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The SeatBelt Law Q3

*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: Thu, 27 Nov 2008 08:35:16 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/27/t12278002063s2ghssv2jjev6f.htm/, Retrieved Thu, 27 Nov 2008 15:37:04 +0000

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/2008/Nov/27/t12278002063s2ghssv2jjev6f.htm/},
    year = {2008},
}
@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 = {2008},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

Feedback Forum:

2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc] [reply] 
test

Post a new message

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

k_vanderheggen

Dataseries X:

» Textbox « » Textfile « » CSV «

5,5 0 5,3 0 5,2 0 5,3 0 5,3 0 5 0 4,8 0 4,9 0 5,3 0 6 0 6,2 0 6,4 0 6,4 0 6,4 0 6,2 0 6,1 0 6 0 5,9 0 6,2 0 6,2 0 6,4 0 6,8 0 6,9 0 7 0 7 1 6,9 1 6,7 1 6,6 1 6,5 1 6,4 1 6,5 1 6,5 1 6,6 1 6,7 1 6,8 1 7,2 1 7,6 1 7,6 1 7,3 1 6,4 1 6,1 1 6,3 1 7,1 1 7,5 1 7,4 1 7,1 1 6,8 1 6,9 1 7,2 1 7,4 1 7,3 1 6,9 1 6,9 1 6,8 1 7,1 1 7,2 1 7,1 1 7 1 6,9 1 7 1 7,4 1 7,5 1 7,5 1 7,4 1 7,3 1 7 1 6,7 1 6,5 1 6,5 1 6,5 1 6,6 1 6,8 1 6,9 1 6,9 1 6,8 1 6,8 1 6,5 1 6,1 1 6 1 5,9 1 5,8 1 5,9 1 5,9 1 6,2 1 6,3 1 6,2 1 6 1 5,8 1 5,5 1 5,5 1 5,7 1 5,8 1

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	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

VAR1[t] = + 6.36969461697723 + 1.27868357487923D1[t] -0.0956863210259885M1[t] -0.0978253680699337M2[t] -0.237464415113870M3[t] -0.439603462157809M4[t] -0.579242509201749M5[t] -0.706381556245686M6[t] -0.558520603289625M7[t] -0.498159650333563M8[t] -0.373940001725327M9[t] -0.235007620197837M10[t] -0.210360952956061M11[t] -0.0103609529560616t + 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)	6.36969461697723	0.225141	28.292	0	0
D1	1.27868357487923	0.195103	6.5539	0	0
M1	-0.0956863210259885	0.275426	-0.3474	0.729217	0.364609
M2	-0.0978253680699337	0.275192	-0.3555	0.72319	0.361595
M3	-0.237464415113870	0.274997	-0.8635	0.390501	0.195251
M4	-0.439603462157809	0.274839	-1.5995	0.113754	0.056877
M5	-0.579242509201749	0.27472	-2.1085	0.038199	0.0191
M6	-0.706381556245686	0.274638	-2.572	0.012009	0.006005
M7	-0.558520603289625	0.274595	-2.034	0.045353	0.022677
M8	-0.498159650333563	0.274589	-1.8142	0.073492	0.036746
M9	-0.373940001725327	0.28372	-1.318	0.191364	0.095682
M10	-0.235007620197837	0.283627	-0.8286	0.409871	0.204936
M11	-0.210360952956061	0.283572	-0.7418	0.460421	0.230211
t	-0.0103609529560616	0.003233	-3.2048	0.001959	0.00098

Multiple Linear Regression - Regression Statistics
Multiple R	0.678282044564129
R-squared	0.460066531978095
Adjusted R-squared	0.370077620641111
F-TEST (value)	5.11248025054188
F-TEST (DF numerator)	13
F-TEST (DF denominator)	78
p-value	1.82579393293025e-06
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.530480415439539
Sum Squared Residuals	21.9499387508626

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	5.5	6.26364734299513	-0.763647342995134
2	5.3	6.25114734299518	-0.951147342995182
3	5.2	6.10114734299517	-0.901147342995172
4	5.3	5.88864734299517	-0.588647342995171
5	5.3	5.73864734299517	-0.438647342995173
6	5	5.60114734299517	-0.60114734299517
7	4.8	5.73864734299517	-0.938647342995168
8	4.9	5.78864734299517	-0.888647342995171
9	5.3	5.90250603864734	-0.602506038647343
10	6	6.03107746721877	-0.0310774672187722
11	6.2	6.04536318150449	0.154636818495514
12	6.4	6.24536318150449	0.154636818495514
13	6.4	6.13931590752243	0.260684092477565
14	6.4	6.12681590752243	0.273184092477571
15	6.2	5.97681590752243	0.22318409247757
16	6.1	5.76431590752243	0.335684092477570
17	6	5.61431590752243	0.38568409247757
18	5.9	5.47681590752243	0.42318409247757
19	6.2	5.61431590752243	0.58568409247757
20	6.2	5.66431590752243	0.53568409247757
21	6.4	5.7781746031746	0.621825396825397
22	6.8	5.90674603174603	0.893253968253967
23	6.9	5.92103174603175	0.978968253968253
24	7	6.12103174603175	0.878968253968253
25	7	7.29366804692892	-0.293668046928921
26	6.9	7.28116804692891	-0.381168046928914
27	6.7	7.13116804692892	-0.431168046928916
28	6.6	6.91866804692892	-0.318668046928916
29	6.5	6.76866804692892	-0.268668046928916
30	6.4	6.63116804692892	-0.231168046928916
31	6.5	6.76866804692892	-0.268668046928916
32	6.5	6.81866804692892	-0.318668046928916
33	6.6	6.93252674258109	-0.332526742581090
34	6.7	7.06109817115252	-0.361098171152518
35	6.8	7.07538388543823	-0.275383885438233
36	7.2	7.27538388543823	-0.0753838854382321
37	7.6	7.16933661145618	0.430663388543819
38	7.6	7.15683661145617	0.443163388543825
39	7.3	7.00683661145618	0.293163388543823
40	6.4	6.79433661145618	-0.394336611456176
41	6.1	6.64433661145618	-0.544336611456176
42	6.3	6.50683661145618	-0.206836611456176
43	7.1	6.64433661145618	0.455663388543824
44	7.5	6.69433661145618	0.805663388543824
45	7.4	6.80819530710835	0.59180469289165
46	7.1	6.93676673567978	0.163233264320221
47	6.8	6.95105244996549	-0.151052449965493
48	6.9	7.15105244996549	-0.251052449965492
49	7.2	7.04500517598344	0.154994824016559
50	7.4	7.03250517598343	0.367494824016565
51	7.3	6.88250517598344	0.417494824016563
52	6.9	6.67000517598344	0.229994824016564
53	6.9	6.52000517598344	0.379994824016564
54	6.8	6.38250517598344	0.417494824016563
55	7.1	6.52000517598344	0.579994824016563
56	7.2	6.57000517598344	0.629994824016564
57	7.1	6.68386387163561	0.416136128364389
58	7	6.81243530020704	0.187564699792961
59	6.9	6.82672101449275	0.073278985507247
60	7	7.02672101449275	-0.0267210144927528
61	7.4	6.9206737405107	0.479326259489299
62	7.5	6.9081737405107	0.591826259489305
63	7.5	6.7581737405107	0.741826259489303
64	7.4	6.5456737405107	0.854326259489304
65	7.3	6.3956737405107	0.904326259489303
66	7	6.2581737405107	0.741826259489303
67	6.7	6.3956737405107	0.304326259489303
68	6.5	6.4456737405107	0.0543262594893032
69	6.5	6.55953243616287	-0.0595324361628709
70	6.5	6.6881038647343	-0.188103864734299
71	6.6	6.70238957902001	-0.102389579020014
72	6.8	6.90238957902001	-0.102389579020013
73	6.9	6.79634230503796	0.103657694962038
74	6.9	6.78384230503796	0.116157694962045
75	6.8	6.63384230503796	0.166157694962043
76	6.8	6.42134230503796	0.378657694962043
77	6.5	6.27134230503796	0.228657694962043
78	6.1	6.13384230503796	-0.0338423050379574
79	6	6.27134230503796	-0.271342305037957
80	5.9	6.32134230503796	-0.421342305037957
81	5.8	6.43520100069013	-0.635201000690131
82	5.9	6.56377242926156	-0.66377242926156
83	5.9	6.57805814354727	-0.678058143547273
84	6.2	6.77805814354727	-0.578058143547273
85	6.3	6.67201086956522	-0.372010869565222
86	6.2	6.65951086956522	-0.459510869565216
87	6	6.50951086956522	-0.509510869565218
88	5.8	6.29701086956522	-0.497010869565218
89	5.5	6.14701086956522	-0.647010869565217
90	5.5	6.00951086956522	-0.509510869565218
91	5.7	6.14701086956522	-0.447010869565217
92	5.8	6.19701086956522	-0.397010869565218

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
17	0.0323328061997257	0.0646656123994514	0.967667193800274
18	0.00771830340722463	0.0154366068144493	0.992281696592775
19	0.0237310483083944	0.0474620966167888	0.976268951691606
20	0.0168885304505532	0.0337770609011065	0.983111469549447
21	0.0066740113088966	0.0133480226177932	0.993325988691103
22	0.00326641867866645	0.00653283735733291	0.996733581321334
23	0.00210706296642195	0.0042141259328439	0.997892937033578
24	0.00181105891082484	0.00362211782164969	0.998188941089175
25	0.000746489768150785	0.00149297953630157	0.99925351023185
26	0.00033147433058808	0.00066294866117616	0.999668525669412
27	0.000162983987388927	0.000325967974777853	0.999837016012611
28	8.2153257824214e-05	0.000164306515648428	0.999917846742176
29	4.26651774795559e-05	8.53303549591119e-05	0.99995733482252
30	1.82894447367149e-05	3.65788894734298e-05	0.999981710555263
31	8.94583100390837e-06	1.78916620078167e-05	0.999991054168996
32	5.18584796590606e-06	1.03716959318121e-05	0.999994814152034
33	5.27277789277074e-06	1.05455557855415e-05	0.999994727222107
34	0.000144309523592133	0.000288619047184267	0.999855690476408
35	0.000880097152436673	0.00176019430487335	0.999119902847563
36	0.000772375827615971	0.00154475165523194	0.999227624172384
37	0.00044285337279202	0.00088570674558404	0.999557146627208
38	0.000218535119774371	0.000437070239548741	0.999781464880226
39	0.000141692871558542	0.000283385743117084	0.999858307128441
40	0.0180133769518817	0.0360267539037634	0.981986623048118
41	0.384134565327293	0.768269130654587	0.615865434672707
42	0.703687487524542	0.592625024950916	0.296312512475458
43	0.668738483242828	0.662523033514343	0.331261516757171
44	0.657794978076653	0.684410043846694	0.342205021923347
45	0.59503092892676	0.80993814214648	0.40496907107324
46	0.624348863047208	0.751302273905585	0.375651136952792
47	0.809351052205517	0.381297895588966	0.190648947794483
48	0.938963251102224	0.122073497795551	0.0610367488977756
49	0.973103249791579	0.0537935004168415	0.0268967502084207
50	0.976492553160132	0.0470148936797357	0.0235074468398678
51	0.979448360743442	0.0411032785131167	0.0205516392565584
52	0.996309613276368	0.00738077344726396	0.00369038672363198
53	0.999054476597779	0.00189104680444242	0.00094552340222121
54	0.999761678394553	0.000476643210893196	0.000238321605446598
55	0.999675694522596	0.00064861095480719	0.000324305477403595
56	0.999378795869929	0.00124240826014300	0.000621204130071502
57	0.998931465409569	0.00213706918086283	0.00106853459043141
58	0.998726328656858	0.00254734268628475	0.00127367134314237
59	0.999025757914874	0.00194848417025239	0.000974242085126197
60	0.999721183675845	0.000557632648310423	0.000278816324155212
61	0.99956699971019	0.000866000579620418	0.000433000289810209
62	0.999067906877335	0.00186418624532897	0.000932093122664486
63	0.99807912189991	0.00384175620017958	0.00192087810008979
64	0.996245478836195	0.00750904232760925	0.00375452116380463
65	0.996348810197633	0.00730237960473469	0.00365118980236735
66	0.995608992174039	0.00878201565192235	0.00439100782596117
67	0.992183720945653	0.0156325581086942	0.00781627905434711
68	0.992935011802656	0.0141299763946875	0.00706498819734377
69	0.988505416333953	0.0229891673320950	0.0114945836660475
70	0.98129235215365	0.0374152956926987	0.0187076478463493
71	0.966381398955038	0.0672372020899231	0.0336186010449615
72	0.937529157166406	0.124941685667188	0.0624708428335938
73	0.882917154270722	0.234165691458555	0.117082845729278
74	0.789894872866096	0.420210254267808	0.210105127133904
75	0.65816247193759	0.683675056124821	0.341837528062411

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	33	0.559322033898305	NOK
5% type I error level	44	0.745762711864407	NOK
10% type I error level	47	0.796610169491525	NOK

Charts produced by software:

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t12278002063s2ghssv2jjev6f/84cgn1227800111.ps (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t12278002063s2ghssv2jjev6f/9omp21227800111.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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