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Paper: Multiple Linear Regression + geslacht

*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, 05 Dec 2010 12:58:27 +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/05/t1291553824xauqqc4w4yz5sjs.htm/, Retrieved Sun, 05 Dec 2010 13:57:15 +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/05/t1291553824xauqqc4w4yz5sjs.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 «

13 13 14 13 3 0 12 8 13 5 0 15 12 16 6 12 12 7 12 6 10 10 10 11 5 12 12 7 12 3 0 15 16 18 8 0 9 11 11 4 12 12 14 14 4 0 11 6 9 4 0 11 16 14 6 0 11 11 12 6 15 15 16 11 5 7 7 12 12 4 11 11 7 13 6 0 11 13 11 4 10 10 11 12 6 0 14 15 16 6 10 10 7 9 4 6 6 9 11 4 11 11 7 13 2 15 15 14 15 7 11 11 15 10 5 14 14 15 13 6 0 9 15 15 7 13 13 14 14 5 16 16 8 14 4 13 13 8 8 4 0 12 14 13 7 0 14 14 15 7 11 11 8 13 4 9 9 11 11 4 16 16 16 15 6 12 12 10 15 6 0 10 8 9 5 13 13 14 13 6 16 16 16 16 7 14 14 13 13 6 15 15 5 11 3 0 5 8 12 3 8 8 10 12 4 11 11 8 12 6 16 16 13 14 7 17 17 15 14 5 9 9 6 8 4 9 9 12 13 5 13 13 16 16 6 12 12 12 14 5 8 8 8 13 4 0 14 13 13 5 12 12 14 13 5 11 11 12 12 4 16 16 16 16 6 8 8 10 15 2 15 15 15 15 8 7 7 8 12 3 0 16 16 14 6 14 14 19 12 6 9 9 6 12 5 14 14 13 13 5 11 11 15 12 6 0 15 13 13 6 15 15 14 13 5 13 13 13 13 5 11 11 11 14 5 0 11 14 17 6 12 12 12 13 6 12 12 15 13 6 12 12 14 12 5 12 12 13 13 5 14 14 8 14 4 6 6 6 11 2 7 7 7 12 4 1 etc...

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits!

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	8 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

Popularity[t] = + 1.59055007677943 + 0.142714990424374`Pop*geslacht`[t] + 0.213531241972043KnowingPeople[t] + 0.25873921064204Liked[t] + 0.591645271703441Celebrity[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)	1.59055007677943	1.11561	1.4257	0.156421	0.078211
`Pop*geslacht`	0.142714990424374	0.033025	4.3215	3.1e-05	1.6e-05
KnowingPeople	0.213531241972043	0.06396	3.3385	0.001108	0.000554
Liked	0.25873921064204	0.099637	2.5968	0.010528	0.005264
Celebrity	0.591645271703441	0.153945	3.8432	0.000192	9.6e-05

Multiple Linear Regression - Regression Statistics
Multiple R	0.730462854365973
R-squared	0.533575981608485
Adjusted R-squared	0.518768869913516
F-TEST (value)	36.035115598526
F-TEST (DF numerator)	4
F-TEST (DF denominator)	126
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1.92784466060862
Sum Squared Residuals	468.289714465082

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	13	11.5738278933616	1.42617210663836
2	12	9.6206361094195	2.3793638905805
3	15	11.8426239809372	3.15737601906279
4	12	11.4525908136013	0.547409186398668
5	10	10.9573700763232	-0.957370076323233
6	12	9.677654998491	2.32234500150900
7	15	14.3975179135164	0.602482086483648
8	9	9.1521061423481	-0.152106142348093
9	12	12.2814973852828	-0.281497385282823
10	11	7.5669715112038	3.4330284887962
11	11	12.1792705275413	-1.17927052754131
12	11	10.5941358963970	0.405864103602983
13	15	12.9521324802774	2.04786751972265
14	7	10.6233815279328	-3.62338152793279
15	11	11.568615033819	-0.568615033818996
16	11	9.57916862629218	1.42083137370782
17	10	12.0212858006408	-2.02128580064075
18	14	12.4832177068533	1.51678229314665
19	10	9.20765265741958	0.79234734258042
20	6	9.58133360095025	-3.58133360095025
21	11	9.20203394700523	1.79796605299477
22	15	14.7433173823083	0.256682617691691
23	11	11.9090020659658	-0.909002065965774
24	14	13.7050099408685	0.294990059131544
25	9	12.8161237679147	-3.81612376791475
26	13	13.0158576474106	-0.0158576474106384
27	16	11.5711698951481	4.42883010485194
28	13	9.5905896600227	3.4094103399773
29	12	12.0851141046586	-0.085114104658626
30	14	12.6025925259427	1.39740747405729
31	11	10.5988557323842	0.401144267615845
32	9	10.4365410561675	-1.43654105616746
33	16	14.7214495849733	1.27855041502667
34	12	12.8694021714436	-0.869402171443577
35	10	8.58567926685133	1.41432073314867
36	13	13.3487637084720	-0.34876370847204
37	16	15.5718340673188	0.428165932681193
38	14	13.2779474569244	0.722052543075628
39	15	9.419998275178	5.580001724822
40	5	8.17860635537057	-3.17860635537056
41	8	10.3390340344131	-2.33903403441308
42	11	11.523407065149	-0.523407065148999
43	16	14.4137619201186	1.5862380798814
44	17	13.8002488510802	3.19975114891982
45	9	8.59266721438112	0.407332785618876
46	9	11.7591959911270	-2.75919599112702
47	13	14.5520438243422	-1.55204382434224
48	12	12.4460801730422	-0.44608017304218
49	8	10.1707107611110	-2.17071076111103
50	14	10.6882923192797	3.3117076807203
51	12	12.6144034463442	-0.614403446344225
52	11	11.1942414896303	-0.194241489630285
53	16	14.9801887956154	1.01981120438463
54	8	9.93196112293232	-1.93196112293232
55	15	15.5484938959838	-0.548493895983793
56	7	9.17761128834118	-2.17761128834118
57	16	12.1792705275413	3.82072947245869
58	14	14.3003956981146	-0.300395698114586
59	9	10.2192693286527	-1.21926932865272
60	14	12.6863021852209	1.31369781477907
61	11	13.0181257589533	-2.01812575895330
62	15	11.2799375909831	3.72006240901686
63	15	13.0425484176173	1.95745158238265
64	13	12.5435871947966	0.456412805203444
65	11	12.0898339406458	-1.08983394064576
66	11	12.5284256755233	-1.52842567552334
67	12	12.7789862341036	-0.778986234103582
68	12	13.4195799600197	-1.41957996001971
69	12	12.3556642357022	-0.355664235702185
70	12	12.4008722043722	-0.400872204372183
71	14	11.2857399142993	2.71426008570068
72	6	7.75744933162724	-1.75744933162724
73	7	9.55572531807258	-2.55572531807258
74	14	14.0541650888505	-0.0541650888504911
75	10	11.4296405289373	-1.42964052893731
76	13	7.53801262945444	5.46198737054556
77	12	12.5202470234615	-0.520247023461542
78	9	9.53720811960929	-0.537208119609288
79	12	10.7787082566197	1.22129174338031
80	16	15.4776776444361	0.522322355563876
81	10	10.4109327732898	-0.410932773289784
82	10	13.2245659165110	-3.22456591651096
83	16	13.2883942205288	2.71160577947117
84	15	14.0612561732649	0.938743826735128
85	10	8.51151241643197	1.48848758356803
86	8	10.4998763366297	-2.49987633662975
87	8	8.58931661550943	-0.589316615509431
88	11	12.9891668772039	-1.98916687720393
89	13	12.7081699825559	0.291830017444087
90	16	15.7853653092908	0.214634690709151
91	14	15.4257684780227	-1.42576847802274
92	9	10.3623742057481	-1.36237420574809
93	8	10.2648671839937	-2.26486718399372
94	8	10.9017204243672	-2.90172042436716
95	11	12.3033651826178	-1.30336518261781
96	12	14.0112252317232	-2.01122523172315
97	14	13.7954258782085	0.204574121791549
98	15	14.5749941090063	0.425005890993736
99	16	14.0356478903872	1.9643521096128
100	16	14.0356478903872	1.9643521096128
101	11	12.5583639077172	-1.55836390771716
102	14	13.9637491515105	0.0362508484895038
103	14	11.6223864609034	2.37761353909659
104	12	11.5956956906967	0.404304309303302
105	13	13.8210341610861	-0.821034161086123
106	12	9.45231283611744	2.54768716388256
107	16	15.7364168550782	0.263583144921837
108	12	13.4195799600197	-1.41957996001971
109	11	11.8763026986737	-0.876302698673722
110	4	6.8441354196911	-2.84413541969110
111	16	15.7364168550782	0.263583144921837
112	10	11.2323583738859	-1.23235837388590
113	13	13.22564840384	-0.225648403839993
114	14	13.9637491515105	0.0362508484895038
115	7	10.2452674982014	-3.24526749820139
116	12	12.8731426569863	-0.873142656986265
117	12	10.7372407734924	1.26275922650761
118	13	13.6075029191141	-0.60750291911408
119	15	13.2271207778400	1.77287922215998
120	12	11.1686332067526	0.831366793247386
121	10	10.7853063174785	-0.785306317478495
122	8	11.0210952434565	-3.02109524345652
123	10	13.6516284004550	-3.65162840045504
124	15	14.3199953839069	0.680004616093088
125	16	15.0506151604920	0.949384839507961
126	13	13.5133464962314	-0.513346496231397
127	16	15.3583028253468	0.641697174653236
128	9	10.2682177828654	-1.26821778286541
129	14	13.5818946362364	0.418105363763591
130	14	13.2327394882544	0.767260511745626
131	12	10.4576131159598	1.54238688404019

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
8	0.0459535442652245	0.0919070885304489	0.954046455734776
9	0.0458934872623727	0.0917869745247454	0.954106512737627
10	0.127743279436854	0.255486558873708	0.872256720563146
11	0.0687360517383393	0.137472103476679	0.93126394826166
12	0.0340428092771499	0.0680856185542998	0.96595719072285
13	0.331229728172681	0.662459456345361	0.66877027182732
14	0.725215881031035	0.54956823793793	0.274784118968965
15	0.703415953314134	0.593168093371733	0.296584046685866
16	0.636024679228908	0.727950641542183	0.363975320771092
17	0.627106076784115	0.74578784643177	0.372893923215885
18	0.561819294117399	0.876361411765202	0.438180705882601
19	0.482596931401864	0.965193862803727	0.517403068598136
20	0.748410310242935	0.50317937951413	0.251589689757065
21	0.693045360980263	0.613909278039475	0.306954639019737
22	0.633492602047735	0.73301479590453	0.366507397952265
23	0.565308378547561	0.869383242904878	0.434691621452439
24	0.505715120159673	0.988569759680653	0.494284879840327
25	0.689466457586018	0.621067084827963	0.310533542413982
26	0.626677633836962	0.746644732326075	0.373322366163038
27	0.733642483197155	0.53271503360569	0.266357516802845
28	0.819122265256642	0.361755469486716	0.180877734743358
29	0.779173084311012	0.441653831377975	0.220826915688988
30	0.758901513966229	0.482196972067543	0.241098486033771
31	0.723460733484106	0.553078533031788	0.276539266515894
32	0.71363670229454	0.572726595410919	0.286363297705459
33	0.682595885040932	0.634808229918137	0.317404114959068
34	0.665153975939829	0.669692048120343	0.334846024060171
35	0.632933977355756	0.734132045288487	0.367066022644244
36	0.576598099156099	0.846803801687801	0.423401900843901
37	0.522946690076296	0.954106619847408	0.477053309923704
38	0.471956956803423	0.943913913606846	0.528043043196577
39	0.743705932498876	0.512588135002248	0.256294067501124
40	0.866073951154957	0.267852097690085	0.133926048845043
41	0.892369713201682	0.215260573596637	0.107630286798318
42	0.875753115657858	0.248493768684284	0.124246884342142
43	0.862275543299379	0.275448913401242	0.137724456700621
44	0.903020888638969	0.193958222722062	0.0969791113610309
45	0.883724175809352	0.232551648381296	0.116275824190648
46	0.91672563829966	0.166548723400682	0.0832743617003408
47	0.91414766687941	0.171704666241181	0.0858523331205903
48	0.895629555389476	0.208740889221047	0.104370444610524
49	0.912347037988906	0.175305924022188	0.087652962011094
50	0.944768410162782	0.110463179674437	0.0552315898372184
51	0.930535845910982	0.138928308178036	0.0694641540890178
52	0.91229959654224	0.175400806915521	0.0877004034577605
53	0.894927276097236	0.210145447805527	0.105072723902764
54	0.899111553705157	0.201776892589685	0.100888446294843
55	0.878178870292653	0.243642259414694	0.121821129707347
56	0.886132234661855	0.227735530676290	0.113867765338145
57	0.940079136179172	0.119841727641656	0.0599208638208278
58	0.923325716391099	0.153348567217803	0.0766742836089014
59	0.91333203628078	0.173335927438442	0.0866679637192208
60	0.902691404550759	0.194617190898482	0.097308595449241
61	0.90438213415077	0.191235731698458	0.0956178658492292
62	0.950308584189414	0.0993828316211712	0.0496914158105856
63	0.951676014162154	0.0966479716756924	0.0483239858378462
64	0.938841683723074	0.122316632553853	0.0611583162769263
65	0.927760544946709	0.144478910106583	0.0722394550532913
66	0.924410875353537	0.151178249292927	0.0755891246464633
67	0.907824088309188	0.184351823381624	0.092175911690812
68	0.896726715822461	0.206546568355078	0.103273284177539
69	0.872267629156807	0.255464741686386	0.127732370843193
70	0.844251909699032	0.311496180601937	0.155748090300968
71	0.883653168038558	0.232693663922885	0.116346831961443
72	0.874302223008163	0.251395553983675	0.125697776991837
73	0.889313407362803	0.221373185274394	0.110686592637197
74	0.862763000616085	0.274473998767829	0.137236999383915
75	0.846812732549008	0.306374534901983	0.153187267450992
76	0.983427349815912	0.0331453003681768	0.0165726501840884
77	0.977380160119567	0.0452396797608656	0.0226198398804328
78	0.97000652633356	0.0599869473328809	0.0299934736664404
79	0.965884658263239	0.0682306834735221	0.0341153417367611
80	0.954994068015835	0.0900118639683305	0.0450059319841652
81	0.941666342815078	0.116667314369844	0.0583336571849218
82	0.966903079995017	0.066193840009966	0.033096920004983
83	0.979870845620403	0.0402583087591942	0.0201291543795971
84	0.974122992169726	0.0517540156605475	0.0258770078302737
85	0.985014699450067	0.0299706010998655	0.0149853005499328
86	0.985312456011374	0.0293750879772512	0.0146875439886256
87	0.979593070825157	0.0408138583496864	0.0204069291748432
88	0.979112410674135	0.0417751786517300	0.0208875893258650
89	0.971436831981545	0.0571263360369105	0.0285631680184552
90	0.96046347218321	0.079073055633579	0.0395365278167895
91	0.958667902926637	0.082664194146726	0.041332097073363
92	0.948653105976234	0.102693788047532	0.051346894023766
93	0.950571190063015	0.0988576198739706	0.0494288099369853
94	0.966451136756683	0.0670977264866346	0.0335488632433173
95	0.95955056404197	0.0808988719160616	0.0404494359580308
96	0.957595199932488	0.0848096001350238	0.0424048000675119
97	0.941276850653867	0.117446298692265	0.0587231493461326
98	0.920715162561674	0.158569674876652	0.0792848374383261
99	0.920575467797918	0.158849064404164	0.0794245322020822
100	0.92338832097843	0.153223358043139	0.0766116790215694
101	0.916069960016446	0.167860079967107	0.0839300399835536
102	0.886930192018945	0.226139615962110	0.113069807981055
103	0.924936904248193	0.150126191503613	0.0750630957518066
104	0.903005028543354	0.193989942913293	0.0969949714566465
105	0.872814983619751	0.254370032760499	0.127185016380249
106	0.969530545057275	0.0609389098854491	0.0304694549427246
107	0.953925454418663	0.0921490911626747	0.0460745455813373
108	0.94384248015414	0.112315039691718	0.056157519845859
109	0.918668739067279	0.162662521865443	0.0813312609327213
110	0.89565344564259	0.208693108714819	0.104346554357410
111	0.85334338077946	0.293313238441079	0.146656619220539
112	0.807078991223225	0.38584201755355	0.192921008776775
113	0.741802146474079	0.516395707051842	0.258197853525921
114	0.665033836770552	0.669932326458895	0.334966163229448
115	0.810405913713478	0.379188172573044	0.189594086286522
116	0.772947603287559	0.454104793424882	0.227052396712441
117	1	1.03952623803669e-141	5.19763119018347e-142
118	1	1.28888100164261e-122	6.44440500821304e-123
119	1	1.51917273998704e-108	7.5958636999352e-109
120	1	2.97616944314037e-92	1.48808472157019e-92
121	1	3.9516372614307e-78	1.97581863071535e-78
122	1	4.50595214666178e-62	2.25297607333089e-62
123	1	5.42176106127711e-48	2.71088053063855e-48

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	7	0.0603448275862069	NOK
5% type I error level	14	0.120689655172414	NOK
10% type I error level	33	0.284482758620690	NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/05/t1291553824xauqqc4w4yz5sjs/10bf5b1291553896.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/05/t1291553824xauqqc4w4yz5sjs/10bf5b1291553896.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/05/t1291553824xauqqc4w4yz5sjs/1xopl1291553896.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/05/t1291553824xauqqc4w4yz5sjs/1xopl1291553896.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/05/t1291553824xauqqc4w4yz5sjs/2xopl1291553896.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/05/t1291553824xauqqc4w4yz5sjs/2xopl1291553896.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/05/t1291553824xauqqc4w4yz5sjs/3xopl1291553896.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/05/t1291553824xauqqc4w4yz5sjs/3xopl1291553896.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/05/t1291553824xauqqc4w4yz5sjs/48f7o1291553896.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/05/t1291553824xauqqc4w4yz5sjs/48f7o1291553896.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/05/t1291553824xauqqc4w4yz5sjs/58f7o1291553896.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/05/t1291553824xauqqc4w4yz5sjs/58f7o1291553896.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/05/t1291553824xauqqc4w4yz5sjs/68f7o1291553896.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/05/t1291553824xauqqc4w4yz5sjs/68f7o1291553896.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/05/t1291553824xauqqc4w4yz5sjs/71o6q1291553896.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/05/t1291553824xauqqc4w4yz5sjs/71o6q1291553896.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/05/t1291553824xauqqc4w4yz5sjs/8bf5b1291553896.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/05/t1291553824xauqqc4w4yz5sjs/8bf5b1291553896.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/05/t1291553824xauqqc4w4yz5sjs/9bf5b1291553896.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/05/t1291553824xauqqc4w4yz5sjs/9bf5b1291553896.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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