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

Title produced by software: Multiple Regression

Date of computation: Mon, 06 Dec 2010 16:31:24 +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/06/t1291653162ppnyrhtj7xcrns2.htm/, Retrieved Mon, 06 Dec 2010 17:32:52 +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/06/t1291653162ppnyrhtj7xcrns2.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 «

3484,74 13830,14 9349,44 7977 -5,6 6 1 3,17 3411,13 14153,22 9327,78 8241 -6,2 3 1 3,17 3288,18 15418,03 9753,63 8444 -7,1 2 1,2 3,36 3280,37 16666,97 10443,5 8490 -1,4 2 1,2 3,11 3173,95 16505,21 10853,87 8388 -0,1 2 0,8 3,11 3165,26 17135,96 10704,02 8099 -0,9 -8 0,7 3,57 3092,71 18033,25 11052,23 7984 0 0 0,7 4,04 3053,05 17671 10935,47 7786 0,1 -2 0,9 4,21 3181,96 17544,22 10714,03 8086 2,6 3 1,2 4,36 2999,93 17677,9 10394,48 9315 6 5 1,3 4,75 3249,57 18470,97 10817,9 9113 6,4 8 1,5 4,43 3210,52 18409,96 11251,2 9023 8,6 8 1,9 4,7 3030,29 18941,6 11281,26 9026 6,4 9 1,8 4,81 2803,47 19685,53 10539,68 9787 7,7 11 1,9 5,01 2767,63 19834,71 10483,39 9536 9,2 13 2,2 5 2882,6 19598,93 10947,43 9490 8,6 12 2,1 4,81 2863,36 17039,97 10580,27 9736 7,4 13 2,2 5,11 2897,06 16969,28 10582,92 9694 8,6 15 2,7 5,1 3012,61 16973,38 10654,41 9647 6,2 13 2,8 5,11 3142,95 16329,89 11014,51 9753 6 16 2,9 5,21 3032,93 16153,34 10967,87 10070 6,6 10 3,4 5,21 3045,78 15311,7 10433,56 10137 5,1 14 3 5,21 3 etc...

Output produced by software:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	9 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

BEL_20[t] = -1471.55250880347 + 0.0954355312113703Nikkei[t] + 0.369163039198861DJ_Indust[t] + 0.0238744986798515Goudprijs[t] -10.6388338055077Conjunct_Seizoenzuiver[t] + 13.4082779421853Cons_vertrouw[t] + 36.2029927235425Alg_consumptie_index_BE[t] -278.729546599587Gem_rente_kasbon_5j[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)	-1471.55250880347	334.820996	-4.395	2.4e-05	1.2e-05
Nikkei	0.0954355312113703	0.01489	6.4094	0	0
DJ_Indust	0.369163039198861	0.034498	10.7009	0	0
Goudprijs	0.0238744986798515	0.008227	2.9019	0.004391	0.002195
Conjunct_Seizoenzuiver	-10.6388338055077	6.686008	-1.5912	0.114109	0.057054
Cons_vertrouw	13.4082779421853	6.24542	2.1469	0.033748	0.016874
Alg_consumptie_index_BE	36.2029927235425	22.797387	1.588	0.114826	0.057413
Gem_rente_kasbon_5j	-278.729546599587	50.979851	-5.4674	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.941641426248589
R-squared	0.886688575627476
Adjusted R-squared	0.880291962961286
F-TEST (value)	138.618456658170
F-TEST (DF numerator)	7
F-TEST (DF denominator)	124
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	260.514793987770
Sum Squared Residuals	8415626.77792477

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	3484.74	2782.9062769675	701.8337230325
2	3411.13	2778.20485107048	632.925148929522
3	3288.18	3011.41592595034	276.764074049664
4	3280.37	3395.42294505136	-115.052945051356
5	3173.95	3500.73185001672	-326.781850016719
6	3165.26	3241.30139670025	-76.0413967002547
7	3092.71	3419.42382524288	-326.713825242876
8	3053.05	3268.99781322394	-215.947813223945
9	3181.96	3191.80915380501	-9.84915380500932
10	2999.93	3001.50298236305	-1.57298236304665
11	3249.57	3361.08175818603	-111.511758186028
12	3210.52	3428.88766156591	-218.367661565914
13	3030.29	3493.32683474948	-463.036834749478
14	2803.47	3269.58921825948	-466.119218259476
15	2767.63	3281.56010261961	-513.930102619609
16	2882.6	3471.57983976385	-588.979839763845
17	2863.36	3043.87167181946	-180.511671819459
18	2897.06	3072.03963437298	-174.979634372979
19	3012.61	3097.24993334053	-84.6399333405251
20	3142.95	3189.40437583695	-46.4543758369476
21	3032.93	3094.17421316021	-61.2442131602135
22	3045.78	2873.31410599627	172.465894003733
23	3110.52	2952.50485978835	158.015140211654
24	3013.24	3039.72840480046	-26.4884048004578
25	2987.1	2996.52224692528	-9.42224692528093
26	2995.55	2943.91454449975	51.6354555002539
27	2833.18	2666.48140967185	166.698590328153
28	2848.96	2826.51939823056	22.4406017694427
29	2794.83	2987.19462930827	-192.364629308267
30	2845.26	3009.92204066049	-164.662040660487
31	2915.02	2810.96679487084	104.053205129165
32	2892.63	2663.17527363360	229.454726366404
33	2604.42	2106.36423852480	498.055761475196
34	2641.65	2171.90268293308	469.747317066924
35	2659.81	2369.79939967285	290.010600327151
36	2638.53	2451.67492933541	186.855070664595
37	2720.25	2506.44299736808	213.807002631916
38	2745.88	2442.06806342782	303.81193657218
39	2735.7	2702.38180906088	33.318190939116
40	2811.7	2508.4193965516	303.2806034484
41	2799.43	2504.98174463288	294.448255367116
42	2555.28	2233.7353243904	321.544675609602
43	2304.98	1908.80279944558	396.177200554424
44	2214.95	1945.60573095747	269.344269042525
45	2065.81	1781.77926015096	284.030739849039
46	1940.49	1698.34022526250	242.149774737498
47	2042	1877.29997118634	164.700028813658
48	1995.37	1815.57251427901	179.797485720992
49	1946.81	1888.86428465092	57.9457153490768
50	1765.9	1715.18955333380	50.7104466662039
51	1635.25	1678.39048532208	-43.1404853220774
52	1833.42	1806.95305272367	26.4669472763262
53	1910.43	2069.59072607337	-159.160726073366
54	1959.67	2429.16326929088	-469.493269290875
55	1969.6	2385.04093186342	-415.440931863422
56	2061.41	2348.56867776170	-287.158677761696
57	2093.48	2554.86041680655	-461.380416806548
58	2120.88	2419.67942614705	-298.799426147051
59	2174.56	2504.58264818782	-330.022648187820
60	2196.72	2630.18922282629	-433.46922282629
61	2350.44	2839.07854317997	-488.638543179968
62	2440.25	2845.13567181262	-404.885671812615
63	2408.64	2820.44757767273	-411.807577672728
64	2472.81	2950.71515592222	-477.905155922219
65	2407.6	2683.68606159096	-276.086061590964
66	2454.62	2901.20733260169	-446.587332601692
67	2448.05	2679.27996319084	-231.229963190844
68	2497.84	2678.89964407652	-181.059644076521
69	2645.64	2739.8367105046	-94.196710504604
70	2756.76	2626.74520724389	130.014792756113
71	2849.27	2787.08769118939	62.1823088106102
72	2921.44	2923.54360488827	-2.10360488827106
73	2981.85	2913.08507269532	68.7649273046758
74	3080.58	3114.46573186389	-33.8857318638916
75	3106.22	3167.1284348135	-60.9084348135003
76	3119.31	2965.75729212929	153.552707870711
77	3061.26	2900.64980171626	160.610198283741
78	3097.31	3026.99739807435	70.3126019256458
79	3161.69	3118.26656397278	43.4234360272214
80	3257.16	3155.36489682314	101.795103176863
81	3277.01	3151.04445248029	125.965547519714
82	3295.32	3161.33003187036	133.989968129645
83	3363.99	3342.80352269739	21.1864773026068
84	3494.17	3551.49276747278	-57.3227674727801
85	3667.03	3644.79645752556	22.2335424744379
86	3813.06	3691.5772318172	121.482768182800
87	3917.96	3667.16351586527	250.796484134733
88	3895.51	3745.20465282433	150.305347175671
89	3801.06	3655.53164839026	145.528351609735
90	3570.12	3391.76836134461	178.351638655387
91	3701.61	3385.78426232281	315.825737677191
92	3862.27	3527.54239550801	334.727604491992
93	3970.1	3648.06199939585	322.038000604154
94	4138.52	3894.07420353413	244.445796465871
95	4199.75	3971.26211885784	228.487881142157
96	4290.89	3965.84238011712	325.047619882884
97	4443.91	4138.07831343244	305.831686567559
98	4502.64	4204.27990036321	298.360099636787
99	4356.98	3986.66242748394	370.317572516063
100	4591.27	4229.92187701452	361.348122985484
101	4696.96	4459.37535235478	237.58464764522
102	4621.4	4394.54378002604	226.856219973956
103	4562.84	4400.90134647826	161.938653521738
104	4202.52	4114.35597350577	88.164026494235
105	4296.49	4262.63786482052	33.8521351794845
106	4435.23	4526.11710050783	-90.8871005078348
107	4105.18	4114.62359388622	-9.4435938862209
108	4116.68	4287.37207046046	-170.692070460459
109	3844.49	3777.55590824415	66.9340917558457
110	3720.98	3824.85307235633	-103.873072356332
111	3674.4	3768.15519271046	-93.7551927104564
112	3857.62	3977.54863426004	-119.928634260039
113	3801.06	4003.90475196433	-202.844751964330
114	3504.37	3598.54192114657	-94.1719211465738
115	3032.6	3125.94758607654	-93.3475860765388
116	3047.03	3168.46584407277	-121.435844072772
117	2962.34	3127.76341408423	-165.423414084230
118	2197.82	2084.53038087081	113.289619129190
119	2014.45	1877.3927155733	137.057284426701
120	1862.83	1914.68332931617	-51.85332931617
121	1905.41	1936.5534971336	-31.1434971335989
122	1810.99	1720.49172292983	90.4982770701676
123	1670.07	1592.63583850985	77.434161490152
124	1864.44	1933.83156176222	-69.3915617622216
125	2052.02	2105.87220617235	-53.8522061723506
126	2029.6	2151.18336073787	-121.583360737874
127	2070.83	2134.4529743431	-63.6229743431011
128	2293.41	2533.19956917905	-239.78956917905
129	2443.27	2609.58390893535	-166.313908935353
130	2513.17	2634.04289735311	-120.872897353108
131	2466.92	2824.88267013467	-357.962670134671
132	2502.66	2904.13932919437	-401.479329194367

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
11	0.0323997973529295	0.0647995947058591	0.96760020264707
12	0.0152863264020716	0.0305726528041432	0.984713673597928
13	0.0057931028295234	0.0115862056590468	0.994206897170477
14	0.0149237053522376	0.0298474107044752	0.985076294647762
15	0.0183047728546225	0.036609545709245	0.981695227145377
16	0.0142997800608265	0.0285995601216531	0.985700219939173
17	0.0445191450343003	0.0890382900686007	0.9554808549657
18	0.0395729103560355	0.079145820712071	0.960427089643965
19	0.0293433678596913	0.0586867357193827	0.970656632140309
20	0.0243308205282003	0.0486616410564005	0.9756691794718
21	0.0174315822609719	0.0348631645219438	0.982568417739028
22	0.0100580981388315	0.0201161962776630	0.989941901861169
23	0.00555452086107098	0.0111090417221420	0.994445479138929
24	0.0085884671821004	0.0171769343642008	0.9914115328179
25	0.0175702265808783	0.0351404531617566	0.982429773419122
26	0.0190867112256686	0.0381734224513372	0.980913288774331
27	0.040983855088241	0.081967710176482	0.959016144911759
28	0.0738656381311821	0.147731276262364	0.926134361868818
29	0.0852814512733487	0.170562902546697	0.914718548726651
30	0.0795956615649018	0.159191323129804	0.920404338435098
31	0.0618332931997419	0.123666586399484	0.938166706800258
32	0.0432863407645455	0.086572681529091	0.956713659235454
33	0.0468844897445634	0.0937689794891268	0.953115510255437
34	0.0399177469397642	0.0798354938795285	0.960082253060236
35	0.0334056195080551	0.0668112390161102	0.966594380491945
36	0.0244593597061334	0.0489187194122668	0.975540640293867
37	0.0185120084008586	0.0370240168017172	0.981487991599141
38	0.0191343857746929	0.0382687715493858	0.980865614225307
39	0.0138170208347216	0.0276340416694432	0.986182979165278
40	0.0157039067489941	0.0314078134979882	0.984296093251006
41	0.0117229977489005	0.0234459954978009	0.9882770022511
42	0.0127973403975877	0.0255946807951754	0.987202659602412
43	0.0462388817752009	0.0924777635504018	0.953761118224799
44	0.111904818028657	0.223809636057314	0.888095181971343
45	0.179435367514818	0.358870735029636	0.820564632485182
46	0.298014518338853	0.596029036677706	0.701985481661147
47	0.40020604897569	0.80041209795138	0.59979395102431
48	0.434650696455188	0.869301392910377	0.565349303544812
49	0.450983314569762	0.901966629139525	0.549016685430238
50	0.414873421083487	0.829746842166974	0.585126578916513
51	0.42769611237162	0.85539222474324	0.57230388762838
52	0.660397133223179	0.679205733553642	0.339602866776821
53	0.770506991615273	0.458986016769453	0.229493008384727
54	0.883201437800972	0.233597124398056	0.116798562199028
55	0.915391216270125	0.169217567459751	0.0846087837298755
56	0.902879798630227	0.194240402739545	0.0971202013697726
57	0.914623813432267	0.170752373135467	0.0853761865677333
58	0.92724853037646	0.145502939247079	0.0727514696235395
59	0.918582560689141	0.162834878621718	0.081417439310859
60	0.92007472187445	0.159850556251098	0.0799252781255492
61	0.934684867081114	0.130630265837772	0.0653151329188861
62	0.931747433823418	0.136505132353165	0.0682525661765824
63	0.954696691251993	0.0906066174960132	0.0453033087480066
64	0.99181097093703	0.0163780581259405	0.00818902906297025
65	0.995975290186268	0.0080494196274635	0.00402470981373175
66	0.999285333466716	0.00142933306656857	0.000714666533284283
67	0.99981891243832	0.000362175123360832	0.000181087561680416
68	0.999932643917329	0.000134712165341802	6.73560826709012e-05
69	0.999975022882783	4.99542344347484e-05	2.49771172173742e-05
70	0.999992098365133	1.58032697344862e-05	7.90163486724312e-06
71	0.999995992629006	8.0147419883021e-06	4.00737099415105e-06
72	0.999996771851818	6.45629636470691e-06	3.22814818235346e-06
73	0.999997391447691	5.21710461742972e-06	2.60855230871486e-06
74	0.999997809315034	4.38136993116523e-06	2.19068496558262e-06
75	0.999998418572012	3.16285597597775e-06	1.58142798798887e-06
76	0.999998661375182	2.67724963630439e-06	1.33862481815219e-06
77	0.999998895676051	2.20864789754283e-06	1.10432394877142e-06
78	0.999998976512405	2.04697519069756e-06	1.02348759534878e-06
79	0.999998702443574	2.59511285117537e-06	1.29755642558768e-06
80	0.99999849470719	3.01058562045257e-06	1.50529281022628e-06
81	0.999998547563251	2.90487349773240e-06	1.45243674886620e-06
82	0.999998516772241	2.96645551698758e-06	1.48322775849379e-06
83	0.999998320580046	3.3588399073991e-06	1.67941995369955e-06
84	0.999999551975966	8.96048068353057e-07	4.48024034176528e-07
85	0.999999876711967	2.46576065540835e-07	1.23288032770418e-07
86	0.999999934008467	1.31983066215823e-07	6.59915331079114e-08
87	0.999999924119762	1.51760475101662e-07	7.58802375508312e-08
88	0.99999996840833	6.31833410290195e-08	3.15916705145098e-08
89	0.999999973725554	5.25488928073461e-08	2.62744464036730e-08
90	0.999999983818538	3.23629239456539e-08	1.61814619728270e-08
91	0.9999999670528	6.58943995559013e-08	3.29471997779507e-08
92	0.999999932474177	1.35051645973568e-07	6.75258229867841e-08
93	0.999999873953766	2.52092468638194e-07	1.26046234319097e-07
94	0.999999891815646	2.16368708985461e-07	1.08184354492731e-07
95	0.99999983788189	3.24236222101166e-07	1.62118111050583e-07
96	0.999999695180636	6.09638726899165e-07	3.04819363449582e-07
97	0.999999460816466	1.07836706715209e-06	5.39183533576043e-07
98	0.999998632535137	2.73492972584283e-06	1.36746486292141e-06
99	0.999996614633194	6.77073361146977e-06	3.38536680573488e-06
100	0.99999330885259	1.33822948188023e-05	6.69114740940116e-06
101	0.99998665195061	2.66960987830777e-05	1.33480493915389e-05
102	0.999975180202826	4.96395943488386e-05	2.48197971744193e-05
103	0.999958199961569	8.36000768627274e-05	4.18000384313637e-05
104	0.999915598799105	0.000168802401790387	8.44012008951936e-05
105	0.999876672647504	0.000246654704991923	0.000123327352495962
106	0.999795378277164	0.000409243445671717	0.000204621722835859
107	0.99978438068514	0.000431238629720175	0.000215619314860088
108	0.999609741649499	0.000780516701002793	0.000390258350501396
109	0.999970517552914	5.89648941717101e-05	2.94824470858551e-05
110	0.999975905570835	4.81888583306757e-05	2.40944291653379e-05
111	0.9999516839502	9.66320995995522e-05	4.83160497997761e-05
112	0.999948156073069	0.000103687853862716	5.18439269313579e-05
113	0.999924755863848	0.000150488272303158	7.52441361515789e-05
114	0.99998479006817	3.04198636579714e-05	1.52099318289857e-05
115	0.999936433633428	0.000127132733144618	6.35663665723088e-05
116	0.999743598292943	0.000512803414113466	0.000256401707056733
117	0.999483164503985	0.00103367099203054	0.000516835496015269
118	0.997972044780435	0.00405591043913022	0.00202795521956511
119	0.999485588313663	0.00102882337267464	0.000514411686337322
120	0.997292038061522	0.0054159238769559	0.00270796193847795
121	0.986326697448695	0.027346605102609	0.0136733025513045

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	56	0.504504504504504	NOK
5% type I error level	77	0.693693693693694	NOK
10% type I error level	88	0.792792792792793	NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291653162ppnyrhtj7xcrns2/10ziq11291653073.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291653162ppnyrhtj7xcrns2/10ziq11291653073.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291653162ppnyrhtj7xcrns2/1szs71291653073.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291653162ppnyrhtj7xcrns2/1szs71291653073.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291653162ppnyrhtj7xcrns2/2lras1291653073.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291653162ppnyrhtj7xcrns2/2lras1291653073.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291653162ppnyrhtj7xcrns2/3lras1291653073.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291653162ppnyrhtj7xcrns2/3lras1291653073.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291653162ppnyrhtj7xcrns2/4lras1291653073.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291653162ppnyrhtj7xcrns2/4lras1291653073.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291653162ppnyrhtj7xcrns2/5e09d1291653073.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291653162ppnyrhtj7xcrns2/5e09d1291653073.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291653162ppnyrhtj7xcrns2/6e09d1291653073.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291653162ppnyrhtj7xcrns2/6e09d1291653073.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291653162ppnyrhtj7xcrns2/7798y1291653073.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291653162ppnyrhtj7xcrns2/7798y1291653073.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291653162ppnyrhtj7xcrns2/8798y1291653073.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291653162ppnyrhtj7xcrns2/8798y1291653073.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291653162ppnyrhtj7xcrns2/9ziq11291653073.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/06/t1291653162ppnyrhtj7xcrns2/9ziq11291653073.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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