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

Title produced by software: Multiple Regression

Date of computation: Sun, 13 Dec 2009 03:32:52 -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/Dec/13/t1260700464bbjs2anchh7n0v7.htm/, Retrieved Sun, 13 Dec 2009 11:34:37 +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/Dec/13/t1260700464bbjs2anchh7n0v7.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 «

6.5 2.77 6.6 6.7 6.8 6.9 6.5 2.64 6.5 6.6 6.7 6.8 7.0 2.56 6.5 6.5 6.6 6.7 7.5 2.07 7.0 6.5 6.5 6.6 7.6 2.32 7.5 7.0 6.5 6.5 7.6 2.16 7.6 7.5 7.0 6.5 7.6 2.23 7.6 7.6 7.5 7.0 7.8 2.40 7.6 7.6 7.6 7.5 8.0 2.84 7.8 7.6 7.6 7.6 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 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	6 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

Y[t] = + 0.103329771420464 + 0.0213844325900316X[t] + 1.38121539673783Y1[t] -0.434524571311922Y2[t] -0.253938773069359Y3[t] + 0.283796486784859Y4[t] -0.0427107358517383M1[t] + 0.0132171205717539M2[t] + 0.562383896769684M3[t] + 0.219755046500052M4[t] -0.00184900361398463M5[t] + 0.159889281175896M6[t] + 0.102181838949999M7[t] + 0.191043321198795M8[t] + 0.121577999327065M9[t] -0.0423727220174399M10[t] -0.0197066669911787M11[t] -0.000546832253316618t + 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)	0.103329771420464	0.159121	0.6494	0.517037	0.258518
X	0.0213844325900316	0.020724	1.0319	0.303706	0.151853
Y1	1.38121539673783	0.076257	18.1127	0	0
Y2	-0.434524571311922	0.132308	-3.2842	0.00126	0.00063
Y3	-0.253938773069359	0.132365	-1.9185	0.056854	0.028427
Y4	0.283796486784859	0.076091	3.7297	0.000267	0.000133
M1	-0.0427107358517383	0.062477	-0.6836	0.495217	0.247609
M2	0.0132171205717539	0.063494	0.2082	0.83537	0.417685
M3	0.562383896769684	0.064013	8.7854	0	0
M4	0.219755046500052	0.079107	2.7779	0.006133	0.003067
M5	-0.00184900361398463	0.08039	-0.023	0.981679	0.490839
M6	0.159889281175896	0.072467	2.2064	0.028801	0.0144
M7	0.102181838949999	0.065869	1.5513	0.122832	0.061416
M8	0.191043321198795	0.061677	3.0975	0.00231	0.001155
M9	0.121577999327065	0.064925	1.8726	0.062973	0.031486
M10	-0.0423727220174399	0.066381	-0.6383	0.524183	0.262091
M11	-0.0197066669911787	0.063727	-0.3092	0.757549	0.378775
t	-0.000546832253316618	0.000269	-2.0362	0.0434	0.0217

Multiple Linear Regression - Regression Statistics
Multiple R	0.988871370422935
R-squared	0.977866587242134
Adjusted R-squared	0.9754851440973
F-TEST (value)	410.619329444628
F-TEST (DF numerator)	17
F-TEST (DF denominator)	158
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.165843506022096
Sum Squared Residuals	4.34564282137274

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	6.5	6.5554261742135	-0.0554261742134966
2	6.5	6.51037236823283	-0.0103723682328288
3	7	7.09774824332988	-0.09774824332988
4	7.5	7.43171611583518	0.0682838841648196
5	7.6	7.6598771056498	-0.0598771056498073
6	7.6	7.61153691645511	-0.0115369164551084
7	7.6	7.52625595198375	0.0737440480162446
8	7.8	7.73471032160503	0.0652896783949673
9	8	7.97873004584565	0.0212699541543462
10	8	8.00207374705171	-0.00207374705171083
11	8	7.8899218101628	0.110078189837195
12	7.9	7.91462549899197	-0.0146254989919655
13	7.9	7.7853011134003	0.114698886599707
14	8	7.87750542059875	0.122494579401249
15	8.5	8.59391766804209	-0.093917668042089
16	9.2	8.8825620819583	0.317437918041701
17	9.4	9.37669357428622	0.0233064257137833
18	9.5	9.40923272513681	0.0907672748631918
19	9.5	9.36227313612076	0.137726863879236
20	9.6	9.55864046866089	0.0413595313391135
21	9.7	9.65212763313445	0.0478723668655492
22	9.7	9.6123895653649	0.0876104346350919
23	9.6	9.56159941150762	0.0384005884923821
24	9.5	9.44776192120225	0.0522380787977494
25	9.4	9.3414225841216	0.0585774158784047
26	9.3	9.33180528957412	-0.0318052895741221
27	9.6	9.7817011579751	-0.181701157975095
28	10.2	9.88758298343383	0.312417016566173
29	10.2	10.3612458849958	-0.161245884995846
30	10.1	10.1498906070654	-0.0498906070653545
31	9.9	9.8835104988695	0.0164895011305049
32	9.8	9.90653244248281	-0.106532442482812
33	9.8	9.8111252289051	-0.0111252289051036
34	9.7	9.71120517241846	-0.0112051724184589
35	9.5	9.56212668086038	-0.0621266808603795
36	9.3	9.31947471172568	-0.0194747117256815
37	9.1	9.10521599308767	-0.005215993087672
38	9	8.99131467052315	0.00868532947685446
39	9.5	9.48103569170606	0.0189643082939415
40	10	9.86787322087322	0.132126779126779
41	10.2	10.0857777322357	0.114222267764316
42	10.1	10.1512424762284	-0.0512424762283885
43	10	9.88823671281827	0.111763287181735
44	9.9	9.97277892472381	-0.0727789247238114
45	10	9.9009430790151	0.099056920984902
46	9.9	9.9133229962435	-0.0133229962434981
47	9.7	9.75409011572842	-0.0540901157284234
48	9.5	9.48689964659039	0.0131003534096119
49	9.2	9.30508361882297	-0.105083618822970
50	9	9.05327460091056	-0.0532746009105622
51	9.3	9.4526034260689	-0.152603426068890
52	9.8	9.63011961139351	0.169880388606489
53	9.8	9.93493708620941	-0.134937086209412
54	9.6	9.75640369578135	-0.156403695781353
55	9.4	9.37793745819635	0.0220625418036537
56	9.3	9.42244754003938	-0.122447540039379
57	9.2	9.347301939947	-0.147301939947001
58	9.2	9.07510689830877	0.124893101691225
59	9	9.09819325321606	-0.0981932532160595
60	8.8	8.8338473507168	-0.0338473507167997
61	8.7	8.57971498727689	0.120285012723111
62	8.7	8.63808864986394	0.0619113501360601
63	9.1	9.22739717308515	-0.127397173085151
64	9.7	9.4044868519037	0.295513148096302
65	9.8	9.80395731088008	-0.00395731088007977
66	9.6	9.73413703264672	-0.134137032646724
67	9.4	9.31990868447188	0.0800913155281188
68	9.4	9.35799538734685	0.0420046126531497
69	9.5	9.43844491498582	0.061555085014176
70	9.4	9.4129403767475	-0.0129403767474939
71	9.3	9.2027139464837	0.0972860535162994
72	9.2	9.11228919334115	0.0877108066588468
73	9	9.03562062008544	-0.0356206200854371
74	8.9	8.84945145386838	0.0505485461316185
75	9.2	9.33189371877963	-0.131893718779630
76	9.8	9.45632640311649	0.343673596883514
77	9.9	9.90930805173243	-0.00930805173243436
78	9.6	9.84420039785994	-0.244200397859937
79	9.2	9.25491708829681	-0.054917088296814
80	9.1	9.06620081008062	0.0337991899193833
81	9.1	9.14413662113826	-0.0441366211382616
82	9	9.04016962084162	-0.0401696208416182
83	8.9	8.84138869468128	0.0586113053187203
84	8.7	8.73621673224266	-0.0362167322426645
85	8.5	8.47850555647346	0.0214944435265415
86	8.3	8.3394242009279	-0.0394242009278998
87	8.5	8.71918948678962	-0.219189486789616
88	8.7	8.73875020760693	-0.038750207606925
89	8.4	8.70595358870686	-0.305953588706861
90	8.1	8.26068074357375	-0.160680743573754
91	7.8	7.92930918370557	-0.129309183705573
92	7.7	7.87532513271297	-0.175325132712971
93	7.5	7.78538383130457	-0.285383831304565
94	7.2	7.38255985059012	-0.182559850590123
95	6.8	7.02410347397849	-0.224103473978491
96	6.7	6.63883805218038	0.0611619478196247
97	6.4	6.65325723940095	-0.253257239400946
98	6.3	6.36677948010137	-0.0667794801013696
99	6.8	6.82036591566237	-0.0203659156623685
100	7.3	7.26097697081495	0.0390230291850474
101	7.1	7.46269096007525	-0.362690960075248
102	7	6.966688083685	0.0333119163149927
103	6.8	6.87492601688885	-0.0749260168888494
104	6.6	6.91009153879434	-0.310091538794336
105	6.3	6.61317431408296	-0.313174314082963
106	6.1	6.14469438329106	-0.0446943832910636
107	6.1	6.01153484615251	0.0884651538474875
108	6.3	6.15199103252962	0.148008967470383
109	6.3	6.35810990375705	-0.0581099037570537
110	6	6.26533598546397	-0.265335985463967
111	6.2	6.34281591464815	-0.142815914648150
112	6.4	6.46342766887512	-0.0634276688751165
113	6.8	6.49802896615184	0.301971033848160
114	7.5	6.99079956140493	0.509200438595075
115	7.5	7.72685320369072	-0.226853203690718
116	7.6	7.46725366352658	0.132746336473417
117	7.6	7.48652129410553	0.113478705894465
118	7.4	7.47145502732661	-0.0714550273266129
119	7.3	7.19279267074866	0.107207329251342
120	7.1	7.17072491672618	-0.070724916726179
121	6.9	6.9351999533754	-0.0351999533754058
122	6.8	6.76025439774485	0.0397456022551489
123	7.5	7.28861959524946	0.211380404750537
124	7.6	7.94934791617929	-0.349347916179288
125	7.8	7.52978595351734	0.270214046482663
126	8	7.71827277142094	0.281727228579061
127	8.1	8.01855728327727	0.0814427167227327
128	8.2	8.14145424954807	0.0585457504519322
129	8.3	8.16866121149431	0.131338788505694
130	8.2	8.14153190976183	0.0584680902381685
131	8	7.98549059575315	0.0145094042468520
132	7.9	7.76885793852098	0.131142061479022
133	7.6	7.71874812065033	-0.118748120650334
134	7.6	7.43802805976795	0.161971940232045
135	8.3	8.0828599788194	0.217140021180596
136	8.4	8.76075238703227	-0.36075238703227
137	8.4	8.2876307427108	0.112369257289203
138	8.4	8.22290802179781	0.177091978202189
139	8.4	8.34390505188627	0.0560949481137286
140	8.6	8.45803321864943	0.141966781350567
141	8.9	8.66105647898345	0.238943521016553
142	8.8	8.81696176738988	-0.0169617673898806
143	8.3	8.5170343482449	-0.217034348244890
144	7.5	7.88651030892732	-0.386510308927318
145	7.2	7.08083079091747	0.119169209082527
146	7.4	7.16057203956552	0.239427960434481
147	8.8	8.18025287420284	0.619747125797162
148	9.3	9.52981061045488	-0.229810610454884
149	9.3	9.24908790647472	0.0509120935252796
150	8.7	8.91201116746492	-0.212011167464921
151	8.2	8.28874417580422	-0.0887441758042202
152	8.3	8.08307647248516	0.216923527514844
153	8.5	8.52059756320557	-0.0205975632055718
154	8.6	8.5522113003908	0.047788699609204
155	8.5	8.46894724417079	0.031052755829211
156	8.2	8.27749580206538	-0.0774958020653822
157	8.1	7.8893453839727	0.210654616027303
158	7.9	7.9984341615805	-0.0984341615804984
159	8.6	8.36783926335037	0.232160736649630
160	8.7	9.01803267110006	-0.318032671100063
161	8.7	8.65331345605303	0.0466865439469646
162	8.5	8.52178075446576	-0.0217807544657625
163	8.4	8.36268550734045	0.0373144926595483
164	8.5	8.43500619903183	0.0649938009681715
165	8.7	8.59179584385222	0.108204156147779
166	8.7	8.62337738427323	0.0766226157267711
167	8.6	8.49006290831124	0.109937091688754
168	8.5	8.35446689423925	0.145533105760753
169	8.3	8.27821796044428	0.0217820395557200
170	8	8.11935922127621	-0.119359221276209
171	8.2	8.331759892291	-0.131759892290998
172	8.1	8.41823429942228	-0.318234299422278
173	8.1	7.98171168032068	0.118288319679319
174	8	8.0502150450132	-0.0502150450132071
175	7.9	7.94198004664933	-0.0419800466493269
176	7.9	7.91045363031223	-0.0104536303122343

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
21	0.0256417733100014	0.0512835466200027	0.974358226689999
22	0.00766050091354612	0.0153210018270922	0.992339499086454
23	0.00188902278872398	0.00377804557744797	0.998110977211276
24	0.000574479905980257	0.00114895981196051	0.99942552009402
25	0.000782325205583507	0.00156465041116701	0.999217674794416
26	0.00431494789586449	0.00862989579172898	0.995685052104135
27	0.00401866360025182	0.00803732720050365	0.995981336399748
28	0.00381485886100847	0.00762971772201694	0.996185141138991
29	0.00216130006952829	0.00432260013905658	0.997838699930472
30	0.000985586760390352	0.00197117352078070	0.99901441323961
31	0.000723857123263818	0.00144771424652764	0.999276142876736
32	0.000348140053746615	0.00069628010749323	0.999651859946253
33	0.000171826473347383	0.000343652946694765	0.999828173526653
34	9.04031170597179e-05	0.000180806234119436	0.99990959688294
35	3.4938712208363e-05	6.9877424416726e-05	0.999965061287792
36	1.30535513669528e-05	2.61071027339055e-05	0.999986946448633
37	4.91284214334274e-06	9.82568428668548e-06	0.999995087157857
38	1.81441482595225e-06	3.6288296519045e-06	0.999998185585174
39	3.15698544580101e-06	6.31397089160203e-06	0.999996843014554
40	2.12991774001641e-06	4.25983548003282e-06	0.99999787008226
41	1.5741883470396e-06	3.1483766940792e-06	0.999998425811653
42	1.60851405194542e-06	3.21702810389085e-06	0.999998391485948
43	8.4633244253762e-07	1.69266488507524e-06	0.999999153667557
44	8.33170012396538e-07	1.66634002479308e-06	0.999999166829988
45	4.23997694732940e-07	8.47995389465879e-07	0.999999576002305
46	1.63483083564452e-07	3.26966167128903e-07	0.999999836516916
47	8.76991808704505e-08	1.75398361740901e-07	0.99999991230082
48	3.33568827539422e-08	6.67137655078844e-08	0.999999966643117
49	2.67706312882558e-08	5.35412625765115e-08	0.999999973229369
50	1.19292433362938e-08	2.38584866725877e-08	0.999999988070757
51	5.02210243548735e-09	1.00442048709747e-08	0.999999994977897
52	4.08834891727955e-09	8.1766978345591e-09	0.99999999591165
53	1.57123206612791e-09	3.14246413225583e-09	0.999999998428768
54	7.98750691677433e-10	1.59750138335487e-09	0.99999999920125
55	3.07078669327455e-10	6.14157338654909e-10	0.999999999692921
56	1.16567420977709e-10	2.33134841955417e-10	0.999999999883433
57	6.25384580045258e-11	1.25076916009052e-10	0.999999999937462
58	2.27528399435147e-10	4.55056798870295e-10	0.999999999772472
59	8.7885927654641e-11	1.75771855309282e-10	0.999999999912114
60	3.41772348202262e-11	6.83544696404525e-11	0.999999999965823
61	2.31561575634861e-11	4.63123151269723e-11	0.999999999976844
62	1.67700254733173e-11	3.35400509466346e-11	0.99999999998323
63	7.2735215312878e-12	1.45470430625756e-11	0.999999999992726
64	9.99755495212846e-12	1.99951099042569e-11	0.999999999990002
65	3.59910306332674e-12	7.19820612665349e-12	0.999999999996401
66	7.22625933509563e-12	1.44525186701913e-11	0.999999999992774
67	4.7839062872756e-12	9.5678125745512e-12	0.999999999995216
68	2.67023883336865e-12	5.34047766673729e-12	0.99999999999733
69	1.63351879801817e-12	3.26703759603635e-12	0.999999999998366
70	7.68882304373706e-13	1.53776460874741e-12	0.99999999999923
71	3.51899125079628e-13	7.03798250159255e-13	0.999999999999648
72	2.16891407430430e-13	4.33782814860861e-13	0.999999999999783
73	9.8742717660507e-14	1.97485435321014e-13	0.9999999999999
74	4.8325907832023e-14	9.6651815664046e-14	0.999999999999952
75	3.22771163065739e-14	6.45542326131477e-14	0.999999999999968
76	3.86349647352105e-13	7.7269929470421e-13	0.999999999999614
77	1.63746365774282e-13	3.27492731548564e-13	0.999999999999836
78	1.14689811258152e-12	2.29379622516304e-12	0.999999999998853
79	1.14441526904209e-11	2.28883053808418e-11	0.999999999988556
80	6.10133596490961e-12	1.22026719298192e-11	0.999999999993899
81	3.05061853071497e-12	6.10123706142994e-12	0.99999999999695
82	1.36626758393504e-12	2.73253516787008e-12	0.999999999998634
83	1.12345678981061e-12	2.24691357962122e-12	0.999999999998877
84	5.25396636565103e-13	1.05079327313021e-12	0.999999999999475
85	3.02605129368044e-13	6.05210258736088e-13	0.999999999999697
86	2.73449182860352e-13	5.46898365720704e-13	0.999999999999727
87	3.11301048128411e-13	6.22602096256821e-13	0.999999999999689
88	1.39856172406620e-11	2.79712344813241e-11	0.999999999986014
89	3.26686383676781e-11	6.53372767353562e-11	0.999999999967331
90	2.47258291768599e-11	4.94516583537198e-11	0.999999999975274
91	1.17428548632938e-11	2.34857097265877e-11	0.999999999988257
92	6.15833587078288e-12	1.23166717415658e-11	0.999999999993842
93	1.93026822267036e-11	3.86053644534072e-11	0.999999999980697
94	1.28884667578524e-11	2.57769335157047e-11	0.999999999987112
95	1.19890830689201e-11	2.39781661378403e-11	0.99999999998801
96	9.19711435906795e-11	1.83942287181359e-10	0.999999999908029
97	1.52295713006762e-10	3.04591426013525e-10	0.999999999847704
98	9.10045517936788e-11	1.82009103587358e-10	0.999999999908995
99	2.40289959694698e-10	4.80579919389396e-10	0.99999999975971
100	4.08816670169946e-10	8.17633340339892e-10	0.999999999591183
101	3.43006997377408e-08	6.86013994754816e-08	0.9999999656993
102	4.42536487452627e-08	8.85072974905255e-08	0.999999955746351
103	2.38031514918584e-08	4.76063029837168e-08	0.999999976196849
104	3.3460621674188e-07	6.6921243348376e-07	0.999999665393783
105	9.35759795158181e-06	1.87151959031636e-05	0.999990642402048
106	7.50111564958514e-06	1.50022312991703e-05	0.99999249888435
107	2.08622339310682e-05	4.17244678621363e-05	0.99997913776607
108	8.0627757661402e-05	0.000161255515322804	0.999919372242339
109	7.825291541669e-05	0.00015650583083338	0.999921747084583
110	0.000417158968586262	0.000834317937172525	0.999582841031414
111	0.00136140968083321	0.00272281936166642	0.998638590319167
112	0.00181075878989082	0.00362151757978163	0.99818924121011
113	0.0218170950181491	0.0436341900362983	0.97818290498185
114	0.155760138959567	0.311520277919134	0.844239861040433
115	0.325181920041366	0.650363840082732	0.674818079958634
116	0.349781569992455	0.699563139984909	0.650218430007546
117	0.302710134020007	0.605420268040015	0.697289865979993
118	0.303250977782286	0.606501955564572	0.696749022217714
119	0.27299247217018	0.54598494434036	0.72700752782982
120	0.298537946998624	0.597075893997249	0.701462053001376
121	0.329678310367624	0.659356620735249	0.670321689632376
122	0.292031504159433	0.584063008318866	0.707968495840567
123	0.359720835016945	0.71944167003389	0.640279164983055
124	0.549460506719191	0.901078986561618	0.450539493280809
125	0.575423723459573	0.849152553080853	0.424576276540427
126	0.566339586288757	0.867320827422486	0.433660413711243
127	0.53406685814822	0.93186628370356	0.46593314185178
128	0.496759638147265	0.99351927629453	0.503240361852735
129	0.446438006253897	0.892876012507794	0.553561993746103
130	0.389281329726987	0.778562659453974	0.610718670273013
131	0.340585500333823	0.681171000667646	0.659414499666177
132	0.318154499222394	0.636308998444788	0.681845500777606
133	0.434906849879327	0.869813699758655	0.565093150120673
134	0.446559761671149	0.893119523342298	0.553440238328851
135	0.449430099775519	0.898860199551038	0.550569900224481
136	0.47929691161258	0.95859382322516	0.52070308838742
137	0.425866092490452	0.851732184980903	0.574133907509548
138	0.425905613631479	0.851811227262958	0.574094386368521
139	0.376962048997573	0.753924097995146	0.623037951002427
140	0.331936301535635	0.66387260307127	0.668063698464365
141	0.42578048456835	0.8515609691367	0.57421951543165
142	0.357702912567595	0.715405825135189	0.642297087432405
143	0.353319475032484	0.706638950064969	0.646680524967516
144	0.691126421474696	0.617747157050607	0.308873578525304
145	0.691025184361162	0.617949631277677	0.308974815638838
146	0.633627779975019	0.732744440049963	0.366372220024981
147	0.888899186742519	0.222201626514962	0.111100813257481
148	0.864416590584326	0.271166818831348	0.135583409415674
149	0.900100804570702	0.199798390858597	0.0998991954292984
150	0.86283809911047	0.274323801779061	0.137161900889530
151	0.820322784801333	0.359354430397333	0.179677215198666
152	0.757787512809985	0.48442497438003	0.242212487190015
153	0.647363567667616	0.705272864664767	0.352636432332384
154	0.502362839441264	0.995274321117472	0.497637160558736
155	0.47023706063907	0.94047412127814	0.52976293936093

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	90	0.666666666666667	NOK
5% type I error level	92	0.681481481481481	NOK
10% type I error level	93	0.688888888888889	NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/13/t1260700464bbjs2anchh7n0v7/10ahn01260700365.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/13/t1260700464bbjs2anchh7n0v7/10ahn01260700365.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/13/t1260700464bbjs2anchh7n0v7/12dhb1260700365.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/13/t1260700464bbjs2anchh7n0v7/12dhb1260700365.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/13/t1260700464bbjs2anchh7n0v7/20d5w1260700365.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/13/t1260700464bbjs2anchh7n0v7/20d5w1260700365.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/13/t1260700464bbjs2anchh7n0v7/30x981260700365.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/13/t1260700464bbjs2anchh7n0v7/30x981260700365.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/13/t1260700464bbjs2anchh7n0v7/4sa5o1260700365.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/13/t1260700464bbjs2anchh7n0v7/4sa5o1260700365.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/13/t1260700464bbjs2anchh7n0v7/5lw9s1260700365.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/13/t1260700464bbjs2anchh7n0v7/5lw9s1260700365.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/13/t1260700464bbjs2anchh7n0v7/67bo11260700365.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/13/t1260700464bbjs2anchh7n0v7/67bo11260700365.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/13/t1260700464bbjs2anchh7n0v7/79xx61260700365.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/13/t1260700464bbjs2anchh7n0v7/79xx61260700365.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/13/t1260700464bbjs2anchh7n0v7/8odl21260700365.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/13/t1260700464bbjs2anchh7n0v7/8odl21260700365.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/13/t1260700464bbjs2anchh7n0v7/9msx01260700365.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/13/t1260700464bbjs2anchh7n0v7/9msx01260700365.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')

}

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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