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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: Sat, 20 Nov 2010 16:08:07 +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/Nov/20/t1290269238ndfudrhyxnc8s1r.htm/, Retrieved Sat, 20 Nov 2010 17:07:21 +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/Nov/20/t1290269238ndfudrhyxnc8s1r.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 «

4 4 4 4 4 4 4 4 4 3 4 4 5 4 4 4 5 5 5 4 5 4 4 4 3 4 4 3 3 2 3 4 2 2 4 3 4 2 3 4 5 4 5 4 5 4 3 4 4 3 4 4 4 3 3 4 2 2 4 2 4 2 4 4 4 4 5 3 4 2 4 4 4 2 2 3 4 4 3 2 4 4 4 4 4 3 4 4 2 2 3 2 4 3 4 3 5 5 5 4 5 4 5 5 3 3 4 4 4 3 3 4 4 4 4 4 4 4 4 3 4 4 5 4 4 4 4 4 3 3 3 3 3 3 3 4 4 4 4 4 5 3 4 4 2 2 4 2 3 2 2 3 4 3 4 4 4 2 4 4 3 4 4 3 4 3 4 4 3 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 4 3 5 3 4 4 5 4 4 4 5 4 4 4 2 4 4 3 4 3 4 4 4 4 4 4 4 4 4 4 4 4 3 4 4 4 3 4 4 4 4 5 2 4 4 4 2 4 4 4 3 3 4 4 4 4 3 4 2 4 4 4 4 5 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 4 4 5 3 5 4 3 3 3 4 4 4 4 4 4 4 4 4 4 3 4 4 4 4 3 4 4 3 4 4 4 3 4 2 3 3 3 3 4 4 4 4 4 3 4 4 4 4 4 4 2 2 3 2 4 2 3 2 2 2 5 2 4 2 2 3 4 4 5 4 4 2 4 4 4 2 4 4 4 4 4 2 5 4 5 5 4 4 4 5 4 4 4 4 4 3 4 4 4 3 4 3 5 3 4 4 4 4 4 4 4 4 4 4 5 4 4 4 5 4 4 4 3 3 4 3 4 4 3 4 2 1 4 4 4 4 2 4 4 4 4 4 4 3 4 4 4 4 4 3 3 4 4 3 2 2 4 3 4 4 4 4 2 2 4 2 3 3 2 3 4 4 4 4 4 3 4 4 4 4 4 4 4 2 4 4 4 3 4 4 3 2 4 4 3 3 4 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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Multiple Linear Regression - Estimated Regression Equation

B[t] = + 1.02830814409858 + 0.0842475032129699A[t] + 0.207213675242005C[t] + 0.38652210968685D[t] -0.134026305664133E[t] + 0.00410101084894533F[t] + 0.279829847242846G[t] -0.0684096369345052H[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)	1.02830814409858	0.478598	2.1486	0.03334	0.01667
A	0.0842475032129699	0.064963	1.2968	0.196758	0.098379
C	0.207213675242005	0.07449	2.7818	0.006131	0.003065
D	0.38652210968685	0.090406	4.2754	3.5e-05	1.7e-05
E	-0.134026305664133	0.071517	-1.8741	0.062949	0.031474
F	0.00410101084894533	0.078835	0.052	0.958585	0.479292
G	0.279829847242846	0.079493	3.5202	0.000578	0.000289
H	-0.0684096369345052	0.062201	-1.0998	0.273251	0.136626

Multiple Linear Regression - Regression Statistics
Multiple R	0.571118664491289
R-squared	0.326176528930313
Adjusted R-squared	0.29342122130887
F-TEST (value)	9.95797483265836
F-TEST (DF numerator)	7
F-TEST (DF denominator)	144
p-value	4.14612011390147e-10
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.604931442781952
Sum Squared Residuals	52.6956552671406

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	4	4.06622095863849	-0.0662209586384934
2	3	3.93219465297436	-0.932194652974361
3	5	4.22365583142934	0.776344168570664
4	4	3.44144578246207	0.55855421753793
5	2	3.22317197358497	-1.22317197358497
6	4	3.94382598418649	0.0561740158135089
7	3	3.7822901005467	-0.782290100546703
8	2	3.11647971114096	-1.11647971114096
9	4	3.87871050249576	0.121289497504242
10	2	3.1222609250938	-1.1222609250938
11	4	4.06211994778955	-0.0621199477895486
12	2	2.98177668368241	-0.981776683682408
13	5	4.43507604173768	0.564923958262323
14	3	3.69804259733373	-0.698042597333733
15	4	4.134630595573	-0.134630595572999
16	4	4.2734346338805	-0.273434633880499
17	3	3.23833311806901	-0.23833311806901
18	4	3.92809364212542	0.0719063578745841
19	2	2.75925595925391	-0.75925595925391
20	3	4.0580189369406	-1.0580189369406
21	4	3.59135033488973	0.408649665110272
22	2	3.77475978018352	-1.77475978018352
23	4	4.06622095863849	-0.0662209586384939
24	4	4.06622095863849	-0.0662209586384939
25	4	4.06622095863849	-0.0662209586384939
26	3	3.54157153243857	-0.541571532438565
27	4	4.01644215618733	-0.016442156187331
28	4	3.50710283167676	0.492897168323241
29	4	4.06622095863849	-0.0662209586384939
30	4	3.57917743615364	0.420822563846357
31	4	4.72079567965361	-0.72079567965361
32	4	4.02765124702774	-0.0276512470277416
33	4	4.12705989472475	-0.127059894724754
34	5	4.06622095863849	0.933779041361506
35	4	4.06622095863849	-0.0662209586384939
36	4	4.13183762736812	-0.131837627368121
37	5	3.72537664055386	1.27462335944614
38	4	4.06622095863849	-0.0662209586384939
39	4	3.97787244457658	0.0221275554234213
40	4	3.62474970353847	0.375250296461529
41	3	3.77475978018352	-0.774759780183519
42	4	4.11879272929453	-0.118792729294534
43	3	3.32440978159118	-0.324409781591183
44	5	3.46331934411607	1.53668065588393
45	5	4.33427356996676	0.66572643003324
46	4	3.26965662079236	0.730343379207642
47	5	4.55326448112335	0.446735518876655
48	4	4.20024726430263	-0.200247264302627
49	4	4.2953081955345	-0.295308195534502
50	4	3.99781132170399	0.00218867829601128
51	4	4.52115270525985	-0.52115270525985
52	4	3.90747804320358	0.0925219567964164
53	4	3.80527642730169	0.194723572698306
54	4	4.20024726430263	-0.200247264302627
55	4	3.3294746003358	0.670525399664197
56	4	3.82733155083956	0.172668449160441
57	4	2.94277092876509	1.05722907123491
58	4	4.20024726430263	-0.200247264302627
59	4	4.33427356996676	-0.334273569966759
60	4	3.93191359400144	0.0680864059985557
61	4	4.25281903495867	-0.252819034958667
62	4	3.34966795888592	0.650332041114084
63	4	3.99781132170399	0.00218867829601128
64	4	4.55230067322767	-0.55230067322767
65	4	4.23852988981213	-0.238529889812126
66	5	5.02813510487211	-0.0281351048721104
67	4	4.3184357036883	-0.318435703688295
68	4	3.58657260224636	0.413427397753639
69	3	3.61322389654373	-0.613223896543731
70	4	3.96149301077416	0.0385069892258415
71	4	3.75004317041274	0.249956829587259
72	2	3.18759050772217	-1.18759050772217
73	4	3.1178728281436	0.8821271718564
74	5	4.38433343139084	0.615666568609161
75	4	4.21608513058109	-0.216085130581091
76	5	4.9397865908102	0.0602134091898047
77	3	3.40668694309615	-0.406686943096148
78	4	4.50348567867218	-0.503485678672182
79	4	4.48668400449804	-0.486684004498042
80	3	3.72059890791049	-0.720598907910494
81	4	3.60241046852483	0.397589531475174
82	4	3.97787244457658	0.0221275554234213
83	4	4.35265769883391	-0.35265769883391
84	4	4.03871138066284	-0.0387113806628387
85	4	3.98472604314534	0.015273956854659
86	4	3.72731132508045	0.272688674919546
87	5	4.10016189481119	0.899838105188808
88	4	4.37521400941067	-0.37521400941067
89	4	3.62496075197325	0.37503924802675
90	4	4.05038309236003	-0.0503830923600292
91	4	3.7478213997849	0.252178600215104
92	5	4.0235502361788	0.976449763821204
93	4	4.06144322599513	-0.0614432259951265
94	4	3.69326486469037	0.306735135309634
95	3	3.031119442827	-0.0311194428270049
96	4	3.18855431561785	0.811445684382152
97	4	3.93151793117994	0.068482068820061
98	4	3.29921243464033	0.700787565359669
99	5	4.30338008342164	0.696619916578358
100	5	4.2030402325075	0.796959767492496
101	4	3.90468507499871	0.095314925001294
102	4	3.74314919135892	0.256850808641082
103	5	4.20024726430263	0.799752735697373
104	5	4.30008592817787	0.69991407182213
105	4	4.3691722869068	-0.369172286906796
106	5	4.48485484418884	0.51514515581116
107	4	4.11599976108966	-0.115999761089657
108	4	3.85900728339649	0.140992716603511
109	4	4.18440939802416	-0.184409398024162
110	4	4.25281903495867	-0.252819034958667
111	2	3.76577551247382	-1.76577551247382
112	4	3.74314919135892	0.256850808641082
113	5	4.62828101101042	0.37171898898958
114	4	3.80459970550727	0.195400294492729
115	4	4.02765124702774	-0.0276512470277416
116	4	3.24243412891796	0.757565871082044
117	4	3.90468507499871	0.095314925001294
118	4	4.18918713066753	-0.18918713066753
119	3	3.48662238702539	-0.486622387025393
120	4	3.6864112661216	0.313588733878396
121	4	4.10729655235287	-0.107296552352871
122	3	4.02765124702774	-1.02765124702774
123	4	3.83616991384681	0.163830086153189
124	5	4.24592505590484	0.754074944095156
125	5	4.2030402325075	0.796959767492496
126	3	4.03938810245726	-1.03938810245726
127	5	4.04348911330621	0.956510886693794
128	4	4.18440939802416	-0.184409398024162
129	4	3.59763273588146	0.402367264118542
130	3	4.341844270815	-1.341844270815
131	3	3.69804259733373	-0.698042597333733
132	4	3.85480074833015	0.145199251669846
133	5	4.52748050719636	0.472519492803644
134	2	3.46752587918241	-1.46752587918241
135	4	4.20024726430263	-0.200247264302627
136	4	4.2030402325075	-0.203040232507504
137	4	3.59135033488973	0.408649665110272
138	5	4.05038309236003	0.94961690763997
139	4	3.2289531875378	0.771046812462197
140	4	4.04218107066214	-0.0421810706621386
141	4	3.96613558914706	0.0338644108529407
142	4	3.71320374181778	0.286796258182224
143	4	4.06622095863849	-0.0662209586384939
144	4	4.20024726430263	-0.200247264302627
145	5	4.11879272929453	0.881207270705465
146	3	3.66392612640551	-0.663926126405508
147	4	4.06622095863849	-0.0662209586384939
148	4	3.75438485974954	0.245615140250457
149	4	4.134630595573	-0.134630595572999
150	4	4.18030838717522	-0.180308387175217
151	4	3.48793042966946	0.51206957033054
152	5	4.89410879920798	0.105891200792022

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
11	0.443885851842148	0.887771703684296	0.556114148157852
12	0.294541690356356	0.589083380712713	0.705458309643644
13	0.223650707405215	0.44730141481043	0.776349292594785
14	0.135927799482064	0.271855598964127	0.864072200517936
15	0.10164954456763	0.203299089135259	0.89835045543237
16	0.206107549821615	0.412215099643229	0.793892450178385
17	0.137148796728727	0.274297593457454	0.862851203271273
18	0.182007492806244	0.364014985612489	0.817992507193756
19	0.143135860989047	0.286271721978095	0.856864139010953
20	0.280606219219672	0.561212438439343	0.719393780780328
21	0.35521233221259	0.71042466442518	0.64478766778741
22	0.513487280285914	0.973025439428171	0.486512719714086
23	0.436514285732802	0.873028571465605	0.563485714267198
24	0.362866539167581	0.725733078335162	0.637133460832419
25	0.294951485823367	0.589902971646734	0.705048514176633
26	0.270556473409092	0.541112946818184	0.729443526590908
27	0.214461441764797	0.428922883529595	0.785538558235203
28	0.479036825101991	0.958073650203983	0.520963174898009
29	0.411844296743771	0.823688593487543	0.588155703256228
30	0.516326636101125	0.96734672779775	0.483673363898875
31	0.550507410491034	0.898985179017931	0.449492589508966
32	0.586076774592414	0.827846450815171	0.413923225407586
33	0.524405070147338	0.951189859705324	0.475594929852662
34	0.646458750105073	0.707082499789854	0.353541249894927
35	0.589009315418137	0.821981369163727	0.410990684581863
36	0.5732827344798	0.8534345310404	0.4267172655202
37	0.751953766406158	0.496092467187684	0.248046233593842
38	0.704425994384084	0.591148011231831	0.295574005615916
39	0.690098759756499	0.619802480487001	0.309901240243501
40	0.685728567212456	0.628542865575089	0.314271432787544
41	0.670207893935998	0.659584212128003	0.329792106064002
42	0.63238048853672	0.73523902292656	0.36761951146328
43	0.658722738196127	0.682554523607747	0.341277261803873
44	0.961130702358003	0.0777385952839939	0.0388692976419969
45	0.959691828530701	0.0806163429385972	0.0403081714692986
46	0.959474833231229	0.0810503335375427	0.0405251667687714
47	0.951362018410335	0.09727596317933	0.048637981589665
48	0.941617701108119	0.116764597783763	0.0583822988918815
49	0.926704542342497	0.146590915315006	0.073295457657503
50	0.908040656613497	0.183918686773005	0.0919593433865027
51	0.892294790792789	0.215410418414422	0.107705209207211
52	0.899987264492845	0.200025471014311	0.100012735507155
53	0.88185800172333	0.236283996553341	0.118141998276671
54	0.860531400906135	0.278937198187731	0.139468599093865
55	0.89555312792535	0.208893744149302	0.104446872074651
56	0.884194380993116	0.231611238013767	0.115805619006884
57	0.931758247185254	0.136483505629492	0.068241752814746
58	0.916712492831902	0.166575014336196	0.083287507168098
59	0.905235140986306	0.189529718027389	0.0947648590136945
60	0.882681604640219	0.234636790719561	0.117318395359781
61	0.859382092636387	0.281235814727225	0.140617907363613
62	0.85480862141358	0.290382757172841	0.145191378586421
63	0.825204849644485	0.34959030071103	0.174795150355515
64	0.819864801346832	0.360270397306336	0.180135198653168
65	0.792383275627782	0.415233448744436	0.207616724372218
66	0.755764798176017	0.488470403647966	0.244235201823983
67	0.722612329152796	0.554775341694409	0.277387670847204
68	0.69855033626513	0.60289932746974	0.30144966373487
69	0.698828433005412	0.602343133989175	0.301171566994588
70	0.657874587738991	0.684250824522017	0.342125412261009
71	0.629205566354853	0.741588867290294	0.370794433645147
72	0.738054485352664	0.523891029294673	0.261945514647336
73	0.781847064332136	0.436305871335727	0.218152935667864
74	0.784972043905073	0.430055912189854	0.215027956094927
75	0.751965161491339	0.496069677017323	0.248034838508661
76	0.713004392554724	0.573991214890553	0.286995607445276
77	0.701470217330904	0.597059565338192	0.298529782669096
78	0.702385753541548	0.595228492916904	0.297614246458452
79	0.675979382257863	0.648041235484275	0.324020617742137
80	0.695636276732323	0.608727446535355	0.304363723267677
81	0.664978093051751	0.670043813896498	0.335021906948249
82	0.621366262148856	0.757267475702288	0.378633737851144
83	0.588726121407263	0.822547757185474	0.411273878592737
84	0.540578142855679	0.918843714288642	0.459421857144321
85	0.492358488445176	0.984716976890352	0.507641511554824
86	0.455075544945198	0.910151089890397	0.544924455054802
87	0.515686510268609	0.968626979462783	0.484313489731391
88	0.480763290678008	0.961526581356017	0.519236709321992
89	0.44489413511752	0.88978827023504	0.55510586488248
90	0.402123728973801	0.804247457947602	0.597876271026199
91	0.364302911080258	0.728605822160516	0.635697088919742
92	0.440052807635176	0.880105615270352	0.559947192364824
93	0.394744067413677	0.789488134827353	0.605255932586323
94	0.362860654842803	0.725721309685605	0.637139345157197
95	0.320993422027729	0.641986844055459	0.67900657797227
96	0.335734418133492	0.671468836266984	0.664265581866508
97	0.305279385762484	0.610558771524968	0.694720614237516
98	0.299006321663415	0.598012643326831	0.700993678336585
99	0.319153723179832	0.638307446359665	0.680846276820168
100	0.337875165942902	0.675750331885805	0.662124834057098
101	0.292550295893007	0.585100591786013	0.707449704106993
102	0.26617200184345	0.5323440036869	0.73382799815655
103	0.292489745978632	0.584979491957264	0.707510254021368
104	0.305169022816939	0.610338045633877	0.694830977183061
105	0.273246172473923	0.546492344947846	0.726753827526077
106	0.253878172472972	0.507756344945944	0.746121827527028
107	0.213349580666494	0.426699161332987	0.786650419333507
108	0.177210121582469	0.354420243164939	0.82278987841753
109	0.145683186007589	0.291366372015178	0.85431681399241
110	0.120583926600066	0.241167853200133	0.879416073399934
111	0.528229035594671	0.943541928810658	0.471770964405329
112	0.493839207298549	0.987678414597099	0.506160792701451
113	0.452518474362608	0.905036948725216	0.547481525637392
114	0.401429451752157	0.802858903504315	0.598570548247843
115	0.352974410608709	0.705948821217419	0.647025589391291
116	0.353485383857779	0.706970767715559	0.64651461614222
117	0.305471354486198	0.610942708972396	0.694528645513802
118	0.256008205016113	0.512016410032227	0.743991794983887
119	0.25850549581793	0.517010991635859	0.74149450418207
120	0.24519500004898	0.490390000097959	0.75480499995102
121	0.215422553229923	0.430845106459847	0.784577446770077
122	0.258064439005416	0.516128878010832	0.741935560994584
123	0.208684344362954	0.417368688725909	0.791315655637046
124	0.291410368109751	0.582820736219502	0.708589631890249
125	0.284466869345719	0.568933738691437	0.715533130654281
126	0.295365557295775	0.59073111459155	0.704634442704225
127	0.584229854914178	0.831540290171644	0.415770145085822
128	0.509376727916594	0.981246544166813	0.490623272083406
129	0.502188811743118	0.995622376513763	0.497811188256882
130	0.890589641869467	0.218820716261067	0.109410358130533
131	0.974885947289066	0.0502281054218688	0.0251140527109344
132	0.97609608861965	0.0478078227607002	0.0239039113803501
133	0.961110853903049	0.0777782921939028	0.0388891460969514
134	0.974232680588313	0.0515346388233749	0.0257673194116874
135	0.952022667345128	0.0959546653097431	0.0479773326548716
136	0.945554063174835	0.108891873650331	0.0544459368251654
137	0.920912900016472	0.158174199967057	0.0790870999835285
138	0.973034891543853	0.0539302169122937	0.0269651084561469
139	0.951210736661153	0.0975785266776947	0.0487892633388474
140	0.888486748020883	0.223026503958233	0.111513251979117
141	0.857304784808674	0.285390430382652	0.142695215191326

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	0	0	OK
5% type I error level	1	0.00763358778625954	OK
10% type I error level	11	0.083969465648855	OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/20/t1290269238ndfudrhyxnc8s1r/10o8ng1290269273.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/20/t1290269238ndfudrhyxnc8s1r/10o8ng1290269273.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/20/t1290269238ndfudrhyxnc8s1r/1h7841290269273.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/20/t1290269238ndfudrhyxnc8s1r/1h7841290269273.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/20/t1290269238ndfudrhyxnc8s1r/2h7841290269273.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/20/t1290269238ndfudrhyxnc8s1r/2h7841290269273.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/20/t1290269238ndfudrhyxnc8s1r/3agpp1290269273.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/20/t1290269238ndfudrhyxnc8s1r/3agpp1290269273.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/20/t1290269238ndfudrhyxnc8s1r/4agpp1290269273.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/20/t1290269238ndfudrhyxnc8s1r/4agpp1290269273.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/20/t1290269238ndfudrhyxnc8s1r/5agpp1290269273.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/20/t1290269238ndfudrhyxnc8s1r/5agpp1290269273.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/20/t1290269238ndfudrhyxnc8s1r/6l7pa1290269273.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/20/t1290269238ndfudrhyxnc8s1r/6l7pa1290269273.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/20/t1290269238ndfudrhyxnc8s1r/7l7pa1290269273.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/20/t1290269238ndfudrhyxnc8s1r/7l7pa1290269273.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/20/t1290269238ndfudrhyxnc8s1r/8vhod1290269273.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/20/t1290269238ndfudrhyxnc8s1r/8vhod1290269273.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/20/t1290269238ndfudrhyxnc8s1r/9vhod1290269273.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/20/t1290269238ndfudrhyxnc8s1r/9vhod1290269273.ps (open in new window)

Parameters (Session):

par1 = 3 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 2 ; 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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