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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: Tue, 15 Dec 2009 07:48:29 -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/Dec/15/t1260888622d8x6y1ryddttmqy.htm/, Retrieved Tue, 15 Dec 2009 15:50:37 +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/Dec/15/t1260888622d8x6y1ryddttmqy.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 «

2350.44 27 2440.25 29 2408.64 27 2472.81 26 2407.6 24 2454.62 30 2448.05 26 2497.84 28 2645.64 28 2756.76 24 2849.27 23 2921.44 24 2981.85 24 3080.58 27 3106.22 28 3119.31 25 3061.26 19 3097.31 19 3161.69 19 3257.16 20 3277.01 16 3295.32 22 3363.99 21 3494.17 25 3667.03 29 3813.06 28 3917.96 25 3895.51 26 3801.06 24 3570.12 28 3701.61 28 3862.27 28 3970.1 28 4138.52 32 4199.75 31 4290.89 22 4443.91 29 4502.64 31 4356.98 29 4591.27 32 4696.96 32 4621.4 31 4562.84 29 4202.52 28 4296.49 28 4435.23 29 4105.18 22 4116.68 26 3844.49 24 3720.98 27 3674.4 27 3857.62 23 3801.06 21 3504.37 19 3032.6 17 3047.03 19 2962.34 21 2197.82 13 2014.45 8 1862.83 5 1905.41 10 1810.99 6 1670.07 6 1864.44 8 2052.02 11 2029.6 12 2070.83 13 2293.41 19 2443.27 19 2513.17 18 2466.92 20

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

Y[t] = + 1230.71723607144 + 87.5267609364537X[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)	1230.71723607144	247.959235	4.9634	5e-06	2e-06
X	87.5267609364537	10.397695	8.4179	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.711795769190165
R-squared	0.506653217037018
Adjusted R-squared	0.499503263660743
F-TEST (value)	70.8610518661828
F-TEST (DF numerator)	1
F-TEST (DF denominator)	69
p-value	3.44013706410351e-12
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	599.406650706703
Sum Squared Residuals	24790894.9708885

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	2350.44	3593.93978135569	-1243.49978135568
2	2440.25	3768.99330322859	-1328.74330322859
3	2408.64	3593.93978135569	-1185.29978135569
4	2472.81	3506.41302041923	-1033.60302041923
5	2407.6	3331.35949854633	-923.759498546327
6	2454.62	3856.52006416505	-1401.90006416505
7	2448.05	3506.41302041923	-1058.36302041923
8	2497.84	3681.46654229214	-1183.62654229214
9	2645.64	3681.46654229214	-1035.82654229214
10	2756.76	3331.35949854633	-574.599498546327
11	2849.27	3243.83273760987	-394.562737609873
12	2921.44	3331.35949854633	-409.919498546327
13	2981.85	3331.35949854633	-349.509498546327
14	3080.58	3593.93978135569	-513.359781355688
15	3106.22	3681.46654229214	-575.246542292142
16	3119.31	3418.88625948278	-299.576259482781
17	3061.26	2893.72569386406	167.534306135942
18	3097.31	2893.72569386406	203.584306135942
19	3161.69	2893.72569386406	267.964306135942
20	3257.16	2981.25245480051	275.907545199488
21	3277.01	2631.14541105470	645.864588945303
22	3295.32	3156.30597667342	139.014023326581
23	3363.99	3068.77921573697	295.210784263034
24	3494.17	3418.88625948278	75.2837405172194
25	3667.03	3768.99330322860	-101.963303228595
26	3813.06	3681.46654229214	131.593457707858
27	3917.96	3418.88625948278	499.07374051722
28	3895.51	3506.41302041923	389.096979580766
29	3801.06	3331.35949854633	469.700501453673
30	3570.12	3681.46654229214	-111.346542292142
31	3701.61	3681.46654229214	20.1434577078583
32	3862.27	3681.46654229214	180.803457707858
33	3970.1	3681.46654229214	288.633457707858
34	4138.52	4031.57358603796	106.946413962044
35	4199.75	3944.0468251015	255.703174898497
36	4290.89	3156.30597667342	1134.58402332658
37	4443.91	3768.99330322860	674.916696771404
38	4502.64	3944.0468251015	558.593174898497
39	4356.98	3768.99330322860	587.986696771404
40	4591.27	4031.57358603796	559.696413962044
41	4696.96	4031.57358603796	665.386413962043
42	4621.4	3944.0468251015	677.353174898497
43	4562.84	3768.99330322860	793.846696771405
44	4202.52	3681.46654229214	521.053457707859
45	4296.49	3681.46654229214	615.023457707858
46	4435.23	3768.99330322860	666.236696771404
47	4105.18	3156.30597667342	948.87402332658
48	4116.68	3506.41302041923	610.266979580766
49	3844.49	3331.35949854633	513.130501453673
50	3720.98	3593.93978135569	127.040218644312
51	3674.4	3593.93978135569	80.460218644312
52	3857.62	3243.83273760987	613.787262390127
53	3801.06	3068.77921573697	732.280784263034
54	3504.37	2893.72569386406	610.644306135942
55	3032.6	2718.67217199115	313.927828008849
56	3047.03	2893.72569386406	153.304306135942
57	2962.34	3068.77921573697	-106.439215736966
58	2197.82	2368.56512824534	-170.745128245336
59	2014.45	1930.93132356307	83.5186764369328
60	1862.83	1668.35104075371	194.478959246294
61	1905.41	2105.98484543597	-200.574845435975
62	1810.99	1755.87780169016	55.1121983098401
63	1670.07	1755.87780169016	-85.80780169016
64	1864.44	1930.93132356307	-66.4913235630672
65	2052.02	2193.51160637243	-141.491606372429
66	2029.6	2281.03836730888	-251.438367308882
67	2070.83	2368.56512824534	-297.735128245336
68	2293.41	2893.72569386406	-600.315693864058
69	2443.27	2893.72569386406	-450.455693864058
70	2513.17	2806.19893292760	-293.028932927605
71	2466.92	2981.25245480051	-514.332454800512

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
5	0.00139129820986984	0.00278259641973968	0.99860870179013
6	0.000173031091682279	0.000346062183364557	0.999826968908318
7	2.26955247597573e-05	4.53910495195146e-05	0.99997730447524
8	8.00560019473845e-06	1.60112003894769e-05	0.999991994399805
9	0.000115603271771806	0.000231206543543612	0.999884396728228
10	0.000898181516208645	0.00179636303241729	0.999101818483791
11	0.00141391138821810	0.00282782277643621	0.998586088611782
12	0.00253652004315325	0.00507304008630649	0.997463479956847
13	0.00396384802538181	0.00792769605076362	0.996036151974618
14	0.0330813128689958	0.0661626257379916	0.966918687131004
15	0.134574786812495	0.269149573624991	0.865425213187505
16	0.185940309267598	0.371880618535196	0.814059690732402
17	0.132205556138417	0.264411112276835	0.867794443861583
18	0.0914310568843392	0.182862113768678	0.90856894311566
19	0.063044025414747	0.126088050829494	0.936955974585253
20	0.0492401471505761	0.0984802943011523	0.950759852849424
21	0.0400543026450805	0.080108605290161	0.95994569735492
22	0.0423939169253681	0.0847878338507362	0.957606083074632
23	0.041911833180375	0.08382366636075	0.958088166819625
24	0.122504697037721	0.245009394075441	0.877495302962279
25	0.499913513470486	0.999827026940972	0.500086486529514
26	0.769064056988565	0.461871886022869	0.230935943011435
27	0.880612254466208	0.238775491067584	0.119387745533792
28	0.930804189714262	0.138391620571476	0.0691958102857382
29	0.94398140786477	0.112037184270460	0.0560185921352301
30	0.958218535738274	0.0835629285234519	0.0417814642617259
31	0.968302702605266	0.0633945947894682	0.0316972973947341
32	0.975987164267529	0.0480256714649426	0.0240128357324713
33	0.981435658597274	0.0371286828054526	0.0185643414027263
34	0.990364041502209	0.0192719169955818	0.00963595849779088
35	0.993259760897316	0.0134804782053674	0.00674023910268372
36	0.998870357348588	0.00225928530282375	0.00112964265141188
37	0.999236060641206	0.00152787871758853	0.000763939358794263
38	0.999331485602202	0.00133702879559548	0.000668514397797741
39	0.999266814643275	0.00146637071344894	0.000733185356724468
40	0.99918683188983	0.00162633622034128	0.00081316811017064
41	0.999085900202096	0.00182819959580755	0.000914099797903774
42	0.998878439679827	0.00224312064034546	0.00112156032017273
43	0.998880508062642	0.00223898387471649	0.00111949193735824
44	0.99826339089889	0.00347321820221945	0.00173660910110972
45	0.997624958619227	0.00475008276154614	0.00237504138077307
46	0.997021433728135	0.00595713254372943	0.00297856627186471
47	0.998941319903612	0.00211736019277644	0.00105868009638822
48	0.99885892895619	0.00228214208761829	0.00114107104380915
49	0.998660671749893	0.00267865650021345	0.00133932825010673
50	0.99736923950844	0.00526152098312127	0.00263076049156064
51	0.994970636385864	0.0100587272282726	0.00502936361413628
52	0.996432220547817	0.00713555890436513	0.00356777945218256
53	0.999364838187062	0.00127032362587688	0.000635161812938438
54	0.999964211331383	7.15773372341817e-05	3.57886686170908e-05
55	0.999994319144778	1.13617104443095e-05	5.68085522215477e-06
56	0.999999692000631	6.159987383117e-07	3.0799936915585e-07
57	0.999999994044788	1.19104242687244e-08	5.95521213436222e-09
58	0.999999968164416	6.36711686589598e-08	3.18355843294799e-08
59	0.999999915260016	1.69479968359174e-07	8.4739984179587e-08
60	0.999999870629	2.58742002736166e-07	1.29371001368083e-07
61	0.999999102302198	1.79539560418813e-06	8.97697802094066e-07
62	0.999995096358603	9.80728279384703e-06	4.90364139692352e-06
63	0.999971541968912	5.69160621756804e-05	2.84580310878402e-05
64	0.999780003615494	0.000439992769012873	0.000219996384506437
65	0.998652971269015	0.00269405746196916	0.00134702873098458
66	0.99113280828997	0.0177343834200587	0.00886719171002934

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	38	0.612903225806452	NOK
5% type I error level	44	0.709677419354839	NOK
10% type I error level	51	0.82258064516129	NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/15/t1260888622d8x6y1ryddttmqy/10ku2i1260888504.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/15/t1260888622d8x6y1ryddttmqy/10ku2i1260888504.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/15/t1260888622d8x6y1ryddttmqy/1mzqq1260888504.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/15/t1260888622d8x6y1ryddttmqy/1mzqq1260888504.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/15/t1260888622d8x6y1ryddttmqy/2rdke1260888504.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/15/t1260888622d8x6y1ryddttmqy/2rdke1260888504.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/15/t1260888622d8x6y1ryddttmqy/3ypyy1260888504.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/15/t1260888622d8x6y1ryddttmqy/3ypyy1260888504.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/15/t1260888622d8x6y1ryddttmqy/4byd01260888504.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/15/t1260888622d8x6y1ryddttmqy/4byd01260888504.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/15/t1260888622d8x6y1ryddttmqy/5ce611260888504.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/15/t1260888622d8x6y1ryddttmqy/5ce611260888504.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/15/t1260888622d8x6y1ryddttmqy/63f911260888504.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/15/t1260888622d8x6y1ryddttmqy/63f911260888504.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/15/t1260888622d8x6y1ryddttmqy/7vgzu1260888504.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/15/t1260888622d8x6y1ryddttmqy/7vgzu1260888504.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/15/t1260888622d8x6y1ryddttmqy/8bc561260888504.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/15/t1260888622d8x6y1ryddttmqy/8bc561260888504.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/15/t1260888622d8x6y1ryddttmqy/9mvh41260888504.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/15/t1260888622d8x6y1ryddttmqy/9mvh41260888504.ps (open in new window)

Parameters (Session):

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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