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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, 08 Dec 2010 19:13:34 +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/08/t1291835543aetyp8l44oscs7s.htm/, Retrieved Wed, 08 Dec 2010 20:12:34 +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/08/t1291835543aetyp8l44oscs7s.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 «

1214,82 1192,72 1206,41 1176,86 1145,11 1199,07 1214,82 1192,72 1206,41 1176,86 1157,47 1199,07 1214,82 1192,72 1206,41 1100,1 1157,47 1199,07 1214,82 1192,72 1095,63 1100,1 1157,47 1199,07 1214,82 1105,63 1095,63 1100,1 1157,47 1199,07 1137,79 1105,63 1095,63 1100,1 1157,47 1124,72 1137,79 1105,63 1095,63 1100,1 1152,6 1124,72 1137,79 1105,63 1095,63 1211,85 1152,6 1124,72 1137,79 1105,63 1239,62 1211,85 1152,6 1124,72 1137,79 1244,13 1239,62 1211,85 1152,6 1124,72 1198,42 1244,13 1239,62 1211,85 1152,6 1227,99 1198,42 1244,13 1239,62 1211,85 1304,92 1227,99 1198,42 1244,13 1239,62 1340,26 1304,92 1227,99 1198,42 1244,13 1307,32 1340,26 1304,92 1227,99 1198,42 1356,51 1307,32 1340,26 1304,92 1227,99 1383,29 1356,51 1307,32 1340,26 1304,92 1437,87 1383,29 1356,51 1307,32 1340,26 1494,56 1437,87 1383,29 1356,51 1307,32 1521,42 1494,56 1437,87 1383,29 1356,51 1498,76 1521,42 1494,56 1437,87 1383,29 1488,75 1498,76 1521,42 1494,56 1437,87 1524,62 1488,75 1498,76 1521,42 1494,56 1439,27 1 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	16 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

BEL_20[t] = + 46.3927350630606 + 1.28080975239333Y1[t] -0.353226463695596Y2[t] + 0.198103762183654Y3[t] -0.142505461121703Y4[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)	46.3927350630606	24.229548	1.9147	0.056907	0.028454
Y1	1.28080975239333	0.068789	18.6195	0	0
Y2	-0.353226463695596	0.111746	-3.161	0.001808	0.000904
Y3	0.198103762183654	0.111861	1.771	0.078035	0.039018
Y4	-0.142505461121703	0.068535	-2.0793	0.038821	0.019411

Multiple Linear Regression - Regression Statistics
Multiple R	0.991510551722486
R-squared	0.98309317417703
Adjusted R-squared	0.98276647222876
F-TEST (value)	3009.14389823190
F-TEST (DF numerator)	4
F-TEST (DF denominator)	207
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	120.02917403868
Sum Squared Residuals	2982249.54242439

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	1214.82	1217.86016984901	-3.04016984901188
2	1199.07	1252.33115344679	-53.2611534467927
3	1157.47	1217.42901811850	-59.9590181184959
4	1100.1	1176.03964212915	-75.9396421291544
5	1095.63	1110.98430257890	-15.3543025789030
6	1105.63	1119.52702971375	-13.8970297137485
7	1137.79	1128.47706387659	9.31293612341217
8	1124.72	1173.42565536419	-48.7056553641922
9	1152.6	1147.94374586101	4.65625413898837
10	1211.85	1193.21535401885	18.6346459811517
11	1239.62	1252.08318623891	-12.4631862389056
12	1244.13	1274.10828435544	-29.9782843554448
13	1198.42	1277.84023309522	-79.4202330952208
14	1227.99	1214.75926086643	13.2307391335663
15	1304.92	1265.71485821233	39.2051417876715
16	1340.26	1344.10462333340	-3.84462333339493
17	1307.32	1374.56658100652	-67.2465810065165
18	1356.51	1330.91992047510	25.5900795249024
19	1383.29	1401.59627374094	-18.3062737409363
20	1437.87	1406.95946823847	30.9105317615273
21	1494.56	1481.84551377749	12.7144862225049
22	1521.42	1533.47089337087	-12.0508933708687
23	1498.76	1554.84524218439	-56.0852421843949
24	1488.75	1519.78698459047	-31.0369845904672
25	1524.62	1512.21262309762	12.4073769023840
26	1439.27	1553.37433788075	-114.104337880747
27	1423.11	1432.63314735077	-9.52314735077478
28	1466.85	1450.61560204387	16.2343979561264
29	1425.83	1490.32653327407	-64.4965332740682
30	1363.45	1431.29907601870	-67.8490760186979
31	1389.18	1376.85946001484	12.3205399851644
32	1395.89	1417.48955655501	-21.5995565550100
33	1368.43	1410.48313441288	-42.0531344128777
34	1349.03	1386.92864950652	-37.8986495065166
35	1299.88	1369.44314973276	-69.563149732758
36	1365.41	1306.94780284463	58.4621971553689
37	1451.04	1408.31033358564	42.7296664143565
38	1433.75	1487.86694855155	-54.116948551546
39	1464.65	1455.46084879644	9.189151203562
40	1475.57	1508.77039799117	-33.2003979911698
41	1471.16	1496.21418607510	-25.0541860751040
42	1429.12	1495.29390775776	-66.173907757763
43	1452.46	1440.76626880643	11.6937311935705
44	1538.09	1483.08021173437	55.0097882656258
45	1631.59	1576.81181209051	54.7781879094948
46	1665.5	1676.93541324795	-11.4354132479503
47	1690.6	1700.97854528928	-10.3785452892757
48	1711.74	1727.46891981875	-15.7289198187506
49	1734.1	1739.07269170635	-4.97269170635476
50	1748.09	1760.38443457152	-12.2944345715173
51	1703.45	1771.01584573767	-67.565845737674
52	1745.74	1710.31589483805	35.4241051619517
53	1751.01	1779.83441812840	-28.8244181284016
54	1795.65	1760.80933502886	34.8406649711434
55	1852.13	1830.86243079924	21.2675692007614
56	1877.1	1882.45198715091	-5.3519871509135
57	1989.31	1902.57592416241	86.7340758375856
58	2097.76	2042.30297838365	55.4570216163496
59	2154.87	2138.46919703700	16.4008029630034
60	2152.18	2191.97969379881	-39.7996937988105
61	2250.27	2173.85536743957	76.414632560432
62	2346.9	2296.29916383883	50.6008361611696
63	2525.56	2376.74444038376	148.815559616238
64	2409.36	2591.25697528246	-181.896975282460
65	2394.36	2384.48384790888	9.87615209112049
66	2401.33	2427.93953214795	-26.6095321479495
67	2354.32	2393.68549022782	-39.3654902278204
68	2450.41	2344.60021346544	105.809786534561
69	2504.67	2487.79676377049	16.8732362295108
70	2661.39	2513.04584911457	148.34415088543
71	2880.4	2720.34325782509	160.056742174913
72	3064.42	2942.55151068328	121.868489316723
73	3141.12	3124.20046879368	16.9195312063165
74	3327.7	3178.49109204184	149.208907958163
75	3564.95	3395.6170391547	169.332960845297
76	3403.13	3622.55486291757	-219.424862917566
77	3149.9	3357.52328135369	-207.623281353690
78	3006.84	3110.75438275233	-103.914382752333
79	3230.66	2951.10270552890	279.557294471103
80	3361.13	3261.20054022681	99.9294597731898
81	3484.74	3356.99457521908	127.745424780925
82	3411.13	3533.95642731407	-122.826427314065
83	3288.18	3389.96472380682	-101.784723806823
84	3280.37	3264.38508327367	15.9849167263318
85	3173.95	3265.61363483526	-91.6636348352577
86	3165.26	3118.20152909971	47.058470900290
87	3092.71	3160.63550868016	-67.9255086801571
88	3053.05	3050.81306439331	2.23693560668846
89	3181.96	3039.08663903370	142.873360966296
90	2999.93	3205.07073027562	-205.140730275618
91	3249.57	2928.87248360864	320.697516391363
92	3210.52	3344.1009659538	-133.580965953799
93	3030.29	3151.47468390238	-121.184683902381
94	2803.47	3009.82272791536	-206.352727915356
95	2767.63	2739.66045020166	27.9695497983353
96	2882.6	2743.73565236977	138.864347630234
97	2863.36	2884.39984998074	-21.0398499807447
98	2897.06	2844.36967366858	52.6903263314226
99	3012.61	2922.21242475059	90.3975752494082
100	3142.95	3038.11089056352	104.839109436476
101	3032.93	3173.65421766801	-140.724217668014
102	3045.78	3004.78844711214	40.9915528878638
103	3110.52	3069.46316629659	41.0568337034147
104	3013.24	3107.47429188999	-94.2342918899924
105	2987.1	2978.23332209419	8.866677905814
106	2995.55	2990.10886794329	5.44113205671213
107	2833.18	2981.66771257377	-148.48771257377
108	2848.96	2779.40236837388	69.5576316261244
109	2794.83	2862.36599672107	-67.5359967210699
110	2845.26	2754.09157221466	91.1684277853362
111	2915.02	2864.06764559729	50.9523544027085
112	2892.63	2922.63163053658	-30.0016305365788
113	2604.42	2887.01741541053	-282.597415410527
114	2641.65	2532.41714524096	109.232854759045
115	2659.81	2667.52836722112	-7.71836722112442
116	2638.53	2623.73246305676	14.7975369432362
117	2720.25	2638.50914096111	81.7408590388943
118	2745.88	2748.98565907782	-3.10565907782441
119	2735.7	2746.14359918522	-10.4435991852235
120	2811.7	2743.27331729966	68.4266827003411
121	2799.43	2837.64255702387	-38.2125570238746
122	2555.28	2789.41269885356	-234.132698853564
123	2304.98	2497.54367803646	-192.563678036455
124	2214.95	2249.93608991644	-34.9860899164423
125	2065.81	2176.41888024230	-110.608880242303
126	1940.49	2002.40722895517	-61.9172289551715
127	2042	1912.41018079017	129.589819209831
128	1995.37	2069.97609075866	-74.6060907586645
129	1946.81	1970.82281466966	-24.0128146696587
130	1765.9	1963.0659403826	-197.165940382599
131	1635.25	1724.80401736509	-89.5540173650926
132	1833.42	1618.39353372254	215.026466277459
133	1910.43	1889.44175341158	20.9882465884183
134	1959.67	1917.97643057507	41.6935694249317
135	1969.6	2011.71809386120	-42.1180938612034
136	2061.41	1994.05932712537	67.350672874627
137	2093.48	2106.92321539705	-13.4432153970478
138	2120.88	2110.51926397726	10.3607360227397
139	2174.56	2151.05830567926	23.5016943207373
140	2196.72	2203.40352935012	-6.6835293501233
141	2350.44	2213.68296983764	136.757030162361
142	2440.25	2409.47110685933	30.7788931406693
143	2408.64	2466.94294493947	-58.3029449394651
144	2472.81	2422.02786926622	50.7821307337752
145	2407.6	2511.26867899281	-103.668678992808
146	2454.62	2386.02005747793	68.5999425220725
147	2448.05	2486.49454577843	-38.4445457784335
148	2497.84	2439.40799561007	58.432004389933
149	2645.64	2524.10783106583	121.532168934167
150	2756.76	2687.82221834267	68.937781657327
151	2849.27	2788.73877389310	60.5312261068951
152	2921.44	2890.16034858265	31.2796514173491
153	2981.85	2950.87039115646	30.9796088435419
154	3080.58	3005.24312661339	75.3368733866063
155	3106.22	3111.47303110376	-5.25303110376167
156	3119.31	3111.12177353882	8.18822646117862
157	3061.26	3129.78087620253	-68.520876202525
158	3097.31	3041.81595195216	55.4940480478393
159	3161.69	3107.43327796729	54.2567220327073
160	3257.16	3163.79267592931	93.367324070695
161	3277.01	3278.74494590241	-1.73494590240833
162	3295.32	3278.06308733434	17.2569126656557
163	3363.99	3304.24163318497	59.7483668150332
164	3494.17	3376.05462563761	118.115374362394
165	3667.03	3519.33292442451	147.69707557549
166	3813.06	3705.74518753534	107.314812464659
167	3917.96	3847.72640690876	70.2335930912414
168	3895.51	3946.19454484359	-50.6845448435939
169	3801.06	3884.68250824288	-83.6225082428776
170	3570.12	3771.61097340476	-201.490973404757
171	3701.61	3489.7867563504	211.823243649599
172	3862.27	3724.2628974824	138.007102517603
173	3970.1	3851.30160255483	118.798397445174
174	4138.52	3991.62082937904	146.899170620961
175	4199.75	4182.33570564636	17.4142943536390
176	4290.89	4199.73588706224	91.1541129377581
177	4443.91	4312.83910327751	131.070896722493
178	4502.64	4464.76467528390	37.8753247160960
179	4356.98	4495.2654860682	-138.285486068202
180	4591.27	4305.28363728446	285.986362715544
181	4696.96	4646.64396916679	50.3160308332056
182	4621.4	4662.03018398665	-40.6301839866545
183	4562.84	4595.09077005682	-32.2507700568223
184	4202.52	4534.32632469250	-331.806324692495
185	4296.49	4063.4797739676	233.010226032403
186	4435.23	4310.27878212768	124.951217872325
187	4105.18	4391.75000859452	-286.570008594522
188	4116.68	3989.97548852775	126.704511472252
189	3844.49	4135.38087280676	-290.890872806757
190	3720.98	3697.53980758558	23.4401924144227
191	3674.4	3684.80382692911	-10.4038269291122
192	3857.62	3613.21003336201	244.409966637994
193	3801.06	3878.65405066987	-77.5940506698651
194	3504.37	3749.86647465682	-245.496474656819
195	3032.6	3432.7759936922	-400.175993692203
196	3047.03	2896.01253694362	151.017463056377
197	2962.34	3030.42097412711	-68.080974127106
198	2197.82	2865.67267170060	-667.852671700603
199	2014.45	1986.47118769293	27.9788123070674
200	1862.83	2002.82403799781	-139.994037997805
201	1905.41	1734.01329922554	171.39670077446
202	1810.99	1914.72836317312	-103.738363173122
203	1670.07	1774.84865751159	-104.778657511587
204	1864.44	1657.75052611551	206.689473884490
205	2052.02	1931.70535119224	120.314648807758
206	2029.6	2088.84160026986	-59.2416002698595
207	2070.83	2052.45492339809	18.3750766019117
208	2293.41	2122.64356403750	170.766435962495
209	2443.27	2361.99001088168	81.2799891183245
210	2513.17	2486.67380463915	26.4961953608454
211	2466.92	2561.48632370682	-94.566323706816
212	2502.66	2475.52730711068	27.1326928893235

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
8	0.0375167946661178	0.0750335893322356	0.962483205333882
9	0.0098639391422238	0.0197278782844476	0.990136060857776
10	0.00446414782770199	0.00892829565540398	0.995535852172298
11	0.00125269368723039	0.00250538737446077	0.99874730631277
12	0.000292148261063697	0.000584296522127394	0.999707851738936
13	9.08039189769603e-05	0.000181607837953921	0.999909196081023
14	0.000157286733761481	0.000314573467522962	0.999842713266239
15	0.000216567943044018	0.000433135886088036	0.999783432056956
16	6.49223378343536e-05	0.000129844675668707	0.999935077662166
17	2.13037220063385e-05	4.2607444012677e-05	0.999978696277994
18	2.62684977893709e-05	5.25369955787417e-05	0.99997373150221
19	8.47801178924865e-06	1.69560235784973e-05	0.99999152198821
20	3.98854876607724e-06	7.97709753215448e-06	0.999996011451234
21	1.30506795987980e-06	2.61013591975959e-06	0.99999869493204
22	3.97036031661677e-07	7.94072063323353e-07	0.999999602963968
23	2.24174799027775e-07	4.48349598055551e-07	0.999999775825201
24	6.8355205633633e-08	1.36710411267266e-07	0.999999931644794
25	1.98157043972371e-08	3.96314087944742e-08	0.999999980184296
26	1.71634169432778e-07	3.43268338865556e-07	0.99999982836583
27	6.04502764317469e-08	1.20900552863494e-07	0.999999939549724
28	2.26640699767705e-08	4.5328139953541e-08	0.99999997733593
29	1.03699011289261e-08	2.07398022578522e-08	0.999999989630099
30	4.33165318919887e-09	8.66330637839775e-09	0.999999995668347
31	1.50255618648793e-09	3.00511237297585e-09	0.999999998497444
32	4.48900445541823e-10	8.97800891083646e-10	0.9999999995511
33	1.32381626840329e-10	2.64763253680658e-10	0.999999999867618
34	4.18907649725226e-11	8.37815299450453e-11	0.99999999995811
35	2.79854373570801e-11	5.59708747141601e-11	0.999999999972015
36	5.46777619156715e-11	1.09355523831343e-10	0.999999999945322
37	4.0887107197132e-11	8.1774214394264e-11	0.999999999959113
38	1.29790467910232e-11	2.59580935820463e-11	0.99999999998702
39	6.64159066245203e-12	1.32831813249041e-11	0.999999999993358
40	2.32318519977718e-12	4.64637039955437e-12	0.999999999997677
41	7.05228678593372e-13	1.41045735718674e-12	0.999999999999295
42	3.5759603035836e-13	7.1519206071672e-13	0.999999999999642
43	1.41650994671543e-13	2.83301989343086e-13	0.999999999999858
44	1.64403121101281e-13	3.28806242202562e-13	0.999999999999836
45	2.97917849129757e-13	5.95835698259513e-13	0.999999999999702
46	1.01896267503596e-13	2.03792535007192e-13	0.999999999999898
47	3.42477261994628e-14	6.84954523989256e-14	0.999999999999966
48	1.03384562816490e-14	2.06769125632981e-14	0.99999999999999
49	3.16878379698653e-15	6.33756759397305e-15	0.999999999999997
50	9.31002741257307e-16	1.86200548251461e-15	1
51	5.61462735371734e-16	1.12292547074347e-15	1
52	3.71778001328558e-16	7.43556002657117e-16	1
53	1.31425842875449e-16	2.62851685750897e-16	1
54	8.57190773701958e-17	1.71438154740392e-16	1
55	3.14962450759021e-17	6.29924901518042e-17	1
56	9.19431195216647e-18	1.83886239043329e-17	1
57	2.90590591768971e-17	5.81181183537942e-17	1
58	1.46272437321875e-17	2.92544874643751e-17	1
59	4.42479229763283e-18	8.84958459526567e-18	1
60	2.32467134561679e-18	4.64934269123358e-18	1
61	1.79475879104012e-18	3.58951758208023e-18	1
62	5.57395446226966e-19	1.11479089245393e-18	1
63	4.26036532225548e-18	8.52073064451095e-18	1
64	6.72335125856328e-15	1.34467025171266e-14	0.999999999999993
65	2.60651395534987e-15	5.21302791069974e-15	0.999999999999997
66	1.46716262646871e-15	2.93432525293742e-15	0.999999999999999
67	1.56422858184180e-15	3.12845716368361e-15	0.999999999999998
68	1.53129955955555e-15	3.06259911911111e-15	0.999999999999998
69	5.50079251875685e-16	1.10015850375137e-15	1
70	1.54883520844503e-15	3.09767041689005e-15	0.999999999999998
71	9.68870594048656e-15	1.93774118809731e-14	0.99999999999999
72	7.57259078370395e-15	1.51451815674079e-14	0.999999999999992
73	3.5090410149616e-15	7.0180820299232e-15	0.999999999999996
74	4.55834250365189e-15	9.11668500730377e-15	0.999999999999995
75	5.50079879539159e-15	1.10015975907832e-14	0.999999999999994
76	3.49601962743435e-11	6.99203925486871e-11	0.99999999996504
77	1.13896898923423e-09	2.27793797846847e-09	0.99999999886103
78	1.16113236449152e-09	2.32226472898303e-09	0.999999998838868
79	1.04424061715381e-08	2.08848123430761e-08	0.999999989557594
80	9.33912139915766e-09	1.86782427983153e-08	0.999999990660879
81	7.19031034100283e-09	1.43806206820057e-08	0.99999999280969
82	1.08991437459891e-08	2.17982874919781e-08	0.999999989100856
83	1.07860256531573e-08	2.15720513063146e-08	0.999999989213974
84	5.69260939072117e-09	1.13852187814423e-08	0.99999999430739
85	1.57910650780063e-08	3.15821301560125e-08	0.999999984208935
86	8.6662648607969e-09	1.73325297215938e-08	0.999999991333735
87	9.05722094051436e-09	1.81144418810287e-08	0.99999999094278
88	5.12707599004084e-09	1.02541519800817e-08	0.999999994872924
89	6.47657999629994e-09	1.29531599925999e-08	0.99999999352342
90	1.20353317501257e-07	2.40706635002513e-07	0.999999879646682
91	4.40809678957179e-06	8.81619357914358e-06	0.99999559190321
92	4.3263143665611e-06	8.6526287331222e-06	0.999995673685633
93	1.08932956399464e-05	2.17865912798928e-05	0.99998910670436
94	2.38291413386166e-05	4.76582826772333e-05	0.999976170858661
95	1.53160934361940e-05	3.06321868723880e-05	0.999984683906564
96	1.42091530447942e-05	2.84183060895884e-05	0.999985790846955
97	1.14250284753858e-05	2.28500569507716e-05	0.999988574971525
98	7.59378005602739e-06	1.51875601120548e-05	0.999992406219944
99	6.98923596072866e-06	1.39784719214573e-05	0.99999301076404
100	6.03189305720379e-06	1.20637861144076e-05	0.999993968106943
101	8.27920643471923e-06	1.65584128694385e-05	0.999991720793565
102	5.64649065355321e-06	1.12929813071064e-05	0.999994353509347
103	3.85267143079439e-06	7.70534286158879e-06	0.99999614732857
104	4.17842749710755e-06	8.3568549942151e-06	0.999995821572503
105	2.58908846951288e-06	5.17817693902576e-06	0.99999741091153
106	1.58756849551228e-06	3.17513699102456e-06	0.999998412431504
107	2.95046538246123e-06	5.90093076492246e-06	0.999997049534618
108	2.04832556325021e-06	4.09665112650041e-06	0.999997951674437
109	1.54464486242535e-06	3.0892897248507e-06	0.999998455355138
110	1.12737166694604e-06	2.25474333389208e-06	0.999998872628333
111	7.46629866775443e-07	1.49325973355089e-06	0.999999253370133
112	4.80069463555475e-07	9.6013892711095e-07	0.999999519930536
113	5.92907018491662e-06	1.18581403698332e-05	0.999994070929815
114	5.37963821260629e-06	1.07592764252126e-05	0.999994620361787
115	3.4009078686071e-06	6.8018157372142e-06	0.999996599092131
116	2.23953406007660e-06	4.47906812015321e-06	0.99999776046594
117	1.74693940607209e-06	3.49387881214417e-06	0.999998253060594
118	1.07030712574746e-06	2.14061425149492e-06	0.999998929692874
119	6.54062549104463e-07	1.30812509820893e-06	0.99999934593745
120	4.79213706200488e-07	9.58427412400976e-07	0.999999520786294
121	3.02591770214801e-07	6.05183540429602e-07	0.99999969740823
122	1.56384810846496e-06	3.12769621692991e-06	0.999998436151892
123	3.79740778164393e-06	7.59481556328785e-06	0.999996202592218
124	2.55553876415477e-06	5.11107752830954e-06	0.999997444461236
125	3.03264864774938e-06	6.06529729549877e-06	0.999996967351352
126	2.37592961377598e-06	4.75185922755195e-06	0.999997624070386
127	2.401213298195e-06	4.80242659639e-06	0.999997598786702
128	1.91874882951051e-06	3.83749765902102e-06	0.99999808125117
129	1.22762646047791e-06	2.45525292095582e-06	0.99999877237354
130	3.04361793970907e-06	6.08723587941814e-06	0.99999695638206
131	2.70160001853254e-06	5.40320003706509e-06	0.999997298399981
132	6.5008020924498e-06	1.30016041848996e-05	0.999993499197908
133	4.07971715488944e-06	8.15943430977888e-06	0.999995920282845
134	2.60903172502592e-06	5.21806345005185e-06	0.999997390968275
135	1.79881688528872e-06	3.59763377057744e-06	0.999998201183115
136	1.28230569698621e-06	2.56461139397242e-06	0.999998717694303
137	7.9974496644959e-07	1.59948993289918e-06	0.999999200255034
138	4.8501519174436e-07	9.7003038348872e-07	0.999999514984808
139	2.98853048920567e-07	5.97706097841133e-07	0.99999970114695
140	1.79393556748714e-07	3.58787113497428e-07	0.999999820606443
141	1.95633161331963e-07	3.91266322663926e-07	0.999999804366839
142	1.17976850372866e-07	2.35953700745732e-07	0.99999988202315
143	8.04312437755413e-08	1.60862487551083e-07	0.999999919568756
144	5.18776691636772e-08	1.03755338327354e-07	0.999999948122331
145	4.76867368929986e-08	9.53734737859973e-08	0.999999952313263
146	3.06023077633849e-08	6.12046155267699e-08	0.999999969397692
147	1.89460618546246e-08	3.78921237092492e-08	0.999999981053938
148	1.13968097411689e-08	2.27936194823377e-08	0.99999998860319
149	1.06210378232880e-08	2.12420756465760e-08	0.999999989378962
150	6.75595164572333e-09	1.35119032914467e-08	0.999999993244048
151	4.15443331781901e-09	8.30886663563802e-09	0.999999995845567
152	2.35303015216498e-09	4.70606030432996e-09	0.99999999764697
153	1.29987706904900e-09	2.59975413809801e-09	0.999999998700123
154	8.46028661106091e-10	1.69205732221218e-09	0.999999999153971
155	4.41804086198182e-10	8.83608172396364e-10	0.999999999558196
156	2.26492371375355e-10	4.52984742750709e-10	0.999999999773508
157	1.45789896744512e-10	2.91579793489024e-10	0.99999999985421
158	8.11716676081666e-11	1.62343335216333e-10	0.999999999918828
159	4.44475174825296e-11	8.88950349650593e-11	0.999999999955552
160	3.02001824962491e-11	6.04003649924981e-11	0.9999999999698
161	1.46293582230891e-11	2.92587164461782e-11	0.99999999998537
162	7.02699785702397e-12	1.40539957140479e-11	0.999999999992973
163	3.83177971638247e-12	7.66355943276494e-12	0.999999999996168
164	3.23494858846526e-12	6.46989717693053e-12	0.999999999996765
165	3.88825463940257e-12	7.77650927880513e-12	0.999999999996112
166	2.97152347702674e-12	5.94304695405349e-12	0.999999999997028
167	1.69374519475089e-12	3.38749038950178e-12	0.999999999998306
168	8.68411068277513e-13	1.73682213655503e-12	0.999999999999132
169	5.48539075779318e-13	1.09707815155864e-12	0.999999999999451
170	1.76138516961273e-12	3.52277033922546e-12	0.999999999998239
171	5.87038534034956e-12	1.17407706806991e-11	0.99999999999413
172	6.33226655242789e-12	1.26645331048558e-11	0.999999999993668
173	6.22116588278321e-12	1.24423317655664e-11	0.99999999999378
174	7.84817810366307e-12	1.56963562073261e-11	0.999999999992152
175	3.61446932337359e-12	7.22893864674717e-12	0.999999999996386
176	2.54992678811299e-12	5.09985357622598e-12	0.99999999999745
177	2.97804311245442e-12	5.95608622490884e-12	0.999999999997022
178	1.71654277992977e-12	3.43308555985955e-12	0.999999999998283
179	1.5379860837443e-12	3.0759721674886e-12	0.999999999998462
180	4.84260235669389e-11	9.68520471338779e-11	0.999999999951574
181	4.15787457658919e-11	8.31574915317838e-11	0.999999999958421
182	3.03360554045220e-11	6.06721108090441e-11	0.999999999969664
183	1.57910393511849e-11	3.15820787023697e-11	0.999999999984209
184	2.54144233601949e-10	5.08288467203898e-10	0.999999999745856
185	2.40090952412455e-09	4.8018190482491e-09	0.99999999759909
186	7.07746041020643e-09	1.41549208204129e-08	0.99999999292254
187	2.12677079981612e-08	4.25354159963223e-08	0.999999978732292
188	6.03377260179185e-08	1.20675452035837e-07	0.999999939662274
189	1.58449565856126e-07	3.16899131712252e-07	0.999999841550434
190	1.98487668564259e-07	3.96975337128519e-07	0.99999980151233
191	1.16928195387702e-07	2.33856390775405e-07	0.999999883071805
192	2.34197186914023e-05	4.68394373828046e-05	0.999976580281309
193	5.87286118646515e-05	0.000117457223729303	0.999941271388135
194	8.18004422836658e-05	0.000163600884567332	0.999918199557716
195	0.000246430474931176	0.000492860949862351	0.999753569525069
196	0.00241016109766978	0.00482032219533956	0.99758983890233
197	0.0209501258793420	0.0419002517586839	0.979049874120658
198	0.333662471944237	0.667324943888473	0.666337528055763
199	0.250767999328418	0.501535998656836	0.749232000671582
200	0.388945833408821	0.777891666817641	0.611054166591179
201	0.710054662481091	0.579890675037819	0.289945337518909
202	0.773808284645185	0.452383430709631	0.226191715354815
203	0.814658964990527	0.370682070018946	0.185341035009473
204	0.686943744852129	0.626112510295742	0.313056255147871

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	187	0.949238578680203	NOK
5% type I error level	189	0.959390862944162	NOK
10% type I error level	190	0.964467005076142	NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291835543aetyp8l44oscs7s/10nmu71291835596.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291835543aetyp8l44oscs7s/10nmu71291835596.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291835543aetyp8l44oscs7s/1ylxd1291835596.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291835543aetyp8l44oscs7s/1ylxd1291835596.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291835543aetyp8l44oscs7s/28cey1291835596.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291835543aetyp8l44oscs7s/28cey1291835596.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291835543aetyp8l44oscs7s/38cey1291835596.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291835543aetyp8l44oscs7s/38cey1291835596.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291835543aetyp8l44oscs7s/48cey1291835596.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291835543aetyp8l44oscs7s/48cey1291835596.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291835543aetyp8l44oscs7s/51ldj1291835596.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291835543aetyp8l44oscs7s/51ldj1291835596.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291835543aetyp8l44oscs7s/61ldj1291835596.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291835543aetyp8l44oscs7s/61ldj1291835596.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291835543aetyp8l44oscs7s/7cvum1291835596.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291835543aetyp8l44oscs7s/7cvum1291835596.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291835543aetyp8l44oscs7s/8cvum1291835596.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291835543aetyp8l44oscs7s/8cvum1291835596.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291835543aetyp8l44oscs7s/9nmu71291835596.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291835543aetyp8l44oscs7s/9nmu71291835596.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; 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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