401671807691
88217196.97337244024120.0266275597589
89204199.1683784289514.83162157104906
90246232.82800622756413.171993772436
91234184.99475001800249.0052499819984
92175222.993964373502-47.9939643735022
93364220.949457765718143.050542234282
94328265.44152938443662.5584706155636
95158233.958764015884-75.9587640158837
964033.10458660100996.89541339899006
97556475.62107385990980.378926140091
98193289.548752016535-96.548752016535
99221261.85394943568-40.8539494356801
100278264.22090951099713.7790904890031
101230258.14067887282-28.1406788728203
102253290.836776945694-37.8367769456945
103240226.92540439957613.0745956004245
104252230.29295763758521.7070423624148
105228298.585389472142-70.5853894721419
106306258.40663266196447.5933673380357
107206195.85064120437610.1493587956239
1084835.725061985669612.2749380143304
109557529.23432760716827.7656723928322
110279274.0948449367914.90515506320867
111399292.552360366641106.447639633359
112364362.6582472212991.34175277870077
113306335.294669833344-29.2946698333441
114471377.57009589432193.4299041056794
115293344.986214958927-51.9862149589275
116333329.5635900861723.43640991382802
117316382.965907087671-66.9659070876714
118329373.059946972107-44.0599469721066
119265250.05303981774114.9469601822593
1206148.350377092728212.6496229072718
121679659.84678440545319.1532155945474
122428336.2446431033291.7553568966803
123394414.14823372035-20.1482337203503
124352422.161388036855-70.1613880368554
125387361.45103035485425.5489696451457
126590459.517675794322130.482324205678
127177387.916111041518-210.916111041518
128199335.843867529765-136.843867529765
129203324.46470148259-121.46470148259
130255300.061606221381-45.061606221381
131261207.89348526925853.1065147307417
13211544.428665846894570.5713341531055







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
133798.764934198416736.443269931118861.086598465714
134423.599640328391358.470806351568488.728474305214
135449.006294923948373.430930102772524.581659745124
136450.855805794138367.23458229841534.477029289866
137430.754629999797342.115602716892519.393657282701
138558.753726183062446.287551520334671.21990084579
139346.786520585885258.925432473894434.647608697875
140379.682964868239279.855464269969479.510465466509
141424.113269898558310.132690828445538.093848968671
142473.055628745454343.840526408369602.27073108254
143375.14755567885262.585480694622487.709630663078
14487.432122371762863.3950033484697111.469241395056

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
133 & 798.764934198416 & 736.443269931118 & 861.086598465714 \tabularnewline
134 & 423.599640328391 & 358.470806351568 & 488.728474305214 \tabularnewline
135 & 449.006294923948 & 373.430930102772 & 524.581659745124 \tabularnewline
136 & 450.855805794138 & 367.23458229841 & 534.477029289866 \tabularnewline
137 & 430.754629999797 & 342.115602716892 & 519.393657282701 \tabularnewline
138 & 558.753726183062 & 446.287551520334 & 671.21990084579 \tabularnewline
139 & 346.786520585885 & 258.925432473894 & 434.647608697875 \tabularnewline
140 & 379.682964868239 & 279.855464269969 & 479.510465466509 \tabularnewline
141 & 424.113269898558 & 310.132690828445 & 538.093848968671 \tabularnewline
142 & 473.055628745454 & 343.840526408369 & 602.27073108254 \tabularnewline
143 & 375.14755567885 & 262.585480694622 & 487.709630663078 \tabularnewline
144 & 87.4321223717628 & 63.3950033484697 & 111.469241395056 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235072&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]798.764934198416[/C][C]736.443269931118[/C][C]861.086598465714[/C][/ROW]
[ROW][C]134[/C][C]423.599640328391[/C][C]358.470806351568[/C][C]488.728474305214[/C][/ROW]
[ROW][C]135[/C][C]449.006294923948[/C][C]373.430930102772[/C][C]524.581659745124[/C][/ROW]
[ROW][C]136[/C][C]450.855805794138[/C][C]367.23458229841[/C][C]534.477029289866[/C][/ROW]
[ROW][C]137[/C][C]430.754629999797[/C][C]342.115602716892[/C][C]519.393657282701[/C][/ROW]
[ROW][C]138[/C][C]558.753726183062[/C][C]446.287551520334[/C][C]671.21990084579[/C][/ROW]
[ROW][C]139[/C][C]346.786520585885[/C][C]258.925432473894[/C][C]434.647608697875[/C][/ROW]
[ROW][C]140[/C][C]379.682964868239[/C][C]279.855464269969[/C][C]479.510465466509[/C][/ROW]
[ROW][C]141[/C][C]424.113269898558[/C][C]310.132690828445[/C][C]538.093848968671[/C][/ROW]
[ROW][C]142[/C][C]473.055628745454[/C][C]343.840526408369[/C][C]602.27073108254[/C][/ROW]
[ROW][C]143[/C][C]375.14755567885[/C][C]262.585480694622[/C][C]487.709630663078[/C][/ROW]
[ROW][C]144[/C][C]87.4321223717628[/C][C]63.3950033484697[/C][C]111.469241395056[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235072&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235072&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
133798.764934198416736.443269931118861.086598465714
134423.599640328391358.470806351568488.728474305214
135449.006294923948373.430930102772524.581659745124
136450.855805794138367.23458229841534.477029289866
137430.754629999797342.115602716892519.393657282701
138558.753726183062446.287551520334671.21990084579
139346.786520585885258.925432473894434.647608697875
140379.682964868239279.855464269969479.510465466509
141424.113269898558310.132690828445538.093848968671
142473.055628745454343.840526408369602.27073108254
143375.14755567885262.585480694622487.709630663078
14487.432122371762863.3950033484697111.469241395056



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')