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multiple -lineaire trend

*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: Thu, 19 Nov 2009 13:41:50 -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/19/t1258663387dqm0ly9zx17p7lm.htm/, Retrieved Thu, 19 Nov 2009 21:43:19 +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/19/t1258663387dqm0ly9zx17p7lm.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 «
0 6,3 0 6,2 0 6,1 0 6,3 0 6,5 0 6,6 0 6,5 0 6,2 0 6,2 0 5,9 0 6,1 0 6,1 0 6,1 0 6,1 0 6,1 0 6,4 0 6,7 0 6,9 0 7 0 7 0 6,8 0 6,4 0 5,9 0 5,5 0 5,5 0 5,6 0 5,8 0 5,9 0 6,1 0 6,1 0 6 0 6 0 5,9 0 5,5 0 5,6 0 5,4 0 5,2 0 5,2 0 5,2 0 5,5 1 5,8 1 5,8 1 5,5 1 5,3 1 5,1 1 5,2 1 5,8 1 5,8 1 5,5 1 5 1 4,9 1 5,3 1 6,1 1 6,5 1 6,8 1 6,6 1 6,4 1 6,4
 
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 time6 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 6.16057692307692 + 0.0480769230769208X[t] -0.0563621794871855M1[t] -0.140608974358974M2[t] -0.124855769230769M3[t] + 0.150897435897435M4[t] + 0.517035256410256M5[t] + 0.672788461538462M6[t] + 0.668541666666667M7[t] + 0.544294871794872M8[t] + 0.420048076923077M9[t] + 0.235801282051282M10[t] + 0.134246794871795M11[t] -0.0157532051282050t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)6.160576923076920.2550224.157200
X0.04807692307692080.2101420.22880.8200980.410049
M1-0.05636217948718550.291549-0.19330.8475980.423799
M2-0.1406089743589740.291203-0.48290.6315920.315796
M3-0.1248557692307690.290971-0.42910.6699430.334972
M40.1508974358974350.2908520.51880.6064920.303246
M50.5170352564102560.2930251.76450.0845930.042297
M60.6727884615384620.2924712.30040.0262280.013114
M70.6685416666666670.292032.28930.0269180.013459
M80.5442948717948720.2917021.86590.0687260.034363
M90.4200480769230770.2914871.44110.156650.078325
M100.2358012820512820.2913870.80920.4227320.211366
M110.1342467948717950.306550.43790.6635810.331791
t-0.01575320512820500.00576-2.7350.0089570.004478


Multiple Linear Regression - Regression Statistics
Multiple R0.695315838819151
R-squared0.48346411571278
Adjusted R-squared0.330851240809738
F-TEST (value)3.16791172448546
F-TEST (DF numerator)13
F-TEST (DF denominator)44
p-value0.0020884763094301
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.433451044170282
Sum Squared Residuals8.26671153846153


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
16.36.088461538461560.211538461538438
26.25.988461538461540.211538461538464
36.15.988461538461540.111538461538463
46.36.248461538461540.0515384615384633
56.56.59884615384615-0.0988461538461528
66.66.73884615384615-0.138846153846152
76.56.71884615384615-0.218846153846152
86.26.57884615384615-0.378846153846153
96.26.43884615384615-0.238846153846152
105.96.23884615384615-0.338846153846153
116.16.12153846153846-0.0215384615384604
126.15.971538461538460.128461538461539
136.15.899423076923070.20057692307693
146.15.799423076923080.300576923076924
156.15.799423076923080.300576923076924
166.46.059423076923080.340576923076924
176.76.409807692307690.290192307692308
186.96.54980769230770.350192307692308
1976.529807692307690.470192307692308
2076.389807692307690.610192307692308
216.86.249807692307690.550192307692308
226.46.049807692307690.350192307692308
235.95.9325-0.0324999999999996
245.55.7825-0.2825
255.55.71038461538461-0.210384615384610
265.65.61038461538462-0.0103846153846166
275.85.610384615384620.189615384615384
285.95.870384615384620.0296153846153845
296.16.22076923076923-0.120769230769232
306.16.36076923076923-0.260769230769232
3166.34076923076923-0.340769230769232
3266.20076923076923-0.200769230769232
335.96.06076923076923-0.160769230769232
345.55.86076923076923-0.360769230769232
355.65.74346153846154-0.143461538461540
365.45.59346153846154-0.193461538461539
375.25.52134615384615-0.321346153846149
385.25.42134615384616-0.221346153846155
395.25.42134615384616-0.221346153846155
405.55.68134615384616-0.181346153846156
415.86.07980769230769-0.279807692307692
425.86.21980769230769-0.419807692307692
435.56.19980769230769-0.699807692307692
445.36.05980769230769-0.759807692307692
455.15.91980769230769-0.819807692307692
465.25.71980769230769-0.519807692307692
475.85.60250.1975
485.85.45250.3475
495.55.380384615384610.119615384615391
5055.28038461538462-0.280384615384616
514.95.28038461538462-0.380384615384615
525.35.54038461538462-0.240384615384616
536.15.890769230769230.209230769230768
546.56.030769230769230.469230769230768
556.86.010769230769230.789230769230768
566.65.870769230769230.729230769230768
576.45.730769230769230.669230769230769
586.45.530769230769230.869230769230769


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.02249527619509500.04499055239019000.977504723804905
180.01403002073354370.02806004146708740.985969979266456
190.01908673950067510.03817347900135010.980913260499325
200.05857915494820750.1171583098964150.941420845051792
210.06455414939777760.1291082987955550.935445850602222
220.05703530245458920.1140706049091780.94296469754541
230.05603417583278370.1120683516655670.943965824167216
240.1104885506884670.2209771013769350.889511449311533
250.2280994369604630.4561988739209270.771900563039537
260.303830628577620.607661257155240.69616937142238
270.5039610855051420.9920778289897160.496038914494858
280.825834362062650.34833127587470.17416563793735
290.8237060920718480.3525878158563030.176293907928152
300.8055733710077040.3888532579845920.194426628992296
310.7814442603524660.4371114792950680.218555739647534
320.7738297038055910.4523405923888170.226170296194409
330.8420720703314080.3158558593371840.157927929668592
340.7998274320291690.4003451359416630.200172567970831
350.7217450127907950.556509974418410.278254987209205
360.7087398958124330.5825202083751340.291260104187567
370.723348837663180.5533023246736420.276651162336821
380.6121555125862260.7756889748275480.387844487413774
390.4854964325675380.9709928651350760.514503567432462
400.3401751351332430.6803502702664860.659824864866757
410.6835219769690710.6329560460618580.316478023030929


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level30.12NOK
10% type I error level30.12NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258663387dqm0ly9zx17p7lm/10p5lr1258663303.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258663387dqm0ly9zx17p7lm/10p5lr1258663303.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258663387dqm0ly9zx17p7lm/1wt431258663303.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258663387dqm0ly9zx17p7lm/1wt431258663303.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258663387dqm0ly9zx17p7lm/247hh1258663303.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258663387dqm0ly9zx17p7lm/247hh1258663303.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258663387dqm0ly9zx17p7lm/3zc481258663303.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258663387dqm0ly9zx17p7lm/3zc481258663303.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258663387dqm0ly9zx17p7lm/4tmjj1258663303.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258663387dqm0ly9zx17p7lm/4tmjj1258663303.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258663387dqm0ly9zx17p7lm/57z0c1258663303.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258663387dqm0ly9zx17p7lm/57z0c1258663303.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258663387dqm0ly9zx17p7lm/6t62s1258663303.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258663387dqm0ly9zx17p7lm/6t62s1258663303.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258663387dqm0ly9zx17p7lm/72qy01258663303.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258663387dqm0ly9zx17p7lm/72qy01258663303.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258663387dqm0ly9zx17p7lm/8ixcc1258663303.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258663387dqm0ly9zx17p7lm/8ixcc1258663303.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Nov/19/t1258663387dqm0ly9zx17p7lm/98kjr1258663303.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Nov/19/t1258663387dqm0ly9zx17p7lm/98kjr1258663303.ps (open in new window)


 
Parameters (Session):
par1 = 2 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
 
Parameters (R input):
par1 = 2 ; par2 = Include Monthly Dummies ; par3 = 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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