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WS 7 (1)

*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, 23 Nov 2010 08:36:41 +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/23/t129050131371j1ktvzq5p2h25.htm/, Retrieved Tue, 23 Nov 2010 09:35:23 +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/23/t129050131371j1ktvzq5p2h25.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 «
1.39 1.08 1.34 1.12 1.33 1.12 1.3 1.16 1.28 1.16 1.29 1.16 1.29 1.16 1.28 1.15 1.27 1.17 1.26 1.16 1.29 1.19 1.36 1.13 1.33 1.14 1.35 1.13 1.31 1.16 1.3 1.17 1.32 1.14 1.33 1.14 1.36 1.11 1.35 1.12 1.4 1.08 1.41 1.07 1.4 1.09 1.4 1.08 1.4 1.08 1.41 1.08 1.4 1.09 1.39 1.08 1.41 1.07 1.42 1.07 1.43 1.07 1.42 1.08 1.42 1.07 1.43 1.06 1.43 1.06 1.43 1.06 1.46 1.04 1.47 1.03 1.47 1.03 1.46 1.04 1.47 1.03 1.49 1.02 1.5 1.01 1.47 1.03 1.48 1.02 1.49 1.01 1.49 1.02 1.5 1.01 1.48 1.02 1.46 1.03 1.43 1.04 1.44 1.04 1.43 1.03
 
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 time12 seconds
R Server'George Udny Yule' @ 72.249.76.132


Multiple Linear Regression - Estimated Regression Equation
us/ch[t] = + 2.10935943686758 -0.734389206628538`eu/us`[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)2.109359436867580.02818174.85100
`eu/us`-0.7343892066285380.02018-36.391600


Multiple Linear Regression - Regression Statistics
Multiple R0.981284059913598
R-squared0.962918406240514
Adjusted R-squared0.962191316166798
F-TEST (value)1324.34541613257
F-TEST (DF numerator)1
F-TEST (DF denominator)51
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.0102367726314117
Sum Squared Residuals0.00534436720926817


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
11.081.08855843965391-0.00855843965390507
21.121.12527789998534-0.00527789998533506
31.121.13262179205162-0.0126217920516204
41.161.154653468250480.0053465317495233
51.161.16934125238305-0.00934125238304747
61.161.16199736031676-0.00199736031676209
71.161.16199736031676-0.00199736031676209
81.151.16934125238305-0.0193412523830475
91.171.17668514444933-0.00668514444933285
101.161.18402903651562-0.0240290365156182
111.191.161997360316760.0280026396832379
121.131.110590115852760.0194098841472356
131.141.132621792051620.00737820794837943
141.131.117934007919050.0120659920809502
151.161.147309576184190.0126904238158087
161.171.154653468250480.0153465317495233
171.141.139965684117913.43158820940498e-05
181.141.132621792051620.00737820794837943
191.111.11059011585276-0.000590115852764216
201.121.117934007919050.00206599208095041
211.081.08121454758762-0.00121454758762287
221.071.07387065552134-0.0038706555213375
231.091.081214547587620.00878545241237714
241.081.08121454758762-0.00121454758762287
251.081.08121454758762-0.00121454758762287
261.081.073870655521340.00612934447866251
271.091.081214547587620.00878545241237714
281.081.08855843965391-0.00855843965390826
291.071.07387065552134-0.0038706555213375
301.071.066526763455050.00347323654494789
311.071.059182871388770.0108171286112333
321.081.066526763455050.0134732365449479
331.071.066526763455050.00347323654494789
341.061.059182871388770.000817128611233264
351.061.059182871388770.000817128611233264
361.061.059182871388770.000817128611233264
371.041.037151195189910.00284880481008939
381.031.029807303123630.000192696876374768
391.031.029807303123630.000192696876374768
401.041.037151195189910.00284880481008939
411.031.029807303123630.000192696876374768
421.021.015119518991050.00488048100894553
431.011.007775626924770.00222437307523091
441.031.029807303123630.000192696876374768
451.021.02246341105734-0.00246341105733985
461.011.01511951899105-0.00511951899105448
471.021.015119518991050.00488048100894553
481.011.007775626924770.00222437307523091
491.021.02246341105734-0.00246341105733985
501.031.03715119518991-0.00715119518991061
511.041.05918287138877-0.0191828713887668
521.041.05183897932248-0.0118389793224814
531.031.05918287138877-0.0291828713887668


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
50.3479733237592850.6959466475185710.652026676240715
60.2011988215325690.4023976430651390.798801178467431
70.1063817489632030.2127634979264050.893618251036797
80.3090076787067550.618015357413510.690992321293245
90.2189501880935100.4379003761870210.78104981190649
100.5948801779585730.8102396440828540.405119822041427
110.9929229584646530.01415408307069350.00707704153534675
120.9980635609062940.003872878187411490.00193643909370575
130.9968087195941570.006382560811686780.00319128040584339
140.996054683413860.00789063317228050.00394531658614025
150.9963188162259840.007362367548031920.00368118377401596
160.997934937683380.004130124633239480.00206506231661974
170.9960638307374290.007872338525142460.00393616926257123
180.9940910151942520.01181796961149540.0059089848057477
190.9904034508714310.01919309825713820.00959654912856912
200.984050272611040.03189945477792070.0159497273889604
210.9772478731455730.04550425370885390.0227521268544269
220.969656930869910.06068613826018080.0303430691300904
230.963754572926050.07249085414790170.0362454270739508
240.9466579097689440.1066841804621120.0533420902310559
250.9228793565458370.1542412869083250.0771206434541626
260.9026959728400330.1946080543199340.097304027159967
270.9017254067510180.1965491864979630.0982745932489817
280.8866881705917920.2266236588164170.113311829408209
290.8499142747173060.3001714505653870.150085725282694
300.809743003366210.3805139932675810.190256996633790
310.8361490235355630.3277019529288750.163850976464437
320.9295583517184440.1408832965631130.0704416482815563
330.9422678227057110.1154643545885780.0577321772942889
340.9447829430968550.1104341138062900.0552170569031448
350.9601306361866540.0797387276266930.0398693638133465
360.9874208510042430.02515829799151470.0125791489957573
370.9909440133827980.01811197323440320.00905598661720162
380.9858871589574340.02822568208513200.0141128410425660
390.9787349933394330.04253001332113320.0212650066605666
400.9915762674765620.01684746504687560.0084237325234378
410.9895157608259350.02096847834813070.0104842391740653
420.9819892328678160.03602153426436760.0180107671321838
430.9652510894215420.06949782115691510.0347489105784576
440.9618381958962340.07632360820753210.0381618041037660
450.9230418511721130.1539162976557740.0769581488278869
460.9140906297399520.1718187405200960.085909370260048
470.8489360883950940.3021278232098110.151063911604906
480.7466071666875550.506785666624890.253392833312445


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level60.136363636363636NOK
5% type I error level180.409090909090909NOK
10% type I error level230.522727272727273NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Nov/23/t129050131371j1ktvzq5p2h25/10j0br1290501388.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/23/t129050131371j1ktvzq5p2h25/10j0br1290501388.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/23/t129050131371j1ktvzq5p2h25/1czdg1290501388.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/23/t129050131371j1ktvzq5p2h25/1czdg1290501388.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/23/t129050131371j1ktvzq5p2h25/24qd11290501388.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/23/t129050131371j1ktvzq5p2h25/24qd11290501388.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/23/t129050131371j1ktvzq5p2h25/34qd11290501388.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/23/t129050131371j1ktvzq5p2h25/34qd11290501388.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/23/t129050131371j1ktvzq5p2h25/44qd11290501388.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/23/t129050131371j1ktvzq5p2h25/44qd11290501388.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/23/t129050131371j1ktvzq5p2h25/5xzul1290501388.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/23/t129050131371j1ktvzq5p2h25/5xzul1290501388.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/23/t129050131371j1ktvzq5p2h25/6xzul1290501388.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/23/t129050131371j1ktvzq5p2h25/6xzul1290501388.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/23/t129050131371j1ktvzq5p2h25/789tp1290501388.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/23/t129050131371j1ktvzq5p2h25/789tp1290501388.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/23/t129050131371j1ktvzq5p2h25/889tp1290501388.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/23/t129050131371j1ktvzq5p2h25/889tp1290501388.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/23/t129050131371j1ktvzq5p2h25/9j0br1290501388.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/23/t129050131371j1ktvzq5p2h25/9j0br1290501388.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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