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Paper - werkloosheid Brussel - MPR (3)

*The author of this computation has been verified*

R Software Module: rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Fri, 12 Dec 2008 03:33:41 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/12/t1229078077d6gj55klhcfrb8x.htm/, Retrieved Fri, 12 Dec 2008 11:34:38 +0100

BibTeX entries for LaTeX users:

@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2008/Dec/12/t1229078077d6gj55klhcfrb8x.htm/},
    year = {2008},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2008},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

51,220 0 50,487 0 49,415 0 49,398 0 48,196 0 47,348 0 49,331 0 49,644 0 49,588 0 49,567 0 49,010 0 49,563 0 49,741 0 49,487 0 48,278 0 47,478 0 46,985 0 45,216 0 46,581 0 49,266 0 48,121 0 46,412 0 46,285 0 46,824 0 46,949 0 45,355 0 44,924 0 45,059 0 44,202 0 44,149 0 46,151 0 47,703 0 48,436 0 47,089 0 47,492 0 49,295 0 49,127 0 50,041 0 48,857 0 48,428 0 48,788 0 48,820 0 50,743 0 52,590 0 51,959 0 53,451 0 55,674 0 56,120 0 55,685 0 56,714 0 54,882 0 55,173 0 53,574 0 53,954 0 58,055 0 61,062 0 58,353 0 59,693 0 58,833 0 60,417 0 61,696 0 62,515 0 62,687 0 61,794 0 63,014 0 63,134 0 68,057 0 67,327 0 68,310 0 69,780 0 69,944 0 69,881 0 71,397 0 70,631 0 70,452 0 69,862 0 69,114 0 69,358 0 71,133 0 73,128 0 73,528 0 73,677 0 72,273 0 71,962 0 73,654 0 73,305 0 73,355 0 73,346 0 72,881 0 72,424 0 74,540 0 74,847 0 75,904 0 76,870 0 76,370 0 77,631 0 78,335 0 77,926 0 77,236 0 76,755 0 74,710 0 73,486 0 76,034 0 76,389 0 77,767 0 78,124 0 76,696 0 77,375 0 77,431 0 77,347 0 77,013 0 76,666 0 75,225 0 75,579 0 77,100 0 78,592 0 79,502 0 78,528 0 77,775 0 77,271 0 78,738 0 77,885 0 76,896 0 75,813 0 74,958 0 75,340 0 77,187 0 78,602 0 81,653 0 78,125 0 76,092 0 74,870 0 75,615 0 74,776 0 72,528 0 71,894 0 71,641 0 71,145 0 73,320 0 72,186 0 72,854 0 74,243 0 74,628 0 72,368 0 75,361 1 72,746 1 70,536 1 69,410 1 66,219 1 66,739 1 67,626 1 70,602 1 71,758 1 71,786 1 69,641 1 68,055 1 70,148 1 69,390 1 68,562 1 68,622 1 68,120 1 68,308 1 70,421 1 69,766 1 72,157 1 72,928 1 75,340 1 74,812 1 74,593 1 76,003 1 75,112 1 75,452 1 75,634 1 75,653 1 78,645 1 73,100 1 79,699 1 82,848 1 81,834 1 81,736 1 82,267 1 84,120 1 83,819 1 82,734 1 81,842 1 81,735 1 83,227 1 81,934 1 89,521 1 88,827 1 85,874 1 85,211 1 87,130 1 88,620 1 89,563 1 89,056 1 88,542 1 89,504 1 89,428 1 86,040 1 96,240 1 94,423 1 93,028 1 92,285 1 91,685 1 94,260 1 93,858 1 92,437 1 92,980 1 92,099 1 92,803 1 88,551 1 98,334 1 98,329 1 96,455 1 97,109 1 97,687 1 98,512 1 98,673 1 96,028 1 98,014 1 95,580 1 97,838 1 97,760 1 99,913 1 97,588 1 93,942 1 93,656 1 93,365 1 92,881 1 93,120 1 91,063 1 90,930 1 91,946 1 94,624 1 95,484 1 95,862 1 95,530 1 94,574 1 94,677 1 93,845 1 91,533 1 91,214 1 90,922 1 89,563 1 89,945 1 91,850 1 92,505 1 92,437 1 93,876 1

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits!

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	16 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Multiple Linear Regression - Estimated Regression Equation

Werkloosheid[t] = + 43.9270269318926 -13.2496295841519dummy[t] + 1.33581659533164M1[t] + 1.00455687388904M2[t] + 0.0819162000654867M3[t] -0.842438759472357M4[t] -1.70336514758163M5[t] -2.15533915473852M6[t] -0.373884590466837M7[t] -0.537572883338013M8[t] + 1.31940549045748M9[t] + 1.03257434044344M10[t] + 0.309312102394984M11[t] + 0.277212102394986t + e[t]

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STAT H0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	43.9270269318926	1.278902	34.3475	0	0
dummy	-13.2496295841519	1.205662	-10.9895	0	0
M1	1.33581659533164	1.519519	0.8791	0.380239	0.190119
M2	1.00455687388904	1.519156	0.6613	0.509091	0.254545
M3	0.0819162000654867	1.518839	0.0539	0.957034	0.478517
M4	-0.842438759472357	1.518566	-0.5548	0.579585	0.289792
M5	-1.70336514758163	1.518338	-1.1219	0.263061	0.131531
M6	-2.15533915473852	1.518155	-1.4197	0.157012	0.078506
M7	-0.373884590466837	1.518017	-0.2463	0.805666	0.402833
M8	-0.537572883338013	1.517924	-0.3542	0.723543	0.361771
M9	1.31940549045748	1.517876	0.8692	0.385596	0.192798
M10	1.03257434044344	1.517872	0.6803	0.496996	0.248498
M11	0.309312102394984	1.536184	0.2014	0.840598	0.420299
t	0.277212102394986	0.00826	33.5618	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.952921548907862
R-squared	0.90805947837296
Adjusted R-squared	0.902994958113843
F-TEST (value)	179.298222124468
F-TEST (DF numerator)	13
F-TEST (DF denominator)	236
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	4.85777064853140
Sum Squared Residuals	5569.11281900104

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	51.22	45.5400556296193	5.67994437038068
2	50.487	45.4860080105716	5.0009919894284
3	49.415	44.840579439143	4.57442056085695
4	49.398	44.1934365820002	5.20456341799982
5	48.196	43.6097222962859	4.58627770371409
6	47.348	43.434960391524	3.913039608476
7	49.331	45.4936270581907	3.83737294180934
8	49.644	45.6071508677145	4.03684913228552
9	49.588	47.7413413439049	1.84665865609505
10	49.567	47.7317222962859	1.83527770371410
11	49.01	47.2856721606324	1.72432783936757
12	49.563	47.2535721606324	2.30942783936757
13	49.741	48.8666008583591	0.874399141640946
14	49.487	48.8125532393114	0.674446760688584
15	48.278	48.1671246678829	0.110875332117125
16	47.478	47.51998181074	-0.0419818107400119
17	46.985	46.9362675250257	0.0487324749742724
18	45.216	46.7615056202638	-1.54550562026382
19	46.581	48.8201722869305	-2.23917228693049
20	49.266	48.9336960964543	0.332303903545699
21	48.121	51.0678865726448	-2.94688657264477
22	46.412	51.0582675250257	-4.64626752502573
23	46.285	50.6122173893723	-4.32721738937226
24	46.824	50.5801173893723	-3.75611738937226
25	46.949	52.1931460870989	-5.24414608709889
26	45.355	52.1390984680513	-6.78409846805127
27	44.924	51.4936698966227	-6.5696698966227
28	45.059	50.8465270394798	-5.78752703947984
29	44.202	50.2628127537656	-6.06081275376556
30	44.149	50.0880508490037	-5.93905084900365
31	46.151	52.1467175156703	-5.99571751567031
32	47.703	52.2602413251941	-4.55724132519412
33	48.436	54.3944318013846	-5.9584318013846
34	47.089	54.3848127537656	-7.29581275376555
35	47.492	53.9387626181121	-6.44676261811208
36	49.295	53.9066626181121	-4.61166261811208
37	49.127	55.5196913158387	-6.39269131583871
38	50.041	55.4656436967911	-5.4246436967911
39	48.857	54.8202151253625	-5.96321512536253
40	48.428	54.1730722682197	-5.74507226821967
41	48.788	53.5893579825054	-4.80135798250538
42	48.82	53.4145960777435	-4.59459607774347
43	50.743	55.4732627444101	-4.73026274441014
44	52.59	55.586786553934	-2.99678655393395
45	51.959	57.7209770301244	-5.76197703012442
46	53.451	57.7113579825054	-4.26035798250538
47	55.674	57.2653078468519	-1.59130784685191
48	56.12	57.2332078468519	-1.11320784685191
49	55.685	58.8462365445785	-3.16123654457853
50	56.714	58.7921889255309	-2.07818892553093
51	54.882	58.1467603541023	-3.26476035410235
52	55.173	57.4996174969595	-2.32661749695949
53	53.574	56.9159032112452	-3.34190321124521
54	53.954	56.7411413064833	-2.78714130648330
55	58.055	58.79980797315	-0.744807973149967
56	61.062	58.9133317826738	2.14866821732622
57	58.353	61.0475222588643	-2.69452225886425
58	59.693	61.0379032112452	-1.34490321124521
59	58.833	60.5918530755917	-1.75885307559173
60	60.417	60.5597530755917	-0.142753075591731
61	61.696	62.1727817733184	-0.476781773318362
62	62.515	62.1187341542707	0.396265845729253
63	62.687	61.4733055828422	1.21369441715782
64	61.794	60.8261627256993	0.967837274300681
65	63.014	60.242448439985	2.77155156001497
66	63.134	60.0676865352231	3.06631346477687
67	68.057	62.1263532018898	5.93064679811021
68	67.327	62.2398770114136	5.08712298858639
69	68.31	64.3740674876041	3.93593251239592
70	69.78	64.364448439985	5.41555156001497
71	69.944	63.9183983043316	6.02560169566845
72	69.881	63.8862983043316	5.99470169566844
73	71.397	65.4993270020582	5.89767299794182
74	70.631	65.4452793830106	5.18572061698943
75	70.452	64.799850811582	5.652149188418
76	69.862	64.1527079544391	5.70929204556086
77	69.114	63.5689936687249	5.54500633127515
78	69.358	63.394231763963	5.96376823603705
79	71.133	65.4528984306296	5.68010156937038
80	73.128	65.5664222401534	7.56157775984657
81	73.528	67.7006127163439	5.8273872836561
82	73.677	67.6909936687249	5.98600633127515
83	72.273	67.2449435330714	5.02805646692862
84	71.962	67.2128435330714	4.74915646692862
85	73.654	68.825872230798	4.82812776920199
86	73.305	68.7718246117504	4.53317538824961
87	73.355	68.1263960403218	5.22860395967818
88	73.346	67.479253183179	5.86674681682104
89	72.881	66.8955388974647	5.98546110253532
90	72.424	66.7207769927028	5.70322300729723
91	74.54	68.7794436593694	5.76055634063056
92	74.847	68.8929674688932	5.95403253110674
93	75.904	71.0271579450837	4.87684205491627
94	76.87	71.0175388974647	5.85246110253533
95	76.37	70.5714887618112	5.7985112381888
96	77.631	70.5393887618112	7.09161123818879
97	78.335	72.1524174595378	6.18258254046216
98	77.926	72.0983698404902	5.82763015950978
99	77.236	71.4529412690617	5.78305873093835
100	76.755	70.8057984119188	5.9492015880812
101	74.71	70.2220841262045	4.48791587379548
102	73.486	70.0473222214426	3.4386777785574
103	76.034	72.1059888881093	3.92801111189074
104	76.389	72.2195126976331	4.16948730236691
105	77.767	74.3537031738236	3.41329682617644
106	78.124	74.3440841262045	3.77991587379549
107	76.696	73.898033990551	2.79796600944896
108	77.375	73.865933990551	3.50906600944896
109	77.431	75.4789626882777	1.95203731172234
110	77.347	75.42491506923	1.92208493076994
111	77.013	74.7794864978015	2.23351350219852
112	76.666	74.1323436406586	2.53365635934138
113	75.225	73.5486293549443	1.67637064505566
114	75.579	73.3738674501824	2.20513254981756
115	77.1	75.4325341168491	1.66746588315090
116	78.592	75.5460579263729	3.04594207362709
117	79.502	77.6802484025634	1.82175159743661
118	78.528	77.6706293549443	0.857370645055674
119	77.775	77.2245792192909	0.550420780709146
120	77.271	77.1924792192909	0.0785207807091393
121	78.738	78.8055079170175	-0.0675079170174872
122	77.885	78.7514602979699	-0.866460297969872
123	76.896	78.1060317265413	-1.21003172654131
124	75.813	77.4588888693985	-1.64588886939844
125	74.958	76.8751745836842	-1.91717458368416
126	75.34	76.7004126789222	-1.36041267892225
127	77.187	78.7590793455889	-1.57207934558892
128	78.602	78.8726031551127	-0.270603155112734
129	81.653	81.0067936313032	0.646206368696799
130	78.125	80.9971745836842	-2.87217458368416
131	76.092	80.5511244480307	-4.45912444803069
132	74.87	80.5190244480307	-5.64902444803068
133	75.615	82.1320531457573	-6.51705314575732
134	74.776	82.0780055267097	-7.3020055267097
135	72.528	81.4325769552811	-8.90457695528112
136	71.894	80.7854340981383	-8.89143409813827
137	71.641	80.201719812424	-8.56071981242398
138	71.145	80.0269579076621	-8.88195790766208
139	73.32	82.0856245743287	-8.76562457432875
140	72.186	82.1991483838526	-10.0131483838525
141	72.854	84.333338860043	-11.4793388600430
142	74.243	84.323719812424	-10.0807198124240
143	74.628	83.8776696767705	-9.2496696767705
144	72.368	83.8455696767705	-11.4775696767705
145	75.361	72.2089687903452	3.15203120965480
146	72.746	72.1549211712976	0.591078828702397
147	70.536	71.509492599869	-0.973492599869027
148	69.41	70.8623497427262	-1.45234974272616
149	66.219	70.2786354570119	-4.05963545701188
150	66.739	70.10387355225	-3.36487355224997
151	67.626	72.1625402189166	-4.53654021891663
152	70.602	72.2760640284405	-1.67406402844045
153	71.758	74.410254504631	-2.65225450463093
154	71.786	74.4006354570119	-2.61463545701188
155	69.641	73.9545853213584	-4.3135853213584
156	68.055	73.9224853213584	-5.8674853213584
157	70.148	75.535514019085	-5.38751401908504
158	69.39	75.4814664000374	-6.09146640003742
159	68.562	74.8360378286089	-6.27403782860885
160	68.622	74.188894971466	-5.56689497146599
161	68.12	73.6051806857517	-5.48518068575169
162	68.308	73.4304187809898	-5.1224187809898
163	70.421	75.4890854476565	-5.06808544765646
164	69.766	75.6026092571803	-5.83660925718027
165	72.157	77.7367997333708	-5.57979973337076
166	72.928	77.7271806857517	-4.79918068575171
167	75.34	77.2811305500982	-1.94113055009823
168	74.812	77.2490305500982	-2.43703055009823
169	74.593	78.8620592478249	-4.26905924782486
170	76.003	78.8080116287773	-2.80501162877725
171	75.112	78.1625830573487	-3.05058305734868
172	75.452	77.5154402002058	-2.06344020020582
173	75.634	76.9317259144915	-1.29772591449153
174	75.653	76.7569640097296	-1.10396400972962
175	78.645	78.8156306763963	-0.170630676396295
176	73.1	78.9291544859201	-5.82915448592011
177	79.699	81.0633449621106	-1.36434496211058
178	82.848	81.0537259144915	1.79427408550847
179	81.834	80.607675778838	1.22632422116195
180	81.736	80.575575778838	1.16042422116195
181	82.267	82.1886044765647	0.0783955234353112
182	84.12	82.134556857517	1.98544314248293
183	83.819	81.4891282860885	2.3298717139115
184	82.734	80.8419854289456	1.89201457105435
185	81.842	80.2582711432314	1.58372885676864
186	81.735	80.0835092384695	1.65149076153054
187	83.227	82.1421759051361	1.08482409486388
188	81.934	82.25569971466	-0.321699714659934
189	89.521	84.3898901908504	5.13110980914959
190	88.827	84.3802711432314	4.44672885676864
191	85.874	83.9342210075779	1.93977899242211
192	85.211	83.9021210075779	1.30887899242211
193	87.13	85.5151497053045	1.61485029469548
194	88.62	85.4611020862569	3.1588979137431
195	89.563	84.8156735148283	4.74732648517168
196	89.056	84.1685306576855	4.88746934231453
197	88.542	83.5848163719712	4.95718362802882
198	89.504	83.4100544672093	6.09394553279072
199	89.428	85.468721133876	3.95927886612405
200	86.04	85.5822449433998	0.457755056600249
201	96.24	87.7164354195902	8.52356458040976
202	94.423	87.7068163719712	6.71618362802881
203	93.028	87.2607662363177	5.7672337636823
204	92.285	87.2286662363177	5.05633376368228
205	91.685	88.8416949340443	2.84330506595566
206	94.26	88.7876473149967	5.47235268500328
207	93.858	88.1422187435682	5.71578125643185
208	92.437	87.4950758864253	4.9419241135747
209	92.98	86.911361600711	6.06863839928899
210	92.099	86.7365996959491	5.3624003040509
211	92.803	88.7952663626158	4.00773363738422
212	88.551	88.9087901721396	-0.357790172139582
213	98.334	91.04298064833	7.29101935166994
214	98.329	91.033361600711	7.29563839928898
215	96.455	90.5873114650575	5.86768853494246
216	97.109	90.5552114650575	6.55378853494245
217	97.687	92.1682401627842	5.51875983721583
218	98.512	92.1141925437366	6.39780745626344
219	98.673	91.468763972308	7.20423602769202
220	96.028	90.8216211151651	5.20637888483488
221	98.014	90.2379068294508	7.77609317054916
222	95.58	90.063144924689	5.51685507531106
223	97.838	92.1218115913556	5.71618840864439
224	97.76	92.2353354008794	5.5246645991206
225	99.913	94.3695258770699	5.54347412293011
226	97.588	94.3599068294508	3.22809317054916
227	93.942	93.9138566937974	0.0281433062026322
228	93.656	93.8817566937974	-0.225756693797359
229	93.365	95.494785391524	-2.12978539152400
230	92.881	95.4407377724764	-2.55973777247638
231	93.12	94.7953092010478	-1.67530920104781
232	91.063	94.148166343905	-3.08516634390495
233	90.93	93.5644520581907	-2.63445205819066
234	91.946	93.3896901534288	-1.44369015342877
235	94.624	95.4483568200954	-0.824356820095435
236	95.484	95.5618806296192	-0.0778806296192438
237	95.862	97.6960711058097	-1.83407110580972
238	95.53	97.6864520581907	-2.15645205819067
239	94.574	97.2404019225372	-2.66640192253719
240	94.677	97.2083019225372	-2.53130192253719
241	93.845	98.8213306202638	-4.97633062026382
242	91.533	98.7672830012162	-7.2342830012162
243	91.214	98.1218544297876	-6.90785442978763
244	90.922	97.4747115726448	-6.55271157264478
245	89.563	96.8909972869305	-7.32799728693049
246	89.945	96.7162353821686	-6.7712353821686
247	91.85	98.7749020488353	-6.92490204883526
248	92.505	98.888425858359	-6.38342585835907
249	92.437	101.022616334550	-8.58561633454954
250	93.876	101.012997286930	-7.13699728693049

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
17	0.000302210598527597	0.000604421197055194	0.999697789401472
18	5.6829966558478e-05	0.000113659933116956	0.999943170033442
19	2.88771109393619e-05	5.77542218787237e-05	0.99997112288906
20	1.00576194578492e-05	2.01152389156984e-05	0.999989942380542
21	1.02674660478786e-06	2.05349320957573e-06	0.999998973253395
22	7.02076494811612e-07	1.40415298962322e-06	0.999999297923505
23	1.59511741571479e-07	3.19023483142958e-07	0.999999840488258
24	3.31920483325430e-08	6.63840966650861e-08	0.999999966807952
25	6.03793334019196e-09	1.20758666803839e-08	0.999999993962067
26	4.779574586241e-09	9.559149172482e-09	0.999999995220425
27	9.08242790749075e-10	1.81648558149815e-09	0.999999999091757
28	1.25445232128618e-10	2.50890464257236e-10	0.999999999874555
29	1.69384078805358e-11	3.38768157610716e-11	0.999999999983062
30	5.94059667532445e-12	1.18811933506489e-11	0.99999999999406
31	2.88781949796594e-12	5.77563899593187e-12	0.999999999997112
32	1.16693051507023e-12	2.33386103014047e-12	0.999999999998833
33	4.58068227673904e-12	9.16136455347807e-12	0.99999999999542
34	3.58771998467783e-12	7.17543996935566e-12	0.999999999996412
35	6.34453954894488e-12	1.26890790978898e-11	0.999999999993655
36	4.7082814408092e-11	9.4165628816184e-11	0.999999999952917
37	7.89127427400869e-11	1.57825485480174e-10	0.999999999921087
38	7.34180498549667e-10	1.46836099709933e-09	0.99999999926582
39	1.69080562296022e-09	3.38161124592045e-09	0.999999998309194
40	2.07394933769768e-09	4.14789867539537e-09	0.99999999792605
41	5.32655602357974e-09	1.06531120471595e-08	0.999999994673444
42	1.94460219473876e-08	3.88920438947751e-08	0.999999980553978
43	4.80101212049979e-08	9.60202424099959e-08	0.999999951989879
44	9.88684530009065e-08	1.97736906001813e-07	0.999999901131547
45	1.32025260479926e-07	2.64050520959853e-07	0.99999986797474
46	6.85889585776754e-07	1.37177917155351e-06	0.999999314110414
47	8.9162063936348e-06	1.78324127872696e-05	0.999991083793606
48	3.47202467880156e-05	6.94404935760312e-05	0.999965279753212
49	5.68239226308138e-05	0.000113647845261628	0.99994317607737
50	0.000126678991125587	0.000253357982251174	0.999873321008874
51	0.000171719203191928	0.000343438406383856	0.999828280796808
52	0.000236436262985853	0.000472872525971707	0.999763563737014
53	0.000234494447103913	0.000468988894207826	0.999765505552896
54	0.000276870264282167	0.000553740528564334	0.999723129735718
55	0.000537245914255769	0.00107449182851154	0.999462754085744
56	0.00126189997974123	0.00252379995948246	0.998738100020259
57	0.00147269598014384	0.00294539196028768	0.998527304019856
58	0.00225100933649184	0.00450201867298369	0.997748990663508
59	0.00243094215027295	0.00486188430054589	0.997569057849727
60	0.00274955125018375	0.0054991025003675	0.997250448749816
61	0.00312663836810878	0.00625327673621756	0.996873361631891
62	0.00388399380161121	0.00776798760322243	0.996116006198389
63	0.00564730260152959	0.0112946052030592	0.99435269739847
64	0.00655371886002543	0.0131074377200509	0.993446281139975
65	0.0098705634415536	0.0197411268831072	0.990129436558446
66	0.0146774202924783	0.0293548405849566	0.985322579707522
67	0.0313615738429606	0.0627231476859212	0.96863842615704
68	0.0380406665491831	0.0760813330983663	0.961959333450817
69	0.0532727079127571	0.106545415825514	0.946727292087243
70	0.0829193496291563	0.165838699258313	0.917080650370844
71	0.115843971356637	0.231687942713274	0.884156028643363
72	0.137325909439752	0.274651818879503	0.862674090560248
73	0.156492971728626	0.312985943457251	0.843507028271374
74	0.162670792399346	0.325341584798692	0.837329207600654
75	0.174032229557627	0.348064459115254	0.825967770442373
76	0.179686796402904	0.359373592805808	0.820313203597096
77	0.179722305524849	0.359444611049698	0.820277694475151
78	0.183949701360873	0.367899402721746	0.816050298639127
79	0.178468149920947	0.356936299841894	0.821531850079053
80	0.184450791209862	0.368901582419724	0.815549208790138
81	0.187085815534446	0.374171631068893	0.812914184465554
82	0.188182618027009	0.376365236054018	0.811817381972991
83	0.175411582626801	0.350823165253603	0.824588417373199
84	0.158240502590252	0.316481005180503	0.841759497409748
85	0.142279205527724	0.284558411055449	0.857720794472276
86	0.126099495986224	0.252198991972448	0.873900504013776
87	0.114782909891023	0.229565819782047	0.885217090108977
88	0.107022033945615	0.214044067891229	0.892977966054386
89	0.10017139275592	0.20034278551184	0.89982860724408
90	0.0924533650135135	0.184906730027027	0.907546634986486
91	0.0851485595842039	0.170297119168408	0.914851440415796
92	0.0794961766154943	0.158992353230989	0.920503823384506
93	0.071019469961015	0.14203893992203	0.928980530038985
94	0.0667968617228591	0.133593723445718	0.93320313827714
95	0.0625385808375232	0.125077161675046	0.937461419162477
96	0.0640699237211117	0.128139847442223	0.935930076278888
97	0.061961482376816	0.123922964753632	0.938038517623184
98	0.0590882394101452	0.118176478820290	0.940911760589855
99	0.0565967275770973	0.113193455154195	0.943403272422903
100	0.0555585700797655	0.111117140159531	0.944441429920234
101	0.051467660274932	0.102935320549864	0.948532339725068
102	0.0463955550185495	0.092791110037099	0.95360444498145
103	0.043265929244016	0.086531858488032	0.956734070755984
104	0.0437391290015168	0.0874782580030335	0.956260870998483
105	0.039156548760677	0.078313097521354	0.960843451239323
106	0.0360223708433834	0.0720447416867668	0.963977629156617
107	0.0329864813498443	0.0659729626996885	0.967013518650156
108	0.0322121912042438	0.0644243824084876	0.967787808795756
109	0.0312783005276874	0.0625566010553748	0.968721699472313
110	0.0301989024085917	0.0603978048171834	0.969801097591408
111	0.0291538480332099	0.0583076960664197	0.97084615196679
112	0.0292003270665243	0.0584006541330486	0.970799672933476
113	0.0290724061270181	0.0581448122540363	0.970927593872982
114	0.0287663502171402	0.0575327004342804	0.97123364978286
115	0.0296542449585146	0.0593084899170292	0.970345755041485
116	0.0355989528353429	0.0711979056706858	0.964401047164657
117	0.0348341738531631	0.0696683477063261	0.965165826146837
118	0.0347127256137434	0.0694254512274868	0.965287274386257
119	0.0352467941711992	0.0704935883423984	0.9647532058288
120	0.0387758584269044	0.0775517168538088	0.961224141573096
121	0.0425152514911755	0.085030502982351	0.957484748508824
122	0.0466092738686364	0.0932185477372729	0.953390726131364
123	0.0511161419145959	0.102232283829192	0.948883858085404
124	0.0583513912688713	0.116702782537743	0.941648608731129
125	0.0655231585687908	0.131046317137582	0.93447684143121
126	0.0717641968946252	0.143528393789250	0.928235803105375
127	0.0819189203760141	0.163837840752028	0.918081079623986
128	0.108817051149350	0.217634102298699	0.89118294885065
129	0.124645494861646	0.249290989723292	0.875354505138354
130	0.137767487958072	0.275534975916144	0.862232512041928
131	0.157273898468591	0.314547796937183	0.842726101531409
132	0.193417914337597	0.386835828675194	0.806582085662403
133	0.235848781819627	0.471697563639255	0.764151218180373
134	0.28224131903743	0.56448263807486	0.71775868096257
135	0.345778300890942	0.691556601781884	0.654221699109058
136	0.409004149546611	0.818008299093221	0.59099585045339
137	0.458441648632717	0.916883297265433	0.541558351367283
138	0.504284793001675	0.99143041399665	0.495715206998325
139	0.548544127365144	0.902911745269712	0.451455872634856
140	0.623471530790606	0.753056938418788	0.376528469209394
141	0.676652220000197	0.646695559999606	0.323347779999803
142	0.701254826683113	0.597490346633774	0.298745173316887
143	0.714315022742435	0.571369954515131	0.285684977257565
144	0.74890289231842	0.50219421536316	0.25109710768158
145	0.734904903703584	0.530190192592832	0.265095096296416
146	0.706048246876244	0.587903506247513	0.293951753123756
147	0.673854533739378	0.652290932521245	0.326145466260622
148	0.640357012231989	0.719285975536023	0.359642987768011
149	0.621492094282635	0.75701581143473	0.378507905717365
150	0.594502595892132	0.810994808215736	0.405497404107868
151	0.576032543412094	0.847934913175811	0.423967456587906
152	0.538431969026885	0.92313606194623	0.461568030973115
153	0.507696292866922	0.984607414266156	0.492303707133078
154	0.477415500699411	0.954831001398821	0.522584499300589
155	0.465375644554372	0.930751289108745	0.534624355445627
156	0.474960319967091	0.949920639934182	0.525039680032909
157	0.466248188619342	0.932496377238685	0.533751811380658
158	0.476782331114625	0.95356466222925	0.523217668885375
159	0.500330848201835	0.99933830359633	0.499669151798165
160	0.509779533565307	0.980440932869386	0.490220466434693
161	0.529000820782571	0.941998358434859	0.470999179217429
162	0.547272054605791	0.905455890788418	0.452727945394209
163	0.564643626302293	0.870712747395414	0.435356373697707
164	0.573850223652373	0.852299552695253	0.426149776347626
165	0.632238775027286	0.735522449945428	0.367761224972714
166	0.68156091453849	0.636878170923019	0.318439085461509
167	0.6870857537001	0.625828492599801	0.312914246299900
168	0.69956342884601	0.60087314230798	0.30043657115399
169	0.721954273401928	0.556091453196145	0.278045726598072
170	0.737287232334825	0.525425535330351	0.262712767665175
171	0.77169559159018	0.456608816819638	0.228304408409819
172	0.786157478071231	0.427685043857538	0.213842521928769
173	0.802608508577987	0.394782982844025	0.197391491422013
174	0.820413088244105	0.359173823511789	0.179586911755895
175	0.825267615105998	0.349464769788005	0.174732384894002
176	0.891423554945111	0.217152890109777	0.108576445054889
177	0.928420348245993	0.143159303508013	0.0715796517540066
178	0.936436645835102	0.127126708329797	0.0635633541648983
179	0.943078248740347	0.113843502519307	0.0569217512596534
180	0.94979930131249	0.100401397375020	0.0502006986875099
181	0.953973282190413	0.0920534356191735	0.0460267178095867
182	0.954409696914281	0.0911806061714377	0.0455903030857189
183	0.95796795785031	0.084064084299379	0.0420320421496895
184	0.960373486754495	0.07925302649101	0.039626513245505
185	0.967951418760205	0.0640971624795893	0.0320485812397947
186	0.975465778140205	0.04906844371959	0.024534221859795
187	0.982543418157006	0.0349131636859875	0.0174565818429937
188	0.988877351622407	0.0222452967551856	0.0111226483775928
189	0.990482056499216	0.0190358870015686	0.0095179435007843
190	0.99200228768461	0.0159954246307800	0.00799771231539001
191	0.995218383367232	0.00956323326553685	0.00478161663276842
192	0.99796765157074	0.00406469685852164	0.00203234842926082
193	0.998663834552338	0.00267233089532394	0.00133616544766197
194	0.99893066191864	0.00213867616272075	0.00106933808136038
195	0.999045775285024	0.00190844942995102	0.00095422471497551
196	0.998986352577612	0.00202729484477538	0.00101364742238769
197	0.999117015479362	0.00176596904127594	0.00088298452063797
198	0.999061323930218	0.00187735213956469	0.000938676069782345
199	0.999354214872804	0.00129157025439169	0.000645785127195847
200	0.999894977095336	0.000210045809327524	0.000105022904663762
201	0.999871912231642	0.000256175536715906	0.000128087768357953
202	0.999876322805307	0.000247354389385439	0.000123677194692720
203	0.99986953341708	0.000260933165841150	0.000130466582920575
204	0.999898412715794	0.000203174568411833	0.000101587284205917
205	0.999938254988134	0.000123490023732367	6.17450118661837e-05
206	0.99991216361307	0.000175672773859329	8.78363869296644e-05
207	0.99989046653231	0.000219066935380118	0.000109533467690059
208	0.999857865835668	0.000284268328663639	0.000142134164331819
209	0.999812912354237	0.000374175291525984	0.000187087645762992
210	0.999792821891286	0.000414356217427033	0.000207178108713516
211	0.999892278656672	0.000215442686655457	0.000107721343327728
212	0.999999979541448	4.09171046782356e-08	2.04585523391178e-08
213	0.999999978457307	4.30853861241341e-08	2.15426930620671e-08
214	0.99999997575784	4.84843207915017e-08	2.42421603957508e-08
215	0.999999953211998	9.35760034475571e-08	4.67880017237786e-08
216	0.999999882118047	2.35763906688318e-07	1.17881953344159e-07
217	0.999999628772913	7.42454173007285e-07	3.71227086503643e-07
218	0.999999371073302	1.25785339578684e-06	6.28926697893421e-07
219	0.999999188336633	1.623326734272e-06	8.11663367136e-07
220	0.99999786204284	4.27591431850855e-06	2.13795715925427e-06
221	0.999999623249277	7.53501445137412e-07	3.76750722568706e-07
222	0.999999036453073	1.92709385342485e-06	9.63546926712423e-07
223	0.99999775801572	4.48396856166685e-06	2.24198428083342e-06
224	0.999992741060243	1.45178795135509e-05	7.25893975677544e-06
225	0.99999751627042	4.96745916079464e-06	2.48372958039732e-06
226	0.999990537123094	1.8925753811791e-05	9.4628769058955e-06
227	0.999980675584127	3.86488317466285e-05	1.93244158733142e-05
228	0.999981610775942	3.67784481151857e-05	1.83892240575928e-05
229	0.999982842636858	3.43147262838729e-05	1.71573631419365e-05
230	0.999905127408266	0.000189745183469000	9.48725917345002e-05
231	0.999413038649721	0.00117392270055777	0.000586961350278883
232	0.99933730174841	0.00132539650318128	0.000662698251590638
233	0.99733876727699	0.00532246544602131	0.00266123272301065

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	89	0.410138248847926	NOK
5% type I error level	98	0.451612903225806	NOK
10% type I error level	126	0.580645161290323	NOK

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/12/t1229078077d6gj55klhcfrb8x/102r3g1229077992.png (open in new window)

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

R code (references can be found in the software module):

library(lattice)

library(lmtest)

n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test

par1 <- as.numeric(par1)

x <- t(y)

k <- length(x[1,])

n <- length(x[,1])

x1 <- cbind(x[,par1], x[,1:k!=par1])

mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])

colnames(x1) <- mycolnames #colnames(x)[par1]

x <- x1

if (par3 == 'First Differences'){

x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))

for (i in 1:n-1) {

for (j in 1:k) {

x2[i,j] <- x[i+1,j] - x[i,j]

}

}

x <- x2

}

if (par2 == 'Include Monthly Dummies'){

x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))

for (i in 1:11){

x2[seq(i,n,12),i] <- 1

}

x <- cbind(x, x2)

}

if (par2 == 'Include Quarterly Dummies'){

x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))

for (i in 1:3){

x2[seq(i,n,4),i] <- 1

}

x <- cbind(x, x2)

}

k <- length(x[1,])

if (par3 == 'Linear Trend'){

x <- cbind(x, c(1:n))

colnames(x)[k+1] <- 't'

}

x

k <- length(x[1,])

df <- as.data.frame(x)

(mylm <- lm(df))

(mysum <- summary(mylm))

if (n > n25) {

kp3 <- k + 3

nmkm3 <- n - k - 3

gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))

numgqtests <- 0

numsignificant1 <- 0

numsignificant5 <- 0

numsignificant10 <- 0

for (mypoint in kp3:nmkm3) {

j <- 0

numgqtests <- numgqtests + 1

for (myalt in c('greater', 'two.sided', 'less')) {

j <- j + 1

gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value

}

if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1

if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1

if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1

}

gqarr

}

bitmap(file='test0.png')

plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')

points(x[,1]-mysum$resid)

grid()

dev.off()

bitmap(file='test1.png')

plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')

grid()

dev.off()

bitmap(file='test2.png')

hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')

grid()

dev.off()

bitmap(file='test3.png')

densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')

dev.off()

bitmap(file='test4.png')

qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')

qqline(mysum$resid)

grid()

dev.off()

(myerror <- as.ts(mysum$resid))

bitmap(file='test5.png')

dum <- cbind(lag(myerror,k=1),myerror)

dum

dum1 <- dum[2:length(myerror),]

dum1

z <- as.data.frame(dum1)

z

plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')

lines(lowess(z))

abline(lm(z))

grid()

dev.off()

bitmap(file='test6.png')

acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')

grid()

dev.off()

bitmap(file='test7.png')

pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')

grid()

dev.off()

bitmap(file='test8.png')

opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))

plot(mylm, las = 1, sub='Residual Diagnostics')

par(opar)

dev.off()

if (n > n25) {

bitmap(file='test9.png')

plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')

grid()

dev.off()

}

load(file='createtable')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)

a<-table.row.end(a)

myeq <- colnames(x)[1]

myeq <- paste(myeq, '[t] = ', sep='')

for (i in 1:k){

if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')

myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')

if (rownames(mysum$coefficients)[i] != '(Intercept)') {

myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')

if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')

}

}

myeq <- paste(myeq, ' + e[t]')

a<-table.row.start(a)

a<-table.element(a, myeq)

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,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'Variable',header=TRUE)

a<-table.element(a,'Parameter',header=TRUE)

a<-table.element(a,'S.D.',header=TRUE)

a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE)

a<-table.element(a,'2-tail p-value',header=TRUE)

a<-table.element(a,'1-tail p-value',header=TRUE)

a<-table.row.end(a)

for (i in 1:k){

a<-table.row.start(a)

a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)

a<-table.element(a,mysum$coefficients[i,1])

a<-table.element(a, round(mysum$coefficients[i,2],6))

a<-table.element(a, round(mysum$coefficients[i,3],4))

a<-table.element(a, round(mysum$coefficients[i,4],6))

a<-table.element(a, round(mysum$coefficients[i,4]/2,6))

a<-table.row.end(a)

}

a<-table.end(a)

table.save(a,file='mytable2.tab')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'Multiple R',1,TRUE)

a<-table.element(a, sqrt(mysum$r.squared))

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'R-squared',1,TRUE)

a<-table.element(a, mysum$r.squared)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'Adjusted R-squared',1,TRUE)

a<-table.element(a, mysum$adj.r.squared)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'F-TEST (value)',1,TRUE)

a<-table.element(a, mysum$fstatistic[1])

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)

a<-table.element(a, mysum$fstatistic[2])

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)

a<-table.element(a, mysum$fstatistic[3])

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'p-value',1,TRUE)

a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'Residual Standard Deviation',1,TRUE)

a<-table.element(a, mysum$sigma)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'Sum Squared Residuals',1,TRUE)

a<-table.element(a, sum(myerror*myerror))

a<-table.row.end(a)

a<-table.end(a)

table.save(a,file='mytable3.tab')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'Time or Index', 1, TRUE)

a<-table.element(a, 'Actuals', 1, TRUE)

a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE)

a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE)

a<-table.row.end(a)

for (i in 1:n) {

a<-table.row.start(a)

a<-table.element(a,i, 1, TRUE)

a<-table.element(a,x[i])

a<-table.element(a,x[i]-mysum$resid[i])

a<-table.element(a,mysum$resid[i])

a<-table.row.end(a)

}

a<-table.end(a)

table.save(a,file='mytable4.tab')

if (n > n25) {

a<-table.start()

a<-table.row.start(a)

a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'p-values',header=TRUE)

a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'breakpoint index',header=TRUE)

a<-table.element(a,'greater',header=TRUE)

a<-table.element(a,'2-sided',header=TRUE)

a<-table.element(a,'less',header=TRUE)

a<-table.row.end(a)

for (mypoint in kp3:nmkm3) {

a<-table.row.start(a)

a<-table.element(a,mypoint,header=TRUE)

a<-table.element(a,gqarr[mypoint-kp3+1,1])

a<-table.element(a,gqarr[mypoint-kp3+1,2])

a<-table.element(a,gqarr[mypoint-kp3+1,3])

a<-table.row.end(a)

}

a<-table.end(a)

table.save(a,file='mytable5.tab')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'Description',header=TRUE)

a<-table.element(a,'# significant tests',header=TRUE)

a<-table.element(a,'% significant tests',header=TRUE)

a<-table.element(a,'OK/NOK',header=TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'1% type I error level',header=TRUE)

a<-table.element(a,numsignificant1)

a<-table.element(a,numsignificant1/numgqtests)

if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'

a<-table.element(a,dum)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'5% type I error level',header=TRUE)

a<-table.element(a,numsignificant5)

a<-table.element(a,numsignificant5/numgqtests)

if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'

a<-table.element(a,dum)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'10% type I error level',header=TRUE)

a<-table.element(a,numsignificant10)

a<-table.element(a,numsignificant10/numgqtests)

if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'

a<-table.element(a,dum)

a<-table.row.end(a)

a<-table.end(a)

table.save(a,file='mytable6.tab')

}

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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