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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 02 Apr 2015 16:07:30 +0100
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/Apr/02/t1427987282tl41bzjphkq6rvy.htm/, Retrieved Thu, 09 May 2024 05:30:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278567, Retrieved Thu, 09 May 2024 05:30:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact108
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-04-02 15:07:30] [9baff654455058ed055e965df18e01ff] [Current]
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Dataseries X:
304040
307100
304330
294710
286890
279050
271860
266710
259590
253830
250640
249140
250840
247590
237830
226380
217230
211420
207620
204310
197490
193580
192330
191970
196070
191940
185620
179410
173920
169190
166840
165170
161450
160830
163670
170830
182690
190940
197770
205090
210720
220210
229730
237070
241620
250370
258570
269860
283220
289610
281770
274700
267650
261380
260500
260730
254200
250450
253380
263740
276240
273820
265890
258400
253520
250710
252850
255260
251170
252500
257780
269900
291590
298870
295570
292100
290870
290580
297970
304010
304340
309850
322320
340170
369280
376690
379700
379520
377770
381560
394580
399320
400370
408200
419070
437730




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278567&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278567&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278567&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999926304594892
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999926304594892 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278567&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]0.999926304594892[/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=278567&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278567&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
alpha0.999926304594892
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
23071003040403060
3304330307099.77449206-2769.77449206036
4294710304330.204119653-9620.20411965327
5286890294710.70896484-7820.70896483981
6279050286890.576350315-7840.57635031542
7271860279050.57781445-7190.57781445037
8266710271860.529912545-5150.529912545
9259590266710.379570388-7120.37957038841
10253830259590.524739257-5760.52473925694
11250640253830.424524204-3190.42452420431
12249140250640.235119628-1500.23511962776
13250840249140.1105604351699.8894395651
14247590250839.874725959-3249.87472595912
15237830247590.239500834-9760.23950083446
16226380237830.719284804-11450.719284804
17217230226380.843865396-9150.84386539648
18211420217230.674375146-5810.67437514573
19207620211420.428220002-3800.42822000201
20204310207620.280074097-3310.28007409725
21197490204310.243952431-6820.2439524311
22193580197490.502620641-3910.50262064103
23192330193580.288186075-1250.28818607482
24191970192330.092140494-360.09214049438
25196070191970.0265371364099.97346286383
26191940196069.697850795-4129.69785079471
27185620191940.304339756-6320.30433975608
28179410185620.465777389-6210.46577738872
29173920179410.457682791-5490.4576827914
30169190173920.404621503-4730.40462150317
31166840169190.348609085-2350.3486090849
32165170166840.173209893-1670.17320989291
33161450165170.123084091-3720.12308409132
34160830161450.274155978-620.274155977735
35163670160830.0457113552839.95428864477
36170830163669.7907084187160.20929158179
37182690170829.47232547611860.5276745244
38190940182689.1259336088250.87406639179
39197770190939.3919484936830.60805150683
40205090197769.4966155737320.50338442749
41210720205089.4605125385630.53948746249
42220210210719.5850551119490.4149448885
43229730220209.3006000269520.69939997399
44237070229729.2983682017340.70163179919
45241620237069.4590240194550.54097598052
46250370241619.6646460398750.33535396069
47258570250369.3551404918200.64485950873
48269860258569.39565015511290.6043498451
49283220269859.16793433913360.8320656614
50289610283219.0153680686390.98463193164
51281770289609.529013799-7839.52901379851
52274700281770.577737267-7070.57773726655
53267650274700.521069091-7050.5210690907
54261380267650.519591006-6270.51959100639
55260500261380.462108482-880.462108481501
56260730260500.064886012229.935113988235
57254200260729.983054839-6529.98305483864
58250450254200.481229747-3750.48122974657
59253380250450.2763932342929.72360676641
60263740253379.78409283210360.2159071681
61276240263739.23649969212500.7635003083
62273820276239.07875117-2419.07875116967
63265890273820.178274989-7930.17827498855
64258400265890.584417701-7490.58441770053
65253520258400.552021653-4880.55202165316
66250710253520.359674258-2810.35967425839
67252850250710.2071105952139.7928894053
68255260252849.8423070962410.15769290383
69251170255259.822382452-4089.82238245246
70252500251170.3014011171329.69859888271
71257780252499.9020073235280.09799267692
72269900257779.61088103912120.3891189606
73291590269899.10678301421690.8932169862
74298870291588.4014808377281.5985191628
75295570298869.463379647-3299.46337964729
76292100295570.24315529-3470.24315529043
77290870292100.255740975-1230.2557409752
78290580290870.090664195-290.090664195188
79297970290580.0213783497389.97862165095
80304010297969.4553925326040.54460746824
81304340304009.554839618330.445160381903
82309850304339.975647715510.02435228997
83322320309849.59393652312470.4060634768
84340170322319.08098837317850.9190116267
85369280340168.68446929229111.3155307081
86376690369277.8546298097412.14537019125
87379700376689.4537589443010.54624105577
88379520379699.778136575-179.778136575129
89377770379520.013248823-1750.01324882259
90381560377770.1289679353789.87103206472
91394580381559.72070391913020.279296081
92399320394579.0404652434740.95953475736
93400370399319.6506130661050.34938693355
94408200400369.9225940767830.07740592357
95419070408199.42295927410870.5770407264
96437730419069.19888842118660.8011115788

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 307100 & 304040 & 3060 \tabularnewline
3 & 304330 & 307099.77449206 & -2769.77449206036 \tabularnewline
4 & 294710 & 304330.204119653 & -9620.20411965327 \tabularnewline
5 & 286890 & 294710.70896484 & -7820.70896483981 \tabularnewline
6 & 279050 & 286890.576350315 & -7840.57635031542 \tabularnewline
7 & 271860 & 279050.57781445 & -7190.57781445037 \tabularnewline
8 & 266710 & 271860.529912545 & -5150.529912545 \tabularnewline
9 & 259590 & 266710.379570388 & -7120.37957038841 \tabularnewline
10 & 253830 & 259590.524739257 & -5760.52473925694 \tabularnewline
11 & 250640 & 253830.424524204 & -3190.42452420431 \tabularnewline
12 & 249140 & 250640.235119628 & -1500.23511962776 \tabularnewline
13 & 250840 & 249140.110560435 & 1699.8894395651 \tabularnewline
14 & 247590 & 250839.874725959 & -3249.87472595912 \tabularnewline
15 & 237830 & 247590.239500834 & -9760.23950083446 \tabularnewline
16 & 226380 & 237830.719284804 & -11450.719284804 \tabularnewline
17 & 217230 & 226380.843865396 & -9150.84386539648 \tabularnewline
18 & 211420 & 217230.674375146 & -5810.67437514573 \tabularnewline
19 & 207620 & 211420.428220002 & -3800.42822000201 \tabularnewline
20 & 204310 & 207620.280074097 & -3310.28007409725 \tabularnewline
21 & 197490 & 204310.243952431 & -6820.2439524311 \tabularnewline
22 & 193580 & 197490.502620641 & -3910.50262064103 \tabularnewline
23 & 192330 & 193580.288186075 & -1250.28818607482 \tabularnewline
24 & 191970 & 192330.092140494 & -360.09214049438 \tabularnewline
25 & 196070 & 191970.026537136 & 4099.97346286383 \tabularnewline
26 & 191940 & 196069.697850795 & -4129.69785079471 \tabularnewline
27 & 185620 & 191940.304339756 & -6320.30433975608 \tabularnewline
28 & 179410 & 185620.465777389 & -6210.46577738872 \tabularnewline
29 & 173920 & 179410.457682791 & -5490.4576827914 \tabularnewline
30 & 169190 & 173920.404621503 & -4730.40462150317 \tabularnewline
31 & 166840 & 169190.348609085 & -2350.3486090849 \tabularnewline
32 & 165170 & 166840.173209893 & -1670.17320989291 \tabularnewline
33 & 161450 & 165170.123084091 & -3720.12308409132 \tabularnewline
34 & 160830 & 161450.274155978 & -620.274155977735 \tabularnewline
35 & 163670 & 160830.045711355 & 2839.95428864477 \tabularnewline
36 & 170830 & 163669.790708418 & 7160.20929158179 \tabularnewline
37 & 182690 & 170829.472325476 & 11860.5276745244 \tabularnewline
38 & 190940 & 182689.125933608 & 8250.87406639179 \tabularnewline
39 & 197770 & 190939.391948493 & 6830.60805150683 \tabularnewline
40 & 205090 & 197769.496615573 & 7320.50338442749 \tabularnewline
41 & 210720 & 205089.460512538 & 5630.53948746249 \tabularnewline
42 & 220210 & 210719.585055111 & 9490.4149448885 \tabularnewline
43 & 229730 & 220209.300600026 & 9520.69939997399 \tabularnewline
44 & 237070 & 229729.298368201 & 7340.70163179919 \tabularnewline
45 & 241620 & 237069.459024019 & 4550.54097598052 \tabularnewline
46 & 250370 & 241619.664646039 & 8750.33535396069 \tabularnewline
47 & 258570 & 250369.355140491 & 8200.64485950873 \tabularnewline
48 & 269860 & 258569.395650155 & 11290.6043498451 \tabularnewline
49 & 283220 & 269859.167934339 & 13360.8320656614 \tabularnewline
50 & 289610 & 283219.015368068 & 6390.98463193164 \tabularnewline
51 & 281770 & 289609.529013799 & -7839.52901379851 \tabularnewline
52 & 274700 & 281770.577737267 & -7070.57773726655 \tabularnewline
53 & 267650 & 274700.521069091 & -7050.5210690907 \tabularnewline
54 & 261380 & 267650.519591006 & -6270.51959100639 \tabularnewline
55 & 260500 & 261380.462108482 & -880.462108481501 \tabularnewline
56 & 260730 & 260500.064886012 & 229.935113988235 \tabularnewline
57 & 254200 & 260729.983054839 & -6529.98305483864 \tabularnewline
58 & 250450 & 254200.481229747 & -3750.48122974657 \tabularnewline
59 & 253380 & 250450.276393234 & 2929.72360676641 \tabularnewline
60 & 263740 & 253379.784092832 & 10360.2159071681 \tabularnewline
61 & 276240 & 263739.236499692 & 12500.7635003083 \tabularnewline
62 & 273820 & 276239.07875117 & -2419.07875116967 \tabularnewline
63 & 265890 & 273820.178274989 & -7930.17827498855 \tabularnewline
64 & 258400 & 265890.584417701 & -7490.58441770053 \tabularnewline
65 & 253520 & 258400.552021653 & -4880.55202165316 \tabularnewline
66 & 250710 & 253520.359674258 & -2810.35967425839 \tabularnewline
67 & 252850 & 250710.207110595 & 2139.7928894053 \tabularnewline
68 & 255260 & 252849.842307096 & 2410.15769290383 \tabularnewline
69 & 251170 & 255259.822382452 & -4089.82238245246 \tabularnewline
70 & 252500 & 251170.301401117 & 1329.69859888271 \tabularnewline
71 & 257780 & 252499.902007323 & 5280.09799267692 \tabularnewline
72 & 269900 & 257779.610881039 & 12120.3891189606 \tabularnewline
73 & 291590 & 269899.106783014 & 21690.8932169862 \tabularnewline
74 & 298870 & 291588.401480837 & 7281.5985191628 \tabularnewline
75 & 295570 & 298869.463379647 & -3299.46337964729 \tabularnewline
76 & 292100 & 295570.24315529 & -3470.24315529043 \tabularnewline
77 & 290870 & 292100.255740975 & -1230.2557409752 \tabularnewline
78 & 290580 & 290870.090664195 & -290.090664195188 \tabularnewline
79 & 297970 & 290580.021378349 & 7389.97862165095 \tabularnewline
80 & 304010 & 297969.455392532 & 6040.54460746824 \tabularnewline
81 & 304340 & 304009.554839618 & 330.445160381903 \tabularnewline
82 & 309850 & 304339.97564771 & 5510.02435228997 \tabularnewline
83 & 322320 & 309849.593936523 & 12470.4060634768 \tabularnewline
84 & 340170 & 322319.080988373 & 17850.9190116267 \tabularnewline
85 & 369280 & 340168.684469292 & 29111.3155307081 \tabularnewline
86 & 376690 & 369277.854629809 & 7412.14537019125 \tabularnewline
87 & 379700 & 376689.453758944 & 3010.54624105577 \tabularnewline
88 & 379520 & 379699.778136575 & -179.778136575129 \tabularnewline
89 & 377770 & 379520.013248823 & -1750.01324882259 \tabularnewline
90 & 381560 & 377770.128967935 & 3789.87103206472 \tabularnewline
91 & 394580 & 381559.720703919 & 13020.279296081 \tabularnewline
92 & 399320 & 394579.040465243 & 4740.95953475736 \tabularnewline
93 & 400370 & 399319.650613066 & 1050.34938693355 \tabularnewline
94 & 408200 & 400369.922594076 & 7830.07740592357 \tabularnewline
95 & 419070 & 408199.422959274 & 10870.5770407264 \tabularnewline
96 & 437730 & 419069.198888421 & 18660.8011115788 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278567&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]307100[/C][C]304040[/C][C]3060[/C][/ROW]
[ROW][C]3[/C][C]304330[/C][C]307099.77449206[/C][C]-2769.77449206036[/C][/ROW]
[ROW][C]4[/C][C]294710[/C][C]304330.204119653[/C][C]-9620.20411965327[/C][/ROW]
[ROW][C]5[/C][C]286890[/C][C]294710.70896484[/C][C]-7820.70896483981[/C][/ROW]
[ROW][C]6[/C][C]279050[/C][C]286890.576350315[/C][C]-7840.57635031542[/C][/ROW]
[ROW][C]7[/C][C]271860[/C][C]279050.57781445[/C][C]-7190.57781445037[/C][/ROW]
[ROW][C]8[/C][C]266710[/C][C]271860.529912545[/C][C]-5150.529912545[/C][/ROW]
[ROW][C]9[/C][C]259590[/C][C]266710.379570388[/C][C]-7120.37957038841[/C][/ROW]
[ROW][C]10[/C][C]253830[/C][C]259590.524739257[/C][C]-5760.52473925694[/C][/ROW]
[ROW][C]11[/C][C]250640[/C][C]253830.424524204[/C][C]-3190.42452420431[/C][/ROW]
[ROW][C]12[/C][C]249140[/C][C]250640.235119628[/C][C]-1500.23511962776[/C][/ROW]
[ROW][C]13[/C][C]250840[/C][C]249140.110560435[/C][C]1699.8894395651[/C][/ROW]
[ROW][C]14[/C][C]247590[/C][C]250839.874725959[/C][C]-3249.87472595912[/C][/ROW]
[ROW][C]15[/C][C]237830[/C][C]247590.239500834[/C][C]-9760.23950083446[/C][/ROW]
[ROW][C]16[/C][C]226380[/C][C]237830.719284804[/C][C]-11450.719284804[/C][/ROW]
[ROW][C]17[/C][C]217230[/C][C]226380.843865396[/C][C]-9150.84386539648[/C][/ROW]
[ROW][C]18[/C][C]211420[/C][C]217230.674375146[/C][C]-5810.67437514573[/C][/ROW]
[ROW][C]19[/C][C]207620[/C][C]211420.428220002[/C][C]-3800.42822000201[/C][/ROW]
[ROW][C]20[/C][C]204310[/C][C]207620.280074097[/C][C]-3310.28007409725[/C][/ROW]
[ROW][C]21[/C][C]197490[/C][C]204310.243952431[/C][C]-6820.2439524311[/C][/ROW]
[ROW][C]22[/C][C]193580[/C][C]197490.502620641[/C][C]-3910.50262064103[/C][/ROW]
[ROW][C]23[/C][C]192330[/C][C]193580.288186075[/C][C]-1250.28818607482[/C][/ROW]
[ROW][C]24[/C][C]191970[/C][C]192330.092140494[/C][C]-360.09214049438[/C][/ROW]
[ROW][C]25[/C][C]196070[/C][C]191970.026537136[/C][C]4099.97346286383[/C][/ROW]
[ROW][C]26[/C][C]191940[/C][C]196069.697850795[/C][C]-4129.69785079471[/C][/ROW]
[ROW][C]27[/C][C]185620[/C][C]191940.304339756[/C][C]-6320.30433975608[/C][/ROW]
[ROW][C]28[/C][C]179410[/C][C]185620.465777389[/C][C]-6210.46577738872[/C][/ROW]
[ROW][C]29[/C][C]173920[/C][C]179410.457682791[/C][C]-5490.4576827914[/C][/ROW]
[ROW][C]30[/C][C]169190[/C][C]173920.404621503[/C][C]-4730.40462150317[/C][/ROW]
[ROW][C]31[/C][C]166840[/C][C]169190.348609085[/C][C]-2350.3486090849[/C][/ROW]
[ROW][C]32[/C][C]165170[/C][C]166840.173209893[/C][C]-1670.17320989291[/C][/ROW]
[ROW][C]33[/C][C]161450[/C][C]165170.123084091[/C][C]-3720.12308409132[/C][/ROW]
[ROW][C]34[/C][C]160830[/C][C]161450.274155978[/C][C]-620.274155977735[/C][/ROW]
[ROW][C]35[/C][C]163670[/C][C]160830.045711355[/C][C]2839.95428864477[/C][/ROW]
[ROW][C]36[/C][C]170830[/C][C]163669.790708418[/C][C]7160.20929158179[/C][/ROW]
[ROW][C]37[/C][C]182690[/C][C]170829.472325476[/C][C]11860.5276745244[/C][/ROW]
[ROW][C]38[/C][C]190940[/C][C]182689.125933608[/C][C]8250.87406639179[/C][/ROW]
[ROW][C]39[/C][C]197770[/C][C]190939.391948493[/C][C]6830.60805150683[/C][/ROW]
[ROW][C]40[/C][C]205090[/C][C]197769.496615573[/C][C]7320.50338442749[/C][/ROW]
[ROW][C]41[/C][C]210720[/C][C]205089.460512538[/C][C]5630.53948746249[/C][/ROW]
[ROW][C]42[/C][C]220210[/C][C]210719.585055111[/C][C]9490.4149448885[/C][/ROW]
[ROW][C]43[/C][C]229730[/C][C]220209.300600026[/C][C]9520.69939997399[/C][/ROW]
[ROW][C]44[/C][C]237070[/C][C]229729.298368201[/C][C]7340.70163179919[/C][/ROW]
[ROW][C]45[/C][C]241620[/C][C]237069.459024019[/C][C]4550.54097598052[/C][/ROW]
[ROW][C]46[/C][C]250370[/C][C]241619.664646039[/C][C]8750.33535396069[/C][/ROW]
[ROW][C]47[/C][C]258570[/C][C]250369.355140491[/C][C]8200.64485950873[/C][/ROW]
[ROW][C]48[/C][C]269860[/C][C]258569.395650155[/C][C]11290.6043498451[/C][/ROW]
[ROW][C]49[/C][C]283220[/C][C]269859.167934339[/C][C]13360.8320656614[/C][/ROW]
[ROW][C]50[/C][C]289610[/C][C]283219.015368068[/C][C]6390.98463193164[/C][/ROW]
[ROW][C]51[/C][C]281770[/C][C]289609.529013799[/C][C]-7839.52901379851[/C][/ROW]
[ROW][C]52[/C][C]274700[/C][C]281770.577737267[/C][C]-7070.57773726655[/C][/ROW]
[ROW][C]53[/C][C]267650[/C][C]274700.521069091[/C][C]-7050.5210690907[/C][/ROW]
[ROW][C]54[/C][C]261380[/C][C]267650.519591006[/C][C]-6270.51959100639[/C][/ROW]
[ROW][C]55[/C][C]260500[/C][C]261380.462108482[/C][C]-880.462108481501[/C][/ROW]
[ROW][C]56[/C][C]260730[/C][C]260500.064886012[/C][C]229.935113988235[/C][/ROW]
[ROW][C]57[/C][C]254200[/C][C]260729.983054839[/C][C]-6529.98305483864[/C][/ROW]
[ROW][C]58[/C][C]250450[/C][C]254200.481229747[/C][C]-3750.48122974657[/C][/ROW]
[ROW][C]59[/C][C]253380[/C][C]250450.276393234[/C][C]2929.72360676641[/C][/ROW]
[ROW][C]60[/C][C]263740[/C][C]253379.784092832[/C][C]10360.2159071681[/C][/ROW]
[ROW][C]61[/C][C]276240[/C][C]263739.236499692[/C][C]12500.7635003083[/C][/ROW]
[ROW][C]62[/C][C]273820[/C][C]276239.07875117[/C][C]-2419.07875116967[/C][/ROW]
[ROW][C]63[/C][C]265890[/C][C]273820.178274989[/C][C]-7930.17827498855[/C][/ROW]
[ROW][C]64[/C][C]258400[/C][C]265890.584417701[/C][C]-7490.58441770053[/C][/ROW]
[ROW][C]65[/C][C]253520[/C][C]258400.552021653[/C][C]-4880.55202165316[/C][/ROW]
[ROW][C]66[/C][C]250710[/C][C]253520.359674258[/C][C]-2810.35967425839[/C][/ROW]
[ROW][C]67[/C][C]252850[/C][C]250710.207110595[/C][C]2139.7928894053[/C][/ROW]
[ROW][C]68[/C][C]255260[/C][C]252849.842307096[/C][C]2410.15769290383[/C][/ROW]
[ROW][C]69[/C][C]251170[/C][C]255259.822382452[/C][C]-4089.82238245246[/C][/ROW]
[ROW][C]70[/C][C]252500[/C][C]251170.301401117[/C][C]1329.69859888271[/C][/ROW]
[ROW][C]71[/C][C]257780[/C][C]252499.902007323[/C][C]5280.09799267692[/C][/ROW]
[ROW][C]72[/C][C]269900[/C][C]257779.610881039[/C][C]12120.3891189606[/C][/ROW]
[ROW][C]73[/C][C]291590[/C][C]269899.106783014[/C][C]21690.8932169862[/C][/ROW]
[ROW][C]74[/C][C]298870[/C][C]291588.401480837[/C][C]7281.5985191628[/C][/ROW]
[ROW][C]75[/C][C]295570[/C][C]298869.463379647[/C][C]-3299.46337964729[/C][/ROW]
[ROW][C]76[/C][C]292100[/C][C]295570.24315529[/C][C]-3470.24315529043[/C][/ROW]
[ROW][C]77[/C][C]290870[/C][C]292100.255740975[/C][C]-1230.2557409752[/C][/ROW]
[ROW][C]78[/C][C]290580[/C][C]290870.090664195[/C][C]-290.090664195188[/C][/ROW]
[ROW][C]79[/C][C]297970[/C][C]290580.021378349[/C][C]7389.97862165095[/C][/ROW]
[ROW][C]80[/C][C]304010[/C][C]297969.455392532[/C][C]6040.54460746824[/C][/ROW]
[ROW][C]81[/C][C]304340[/C][C]304009.554839618[/C][C]330.445160381903[/C][/ROW]
[ROW][C]82[/C][C]309850[/C][C]304339.97564771[/C][C]5510.02435228997[/C][/ROW]
[ROW][C]83[/C][C]322320[/C][C]309849.593936523[/C][C]12470.4060634768[/C][/ROW]
[ROW][C]84[/C][C]340170[/C][C]322319.080988373[/C][C]17850.9190116267[/C][/ROW]
[ROW][C]85[/C][C]369280[/C][C]340168.684469292[/C][C]29111.3155307081[/C][/ROW]
[ROW][C]86[/C][C]376690[/C][C]369277.854629809[/C][C]7412.14537019125[/C][/ROW]
[ROW][C]87[/C][C]379700[/C][C]376689.453758944[/C][C]3010.54624105577[/C][/ROW]
[ROW][C]88[/C][C]379520[/C][C]379699.778136575[/C][C]-179.778136575129[/C][/ROW]
[ROW][C]89[/C][C]377770[/C][C]379520.013248823[/C][C]-1750.01324882259[/C][/ROW]
[ROW][C]90[/C][C]381560[/C][C]377770.128967935[/C][C]3789.87103206472[/C][/ROW]
[ROW][C]91[/C][C]394580[/C][C]381559.720703919[/C][C]13020.279296081[/C][/ROW]
[ROW][C]92[/C][C]399320[/C][C]394579.040465243[/C][C]4740.95953475736[/C][/ROW]
[ROW][C]93[/C][C]400370[/C][C]399319.650613066[/C][C]1050.34938693355[/C][/ROW]
[ROW][C]94[/C][C]408200[/C][C]400369.922594076[/C][C]7830.07740592357[/C][/ROW]
[ROW][C]95[/C][C]419070[/C][C]408199.422959274[/C][C]10870.5770407264[/C][/ROW]
[ROW][C]96[/C][C]437730[/C][C]419069.198888421[/C][C]18660.8011115788[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278567&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278567&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
23071003040403060
3304330307099.77449206-2769.77449206036
4294710304330.204119653-9620.20411965327
5286890294710.70896484-7820.70896483981
6279050286890.576350315-7840.57635031542
7271860279050.57781445-7190.57781445037
8266710271860.529912545-5150.529912545
9259590266710.379570388-7120.37957038841
10253830259590.524739257-5760.52473925694
11250640253830.424524204-3190.42452420431
12249140250640.235119628-1500.23511962776
13250840249140.1105604351699.8894395651
14247590250839.874725959-3249.87472595912
15237830247590.239500834-9760.23950083446
16226380237830.719284804-11450.719284804
17217230226380.843865396-9150.84386539648
18211420217230.674375146-5810.67437514573
19207620211420.428220002-3800.42822000201
20204310207620.280074097-3310.28007409725
21197490204310.243952431-6820.2439524311
22193580197490.502620641-3910.50262064103
23192330193580.288186075-1250.28818607482
24191970192330.092140494-360.09214049438
25196070191970.0265371364099.97346286383
26191940196069.697850795-4129.69785079471
27185620191940.304339756-6320.30433975608
28179410185620.465777389-6210.46577738872
29173920179410.457682791-5490.4576827914
30169190173920.404621503-4730.40462150317
31166840169190.348609085-2350.3486090849
32165170166840.173209893-1670.17320989291
33161450165170.123084091-3720.12308409132
34160830161450.274155978-620.274155977735
35163670160830.0457113552839.95428864477
36170830163669.7907084187160.20929158179
37182690170829.47232547611860.5276745244
38190940182689.1259336088250.87406639179
39197770190939.3919484936830.60805150683
40205090197769.4966155737320.50338442749
41210720205089.4605125385630.53948746249
42220210210719.5850551119490.4149448885
43229730220209.3006000269520.69939997399
44237070229729.2983682017340.70163179919
45241620237069.4590240194550.54097598052
46250370241619.6646460398750.33535396069
47258570250369.3551404918200.64485950873
48269860258569.39565015511290.6043498451
49283220269859.16793433913360.8320656614
50289610283219.0153680686390.98463193164
51281770289609.529013799-7839.52901379851
52274700281770.577737267-7070.57773726655
53267650274700.521069091-7050.5210690907
54261380267650.519591006-6270.51959100639
55260500261380.462108482-880.462108481501
56260730260500.064886012229.935113988235
57254200260729.983054839-6529.98305483864
58250450254200.481229747-3750.48122974657
59253380250450.2763932342929.72360676641
60263740253379.78409283210360.2159071681
61276240263739.23649969212500.7635003083
62273820276239.07875117-2419.07875116967
63265890273820.178274989-7930.17827498855
64258400265890.584417701-7490.58441770053
65253520258400.552021653-4880.55202165316
66250710253520.359674258-2810.35967425839
67252850250710.2071105952139.7928894053
68255260252849.8423070962410.15769290383
69251170255259.822382452-4089.82238245246
70252500251170.3014011171329.69859888271
71257780252499.9020073235280.09799267692
72269900257779.61088103912120.3891189606
73291590269899.10678301421690.8932169862
74298870291588.4014808377281.5985191628
75295570298869.463379647-3299.46337964729
76292100295570.24315529-3470.24315529043
77290870292100.255740975-1230.2557409752
78290580290870.090664195-290.090664195188
79297970290580.0213783497389.97862165095
80304010297969.4553925326040.54460746824
81304340304009.554839618330.445160381903
82309850304339.975647715510.02435228997
83322320309849.59393652312470.4060634768
84340170322319.08098837317850.9190116267
85369280340168.68446929229111.3155307081
86376690369277.8546298097412.14537019125
87379700376689.4537589443010.54624105577
88379520379699.778136575-179.778136575129
89377770379520.013248823-1750.01324882259
90381560377770.1289679353789.87103206472
91394580381559.72070391913020.279296081
92399320394579.0404652434740.95953475736
93400370399319.6506130661050.34938693355
94408200400369.9225940767830.07740592357
95419070408199.42295927410870.5770407264
96437730419069.19888842118660.8011115788







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
97437728.624784702422490.078677168452967.170892237
98437728.624784702416178.860282521459278.389286884
99437728.624784702411335.985418253464121.264151152
100437728.624784702407253.217070358468204.032499046
101437728.624784702403656.208698027471801.040871378
102437728.624784702400404.254721545475052.99484786
103437728.624784702397413.768177745478043.48139166
104437728.624784702394630.286929658480826.962639747
105437728.624784702392015.981145381483441.268424024
106437728.624784702389543.306988473485913.942580932
107437728.624784702387191.470989187488265.778580218
108437728.624784702384944.318628614490512.930940791

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 437728.624784702 & 422490.078677168 & 452967.170892237 \tabularnewline
98 & 437728.624784702 & 416178.860282521 & 459278.389286884 \tabularnewline
99 & 437728.624784702 & 411335.985418253 & 464121.264151152 \tabularnewline
100 & 437728.624784702 & 407253.217070358 & 468204.032499046 \tabularnewline
101 & 437728.624784702 & 403656.208698027 & 471801.040871378 \tabularnewline
102 & 437728.624784702 & 400404.254721545 & 475052.99484786 \tabularnewline
103 & 437728.624784702 & 397413.768177745 & 478043.48139166 \tabularnewline
104 & 437728.624784702 & 394630.286929658 & 480826.962639747 \tabularnewline
105 & 437728.624784702 & 392015.981145381 & 483441.268424024 \tabularnewline
106 & 437728.624784702 & 389543.306988473 & 485913.942580932 \tabularnewline
107 & 437728.624784702 & 387191.470989187 & 488265.778580218 \tabularnewline
108 & 437728.624784702 & 384944.318628614 & 490512.930940791 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278567&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]97[/C][C]437728.624784702[/C][C]422490.078677168[/C][C]452967.170892237[/C][/ROW]
[ROW][C]98[/C][C]437728.624784702[/C][C]416178.860282521[/C][C]459278.389286884[/C][/ROW]
[ROW][C]99[/C][C]437728.624784702[/C][C]411335.985418253[/C][C]464121.264151152[/C][/ROW]
[ROW][C]100[/C][C]437728.624784702[/C][C]407253.217070358[/C][C]468204.032499046[/C][/ROW]
[ROW][C]101[/C][C]437728.624784702[/C][C]403656.208698027[/C][C]471801.040871378[/C][/ROW]
[ROW][C]102[/C][C]437728.624784702[/C][C]400404.254721545[/C][C]475052.99484786[/C][/ROW]
[ROW][C]103[/C][C]437728.624784702[/C][C]397413.768177745[/C][C]478043.48139166[/C][/ROW]
[ROW][C]104[/C][C]437728.624784702[/C][C]394630.286929658[/C][C]480826.962639747[/C][/ROW]
[ROW][C]105[/C][C]437728.624784702[/C][C]392015.981145381[/C][C]483441.268424024[/C][/ROW]
[ROW][C]106[/C][C]437728.624784702[/C][C]389543.306988473[/C][C]485913.942580932[/C][/ROW]
[ROW][C]107[/C][C]437728.624784702[/C][C]387191.470989187[/C][C]488265.778580218[/C][/ROW]
[ROW][C]108[/C][C]437728.624784702[/C][C]384944.318628614[/C][C]490512.930940791[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278567&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278567&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
97437728.624784702422490.078677168452967.170892237
98437728.624784702416178.860282521459278.389286884
99437728.624784702411335.985418253464121.264151152
100437728.624784702407253.217070358468204.032499046
101437728.624784702403656.208698027471801.040871378
102437728.624784702400404.254721545475052.99484786
103437728.624784702397413.768177745478043.48139166
104437728.624784702394630.286929658480826.962639747
105437728.624784702392015.981145381483441.268424024
106437728.624784702389543.306988473485913.942580932
107437728.624784702387191.470989187488265.778580218
108437728.624784702384944.318628614490512.930940791



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')