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*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: Sat, 27 Nov 2010 13:51:50 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/27/t12908659926510i07axf12akg.htm/, Retrieved Sat, 27 Nov 2010 14:53:22 +0100

BibTeX entries for LaTeX users:

@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Nov/27/t12908659926510i07axf12akg.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 «

1579 0 2146 0 2462 0 3695 0 4831 0 5134 0 6250 0 5760 0 6249 0 2917 0 1741 0 2359 0 1511 1 2059 0 2635 0 2867 0 4403 0 5720 0 4502 0 5749 0 5627 0 2846 0 1762 0 2429 0 1169 0 2154 1 2249 0 2687 0 4359 0 5382 0 4459 0 6398 0 4596 0 3024 0 1887 0 2070 0 1351 0 2218 0 2461 1 3028 0 4784 0 4975 0 4607 0 6249 0 4809 0 3157 0 1910 0 2228 0 1594 0 2467 0 2222 0 3607 1 4685 0 4962 0 5770 0 5480 0 5000 0 3228 0 1993 0 2288 0 1580 0 2111 0 2192 0 3601 0 4665 1 4876 0 5813 0 5589 0 5331 0 3075 0 2002 0 2306 0 1507 0 1992 0 2487 0 3490 0 4647 0 5594 1 5611 0 5788 0 6204 0 3013 0 1931 0 2549 0 1504 0 2090 0 2702 0 2939 0 4500 0 6208 0 6415 1 5657 0 5964 0 3163 0 1997 0 2422 0 1376 0 2202 0 2683 0 3303 0 5202 0 5231 0 4880 0 7998 1 4977 0 3531 0 2025 0 2205 0 1442 0 2238 0 2179 0 3218 0 5139 0 4990 0 4914 0 6084 0 5672 1 3548 0 1793 0 2086 0

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	10 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

Y[t] = + 3559.40540540541 + 893.594594594594X[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)	3559.40540540541	153.055004	23.2557	0	0
X	893.594594594594	558.877855	1.5989	0.112515	0.056258

Multiple Linear Regression - Regression Statistics
Multiple R	0.145622439036970
R-squared	0.0212058947510761
Adjusted R-squared	0.0129110294523564
F-TEST (value)	2.55650863364222
F-TEST (DF numerator)	1
F-TEST (DF denominator)	118
p-value	0.112515184877864
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1612.53452664851
Sum Squared Residuals	306831576.756757

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	1579	3559.4054054054	-1980.40540540540
2	2146	3559.4054054054	-1413.40540540540
3	2462	3559.40540540540	-1097.40540540541
4	3695	3559.40540540541	135.594594594595
5	4831	3559.40540540540	1271.59459459459
6	5134	3559.40540540540	1574.59459459459
7	6250	3559.40540540541	2690.59459459459
8	5760	3559.40540540541	2200.59459459459
9	6249	3559.40540540541	2689.59459459459
10	2917	3559.40540540541	-642.405405405405
11	1741	3559.40540540540	-1818.40540540541
12	2359	3559.40540540540	-1200.40540540541
13	1511	4453	-2942
14	2059	3559.40540540540	-1500.40540540541
15	2635	3559.40540540541	-924.405405405405
16	2867	3559.40540540541	-692.405405405405
17	4403	3559.40540540541	843.594594594595
18	5720	3559.40540540541	2160.59459459459
19	4502	3559.40540540541	942.594594594595
20	5749	3559.40540540541	2189.59459459459
21	5627	3559.40540540541	2067.59459459459
22	2846	3559.40540540541	-713.405405405405
23	1762	3559.40540540540	-1797.40540540541
24	2429	3559.40540540540	-1130.40540540541
25	1169	3559.40540540541	-2390.40540540541
26	2154	4453	-2299
27	2249	3559.40540540540	-1310.40540540541
28	2687	3559.40540540541	-872.405405405405
29	4359	3559.40540540541	799.594594594595
30	5382	3559.40540540540	1822.59459459459
31	4459	3559.40540540541	899.594594594595
32	6398	3559.40540540541	2838.59459459459
33	4596	3559.40540540540	1036.59459459459
34	3024	3559.40540540541	-535.405405405405
35	1887	3559.40540540540	-1672.40540540541
36	2070	3559.40540540540	-1489.40540540541
37	1351	3559.40540540541	-2208.40540540541
38	2218	3559.40540540540	-1341.40540540541
39	2461	4453	-1992
40	3028	3559.40540540541	-531.405405405405
41	4784	3559.40540540540	1224.59459459459
42	4975	3559.40540540540	1415.59459459459
43	4607	3559.40540540540	1047.59459459459
44	6249	3559.40540540541	2689.59459459459
45	4809	3559.40540540540	1249.59459459459
46	3157	3559.40540540541	-402.405405405405
47	1910	3559.40540540540	-1649.40540540541
48	2228	3559.40540540540	-1331.40540540541
49	1594	3559.40540540540	-1965.40540540541
50	2467	3559.40540540540	-1092.40540540541
51	2222	3559.40540540540	-1337.40540540541
52	3607	4453	-846
53	4685	3559.40540540540	1125.59459459459
54	4962	3559.40540540540	1402.59459459459
55	5770	3559.40540540541	2210.59459459459
56	5480	3559.40540540541	1920.59459459459
57	5000	3559.40540540540	1440.59459459459
58	3228	3559.40540540541	-331.405405405405
59	1993	3559.40540540540	-1566.40540540541
60	2288	3559.40540540540	-1271.40540540541
61	1580	3559.40540540540	-1979.40540540541
62	2111	3559.40540540540	-1448.40540540541
63	2192	3559.40540540540	-1367.40540540541
64	3601	3559.40540540541	41.5945945945947
65	4665	4453	212.000000000000
66	4876	3559.40540540540	1316.59459459459
67	5813	3559.40540540541	2253.59459459459
68	5589	3559.40540540541	2029.59459459459
69	5331	3559.40540540540	1771.59459459459
70	3075	3559.40540540541	-484.405405405405
71	2002	3559.40540540540	-1557.40540540541
72	2306	3559.40540540540	-1253.40540540541
73	1507	3559.40540540541	-2052.40540540541
74	1992	3559.40540540540	-1567.40540540541
75	2487	3559.40540540540	-1072.40540540541
76	3490	3559.40540540541	-69.4054054054053
77	4647	3559.40540540540	1087.59459459459
78	5594	4453	1141
79	5611	3559.40540540541	2051.59459459459
80	5788	3559.40540540541	2228.59459459459
81	6204	3559.40540540541	2644.59459459459
82	3013	3559.40540540541	-546.405405405405
83	1931	3559.40540540540	-1628.40540540541
84	2549	3559.40540540541	-1010.40540540541
85	1504	3559.40540540541	-2055.40540540541
86	2090	3559.40540540540	-1469.40540540541
87	2702	3559.40540540541	-857.405405405405
88	2939	3559.40540540541	-620.405405405405
89	4500	3559.40540540541	940.594594594595
90	6208	3559.40540540541	2648.59459459459
91	6415	4453	1962
92	5657	3559.40540540541	2097.59459459459
93	5964	3559.40540540541	2404.59459459459
94	3163	3559.40540540541	-396.405405405405
95	1997	3559.40540540540	-1562.40540540541
96	2422	3559.40540540540	-1137.40540540541
97	1376	3559.40540540541	-2183.40540540541
98	2202	3559.40540540540	-1357.40540540541
99	2683	3559.40540540541	-876.405405405405
100	3303	3559.40540540541	-256.405405405405
101	5202	3559.40540540540	1642.59459459459
102	5231	3559.40540540540	1671.59459459459
103	4880	3559.40540540540	1320.59459459459
104	7998	4453	3545
105	4977	3559.40540540540	1417.59459459459
106	3531	3559.40540540541	-28.4054054054053
107	2025	3559.40540540540	-1534.40540540541
108	2205	3559.40540540540	-1354.40540540541
109	1442	3559.40540540541	-2117.40540540541
110	2238	3559.40540540540	-1321.40540540541
111	2179	3559.40540540540	-1380.40540540541
112	3218	3559.40540540541	-341.405405405405
113	5139	3559.40540540540	1579.59459459459
114	4990	3559.40540540540	1430.59459459459
115	4914	3559.40540540540	1354.59459459459
116	6084	3559.40540540541	2524.59459459459
117	5672	4453	1219
118	3548	3559.40540540541	-11.4054054054053
119	1793	3559.40540540540	-1766.40540540541
120	2086	3559.40540540540	-1473.40540540541

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
5	0.539377372347707	0.921245255304586	0.460622627652293
6	0.60428684136613	0.79142631726774	0.39571315863387
7	0.772870687310764	0.454258625378473	0.227129312689236
8	0.785205296890918	0.429589406218164	0.214794703109082
9	0.82285069029481	0.354298619410381	0.177149309705190
10	0.783380159216758	0.433239681566484	0.216619840783242
11	0.821371674194893	0.357256651610215	0.178628325805107
12	0.799492809690753	0.401014380618495	0.200507190309247
13	0.757859949552731	0.484280100894537	0.242140050447269
14	0.75110831872541	0.49778336254918	0.24889168127459
15	0.703464400311323	0.593071199377354	0.296535599688677
16	0.641474397575283	0.717051204849434	0.358525602424717
17	0.585761892109765	0.82847621578047	0.414238107890235
18	0.633493442868743	0.733013114262514	0.366506557131257
19	0.578672293168481	0.842655413663039	0.421327706831519
20	0.615075419537495	0.76984916092501	0.384924580462505
21	0.63092740972851	0.73814518054298	0.36907259027149
22	0.588700409997802	0.822599180004396	0.411299590002198
23	0.623928859444163	0.752142281111674	0.376071140555837
24	0.599095632147931	0.801808735704138	0.400904367852069
25	0.67911646200187	0.641767075996261	0.320883537998131
26	0.663856776334902	0.672286447330197	0.336143223665098
27	0.644932592997377	0.710134814005245	0.355067407002623
28	0.601968506758813	0.796062986482374	0.398031493241187
29	0.556080459745935	0.88783908050813	0.443919540254065
30	0.572409835682349	0.855180328635303	0.427590164317651
31	0.528691822892864	0.942616354214272	0.471308177107136
32	0.643940719528894	0.712118560942212	0.356059280471106
33	0.605989636570285	0.788020726859431	0.394010363429715
34	0.558321568725133	0.883356862549735	0.441678431274867
35	0.572142730285961	0.855714539428078	0.427857269714039
36	0.569332705783754	0.861334588432493	0.430667294216246
37	0.623077203843115	0.75384559231377	0.376922796156885
38	0.606912955823023	0.786174088353954	0.393087044176977
39	0.618776350311813	0.762447299376374	0.381223649688187
40	0.570088342676904	0.859823314646192	0.429911657323096
41	0.548773486535572	0.902453026928855	0.451226513464428
42	0.537899045338056	0.924201909323887	0.462100954661944
43	0.50629213787446	0.98741572425108	0.49370786212554
44	0.607246876309098	0.785506247381804	0.392753123690902
45	0.585244579111929	0.829510841776143	0.414755420888071
46	0.536396325905693	0.927207348188615	0.463603674094308
47	0.545910746944334	0.908178506111333	0.454089253055666
48	0.532871542213808	0.934256915572384	0.467128457786192
49	0.564842693021393	0.870314613957214	0.435157306978607
50	0.537712086101019	0.924575827797962	0.462287913898981
51	0.523117934485476	0.953764131029048	0.476882065514524
52	0.540251279507454	0.919497440985093	0.459748720492546
53	0.515104021537753	0.969791956924495	0.484895978462247
54	0.505034783852826	0.989930432294347	0.494965216147174
55	0.558176170992368	0.883647658015264	0.441823829007632
56	0.584868621267326	0.830262757465349	0.415131378732674
57	0.577340957940296	0.845318084119407	0.422659042059704
58	0.527847144917119	0.944305710165761	0.472152855082881
59	0.529295008551535	0.94140998289693	0.470704991448465
60	0.512035564181562	0.975928871636876	0.487964435818438
61	0.544635093781997	0.910729812436006	0.455364906218003
62	0.537611006217464	0.924777987565071	0.462388993782536
63	0.525726930507313	0.948546138985375	0.474273069492687
64	0.472946201007433	0.945892402014867	0.527053798992567
65	0.48910658061322	0.97821316122644	0.51089341938678
66	0.473795724357078	0.947591448714157	0.526204275642922
67	0.532135448810771	0.935729102378457	0.467864551189229
68	0.570775346834766	0.858449306330467	0.429224653165233
69	0.589211731723462	0.821576536553076	0.410788268276538
70	0.540998960181094	0.918002079637811	0.459001039818906
71	0.53895213563981	0.92209572872038	0.46104786436019
72	0.518619183798245	0.96276163240351	0.481380816201755
73	0.556874572373497	0.886250855253006	0.443125427626503
74	0.557572130851967	0.884855738296066	0.442427869148033
75	0.529631410026264	0.940737179947472	0.470368589973736
76	0.475056443783657	0.950112887567315	0.524943556216343
77	0.446193727989762	0.892387455979524	0.553806272010238
78	0.452861492294449	0.905722984588898	0.547138507705551
79	0.491788791587641	0.983577583175281	0.508211208412359
80	0.551972299905105	0.89605540018979	0.448027700094895
81	0.663253618125037	0.673492763749927	0.336746381874963
82	0.614290534774079	0.771418930451843	0.385709465225921
83	0.613630857729198	0.772738284541604	0.386369142270802
84	0.578063139357664	0.843873721284672	0.421936860642336
85	0.616212361992126	0.767575276015748	0.383787638007874
86	0.609512085202908	0.780975829594184	0.390487914797092
87	0.569583426985726	0.860833146028549	0.430416573014274
88	0.520214785435949	0.959570429128102	0.479785214564051
89	0.479602363497096	0.959204726994193	0.520397636502903
90	0.594248159473679	0.811503681052642	0.405751840526321
91	0.580199809078393	0.839600381843214	0.419800190921607
92	0.635486817486701	0.729026365026598	0.364513182513299
93	0.733379912393756	0.533240175212488	0.266620087606244
94	0.677632096623514	0.644735806752971	0.322367903376486
95	0.666255499977132	0.667489000045736	0.333744500022868
96	0.629601349165579	0.740797301668842	0.370398650834421
97	0.683092107960926	0.633815784078147	0.316907892039074
98	0.667471409059218	0.665057181881564	0.332528590940782
99	0.623280680173759	0.753438639652482	0.376719319826241
100	0.554672521808984	0.890654956382032	0.445327478191016
101	0.557015062882748	0.885969874234503	0.442984937117252
102	0.571050438698396	0.857899122603208	0.428949561301604
103	0.559370158445352	0.881259683109295	0.440629841554648
104	0.611698513996306	0.776602972007388	0.388301486003694
105	0.618074401267422	0.763851197465156	0.381925598732578
106	0.534692531439566	0.930614937120869	0.465307468560434
107	0.500400299828722	0.999199400342555	0.499599700171277
108	0.455528199826782	0.911056399653564	0.544471800173218
109	0.516377816689874	0.967244366620251	0.483622183310126
110	0.494285564768084	0.988571129536168	0.505714435231916
111	0.500279721955381	0.999440556089238	0.499720278044619
112	0.408704700600983	0.817409401201967	0.591295299399017
113	0.344771187434488	0.689542374868977	0.655228812565512
114	0.278851029169539	0.557702058339078	0.721148970830461
115	0.223761423588485	0.44752284717697	0.776238576411515

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	0	0	OK
10% type I error level	0	0	OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/27/t12908659926510i07axf12akg/10vgdt1290865899.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t12908659926510i07axf12akg/10vgdt1290865899.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t12908659926510i07axf12akg/16xg01290865899.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t12908659926510i07axf12akg/16xg01290865899.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t12908659926510i07axf12akg/2hpx21290865899.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t12908659926510i07axf12akg/2hpx21290865899.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t12908659926510i07axf12akg/3hpx21290865899.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t12908659926510i07axf12akg/3hpx21290865899.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t12908659926510i07axf12akg/4hpx21290865899.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t12908659926510i07axf12akg/4hpx21290865899.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t12908659926510i07axf12akg/5rye51290865899.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t12908659926510i07axf12akg/5rye51290865899.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t12908659926510i07axf12akg/6rye51290865899.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t12908659926510i07axf12akg/6rye51290865899.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t12908659926510i07axf12akg/727eq1290865899.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t12908659926510i07axf12akg/727eq1290865899.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t12908659926510i07axf12akg/827eq1290865899.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t12908659926510i07axf12akg/827eq1290865899.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t12908659926510i07axf12akg/9vgdt1290865899.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t12908659926510i07axf12akg/9vgdt1290865899.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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