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Multiple Regression werklh ecogr 2 vertragingen

*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, 17 Dec 2009 07:43:11 -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/17/t1261061058br7p8r69t2o2xuz.htm/, Retrieved Thu, 17 Dec 2009 15:44:30 +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/17/t1261061058br7p8r69t2o2xuz.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 «
8,7 110,3 9,3 9,3 8,2 103,9 8,7 9,3 8,3 101,6 8,2 8,7 8,5 94,6 8,3 8,2 8,6 95,9 8,5 8,3 8,5 104,7 8,6 8,5 8,2 102,8 8,5 8,6 8,1 98,1 8,2 8,5 7,9 113,9 8,1 8,2 8,6 80,9 7,9 8,1 8,7 95,7 8,6 7,9 8,7 113,2 8,7 8,6 8,5 105,9 8,7 8,7 8,4 108,8 8,5 8,7 8,5 102,3 8,4 8,5 8,7 99 8,5 8,4 8,7 100,7 8,7 8,5 8,6 115,5 8,7 8,7 8,5 100,7 8,6 8,7 8,3 109,9 8,5 8,6 8 114,6 8,3 8,5 8,2 85,4 8 8,3 8,1 100,5 8,2 8 8,1 114,8 8,1 8,2 8 116,5 8,1 8,1 7,9 112,9 8 8,1 7,9 102 7,9 8 8 106 7,9 7,9 8 105,3 8 7,9 7,9 118,8 8 8 8 106,1 7,9 8 7,7 109,3 8 7,9 7,2 117,2 7,7 8 7,5 92,5 7,2 7,7 7,3 104,2 7,5 7,2 7 112,5 7,3 7,5 7 122,4 7 7,3 7 113,3 7 7 7,2 100 7 7 7,3 110,7 7,2 7 7,1 112,8 7,3 7,2 6,8 109,8 7,1 7,3 6,4 117,3 6,8 7,1 6,1 109,1 6,4 6,8 6,5 115,9 6,1 6,4 7,7 96 6,5 6,1 7,9 99,8 7,7 6,5 7,5 116,8 7,9 7,7 6,9 115,7 7,5 7,9 6,6 99,4 6,9 7,5 6,9 94,3 6,6 6,9 7,7 91 6,9 6,6 8 93,2 7,7 6,9 8 103,1 8 7,7 7,7 94,1 8 8 7,3 91,8 7,7 8 7,4 102,7 7,3 7,7 8,1 82,6 7,4 7,3
 
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] = + 3.62399518778054 -0.0116550205248898X[t] + 1.33908375456985Y1[t] -0.61955467605507Y2[t] -0.0436568455591268M1[t] + 0.00299857923202550M2[t] + 0.143563257409505M3[t] + 0.122170287553879M4[t] -0.103225295505422M5[t] + 0.00667643070592493M6[t] -0.072453772067619M7[t] -0.138084807294505M8[t] + 0.101050909401817M9[t] + 0.405496234642471M10[t] -0.370533810105535M11[t] -0.00742558647969111t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)3.623995187780540.9617843.7680.0005070.000254
X-0.01165502052488980.004553-2.56010.0141510.007075
Y11.339083754569850.11725611.420200
Y2-0.619554676055070.119921-5.16636e-063e-06
M1-0.04365684555912680.123152-0.35450.7247420.362371
M20.002998579232025500.1318820.02270.9819680.490984
M30.1435632574095050.1475430.9730.336110.168055
M40.1221702875538790.145720.83840.4065580.203279
M5-0.1032252955054220.140214-0.73620.4657030.232852
M60.006676430705924930.1231970.05420.9570380.478519
M7-0.0724537720676190.130933-0.55340.5829460.291473
M8-0.1380848072945050.134657-1.02550.3110190.15551
M90.1010509094018170.1276550.79160.4330440.216522
M100.4054962346424710.1842132.20120.0332670.016634
M11-0.3705338101055350.164088-2.25810.0291920.014596
t-0.007425586479691110.00262-2.83420.0070320.003516


Multiple Linear Regression - Regression Statistics
Multiple R0.972152036416714
R-squared0.945079581909165
Adjusted R-squared0.925465146876724
F-TEST (value)48.1828602427782
F-TEST (DF numerator)15
F-TEST (DF denominator)42
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.181892943332620
Sum Squared Residuals1.38957179903655


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
18.78.97898442203381-0.278984422033815
28.28.28935613896266-0.0893561389626577
38.38.151492706215810.148507293784190
48.58.64794500703924-0.147945007039241
58.68.60583359412635-0.00583359412635362
68.58.61574299348495-0.115742993484950
78.28.35546790016651-0.155467900166515
88.17.997420216161470.102579783838529
97.98.09693904944438-0.196939049444379
108.68.572713182218240.0272868177817554
118.78.678032810632080.021967189367915
128.78.53739827729080.162601722709207
138.58.50944202747816-0.00944202747816331
148.48.247055555353470.152944444646525
158.58.445954840217080.0540451597829233
168.78.651461694676390.0485383053236123
178.78.604688273553540.0953117264464555
188.68.410759174305820.189240825694183
198.58.362789313363970.137210686636033
208.38.110553594976930.189446405023075
2188.08162384541811-0.0816238454181131
228.28.44115599234592-0.241155992345917
238.17.935392704922870.164607295077126
248.17.87401482437480.225985175625205
2587.865074325049170.134925674950829
267.97.812353861793250.0876461382067493
277.98.00057976936086-0.100579769360861
2887.98709659853150.0129034014685088
2987.89634231881690.103657681183094
307.97.779520213857040.120479786142958
3187.707074809812920.292925190187076
327.77.79258596548919-0.0925859654891908
337.27.46854083958273-0.268540839582731
347.57.56976411084007-0.0697641108400692
357.37.36144720386965-0.0614472038696505
3677.17413560340842-0.174135603408418
3776.729854277013250.270145722986750
3877.06101120491773-0.0610112049177301
397.27.34916206959655-0.149162069596553
407.37.46345154455888-0.163451544558885
417.17.21615227216359-0.116152272163594
426.87.02382125495044-0.223821254950443
436.46.5720386206006-0.172038620600593
446.16.2447860681867-0.144786068186696
456.56.243338802885150.256661197114851
467.77.493793354735880.206206645264122
477.98.0251272805754-0.125127280575391
487.57.714451294926-0.214451294925994
496.97.0166449484256-0.116644948425601
506.66.69022323897289-0.0902232389728868
516.96.85281061460970.0471893853903009
527.77.4500451551940.249954844806005
5388.0769835413396-0.0769835413396017
5487.970156363401750.0298436365982526
557.77.802629356056-0.102629356056000
567.37.35465415518572-0.0546541551857161
577.47.109557462669630.290442537330372
588.18.022573359859890.0774266401401095


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
190.1103866840216650.220773368043330.889613315978335
200.04742353471522110.09484706943044220.95257646528478
210.01992951540489470.03985903080978940.980070484595105
220.336262850682180.672525701364360.66373714931782
230.2568939831211800.5137879662423590.743106016878820
240.2434235598018910.4868471196037830.756576440198109
250.1622353606671810.3244707213343610.83776463933282
260.1439442822983910.2878885645967820.856055717701609
270.2122501470579550.4245002941159100.787749852942045
280.1524822128982690.3049644257965390.84751778710173
290.1178966069322360.2357932138644730.882103393067764
300.1276007061912160.2552014123824320.872399293808784
310.2973351191471140.5946702382942290.702664880852885
320.4447271324414780.8894542648829570.555272867558521
330.5376454402919640.9247091194160720.462354559708036
340.4459767259224430.8919534518448860.554023274077557
350.4610524929188660.9221049858377330.538947507081134
360.4247552922634220.8495105845268440.575244707736578
370.7861162151292410.4277675697415170.213883784870759
380.6988850284556850.6022299430886290.301114971544315
390.544750916409260.910498167181480.45524908359074


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level10.0476190476190476OK
10% type I error level20.0952380952380952OK
 
Charts produced by software:
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Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
 
Parameters (R input):
par1 = 1 ; 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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