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workshop 7

*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, 20 Nov 2009 07:31:26 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/20/t1258727590js7ojf76qskiydm.htm/, Retrieved Fri, 20 Nov 2009 15:33:23 +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/2009/Nov/20/t1258727590js7ojf76qskiydm.htm/},
    year = {2009},
}
@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 = {2009},
    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 «

8.0 2.77 8.0 7.8 7.6 7.6 8.0 2.93 8.0 8.0 7.8 7.6 7.9 2.91 8.0 8.0 8.0 7.8 7.9 2.69 7.9 8.0 8.0 8.0 8.0 2.38 7.9 7.9 8.0 8.0 8.5 2.58 8.0 7.9 7.9 8.0 9.2 3.19 8.5 8.0 7.9 7.9 9.4 2.82 9.2 8.5 8.0 7.9 9.5 2.72 9.4 9.2 8.5 8.0 9.5 2.53 9.5 9.4 9.2 8.5 9.6 2.70 9.5 9.5 9.4 9.2 9.7 2.42 9.6 9.5 9.5 9.4 9.7 2.50 9.7 9.6 9.5 9.5 9.6 2.31 9.7 9.7 9.6 9.5 9.5 2.41 9.6 9.7 9.7 9.6 9.4 2.56 9.5 9.6 9.7 9.7 9.3 2.76 9.4 9.5 9.6 9.7 9.6 2.71 9.3 9.4 9.5 9.6 10.2 2.44 9.6 9.3 9.4 9.5 10.2 2.46 10.2 9.6 9.3 9.4 10.1 2.12 10.2 10.2 9.6 9.3 9.9 1.99 10.1 10.2 10.2 9.6 9.8 1.86 9.9 10.1 10.2 10.2 9.8 1.88 9.8 9.9 10.1 10.2 9.7 1.82 9.8 9.8 9.9 10.1 9.5 1.74 9.7 9.8 9.8 9.9 9.3 1.71 9.5 9.7 9.8 9.8 9.1 1.38 9.3 9.5 9.7 9.8 9.0 1.27 9.1 9.3 9.5 9.7 9.5 1.19 9.0 9.1 9.3 9.5 10.0 1.28 9.5 9.0 9.1 9.3 10.2 1.19 10.0 9.5 9.0 9.1 10.1 1.22 10.2 10.0 9.5 9.0 10.0 1.47 10.1 10.2 10.0 9.5 9.9 1.46 10.0 10.1 10.2 10.0 10.0 1.96 9.9 10.0 10.1 10.2 9.9 1.88 10.0 9.9 10.0 10.1 9.7 2.03 9.9 10.0 9.9 10.0 etc...

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	5 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

Y[t] = + 0.218696812913364 + 0.0214033923580752X[t] + 1.38294217269954Y1[t] -0.440570189496239Y2[t] -0.255229751929124Y3[t] + 0.289096046118345Y4[t] -0.161991160311381M1[t] -0.138075749392786M2[t] -0.118629659389799M3[t] -0.158456291128355M4[t] -0.106289572157702M5[t] + 0.448837334806040M6[t] + 0.0935944507375918M7[t] -0.115701160265447M8[t] + 0.0501367232538751M9[t] -0.0165214692594234M10[t] + 0.0682679561748867M11[t] -0.000532440156977438t + 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)	0.218696812913364	0.189627	1.1533	0.250673	0.125337
X	0.0214033923580752	0.021647	0.9887	0.324425	0.162213
Y1	1.38294217269954	0.079547	17.3852	0	0
Y2	-0.440570189496239	0.139215	-3.1647	0.00189	0.000945
Y3	-0.255229751929124	0.139883	-1.8246	0.070106	0.035053
Y4	0.289096046118345	0.080791	3.5783	0.00047	0.000235
M1	-0.161991160311381	0.068284	-2.3723	0.01898	0.00949
M2	-0.138075749392786	0.069296	-1.9926	0.048174	0.024087
M3	-0.118629659389799	0.068567	-1.7301	0.085723	0.042861
M4	-0.158456291128355	0.06797	-2.3313	0.021107	0.010553
M5	-0.106289572157702	0.068547	-1.5506	0.123161	0.06158
M6	0.448837334806040	0.067849	6.6152	0	0
M7	0.0935944507375918	0.075713	1.2362	0.21838	0.10919
M8	-0.115701160265447	0.084064	-1.3763	0.170823	0.085411
M9	0.0501367232538751	0.084889	0.5906	0.555693	0.277847
M10	-0.0165214692594234	0.076516	-0.2159	0.829349	0.414675
M11	0.0682679561748867	0.069499	0.9823	0.32758	0.16379
t	-0.000532440156977438	0.000333	-1.5975	0.112312	0.056156

Multiple Linear Regression - Regression Statistics
Multiple R	0.988075861397124
R-squared	0.97629390787567
Adjusted R-squared	0.97353360947763
F-TEST (value)	353.691437334976
F-TEST (DF numerator)	17
F-TEST (DF denominator)	146
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.171762517264902
Sum Squared Residuals	4.30734490122769

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	8	7.99993434864062	6.56513593800204e-05
2	8	7.88758187389446	0.112418126105540
3	7.9	7.91284071473113	-0.0128407147311306
4	7.9	7.78729788847055	0.112702111529449
5	8	7.87635413460285	0.123645865397153
6	8.5	8.5990464723441	-0.0990464723440924
7	9.2	8.8748316802454	0.325168319754592
8	9.4	9.37933582486155	0.0206641751384513
9	9.5	9.4119849595279	0.0880150404720975
10	9.5	9.35679505838908	0.143204941610919
11	9.6	9.55195488331468	0.0480451166853189
12	9.7	9.64775198842327	0.0522480115767324
13	9.7	9.61008746227572	0.0899125377242815
14	9.6	9.55982379434677	0.0401762056532345
15	9.5	9.44597019557755	0.0540298044224499
16	9.4	9.34349403882723	0.0565059611727672
17	9.3	9.3306947729851	-0.0306947729851053
18	9.6	9.78659524243471	-0.186595242434714
19	10.2	9.88059404361317	0.319405956386828
20	10.2	10.3654016776522	-0.165401677652248
21	10.1	10.1536093237245	-0.0536093237245325
22	9.9	9.87893299545578	0.0210670045442195
23	9.8	9.90133375180729	-0.101333751807287
24	9.8	9.80830421914479	-0.00830421914478972
25	9.7	9.71068977985856	-0.010689779858562
26	9.5	9.56177002793082	-0.0617700279308206
27	9.3	9.31860055580397	-0.0186005558039693
28	9.1	9.10822694298252	-0.00822694298252507
29	9	8.99116879777014	0.00883120222986119
30	9.5	9.4870975549797	0.0129024450202934
31	10	9.86200338252806	0.137996617471940
32	10.2	10.0891387836267	0.110861216373288
33	10.1	10.1548651879752	-0.0548651879751908
34	10	9.88355029531984	0.116449704680158
35	9.9	9.96685812102661	-0.0668581210266119
36	10	9.89786440697004	0.102135593029963
37	9.9	9.91259314191369	-0.0125931419136879
38	9.7	9.75344875589052	-0.053448755890519
39	9.5	9.48561244426507	0.0143875557349250
40	9.2	9.3082150806035	-0.108215080603500
41	9	9.05307675204474	-0.0530767520447411
42	9.3	9.4590489894056	-0.159048989405593
43	9.8	9.62502007124435	0.174979928755652
44	9.8	9.93987935575346	-0.139879355753456
45	9.6	9.76099923182073	-0.160999231820733
46	9.4	9.37419376324568	0.0258062367543196
47	9.3	9.4181629516424	-0.118162951642399
48	9.2	9.34551958000688	-0.145519580006878
49	9.2	9.07492240290218	0.125077597097823
50	9	9.09893639455646	-0.0989363945564631
51	8.8	8.83359430197203	-0.033594301972027
52	8.7	8.58270031437858	0.117299685621415
53	8.7	8.63862490698467	0.0613750930153314
54	9.1	9.23371364275692	-0.133713642756924
55	9.7	9.39796281788624	0.302037182113762
56	9.8	9.80783960969326	-0.00783960969325669
57	9.6	9.73815617030158	-0.138156170301581
58	9.4	9.3153890585146	0.0846109414853975
59	9.4	9.35332738369269	0.0466726163073101
60	9.5	9.43697210383634	0.0630278961636623
61	9.4	9.41281854735467	-0.0128185473546724
62	9.3	9.20202402253331	0.0979759774666949
63	9.2	9.11166516112153	0.0883348388784693
64	9	9.03899265803574	-0.0389926580357383
65	8.9	8.84892997590353	0.0510700240964726
66	9.2	9.33797173420014	-0.137971734200141
67	9.8	9.45064442501693	0.349355574983075
68	9.9	9.91424767569308	-0.0142476756930777
69	9.6	9.84888282813138	-0.248882828131385
70	9.2	9.25035053751939	-0.0503505375193881
71	9.1	9.06175039696745	0.0382496030325490
72	9.1	9.1440676106036	-0.0440676106036082
73	9	9.04160621779176	-0.0416062177917615
74	8.9	8.84193037611852	0.0580696238814814
75	8.7	8.73641301949088	-0.0364130194908797
76	8.5	8.4819823877198	0.0180176122801927
77	8.3	8.3396153012381	-0.0396153012380927
78	8.5	8.72594541186596	-0.225945411865961
79	8.7	8.73366418325495	-0.0336641832549470
80	8.4	8.711530219758	-0.311530219758007
81	8.1	8.26732818696114	-0.167328186961138
82	7.8	7.92912199841007	-0.129121998410071
83	7.7	7.87383091439563	-0.173830914395631
84	7.5	7.7855369605322	-0.285536960532207
85	7.2	7.38374659899409	-0.183746598994089
86	6.8	7.0257901688335	-0.225790168833505
87	6.7	6.64112560590378	0.0588743940962178
88	6.4	6.66001851597483	-0.260018515974828
89	6.3	6.36881825035568	-0.068818250355677
90	6.8	6.82803024918125	-0.0280302491812544
91	7.3	7.25736865653435	0.0426313434656451
92	7.1	7.46779438666528	-0.367794386665276
93	7	6.97135449714355	0.0286455028564546
94	6.8	6.87369927320372	-0.0736992732037239
95	6.6	6.90796274699734	-0.307962746997343
96	6.3	6.61218473621022	-0.312184736210219
97	6.1	6.14609903722314	-0.04609903722314
98	6.1	6.01486682867858	0.0851331713214155
99	6.3	6.15562660742956	0.144373392570437
100	6.3	6.36366429394959	-0.0636642939495871
101	6	6.26487061324515	-0.264870613245149
102	6.2	6.34754352799597	-0.147543527995965
103	6.4	6.45877497223015	-0.0587749722301495
104	6.8	6.50521485242272	0.294785147577279
105	7.5	6.99973466805653	0.500265331943468
106	7.5	7.72643999299651	-0.226439992996508
107	7.6	7.4590953236964	0.140904676303603
108	7.6	7.48097717922925	0.119022820770747
109	7.4	7.47098487615743	-0.0709848761574307
110	7.3	7.19311257288055	0.106887427119448
111	7.1	7.17234873053974	-0.0723487305397426
112	6.9	6.94023056510787	-0.0402305651078727
113	6.8	6.761462686689	0.0385373133110015
114	7.5	7.29657467684228	0.203425323157725
115	7.6	7.94571456577115	-0.345714565771149
116	7.8	7.53348536520296	0.266514634797038
117	8	7.72439389496411	0.275606105035888
118	8.1	8.0184552714764	0.0815447285236073
119	8.2	8.13653500628712	0.0634649937128786
120	8.3	8.16532052433614	0.134679475663862
121	8.2	8.14067415416865	0.0593258458313496
122	8	7.98552058597677	0.0144794140232293
123	7.9	7.76929649979116	0.130703500208844
124	7.6	7.72377233569211	-0.123772335692112
125	7.6	7.43913129498722	0.160868705012778
126	8.3	8.09081814360555	0.209181856394451
127	8.4	8.75718267894413	-0.357182678944133
128	8.4	8.29073493249478	0.109265067505221
129	8.4	8.22861378423834	0.171386215761664
130	8.4	8.34426035851825	0.0557396414817489
131	8.6	8.45485854132445	0.145141458675550
132	8.9	8.65943607067878	0.240563929321219
133	8.8	8.81661796464287	-0.0166179646428731
134	8.3	8.51570726989329	-0.215707269893291
135	7.5	7.88536581594696	-0.385365815946965
136	7.2	7.08595823039541	0.114041769604595
137	7.4	7.16638009302361	0.23361990697639
138	8.8	8.192580338557	0.607419661443008
139	9.3	9.52689159804203	-0.226891598042029
140	9.3	9.24903882347336	0.0509611765266366
141	8.7	8.91232154426769	-0.212321544267688
142	8.2	8.2858501449478	-0.0858501449478024
143	8.3	8.08153323077202	0.218466769227983
144	8.5	8.52423596369212	-0.0242359636921239
145	8.6	8.5550360787386	0.0449639212613928
146	8.5	8.46922992679788	0.0307700732021162
147	8.2	8.27702094301932	-0.0770209430193227
148	8.1	7.89278162420479	0.207218375795213
149	7.9	8.00043054365104	-0.100430543651034
150	8.6	8.3759318317711	0.224068168228902
151	8.7	9.01448212592127	-0.314482125921266
152	8.7	8.65775567477573	0.0422443252242692
153	8.5	8.52775572288732	-0.0277557228873226
154	8.4	8.36296125200288	0.0370387479971244
155	8.5	8.43279674807592	0.0672032519240788
156	8.7	8.59182865633636	0.108171343663640
157	8.7	8.624189389338	0.0758106106619902
158	8.6	8.49025740166856	0.109742598331439
159	8.5	8.3545194044073	0.145480595592694
160	8.3	8.28266512365747	0.0173348763425314
161	8	8.12044187651919	-0.120441876519189
162	8.2	8.33910218405973	-0.139102184059734
163	8.1	8.41486479876782	-0.314864798767821
164	8.1	7.98860281792686	0.111397182073139

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
21	0.0163357686074060	0.0326715372148121	0.983664231392594
22	0.00334829218077274	0.00669658436154549	0.996651707819227
23	0.000627985354217949	0.00125597070843590	0.999372014645782
24	0.00216674968245384	0.00433349936490768	0.997833250317546
25	0.000857920630618136	0.00171584126123627	0.999142079369382
26	0.000298430339332507	0.000596860678665013	0.999701569660667
27	8.8473222566525e-05	0.00017694644513305	0.999911526777433
28	7.33684069859946e-05	0.000146736813971989	0.999926631593014
29	1.92346611245317e-05	3.84693222490634e-05	0.999980765338875
30	4.11374083538347e-05	8.22748167076694e-05	0.999958862591646
31	7.00045475054603e-05	0.000140009095010921	0.999929995452495
32	2.94832686394765e-05	5.8966537278953e-05	0.99997051673136
33	1.27262529376994e-05	2.54525058753989e-05	0.999987273747062
34	4.97329109433351e-06	9.94658218866703e-06	0.999995026708906
35	1.60252834949155e-06	3.20505669898311e-06	0.99999839747165
36	3.54621980007247e-06	7.09243960014494e-06	0.9999964537802
37	1.99721306392272e-06	3.99442612784544e-06	0.999998002786936
38	6.91888596496511e-07	1.38377719299302e-06	0.999999308111404
39	2.26592062592814e-07	4.53184125185629e-07	0.999999773407937
40	1.43158813397703e-07	2.86317626795407e-07	0.999999856841187
41	6.5376260532538e-08	1.30752521065076e-07	0.99999993462374
42	2.51617845274439e-08	5.03235690548878e-08	0.999999974838215
43	1.52183432237809e-08	3.04366864475618e-08	0.999999984781657
44	4.94393360118467e-09	9.88786720236934e-09	0.999999995056066
45	1.63997542157751e-09	3.27995084315503e-09	0.999999998360025
46	6.24852466291475e-10	1.24970493258295e-09	0.999999999375148
47	4.09357080156452e-10	8.18714160312904e-10	0.999999999590643
48	1.70913854819413e-10	3.41827709638826e-10	0.999999999829086
49	5.84910290747484e-10	1.16982058149497e-09	0.99999999941509
50	2.39178133890418e-10	4.78356267780836e-10	0.999999999760822
51	8.5855446840273e-11	1.71710893680546e-10	0.999999999914145
52	4.420510174586e-11	8.841020349172e-11	0.999999999955795
53	5.42119935740874e-11	1.08423987148175e-10	0.999999999945788
54	1.85663213541309e-11	3.71326427082619e-11	0.999999999981434
55	2.23924783037401e-11	4.47849566074802e-11	0.999999999977607
56	7.6881190342904e-12	1.53762380685808e-11	0.999999999992312
57	1.7243596343106e-11	3.4487192686212e-11	0.999999999982756
58	1.22749157836800e-11	2.45498315673600e-11	0.999999999987725
59	7.66765689909576e-12	1.53353137981915e-11	0.999999999992332
60	4.54497325590115e-12	9.08994651180231e-12	0.999999999995455
61	1.86311092168957e-12	3.72622184337915e-12	0.999999999998137
62	7.98045748313551e-13	1.59609149662710e-12	0.999999999999202
63	6.88591880002961e-13	1.37718376000592e-12	0.999999999999311
64	2.53374393601352e-13	5.06748787202704e-13	0.999999999999747
65	1.25864909964112e-13	2.51729819928224e-13	0.999999999999874
66	8.69348486020997e-14	1.73869697204199e-13	0.999999999999913
67	5.86863166892948e-13	1.17372633378590e-12	0.999999999999413
68	2.26804408845946e-13	4.53608817691891e-13	0.999999999999773
69	1.73224548716259e-12	3.46449097432517e-12	0.999999999998268
70	4.88195073662597e-11	9.76390147325194e-11	0.99999999995118
71	2.38619373968637e-11	4.77238747937274e-11	0.999999999976138
72	1.12506749867814e-11	2.25013499735628e-11	0.99999999998875
73	4.98351452800972e-12	9.96702905601944e-12	0.999999999995016
74	4.82383798642279e-12	9.64767597284558e-12	0.999999999995176
75	2.35688423201181e-12	4.71376846402361e-12	0.999999999997643
76	1.64621893326811e-12	3.29243786653623e-12	0.999999999998354
77	2.24912145522489e-12	4.49824291044979e-12	0.99999999999775
78	2.90436416481181e-12	5.80872832962361e-12	0.999999999997096
79	8.67104538361769e-10	1.73420907672354e-09	0.999999999132895
80	1.98815290012723e-09	3.97630580025446e-09	0.999999998011847
81	1.56792090286952e-09	3.13584180573904e-09	0.99999999843208
82	8.27460677297655e-10	1.65492135459531e-09	0.99999999917254
83	4.08507591418838e-10	8.17015182837677e-10	0.999999999591492
84	1.04466830262749e-09	2.08933660525498e-09	0.999999998955332
85	6.28386355368256e-10	1.25677271073651e-09	0.999999999371614
86	4.51835107943857e-10	9.03670215887715e-10	0.999999999548165
87	2.69893375264926e-09	5.39786750529853e-09	0.999999997301066
88	3.43094130953231e-09	6.86188261906462e-09	0.999999996569059
89	1.90995312236469e-09	3.81990624472938e-09	0.999999998090047
90	4.69310062633659e-09	9.38620125267318e-09	0.9999999953069
91	1.25977690588088e-08	2.51955381176177e-08	0.99999998740223
92	2.64527356865801e-07	5.29054713731602e-07	0.999999735472643
93	3.55623996672693e-07	7.11247993345387e-07	0.999999644376003
94	1.90691352123106e-07	3.81382704246212e-07	0.999999809308648
95	1.9511354252912e-06	3.9022708505824e-06	0.999998048864575
96	4.77896846057607e-05	9.55793692115214e-05	0.999952210315394
97	3.86734850744292e-05	7.73469701488584e-05	0.999961326514926
98	9.10359430658777e-05	0.000182071886131755	0.999908964056934
99	0.000322985609240111	0.000645971218480222	0.99967701439076
100	0.000304684703127305	0.000609369406254610	0.999695315296873
101	0.00124104794189170	0.00248209588378339	0.998758952058108
102	0.00354224977905592	0.00708449955811184	0.996457750220944
103	0.00487207400573916	0.00974414801147833	0.99512792599426
104	0.0372121725070368	0.0744243450140736	0.962787827492963
105	0.186470013727103	0.372940027454206	0.813529986272897
106	0.395983083014587	0.791966166029175	0.604016916985413
107	0.42351218032527	0.84702436065054	0.57648781967473
108	0.376043272440850	0.752086544881699	0.62395672755915
109	0.365053977457289	0.730107954914578	0.634946022542711
110	0.337250546920059	0.674501093840118	0.662749453079941
111	0.359940833842836	0.719881667685673	0.640059166157164
112	0.415210373437472	0.830420746874944	0.584789626562528
113	0.379996419091606	0.759992838183211	0.620003580908394
114	0.459426932393181	0.918853864786363	0.540573067606819
115	0.667899139590394	0.664201720819213	0.332100860409606
116	0.683497310414454	0.633005379171091	0.316502689585546
117	0.651841874700923	0.696316250598155	0.348158125299077
118	0.659198834167727	0.681602331664546	0.340801165832273
119	0.712972035124655	0.57405592975069	0.287027964875345
120	0.6741537368076	0.651692526384801	0.325846263192401
121	0.623910713011932	0.752178573976136	0.376089286988068
122	0.572940334141905	0.854119331716189	0.427059665858094
123	0.540373850230188	0.919252299539625	0.459626149769812
124	0.691056157599604	0.617887684800792	0.308943842400396
125	0.66616746750339	0.66766506499322	0.33383253249661
126	0.661774238265537	0.676451523468925	0.338225761734463
127	0.671493073790399	0.657013852419203	0.328506926209601
128	0.61427447775874	0.77145104448252	0.38572552224126
129	0.570101869618859	0.859796260762282	0.429898130381141
130	0.543382415710049	0.913235168579902	0.456617584289951
131	0.505333532486843	0.989332935026314	0.494666467513157
132	0.550141811583726	0.899716376832549	0.449858188416274
133	0.484087630039703	0.968175260079406	0.515912369960297
134	0.44035306235108	0.88070612470216	0.55964693764892
135	0.699038384458634	0.601923231082733	0.300961615541366
136	0.712107463607792	0.575785072784415	0.287892536392208
137	0.644727674088471	0.710544651823058	0.355272325911529
138	0.804223915557246	0.391552168885507	0.195776084442753
139	0.736208480156524	0.527583039686952	0.263791519843476
140	0.718094712965841	0.563810574068317	0.281905287034159
141	0.619994197232253	0.760011605535495	0.380005802767747
142	0.498399200924907	0.996798401849814	0.501600799075093
143	0.411699859261908	0.823399718523816	0.588300140738092

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	82	0.666666666666667	NOK
5% type I error level	83	0.67479674796748	NOK
10% type I error level	84	0.682926829268293	NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/20/t1258727590js7ojf76qskiydm/10ltd41258727480.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t1258727590js7ojf76qskiydm/10ltd41258727480.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t1258727590js7ojf76qskiydm/1n58j1258727480.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t1258727590js7ojf76qskiydm/1n58j1258727480.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t1258727590js7ojf76qskiydm/242qr1258727480.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t1258727590js7ojf76qskiydm/242qr1258727480.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t1258727590js7ojf76qskiydm/3e8x11258727480.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t1258727590js7ojf76qskiydm/3e8x11258727480.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t1258727590js7ojf76qskiydm/4lwkn1258727480.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t1258727590js7ojf76qskiydm/4lwkn1258727480.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t1258727590js7ojf76qskiydm/5z2bs1258727480.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t1258727590js7ojf76qskiydm/5z2bs1258727480.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t1258727590js7ojf76qskiydm/66mrq1258727480.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t1258727590js7ojf76qskiydm/66mrq1258727480.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t1258727590js7ojf76qskiydm/7lk5b1258727480.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t1258727590js7ojf76qskiydm/7lk5b1258727480.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t1258727590js7ojf76qskiydm/809pv1258727480.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t1258727590js7ojf76qskiydm/809pv1258727480.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t1258727590js7ojf76qskiydm/9st4n1258727480.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/20/t1258727590js7ojf76qskiydm/9st4n1258727480.ps (open in new window)

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')

}

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Software written by Ed van Stee & Patrick Wessa

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