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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 17:25:01 +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/t1290878581clnucj6wtjy5hdp.htm/, Retrieved Sat, 27 Nov 2010 18:23:04 +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/t1290878581clnucj6wtjy5hdp.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 «
4754 4531 4690 4716 4824 5270 5172 5150 5245 5300 4836 4663 4592 4553 4217 4366 4532 4743 4776 4949 5069 4980 5213 5394 6075 5919 5758 5916 6474 6704 7553 7891 7840 7007 6680 6102 5238 4237 3983 3879 3733 3940 3945 4324 4233 4550 4344 4388 4561 4512 4756 4704 5107 5472 5537 5539 5313 5371 5459 5461
 
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 time7 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk


Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 5201.6 -157.600000000001M1[t] -451.2M2[t] -520.8M3[t] -485.4M4[t] -267.6M5[t] + 24.1999999999999M6[t] + 195M7[t] + 369M8[t] + 338.4M9[t] + 240M10[t] + 104.8M11[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)5201.6438.60107911.859500
M1-157.600000000001620.275595-0.25410.8005190.400259
M2-451.2620.275595-0.72740.4705030.235251
M3-520.8620.275595-0.83960.405280.20264
M4-485.4620.275595-0.78260.4377320.218866
M5-267.6620.275595-0.43140.6680940.334047
M624.1999999999999620.2755950.0390.969040.48452
M7195620.2755950.31440.7545980.377299
M8369620.2755950.59490.5547070.277353
M9338.4620.2755950.54560.5878920.293946
M10240620.2755950.38690.7005220.350261
M11104.8620.2755950.1690.866540.43327


Multiple Linear Regression - Regression Statistics
Multiple R0.330671852624358
R-squared0.109343874118025
Adjusted R-squared-0.094764821396594
F-TEST (value)0.535713943212153
F-TEST (DF numerator)11
F-TEST (DF denominator)48
p-value0.869091752881583
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation980.741828073695
Sum Squared Residuals46169017.6


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
147545044-290.000000000002
245314750.4-219.4
346904680.89.19999999999978
447164716.2-0.199999999999998
548244934-110
652705225.844.2000000000003
751725396.6-224.6
851505570.6-420.6
952455540-295
1053005441.6-141.6
1148365306.4-470.4
1246635201.6-538.6
1345925044-451.999999999999
1445534750.4-197.4
1542174680.8-463.8
1643664716.2-350.2
1745324934-402
1847435225.8-482.8
1947765396.6-620.6
2049495570.6-621.6
2150695540-471
2249805441.6-461.6
2352135306.4-93.4
2453945201.6192.4
25607550441031
2659194750.41168.6
2757584680.81077.2
2859164716.21199.8
29647449341540
3067045225.81478.2
3175535396.62156.4
3278915570.62320.4
33784055402300
3470075441.61565.4
3566805306.41373.6
3661025201.6900.4
3752385044194
3842374750.4-513.4
3939834680.8-697.8
4038794716.2-837.2
4137334934-1201
4239405225.8-1285.8
4339455396.6-1451.6
4443245570.6-1246.6
4542335540-1307
4645505441.6-891.6
4743445306.4-962.4
4843885201.6-813.6
4945615044-482.999999999999
5045124750.4-238.4
5147564680.875.2
5247044716.2-12.2
5351074934173
5454725225.8246.2
5555375396.6140.4
5655395570.6-31.6
5753135540-227
5853715441.6-70.6
5954595306.4152.6
6054615201.6259.4


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
150.007543066501434460.01508613300286890.992456933498566
160.002319204350044740.004638408700089490.997680795649955
170.0005921294975639790.001184258995127960.999407870502436
180.0003678171617777380.0007356343235554770.999632182838222
190.0001319412183583150.0002638824367166290.999868058781642
203.04473499258097e-056.08946998516194e-050.999969552650074
216.39228931629099e-061.2784578632582e-050.999993607710684
221.8017560271664e-063.6035120543328e-060.999998198243973
235.80957123210544e-071.16191424642109e-060.999999419042877
247.83306825342432e-071.56661365068486e-060.999999216693175
254.03476967523565e-058.0695393504713e-050.999959652303248
260.0002214601909737140.0004429203819474280.999778539809026
270.0005084716299757470.001016943259951490.999491528370024
280.001104642356554150.002209284713108310.998895357643446
290.004581366009257790.009162732018515580.995418633990742
300.01115730018190870.02231460036381730.98884269981809
310.08018148035869170.1603629607173830.919818519641308
320.3332862798671460.6665725597342910.666713720132854
330.7214056518575330.5571886962849340.278594348142467
340.8402112133464610.3195775733070780.159788786653539
350.9032656407525920.1934687184948160.096734359247408
360.903659804585390.1926803908292190.0963401954146093
370.8617110027445470.2765779945109050.138288997255453
380.8006340616857780.3987318766284430.199365938314222
390.7473307748730590.5053384502538820.252669225126941
400.6932116702085650.613576659582870.306788329791435
410.7032644436244750.5934711127510490.296735556375525
420.7393858535162190.5212282929675630.260614146483781
430.7977555436916540.4044889126166920.202244456308346
440.7905456861858780.4189086276282440.209454313814122
450.7558495895700020.4883008208599960.244150410429998


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level140.451612903225806NOK
5% type I error level160.516129032258065NOK
10% type I error level160.516129032258065NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Nov/27/t1290878581clnucj6wtjy5hdp/10fcvi1290878691.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/27/t1290878581clnucj6wtjy5hdp/10fcvi1290878691.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/27/t1290878581clnucj6wtjy5hdp/1qtg61290878691.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/27/t1290878581clnucj6wtjy5hdp/1qtg61290878691.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/27/t1290878581clnucj6wtjy5hdp/2qtg61290878691.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/27/t1290878581clnucj6wtjy5hdp/2qtg61290878691.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/27/t1290878581clnucj6wtjy5hdp/3qtg61290878691.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/27/t1290878581clnucj6wtjy5hdp/3qtg61290878691.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/27/t1290878581clnucj6wtjy5hdp/4j2fr1290878691.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/27/t1290878581clnucj6wtjy5hdp/4j2fr1290878691.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/27/t1290878581clnucj6wtjy5hdp/5j2fr1290878691.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/27/t1290878581clnucj6wtjy5hdp/5j2fr1290878691.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/27/t1290878581clnucj6wtjy5hdp/6j2fr1290878691.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/27/t1290878581clnucj6wtjy5hdp/6j2fr1290878691.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/27/t1290878581clnucj6wtjy5hdp/7utwc1290878691.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/27/t1290878581clnucj6wtjy5hdp/7utwc1290878691.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/27/t1290878581clnucj6wtjy5hdp/8m2vf1290878691.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/27/t1290878581clnucj6wtjy5hdp/8m2vf1290878691.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/27/t1290878581clnucj6wtjy5hdp/9m2vf1290878691.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/27/t1290878581clnucj6wtjy5hdp/9m2vf1290878691.ps (open in new window)


 
Parameters (Session):
par1 = 1 ; par2 = Do not include Seasonal 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')
}
 





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