ws 7 regressie analyse 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: Wed, 18 Nov 2009 09:16:40 -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/t1258561118h7smb73l8sth9w5.htm/, Retrieved Wed, 18 Nov 2009 17:18:51 +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/t1258561118h7smb73l8sth9w5.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:

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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 Input view raw input (R code) Raw Output view raw output of R engine Computing time 5 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation aanbod[t] = + 2545.66561777526 -0.0536921662865609invoer[t] -49.4740910207108M1[t] -403.725971096605M2[t] -47.9857236889952M3[t] -180.392078283739M4[t] -371.644328074481M5[t] -376.900740873810M6[t] -571.809334244978M7[t] -571.89257984978M8[t] -608.615941886095M9[t] -437.601930818772M10[t] -265.63400289473M11[t] + 8.10466936063765t + e[t] Multiple Linear Regression - Ordinary Least Squares Variable Parameter S.D. T-STAT H0: parameter = 0 2-tail p-value 1-tail p-value (Intercept) 2545.66561777526 2879.398862 0.8841 0.381242 0.190621 invoer -0.0536921662865609 0.282425 -0.1901 0.850059 0.425029 M1 -49.4740910207108 183.414737 -0.2697 0.788568 0.394284 M2 -403.725971096605 285.806045 -1.4126 0.164507 0.082254 M3 -47.9857236889952 175.672248 -0.2732 0.785957 0.392978 M4 -180.392078283739 399.731224 -0.4513 0.653906 0.326953 M5 -371.644328074481 383.34472 -0.9695 0.337377 0.168688 M6 -376.900740873810 405.790831 -0.9288 0.357838 0.178919 M7 -571.809334244978 380.208117 -1.5039 0.139433 0.069716 M8 -571.89257984978 398.964519 -1.4334 0.158494 0.079247 M9 -608.615941886095 374.505608 -1.6251 0.11097 0.055485 M10 -437.601930818772 234.246234 -1.8681 0.068122 0.034061 M11 -265.63400289473 213.69312 -1.2431 0.220143 0.110072 t 8.10466936063765 4.696567 1.7257 0.091122 0.045561 Multiple Linear Regression - Regression Statistics Multiple R 0.678316987506086 R-squared 0.460113935539331 Adjusted R-squared 0.307537439061316 F-TEST (value) 3.01562787297079 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 0.00285871719941422 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 270.527201060377 Sum Squared Residuals 3366508.45962384 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1901 1943.96474874864 -42.9647487486426 2 1395 1658.06014860691 -263.060148606905 3 1639 2000.26712236167 -361.267122361669 4 1643 1914.62379685389 -271.623796853887 5 1751 1727.98622561516 23.0137743848437 6 1797 1740.33799560919 56.6620043908133 7 1373 1544.24532683108 -171.245326831081 8 1558 1550.28014043431 7.71985956568655 9 1555 1518.76207077916 36.2379292208376 10 2061 1659.86669747624 401.133302523763 11 2010 1840.42252425750 169.577475742504 12 2119 2091.55679450622 27.4432054937782 13 1985 2046.32153687352 -61.3215368735163 14 1963 1735.12792641081 227.872073589189 15 2017 2075.61675084440 -58.6167508444045 16 1975 1992.98018664867 -17.9801866486696 17 1589 1816.54412700439 -227.544127004385 18 1679 1819.39238356569 -140.392383565694 19 1392 1620.23926130925 -228.239261309255 20 1511 1634.00574685775 -123.005746857752 21 1449 1600.93060438029 -151.930604380290 22 1767 1753.04212516611 13.9578748338893 23 1899 1921.57090669918 -22.5709066991798 24 2179 2166.90642298896 12.0935770110430 25 2217 2122.42285568426 94.5771443157367 26 2049 1828.62550709840 220.374492901596 27 2343 2149.14084567340 193.859154326604 28 2175 2091.09529363691 83.9047063630936 29 1607 1903.86710856902 -296.867108569023 30 1702 1901.72199366568 -199.721993665682 31 1764 1723.18666326328 40.8133367367182 32 1766 1732.76515984143 33.2348401585723 33 1615 1689.38112143695 -74.3811214369463 34 1953 1838.11003574671 114.889964253287 35 2091 2017.00140537309 73.9985946269115 36 2411 2257.02139720050 153.978602799504 37 2550 2199.81278648589 350.187213514112 38 2351 1919.76063246939 431.239367530612 39 2786 2225.40324098300 560.596759016997 40 2525 2189.53255362286 335.467446377138 41 2474 1990.33101547308 483.668984526924 42 2332 2004.56201128714 327.437988712863 43 1978 1797.03291108999 180.967088910007 44 1789 1824.32982254270 -35.329822542704 45 1904 1788.6237639172 115.376236082799 46 1997 1935.04391507665 61.9560849233543 47 2207 2105.93515192632 101.064848073677 48 2453 2356.42511617961 96.5748838203896 49 1948 2288.47807220769 -340.47807220769 50 1384 2000.42578541449 -616.425785414492 51 1989 2323.57204013753 -334.572040137527 52 2140 2269.76816923767 -129.768169237675 53 2100 2082.27152333836 17.7284766616413 54 2045 2088.9856158723 -43.9856158723002 55 2083 1905.29583750639 177.70416249361 56 2022 1904.61913032380 117.380869676197 57 1950 1875.3024394864 74.6975605135999 58 1422 2013.93722653429 -591.937226534293 59 1859 2181.07001174391 -322.070011743912 60 2147 2437.09026912472 -290.090269124715 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.233400501451395 0.466801002902791 0.766599498548605 18 0.294616405823607 0.589232811647215 0.705383594176393 19 0.229223836061663 0.458447672123326 0.770776163938337 20 0.156308157772842 0.312616315545684 0.843691842227158 21 0.120480170366888 0.240960340733777 0.879519829633112 22 0.0914591769819509 0.182918353963902 0.908540823018049 23 0.0625390143109303 0.125078028621861 0.93746098568907 24 0.0349654507119113 0.0699309014238226 0.965034549288089 25 0.026805581646395 0.05361116329279 0.973194418353605 26 0.0266028013906094 0.0532056027812187 0.97339719860939 27 0.0183622376448618 0.0367244752897236 0.981637762355138 28 0.0155990194907077 0.0311980389814153 0.984400980509292 29 0.0311784193951111 0.0623568387902223 0.968821580604889 30 0.0381007780524057 0.0762015561048113 0.961899221947594 31 0.0600058613505894 0.120011722701179 0.93999413864941 32 0.0550514820012164 0.110102964002433 0.944948517998784 33 0.0701847461360006 0.140369492272001 0.929815253864 34 0.0460672920786607 0.0921345841573214 0.95393270792134 35 0.0451749201919385 0.090349840383877 0.954825079808062 36 0.037896395601428 0.075792791202856 0.962103604398572 37 0.0335233607390545 0.0670467214781091 0.966476639260945 38 0.114791404842483 0.229582809684966 0.885208595157517 39 0.420637040298647 0.841274080597294 0.579362959701353 40 0.388721599206464 0.777443198412929 0.611278400793536 41 0.453186020572846 0.906372041145691 0.546813979427154 42 0.351204515244852 0.702409030489704 0.648795484755148 43 0.278390689822325 0.556781379644649 0.721609310177675 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 2 0.0740740740740741 NOK 10% type I error level 11 0.407407407407407 NOK

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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