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Multiple Regression Lineaire trend werkloosheid ecogr

*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 06:58:51 -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/t1261058410xlrs73qhl8eco95.htm/, Retrieved Thu, 17 Dec 2009 15:00:22 +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/t1261058410xlrs73qhl8eco95.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 time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
werklh[t] = + 12.1281080048809 -0.0347898199866124ecogr[t] + 0.329371318768953M1[t] + 0.73661868884898M2[t] + 0.462018759129809M3[t] + 0.0654597778960518M4[t] -0.0300638017227109M5[t] + 0.287164807353566M6[t] + 0.402662218415118M7[t] + 0.61838748297653M8[t] + 0.232961244138489M9[t] -0.0169462063747899M10[t] + 0.233390782581000M11[t] -0.0295748486792233t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)12.12810800488090.85855514.126200
ecogr-0.03478981998661240.009502-3.66130.0006460.000323
M10.3293713187689530.2912571.13090.2639750.131988
M20.736618688848980.3697831.9920.0523230.026162
M30.4620187591298090.3687071.25310.2165090.108255
M40.06545977789605180.3289530.1990.8431440.421572
M5-0.03006380172271090.292363-0.10280.9185450.459272
M60.2871648073535660.2929810.98010.332140.16607
M70.4026622184151180.2982021.35030.1835260.091763
M80.618387482976530.3438691.79830.078690.039345
M90.2329612441384890.3098960.75170.4560370.228018
M10-0.01694620637478990.307097-0.05520.9562320.478116
M110.2333907825810000.358960.65020.5188060.259403
t-0.02957484867922330.003198-9.248900


Multiple Linear Regression - Regression Statistics
Multiple R0.851639257562177
R-squared0.725289425021056
Adjusted R-squared0.647653827744398
F-TEST (value)9.34222766956312
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value5.09720377017686e-09
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.420311541905972
Sum Squared Residuals8.1264424439313


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
19.39.06024990026660.239750099733406
29.38.836058535898950.463941464101053
38.78.664085073449680.0359149265503157
48.28.46060609145102-0.260606091451024
58.38.41552424912224-0.115524249122243
68.58.94670674942559-0.446706749425586
78.68.98740254582532-0.387402545825318
88.58.86740254582532-0.367402545825317
98.28.51850211628262-0.318502116282617
108.18.40253197102719-0.302531971027192
117.98.07361495551528-0.173614955515282
128.68.95871338381327-0.358713383813269
138.78.74362051810114-0.0436205181011353
148.78.512471189736220.187528810263777
158.58.46226209724010.0377379027599024
168.47.935237789365940.464762210634059
178.58.036273190980940.463726809019064
188.78.438733357333810.261266642666188
198.78.46551322573890.234486774261101
208.68.136774305819230.463225694180775
218.58.236662554103820.263337445896177
228.37.637113911034490.662886088965515
2387.694363897373970.305636102626026
248.28.44726100972283-0.247261009722834
258.18.22173119801472-0.121731198014716
268.18.10190929360696-0.00190929360696137
2787.738591821231330.261408178768673
287.97.437701343270150.46229865672985
297.97.691811952826240.208188047173760
3087.840306433276840.159693566723155
3187.95058186964980.0494181303501983
327.97.667069715712720.232930284287277
3387.693899342025440.306100657974564
347.77.303089618875770.396910381124226
357.27.2490121812581-0.0490121812581021
367.57.8453551036672-0.345355103667206
377.37.73811067991357-0.43811067991357
3877.82702769542549-0.82702769542549
3977.17843369915963-0.178433699159634
4077.06888723112483-0.068887231124826
417.27.40649340864879-0.206493408648785
427.37.32189609518909-0.0218960951890868
437.17.33476003559953-0.234760035599529
446.87.62527991144156-0.825279911441556
456.46.9493551740247-0.549355174024697
466.16.95514939872242-0.855149398722417
476.56.93934076309002-0.439340763090019
487.77.368692549563380.331307450436618
497.97.536287703703980.363712296296015
507.57.322533285332380.177466714667623
516.97.05662730891926-0.156627308919257
526.67.19756754478806-0.597567544788059
536.97.2498971984218-0.349897198421796
547.77.652357364774670.0476426352253289
5587.661742323186450.338257676813547
5687.503473521201180.496526478798821
577.77.401580813563430.298419186436574
587.37.202115100340130.0978848996598677
597.47.043668202762620.356331797237377
608.17.479977953233310.62002204676669


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.2327985359456230.4655970718912450.767201464054377
180.1114782980393980.2229565960787950.888521701960602
190.04814243192083680.09628486384167360.951857568079163
200.03137777814406580.06275555628813160.968622221855934
210.0377958121788820.0755916243577640.962204187821118
220.02161068399653480.04322136799306960.978389316003465
230.01084456047951760.02168912095903520.989155439520482
240.01253271118464960.02506542236929920.98746728881535
250.04850421317126220.09700842634252440.951495786828738
260.05335741834260690.1067148366852140.946642581657393
270.04088865551118820.08177731102237650.959111344488812
280.03472179407341330.06944358814682660.965278205926587
290.02339593792097080.04679187584194160.97660406207903
300.01632972187717170.03265944375434340.983670278122828
310.01004402413097460.02008804826194910.989955975869026
320.009388348338867330.01877669667773470.990611651661133
330.00783531141762110.01567062283524220.99216468858238
340.03537963070888950.0707592614177790.96462036929111
350.05175680187323660.1035136037464730.948243198126763
360.04499672972590130.08999345945180260.95500327027410
370.06419169078216160.1283833815643230.935808309217838
380.1158955380272530.2317910760545060.884104461972747
390.1193648519957110.2387297039914220.880635148004289
400.2743585997361690.5487171994723390.72564140026383
410.5324635135828590.9350729728342820.467536486417141
420.619650559972950.7606988800541010.380349440027050
430.4877098176823280.9754196353646560.512290182317672


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level80.296296296296296NOK
10% type I error level160.592592592592593NOK
 
Charts produced by software:
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http://www.freestatistics.org/blog/date/2009/Dec/17/t1261058410xlrs73qhl8eco95/8d30r1261058326.png (open in new window)
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http://www.freestatistics.org/blog/date/2009/Dec/17/t1261058410xlrs73qhl8eco95/9861h1261058326.png (open in new window)
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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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