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Multiple Regression werkloosheid ecogr 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, 17 Dec 2009 11:34:08 -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/t1261074934y5mjd98wpgfcgy3.htm/, Retrieved Thu, 17 Dec 2009 19:35:46 +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/t1261074934y5mjd98wpgfcgy3.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 «
9.3 96.8 9.3 114.1 8.7 110.3 8.2 103.9 8.3 101.6 8.5 94.6 8.6 95.9 8.5 104.7 8.2 102.8 8.1 98.1 7.9 113.9 8.6 80.9 8.7 95.7 8.7 113.2 8.5 105.9 8.4 108.8 8.5 102.3 8.7 99 8.7 100.7 8.6 115.5 8.5 100.7 8.3 109.9 8 114.6 8.2 85.4 8.1 100.5 8.1 114.8 8 116.5 7.9 112.9 7.9 102 8 106 8 105.3 7.9 118.8 8 106.1 7.7 109.3 7.2 117.2 7.5 92.5 7.3 104.2 7 112.5 7 122.4 7 113.3 7.2 100 7.3 110.7 7.1 112.8 6.8 109.8 6.4 117.3 6.1 109.1 6.5 115.9 7.7 96 7.9 99.8 7.5 116.8 6.9 115.7 6.6 99.4 6.9 94.3 7.7 91 8 93.2 8 103.1 7.7 94.1 7.3 91.8 7.4 102.7 8.1 82.6
 
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 time10 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
werklh[t] = + 11.1603438237684 -0.0226357640168363ecogr[t] -0.0304780448795493t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)11.16034382376840.64038817.427500
ecogr-0.02263576401683630.00598-3.78540.0003710.000185
t-0.03047804487954930.003241-9.403200


Multiple Linear Regression - Regression Statistics
Multiple R0.797775107475138
R-squared0.636445122106969
Adjusted R-squared0.62368881060195
F-TEST (value)49.8925666605567
F-TEST (DF numerator)2
F-TEST (DF denominator)57
p-value2.99316127438942e-13
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.434370280342442
Sum Squared Residuals10.754619805352


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
19.38.938723822059120.361276177940882
29.38.516647059688250.783352940311753
38.78.572184918072670.127815081927326
48.28.68657576290088-0.486575762900879
58.38.70815997526005-0.408159975260052
68.58.83613227849836-0.336132278498358
78.68.77622774039692-0.176227740396921
88.58.54655497216921-0.0465549721692125
98.28.55908487892165-0.359084878921653
108.18.63499492492123-0.534994924921234
117.98.24687180857567-0.346871808575671
128.68.96337397625172-0.363373976251719
138.78.597886623922990.102113376077007
148.78.171282708748810.528717291251191
158.58.306045741192160.193954258807836
168.48.209923980663790.190076019336211
178.58.326578401893680.173421598106324
188.78.370798378269690.329201621730313
198.78.301839534561520.398160465438484
208.67.936352182232790.66364781776721
218.58.240883444802420.259116555197583
228.38.002156370967970.297843629032027
2387.86529023520930.134709764790706
248.28.49577649962136-0.295776499621365
258.18.12349841808759-0.0234984180875875
268.17.769328947767280.330671052232720
2787.700370104059110.299629895940892
287.97.751380809640170.148619190359831
297.97.96763259254414-0.0676325925441353
3087.846611491597240.153388508402759
3187.831978481529480.168021518470523
327.97.495917622422640.404082377577362
3387.752913780556910.24708621944309
347.77.650001290823480.0499987091765157
357.27.44070071021093-0.240700710210928
367.57.96932603654724-0.469326036547235
377.37.6740095526707-0.374009552670702
3877.45565466645141-0.455654666451411
3977.20108255780518-0.201082557805183
4077.37658996547884-0.376589965478844
417.27.64716758202322-0.447167582023217
427.37.37448686216352-0.0744868621635195
437.17.29647371284861-0.196473712848614
446.87.33390296001957-0.533902960019574
456.47.13365668501375-0.733656685013752
466.17.28879190507226-1.18879190507226
476.57.10439066487822-0.604390664878224
487.77.524364323933720.175635676066283
497.97.407870375790190.49212962420981
507.56.992584342624420.507415657375576
516.96.9870056381634-0.087005638163394
526.67.32549054675828-0.725490546758277
536.97.41045489836459-0.510454898364592
547.77.45467487474060.245325125259398
5587.374398149024010.625601850975987
5687.119826040377790.880173959622215
577.77.293069871649760.406930128350238
587.37.31465408400894-0.0146540840089365
597.47.037446211345870.362553788654129
608.17.461947023204730.638052976795268


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
60.4103422979217620.8206845958435250.589657702078238
70.436673087726790.873346175453580.56332691227321
80.3692747447069290.7385494894138570.630725255293071
90.2526729109573640.5053458219147290.747327089042636
100.1742975125961590.3485950251923170.825702487403841
110.1115818545487590.2231637090975170.888418145451241
120.1648121521048580.3296243042097150.835187847895142
130.2653242707174060.5306485414348120.734675729282594
140.3826798571265640.7653597142531280.617320142873436
150.3207550499619100.6415100999238210.67924495003809
160.24812466327050.4962493265410.7518753367295
170.1944049713383080.3888099426766160.805595028661692
180.1752051259057410.3504102518114820.824794874094259
190.1515670276905410.3031340553810820.848432972309459
200.1445363133668630.2890726267337250.855463686633137
210.1050503892749670.2101007785499340.894949610725033
220.07964605047774420.1592921009554880.920353949522256
230.07046408709674050.1409281741934810.92953591290326
240.05407691750873480.1081538350174700.945923082491265
250.03723721832147930.07447443664295860.96276278167852
260.02898991072467050.05797982144934110.97101008927533
270.02426535736748790.04853071473497570.975734642632512
280.01914860998794030.03829721997588060.98085139001206
290.01278974914290180.02557949828580360.987210250857098
300.008763741287968960.01752748257593790.991236258712031
310.006302349310254850.01260469862050970.993697650689745
320.009119893820184330.01823978764036870.990880106179816
330.01045688829517880.02091377659035750.989543111704821
340.01204074445895160.02408148891790320.987959255541048
350.02231435801401330.04462871602802660.977685641985987
360.01745259488551560.03490518977103130.982547405114484
370.01591024351498540.03182048702997090.984089756485015
380.01968028384859240.03936056769718480.980319716151408
390.02258253659985460.04516507319970910.977417463400145
400.01982031755764590.03964063511529170.980179682442354
410.01303330891273290.02606661782546590.986966691087267
420.01229204948929810.02458409897859620.987707950510702
430.01071782733341090.02143565466682170.98928217266659
440.008096623520932950.01619324704186590.991903376479067
450.009848285280181240.01969657056036250.990151714719819
460.05785634792335640.1157126958467130.942143652076644
470.07089930790339740.1417986158067950.929100692096603
480.07389921838429060.1477984367685810.92610078161571
490.1790295404192230.3580590808384460.820970459580777
500.2587669026727230.5175338053454460.741233097327277
510.1776416367639940.3552832735279870.822358363236006
520.2382859398647050.4765718797294110.761714060135295
530.4992185275201720.9984370550403440.500781472479828
540.441614036592080.883228073184160.55838596340792


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level190.387755102040816NOK
10% type I error level210.428571428571429NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Dec/17/t1261074934y5mjd98wpgfcgy3/10qs7y1261074836.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Dec/17/t1261074934y5mjd98wpgfcgy3/1gsko1261074836.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/17/t1261074934y5mjd98wpgfcgy3/1gsko1261074836.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/17/t1261074934y5mjd98wpgfcgy3/2qqxe1261074836.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/17/t1261074934y5mjd98wpgfcgy3/2qqxe1261074836.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/17/t1261074934y5mjd98wpgfcgy3/3ogur1261074836.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Dec/17/t1261074934y5mjd98wpgfcgy3/4rzw21261074836.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Dec/17/t1261074934y5mjd98wpgfcgy3/576o91261074836.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Dec/17/t1261074934y5mjd98wpgfcgy3/611ow1261074836.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Dec/17/t1261074934y5mjd98wpgfcgy3/8k4ku1261074836.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Dec/17/t1261074934y5mjd98wpgfcgy3/9nnlz1261074836.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/17/t1261074934y5mjd98wpgfcgy3/9nnlz1261074836.ps (open in new window)


 
Parameters (Session):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;
 
Parameters (R input):
par1 = 1 ; par2 = Do not include Seasonal 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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