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Multiple Regression 6

*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: Tue, 29 Dec 2009 04:48:04 -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/29/t12620873577p07r06hcxgqmpr.htm/, Retrieved Tue, 29 Dec 2009 12:49:30 +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/29/t12620873577p07r06hcxgqmpr.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 «

10.8 4.3 11.1 11.2 11.4 11.7 10.4 4.1 10.8 11.1 11.2 11.4 10.1 3.9 10.4 10.8 11.1 11.2 9.8 3.7 10.1 10.4 10.8 11.1 9.7 3.6 9.8 10.1 10.4 10.8 10.3 3.9 9.7 9.8 10.1 10.4 10.9 4.2 10.3 9.7 9.8 10.1 10.8 4.2 10.9 10.3 9.7 9.8 10.6 4.1 10.8 10.9 10.3 9.7 10.4 4.1 10.6 10.8 10.9 10.3 10.3 4.1 10.4 10.6 10.8 10.9 10.2 4.1 10.3 10.4 10.6 10.8 10 4.1 10.2 10.3 10.4 10.6 9.7 4 10 10.2 10.3 10.4 9.4 3.9 9.7 10 10.2 10.3 9.2 3.8 9.4 9.7 10 10.2 9.1 3.8 9.2 9.4 9.7 10 9.6 4 9.1 9.2 9.4 9.7 10.2 4.4 9.6 9.1 9.2 9.4 10.2 4.6 10.2 9.6 9.1 9.2 10 4.6 10.2 10.2 9.6 9.1 9.9 4.6 10 10.2 10.2 9.6 9.9 4.7 9.9 10 10.2 10.2 9.9 4.8 9.9 9.9 10 10.2 9.7 4.8 9.9 9.9 9.9 10 9.5 4.7 9.7 9.9 9.9 9.9 9.4 4.7 9.5 9.7 9.9 9.9 9.3 4.7 9.4 9.5 9.7 9.9 9.3 4.6 9.3 9.4 9.5 9.7 9.9 5 9.3 9.3 9.4 9.5 10.5 5.4 9.9 9.3 9.3 9.4 10.6 5.5 10.5 9.9 9.3 9.3 10.6 5.6 10.6 10.5 9.9 9.3 10.5 5.6 10.6 10.6 10.5 9.9 10.6 5.8 10.5 10.6 10.6 10.5 10.8 6 10.6 10.5 10.6 10.6 10.8 6.1 10.8 10.6 10.5 10.6 10.7 6.1 10.8 10.8 10. 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	8 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

Y[t] = + 0.406327472245542 + 0.132002787047602X[t] + 1.33719141843655Y1[t] -0.523857828846532Y2[t] -0.238580032736566Y3[t] + 0.322342059837373Y4[t] -0.170474709866218M1[t] -0.123311871032308M2[t] -0.0849884362519037M3[t] -0.0917642589554215M4[t] + 0.0375192409404774M5[t] + 0.662186968591818M6[t] + 0.136244777286711M7[t] -0.0875822905375944M8[t] + 0.171234680238685M9[t] + 0.0642899482917782M10[t] + 0.160873466453772M11[t] -0.00279915567983406t + 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)	0.406327472245542	0.139359	2.9157	0.00392	0.00196
X	0.132002787047602	0.022146	5.9606	0	0
Y1	1.33719141843655	0.064476	20.7393	0	0
Y2	-0.523857828846532	0.110877	-4.7247	4e-06	2e-06
Y3	-0.238580032736566	0.109924	-2.1704	0.031057	0.015528
Y4	0.322342059837373	0.059345	5.4317	0	0
M1	-0.170474709866218	0.063764	-2.6735	0.008074	0.004037
M2	-0.123311871032308	0.065029	-1.8963	0.059249	0.029625
M3	-0.0849884362519037	0.064575	-1.3161	0.189515	0.094758
M4	-0.0917642589554215	0.063158	-1.4529	0.14768	0.07384
M5	0.0375192409404774	0.062731	0.5981	0.550396	0.275198
M6	0.662186968591818	0.061679	10.736	0	0
M7	0.136244777286711	0.071741	1.8991	0.05887	0.029435
M8	-0.0875822905375944	0.081154	-1.0792	0.281686	0.140843
M9	0.171234680238685	0.081354	2.1048	0.036454	0.018227
M10	0.0642899482917782	0.071796	0.8955	0.371534	0.185767
M11	0.160873466453772	0.064166	2.5071	0.012901	0.00645
t	-0.00279915567983406	0.000478	-5.8527	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.994382149367365
R-squared	0.98879585898046
Adjusted R-squared	0.987922141561505
F-TEST (value)	1131.71128047690
F-TEST (DF numerator)	17
F-TEST (DF denominator)	218
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.189540022317192
Sum Squared Residuals	7.83174157308037

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	10.8	10.8278723794691	-0.0278723794690997
2	10.4	10.4480772511634	-0.0480772511634411
3	10.1	10.03887134544	0.0611286545600049
4	9.8	9.85062131949202	-0.0506213194920155
5	9.7	9.71863470326973	-0.0186347032697343
6	10.3	10.3461795040518	-0.0461795040518444
7	10.9	10.6866110189975	0.213388981002476
8	10.8	10.8751403345698	-0.0751403345698372
9	10.6	10.4945418061843	0.105458193815727
10	10.4	10.2200026340154	0.179997365984642
11	10.3	10.3683835177556	-0.0683835177555948
12	10.2	10.1912451201112	0.00875487988878097
13	10	9.919885490186	0.0801145098139981
14	9.7	9.69538598513885	0.00461401486115476
15	9.4	9.41294792306292	-0.0129479230629162
16	9.2	9.16165438966138	0.0383456103386212
17	9.1	9.18496339669759	-0.084963396697587
18	9.6	9.77915634187403	-0.179156341874026
19	10.2	9.97521099040715	0.224789009592847
20	10.2	10.2747608522574	-0.074760852257376
21	10	10.0649397476939	-0.0649397476938813
22	9.9	9.70578058665658	0.194219413343422
23	9.9	9.97722288767157	-0.0772228876715738
24	9.9	9.9268523336747	-0.0268523336746943
25	9.7	9.71296805943483	-0.0129680594348255
26	9.5	9.4444589742131	0.0555410257869075
27	9.4	9.31731653539566	0.0826834646043384
28	9.3	9.32650998748528	-0.0265099874852751
29	9.3	9.34170828861742	-0.0417082886174169
30	9.9	10.0281533495988	-0.1281533495988
31	10.5	10.3461517657847	0.153848234215254
32	10.6	10.5884917687556	0.0115082312443625
33	10.6	10.5339662874506	0.0660337125493615
34	10.5	10.4220938331997	0.077906166800272
35	10.6	10.5781068438765	0.0218931561234788
36	10.8	10.6591739098645	0.140826090135521
37	10.8	10.7380108270995	0.0619891729004987
38	10.7	10.6215107352269	0.0784892647731225
39	10.6	10.4946337932155	0.105366206784546
40	10.6	10.4681938678406	0.131806132159422
41	10.8	10.6841222769197	0.115877723080288
42	11.4	11.6178540446875	-0.217854044687489
43	12.2	11.83362344924	0.366376550760007
44	12.4	12.3543204927441	0.0456795072558651
45	12.4	12.3800107207762	0.0199892792237989
46	12.3	12.1812367557981	0.118763244201916
47	12.4	12.3646598964639	0.0353401035360656
48	12.5	12.4779611684356	0.0220388315643688
49	12.5	12.4098786651222	0.0901213348777636
50	12.4	12.3325640774295	0.0674359225704956
51	12.3	12.2295451386917	0.070454861308259
52	12.2	12.1576707286284	0.0423292713716335
53	12.1	12.2002791597496	-0.100279159749564
54	12.6	12.7720390061663	-0.172039006166271
55	13.2	13.0087040633932	0.191295936606783
56	13.4	13.3140875738177	0.0859124261823443
57	13.2	13.3585044742367	-0.158504474236713
58	12.9	12.8813734687253	0.0186265312746604
59	12.8	12.8112609220962	-0.011260922096193
60	12.7	12.7964112039924	-0.0964112039924424
61	12.6	12.5357092986361	0.0642907013638791
62	12.4	12.3994944507441	0.000505549255879314
63	12.1	12.1851894689224	-0.0851894689224362
64	12	11.8444518706578	0.155548129342176
65	11.9	11.996655943543	-0.09665594354301
66	12.5	12.5838975905233	-0.0838975905232926
67	13.2	12.9030136563312	0.296986343668823
68	13.4	13.3029308044194	0.0970691955806218
69	13.3	13.2843041973849	0.0156958026151152
70	13	12.9492685364273	0.0507314635727493
71	12.9	12.8722046916019	0.0277953083980552
72	13	12.8334969702245	0.166503029775463
73	12.9	12.8724675545393	0.0275324454607355
74	12.6	12.6314811408780	-0.0314811408779579
75	12.4	12.2357410106653	0.164258989334698
76	12.1	12.1455767490965	-0.0455767490964766
77	11.9	11.9754142012738	-0.0754142012738348
78	12.3	12.4644157842176	-0.164415784217614
79	13	12.6352292830491	0.364770716950865
80	13	13.0993075882128	-0.099307588212824
81	12.6	12.8023239406451	-0.202323940645077
82	12.2	12.1064340079583	0.0935659920416899
83	12.1	12.0873240977859	0.0126759022141359
84	12	12.1081077571466	-0.108107757146604
85	11.8	11.8067954430965	-0.00679544309646715
86	11.6	11.5178275260818	0.0821724739181641
87	11.4	11.3691086058496	0.0308913941504401
88	11.2	11.1991484314070	0.000851568592975974
89	11.2	11.1330133735802	0.0669866264198363
90	11.8	11.8957022207199	-0.095702220719855
91	12.5	12.2053244341957	0.294675565804276
92	12.6	12.5491493730265	0.05085062697347
93	12.4	12.4158375514274	-0.0158375514273565
94	12.1	11.9994685315107	0.100531468489277
95	12	11.9986484728437	0.00135152715627272
96	12	11.9515645487562	0.0484354512437615
97	11.9	11.8377820639483	0.0622179360516651
98	11.8	11.6755819905812	0.124418009418799
99	11.5	11.5843384260343	-0.0843384260342731
100	11.3	11.2234492508687	0.0765507491312545
101	11.2	11.2180761786366	-0.0180761786366228
102	11.6	11.8767375357805	-0.276737535780532
103	12.2	11.9654735998795	0.234526400120474
104	12.2	12.3174092446144	-0.117409244614403
105	11.7	12.1050455859150	-0.405045585915045
106	11.2	11.2728939572488	-0.0728939572487603
107	11	11.1534167608383	-0.153416760838336
108	10.9	11.1167250645137	-0.216725064513731
109	10.8	10.8726226093429	-0.0726226093429273
110	10.5	10.7089976314619	-0.208997631461869
111	10.2	10.3287393018128	-0.128739301812791
112	10	10.0403874864328	-0.0403874864328324
113	9.9	10.0695301420433	-0.169530142043262
114	10.3	10.6373225298102	-0.337322529810178
115	10.7	10.6600572003854	0.0399427996146291
116	10.4	10.6653528892044	-0.265352889204375
117	10.1	10.1566033707434	-0.0566033707433625
118	9.7	9.80996365967042	-0.109963659670419
119	9.4	9.72653963718784	-0.326539637187837
120	8.9	9.3593243916364	-0.459324391636401
121	8.4	8.64694100325993	-0.246941003259930
122	8.1	8.17447396268598	-0.0744739626859784
123	8.3	8.04055601427688	0.259443985723120
124	8.1	8.37409481857012	-0.274094818570116
125	8	7.99917145711757	0.00082854288243362
126	8.7	8.51367522204	0.186324777959997
127	9.2	9.13833918417912	0.0616608158208758
128	9	9.15979750230211	-0.159797502302106
129	8.9	8.67400761168388	0.225992388316117
130	8.5	8.62846529479591	-0.128465294795912
131	8.1	8.43544563054935	-0.335445630549346
132	7.5	7.90582916388592	-0.405829163885916
133	7.1	7.20298138592744	-0.10298138592744
134	6.9	7.00647866687925	-0.106478666879253
135	7.1	7.0379198256524	0.0620801743475994
136	7	7.2893811952131	-0.289381195213105
137	6.7	7.0565531783143	-0.356553178314293
138	7	7.24386624653422	-0.243866246534223
139	7.3	7.38816664638486	-0.0881666463848558
140	7.7	7.497681418414	0.202318581586007
141	8.4	8.04234349668748	0.357656503312524
142	8.4	8.67101879985319	-0.271018799853187
143	8.8	8.39937328699936	0.400626713000642
144	9.1	8.69290719714544	0.407092802854556
145	9	8.92368678877314	0.0763132112268579
146	8.6	8.58174196833498	0.0182580316650219
147	7.9	8.20533855576432	-0.305338555764322
148	7.7	7.57663305853411	0.123366941465890
149	7.8	7.82597657025205	-0.0259765702520479
150	9.2	8.76400588493144	0.435994115068557
151	9.4	9.87702330553416	-0.477023305534163
152	9.2	9.13570882620534	0.0642911737946601
153	8.7	8.83654146034055	-0.136541460340554
154	8.4	8.60613714260414	-0.206137142604136
155	8.6	8.68607769119815	-0.0860776911981478
156	9	8.98862202710186	0.0113779728981428
157	9.1	9.12945558565388	-0.0294555856538811
158	8.7	8.94037637590971	-0.240376375909713
159	8.2	8.37087498232862	-0.170874982328620
160	7.9	7.99412596822214	-0.0941259682221396
161	7.9	8.08264746299935	-0.182647462999352
162	9.1	8.89162741217243	0.208372587827567
163	9.4	9.86471846850887	-0.464718468508868
164	9.4	9.3271179366734	0.0728820633265968
165	9.1	9.17928319994629	-0.0792831999462903
166	9	8.98361834877246	0.0163816512275383
167	9.3	9.22394409342566	0.076055906574341
168	9.9	9.5985889682334	0.301411031766599
169	9.8	9.97122743300824	-0.171227433008240
170	9.3	9.39774766768223	-0.0977476676822338
171	8.3	8.67821466782514	-0.378214667825135
172	8	7.7710395884903	0.228960411509695
173	8.5	8.12048042511124	0.379519574888757
174	10.4	9.77751384482047	0.622486155179535
175	11.1	11.3295403432443	-0.229540343244333
176	10.9	10.8408258822226	0.0591741177773727
177	10	10.1177727863394	-0.117772786339362
178	9.2	9.32837152125493	-0.128371521254929
179	9.2	9.11043052208796	0.0895694779120363
180	9.5	9.54249833793654	-0.0424983379365393
181	9.6	9.67113807025707	-0.0711380702570696
182	9.5	9.43418989873094	0.0658101012690597
183	9.1	9.17243440716795	-0.0724344071679533
184	8.9	8.7532132589722	0.146786741027809
185	9	8.82509354547791	0.174906454522086
186	10.1	9.80145174699231	0.298548253007688
187	10.3	10.6100143600153	-0.310014360015279
188	10.2	9.9994566719309	0.200543328069104
189	9.6	9.79998022809265	-0.199980228092652
190	9.2	9.24716753156243	-0.0471675315624352
191	9.3	9.23511699662855	0.0648830033714542
192	9.4	9.55202101894493	-0.152021018944933
193	9.4	9.37530756825484	0.0246924317451564
194	9.2	9.21449064131566	-0.0144906413156608
195	9	8.990952839439	0.0090471605609987
196	9	8.8113445130071	0.188655486992895
197	9	9.01111475731123	-0.0111147573112289
198	9.8	9.56342980904353	0.236570190956468
199	10	10.0003723487261	-0.000372348726073684
200	9.8	9.63529842453678	0.164701575463224
201	9.3	9.35464292139688	-0.0546429213968742
202	9	8.90443281034851	0.0955671896514872
203	9	8.98437335894252	0.0156266410574788
204	9.1	9.04587996856844	0.0541200314315553
205	9.1	8.90352794606357	0.196472053936430
206	9.1	8.77240267097226	0.32759732902774
207	9.2	8.79726922550393	0.402730774496065
208	8.8	8.92724703753845	-0.127247037538453
209	8.3	8.4136679166762	-0.113667916676207
210	8.4	8.59222674380868	-0.192226743808678
211	8.1	8.57359939346426	-0.473599393464261
212	7.7	7.85738259656832	-0.157382596568317
213	7.9	7.537451881047	0.362548118952998
214	7.9	7.99529734574613	-0.0952973457461306
215	8	8.02264037371668	-0.0226403737166777
216	7.9	7.85563489905874	0.044365100941256
217	7.6	7.56072452075186	0.03927547924814
218	7.1	7.17965744316693	-0.0796574431669274
219	6.8	6.7202347348463	0.0797652651537024
220	6.5	6.5711702130782	-0.0711702130782014
221	6.9	6.51584271494861	0.384157285051386
222	8.2	7.88535124860334	0.314648751396655
223	8.7	8.87348728462182	-0.173487284621817
224	8.3	8.38950584697058	-0.0895058469705781
225	7.9	7.56189873200847	0.338101267991527
226	7.5	7.38697523385175	0.113024766148253
227	7.8	7.46483031833025	0.335169681669745
228	8.3	7.99715595076874	0.302844049231257
229	8.4	8.38101730717525	0.0189826928247552
230	8.2	8.12306094140331	0.0769390585966898
231	7.7	7.78977319810532	-0.0897731981053238
232	7.2	7.31408626680376	-0.114086266803758
233	7.3	7.12705430746063	0.172945692539374
234	8.1	8.26539393362366	-0.165393933623663
235	8.5	8.72533920365766	-0.225339203657662
236	8.4	8.41627397255381	-0.0162739725538122

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
21	0.00468034236180840	0.00936068472361681	0.995319657638192
22	0.00064468828222294	0.00128937656444588	0.999355311717777
23	7.80028630655313e-05	0.000156005726131063	0.999921997136934
24	3.12667336796914e-05	6.25334673593828e-05	0.99996873326632
25	5.28354791017982e-06	1.05670958203596e-05	0.99999471645209
26	3.23463165899134e-05	6.46926331798268e-05	0.99996765368341
27	7.35783727773474e-05	0.000147156745554695	0.999926421627223
28	2.22316962273037e-05	4.44633924546074e-05	0.999977768303773
29	5.34870308814221e-06	1.06974061762844e-05	0.999994651296912
30	1.95018691783463e-06	3.90037383566926e-06	0.999998049813082
31	5.09035872959235e-07	1.01807174591847e-06	0.999999490964127
32	9.74467451521214e-07	1.94893490304243e-06	0.999999025532548
33	4.77537701670907e-07	9.55075403341814e-07	0.999999522462298
34	1.33602445881224e-07	2.67204891762448e-07	0.999999866397554
35	5.879860624564e-08	1.1759721249128e-07	0.999999941201394
36	2.34444215390459e-08	4.68888430780917e-08	0.999999976555578
37	9.80478249458747e-09	1.96095649891749e-08	0.999999990195217
38	2.50067321666301e-09	5.00134643332602e-09	0.999999997499327
39	9.516947918251e-10	1.9033895836502e-09	0.999999999048305
40	2.76578087878964e-10	5.53156175757928e-10	0.999999999723422
41	8.95961758708269e-11	1.79192351741654e-10	0.999999999910404
42	3.37850306033759e-10	6.75700612067517e-10	0.99999999966215
43	1.62051236684262e-10	3.24102473368524e-10	0.999999999837949
44	7.68050663952966e-11	1.53610132790593e-10	0.999999999923195
45	2.02520476066788e-11	4.05040952133576e-11	0.999999999979748
46	4.03074415966445e-11	8.0614883193289e-11	0.999999999959693
47	1.20299304160804e-11	2.40598608321607e-11	0.99999999998797
48	4.73926986160861e-12	9.47853972321722e-12	0.99999999999526
49	2.63896246742893e-12	5.27792493485786e-12	0.99999999999736
50	7.43467017208196e-13	1.48693403441639e-12	0.999999999999257
51	2.03010102522181e-13	4.06020205044361e-13	0.999999999999797
52	6.32402253814971e-14	1.26480450762994e-13	0.999999999999937
53	6.27601636470225e-14	1.25520327294045e-13	0.999999999999937
54	1.82564010080091e-14	3.65128020160181e-14	0.999999999999982
55	5.88838389805992e-15	1.17767677961198e-14	0.999999999999994
56	2.24262539714358e-13	4.48525079428717e-13	0.999999999999776
57	1.13121135550702e-13	2.26242271101404e-13	0.999999999999887
58	4.00785131564075e-14	8.0157026312815e-14	0.99999999999996
59	1.16118696069211e-14	2.32237392138423e-14	0.999999999999988
60	3.60823411182666e-15	7.21646822365331e-15	0.999999999999996
61	8.34607142398277e-15	1.66921428479655e-14	0.999999999999992
62	4.6134985171474e-15	9.2269970342948e-15	0.999999999999995
63	1.39553470614415e-15	2.79106941228829e-15	0.999999999999999
64	4.42703071681576e-15	8.85406143363153e-15	0.999999999999996
65	1.39468496765448e-15	2.78936993530896e-15	0.999999999999999
66	2.31695508402027e-15	4.63391016804054e-15	0.999999999999998
67	2.62992088491929e-15	5.25984176983859e-15	0.999999999999997
68	5.72248805620978e-15	1.14449761124196e-14	0.999999999999994
69	1.94694304780188e-15	3.89388609560375e-15	0.999999999999998
70	1.17254480296331e-15	2.34508960592662e-15	0.999999999999999
71	3.81562942914398e-16	7.63125885828796e-16	1
72	6.20103929615346e-16	1.24020785923069e-15	1
73	2.31483605454497e-16	4.62967210908994e-16	1
74	7.93467664357183e-17	1.58693532871437e-16	1
75	4.3148360285712e-17	8.6296720571424e-17	1
76	4.00835313012862e-17	8.01670626025725e-17	1
77	1.42922128516097e-17	2.85844257032194e-17	1
78	6.51434631473837e-18	1.30286926294767e-17	1
79	3.95289723796886e-17	7.90579447593773e-17	1
80	1.60559614024445e-17	3.21119228048891e-17	1
81	3.16519133726147e-17	6.33038267452293e-17	1
82	1.95821816940309e-17	3.91643633880618e-17	1
83	6.87077562999184e-18	1.37415512599837e-17	1
84	2.78574180786551e-18	5.57148361573103e-18	1
85	9.58405649259454e-19	1.91681129851891e-18	1
86	5.1577359593891e-19	1.03154719187782e-18	1
87	1.83941362200003e-19	3.67882724400006e-19	1
88	6.07113389630245e-20	1.21422677926049e-19	1
89	3.78123423572719e-20	7.56246847145438e-20	1
90	1.46292169254294e-20	2.92584338508588e-20	1
91	2.74696444671242e-20	5.49392889342483e-20	1
92	1.02167098360439e-20	2.04334196720879e-20	1
93	3.32433310226576e-21	6.64866620453152e-21	1
94	1.82740064493995e-21	3.65480128987991e-21	1
95	6.39731326913074e-22	1.27946265382615e-21	1
96	2.45309643334812e-22	4.90619286669624e-22	1
97	1.09627903086292e-22	2.19255806172583e-22	1
98	1.23297055789773e-22	2.46594111579546e-22	1
99	1.75057998714631e-22	3.50115997429262e-22	1
100	7.92095415288039e-23	1.58419083057608e-22	1
101	3.83043134266089e-23	7.66086268532179e-23	1
102	6.35053586570662e-23	1.27010717314132e-22	1
103	2.90529155003505e-22	5.81058310007009e-22	1
104	3.45296172845869e-22	6.90592345691738e-22	1
105	3.15202202478562e-19	6.30404404957123e-19	1
106	5.25006508869064e-19	1.05001301773813e-18	1
107	2.83288246512103e-19	5.66576493024206e-19	1
108	1.14439400248882e-19	2.28878800497763e-19	1
109	5.96939808867683e-20	1.19387961773537e-19	1
110	5.61985725528464e-20	1.12397145105693e-19	1
111	2.43067273881754e-20	4.86134547763509e-20	1
112	1.02563571675040e-20	2.05127143350081e-20	1
113	4.09523729579408e-21	8.19047459158816e-21	1
114	6.94171562343563e-21	1.38834312468713e-20	1
115	3.91074920343275e-20	7.8214984068655e-20	1
116	1.17343671730961e-19	2.34687343461922e-19	1
117	1.50723420564293e-19	3.01446841128586e-19	1
118	6.06494033762475e-20	1.21298806752495e-19	1
119	5.63454425498692e-20	1.12690885099738e-19	1
120	1.17473502404606e-17	2.34947004809211e-17	1
121	6.75285814805208e-18	1.35057162961042e-17	1
122	7.46345832432192e-18	1.49269166486438e-17	1
123	1.41313030296940e-13	2.82626060593879e-13	0.999999999999859
124	2.4130502456517e-13	4.8261004913034e-13	0.999999999999759
125	3.53057690551168e-13	7.06115381102337e-13	0.999999999999647
126	8.30402208141236e-13	1.66080441628247e-12	0.99999999999917
127	3.10963475797579e-12	6.21926951595157e-12	0.99999999999689
128	1.98196772997160e-12	3.96393545994319e-12	0.999999999998018
129	5.8548169918591e-12	1.17096339837182e-11	0.999999999994145
130	4.46372376682009e-12	8.92744753364018e-12	0.999999999995536
131	1.13780421022587e-11	2.27560842045174e-11	0.999999999988622
132	5.08419553604622e-10	1.01683910720924e-09	0.99999999949158
133	2.99998194910352e-10	5.99996389820704e-10	0.999999999700002
134	2.17428583288045e-10	4.34857166576091e-10	0.999999999782571
135	1.03843478318746e-09	2.07686956637491e-09	0.999999998961565
136	2.69841022232531e-09	5.39682044465063e-09	0.99999999730159
137	2.62756562656667e-08	5.25513125313335e-08	0.999999973724344
138	1.07226764141233e-07	2.14453528282466e-07	0.999999892773236
139	2.08393799210078e-07	4.16787598420157e-07	0.9999997916062
140	2.74734474546320e-06	5.49468949092641e-06	0.999997252655255
141	3.08767140877996e-05	6.17534281755992e-05	0.999969123285912
142	5.5325392515099e-05	0.000110650785030198	0.999944674607485
143	0.000645275602238986	0.00129055120447797	0.99935472439776
144	0.00219508976441682	0.00439017952883364	0.997804910235583
145	0.00171554000489942	0.00343108000979884	0.9982844599951
146	0.00138272126942045	0.00276544253884089	0.99861727873058
147	0.00411421343577655	0.0082284268715531	0.995885786564223
148	0.00439307234268454	0.00878614468536909	0.995606927657315
149	0.00367452126830276	0.00734904253660553	0.996325478731697
150	0.0450276698875016	0.0900553397750031	0.954972330112498
151	0.123269076497423	0.246538152994846	0.876730923502577
152	0.106350484046530	0.212700968093060	0.89364951595347
153	0.103780215148700	0.207560430297400	0.8962197848513
154	0.094437324873486	0.188874649746972	0.905562675126514
155	0.0798710409962537	0.159742081992507	0.920128959003746
156	0.0690066000387975	0.138013200077595	0.930993399961202
157	0.0559145069094044	0.111829013818809	0.944085493090596
158	0.0699561928798328	0.139912385759666	0.930043807120167
159	0.0672578835458807	0.134515767091761	0.932742116454119
160	0.0556583154478873	0.111316630895775	0.944341684552113
161	0.0732513123702097	0.146502624740419	0.92674868762979
162	0.0837488573492213	0.167497714698443	0.916251142650779
163	0.146379048366516	0.292758096733033	0.853620951633484
164	0.124717450275605	0.249434900551210	0.875282549724395
165	0.113051471941619	0.226102943883239	0.88694852805838
166	0.0941801297246446	0.188360259449289	0.905819870275355
167	0.0820846392381656	0.164169278476331	0.917915360761834
168	0.112844882543054	0.225689765086107	0.887155117456946
169	0.111514452613941	0.223028905227882	0.88848554738606
170	0.107121876341937	0.214243752683874	0.892878123658063
171	0.215888181560001	0.431776363120003	0.784111818439999
172	0.224970819121477	0.449941638242953	0.775029180878523
173	0.307680302207068	0.615360604414136	0.692319697792932
174	0.597187346199285	0.805625307601431	0.402812653800715
175	0.568136515063745	0.86372696987251	0.431863484936255
176	0.525049317081721	0.949901365836558	0.474950682918279
177	0.497010533110073	0.994021066220146	0.502989466889927
178	0.449615279211625	0.89923055842325	0.550384720788375
179	0.420916722148895	0.84183344429779	0.579083277851105
180	0.376060330075765	0.75212066015153	0.623939669924235
181	0.356421262570105	0.712842525140209	0.643578737429895
182	0.317558221095959	0.635116442191918	0.682441778904041
183	0.308253179891112	0.616506359782225	0.691746820108888
184	0.303115189657991	0.606230379315982	0.696884810342009
185	0.280791984778026	0.561583969556051	0.719208015221974
186	0.313783979361511	0.627567958723022	0.686216020638489
187	0.294803289162083	0.589606578324165	0.705196710837917
188	0.323739924950054	0.647479849900108	0.676260075049946
189	0.396969693294167	0.793939386588335	0.603030306705833
190	0.351757445324744	0.703514890649488	0.648242554675256
191	0.305087443906993	0.610174887813985	0.694912556093007
192	0.300346706971858	0.600693413943716	0.699653293028142
193	0.251789317400742	0.503578634801484	0.748210682599258
194	0.215407614139322	0.430815228278643	0.784592385860678
195	0.18268044591747	0.36536089183494	0.81731955408253
196	0.245334522666138	0.490669045332275	0.754665477333862
197	0.230265440260814	0.460530880521628	0.769734559739186
198	0.269835601806628	0.539671203613257	0.730164398193372
199	0.263959883899408	0.527919767798816	0.736040116100592
200	0.308963962397748	0.617927924795496	0.691036037602252
201	0.406525654679615	0.81305130935923	0.593474345320385
202	0.546089292600805	0.90782141479839	0.453910707399195
203	0.536259504535698	0.927480990928603	0.463740495464302
204	0.478102910939407	0.956205821878814	0.521897089060593
205	0.448733065595161	0.897466131190322	0.551266934404839
206	0.550883737804591	0.898232524390818	0.449116262195409
207	0.861379776423097	0.277240447153807	0.138620223576903
208	0.875693227072274	0.248613545855453	0.124306772927726
209	0.816020724013194	0.367958551973612	0.183979275986806
210	0.800985181288244	0.398029637423513	0.199014818711756
211	0.742518299768306	0.514963400463387	0.257481700231694
212	0.778048301500464	0.443903396999072	0.221951698499536
213	0.838653337169267	0.322693325661465	0.161346662830733
214	0.825649620716244	0.348700758567512	0.174350379283756
215	0.680563866594093	0.638872266811814	0.319436133405907

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	129	0.661538461538462	NOK
5% type I error level	129	0.661538461538462	NOK
10% type I error level	130	0.666666666666667	NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/29/t12620873577p07r06hcxgqmpr/1044vj1262087273.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/29/t12620873577p07r06hcxgqmpr/1044vj1262087273.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/29/t12620873577p07r06hcxgqmpr/1s4tw1262087273.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/29/t12620873577p07r06hcxgqmpr/1s4tw1262087273.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/29/t12620873577p07r06hcxgqmpr/2cqnr1262087273.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/29/t12620873577p07r06hcxgqmpr/2cqnr1262087273.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/29/t12620873577p07r06hcxgqmpr/30tck1262087273.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/29/t12620873577p07r06hcxgqmpr/30tck1262087273.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/29/t12620873577p07r06hcxgqmpr/4lmvc1262087273.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/29/t12620873577p07r06hcxgqmpr/4lmvc1262087273.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/29/t12620873577p07r06hcxgqmpr/5znr51262087273.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/29/t12620873577p07r06hcxgqmpr/5znr51262087273.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/29/t12620873577p07r06hcxgqmpr/6cwr11262087273.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/29/t12620873577p07r06hcxgqmpr/6cwr11262087273.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/29/t12620873577p07r06hcxgqmpr/7pcig1262087273.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/29/t12620873577p07r06hcxgqmpr/7pcig1262087273.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/29/t12620873577p07r06hcxgqmpr/8a2wj1262087273.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/29/t12620873577p07r06hcxgqmpr/8a2wj1262087273.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/29/t12620873577p07r06hcxgqmpr/9tn6f1262087273.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/29/t12620873577p07r06hcxgqmpr/9tn6f1262087273.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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