Meervoudige regressie 2

*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: Sun, 21 Nov 2010 11:20:12 +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/Nov/21/t12903385051gng93sz3nptcos.htm/, Retrieved Sun, 21 Nov 2010 12:21:47 +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/Nov/21/t12903385051gng93sz3nptcos.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:

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User-defined keywords:

Dataseries X:

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16198.9 16896.2 0 16554.2 16698 0 19554.2 19691.6 0 15903.8 15930.7 0 18003.8 17444.6 0 18329.6 17699.4 0 16260.7 15189.8 0 14851.9 15672.7 0 18174.1 17180.8 0 18406.6 17664.9 0 18466.5 17862.9 0 16016.5 16162.3 0 17428.5 17463.6 0 17167.2 16772.1 0 19630 19106.9 0 17183.6 16721.3 0 18344.7 18161.3 0 19301.4 18509.9 0 18147.5 17802.7 0 16192.9 16409.9 0 18374.4 17967.7 0 20515.2 20286.6 0 18957.2 19537.3 0 16471.5 18021.9 0 18746.8 20194.3 0 19009.5 19049.6 0 19211.2 20244.7 0 20547.7 21473.3 0 19325.8 19673.6 0 20605.5 21053.2 0 20056.9 20159.5 0 16141.4 18203.6 0 20359.8 21289.5 0 19711.6 20432.3 1 15638.6 17180.4 1 14384.5 15816.8 1 13855.6 15071.8 1 14308.3 14521.1 1 15290.6 15668.8 1 14423.8 14346.9 1 13779.7 13881 1 15686.3 15465.9 1 14733.8 14238.2 1 12522.5 13557.7 1 16189.4 16127.6 1 16059.1 16793.9 1 16007.1 16014 1 15806.8 16867.9 1 15160 16014.6 0 15692.1 15878.6 0 18908.9 18664.9 0 16969.9 17962.5 0 16997.5 17332.7 0 19858.9 19542.1 0 17681.2 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 7 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation uitvoer[t] = + 3885.44637298981 + 0.734871978147498invoer[t] -1001.28315575325crisis[t] + 5.8095292526758M1[t] + 674.041557200105M2[t] + 1109.77681490461M3[t] + 616.882464243724M4[t] + 892.824462099399M5[t] + 1509.74928622909M6[t] + 1257.70762915807M7[t] -437.223855464267M8[t] + 1307.69291158347M9[t] + 1476.82392699202M10[t] + 913.046867753967M11[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) 3885.44637298981 829.835086 4.6822 3.1e-05 1.5e-05 invoer 0.734871978147498 0.044183 16.6325 0 0 crisis -1001.28315575325 181.284847 -5.5233 2e-06 1e-06 M1 5.8095292526758 298.298304 0.0195 0.984556 0.492278 M2 674.041557200105 300.628428 2.2421 0.030427 0.015213 M3 1109.77681490461 302.210893 3.6722 0.000688 0.000344 M4 616.882464243724 297.980799 2.0702 0.044771 0.022385 M5 892.824462099399 297.963935 2.9964 0.004621 0.00231 M6 1509.74928622909 300.703549 5.0207 1e-05 5e-06 M7 1257.70762915807 298.967974 4.2068 0.000137 6.9e-05 M8 -437.223855464267 319.001819 -1.3706 0.177957 0.088979 M9 1307.69291158347 314.581072 4.1569 0.00016 8e-05 M10 1476.82392699202 324.125162 4.5563 4.6e-05 2.3e-05 M11 913.046867753967 313.572579 2.9118 0.00579 0.002895 Multiple Linear Regression - Regression Statistics Multiple R 0.981837209466541 R-squared 0.964004305893045 Adjusted R-squared 0.952591037029864 F-TEST (value) 84.4634711973627 F-TEST (DF numerator) 13 F-TEST (DF denominator) 41 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 439.623013186437 Sum Squared Residuals 7924004.14264802 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 16198.9 16307.7998194182 -108.899819418234 2 16554.2 16830.3802212968 -276.180221296841 3 19554.2 19466.0282327837 88.1717672163014 4 15903.8 16209.3538595079 -305.553859507887 5 18003.8 17597.8185450811 405.981454918942 6 18329.6 18401.9887492427 -72.3887492427348 7 16260.7 16305.7123758128 -45.0123758127501 8 14851.9 14965.6505694378 -113.750569437842 9 18174.1 17818.8277667298 355.272233270175 10 18406.6 18343.7103067596 62.8896932404287 11 18466.5 17925.4378991947 541.062100805274 12 16016.5 15762.6677454031 253.832254596878 13 17428.5 16724.7661798191 703.733820180863 14 17167.2 16884.8342348776 282.36576512243 15 19630 19036.3485871609 593.651412839141 16 17183.6 16790.3436454313 393.256354568701 17 18344.7 18124.5012918194 220.198708180631 18 19301.4 18997.6024875313 303.797512468721 19 18147.5 18225.8593675143 -78.3593675143502 20 16192.9 15507.3981917282 685.501808271822 21 18374.4 18397.0985263341 -22.69852633409 22 20515.2 20270.3241718689 244.875828131135 23 18957.2 19155.9075394049 -198.707539404895 24 16471.5 17129.2356759662 -657.735675966212 25 18746.8 18731.4810905465 15.3189094534879 26 19009.5 18558.5051651085 450.994834891502 27 19211.2 19872.4859238971 -661.285923897082 28 20547.7 20282.4552855882 265.244714411791 29 19325.8 19235.8481843718 89.9518156281678 30 20605.5 20866.6023895538 -261.102389553813 31 20056.9 19957.8056456124 99.0943543876275 32 16141.4 16825.5380589313 -684.138058931344 33 20359.8 20838.1962633445 -478.396263344452 34 19711.6 19376.1118633317 335.488136668289 35 15638.6 16422.6046183558 -784.004618355811 36 14384.5 14507.4863211999 -122.986321199915 37 13855.6 13965.8162267327 -110.216226732704 38 14308.3 14229.3542563143 78.945743685692 39 15290.6 15508.5020833387 -217.902083338696 40 14423.8 14044.1804647646 379.619535235368 41 13779.7 13977.7456080014 -198.045608001386 42 15686.3 15759.369030297 -73.0690302970484 43 14733.8 14605.1250456543 128.674954345654 44 12522.5 12410.1131799026 112.386820097364 45 16189.4 16043.5774435916 145.822556408367 46 16059.1 16702.3536580399 -643.253658039852 47 16007.1 15565.4499430446 441.650056955432 48 15806.8 15279.9102574308 526.889742569248 49 15160 15659.9366834834 -499.936683483413 50 15692.1 16228.2261224028 -536.126122402782 51 18908.9 18711.5351728197 197.364827180337 52 16969.9 17702.466744708 -732.566744707972 53 16997.5 17515.5863707264 -518.086370726354 54 19858.9 19756.1373433751 102.762656624875 55 17681.2 17785.5975654062 -104.397565406181 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.681846654831882 0.636306690336237 0.318153345168118 18 0.536750737419235 0.92649852516153 0.463249262580765 19 0.464491796406699 0.928983592813398 0.535508203593301 20 0.580707349210767 0.838585301578466 0.419292650789233 21 0.53277069326962 0.93445861346076 0.46722930673038 22 0.509326971140965 0.98134605771807 0.490673028859035 23 0.570925119517281 0.858149760965438 0.429074880482719 24 0.609066467822395 0.78186706435521 0.390933532177605 25 0.500461579701486 0.999076840597028 0.499538420298514 26 0.522142780300304 0.955714439399391 0.477857219699696 27 0.653896873439595 0.69220625312081 0.346103126560405 28 0.578568087917562 0.842863824164875 0.421431912082438 29 0.513440124115843 0.973119751768313 0.486559875884157 30 0.42597809140531 0.851956182810621 0.57402190859469 31 0.327082793683125 0.65416558736625 0.672917206316875 32 0.371744339604474 0.743488679208948 0.628255660395526 33 0.336630961150833 0.673261922301666 0.663369038849167 34 0.297513413378628 0.595026826757256 0.702486586621372 35 0.650531179251794 0.698937641496411 0.349468820748206 36 0.609346258532553 0.781307482934895 0.390653741467447 37 0.45723412017654 0.914468240353081 0.54276587982346 38 0.328839158403053 0.657678316806106 0.671160841596947 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 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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