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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, 21 Dec 2010 13:17:04 +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/Dec/21/t12929373207uh6wa2al3rom5o.htm/, Retrieved Tue, 21 Dec 2010 14:15:32 +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/Dec/21/t12929373207uh6wa2al3rom5o.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 «
6.3 2 4.5 1 6.6 42 3 1 3 2.1 1.8 69 2547 4603 624 3 5 4 9.1 0.7 27 10.55 179.5 180 4 4 4 15.8 3.9 19 0.023 0.3 35 1 1 1 5.2 1 30.4 160 169 392 4 5 4 10.9 3.6 28 3.3 25.6 63 1 2 1 8.3 1.4 50 52.16 440 230 1 1 1 11 1.5 7 0.425 6.4 112 5 4 4 3.2 0.7 30 465 423 281 5 5 5 6.3 2.1 3.5 0.075 1.2 42 1 1 1 8.6 0 50 3 25 28 2 2 2 6.6 4.1 6 0.785 3.5 42 2 2 2 9.5 1.2 10.4 0.2 5 120 2 2 2 3.3 0.5 20 27.66 115 148 5 5 5 11 3.4 3.9 0.12 1 16 3 1 2 4.7 1.5 41 85 325 310 1 3 1 10.4 3.4 9 0.101 4 28 5 1 3 7.4 0.8 7.6 1.04 5.5 68 5 3 4 2.1 0.8 46 521 655 336 5 5 5 7.7 1.4 2.6 0.005 0.14 21.5 5 2 4 17.9 2 24 0.01 0.25 50 1 1 1 6.1 1.9 100 62 1320 267 1 1 1 11.9 1.3 3.2 0.023 0.4 19 4 1 3 10.8 2 2 0.048 0.33 30 4 1 3 13.8 5.6 5 1.7 6.3 12 2 1 1 14.3 3.1 6.5 3.5 10.8 120 2 1 1 15.2 1.8 12 0.48 15.5 140 2 2 2 10 0.9 20.2 10 115 170 4 4 4 11.9 1.8 13 1.62 11.4 17 2 1 2 6.5 1.9 27 192 180 115 4 4 4 7.5 0.9 18 2.5 12.1 31 5 5 5 10.6 2.6 4.7 0.28 1.9 21 3 1 3 7.4 2.4 9.8 4.235 50.4 52 1 1 1 8.4 1.2 29 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 time9 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135
R Framework
error message
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.


Multiple Linear Regression - Estimated Regression Equation
PS[t] = + 3.62388684905666 + 0.0115328862754582SWS[t] -0.0133813431715984L[t] + 0.00133188408343262WB[t] + 0.000311047350003712WBR[t] -0.00484781985414119TG[t] + 0.8840450491086P[t] + 0.357433139265944S[t] -1.70617590983705`D `[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)3.623886849056660.8704444.16330.0002110.000106
SWS0.01153288627545820.0572210.20160.8415050.420753
L-0.01338134317159840.014517-0.92180.3633430.181672
WB0.001331884083432620.0018670.71320.4807240.240362
WBR0.0003110473500037120.0011170.27840.7824620.391231
TG-0.004847819854141190.002328-2.08270.0451110.022555
P0.88404504910860.3522072.510.0171560.008578
S0.3574331392659440.2151371.66140.1061010.05305
`D `-1.706175909837050.454756-3.75190.0006770.000338


Multiple Linear Regression - Regression Statistics
Multiple R0.787947573648145
R-squared0.620861378817999
Adjusted R-squared0.52894898580418
F-TEST (value)6.75492562493347
F-TEST (DF numerator)8
F-TEST (DF denominator)33
p-value3.14250718375098e-05
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.953180992750902
Sum Squared Residuals29.9822821630727


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
121.327144908120000.672855091880002
21.82.13841055928803-0.338410559288035
30.70.706025765340633-0.00602576534063304
43.92.917613463130010.982386536869987
510.1410303513648910.85896964863511
63.62.974598497282380.625401502717623
71.41.67717826644156-0.277178266441559
81.52.14193428925577-0.641934289255774
90.70.3245249315117320.375475068488268
102.12.98187632428129-0.88187632428129
1102.00063994960512-2.00063994960512
124.12.488846157376671.61115384262333
131.22.08497108783365-0.884971087833654
140.50.4259629236064750.0740370763935246
153.43.218683582408880.18131641759112
161.52.09110128264438-0.591101282644382
173.43.148167186851340.251832813148663
180.81.94879719317374-1.14879719317374
190.8-0.02214433224152360.822144332241524
201.41.88410854504362-0.484108545043622
2122.80217564377778-0.80217564377778
221.91.090196830836640.809803169163356
231.32.40143997881994-1.10143997881994
2422.35149692111489-0.351496921114892
255.64.081531254443261.51846874555674
263.13.54745824300154-0.447458243001537
271.82.03598091816478-0.235980918164783
280.90.83508160477570.0649183952242993
291.82.22363280679769-0.423632806797694
301.91.232974442157470.667025557842527
310.91.00284167938657-0.102841679386569
322.61.473443388322021.12655661167798
332.42.88262600606907-0.482626006069074
341.22.03043366947395-0.830433669473952
350.91.58062478398644-0.680624783986437
360.50.769150938992037-0.269150938992037
370.60.4660086692994920.133991330700508
382.32.114842199160190.185157800839807
390.50.508004154843701-0.0080041548437012
402.63.47790988581082-0.877909885810824
410.60.2039587559344430.396041244065557
426.64.088716292512882.51128370748712


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
120.8471979779289710.3056040441420570.152802022071029
130.9185188104889640.1629623790220710.0814811895110357
140.8519286656087180.2961426687825630.148071334391282
150.7923076590701760.4153846818596480.207692340929824
160.6889338664599960.6221322670800080.311066133540004
170.6377610429150910.7244779141698170.362238957084909
180.6158016599972830.7683966800054340.384198340002717
190.5521404872209820.8957190255580350.447859512779018
200.4555683192063170.9111366384126350.544431680793683
210.4266133705035530.8532267410071060.573386629496447
220.4337156036212550.8674312072425110.566284396378745
230.4942375940282620.9884751880565240.505762405971738
240.5330648672123020.9338702655753970.466935132787698
250.5975597640380820.8048804719238360.402440235961918
260.5436022649325010.9127954701349970.456397735067499
270.4157331849398440.8314663698796890.584266815060156
280.3057901602358670.6115803204717340.694209839764133
290.2444414074902590.4888828149805190.755558592509741
300.242229251538890.484458503077780.75777074846111


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level00OK
10% type I error level00OK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929373207uh6wa2al3rom5o/10fdd01292937414.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929373207uh6wa2al3rom5o/10fdd01292937414.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t12929373207uh6wa2al3rom5o/11lfa1292937414.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929373207uh6wa2al3rom5o/11lfa1292937414.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t12929373207uh6wa2al3rom5o/21lfa1292937414.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929373207uh6wa2al3rom5o/21lfa1292937414.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t12929373207uh6wa2al3rom5o/3ucfv1292937414.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929373207uh6wa2al3rom5o/3ucfv1292937414.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t12929373207uh6wa2al3rom5o/4m4ef1292937414.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929373207uh6wa2al3rom5o/4m4ef1292937414.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t12929373207uh6wa2al3rom5o/5m4ef1292937414.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929373207uh6wa2al3rom5o/5m4ef1292937414.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t12929373207uh6wa2al3rom5o/6m4ef1292937414.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929373207uh6wa2al3rom5o/6m4ef1292937414.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t12929373207uh6wa2al3rom5o/7m4ef1292937414.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929373207uh6wa2al3rom5o/7m4ef1292937414.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t12929373207uh6wa2al3rom5o/8fdd01292937414.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929373207uh6wa2al3rom5o/8fdd01292937414.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t12929373207uh6wa2al3rom5o/9fdd01292937414.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929373207uh6wa2al3rom5o/9fdd01292937414.ps (open in new window)


 
Parameters (Session):
par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
 
Parameters (R input):
par1 = 2 ; 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')
}
 





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