paper multiple lineair regression: berekening 1

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R Software Module: rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Thu, 11 Dec 2008 13:14:55 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/11/t1229026614mmpagxckps1jez8.htm/, Retrieved Thu, 11 Dec 2008 20:17:09 +0000

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@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/2008/Dec/11/t1229026614mmpagxckps1jez8.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

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Dataseries X:

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103,3 0 101,2 0 107,7 0 110,4 0 101,9 0 115,9 0 89,9 0 88,6 0 117,2 0 123,9 0 100 0 103,6 0 94,1 0 98,7 0 119,5 0 112,7 0 104,4 0 124,7 0 89,1 0 97 0 121,6 0 118,8 0 114 0 111,5 0 97,2 0 102,5 0 113,4 0 109,8 0 104,9 0 126,1 0 80 0 96,8 0 117,2 1 112,3 1 117,3 1 111,1 1 102,2 1 104,3 1 122,9 1 107,6 1 121,3 1 131,5 1 89 1 104,4 1 128,9 1 135,9 1 133,3 1 121,3 1 120,5 1 120,4 1 137,9 1 126,1 1 133,2 1 151,1 1 105 1 119 1 140,4 1 156,6 1 137,1 1 122,7 1

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 4 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation metaal[t] = + 106.2625 + 16.2553571428571conjunctuur[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) 106.2625 2.380019 44.6477 0 0 conjunctuur 16.2553571428571 3.483991 4.6657 1.9e-05 9e-06 Multiple Linear Regression - Regression Statistics Multiple R 0.522398973464736 R-squared 0.27290068747701 Adjusted R-squared 0.26036449243351 F-TEST (value) 21.7690205465104 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 1.85786028988888e-05 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 13.4634217556109 Sum Squared Residuals 10513.2960714286 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 103.3 106.2625 -2.96249999999995 2 101.2 106.2625 -5.06250000000001 3 107.7 106.2625 1.4375 4 110.4 106.2625 4.1375 5 101.9 106.2625 -4.3625 6 115.9 106.2625 9.6375 7 89.9 106.2625 -16.3625 8 88.6 106.2625 -17.6625 9 117.2 106.2625 10.9375 10 123.9 106.2625 17.6375 11 100 106.2625 -6.2625 12 103.6 106.2625 -2.66250000000001 13 94.1 106.2625 -12.1625 14 98.7 106.2625 -7.5625 15 119.5 106.2625 13.2375 16 112.7 106.2625 6.4375 17 104.4 106.2625 -1.86250000000000 18 124.7 106.2625 18.4375 19 89.1 106.2625 -17.1625 20 97 106.2625 -9.2625 21 121.6 106.2625 15.3375 22 118.8 106.2625 12.5375 23 114 106.2625 7.7375 24 111.5 106.2625 5.2375 25 97.2 106.2625 -9.0625 26 102.5 106.2625 -3.7625 27 113.4 106.2625 7.1375 28 109.8 106.2625 3.53749999999999 29 104.9 106.2625 -1.36250000000000 30 126.1 106.2625 19.8375 31 80 106.2625 -26.2625 32 96.8 106.2625 -9.4625 33 117.2 122.517857142857 -5.31785714285714 34 112.3 122.517857142857 -10.2178571428571 35 117.3 122.517857142857 -5.21785714285715 36 111.1 122.517857142857 -11.4178571428571 37 102.2 122.517857142857 -20.3178571428571 38 104.3 122.517857142857 -18.2178571428571 39 122.9 122.517857142857 0.382142857142862 40 107.6 122.517857142857 -14.9178571428571 41 121.3 122.517857142857 -1.21785714285715 42 131.5 122.517857142857 8.98214285714286 43 89 122.517857142857 -33.5178571428571 44 104.4 122.517857142857 -18.1178571428571 45 128.9 122.517857142857 6.38214285714286 46 135.9 122.517857142857 13.3821428571429 47 133.3 122.517857142857 10.7821428571429 48 121.3 122.517857142857 -1.21785714285715 49 120.5 122.517857142857 -2.01785714285714 50 120.4 122.517857142857 -2.11785714285714 51 137.9 122.517857142857 15.3821428571429 52 126.1 122.517857142857 3.58214285714285 53 133.2 122.517857142857 10.6821428571428 54 151.1 122.517857142857 28.5821428571429 55 105 122.517857142857 -17.5178571428571 56 119 122.517857142857 -3.51785714285714 57 140.4 122.517857142857 17.8821428571429 58 156.6 122.517857142857 34.0821428571429 59 137.1 122.517857142857 14.5821428571429 60 122.7 122.517857142857 0.182142857142860 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.0444721080817364 0.0889442161634729 0.955527891918264 6 0.0661849938961953 0.132369987792391 0.933815006103805 7 0.161890575450578 0.323781150901155 0.838109424549422 8 0.220318637080875 0.440637274161749 0.779681362919125 9 0.243524693066176 0.487049386132353 0.756475306933824 10 0.356895688992769 0.713791377985538 0.64310431100723 11 0.276023331625871 0.552046663251743 0.723976668374129 12 0.194549891090185 0.389099782180369 0.805450108909815 13 0.177779641663337 0.355559283326674 0.822220358336663 14 0.131760986361606 0.263521972723212 0.868239013638394 15 0.150020687333777 0.300041374667553 0.849979312666223 16 0.115319069964796 0.230638139929592 0.884680930035204 17 0.0765801301340837 0.153160260268167 0.923419869865916 18 0.121697589727260 0.243395179454519 0.87830241027274 19 0.157133598392364 0.314267196784729 0.842866401607636 20 0.131301156129156 0.262602312258313 0.868698843870844 21 0.150836333860679 0.301672667721358 0.849163666139321 22 0.146047618497630 0.292095236995260 0.85395238150237 23 0.117394831393811 0.234789662787621 0.88260516860619 24 0.0874546214006686 0.174909242801337 0.912545378599331 25 0.0718567313860037 0.143713462772007 0.928143268613996 26 0.0499540166718558 0.0999080333437116 0.950045983328144 27 0.0376511038820428 0.0753022077640857 0.962348896117957 28 0.0254871020406414 0.0509742040812827 0.97451289795936 29 0.0161528451064725 0.0323056902129449 0.983847154893527 30 0.0441664791622831 0.0883329583245662 0.955833520837717 31 0.0910667299370688 0.182133459874138 0.908933270062931 32 0.0709872080970208 0.141974416194042 0.92901279190298 33 0.0496038484665386 0.0992076969330771 0.95039615153346 34 0.0369909503629302 0.0739819007258604 0.96300904963707 35 0.0248859640919403 0.0497719281838805 0.97511403590806 36 0.0188256541320417 0.0376513082640834 0.981174345867958 37 0.0240404343822272 0.0480808687644545 0.975959565617773 38 0.0271232003028498 0.0542464006056996 0.97287679969715 39 0.0205558510019059 0.0411117020038119 0.979444148998094 40 0.0205891843952292 0.0411783687904583 0.97941081560477 41 0.0146660163033619 0.0293320326067238 0.985333983696638 42 0.0138726548936591 0.0277453097873181 0.98612734510634 43 0.130672341901526 0.261344683803052 0.869327658098474 44 0.224812890138566 0.449625780277131 0.775187109861434 45 0.194492586892968 0.388985173785937 0.805507413107032 46 0.190471004175251 0.380942008350501 0.80952899582475 47 0.161988042171294 0.323976084342587 0.838011957828706 48 0.127585843168653 0.255171686337306 0.872414156831347 49 0.102428227282271 0.204856454564542 0.897571772717729 50 0.083950929266073 0.167901858532146 0.916049070733927 51 0.0680238335993984 0.136047667198797 0.931976166400602 52 0.0437682160887157 0.0875364321774313 0.956231783911284 53 0.0258207496575438 0.0516414993150876 0.974179250342456 54 0.0482086559332499 0.0964173118664998 0.95179134406675 55 0.148179500984737 0.296359001969474 0.851820499015263 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 8 0.156862745098039 NOK 10% type I error level 19 0.372549019607843 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; 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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