Home » date » 2009 » Nov » 18 »

WS 7 regressie analyse: seizoenaliteit modelleren

*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 09:09:15 -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/t125856083378nicvble1y2642.htm/, Retrieved Wed, 18 Nov 2009 17:14:05 +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/t125856083378nicvble1y2642.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 «
1901 10436 1395 9314 1639 9717 1643 8997 1751 9062 1797 8885 1373 9058 1558 9095 1555 9149 2061 9857 2010 9848 2119 10269 1985 10341 1963 9690 2017 10125 1975 9349 1589 9224 1679 9224 1392 9454 1511 9347 1449 9430 1767 9933 1899 10148 2179 10677 2217 10735 2049 9760 2343 10567 2175 9333 1607 9409 1702 9502 1764 9348 1766 9319 1615 9594 1953 10160 2091 10182 2411 10810 2550 11105 2351 9874 2786 10958 2525 9311 2474 9610 2332 9398 1978 9784 1789 9425 1904 9557 1997 10166 2207 10337 2453 10770 1948 11265 1384 10183 1989 10941 2140 9628 2100 9709 2045 9637 2083 9579 2022 9741 1950 9754 1422 10508 1859 10749 2147 11079
 
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 time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
aanbod[t] = -1859.31715563635 + 0.384396712586172invoer[t] -162.895577877275M1[t] -65.6092253975502M2[t] -7.28749275514697M3[t] + 366.955966167917M4[t] + 149.111746531092M5[t] + 184.203344577435M6[t] -53.1560360550097M7[t] -19.1997506699084M8[t] -96.6215444520079M9[t] -192.622679956124M10[t] -68.6254591671542M11[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)-1859.317155636351360.024466-1.36710.1780910.089045
invoer0.3843967125861720.1263323.04280.003830.001915
M1-162.895577877275174.79961-0.93190.3561510.178076
M2-65.6092253975502212.406574-0.30890.7587740.379387
M3-7.28749275514697177.70714-0.0410.9674630.483731
M4366.955966167917248.3364521.47770.146170.073085
M5149.111746531092241.3264120.61790.5396340.269817
M6184.203344577435247.8340360.74330.4610280.230514
M7-53.1560360550097237.713129-0.22360.8240270.412013
M8-19.1997506699084242.848508-0.07910.937320.46866
M9-96.6215444520079233.290124-0.41420.6806340.340317
M10-192.622679956124190.207498-1.01270.316390.158195
M11-68.6254591671542184.403042-0.37210.7114540.355727


Multiple Linear Regression - Regression Statistics
Multiple R0.652045551001417
R-squared0.425163400580741
Adjusted R-squared0.278396609239654
F-TEST (value)2.89686377071948
F-TEST (DF numerator)12
F-TEST (DF denominator)47
p-value0.00451362788080933
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation276.160826034476
Sum Squared Residuals3584445.68629409


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
119011989.35135903567-88.3513590356689
213951655.34459999370-260.344599993704
316391868.57820780834-229.578207808336
416431966.05603366936-323.056033669356
517511773.19760035063-22.1976003506323
617971740.2509802692256.7490197307776
713731569.39223091419-196.392230914186
815581617.57119466498-59.5711946649756
915551560.90682336253-5.90682336252936
1020611737.05856036942323.941439630577
1120101857.59621074512152.403789254883
1221192088.0526859110530.9473140889499
1319851952.8336713399832.1663286600199
1419631799.87776392611163.122236073894
1520172025.41206654349-8.41206654349432
1619752101.36367649969-126.363676499689
1715891835.46986778959-246.469867789592
1816791870.56146583593-191.561465835935
1913921721.61332909831-329.61332909831
2015111714.43916623669-203.439166236691
2114491668.92229959924-219.922299599244
2217671766.272710525970.727289474027781
2318991972.91522452097-73.9152245209692
2421792244.88654464621-65.8865446462085
2522172104.28597609893112.714023901068
2620491826.78553380714222.214466192862
2723432195.31541350658147.684586493417
2821752095.2133290983179.78667090169
2916071906.58325961803-299.583259618034
3017021977.42375193489-275.423751934890
3117641680.8672775641883.1327224358243
3217661703.6760582842862.3239417157218
3316151731.96336046338-116.963360463376
3419531853.5307642830399.4692357169667
3520911985.9847127489105.015287251101
3624112296.01130742017114.988692579831
3725502246.51275975582303.487240244184
3823511870.60675904196480.393240958038
3927862345.61452812778440.385471872224
4025252086.75660142141438.243398578586
4124741983.84699884786490.153001152145
4223321937.44649382593394.553506174071
4319781848.46424425175129.535755748253
4417891744.4221098184144.5778901815875
4519041717.74068209769186.259317902312
4619971855.83714455855141.162855441450
4722072045.56620319976161.433796800244
4824532280.63543891672172.364561083277
4919482308.01623376960-360.016233769603
5013841989.38534323109-605.385343231089
5119892339.07978401381-350.079784013811
5221402208.61035931123-68.6103593112309
5321002021.9022733938978.097726606114
5420452029.3173081340215.6826918659762
5520831769.66291817158313.337081828418
5620221865.89147099564156.108529004357
5719501793.46683447716156.533165522837
5814221987.30082026302-565.300820263021
5918592203.93764878526-344.937648785259
6021472399.41402310585-252.41402310585


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.05351119122570770.1070223824514150.946488808774292
170.0887198169482170.1774396338964340.911280183051783
180.1375178764709400.2750357529418790.86248212352906
190.1171177167882650.2342354335765290.882882283211735
200.08285752858559430.1657150571711890.917142471414406
210.07051182071344580.1410236414268920.929488179286554
220.06778175277176160.1355635055435230.932218247228238
230.04989776391615490.09979552783230970.950102236083845
240.02874991408785630.05749982817571250.971250085912144
250.01862799274035530.03725598548071060.981372007259645
260.01635493054717440.03270986109434880.983645069452826
270.01164471593618980.02328943187237960.98835528406381
280.01080697397765910.02161394795531820.98919302602234
290.02474444152281090.04948888304562180.97525555847719
300.03340322399258830.06680644798517670.966596776007412
310.06215037456425360.1243007491285070.937849625435746
320.06182712664635210.1236542532927040.938172873353648
330.05451468655791590.1090293731158320.945485313442084
340.03356666492982140.06713332985964280.966433335070179
350.02721715021749390.05443430043498780.972782849782506
360.01551978510025550.0310395702005110.984480214899744
370.01753007796595500.03506015593191010.982469922034045
380.0797171094992020.1594342189984040.920282890500798
390.4960107087487930.9920214174975860.503989291251207
400.5480022300375660.9039955399248680.451997769962434
410.6568135678420430.6863728643159140.343186432157957
420.6009299556362560.7981400887274880.399070044363744
430.4492941738314020.8985883476628040.550705826168598
440.7388810673763960.5222378652472080.261118932623604


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level70.241379310344828NOK
10% type I error level120.413793103448276NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Nov/18/t125856083378nicvble1y2642/10rffv1258560550.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/18/t125856083378nicvble1y2642/8ty201258560550.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Nov/18/t125856083378nicvble1y2642/9ta7w1258560550.png (open in new window)
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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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