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Multiple regression - OPJV

*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: Mon, 27 Dec 2010 15:00:15 +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/27/t1293461971aan1k9rkjccauiz.htm/, Retrieved Mon, 27 Dec 2010 15:59:33 +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/27/t1293461971aan1k9rkjccauiz.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 «

20503 22885 26217 26583 27751 28158 27373 28367 26851 26733 26849 26733 27951 29781 32914 33488 35652 36488 35387 35676 34844 32447 31068 29010 29812 30951 32974 32936 34012 32946 31948 30599 27691 25073 23406 22248 22896 25317 26558 26471 27543 26198 24725 25005 23462 20780 19815 19761 21454 23899 24939 23580 24562 24696 23785 23812 21917 19713 19282 18788 21453 24482 27474 27264 27349 30632 29429 30084 26290 24379 23335 21346 21106 24514 28353 30805 31348 34556 33855 34787 32529 29998 29257 28155 30466 35704 39327 39351 42234 43630 43722 43121 37985 37135 34646 33026 35087 38846 42013 43908 42868 44423 44167 43636 44382 42142 43452 36912 42413 45344 44873 47510 49554 47369 45998 48140 48441 44928 40454 38661 37246 36843 36424 37594 38144 38737 34560 36080 33508 35462 33374 32110 35533 35532 37903 36763 40399 44164 44496 43110 43880 43930 44327

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	7 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

Multiple Linear Regression - Estimated Regression Equation

OPJV[t] = + 23615.8972717423 + 126.744045273975t + 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)	23615.8972717423	999.993581	23.616	0	0
t	126.744045273975	12.04899	10.5191	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.663098309947825
R-squared	0.439699368655662
Adjusted R-squared	0.435725605312794
F-TEST (value)	110.650617743722
F-TEST (DF numerator)	1
F-TEST (DF denominator)	141
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	5947.76028766207
Sum Squared Residuals	4987995193.96808

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	20503	23742.6413170163	-3239.6413170163
2	22885	23869.3853622903	-984.385362290291
3	26217	23996.1294075643	2220.87059243573
4	26583	24122.8734528382	2460.12654716176
5	27751	24249.6174981122	3501.38250188778
6	28158	24376.3615433862	3781.63845661381
7	27373	24503.1055886602	2869.89441133983
8	28367	24629.8496339341	3737.15036606586
9	26851	24756.5936792081	2094.40632079188
10	26733	24883.3377244821	1849.66227551791
11	26849	25010.0817697561	1838.91823024393
12	26733	25136.82581503	1596.17418496996
13	27951	25263.569860304	2687.43013969598
14	29781	25390.313905578	4390.68609442201
15	32914	25517.057950852	7396.94204914803
16	33488	25643.8019961259	7844.19800387406
17	35652	25770.5460413999	9881.45395860008
18	36488	25897.2900866739	10590.7099133261
19	35387	26024.0341319479	9362.96586805214
20	35676	26150.7781772218	9525.22182277816
21	34844	26277.5222224958	8566.47777750419
22	32447	26404.2662677698	6042.73373223021
23	31068	26531.0103130438	4536.98968695623
24	29010	26657.7543583177	2352.24564168226
25	29812	26784.4984035917	3027.50159640829
26	30951	26911.2424488657	4039.75755113431
27	32974	27037.9864941397	5936.01350586034
28	32936	27164.7305394136	5771.26946058636
29	34012	27291.4745846876	6720.52541531239
30	32946	27418.2186299616	5527.78137003841
31	31948	27544.9626752356	4403.03732476444
32	30599	27671.7067205095	2927.29327949046
33	27691	27798.4507657835	-107.450765783513
34	25073	27925.1948110575	-2852.19481105749
35	23406	28051.9388563315	-4645.93885633146
36	22248	28178.6829016054	-5930.68290160544
37	22896	28305.4269468794	-5409.42694687941
38	25317	28432.1709921534	-3115.17099215339
39	26558	28558.9150374274	-2000.91503742736
40	26471	28685.6590827013	-2214.65908270134
41	27543	28812.4031279753	-1269.40312797531
42	26198	28939.1471732493	-2741.14717324929
43	24725	29065.8912185233	-4340.89121852326
44	25005	29192.6352637972	-4187.63526379724
45	23462	29319.3793090712	-5857.37930907121
46	20780	29446.1233543452	-8666.12335434519
47	19815	29572.8673996192	-9757.86739961916
48	19761	29699.6114448931	-9938.61144489313
49	21454	29826.3554901671	-8372.3554901671
50	23899	29953.0995354411	-6054.09953544109
51	24939	30079.8435807151	-5140.84358071506
52	23580	30206.587625989	-6626.58762598903
53	24562	30333.331671263	-5771.33167126301
54	24696	30460.075716537	-5764.07571653698
55	23785	30586.819761811	-6801.81976181096
56	23812	30713.5638070849	-6901.56380708494
57	21917	30840.3078523589	-8923.3078523589
58	19713	30967.0518976329	-11254.0518976329
59	19282	31093.7959429069	-11811.7959429069
60	18788	31220.5399881808	-12432.5399881808
61	21453	31347.2840334548	-9894.2840334548
62	24482	31474.0280787288	-6992.02807872878
63	27474	31600.7721240028	-4126.77212400276
64	27264	31727.5161692767	-4463.51616927673
65	27349	31854.2602145507	-4505.26021455071
66	30632	31981.0042598247	-1349.00425982468
67	29429	32107.7483050987	-2678.74830509866
68	30084	32234.4923503726	-2150.49235037263
69	26290	32361.2363956466	-6071.23639564661
70	24379	32487.9804409206	-8108.98044092058
71	23335	32614.7244861946	-9279.72448619455
72	21346	32741.4685314685	-11395.4685314685
73	21106	32868.2125767425	-11762.2125767425
74	24514	32994.9566220165	-8480.95662201648
75	28353	33121.7006672905	-4768.70066729046
76	30805	33248.4447125644	-2443.44471256443
77	31348	33375.1887578384	-2027.18875783841
78	34556	33501.9328031124	1054.06719688762
79	33855	33628.6768483864	226.323151613644
80	34787	33755.4208936603	1031.57910633967
81	32529	33882.1649389343	-1353.16493893431
82	29998	34008.9089842083	-4010.90898420828
83	29257	34135.6530294823	-4878.65302948226
84	28155	34262.3970747562	-6107.39707475623
85	30466	34389.1411200302	-3923.1411200302
86	35704	34515.8851653042	1188.11483469582
87	39327	34642.6292105782	4684.37078942185
88	39351	34769.3732558521	4581.62674414787
89	42234	34896.1173011261	7337.8826988739
90	43630	35022.8613464001	8607.13865359992
91	43722	35149.605391674	8572.39460832595
92	43121	35276.349436948	7844.65056305197
93	37985	35403.093482222	2581.906517778
94	37135	35529.837527496	1605.16247250402
95	34646	35656.58157277	-1010.58157276995
96	33026	35783.3256180439	-2757.32561804393
97	35087	35910.0696633179	-823.069663317903
98	38846	36036.8137085919	2809.18629140812
99	42013	36163.5577538659	5849.44224613415
100	43908	36290.3017991398	7617.69820086017
101	42868	36417.0458444138	6450.9541555862
102	44423	36543.7898896878	7879.21011031222
103	44167	36670.5339349617	7496.46606503825
104	43636	36797.2779802357	6838.72201976427
105	44382	36924.0220255097	7457.9779744903
106	42142	37050.7660707837	5091.23392921632
107	43452	37177.5101160577	6274.48988394235
108	36912	37304.2541613316	-392.254161331627
109	42413	37430.9982066056	4982.0017933944
110	45344	37557.7422518796	7786.25774812042
111	44873	37684.4862971535	7188.51370284645
112	47510	37811.2303424275	9698.76965757247
113	49554	37937.9743877015	11616.0256122985
114	47369	38064.7184329755	9304.28156702452
115	45998	38191.4624782495	7806.53752175055
116	48140	38318.2065235234	9821.79347647658
117	48441	38444.9505687974	9996.0494312026
118	44928	38571.6946140714	6356.30538592863
119	40454	38698.4386593454	1755.56134065465
120	38661	38825.1827046193	-164.182704619325
121	37246	38951.9267498933	-1705.9267498933
122	36843	39078.6707951673	-2235.67079516727
123	36424	39205.4148404412	-2781.41484044125
124	37594	39332.1588857152	-1738.15888571522
125	38144	39458.9029309892	-1314.9029309892
126	38737	39585.6469762632	-848.646976263175
127	34560	39712.3910215372	-5152.39102153715
128	36080	39839.1350668111	-3759.13506681112
129	33508	39965.8791120851	-6457.8791120851
130	35462	40092.6231573591	-4630.62315735907
131	33374	40219.367202633	-6845.36720263305
132	32110	40346.111247907	-8236.11124790702
133	35533	40472.855293181	-4939.855293181
134	35532	40599.599338455	-5067.59933845497
135	37903	40726.3433837289	-2823.34338372895
136	36763	40853.0874290029	-4090.08742900292
137	40399	40979.8314742769	-580.831474276896
138	44164	41106.5755195509	3057.42448044913
139	44496	41233.3195648248	3262.68043517515
140	43110	41360.0636100988	1749.93638990118
141	43880	41486.8076553728	2393.1923446272
142	43930	41613.5517006468	2316.44829935323
143	44327	41740.2957459207	2586.70425407926

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
5	0.00593620333761853	0.0118724066752371	0.994063796662381
6	0.00226266623845864	0.00452533247691728	0.997737333761541
7	0.00231244030564355	0.0046248806112871	0.997687559694356
8	0.000835234444628007	0.00167046888925601	0.999164765555372
9	0.000923153607940709	0.00184630721588142	0.99907684639206
10	0.000641456552052668	0.00128291310410534	0.999358543447947
11	0.000327319212509255	0.00065463842501851	0.99967268078749
12	0.00015478020697483	0.00030956041394966	0.999845219793025
13	4.74929537634695e-05	9.4985907526939e-05	0.999952507046237
14	1.46489675953808e-05	2.92979351907616e-05	0.999985351032405
15	1.52236012432148e-05	3.04472024864296e-05	0.999984776398757
16	1.01354138499734e-05	2.02708276999467e-05	0.99998986458615
17	1.311633363052e-05	2.62326672610399e-05	0.99998688366637
18	1.24311917603434e-05	2.48623835206869e-05	0.99998756880824
19	5.46692534108743e-06	1.09338506821749e-05	0.99999453307466
20	2.38325609227969e-06	4.76651218455937e-06	0.999997616743908
21	1.2076659677044e-06	2.4153319354088e-06	0.999998792334032
22	2.29815262165781e-06	4.59630524331561e-06	0.999997701847378
23	8.73389424742873e-06	1.74677884948575e-05	0.999991266105753
24	6.79360924955904e-05	0.000135872184991181	0.999932063907504
25	0.000144105060046371	0.000288210120092742	0.999855894939954
26	0.00015894654096919	0.000317893081938379	0.99984105345903
27	0.000116259659101918	0.000232519318203836	0.999883740340898
28	8.96723337983079e-05	0.000179344667596616	0.999910327666202
29	6.79694660911525e-05	0.000135938932182305	0.999932030533909
30	6.01596885542458e-05	0.000120319377108492	0.999939840311446
31	6.65917356236504e-05	0.000133183471247301	0.999933408264376
32	0.000103192015921477	0.000206384031842955	0.999896807984079
33	0.000386333898758198	0.000772667797516396	0.999613666101242
34	0.00228725320803382	0.00457450641606763	0.997712746791966
35	0.0103523809250832	0.0207047618501664	0.989647619074917
36	0.0312565248134495	0.062513049626899	0.96874347518655
37	0.0515679541323565	0.103135908264713	0.948432045867644
38	0.0521202468385109	0.104240493677022	0.947879753161489
39	0.0459746806529864	0.0919493613059728	0.954025319347014
40	0.0397024787667966	0.0794049575335931	0.960297521233203
41	0.0324118444877413	0.0648236889754827	0.967588155512259
42	0.0272418094965651	0.0544836189931302	0.972758190503435
43	0.0245430906277959	0.0490861812555918	0.975456909372204
44	0.020806502340276	0.041613004680552	0.979193497659724
45	0.019425354835471	0.0388507096709421	0.980574645164529
46	0.0242823918498002	0.0485647836996004	0.9757176081502
47	0.031573191176676	0.063146382353352	0.968426808823324
48	0.0373117071975154	0.0746234143950308	0.962688292802485
49	0.0339980130195198	0.0679960260390396	0.96600198698048
50	0.0258514819705041	0.0517029639410082	0.974148518029496
51	0.018950322051244	0.0379006441024879	0.981049677948756
52	0.0141563436144927	0.0283126872289855	0.985843656385507
53	0.0101510723720294	0.0203021447440588	0.98984892762797
54	0.00718186434286482	0.0143637286857296	0.992818135657135
55	0.00514038254562817	0.0102807650912563	0.994859617454372
56	0.00364788553258648	0.00729577106517297	0.996352114467414
57	0.00293663437944306	0.00587326875888613	0.997063365620557
58	0.00318847054752973	0.00637694109505945	0.99681152945247
59	0.00375233172625396	0.00750466345250792	0.996247668273746
60	0.00492562192706723	0.00985124385413445	0.995074378072933
61	0.00458669163506942	0.00917338327013885	0.99541330836493
62	0.0037720591760309	0.00754411835206179	0.99622794082397
63	0.0035501620225084	0.0071003240450168	0.996449837977492
64	0.00324434040162718	0.00648868080325436	0.996755659598373
65	0.00296153004380228	0.00592306008760456	0.997038469956198
66	0.00381904805827663	0.00763809611655326	0.996180951941723
67	0.00393589062790012	0.00787178125580024	0.9960641093721
68	0.00419484452618832	0.00838968905237664	0.995805155473812
69	0.00361378488391227	0.00722756976782454	0.996386215116088
70	0.00350671511542487	0.00701343023084974	0.996493284884575
71	0.00404693434989257	0.00809386869978514	0.995953065650107
72	0.00704010556991516	0.0140802111398303	0.992959894430085
73	0.0148306749174065	0.0296613498348129	0.985169325082594
74	0.0218053973120551	0.0436107946241102	0.978194602687945
75	0.0282029174662188	0.0564058349324375	0.971797082533781
76	0.0383385349904587	0.0766770699809173	0.961661465009541
77	0.05156624463244	0.10313248926488	0.94843375536756
78	0.0795631841534707	0.159126368306941	0.92043681584653
79	0.1050351603284	0.210070320656801	0.8949648396716
80	0.136102300224601	0.272204600449203	0.863897699775399
81	0.157131688735649	0.314263377471298	0.842868311264351
82	0.191228059160617	0.382456118321235	0.808771940839383
83	0.251618693504464	0.503237387008928	0.748381306495536
84	0.372157727777732	0.744315455555464	0.627842272222268
85	0.490427108255046	0.980854216510091	0.509572891744954
86	0.570384685201117	0.859230629597766	0.429615314798883
87	0.659808980195565	0.68038203960887	0.340191019804435
88	0.723935612824094	0.552128774351813	0.276064387175906
89	0.798870858613466	0.402258282773067	0.201129141386534
90	0.862058727422087	0.275882545155826	0.137941272577913
91	0.900532862609416	0.198934274781167	0.0994671373905835
92	0.919551381746613	0.160897236506773	0.0804486182533867
93	0.917589280417913	0.164821439164175	0.0824107195820874
94	0.917117907479115	0.16576418504177	0.0828820925208848
95	0.930700707193265	0.138598585613471	0.0692992928067354
96	0.95839117965094	0.083217640698121	0.0416088203490605
97	0.97241686243599	0.055166275128018	0.027583137564009
98	0.975052530512796	0.0498949389744087	0.0249474694872044
99	0.974859722220316	0.0502805555593689	0.0251402777796844
100	0.974949111325204	0.0501017773495914	0.0250508886747957
101	0.972969573470964	0.0540608530580711	0.0270304265290356
102	0.971564258054556	0.0568714838908882	0.0284357419454441
103	0.968625857549887	0.0627482849002263	0.0313741424501132
104	0.963671148115876	0.0726577037682473	0.0363288518841236
105	0.958510790846436	0.0829784183071279	0.0414892091535639
106	0.948930608844838	0.102138782310324	0.0510693911551622
107	0.938076167181927	0.123847665636147	0.0619238328180735
108	0.942474378266305	0.115051243467391	0.0575256217336953
109	0.928566207143217	0.142867585713566	0.071433792856783
110	0.917572556494976	0.164854887010048	0.0824274435050242
111	0.902615319809044	0.194769360381911	0.0973846801909556
112	0.907086518766088	0.185826962467823	0.0929134812339117
113	0.938772435241015	0.12245512951797	0.061227564758985
114	0.951308367407063	0.0973832651858738	0.0486916325929369
115	0.95813860046119	0.0837227990776204	0.0418613995388102
116	0.98284985441015	0.0343002911797014	0.0171501455898507
117	0.997727560805182	0.00454487838963579	0.00227243919481789
118	0.999642699084596	0.000714601830808579	0.000357300915404289
119	0.999784515710722	0.000430968578555813	0.000215484289277907
120	0.999803013465073	0.000393973069853378	0.000196986534926689
121	0.9997491327932	0.000501734413600406	0.000250867206800203
122	0.999663008444248	0.00067398311150294	0.00033699155575147
123	0.999513553535808	0.00097289292838487	0.000486446464192435
124	0.999550418926583	0.000899162146833466	0.000449581073416733
125	0.999766101410902	0.000467797178195007	0.000233898589097504
126	0.999974216219376	5.15675612481918e-05	2.57837806240959e-05
127	0.999964140034467	7.17199310650398e-05	3.58599655325199e-05
128	0.99998565204774	2.86959045173857e-05	1.43479522586929e-05
129	0.999965254085714	6.94918285729527e-05	3.47459142864764e-05
130	0.9999682400889	6.35198222014498e-05	3.17599111007249e-05
131	0.99989300285009	0.000213994299821896	0.000106997149910948
132	0.999824966497792	0.000350067004417025	0.000175033502208512
133	0.9993859420073	0.0012281159854016	0.000614057992700802
134	0.99857183692197	0.0028563261560606	0.0014281630780303
135	0.995507733673288	0.00898453265342383	0.00449226632671191
136	0.998851871781467	0.00229625643706663	0.00114812821853332
137	0.999867408976401	0.000265182047198447	0.000132591023599223
138	0.99855574930957	0.00288850138086132	0.00144425069043066

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	67	0.5	NOK
5% type I error level	83	0.619402985074627	NOK
10% type I error level	105	0.783582089552239	NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293461971aan1k9rkjccauiz/10tgbl1293462005.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293461971aan1k9rkjccauiz/10tgbl1293462005.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293461971aan1k9rkjccauiz/1mfe91293462005.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293461971aan1k9rkjccauiz/1mfe91293462005.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293461971aan1k9rkjccauiz/2xodu1293462005.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293461971aan1k9rkjccauiz/2xodu1293462005.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293461971aan1k9rkjccauiz/3xodu1293462005.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293461971aan1k9rkjccauiz/3xodu1293462005.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293461971aan1k9rkjccauiz/4xodu1293462005.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293461971aan1k9rkjccauiz/4xodu1293462005.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293461971aan1k9rkjccauiz/5pfuf1293462005.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293461971aan1k9rkjccauiz/5pfuf1293462005.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293461971aan1k9rkjccauiz/6pfuf1293462005.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293461971aan1k9rkjccauiz/6pfuf1293462005.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293461971aan1k9rkjccauiz/7na0o1293462005.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293461971aan1k9rkjccauiz/7na0o1293462005.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293461971aan1k9rkjccauiz/8tgbl1293462005.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293461971aan1k9rkjccauiz/8tgbl1293462005.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293461971aan1k9rkjccauiz/9tgbl1293462005.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293461971aan1k9rkjccauiz/9tgbl1293462005.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; 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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