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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: Thu, 17 Dec 2009 21:38:42 +0100

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/17/t12610824195fwi2n0lvlyhu03.htm/, Retrieved Thu, 17 Dec 2009 21:40:22 +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/17/t12610824195fwi2n0lvlyhu03.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 «

277 7.7 0 260.6 7.5 0 291.6 8.3 0 275.4 7.8 0 275.3 7.9 0 231.7 6.6 0 238.8 7 0 274.2 8.2 0 277.8 8.2 0 299.1 9.1 0 286.6 9 0 232.3 7.1 0 294.1 8.9 0 267.5 8.5 0 309.7 9.8 0 280.7 8.8 0 287.3 9.2 0 235.7 7.4 0 256.4 8.3 0 289 9.7 0 290.8 9.7 0 321.9 10.8 0 291.8 9.8 0 241.4 7.9 0 295.5 9.8 0 258.2 9 0 306.1 10.5 0 281.5 9.5 0 283.1 9.7 0 237.4 8.1 0 274.8 10.1 0 299.3 11.1 0 300.4 11.2 0 340.9 12.6 0 318.8 12.2 0 265.7 9.9 0 322.7 11.8 0 281.6 11.1 0 323.5 12.6 0 312.6 11.9 0 310.8 11.9 0 262.8 10 0 273.8 10.8 0 320 12.9 0 310.3 12.5 0 342.2 13.8 0 320.1 13.1 0 265.6 10.5 0 327 12.9 0 300.7 12.9 0 346.4 14.4 0 317.3 12.7 0 326.2 13.3 0 270.7 11 0 278.2 11.9 0 324.6 14.1 0 321.8 14.4 0 343.5 14.9 0 354 15.7 0 278.2 12 0 330.2 14.3 0 307.3 14.2 0 375.9 17.4 0 335.3 15.1 0 339.3 15.3 0 280.3 12.6 0 293.7 14 0 341.2 16.6 0 345.1 16.7 0 368.7 17.6 0 369.4 18.3 0 288.4 13.6 0 341 15.8 0 319.1 16.1 0 374.2 18.6 0 344.5 17.3 0 337.3 17 0 281 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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Multiple Linear Regression - Estimated Regression Equation

Y[t][t] = + 209.71550546094 + 4.16064886875658`X[t]`[t] + 35.6139613188847`D[t]`[t] + 44.4881074624471M1[t] + 17.0595132695103M2[t] + 59.9012520404552M3[t] + 42.3320083056181M4[t] + 28.2672223253406M5[t] -5.12091858711014M6[t] + 7.38449939264906M7[t] + 18.1204695726691M8[t] + 31.4270415324802M9[t] + 58.1708547316912M10[t] + 48.8622437145571M11[t] + 0.251010465555662t + 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)	209.71550546094	3.460082	60.61	0	0
`X[t]`	4.16064886875658	0.401932	10.3516	0	0
`D[t]`	35.6139613188847	12.393559	2.8736	0.004573	0.002287
M1	44.4881074624471	4.489905	9.9085	0	0
M2	17.0595132695103	4.436226	3.8455	0.00017	8.5e-05
M3	59.9012520404552	4.957355	12.0833	0	0
M4	42.3320083056181	4.524593	9.356	0	0
M5	28.2672223253406	4.414463	6.4033	0	0
M6	-5.12091858711014	4.269829	-1.1993	0.23206	0.11603
M7	7.38449939264906	4.387731	1.683	0.094202	0.047101
M8	18.1204695726691	4.462031	4.061	7.4e-05	3.7e-05
M9	31.4270415324802	4.580635	6.8608	0	0
M10	58.1708547316912	4.962148	11.7229	0	0
M11	48.8622437145571	5.024604	9.7246	0	0
t	0.251010465555662	0.082161	3.0551	0.002611	0.001305

Multiple Linear Regression - Regression Statistics
Multiple R	0.985444142850747
R-squared	0.971100158678844
Adjusted R-squared	0.96873408979875
F-TEST (value)	410.427678943987
F-TEST (DF numerator)	14
F-TEST (DF denominator)	171
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	11.8764006811788
Sum Squared Residuals	24119.3607269236

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	277	286.491619678368	-9.49161967836769
2	260.6	258.481906177236	2.11809382276373
3	291.6	304.903174508742	-13.3031745087422
4	275.4	285.504616805082	-10.1046168050825
5	275.3	272.106906177236	3.19309382276364
6	231.7	233.560932200958	-1.86093220095773
7	238.8	247.981620193775	-9.18162019377515
8	274.2	263.961379481859	10.2386205181412
9	277.8	277.518961907226	0.281038092774518
10	299.1	308.258369553873	-9.15836955387306
11	286.6	298.784704115419	-12.184704115419
12	232.3	242.26823801578	-9.96823801578005
13	294.1	294.496523907545	-0.396523907544678
14	267.5	265.654680632661	1.84531936733911
15	309.7	314.156273398545	-4.45627339854505
16	280.7	292.677391260507	-11.977391260507
17	287.3	280.527875293288	6.77212470671217
18	235.7	239.901576882631	-4.2015768826309
19	256.4	256.402589309827	-0.00258930982670624
20	289	273.214478371662	15.7855216283384
21	290.8	286.772060797028	4.02793920297172
22	321.9	318.343598217427	3.5564017825728
23	291.8	305.125348797092	-13.3253487970922
24	241.4	248.608882697453	-7.2088826974533
25	295.5	301.253233476094	-5.75323347609356
26	258.2	270.747130653707	-12.5471306537071
27	306.1	320.080853193343	-13.9808531933426
28	281.5	298.601971055304	-17.1019710553045
29	283.1	285.620325314334	-2.52032531433405
30	237.4	245.826156677428	-8.42615667742844
31	274.8	266.903882860256	7.89611713974356
32	299.3	282.051512374589	17.2484876254113
33	300.4	296.025159686831	4.37484031316887
34	340.9	328.844891767857	12.055108232143
35	318.8	318.123031668776	0.676968331224044
36	265.7	259.942306021634	5.75769397836559
37	322.7	312.586656800275	10.1133431997253
38	281.6	282.496618864764	-0.89661886476384
39	323.5	331.830341404399	-8.33034140439935
40	312.6	311.599653926988	1.00034607301177
41	310.8	297.785878412266	13.0141215877335
42	262.8	256.743515114734	6.05648488526613
43	273.8	272.828462655054	0.971537344946015
44	320	292.552805925019	27.4471940749815
45	310.3	304.446128802883	5.85387119711742
46	342.2	336.849795997033	5.35020400296718
47	320.1	324.879741237325	-4.77974123732481
48	265.6	265.450820929556	0.149179070443747
49	327	320.175496142575	6.82450385742518
50	300.7	292.997912415194	7.70208758480634
51	346.4	342.331634954829	4.06836504517085
52	317.3	317.940298608661	-0.640298608661439
53	326.2	306.622912415194	19.5770875848063
54	270.7	263.916289570158	6.78371042984159
55	278.2	280.417301997354	-2.21730199735419
56	324.6	300.557710154194	24.0422898458057
57	321.8	315.363487240188	6.43651275981197
58	343.5	344.438635339333	-0.938635339332994
59	354	338.70955388276	15.2904461172401
60	278.2	274.703919819359	3.49608018064089
61	330.2	329.012530145502	1.187469854498
62	307.3	301.418881531245	5.88111846875488
63	375.9	357.825707147767	18.0742928522332
64	335.3	330.937981480345	4.36201851965484
65	339.3	317.956335739375	21.3436642606253
66	280.3	273.585453346837	6.71454665316315
67	293.7	292.166790208411	1.53320979158906
68	341.2	313.971457912754	27.2285420872462
69	345.1	327.945105224996	17.1548947750039
70	368.7	358.684512871644	10.0154871283563
71	369.4	352.539366528195	16.8606334718051
72	288.4	284.373083596038	4.02691640396243
73	341	338.265629035305	2.73437096469521
74	319.1	312.336239968551	6.76376003144944
75	374.2	365.830611376943	8.36938862305736
76	344.5	343.103534578278	1.39646542172241
77	337.3	328.041564402929	9.25843559707116
78	281	282.006422462888	-1.00642246288836
79	282.2	300.171694437587	-17.9716944375868
80	321	321.97636214193	-0.976362141929565
81	325.4	336.366074341048	-10.9660743410476
82	366.3	369.185806422073	-2.88580642207345
83	380.3	370.113763155511	10.1862368444891
84	300.7	298.202896241473	2.4971037585274
85	359.3	355.423960775745	3.87603922425493
86	327.6	329.494571708991	-1.89457170899085
87	383.6	382.988943117383	0.611056882617091
88	352.4	357.349412110588	-4.94941211058831
89	329.4	340.207117500861	-10.8071175008613
90	294.5	297.500494655826	-3.00049465582602
91	333.5	323.154934594286	10.3450654057137
92	334.3	335.806174787365	-1.5061747873646
93	358	355.188665628991	2.81133437100946
94	396.1	395.497565673778	0.602434326221781
95	387	389.768484217205	-2.76848421720514
96	307.2	314.529098208162	-7.32909820816158
97	363.9	372.582292516185	-8.68229251618542
98	344.7	351.645682091939	-6.94568209193909
99	397.6	406.388248160958	-8.78824816095807
100	376.8	380.748717154163	-3.94871715416343
101	337.1	360.277903449431	-23.1779034494312
102	299.3	314.658826396266	-15.3588263962663
103	323.1	335.736552579094	-12.6365525790943
104	329.1	352.548441640929	-23.4484416409292
105	347	368.60241338755	-21.6024133875499
106	462	462	3.8838832323862e-15
107	436.5	419.408762563915	17.0912374360848
108	360.4	342.505117007369	17.894882992631
109	415.5	400.558311315393	14.9416886846072
110	382.1	373.796792474887	8.30320752511276
111	432.2	426.042969222652	6.15703077734764
112	424.3	410.805060387749	13.4949396122509
113	386.7	387.421792474887	-0.721792474887278
114	354.5	342.634845195474	11.8651548045263
115	375.8	366.208960699556	9.59103930044433
116	368	377.195941345131	-9.1959413451314
117	402.4	399.490886394887	2.90911360511305
118	426.5	436.471267344669	-9.97126734466937
119	433.3	437.815288964982	-4.51528896498242
120	338.5	347.18150214154	-8.68150214153956
121	416.8	414.388123960828	2.41187603917217
122	381.1	389.290864667825	-8.19086466782492
123	445.7	451.10653381373	-5.40653381373016
124	412.4	416.313575295671	-3.91357529567105
125	394	402.915864667825	-8.91586466782494
126	348.2	353.136138745904	-4.93613874590352
127	380.1	378.374513797488	1.72548620251191
128	373.7	392.690013538069	-18.9900135380691
129	393.6	406.663660850311	-13.0636608503114
130	434.2	452.797469311358	-18.5974693113584
131	430.7	449.980842062915	-19.2808420629149
132	344.5	359.763120126348	-15.2631201263476
133	411.9	424.473352624382	-12.573352624382
134	370.5	388.142341385736	-17.6423413857363
135	437.3	450.790140305393	-13.4901403053928
136	411.3	426.398803959225	-15.0988039592251
137	385.5	403.847665820115	-18.3476658201146
138	341.3	355.31613455882	-14.0161345588201
139	384.2	385.963353139788	-1.7633531397883
140	373.2	397.36639867224	-24.1663986722396
141	415.8	423.405927703876	-7.60592770387606
142	448.6	458.30598421928	-9.70598421928026
143	454.3	459.233940952718	-4.93394095271766
144	350.3	364.023440373643	-13.7234403736425
145	419.1	431.646127079806	-12.5461270798065
146	398	403.636413578674	-5.63641357867399
147	456.1	465.868147611455	-9.76814761145483
148	430.1	433.155513527774	-3.055513527774
149	399.8	411.436505162415	-11.6365051624148
150	362.7	364.985298335499	-2.28529833549861
151	384.9	388.143348952705	-3.24334895270493
152	385.3	404.123108240788	-18.8231082407885
153	432.3	432.242961706803	0.0570382931967554
154	468.9	467.143018222207	1.75698177779256
155	442.7	456.005093236251	-13.3050932362508
156	370.2	372.86047437657	-2.66047437656971
157	439.4	441.731355743361	-2.33135574336064
158	393.9	404.568214730964	-10.6682147309637
159	468.7	471.376662519377	-2.67666251937675
160	438.8	436.999768888193	1.80023111180674
161	430.1	433.171550658487	-3.0715506584873
162	366.3	368.829553695918	-2.52955369591785
163	391	391.987604313124	-0.987604313124178
164	380.9	402.558520071824	-21.6585200718242
165	431.4	433.590827745969	-2.19082774596857
166	465.4	469.323014035124	-3.92301403512405
167	471.5	470.250970768561	1.24902923143856
168	387.5	382.113573266372	5.3864267336275
169	446.4	447.239870651283	-0.839870651282532
170	421.5	415.485573168269	6.01442683173091
171	504.8	496.024162223579	8.77583777642112
172	492.1	458.734814384266	33.3651856157342
173	421.3	423.28566475201	-1.98566475200986
174	396.7	383.075431228229	13.6245687717714
175	428	412.058390261694	15.9416097383059
176	421.9	425.125695341648	-3.22569534164808
177	465.6	454.077678581414	11.5223214185859
178	525.8	503.956071024342	21.843928975658
179	499.9	486.161107848375	13.7388921516252
180	435.3	409.673527178704	25.6264728212957
181	479.5	468.974916147355	10.5250838526449
182	473	447.206175949357	25.7938240506426
183	554.4	520.255597040905	34.1444029590946
184	489.6	474.228886577203	15.3711134227965
185	462.2	454.174137759347	8.02586224065313
186	420.3	407.722930932431	12.5770690675693

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
18	0.0115417720170148	0.0230835440340297	0.988458227982985
19	0.00293945906690321	0.00587891813380643	0.997060540933097
20	0.000988668460565814	0.00197733692113163	0.999011331539434
21	0.000375914989727729	0.000751829979455458	0.999624085010272
22	8.41380379049754e-05	0.000168276075809951	0.999915861962095
23	1.64806922023281e-05	3.29613844046562e-05	0.999983519307798
24	6.37602709202849e-06	1.2752054184057e-05	0.999993623972908
25	1.85970140714245e-06	3.71940281428491e-06	0.999998140298593
26	3.91742712762915e-06	7.8348542552583e-06	0.999996082572872
27	1.49004024138338e-06	2.98008048276677e-06	0.999998509959759
28	3.75370407704599e-07	7.50740815409197e-07	0.999999624629592
29	8.02542235370713e-08	1.60508447074143e-07	0.999999919745777
30	2.39196064452785e-08	4.78392128905571e-08	0.999999976080394
31	6.84023583690318e-09	1.36804716738064e-08	0.999999993159764
32	4.73155686291205e-09	9.4631137258241e-09	0.999999995268443
33	8.3044967809025e-09	1.6608993561805e-08	0.999999991695503
34	2.01032746375371e-09	4.02065492750742e-09	0.999999997989673
35	6.07144735961084e-10	1.21428947192217e-09	0.999999999392855
36	2.34764311435118e-10	4.69528622870237e-10	0.999999999765236
37	8.80132969890297e-11	1.76026593978059e-10	0.999999999911987
38	1.19056239752013e-10	2.38112479504026e-10	0.999999999880944
39	6.44570998374905e-10	1.28914199674981e-09	0.99999999935543
40	1.80955498112548e-10	3.61910996225097e-10	0.999999999819045
41	5.14852912589011e-11	1.02970582517802e-10	0.999999999948515
42	3.13787757038802e-11	6.27575514077603e-11	0.999999999968621
43	8.17335635694335e-12	1.63467127138867e-11	0.999999999991827
44	3.98665041802543e-12	7.97330083605087e-12	0.999999999996013
45	2.30531757879219e-12	4.61063515758437e-12	0.999999999997695
46	2.27809043256419e-12	4.55618086512838e-12	0.999999999997722
47	8.88694141330038e-13	1.77738828266008e-12	0.999999999999111
48	4.1674006749575e-13	8.33480134991501e-13	0.999999999999583
49	1.14815009001251e-13	2.29630018002502e-13	0.999999999999885
50	4.72881160856874e-14	9.45762321713748e-14	0.999999999999953
51	1.39030828657127e-14	2.78061657314254e-14	0.999999999999986
52	5.72417177198805e-15	1.14483435439761e-14	0.999999999999994
53	3.70257526576955e-15	7.40515053153909e-15	0.999999999999996
54	2.96962155945202e-15	5.93924311890403e-15	0.999999999999997
55	1.28394774167804e-15	2.56789548335609e-15	0.999999999999999
56	1.75329449085286e-15	3.50658898170571e-15	0.999999999999998
57	2.65314672898131e-14	5.30629345796262e-14	0.999999999999973
58	1.01245787509608e-13	2.02491575019216e-13	0.999999999999899
59	3.98275659680681e-14	7.96551319361363e-14	0.99999999999996
60	1.3651527080515e-14	2.73030541610301e-14	0.999999999999986
61	1.5218500971959e-14	3.04370019439179e-14	0.999999999999985
62	9.28863128726393e-15	1.85772625745279e-14	0.99999999999999
63	8.08956700039195e-15	1.61791340007839e-14	0.999999999999992
64	3.72912247521907e-15	7.45824495043814e-15	0.999999999999996
65	3.49502492270536e-15	6.99004984541071e-15	0.999999999999997
66	1.22718729968773e-15	2.45437459937547e-15	0.999999999999999
67	1.7481426460481e-15	3.4962852920962e-15	0.999999999999998
68	8.8355051201432e-14	1.76710102402864e-13	0.999999999999912
69	1.56651476198597e-13	3.13302952397195e-13	0.999999999999843
70	4.31859655019541e-13	8.63719310039081e-13	0.999999999999568
71	4.83182400007517e-13	9.66364800015034e-13	0.999999999999517
72	2.04852134499339e-13	4.09704268998678e-13	0.999999999999795
73	1.68162156346977e-13	3.36324312693954e-13	0.999999999999832
74	2.15349613295151e-13	4.30699226590302e-13	0.999999999999785
75	3.50346136099156e-13	7.00692272198312e-13	0.99999999999965
76	8.72187528544341e-13	1.74437505708868e-12	0.999999999999128
77	1.84701477735864e-11	3.69402955471728e-11	0.99999999998153
78	1.57167413852305e-11	3.14334827704611e-11	0.999999999984283
79	4.63313055480943e-09	9.26626110961886e-09	0.99999999536687
80	6.73191911516217e-06	1.34638382303243e-05	0.999993268080885
81	0.000135817033933534	0.000271634067867068	0.999864182966066
82	0.00031327144782931	0.00062654289565862	0.99968672855217
83	0.000604139077289723	0.00120827815457945	0.99939586092271
84	0.000504046762284541	0.00100809352456908	0.999495953237715
85	0.000580727531360259	0.00116145506272052	0.99941927246864
86	0.000976284755217779	0.00195256951043556	0.999023715244782
87	0.00119477226557765	0.0023895445311553	0.998805227734422
88	0.00109544636793209	0.00219089273586418	0.998904553632068
89	0.00547820129102239	0.0109564025820448	0.994521798708978
90	0.00513445483927736	0.0102689096785547	0.994865545160723
91	0.00595735806904493	0.0119147161380899	0.994042641930955
92	0.0300307055340758	0.0600614110681516	0.969969294465924
93	0.0422638775678509	0.0845277551357018	0.95773612243215
94	0.0620126400509058	0.124025280101812	0.937987359949094
95	0.0791801555845664	0.158360311169133	0.920819844415434
96	0.0765405394784703	0.153081078956941	0.92345946052153
97	0.0847646464856772	0.169529292971354	0.915235353514323
98	0.0809162915485668	0.161832583097134	0.919083708451433
99	0.0779282776698621	0.155856555339724	0.922071722330138
100	0.0678285104716384	0.135657020943277	0.932171489528362
101	0.145824129897711	0.291648259795422	0.854175870102289
102	0.149601569364463	0.299203138728926	0.850398430635537
103	0.136953488058862	0.273906976117723	0.863046511941138
104	0.300208766977145	0.600417533954291	0.699791233022855
105	0.334131394947031	0.668262789894062	0.665868605052969
106	0.293367691451341	0.586735382902683	0.706632308548659
107	0.603499704419208	0.793000591161585	0.396500295580792
108	0.75597730484738	0.48804539030524	0.24402269515262
109	0.89299344859243	0.214013102815141	0.10700655140757
110	0.925959356251244	0.148081287497512	0.074040643748756
111	0.97666679710786	0.0466664057842785	0.0233332028921392
112	0.986575701681012	0.0268485966379766	0.0134242983189883
113	0.992215652141435	0.0155686957171307	0.00778434785856537
114	0.9974654183518	0.00506916329640175	0.00253458164820088
115	0.998622224442739	0.00275555111452307	0.00137777555726153
116	0.999754808793942	0.000490382412115815	0.000245191206057908
117	0.999949296203281	0.000101407593437636	5.07037967188182e-05
118	0.99996264516037	7.47096792584925e-05	3.73548396292463e-05
119	0.999979536239334	4.09275213313677e-05	2.04637606656839e-05
120	0.99997919692069	4.16061586181105e-05	2.08030793090553e-05
121	0.999998945923824	2.10815235191308e-06	1.05407617595654e-06
122	0.999998467566429	3.0648671422762e-06	1.5324335711381e-06
123	0.999998590029924	2.81994015157492e-06	1.40997007578746e-06
124	0.999998418677601	3.16264479787431e-06	1.58132239893716e-06
125	0.999998997667468	2.00466506487054e-06	1.00233253243527e-06
126	0.999999020964377	1.95807124577532e-06	9.7903562288766e-07
127	0.999999339389112	1.32122177589362e-06	6.6061088794681e-07
128	0.999999745855378	5.08289243711268e-07	2.54144621855634e-07
129	0.999999726572661	5.46854677459003e-07	2.73427338729501e-07
130	0.999999672627772	6.5474445662492e-07	3.2737222831246e-07
131	0.999999622286879	7.5542624192508e-07	3.7771312096254e-07
132	0.999999397981064	1.20403787191137e-06	6.02018935955683e-07
133	0.999999093020685	1.81395862980935e-06	9.06979314904673e-07
134	0.999998472560713	3.05487857319203e-06	1.52743928659601e-06
135	0.99999745506065	5.0898787000073e-06	2.54493935000365e-06
136	0.999998376567704	3.24686459175462e-06	1.62343229587731e-06
137	0.999997360324484	5.27935103169287e-06	2.63967551584643e-06
138	0.99999505462225	9.89075549941745e-06	4.94537774970873e-06
139	0.99999020657273	1.9586854538394e-05	9.793427269197e-06
140	0.99998756886002	2.48622799608513e-05	1.24311399804257e-05
141	0.999974378418346	5.12431633072378e-05	2.56215816536189e-05
142	0.999949384175153	0.000101231649694197	5.06158248470987e-05
143	0.999905121962164	0.000189756075672831	9.48780378364156e-05
144	0.999882989592653	0.000234020814694942	0.000117010407347471
145	0.999780784136265	0.000438431727470417	0.000219215863735208
146	0.999578453870435	0.000843092259130523	0.000421546129565261
147	0.999292440523464	0.00141511895307227	0.000707559476536133
148	0.998951419220205	0.00209716155959062	0.00104858077979531
149	0.99823449344514	0.00353101310971868	0.00176550655485934
150	0.99705337754382	0.00589324491235972	0.00294662245617986
151	0.9948870754572	0.0102258490856013	0.00511292454280066
152	0.992130472101828	0.0157390557963432	0.00786952789817162
153	0.987303642201395	0.0253927155972093	0.0126963577986047
154	0.98237920867974	0.0352415826405192	0.0176207913202596
155	0.975814059546182	0.0483718809076354	0.0241859404538177
156	0.962800847673742	0.0743983046525164	0.0371991523262582
157	0.943789373386369	0.112421253227263	0.0562106266136315
158	0.939676554098888	0.120646891802225	0.0603234459011125
159	0.9082085543038	0.1835828913924	0.0917914456961998
160	0.876910718650974	0.246178562698052	0.123089281349026
161	0.847894987334548	0.304210025330903	0.152105012665452
162	0.793967492039826	0.412065015920349	0.206032507960174
163	0.7478941407024	0.504211718595199	0.252105859297599
164	0.702025635265905	0.59594872946819	0.297974364734095
165	0.620678428432641	0.758643143134718	0.379321571567359
166	0.492480673405369	0.984961346810738	0.507519326594631
167	0.512960012468199	0.974079975063602	0.487039987531801
168	0.384104987713837	0.768209975427674	0.615895012286163

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	107	0.708609271523179	NOK
5% type I error level	119	0.788079470198676	NOK
10% type I error level	122	0.80794701986755	NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/17/t12610824195fwi2n0lvlyhu03/10wzh01261082312.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t12610824195fwi2n0lvlyhu03/10wzh01261082312.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t12610824195fwi2n0lvlyhu03/1vi191261082312.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t12610824195fwi2n0lvlyhu03/1vi191261082312.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t12610824195fwi2n0lvlyhu03/2zlbw1261082312.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t12610824195fwi2n0lvlyhu03/2zlbw1261082312.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t12610824195fwi2n0lvlyhu03/3vge31261082312.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t12610824195fwi2n0lvlyhu03/3vge31261082312.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t12610824195fwi2n0lvlyhu03/45qcd1261082312.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t12610824195fwi2n0lvlyhu03/45qcd1261082312.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t12610824195fwi2n0lvlyhu03/5i7561261082312.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t12610824195fwi2n0lvlyhu03/5i7561261082312.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t12610824195fwi2n0lvlyhu03/6x8sm1261082312.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t12610824195fwi2n0lvlyhu03/6x8sm1261082312.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t12610824195fwi2n0lvlyhu03/74n5y1261082312.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t12610824195fwi2n0lvlyhu03/74n5y1261082312.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t12610824195fwi2n0lvlyhu03/8e3zy1261082312.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t12610824195fwi2n0lvlyhu03/8e3zy1261082312.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t12610824195fwi2n0lvlyhu03/95pzq1261082312.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t12610824195fwi2n0lvlyhu03/95pzq1261082312.ps (open in new window)

Parameters (Session):

par1 = FALSE ; par2 = 0.0 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; par8 = 2 ; par9 = 1 ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; par8 = 2 ; par9 = 1 ;

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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