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Multiple regression 1

*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: Sun, 21 Nov 2010 12:49:51 +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/21/t1290343724obbctt2vg5gv0rj.htm/, Retrieved Sun, 21 Nov 2010 13:48:56 +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/21/t1290343724obbctt2vg5gv0rj.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	'George Udny Yule' @ 72.249.76.132

Multiple Linear Regression - Estimated Regression Equation

Leadership[t] = + 1.02830814409858 + 0.0842475032129696Preferleader[t] + 0.207213675242005Jobcontrol[t] + 0.386522109686850Influenceothers[t] -0.134026305664132Destinycontrol[t] + 0.00410101084894554Handlingsituations[t] + 0.279829847242845Organization[t] -0.068409636934505Ability[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
Preferleader	0.0842475032129696	0.064963	1.2968	0.196758	0.098379
Jobcontrol	0.207213675242005	0.07449	2.7818	0.006131	0.003065
Influenceothers	0.386522109686850	0.090406	4.2754	3.5e-05	1.7e-05
Destinycontrol	-0.134026305664132	0.071517	-1.8741	0.062949	0.031474
Handlingsituations	0.00410101084894554	0.078835	0.052	0.958585	0.479292
Organization	0.279829847242845	0.079493	3.5202	0.000578	0.000289
Ability	-0.068409636934505	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	4.06622095863846	-0.0662209586384641
2	3	3.93219465297436	-0.932194652974364
3	5	4.22365583142934	0.776344168570663
4	4	3.44144578246207	0.55855421753793
5	2	3.22317197358497	-1.22317197358497
6	4	3.94382598418649	0.0561740158135078
7	3	3.7822901005467	-0.782290100546702
8	2	3.11647971114096	-1.11647971114096
9	4	3.87871050249576	0.121289497504241
10	2	3.1222609250938	-1.12226092509380
11	4	4.06211994778955	-0.0621199477895489
12	2	2.98177668368241	-0.98177668368241
13	5	4.43507604173768	0.564923958262323
14	3	3.69804259733373	-0.698042597333733
15	4	4.134630595573	-0.134630595573000
16	4	4.2734346338805	-0.273434633880500
17	3	3.23833311806901	-0.238333118069011
18	4	3.92809364212542	0.0719063578745837
19	2	2.75925595925391	-0.75925595925391
20	3	4.0580189369406	-1.05801893694060
21	4	3.59135033488973	0.408649665110271
22	2	3.77475978018352	-1.77475978018352
23	4	4.06622095863849	-0.0662209586384942
24	4	4.06622095863849	-0.0662209586384942
25	4	4.06622095863849	-0.0662209586384942
26	3	3.54157153243857	-0.541571532438566
27	4	4.01644215618733	-0.0164421561873315
28	4	3.50710283167676	0.492897168323241
29	4	4.06622095863849	-0.0662209586384942
30	4	3.57917743615364	0.420822563846357
31	4	4.72079567965361	-0.72079567965361
32	4	4.02765124702774	-0.0276512470277418
33	4	4.12705989472475	-0.127059894724754
34	5	4.06622095863849	0.933779041361506
35	4	4.06622095863849	-0.0662209586384942
36	4	4.13183762736812	-0.131837627368122
37	5	3.72537664055386	1.27462335944614
38	4	4.06622095863849	-0.0662209586384942
39	4	3.97787244457658	0.022127555423421
40	4	3.62474970353847	0.375250296461529
41	3	3.77475978018352	-0.774759780183519
42	4	4.11879272929453	-0.118792729294535
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	-0.295308195534501
50	4	3.99781132170399	0.00218867829601101
51	4	4.52115270525985	-0.52115270525985
52	4	3.90747804320358	0.092521956796416
53	4	3.80527642730169	0.194723572698306
54	4	4.20024726430263	-0.200247264302627
55	4	3.32947460033580	0.670525399664196
56	4	3.82733155083956	0.172668449160441
57	4	2.94277092876509	1.05722907123491
58	4	4.20024726430263	-0.200247264302627
59	4	4.33427356996676	-0.33427356996676
60	4	3.93191359400145	0.0680864059985549
61	4	4.25281903495867	-0.252819034958668
62	4	3.34966795888592	0.650332041114084
63	4	3.99781132170399	0.00218867829601101
64	4	4.55230067322767	-0.55230067322767
65	4	4.23852988981213	-0.238529889812126
66	5	5.02813510487211	-0.0281351048721104
67	4	4.31843570368830	-0.318435703688295
68	4	3.58657260224636	0.413427397753639
69	3	3.61322389654373	-0.61322389654373
70	4	3.96149301077416	0.0385069892258418
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	-0.216085130581092
76	5	4.9397865908102	0.0602134091898048
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	0.022127555423421
83	4	4.35265769883391	-0.352657698833910
84	4	4.03871138066284	-0.0387113806628388
85	4	3.98472604314534	0.0152739568546587
86	4	3.72731132508045	0.272688674919547
87	5	4.10016189481119	0.899838105188808
88	4	4.37521400941067	-0.37521400941067
89	4	3.62496075197325	0.375039248026750
90	4	4.05038309236003	-0.0503830923600296
91	4	3.7478213997849	0.252178600215104
92	5	4.0235502361788	0.976449763821204
93	4	4.06144322599513	-0.0614432259951267
94	4	3.69326486469037	0.306735135309634
95	3	3.03111944282701	-0.0311194428270053
96	4	3.18855431561785	0.811445684382152
97	4	3.93151793117994	0.0684820688200606
98	4	3.29921243464033	0.700787565359668
99	5	4.30338008342164	0.696619916578358
100	5	4.20304023250750	0.796959767492496
101	4	3.90468507499871	0.0953149250012938
102	4	3.74314919135892	0.256850808641082
103	5	4.20024726430263	0.799752735697373
104	5	4.30008592817787	0.699914071822131
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	-0.252819034958668
111	2	3.76577551247382	-1.76577551247382
112	4	3.74314919135892	0.256850808641082
113	5	4.62828101101042	0.37171898898958
114	4	3.80459970550727	0.195400294492728
115	4	4.02765124702774	-0.0276512470277418
116	4	3.24243412891796	0.757565871082044
117	4	3.90468507499871	0.0953149250012938
118	4	4.18918713066753	-0.189187130667530
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	4.20304023250750	0.796959767492496
126	3	4.03938810245726	-1.03938810245726
127	5	4.04348911330621	0.956510886693793
128	4	4.18440939802416	-0.184409398024162
129	4	3.59763273588146	0.402367264118541
130	3	4.341844270815	-1.34184427081501
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	4.20304023250750	-0.203040232507505
137	4	3.59135033488973	0.408649665110271
138	5	4.05038309236003	0.94961690763997
139	4	3.22895318753780	0.771046812462197
140	4	4.04218107066214	-0.0421810706621389
141	4	3.96613558914706	0.0338644108529403
142	4	3.71320374181778	0.286796258182224
143	4	4.06622095863849	-0.0662209586384942
144	4	4.20024726430263	-0.200247264302627
145	5	4.11879272929453	0.881207270705465
146	3	3.66392612640551	-0.663926126405508
147	4	4.06622095863849	-0.0662209586384942
148	4	3.75438485974954	0.245615140250458
149	4	4.134630595573	-0.134630595573000
150	4	4.18030838717522	-0.180308387175217
151	4	3.48793042966946	0.512069570330539
152	5	4.89410879920798	0.105891200792022

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
11	0.443885851842151	0.887771703684301	0.55611414815785
12	0.294541690356356	0.589083380712712	0.705458309643644
13	0.223650707405217	0.447301414810433	0.776349292594783
14	0.135927799482062	0.271855598964125	0.864072200517938
15	0.101649544567628	0.203299089135257	0.898350455432372
16	0.206107549821615	0.412215099643230	0.793892450178385
17	0.137148796728726	0.274297593457452	0.862851203271274
18	0.182007492806244	0.364014985612488	0.817992507193756
19	0.143135860989047	0.286271721978095	0.856864139010953
20	0.280606219219671	0.561212438439343	0.719393780780329
21	0.355212332212593	0.710424664425185	0.644787667787407
22	0.513487280285913	0.973025439428173	0.486512719714087
23	0.436514285732803	0.873028571465605	0.563485714267197
24	0.362866539167581	0.725733078335162	0.637133460832419
25	0.294951485823366	0.589902971646732	0.705048514176634
26	0.270556473409092	0.541112946818184	0.729443526590908
27	0.214461441764797	0.428922883529595	0.785538558235203
28	0.479036825101992	0.958073650203985	0.520963174898007
29	0.411844296743774	0.823688593487548	0.588155703256226
30	0.516326636101126	0.967346727797748	0.483673363898874
31	0.550507410491033	0.898985179017933	0.449492589508966
32	0.586076774592415	0.82784645081517	0.413923225407585
33	0.524405070147337	0.951189859705327	0.475594929852663
34	0.646458750105074	0.707082499789853	0.353541249894926
35	0.589009315418137	0.821981369163726	0.410990684581863
36	0.573282734479799	0.853434531040402	0.426717265520201
37	0.751953766406159	0.496092467187683	0.248046233593841
38	0.704425994384085	0.59114801123183	0.295574005615915
39	0.690098759756501	0.619802480486998	0.309901240243499
40	0.68572856721246	0.62854286557508	0.31427143278754
41	0.670207893935998	0.659584212128004	0.329792106064002
42	0.63238048853672	0.73523902292656	0.36761951146328
43	0.658722738196123	0.682554523607754	0.341277261803877
44	0.961130702358003	0.0777385952839933	0.0388692976419966
45	0.959691828530702	0.0806163429385967	0.0403081714692983
46	0.959474833231229	0.0810503335375424	0.0405251667687712
47	0.951362018410335	0.0972759631793302	0.0486379815896651
48	0.941617701108118	0.116764597783763	0.0583822988918816
49	0.926704542342497	0.146590915315006	0.0732954576575028
50	0.908040656613497	0.183918686773005	0.0919593433865027
51	0.89229479079279	0.215410418414422	0.107705209207211
52	0.899987264492846	0.200025471014307	0.100012735507154
53	0.88185800172333	0.236283996553340	0.118141998276670
54	0.860531400906133	0.278937198187734	0.139468599093867
55	0.89555312792535	0.208893744149302	0.104446872074651
56	0.884194380993118	0.231611238013765	0.115805619006882
57	0.931758247185255	0.136483505629491	0.0682417528147453
58	0.916712492831901	0.166575014336197	0.0832875071680986
59	0.905235140986306	0.189529718027388	0.094764859013694
60	0.882681604640219	0.234636790719562	0.117318395359781
61	0.859382092636387	0.281235814727225	0.140617907363613
62	0.854808621413579	0.290382757172843	0.145191378586421
63	0.825204849644486	0.349590300711027	0.174795150355514
64	0.819864801346832	0.360270397306336	0.180135198653168
65	0.79238327562778	0.415233448744439	0.207616724372220
66	0.755764798176016	0.488470403647967	0.244235201823984
67	0.722612329152795	0.55477534169441	0.277387670847205
68	0.698550336265128	0.602899327469745	0.301449663734872
69	0.698828433005413	0.602343133989175	0.301171566994587
70	0.657874587738991	0.684250824522018	0.342125412261009
71	0.629205566354851	0.741588867290298	0.370794433645149
72	0.738054485352662	0.523891029294675	0.261945514647337
73	0.781847064332134	0.436305871335731	0.218152935667866
74	0.784972043905073	0.430055912189854	0.215027956094927
75	0.751965161491338	0.496069677017325	0.248034838508662
76	0.713004392554724	0.573991214890552	0.286995607445276
77	0.701470217330902	0.597059565338197	0.298529782669098
78	0.702385753541549	0.595228492916901	0.297614246458451
79	0.675979382257867	0.648041235484266	0.324020617742133
80	0.695636276732322	0.608727446535356	0.304363723267678
81	0.664978093051752	0.670043813896496	0.335021906948248
82	0.621366262148856	0.757267475702288	0.378633737851144
83	0.588726121407263	0.822547757185474	0.411273878592737
84	0.54057814285568	0.91884371428864	0.45942185714432
85	0.492358488445176	0.984716976890352	0.507641511554824
86	0.455075544945199	0.910151089890398	0.544924455054801
87	0.515686510268614	0.968626979462773	0.484313489731386
88	0.480763290678006	0.961526581356013	0.519236709321994
89	0.444894135117521	0.889788270235041	0.555105864882479
90	0.4021237289738	0.8042474579476	0.5978762710262
91	0.364302911080257	0.728605822160514	0.635697088919743
92	0.44005280763518	0.88010561527036	0.55994719236482
93	0.394744067413676	0.789488134827352	0.605255932586324
94	0.362860654842802	0.725721309685605	0.637139345157198
95	0.320993422027729	0.641986844055459	0.67900657797227
96	0.335734418133493	0.671468836266987	0.664265581866507
97	0.305279385762485	0.61055877152497	0.694720614237515
98	0.299006321663417	0.598012643326834	0.700993678336583
99	0.319153723179832	0.638307446359664	0.680846276820168
100	0.337875165942901	0.675750331885802	0.662124834057099
101	0.292550295893007	0.585100591786014	0.707449704106993
102	0.26617200184345	0.5323440036869	0.73382799815655
103	0.292489745978633	0.584979491957265	0.707510254021367
104	0.305169022816940	0.610338045633879	0.69483097718306
105	0.273246172473922	0.546492344947845	0.726753827526078
106	0.253878172472972	0.507756344945944	0.746121827527028
107	0.213349580666493	0.426699161332987	0.786650419333507
108	0.177210121582470	0.354420243164940	0.82278987841753
109	0.145683186007588	0.291366372015177	0.854316813992412
110	0.120583926600067	0.241167853200134	0.879416073399933
111	0.528229035594669	0.943541928810662	0.471770964405331
112	0.49383920729855	0.9876784145971	0.50616079270145
113	0.452518474362607	0.905036948725214	0.547481525637393
114	0.401429451752158	0.802858903504316	0.598570548247842
115	0.352974410608707	0.705948821217415	0.647025589391293
116	0.353485383857780	0.706970767715559	0.64651461614222
117	0.305471354486197	0.610942708972394	0.694528645513803
118	0.256008205016115	0.512016410032229	0.743991794983885
119	0.258505495817930	0.517010991635859	0.74149450418207
120	0.245195000048979	0.490390000097958	0.754804999951021
121	0.215422553229923	0.430845106459846	0.784577446770077
122	0.258064439005415	0.51612887801083	0.741935560994585
123	0.208684344362956	0.417368688725911	0.791315655637044
124	0.291410368109751	0.582820736219501	0.708589631890249
125	0.284466869345718	0.568933738691436	0.715533130654282
126	0.295365557295776	0.590731114591551	0.704634442704224
127	0.584229854914177	0.831540290171645	0.415770145085823
128	0.509376727916595	0.98124654416681	0.490623272083405
129	0.502188811743121	0.995622376513758	0.497811188256879
130	0.890589641869466	0.218820716261069	0.109410358130534
131	0.974885947289066	0.0502281054218686	0.0251140527109343
132	0.97609608861965	0.0478078227607003	0.0239039113803501
133	0.961110853903048	0.0777782921939031	0.0388891460969515
134	0.974232680588313	0.0515346388233749	0.0257673194116875
135	0.952022667345129	0.0959546653097426	0.0479773326548713
136	0.945554063174834	0.108891873650331	0.0544459368251655
137	0.920912900016472	0.158174199967057	0.0790870999835284
138	0.973034891543853	0.0539302169122937	0.0269651084561468
139	0.951210736661153	0.0975785266776948	0.0487892633388474
140	0.888486748020883	0.223026503958234	0.111513251979117
141	0.857304784808674	0.285390430382653	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/21/t1290343724obbctt2vg5gv0rj/10fg691290343780.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290343724obbctt2vg5gv0rj/10fg691290343780.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290343724obbctt2vg5gv0rj/18x8x1290343780.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290343724obbctt2vg5gv0rj/18x8x1290343780.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290343724obbctt2vg5gv0rj/28x8x1290343780.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290343724obbctt2vg5gv0rj/28x8x1290343780.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290343724obbctt2vg5gv0rj/31pq01290343780.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290343724obbctt2vg5gv0rj/31pq01290343780.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290343724obbctt2vg5gv0rj/41pq01290343780.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290343724obbctt2vg5gv0rj/41pq01290343780.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290343724obbctt2vg5gv0rj/51pq01290343780.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290343724obbctt2vg5gv0rj/51pq01290343780.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290343724obbctt2vg5gv0rj/6uy7l1290343780.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290343724obbctt2vg5gv0rj/6uy7l1290343780.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290343724obbctt2vg5gv0rj/7uy7l1290343780.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290343724obbctt2vg5gv0rj/7uy7l1290343780.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290343724obbctt2vg5gv0rj/847oo1290343780.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290343724obbctt2vg5gv0rj/847oo1290343780.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290343724obbctt2vg5gv0rj/947oo1290343780.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/21/t1290343724obbctt2vg5gv0rj/947oo1290343780.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 = 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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