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*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: Wed, 22 Dec 2010 20:33:29 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/22/t1293049903mtwrrzaw87vwk3j.htm/, Retrieved Wed, 22 Dec 2010 21:31:46 +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/2010/Dec/22/t1293049903mtwrrzaw87vwk3j.htm/},
    year = {2010},
}
@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 = {2010},
    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 «

5 4 3 2 12 4 4 3 2 11 5 5 5 2 15 2 2 2 1 6 4 5 4 2 13 3 3 4 2 10 5 3 4 2 12 5 5 4 2 14 4 3 5 2 12 3 3 2 6 2 4 4 1 10 4 4 4 2 12 4 4 4 1 12 4 3 4 2 11 5 5 5 2 15 5 4 3 1 12 4 4 2 1 10 4 4 4 2 12 4 4 3 1 11 4 4 4 2 12 4 4 3 1 11 4 4 4 2 12 5 4 4 2 13 3 4 4 2 11 5 4 1 9 4 4 5 2 13 4 3 3 1 10 5 5 4 2 14 4 4 4 2 12 3 4 3 1 10 4 4 4 2 12 4 2 2 1 8 4 3 3 2 10 4 4 4 2 12 4 4 4 1 12 2 2 3 1 7 3 3 1 6 4 4 4 1 12 3 4 3 2 10 4 3 3 1 10 2 4 4 1 10 4 4 4 2 12 5 5 5 1 15 4 3 3 1 10 4 4 2 2 10 4 4 4 2 12 5 4 4 2 13 3 4 4 2 11 4 4 3 2 11 4 4 4 1 12 5 5 4 2 14 3 3 4 1 10 4 4 4 1 12 5 4 4 2 13 2 1 2 1 5 2 2 2 2 6 4 4 4 2 12 4 4 4 2 12 4 3 4 1 11 4 3 3 2 10 2 2 3 1 7 4 4 4 1 12 5 5 4 2 14 3 4 4 2 11 4 4 4 2 12 5 4 4 1 13 5 5 4 2 14 4 4 3 1 11 4 4 4 2 12 4 4 4 1 12 2 3 3 1 8 3 4 4 2 11 5 5 4 2 14 4 5 5 1 14 4 4 4 1 12 3 2 4 2 9 4 4 5 2 13 3 4 4 2 11 4 4 4 1 12 4 4 4 1 12 4 4 4 1 12 4 4 4 1 12 4 4 4 2 12 4 4 4 1 12 4 4 3 2 11 3 4 3 2 10 4 3 2 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	7 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk
R Framework error message	Warning: there are blank lines in the 'Data X' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

Multiple Linear Regression - Estimated Regression Equation

PCCS [t] = + 3.81711992673291 + 1.40873728291067CCS[t] -0.0100990965644928CHCS[t] -0.247946566002252AORT[t] -0.380978135850004G[t] + 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)	3.81711992673291	0.888898	4.2942	3.1e-05	1.5e-05
CCS	1.40873728291067	0.175947	8.0066	0	0
CHCS	-0.0100990965644928	0.048768	-0.2071	0.836214	0.418107
AORT	-0.247946566002252	0.066991	-3.7012	0.000297	0.000148
G	-0.380978135850004	0.064076	-5.9457	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.628911596512203
R-squared	0.395529796227527
Adjusted R-squared	0.380129281481732
F-TEST (value)	25.6828945497105
F-TEST (DF numerator)	4
F-TEST (DF denominator)	157
p-value	2.22044604925031e-16
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1.65775037263514
Sum Squared Residuals	431.457398781596

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	12	9.31461398532156	2.68538601467844
2	11	7.90587670241088	3.09412329758912
3	15	8.80862175675255	6.19137824324745
4	6	5.73752503157077	0.262474968429231
5	13	7.64783103984413	5.35216896015587
6	10	6.25929195006244	3.74070804993756
7	12	9.07676651588379	2.92323348411621
8	14	9.0565683227548	4.9434316772452
9	12	7.42008266697087	4.57991733302913
10	2	5.23127253866693	-3.23127253866693
11	4	5.35394474761535	-1.35394474761535
12	4	4.34404190991309	-0.344041909913094
13	4	4.59198847591535	-0.591988475915345
14	5	3.31628276285242	1.68371723714758
15	5	4.59974568870927	0.400254311290735
16	4	4.60208757247984	-0.602087572479838
17	4	5.37414294074434	-1.37414294074434
18	4	4.34404190991309	-0.344041909913094
19	4	4.98306570832984	-0.983065708329842
20	4	4.34404190991309	-0.344041909913094
21	4	4.98306570832984	-0.983065708329842
22	5	4.34404190991309	0.655958090086907
23	3	3.96306377406309	-0.96306377406309
24	5	4.7250200457631	0.274979954236904
25	4	5.68653832439084	-1.68653832439084
26	3	6.09339024672801	-3.09339024672801
27	5	3.64887633962791	1.35112366037209
28	4	4.43670639781508	-0.436706397815085
29	4	5.31357766566959	-1.31357766566959
30	4	4.02985447547791	-0.0298544754779104
31	2	4.93259952981959	-2.93259952981959
32	3	3.11701032457174	-0.11701032457174
33	4	4.01975537891342	-0.0197553789134175
34	4	4.93259952981959	-0.932599529819588
35	2	5.70465489808409	-3.70465489808409
36	3	5.15467230933467	-2.15467230933467
37	4	2.64956382284761	1.35043617715239
38	3	2.8369158094629	0.163084190537096
39	3	4.39888285535032	-1.39888285535032
40	4	3.10506056859414	0.894939431405859
41	4	2.60916743658964	1.39083256341036
42	5	3.36878182451907	1.63121817548093
43	3	2.93965008961718	0.0603499103828226
44	2	2.60916743658964	-0.609167436589638
45	4	4.01790471950031	-0.017904719500312
46	4	3.74975996036907	0.250240039630925
47	4	4.23555399580909	-0.235553995809086
48	3	4.00780562293582	-1.00780562293582
49	4	4.00780562293582	-0.00780562293581912
50	4	1.9600445416084	2.0399554583916
51	4	4.6064330350946	-0.606433035094596
52	4	2.60916743658964	1.39083256341036
53	4	2.3410226774584	1.6589773225416
54	2	5.62643496936135	-3.62643496936135
55	2	3.91751232311661	-1.91751232311661
56	4	4.05830110575828	-0.0583011057582832
57	4	3.99770652637133	0.00229347362867353
58	4	4.37868466222133	-0.37868466222133
59	3	2.98004647587515	0.0199535241248514
60	3	5.27575412320482	-2.27575412320482
61	4	2.63946472628312	1.36053527371688
62	4	1.9600445416084	2.0399554583916
63	4	4.22545489924459	-0.225454899244593
64	4	4.00780562293582	-0.00780562293581912
65	4	3.74975996036907	0.250240039630925
66	4	1.9499454450439	2.0500545549561
67	3	3.97750833324234	-0.977508333242341
68	4	2.59906834002514	1.40093165997485
69	4	3.99770652637133	0.00229347362867353
70	3	3.46584051131516	-0.46584051131516
71	4	2.87731219572087	1.12268780427913
72	4	3.37888092108356	0.621119078916436
73	5	3.59653019739234	1.40346980260766
74	4	2.56877105033167	1.43122894966833
75	4	3.59887208116291	0.401127918837089
76	5	4.02800381606481	0.971996183935195
77	4	4.23555399580909	-0.235553995809086
78	4	4.00780562293582	-0.00780562293581912
79	4	2.58896924346065	1.41103075653935
80	4	2.58896924346065	1.41103075653935
81	4	2.58896924346065	1.41103075653935
82	4	2.58896924346065	1.41103075653935
83	4	3.99770652637133	0.00229347362867353
84	3	2.58896924346065	0.411030756539348
85	3	4.25575218893807	-1.25575218893807
86	2	4.39888285535032	-2.39888285535031
87	4	2.61926653315413	1.38073346684587
88	4	3.99770652637133	0.00229347362867353
89	4	3.99770652637133	0.00229347362867353
90	3	4.62663122822358	-1.62663122822358
91	5	3.39907911421255	1.60092088578745
92	4	3.96740923667785	0.0325907633221519
93	4	3.99770652637133	0.00229347362867353
94	4	3.99770652637133	0.00229347362867353
95	2	3.99770652637133	-1.99770652637133
96	4	3.76995815349806	0.23004184650194
97	2	4.36858556565684	-2.36858556565684
98	4	4.02800381606481	-0.0280038160648048
99	4	3.08486237546516	0.915137624534844
100	4	1.98024273473738	2.01975726526262
101	3	3.97750833324234	-0.977508333242341
102	5	1.97014363817289	3.02985636182711
103	3	3.96740923667785	-0.967409236677848
104	3	2.59906834002515	0.400931659974855
105	4	4.00780562293582	-0.00780562293581912
106	4	2.58896924346065	1.41103075653935
107	4	3.99770652637133	0.00229347362867353
108	4	2.96994737931066	1.03005262068934
109	1	3.09496147202965	-2.09496147202965
110	4	4.04820200919379	-0.0482020091937904
111	4	3.36878182451907	0.631218175480929
112	3	3.97750833324234	-0.977508333242341
113	4	4.38878375878582	-0.388783758785823
114	4	3.09496147202965	0.905038527970351
115	4	3.76995815349806	0.23004184650194
116	3	1.9499454450439	1.0500545549561
117	4	5.24545683351134	-1.24545683351134
118	3	4.0381029126293	-1.0381029126293
119	4	4.00780562293582	-0.00780562293581912
120	3	3.99770652637133	-0.997706526371327
121	4	3.75985905693357	0.240140943066433
122	4	3.98760742980683	0.0123925701931664
123	4	3.36878182451907	0.631218175480929
124	4	3.72956176724009	0.270438232759911
125	5	3.35868272795458	1.64131727204542
126	4	4.5963339385301	-0.596333938530103
127	3	2.60916743658964	0.390832563410362
128	2	4.38878375878582	-2.38878375878582
129	3	4.02800381606481	-1.02800381606481
130	3	4.25575218893807	-1.25575218893807
131	3	2.60916743658964	0.390832563410362
132	2	3.36102461172515	-1.36102461172515
133	3	4.0381029126293	-1.0381029126293
134	4	2.59906834002514	1.40093165997485
135	4	2.58896924346065	1.41103075653935
136	2	4.37868466222133	-2.37868466222133
137	3	2.61926653315413	0.380733466845869
138	3	2.8470149060274	0.152985093972603
139	3	4.89477598735482	-1.89477598735482
140	4	4.9149741804838	-0.914974180483804
141	2	3.38122280485414	-1.38122280485414
142	3	4.5339960446338	-1.5339960446338
143	5	1.99034183130188	3.00965816869812
144	4	4.2153558026801	-0.2153558026801
145	2	3.09496147202965	-1.09496147202965
146	4	3.79015634662705	0.209843653372954
147	4	3.98760742980683	0.0123925701931664
148	4	2.58896924346065	1.41103075653935
149	4	3.46584051131516	0.534159488684841
150	2	3.62916937085639	-1.62916937085639
151	4	3.80025544319154	0.199744556808461
152	3	4.74956370150684	-1.74956370150684
153	2	3.87711593685864	-1.87711593685864
154	3	4.93517237361279	-1.93517237361279
155	3	4.9149741804838	-1.9149741804838
156	5	3.40917821077704	1.59082178922296
157	2	5.22525864038236	-3.22525864038236
158	2	4.43927924160829	-2.43927924160829
159	3	4.02800381606481	-1.02800381606481
160	4	5.26565502664033	-1.26565502664033
161	3	4.9149741804838	-1.9149741804838
162	3	3.79015634662705	-0.790156346627046

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
8	1.21428466663986e-46	2.42856933327971e-46	1
9	9.72401155657777e-62	1.94480231131555e-61	1
10	0.02906273032516	0.05812546065032	0.97093726967484
11	0.973337272482394	0.0533254550352128	0.0266627275176064
12	0.976210908032794	0.0475781839344128	0.0237890919672064
13	0.988425066690536	0.0231498666189281	0.011574933309464
14	0.994180741053972	0.0116385178920567	0.00581925894602837
15	0.989859941958573	0.0202801160828538	0.0101400580414269
16	0.996863123825761	0.00627375234847755	0.00313687617423877
17	0.99718238933764	0.00563522132472059	0.0028176106623603
18	0.996327227837604	0.00734554432479211	0.00367277216239605
19	0.994887906072302	0.0102241878553949	0.00511209392769746
20	0.993495335676022	0.0130093286479553	0.00650466432397766
21	0.991145730216324	0.0177085395673517	0.00885426978367586
22	0.98688092613473	0.0262381477305381	0.0131190738652691
23	0.996021490796494	0.00795701840701147	0.00397850920350573
24	0.995830113730483	0.00833977253903468	0.00416988626951734
25	0.999991322899225	1.73542015507761e-05	8.67710077538803e-06
26	0.999999851916744	2.96166511527877e-07	1.48083255763939e-07
27	0.99999999943766	1.1246816272245e-09	5.62340813612249e-10
28	0.9999999988635	2.2729996830664e-09	1.1364998415332e-09
29	0.999999999336314	1.32737233286993e-09	6.63686166434965e-10
30	0.999999999411984	1.17603231544471e-09	5.88016157722354e-10
31	0.999999999973402	5.31961083909417e-11	2.65980541954709e-11
32	0.99999999996062	7.87605576346731e-11	3.93802788173366e-11
33	0.999999999912497	1.75006683240076e-10	8.75033416200382e-11
34	0.99999999981766	3.64679894058352e-10	1.82339947029176e-10
35	0.99999999996838	6.32391423207172e-11	3.16195711603586e-11
36	0.9999999999545	9.09986349273783e-11	4.54993174636892e-11
37	0.99999999999854	2.91968047635638e-12	1.45984023817819e-12
38	0.999999999999998	3.1149472320037e-15	1.55747361600185e-15
39	1	1.83785966735159e-16	9.18929833675794e-17
40	1	4.10677367715446e-16	2.05338683857723e-16
41	1	7.64031272289909e-16	3.82015636144954e-16
42	1	1.44285936816876e-15	7.21429684084381e-16
43	1	1.71423862801823e-15	8.57119314009114e-16
44	1	8.08675799135246e-16	4.04337899567623e-16
45	1	1.52844246175317e-15	7.64221230876587e-16
46	0.999999999999998	3.5841898490094e-15	1.7920949245047e-15
47	0.999999999999998	4.10463280398183e-15	2.05231640199091e-15
48	0.999999999999998	3.47133988275581e-15	1.7356699413779e-15
49	0.999999999999996	7.61956901065666e-15	3.80978450532833e-15
50	0.999999999999998	3.31960766579632e-15	1.65980383289816e-15
51	1	1.81711498988295e-15	9.08557494941473e-16
52	0.999999999999999	2.62746809316963e-15	1.31373404658481e-15
53	0.999999999999998	3.13697464127366e-15	1.56848732063683e-15
54	1	6.54826117433778e-18	3.27413058716889e-18
55	1	4.52733156080127e-18	2.26366578040063e-18
56	1	1.11353539596407e-17	5.56767697982035e-18
57	1	2.82525859347071e-17	1.41262929673536e-17
58	1	4.27121248548555e-17	2.13560624274278e-17
59	1	1.15221756325757e-16	5.76108781628786e-17
60	1	3.23960004725349e-17	1.61980002362674e-17
61	1	4.25220292832256e-17	2.12610146416128e-17
62	1	3.58271349971884e-17	1.79135674985942e-17
63	1	8.1422313729339e-17	4.07111568646694e-17
64	1	2.02169584849665e-16	1.01084792424832e-16
65	1	5.22016079244816e-16	2.61008039622408e-16
66	1	5.19282916474025e-16	2.59641458237012e-16
67	1	6.79131901155856e-16	3.39565950577928e-16
68	1	1.19145355842847e-15	5.95726779214236e-16
69	0.999999999999999	2.89222884394136e-15	1.44611442197068e-15
70	0.999999999999997	6.43015490756988e-15	3.21507745378494e-15
71	0.999999999999994	1.11808684303058e-14	5.5904342151529e-15
72	0.999999999999987	2.56604709640991e-14	1.28302354820496e-14
73	0.99999999999998	3.95919058034335e-14	1.97959529017167e-14
74	0.999999999999963	7.47543850495267e-14	3.73771925247634e-14
75	0.999999999999978	4.4235366425544e-14	2.2117683212772e-14
76	0.999999999999985	2.98468569070157e-14	1.49234284535078e-14
77	0.99999999999997	6.179554332207e-14	3.0897771661035e-14
78	0.99999999999993	1.38989390507797e-13	6.94946952538983e-14
79	0.999999999999878	2.43043275579919e-13	1.21521637789959e-13
80	0.999999999999787	4.25197253724514e-13	2.12598626862257e-13
81	0.99999999999963	7.417953485012e-13	3.708976742506e-13
82	0.999999999999357	1.28635864727105e-12	6.43179323635525e-13
83	0.999999999998608	2.78491398800905e-12	1.39245699400453e-12
84	0.999999999997133	5.7334231193578e-12	2.8667115596789e-12
85	0.999999999996255	7.49033165512327e-12	3.74516582756164e-12
86	0.99999999999838	3.23869245703562e-12	1.61934622851781e-12
87	0.99999999999741	5.17903746221495e-12	2.58951873110748e-12
88	0.999999999994311	1.13779627598971e-11	5.68898137994855e-12
89	0.999999999987652	2.46969769026866e-11	1.23484884513433e-11
90	0.999999999983306	3.33885731367904e-11	1.66942865683952e-11
91	0.999999999980355	3.92907669516658e-11	1.96453834758329e-11
92	0.999999999956638	8.67230921168988e-11	4.33615460584494e-11
93	0.999999999908646	1.82708527527122e-10	9.1354263763561e-11
94	0.99999999981012	3.79758450457725e-10	1.89879225228863e-10
95	0.999999999946446	1.071086039332e-10	5.35543019665999e-11
96	0.999999999883295	2.33410367279045e-10	1.16705183639522e-10
97	0.999999999947708	1.0458466621165e-10	5.2292333105825e-11
98	0.999999999891682	2.16635291488893e-10	1.08317645744447e-10
99	0.999999999826023	3.47954718708567e-10	1.73977359354283e-10
100	0.9999999997271	5.45801616220406e-10	2.72900808110203e-10
101	0.999999999617147	7.65705396203761e-10	3.82852698101881e-10
102	0.99999999980971	3.80581200049977e-10	1.90290600024989e-10
103	0.99999999975739	4.85218148987176e-10	2.42609074493588e-10
104	0.999999999469255	1.06148950960751e-09	5.30744754803753e-10
105	0.999999998845722	2.30855531471509e-09	1.15427765735754e-09
106	0.99999999809585	3.80830106235355e-09	1.90415053117677e-09
107	0.999999995850405	8.2991905068539e-09	4.14959525342695e-09
108	0.99999999553824	8.9235194183864e-09	4.4617597091932e-09
109	0.999999999797398	4.05203703347885e-10	2.02601851673943e-10
110	0.999999999615804	7.68393014411982e-10	3.84196507205991e-10
111	0.999999999112966	1.77406815991051e-09	8.87034079955254e-10
112	0.999999998938257	2.12348687329033e-09	1.06174343664516e-09
113	0.99999999854306	2.91387936291309e-09	1.45693968145655e-09
114	0.999999997315895	5.36820990152843e-09	2.68410495076421e-09
115	0.999999994258794	1.14824109408404e-08	5.74120547042022e-09
116	0.999999994889715	1.02205696584199e-08	5.11028482920996e-09
117	0.999999997606226	4.7875483148114e-09	2.3937741574057e-09
118	0.999999995424387	9.15122631469904e-09	4.57561315734952e-09
119	0.999999989491358	2.10172831876253e-08	1.05086415938126e-08
120	0.999999985063579	2.98728422690446e-08	1.49364211345223e-08
121	0.999999965490012	6.90199765845291e-08	3.45099882922646e-08
122	0.999999917753845	1.64492310414121e-07	8.22461552070603e-08
123	0.999999831471313	3.37057374587674e-07	1.68528687293837e-07
124	0.999999603600963	7.92798073472457e-07	3.96399036736229e-07
125	0.999999336894352	1.32621129664098e-06	6.63105648320488e-07
126	0.999999029283096	1.94143380708242e-06	9.70716903541212e-07
127	0.999998034637689	3.93072462293769e-06	1.96536231146885e-06
128	0.999998396992887	3.20601422668481e-06	1.60300711334241e-06
129	0.999997254432658	5.4911346834239e-06	2.74556734171195e-06
130	0.999995901889877	8.19622024616001e-06	4.09811012308e-06
131	0.999991966385274	1.60672294517402e-05	8.0336147258701e-06
132	0.999984337602323	3.13247953546438e-05	1.56623976773219e-05
133	0.99997396818609	5.20636278178865e-05	2.60318139089432e-05
134	0.99995121446285	9.75710743018743e-05	4.87855371509371e-05
135	0.999909925879274	0.000180148241451718	9.00741207258591e-05
136	0.999945348824718	0.000109302350564171	5.46511752820853e-05
137	0.999888224704207	0.000223550591585896	0.000111775295792948
138	0.999789154833453	0.000421690333093719	0.000210845166546859
139	0.99958912914272	0.000821741714559993	0.000410870857279996
140	0.999617084687717	0.000765830624565669	0.000382915312282834
141	0.999282076339594	0.00143584732081112	0.00071792366040556
142	0.998630778634338	0.00273844273132374	0.00136922136566187
143	0.99842146660076	0.00315706679847983	0.00157853339923991
144	0.99658492064431	0.00683015871137836	0.00341507935568918
145	0.998933977964526	0.00213204407094791	0.00106602203547395
146	0.997792487631185	0.00441502473762933	0.00220751236881467
147	0.994940947564282	0.0101181048714351	0.00505905243571756
148	0.988754148860438	0.0224917022791248	0.0112458511395624
149	0.981674504078836	0.0366509918423275	0.0183254959211638
150	0.961804875401867	0.0763902491962662	0.0381951245981331
151	0.934403082406582	0.131193835186837	0.0655969175934183
152	0.898500158082424	0.202999683835151	0.101499841917576
153	0.807375494300686	0.385249011398627	0.192624505699314
154	0.661815395008993	0.676369209982014	0.338184604991007

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	129	0.877551020408163	NOK
5% type I error level	140	0.952380952380952	NOK
10% type I error level	143	0.972789115646258	NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293049903mtwrrzaw87vwk3j/106ais1293049998.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293049903mtwrrzaw87vwk3j/106ais1293049998.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293049903mtwrrzaw87vwk3j/1hrly1293049998.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293049903mtwrrzaw87vwk3j/1hrly1293049998.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293049903mtwrrzaw87vwk3j/2hrly1293049998.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293049903mtwrrzaw87vwk3j/2hrly1293049998.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293049903mtwrrzaw87vwk3j/3sjlk1293049998.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293049903mtwrrzaw87vwk3j/3sjlk1293049998.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293049903mtwrrzaw87vwk3j/4sjlk1293049998.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293049903mtwrrzaw87vwk3j/4sjlk1293049998.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293049903mtwrrzaw87vwk3j/5sjlk1293049998.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293049903mtwrrzaw87vwk3j/5sjlk1293049998.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293049903mtwrrzaw87vwk3j/63sk41293049998.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293049903mtwrrzaw87vwk3j/63sk41293049998.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293049903mtwrrzaw87vwk3j/7d1jp1293049998.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293049903mtwrrzaw87vwk3j/7d1jp1293049998.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293049903mtwrrzaw87vwk3j/8d1jp1293049998.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293049903mtwrrzaw87vwk3j/8d1jp1293049998.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293049903mtwrrzaw87vwk3j/9d1jp1293049998.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293049903mtwrrzaw87vwk3j/9d1jp1293049998.ps (open in new window)

Parameters (Session):

par1 = 5 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 5 ; par2 = Do not include Seasonal Dummies ; par3 = No 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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We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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