Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 02 Jan 2011 15:47:21 +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/2011/Jan/02/t12939831295n17194aay37qyf.htm/, Retrieved Thu, 31 Oct 2024 23:53:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=117243, Retrieved Thu, 31 Oct 2024 23:53:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact232
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Aantal niet-werke...] [2011-01-02 15:47:21] [3ed99328c0a6512dc7383724785cc652] [Current]
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Dataseries X:
180144
173666
165688
161570
156145
153730
182698
200765
176512
166618
158644
159585
163095
159044
155511
153745
150569
150605
179612
194690
189917
184128
175335
179566
181140
177876
175041
169292
166070
166972
206348
215706
202108
195411
193111
195198
198770
194163
190420
189733
186029
191531
232571
243477
227247
217859
208679
213188
216234
213586
209465
204045
200237
203666
241476
260307
243324
244460
233575
237217
235243
230354
227184
221678
217142
219452
256446
265845
248624
241114
229245
231805
219277
219313
212610
214771
211142
211457
240048
240636
230580
208795
197922
194596
194581
185686
178106
172608
167302
168053
202300
202388
182516
173476
166444
171297
169701
164182
161914
159612
151001
158114
186530
187069
174330
169362
166827
178037
186413
189226
191563
188906
186005
195309
223532
226899
214126
206903
204442
220375




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117243&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117243&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117243&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117243&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]0[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117243&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117243&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
beta0
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3165688173666-7978
4161570165688-4118
5156145161570-5425
6153730156145-2415
718269815373028968
820076518269818067
9176512200765-24253
10166618176512-9894
11158644166618-7974
12159585158644941
131630951595853510
14159044163095-4051
15155511159044-3533
16153745155511-1766
17150569153745-3176
1815060515056936
1917961215060529007
2019469017961215078
21189917194690-4773
22184128189917-5789
23175335184128-8793
241795661753354231
251811401795661574
26177876181140-3264
27175041177876-2835
28169292175041-5749
29166070169292-3222
30166972166070902
3120634816697239376
322157062063489358
33202108215706-13598
34195411202108-6697
35193111195411-2300
361951981931112087
371987701951983572
38194163198770-4607
39190420194163-3743
40189733190420-687
41186029189733-3704
421915311860295502
4323257119153141040
4424347723257110906
45227247243477-16230
46217859227247-9388
47208679217859-9180
482131882086794509
492162342131883046
50213586216234-2648
51209465213586-4121
52204045209465-5420
53200237204045-3808
542036662002373429
5524147620366637810
5626030724147618831
57243324260307-16983
582444602433241136
59233575244460-10885
602372172335753642
61235243237217-1974
62230354235243-4889
63227184230354-3170
64221678227184-5506
65217142221678-4536
662194522171422310
6725644621945236994
682658452564469399
69248624265845-17221
70241114248624-7510
71229245241114-11869
722318052292452560
73219277231805-12528
7421931321927736
75212610219313-6703
762147712126102161
77211142214771-3629
78211457211142315
7924004821145728591
80240636240048588
81230580240636-10056
82208795230580-21785
83197922208795-10873
84194596197922-3326
85194581194596-15
86185686194581-8895
87178106185686-7580
88172608178106-5498
89167302172608-5306
90168053167302751
9120230016805334247
9220238820230088
93182516202388-19872
94173476182516-9040
95166444173476-7032
961712971664444853
97169701171297-1596
98164182169701-5519
99161914164182-2268
100159612161914-2302
101151001159612-8611
1021581141510017113
10318653015811428416
104187069186530539
105174330187069-12739
106169362174330-4968
107166827169362-2535
10817803716682711210
1091864131780378376
1101892261864132813
1111915631892262337
112188906191563-2657
113186005188906-2901
1141953091860059304
11522353219530928223
1162268992235323367
117214126226899-12773
118206903214126-7223
119204442206903-2461
12022037520444215933

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 165688 & 173666 & -7978 \tabularnewline
4 & 161570 & 165688 & -4118 \tabularnewline
5 & 156145 & 161570 & -5425 \tabularnewline
6 & 153730 & 156145 & -2415 \tabularnewline
7 & 182698 & 153730 & 28968 \tabularnewline
8 & 200765 & 182698 & 18067 \tabularnewline
9 & 176512 & 200765 & -24253 \tabularnewline
10 & 166618 & 176512 & -9894 \tabularnewline
11 & 158644 & 166618 & -7974 \tabularnewline
12 & 159585 & 158644 & 941 \tabularnewline
13 & 163095 & 159585 & 3510 \tabularnewline
14 & 159044 & 163095 & -4051 \tabularnewline
15 & 155511 & 159044 & -3533 \tabularnewline
16 & 153745 & 155511 & -1766 \tabularnewline
17 & 150569 & 153745 & -3176 \tabularnewline
18 & 150605 & 150569 & 36 \tabularnewline
19 & 179612 & 150605 & 29007 \tabularnewline
20 & 194690 & 179612 & 15078 \tabularnewline
21 & 189917 & 194690 & -4773 \tabularnewline
22 & 184128 & 189917 & -5789 \tabularnewline
23 & 175335 & 184128 & -8793 \tabularnewline
24 & 179566 & 175335 & 4231 \tabularnewline
25 & 181140 & 179566 & 1574 \tabularnewline
26 & 177876 & 181140 & -3264 \tabularnewline
27 & 175041 & 177876 & -2835 \tabularnewline
28 & 169292 & 175041 & -5749 \tabularnewline
29 & 166070 & 169292 & -3222 \tabularnewline
30 & 166972 & 166070 & 902 \tabularnewline
31 & 206348 & 166972 & 39376 \tabularnewline
32 & 215706 & 206348 & 9358 \tabularnewline
33 & 202108 & 215706 & -13598 \tabularnewline
34 & 195411 & 202108 & -6697 \tabularnewline
35 & 193111 & 195411 & -2300 \tabularnewline
36 & 195198 & 193111 & 2087 \tabularnewline
37 & 198770 & 195198 & 3572 \tabularnewline
38 & 194163 & 198770 & -4607 \tabularnewline
39 & 190420 & 194163 & -3743 \tabularnewline
40 & 189733 & 190420 & -687 \tabularnewline
41 & 186029 & 189733 & -3704 \tabularnewline
42 & 191531 & 186029 & 5502 \tabularnewline
43 & 232571 & 191531 & 41040 \tabularnewline
44 & 243477 & 232571 & 10906 \tabularnewline
45 & 227247 & 243477 & -16230 \tabularnewline
46 & 217859 & 227247 & -9388 \tabularnewline
47 & 208679 & 217859 & -9180 \tabularnewline
48 & 213188 & 208679 & 4509 \tabularnewline
49 & 216234 & 213188 & 3046 \tabularnewline
50 & 213586 & 216234 & -2648 \tabularnewline
51 & 209465 & 213586 & -4121 \tabularnewline
52 & 204045 & 209465 & -5420 \tabularnewline
53 & 200237 & 204045 & -3808 \tabularnewline
54 & 203666 & 200237 & 3429 \tabularnewline
55 & 241476 & 203666 & 37810 \tabularnewline
56 & 260307 & 241476 & 18831 \tabularnewline
57 & 243324 & 260307 & -16983 \tabularnewline
58 & 244460 & 243324 & 1136 \tabularnewline
59 & 233575 & 244460 & -10885 \tabularnewline
60 & 237217 & 233575 & 3642 \tabularnewline
61 & 235243 & 237217 & -1974 \tabularnewline
62 & 230354 & 235243 & -4889 \tabularnewline
63 & 227184 & 230354 & -3170 \tabularnewline
64 & 221678 & 227184 & -5506 \tabularnewline
65 & 217142 & 221678 & -4536 \tabularnewline
66 & 219452 & 217142 & 2310 \tabularnewline
67 & 256446 & 219452 & 36994 \tabularnewline
68 & 265845 & 256446 & 9399 \tabularnewline
69 & 248624 & 265845 & -17221 \tabularnewline
70 & 241114 & 248624 & -7510 \tabularnewline
71 & 229245 & 241114 & -11869 \tabularnewline
72 & 231805 & 229245 & 2560 \tabularnewline
73 & 219277 & 231805 & -12528 \tabularnewline
74 & 219313 & 219277 & 36 \tabularnewline
75 & 212610 & 219313 & -6703 \tabularnewline
76 & 214771 & 212610 & 2161 \tabularnewline
77 & 211142 & 214771 & -3629 \tabularnewline
78 & 211457 & 211142 & 315 \tabularnewline
79 & 240048 & 211457 & 28591 \tabularnewline
80 & 240636 & 240048 & 588 \tabularnewline
81 & 230580 & 240636 & -10056 \tabularnewline
82 & 208795 & 230580 & -21785 \tabularnewline
83 & 197922 & 208795 & -10873 \tabularnewline
84 & 194596 & 197922 & -3326 \tabularnewline
85 & 194581 & 194596 & -15 \tabularnewline
86 & 185686 & 194581 & -8895 \tabularnewline
87 & 178106 & 185686 & -7580 \tabularnewline
88 & 172608 & 178106 & -5498 \tabularnewline
89 & 167302 & 172608 & -5306 \tabularnewline
90 & 168053 & 167302 & 751 \tabularnewline
91 & 202300 & 168053 & 34247 \tabularnewline
92 & 202388 & 202300 & 88 \tabularnewline
93 & 182516 & 202388 & -19872 \tabularnewline
94 & 173476 & 182516 & -9040 \tabularnewline
95 & 166444 & 173476 & -7032 \tabularnewline
96 & 171297 & 166444 & 4853 \tabularnewline
97 & 169701 & 171297 & -1596 \tabularnewline
98 & 164182 & 169701 & -5519 \tabularnewline
99 & 161914 & 164182 & -2268 \tabularnewline
100 & 159612 & 161914 & -2302 \tabularnewline
101 & 151001 & 159612 & -8611 \tabularnewline
102 & 158114 & 151001 & 7113 \tabularnewline
103 & 186530 & 158114 & 28416 \tabularnewline
104 & 187069 & 186530 & 539 \tabularnewline
105 & 174330 & 187069 & -12739 \tabularnewline
106 & 169362 & 174330 & -4968 \tabularnewline
107 & 166827 & 169362 & -2535 \tabularnewline
108 & 178037 & 166827 & 11210 \tabularnewline
109 & 186413 & 178037 & 8376 \tabularnewline
110 & 189226 & 186413 & 2813 \tabularnewline
111 & 191563 & 189226 & 2337 \tabularnewline
112 & 188906 & 191563 & -2657 \tabularnewline
113 & 186005 & 188906 & -2901 \tabularnewline
114 & 195309 & 186005 & 9304 \tabularnewline
115 & 223532 & 195309 & 28223 \tabularnewline
116 & 226899 & 223532 & 3367 \tabularnewline
117 & 214126 & 226899 & -12773 \tabularnewline
118 & 206903 & 214126 & -7223 \tabularnewline
119 & 204442 & 206903 & -2461 \tabularnewline
120 & 220375 & 204442 & 15933 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117243&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]165688[/C][C]173666[/C][C]-7978[/C][/ROW]
[ROW][C]4[/C][C]161570[/C][C]165688[/C][C]-4118[/C][/ROW]
[ROW][C]5[/C][C]156145[/C][C]161570[/C][C]-5425[/C][/ROW]
[ROW][C]6[/C][C]153730[/C][C]156145[/C][C]-2415[/C][/ROW]
[ROW][C]7[/C][C]182698[/C][C]153730[/C][C]28968[/C][/ROW]
[ROW][C]8[/C][C]200765[/C][C]182698[/C][C]18067[/C][/ROW]
[ROW][C]9[/C][C]176512[/C][C]200765[/C][C]-24253[/C][/ROW]
[ROW][C]10[/C][C]166618[/C][C]176512[/C][C]-9894[/C][/ROW]
[ROW][C]11[/C][C]158644[/C][C]166618[/C][C]-7974[/C][/ROW]
[ROW][C]12[/C][C]159585[/C][C]158644[/C][C]941[/C][/ROW]
[ROW][C]13[/C][C]163095[/C][C]159585[/C][C]3510[/C][/ROW]
[ROW][C]14[/C][C]159044[/C][C]163095[/C][C]-4051[/C][/ROW]
[ROW][C]15[/C][C]155511[/C][C]159044[/C][C]-3533[/C][/ROW]
[ROW][C]16[/C][C]153745[/C][C]155511[/C][C]-1766[/C][/ROW]
[ROW][C]17[/C][C]150569[/C][C]153745[/C][C]-3176[/C][/ROW]
[ROW][C]18[/C][C]150605[/C][C]150569[/C][C]36[/C][/ROW]
[ROW][C]19[/C][C]179612[/C][C]150605[/C][C]29007[/C][/ROW]
[ROW][C]20[/C][C]194690[/C][C]179612[/C][C]15078[/C][/ROW]
[ROW][C]21[/C][C]189917[/C][C]194690[/C][C]-4773[/C][/ROW]
[ROW][C]22[/C][C]184128[/C][C]189917[/C][C]-5789[/C][/ROW]
[ROW][C]23[/C][C]175335[/C][C]184128[/C][C]-8793[/C][/ROW]
[ROW][C]24[/C][C]179566[/C][C]175335[/C][C]4231[/C][/ROW]
[ROW][C]25[/C][C]181140[/C][C]179566[/C][C]1574[/C][/ROW]
[ROW][C]26[/C][C]177876[/C][C]181140[/C][C]-3264[/C][/ROW]
[ROW][C]27[/C][C]175041[/C][C]177876[/C][C]-2835[/C][/ROW]
[ROW][C]28[/C][C]169292[/C][C]175041[/C][C]-5749[/C][/ROW]
[ROW][C]29[/C][C]166070[/C][C]169292[/C][C]-3222[/C][/ROW]
[ROW][C]30[/C][C]166972[/C][C]166070[/C][C]902[/C][/ROW]
[ROW][C]31[/C][C]206348[/C][C]166972[/C][C]39376[/C][/ROW]
[ROW][C]32[/C][C]215706[/C][C]206348[/C][C]9358[/C][/ROW]
[ROW][C]33[/C][C]202108[/C][C]215706[/C][C]-13598[/C][/ROW]
[ROW][C]34[/C][C]195411[/C][C]202108[/C][C]-6697[/C][/ROW]
[ROW][C]35[/C][C]193111[/C][C]195411[/C][C]-2300[/C][/ROW]
[ROW][C]36[/C][C]195198[/C][C]193111[/C][C]2087[/C][/ROW]
[ROW][C]37[/C][C]198770[/C][C]195198[/C][C]3572[/C][/ROW]
[ROW][C]38[/C][C]194163[/C][C]198770[/C][C]-4607[/C][/ROW]
[ROW][C]39[/C][C]190420[/C][C]194163[/C][C]-3743[/C][/ROW]
[ROW][C]40[/C][C]189733[/C][C]190420[/C][C]-687[/C][/ROW]
[ROW][C]41[/C][C]186029[/C][C]189733[/C][C]-3704[/C][/ROW]
[ROW][C]42[/C][C]191531[/C][C]186029[/C][C]5502[/C][/ROW]
[ROW][C]43[/C][C]232571[/C][C]191531[/C][C]41040[/C][/ROW]
[ROW][C]44[/C][C]243477[/C][C]232571[/C][C]10906[/C][/ROW]
[ROW][C]45[/C][C]227247[/C][C]243477[/C][C]-16230[/C][/ROW]
[ROW][C]46[/C][C]217859[/C][C]227247[/C][C]-9388[/C][/ROW]
[ROW][C]47[/C][C]208679[/C][C]217859[/C][C]-9180[/C][/ROW]
[ROW][C]48[/C][C]213188[/C][C]208679[/C][C]4509[/C][/ROW]
[ROW][C]49[/C][C]216234[/C][C]213188[/C][C]3046[/C][/ROW]
[ROW][C]50[/C][C]213586[/C][C]216234[/C][C]-2648[/C][/ROW]
[ROW][C]51[/C][C]209465[/C][C]213586[/C][C]-4121[/C][/ROW]
[ROW][C]52[/C][C]204045[/C][C]209465[/C][C]-5420[/C][/ROW]
[ROW][C]53[/C][C]200237[/C][C]204045[/C][C]-3808[/C][/ROW]
[ROW][C]54[/C][C]203666[/C][C]200237[/C][C]3429[/C][/ROW]
[ROW][C]55[/C][C]241476[/C][C]203666[/C][C]37810[/C][/ROW]
[ROW][C]56[/C][C]260307[/C][C]241476[/C][C]18831[/C][/ROW]
[ROW][C]57[/C][C]243324[/C][C]260307[/C][C]-16983[/C][/ROW]
[ROW][C]58[/C][C]244460[/C][C]243324[/C][C]1136[/C][/ROW]
[ROW][C]59[/C][C]233575[/C][C]244460[/C][C]-10885[/C][/ROW]
[ROW][C]60[/C][C]237217[/C][C]233575[/C][C]3642[/C][/ROW]
[ROW][C]61[/C][C]235243[/C][C]237217[/C][C]-1974[/C][/ROW]
[ROW][C]62[/C][C]230354[/C][C]235243[/C][C]-4889[/C][/ROW]
[ROW][C]63[/C][C]227184[/C][C]230354[/C][C]-3170[/C][/ROW]
[ROW][C]64[/C][C]221678[/C][C]227184[/C][C]-5506[/C][/ROW]
[ROW][C]65[/C][C]217142[/C][C]221678[/C][C]-4536[/C][/ROW]
[ROW][C]66[/C][C]219452[/C][C]217142[/C][C]2310[/C][/ROW]
[ROW][C]67[/C][C]256446[/C][C]219452[/C][C]36994[/C][/ROW]
[ROW][C]68[/C][C]265845[/C][C]256446[/C][C]9399[/C][/ROW]
[ROW][C]69[/C][C]248624[/C][C]265845[/C][C]-17221[/C][/ROW]
[ROW][C]70[/C][C]241114[/C][C]248624[/C][C]-7510[/C][/ROW]
[ROW][C]71[/C][C]229245[/C][C]241114[/C][C]-11869[/C][/ROW]
[ROW][C]72[/C][C]231805[/C][C]229245[/C][C]2560[/C][/ROW]
[ROW][C]73[/C][C]219277[/C][C]231805[/C][C]-12528[/C][/ROW]
[ROW][C]74[/C][C]219313[/C][C]219277[/C][C]36[/C][/ROW]
[ROW][C]75[/C][C]212610[/C][C]219313[/C][C]-6703[/C][/ROW]
[ROW][C]76[/C][C]214771[/C][C]212610[/C][C]2161[/C][/ROW]
[ROW][C]77[/C][C]211142[/C][C]214771[/C][C]-3629[/C][/ROW]
[ROW][C]78[/C][C]211457[/C][C]211142[/C][C]315[/C][/ROW]
[ROW][C]79[/C][C]240048[/C][C]211457[/C][C]28591[/C][/ROW]
[ROW][C]80[/C][C]240636[/C][C]240048[/C][C]588[/C][/ROW]
[ROW][C]81[/C][C]230580[/C][C]240636[/C][C]-10056[/C][/ROW]
[ROW][C]82[/C][C]208795[/C][C]230580[/C][C]-21785[/C][/ROW]
[ROW][C]83[/C][C]197922[/C][C]208795[/C][C]-10873[/C][/ROW]
[ROW][C]84[/C][C]194596[/C][C]197922[/C][C]-3326[/C][/ROW]
[ROW][C]85[/C][C]194581[/C][C]194596[/C][C]-15[/C][/ROW]
[ROW][C]86[/C][C]185686[/C][C]194581[/C][C]-8895[/C][/ROW]
[ROW][C]87[/C][C]178106[/C][C]185686[/C][C]-7580[/C][/ROW]
[ROW][C]88[/C][C]172608[/C][C]178106[/C][C]-5498[/C][/ROW]
[ROW][C]89[/C][C]167302[/C][C]172608[/C][C]-5306[/C][/ROW]
[ROW][C]90[/C][C]168053[/C][C]167302[/C][C]751[/C][/ROW]
[ROW][C]91[/C][C]202300[/C][C]168053[/C][C]34247[/C][/ROW]
[ROW][C]92[/C][C]202388[/C][C]202300[/C][C]88[/C][/ROW]
[ROW][C]93[/C][C]182516[/C][C]202388[/C][C]-19872[/C][/ROW]
[ROW][C]94[/C][C]173476[/C][C]182516[/C][C]-9040[/C][/ROW]
[ROW][C]95[/C][C]166444[/C][C]173476[/C][C]-7032[/C][/ROW]
[ROW][C]96[/C][C]171297[/C][C]166444[/C][C]4853[/C][/ROW]
[ROW][C]97[/C][C]169701[/C][C]171297[/C][C]-1596[/C][/ROW]
[ROW][C]98[/C][C]164182[/C][C]169701[/C][C]-5519[/C][/ROW]
[ROW][C]99[/C][C]161914[/C][C]164182[/C][C]-2268[/C][/ROW]
[ROW][C]100[/C][C]159612[/C][C]161914[/C][C]-2302[/C][/ROW]
[ROW][C]101[/C][C]151001[/C][C]159612[/C][C]-8611[/C][/ROW]
[ROW][C]102[/C][C]158114[/C][C]151001[/C][C]7113[/C][/ROW]
[ROW][C]103[/C][C]186530[/C][C]158114[/C][C]28416[/C][/ROW]
[ROW][C]104[/C][C]187069[/C][C]186530[/C][C]539[/C][/ROW]
[ROW][C]105[/C][C]174330[/C][C]187069[/C][C]-12739[/C][/ROW]
[ROW][C]106[/C][C]169362[/C][C]174330[/C][C]-4968[/C][/ROW]
[ROW][C]107[/C][C]166827[/C][C]169362[/C][C]-2535[/C][/ROW]
[ROW][C]108[/C][C]178037[/C][C]166827[/C][C]11210[/C][/ROW]
[ROW][C]109[/C][C]186413[/C][C]178037[/C][C]8376[/C][/ROW]
[ROW][C]110[/C][C]189226[/C][C]186413[/C][C]2813[/C][/ROW]
[ROW][C]111[/C][C]191563[/C][C]189226[/C][C]2337[/C][/ROW]
[ROW][C]112[/C][C]188906[/C][C]191563[/C][C]-2657[/C][/ROW]
[ROW][C]113[/C][C]186005[/C][C]188906[/C][C]-2901[/C][/ROW]
[ROW][C]114[/C][C]195309[/C][C]186005[/C][C]9304[/C][/ROW]
[ROW][C]115[/C][C]223532[/C][C]195309[/C][C]28223[/C][/ROW]
[ROW][C]116[/C][C]226899[/C][C]223532[/C][C]3367[/C][/ROW]
[ROW][C]117[/C][C]214126[/C][C]226899[/C][C]-12773[/C][/ROW]
[ROW][C]118[/C][C]206903[/C][C]214126[/C][C]-7223[/C][/ROW]
[ROW][C]119[/C][C]204442[/C][C]206903[/C][C]-2461[/C][/ROW]
[ROW][C]120[/C][C]220375[/C][C]204442[/C][C]15933[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117243&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117243&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
3165688173666-7978
4161570165688-4118
5156145161570-5425
6153730156145-2415
718269815373028968
820076518269818067
9176512200765-24253
10166618176512-9894
11158644166618-7974
12159585158644941
131630951595853510
14159044163095-4051
15155511159044-3533
16153745155511-1766
17150569153745-3176
1815060515056936
1917961215060529007
2019469017961215078
21189917194690-4773
22184128189917-5789
23175335184128-8793
241795661753354231
251811401795661574
26177876181140-3264
27175041177876-2835
28169292175041-5749
29166070169292-3222
30166972166070902
3120634816697239376
322157062063489358
33202108215706-13598
34195411202108-6697
35193111195411-2300
361951981931112087
371987701951983572
38194163198770-4607
39190420194163-3743
40189733190420-687
41186029189733-3704
421915311860295502
4323257119153141040
4424347723257110906
45227247243477-16230
46217859227247-9388
47208679217859-9180
482131882086794509
492162342131883046
50213586216234-2648
51209465213586-4121
52204045209465-5420
53200237204045-3808
542036662002373429
5524147620366637810
5626030724147618831
57243324260307-16983
582444602433241136
59233575244460-10885
602372172335753642
61235243237217-1974
62230354235243-4889
63227184230354-3170
64221678227184-5506
65217142221678-4536
662194522171422310
6725644621945236994
682658452564469399
69248624265845-17221
70241114248624-7510
71229245241114-11869
722318052292452560
73219277231805-12528
7421931321927736
75212610219313-6703
762147712126102161
77211142214771-3629
78211457211142315
7924004821145728591
80240636240048588
81230580240636-10056
82208795230580-21785
83197922208795-10873
84194596197922-3326
85194581194596-15
86185686194581-8895
87178106185686-7580
88172608178106-5498
89167302172608-5306
90168053167302751
9120230016805334247
9220238820230088
93182516202388-19872
94173476182516-9040
95166444173476-7032
961712971664444853
97169701171297-1596
98164182169701-5519
99161914164182-2268
100159612161914-2302
101151001159612-8611
1021581141510017113
10318653015811428416
104187069186530539
105174330187069-12739
106169362174330-4968
107166827169362-2535
10817803716682711210
1091864131780378376
1101892261864132813
1111915631892262337
112188906191563-2657
113186005188906-2901
1141953091860059304
11522353219530928223
1162268992235323367
117214126226899-12773
118206903214126-7223
119204442206903-2461
12022037520444215933







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121220375195827.339684944244922.660315056
122220375185659.365857920255090.63414208
123220375177857.205127381262892.794872619
124220375171279.679369888269470.320630112
125220375165484.762846961275265.237153039
126220375160245.757848945280504.242151055
127220375155427.995537873285322.004462127
128220375150943.731715840289806.268284160
129220375146732.019054832294017.980945168
130220375142748.482176297298001.517823703
131220375138959.621253862301790.378746138
132220375135339.410254762305410.589745238

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 220375 & 195827.339684944 & 244922.660315056 \tabularnewline
122 & 220375 & 185659.365857920 & 255090.63414208 \tabularnewline
123 & 220375 & 177857.205127381 & 262892.794872619 \tabularnewline
124 & 220375 & 171279.679369888 & 269470.320630112 \tabularnewline
125 & 220375 & 165484.762846961 & 275265.237153039 \tabularnewline
126 & 220375 & 160245.757848945 & 280504.242151055 \tabularnewline
127 & 220375 & 155427.995537873 & 285322.004462127 \tabularnewline
128 & 220375 & 150943.731715840 & 289806.268284160 \tabularnewline
129 & 220375 & 146732.019054832 & 294017.980945168 \tabularnewline
130 & 220375 & 142748.482176297 & 298001.517823703 \tabularnewline
131 & 220375 & 138959.621253862 & 301790.378746138 \tabularnewline
132 & 220375 & 135339.410254762 & 305410.589745238 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117243&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]121[/C][C]220375[/C][C]195827.339684944[/C][C]244922.660315056[/C][/ROW]
[ROW][C]122[/C][C]220375[/C][C]185659.365857920[/C][C]255090.63414208[/C][/ROW]
[ROW][C]123[/C][C]220375[/C][C]177857.205127381[/C][C]262892.794872619[/C][/ROW]
[ROW][C]124[/C][C]220375[/C][C]171279.679369888[/C][C]269470.320630112[/C][/ROW]
[ROW][C]125[/C][C]220375[/C][C]165484.762846961[/C][C]275265.237153039[/C][/ROW]
[ROW][C]126[/C][C]220375[/C][C]160245.757848945[/C][C]280504.242151055[/C][/ROW]
[ROW][C]127[/C][C]220375[/C][C]155427.995537873[/C][C]285322.004462127[/C][/ROW]
[ROW][C]128[/C][C]220375[/C][C]150943.731715840[/C][C]289806.268284160[/C][/ROW]
[ROW][C]129[/C][C]220375[/C][C]146732.019054832[/C][C]294017.980945168[/C][/ROW]
[ROW][C]130[/C][C]220375[/C][C]142748.482176297[/C][C]298001.517823703[/C][/ROW]
[ROW][C]131[/C][C]220375[/C][C]138959.621253862[/C][C]301790.378746138[/C][/ROW]
[ROW][C]132[/C][C]220375[/C][C]135339.410254762[/C][C]305410.589745238[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117243&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117243&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
121220375195827.339684944244922.660315056
122220375185659.365857920255090.63414208
123220375177857.205127381262892.794872619
124220375171279.679369888269470.320630112
125220375165484.762846961275265.237153039
126220375160245.757848945280504.242151055
127220375155427.995537873285322.004462127
128220375150943.731715840289806.268284160
129220375146732.019054832294017.980945168
130220375142748.482176297298001.517823703
131220375138959.621253862301790.378746138
132220375135339.410254762305410.589745238



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')