MR interventie

*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: Tue, 14 Dec 2010 17:29:42 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/14/t12923477023chngdhttgaq8oo.htm/, Retrieved Tue, 14 Dec 2010 18:28:32 +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/2010/Dec/14/t12923477023chngdhttgaq8oo.htm/}, year = {2010}, } @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 = {2010}, 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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1606 6 3,74 16 1391 1634 6,81 4,17 29 1621 2013 9,75 4,84 22 1837 1654 6,96 4,21 30 2132 1003 3,94 3,93 20 1489 1029 5 4,9 39 1817 1052 4,9 4,7 18 1586 1653 5,7 3,5 9,6 1565 1918 6,5 3,4 10,2 1787 1926 7,1 3,7 20,2 1804 1862 7,5 4 50 1763 1816 7,8 4,3 120 1675 1712 7 4,1 19,8 1575 1646 7,4 4,5 18 1524 1555 8,55 5,5 3 1686 1402 7,43 5,3 11 1800 1047 4,7 4,5 15 1442 891 4,7 5,3 27 1345 940 5,3 5,6 28 1500 1372 6,2 4,5 14 1556 2012 7,4 3,7 5,6 2012 1879 7,5 4 6,5 1618 1667 7,32 4,4 8,5 1487 1856 8,15 4,4 87,9 1607 1771 7,24 4,1 5,8 1308 1721 7,4 4,3 25,2 1429 1773 9,4 5,3 7,5 1596 1507 8,9 5,9 13,7 1884 1033 4,5 4,4 34 1262 1011 4,9 4,9 17 1283 1111 5,6 5,1 9 1346 1736 6,4 3,7 9,2 1505 1865 6 3,2 5 1151 2078 6,9 3,3 24 1600 1947 6,7 3,5 40 1420 1428 5,4 3,8 86,5 1073 1500 5,6 3,8 0,54 1076 1950 6,9 3,5 14 1510 1591 6,9 4,3 4,8 1345 1613 7 4,3 28 1631 1077 4 3,7 16 1135 880 3,7 4,2 5,8 1009 1128 4,9 4,3 16 1155 1320 5 3,8 9,1 1184 1692 5,7 3,4 6 1285 1575 6,1 3,9 17 12 etc...

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 6 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation interventie[t] = + 123.434346672544 -0.0516942369122776aanvoer[t] + 12.9120345060052aanvoerwaarde[t] -22.1857340589894prijzen[t] -0.00417148774698359visserijen[t] + 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) 123.434346672544 128.114625 0.9635 0.33953 0.169765 aanvoer -0.0516942369122776 0.083763 -0.6171 0.539683 0.269842 aanvoerwaarde 12.9120345060052 19.215943 0.6719 0.504432 0.252216 prijzen -22.1857340589894 29.722792 -0.7464 0.458592 0.229296 visserijen -0.00417148774698359 0.01674 -0.2492 0.804136 0.402068 Multiple Linear Regression - Regression Statistics Multiple R 0.136346528217409 R-squared 0.0185903757569407 Adjusted R-squared -0.0527848696425544 F-TEST (value) 0.260459710546539 F-TEST (DF numerator) 4 F-TEST (DF denominator) 55 p-value 0.902019020498443 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 30.6178976353531 Sum Squared Residuals 51560.0610584928 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 16 29.1084243907833 -13.1084243907833 2 29 27.6204258799319 1.37957412006813 3 22 30.2242083649627 -8.22420836496268 4 30 25.504286716519 4.495713283481 5 20 29.0571628961035 -9.0571628961035 6 39 18.5114592945195 20.4885407054805 7 18 21.4320488762877 -3.43204887628766 8 9.6 27.4039222102869 -17.8039222102869 9 10.2 25.3270801594061 -15.1270801594061 10 20.2 25.9341114583154 -5.73411145831542 11 50 27.9226672030328 22.0773327969672 12 120 27.8855831568368 92.1144168431632 13 19.8 27.7864517774058 -7.9864517774058 14 18 27.7015374675186 -9.70153746751861 15 3 24.3930376344411 -21.3930376344411 16 11 21.8023744439355 -10.8023744439355 17 15 24.1459542070115 -9.14595420701153 18 27 14.8663022295927 12.1336977704073 19 28 12.7782045060150 15.2217954939850 20 14 26.2378293663730 -12.2378293663730 21 5.6 24.4943479842885 -18.8943479842885 22 6.5 27.6487308988367 -21.1487308988367 23 8.5 27.9559141844177 -19.4559141844177 24 87.9 28.4021135183435 59.4978864816565 25 5.8 28.9491673094673 -23.1491673094673 26 25.2 28.6579078468591 -3.45790784685911 27 7.5 28.9115040266954 -21.4115040266954 28 13.7 21.6933248858338 -7.99332488583376 29 34 25.2567078229383 8.74329217706165 30 17 20.3783265652292 -3.37832656522919 31 9 19.5473764883472 -10.5473764883472 32 9.2 27.9648671537926 -18.7648671537926 33 5 28.7010704816336 -23.7010704816336 34 24 25.2194576704286 -1.21945767042860 35 40 25.7227167873951 14.2772832126049 36 86.5 30.5581669175669 55.9418330824331 37 0.54 29.406074297843 -28.866074297843 38 14 27.7746070806308 -13.7746070806308 39 4.8 29.2725463631992 -24.4725463631992 40 28 28.2334311060923 -0.233431106092329 41 16 32.585936930955 -16.5859369309550 42 5.8 28.3288316774974 -22.5288316774974 43 16 28.1754917135003 -12.1754917135003 44 9.1 30.5132955617756 -21.4132955617756 45 6 28.7744369457624 -22.7744369457624 46 17 29.0114110943218 -12.0114110943218 47 26 30.8774521438253 -4.87745214382533 48 99.6 31.7260630851376 67.8739369148624 49 41 32.1548445924816 8.84515540751839 50 72 31.2762691769448 40.7237308230552 51 23 29.1505781071334 -6.15057810713337 52 42 31.9604602450021 10.0395397549979 53 40 30.3549264169554 9.64507358304456 54 18 30.3534817716875 -12.3534817716875 55 45 24.4709154431683 20.5290845568317 56 18 27.7469200956395 -9.7469200956395 57 2 32.6480638005764 -30.6480638005764 58 10 32.0171923313043 -22.0171923313043 59 13.6 30.4929668009589 -16.8929668009589 60 160 29.6290304362546 130.370969563745 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.0272153906322807 0.0544307812645614 0.97278460936772 9 0.00713915802649459 0.0142783160529892 0.992860841973505 10 0.00164747709857523 0.00329495419715045 0.998352522901425 11 0.0137891180635031 0.0275782361270062 0.986210881936497 12 0.705611227840192 0.588777544319617 0.294388772159808 13 0.622879514513906 0.754240970972187 0.377120485486094 14 0.557595531920182 0.884808936159635 0.442404468079818 15 0.569599522250554 0.860800955498892 0.430400477749446 16 0.487939231568201 0.975878463136403 0.512060768431799 17 0.392950593722921 0.785901187445843 0.607049406277079 18 0.322933530455556 0.645867060911113 0.677066469544444 19 0.25522006303491 0.51044012606982 0.74477993696509 20 0.19321937818874 0.38643875637748 0.80678062181126 21 0.165838378741044 0.331676757482088 0.834161621258956 22 0.136058688493897 0.272117376987795 0.863941311506103 23 0.105719148718830 0.211438297437659 0.89428085128117 24 0.251685396647897 0.503370793295794 0.748314603352103 25 0.215859905314930 0.431719810629860 0.78414009468507 26 0.159676579889373 0.319353159778746 0.840323420110627 27 0.139239338252906 0.278478676505813 0.860760661747094 28 0.106525150917190 0.213050301834381 0.89347484908281 29 0.078568166561932 0.157136333123864 0.921431833438068 30 0.0532761416384311 0.106552283276862 0.946723858361569 31 0.0357319579904049 0.0714639159808098 0.964268042009595 32 0.0262530902120891 0.0525061804241781 0.973746909787911 33 0.0186935461454002 0.0373870922908004 0.9813064538546 34 0.0113043453133644 0.0226086906267287 0.988695654686636 35 0.00770642563948841 0.0154128512789768 0.992293574360512 36 0.0258894177190435 0.051778835438087 0.974110582280956 37 0.0233305009355346 0.0466610018710693 0.976669499064465 38 0.0170449138418293 0.0340898276836587 0.98295508615817 39 0.0171683542670511 0.0343367085341022 0.98283164573295 40 0.019365008301455 0.03873001660291 0.980634991698545 41 0.0122221739961773 0.0244443479923545 0.987777826003823 42 0.0072831488332602 0.0145662976665204 0.99271685116674 43 0.00501934402924645 0.0100386880584929 0.994980655970753 44 0.00415356552535167 0.00830713105070334 0.995846434474648 45 0.00254872563795511 0.00509745127591021 0.997451274362045 46 0.0045960113304431 0.0091920226608862 0.995403988669557 47 0.00276964020101258 0.00553928040202515 0.997230359798987 48 0.00836424138162576 0.0167284827632515 0.991635758618374 49 0.00417041990678482 0.00834083981356964 0.995829580093215 50 0.0043468871617991 0.0086937743235982 0.995653112838201 51 0.00469888430938015 0.0093977686187603 0.99530111569062 52 0.00184196024410956 0.00368392048821911 0.99815803975589 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 9 0.2 NOK 5% type I error level 22 0.488888888888889 NOK 10% type I error level 26 0.577777777777778 NOK

Charts produced by software:

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Parameters (Session):

par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 4 ; par2 = Do not include Seasonal 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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