meervoudige regressie

*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: Fri, 17 Dec 2010 13:03:18 +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/17/t1292590909dauir53q710zv5s.htm/, Retrieved Fri, 17 Dec 2010 14:01:49 +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/17/t1292590909dauir53q710zv5s.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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14544.5 94.6 -3.0 14097.8 15116.3 95.9 -3.7 14776.8 17413.2 104.7 -4.7 16833.3 16181.5 102.8 -6.4 15385.5 15607.4 98.1 -7.5 15172.6 17160.9 113.9 -7.8 16858.9 14915.8 80.9 -7.7 14143.5 13768 95.7 -6.6 14731.8 17487.5 113.2 -4.2 16471.6 16198.1 105.9 -2.0 15214 17535.2 108.8 -0.7 17637.4 16571.8 102.3 0.1 17972.4 16198.9 99 0.9 16896.2 16554.2 100.7 2.1 16698 19554.2 115.5 3.5 19691.6 15903.8 100.7 4.9 15930.7 18003.8 109.9 5.7 17444.6 18329.6 114.6 6.2 17699.4 16260.7 85.4 6.5 15189.8 14851.9 100.5 6.5 15672.7 18174.1 114.8 6.3 17180.8 18406.6 116.5 6.2 17664.9 18466.5 112.9 6.4 17862.9 16016.5 102 6.3 16162.3 17428.5 106 5.8 17463.6 17167.2 105.3 5.1 16772.1 19630 118.8 5.1 19106.9 17183.6 106.1 5.8 16721.3 18344.7 109.3 6.7 18161.3 19301.4 117.2 7.1 18509.9 18147.5 92.5 6.7 17802.7 16192.9 104.2 5.5 16409.9 18374.4 112.5 4.2 17967.7 20515.2 122.4 3.0 20286.6 18957.2 113.3 2.2 19537.3 16471.5 100 2.0 18021.9 18746.8 110.7 1.8 20194.3 19009.5 112.8 1.8 19049.6 19211.2 109 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 5 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation productie[t] = + 36.1042160237842 + 0.0041262686906565uitvoer[t] + 0.00869642083370103ondernemersvertrouwen[t] -0.000179360815770516invoer[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) 36.1042160237842 8.514739 4.2402 7.3e-05 3.7e-05 uitvoer 0.0041262686906565 0.001191 3.4653 0.000951 0.000475 ondernemersvertrouwen 0.00869642083370103 0.089827 0.0968 0.923177 0.461589 invoer -0.000179360815770516 0.001098 -0.1634 0.870709 0.435355 Multiple Linear Regression - Regression Statistics Multiple R 0.77813978797093 R-squared 0.605501529623444 Adjusted R-squared 0.587009413824542 F-TEST (value) 32.7437669225187 F-TEST (DF numerator) 3 F-TEST (DF denominator) 64 p-value 6.00852700927135e-13 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 6.39432806256235 Sum Squared Residuals 2616.79560778703 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 94.6 93.564048823967 1.03595117603298 2 95.9 95.7955757727927 0.104424227207334 3 104.7 104.895650389896 -0.195650389895822 4 102.8 100.058219917269 2.74178008273053 5 98.1 97.717948916724 0.382051083275955 6 113.9 103.823042257775 10.0769577422250 7 80.9 95.0470624216087 -14.1470624216087 8 95.7 90.2149793134724 5.48502068652756 9 113.2 105.271455171093 7.92854482890736 10 105.9 100.195740609107 5.70425939089271 11 108.8 105.289616821530 3.51038317847035 12 102.3 101.261240828335 1.03875917166499 13 99 99.9225404801884 -0.922540480188387 14 100.7 101.434588764665 -0.734588764664802 15 115.5 113.288635287711 2.21136471228912 16 100.7 98.9128371405369 1.78716285946311 17 109.9 107.313424188588 2.58657581141248 18 114.6 108.616409602562 5.98359039743806 19 85.4 100.532305137970 -15.1323051379705 20 100.5 94.632604468638 5.86739553136197 21 114.8 108.068660982307 6.73133901769319 22 116.5 108.940320239887 7.55967976011343 23 112.9 109.153709577101 3.74629042289893 24 102 99.3485026462086 2.65149735379139 25 106 104.937043597437 1.06295640256343 26 105.3 103.976790098090 1.32320990191025 27 118.8 113.720192996778 5.07980700322241 28 106.1 104.059659928641 2.04034007135875 29 109.3 108.600217709403 0.699782290596693 30 117.2 112.488772353710 4.71122764628974 31 92.5 107.850836312141 -15.3508363121411 32 104.2 100.025009568589 4.17499043141133 33 112.5 108.735751091365 3.76424890863527 34 122.4 117.142911603631 5.25708839636853 35 113.3 110.841622906179 2.45837709382147 36 100 100.855020917866 -0.855020917865553 37 110.7 109.852137349370 0.847862650630318 38 112.8 111.141422460218 1.65857753978234 39 109.8 111.756727817946 -1.95672781794563 40 117.3 117.041557161835 0.258442838164681 41 109.1 112.311159761781 -3.21115976178052 42 115.9 117.337142487110 -1.43714248710968 43 96 115.225939465719 -19.2259394657193 44 99.8 99.4046926695187 0.395307330481347 45 116.8 116.223538931546 0.576461068453622 46 115.7 113.649591490456 2.05040850954427 47 99.4 97.3665572464634 2.0334427535366 48 94.3 92.3911587015605 1.90884129843948 49 91 90.3189186625703 0.681081337429666 50 93.2 92.2717402267414 0.928259773258573 51 103.1 96.1182519112301 6.98174808876987 52 94.1 92.7908742617033 1.30912573829670 53 91.8 90.2375802121198 1.56241978788019 54 102.7 97.8439354770618 4.85606452293821 55 82.6 94.1556068748172 -11.5556068748172 56 89.1 85.175854648468 3.92414535153207 57 104.5 99.8655317177051 4.63446828229488 58 105.1 99.2361993424325 5.86380065756746 59 95.1 99.1954329119893 -4.09543291198926 60 88.7 98.2331779343317 -9.5331779343317 61 86.3 95.7234434238957 -9.42344342389566 62 91.8 97.9521204859725 -6.15212048597248 63 111.5 110.740532484512 0.759467515487776 64 99.7 102.870898382827 -3.17089838282669 65 97.5 103.088178777544 -5.58817877754401 66 111.7 114.488368517625 -2.78836851762471 67 86.2 105.922898099745 -19.7228980997448 68 95.4 99.135881259426 -3.73588125942590 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 7 0.594688832535905 0.81062233492819 0.405311167464095 8 0.505101402055792 0.989797195888415 0.494898597944208 9 0.433177460771816 0.866354921543633 0.566822539228184 10 0.347884511050518 0.695769022101037 0.652115488949481 11 0.547584375294617 0.904831249410765 0.452415624705383 12 0.558600597951264 0.882798804097472 0.441399402048736 13 0.479791705263992 0.959583410527984 0.520208294736008 14 0.386673562116375 0.77334712423275 0.613326437883625 15 0.318153434749659 0.636306869499318 0.681846565250341 16 0.25281723464608 0.50563446929216 0.74718276535392 17 0.186341328409153 0.372682656818307 0.813658671590847 18 0.153498403156775 0.306996806313549 0.846501596843225 19 0.374947555572274 0.749895111144549 0.625052444427726 20 0.417706419338692 0.835412838677384 0.582293580661308 21 0.427161753945536 0.854323507891071 0.572838246054464 22 0.427907417886914 0.855814835773829 0.572092582113086 23 0.368346565118962 0.736693130237924 0.631653434881038 24 0.314104713164661 0.628209426329322 0.685895286835339 25 0.257882275920072 0.515764551840145 0.742117724079928 26 0.207065043349971 0.414130086699943 0.792934956650029 27 0.182676029584689 0.365352059169379 0.81732397041531 28 0.152569440008494 0.305138880016987 0.847430559991506 29 0.128061839655430 0.256123679310861 0.87193816034457 30 0.134281361667828 0.268562723335655 0.865718638332172 31 0.459773781106228 0.919547562212455 0.540226218893772 32 0.485117678874531 0.970235357749063 0.514882321125469 33 0.526054337341421 0.947891325317157 0.473945662658579 34 0.584472100207873 0.831055799584255 0.415527899792127 35 0.584686120039383 0.830627759921235 0.415313879960617 36 0.540430807563085 0.91913838487383 0.459569192436915 37 0.497504586396286 0.995009172792571 0.502495413603714 38 0.54368250466706 0.91263499066588 0.45631749533294 39 0.51183906401055 0.9763218719789 0.48816093598945 40 0.470029370325011 0.940058740650021 0.529970629674989 41 0.442412691502233 0.884825383004466 0.557587308497767 42 0.402345125005885 0.80469025001177 0.597654874994115 43 0.861722595811742 0.276554808376516 0.138277404188258 44 0.817340848996841 0.365318302006317 0.182659151003159 45 0.762016232789749 0.475967534420503 0.237983767210251 46 0.704324095076542 0.591351809846916 0.295675904923458 47 0.648063449937081 0.703873100125837 0.351936550062919 48 0.609474232468286 0.781051535063428 0.390525767531714 49 0.6451546522754 0.709690695449199 0.354845347724599 50 0.605842566668622 0.788314866662757 0.394157433331378 51 0.578228413849585 0.84354317230083 0.421771586150415 52 0.520110416392224 0.959779167215552 0.479889583607776 53 0.432532787431035 0.86506557486207 0.567467212568965 54 0.344414452045160 0.688828904090319 0.65558554795484 55 0.556606379841042 0.886787240317915 0.443393620158958 56 0.45349695352871 0.90699390705742 0.54650304647129 57 0.360130914347265 0.72026182869453 0.639869085652735 58 0.354527586282574 0.709055172565148 0.645472413717426 59 0.491179680843493 0.982359361686987 0.508820319156507 60 0.386256321026720 0.772512642053439 0.61374367897328 61 0.264164378490354 0.528328756980707 0.735835621509646 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 0 0 OK 10% type I error level 0 0 OK

Charts produced by software:

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Parameters (Session):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 2 ; 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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