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Liniear Trend on - Priems

*The author of this computation has been verified*

R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Wed, 24 Nov 2010 08:24:56 +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/24/t12905870144o40nxvyldecvsh.htm/, Retrieved Wed, 24 Nov 2010 09:23:46 +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/24/t12905870144o40nxvyldecvsh.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 «

8 3 3 4 4 4 8 4 3 4 3 4 8 4 4 3 4 3 8 3 3 4 3 2 8 2 3 4 4 4 8 5 4 4 4 5 8 3 2 4 3 4 8 2 3 4 4 4 8 2 4 2 3 2 8 4 3 2 4 2 8 3 3 4 3 4 8 3 4 4 4 4 8 4 2 4 3 5 8 4 2 4 3 5 8 2 3 3 4 4 8 3 2 4 3 3 8 4 4 4 4 4 8 2 2 3 3 4 8 2 1 2 3 2 8 3 3 2 4 4 8 4 4 4 4 4 8 2 2 3 3 4 8 2 3 4 3 4 8 3 3 4 4 4 8 4 4 3 4 4 8 4 3 3 4 4 8 3 3 2 4 3 8 3 4 3 4 3 8 4 4 4 4 4 8 2 4 3 2 3 8 3 3 3 4 4 8 4 4 4 4 4 8 2 2 4 3 4 8 4 4 3 4 4 8 4 3 4 4 4 8 2 2 2 3 3 8 3 4 3 4 4 9 4 4 4 4 4 9 4 4 4 3 4 9 3 4 3 4 3 9 4 2 5 3 5 9 3 2 3 3 4 9 3 3 3 3 4 9 3 4 4 3 4 9 3 5 4 4 4 9 2 2 5 2 5 9 4 3 3 3 4 9 4 3 4 4 4 9 3 3 4 4 4 9 3 2 4 3 4 9 3 4 4 4 5 9 3 3 3 4 4 9 2 3 3 4 3 9 4 4 3 5 3 9 4 1 2 4 4 9 4 4 4 4 4 9 3 2 4 3 4 9 4 4 4 3 4 9 3 4 3 3 3 9 4 4 4 4 3 9 3 2 3 3 3 9 3 4 4 4 4 9 3 2 4 3 4 9 3 4 4 3 4 9 4 4 4 3 4 9 1 1 4 1 5 9 4 4 4 4 3 9 4 4 4 4 4 9 3 3 4 4 3 9 5 3 2 4 2 9 3 3 3 4 4 9 3 3 4 4 4 9 3 3 4 3 5 9 4 3 3 3 2 10 4 4 4 3 4 10 3 1 4 3 4 10 3 3 4 4 4 10 4 3 3 4 4 10 2 3 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

SocialVisible[t] = + 1.28655442281463 -0.0116291252388734Tijd[t] + 0.200736343687531ManyFriends[t] + 0.0194771930298669MakeNewFriends[t] + 0.234334548584778QuiteAccepted[t] + 0.111076713012465IntendMakeNewFriends[t] + 0.00371329634067004t + 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)	1.28655442281463	1.629028	0.7898	0.430989	0.215495
Tijd	-0.0116291252388734	0.208366	-0.0558	0.955571	0.477786
ManyFriends	0.200736343687531	0.073589	2.7278	0.007187	0.003594
MakeNewFriends	0.0194771930298669	0.09711	0.2006	0.841324	0.420662
QuiteAccepted	0.234334548584778	0.093916	2.4952	0.013743	0.006872
IntendMakeNewFriends	0.111076713012465	0.091974	1.2077	0.229184	0.114592
t	0.00371329634067004	0.005429	0.684	0.495122	0.247561

Multiple Linear Regression - Regression Statistics
Multiple R	0.463319910208726
R-squared	0.214665339195822
Adjusted R-squared	0.181246842991389
F-TEST (value)	6.42354874027353
F-TEST (DF numerator)	6
F-TEST (DF denominator)	141
p-value	5.28252382958616e-06
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.698807226015477
Sum Squared Residuals	68.8547470175339

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	3	3.25899756681534	-0.25899756681534
2	4	3.02837631457124	0.971623685428758
3	4	3.33660659714189	0.663393402858115
4	3	2.81364948122765	0.186350518772350
5	2	3.27385075217803	-1.27385075217803
6	5	3.58937710521869	1.41062289478130
7	3	2.84620645258706	0.153793547412941
8	2	3.28499064120004	-1.28499064120004
9	2	2.99399792055880	-0.993997920558796
10	4	3.03130942179671	0.968690578203287
11	3	3.06179598163727	-0.0617959816372699
12	3	3.50058017025025	-0.500580170250248
13	4	2.97956294364354	1.02043705635646
14	4	2.98327623998421	1.01672376001579
15	2	3.29150652255486	-1.29150652255486
16	3	2.76854940664062	0.231450593359376
17	4	3.5191466519536	0.480853348046401
18	2	2.86757551930456	-0.867575519304562
19	2	2.42892185290290	-0.428921852902904
20	3	3.29059581122834	-0.290595811228344
21	4	3.53399983731628	0.466000162683721
22	2	2.88242870466724	-0.882428704667243
23	2	3.10635553772531	-1.10635553772531
24	3	3.34440338265076	-0.344403382650758
25	4	3.52937582964909	0.470624170350908
26	4	3.33235278230223	0.667647217697769
27	3	3.20551217260057	-0.205512172600569
28	3	3.42943900565864	-0.429439005658637
29	4	3.56370620804164	0.436293791958361
30	2	2.96819650117042	-0.968196501170422
31	3	3.35091926400558	-0.350919264005582
32	4	3.57484609706365	0.425153902936351
33	2	2.94275215744448	-0.94275215744448
34	4	3.56279549671512	0.437204503284877
35	4	3.38524964239813	0.614750357601871
36	2	2.80386094739429	-0.803860947394291
37	3	3.57393538573713	-0.573935385737133
38	4	3.58549674986880	0.414503250131204
39	4	3.35487549762469	0.645124502375312
40	3	3.4623694365078	-0.462369436507804
41	4	3.0913833089733	0.908616691026701
42	3	2.94506550624177	0.0549344937582302
43	3	3.14951514626997	-0.149515146269971
44	3	3.37344197932804	-0.373441979328039
45	3	3.81222616794102	-0.812226167941017
46	2	2.87561524209187	-0.875615242091871
47	4	3.16436833163265	0.835631668367349
48	4	3.42189336958797	0.578106630412035
49	3	3.42560666592864	-0.425606665928635
50	3	2.994249069997	0.00575093000300298
51	3	3.74484631530997	-0.744846315309972
52	3	3.41726936192078	-0.417269361920779
53	2	3.30990594524898	-1.30990594524898
54	4	3.74869013386196	0.251309866138038
55	4	3.00745937053786	0.99254062946214
56	4	3.65233608400086	0.347663915999143
57	3	3.02024214438169	-0.0202421443816873
58	4	3.42542812809742	0.574571871902581
59	3	3.29858751839576	-0.298587518395757
60	4	3.55611255635107	0.443887443648929
61	3	2.90454142370204	0.0954585762979647
62	3	3.67461586204488	-0.674615862044877
63	3	3.04252192242571	-0.0425219224257076
64	3	3.44770790614144	-0.447707906141439
65	4	3.45142120248211	0.548578797517891
66	1	2.49533308360310	-1.49533308360310
67	4	3.58210563073576	0.417894369264238
68	4	3.6968956400889	0.303104359911103
69	3	3.38879587972957	-0.388795879729571
70	5	3.24247807699804	1.75752192300196
71	3	3.48782199239351	-0.48782199239351
72	3	3.51101248176405	-0.511012481764046
73	3	3.3914679425324	-0.391467942532404
74	4	3.04247390680581	0.957526093194189
75	4	3.47692504064994	0.523074959350064
76	3	2.87842930592801	0.121570694071986
77	3	3.51794983822852	-0.517949838228523
78	4	3.50218594153933	0.497814058460674
79	2	3.39482252486753	-1.39482252486753
80	4	3.24167978073864	0.758320219261358
81	3	3.40954518801889	-0.409545188018891
82	2	2.87929200163463	-0.879292001634634
83	4	3.27912180418788	0.720878195812121
84	4	3.74467925630074	0.255320743699256
85	3	3.52817901592402	-0.528179015924017
86	4	3.64102913596962	0.358970864030381
87	4	3.53560560860536	0.464394391394643
88	4	3.75953244166342	0.240467558336575
89	3	3.74376854497423	-0.743768544974228
90	3	3.31241094904259	-0.312410949042589
91	4	3.13486509472559	0.865134905274405
92	5	2.46187687973916	2.53812312026084
93	3	2.90795713882216	0.0920428611778425
94	4	3.34138514627265	0.658614853727351
95	4	3.35045462377581	0.649545376224194
96	4	3.78923881238878	0.210761187611215
97	4	3.79295210872945	0.207047891270545
98	5	3.94134032297984	1.05865967702016
99	4	3.36530780913849	0.634692190861514
100	3	2.47940212790467	0.520597872095328
101	4	3.6070689504046	0.392931049595396
102	4	3.24589379211816	0.754106207881836
103	4	3.81523188677347	0.184768113226525
104	4	3.39799530270922	0.602004697290784
105	4	3.60244494273742	0.397555057262582
106	3	3.47560433303576	-0.475604333035755
107	4	3.39501417986385	0.604985820136153
108	4	3.83379836847683	0.166201631523175
109	4	3.83751166481750	0.162488335182505
110	4	3.65953554649625	0.340464453503748
111	4	3.61060370891406	0.389396291085942
112	4	3.43554974122557	0.56445025877443
113	4	3.63999938125377	0.360000618746229
114	3	3.59063727966733	-0.590637279667327
115	4	3.41309142535033	0.586908574649667
116	3	3.61754106537853	-0.617541065378534
117	3	3.43463902989905	-0.434639029899053
118	4	3.85930220664465	0.140697793355348
119	4	3.62868095440054	0.371319045599456
120	4	3.43165790705368	0.568342092946316
121	4	3.87044209566666	0.129557904333338
122	3	3.6734190483198	-0.673419048319801
123	3	3.54657843861814	-0.546578438618139
124	1	2.22366197580448	-1.22366197580448
125	4	3.88529528102934	0.114704718970658
126	3	3.88900857737001	-0.889008577370012
127	4	3.49124918633562	0.508750813664379
128	4	3.69569882636382	0.304301173636178
129	3	3.90014846639202	-0.900148466392023
130	4	3.70312541904516	0.296874580954838
131	4	3.90757505907336	0.0924249409266374
132	2	3.50981566803897	-1.50981566803897
133	4	4.11573799544223	-0.115737995442234
134	3	3.58742469836551	-0.58742469836551
135	3	3.90295105140618	-0.902951051406176
136	4	3.72540519708918	0.274594802910818
137	4	3.92985483711738	0.0701451628826171
138	3	3.73283178977052	-0.732831789770522
139	3	3.73654508611119	-0.736545086111192
140	3	3.53952203876433	-0.539522038764331
141	4	3.94470802248006	0.055291977519937
142	4	3.94842131882073	0.0515786811792669
143	3	3.75139827147387	-0.751398271473872
144	4	4.19018246008685	-0.190182460086851
145	3	3.21267725887044	-0.212677258870438
146	4	3.85219779117095	0.147802208829052
147	4	3.73265325193931	0.267346748060694
148	4	3.42455349157998	0.57544650842002

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
10	0.99858910788783	0.00282178422434138	0.00141089211217069
11	0.996483894355613	0.00703221128877318	0.00351610564438659
12	0.99215165572289	0.0156966885542185	0.00784834427710927
13	0.990795953888255	0.0184080922234906	0.0092040461117453
14	0.986525242315786	0.0269495153684271	0.0134747576842136
15	0.991895492373643	0.0162090152527135	0.00810450762635674
16	0.99008787933023	0.0198242413395397	0.00991212066976985
17	0.991074195544875	0.01785160891025	0.008925804455125
18	0.9925117964326	0.0149764071348015	0.00748820356740073
19	0.988033646154905	0.0239327076901900	0.0119663538450950
20	0.98091633390308	0.0381673321938413	0.0190836660969207
21	0.976627199045353	0.0467456019092930	0.0233728009546465
22	0.97685160221351	0.0462967955729813	0.0231483977864907
23	0.982522653476458	0.0349546930470834	0.0174773465235417
24	0.974509201365195	0.0509815972696101	0.0254907986348051
25	0.973040875519453	0.0539182489610937	0.0269591244805469
26	0.976528692625557	0.0469426147488853	0.0234713073744426
27	0.966785875139853	0.0664282497202932	0.0332141248601466
28	0.955119565743614	0.0897608685127718	0.0448804342563859
29	0.9455211588551	0.108957682289801	0.0544788411449007
30	0.947268315726784	0.105463368546431	0.0527316842732155
31	0.930729374204817	0.138541251590365	0.0692706257951825
32	0.918040934209108	0.163918131581785	0.0819590657908925
33	0.91661240784859	0.166775184302818	0.083387592151409
34	0.903917578639119	0.192164842721762	0.096082421360881
35	0.900148078960379	0.199703842079243	0.0998519210396215
36	0.891542988323364	0.216914023353273	0.108457011676636
37	0.881411196623605	0.237177606752789	0.118588803376395
38	0.854250996969145	0.29149800606171	0.145749003030855
39	0.833358377079102	0.333283245841796	0.166641622920898
40	0.82498038555368	0.350039228892639	0.175019614446319
41	0.829162570337736	0.341674859324529	0.170837429662264
42	0.79173166866348	0.416536662673042	0.208268331336521
43	0.754721308876258	0.490557382247485	0.245278691123742
44	0.733106289467563	0.533787421064874	0.266893710532437
45	0.76941605761523	0.461167884769539	0.230583942384769
46	0.781102617621714	0.437794764756572	0.218897382378286
47	0.80865654851077	0.382686902978461	0.191343451489230
48	0.789542770674828	0.420914458650344	0.210457229325172
49	0.770425211426741	0.459149577146518	0.229574788573259
50	0.729951198415377	0.540097603169245	0.270048801584623
51	0.749938720280529	0.500122559438942	0.250061279719471
52	0.72351604803449	0.552967903931021	0.276483951965510
53	0.806735669151369	0.386528661697263	0.193264330848632
54	0.782600774609256	0.434798450781487	0.217399225390744
55	0.813273563485362	0.373452873029275	0.186726436514638
56	0.788597416242458	0.422805167515084	0.211402583757542
57	0.75274215815608	0.49451568368784	0.24725784184392
58	0.753135916924459	0.493728166151082	0.246864083075541
59	0.729243346422347	0.541513307155306	0.270756653577653
60	0.707518482188623	0.584963035622754	0.292481517811377
61	0.67334576896615	0.653308462067701	0.326654231033850
62	0.681616367601273	0.636767264797454	0.318383632398727
63	0.638592569989613	0.722814860020773	0.361407430010387
64	0.618563718889721	0.762872562220557	0.381436281110279
65	0.60598270133786	0.78803459732428	0.39401729866214
66	0.768756376481329	0.462487247037342	0.231243623518671
67	0.741521043945689	0.516957912108622	0.258478956054311
68	0.704546189239639	0.590907621520723	0.295453810760362
69	0.69869257445956	0.60261485108088	0.30130742554044
70	0.866650842802714	0.266698314394573	0.133349157197286
71	0.870361549862512	0.259276900274976	0.129638450137488
72	0.886208904357803	0.227582191284393	0.113791095642197
73	0.912239128512193	0.175521742975613	0.0877608714878066
74	0.91874509823104	0.162509803537918	0.0812549017689592
75	0.904036204930536	0.191927590138928	0.0959637950694638
76	0.88383205666202	0.23233588667596	0.11616794333798
77	0.891375451174184	0.217249097651632	0.108624548825816
78	0.87329244272934	0.253415114541318	0.126707557270659
79	0.951407449418854	0.0971851011622912	0.0485925505811456
80	0.95128896865352	0.0974220626929606	0.0487110313464803
81	0.95576154562473	0.0884769087505419	0.0442384543752710
82	0.978589887531351	0.0428202249372977	0.0214101124686488
83	0.979041860161708	0.0419162796765832	0.0209581398382916
84	0.972165021993753	0.0556699560124939	0.0278349780062470
85	0.97536722912840	0.0492655417431978	0.0246327708715989
86	0.967521462072935	0.0649570758541292	0.0324785379270646
87	0.95869652708805	0.0826069458239022	0.0413034729119511
88	0.947327615491328	0.105344769017343	0.0526723845086715
89	0.963740815334768	0.0725183693304631	0.0362591846652315
90	0.96620261031726	0.0675947793654822	0.0337973896827411
91	0.962739039217887	0.0745219215642265	0.0372609607821133
92	0.999643840111554	0.000712319776892065	0.000356159888446032
93	0.99961565997002	0.000768680059961131	0.000384340029980566
94	0.99959263698602	0.00081472602796107	0.000407363013980535
95	0.999384840057197	0.00123031988560692	0.000615159942803458
96	0.999098278043738	0.00180344391252411	0.000901721956262056
97	0.998724615227296	0.00255076954540881	0.00127538477270441
98	0.998590420473798	0.00281915905240385	0.00140957952620193
99	0.997892775859363	0.00421444828127398	0.00210722414063699
100	0.996918719488557	0.00616256102288622	0.00308128051144311
101	0.995351989292972	0.00929602141405634	0.00464801070702817
102	0.99548260692966	0.00903478614068071	0.00451739307034036
103	0.99360320974608	0.0127935805078406	0.00639679025392029
104	0.992284578162457	0.0154308436750861	0.00771542183754303
105	0.989587721691809	0.0208245566163828	0.0104122783081914
106	0.986158256214966	0.027683487570069	0.0138417437850345
107	0.980619870477796	0.0387602590444078	0.0193801295222039
108	0.97305511726305	0.0538897654739016	0.0269448827369508
109	0.964896168000487	0.0702076639990259	0.0351038319995129
110	0.97214046798392	0.0557190640321602	0.0278595320160801
111	0.960760944866861	0.0784781102662769	0.0392390551331385
112	0.95954335726529	0.0809132854694212	0.0404566427347106
113	0.951524548434362	0.0969509031312753	0.0484754515656376
114	0.939222426242773	0.121555147514454	0.0607775737572272
115	0.937657481140573	0.124685037718854	0.0623425188594269
116	0.946638340933345	0.106723318133311	0.0533616590666553
117	0.943560500563597	0.112878998872805	0.0564394994364027
118	0.92247335436385	0.155053291272301	0.0775266456361507
119	0.897949827650417	0.204100344699167	0.102050172349583
120	0.911993650367392	0.176012699265217	0.0880063496326084
121	0.888784277392061	0.222431445215877	0.111215722607939
122	0.86789756938858	0.264204861222840	0.132102430611420
123	0.845473876333832	0.309052247332336	0.154526123666168
124	0.87093035010909	0.258139299781821	0.129069649890911
125	0.830516207568033	0.338967584863934	0.169483792431967
126	0.870743008140704	0.258513983718593	0.129256991859296
127	0.92925656264239	0.141486874715219	0.0707434373576097
128	0.94730696540994	0.105386069180121	0.0526930345900603
129	0.967151047271548	0.0656979054569047	0.0328489527284523
130	0.982262646571668	0.0354747068566633	0.0177373534283316
131	0.97477247405783	0.0504550518843387	0.0252275259421694
132	0.984061746649693	0.0318765067006134	0.0159382533503067
133	0.980470347634979	0.039059304730043	0.0195296523650215
134	0.96185240480981	0.0762951903803819	0.0381475951901909
135	0.924847560026967	0.150304879946067	0.0751524399730334
136	0.958161543232746	0.083676913534508	0.041838456767254
137	0.926581758414778	0.146836483170444	0.073418241585222
138	0.839790045417048	0.320419909165904	0.160209954582952

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	13	0.100775193798450	NOK
5% type I error level	37	0.286821705426357	NOK
10% type I error level	60	0.465116279069767	NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/24/t12905870144o40nxvyldecvsh/106ruu1290587086.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t12905870144o40nxvyldecvsh/106ruu1290587086.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t12905870144o40nxvyldecvsh/1ahf41290587086.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t12905870144o40nxvyldecvsh/1ahf41290587086.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t12905870144o40nxvyldecvsh/2ahf41290587086.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t12905870144o40nxvyldecvsh/2ahf41290587086.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t12905870144o40nxvyldecvsh/3ahf41290587086.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t12905870144o40nxvyldecvsh/3ahf41290587086.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t12905870144o40nxvyldecvsh/4l8e71290587086.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t12905870144o40nxvyldecvsh/4l8e71290587086.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t12905870144o40nxvyldecvsh/5l8e71290587086.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t12905870144o40nxvyldecvsh/5l8e71290587086.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t12905870144o40nxvyldecvsh/6l8e71290587086.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t12905870144o40nxvyldecvsh/6l8e71290587086.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t12905870144o40nxvyldecvsh/7dhdr1290587086.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t12905870144o40nxvyldecvsh/7dhdr1290587086.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t12905870144o40nxvyldecvsh/86ruu1290587086.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t12905870144o40nxvyldecvsh/86ruu1290587086.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t12905870144o40nxvyldecvsh/96ruu1290587086.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/24/t12905870144o40nxvyldecvsh/96ruu1290587086.ps (open in new window)

Parameters (Session):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 2 ; 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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