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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: Fri, 24 Dec 2010 10:52:02 +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/24/t1293187830erjtqmqx7w62udr.htm/, Retrieved Fri, 24 Dec 2010 11:50:45 +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/24/t1293187830erjtqmqx7w62udr.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 «

9,1 4,5 1,0 -1,0 1989,3 9,0 4,3 1,0 3,0 2097,8 9,0 4,3 1,3 2,0 2154,9 8,9 4,2 1,1 3,0 2152,2 8,8 4,0 0,8 5,0 2250,3 8,7 3,8 0,7 5,0 2346,9 8,5 4,1 0,7 3,0 2525,6 8,3 4,2 0,9 2,0 2409,4 8,1 4,0 1,3 1,0 2394,4 7,9 4,3 1,4 -4,0 2401,3 7,8 4,7 1,6 1,0 2354,3 7,6 5,0 2,1 1,0 2450,4 7,4 5,1 0,3 6,0 2504,7 7,2 5,4 2,1 3,0 2661,4 7,0 5,4 2,5 2,0 2880,4 7,0 5,4 2,3 2,0 3064,4 6,8 5,5 2,4 2,0 3141,1 6,8 5,8 3,0 -8,0 3327,7 6,7 5,7 1,7 0,0 3565,0 6,8 5,5 3,5 -2,0 3403,1 6,7 5,6 4,0 3,0 3149,9 6,7 5,6 3,7 5,0 3006,8 6,7 5,5 3,7 8,0 3230,7 6,5 5,5 3,0 8,0 3361,1 6,3 5,7 2,7 9,0 3484,7 6,3 5,6 2,5 11,0 3411,1 6,3 5,6 2,2 13,0 3288,2 6,5 5,4 2,9 12,0 3280,4 6,6 5,2 3,1 13,0 3174,0 6,5 5,1 3,0 15,0 3165,3 6,3 5,1 2,8 13,0 3092,7 6,3 5,0 2,5 16,0 3053,1 6,5 5,3 1,9 10,0 3182,0 7,0 5,4 1,9 14,0 2999,9 7,1 5,3 1,8 14,0 3249,6 7,3 5,1 2,0 15,0 3210,5 7,3 5,0 2,6 13,0 3030,3 7,4 5,0 2,5 8,0 2803,5 7,4 4,6 2,5 7,0 2767,6 7,3 4,8 1,6 3,0 2882,6 7,4 5,1 1,4 3,0 2863,4 7,5 5,1 0,8 4,0 2897,1 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	9 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

Werkloosheid[t] = + 11.6359824396043 -0.559320335978252rente[t] -0.143899561563292inflatie[t] -0.0296059693049306consumer[t] -0.000333689284785689Bel20[t] -0.00268120125236932t + 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)	11.6359824396043	0.267369	43.5204	0	0
rente	-0.559320335978252	0.075582	-7.4002	0	0
inflatie	-0.143899561563292	0.024294	-5.9232	0	0
consumer	-0.0296059693049306	0.004442	-6.6647	0	0
Bel20	-0.000333689284785689	7e-05	-4.7938	4e-06	2e-06
t	-0.00268120125236932	0.001503	-1.7839	0.076666	0.038333

Multiple Linear Regression - Regression Statistics
Multiple R	0.906296630636011
R-squared	0.821373582702186
Adjusted R-squared	0.814806435007414
F-TEST (value)	125.073109495618
F-TEST (DF numerator)	5
F-TEST (DF denominator)	136
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.307203185474167
Sum Squared Residuals	12.8348364145047

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	9.1	8.33825803996732	0.761741960032681
2	9	8.29281174129161	0.70718825870839
3	9	8.25751298271392	0.74248701728608
4	8.9	8.31083871913602	0.589161280863977
5	8.8	8.37124459610096	0.428755403899044
6	8.7	8.46258303329027	0.237416966709730
7	8.5	8.29168739466308	0.208312605336917
8	8.3	8.27267491169726	0.0273250883027432
9	8.1	8.35890926159194	-0.258909261591938
10	7.9	8.3197693938494	-0.419769393849395
11	7.8	7.93223369575334	-0.132233695753342
12	7.6	7.65773907265795	-0.0577390726579463
13	7.4	7.69199587393316	-0.291995873933161
14	7.2	7.29902815806226	-0.0990281580622647
15	7	7.19531514812144	-0.195315148121443
16	7	7.16001503078117	-0.160015030781166
17	6.8	7.06141787163158	-0.26141787163158
18	6.8	7.03839410515606	-0.238394105156057
19	6.7	6.9626821458147	-0.262682145814703
20	6.8	6.92608203476072	-0.126082034760723
21	6.7	6.73197929951197	-0.0319792995119653
22	6.7	6.76100696477155	-0.0610069647715545
23	6.7	6.6507268583387	0.0492731416612976
24	6.5	6.70526226744458	-0.205262267444584
25	6.3	6.56303690256111	-0.263036902561110
26	6.3	6.61041523996959	-0.31041523996959
27	6.3	6.63270238167651	-0.332702381676508
28	6.5	6.67336430025174	-0.173364300251743
29	6.6	6.75966582447863	-0.159665824478633
30	6.5	6.77099777114819	-0.270997771148192
31	6.3	6.88053426289378	-0.580534262893784
32	6.3	6.90135115147095	-0.601351151470949
33	6.5	6.95183685338379	-0.451836853383787
34	7	6.83556456007334	0.164435439926656
35	7.1	6.81988313416414	0.280116865835857
36	7.3	6.88372736952496	0.416272630475044
37	7.3	6.96998121266068	0.330018787339322
38	7.4	7.20540054387869	0.194599456121315
39	7.4	7.46803289164635	-0.0680328916463535
40	7.3	7.56304683807467	-0.263046838074666
41	7.4	7.42775628260936	-0.0277562826093639
42	7.5	7.47056352009276	0.0294364799072381
43	7.7	7.38617133797866	0.313828662021342
44	7.7	7.26182491810382	0.438175081896177
45	7.7	7.48462877408024	0.215371225919765
46	7.7	7.75931271794711	-0.0593127179471072
47	7.7	7.99410967669714	-0.294109676697135
48	7.8	7.8109209046881	-0.0109209046880991
49	8	7.7359612319861	0.264038768013899
50	8.1	7.78146800937135	0.318531990628649
51	8.1	7.67711795531127	0.422882044688732
52	8.2	7.81308834787963	0.38691165212037
53	8.2	8.05302297428916	0.146977025710835
54	8.2	8.08862076371772	0.111379236282276
55	8.1	8.16260937837488	-0.0626093783748768
56	8.1	8.08597077620326	0.0140292237967404
57	8.2	8.1650688706698	0.0349311293302029
58	8.3	8.41683906195521	-0.116839061955208
59	8.3	8.32423219573	-0.0242321957300066
60	8.4	8.29367630882615	0.106323691173851
61	8.5	8.33647516185223	0.163524838147771
62	8.5	8.52838733803955	-0.028387338039552
63	8.4	8.53812342553583	-0.138123425535833
64	8	8.1461783268131	-0.146178326813107
65	7.9	8.09952393925509	-0.199523939255086
66	8.1	8.26546208634915	-0.165462086349151
67	8.5	8.53259533203275	-0.032595332032753
68	8.8	8.51512418395756	0.284875816042437
69	8.8	8.24557741968482	0.554422580315182
70	8.6	8.39532553986061	0.204674460139386
71	8.3	8.14988097708344	0.150119022916562
72	8.3	8.27624155472522	0.0237584452747763
73	8.3	8.29843385583797	0.00156614416203172
74	8.4	8.25373523912448	0.146264760875518
75	8.4	8.39376008348899	0.00623991651101146
76	8.5	8.46807286244865	0.0319271375513528
77	8.6	8.5692315146318	0.0307684853682044
78	8.6	8.42676785838024	0.173232141619758
79	8.6	8.42734294323257	0.172657056767434
80	8.6	8.30603721471435	0.293962785285649
81	8.6	8.39011869845968	0.209881301540318
82	8.5	8.72370200447019	-0.223702004470191
83	8.4	8.77424973537126	-0.374249735371256
84	8.4	8.60670621724072	-0.206706217240722
85	8.4	8.66460104011244	-0.264601040112442
86	8.5	8.48717123064522	0.0128287693547775
87	8.5	8.43993768015795	0.060062319842046
88	8.6	8.391159676514	0.208840323486006
89	8.6	8.67095498734223	-0.070954987342227
90	8.4	8.58389619097827	-0.183896190978267
91	8.2	8.59777392623333	-0.397773926233335
92	8	8.39549625358504	-0.395496253585039
93	8	8.40761541069073	-0.407615410690734
94	8	8.21897205745327	-0.218972057453271
95	8	8.11592866459634	-0.115928664596343
96	7.9	8.0123066661327	-0.112306666132699
97	7.9	8.04043727775204	-0.140437277752040
98	7.8	8.07596899083775	-0.275968990837750
99	7.8	8.09763121821183	-0.297631218211834
100	8	8.11690475162167	-0.116904751621666
101	7.8	8.0969431474849	-0.296943147484899
102	7.4	7.85196118756487	-0.451961187564871
103	7.2	7.93965446356795	-0.739654463567954
104	7	7.86356385817706	-0.863563858177056
105	7	7.76956366317545	-0.769563663175446
106	7.2	7.35943632074767	-0.159436320747667
107	7.2	7.20677490824332	-0.00677490824332195
108	7.2	7.4542532071414	-0.254253207141398
109	7	7.12910888771823	-0.129108887718231
110	6.9	7.00407378719248	-0.104073787192481
111	6.8	6.96641290292315	-0.166412902923146
112	6.8	6.98152370473048	-0.181523704730476
113	6.8	6.75457914320293	0.0454208567970666
114	6.9	6.98158457733799	-0.0815845773379848
115	7.2	6.97984521758983	0.220154782410171
116	7.2	6.91323183116333	0.286768168836674
117	7.2	6.8042569352569	0.395743064743095
118	7.1	6.64871008144252	0.451289918557476
119	7.2	6.8952587098751	0.304741290124902
120	7.3	6.98350041913415	0.316499580865848
121	7.5	7.18718050005306	0.312819499946941
122	7.6	7.10487374218164	0.495126257818364
123	7.7	7.33784713082634	0.362152869173657
124	7.7	6.80169611523383	0.898303884766172
125	7.7	7.51178583657469	0.188214163425313
126	7.8	7.76459516671044	0.0354048332895637
127	8	8.05327385644632	-0.0532738564463242
128	8.1	8.13550550512256	-0.0355055051225612
129	8.1	8.08541544095946	0.0145845590405365
130	8	8.09111323339696	-0.0911132333969588
131	8.1	8.3289338044372	-0.228933804437208
132	8.2	8.47992728305126	-0.279927283051258
133	8.3	8.40402871140908	-0.104028711409078
134	8.4	8.56098201404746	-0.160982014047464
135	8.4	8.41556121574649	-0.0155612157464867
136	8.4	8.26375628659886	0.136243713401140
137	8.5	8.13355079739677	0.366449202603227
138	8.5	8.1155572917249	0.384442708275096
139	8.6	8.3398066277963	0.260193372203695
140	8.6	8.26654855220909	0.333451447790911
141	8.5	8.22018105259642	0.279818947403579
142	8.5	8.69715950094628	-0.197159500946283

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
9	0.0315400249677409	0.0630800499354818	0.96845997503226
10	0.00881164890753935	0.0176232978150787	0.99118835109246
11	0.00194598048169021	0.00389196096338043	0.99805401951831
12	0.000438071992968715	0.00087614398593743	0.999561928007031
13	0.000123259205226788	0.000246518410453576	0.999876740794773
14	4.75379913333986e-05	9.50759826667972e-05	0.999952462008667
15	1.69271248550467e-05	3.38542497100934e-05	0.999983072875145
16	7.9031314218711e-06	1.58062628437422e-05	0.999992096868578
17	1.69267735581695e-06	3.38535471163391e-06	0.999998307322644
18	1.18167725473103e-05	2.36335450946206e-05	0.999988183227453
19	3.6173365798665e-06	7.234673159733e-06	0.99999638266342
20	4.04591394702583e-05	8.09182789405167e-05	0.99995954086053
21	9.91331545541987e-05	0.000198266309108397	0.999900866845446
22	0.000339439820799879	0.000678879641599758	0.9996605601792
23	0.000300486658964447	0.000600973317928894	0.999699513341036
24	0.000207055905852020	0.000414111811704039	0.999792944094148
25	0.000122863385490216	0.000245726770980432	0.99987713661451
26	9.85592687716826e-05	0.000197118537543365	0.999901440731228
27	0.000142292553613691	0.000284585107227382	0.999857707446386
28	0.000462566728224932	0.000925133456449864	0.999537433271775
29	0.000895548271196113	0.00179109654239223	0.999104451728804
30	0.000642689474519676	0.00128537894903935	0.99935731052548
31	0.00056201713553856	0.00112403427107712	0.999437982864462
32	0.000524780677441409	0.00104956135488282	0.999475219322559
33	0.0146723782286312	0.0293447564572624	0.985327621771369
34	0.216878379253501	0.433756758507002	0.783121620746499
35	0.570804575259894	0.858390849480213	0.429195424740106
36	0.811473102260594	0.377053795478811	0.188526897739406
37	0.865362953055865	0.269274093888270	0.134637046944135
38	0.850255730845816	0.299488538308368	0.149744269154184
39	0.818195538207716	0.363608923584569	0.181804461792284
40	0.799944204555929	0.400111590888143	0.200055795444071
41	0.770230204016925	0.45953959196615	0.229769795983075
42	0.738065593755321	0.523868812489358	0.261934406244679
43	0.764564391738434	0.470871216523131	0.235435608261566
44	0.817697555869343	0.364604888261315	0.182302444130657
45	0.788164455493494	0.423671089013011	0.211835544506506
46	0.761569923165052	0.476860153669895	0.238430076834948
47	0.782407906476811	0.435184187046377	0.217592093523188
48	0.750222311461213	0.499555377077574	0.249777688538787
49	0.731458326989038	0.537083346021924	0.268541673010962
50	0.730149593324594	0.539700813350812	0.269850406675406
51	0.733487147059515	0.53302570588097	0.266512852940485
52	0.730284151211344	0.539431697577312	0.269715848788656
53	0.704905075515971	0.590189848968057	0.295094924484029
54	0.677064166582068	0.645871666835863	0.322935833417931
55	0.648101696244538	0.703796607510925	0.351898303755462
56	0.608454078011228	0.783091843977544	0.391545921988772
57	0.583588767316707	0.832822465366586	0.416411232683293
58	0.572970044453431	0.854059911093138	0.427029955546569
59	0.539611705790919	0.920776588418162	0.460388294209081
60	0.501110565875597	0.997778868248806	0.498889434124403
61	0.475077716032616	0.950155432065231	0.524922283967384
62	0.435270455183238	0.870540910366477	0.564729544816762
63	0.407286543929364	0.814573087858727	0.592713456070636
64	0.375733271759978	0.751466543519957	0.624266728240022
65	0.346592907833899	0.693185815667798	0.653407092166101
66	0.330086960043886	0.660173920087773	0.669913039956114
67	0.293888080133488	0.587776160266977	0.706111919866512
68	0.277644231237066	0.555288462474131	0.722355768762935
69	0.328049864390662	0.656099728781323	0.671950135609338
70	0.290382897841211	0.580765795682422	0.709617102158789
71	0.264899785899724	0.529799571799447	0.735100214100276
72	0.254352880937399	0.508705761874798	0.7456471190626
73	0.243845166285309	0.487690332570618	0.756154833714691
74	0.229928676451627	0.459857352903254	0.770071323548373
75	0.212499410382830	0.424998820765659	0.78750058961717
76	0.195341505972503	0.390683011945005	0.804658494027497
77	0.180414969969573	0.360829939939147	0.819585030030427
78	0.191264263739897	0.382528527479793	0.808735736260103
79	0.204881489181816	0.409762978363632	0.795118510818184
80	0.277080174247669	0.554160348495339	0.722919825752331
81	0.342039799113215	0.68407959822643	0.657960200886785
82	0.343376669786756	0.686753339573512	0.656623330213244
83	0.348906675427514	0.697813350855028	0.651093324572486
84	0.321095907807048	0.642191815614096	0.678904092192952
85	0.286824327357248	0.573648654714496	0.713175672642752
86	0.305768428379046	0.611536856758091	0.694231571620954
87	0.374078816280709	0.748157632561419	0.62592118371929
88	0.567882024036187	0.864235951927625	0.432117975963813
89	0.636163246386483	0.727673507227034	0.363836753613517
90	0.667453289850228	0.665093420299545	0.332546710149772
91	0.669064539822376	0.661870920355248	0.330935460177624
92	0.656218748452274	0.687562503095452	0.343781251547726
93	0.632967978574563	0.734064042850873	0.367032021425437
94	0.629972193538685	0.74005561292263	0.370027806461315
95	0.663086204965654	0.673827590068693	0.336913795034346
96	0.722834752449057	0.554330495101887	0.277165247550943
97	0.803950543174934	0.392098913650133	0.196049456825066
98	0.853538629130638	0.292922741738724	0.146461370869362
99	0.906189236569353	0.187621526861293	0.0938107634306467
100	0.996124944518373	0.00775011096325427	0.00387505548162713
101	0.999943526082175	0.000112947835649588	5.64739178247939e-05
102	0.99998978787094	2.04242581215696e-05	1.02121290607848e-05
103	0.999993443224175	1.31135516509342e-05	6.55677582546711e-06
104	0.999993305230107	1.33895397863576e-05	6.69476989317878e-06
105	0.999992036774378	1.59264512433291e-05	7.96322562166453e-06
106	0.999992793639745	1.44127205095094e-05	7.20636025475472e-06
107	0.99999853916078	2.9216784410777e-06	1.46083922053885e-06
108	0.999999832154825	3.35690349142549e-07	1.67845174571275e-07
109	0.99999997682496	4.63500801424569e-08	2.31750400712285e-08
110	0.99999998777983	2.44403394219493e-08	1.22201697109747e-08
111	0.99999996978478	6.04304412126695e-08	3.02152206063347e-08
112	0.999999938776748	1.22446504004248e-07	6.1223252002124e-08
113	0.999999917672857	1.64654285255342e-07	8.2327142627671e-08
114	0.999999874131152	2.51737695795819e-07	1.25868847897910e-07
115	0.999999880507252	2.38985495621698e-07	1.19492747810849e-07
116	0.999999876969113	2.46061774139566e-07	1.23030887069783e-07
117	0.999999858370198	2.83259604450322e-07	1.41629802225161e-07
118	0.999999741634274	5.16731451300734e-07	2.58365725650367e-07
119	0.99999955496023	8.90079540227023e-07	4.45039770113512e-07
120	0.999999510874158	9.78251683741077e-07	4.89125841870538e-07
121	0.99999887734003	2.24531994183964e-06	1.12265997091982e-06
122	0.999997187073018	5.62585396374125e-06	2.81292698187063e-06
123	0.999991663236751	1.66735264973201e-05	8.33676324866005e-06
124	0.999991958174869	1.60836502626534e-05	8.04182513132669e-06
125	0.999979262098394	4.14758032111096e-05	2.07379016055548e-05
126	0.99997658111236	4.68377752782574e-05	2.34188876391287e-05
127	0.999908265097957	0.000183469804085118	9.1734902042559e-05
128	0.999667368336306	0.000665263327388217	0.000332631663694109
129	0.99960356550223	0.00079286899553935	0.000396434497769675
130	0.998718888661592	0.00256222267681535	0.00128111133840768
131	0.99821830770531	0.00356338458938157	0.00178169229469078
132	0.997595668639463	0.00480866272107447	0.00240433136053724
133	0.989861781664316	0.0202764366713684	0.0101382183356842

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	55	0.44	NOK
5% type I error level	58	0.464	NOK
10% type I error level	59	0.472	NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293187830erjtqmqx7w62udr/10eeek1293187912.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293187830erjtqmqx7w62udr/10eeek1293187912.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293187830erjtqmqx7w62udr/17dzq1293187912.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293187830erjtqmqx7w62udr/17dzq1293187912.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293187830erjtqmqx7w62udr/27dzq1293187912.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293187830erjtqmqx7w62udr/27dzq1293187912.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293187830erjtqmqx7w62udr/3inyt1293187912.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293187830erjtqmqx7w62udr/3inyt1293187912.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293187830erjtqmqx7w62udr/4inyt1293187912.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293187830erjtqmqx7w62udr/4inyt1293187912.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293187830erjtqmqx7w62udr/5inyt1293187912.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293187830erjtqmqx7w62udr/5inyt1293187912.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293187830erjtqmqx7w62udr/6awxe1293187912.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293187830erjtqmqx7w62udr/6awxe1293187912.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293187830erjtqmqx7w62udr/7lnwz1293187912.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293187830erjtqmqx7w62udr/7lnwz1293187912.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293187830erjtqmqx7w62udr/8lnwz1293187912.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293187830erjtqmqx7w62udr/8lnwz1293187912.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293187830erjtqmqx7w62udr/9lnwz1293187912.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/24/t1293187830erjtqmqx7w62udr/9lnwz1293187912.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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