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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 07:44:06 -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/t1258555649xselnkojxyuuzbp.htm/, Retrieved Wed, 18 Nov 2009 15:47:41 +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/t1258555649xselnkojxyuuzbp.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 «
8,2 25,5 8,3 25,5 8,1 25,5 7,4 20,9 7,3 20,9 7,7 20,9 8 22,3 8 22,3 7,7 22,3 6,9 19,9 6,6 19,9 6,9 19,9 7,5 24,1 7,9 24,1 7,7 24,1 6,5 13,8 6,1 13,8 6,4 13,8 6,8 16,2 7,1 16,2 7,3 16,2 7,2 18,6 7 18,6 7 18,6 7 22,4 7,3 22,4 7,5 22,4 7,2 22,6 7,7 22,6 8 22,6 7,9 20 8 20 8 20 7,9 21,8 7,9 21,8 8 21,8 8,1 28,7 8,1 28,7 8,2 28,7 8 19,5 8,3 19,5 8,5 19,5 8,6 19,4 8,7 19,4 8,7 19,4 8,5 21,7 8,4 21,7 8,5 21,7 8,7 26,2 8,7 26,2 8,6 26,2 7,9 19,1 8,1 19,1 8,2 19,1 8,5 21,3 8,6 21,3 8,5 21,3 8,3 24,1 8,2 24,1 8,7 24,1
 
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 time7 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 3.89013097776424 + 0.18519646664636X[t] -0.690417301248855M1[t] -0.530417301248857M2[t] -0.570417301248857M3[t] -0.0421992080414256M4[t] + 0.0578007919585741M5[t] + 0.317800791958574M6[t] + 0.395571123971977M7[t] + 0.515571123971976M8[t] + 0.475571123971977M9[t] -0.0599999999999998M10[t] -0.200000000000000M11[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)3.890130977764240.6466.021900
X0.185196466646360.0285136.495200
M1-0.6904173012488550.341406-2.02230.048860.02443
M2-0.5304173012488570.341406-1.55360.1269820.063491
M3-0.5704173012488570.341406-1.67080.101410.050705
M4-0.04219920804142560.32538-0.12970.8973640.448682
M50.05780079195857410.325380.17760.8597680.429884
M60.3178007919585740.325380.97670.3337150.166858
M70.3955711239719770.3225481.22640.2261590.11308
M80.5155711239719760.3225481.59840.1166490.058324
M90.4755711239719770.3225481.47440.1470360.073518
M10-0.05999999999999980.320139-0.18740.8521390.42607
M11-0.2000000000000000.320139-0.62470.535170.267585


Multiple Linear Regression - Regression Statistics
Multiple R0.728703258736597
R-squared0.531008439293335
Adjusted R-squared0.411265913155463
F-TEST (value)4.43458524235517
F-TEST (DF numerator)12
F-TEST (DF denominator)47
p-value0.000103242332424536
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.506184152739685
Sum Squared Residuals12.0424526347853


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
18.27.922223575997550.277776424002445
28.38.082223575997560.217776424002437
38.18.042223575997560.0577764240024357
47.47.71853792263174-0.318537922631738
57.37.81853792263174-0.518537922631739
67.78.07853792263174-0.378537922631739
788.41558330795005-0.415583307950046
888.53558330795004-0.535583307950045
97.78.49558330795005-0.795583307950046
106.97.5155406640268-0.615540664026804
116.67.3755406640268-0.775540664026805
126.97.5755406640268-0.675540664026804
137.57.66294852269266-0.162948522692661
147.97.822948522692660.0770514773073407
157.77.78294852269266-0.0829485226926589
166.56.403643009442580.0963569905574161
176.16.50364300944258-0.403643009442584
186.46.76364300944258-0.363643009442583
196.87.28588486140725-0.48588486140725
207.17.40588486140725-0.30588486140725
217.37.36588486140725-0.0658848614072498
227.27.27478525738654-0.0747852573865374
2377.13478525738654-0.134785257386537
2477.33478525738654-0.334785257386537
2577.34811452939385-0.348114529393849
267.37.50811452939385-0.208114529393847
277.57.468114529393850.0318854706061531
287.28.03337191593055-0.833371915930551
297.78.13337191593055-0.433371915930551
3088.39337191593055-0.393371915930551
317.97.98963143466342-0.089631434663417
3288.10963143466342-0.109631434663417
3388.06963143466342-0.0696314346634173
347.97.867413950654890.0325860493451112
357.97.727413950654890.172586049345112
3687.927413950654890.0725860493451112
378.18.51485226926592-0.414852269265917
388.18.67485226926591-0.574852269265915
398.28.63485226926591-0.434852269265915
4087.459262869326840.540737130673165
418.37.559262869326830.740737130673166
428.57.819262869326830.680737130673166
438.67.87851355467560.721486445324399
448.77.99851355467560.701486445324398
458.77.95851355467560.741486445324398
468.57.848894303990250.651105696009747
478.47.708894303990250.691105696009748
488.57.908894303990250.591105696009747
498.78.051861102650020.648138897349982
508.78.211861102650020.488138897349984
518.68.171861102650010.428138897349985
527.97.385184282668290.514815717331709
538.17.485184282668290.614815717331708
548.27.74518428266830.454815717331708
558.58.230386841303690.269613158696315
568.68.350386841303680.249613158696314
578.58.310386841303690.189613158696315
588.38.293365823941520.0066341760584837
598.28.153365823941520.0466341760584828
608.78.353365823941520.346634176058482


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.1186769670489080.2373539340978160.881323032951092
170.04830983690677140.09661967381354290.951690163093229
180.01999360945124030.03998721890248060.98000639054876
190.009517611946391750.01903522389278350.990482388053608
200.004212472713791890.008424945427583780.995787527286208
210.01143309922990780.02286619845981550.988566900770092
220.01409077965155570.02818155930311140.985909220348444
230.02399952029878330.04799904059756670.976000479701217
240.02710969416475630.05421938832951270.972890305835244
250.06234512065527410.1246902413105480.937654879344726
260.1209631826154490.2419263652308980.87903681738455
270.2276486676361990.4552973352723970.772351332363801
280.3104502122263110.6209004244526220.689549787773689
290.2640590107620040.5281180215240080.735940989237996
300.2042640055060720.4085280110121450.795735994493928
310.2813149179568910.5626298359137830.718685082043109
320.3815608641073040.7631217282146090.618439135892696
330.5090177279569510.9819645440860990.490982272043049
340.651362336713440.697275326573120.34863766328656
350.8025632264634980.3948735470730030.197436773536502
360.9746102248640310.0507795502719380.025389775135969
370.9782546762636830.04349064747263490.0217453237363174
380.9909923656236770.01801526875264540.0090076343763227
390.9912406317268670.01751873654626630.00875936827313316
400.989835725916660.02032854816668110.0101642740833405
410.9923927919335060.01521441613298730.00760720806649367
420.9960491230997670.007901753800466420.00395087690023321
430.988104348147190.02379130370562260.0118956518528113
440.9615473152565380.0769053694869240.038452684743462


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level20.0689655172413793NOK
5% type I error level130.448275862068966NOK
10% type I error level170.586206896551724NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258555649xselnkojxyuuzbp/10jxq01258555437.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/18/t1258555649xselnkojxyuuzbp/9mx611258555437.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/18/t1258555649xselnkojxyuuzbp/9mx611258555437.ps (open in new window)


 
Parameters (Session):
par1 = 1 ; par2 = Include Monthly 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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Software written by Ed van Stee & Patrick Wessa


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