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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, 16 Dec 2009 07:02:04 -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/16/t1260972294f8fwe4c5c9rdkaq.htm/, Retrieved Wed, 16 Dec 2009 15:05:07 +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/16/t1260972294f8fwe4c5c9rdkaq.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 «
20366 0 22782 0 19169 0 13807 0 29743 0 25591 0 29096 0 26482 0 22405 0 27044 0 17970 0 18730 0 19684 0 19785 0 18479 0 10698 0 31956 0 29506 0 34506 0 27165 0 26736 0 23691 0 18157 0 17328 0 18205 0 20995 0 17382 0 9367 0 31124 0 26551 0 30651 0 25859 0 25100 0 25778 0 20418 0 18688 0 20424 0 24776 0 19814 0 12738 0 31566 0 30111 0 30019 0 31934 1 25826 1 26835 1 20205 1 17789 1 20520 1 22518 1 15572 1 11509 1 25447 1 24090 1 27786 1 26195 1 20516 1 22759 1 19028 1 16971 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 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
Y[t] = + 18301.5517241379 -1000.87931034482X[t] + 1738.42413793102M1[t] + 4069.82413793103M2[t] -18.1758620689729M3[t] -6477.57586206898M4[t] + 11865.8241379310M5[t] + 9068.42413793104M6[t] + 12310.2241379310M7[t] + 9625.8M8[t] + 6215.4M9[t] + 7320.2M10[t] + 1254.40000000000M11[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)18301.5517241379915.18169919.997700
X-1000.87931034482581.14096-1.72230.0915970.045798
M11738.424137931021257.2001181.38280.1732690.086634
M24069.824137931031257.2001183.23720.0022160.001108
M3-18.17586206897291257.200118-0.01450.9885260.494263
M4-6477.575862068981257.200118-5.15245e-063e-06
M511865.82413793101257.2001189.438300
M69068.424137931041257.2001187.213200
M712310.22413793101257.2001189.791800
M89625.81251.8159397.689500
M96215.41251.8159394.96519e-065e-06
M107320.21251.8159395.847700
M111254.400000000001251.8159391.00210.3214440.160722


Multiple Linear Regression - Regression Statistics
Multiple R0.951753185657985
R-squared0.905834126410122
Adjusted R-squared0.881791775706323
F-TEST (value)37.6766039881035
F-TEST (DF numerator)12
F-TEST (DF denominator)47
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation1979.29478861406
Sum Squared Residuals184127569.431034


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
12036620039.975862069326.024137930996
22278222371.3758620690410.62413793103
31916918283.3758620690885.624137931035
41380711823.97586206901983.02413793103
52974330167.3758620690-424.375862068960
62559127369.9758620689-1778.97586206895
72909630611.775862069-1515.77586206897
82648227927.3517241379-1445.35172413794
92240524516.9517241379-2111.95172413793
102704425621.75172413791422.24827586208
111797019555.9517241379-1585.95172413793
121873018301.5517241379428.448275862066
131968420039.9758620690-355.975862068954
141978522371.3758620690-2586.37586206897
151847918283.3758620690195.624137931036
161069811823.9758620690-1125.97586206896
173195630167.37586206901788.62413793103
182950627369.97586206902136.02413793103
193450630611.77586206903894.22413793104
202716527927.3517241379-762.351724137928
212673624516.95172413792219.04827586207
222369125621.7517241379-1930.75172413793
231815719555.9517241379-1398.95172413793
241732818301.5517241379-973.551724137935
251820520039.9758620690-1834.97586206895
262099522371.3758620690-1376.37586206896
271738218283.3758620690-901.375862068965
28936711823.9758620690-2456.97586206896
293112430167.3758620690956.624137931035
302655127369.975862069-818.97586206897
313065130611.775862069039.2241379310378
322585927927.3517241379-2068.35172413793
332510024516.9517241379583.048275862069
342577825621.7517241379156.248275862067
352041819555.9517241379862.048275862068
361868818301.5517241379386.448275862067
372042420039.9758620690384.024137931045
382477622371.37586206902404.62413793104
391981418283.37586206901530.62413793103
401273811823.9758620690914.024137931036
413156630167.37586206901398.62413793103
423011127369.97586206902741.02413793103
433001930611.7758620690-592.775862068962
443193426926.47241379315007.5275862069
452582623516.07241379312309.9275862069
462683524620.87241379312214.12758620690
472020518555.07241379311649.92758620690
481778917300.6724137931488.327586206894
492052019039.09655172411480.90344827587
502251821370.49655172411147.50344827586
511557217282.4965517241-1710.49655172414
521150910823.0965517241685.903448275864
532544729166.4965517241-3719.49655172414
542409026369.0965517241-2279.09655172415
552778629610.8965517241-1824.89655172414
562619526926.4724137931-731.472413793099
572051623516.0724137931-3000.0724137931
582275924620.8724137931-1861.87241379311
591902818555.0724137931472.927586206896
601697117300.6724137931-329.672413793106


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.4342153707574910.8684307415149820.565784629242509
170.3620343452649230.7240686905298460.637965654735077
180.4582749525991640.9165499051983290.541725047400836
190.7122778366764020.5754443266471960.287722163323598
200.6096846595074020.7806306809851960.390315340492598
210.6709055127084720.6581889745830560.329094487291528
220.6651794591411950.669641081717610.334820540858805
230.5907932575653730.8184134848692540.409206742434627
240.508083853045240.983832293909520.49191614695476
250.4777645043045050.955529008609010.522235495695495
260.4369283456131330.8738566912262660.563071654386867
270.3646944414752420.7293888829504840.635305558524758
280.417189559250580.834379118501160.58281044074942
290.3406257718319030.6812515436638070.659374228168097
300.2729859907928430.5459719815856870.727014009207157
310.2084709001560620.4169418003121240.791529099843938
320.3018243573950610.6036487147901220.698175642604939
330.2238208357247830.4476416714495670.776179164275217
340.1687172939835730.3374345879671460.831282706016427
350.1546391803343030.3092783606686070.845360819665697
360.1150156736539420.2300313473078840.884984326346058
370.1122962931174080.2245925862348160.887703706882592
380.1201535894615570.2403071789231150.879846410538443
390.07944118254924060.1588823650984810.92055881745076
400.07114103935205180.1422820787041040.928858960647948
410.04427138764176160.08854277528352320.955728612358238
420.04196027894081370.08392055788162740.958039721059186
430.02094829678908960.04189659357817920.97905170321091
440.05957784888221260.1191556977644250.940422151117787


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level10.0344827586206897OK
10% type I error level30.103448275862069NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Dec/16/t1260972294f8fwe4c5c9rdkaq/10vbkz1260972119.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Dec/16/t1260972294f8fwe4c5c9rdkaq/2s1fm1260972119.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Dec/16/t1260972294f8fwe4c5c9rdkaq/3sy1k1260972119.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Dec/16/t1260972294f8fwe4c5c9rdkaq/486c61260972119.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Dec/16/t1260972294f8fwe4c5c9rdkaq/6ypmw1260972119.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Dec/16/t1260972294f8fwe4c5c9rdkaq/71gqp1260972119.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/16/t1260972294f8fwe4c5c9rdkaq/71gqp1260972119.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/16/t1260972294f8fwe4c5c9rdkaq/8k2w91260972119.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/16/t1260972294f8fwe4c5c9rdkaq/8k2w91260972119.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/16/t1260972294f8fwe4c5c9rdkaq/9zc8x1260972119.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/16/t1260972294f8fwe4c5c9rdkaq/9zc8x1260972119.ps (open in new window)


 
Parameters (Session):
par1 = 0 ; par2 = 36 ;
 
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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