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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 29 Nov 2015 22:09:36 +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/2015/Nov/29/t1448835012iu20ttcngnvmmn1.htm/, Retrieved Wed, 15 May 2024 08:36:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284536, Retrieved Wed, 15 May 2024 08:36:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact161
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Opgave 10-oefenin...] [2015-11-29 22:09:36] [df110f336183c9d15b985c5fac87d8f5] [Current]
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Dataseries X:
169701
164182
161914
159612
151001
158114
186530
187069
174330
169362
166827
178037
186412
189226
191563
188906
186005
195309
223532
226899
214126
206903
204442
220376
214320
212588
205816
202196
195722
198563
229139
229527
211868
203555
195770
199834
203089
198480
192684
187827
182414
182510
211524
211451
200140
191568
186424
191987
203583
201920
195978
191395
188222
189422
214419
224325
216222
210506
207221
210027
215191
215177
211701
210176
205491
206996
235980
241292
236675
229127
225436
229570
239973
236168
230703
224790
217811
219576
245472
248511
242084
235572
229827
229697




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284536&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284536&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284536&T=0

As an alternative you can also use a QR Code:  

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

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







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999933893038648
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999933893038648 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284536&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]0.999933893038648[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284536&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284536&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
alpha0.999933893038648
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2164182169701-5519
3161914164182.36484432-2268.3648443197
4159612161914.149954707-2302.1499547071
5151001159612.152188138-8611.15218813808
6158114151001.5692571057112.43074289509
7186530158113.52981881628416.4701811842
8187069186528.121473504540.878526496032
9174330187068.964244164-12738.9642441641
10169362174330.842134217-4968.84213421695
11166827169362.328475055-2535.32847505494
12178037166827.16760286211209.8323971385
13186412178036.2589520438375.74104795704
14189226186411.446305212814.55369478973
15191563189225.8139384082337.18606159234
16188906191562.845495731-2656.84549573137
17186005188906.175635983-2901.17563598251
18195309186005.1917879069303.80821209436
19223532195308.3849535128223.6150464899
20226899223530.1342225713368.86577742908
21214126226898.77729452-12772.7772945203
22206903214126.844369495-7223.84436949497
23204442206903.477546401-2461.47754640057
24220376204442.16272080115933.837279199
25214320220374.946662435-6054.94666243478
26212588214320.400274125-1732.40027412499
27205816212588.114523718-6772.11452371799
28202196205816.447683913-3620.44768391308
29195722202196.239336795-6474.23933679512
30198563195722.427992292840.57200771038
31229139198562.81221841630576.1877815839
32229527229136.978701136390.021298863983
33211868229526.974216877-17658.974216877
34203555211869.167381126-8314.16738112606
35195770203555.549624342-7785.54962434174
36199834195770.5146790284063.48532097187
37203089199833.7313753333255.26862466705
38198480203088.784804083-4608.78480408282
39192684198480.304672759-5796.30467275894
40187827192684.383176089-4857.383176089
41182414187827.321106842-5413.32110684188
42182510182414.35785820995.6421417908277
43211524182509.99367738929014.0063226114
44211451211522.081972205-71.081972205342
45200140211451.004699013-11311.0046990132
46191568200140.747736151-8572.74773615052
47186424191568.566718303-5144.56671830328
48191987186424.3400916735562.65990832678
49203583191986.63226945611596.3677305436
50201920203582.233399367-1662.23339936661
51195978201920.109885199-5942.10988519908
52191395195978.392814829-4583.39281482852
53188222191395.302994172-3173.30299417165
54189422188222.2097774181199.79022258162
55214419189421.92068551424997.0793144859
56224325214417.3475190449907.65248095614
57216222224324.3450352-8102.34503520036
58210506216222.53562141-5716.53562141009
59207221210506.377902799-3285.3779027994
60210027207221.217186352805.78281364997
61215191210026.8145182245164.18548177605
62215177215190.65861139-13.6586113899539
63211701215177.000902929-3476.00090292929
64210176211701.229787857-1525.22978785736
65205491210176.100828307-4685.10082830663
66206996205491.3097177791504.69028222063
67235980206995.90052949828984.0994705023
68241292235978.0839492565313.91605074352
69236675241291.648713157-4616.64871315702
70229127236675.305192618-7548.30519261805
71225436229127.49899552-3691.49899551965
72229570225436.2440337814133.7559662186
73239973229569.72672995410403.2732700459
74236168239972.312271216-3804.31227121601
75230703236168.251491524-5465.25149152428
76224790230703.361291169-5913.36129116913
77217811224790.390914346-6979.39091434632
78219576217811.4613863251764.53861367458
79245472219575.88335171425896.1166482859
80248511245470.2880864183040.71191358243
81242084248510.798987775-6426.79898777505
82235572242084.424856152-6512.4248561523
83229827235572.430516618-5745.43051661827
84229697229827.379812953-130.379812953091

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 164182 & 169701 & -5519 \tabularnewline
3 & 161914 & 164182.36484432 & -2268.3648443197 \tabularnewline
4 & 159612 & 161914.149954707 & -2302.1499547071 \tabularnewline
5 & 151001 & 159612.152188138 & -8611.15218813808 \tabularnewline
6 & 158114 & 151001.569257105 & 7112.43074289509 \tabularnewline
7 & 186530 & 158113.529818816 & 28416.4701811842 \tabularnewline
8 & 187069 & 186528.121473504 & 540.878526496032 \tabularnewline
9 & 174330 & 187068.964244164 & -12738.9642441641 \tabularnewline
10 & 169362 & 174330.842134217 & -4968.84213421695 \tabularnewline
11 & 166827 & 169362.328475055 & -2535.32847505494 \tabularnewline
12 & 178037 & 166827.167602862 & 11209.8323971385 \tabularnewline
13 & 186412 & 178036.258952043 & 8375.74104795704 \tabularnewline
14 & 189226 & 186411.44630521 & 2814.55369478973 \tabularnewline
15 & 191563 & 189225.813938408 & 2337.18606159234 \tabularnewline
16 & 188906 & 191562.845495731 & -2656.84549573137 \tabularnewline
17 & 186005 & 188906.175635983 & -2901.17563598251 \tabularnewline
18 & 195309 & 186005.191787906 & 9303.80821209436 \tabularnewline
19 & 223532 & 195308.38495351 & 28223.6150464899 \tabularnewline
20 & 226899 & 223530.134222571 & 3368.86577742908 \tabularnewline
21 & 214126 & 226898.77729452 & -12772.7772945203 \tabularnewline
22 & 206903 & 214126.844369495 & -7223.84436949497 \tabularnewline
23 & 204442 & 206903.477546401 & -2461.47754640057 \tabularnewline
24 & 220376 & 204442.162720801 & 15933.837279199 \tabularnewline
25 & 214320 & 220374.946662435 & -6054.94666243478 \tabularnewline
26 & 212588 & 214320.400274125 & -1732.40027412499 \tabularnewline
27 & 205816 & 212588.114523718 & -6772.11452371799 \tabularnewline
28 & 202196 & 205816.447683913 & -3620.44768391308 \tabularnewline
29 & 195722 & 202196.239336795 & -6474.23933679512 \tabularnewline
30 & 198563 & 195722.42799229 & 2840.57200771038 \tabularnewline
31 & 229139 & 198562.812218416 & 30576.1877815839 \tabularnewline
32 & 229527 & 229136.978701136 & 390.021298863983 \tabularnewline
33 & 211868 & 229526.974216877 & -17658.974216877 \tabularnewline
34 & 203555 & 211869.167381126 & -8314.16738112606 \tabularnewline
35 & 195770 & 203555.549624342 & -7785.54962434174 \tabularnewline
36 & 199834 & 195770.514679028 & 4063.48532097187 \tabularnewline
37 & 203089 & 199833.731375333 & 3255.26862466705 \tabularnewline
38 & 198480 & 203088.784804083 & -4608.78480408282 \tabularnewline
39 & 192684 & 198480.304672759 & -5796.30467275894 \tabularnewline
40 & 187827 & 192684.383176089 & -4857.383176089 \tabularnewline
41 & 182414 & 187827.321106842 & -5413.32110684188 \tabularnewline
42 & 182510 & 182414.357858209 & 95.6421417908277 \tabularnewline
43 & 211524 & 182509.993677389 & 29014.0063226114 \tabularnewline
44 & 211451 & 211522.081972205 & -71.081972205342 \tabularnewline
45 & 200140 & 211451.004699013 & -11311.0046990132 \tabularnewline
46 & 191568 & 200140.747736151 & -8572.74773615052 \tabularnewline
47 & 186424 & 191568.566718303 & -5144.56671830328 \tabularnewline
48 & 191987 & 186424.340091673 & 5562.65990832678 \tabularnewline
49 & 203583 & 191986.632269456 & 11596.3677305436 \tabularnewline
50 & 201920 & 203582.233399367 & -1662.23339936661 \tabularnewline
51 & 195978 & 201920.109885199 & -5942.10988519908 \tabularnewline
52 & 191395 & 195978.392814829 & -4583.39281482852 \tabularnewline
53 & 188222 & 191395.302994172 & -3173.30299417165 \tabularnewline
54 & 189422 & 188222.209777418 & 1199.79022258162 \tabularnewline
55 & 214419 & 189421.920685514 & 24997.0793144859 \tabularnewline
56 & 224325 & 214417.347519044 & 9907.65248095614 \tabularnewline
57 & 216222 & 224324.3450352 & -8102.34503520036 \tabularnewline
58 & 210506 & 216222.53562141 & -5716.53562141009 \tabularnewline
59 & 207221 & 210506.377902799 & -3285.3779027994 \tabularnewline
60 & 210027 & 207221.21718635 & 2805.78281364997 \tabularnewline
61 & 215191 & 210026.814518224 & 5164.18548177605 \tabularnewline
62 & 215177 & 215190.65861139 & -13.6586113899539 \tabularnewline
63 & 211701 & 215177.000902929 & -3476.00090292929 \tabularnewline
64 & 210176 & 211701.229787857 & -1525.22978785736 \tabularnewline
65 & 205491 & 210176.100828307 & -4685.10082830663 \tabularnewline
66 & 206996 & 205491.309717779 & 1504.69028222063 \tabularnewline
67 & 235980 & 206995.900529498 & 28984.0994705023 \tabularnewline
68 & 241292 & 235978.083949256 & 5313.91605074352 \tabularnewline
69 & 236675 & 241291.648713157 & -4616.64871315702 \tabularnewline
70 & 229127 & 236675.305192618 & -7548.30519261805 \tabularnewline
71 & 225436 & 229127.49899552 & -3691.49899551965 \tabularnewline
72 & 229570 & 225436.244033781 & 4133.7559662186 \tabularnewline
73 & 239973 & 229569.726729954 & 10403.2732700459 \tabularnewline
74 & 236168 & 239972.312271216 & -3804.31227121601 \tabularnewline
75 & 230703 & 236168.251491524 & -5465.25149152428 \tabularnewline
76 & 224790 & 230703.361291169 & -5913.36129116913 \tabularnewline
77 & 217811 & 224790.390914346 & -6979.39091434632 \tabularnewline
78 & 219576 & 217811.461386325 & 1764.53861367458 \tabularnewline
79 & 245472 & 219575.883351714 & 25896.1166482859 \tabularnewline
80 & 248511 & 245470.288086418 & 3040.71191358243 \tabularnewline
81 & 242084 & 248510.798987775 & -6426.79898777505 \tabularnewline
82 & 235572 & 242084.424856152 & -6512.4248561523 \tabularnewline
83 & 229827 & 235572.430516618 & -5745.43051661827 \tabularnewline
84 & 229697 & 229827.379812953 & -130.379812953091 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284536&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]2[/C][C]164182[/C][C]169701[/C][C]-5519[/C][/ROW]
[ROW][C]3[/C][C]161914[/C][C]164182.36484432[/C][C]-2268.3648443197[/C][/ROW]
[ROW][C]4[/C][C]159612[/C][C]161914.149954707[/C][C]-2302.1499547071[/C][/ROW]
[ROW][C]5[/C][C]151001[/C][C]159612.152188138[/C][C]-8611.15218813808[/C][/ROW]
[ROW][C]6[/C][C]158114[/C][C]151001.569257105[/C][C]7112.43074289509[/C][/ROW]
[ROW][C]7[/C][C]186530[/C][C]158113.529818816[/C][C]28416.4701811842[/C][/ROW]
[ROW][C]8[/C][C]187069[/C][C]186528.121473504[/C][C]540.878526496032[/C][/ROW]
[ROW][C]9[/C][C]174330[/C][C]187068.964244164[/C][C]-12738.9642441641[/C][/ROW]
[ROW][C]10[/C][C]169362[/C][C]174330.842134217[/C][C]-4968.84213421695[/C][/ROW]
[ROW][C]11[/C][C]166827[/C][C]169362.328475055[/C][C]-2535.32847505494[/C][/ROW]
[ROW][C]12[/C][C]178037[/C][C]166827.167602862[/C][C]11209.8323971385[/C][/ROW]
[ROW][C]13[/C][C]186412[/C][C]178036.258952043[/C][C]8375.74104795704[/C][/ROW]
[ROW][C]14[/C][C]189226[/C][C]186411.44630521[/C][C]2814.55369478973[/C][/ROW]
[ROW][C]15[/C][C]191563[/C][C]189225.813938408[/C][C]2337.18606159234[/C][/ROW]
[ROW][C]16[/C][C]188906[/C][C]191562.845495731[/C][C]-2656.84549573137[/C][/ROW]
[ROW][C]17[/C][C]186005[/C][C]188906.175635983[/C][C]-2901.17563598251[/C][/ROW]
[ROW][C]18[/C][C]195309[/C][C]186005.191787906[/C][C]9303.80821209436[/C][/ROW]
[ROW][C]19[/C][C]223532[/C][C]195308.38495351[/C][C]28223.6150464899[/C][/ROW]
[ROW][C]20[/C][C]226899[/C][C]223530.134222571[/C][C]3368.86577742908[/C][/ROW]
[ROW][C]21[/C][C]214126[/C][C]226898.77729452[/C][C]-12772.7772945203[/C][/ROW]
[ROW][C]22[/C][C]206903[/C][C]214126.844369495[/C][C]-7223.84436949497[/C][/ROW]
[ROW][C]23[/C][C]204442[/C][C]206903.477546401[/C][C]-2461.47754640057[/C][/ROW]
[ROW][C]24[/C][C]220376[/C][C]204442.162720801[/C][C]15933.837279199[/C][/ROW]
[ROW][C]25[/C][C]214320[/C][C]220374.946662435[/C][C]-6054.94666243478[/C][/ROW]
[ROW][C]26[/C][C]212588[/C][C]214320.400274125[/C][C]-1732.40027412499[/C][/ROW]
[ROW][C]27[/C][C]205816[/C][C]212588.114523718[/C][C]-6772.11452371799[/C][/ROW]
[ROW][C]28[/C][C]202196[/C][C]205816.447683913[/C][C]-3620.44768391308[/C][/ROW]
[ROW][C]29[/C][C]195722[/C][C]202196.239336795[/C][C]-6474.23933679512[/C][/ROW]
[ROW][C]30[/C][C]198563[/C][C]195722.42799229[/C][C]2840.57200771038[/C][/ROW]
[ROW][C]31[/C][C]229139[/C][C]198562.812218416[/C][C]30576.1877815839[/C][/ROW]
[ROW][C]32[/C][C]229527[/C][C]229136.978701136[/C][C]390.021298863983[/C][/ROW]
[ROW][C]33[/C][C]211868[/C][C]229526.974216877[/C][C]-17658.974216877[/C][/ROW]
[ROW][C]34[/C][C]203555[/C][C]211869.167381126[/C][C]-8314.16738112606[/C][/ROW]
[ROW][C]35[/C][C]195770[/C][C]203555.549624342[/C][C]-7785.54962434174[/C][/ROW]
[ROW][C]36[/C][C]199834[/C][C]195770.514679028[/C][C]4063.48532097187[/C][/ROW]
[ROW][C]37[/C][C]203089[/C][C]199833.731375333[/C][C]3255.26862466705[/C][/ROW]
[ROW][C]38[/C][C]198480[/C][C]203088.784804083[/C][C]-4608.78480408282[/C][/ROW]
[ROW][C]39[/C][C]192684[/C][C]198480.304672759[/C][C]-5796.30467275894[/C][/ROW]
[ROW][C]40[/C][C]187827[/C][C]192684.383176089[/C][C]-4857.383176089[/C][/ROW]
[ROW][C]41[/C][C]182414[/C][C]187827.321106842[/C][C]-5413.32110684188[/C][/ROW]
[ROW][C]42[/C][C]182510[/C][C]182414.357858209[/C][C]95.6421417908277[/C][/ROW]
[ROW][C]43[/C][C]211524[/C][C]182509.993677389[/C][C]29014.0063226114[/C][/ROW]
[ROW][C]44[/C][C]211451[/C][C]211522.081972205[/C][C]-71.081972205342[/C][/ROW]
[ROW][C]45[/C][C]200140[/C][C]211451.004699013[/C][C]-11311.0046990132[/C][/ROW]
[ROW][C]46[/C][C]191568[/C][C]200140.747736151[/C][C]-8572.74773615052[/C][/ROW]
[ROW][C]47[/C][C]186424[/C][C]191568.566718303[/C][C]-5144.56671830328[/C][/ROW]
[ROW][C]48[/C][C]191987[/C][C]186424.340091673[/C][C]5562.65990832678[/C][/ROW]
[ROW][C]49[/C][C]203583[/C][C]191986.632269456[/C][C]11596.3677305436[/C][/ROW]
[ROW][C]50[/C][C]201920[/C][C]203582.233399367[/C][C]-1662.23339936661[/C][/ROW]
[ROW][C]51[/C][C]195978[/C][C]201920.109885199[/C][C]-5942.10988519908[/C][/ROW]
[ROW][C]52[/C][C]191395[/C][C]195978.392814829[/C][C]-4583.39281482852[/C][/ROW]
[ROW][C]53[/C][C]188222[/C][C]191395.302994172[/C][C]-3173.30299417165[/C][/ROW]
[ROW][C]54[/C][C]189422[/C][C]188222.209777418[/C][C]1199.79022258162[/C][/ROW]
[ROW][C]55[/C][C]214419[/C][C]189421.920685514[/C][C]24997.0793144859[/C][/ROW]
[ROW][C]56[/C][C]224325[/C][C]214417.347519044[/C][C]9907.65248095614[/C][/ROW]
[ROW][C]57[/C][C]216222[/C][C]224324.3450352[/C][C]-8102.34503520036[/C][/ROW]
[ROW][C]58[/C][C]210506[/C][C]216222.53562141[/C][C]-5716.53562141009[/C][/ROW]
[ROW][C]59[/C][C]207221[/C][C]210506.377902799[/C][C]-3285.3779027994[/C][/ROW]
[ROW][C]60[/C][C]210027[/C][C]207221.21718635[/C][C]2805.78281364997[/C][/ROW]
[ROW][C]61[/C][C]215191[/C][C]210026.814518224[/C][C]5164.18548177605[/C][/ROW]
[ROW][C]62[/C][C]215177[/C][C]215190.65861139[/C][C]-13.6586113899539[/C][/ROW]
[ROW][C]63[/C][C]211701[/C][C]215177.000902929[/C][C]-3476.00090292929[/C][/ROW]
[ROW][C]64[/C][C]210176[/C][C]211701.229787857[/C][C]-1525.22978785736[/C][/ROW]
[ROW][C]65[/C][C]205491[/C][C]210176.100828307[/C][C]-4685.10082830663[/C][/ROW]
[ROW][C]66[/C][C]206996[/C][C]205491.309717779[/C][C]1504.69028222063[/C][/ROW]
[ROW][C]67[/C][C]235980[/C][C]206995.900529498[/C][C]28984.0994705023[/C][/ROW]
[ROW][C]68[/C][C]241292[/C][C]235978.083949256[/C][C]5313.91605074352[/C][/ROW]
[ROW][C]69[/C][C]236675[/C][C]241291.648713157[/C][C]-4616.64871315702[/C][/ROW]
[ROW][C]70[/C][C]229127[/C][C]236675.305192618[/C][C]-7548.30519261805[/C][/ROW]
[ROW][C]71[/C][C]225436[/C][C]229127.49899552[/C][C]-3691.49899551965[/C][/ROW]
[ROW][C]72[/C][C]229570[/C][C]225436.244033781[/C][C]4133.7559662186[/C][/ROW]
[ROW][C]73[/C][C]239973[/C][C]229569.726729954[/C][C]10403.2732700459[/C][/ROW]
[ROW][C]74[/C][C]236168[/C][C]239972.312271216[/C][C]-3804.31227121601[/C][/ROW]
[ROW][C]75[/C][C]230703[/C][C]236168.251491524[/C][C]-5465.25149152428[/C][/ROW]
[ROW][C]76[/C][C]224790[/C][C]230703.361291169[/C][C]-5913.36129116913[/C][/ROW]
[ROW][C]77[/C][C]217811[/C][C]224790.390914346[/C][C]-6979.39091434632[/C][/ROW]
[ROW][C]78[/C][C]219576[/C][C]217811.461386325[/C][C]1764.53861367458[/C][/ROW]
[ROW][C]79[/C][C]245472[/C][C]219575.883351714[/C][C]25896.1166482859[/C][/ROW]
[ROW][C]80[/C][C]248511[/C][C]245470.288086418[/C][C]3040.71191358243[/C][/ROW]
[ROW][C]81[/C][C]242084[/C][C]248510.798987775[/C][C]-6426.79898777505[/C][/ROW]
[ROW][C]82[/C][C]235572[/C][C]242084.424856152[/C][C]-6512.4248561523[/C][/ROW]
[ROW][C]83[/C][C]229827[/C][C]235572.430516618[/C][C]-5745.43051661827[/C][/ROW]
[ROW][C]84[/C][C]229697[/C][C]229827.379812953[/C][C]-130.379812953091[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284536&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284536&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
2164182169701-5519
3161914164182.36484432-2268.3648443197
4159612161914.149954707-2302.1499547071
5151001159612.152188138-8611.15218813808
6158114151001.5692571057112.43074289509
7186530158113.52981881628416.4701811842
8187069186528.121473504540.878526496032
9174330187068.964244164-12738.9642441641
10169362174330.842134217-4968.84213421695
11166827169362.328475055-2535.32847505494
12178037166827.16760286211209.8323971385
13186412178036.2589520438375.74104795704
14189226186411.446305212814.55369478973
15191563189225.8139384082337.18606159234
16188906191562.845495731-2656.84549573137
17186005188906.175635983-2901.17563598251
18195309186005.1917879069303.80821209436
19223532195308.3849535128223.6150464899
20226899223530.1342225713368.86577742908
21214126226898.77729452-12772.7772945203
22206903214126.844369495-7223.84436949497
23204442206903.477546401-2461.47754640057
24220376204442.16272080115933.837279199
25214320220374.946662435-6054.94666243478
26212588214320.400274125-1732.40027412499
27205816212588.114523718-6772.11452371799
28202196205816.447683913-3620.44768391308
29195722202196.239336795-6474.23933679512
30198563195722.427992292840.57200771038
31229139198562.81221841630576.1877815839
32229527229136.978701136390.021298863983
33211868229526.974216877-17658.974216877
34203555211869.167381126-8314.16738112606
35195770203555.549624342-7785.54962434174
36199834195770.5146790284063.48532097187
37203089199833.7313753333255.26862466705
38198480203088.784804083-4608.78480408282
39192684198480.304672759-5796.30467275894
40187827192684.383176089-4857.383176089
41182414187827.321106842-5413.32110684188
42182510182414.35785820995.6421417908277
43211524182509.99367738929014.0063226114
44211451211522.081972205-71.081972205342
45200140211451.004699013-11311.0046990132
46191568200140.747736151-8572.74773615052
47186424191568.566718303-5144.56671830328
48191987186424.3400916735562.65990832678
49203583191986.63226945611596.3677305436
50201920203582.233399367-1662.23339936661
51195978201920.109885199-5942.10988519908
52191395195978.392814829-4583.39281482852
53188222191395.302994172-3173.30299417165
54189422188222.2097774181199.79022258162
55214419189421.92068551424997.0793144859
56224325214417.3475190449907.65248095614
57216222224324.3450352-8102.34503520036
58210506216222.53562141-5716.53562141009
59207221210506.377902799-3285.3779027994
60210027207221.217186352805.78281364997
61215191210026.8145182245164.18548177605
62215177215190.65861139-13.6586113899539
63211701215177.000902929-3476.00090292929
64210176211701.229787857-1525.22978785736
65205491210176.100828307-4685.10082830663
66206996205491.3097177791504.69028222063
67235980206995.90052949828984.0994705023
68241292235978.0839492565313.91605074352
69236675241291.648713157-4616.64871315702
70229127236675.305192618-7548.30519261805
71225436229127.49899552-3691.49899551965
72229570225436.2440337814133.7559662186
73239973229569.72672995410403.2732700459
74236168239972.312271216-3804.31227121601
75230703236168.251491524-5465.25149152428
76224790230703.361291169-5913.36129116913
77217811224790.390914346-6979.39091434632
78219576217811.4613863251764.53861367458
79245472219575.88335171425896.1166482859
80248511245470.2880864183040.71191358243
81242084248510.798987775-6426.79898777505
82235572242084.424856152-6512.4248561523
83229827235572.430516618-5745.43051661827
84229697229827.379812953-130.379812953091







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85229697.008619013209622.339824105249771.677413922
86229697.008619013201308.078117579258085.939120448
87229697.008619013194928.194678856264465.822559171
88229697.008619013189549.661625777269844.355612249
89229697.008619013184811.058496672274582.958741355
90229697.008619013180527.022182414278866.995055612
91229697.008619013176587.436845506282806.580392521
92229697.008619013172920.555209564286473.462028462
93229697.008619013169476.541088901289917.476149126
94229697.008619013166219.108863781293174.908374246
95229697.008619013163120.865706365296273.151531662
96229697.008619013160160.530041828299233.487196199

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 229697.008619013 & 209622.339824105 & 249771.677413922 \tabularnewline
86 & 229697.008619013 & 201308.078117579 & 258085.939120448 \tabularnewline
87 & 229697.008619013 & 194928.194678856 & 264465.822559171 \tabularnewline
88 & 229697.008619013 & 189549.661625777 & 269844.355612249 \tabularnewline
89 & 229697.008619013 & 184811.058496672 & 274582.958741355 \tabularnewline
90 & 229697.008619013 & 180527.022182414 & 278866.995055612 \tabularnewline
91 & 229697.008619013 & 176587.436845506 & 282806.580392521 \tabularnewline
92 & 229697.008619013 & 172920.555209564 & 286473.462028462 \tabularnewline
93 & 229697.008619013 & 169476.541088901 & 289917.476149126 \tabularnewline
94 & 229697.008619013 & 166219.108863781 & 293174.908374246 \tabularnewline
95 & 229697.008619013 & 163120.865706365 & 296273.151531662 \tabularnewline
96 & 229697.008619013 & 160160.530041828 & 299233.487196199 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284536&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]85[/C][C]229697.008619013[/C][C]209622.339824105[/C][C]249771.677413922[/C][/ROW]
[ROW][C]86[/C][C]229697.008619013[/C][C]201308.078117579[/C][C]258085.939120448[/C][/ROW]
[ROW][C]87[/C][C]229697.008619013[/C][C]194928.194678856[/C][C]264465.822559171[/C][/ROW]
[ROW][C]88[/C][C]229697.008619013[/C][C]189549.661625777[/C][C]269844.355612249[/C][/ROW]
[ROW][C]89[/C][C]229697.008619013[/C][C]184811.058496672[/C][C]274582.958741355[/C][/ROW]
[ROW][C]90[/C][C]229697.008619013[/C][C]180527.022182414[/C][C]278866.995055612[/C][/ROW]
[ROW][C]91[/C][C]229697.008619013[/C][C]176587.436845506[/C][C]282806.580392521[/C][/ROW]
[ROW][C]92[/C][C]229697.008619013[/C][C]172920.555209564[/C][C]286473.462028462[/C][/ROW]
[ROW][C]93[/C][C]229697.008619013[/C][C]169476.541088901[/C][C]289917.476149126[/C][/ROW]
[ROW][C]94[/C][C]229697.008619013[/C][C]166219.108863781[/C][C]293174.908374246[/C][/ROW]
[ROW][C]95[/C][C]229697.008619013[/C][C]163120.865706365[/C][C]296273.151531662[/C][/ROW]
[ROW][C]96[/C][C]229697.008619013[/C][C]160160.530041828[/C][C]299233.487196199[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284536&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284536&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
85229697.008619013209622.339824105249771.677413922
86229697.008619013201308.078117579258085.939120448
87229697.008619013194928.194678856264465.822559171
88229697.008619013189549.661625777269844.355612249
89229697.008619013184811.058496672274582.958741355
90229697.008619013180527.022182414278866.995055612
91229697.008619013176587.436845506282806.580392521
92229697.008619013172920.555209564286473.462028462
93229697.008619013169476.541088901289917.476149126
94229697.008619013166219.108863781293174.908374246
95229697.008619013163120.865706365296273.151531662
96229697.008619013160160.530041828299233.487196199



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