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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: Wed, 18 Nov 2009 09:29:33 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561810mp949xtjuso2a0m.htm/, Retrieved Wed, 18 Nov 2009 17:30:23 +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/2009/Nov/18/t1258561810mp949xtjuso2a0m.htm/},
    year = {2009},
}
@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 = {2009},
    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 «

274412 244752 272433 244576 268361 241572 268586 240541 264768 236089 269974 236997 304744 264579 309365 270349 308347 269645 298427 267037 289231 258113 291975 262813 294912 267413 293488 267366 290555 264777 284736 258863 281818 254844 287854 254868 316263 277267 325412 285351 326011 286602 328282 283042 317480 276687 317539 277915 313737 277128 312276 277103 309391 275037 302950 270150 300316 267140 304035 264993 333476 287259 337698 291186 335932 292300 323931 288186 313927 281477 314485 282656 313218 280190 309664 280408 302963 276836 298989 275216 298423 274352 301631 271311 329765 289802 335083 290726 327616 292300 309119 278506 295916 269826 291413 265861 291542 269034 284678 264176 276475 255198 272566 253353 264981 246057 263290 235372 296806 258556 303598 260993 286994 254663 276427 250643 266424 243422 267153 247105 268381 248541 262522 245039 255542 237080 253158 237085 243803 225554 250741 226839 280445 247934 285257 248333 2709 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	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

Y[t] = + 3078.3269626413 + 1.08313220981157X[t] -961.335706115605M1[t] -3251.10389194446M2[t] -4303.81391593477M3[t] -5366.09598507172M4[t] -4286.31027493667M5[t] + 1616.39275132285M6[t] + 8035.3196709235M7[t] + 15681.9071435834M8[t] + 9730.68823084167M9[t] + 5371.39205274557M10[t] + 2220.71659826559M11[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)	3078.3269626413	25064.660906	0.1228	0.902626	0.451313
X	1.08313220981157	0.092468	11.7136	0	0
M1	-961.335706115605	6975.557974	-0.1378	0.890806	0.445403
M2	-3251.10389194446	6976.460471	-0.466	0.642742	0.321371
M3	-4303.81391593477	6989.472234	-0.6158	0.540173	0.270086
M4	-5366.09598507172	7004.209797	-0.7661	0.446334	0.223167
M5	-4286.31027493667	7067.004043	-0.6065	0.546247	0.273124
M6	1616.39275132285	7087.30471	0.2281	0.820298	0.410149
M7	8035.3196709235	7020.938706	1.1445	0.256559	0.128279
M8	15681.9071435834	7287.539704	2.1519	0.03507	0.017535
M9	9730.68823084167	7279.89267	1.3367	0.185926	0.092963
M10	5371.39205274557	7245.219445	0.7414	0.461099	0.230549
M11	2220.71659826559	7242.769181	0.3066	0.760104	0.380052

Multiple Linear Regression - Regression Statistics
Multiple R	0.879926325621267
R-squared	0.774270338521344
Adjusted R-squared	0.73322858188886
F-TEST (value)	18.8654288230085
F-TEST (DF numerator)	12
F-TEST (DF denominator)	66
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	12537.2715860660
Sum Squared Residuals	10374089802.3033

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	274412	267215.765872328	7196.23412767223
2	272433	264735.366417572	7697.63358242789
3	268361	260428.927235308	7932.07276469219
4	268586	258249.935857855	10336.0641421449
5	264768	254507.616969909	10260.3830300910
6	269974	261393.804042677	8580.19595732252
7	304744	297687.683573301	7056.3164266991
8	309365	311583.943896574	-2218.94389657356
9	308347	304870.199908125	3476.80009187549
10	298427	297686.09492684	740.905073160178
11	289231	284869.547632001	4361.45236799862
12	291975	287739.55241985	4235.44758014982
13	294912	291760.624878868	3151.37512113221
14	293488	289419.949479178	4068.0505208222
15	290555	285563.010163985	4991.98983601467
16	284736	278095.084206023	6640.91579397725
17	281818	274821.761564925	6996.23843507491
18	287854	280750.45976422	7103.54023577992
19	316263	311430.46505139	4832.53494860986
20	325412	327833.093308167	-2421.09330816676
21	326011	323236.872789899	2774.12721010067
22	328282	315021.625944874	13260.3740551260
23	317480	304987.645297042	12492.3547029585
24	317539	304097.015052425	13441.9849475755
25	313737	302283.254297187	11453.7457028128
26	312276	299966.407806113	12309.5921938869
27	309391	296675.946636652	12715.0533633479
28	302950	290320.397458166	12629.6025418340
29	300316	288139.955216768	12176.0447832318
30	304035	291717.173388562	12317.8266114378
31	333476	322253.122091827	11222.8779081726
32	337698	334153.169752417	3544.83024758272
33	335932	329408.560121406	6523.43987859433
34	323931	320593.258032145	3337.74196785524
35	313927	310175.848582039	3751.15141796105
36	314485	309232.144859141	5252.8551408588
37	313218	305599.80512363	7618.19487636974
38	309664	303546.159759540	6117.84024045968
39	302963	298624.501482103	4338.49851789692
40	298989	295807.545233071	3181.45476692862
41	298423	295951.504713929	2471.49528607077
42	301631	298560.402690152	3070.59730984824
43	329765	325007.527301378	4757.4726986218
44	335083	333654.928935904	1428.07106409604
45	327616	329408.560121406	-1792.56012140567
46	309119	310108.538241169	-989.53824116874
47	295916	297556.275205524	-1640.27520552432
48	291413	291040.939395356	372.060604644147
49	291542	293516.382190972	-1974.38219097236
50	284678	285964.757729879	-1286.75772987889
51	276475	275187.686726200	1287.31327379972
52	272566	272127.025729961	438.974270039016
53	264981	265304.278837311	-323.278837310803
54	263290	259633.714201734	3656.28579826633
55	296806	291163.978273606	5642.02172639418
56	303598	301450.158941576	2147.84105842352
57	286994	288642.713140728	-1648.71314072754
58	276427	279929.225479189	-3502.22547918891
59	266424	268957.252337660	-2533.25233765957
60	267153	270725.71166813	-3572.71166813000
61	268381	271319.753815304	-2938.75381530381
62	262522	265236.856630715	-2714.85663071483
63	255542	255563.497348834	-21.4973488342223
64	253158	254506.630940746	-1348.63094074633
65	243803	243096.819139544	706.180860455863
66	250741	250391.347055412	349.652944588481
67	280445	279658.947940987	786.052059012698
68	285257	287737.705165362	-2480.70516536198
69	270976	280309.093918437	-9333.0939184373
70	261076	273923.257375784	-12847.2573757837
71	255603	272034.430945734	-16431.4309457343
72	260376	280105.636605098	-19729.6366050982
73	263903	288409.413821711	-24506.4138217108
74	264291	290482.502177003	-26191.5021770030
75	263276	294519.430406917	-31243.4304069172
76	262572	294450.380574177	-31878.3805741775
77	256167	288454.063557614	-32287.0635576135
78	264221	299299.098857243	-35078.0988572433
79	293860	328157.27576751	-34297.2757675103

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
16	5.7207133695348e-05	0.000114414267390696	0.999942792866305
17	1.70342598241517e-06	3.40685196483034e-06	0.999998296574018
18	3.74585589660166e-07	7.49171179320333e-07	0.99999962541441
19	1.42839766216999e-08	2.85679532433998e-08	0.999999985716023
20	8.2560940858686e-09	1.65121881717372e-08	0.999999991743906
21	1.3534045091508e-09	2.7068090183016e-09	0.999999998646596
22	4.63293594591837e-05	9.26587189183674e-05	0.99995367064054
23	5.10772904393807e-05	0.000102154580878761	0.99994892270956
24	5.33274119991281e-05	0.000106654823998256	0.999946672588001
25	2.92112245145796e-05	5.84224490291591e-05	0.999970788775485
26	1.51749045272047e-05	3.03498090544095e-05	0.999984825095473
27	7.27738349206225e-06	1.45547669841245e-05	0.999992722616508
28	2.8385652726953e-06	5.6771305453906e-06	0.999997161434727
29	1.05991474341712e-06	2.11982948683425e-06	0.999998940085257
30	4.3465293534018e-07	8.6930587068036e-07	0.999999565347065
31	1.91032491350543e-07	3.82064982701085e-07	0.999999808967509
32	7.20405863871459e-08	1.44081172774292e-07	0.999999927959414
33	2.25210225448778e-08	4.50420450897557e-08	0.999999977478977
34	1.28622964255499e-08	2.57245928510997e-08	0.999999987137704
35	9.93604380500276e-09	1.98720876100055e-08	0.999999990063956
36	6.0381869581386e-09	1.20763739162772e-08	0.999999993961813
37	2.92191725443628e-09	5.84383450887257e-09	0.999999997078083
38	1.92006722985033e-09	3.84013445970066e-09	0.999999998079933
39	1.95863853602547e-09	3.91727707205094e-09	0.999999998041361
40	4.2397026184458e-09	8.4794052368916e-09	0.999999995760297
41	1.1763895803834e-08	2.3527791607668e-08	0.999999988236104
42	2.40896516120065e-08	4.8179303224013e-08	0.999999975910348
43	3.21049914528154e-08	6.42099829056308e-08	0.999999967895009
44	2.20040651643811e-08	4.40081303287622e-08	0.999999977995935
45	7.41990489896872e-08	1.48398097979374e-07	0.99999992580095
46	4.12681043886369e-07	8.25362087772739e-07	0.999999587318956
47	3.9873295947815e-06	7.974659189563e-06	0.999996012670405
48	2.43583328230076e-05	4.87166656460153e-05	0.999975641667177
49	0.000236579964350939	0.000473159928701879	0.99976342003565
50	0.00139140343122109	0.00278280686244219	0.99860859656878
51	0.00419697974701703	0.00839395949403406	0.995803020252983
52	0.0118058822437479	0.0236117644874958	0.988194117756252
53	0.0346753642743975	0.0693507285487951	0.965324635725602
54	0.0369019330390639	0.0738038660781279	0.963098066960936
55	0.0642416407344497	0.128483281468899	0.93575835926555
56	0.130823640504872	0.261647281009744	0.869176359495128
57	0.251842642129124	0.503685284258248	0.748157357870876
58	0.514594018552645	0.97081196289471	0.485405981447355
59	0.749382912087347	0.501234175825306	0.250617087912653
60	0.88230416789119	0.235391664217619	0.117695832108809
61	0.984536207953748	0.0309275840925041	0.0154637920462520
62	0.995957134085036	0.00808573182992877	0.00404286591496438
63	0.997396266892615	0.0052074662147703	0.00260373310738515

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	38	0.791666666666667	NOK
5% type I error level	40	0.833333333333333	NOK
10% type I error level	42	0.875	NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561810mp949xtjuso2a0m/107rhj1258561768.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561810mp949xtjuso2a0m/107rhj1258561768.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561810mp949xtjuso2a0m/1z6gg1258561768.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561810mp949xtjuso2a0m/1z6gg1258561768.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561810mp949xtjuso2a0m/2k1bw1258561768.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561810mp949xtjuso2a0m/2k1bw1258561768.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561810mp949xtjuso2a0m/3ak9g1258561768.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561810mp949xtjuso2a0m/3ak9g1258561768.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561810mp949xtjuso2a0m/4qo7s1258561768.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561810mp949xtjuso2a0m/4qo7s1258561768.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561810mp949xtjuso2a0m/56oob1258561768.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561810mp949xtjuso2a0m/56oob1258561768.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561810mp949xtjuso2a0m/6bdrr1258561768.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561810mp949xtjuso2a0m/6bdrr1258561768.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561810mp949xtjuso2a0m/7uuyc1258561768.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561810mp949xtjuso2a0m/7uuyc1258561768.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561810mp949xtjuso2a0m/8p1ak1258561768.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561810mp949xtjuso2a0m/8p1ak1258561768.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561810mp949xtjuso2a0m/96j0p1258561768.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561810mp949xtjuso2a0m/96j0p1258561768.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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