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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 14:44:38 +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/t1290869466cro4oybhb4zmzj3.htm/, Retrieved Sat, 27 Nov 2010 15:51:16 +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/t1290869466cro4oybhb4zmzj3.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 «

4831 0 3695 2462 2146 1579 5134 0 4831 3695 2462 2146 6250 0 5134 4831 3695 2462 5760 0 6250 5134 4831 3695 6249 0 5760 6250 5134 4831 2917 0 6249 5760 6250 5134 1741 0 2917 6249 5760 6250 2359 0 1741 2917 6249 5760 1511 1 2359 1741 2917 6249 2059 0 1511 2359 1741 2917 2635 0 2059 1511 2359 1741 2867 0 2635 2059 1511 2359 4403 0 2867 2635 2059 1511 5720 0 4403 2867 2635 2059 4502 0 5720 4403 2867 2635 5749 0 4502 5720 4403 2867 5627 0 5749 4502 5720 4403 2846 0 5627 5749 4502 5720 1762 0 2846 5627 5749 4502 2429 0 1762 2846 5627 5749 1169 0 2429 1762 2846 5627 2154 1 1169 2429 1762 2846 2249 0 2154 1169 2429 1762 2687 0 2249 2154 1169 2429 4359 0 2687 2249 2154 1169 5382 0 4359 2687 2249 2154 4459 0 5382 4359 2687 2249 6398 0 4459 5382 4359 2687 4596 0 6398 4459 5382 4359 3024 0 4596 6398 4459 5382 1887 0 3024 4596 6398 4459 2070 0 1887 3024 4596 6398 1351 0 2070 1887 3024 4596 2218 0 1351 2070 1887 3024 2461 1 2218 1351 2070 1887 3028 0 2461 2218 1351 2070 4784 0 3028 2461 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	'George Udny Yule' @ 72.249.76.132

Multiple Linear Regression - Estimated Regression Equation

Y[t] = + 2965.25393399467 + 528.345055465305X[t] -0.298382874958045Y1[t] + 0.104830390324839Y2[t] + 0.343772803301765Y3[t] + 0.0254522282235195Y4[t] + 1535.27129445461M1[t] + 2367.41761862446M2[t] + 2113.11253810597M3[t] + 2278.58440522865M4[t] + 1628.66643041343M5[t] -900.645928591427M6[t] -3025.6406474945M7[t] -2570.61346255146M8[t] -2393.54530684769M9[t] -1507.04339002879M10[t] -1056.65250730958M11[t] + 1.80202092207090t + 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)	2965.25393399467	397.59171	7.458	0	0
X	528.345055465305	123.256157	4.2866	4.2e-05	2.1e-05
Y1	-0.298382874958045	0.092271	-3.2338	0.001665	0.000833
Y2	0.104830390324839	0.091343	1.1477	0.253905	0.126953
Y3	0.343772803301765	0.09124	3.7678	0.000281	0.000141
Y4	0.0254522282235195	0.092713	0.2745	0.784259	0.392129
M1	1535.27129445461	211.525132	7.2581	0	0
M2	2367.41761862446	320.263045	7.3921	0	0
M3	2113.11253810597	470.469339	4.4915	1.9e-05	1e-05
M4	2278.58440522865	580.70304	3.9238	0.000162	8.1e-05
M5	1628.66643041343	674.185732	2.4158	0.017555	0.008778
M6	-900.645928591427	712.944589	-1.2633	0.209487	0.104744
M7	-3025.6406474945	686.72077	-4.4059	2.7e-05	1.3e-05
M8	-2570.61346255146	616.133527	-4.1722	6.5e-05	3.3e-05
M9	-2393.54530684769	399.431255	-5.9924	0	0
M10	-1507.04339002879	219.894571	-6.8535	0	0
M11	-1056.65250730958	188.321523	-5.6109	0	0
t	1.80202092207090	1.044326	1.7255	0.087583	0.043792

Multiple Linear Regression - Regression Statistics
Multiple R	0.980496299065626
R-squared	0.961372992481389
Adjusted R-squared	0.954672389136324
F-TEST (value)	143.475586148434
F-TEST (DF numerator)	17
F-TEST (DF denominator)	98
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	347.035679883005
Sum Squared Residuals	11802508.7849622

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	4831	4435.82045163164	395.179548368358
2	5134	5183.12534128784	-49.1253412878383
3	6250	5391.21436457787	858.785635422132
4	5760	5679.16507438827	80.8349256117315
5	6249	5427.32433548944	821.675664510558
6	2917	3093.9003539295	-176.900353929499
7	1741	1876.13746925713	-135.137469257125
8	2359	2490.20338449557	-131.203384495573
9	1511	1756.73261984046	-245.732619840460
10	2059	1945.42172017765	113.578279822347
11	2635	2327.72440939609	307.275590603906
12	2867	2995.96759539216	-128.967595392162
13	4403	4691.0023952815	-288.002395281504
14	5720	5302.91625076154	417.083749238463
15	4502	4912.87819820708	-410.878198207081
16	5749	6115.58399482791	-366.583994827911
17	5627	5459.54458494618	167.455415053817
18	2846	2713.96576449217	132.034235507825
19	1762	1805.47040589092	-43.470405890918
20	2429	2284.01197930909	144.988020690912
21	1169	1191.08729740031	-22.0872974003102
22	2154	2610.18821793167	-456.188217931672
23	2249	2309.74888687266	-60.7488868726552
24	2687	3026.93788051812	-339.937880518121
25	4359	4749.82478743464	-390.82478743464
26	5382	5188.52153767282	193.478462327175
27	4459	4959.03965914486	-500.039659144862
28	6398	6094.89863316065	303.101366839349
29	4596	5165.69553782146	-569.695537821463
30	3024	3087.87259927807	-63.872599278065
31	1887	1887.91647631756	-0.916476317562584
32	2070	1949.08691639495	120.913083605051
33	1351	1367.88511105497	-16.8851110549693
34	2218	2059.02971719874	158.970282801261
35	2461	2739.46791258723	-278.467912587227
36	3028	3045.44340734133	-17.4434073413343
37	4784	4718.55828583566	65.4417141643435
38	4975	5193.58900688756	-218.589006887556
39	4607	5269.28105451498	-662.281054514983
40	6249	6184.47890109697	64.5210989030287
41	4809	5118.19540107432	-309.195401074316
42	3157	3070.84088782014	86.15911217986
43	1910	1844.72946023730	65.2705397626976
44	2228	2047.22202834694	180.777971653060
45	1594	1395.91907430466	198.080925695335
46	2467	2036.00205214978	430.997947850222
47	2222	2238.82506134197	-16.8250613419717
48	3607	3780.387231439	-173.387231438997
49	4685	4634.14870849262	50.8512915073828
50	4962	5229.62586340987	-267.62586340987
51	5770	5477.36744487843	292.63255512157
52	5480	5838.42440612594	-358.424406125936
53	5000	5484.20500989264	-484.20500989264
54	3228	3354.33633088125	-126.336330881250
55	1993	1630.43078741707	362.569212582929
56	2288	2097.61130043009	190.388699569913
57	1580	1437.61051989411	142.389480105888
58	2111	2098.43373776145	12.5662622385519
59	2192	2387.94489356800	-195.944893567997
60	3601	3242.01260877882	358.987391221176
61	4665	5060.02395139222	-395.023951392222
62	4876	5237.21461228531	-361.214612285307
63	5813	5519.72981171666	293.27018828334
64	5589	5831.17461056428	-242.174610564277
65	5331	5447.73972872261	-116.739728722610
66	3075	3301.21570179515	-226.215701795149
67	2002	1770.97215892153	231.027841078471
68	2306	2217.07414666986	88.9258533301374
69	1507	1410.63480135946	96.3651986405435
70	1992	2142.9266500356	-150.926650035601
71	2487	2443.84106877259	43.1589312274148
72	3490	3138.50182074939	351.498179250611
73	4647	4574.58163500471	72.4183649952922
74	5594	5879.30279905408	-285.302799054077
75	5611	5294.57783769523	316.422162304771
76	5788	5979.32731483165	-191.327314831647
77	6204	5635.18078148784	568.819218512163
78	3013	3032.0455442938	-19.0455442937992
79	1931	1965.88251674326	-34.8825167432633
80	2549	2558.56274835552	-9.56274835551595
81	1504	1353.21493753086	150.785062469139
82	2090	2164.93392738998	-74.9339273899778
83	2702	2517.63898991903	184.361010080968
84	2939	3111.40070499850	-172.400704998505
85	4500	4816.76676213019	-316.766762130185
86	6208	5435.08820327925	772.91179672075
87	6415	5461.98340607218	953.016593927818
88	5657	5760.85881425316	-103.858814253161
89	5964	5987.51184667179	-23.5118466717879
90	3163	3403.56990619989	-240.569906199886
91	1997	1893.01939714562	103.980602854376
92	2422	2490.37857353216	-68.3785735321568
93	1376	1465.11000519844	-89.110005198444
94	2202	2237.94456612965	-35.9445661296484
95	2683	2450.44677007043	232.553229929570
96	3303	3103.19988259693	199.800117403072
97	5202	4763.03253805132	438.967461948678
98	5231	5281.72490450009	-50.7249045000937
99	4880	5445.02331257937	-565.023312579367
100	7998	6917.01966148775	1080.98033851225
101	4977	4831.70857369831	145.291426301688
102	3531	3412.54791855619	118.452081443810
103	2025	2467.07411718163	-442.074117181627
104	2205	2262.50559715014	-57.5055971501397
105	1442	1655.80563341672	-213.805633416722
106	2238	2236.11941122548	1.88058877451727
107	2179	2394.36200747201	-215.362007472007
108	3218	3296.14886818574	-78.1488681857402
109	5139	4771.2404847455	367.759515254496
110	4990	5140.89148086165	-150.891480861647
111	4914	5489.90491061334	-575.904910613338
112	6084	6351.06858926342	-267.068589263424
113	5672	5871.89420019541	-199.894200195409
114	3548	3031.70499275385	516.295007246151
115	1793	1899.36721088798	-106.367210887977
116	2086	2545.34332531569	-459.34332531569

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
21	0.977996689939066	0.0440066201218676	0.0220033100609338
22	0.967163269190447	0.0656734616191054	0.0328367308095527
23	0.936298360044544	0.127403279910912	0.063701639955456
24	0.894814447927818	0.210371104144364	0.105185552072182
25	0.841637108456265	0.316725783087471	0.158362891543735
26	0.818423680070123	0.363152639859754	0.181576319929877
27	0.795967518174697	0.408064963650605	0.204032481825303
28	0.852737883669282	0.294524232661436	0.147262116330718
29	0.847661920947159	0.304676158105682	0.152338079052841
30	0.790478688272135	0.41904262345573	0.209521311727865
31	0.792762693917551	0.414474612164897	0.207237306082449
32	0.81056222024591	0.378875559508179	0.189437779754090
33	0.762577150068261	0.474845699863478	0.237422849931739
34	0.740420031670686	0.519159936658628	0.259579968329314
35	0.728840973975326	0.542318052049348	0.271159026024674
36	0.702126666933158	0.595746666133683	0.297873333066842
37	0.655695812579926	0.688608374840149	0.344304187420074
38	0.606213495404496	0.787573009191008	0.393786504595504
39	0.6896980484159	0.6206039031682	0.3103019515841
40	0.640646955269802	0.718706089460395	0.359353044730198
41	0.601188897381349	0.797622205237301	0.398811102618651
42	0.551379570235905	0.89724085952819	0.448620429764095
43	0.531098230846540	0.937803538306921	0.468901769153460
44	0.497159609765746	0.994319219531492	0.502840390234254
45	0.447822999735352	0.895645999470704	0.552177000264648
46	0.462378607057366	0.924757214114731	0.537621392942634
47	0.400307703445326	0.800615406890652	0.599692296554674
48	0.388796440133722	0.777592880267444	0.611203559866278
49	0.334315036793749	0.668630073587497	0.665684963206251
50	0.315434995450432	0.630869990900864	0.684565004549568
51	0.298964446870471	0.597928893740942	0.701035553129529
52	0.279035482166561	0.558070964333121	0.72096451783344
53	0.345093124502053	0.690186249004105	0.654906875497947
54	0.305545316270471	0.611090632540943	0.694454683729529
55	0.328763572654128	0.657527145308257	0.671236427345872
56	0.289758239699939	0.579516479399879	0.71024176030006
57	0.240705651492122	0.481411302984245	0.759294348507878
58	0.196365807942924	0.392731615885848	0.803634192057076
59	0.171857443373467	0.343714886746935	0.828142556626533
60	0.168802888341375	0.33760577668275	0.831197111658625
61	0.2303141410359	0.4606282820718	0.7696858589641
62	0.225259014926522	0.450518029853044	0.774740985073478
63	0.20939810612825	0.4187962122565	0.79060189387175
64	0.195304966520725	0.39060993304145	0.804695033479275
65	0.167782868098302	0.335565736196604	0.832217131901698
66	0.175808155728939	0.351616311457878	0.824191844271061
67	0.143956092380609	0.287912184761219	0.85604390761939
68	0.111696929495347	0.223393858990695	0.888303070504653
69	0.0840044195616697	0.168008839123339	0.91599558043833
70	0.0710833359831426	0.142166671966285	0.928916664016857
71	0.0537543134473073	0.107508626894615	0.946245686552693
72	0.0472781239070489	0.0945562478140978	0.95272187609295
73	0.0379886761693622	0.0759773523387244	0.962011323830638
74	0.133446867663141	0.266893735326283	0.866553132336859
75	0.134913161900216	0.269826323800433	0.865086838099784
76	0.130488013977086	0.260976027954172	0.869511986022914
77	0.192827234595107	0.385654469190214	0.807172765404893
78	0.181048796836782	0.362097593673564	0.818951203163218
79	0.150653757302872	0.301307514605745	0.849346242697128
80	0.118704120495735	0.23740824099147	0.881295879504265
81	0.0865197459780516	0.173039491956103	0.913480254021948
82	0.0711743542110573	0.142348708422115	0.928825645788943
83	0.04898634617079	0.09797269234158	0.95101365382921
84	0.047606557394901	0.095213114789802	0.9523934426051
85	0.214504976801004	0.429009953602008	0.785495023198996
86	0.304292600561865	0.60858520112373	0.695707399438135
87	0.478710915609278	0.957421831218556	0.521289084390722
88	0.752829217873552	0.494341564252896	0.247170782126448
89	0.951417590403074	0.0971648191938516	0.0485824095969258
90	0.985029874751647	0.0299402504967060	0.0149701252483530
91	0.978460949026727	0.0430781019465465	0.0215390509732733
92	0.952142814777196	0.0957143704456076	0.0478571852228038
93	0.914126378584064	0.171747242831872	0.0858736214159358
94	0.8498789023184	0.300242195363201	0.150121097681600
95	0.950314464901982	0.0993710701960357	0.0496855350980178

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	0	0	OK
5% type I error level	3	0.04	OK
10% type I error level	11	0.146666666666667	NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290869466cro4oybhb4zmzj3/104fhj1290869069.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290869466cro4oybhb4zmzj3/104fhj1290869069.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290869466cro4oybhb4zmzj3/1nmiv1290869068.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290869466cro4oybhb4zmzj3/1nmiv1290869068.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290869466cro4oybhb4zmzj3/285ka1290869069.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290869466cro4oybhb4zmzj3/285ka1290869069.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290869466cro4oybhb4zmzj3/385ka1290869069.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290869466cro4oybhb4zmzj3/385ka1290869069.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290869466cro4oybhb4zmzj3/485ka1290869069.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290869466cro4oybhb4zmzj3/485ka1290869069.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290869466cro4oybhb4zmzj3/585ka1290869069.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290869466cro4oybhb4zmzj3/585ka1290869069.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290869466cro4oybhb4zmzj3/6jxjd1290869069.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290869466cro4oybhb4zmzj3/6jxjd1290869069.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290869466cro4oybhb4zmzj3/7bo0g1290869069.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290869466cro4oybhb4zmzj3/7bo0g1290869069.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290869466cro4oybhb4zmzj3/8bo0g1290869069.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290869466cro4oybhb4zmzj3/8bo0g1290869069.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290869466cro4oybhb4zmzj3/9bo0g1290869069.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290869466cro4oybhb4zmzj3/9bo0g1290869069.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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