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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 10:51:37 -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/t1258566979xie77iujj9rgwwg.htm/, Retrieved Wed, 18 Nov 2009 18:56:31 +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/t1258566979xie77iujj9rgwwg.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 «
2863,36 99.9 2882,6 2767,63 2803,47 3030,29 2897,06 99.7 2863,36 2882,6 2767,63 2803,47 3012,61 99.5 2897,06 2863,36 2882,6 2767,63 3142,95 99.2 3012,61 2897,06 2863,36 2882,6 3032,93 99 3142,95 3012,61 2897,06 2863,36 3045,78 99 3032,93 3142,95 3012,61 2897,06 3110,52 99.3 3045,78 3032,93 3142,95 3012,61 3013,24 99.5 3110,52 3045,78 3032,93 3142,95 2987,1 99.7 3013,24 3110,52 3045,78 3032,93 2995,55 100 2987,1 3013,24 3110,52 3045,78 2833,18 100.4 2995,55 2987,1 3013,24 3110,52 2848,96 100.6 2833,18 2995,55 2987,1 3013,24 2794,83 100.7 2848,96 2833,18 2995,55 2987,1 2845,26 100.7 2794,83 2848,96 2833,18 2995,55 2915,02 100.6 2845,26 2794,83 2848,96 2833,18 2892,63 100.5 2915,02 2845,26 2794,83 2848,96 2604,42 100.6 2892,63 2915,02 2845,26 2794,83 2641,65 100.5 2604,42 2892,63 2915,02 2845,26 2659,81 100.4 2641,65 2604,42 2892,63 2915,02 2638,53 100.3 2659,81 2641,65 2604,42 2892,63 2720,25 100.4 2638,53 2659,81 2641,65 2604,42 2745,88 100.4 2720,25 2638,53 2659,81 2641,65 2735,7 100.4 2 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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
Bel20[t] = -1092.78270532526 + 12.5769027972356Gzhind[t] + 1.54924150207039Y1[t] -0.763672660876186Y2[t] + 0.338991410113042Y3[t] -0.141990563713654Y4[t] -199.107040330143M1[t] -101.49182241988M2[t] -148.393128332664M3[t] -88.7734804200535M4[t] -218.605515568737M5[t] -65.3177530628458M6[t] -88.7273869252064M7[t] -167.702931515144M8[t] -49.6419680958159M9[t] -175.368415813703M10[t] -187.01519336378M11[t] -0.282093134491550t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)-1092.782705325262068.766542-0.52820.6004120.300206
Gzhind12.576902797235620.3265030.61870.5397770.269888
Y11.549241502070390.1613629.60100
Y2-0.7636726608761860.29179-2.61720.0126560.006328
Y30.3389914101130420.2818921.20260.2365870.118293
Y4-0.1419905637136540.162602-0.87320.3880180.194009
M1-199.10704033014370.766654-2.81360.0077160.003858
M2-101.4918224198867.987818-1.49280.1437480.071874
M3-148.39312833266463.416287-2.340.0246380.012319
M4-88.773480420053563.122114-1.40640.1677380.083869
M5-218.60551556873764.554411-3.38640.0016580.000829
M6-65.317753062845862.930493-1.03790.305860.15293
M7-88.727386925206465.533452-1.35390.1837580.091879
M8-167.70293151514468.114055-2.46210.0184620.009231
M9-49.641968095815966.70994-0.74410.4613650.230682
M10-175.36841581370368.657013-2.55430.0147730.007386
M11-187.0151933637866.91962-2.79460.0080990.00405
t-0.2820931344915501.512973-0.18640.8530840.426542


Multiple Linear Regression - Regression Statistics
Multiple R0.982311884103085
R-squared0.964936637650153
Adjusted R-squared0.949250396598906
F-TEST (value)61.5148418603080
F-TEST (DF numerator)17
F-TEST (DF denominator)38
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation91.233745581805
Sum Squared Residuals316296.660649649


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
12863.362836.6206012950526.7393987049488
22897.062833.8883407136963.1716592863088
33012.612895.15484594619117.455154053808
43142.953081.1515669371161.7984330628865
53032.933076.36372847676-43.4337284767624
63045.782993.7701286131952.0098713868124
73110.523105.555622663734.96437733626984
83013.243063.49518163545-50.255181635452
92987.13003.61689253293-16.5168925329319
102995.552935.2960512526460.253948747363
112833.182919.28188226414-86.1018822641426
122848.962855.47859295501-6.51859295501351
132794.832812.36782137017-17.5378213701703
142845.262757.5478935268187.7121064731903
152915.022856.9769465642258.0430534357808
162892.632964.02966983424-71.3996698342379
172604.422771.99319580253-167.573195802529
182641.652510.82036910092130.829630899079
192659.812746.15203114046-86.342031140456
202638.532570.8178500623567.7121499376502
212720.252696.5620065077623.6879934922381
222745.882714.2782107486131.6017892513861
232735.72669.8567840710665.8432159289373
242811.72851.96961274128-40.2696127412817
252799.432775.1819020962324.2480979037658
262555.282789.6342509918-234.354250991803
272304.982402.04030414991-97.0603041499127
282214.952245.10268366841-30.1526836684080
292065.812084.37739112909-18.5673911290882
301940.492024.90007871979-84.4100787197871
3120421928.48776933105113.512230668955
321995.372069.45408700856-74.0840870085609
331946.812021.19624452210-74.3862445220955
341765.91912.8026291099-146.902629109899
351635.251629.979171681235.27082831877324
361833.421742.6194878550190.8005121449927
371910.431895.5855017695214.8444982304792
381959.671946.0600594032413.6099405967615
391969.62007.11063631402-37.5106363140189
402061.412045.9694467069915.4405532930057
412093.482056.2651549287837.2148450712213
422120.882182.70140106225-61.8214010622488
432174.562200.39229265401-25.8322926540103
442196.722174.9201573218721.7998426781308
452350.442283.2248564372167.2151435627893
462440.252385.2031088888555.0468911111502
472408.642393.6521619835714.9878380164321
482472.812516.82230644870-44.0123064486975
492407.62455.89417346902-48.2941734690235
502454.622384.7594553644669.8605446355425
512448.052488.97726702566-40.9272670256572
522497.842473.5266328532524.3133671467537
532645.642453.28052966284192.359470337158
542756.762793.36802250386-36.6080225038557
552849.272855.57228421076-6.30228421075798
562921.442886.6127239717734.8272760282317


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.2364608480771820.4729216961543630.763539151922818
220.1595158151742210.3190316303484410.84048418482578
230.09610974898740670.1922194979748130.903890251012593
240.07145644245186790.1429128849037360.928543557548132
250.1565055862057490.3130111724114980.843494413794251
260.7531664922087770.4936670155824450.246833507791223
270.8444134847581060.3111730304837880.155586515241894
280.7841960831399150.431607833720170.215803916860085
290.695594636682640.608810726634720.30440536331736
300.7483408101751160.5033183796497670.251659189824884
310.9544502242888690.09109955142226250.0455497757111313
320.949790205415830.1004195891683400.0502097945841699
330.9970859263994750.005828147201049350.00291407360052468
340.9947536096649520.01049278067009660.00524639033504832
350.9801254444306830.03974911113863460.0198745555693173


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level10.0666666666666667NOK
5% type I error level30.2NOK
10% type I error level40.266666666666667NOK
 
Charts produced by software:
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http://www.freestatistics.org/blog/date/2009/Nov/18/t1258566979xie77iujj9rgwwg/1pjg21258566690.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/18/t1258566979xie77iujj9rgwwg/2vqcj1258566690.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/18/t1258566979xie77iujj9rgwwg/932su1258566690.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258566979xie77iujj9rgwwg/932su1258566690.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')
}
 





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Software written by Ed van Stee & Patrick Wessa


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