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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 19 May 2011 19:16:56 +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/May/19/t1305832410ftq0lxdgkw29s9g.htm/, Retrieved Sat, 11 May 2024 06:04:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=122207, Retrieved Sat, 11 May 2024 06:04:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact94
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [inflation in cons...] [2011-05-19 19:16:56] [5e78ed906b09bab42b8ec3dd93b6358a] [Current]
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Dataseries X:
0.440
0.548
0.163
0.381
0.164
0.109
0.328
0.435
0.325
0.108
0.054
0.270
0.431
0.215
0.214
0.160
0.427
0.372
0.106
0.053
0.317
0.527
0.472
0.001
0.051
0.418
0.364
0.311
0.052
0.052
0.620
0.616
1.377
0.151
0.501
0.001
0.606
0.050
0.150
0.501
0.299
0.248
0.545
0.444
0.491
0.444
0.050
0.545
0.138
0.423
0.495
0.370
0.388
0.169
0.241
0.014
0.376
0.331
0.789
0.289
0.359
0.236
0.367
0.309
0.551
0.901
0.870
0.160
0.032
0.877
1.812
0.784
0.270
0.462
0.146
0.108
0.132
0.680
0.117
0.345
0.204
0.227
0.236
0.092
0.138
0.046
0.023
0.009
0.142
0.207
0.346
0.207
0.165
0.247
0.123
0.433




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ www.yougetit.org

\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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ www.yougetit.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122207&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ www.yougetit.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122207&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122207&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 time1 seconds
R Server'Herman Ole Andreas Wold' @ www.yougetit.org







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0
beta0
gamma0.144366894147601

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.144366894147601 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122207&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[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.144366894147601[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122207&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122207&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
beta0
gamma0.144366894147601







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
130.4310.3863238063091580.0446761936908425
140.2150.2129791805050960.00202081949490351
150.2140.22752494958839-0.0135249495883902
160.160.1584854983252490.00151450167475148
170.4270.370848190860210.0561518091397898
180.3720.3166160137288860.0553839862711142
190.1060.288834925031666-0.182834925031666
200.0530.404561238766747-0.351561238766747
210.3170.3169756731608552.43268391449947e-05
220.5270.1085845142551590.418415485744841
230.4720.05399863424854370.418001365751456
240.0010.248284557096173-0.247284557096173
250.0510.401086340442924-0.350086340442924
260.4180.2177766991510860.200223300848914
270.3640.2303296917227750.133670308277225
280.3110.1620453231130630.148954676886937
290.0520.38691877155086-0.33491877155086
300.0520.331421745336218-0.279421745336218
310.620.2679357995202840.352064200479716
320.6160.3612041959709190.254795804029081
331.3770.3235944834944261.05340551650557
340.1510.172510523248285-0.0215105232482846
350.5010.1167222641788450.384277735821155
360.0010.216998433463264-0.215998433463264
370.6060.3578107415993150.248189258400685
380.050.25178614889252-0.20178614889252
390.150.254783133690003-0.104783133690003
400.5010.1873340174052960.313665982594704
410.2990.345536473558083-0.0465364735580834
420.2480.297063714700177-0.0490637147001771
430.5450.3253010050534280.219698994946572
440.4440.4061383027774860.0378616972225141
450.4910.4853955987135380.0056044012864615
460.4440.1728624042516450.271137595748355
470.050.175707592952947-0.125707592952947
480.5450.189594751825420.35540524817458
490.1380.401633860459003-0.263633860459003
500.4230.2271682378717280.195831762128272
510.4950.2445056735658490.250494326434151
520.370.2373163898702150.132683610129785
530.3880.3456515350054590.0423484649945405
540.1690.295819141529303-0.126819141529303
550.2410.364194597344315-0.123194597344315
560.0140.419863992763976-0.405863992763976
570.3760.495945130248409-0.119945130248409
580.3310.2162458602615810.114754139738419
590.7890.1607055631608670.628294436839133
600.2890.2457056227251220.0432943772748776
610.3590.370809243532144-0.0118092435321445
620.2360.260514884114387-0.0245148841143871
630.3670.2862358096113170.0807641903886827
640.3090.2615502130309410.0474497869690593
650.5510.3587195046069860.192280495393014
660.9010.2829879030328760.618012096967124
670.870.3532352549510570.516764745048943
680.160.368377714245271-0.208377714245271
690.0320.488029374769362-0.456029374769362
700.8770.2373775633785690.639622436621431
711.8120.2563321112988191.55566788870118
720.7840.2568801731640050.527119826835996
730.270.3763064984068-0.1063064984068
740.4620.2619818243788540.200018175621146
750.1460.303689304048226-0.157689304048226
760.1080.273612108545154-0.165612108545154
770.1320.393970839588824-0.261970839588824
780.680.3794125047421730.300587495257827
790.1170.436106489258548-0.319106489258548
800.3450.3448215334585320.000178466541468136
810.2040.43032606610757-0.22632606610757
820.2270.336058667370351-0.10905866737035
830.2360.490152801987282-0.254152801987282
840.0920.339361877491228-0.247361877491228
850.1380.367867749660774-0.229867749660774
860.0460.29641568201754-0.25041568201754
870.0230.286283692638016-0.263283692638016
880.0090.254459507152157-0.245459507152157
890.1420.362924074480643-0.220924074480643
900.2070.430835465183252-0.223835465183252
910.3460.397432245061054-0.0514322450610543
920.2070.351374448411832-0.144374448411832
930.1650.405166842631687-0.240166842631687
940.2470.326357937097361-0.0793579370973606
950.1230.462004092043866-0.339004092043866
960.4330.309362378487950.12363762151205

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 0.431 & 0.386323806309158 & 0.0446761936908425 \tabularnewline
14 & 0.215 & 0.212979180505096 & 0.00202081949490351 \tabularnewline
15 & 0.214 & 0.22752494958839 & -0.0135249495883902 \tabularnewline
16 & 0.16 & 0.158485498325249 & 0.00151450167475148 \tabularnewline
17 & 0.427 & 0.37084819086021 & 0.0561518091397898 \tabularnewline
18 & 0.372 & 0.316616013728886 & 0.0553839862711142 \tabularnewline
19 & 0.106 & 0.288834925031666 & -0.182834925031666 \tabularnewline
20 & 0.053 & 0.404561238766747 & -0.351561238766747 \tabularnewline
21 & 0.317 & 0.316975673160855 & 2.43268391449947e-05 \tabularnewline
22 & 0.527 & 0.108584514255159 & 0.418415485744841 \tabularnewline
23 & 0.472 & 0.0539986342485437 & 0.418001365751456 \tabularnewline
24 & 0.001 & 0.248284557096173 & -0.247284557096173 \tabularnewline
25 & 0.051 & 0.401086340442924 & -0.350086340442924 \tabularnewline
26 & 0.418 & 0.217776699151086 & 0.200223300848914 \tabularnewline
27 & 0.364 & 0.230329691722775 & 0.133670308277225 \tabularnewline
28 & 0.311 & 0.162045323113063 & 0.148954676886937 \tabularnewline
29 & 0.052 & 0.38691877155086 & -0.33491877155086 \tabularnewline
30 & 0.052 & 0.331421745336218 & -0.279421745336218 \tabularnewline
31 & 0.62 & 0.267935799520284 & 0.352064200479716 \tabularnewline
32 & 0.616 & 0.361204195970919 & 0.254795804029081 \tabularnewline
33 & 1.377 & 0.323594483494426 & 1.05340551650557 \tabularnewline
34 & 0.151 & 0.172510523248285 & -0.0215105232482846 \tabularnewline
35 & 0.501 & 0.116722264178845 & 0.384277735821155 \tabularnewline
36 & 0.001 & 0.216998433463264 & -0.215998433463264 \tabularnewline
37 & 0.606 & 0.357810741599315 & 0.248189258400685 \tabularnewline
38 & 0.05 & 0.25178614889252 & -0.20178614889252 \tabularnewline
39 & 0.15 & 0.254783133690003 & -0.104783133690003 \tabularnewline
40 & 0.501 & 0.187334017405296 & 0.313665982594704 \tabularnewline
41 & 0.299 & 0.345536473558083 & -0.0465364735580834 \tabularnewline
42 & 0.248 & 0.297063714700177 & -0.0490637147001771 \tabularnewline
43 & 0.545 & 0.325301005053428 & 0.219698994946572 \tabularnewline
44 & 0.444 & 0.406138302777486 & 0.0378616972225141 \tabularnewline
45 & 0.491 & 0.485395598713538 & 0.0056044012864615 \tabularnewline
46 & 0.444 & 0.172862404251645 & 0.271137595748355 \tabularnewline
47 & 0.05 & 0.175707592952947 & -0.125707592952947 \tabularnewline
48 & 0.545 & 0.18959475182542 & 0.35540524817458 \tabularnewline
49 & 0.138 & 0.401633860459003 & -0.263633860459003 \tabularnewline
50 & 0.423 & 0.227168237871728 & 0.195831762128272 \tabularnewline
51 & 0.495 & 0.244505673565849 & 0.250494326434151 \tabularnewline
52 & 0.37 & 0.237316389870215 & 0.132683610129785 \tabularnewline
53 & 0.388 & 0.345651535005459 & 0.0423484649945405 \tabularnewline
54 & 0.169 & 0.295819141529303 & -0.126819141529303 \tabularnewline
55 & 0.241 & 0.364194597344315 & -0.123194597344315 \tabularnewline
56 & 0.014 & 0.419863992763976 & -0.405863992763976 \tabularnewline
57 & 0.376 & 0.495945130248409 & -0.119945130248409 \tabularnewline
58 & 0.331 & 0.216245860261581 & 0.114754139738419 \tabularnewline
59 & 0.789 & 0.160705563160867 & 0.628294436839133 \tabularnewline
60 & 0.289 & 0.245705622725122 & 0.0432943772748776 \tabularnewline
61 & 0.359 & 0.370809243532144 & -0.0118092435321445 \tabularnewline
62 & 0.236 & 0.260514884114387 & -0.0245148841143871 \tabularnewline
63 & 0.367 & 0.286235809611317 & 0.0807641903886827 \tabularnewline
64 & 0.309 & 0.261550213030941 & 0.0474497869690593 \tabularnewline
65 & 0.551 & 0.358719504606986 & 0.192280495393014 \tabularnewline
66 & 0.901 & 0.282987903032876 & 0.618012096967124 \tabularnewline
67 & 0.87 & 0.353235254951057 & 0.516764745048943 \tabularnewline
68 & 0.16 & 0.368377714245271 & -0.208377714245271 \tabularnewline
69 & 0.032 & 0.488029374769362 & -0.456029374769362 \tabularnewline
70 & 0.877 & 0.237377563378569 & 0.639622436621431 \tabularnewline
71 & 1.812 & 0.256332111298819 & 1.55566788870118 \tabularnewline
72 & 0.784 & 0.256880173164005 & 0.527119826835996 \tabularnewline
73 & 0.27 & 0.3763064984068 & -0.1063064984068 \tabularnewline
74 & 0.462 & 0.261981824378854 & 0.200018175621146 \tabularnewline
75 & 0.146 & 0.303689304048226 & -0.157689304048226 \tabularnewline
76 & 0.108 & 0.273612108545154 & -0.165612108545154 \tabularnewline
77 & 0.132 & 0.393970839588824 & -0.261970839588824 \tabularnewline
78 & 0.68 & 0.379412504742173 & 0.300587495257827 \tabularnewline
79 & 0.117 & 0.436106489258548 & -0.319106489258548 \tabularnewline
80 & 0.345 & 0.344821533458532 & 0.000178466541468136 \tabularnewline
81 & 0.204 & 0.43032606610757 & -0.22632606610757 \tabularnewline
82 & 0.227 & 0.336058667370351 & -0.10905866737035 \tabularnewline
83 & 0.236 & 0.490152801987282 & -0.254152801987282 \tabularnewline
84 & 0.092 & 0.339361877491228 & -0.247361877491228 \tabularnewline
85 & 0.138 & 0.367867749660774 & -0.229867749660774 \tabularnewline
86 & 0.046 & 0.29641568201754 & -0.25041568201754 \tabularnewline
87 & 0.023 & 0.286283692638016 & -0.263283692638016 \tabularnewline
88 & 0.009 & 0.254459507152157 & -0.245459507152157 \tabularnewline
89 & 0.142 & 0.362924074480643 & -0.220924074480643 \tabularnewline
90 & 0.207 & 0.430835465183252 & -0.223835465183252 \tabularnewline
91 & 0.346 & 0.397432245061054 & -0.0514322450610543 \tabularnewline
92 & 0.207 & 0.351374448411832 & -0.144374448411832 \tabularnewline
93 & 0.165 & 0.405166842631687 & -0.240166842631687 \tabularnewline
94 & 0.247 & 0.326357937097361 & -0.0793579370973606 \tabularnewline
95 & 0.123 & 0.462004092043866 & -0.339004092043866 \tabularnewline
96 & 0.433 & 0.30936237848795 & 0.12363762151205 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122207&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]0.431[/C][C]0.386323806309158[/C][C]0.0446761936908425[/C][/ROW]
[ROW][C]14[/C][C]0.215[/C][C]0.212979180505096[/C][C]0.00202081949490351[/C][/ROW]
[ROW][C]15[/C][C]0.214[/C][C]0.22752494958839[/C][C]-0.0135249495883902[/C][/ROW]
[ROW][C]16[/C][C]0.16[/C][C]0.158485498325249[/C][C]0.00151450167475148[/C][/ROW]
[ROW][C]17[/C][C]0.427[/C][C]0.37084819086021[/C][C]0.0561518091397898[/C][/ROW]
[ROW][C]18[/C][C]0.372[/C][C]0.316616013728886[/C][C]0.0553839862711142[/C][/ROW]
[ROW][C]19[/C][C]0.106[/C][C]0.288834925031666[/C][C]-0.182834925031666[/C][/ROW]
[ROW][C]20[/C][C]0.053[/C][C]0.404561238766747[/C][C]-0.351561238766747[/C][/ROW]
[ROW][C]21[/C][C]0.317[/C][C]0.316975673160855[/C][C]2.43268391449947e-05[/C][/ROW]
[ROW][C]22[/C][C]0.527[/C][C]0.108584514255159[/C][C]0.418415485744841[/C][/ROW]
[ROW][C]23[/C][C]0.472[/C][C]0.0539986342485437[/C][C]0.418001365751456[/C][/ROW]
[ROW][C]24[/C][C]0.001[/C][C]0.248284557096173[/C][C]-0.247284557096173[/C][/ROW]
[ROW][C]25[/C][C]0.051[/C][C]0.401086340442924[/C][C]-0.350086340442924[/C][/ROW]
[ROW][C]26[/C][C]0.418[/C][C]0.217776699151086[/C][C]0.200223300848914[/C][/ROW]
[ROW][C]27[/C][C]0.364[/C][C]0.230329691722775[/C][C]0.133670308277225[/C][/ROW]
[ROW][C]28[/C][C]0.311[/C][C]0.162045323113063[/C][C]0.148954676886937[/C][/ROW]
[ROW][C]29[/C][C]0.052[/C][C]0.38691877155086[/C][C]-0.33491877155086[/C][/ROW]
[ROW][C]30[/C][C]0.052[/C][C]0.331421745336218[/C][C]-0.279421745336218[/C][/ROW]
[ROW][C]31[/C][C]0.62[/C][C]0.267935799520284[/C][C]0.352064200479716[/C][/ROW]
[ROW][C]32[/C][C]0.616[/C][C]0.361204195970919[/C][C]0.254795804029081[/C][/ROW]
[ROW][C]33[/C][C]1.377[/C][C]0.323594483494426[/C][C]1.05340551650557[/C][/ROW]
[ROW][C]34[/C][C]0.151[/C][C]0.172510523248285[/C][C]-0.0215105232482846[/C][/ROW]
[ROW][C]35[/C][C]0.501[/C][C]0.116722264178845[/C][C]0.384277735821155[/C][/ROW]
[ROW][C]36[/C][C]0.001[/C][C]0.216998433463264[/C][C]-0.215998433463264[/C][/ROW]
[ROW][C]37[/C][C]0.606[/C][C]0.357810741599315[/C][C]0.248189258400685[/C][/ROW]
[ROW][C]38[/C][C]0.05[/C][C]0.25178614889252[/C][C]-0.20178614889252[/C][/ROW]
[ROW][C]39[/C][C]0.15[/C][C]0.254783133690003[/C][C]-0.104783133690003[/C][/ROW]
[ROW][C]40[/C][C]0.501[/C][C]0.187334017405296[/C][C]0.313665982594704[/C][/ROW]
[ROW][C]41[/C][C]0.299[/C][C]0.345536473558083[/C][C]-0.0465364735580834[/C][/ROW]
[ROW][C]42[/C][C]0.248[/C][C]0.297063714700177[/C][C]-0.0490637147001771[/C][/ROW]
[ROW][C]43[/C][C]0.545[/C][C]0.325301005053428[/C][C]0.219698994946572[/C][/ROW]
[ROW][C]44[/C][C]0.444[/C][C]0.406138302777486[/C][C]0.0378616972225141[/C][/ROW]
[ROW][C]45[/C][C]0.491[/C][C]0.485395598713538[/C][C]0.0056044012864615[/C][/ROW]
[ROW][C]46[/C][C]0.444[/C][C]0.172862404251645[/C][C]0.271137595748355[/C][/ROW]
[ROW][C]47[/C][C]0.05[/C][C]0.175707592952947[/C][C]-0.125707592952947[/C][/ROW]
[ROW][C]48[/C][C]0.545[/C][C]0.18959475182542[/C][C]0.35540524817458[/C][/ROW]
[ROW][C]49[/C][C]0.138[/C][C]0.401633860459003[/C][C]-0.263633860459003[/C][/ROW]
[ROW][C]50[/C][C]0.423[/C][C]0.227168237871728[/C][C]0.195831762128272[/C][/ROW]
[ROW][C]51[/C][C]0.495[/C][C]0.244505673565849[/C][C]0.250494326434151[/C][/ROW]
[ROW][C]52[/C][C]0.37[/C][C]0.237316389870215[/C][C]0.132683610129785[/C][/ROW]
[ROW][C]53[/C][C]0.388[/C][C]0.345651535005459[/C][C]0.0423484649945405[/C][/ROW]
[ROW][C]54[/C][C]0.169[/C][C]0.295819141529303[/C][C]-0.126819141529303[/C][/ROW]
[ROW][C]55[/C][C]0.241[/C][C]0.364194597344315[/C][C]-0.123194597344315[/C][/ROW]
[ROW][C]56[/C][C]0.014[/C][C]0.419863992763976[/C][C]-0.405863992763976[/C][/ROW]
[ROW][C]57[/C][C]0.376[/C][C]0.495945130248409[/C][C]-0.119945130248409[/C][/ROW]
[ROW][C]58[/C][C]0.331[/C][C]0.216245860261581[/C][C]0.114754139738419[/C][/ROW]
[ROW][C]59[/C][C]0.789[/C][C]0.160705563160867[/C][C]0.628294436839133[/C][/ROW]
[ROW][C]60[/C][C]0.289[/C][C]0.245705622725122[/C][C]0.0432943772748776[/C][/ROW]
[ROW][C]61[/C][C]0.359[/C][C]0.370809243532144[/C][C]-0.0118092435321445[/C][/ROW]
[ROW][C]62[/C][C]0.236[/C][C]0.260514884114387[/C][C]-0.0245148841143871[/C][/ROW]
[ROW][C]63[/C][C]0.367[/C][C]0.286235809611317[/C][C]0.0807641903886827[/C][/ROW]
[ROW][C]64[/C][C]0.309[/C][C]0.261550213030941[/C][C]0.0474497869690593[/C][/ROW]
[ROW][C]65[/C][C]0.551[/C][C]0.358719504606986[/C][C]0.192280495393014[/C][/ROW]
[ROW][C]66[/C][C]0.901[/C][C]0.282987903032876[/C][C]0.618012096967124[/C][/ROW]
[ROW][C]67[/C][C]0.87[/C][C]0.353235254951057[/C][C]0.516764745048943[/C][/ROW]
[ROW][C]68[/C][C]0.16[/C][C]0.368377714245271[/C][C]-0.208377714245271[/C][/ROW]
[ROW][C]69[/C][C]0.032[/C][C]0.488029374769362[/C][C]-0.456029374769362[/C][/ROW]
[ROW][C]70[/C][C]0.877[/C][C]0.237377563378569[/C][C]0.639622436621431[/C][/ROW]
[ROW][C]71[/C][C]1.812[/C][C]0.256332111298819[/C][C]1.55566788870118[/C][/ROW]
[ROW][C]72[/C][C]0.784[/C][C]0.256880173164005[/C][C]0.527119826835996[/C][/ROW]
[ROW][C]73[/C][C]0.27[/C][C]0.3763064984068[/C][C]-0.1063064984068[/C][/ROW]
[ROW][C]74[/C][C]0.462[/C][C]0.261981824378854[/C][C]0.200018175621146[/C][/ROW]
[ROW][C]75[/C][C]0.146[/C][C]0.303689304048226[/C][C]-0.157689304048226[/C][/ROW]
[ROW][C]76[/C][C]0.108[/C][C]0.273612108545154[/C][C]-0.165612108545154[/C][/ROW]
[ROW][C]77[/C][C]0.132[/C][C]0.393970839588824[/C][C]-0.261970839588824[/C][/ROW]
[ROW][C]78[/C][C]0.68[/C][C]0.379412504742173[/C][C]0.300587495257827[/C][/ROW]
[ROW][C]79[/C][C]0.117[/C][C]0.436106489258548[/C][C]-0.319106489258548[/C][/ROW]
[ROW][C]80[/C][C]0.345[/C][C]0.344821533458532[/C][C]0.000178466541468136[/C][/ROW]
[ROW][C]81[/C][C]0.204[/C][C]0.43032606610757[/C][C]-0.22632606610757[/C][/ROW]
[ROW][C]82[/C][C]0.227[/C][C]0.336058667370351[/C][C]-0.10905866737035[/C][/ROW]
[ROW][C]83[/C][C]0.236[/C][C]0.490152801987282[/C][C]-0.254152801987282[/C][/ROW]
[ROW][C]84[/C][C]0.092[/C][C]0.339361877491228[/C][C]-0.247361877491228[/C][/ROW]
[ROW][C]85[/C][C]0.138[/C][C]0.367867749660774[/C][C]-0.229867749660774[/C][/ROW]
[ROW][C]86[/C][C]0.046[/C][C]0.29641568201754[/C][C]-0.25041568201754[/C][/ROW]
[ROW][C]87[/C][C]0.023[/C][C]0.286283692638016[/C][C]-0.263283692638016[/C][/ROW]
[ROW][C]88[/C][C]0.009[/C][C]0.254459507152157[/C][C]-0.245459507152157[/C][/ROW]
[ROW][C]89[/C][C]0.142[/C][C]0.362924074480643[/C][C]-0.220924074480643[/C][/ROW]
[ROW][C]90[/C][C]0.207[/C][C]0.430835465183252[/C][C]-0.223835465183252[/C][/ROW]
[ROW][C]91[/C][C]0.346[/C][C]0.397432245061054[/C][C]-0.0514322450610543[/C][/ROW]
[ROW][C]92[/C][C]0.207[/C][C]0.351374448411832[/C][C]-0.144374448411832[/C][/ROW]
[ROW][C]93[/C][C]0.165[/C][C]0.405166842631687[/C][C]-0.240166842631687[/C][/ROW]
[ROW][C]94[/C][C]0.247[/C][C]0.326357937097361[/C][C]-0.0793579370973606[/C][/ROW]
[ROW][C]95[/C][C]0.123[/C][C]0.462004092043866[/C][C]-0.339004092043866[/C][/ROW]
[ROW][C]96[/C][C]0.433[/C][C]0.30936237848795[/C][C]0.12363762151205[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122207&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122207&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
130.4310.3863238063091580.0446761936908425
140.2150.2129791805050960.00202081949490351
150.2140.22752494958839-0.0135249495883902
160.160.1584854983252490.00151450167475148
170.4270.370848190860210.0561518091397898
180.3720.3166160137288860.0553839862711142
190.1060.288834925031666-0.182834925031666
200.0530.404561238766747-0.351561238766747
210.3170.3169756731608552.43268391449947e-05
220.5270.1085845142551590.418415485744841
230.4720.05399863424854370.418001365751456
240.0010.248284557096173-0.247284557096173
250.0510.401086340442924-0.350086340442924
260.4180.2177766991510860.200223300848914
270.3640.2303296917227750.133670308277225
280.3110.1620453231130630.148954676886937
290.0520.38691877155086-0.33491877155086
300.0520.331421745336218-0.279421745336218
310.620.2679357995202840.352064200479716
320.6160.3612041959709190.254795804029081
331.3770.3235944834944261.05340551650557
340.1510.172510523248285-0.0215105232482846
350.5010.1167222641788450.384277735821155
360.0010.216998433463264-0.215998433463264
370.6060.3578107415993150.248189258400685
380.050.25178614889252-0.20178614889252
390.150.254783133690003-0.104783133690003
400.5010.1873340174052960.313665982594704
410.2990.345536473558083-0.0465364735580834
420.2480.297063714700177-0.0490637147001771
430.5450.3253010050534280.219698994946572
440.4440.4061383027774860.0378616972225141
450.4910.4853955987135380.0056044012864615
460.4440.1728624042516450.271137595748355
470.050.175707592952947-0.125707592952947
480.5450.189594751825420.35540524817458
490.1380.401633860459003-0.263633860459003
500.4230.2271682378717280.195831762128272
510.4950.2445056735658490.250494326434151
520.370.2373163898702150.132683610129785
530.3880.3456515350054590.0423484649945405
540.1690.295819141529303-0.126819141529303
550.2410.364194597344315-0.123194597344315
560.0140.419863992763976-0.405863992763976
570.3760.495945130248409-0.119945130248409
580.3310.2162458602615810.114754139738419
590.7890.1607055631608670.628294436839133
600.2890.2457056227251220.0432943772748776
610.3590.370809243532144-0.0118092435321445
620.2360.260514884114387-0.0245148841143871
630.3670.2862358096113170.0807641903886827
640.3090.2615502130309410.0474497869690593
650.5510.3587195046069860.192280495393014
660.9010.2829879030328760.618012096967124
670.870.3532352549510570.516764745048943
680.160.368377714245271-0.208377714245271
690.0320.488029374769362-0.456029374769362
700.8770.2373775633785690.639622436621431
711.8120.2563321112988191.55566788870118
720.7840.2568801731640050.527119826835996
730.270.3763064984068-0.1063064984068
740.4620.2619818243788540.200018175621146
750.1460.303689304048226-0.157689304048226
760.1080.273612108545154-0.165612108545154
770.1320.393970839588824-0.261970839588824
780.680.3794125047421730.300587495257827
790.1170.436106489258548-0.319106489258548
800.3450.3448215334585320.000178466541468136
810.2040.43032606610757-0.22632606610757
820.2270.336058667370351-0.10905866737035
830.2360.490152801987282-0.254152801987282
840.0920.339361877491228-0.247361877491228
850.1380.367867749660774-0.229867749660774
860.0460.29641568201754-0.25041568201754
870.0230.286283692638016-0.263283692638016
880.0090.254459507152157-0.245459507152157
890.1420.362924074480643-0.220924074480643
900.2070.430835465183252-0.223835465183252
910.3460.397432245061054-0.0514322450610543
920.2070.351374448411832-0.144374448411832
930.1650.405166842631687-0.240166842631687
940.2470.326357937097361-0.0793579370973606
950.1230.462004092043866-0.339004092043866
960.4330.309362378487950.12363762151205







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
970.3409676420123450.2486713588201450.433263925204545
980.2651439501756770.1728476669834770.357440233367878
990.2529221741862560.1606258909940550.345218457378456
1000.2231172182142270.1308209350220270.315413501406427
1010.3372078722026580.2449115890104580.429504155394859
1020.4059469728052010.3136506896130.498243255997401
1030.397263156995720.304966873803520.48955944018792
1040.3366715293557680.2443752461635670.428967812547968
1050.3773663931976180.2850701100054170.469662676389818
1060.3207328463649130.2284365631727130.413029129557113
1070.4207007373844180.3284044541922180.512997020576619
1080.333252451748585-228.341438594071229.007943497568

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 0.340967642012345 & 0.248671358820145 & 0.433263925204545 \tabularnewline
98 & 0.265143950175677 & 0.172847666983477 & 0.357440233367878 \tabularnewline
99 & 0.252922174186256 & 0.160625890994055 & 0.345218457378456 \tabularnewline
100 & 0.223117218214227 & 0.130820935022027 & 0.315413501406427 \tabularnewline
101 & 0.337207872202658 & 0.244911589010458 & 0.429504155394859 \tabularnewline
102 & 0.405946972805201 & 0.313650689613 & 0.498243255997401 \tabularnewline
103 & 0.39726315699572 & 0.30496687380352 & 0.48955944018792 \tabularnewline
104 & 0.336671529355768 & 0.244375246163567 & 0.428967812547968 \tabularnewline
105 & 0.377366393197618 & 0.285070110005417 & 0.469662676389818 \tabularnewline
106 & 0.320732846364913 & 0.228436563172713 & 0.413029129557113 \tabularnewline
107 & 0.420700737384418 & 0.328404454192218 & 0.512997020576619 \tabularnewline
108 & 0.333252451748585 & -228.341438594071 & 229.007943497568 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122207&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]0.340967642012345[/C][C]0.248671358820145[/C][C]0.433263925204545[/C][/ROW]
[ROW][C]98[/C][C]0.265143950175677[/C][C]0.172847666983477[/C][C]0.357440233367878[/C][/ROW]
[ROW][C]99[/C][C]0.252922174186256[/C][C]0.160625890994055[/C][C]0.345218457378456[/C][/ROW]
[ROW][C]100[/C][C]0.223117218214227[/C][C]0.130820935022027[/C][C]0.315413501406427[/C][/ROW]
[ROW][C]101[/C][C]0.337207872202658[/C][C]0.244911589010458[/C][C]0.429504155394859[/C][/ROW]
[ROW][C]102[/C][C]0.405946972805201[/C][C]0.313650689613[/C][C]0.498243255997401[/C][/ROW]
[ROW][C]103[/C][C]0.39726315699572[/C][C]0.30496687380352[/C][C]0.48955944018792[/C][/ROW]
[ROW][C]104[/C][C]0.336671529355768[/C][C]0.244375246163567[/C][C]0.428967812547968[/C][/ROW]
[ROW][C]105[/C][C]0.377366393197618[/C][C]0.285070110005417[/C][C]0.469662676389818[/C][/ROW]
[ROW][C]106[/C][C]0.320732846364913[/C][C]0.228436563172713[/C][C]0.413029129557113[/C][/ROW]
[ROW][C]107[/C][C]0.420700737384418[/C][C]0.328404454192218[/C][C]0.512997020576619[/C][/ROW]
[ROW][C]108[/C][C]0.333252451748585[/C][C]-228.341438594071[/C][C]229.007943497568[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122207&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122207&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
970.3409676420123450.2486713588201450.433263925204545
980.2651439501756770.1728476669834770.357440233367878
990.2529221741862560.1606258909940550.345218457378456
1000.2231172182142270.1308209350220270.315413501406427
1010.3372078722026580.2449115890104580.429504155394859
1020.4059469728052010.3136506896130.498243255997401
1030.397263156995720.304966873803520.48955944018792
1040.3366715293557680.2443752461635670.428967812547968
1050.3773663931976180.2850701100054170.469662676389818
1060.3207328463649130.2284365631727130.413029129557113
1070.4207007373844180.3284044541922180.512997020576619
1080.333252451748585-228.341438594071229.007943497568



Parameters (Session):
par1 = Studio 100 PRIJS 2005 ; par2 = Studio 100 PRIJS 2005 ; par3 = Studio 100 PRIJS 2005 ; par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')