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Workshop 4 - Mini tutorial (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: Wed, 01 Dec 2010 17:46:18 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/01/t1291229375yk23pnu6cutl9lp.htm/, Retrieved Wed, 01 Dec 2010 19:49:35 +0100

BibTeX entries for LaTeX users:

@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/01/t1291229375yk23pnu6cutl9lp.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 «

2 2 4 2 2 2 4 1 4 2 5 4 2 2 2 2 3 2 2 2 4 1 4 2 3 1 4 2 3 3 4 2 3 2 4 1 2 1 2 4 4 4 3 2 4 2 4 3 3 3 3 2 3 2 4 2 4 1 4 1 4 1 4 3 3 2 4 1 3 2 2 2 3 2 4 4 4 2 4 4 2 1 4 3 5 2 3 2 4 4 2 3 2 2 4 2 3 2 2 2 4 2 3 3 4 2 4 3 3 2 3 2 4 3 4 4 4 2 4 2 1 1 4 2 4 4 4 3 5 1 4 5 2 2 4 2 4 2 4 3 3 2 5 1 2 2 4 2 4 2 2 2 5 2 4 4 4 2 4 2 4 2 5 4 4 2 4 3 3 2 2 2 4 2 4 4 2 2 4 2 2 1 4 2 4 2 2 2 2 1 5 2 4 2 4 2 4 1 4 3 1 1 4 1 4 2 4 2 2 2 4 2 1 1 3 1 4 5 5 5 3 2 4 2 2 2 4 2 4 1 4 2 3 1 4 1 2 2 2 2 2 2 4 2 3 1 4 2 2 1 4 4 1 2 4 2 3 1 3 1 2 1 4 2 3 2 2 2 3 1 4 2 3 1 4 1 2 2 4 2 3 1 4 2 2 1 4 2 4 3 4 3 4 3 3 3 4 2 4 2 2 2 4 2 3 1 4 3 4 3 4 2 3 2 4 2 4 2 4 2 2 2 4 2 3 2 2 2 3 1 3 1 4 4 5 3 2 1 3 2 4 1 3 4 2 1 4 2 2 1 4 1 4 4 4 4 3 2 4 3 4 2 4 2 2 1 3 3 2 1 4 2 3 1 4 3 3 3 4 2 5 4 5 5 2 4 4 3 3 3 4 4 4 2 2 2 3 2 3 2 4 3 3 2 3 1 3 3 3 3 4 4 2 2 4 3 3 2 2 2 2 2 3 2 3 2 3 3 2 4 4 2 4 3 4 2 2 1 2 2 4 1 3 2 4 2 4 3 1 1 4 2 5 3 5 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	6 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Multiple Linear Regression - Estimated Regression Equation

Q1[t] = + 2.23897194643045 + 0.243785460782962Q2[t] -0.122438966674107Q3[t] + 0.347603426744458Q4[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)	2.23897194643045	0.335983	6.664	0	0
Q2	0.243785460782962	0.079459	3.0681	0.002543	0.001272
Q3	-0.122438966674107	0.086368	-1.4176	0.158301	0.07915
Q4	0.347603426744458	0.079707	4.361	2.4e-05	1.2e-05

Multiple Linear Regression - Regression Statistics
Multiple R	0.479336441707
R-squared	0.229763424348329
Adjusted R-squared	0.214855619658296
F-TEST (value)	15.4122910197471
F-TEST (DF numerator)	3
F-TEST (DF denominator)	155
p-value	7.9837040312114e-09
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.856089324065147
Sum Squared Residuals	113.597784270640

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	2	2.93199385478886	-0.93199385478886
2	2	2.5843904280444	-0.5843904280444
3	4	3.50476174160366	0.495238258396335
4	2	3.17687178813707	-1.17687178813707
5	3	3.17687178813707	-0.176871788137071
6	4	2.68820839400589	1.31179160599410
7	3	2.68820839400590	0.311791605994105
8	3	3.17577931557182	-0.175779315571818
9	3	2.5843904280444	0.415609571955601
10	2	3.62829318084302	-1.62829318084302
11	4	3.54200374302889	0.457996256971113
12	4	3.27959728153331	0.720402718466686
13	3	3.29821828224593	-0.298218282245925
14	3	2.93199385478886	0.0680061452111432
15	4	2.34060496726144	1.65939503273856
16	4	3.03581182075035	0.964188179249647
17	3	2.5843904280444	0.415609571955601
18	3	3.17687178813707	-0.176871788137071
19	3	3.62720070827777	-0.627200708277772
20	4	3.62720070827777	0.372799291722228
21	2	3.03581182075035	-1.03581182075035
22	5	3.05443282146296	1.94556717853704
23	4	4.01204613644745	-0.0120461364474518
24	2	2.93199385478886	-0.931993854788857
25	3	3.17687178813707	-0.176871788137071
26	4	3.40203624820742	0.597963751792578
27	4	3.27959728153331	0.720402718466686
28	3	3.05443282146296	-0.054432821462964
29	4	3.87098616906073	0.129013830939266
30	4	2.93199385478886	1.06800614521114
31	1	2.68820839400589	-1.68820839400590
32	4	3.76716820309924	0.232831796900762
33	5	3.73101867423927	1.26898132576073
34	2	2.93199385478886	-0.931993854788857
35	4	3.27959728153331	0.720402718466686
36	3	2.46195146137029	0.538048538629708
37	2	2.93199385478886	-0.931993854788857
38	4	3.17687178813707	0.823128211862929
39	5	3.62720070827777	1.37279929172223
40	4	2.93199385478886	1.06800614521114
41	4	3.50476174160366	0.495238258396335
42	4	3.27959728153331	0.720402718466686
43	3	3.17687178813707	-0.176871788137071
44	4	3.62720070827777	0.372799291722228
45	2	2.93199385478886	-0.931993854788857
46	2	2.68820839400590	-0.688208394005895
47	4	3.17687178813707	0.823128211862929
48	2	2.56576942733179	-0.565769427331788
49	4	2.93199385478886	1.06800614521114
50	4	3.03581182075035	0.964188179249647
51	1	2.34060496726144	-1.34060496726144
52	4	2.93199385478886	1.06800614521114
53	2	2.93199385478886	-0.931993854788857
54	1	2.46304393393554	-1.46304393393554
55	4	4.58372155069701	-0.583721550697007
56	3	2.93199385478886	0.0680061452111432
57	2	2.93199385478886	-0.931993854788857
58	4	2.68820839400589	1.31179160599410
59	3	2.34060496726144	0.659395032738562
60	2	3.17687178813707	-1.17687178813707
61	2	2.93199385478886	-0.931993854788857
62	3	2.68820839400590	0.311791605994105
63	2	3.38341524749481	-1.38341524749481
64	1	2.93199385478886	-1.93199385478886
65	3	2.46304393393554	0.536956066064455
66	2	2.68820839400590	-0.688208394005895
67	3	3.17687178813707	-0.176871788137071
68	3	2.68820839400590	0.311791605994105
69	3	2.34060496726144	0.659395032738562
70	2	2.93199385478886	-0.931993854788857
71	3	2.68820839400590	0.311791605994105
72	2	2.68820839400590	-0.688208394005895
73	4	3.52338274231628	0.476617257683724
74	4	3.64582170899038	0.354178291009617
75	4	2.93199385478886	1.06800614521114
76	2	2.93199385478886	-0.931993854788857
77	3	3.03581182075035	-0.035811820750353
78	4	3.17577931557182	0.824220684428182
79	3	2.93199385478886	0.0680061452111432
80	4	2.93199385478886	1.06800614521114
81	2	2.93199385478886	-0.931993854788857
82	3	3.17687178813707	-0.176871788137071
83	3	2.46304393393554	0.536956066064455
84	4	3.64472923642513	0.355270763574870
85	2	2.81064736068	-0.810647360680002
86	4	3.50585421416892	0.494145785831082
87	2	2.68820839400590	-0.688208394005895
88	2	2.34060496726144	-0.340604967261437
89	4	4.11477162984369	-0.114771629843695
90	3	3.27959728153331	-0.279597281533314
91	4	2.93199385478886	1.06800614521114
92	2	3.15825078742446	-1.15825078742446
93	2	2.68820839400590	-0.688208394005895
94	3	3.03581182075035	-0.035811820750353
95	3	3.17577931557182	-0.175779315571818
96	5	4.33993608991405	0.660063910085955
97	2	3.76716820309924	-1.76716820309924
98	3	3.87098616906073	-0.870986169060734
99	4	3.17687178813707	0.823128211862929
100	3	3.05443282146296	-0.054432821462964
101	4	3.29821828224593	0.701781717754074
102	3	3.15825078742446	-0.15825078742446
103	3	3.87098616906073	-0.870986169060734
104	2	3.27959728153331	-1.27959728153331
105	3	3.17687178813707	-0.176871788137071
106	2	3.05443282146296	-1.05443282146296
107	3	3.40203624820742	-0.402036248207422
108	2	3.41956477635478	-1.41956477635478
109	4	3.17577931557182	0.824220684428182
110	2	2.93308632735411	-0.93308632735411
111	4	2.81064736068	1.18935263932000
112	4	3.27959728153331	0.720402718466686
113	1	2.68820839400589	-1.68820839400590
114	5	3.74854720238663	1.25145279761337
115	2	2.70682939471851	-0.706829394718506
116	3	3.05443282146296	-0.054432821462964
117	4	3.62720070827777	0.372799291722228
118	1	2.81064736068	-1.81064736068000
119	5	3.29821828224593	1.70178171775407
120	3	2.58548290060965	0.414517099390348
121	3	2.34060496726144	0.659395032738562
122	3	3.40203624820742	-0.402036248207422
123	3	3.52338274231628	-0.523382742316276
124	2	2.46195146137029	-0.461951461370292
125	2	2.34060496726144	-0.340604967261437
126	4	3.40203624820742	0.597963751792578
127	4	2.46304393393554	1.53695606606446
128	3	3.05443282146296	-0.054432821462964
129	3	3.15825078742446	-0.15825078742446
130	3	2.93199385478886	0.0680061452111432
131	4	3.17577931557182	0.824220684428182
132	3	3.05443282146296	-0.054432821462964
133	4	2.93308632735411	1.06691367264589
134	4	2.81064736068	1.18935263932000
135	2	3.17687178813707	-1.17687178813707
136	4	3.62720070827777	0.372799291722228
137	2	2.68820839400590	-0.688208394005895
138	4	2.93199385478886	1.06800614521114
139	3	3.52338274231628	-0.523382742316276
140	3	3.41956477635478	-0.41956477635478
141	2	2.93199385478886	-0.931993854788857
142	2	3.99233266316959	-1.99233266316959
143	5	4.48099605730076	0.519003942699236
144	2	2.34060496726144	-0.340604967261437
145	4	3.52338274231628	0.476617257683724
146	3	2.93199385478886	0.0680061452111432
147	3	3.50476174160366	-0.504761741603665
148	3	3.05443282146296	-0.054432821462964
149	3	2.58548290060965	0.414517099390348
150	4	3.41956477635478	0.58043522364522
151	4	3.05443282146296	0.945567178537036
152	4	3.27959728153331	0.720402718466686
153	4	4.09615062913108	-0.096150629131084
154	4	2.81064736068	1.18935263932000
155	5	4.2372105965178	0.762789403482198
156	3	3.05443282146296	-0.054432821462964
157	3	2.80955488811475	0.190445111885250
158	4	3.76716820309924	0.232831796900762
159	4	4.35964956319191	-0.359649563191909

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
7	0.374778290690061	0.749556581380123	0.625221709309938
8	0.445023871997149	0.890047743994299	0.554976128002851
9	0.382697881968956	0.765395763937911	0.617302118031044
10	0.458237247831948	0.916474495663897	0.541762752168052
11	0.529385249723225	0.94122950055355	0.470614750276775
12	0.485034154915191	0.970068309830383	0.514965845084809
13	0.382523277001251	0.765046554002502	0.617476722998749
14	0.291675672994694	0.583351345989387	0.708324327005306
15	0.417372997754567	0.834745995509134	0.582627002245433
16	0.397649037230417	0.795298074460834	0.602350962769583
17	0.319265600774192	0.638531201548385	0.680734399225808
18	0.273415696024939	0.546831392049877	0.726584303975061
19	0.236913072229273	0.473826144458545	0.763086927770727
20	0.198880203291997	0.397760406583995	0.801119796708003
21	0.279419062587415	0.55883812517483	0.720580937412585
22	0.618771362478365	0.76245727504327	0.381228637521635
23	0.582405358768509	0.835189282462983	0.417594641231491
24	0.642489801810588	0.715020396378823	0.357510198189412
25	0.580143673157277	0.839712653685446	0.419856326842723
26	0.56508639564939	0.86982720870122	0.43491360435061
27	0.53336953657518	0.933260926849639	0.466630463424820
28	0.469697043023122	0.939394086046244	0.530302956976878
29	0.408330927474781	0.816661854949563	0.591669072525219
30	0.402697635937668	0.805395271875337	0.597302364062332
31	0.630059647813811	0.739880704372378	0.369940352186189
32	0.574486050614173	0.851027898771655	0.425513949385827
33	0.64629707609601	0.70740584780798	0.35370292390399
34	0.677892332475199	0.644215335049602	0.322107667524801
35	0.64848929231282	0.70302141537436	0.35151070768718
36	0.602270040562342	0.795459918875316	0.397729959437658
37	0.630555024686505	0.738889950626991	0.369444975313495
38	0.64873118761508	0.70253762476984	0.35126881238492
39	0.694874774222383	0.610250451555235	0.305125225777617
40	0.701579535513153	0.596840928973694	0.298420464486847
41	0.661789799241109	0.676420401517782	0.338210200758891
42	0.63419629580567	0.73160740838866	0.36580370419433
43	0.584876346532735	0.830247306934529	0.415123653467265
44	0.538619733240357	0.922760533519286	0.461380266759643
45	0.56830680751865	0.8633863849627	0.43169319248135
46	0.557485387512356	0.885029224975288	0.442514612487644
47	0.565862540831114	0.868274918337773	0.434137459168886
48	0.54894340858668	0.90211318282664	0.45105659141332
49	0.563913400699232	0.872173198601535	0.436086599300768
50	0.569468778394227	0.861062443211546	0.430531221605773
51	0.633532123245473	0.732935753509054	0.366467876754527
52	0.64904684275534	0.701906314489321	0.350953157244661
53	0.665699171537022	0.668601656925957	0.334300828462978
54	0.722532205881726	0.554935588236548	0.277467794118274
55	0.747835137384785	0.50432972523043	0.252164862615215
56	0.707862579292357	0.584274841415287	0.292137420707643
57	0.716786919784025	0.56642616043195	0.283213080215975
58	0.765954977725335	0.468090044549329	0.234045022274665
59	0.750553416930239	0.498893166139522	0.249446583069761
60	0.778633000928734	0.442733998142533	0.221366999071266
61	0.786273022338975	0.42745395532205	0.213726977661025
62	0.75557426511813	0.488851469763739	0.244425734881869
63	0.814021492892214	0.371957014215572	0.185978507107786
64	0.912831219220578	0.174337561558844	0.0871687807794218
65	0.902082186417057	0.195835627165886	0.097917813582943
66	0.893661873047822	0.212676253904357	0.106338126952178
67	0.872311455370715	0.255377089258571	0.127688544629285
68	0.850450029671153	0.299099940657694	0.149549970328847
69	0.839720205908489	0.320559588183022	0.160279794091511
70	0.843941521866012	0.312116956267976	0.156058478133988
71	0.819296446518641	0.361407106962718	0.180703553481359
72	0.80651606714366	0.38696786571268	0.19348393285634
73	0.78300245931902	0.433995081361960	0.216997540680980
74	0.753031069350287	0.493937861299426	0.246968930649713
75	0.772158370955865	0.45568325808827	0.227841629044135
76	0.777463783266586	0.445072433466828	0.222536216733414
77	0.742083566578456	0.515832866843087	0.257916433421544
78	0.736593933466275	0.526812133067449	0.263406066533725
79	0.697924217984631	0.604151564030738	0.302075782015369
80	0.720454821512502	0.559090356974996	0.279545178487498
81	0.72590825262061	0.54818349475878	0.27409174737939
82	0.689423095168575	0.62115380966285	0.310576904831425
83	0.665968046455304	0.668063907089392	0.334031953544696
84	0.632016151665758	0.735967696668485	0.367983848334242
85	0.624845063578691	0.750309872842618	0.375154936421309
86	0.596960560872602	0.806078878254796	0.403039439127398
87	0.576846903634023	0.846306192731954	0.423153096365977
88	0.536711322722032	0.926577354555936	0.463288677277968
89	0.49319988558539	0.98639977117078	0.506800114414609
90	0.451361708400619	0.902723416801238	0.548638291599381
91	0.478315204893607	0.956630409787215	0.521684795106393
92	0.51317411503645	0.973651769927101	0.486825884963551
93	0.493309090092435	0.98661818018487	0.506690909907565
94	0.446534942493333	0.893069884986666	0.553465057506667
95	0.402633705446227	0.805267410892454	0.597366294553773
96	0.395738037328478	0.791476074656957	0.604261962671522
97	0.543980913467317	0.912038173065367	0.456019086532683
98	0.540471190476433	0.919057619047135	0.459528809523567
99	0.531152870392716	0.937694259214568	0.468847129607284
100	0.484074216178035	0.96814843235607	0.515925783821965
101	0.464273619737135	0.92854723947427	0.535726380262865
102	0.418385340212127	0.836770680424253	0.581614659787873
103	0.415900085901055	0.83180017180211	0.584099914098945
104	0.471193287941412	0.942386575882824	0.528806712058588
105	0.428502184544098	0.857004369088197	0.571497815455902
106	0.459419331351806	0.918838662703612	0.540580668648194
107	0.426221340891763	0.852442681783525	0.573778659108237
108	0.51654733724562	0.96690532550876	0.48345266275438
109	0.506959145445685	0.98608170910863	0.493040854554315
110	0.543007376391255	0.913985247217491	0.456992623608745
111	0.574269073659107	0.851461852681786	0.425730926340893
112	0.559575511302245	0.88084897739551	0.440424488697755
113	0.702687896106623	0.594624207786755	0.297312103893378
114	0.77431289555669	0.451374208886621	0.225687104443310
115	0.784129534649345	0.431740930701309	0.215870465350655
116	0.74762823470347	0.504743530593059	0.252371765296530
117	0.719844324245086	0.560311351509828	0.280155675754914
118	0.897960906955542	0.204078186088916	0.102039093044458
119	0.94829649125816	0.103407017483680	0.0517035087418399
120	0.934675999843293	0.130648000313414	0.0653240001567069
121	0.92353062775851	0.152938744482979	0.0764693722414893
122	0.91422001326533	0.171559973469339	0.0857799867346696
123	0.89867081735236	0.202658365295279	0.101329182647640
124	0.876468780368465	0.247062439263069	0.123531219631535
125	0.859095719318141	0.281808561363718	0.140904280681859
126	0.832757530025908	0.334484939948184	0.167242469974092
127	0.875779240288612	0.248441519422776	0.124220759711388
128	0.845626916994732	0.308746166010536	0.154373083005268
129	0.816830469011507	0.366339061976985	0.183169530988493
130	0.771321092596035	0.45735781480793	0.228678907403965
131	0.775315774079142	0.449368451841715	0.224684225920858
132	0.730054960416882	0.539890079166237	0.269945039583118
133	0.705002122988244	0.589995754023511	0.294997877011756
134	0.724896581624881	0.550206836750237	0.275103418375119
135	0.869106762091254	0.261786475817491	0.130893237908746
136	0.83691419886101	0.326171602277981	0.163085801138991
137	0.836899462853213	0.326201074293574	0.163100537146787
138	0.867181641251044	0.265636717497913	0.132818358748956
139	0.837170122276516	0.325659755446968	0.162829877723484
140	0.793131677526034	0.413736644947933	0.206868322473966
141	0.831012243017961	0.337975513964077	0.168987756982039
142	0.986035812248661	0.0279283755026774	0.0139641877513387
143	0.97577140108915	0.0484571978217005	0.0242285989108502
144	0.978893022821635	0.0422139543567297	0.0211069771783648
145	0.96406327120947	0.0718734575810583	0.0359367287905291
146	0.94315965455635	0.113680690887301	0.0568403454436506
147	0.941461802519	0.117076394961999	0.0585381974809996
148	0.92794249185595	0.144115016288099	0.0720575081440496
149	0.892944793303478	0.214110413393043	0.107055206696522
150	0.828539792427558	0.342920415144884	0.171460207572442
151	0.742471431830197	0.515057136339606	0.257528568169803
152	0.605076237990254	0.789847524019492	0.394923762009746

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	3	0.0205479452054795	OK
10% type I error level	4	0.0273972602739726	OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/01/t1291229375yk23pnu6cutl9lp/105ty81291225568.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/01/t1291229375yk23pnu6cutl9lp/105ty81291225568.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/01/t1291229375yk23pnu6cutl9lp/1ya1w1291225568.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/01/t1291229375yk23pnu6cutl9lp/1ya1w1291225568.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/01/t1291229375yk23pnu6cutl9lp/2ya1w1291225568.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/01/t1291229375yk23pnu6cutl9lp/2ya1w1291225568.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/01/t1291229375yk23pnu6cutl9lp/391ii1291225568.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/01/t1291229375yk23pnu6cutl9lp/391ii1291225568.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/01/t1291229375yk23pnu6cutl9lp/491ii1291225568.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/01/t1291229375yk23pnu6cutl9lp/491ii1291225568.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/01/t1291229375yk23pnu6cutl9lp/591ii1291225568.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/01/t1291229375yk23pnu6cutl9lp/591ii1291225568.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/01/t1291229375yk23pnu6cutl9lp/6ks031291225568.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/01/t1291229375yk23pnu6cutl9lp/6ks031291225568.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/01/t1291229375yk23pnu6cutl9lp/7d1z51291225568.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/01/t1291229375yk23pnu6cutl9lp/7d1z51291225568.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/01/t1291229375yk23pnu6cutl9lp/8d1z51291225568.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/01/t1291229375yk23pnu6cutl9lp/8d1z51291225568.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/01/t1291229375yk23pnu6cutl9lp/9d1z51291225568.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/01/t1291229375yk23pnu6cutl9lp/9d1z51291225568.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; 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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