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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 12 Jan 2014 06:59:49 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Jan/12/t1389528238k7o7ab222no5r99.htm/, Retrieved Mon, 27 May 2024 01:44:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232987, Retrieved Mon, 27 May 2024 01:44:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact133
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Wekelijkse verkoc...] [2014-01-12 11:59:49] [74a92a9d3a2c9c03f2186ea574174bd1] [Current]
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Dataseries X:
221102
220892
225537
219334
216126
224573
213991
221865
215382
213962
217009
318110
219662
212650
209307
210541
210609
208910
207541
207699
205005
205747
203644
229937
214446
210194
206535
216524
198243
208274
207493
215525
207562
213355
209048
220497
214563
211571
216385
211496
209683
206304
213925
204829
205729
200296
207960
207729
208327
207794
213700
213136
210354
202205
220425
210038
205201
197441
200021
203165
201699
201003
232308
211412
209661
213587
193611
192543
196040
191407
189726
191272
187924
198213
199352
199289
195475
198045
197615
189015
189668
189120
194168
192304
185913
197599
186085
190566
187054
193222
189856
190608
190588
186773
183510
180106
180150
178412
182353
203805
186054
184290
187483
187111
189561
184439
182985
183828
184036
183214
183464
173718
180210
171252
172705
174006
172043
169445
169449
177073
170799
171648
172220
165795
167466
165528
162851
165864
162094
162385
164293
165983
159680
161739
159302
167795
164242
159743
160887
163844
161172
159330
155570
156749
155012
163419
153630
154535
151543
152955
150166
151416
150332
152196
153422
147435




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 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 & 6 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232987&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]6 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=232987&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232987&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 time6 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta1
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 1 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232987&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]1[/C][/ROW]
[ROW][C]beta[/C][C]1[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232987&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232987&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
alpha1
beta1
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
32255372206824855
4219334230182-10848
52161262131312995
622457321291811655
7213991233020-19029
822186520340918456
9215382229739-14357
102139622088995063
112170092125424467
1231811022005698054
13219662419211-199549
1421265012121491436
152093072056383669
162105412059644577
17210609211775-1166
18208910210677-1767
19207541207211330
202076992061721527
21205005207857-2852
222057472023113436
23203644206489-2845
2422993720154128396
25214446256230-41784
2621019419895511239
27206535205942593
2821652420287613648
29198243226513-28270
3020827417996228312
31207493218305-10812
322155252067128813
33207562223557-15995
3421335519959913756
35209048219148-10100
3622049720474115756
37214563231946-17383
382115712086292942
392163852085797806
40211496221199-9703
412096832066073076
42206304207870-1566
4321392520292511000
44204829221546-16717
452057291957339996
46200296206629-6333
4720796019486313097
48207729215624-7895
49208327207498829
50207794208925-1131
512137002072616439
52213136219606-6470
53210354212572-2218
54202205207572-5367
5522042519405626369
56210038238645-28607
572052011996515550
58197441200364-2923
5920002118968110340
60203165202601564
61201699206309-4610
62201003200233770
6323230820030732001
64211412263613-52201
6520966119051619145
662135872079105677
67193611217513-23902
6819254317363518908
691960401914754565
70191407199537-8130
711897261867742952
721912721880453227
73187924192818-4894
7419821318457613637
75199352208502-9150
76199289200491-1202
77195475199226-3751
781980451916616384
79197615200615-3000
80189015197185-8170
811896681804159253
82189120190321-1201
831941681885725596
84192304199216-6912
85185913190440-4527
8619759917952218077
87186085209285-23200
8819056617457115995
89187054195047-7993
901932221835429680
91189856199390-9534
921906081864904118
93190588191360-772
94186773190568-3795
95183510182958552
96180106180247-141
971801501767023448
98178412180194-1782
991823531766745679
10020380518629417511
101186054225257-39203
10218429016830315987
1031874831825264957
104187111190676-3565
1051895611867392822
106184439192011-7572
1071829851793173668
1081838281815312297
109184036184671-635
110183214184244-1030
1111834641823921072
112173718183714-9996
11318021016397216238
114171252186702-15450
11517270516229410411
116174006174158-152
117172043175307-3264
118169445170080-635
1191694491668472602
1201770731694537620
121170799184697-13898
1221716481645257123
123172220172497-277
124165795172792-6997
1251674661593708096
126165528169137-3609
127162851163590-739
1281658641601745690
129162094168877-6783
1301623851583244061
1311642931626761617
132165983166201-218
133159680167673-7993
1341617391533778362
135159302163798-4496
13616779515686510930
137164242176288-12046
138159743160689-946
1391608871552445643
1401638441620311813
141161172166801-5629
142159330158500830
143155570157488-1918
1441567491518104939
145155012157928-2916
14616341915327510144
147153630171826-18196
14815453514384110694
149151543155440-3897
1501529551485514404
151150166154367-4201
1521514161473774039
153150332152666-2334
1541521961492482948
155153422154060-638
156147435154648-7213

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 225537 & 220682 & 4855 \tabularnewline
4 & 219334 & 230182 & -10848 \tabularnewline
5 & 216126 & 213131 & 2995 \tabularnewline
6 & 224573 & 212918 & 11655 \tabularnewline
7 & 213991 & 233020 & -19029 \tabularnewline
8 & 221865 & 203409 & 18456 \tabularnewline
9 & 215382 & 229739 & -14357 \tabularnewline
10 & 213962 & 208899 & 5063 \tabularnewline
11 & 217009 & 212542 & 4467 \tabularnewline
12 & 318110 & 220056 & 98054 \tabularnewline
13 & 219662 & 419211 & -199549 \tabularnewline
14 & 212650 & 121214 & 91436 \tabularnewline
15 & 209307 & 205638 & 3669 \tabularnewline
16 & 210541 & 205964 & 4577 \tabularnewline
17 & 210609 & 211775 & -1166 \tabularnewline
18 & 208910 & 210677 & -1767 \tabularnewline
19 & 207541 & 207211 & 330 \tabularnewline
20 & 207699 & 206172 & 1527 \tabularnewline
21 & 205005 & 207857 & -2852 \tabularnewline
22 & 205747 & 202311 & 3436 \tabularnewline
23 & 203644 & 206489 & -2845 \tabularnewline
24 & 229937 & 201541 & 28396 \tabularnewline
25 & 214446 & 256230 & -41784 \tabularnewline
26 & 210194 & 198955 & 11239 \tabularnewline
27 & 206535 & 205942 & 593 \tabularnewline
28 & 216524 & 202876 & 13648 \tabularnewline
29 & 198243 & 226513 & -28270 \tabularnewline
30 & 208274 & 179962 & 28312 \tabularnewline
31 & 207493 & 218305 & -10812 \tabularnewline
32 & 215525 & 206712 & 8813 \tabularnewline
33 & 207562 & 223557 & -15995 \tabularnewline
34 & 213355 & 199599 & 13756 \tabularnewline
35 & 209048 & 219148 & -10100 \tabularnewline
36 & 220497 & 204741 & 15756 \tabularnewline
37 & 214563 & 231946 & -17383 \tabularnewline
38 & 211571 & 208629 & 2942 \tabularnewline
39 & 216385 & 208579 & 7806 \tabularnewline
40 & 211496 & 221199 & -9703 \tabularnewline
41 & 209683 & 206607 & 3076 \tabularnewline
42 & 206304 & 207870 & -1566 \tabularnewline
43 & 213925 & 202925 & 11000 \tabularnewline
44 & 204829 & 221546 & -16717 \tabularnewline
45 & 205729 & 195733 & 9996 \tabularnewline
46 & 200296 & 206629 & -6333 \tabularnewline
47 & 207960 & 194863 & 13097 \tabularnewline
48 & 207729 & 215624 & -7895 \tabularnewline
49 & 208327 & 207498 & 829 \tabularnewline
50 & 207794 & 208925 & -1131 \tabularnewline
51 & 213700 & 207261 & 6439 \tabularnewline
52 & 213136 & 219606 & -6470 \tabularnewline
53 & 210354 & 212572 & -2218 \tabularnewline
54 & 202205 & 207572 & -5367 \tabularnewline
55 & 220425 & 194056 & 26369 \tabularnewline
56 & 210038 & 238645 & -28607 \tabularnewline
57 & 205201 & 199651 & 5550 \tabularnewline
58 & 197441 & 200364 & -2923 \tabularnewline
59 & 200021 & 189681 & 10340 \tabularnewline
60 & 203165 & 202601 & 564 \tabularnewline
61 & 201699 & 206309 & -4610 \tabularnewline
62 & 201003 & 200233 & 770 \tabularnewline
63 & 232308 & 200307 & 32001 \tabularnewline
64 & 211412 & 263613 & -52201 \tabularnewline
65 & 209661 & 190516 & 19145 \tabularnewline
66 & 213587 & 207910 & 5677 \tabularnewline
67 & 193611 & 217513 & -23902 \tabularnewline
68 & 192543 & 173635 & 18908 \tabularnewline
69 & 196040 & 191475 & 4565 \tabularnewline
70 & 191407 & 199537 & -8130 \tabularnewline
71 & 189726 & 186774 & 2952 \tabularnewline
72 & 191272 & 188045 & 3227 \tabularnewline
73 & 187924 & 192818 & -4894 \tabularnewline
74 & 198213 & 184576 & 13637 \tabularnewline
75 & 199352 & 208502 & -9150 \tabularnewline
76 & 199289 & 200491 & -1202 \tabularnewline
77 & 195475 & 199226 & -3751 \tabularnewline
78 & 198045 & 191661 & 6384 \tabularnewline
79 & 197615 & 200615 & -3000 \tabularnewline
80 & 189015 & 197185 & -8170 \tabularnewline
81 & 189668 & 180415 & 9253 \tabularnewline
82 & 189120 & 190321 & -1201 \tabularnewline
83 & 194168 & 188572 & 5596 \tabularnewline
84 & 192304 & 199216 & -6912 \tabularnewline
85 & 185913 & 190440 & -4527 \tabularnewline
86 & 197599 & 179522 & 18077 \tabularnewline
87 & 186085 & 209285 & -23200 \tabularnewline
88 & 190566 & 174571 & 15995 \tabularnewline
89 & 187054 & 195047 & -7993 \tabularnewline
90 & 193222 & 183542 & 9680 \tabularnewline
91 & 189856 & 199390 & -9534 \tabularnewline
92 & 190608 & 186490 & 4118 \tabularnewline
93 & 190588 & 191360 & -772 \tabularnewline
94 & 186773 & 190568 & -3795 \tabularnewline
95 & 183510 & 182958 & 552 \tabularnewline
96 & 180106 & 180247 & -141 \tabularnewline
97 & 180150 & 176702 & 3448 \tabularnewline
98 & 178412 & 180194 & -1782 \tabularnewline
99 & 182353 & 176674 & 5679 \tabularnewline
100 & 203805 & 186294 & 17511 \tabularnewline
101 & 186054 & 225257 & -39203 \tabularnewline
102 & 184290 & 168303 & 15987 \tabularnewline
103 & 187483 & 182526 & 4957 \tabularnewline
104 & 187111 & 190676 & -3565 \tabularnewline
105 & 189561 & 186739 & 2822 \tabularnewline
106 & 184439 & 192011 & -7572 \tabularnewline
107 & 182985 & 179317 & 3668 \tabularnewline
108 & 183828 & 181531 & 2297 \tabularnewline
109 & 184036 & 184671 & -635 \tabularnewline
110 & 183214 & 184244 & -1030 \tabularnewline
111 & 183464 & 182392 & 1072 \tabularnewline
112 & 173718 & 183714 & -9996 \tabularnewline
113 & 180210 & 163972 & 16238 \tabularnewline
114 & 171252 & 186702 & -15450 \tabularnewline
115 & 172705 & 162294 & 10411 \tabularnewline
116 & 174006 & 174158 & -152 \tabularnewline
117 & 172043 & 175307 & -3264 \tabularnewline
118 & 169445 & 170080 & -635 \tabularnewline
119 & 169449 & 166847 & 2602 \tabularnewline
120 & 177073 & 169453 & 7620 \tabularnewline
121 & 170799 & 184697 & -13898 \tabularnewline
122 & 171648 & 164525 & 7123 \tabularnewline
123 & 172220 & 172497 & -277 \tabularnewline
124 & 165795 & 172792 & -6997 \tabularnewline
125 & 167466 & 159370 & 8096 \tabularnewline
126 & 165528 & 169137 & -3609 \tabularnewline
127 & 162851 & 163590 & -739 \tabularnewline
128 & 165864 & 160174 & 5690 \tabularnewline
129 & 162094 & 168877 & -6783 \tabularnewline
130 & 162385 & 158324 & 4061 \tabularnewline
131 & 164293 & 162676 & 1617 \tabularnewline
132 & 165983 & 166201 & -218 \tabularnewline
133 & 159680 & 167673 & -7993 \tabularnewline
134 & 161739 & 153377 & 8362 \tabularnewline
135 & 159302 & 163798 & -4496 \tabularnewline
136 & 167795 & 156865 & 10930 \tabularnewline
137 & 164242 & 176288 & -12046 \tabularnewline
138 & 159743 & 160689 & -946 \tabularnewline
139 & 160887 & 155244 & 5643 \tabularnewline
140 & 163844 & 162031 & 1813 \tabularnewline
141 & 161172 & 166801 & -5629 \tabularnewline
142 & 159330 & 158500 & 830 \tabularnewline
143 & 155570 & 157488 & -1918 \tabularnewline
144 & 156749 & 151810 & 4939 \tabularnewline
145 & 155012 & 157928 & -2916 \tabularnewline
146 & 163419 & 153275 & 10144 \tabularnewline
147 & 153630 & 171826 & -18196 \tabularnewline
148 & 154535 & 143841 & 10694 \tabularnewline
149 & 151543 & 155440 & -3897 \tabularnewline
150 & 152955 & 148551 & 4404 \tabularnewline
151 & 150166 & 154367 & -4201 \tabularnewline
152 & 151416 & 147377 & 4039 \tabularnewline
153 & 150332 & 152666 & -2334 \tabularnewline
154 & 152196 & 149248 & 2948 \tabularnewline
155 & 153422 & 154060 & -638 \tabularnewline
156 & 147435 & 154648 & -7213 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232987&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]225537[/C][C]220682[/C][C]4855[/C][/ROW]
[ROW][C]4[/C][C]219334[/C][C]230182[/C][C]-10848[/C][/ROW]
[ROW][C]5[/C][C]216126[/C][C]213131[/C][C]2995[/C][/ROW]
[ROW][C]6[/C][C]224573[/C][C]212918[/C][C]11655[/C][/ROW]
[ROW][C]7[/C][C]213991[/C][C]233020[/C][C]-19029[/C][/ROW]
[ROW][C]8[/C][C]221865[/C][C]203409[/C][C]18456[/C][/ROW]
[ROW][C]9[/C][C]215382[/C][C]229739[/C][C]-14357[/C][/ROW]
[ROW][C]10[/C][C]213962[/C][C]208899[/C][C]5063[/C][/ROW]
[ROW][C]11[/C][C]217009[/C][C]212542[/C][C]4467[/C][/ROW]
[ROW][C]12[/C][C]318110[/C][C]220056[/C][C]98054[/C][/ROW]
[ROW][C]13[/C][C]219662[/C][C]419211[/C][C]-199549[/C][/ROW]
[ROW][C]14[/C][C]212650[/C][C]121214[/C][C]91436[/C][/ROW]
[ROW][C]15[/C][C]209307[/C][C]205638[/C][C]3669[/C][/ROW]
[ROW][C]16[/C][C]210541[/C][C]205964[/C][C]4577[/C][/ROW]
[ROW][C]17[/C][C]210609[/C][C]211775[/C][C]-1166[/C][/ROW]
[ROW][C]18[/C][C]208910[/C][C]210677[/C][C]-1767[/C][/ROW]
[ROW][C]19[/C][C]207541[/C][C]207211[/C][C]330[/C][/ROW]
[ROW][C]20[/C][C]207699[/C][C]206172[/C][C]1527[/C][/ROW]
[ROW][C]21[/C][C]205005[/C][C]207857[/C][C]-2852[/C][/ROW]
[ROW][C]22[/C][C]205747[/C][C]202311[/C][C]3436[/C][/ROW]
[ROW][C]23[/C][C]203644[/C][C]206489[/C][C]-2845[/C][/ROW]
[ROW][C]24[/C][C]229937[/C][C]201541[/C][C]28396[/C][/ROW]
[ROW][C]25[/C][C]214446[/C][C]256230[/C][C]-41784[/C][/ROW]
[ROW][C]26[/C][C]210194[/C][C]198955[/C][C]11239[/C][/ROW]
[ROW][C]27[/C][C]206535[/C][C]205942[/C][C]593[/C][/ROW]
[ROW][C]28[/C][C]216524[/C][C]202876[/C][C]13648[/C][/ROW]
[ROW][C]29[/C][C]198243[/C][C]226513[/C][C]-28270[/C][/ROW]
[ROW][C]30[/C][C]208274[/C][C]179962[/C][C]28312[/C][/ROW]
[ROW][C]31[/C][C]207493[/C][C]218305[/C][C]-10812[/C][/ROW]
[ROW][C]32[/C][C]215525[/C][C]206712[/C][C]8813[/C][/ROW]
[ROW][C]33[/C][C]207562[/C][C]223557[/C][C]-15995[/C][/ROW]
[ROW][C]34[/C][C]213355[/C][C]199599[/C][C]13756[/C][/ROW]
[ROW][C]35[/C][C]209048[/C][C]219148[/C][C]-10100[/C][/ROW]
[ROW][C]36[/C][C]220497[/C][C]204741[/C][C]15756[/C][/ROW]
[ROW][C]37[/C][C]214563[/C][C]231946[/C][C]-17383[/C][/ROW]
[ROW][C]38[/C][C]211571[/C][C]208629[/C][C]2942[/C][/ROW]
[ROW][C]39[/C][C]216385[/C][C]208579[/C][C]7806[/C][/ROW]
[ROW][C]40[/C][C]211496[/C][C]221199[/C][C]-9703[/C][/ROW]
[ROW][C]41[/C][C]209683[/C][C]206607[/C][C]3076[/C][/ROW]
[ROW][C]42[/C][C]206304[/C][C]207870[/C][C]-1566[/C][/ROW]
[ROW][C]43[/C][C]213925[/C][C]202925[/C][C]11000[/C][/ROW]
[ROW][C]44[/C][C]204829[/C][C]221546[/C][C]-16717[/C][/ROW]
[ROW][C]45[/C][C]205729[/C][C]195733[/C][C]9996[/C][/ROW]
[ROW][C]46[/C][C]200296[/C][C]206629[/C][C]-6333[/C][/ROW]
[ROW][C]47[/C][C]207960[/C][C]194863[/C][C]13097[/C][/ROW]
[ROW][C]48[/C][C]207729[/C][C]215624[/C][C]-7895[/C][/ROW]
[ROW][C]49[/C][C]208327[/C][C]207498[/C][C]829[/C][/ROW]
[ROW][C]50[/C][C]207794[/C][C]208925[/C][C]-1131[/C][/ROW]
[ROW][C]51[/C][C]213700[/C][C]207261[/C][C]6439[/C][/ROW]
[ROW][C]52[/C][C]213136[/C][C]219606[/C][C]-6470[/C][/ROW]
[ROW][C]53[/C][C]210354[/C][C]212572[/C][C]-2218[/C][/ROW]
[ROW][C]54[/C][C]202205[/C][C]207572[/C][C]-5367[/C][/ROW]
[ROW][C]55[/C][C]220425[/C][C]194056[/C][C]26369[/C][/ROW]
[ROW][C]56[/C][C]210038[/C][C]238645[/C][C]-28607[/C][/ROW]
[ROW][C]57[/C][C]205201[/C][C]199651[/C][C]5550[/C][/ROW]
[ROW][C]58[/C][C]197441[/C][C]200364[/C][C]-2923[/C][/ROW]
[ROW][C]59[/C][C]200021[/C][C]189681[/C][C]10340[/C][/ROW]
[ROW][C]60[/C][C]203165[/C][C]202601[/C][C]564[/C][/ROW]
[ROW][C]61[/C][C]201699[/C][C]206309[/C][C]-4610[/C][/ROW]
[ROW][C]62[/C][C]201003[/C][C]200233[/C][C]770[/C][/ROW]
[ROW][C]63[/C][C]232308[/C][C]200307[/C][C]32001[/C][/ROW]
[ROW][C]64[/C][C]211412[/C][C]263613[/C][C]-52201[/C][/ROW]
[ROW][C]65[/C][C]209661[/C][C]190516[/C][C]19145[/C][/ROW]
[ROW][C]66[/C][C]213587[/C][C]207910[/C][C]5677[/C][/ROW]
[ROW][C]67[/C][C]193611[/C][C]217513[/C][C]-23902[/C][/ROW]
[ROW][C]68[/C][C]192543[/C][C]173635[/C][C]18908[/C][/ROW]
[ROW][C]69[/C][C]196040[/C][C]191475[/C][C]4565[/C][/ROW]
[ROW][C]70[/C][C]191407[/C][C]199537[/C][C]-8130[/C][/ROW]
[ROW][C]71[/C][C]189726[/C][C]186774[/C][C]2952[/C][/ROW]
[ROW][C]72[/C][C]191272[/C][C]188045[/C][C]3227[/C][/ROW]
[ROW][C]73[/C][C]187924[/C][C]192818[/C][C]-4894[/C][/ROW]
[ROW][C]74[/C][C]198213[/C][C]184576[/C][C]13637[/C][/ROW]
[ROW][C]75[/C][C]199352[/C][C]208502[/C][C]-9150[/C][/ROW]
[ROW][C]76[/C][C]199289[/C][C]200491[/C][C]-1202[/C][/ROW]
[ROW][C]77[/C][C]195475[/C][C]199226[/C][C]-3751[/C][/ROW]
[ROW][C]78[/C][C]198045[/C][C]191661[/C][C]6384[/C][/ROW]
[ROW][C]79[/C][C]197615[/C][C]200615[/C][C]-3000[/C][/ROW]
[ROW][C]80[/C][C]189015[/C][C]197185[/C][C]-8170[/C][/ROW]
[ROW][C]81[/C][C]189668[/C][C]180415[/C][C]9253[/C][/ROW]
[ROW][C]82[/C][C]189120[/C][C]190321[/C][C]-1201[/C][/ROW]
[ROW][C]83[/C][C]194168[/C][C]188572[/C][C]5596[/C][/ROW]
[ROW][C]84[/C][C]192304[/C][C]199216[/C][C]-6912[/C][/ROW]
[ROW][C]85[/C][C]185913[/C][C]190440[/C][C]-4527[/C][/ROW]
[ROW][C]86[/C][C]197599[/C][C]179522[/C][C]18077[/C][/ROW]
[ROW][C]87[/C][C]186085[/C][C]209285[/C][C]-23200[/C][/ROW]
[ROW][C]88[/C][C]190566[/C][C]174571[/C][C]15995[/C][/ROW]
[ROW][C]89[/C][C]187054[/C][C]195047[/C][C]-7993[/C][/ROW]
[ROW][C]90[/C][C]193222[/C][C]183542[/C][C]9680[/C][/ROW]
[ROW][C]91[/C][C]189856[/C][C]199390[/C][C]-9534[/C][/ROW]
[ROW][C]92[/C][C]190608[/C][C]186490[/C][C]4118[/C][/ROW]
[ROW][C]93[/C][C]190588[/C][C]191360[/C][C]-772[/C][/ROW]
[ROW][C]94[/C][C]186773[/C][C]190568[/C][C]-3795[/C][/ROW]
[ROW][C]95[/C][C]183510[/C][C]182958[/C][C]552[/C][/ROW]
[ROW][C]96[/C][C]180106[/C][C]180247[/C][C]-141[/C][/ROW]
[ROW][C]97[/C][C]180150[/C][C]176702[/C][C]3448[/C][/ROW]
[ROW][C]98[/C][C]178412[/C][C]180194[/C][C]-1782[/C][/ROW]
[ROW][C]99[/C][C]182353[/C][C]176674[/C][C]5679[/C][/ROW]
[ROW][C]100[/C][C]203805[/C][C]186294[/C][C]17511[/C][/ROW]
[ROW][C]101[/C][C]186054[/C][C]225257[/C][C]-39203[/C][/ROW]
[ROW][C]102[/C][C]184290[/C][C]168303[/C][C]15987[/C][/ROW]
[ROW][C]103[/C][C]187483[/C][C]182526[/C][C]4957[/C][/ROW]
[ROW][C]104[/C][C]187111[/C][C]190676[/C][C]-3565[/C][/ROW]
[ROW][C]105[/C][C]189561[/C][C]186739[/C][C]2822[/C][/ROW]
[ROW][C]106[/C][C]184439[/C][C]192011[/C][C]-7572[/C][/ROW]
[ROW][C]107[/C][C]182985[/C][C]179317[/C][C]3668[/C][/ROW]
[ROW][C]108[/C][C]183828[/C][C]181531[/C][C]2297[/C][/ROW]
[ROW][C]109[/C][C]184036[/C][C]184671[/C][C]-635[/C][/ROW]
[ROW][C]110[/C][C]183214[/C][C]184244[/C][C]-1030[/C][/ROW]
[ROW][C]111[/C][C]183464[/C][C]182392[/C][C]1072[/C][/ROW]
[ROW][C]112[/C][C]173718[/C][C]183714[/C][C]-9996[/C][/ROW]
[ROW][C]113[/C][C]180210[/C][C]163972[/C][C]16238[/C][/ROW]
[ROW][C]114[/C][C]171252[/C][C]186702[/C][C]-15450[/C][/ROW]
[ROW][C]115[/C][C]172705[/C][C]162294[/C][C]10411[/C][/ROW]
[ROW][C]116[/C][C]174006[/C][C]174158[/C][C]-152[/C][/ROW]
[ROW][C]117[/C][C]172043[/C][C]175307[/C][C]-3264[/C][/ROW]
[ROW][C]118[/C][C]169445[/C][C]170080[/C][C]-635[/C][/ROW]
[ROW][C]119[/C][C]169449[/C][C]166847[/C][C]2602[/C][/ROW]
[ROW][C]120[/C][C]177073[/C][C]169453[/C][C]7620[/C][/ROW]
[ROW][C]121[/C][C]170799[/C][C]184697[/C][C]-13898[/C][/ROW]
[ROW][C]122[/C][C]171648[/C][C]164525[/C][C]7123[/C][/ROW]
[ROW][C]123[/C][C]172220[/C][C]172497[/C][C]-277[/C][/ROW]
[ROW][C]124[/C][C]165795[/C][C]172792[/C][C]-6997[/C][/ROW]
[ROW][C]125[/C][C]167466[/C][C]159370[/C][C]8096[/C][/ROW]
[ROW][C]126[/C][C]165528[/C][C]169137[/C][C]-3609[/C][/ROW]
[ROW][C]127[/C][C]162851[/C][C]163590[/C][C]-739[/C][/ROW]
[ROW][C]128[/C][C]165864[/C][C]160174[/C][C]5690[/C][/ROW]
[ROW][C]129[/C][C]162094[/C][C]168877[/C][C]-6783[/C][/ROW]
[ROW][C]130[/C][C]162385[/C][C]158324[/C][C]4061[/C][/ROW]
[ROW][C]131[/C][C]164293[/C][C]162676[/C][C]1617[/C][/ROW]
[ROW][C]132[/C][C]165983[/C][C]166201[/C][C]-218[/C][/ROW]
[ROW][C]133[/C][C]159680[/C][C]167673[/C][C]-7993[/C][/ROW]
[ROW][C]134[/C][C]161739[/C][C]153377[/C][C]8362[/C][/ROW]
[ROW][C]135[/C][C]159302[/C][C]163798[/C][C]-4496[/C][/ROW]
[ROW][C]136[/C][C]167795[/C][C]156865[/C][C]10930[/C][/ROW]
[ROW][C]137[/C][C]164242[/C][C]176288[/C][C]-12046[/C][/ROW]
[ROW][C]138[/C][C]159743[/C][C]160689[/C][C]-946[/C][/ROW]
[ROW][C]139[/C][C]160887[/C][C]155244[/C][C]5643[/C][/ROW]
[ROW][C]140[/C][C]163844[/C][C]162031[/C][C]1813[/C][/ROW]
[ROW][C]141[/C][C]161172[/C][C]166801[/C][C]-5629[/C][/ROW]
[ROW][C]142[/C][C]159330[/C][C]158500[/C][C]830[/C][/ROW]
[ROW][C]143[/C][C]155570[/C][C]157488[/C][C]-1918[/C][/ROW]
[ROW][C]144[/C][C]156749[/C][C]151810[/C][C]4939[/C][/ROW]
[ROW][C]145[/C][C]155012[/C][C]157928[/C][C]-2916[/C][/ROW]
[ROW][C]146[/C][C]163419[/C][C]153275[/C][C]10144[/C][/ROW]
[ROW][C]147[/C][C]153630[/C][C]171826[/C][C]-18196[/C][/ROW]
[ROW][C]148[/C][C]154535[/C][C]143841[/C][C]10694[/C][/ROW]
[ROW][C]149[/C][C]151543[/C][C]155440[/C][C]-3897[/C][/ROW]
[ROW][C]150[/C][C]152955[/C][C]148551[/C][C]4404[/C][/ROW]
[ROW][C]151[/C][C]150166[/C][C]154367[/C][C]-4201[/C][/ROW]
[ROW][C]152[/C][C]151416[/C][C]147377[/C][C]4039[/C][/ROW]
[ROW][C]153[/C][C]150332[/C][C]152666[/C][C]-2334[/C][/ROW]
[ROW][C]154[/C][C]152196[/C][C]149248[/C][C]2948[/C][/ROW]
[ROW][C]155[/C][C]153422[/C][C]154060[/C][C]-638[/C][/ROW]
[ROW][C]156[/C][C]147435[/C][C]154648[/C][C]-7213[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232987&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232987&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
32255372206824855
4219334230182-10848
52161262131312995
622457321291811655
7213991233020-19029
822186520340918456
9215382229739-14357
102139622088995063
112170092125424467
1231811022005698054
13219662419211-199549
1421265012121491436
152093072056383669
162105412059644577
17210609211775-1166
18208910210677-1767
19207541207211330
202076992061721527
21205005207857-2852
222057472023113436
23203644206489-2845
2422993720154128396
25214446256230-41784
2621019419895511239
27206535205942593
2821652420287613648
29198243226513-28270
3020827417996228312
31207493218305-10812
322155252067128813
33207562223557-15995
3421335519959913756
35209048219148-10100
3622049720474115756
37214563231946-17383
382115712086292942
392163852085797806
40211496221199-9703
412096832066073076
42206304207870-1566
4321392520292511000
44204829221546-16717
452057291957339996
46200296206629-6333
4720796019486313097
48207729215624-7895
49208327207498829
50207794208925-1131
512137002072616439
52213136219606-6470
53210354212572-2218
54202205207572-5367
5522042519405626369
56210038238645-28607
572052011996515550
58197441200364-2923
5920002118968110340
60203165202601564
61201699206309-4610
62201003200233770
6323230820030732001
64211412263613-52201
6520966119051619145
662135872079105677
67193611217513-23902
6819254317363518908
691960401914754565
70191407199537-8130
711897261867742952
721912721880453227
73187924192818-4894
7419821318457613637
75199352208502-9150
76199289200491-1202
77195475199226-3751
781980451916616384
79197615200615-3000
80189015197185-8170
811896681804159253
82189120190321-1201
831941681885725596
84192304199216-6912
85185913190440-4527
8619759917952218077
87186085209285-23200
8819056617457115995
89187054195047-7993
901932221835429680
91189856199390-9534
921906081864904118
93190588191360-772
94186773190568-3795
95183510182958552
96180106180247-141
971801501767023448
98178412180194-1782
991823531766745679
10020380518629417511
101186054225257-39203
10218429016830315987
1031874831825264957
104187111190676-3565
1051895611867392822
106184439192011-7572
1071829851793173668
1081838281815312297
109184036184671-635
110183214184244-1030
1111834641823921072
112173718183714-9996
11318021016397216238
114171252186702-15450
11517270516229410411
116174006174158-152
117172043175307-3264
118169445170080-635
1191694491668472602
1201770731694537620
121170799184697-13898
1221716481645257123
123172220172497-277
124165795172792-6997
1251674661593708096
126165528169137-3609
127162851163590-739
1281658641601745690
129162094168877-6783
1301623851583244061
1311642931626761617
132165983166201-218
133159680167673-7993
1341617391533778362
135159302163798-4496
13616779515686510930
137164242176288-12046
138159743160689-946
1391608871552445643
1401638441620311813
141161172166801-5629
142159330158500830
143155570157488-1918
1441567491518104939
145155012157928-2916
14616341915327510144
147153630171826-18196
14815453514384110694
149151543155440-3897
1501529551485514404
151150166154367-4201
1521514161473774039
153150332152666-2334
1541521961492482948
155153422154060-638
156147435154648-7213







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
15714144896758.4839974342186137.516002566
15813546135532.2043366983235389.795663302
159129474-37738.8576623524296686.857662352
160123487-121287.559985934368261.559985934
161117500-213926.320967266448926.320967266
162111513-314797.812071974537823.812071974
163105526-423247.484278572634299.484278572
16499539-538754.960077087737832.960077087
16593552-660893.86257393847997.86257393
16687565-789306.623220457964436.623220457
16781578-923687.804310011086843.80431001
16875591-1063772.57075051214954.5707505

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
157 & 141448 & 96758.4839974342 & 186137.516002566 \tabularnewline
158 & 135461 & 35532.2043366983 & 235389.795663302 \tabularnewline
159 & 129474 & -37738.8576623524 & 296686.857662352 \tabularnewline
160 & 123487 & -121287.559985934 & 368261.559985934 \tabularnewline
161 & 117500 & -213926.320967266 & 448926.320967266 \tabularnewline
162 & 111513 & -314797.812071974 & 537823.812071974 \tabularnewline
163 & 105526 & -423247.484278572 & 634299.484278572 \tabularnewline
164 & 99539 & -538754.960077087 & 737832.960077087 \tabularnewline
165 & 93552 & -660893.86257393 & 847997.86257393 \tabularnewline
166 & 87565 & -789306.623220457 & 964436.623220457 \tabularnewline
167 & 81578 & -923687.80431001 & 1086843.80431001 \tabularnewline
168 & 75591 & -1063772.5707505 & 1214954.5707505 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232987&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]157[/C][C]141448[/C][C]96758.4839974342[/C][C]186137.516002566[/C][/ROW]
[ROW][C]158[/C][C]135461[/C][C]35532.2043366983[/C][C]235389.795663302[/C][/ROW]
[ROW][C]159[/C][C]129474[/C][C]-37738.8576623524[/C][C]296686.857662352[/C][/ROW]
[ROW][C]160[/C][C]123487[/C][C]-121287.559985934[/C][C]368261.559985934[/C][/ROW]
[ROW][C]161[/C][C]117500[/C][C]-213926.320967266[/C][C]448926.320967266[/C][/ROW]
[ROW][C]162[/C][C]111513[/C][C]-314797.812071974[/C][C]537823.812071974[/C][/ROW]
[ROW][C]163[/C][C]105526[/C][C]-423247.484278572[/C][C]634299.484278572[/C][/ROW]
[ROW][C]164[/C][C]99539[/C][C]-538754.960077087[/C][C]737832.960077087[/C][/ROW]
[ROW][C]165[/C][C]93552[/C][C]-660893.86257393[/C][C]847997.86257393[/C][/ROW]
[ROW][C]166[/C][C]87565[/C][C]-789306.623220457[/C][C]964436.623220457[/C][/ROW]
[ROW][C]167[/C][C]81578[/C][C]-923687.80431001[/C][C]1086843.80431001[/C][/ROW]
[ROW][C]168[/C][C]75591[/C][C]-1063772.5707505[/C][C]1214954.5707505[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232987&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232987&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
15714144896758.4839974342186137.516002566
15813546135532.2043366983235389.795663302
159129474-37738.8576623524296686.857662352
160123487-121287.559985934368261.559985934
161117500-213926.320967266448926.320967266
162111513-314797.812071974537823.812071974
163105526-423247.484278572634299.484278572
16499539-538754.960077087737832.960077087
16593552-660893.86257393847997.86257393
16687565-789306.623220457964436.623220457
16781578-923687.804310011086843.80431001
16875591-1063772.57075051214954.5707505



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